diff --git a/exercises/ex07_solution/hamiltonians.nb b/exercises/ex07_solution/hamiltonians.nb
new file mode 100644
index 0000000000000000000000000000000000000000..6d80b391df4b72ea8fb9ce1ebc368dc7f08ba2ce
--- /dev/null
+++ b/exercises/ex07_solution/hamiltonians.nb
@@ -0,0 +1,5526 @@
+(* Content-type: application/mathematica *)
+
+(*** Wolfram Notebook File ***)
+(* http://www.wolfram.com/nb *)
+
+(* CreatedBy='Mathematica 7.0' *)
+
+(*CacheID: 234*)
+(* Internal cache information:
+NotebookFileLineBreakTest
+NotebookFileLineBreakTest
+NotebookDataPosition[ 145, 7]
+NotebookDataLength[ 196404, 5517]
+NotebookOptionsPosition[ 182115, 5064]
+NotebookOutlinePosition[ 182493, 5081]
+CellTagsIndexPosition[ 182450, 5078]
+WindowFrame->Normal*)
+
+(* Beginning of Notebook Content *)
+Notebook[{
+
+Cell[CellGroupData[{
+Cell["S = 1/2 Heisenberg model", "Section",
+ CellChangeTimes->{{3.508786172194064*^9, 3.508786182305313*^9}, {
+ 3.508788750786186*^9, 3.508788750882126*^9}}],
+
+Cell[BoxData[
+ RowBox[{
+ SubscriptBox["H", "Heisenberg"], "=", " ",
+ RowBox[{"J", " ",
+ RowBox[{
+ SubscriptBox["\[Sum]",
+ RowBox[{
+ RowBox[{"<", "i"}], ",",
+ RowBox[{"j", ">"}]}]],
+ RowBox[{
+ SubscriptBox["S", "i"], ".",
+ SubscriptBox["S", "j"]}]}]}]}]], "Text",
+ CellChangeTimes->{{3.508788774779942*^9, 3.508788814118443*^9}}],
+
+Cell["\<\
+Basis representation : Direct product of spinors for both sites\
+\>", "Text",
+ CellChangeTimes->{{3.5099647516573553`*^9, 3.5099647672152348`*^9}, {
+ 3.509964803425087*^9, 3.509964833873074*^9}}],
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{"S12basis", " ", "=", " ",
+ RowBox[{"{", "\[IndentingNewLine]",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"0", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"0", ",", "1"}], "}"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"0", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "0"}], "}"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"1", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"0", ",", "1"}], "}"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"1", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "0"}], "}"}]}], "}"}]}], "}"}]}], ";"}]], "Input",
+ CellChangeTimes->{{3.508788879637247*^9, 3.508788898991542*^9}, {
+ 3.508788932053474*^9, 3.50878893450756*^9}, {3.508788970691636*^9,
+ 3.508789016790594*^9}, {3.508789132006886*^9, 3.508789167693777*^9}, {
+ 3.5087895524623213`*^9, 3.508789574787383*^9}}],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[{
+ RowBox[{
+ RowBox[{"HS12", "[",
+ RowBox[{"f_", ",", "i_"}], "]"}], " ", ":=", " ",
+ RowBox[{
+ FractionBox["J", "4"], " ",
+ RowBox[{"Sum", "[", " ",
+ RowBox[{
+ RowBox[{
+ RowBox[{
+ RowBox[{"f", "[",
+ RowBox[{"[", "1", "]"}], "]"}], ".",
+ RowBox[{"PauliMatrix", "[", "\[Alpha]", "]"}], ".",
+ RowBox[{"i", "[",
+ RowBox[{"[", "1", "]"}], "]"}]}], "*",
+ RowBox[{
+ RowBox[{"f", "[",
+ RowBox[{"[", "2", "]"}], "]"}], ".",
+ RowBox[{"PauliMatrix", "[", "\[Alpha]", "]"}], ".",
+ RowBox[{"i", "[",
+ RowBox[{"[", "2", "]"}], "]"}]}]}], ",", " ",
+ RowBox[{"{",
+ RowBox[{"\[Alpha]", ",", "3"}], "}"}]}], " ",
+ "]"}]}]}], "\[IndentingNewLine]",
+ RowBox[{
+ RowBox[{"HS12matrix", " ", "=", " ",
+ RowBox[{"Table", "[", " ",
+ RowBox[{
+ RowBox[{"HS12", "[",
+ RowBox[{"f", ",", "i"}], "]"}], ",", " ",
+ RowBox[{"{",
+ RowBox[{"f", ",", "S12basis"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"i", ",", "S12basis"}], "}"}]}], "]"}]}],
+ ";"}], "\[IndentingNewLine]",
+ RowBox[{"HS12matrix", "//", "MatrixForm"}]}], "Input",
+ CellChangeTimes->{{3.508789248939413*^9, 3.508789423575313*^9}, {
+ 3.509079076323452*^9, 3.509079094436656*^9}}],
+
+Cell[BoxData[
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {
+ FractionBox["J", "4"], "0", "0", "0"},
+ {"0",
+ RowBox[{"-",
+ FractionBox["J", "4"]}],
+ FractionBox["J", "2"], "0"},
+ {"0",
+ FractionBox["J", "2"],
+ RowBox[{"-",
+ FractionBox["J", "4"]}], "0"},
+ {"0", "0", "0",
+ FractionBox["J", "4"]}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
+ "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]], "Output",
+ CellChangeTimes->{3.5090791028068733`*^9, 3.509173187234962*^9,
+ 3.5099658620160637`*^9, 3.5100302887507687`*^9, 3.5103256240675163`*^9}]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell["Sectors", "Subsection",
+ CellChangeTimes->{{3.5099648816219482`*^9, 3.509964883105729*^9}}],
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{
+ "The", " ", "total", " ", "spin", " ", "component", " ", "along", " ",
+ "one", " ", "direction", " ", "is", " ", "conserved"}], ",", " ",
+ RowBox[{
+ RowBox[{
+ "hence", " ", "we", " ", "can", " ", "split", " ", "the", " ",
+ "Hamiltonian", " ", "into", " ", "sectors", " ",
+ SubsuperscriptBox["S", "z",
+ RowBox[{"(", "tot", ")"}]]}], "=",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "1"}], ",", "0", ",", "1"}], "}"}], "."}]}]}]], "Text",
+ CellChangeTimes->{{3.509966389957258*^9, 3.509966491396262*^9}}],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"Module", "[",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"basis", ",", "H", ",", "evals", ",", "evecs"}], "}"}], ",",
+ "\[IndentingNewLine]",
+ RowBox[{"Do", "[", "\[IndentingNewLine]",
+ RowBox[{
+ RowBox[{
+ RowBox[{"Print", "[",
+ RowBox[{"\"\<\!\(\*SubscriptBox[\(S\), \(z\)]\)=\>\"", ",",
+ RowBox[{
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{
+ RowBox[{
+ RowBox[{"basis", "[",
+ RowBox[{"[", "1", "]"}], "]"}], "[",
+ RowBox[{"[", "1", "]"}], "]"}], ".",
+ RowBox[{"PauliMatrix", "[", "3", "]"}], ".",
+ RowBox[{
+ RowBox[{"basis", "[",
+ RowBox[{"[", "1", "]"}], "]"}], "[",
+ RowBox[{"[", "1", "]"}], "]"}]}], "+",
+ RowBox[{
+ RowBox[{
+ RowBox[{"basis", "[",
+ RowBox[{"[", "1", "]"}], "]"}], "[",
+ RowBox[{"[", "2", "]"}], "]"}], ".",
+ RowBox[{"PauliMatrix", "[", "3", "]"}], ".",
+ RowBox[{
+ RowBox[{"basis", "[",
+ RowBox[{"[", "1", "]"}], "]"}], "[",
+ RowBox[{"[", "2", "]"}], "]"}]}]}], ")"}], "/", "2"}], ",",
+ "\"\<:\>\""}], "]"}], ";", "\[IndentingNewLine]",
+ RowBox[{"Print", "[",
+ RowBox[{"\"\<\\tStates: \>\"", ",", " ", "basis"}], "]"}], ";",
+ "\[IndentingNewLine]",
+ RowBox[{"H", " ", "=", " ",
+ RowBox[{"Table", "[", " ",
+ RowBox[{
+ RowBox[{"HS12", "[",
+ RowBox[{"f", ",", "i"}], "]"}], ",", " ",
+ RowBox[{"{",
+ RowBox[{"f", ",", "basis"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"i", ",", "basis"}], "}"}]}], "]"}]}], ";",
+ "\[IndentingNewLine]",
+ RowBox[{"Print", "[",
+ RowBox[{"\"\<\\tH:\>\"", ",",
+ RowBox[{"MatrixForm", "[", "H", "]"}]}], "]"}], ";",
+ "\[IndentingNewLine]",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"evals", ",", "evecs"}], "}"}], " ", "=", " ",
+ RowBox[{"Eigensystem", "[", "H", "]"}]}], ";", "\[IndentingNewLine]",
+ RowBox[{"Print", "[", "\"\<\\tEigenstates:\>\"", "]"}], ";",
+ "\[IndentingNewLine]",
+ RowBox[{"Do", "[",
+ RowBox[{
+ RowBox[{"Print", "[",
+ RowBox[{"\"\<\\t\\tE=\>\"", ",",
+ RowBox[{"evals", "[",
+ RowBox[{"[", "i", "]"}], "]"}], ",", "\"\<: \>\"", ",",
+ RowBox[{"evecs", "[",
+ RowBox[{"[", "i", "]"}], "]"}]}], "]"}], ",",
+ RowBox[{"{",
+ RowBox[{"i", ",",
+ RowBox[{"Length", "[", "evals", "]"}]}], "}"}]}], "]"}], ";"}],
+ "\[IndentingNewLine]", ",",
+ RowBox[{"{",
+ RowBox[{"basis", ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"S12basis", "[",
+ RowBox[{"[", "1", "]"}], "]"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"S12basis", "[",
+ RowBox[{"[", "2", "]"}], "]"}], ",",
+ RowBox[{"S12basis", "[",
+ RowBox[{"[", "3", "]"}], "]"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"S12basis", "[",
+ RowBox[{"[", "4", "]"}], "]"}], "}"}]}], "}"}]}], "}"}]}],
+ "\[IndentingNewLine]", "]"}]}], "\[IndentingNewLine]", "]"}]], "Input",
+ CellChangeTimes->{{3.509965143823481*^9, 3.509965191117568*^9}, {
+ 3.509965264742386*^9, 3.509965358552906*^9}, {3.509965390504612*^9,
+ 3.509965435745974*^9}, {3.509965468672267*^9, 3.509965808634406*^9}, {
+ 3.509965946931533*^9, 3.509966095886098*^9}, {3.509966166089438*^9,
+ 3.5099662664330482`*^9}}],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\!\\(\\*SubscriptBox[\\(S\\), \\(z\\)]\\)=\"\>",
+ "\[InvisibleSpace]",
+ RowBox[{"-", "1"}], "\[InvisibleSpace]", "\<\":\"\>"}],
+ SequenceForm["\!\(\*SubscriptBox[\(S\), \(z\)]\)=", -1, ":"],
+ Editable->False]], "Print",
+ CellChangeTimes->{
+ 3.50996609909663*^9, {3.509966180378068*^9, 3.509966199650675*^9},
+ 3.509966232338327*^9, 3.509966267432103*^9, 3.510030289675577*^9,
+ 3.510325624153186*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tStates: \"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"0", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"0", ",", "1"}], "}"}]}], "}"}], "}"}]}],
+ SequenceForm["\tStates: ", {{{0, 1}, {0, 1}}}],
+ Editable->False]], "Print",
+ CellChangeTimes->{
+ 3.50996609909663*^9, {3.509966180378068*^9, 3.509966199650675*^9},
+ 3.509966232338327*^9, 3.509966267432103*^9, 3.510030289675577*^9,
+ 3.5103256241557083`*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tH:\"\>", "\[InvisibleSpace]",
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {
+ FractionBox["J", "4"]}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {},
+ "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]}],
+ SequenceForm["\tH:",
+ MatrixForm[{{Rational[1, 4] $CellContext`J}}]],
+ Editable->False]], "Print",
+ CellChangeTimes->{
+ 3.50996609909663*^9, {3.509966180378068*^9, 3.509966199650675*^9},
+ 3.509966232338327*^9, 3.509966267432103*^9, 3.510030289675577*^9,
+ 3.5103256241587877`*^9}],
+
+Cell[BoxData["\<\"\\tEigenstates:\"\>"], "Print",
+ CellChangeTimes->{
+ 3.50996609909663*^9, {3.509966180378068*^9, 3.509966199650675*^9},
+ 3.509966232338327*^9, 3.509966267432103*^9, 3.510030289675577*^9,
+ 3.5103256241618233`*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]",
+ FractionBox["J", "4"], "\[InvisibleSpace]", "\<\": \"\>",
+ "\[InvisibleSpace]",
+ RowBox[{"{", "1", "}"}]}],
+ SequenceForm["\t\tE=", Rational[1, 4] $CellContext`J, ": ", {1}],
+ Editable->False]], "Print",
+ CellChangeTimes->{
+ 3.50996609909663*^9, {3.509966180378068*^9, 3.509966199650675*^9},
+ 3.509966232338327*^9, 3.509966267432103*^9, 3.510030289675577*^9,
+ 3.510325624164914*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\!\\(\\*SubscriptBox[\\(S\\), \\(z\\)]\\)=\"\>",
+ "\[InvisibleSpace]", "0", "\[InvisibleSpace]", "\<\":\"\>"}],
+ SequenceForm["\!\(\*SubscriptBox[\(S\), \(z\)]\)=", 0, ":"],
+ Editable->False]], "Print",
+ CellChangeTimes->{
+ 3.50996609909663*^9, {3.509966180378068*^9, 3.509966199650675*^9},
+ 3.509966232338327*^9, 3.509966267432103*^9, 3.510030289675577*^9,
+ 3.510325624167997*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tStates: \"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"0", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "0"}], "}"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"1", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"0", ",", "1"}], "}"}]}], "}"}]}], "}"}]}],
+ SequenceForm["\tStates: ", {{{0, 1}, {1, 0}}, {{1, 0}, {0, 1}}}],
+ Editable->False]], "Print",
+ CellChangeTimes->{
+ 3.50996609909663*^9, {3.509966180378068*^9, 3.509966199650675*^9},
+ 3.509966232338327*^9, 3.509966267432103*^9, 3.510030289675577*^9,
+ 3.5103256241713867`*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tH:\"\>", "\[InvisibleSpace]",
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {
+ RowBox[{"-",
+ FractionBox["J", "4"]}],
+ FractionBox["J", "2"]},
+ {
+ FractionBox["J", "2"],
+ RowBox[{"-",
+ FractionBox["J", "4"]}]}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {},
+ "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]}],
+ SequenceForm["\tH:",
+ MatrixForm[{{
+ Rational[-1, 4] $CellContext`J, Rational[1, 2] $CellContext`J}, {
+ Rational[1, 2] $CellContext`J, Rational[-1, 4] $CellContext`J}}]],
+ Editable->False]], "Print",
+ CellChangeTimes->{
+ 3.50996609909663*^9, {3.509966180378068*^9, 3.509966199650675*^9},
+ 3.509966232338327*^9, 3.509966267432103*^9, 3.510030289675577*^9,
+ 3.510325624174748*^9}],
+
+Cell[BoxData["\<\"\\tEigenstates:\"\>"], "Print",
+ CellChangeTimes->{
+ 3.50996609909663*^9, {3.509966180378068*^9, 3.509966199650675*^9},
+ 3.509966232338327*^9, 3.509966267432103*^9, 3.510030289675577*^9,
+ 3.5103256241777554`*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]",
+ RowBox[{"-",
+ FractionBox[
+ RowBox[{"3", " ", "J"}], "4"]}], "\[InvisibleSpace]", "\<\": \"\>",
+ "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "1"}], ",", "1"}], "}"}]}],
+ SequenceForm["\t\tE=", Rational[-3, 4] $CellContext`J, ": ", {-1, 1}],
+ Editable->False]], "Print",
+ CellChangeTimes->{
+ 3.50996609909663*^9, {3.509966180378068*^9, 3.509966199650675*^9},
+ 3.509966232338327*^9, 3.509966267432103*^9, 3.510030289675577*^9,
+ 3.5103256241811113`*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]",
+ FractionBox["J", "4"], "\[InvisibleSpace]", "\<\": \"\>",
+ "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{"1", ",", "1"}], "}"}]}],
+ SequenceForm["\t\tE=", Rational[1, 4] $CellContext`J, ": ", {1, 1}],
+ Editable->False]], "Print",
+ CellChangeTimes->{
+ 3.50996609909663*^9, {3.509966180378068*^9, 3.509966199650675*^9},
+ 3.509966232338327*^9, 3.509966267432103*^9, 3.510030289675577*^9,
+ 3.510325624184245*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\!\\(\\*SubscriptBox[\\(S\\), \\(z\\)]\\)=\"\>",
+ "\[InvisibleSpace]", "1", "\[InvisibleSpace]", "\<\":\"\>"}],
+ SequenceForm["\!\(\*SubscriptBox[\(S\), \(z\)]\)=", 1, ":"],
+ Editable->False]], "Print",
+ CellChangeTimes->{
+ 3.50996609909663*^9, {3.509966180378068*^9, 3.509966199650675*^9},
+ 3.509966232338327*^9, 3.509966267432103*^9, 3.510030289675577*^9,
+ 3.510325624187385*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tStates: \"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"1", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "0"}], "}"}]}], "}"}], "}"}]}],
+ SequenceForm["\tStates: ", {{{1, 0}, {1, 0}}}],
+ Editable->False]], "Print",
+ CellChangeTimes->{
+ 3.50996609909663*^9, {3.509966180378068*^9, 3.509966199650675*^9},
+ 3.509966232338327*^9, 3.509966267432103*^9, 3.510030289675577*^9,
+ 3.5103256241905603`*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tH:\"\>", "\[InvisibleSpace]",
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {
+ FractionBox["J", "4"]}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {},
+ "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]}],
+ SequenceForm["\tH:",
+ MatrixForm[{{Rational[1, 4] $CellContext`J}}]],
+ Editable->False]], "Print",
+ CellChangeTimes->{
+ 3.50996609909663*^9, {3.509966180378068*^9, 3.509966199650675*^9},
+ 3.509966232338327*^9, 3.509966267432103*^9, 3.510030289675577*^9,
+ 3.510325624193729*^9}],
+
+Cell[BoxData["\<\"\\tEigenstates:\"\>"], "Print",
+ CellChangeTimes->{
+ 3.50996609909663*^9, {3.509966180378068*^9, 3.509966199650675*^9},
+ 3.509966232338327*^9, 3.509966267432103*^9, 3.510030289675577*^9,
+ 3.510325624196755*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]",
+ FractionBox["J", "4"], "\[InvisibleSpace]", "\<\": \"\>",
+ "\[InvisibleSpace]",
+ RowBox[{"{", "1", "}"}]}],
+ SequenceForm["\t\tE=", Rational[1, 4] $CellContext`J, ": ", {1}],
+ Editable->False]], "Print",
+ CellChangeTimes->{
+ 3.50996609909663*^9, {3.509966180378068*^9, 3.509966199650675*^9},
+ 3.509966232338327*^9, 3.509966267432103*^9, 3.510030289675577*^9,
+ 3.510325624199864*^9}]
+}, Open ]]
+}, Open ]],
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{
+ RowBox[{"We", " ", "see", " ", "the", " ", "S"}], "=",
+ RowBox[{
+ RowBox[{"1", " ", "triplet", " ", "with", " ", "energy", " ",
+ FractionBox["J", "4"], " ", "and", " ", "the", " ", "S"}], "=",
+ RowBox[{
+ RowBox[{"0", " ", "singlet", " ", "at", " ", "E"}], "=",
+ RowBox[{
+ RowBox[{"-",
+ FractionBox["3", "4"]}],
+ RowBox[{"J", ".", " ", "The"}], " ", "former", " ", "is", " ", "the",
+ " ", "ground", " ", "state", " ", "for", " ", "ferromagnetic", " ",
+ "coupling", " ",
+ RowBox[{"(",
+ RowBox[{"J", "<", "0"}], ")"}]}]}]}]}], ",", " ",
+ RowBox[{"the", " ", "latter", " ", "for", " ", "antiferromagnetic", " ",
+ RowBox[{
+ RowBox[{"(",
+ RowBox[{"J", ">", "0"}], ")"}], "."}]}]}]], "Text",
+ CellChangeTimes->{{3.509966525102811*^9, 3.509966644198653*^9}, {
+ 3.509967249518231*^9, 3.509967262909925*^9}}]
+}, Open ]]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell["S = 1 Heisenberg model", "Section",
+ CellChangeTimes->{{3.508786172194064*^9, 3.508786182305313*^9}}],
+
+Cell[BoxData[
+ RowBox[{"Basis", " ",
+ RowBox[{"representation", " ", ":", " ",
+ RowBox[{"Direct", " ", "product", " ", "of", " ",
+ SubscriptBox["S", "z"], " ", "eigenstates", " ",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"|",
+ RowBox[{"m", ">"}]}], ",",
+ RowBox[{"m", "=",
+ RowBox[{"-", "1"}]}], ",", "0", ",", "1"}], "}"}], " ", "for", " ",
+ "both", " ", "sites"}]}]}]], "Text",
+ CellChangeTimes->{{3.509966763800754*^9, 3.509966825488346*^9}}],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"S1basis", " ", "=", " ",
+ RowBox[{"Flatten", "[", " ",
+ RowBox[{
+ RowBox[{"Table", "[",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"m", ",", "n"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"m", ",",
+ RowBox[{"-", "1"}], ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"n", ",",
+ RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "]"}], ",", " ", "1"}],
+ "]"}]}]], "Input",
+ CellChangeTimes->{{3.5087862610990973`*^9, 3.508786332818791*^9}}],
+
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "1"}], ",",
+ RowBox[{"-", "1"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "1"}], ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "1"}], ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"0", ",",
+ RowBox[{"-", "1"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"0", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"0", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",",
+ RowBox[{"-", "1"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "1"}], "}"}]}], "}"}]], "Output",
+ CellChangeTimes->{3.50878633369862*^9, 3.509173187405579*^9,
+ 3.509966879484519*^9, 3.510030290495617*^9, 3.510325624289016*^9}]
+}, Open ]],
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{"Splus", "[",
+ RowBox[{"mf_", ",", "mi_"}], "]"}], " ", ":=", " ",
+ RowBox[{
+ SqrtBox[
+ RowBox[{"2", "-",
+ RowBox[{"mi",
+ RowBox[{"(",
+ RowBox[{"mi", "+", "1"}], ")"}]}]}]],
+ RowBox[{"KroneckerDelta", "[",
+ RowBox[{"mf", ",",
+ RowBox[{"mi", "+", "1"}]}], "]"}]}]}]], "Input",
+ CellChangeTimes->{{3.5087863983563547`*^9, 3.508786556485632*^9}}],
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{"Sminus", "[",
+ RowBox[{"mf_", ",", "mi_"}], "]"}], " ", ":=", " ",
+ RowBox[{
+ SqrtBox[
+ RowBox[{"2", "-",
+ RowBox[{"mi",
+ RowBox[{"(",
+ RowBox[{"mi", "-", "1"}], ")"}]}]}]],
+ RowBox[{"KroneckerDelta", "[",
+ RowBox[{"mf", ",",
+ RowBox[{"mi", "-", "1"}]}], "]"}]}]}]], "Input",
+ CellChangeTimes->{{3.5087863983563547`*^9, 3.50878657977427*^9}}],
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{"Sx", "[", "i__", "]"}], " ", ":=", " ",
+ RowBox[{
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{"Splus", "[", "i", "]"}], "+",
+ RowBox[{"Sminus", "[", "i", "]"}]}], ")"}], "/", "2"}]}]], "Input",
+ CellChangeTimes->{{3.508786586401273*^9, 3.508786643215939*^9}}],
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{"Sy", "[", "i__", "]"}], " ", ":=", " ",
+ RowBox[{
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{"Splus", "[", "i", "]"}], "-",
+ RowBox[{"Sminus", "[", "i", "]"}]}], ")"}], "/",
+ RowBox[{"(",
+ RowBox[{"2", " ", "I"}], ")"}]}]}]], "Input",
+ CellChangeTimes->{{3.508786586401273*^9, 3.50878666393498*^9}}],
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{"Sz", "[",
+ RowBox[{"mf_", ",", "mi_"}], "]"}], " ", ":=", " ",
+ RowBox[{"mi", " ",
+ RowBox[{"KroneckerDelta", "[",
+ RowBox[{"mf", ",", "mi"}], "]"}]}]}]], "Input",
+ CellChangeTimes->{{3.508786675973007*^9, 3.508786707775208*^9}}],
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{"HS1", "[",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"mf_", ",", "nf_"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"mi_", ",", "ni_"}], "}"}]}], "]"}], " ", ":=", " ",
+ RowBox[{"J", " ",
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{
+ RowBox[{"Sx", "[",
+ RowBox[{"mf", ",", "mi"}], "]"}], " ",
+ RowBox[{"Sx", "[",
+ RowBox[{"nf", ",", "ni"}], "]"}]}], "+",
+ RowBox[{
+ RowBox[{"Sy", "[",
+ RowBox[{"mf", ",", "mi"}], "]"}], " ",
+ RowBox[{"Sy", "[",
+ RowBox[{"nf", ",", "ni"}], "]"}]}], "+",
+ RowBox[{
+ RowBox[{"Sz", "[",
+ RowBox[{"mf", ",", "mi"}], "]"}], " ",
+ RowBox[{"Sz", "[",
+ RowBox[{"nf", ",", "ni"}], "]"}]}]}], ")"}]}]}]], "Input",
+ CellChangeTimes->{{3.508786347779708*^9, 3.508786369466791*^9}, {
+ 3.508786727583376*^9, 3.50878676062428*^9}, {3.508786793341441*^9,
+ 3.5087868517415657`*^9}}],
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{"HS1matrix", " ", "=", " ",
+ RowBox[{"Table", "[", " ",
+ RowBox[{
+ RowBox[{"HS1", "[",
+ RowBox[{"f", ",", "i"}], "]"}], ",", " ",
+ RowBox[{"{",
+ RowBox[{"f", ",", "S1basis"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"i", ",", "S1basis"}], "}"}]}], "]"}]}], ";"}]], "Input",
+ CellChangeTimes->{{3.5087868796564083`*^9, 3.508786920936434*^9}}],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"HS1matrix", "//", "MatrixForm"}]], "Input",
+ CellChangeTimes->{{3.508786923121214*^9, 3.508786931311994*^9}}],
+
+Cell[BoxData[
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {"J", "0", "0", "0", "0", "0", "0", "0", "0"},
+ {"0", "0", "0", "J", "0", "0", "0", "0", "0"},
+ {"0", "0",
+ RowBox[{"-", "J"}], "0", "J", "0", "0", "0", "0"},
+ {"0", "J", "0", "0", "0", "0", "0", "0", "0"},
+ {"0", "0", "J", "0", "0", "0", "J", "0", "0"},
+ {"0", "0", "0", "0", "0", "0", "0", "J", "0"},
+ {"0", "0", "0", "0", "J", "0",
+ RowBox[{"-", "J"}], "0", "0"},
+ {"0", "0", "0", "0", "0", "J", "0", "0", "0"},
+ {"0", "0", "0", "0", "0", "0", "0", "0", "J"}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
+ "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]], "Output",
+ CellChangeTimes->{3.508786931886113*^9, 3.5099668798027277`*^9,
+ 3.5100302907184362`*^9, 3.5103256245670757`*^9}]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell["Sectors", "Subsection",
+ CellChangeTimes->{{3.5099668911983957`*^9, 3.509966892640156*^9}}],
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{"Again", ":", " ",
+ RowBox[{
+ "The", " ", "total", " ", "spin", " ", "component", " ", "along", " ",
+ "one", " ", "direction", " ", "is", " ", "conserved"}]}], ",", " ",
+ RowBox[{
+ RowBox[{
+ "hence", " ", "we", " ", "can", " ", "split", " ", "the", " ",
+ "Hamiltonian", " ", "into", " ", "sectors", " ",
+ SubsuperscriptBox["S", "z",
+ RowBox[{"(", "tot", ")"}]]}], "=",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "2"}], ",",
+ RowBox[{"-", "1"}], ",", "0", ",", "1", ",", "2"}], "}"}],
+ "."}]}]}]], "Text",
+ CellChangeTimes->{{3.509966389957258*^9, 3.509966491396262*^9}, {
+ 3.509967538545294*^9, 3.509967548280451*^9}}],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"Module", "[",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"sz", ",", "basis", ",", "H", ",", "evals", ",", "evecs"}], "}"}],
+ ",", "\[IndentingNewLine]",
+ RowBox[{"Do", "[", "\[IndentingNewLine]",
+ RowBox[{
+ RowBox[{
+ RowBox[{"Print", "[",
+ RowBox[{
+ "\"\<\!\(\*SubscriptBox[\(S\), \(z\)]\) = \>\"", ",", "sz", ",",
+ "\"\<:\>\""}], "]"}], ";", "\[IndentingNewLine]",
+ RowBox[{"basis", " ", "=", " ",
+ RowBox[{"Select", "[",
+ RowBox[{"S1basis", ",",
+ RowBox[{
+ RowBox[{
+ RowBox[{
+ RowBox[{"#", "[",
+ RowBox[{"[", "1", "]"}], "]"}], "+",
+ RowBox[{"#", "[",
+ RowBox[{"[", "2", "]"}], "]"}]}], "\[Equal]", "sz"}], "&"}]}],
+ "]"}]}], ";", "\[IndentingNewLine]",
+ RowBox[{"Print", "[",
+ RowBox[{"\"\<\\tBasis: \>\"", ",", "basis"}], "]"}], ";",
+ "\[IndentingNewLine]",
+ RowBox[{"H", "=",
+ RowBox[{"Table", "[",
+ RowBox[{
+ RowBox[{"HS1", "[",
+ RowBox[{"f", ",", "i"}], "]"}], ",",
+ RowBox[{"{",
+ RowBox[{"f", ",", "basis"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"i", ",", "basis"}], "}"}]}], "]"}]}], ";",
+ "\[IndentingNewLine]",
+ RowBox[{"Print", "[",
+ RowBox[{"\"\<\\tHamiltonian: \>\"", ",",
+ RowBox[{"MatrixForm", "[", "H", "]"}]}], "]"}], ";",
+ "\[IndentingNewLine]",
+ RowBox[{"Print", "[",
+ RowBox[{"\"\<\\tEigensystem: \>\"", ",",
+ RowBox[{"Eigensystem", "[", "H", "]"}]}], "]"}], ";"}],
+ "\[IndentingNewLine]", ",",
+ RowBox[{"{",
+ RowBox[{"sz", ",",
+ RowBox[{"-", "2"}], ",", "2"}], "}"}]}], "\[IndentingNewLine]",
+ "]"}]}], "\[IndentingNewLine]", "]"}]], "Input",
+ CellChangeTimes->{{3.509966931310486*^9, 3.509967156311015*^9}}],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\!\\(\\*SubscriptBox[\\(S\\), \\(z\\)]\\) = \"\>",
+ "\[InvisibleSpace]",
+ RowBox[{"-", "2"}], "\[InvisibleSpace]", "\<\":\"\>"}],
+ SequenceForm["\!\(\*SubscriptBox[\(S\), \(z\)]\) = ", -2, ":"],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099671576323977`*^9, 3.510030291144125*^9,
+ 3.5103256246507673`*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tBasis: \"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "1"}], ",",
+ RowBox[{"-", "1"}]}], "}"}], "}"}]}],
+ SequenceForm["\tBasis: ", {{-1, -1}}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099671576323977`*^9, 3.510030291144125*^9,
+ 3.510325624652732*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tHamiltonian: \"\>", "\[InvisibleSpace]",
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {"J"}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {},
+ "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]}],
+ SequenceForm["\tHamiltonian: ",
+ MatrixForm[{{$CellContext`J}}]],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099671576323977`*^9, 3.510030291144125*^9,
+ 3.5103256246565313`*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tEigensystem: \"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{", "J", "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"{", "1", "}"}], "}"}]}], "}"}]}],
+ SequenceForm["\tEigensystem: ", {{$CellContext`J}, {{1}}}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099671576323977`*^9, 3.510030291144125*^9,
+ 3.510325624660328*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\!\\(\\*SubscriptBox[\\(S\\), \\(z\\)]\\) = \"\>",
+ "\[InvisibleSpace]",
+ RowBox[{"-", "1"}], "\[InvisibleSpace]", "\<\":\"\>"}],
+ SequenceForm["\!\(\*SubscriptBox[\(S\), \(z\)]\) = ", -1, ":"],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099671576323977`*^9, 3.510030291144125*^9,
+ 3.510325624664104*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tBasis: \"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "1"}], ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"0", ",",
+ RowBox[{"-", "1"}]}], "}"}]}], "}"}]}],
+ SequenceForm["\tBasis: ", {{-1, 0}, {0, -1}}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099671576323977`*^9, 3.510030291144125*^9,
+ 3.510325624667982*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tHamiltonian: \"\>", "\[InvisibleSpace]",
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {"0", "J"},
+ {"J", "0"}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {},
+ "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]}],
+ SequenceForm["\tHamiltonian: ",
+ MatrixForm[{{0, $CellContext`J}, {$CellContext`J, 0}}]],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099671576323977`*^9, 3.510030291144125*^9,
+ 3.510325624671771*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tEigensystem: \"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "J"}], ",", "J"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "1"}], ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "1"}], "}"}]}], "}"}]}], "}"}]}],
+ SequenceForm[
+ "\tEigensystem: ", {{-$CellContext`J, $CellContext`J}, {{-1, 1}, {1, 1}}}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099671576323977`*^9, 3.510030291144125*^9,
+ 3.5103256246758947`*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\!\\(\\*SubscriptBox[\\(S\\), \\(z\\)]\\) = \"\>",
+ "\[InvisibleSpace]", "0", "\[InvisibleSpace]", "\<\":\"\>"}],
+ SequenceForm["\!\(\*SubscriptBox[\(S\), \(z\)]\) = ", 0, ":"],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099671576323977`*^9, 3.510030291144125*^9,
+ 3.5103256246800117`*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tBasis: \"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "1"}], ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"0", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",",
+ RowBox[{"-", "1"}]}], "}"}]}], "}"}]}],
+ SequenceForm["\tBasis: ", {{-1, 1}, {0, 0}, {1, -1}}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099671576323977`*^9, 3.510030291144125*^9,
+ 3.510325624684224*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tHamiltonian: \"\>", "\[InvisibleSpace]",
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {
+ RowBox[{"-", "J"}], "J", "0"},
+ {"J", "0", "J"},
+ {"0", "J",
+ RowBox[{"-", "J"}]}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {},
+ "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]}],
+ SequenceForm["\tHamiltonian: ",
+ MatrixForm[{{-$CellContext`J, $CellContext`J, 0}, {$CellContext`J,
+ 0, $CellContext`J}, {0, $CellContext`J, -$CellContext`J}}]],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099671576323977`*^9, 3.510030291144125*^9,
+ 3.510325624688529*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tEigensystem: \"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{
+ RowBox[{"-", "2"}], " ", "J"}], ",",
+ RowBox[{"-", "J"}], ",", "J"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"1", ",",
+ RowBox[{"-", "1"}], ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "1"}], ",", "0", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "2", ",", "1"}], "}"}]}], "}"}]}], "}"}]}],
+ SequenceForm[
+ "\tEigensystem: ", {{(-2) $CellContext`J, -$CellContext`J, $CellContext`J}, \
+{{1, -1, 1}, {-1, 0, 1}, {1, 2, 1}}}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099671576323977`*^9, 3.510030291144125*^9,
+ 3.510325624692791*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\!\\(\\*SubscriptBox[\\(S\\), \\(z\\)]\\) = \"\>",
+ "\[InvisibleSpace]", "1", "\[InvisibleSpace]", "\<\":\"\>"}],
+ SequenceForm["\!\(\*SubscriptBox[\(S\), \(z\)]\) = ", 1, ":"],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099671576323977`*^9, 3.510030291144125*^9,
+ 3.510325624696945*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tBasis: \"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"0", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "0"}], "}"}]}], "}"}]}],
+ SequenceForm["\tBasis: ", {{0, 1}, {1, 0}}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099671576323977`*^9, 3.510030291144125*^9,
+ 3.5103256247011633`*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tHamiltonian: \"\>", "\[InvisibleSpace]",
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {"0", "J"},
+ {"J", "0"}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {},
+ "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]}],
+ SequenceForm["\tHamiltonian: ",
+ MatrixForm[{{0, $CellContext`J}, {$CellContext`J, 0}}]],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099671576323977`*^9, 3.510030291144125*^9,
+ 3.510325624705394*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tEigensystem: \"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "J"}], ",", "J"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "1"}], ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "1"}], "}"}]}], "}"}]}], "}"}]}],
+ SequenceForm[
+ "\tEigensystem: ", {{-$CellContext`J, $CellContext`J}, {{-1, 1}, {1, 1}}}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099671576323977`*^9, 3.510030291144125*^9,
+ 3.5103256247095957`*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\!\\(\\*SubscriptBox[\\(S\\), \\(z\\)]\\) = \"\>",
+ "\[InvisibleSpace]", "2", "\[InvisibleSpace]", "\<\":\"\>"}],
+ SequenceForm["\!\(\*SubscriptBox[\(S\), \(z\)]\) = ", 2, ":"],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099671576323977`*^9, 3.510030291144125*^9,
+ 3.5103256247136393`*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tBasis: \"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{"{",
+ RowBox[{"1", ",", "1"}], "}"}], "}"}]}],
+ SequenceForm["\tBasis: ", {{1, 1}}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099671576323977`*^9, 3.510030291144125*^9,
+ 3.510325624717375*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tHamiltonian: \"\>", "\[InvisibleSpace]",
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {"J"}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {},
+ "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]}],
+ SequenceForm["\tHamiltonian: ",
+ MatrixForm[{{$CellContext`J}}]],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099671576323977`*^9, 3.510030291144125*^9,
+ 3.510325624721262*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tEigensystem: \"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{", "J", "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"{", "1", "}"}], "}"}]}], "}"}]}],
+ SequenceForm["\tEigensystem: ", {{$CellContext`J}, {{1}}}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099671576323977`*^9, 3.510030291144125*^9,
+ 3.510325624724963*^9}]
+}, Open ]]
+}, Open ]]
+}, Open ]]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell["Bose - Hubbard model", "Section",
+ CellChangeTimes->{{3.50878589074474*^9, 3.50878589768194*^9}}],
+
+Cell[BoxData[
+ RowBox[{
+ SubscriptBox["H", "BH"], "=",
+ RowBox[{
+ RowBox[{
+ RowBox[{"-", "t"}],
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{
+ SubsuperscriptBox["b", "1", "\[Dagger]"],
+ SubscriptBox["b", "2"]}], "+",
+ RowBox[{
+ SubsuperscriptBox["b", "2", "\[Dagger]"],
+ SubscriptBox["b", "1"]}]}], ")"}]}], " ", "+", " ",
+ RowBox[{
+ FractionBox["U", "2"],
+ RowBox[{
+ SubscriptBox["\[Sum]", "i"],
+ RowBox[{
+ SubscriptBox["n", "i"],
+ RowBox[{"(",
+ RowBox[{
+ SubscriptBox["n", "i"], "-", "1"}], ")"}]}]}]}]}]}]], "Text",
+ CellChangeTimes->{{3.508785909962515*^9, 3.508786058066607*^9}, {
+ 3.604145727373187*^9, 3.604145764200634*^9}}],
+
+Cell[CellGroupData[{
+
+Cell["Basis", "Subsection",
+ CellChangeTimes->{{3.509082062674439*^9, 3.509082063268136*^9}}],
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{
+ "The", " ", "basis", " ", "can", " ", "be", " ", "enumerated", " ", "by",
+ " ", "the", " ", "number", " ", "of", " ", "particles", " ", "on", " ",
+ "each", " ",
+ RowBox[{"site", ".", " ", "\[IndentingNewLine]", "We"}], " ", "employ",
+ " ", "a", " ", "maximum", " ", "number", " ", "of", " ", "particles", " ",
+ "in", " ", "the", " ", "system", " ",
+ SubscriptBox["N", "max"]}], "=", "4."}]], "Text",
+ CellChangeTimes->{{3.510325278460219*^9, 3.5103253468115997`*^9}}],
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{
+ RowBox[{"maxN", " ", "=", " ", "4"}], ";"}], " ",
+ RowBox[{"(*", " ",
+ RowBox[{
+ RowBox[{"Particle", " ", "number", " ", "cut"}], "-", "off"}], " ",
+ "*)"}]}]], "Input",
+ CellChangeTimes->{{3.508783742570593*^9, 3.508783747959845*^9}, {
+ 3.5090820761803417`*^9, 3.509082079140167*^9}}],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"BHBasis", " ", "=", " ",
+ RowBox[{"Flatten", "[", " ",
+ RowBox[{
+ RowBox[{"Table", "[", " ",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"k", ",",
+ RowBox[{"n", "-", "k"}]}], "}"}], ",", " ",
+ RowBox[{"{",
+ RowBox[{"n", ",", "0", ",", "maxN"}], "}"}], ",", " ",
+ RowBox[{"{",
+ RowBox[{"k", ",", "0", ",", "n"}], "}"}]}], "]"}], ",", " ", "1"}],
+ "]"}]}]], "Input",
+ CellChangeTimes->{{3.508783880127376*^9, 3.508783991254715*^9}, {
+ 3.508784023788666*^9, 3.508784071702196*^9}}],
+
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"0", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"0", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"0", ",", "2"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"2", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"0", ",", "3"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "2"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"2", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"3", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"0", ",", "4"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "3"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"2", ",", "2"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"3", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"4", ",", "0"}], "}"}]}], "}"}]], "Output",
+ CellChangeTimes->{3.5087839933307667`*^9, 3.508784032836603*^9,
+ 3.508784072438197*^9, 3.508837210475828*^9, 3.5099677524359627`*^9,
+ 3.510030291498403*^9, 3.510325624801455*^9, 3.540571399199623*^9,
+ 3.5405714508984327`*^9}]
+}, Open ]]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell["Hamiltonian", "Subsection",
+ CellChangeTimes->{{3.5090820847471533`*^9, 3.5090820861656647`*^9}}],
+
+Cell["Creation/annihilation operators", "Text",
+ CellChangeTimes->{{3.5099682689662123`*^9, 3.509968276663623*^9}}],
+
+Cell[BoxData[{
+ RowBox[{
+ RowBox[{
+ RowBox[{"Bcrt", "[",
+ RowBox[{"f_", ",", "i_"}], "]"}], ":=",
+ RowBox[{
+ SqrtBox["f"],
+ RowBox[{"KroneckerDelta", "[",
+ RowBox[{"f", ",",
+ RowBox[{"i", "+", "1"}]}], "]"}]}]}], ";"}], "\[IndentingNewLine]",
+ RowBox[{
+ RowBox[{
+ RowBox[{"Bann", "[",
+ RowBox[{"f_", ",", "i_"}], "]"}], ":=",
+ RowBox[{
+ SqrtBox["i"],
+ RowBox[{"KroneckerDelta", "[",
+ RowBox[{"f", ",",
+ RowBox[{"i", "-", "1"}]}], "]"}]}]}],
+ ";"}], "\[IndentingNewLine]"}], "Input",
+ CellChangeTimes->{{3.509968078139415*^9, 3.509968094293738*^9}, {
+ 3.509968191759656*^9, 3.509968259817408*^9}}],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[{
+ RowBox[{
+ RowBox[{
+ RowBox[{"HBH", "[",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"k_", ",", "l_"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"m_", ",", "n_"}], "}"}]}], "]"}], " ", ":=", " ",
+ RowBox[{
+ RowBox[{
+ RowBox[{"-", "t"}], " ",
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{
+ RowBox[{"Bcrt", "[",
+ RowBox[{"k", ",", "m"}], "]"}],
+ RowBox[{"Bann", "[",
+ RowBox[{"l", ",", "n"}], "]"}]}], "+",
+ RowBox[{
+ RowBox[{"Bann", "[",
+ RowBox[{"k", ",", "m"}], "]"}],
+ RowBox[{"Bcrt", "[",
+ RowBox[{"l", ",", "n"}], "]"}]}]}], ")"}]}], " ", "+",
+ RowBox[{
+ FractionBox["U", "2"],
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{"m",
+ RowBox[{"(",
+ RowBox[{"m", "-", "1"}], ")"}]}], "+",
+ RowBox[{"n",
+ RowBox[{"(",
+ RowBox[{"n", "-", "1"}], ")"}]}]}], ")"}],
+ RowBox[{"DiscreteDelta", "[",
+ RowBox[{
+ RowBox[{"k", "-", "m"}], ",",
+ RowBox[{"l", "-", "n"}]}], "]"}]}]}]}], ";"}], "\[IndentingNewLine]",
+ RowBox[{
+ RowBox[{"HBHmatrix", " ", "=", " ",
+ RowBox[{"Table", "[", " ",
+ RowBox[{
+ RowBox[{"HBH", "[",
+ RowBox[{"f", ",", "i"}], "]"}], ",", " ",
+ RowBox[{"{",
+ RowBox[{"f", ",", "BHBasis"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"i", ",", "BHBasis"}], "}"}]}], " ", "]"}]}],
+ ";"}], "\[IndentingNewLine]",
+ RowBox[{"HBHmatrix", "//", "MatrixForm"}]}], "Input",
+ CellChangeTimes->{{3.5087832565532103`*^9, 3.508783258500182*^9}, {
+ 3.508783348190814*^9, 3.5087836326748962`*^9}, {3.508783843170176*^9,
+ 3.508783850313211*^9}, {3.508785074190639*^9, 3.508785080524797*^9}, {
+ 3.508837185610881*^9, 3.508837187974235*^9}, {3.50908212588087*^9,
+ 3.509082126938532*^9}, {3.5099682998047523`*^9, 3.509968388579712*^9}}],
+
+Cell[BoxData[
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {"0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
+ "0"},
+ {"0", "0",
+ RowBox[{"-", "t"}], "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
+ "0", "0"},
+ {"0",
+ RowBox[{"-", "t"}], "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
+ "0", "0", "0"},
+ {"0", "0", "0", "U",
+ RowBox[{
+ RowBox[{"-",
+ SqrtBox["2"]}], " ", "t"}], "0", "0", "0", "0", "0", "0", "0", "0",
+ "0", "0"},
+ {"0", "0", "0",
+ RowBox[{
+ RowBox[{"-",
+ SqrtBox["2"]}], " ", "t"}], "0",
+ RowBox[{
+ RowBox[{"-",
+ SqrtBox["2"]}], " ", "t"}], "0", "0", "0", "0", "0", "0", "0", "0",
+ "0"},
+ {"0", "0", "0", "0",
+ RowBox[{
+ RowBox[{"-",
+ SqrtBox["2"]}], " ", "t"}], "U", "0", "0", "0", "0", "0", "0", "0",
+ "0", "0"},
+ {"0", "0", "0", "0", "0", "0",
+ RowBox[{"3", " ", "U"}],
+ RowBox[{
+ RowBox[{"-",
+ SqrtBox["3"]}], " ", "t"}], "0", "0", "0", "0", "0", "0", "0"},
+ {"0", "0", "0", "0", "0", "0",
+ RowBox[{
+ RowBox[{"-",
+ SqrtBox["3"]}], " ", "t"}], "U",
+ RowBox[{
+ RowBox[{"-", "2"}], " ", "t"}], "0", "0", "0", "0", "0", "0"},
+ {"0", "0", "0", "0", "0", "0", "0",
+ RowBox[{
+ RowBox[{"-", "2"}], " ", "t"}], "U",
+ RowBox[{
+ RowBox[{"-",
+ SqrtBox["3"]}], " ", "t"}], "0", "0", "0", "0", "0"},
+ {"0", "0", "0", "0", "0", "0", "0", "0",
+ RowBox[{
+ RowBox[{"-",
+ SqrtBox["3"]}], " ", "t"}],
+ RowBox[{"3", " ", "U"}], "0", "0", "0", "0", "0"},
+ {"0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
+ RowBox[{"6", " ", "U"}],
+ RowBox[{
+ RowBox[{"-", "2"}], " ", "t"}], "0", "0", "0"},
+ {"0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
+ RowBox[{
+ RowBox[{"-", "2"}], " ", "t"}],
+ RowBox[{"3", " ", "U"}],
+ RowBox[{
+ RowBox[{"-",
+ SqrtBox["6"]}], " ", "t"}], "0", "0"},
+ {"0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
+ RowBox[{
+ RowBox[{"-",
+ SqrtBox["6"]}], " ", "t"}],
+ RowBox[{"2", " ", "U"}],
+ RowBox[{
+ RowBox[{"-",
+ SqrtBox["6"]}], " ", "t"}], "0"},
+ {"0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
+ RowBox[{
+ RowBox[{"-",
+ SqrtBox["6"]}], " ", "t"}],
+ RowBox[{"3", " ", "U"}],
+ RowBox[{
+ RowBox[{"-", "2"}], " ", "t"}]},
+ {"0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
+ RowBox[{
+ RowBox[{"-", "2"}], " ", "t"}],
+ RowBox[{"6", " ", "U"}]}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
+ "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]], "Output",
+ CellChangeTimes->{3.509082131779736*^9, 3.509967752469507*^9,
+ 3.509968401732951*^9, 3.5100302916118517`*^9, 3.510325624884994*^9,
+ 3.540571399332176*^9, 3.540571450965391*^9}]
+}, Open ]]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell["Sectors", "Subsection",
+ CellChangeTimes->{{3.509082181075365*^9, 3.509082182381535*^9}}],
+
+Cell["\<\
+The Hamiltonian conserves the total particle number (U (1) symmetry), hence \
+we can split into N - sectors\
+\>", "Text",
+ CellChangeTimes->{{3.509968520289266*^9, 3.509968574091744*^9}}],
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{"doBHSector", "[", "n_", "]"}], ":=",
+ RowBox[{"Module", "[",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"basis", ",", "hmatrix", ",", "evals", ",", "evecs"}], "}"}],
+ ",", "\[IndentingNewLine]",
+ RowBox[{
+ RowBox[{"Print", "[",
+ RowBox[{"\"\<N = \>\"", ",", "n", ",", "\"\<:\>\""}], "]"}], ";",
+ "\[IndentingNewLine]",
+ RowBox[{"basis", " ", "=", " ",
+ RowBox[{"Select", "[",
+ RowBox[{"BHBasis", ",",
+ RowBox[{
+ RowBox[{
+ RowBox[{
+ RowBox[{"#", "[",
+ RowBox[{"[", "1", "]"}], "]"}], "+",
+ RowBox[{"#", "[",
+ RowBox[{"[", "2", "]"}], "]"}]}], "\[Equal]", "n"}], "&"}]}],
+ "]"}]}], ";", "\[IndentingNewLine]",
+ RowBox[{"Print", "[",
+ RowBox[{"\"\<\\tBasis: \>\"", ",", "basis"}], "]"}], ";",
+ "\[IndentingNewLine]",
+ RowBox[{"hmatrix", "=",
+ RowBox[{"Table", "[",
+ RowBox[{
+ RowBox[{"HBH", "[",
+ RowBox[{"f", ",", "i"}], "]"}], ",",
+ RowBox[{"{",
+ RowBox[{"f", ",", "basis"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"i", ",", "basis"}], "}"}]}], "]"}]}], ";",
+ "\[IndentingNewLine]",
+ RowBox[{"Print", "[",
+ RowBox[{"\"\<\\tHamiltonian: \>\"", ",",
+ RowBox[{"MatrixForm", "[", "hmatrix", "]"}]}], "]"}], ";",
+ "\[IndentingNewLine]",
+ RowBox[{"Do", "[", "\[IndentingNewLine]",
+ RowBox[{
+ RowBox[{
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"evals", ",", "evecs"}], "}"}], "=",
+ RowBox[{"Eigensystem", "[",
+ RowBox[{"hmatrix", "/.",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"t", "\[Rule]", "1."}], ",",
+ RowBox[{"U", "\[Rule]", "u"}]}], "}"}]}], "]"}]}], ";",
+ "\[IndentingNewLine]",
+ RowBox[{"Print", "[",
+ RowBox[{"\"\<\\tU=\>\"", ",", "u", ",", "\"\<:\>\""}], "]"}], ";",
+ "\[IndentingNewLine]",
+ RowBox[{"Do", "[", " ",
+ RowBox[{
+ RowBox[{"Print", "[",
+ RowBox[{"\"\<\\t\\tE=\>\"", ",",
+ RowBox[{"evals", "[",
+ RowBox[{"[", "i", "]"}], "]"}], ",", "\"\<\\t\>\"", ",",
+ RowBox[{"evecs", "[",
+ RowBox[{"[", "i", "]"}], "]"}]}], "]"}], ",",
+ RowBox[{"{",
+ RowBox[{"i", ",",
+ RowBox[{"Length", "[", "evals", "]"}]}], "}"}]}], "]"}]}],
+ "\[IndentingNewLine]", ",",
+ RowBox[{"{",
+ RowBox[{"u", ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "1"}], ",", "1", ",", "4"}], "}"}]}], "}"}]}],
+ "\[IndentingNewLine]", "]"}]}]}], "\[IndentingNewLine]",
+ "]"}]}]], "Input",
+ CellChangeTimes->{{3.50908224727859*^9, 3.509082288139579*^9}, {
+ 3.509082320253356*^9, 3.509082470192093*^9}, {3.509082502426523*^9,
+ 3.509082652102894*^9}, {3.509082847502182*^9, 3.5090828601355143`*^9}, {
+ 3.509082946714623*^9, 3.5090829706468163`*^9}, {3.509967733608123*^9,
+ 3.509967737366346*^9}, {3.509967793863312*^9, 3.509967827009042*^9},
+ 3.509968584801321*^9, {3.510030751538084*^9, 3.510030915952474*^9}, {
+ 3.510031123165592*^9, 3.510031207096511*^9}, {3.510031247272181*^9,
+ 3.510031252013926*^9}, 3.5405714450428543`*^9}],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"For", "[",
+ RowBox[{
+ RowBox[{"n", "=", "0"}], ",",
+ RowBox[{"n", "\[LessEqual]", "maxN"}], ",",
+ RowBox[{"n", "++"}], ",",
+ RowBox[{"doBHSector", "[", "n", "]"}]}], "]"}]], "Input",
+ CellChangeTimes->{{3.509082832796688*^9, 3.509082833933125*^9}, {
+ 3.509082874846966*^9, 3.5090829227496147`*^9}}],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"N = \"\>", "\[InvisibleSpace]", "0",
+ "\[InvisibleSpace]", "\<\":\"\>"}],
+ SequenceForm["N = ", 0, ":"],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451033278*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tBasis: \"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{"{",
+ RowBox[{"0", ",", "0"}], "}"}], "}"}]}],
+ SequenceForm["\tBasis: ", {{0, 0}}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.5405714510347147`*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tHamiltonian: \"\>", "\[InvisibleSpace]",
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {"0"}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {},
+ "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]}],
+ SequenceForm["\tHamiltonian: ",
+ MatrixForm[{{0}}]],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451036318*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tU=\"\>", "\[InvisibleSpace]",
+ RowBox[{"-", "1"}], "\[InvisibleSpace]", "\<\":\"\>"}],
+ SequenceForm["\tU=", -1, ":"],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451037891*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]", "0",
+ "\[InvisibleSpace]", "\<\"\\t\"\>", "\[InvisibleSpace]",
+ RowBox[{"{", "1", "}"}]}],
+ SequenceForm["\t\tE=", 0, "\t", {1}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451039425*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tU=\"\>", "\[InvisibleSpace]", "1",
+ "\[InvisibleSpace]", "\<\":\"\>"}],
+ SequenceForm["\tU=", 1, ":"],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451040916*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]", "0",
+ "\[InvisibleSpace]", "\<\"\\t\"\>", "\[InvisibleSpace]",
+ RowBox[{"{", "1", "}"}]}],
+ SequenceForm["\t\tE=", 0, "\t", {1}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451042637*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tU=\"\>", "\[InvisibleSpace]", "4",
+ "\[InvisibleSpace]", "\<\":\"\>"}],
+ SequenceForm["\tU=", 4, ":"],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451044293*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]", "0",
+ "\[InvisibleSpace]", "\<\"\\t\"\>", "\[InvisibleSpace]",
+ RowBox[{"{", "1", "}"}]}],
+ SequenceForm["\t\tE=", 0, "\t", {1}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451045948*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"N = \"\>", "\[InvisibleSpace]", "1",
+ "\[InvisibleSpace]", "\<\":\"\>"}],
+ SequenceForm["N = ", 1, ":"],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451047605*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tBasis: \"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"0", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "0"}], "}"}]}], "}"}]}],
+ SequenceForm["\tBasis: ", {{0, 1}, {1, 0}}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.5405714510493097`*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tHamiltonian: \"\>", "\[InvisibleSpace]",
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {"0",
+ RowBox[{"-", "t"}]},
+ {
+ RowBox[{"-", "t"}], "0"}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {},
+ "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]}],
+ SequenceForm["\tHamiltonian: ",
+ MatrixForm[{{0, -$CellContext`t}, {-$CellContext`t, 0}}]],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.5405714510511723`*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tU=\"\>", "\[InvisibleSpace]",
+ RowBox[{"-", "1"}], "\[InvisibleSpace]", "\<\":\"\>"}],
+ SequenceForm["\tU=", -1, ":"],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451052959*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]",
+ RowBox[{"-", "1.`"}], "\[InvisibleSpace]", "\<\"\\t\"\>",
+ "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "0.7071067811865475`"}], ",",
+ RowBox[{"-", "0.7071067811865475`"}]}], "}"}]}],
+ SequenceForm[
+ "\t\tE=", -1., "\t", {-0.7071067811865475, -0.7071067811865475}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.5405714510546703`*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]", "1.`",
+ "\[InvisibleSpace]", "\<\"\\t\"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "0.7071067811865475`"}], ",", "0.7071067811865475`"}],
+ "}"}]}],
+ SequenceForm["\t\tE=", 1., "\t", {-0.7071067811865475, 0.7071067811865475}],
+
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451056407*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tU=\"\>", "\[InvisibleSpace]", "1",
+ "\[InvisibleSpace]", "\<\":\"\>"}],
+ SequenceForm["\tU=", 1, ":"],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451058135*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]",
+ RowBox[{"-", "1.`"}], "\[InvisibleSpace]", "\<\"\\t\"\>",
+ "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "0.7071067811865475`"}], ",",
+ RowBox[{"-", "0.7071067811865475`"}]}], "}"}]}],
+ SequenceForm[
+ "\t\tE=", -1., "\t", {-0.7071067811865475, -0.7071067811865475}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451059902*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]", "1.`",
+ "\[InvisibleSpace]", "\<\"\\t\"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "0.7071067811865475`"}], ",", "0.7071067811865475`"}],
+ "}"}]}],
+ SequenceForm["\t\tE=", 1., "\t", {-0.7071067811865475, 0.7071067811865475}],
+
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.54057145106172*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tU=\"\>", "\[InvisibleSpace]", "4",
+ "\[InvisibleSpace]", "\<\":\"\>"}],
+ SequenceForm["\tU=", 4, ":"],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451063243*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]",
+ RowBox[{"-", "1.`"}], "\[InvisibleSpace]", "\<\"\\t\"\>",
+ "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "0.7071067811865475`"}], ",",
+ RowBox[{"-", "0.7071067811865475`"}]}], "}"}]}],
+ SequenceForm[
+ "\t\tE=", -1., "\t", {-0.7071067811865475, -0.7071067811865475}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451064823*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]", "1.`",
+ "\[InvisibleSpace]", "\<\"\\t\"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "0.7071067811865475`"}], ",", "0.7071067811865475`"}],
+ "}"}]}],
+ SequenceForm["\t\tE=", 1., "\t", {-0.7071067811865475, 0.7071067811865475}],
+
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451066381*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"N = \"\>", "\[InvisibleSpace]", "2",
+ "\[InvisibleSpace]", "\<\":\"\>"}],
+ SequenceForm["N = ", 2, ":"],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451067906*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tBasis: \"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"0", ",", "2"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"2", ",", "0"}], "}"}]}], "}"}]}],
+ SequenceForm["\tBasis: ", {{0, 2}, {1, 1}, {2, 0}}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451069434*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tHamiltonian: \"\>", "\[InvisibleSpace]",
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {"U",
+ RowBox[{
+ RowBox[{"-",
+ SqrtBox["2"]}], " ", "t"}], "0"},
+ {
+ RowBox[{
+ RowBox[{"-",
+ SqrtBox["2"]}], " ", "t"}], "0",
+ RowBox[{
+ RowBox[{"-",
+ SqrtBox["2"]}], " ", "t"}]},
+ {"0",
+ RowBox[{
+ RowBox[{"-",
+ SqrtBox["2"]}], " ", "t"}], "U"}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {},
+ "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]}],
+ SequenceForm["\tHamiltonian: ",
+ MatrixForm[{{$CellContext`U, -2^Rational[1, 2] $CellContext`t,
+ 0}, {-2^Rational[1, 2] $CellContext`t,
+ 0, -2^Rational[1, 2] $CellContext`t}, {
+ 0, -2^Rational[1, 2] $CellContext`t, $CellContext`U}}]],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451071168*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tU=\"\>", "\[InvisibleSpace]",
+ RowBox[{"-", "1"}], "\[InvisibleSpace]", "\<\":\"\>"}],
+ SequenceForm["\tU=", -1, ":"],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451072918*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]",
+ RowBox[{"-", "2.5615528128088276`"}], "\[InvisibleSpace]", "\<\"\\t\"\>",
+ "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ "0.5573454101893045`", ",", "0.6154122094026357`", ",",
+ "0.557345410189303`"}], "}"}]}],
+ SequenceForm[
+ "\t\tE=", -2.5615528128088276`, "\t", {0.5573454101893045,
+ 0.6154122094026357, 0.557345410189303}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.5405714510745068`*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]", "1.5615528128088303`",
+ "\[InvisibleSpace]", "\<\"\\t\"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{"0.43516214649359936`", ",",
+ RowBox[{"-", "0.7882054380161091`"}], ",", "0.4351621464935993`"}],
+ "}"}]}],
+ SequenceForm[
+ "\t\tE=", 1.5615528128088303`, "\t", {
+ 0.43516214649359936`, -0.7882054380161091, 0.4351621464935993}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451076109*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]",
+ RowBox[{"-", "0.9999999999999978`"}], "\[InvisibleSpace]", "\<\"\\t\"\>",
+ "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{"0.7071067811865467`", ",",
+ RowBox[{"-", "8.881784197001278`*^-16"}], ",",
+ RowBox[{"-", "0.7071067811865485`"}]}], "}"}]}],
+ SequenceForm[
+ "\t\tE=", -0.9999999999999978, "\t", {
+ 0.7071067811865467, -8.881784197001278*^-16, -0.7071067811865485}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451077704*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tU=\"\>", "\[InvisibleSpace]", "1",
+ "\[InvisibleSpace]", "\<\":\"\>"}],
+ SequenceForm["\tU=", 1, ":"],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.5405714510793133`*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]", "2.5615528128088303`",
+ "\[InvisibleSpace]", "\<\"\\t\"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "0.557345410189304`"}], ",", "0.6154122094026356`", ",",
+ RowBox[{"-", "0.5573454101893036`"}]}], "}"}]}],
+ SequenceForm[
+ "\t\tE=", 2.5615528128088303`, "\t", {-0.557345410189304,
+ 0.6154122094026356, -0.5573454101893036}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451080858*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]",
+ RowBox[{"-", "1.5615528128088263`"}], "\[InvisibleSpace]", "\<\"\\t\"\>",
+ "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ "0.43516214649359997`", ",", "0.7882054380161091`", ",",
+ "0.4351621464935987`"}], "}"}]}],
+ SequenceForm[
+ "\t\tE=", -1.5615528128088263`, "\t", {0.43516214649359997`,
+ 0.7882054380161091, 0.4351621464935987}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451082486*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]", "1.0000000000000016`",
+ "\[InvisibleSpace]", "\<\"\\t\"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{"0.7071067811865471`", ",",
+ RowBox[{"-", "5.551115123125796`*^-16"}], ",",
+ RowBox[{"-", "0.7071067811865479`"}]}], "}"}]}],
+ SequenceForm[
+ "\t\tE=", 1.0000000000000016`, "\t", {
+ 0.7071067811865471, -5.551115123125796*^-16, -0.7071067811865479}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451084113*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tU=\"\>", "\[InvisibleSpace]", "4",
+ "\[InvisibleSpace]", "\<\":\"\>"}],
+ SequenceForm["\tU=", 4, ":"],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451085703*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]", "4.82842712474619`",
+ "\[InvisibleSpace]", "\<\"\\t\"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{"0.6532814824381884`", ",",
+ RowBox[{"-", "0.3826834323650897`"}], ",", "0.6532814824381881`"}],
+ "}"}]}],
+ SequenceForm[
+ "\t\tE=", 4.82842712474619, "\t", {0.6532814824381884, -0.3826834323650897,
+ 0.6532814824381881}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451087323*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]", "4.000000000000001`",
+ "\[InvisibleSpace]", "\<\"\\t\"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{"0.7071067811865472`", ",",
+ RowBox[{"-", "2.775557561562897`*^-16"}], ",",
+ RowBox[{"-", "0.7071067811865477`"}]}], "}"}]}],
+ SequenceForm[
+ "\t\tE=", 4.000000000000001, "\t", {
+ 0.7071067811865472, -2.775557561562897*^-16, -0.7071067811865477}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451088966*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]",
+ RowBox[{"-", "0.8284271247461872`"}], "\[InvisibleSpace]", "\<\"\\t\"\>",
+ "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ "0.27059805007309873`", ",", "0.9238795325112868`", ",",
+ "0.2705980500730982`"}], "}"}]}],
+ SequenceForm[
+ "\t\tE=", -0.8284271247461872, "\t", {0.27059805007309873`,
+ 0.9238795325112868, 0.2705980500730982}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451090748*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"N = \"\>", "\[InvisibleSpace]", "3",
+ "\[InvisibleSpace]", "\<\":\"\>"}],
+ SequenceForm["N = ", 3, ":"],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.54057145109268*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tBasis: \"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"0", ",", "3"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "2"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"2", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"3", ",", "0"}], "}"}]}], "}"}]}],
+ SequenceForm["\tBasis: ", {{0, 3}, {1, 2}, {2, 1}, {3, 0}}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.5405714510943413`*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tHamiltonian: \"\>", "\[InvisibleSpace]",
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {
+ RowBox[{"3", " ", "U"}],
+ RowBox[{
+ RowBox[{"-",
+ SqrtBox["3"]}], " ", "t"}], "0", "0"},
+ {
+ RowBox[{
+ RowBox[{"-",
+ SqrtBox["3"]}], " ", "t"}], "U",
+ RowBox[{
+ RowBox[{"-", "2"}], " ", "t"}], "0"},
+ {"0",
+ RowBox[{
+ RowBox[{"-", "2"}], " ", "t"}], "U",
+ RowBox[{
+ RowBox[{"-",
+ SqrtBox["3"]}], " ", "t"}]},
+ {"0", "0",
+ RowBox[{
+ RowBox[{"-",
+ SqrtBox["3"]}], " ", "t"}],
+ RowBox[{"3", " ", "U"}]}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {},
+ "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]}],
+ SequenceForm["\tHamiltonian: ",
+ MatrixForm[{{
+ 3 $CellContext`U, -3^Rational[1, 2] $CellContext`t, 0,
+ 0}, {-3^Rational[
+ 1, 2] $CellContext`t, $CellContext`U, (-2) $CellContext`t, 0}, {
+ 0, (-2) $CellContext`t, $CellContext`U, -3^
+ Rational[1, 2] $CellContext`t}, {
+ 0, 0, -3^Rational[1, 2] $CellContext`t, 3 $CellContext`U}}]],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451096223*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tU=\"\>", "\[InvisibleSpace]",
+ RowBox[{"-", "1"}], "\[InvisibleSpace]", "\<\":\"\>"}],
+ SequenceForm["\tU=", -1, ":"],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451097972*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]",
+ RowBox[{"-", "4.732050807568877`"}], "\[InvisibleSpace]", "\<\"\\t\"\>",
+ "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ "0.4999999999999997`", ",", "0.4999999999999997`", ",",
+ "0.5000000000000002`", ",", "0.5000000000000002`"}], "}"}]}],
+ SequenceForm[
+ "\t\tE=", -4.732050807568877, "\t", {0.4999999999999997, 0.4999999999999997,
+ 0.5000000000000002, 0.5000000000000002}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451099531*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]",
+ RowBox[{"-", "3.645751311064592`"}], "\[InvisibleSpace]", "\<\"\\t\"\>",
+ "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{"0.6625573458234493`", ",", "0.24701773923219902`", ",",
+ RowBox[{"-", "0.24701773923219866`"}], ",",
+ RowBox[{"-", "0.6625573458234487`"}]}], "}"}]}],
+ SequenceForm[
+ "\t\tE=", -3.645751311064592, "\t", {0.6625573458234493,
+ 0.24701773923219902`, -0.24701773923219866`, -0.6625573458234487}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451101159*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]", "1.6457513110645792`",
+ "\[InvisibleSpace]", "\<\"\\t\"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{"0.2470177392321991`", ",",
+ RowBox[{"-", "0.6625573458234495`"}], ",", "0.6625573458234485`", ",",
+ RowBox[{"-", "0.2470177392321986`"}]}], "}"}]}],
+ SequenceForm[
+ "\t\tE=", 1.6457513110645792`, "\t", {
+ 0.2470177392321991, -0.6625573458234495,
+ 0.6625573458234485, -0.2470177392321986}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451102783*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]",
+ RowBox[{"-", "1.2679491924311241`"}], "\[InvisibleSpace]", "\<\"\\t\"\>",
+ "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{"0.4999999999999998`", ",",
+ RowBox[{"-", "0.49999999999999967`"}], ",",
+ RowBox[{"-", "0.5000000000000004`"}], ",", "0.5000000000000002`"}],
+ "}"}]}],
+ SequenceForm[
+ "\t\tE=", -1.2679491924311241`, "\t", {
+ 0.4999999999999998, -0.49999999999999967`, -0.5000000000000004,
+ 0.5000000000000002}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.5405714511045856`*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tU=\"\>", "\[InvisibleSpace]", "1",
+ "\[InvisibleSpace]", "\<\":\"\>"}],
+ SequenceForm["\tU=", 1, ":"],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.5405714511061993`*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]", "4.732050807568877`",
+ "\[InvisibleSpace]", "\<\"\\t\"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{"0.4999999999999997`", ",",
+ RowBox[{"-", "0.4999999999999997`"}], ",", "0.5000000000000002`", ",",
+ RowBox[{"-", "0.5000000000000002`"}]}], "}"}]}],
+ SequenceForm[
+ "\t\tE=", 4.732050807568877, "\t", {0.4999999999999997, -0.4999999999999997,
+ 0.5000000000000002, -0.5000000000000002}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451107786*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]", "3.645751311064592`",
+ "\[InvisibleSpace]", "\<\"\\t\"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{"0.6625573458234493`", ",",
+ RowBox[{"-", "0.24701773923219902`"}], ",",
+ RowBox[{"-", "0.24701773923219866`"}], ",", "0.6625573458234487`"}],
+ "}"}]}],
+ SequenceForm[
+ "\t\tE=", 3.645751311064592, "\t", {
+ 0.6625573458234493, -0.24701773923219902`, -0.24701773923219866`,
+ 0.6625573458234487}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451109453*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]",
+ RowBox[{"-", "1.6457513110645792`"}], "\[InvisibleSpace]", "\<\"\\t\"\>",
+ "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ "0.2470177392321991`", ",", "0.6625573458234495`", ",",
+ "0.6625573458234485`", ",", "0.2470177392321986`"}], "}"}]}],
+ SequenceForm[
+ "\t\tE=", -1.6457513110645792`, "\t", {0.2470177392321991,
+ 0.6625573458234495, 0.6625573458234485, 0.2470177392321986}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451111092*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]", "1.2679491924311241`",
+ "\[InvisibleSpace]", "\<\"\\t\"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "0.4999999999999998`"}], ",",
+ RowBox[{"-", "0.49999999999999967`"}], ",", "0.5000000000000004`", ",",
+ "0.5000000000000002`"}], "}"}]}],
+ SequenceForm[
+ "\t\tE=", 1.2679491924311241`,
+ "\t", {-0.4999999999999998, -0.49999999999999967`, 0.5000000000000004,
+ 0.5000000000000002}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451112754*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tU=\"\>", "\[InvisibleSpace]", "4",
+ "\[InvisibleSpace]", "\<\":\"\>"}],
+ SequenceForm["\tU=", 4, ":"],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451114336*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]", "12.464101615137755`",
+ "\[InvisibleSpace]", "\<\"\\t\"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "0.6830127018922189`"}], ",", "0.18301270189221922`", ",",
+ RowBox[{"-", "0.1830127018922194`"}], ",", "0.6830127018922196`"}],
+ "}"}]}],
+ SequenceForm[
+ "\t\tE=", 12.464101615137755`, "\t", {-0.6830127018922189,
+ 0.18301270189221922`, -0.1830127018922194, 0.6830127018922196}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.5405714511159*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]", "12.291502622129181`",
+ "\[InvisibleSpace]", "\<\"\\t\"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{"0.697300362563198`", ",",
+ RowBox[{"-", "0.11735503555124092`"}], ",",
+ RowBox[{"-", "0.11735503555124085`"}], ",", "0.6973003625631974`"}],
+ "}"}]}],
+ SequenceForm[
+ "\t\tE=", 12.291502622129181`, "\t", {
+ 0.697300362563198, -0.11735503555124092`, -0.11735503555124085`,
+ 0.6973003625631974}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.54057145111756*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]", "5.535898384862242`",
+ "\[InvisibleSpace]", "\<\"\\t\"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{"0.18301270189221913`", ",", "0.6830127018922187`", ",",
+ RowBox[{"-", "0.68301270189222`"}], ",",
+ RowBox[{"-", "0.18301270189221946`"}]}], "}"}]}],
+ SequenceForm[
+ "\t\tE=", 5.535898384862242, "\t", {0.18301270189221913`,
+ 0.6830127018922187, -0.68301270189222, -0.18301270189221946`}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.54057145111919*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]", "1.7084973778708186`",
+ "\[InvisibleSpace]", "\<\"\\t\"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ "0.1173550355512409`", ",", "0.6973003625631979`", ",",
+ "0.6973003625631975`", ",", "0.11735503555124083`"}], "}"}]}],
+ SequenceForm[
+ "\t\tE=", 1.7084973778708186`, "\t", {0.1173550355512409,
+ 0.6973003625631979, 0.6973003625631975, 0.11735503555124083`}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.54057145112082*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"N = \"\>", "\[InvisibleSpace]", "4",
+ "\[InvisibleSpace]", "\<\":\"\>"}],
+ SequenceForm["N = ", 4, ":"],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.5405714511224203`*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tBasis: \"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"0", ",", "4"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "3"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"2", ",", "2"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"3", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"4", ",", "0"}], "}"}]}], "}"}]}],
+ SequenceForm["\tBasis: ", {{0, 4}, {1, 3}, {2, 2}, {3, 1}, {4, 0}}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451124012*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tHamiltonian: \"\>", "\[InvisibleSpace]",
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {
+ RowBox[{"6", " ", "U"}],
+ RowBox[{
+ RowBox[{"-", "2"}], " ", "t"}], "0", "0", "0"},
+ {
+ RowBox[{
+ RowBox[{"-", "2"}], " ", "t"}],
+ RowBox[{"3", " ", "U"}],
+ RowBox[{
+ RowBox[{"-",
+ SqrtBox["6"]}], " ", "t"}], "0", "0"},
+ {"0",
+ RowBox[{
+ RowBox[{"-",
+ SqrtBox["6"]}], " ", "t"}],
+ RowBox[{"2", " ", "U"}],
+ RowBox[{
+ RowBox[{"-",
+ SqrtBox["6"]}], " ", "t"}], "0"},
+ {"0", "0",
+ RowBox[{
+ RowBox[{"-",
+ SqrtBox["6"]}], " ", "t"}],
+ RowBox[{"3", " ", "U"}],
+ RowBox[{
+ RowBox[{"-", "2"}], " ", "t"}]},
+ {"0", "0", "0",
+ RowBox[{
+ RowBox[{"-", "2"}], " ", "t"}],
+ RowBox[{"6", " ", "U"}]}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {},
+ "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]}],
+ SequenceForm["\tHamiltonian: ",
+ MatrixForm[{{
+ 6 $CellContext`U, (-2) $CellContext`t, 0, 0, 0}, {(-2) $CellContext`t,
+ 3 $CellContext`U, -6^Rational[1, 2] $CellContext`t, 0, 0}, {
+ 0, -6^Rational[1, 2] $CellContext`t,
+ 2 $CellContext`U, -6^Rational[1, 2] $CellContext`t, 0}, {
+ 0, 0, -6^Rational[1, 2] $CellContext`t,
+ 3 $CellContext`U, (-2) $CellContext`t}, {
+ 0, 0, 0, (-2) $CellContext`t, 6 $CellContext`U}}]],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451125925*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tU=\"\>", "\[InvisibleSpace]",
+ RowBox[{"-", "1"}], "\[InvisibleSpace]", "\<\":\"\>"}],
+ SequenceForm["\tU=", -1, ":"],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451127733*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]",
+ RowBox[{"-", "7.614627004194527`"}], "\[InvisibleSpace]", "\<\"\\t\"\>",
+ "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ "0.5130089636809934`", ",", "0.41415906307659095`", ",",
+ "0.36136982069473644`", ",", "0.4141590630765912`", ",",
+ "0.5130089636809946`"}], "}"}]}],
+ SequenceForm[
+ "\t\tE=", -7.614627004194527, "\t", {0.5130089636809934,
+ 0.41415906307659095`, 0.36136982069473644`, 0.4141590630765912,
+ 0.5130089636809946}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451129314*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]",
+ RowBox[{"-", "7.`"}], "\[InvisibleSpace]", "\<\"\\t\"\>",
+ "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "0.632455532033676`"}], ",",
+ RowBox[{"-", "0.3162277660168385`"}], ",",
+ RowBox[{"-", "2.8665835232995152`*^-16"}], ",", "0.3162277660168377`",
+ ",", "0.6324555320336755`"}], "}"}]}],
+ SequenceForm[
+ "\t\tE=", -7.,
+ "\t", {-0.632455532033676, -0.3162277660168385, -2.8665835232995152`*^-16,
+ 0.3162277660168377, 0.6324555320336755}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451131008*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]",
+ RowBox[{"-", "4.632676330081332`"}], "\[InvisibleSpace]", "\<\"\\t\"\>",
+ "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "0.46864061744857904`"}], ",", "0.3203917044613714`", ",",
+ "0.5961964900764719`", ",", "0.32039170446137066`", ",",
+ RowBox[{"-", "0.4686406174485783`"}]}], "}"}]}],
+ SequenceForm[
+ "\t\tE=", -4.632676330081332, "\t", {-0.46864061744857904`,
+ 0.3203917044613714, 0.5961964900764719,
+ 0.32039170446137066`, -0.4686406174485783}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451132793*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]",
+ RowBox[{"-", "2.000000000000009`"}], "\[InvisibleSpace]", "\<\"\\t\"\>",
+ "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{"0.3162277660168381`", ",",
+ RowBox[{"-", "0.6324555320336759`"}], ",", "3.4399002279594126`*^-16",
+ ",", "0.6324555320336755`", ",",
+ RowBox[{"-", "0.31622776601683833`"}]}], "}"}]}],
+ SequenceForm[
+ "\t\tE=", -2.000000000000009, "\t", {
+ 0.3162277660168381, -0.6324555320336759, 3.4399002279594126`*^-16,
+ 0.6324555320336755, -0.31622776601683833`}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.5405714511344748`*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]", "1.2473033342758466`",
+ "\[InvisibleSpace]", "\<\"\\t\"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{"0.13114028694633678`", ",",
+ RowBox[{"-", "0.47520671942203957`"}], ",", "0.7169111506397076`", ",",
+ RowBox[{"-", "0.47520671942204074`"}], ",", "0.1311402869463372`"}],
+ "}"}]}],
+ SequenceForm[
+ "\t\tE=", 1.2473033342758466`, "\t", {
+ 0.13114028694633678`, -0.47520671942203957`,
+ 0.7169111506397076, -0.47520671942204074`, 0.1311402869463372}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.5405714511361732`*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tU=\"\>", "\[InvisibleSpace]", "1",
+ "\[InvisibleSpace]", "\<\":\"\>"}],
+ SequenceForm["\tU=", 1, ":"],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451137783*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]", "7.614627004194527`",
+ "\[InvisibleSpace]", "\<\"\\t\"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{"0.5130089636809934`", ",",
+ RowBox[{"-", "0.41415906307659095`"}], ",", "0.36136982069473644`", ",",
+
+ RowBox[{"-", "0.4141590630765912`"}], ",", "0.5130089636809946`"}],
+ "}"}]}],
+ SequenceForm[
+ "\t\tE=", 7.614627004194527, "\t", {
+ 0.5130089636809934, -0.41415906307659095`,
+ 0.36136982069473644`, -0.4141590630765912, 0.5130089636809946}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.5405714511394043`*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]", "7.`",
+ "\[InvisibleSpace]", "\<\"\\t\"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "0.632455532033676`"}], ",", "0.3162277660168385`", ",",
+ RowBox[{"-", "2.8665835232995152`*^-16"}], ",",
+ RowBox[{"-", "0.3162277660168377`"}], ",", "0.6324555320336755`"}],
+ "}"}]}],
+ SequenceForm[
+ "\t\tE=", 7., "\t", {-0.632455532033676,
+ 0.3162277660168385, -2.8665835232995152`*^-16, -0.3162277660168377,
+ 0.6324555320336755}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451141101*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]", "4.632676330081332`",
+ "\[InvisibleSpace]", "\<\"\\t\"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "0.46864061744857904`"}], ",",
+ RowBox[{"-", "0.3203917044613714`"}], ",", "0.5961964900764719`", ",",
+ RowBox[{"-", "0.32039170446137066`"}], ",",
+ RowBox[{"-", "0.4686406174485783`"}]}], "}"}]}],
+ SequenceForm[
+ "\t\tE=", 4.632676330081332,
+ "\t", {-0.46864061744857904`, -0.3203917044613714,
+ 0.5961964900764719, -0.32039170446137066`, -0.4686406174485783}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451142831*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]", "2.000000000000009`",
+ "\[InvisibleSpace]", "\<\"\\t\"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "0.3162277660168381`"}], ",",
+ RowBox[{"-", "0.6324555320336759`"}], ",",
+ RowBox[{"-", "3.4399002279594126`*^-16"}], ",", "0.6324555320336755`",
+ ",", "0.31622776601683833`"}], "}"}]}],
+ SequenceForm[
+ "\t\tE=", 2.000000000000009,
+ "\t", {-0.3162277660168381, -0.6324555320336759, -3.4399002279594126`*^-16,
+ 0.6324555320336755, 0.31622776601683833`}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451144492*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]",
+ RowBox[{"-", "1.2473033342758466`"}], "\[InvisibleSpace]", "\<\"\\t\"\>",
+ "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ "0.13114028694633678`", ",", "0.47520671942203957`", ",",
+ "0.7169111506397076`", ",", "0.47520671942204074`", ",",
+ "0.1311402869463372`"}], "}"}]}],
+ SequenceForm[
+ "\t\tE=", -1.2473033342758466`, "\t", {0.13114028694633678`,
+ 0.47520671942203957`, 0.7169111506397076, 0.47520671942204074`,
+ 0.1311402869463372}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451146185*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\tU=\"\>", "\[InvisibleSpace]", "4",
+ "\[InvisibleSpace]", "\<\":\"\>"}],
+ SequenceForm["\tU=", 4, ":"],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.5405714511478033`*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]", "24.344520790605976`",
+ "\[InvisibleSpace]", "\<\"\\t\"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{"0.6963928199041625`", ",",
+ RowBox[{"-", "0.1199609024428538`"}], ",", "0.03595614748615579`", ",",
+ RowBox[{"-", "0.11996090244285405`"}], ",", "0.6963928199041649`"}],
+ "}"}]}],
+ SequenceForm[
+ "\t\tE=", 24.344520790605976`, "\t", {
+ 0.6963928199041625, -0.1199609024428538,
+ 0.03595614748615579, -0.11996090244285405`, 0.6963928199041649}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451149425*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]", "24.32455532033676`",
+ "\[InvisibleSpace]", "\<\"\\t\"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "0.6979762349196642`"}], ",", "0.11326595025589832`", ",",
+ RowBox[{"-", "9.240734289708722`*^-17"}], ",",
+ RowBox[{"-", "0.11326595025589768`"}], ",", "0.6979762349196614`"}],
+ "}"}]}],
+ SequenceForm[
+ "\t\tE=", 24.32455532033676, "\t", {-0.6979762349196642,
+ 0.11326595025589832`, -9.240734289708722*^-17, -0.11326595025589768`,
+ 0.6979762349196614}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451151103*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]", "13.712026926735188`",
+ "\[InvisibleSpace]", "\<\"\\t\"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{"0.1159463200906007`", ",", "0.5964263095181217`", ",",
+ RowBox[{"-", "0.5115312466937821`"}], ",", "0.5964263095181122`", ",",
+ "0.11594632009059898`"}], "}"}]}],
+ SequenceForm[
+ "\t\tE=", 13.712026926735188`, "\t", {0.1159463200906007,
+ 0.5964263095181217, -0.5115312466937821, 0.5964263095181122,
+ 0.11594632009059898`}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451152831*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]", "11.675444679663245`",
+ "\[InvisibleSpace]", "\<\"\\t\"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "0.1132659502558974`"}], ",",
+ RowBox[{"-", "0.6979762349196597`"}], ",",
+ RowBox[{"-", "4.397339942392373`*^-15"}], ",", "0.697976234919666`", ",",
+ "0.11326595025589856`"}], "}"}]}],
+ SequenceForm[
+ "\t\tE=", 11.675444679663245`,
+ "\t", {-0.1132659502558974, -0.6979762349196597, -4.397339942392373*^-15,
+ 0.697976234919666, 0.11326595025589856`}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451154538*^9}],
+
+Cell[BoxData[
+ InterpretationBox[
+ RowBox[{"\<\"\\t\\tE=\"\>", "\[InvisibleSpace]", "5.943452282658837`",
+ "\[InvisibleSpace]", "\<\"\\t\"\>", "\[InvisibleSpace]",
+ RowBox[{"{",
+ RowBox[{
+ "0.03991855763144709`", ",", "0.36039567033982894`", ",",
+ "0.8585120494867028`", ",", "0.360395670339831`", ",",
+ "0.039918557631447374`"}], "}"}]}],
+ SequenceForm[
+ "\t\tE=", 5.943452282658837, "\t", {0.03991855763144709,
+ 0.36039567033982894`, 0.8585120494867028, 0.360395670339831,
+ 0.039918557631447374`}],
+ Editable->False]], "Print",
+ CellChangeTimes->{3.5099677527691174`*^9, 3.509967830061452*^9,
+ 3.5099684499525023`*^9, 3.509968589492371*^9, 3.510030292003498*^9,
+ 3.510031175129266*^9, 3.5100312099009533`*^9, 3.510031254165797*^9,
+ 3.5103256250705147`*^9, 3.5405713993782797`*^9, 3.540571451194001*^9}]
+}, Open ]]
+}, Open ]],
+
+Cell["\<\
+In the attractive case (U < 0), the system can gain energy by attracting \
+additional particles from the environment. With positive or vanishing \
+chemical potential \[Mu] >= 0 the ground state has infinitely many particles.
+For U=1, \[Mu]=0, the ground state among those considered here has N=3 \
+particles. The first excitations have 2 and 4 particles, respectively. \
+Therefore a higher cut-off than N=4 may make sense.
+For U=4, \[Mu]=0, the ground state has N=1 one particle and all states with \
+more than 2 particles have such high energies that they are probably \
+irrelevant for most purposes.\
+\>", "Text",
+ CellChangeTimes->{{3.509968717767687*^9, 3.509968750261797*^9}, {
+ 3.50996886551903*^9, 3.509968892119748*^9}, {3.509969001344927*^9,
+ 3.509969037041493*^9}, {3.50996929703123*^9, 3.509969392901599*^9}, {
+ 3.509969534477647*^9, 3.50996968740697*^9}, {3.509969754048749*^9,
+ 3.509969807616721*^9}, {3.5099698937624397`*^9, 3.5099699983311977`*^9}}]
+}, Open ]]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell["Fermi - Hubbard model", "Section",
+ CellChangeTimes->{{3.50878589074474*^9, 3.50878589768194*^9}, {
+ 3.5088377030353937`*^9, 3.508837704096752*^9}}],
+
+Cell[BoxData[
+ RowBox[{
+ SubscriptBox["H", "FH"], "=",
+ RowBox[{
+ RowBox[{
+ RowBox[{"-", "t"}],
+ RowBox[{
+ SubscriptBox["\[Sum]", "\[Sigma]"],
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{
+ SubsuperscriptBox["c",
+ RowBox[{"1", ",", "\[Sigma]"}], "\[Dagger]"],
+ SubscriptBox["c",
+ RowBox[{"2", ",", "\[Sigma]"}]]}], "+",
+ RowBox[{
+ SubsuperscriptBox["c",
+ RowBox[{"2", ",", "\[Sigma]"}], "\[Dagger]"],
+ SubscriptBox["c",
+ RowBox[{"1", ",", "\[Sigma]"}]]}]}], ")"}]}]}], " ", "+", " ",
+ RowBox[{"U",
+ RowBox[{
+ SubscriptBox["\[Sum]", "i"],
+ RowBox[{
+ SubscriptBox["n",
+ RowBox[{"i", ",", "\[UpArrow]"}]],
+ SubscriptBox["n",
+ RowBox[{"i", ",", "\[DownArrow]"}]]}]}]}]}]}]], "Text",
+ CellChangeTimes->{{3.508785909962515*^9, 3.508786058066607*^9}, {
+ 3.508837708148725*^9, 3.5088377082770853`*^9}, {3.5088379322201977`*^9,
+ 3.508837936950053*^9}, {3.6041457814883833`*^9, 3.6041457839908*^9}, {
+ 3.604145839931108*^9, 3.60414594383324*^9}}],
+
+Cell[CellGroupData[{
+
+Cell["Basis", "Subsection",
+ CellChangeTimes->{{3.5090804841292953`*^9, 3.5090804850501823`*^9}}],
+
+Cell["\<\
+Basis representation : Number of up and down spins on site 1, number of up \
+and down spins on site 2.
+We are dealing with fermions, so each site can hold at most one particle of \
+each spin.\
+\>", "Text",
+ CellChangeTimes->{{3.5103254085755367`*^9, 3.510325490075185*^9},
+ 3.604145039062447*^9}],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"FHBasis", " ", "=", " ",
+ RowBox[{"Flatten", "[", " ",
+ RowBox[{
+ RowBox[{"Table", "[", " ",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"i", ",", "j", ",", "k", ",", "l"}], "}"}], ",", " ",
+ RowBox[{"{",
+ RowBox[{"i", ",", "0", ",", "1"}], "}"}], ",", " ",
+ RowBox[{"{",
+ RowBox[{"j", ",", "0", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"k", ",", "0", ",", "1"}], "}"}], ",", " ",
+ RowBox[{"{",
+ RowBox[{"l", ",", "0", ",", "1"}], "}"}]}], "]"}], ",", " ", "3"}],
+ "]"}]}]], "Input",
+ CellChangeTimes->{{3.508783880127376*^9, 3.508783991254715*^9}, {
+ 3.508784023788666*^9, 3.508784071702196*^9}, {3.508837729976532*^9,
+ 3.508837730106048*^9}, {3.508837770902673*^9, 3.508837837983169*^9}}],
+
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"0", ",", "0", ",", "0", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"0", ",", "0", ",", "0", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"0", ",", "0", ",", "1", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"0", ",", "0", ",", "1", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"0", ",", "1", ",", "0", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"0", ",", "1", ",", "0", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"0", ",", "1", ",", "1", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"0", ",", "1", ",", "1", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "0", ",", "0", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "0", ",", "0", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "0", ",", "1", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "0", ",", "1", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "1", ",", "0", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "1", ",", "0", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "1", ",", "1", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "1", ",", "1", ",", "1"}], "}"}]}], "}"}]], "Output",
+ CellChangeTimes->{
+ 3.5087839933307667`*^9, 3.508784032836603*^9, 3.508784072438197*^9,
+ 3.508837210475828*^9, {3.508837821810259*^9, 3.508837838684524*^9},
+ 3.509970045837077*^9, 3.510030292269497*^9, 3.510325625420429*^9}]
+}, Open ]]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell["Hamiltonian", "Subsection",
+ CellChangeTimes->{{3.5090804925886374`*^9, 3.509080494178164*^9}}],
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{"HFH", "[",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"kf_", ",", "lf_", ",", "mf_", ",", "nf_"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"ki_", ",", "li_", ",", "mi_", ",", "ni_"}], "}"}]}], "]"}], " ",
+ ":=", " ", "\[IndentingNewLine]",
+ RowBox[{
+ RowBox[{
+ RowBox[{"-", "t"}], " ",
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{"DiscreteDelta", "[",
+ RowBox[{
+ RowBox[{"kf", "-", "ki", "-", "1"}], ",",
+ RowBox[{"mf", "-", "mi", "+", "1"}], ",",
+ RowBox[{"lf", "-", "li"}], ",",
+ RowBox[{"nf", "-", "ni"}]}], "]"}], "+",
+ RowBox[{"DiscreteDelta", "[",
+ RowBox[{
+ RowBox[{"kf", "-", "ki", "+", "1"}], ",",
+ RowBox[{"mf", "-", "mi", "-", "1"}], ",",
+ RowBox[{"lf", "-", "li"}], ",",
+ RowBox[{"nf", "-", "ni"}]}], "]"}], "+",
+ RowBox[{"DiscreteDelta", "[",
+ RowBox[{
+ RowBox[{"kf", "-", "ki"}], ",",
+ RowBox[{"mf", "-", "mi"}], ",",
+ RowBox[{"lf", "-", "li", "-", "1"}], ",",
+ RowBox[{"nf", "-", "ni", "+", "1"}]}], "]"}], "+",
+ RowBox[{"DiscreteDelta", "[",
+ RowBox[{
+ RowBox[{"kf", "-", "ki"}], ",",
+ RowBox[{"mf", "-", "mi"}], ",",
+ RowBox[{"lf", "-", "li", "+", "1"}], ",",
+ RowBox[{"nf", "-", "ni", "-", "1"}]}], "]"}]}], ")"}]}], " ", "+",
+ "\[IndentingNewLine]",
+ RowBox[{"U",
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{"kf", " ", "lf"}], " ", "+", " ",
+ RowBox[{"mf", " ", "nf"}]}], ")"}],
+ RowBox[{"DiscreteDelta", "[",
+ RowBox[{
+ RowBox[{"kf", "-", "ki"}], ",",
+ RowBox[{"lf", "-", "li"}], ",",
+ RowBox[{"mf", "-", "mi"}], ",",
+ RowBox[{"nf", "-", "ni"}]}], "]"}],
+ RowBox[{"(*",
+ RowBox[{
+ RowBox[{"+", "\[IndentingNewLine]",
+ RowBox[{"-", "\[Mu]"}]}],
+ RowBox[{"(",
+ RowBox[{"m", "+", "n"}], ")"}],
+ RowBox[{"DiscreteDelta", "[",
+ RowBox[{
+ RowBox[{"k", "-", "m"}], ",",
+ RowBox[{"l", "-", "n"}]}], "]"}]}], "*)"}]}]}]}]], "Input",
+ CellChangeTimes->{{3.5087832565532103`*^9, 3.508783258500182*^9}, {
+ 3.508783348190814*^9, 3.5087836326748962`*^9}, {3.508783843170176*^9,
+ 3.508783850313211*^9}, {3.508785074190639*^9, 3.508785080524797*^9}, {
+ 3.508837185610881*^9, 3.508837187974235*^9}, {3.5088377114253597`*^9,
+ 3.5088377115681562`*^9}, {3.5088378907530746`*^9, 3.508837918838941*^9}, {
+ 3.50883796354082*^9, 3.508837969300885*^9}, {3.508838011485293*^9,
+ 3.508838143990327*^9}}],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[{
+ RowBox[{
+ RowBox[{"HFHmatrix", " ", "=", " ",
+ RowBox[{"Table", "[", " ",
+ RowBox[{
+ RowBox[{"HFH", "[",
+ RowBox[{"f", ",", "i"}], "]"}], ",", " ",
+ RowBox[{"{",
+ RowBox[{"f", ",", "FHBasis"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"i", ",", "FHBasis"}], "}"}]}], " ", "]"}]}],
+ ";"}], "\[IndentingNewLine]",
+ RowBox[{"HFHmatrix", "//", "MatrixForm"}]}], "Input",
+ CellChangeTimes->{{3.508783670539372*^9, 3.508783704346925*^9}, {
+ 3.5087837778192*^9, 3.5087837828681717`*^9}, {3.508784092387499*^9,
+ 3.508784122553347*^9}, 3.508784221180039*^9, {3.508838154137784*^9,
+ 3.508838167857397*^9}, {3.508838199737981*^9, 3.5088382000263166`*^9}, {
+ 3.5088386843965683`*^9, 3.508838684823778*^9}}],
+
+Cell[BoxData[
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {"0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
+ "0", "0"},
+ {"0", "0", "0", "0",
+ RowBox[{"-", "t"}], "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
+ "0"},
+ {"0", "0", "0", "0", "0", "0", "0", "0",
+ RowBox[{"-", "t"}], "0", "0", "0", "0", "0", "0", "0"},
+ {"0", "0", "0", "U", "0", "0",
+ RowBox[{"-", "t"}], "0", "0",
+ RowBox[{"-", "t"}], "0", "0", "0", "0", "0", "0"},
+ {"0",
+ RowBox[{"-", "t"}], "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
+ "0", "0", "0", "0"},
+ {"0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
+ "0", "0"},
+ {"0", "0", "0",
+ RowBox[{"-", "t"}], "0", "0", "0", "0", "0", "0", "0", "0",
+ RowBox[{"-", "t"}], "0", "0", "0"},
+ {"0", "0", "0", "0", "0", "0", "0", "U", "0", "0", "0", "0", "0",
+ RowBox[{"-", "t"}], "0", "0"},
+ {"0", "0",
+ RowBox[{"-", "t"}], "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
+ "0", "0", "0"},
+ {"0", "0", "0",
+ RowBox[{"-", "t"}], "0", "0", "0", "0", "0", "0", "0", "0",
+ RowBox[{"-", "t"}], "0", "0", "0"},
+ {"0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
+ "0", "0"},
+ {"0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "U", "0", "0",
+ RowBox[{"-", "t"}], "0"},
+ {"0", "0", "0", "0", "0", "0",
+ RowBox[{"-", "t"}], "0", "0",
+ RowBox[{"-", "t"}], "0", "0", "U", "0", "0", "0"},
+ {"0", "0", "0", "0", "0", "0", "0",
+ RowBox[{"-", "t"}], "0", "0", "0", "0", "0", "U", "0", "0"},
+ {"0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
+ RowBox[{"-", "t"}], "0", "0", "U", "0"},
+ {"0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0",
+ "0",
+ RowBox[{"2", " ", "U"}]}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
+ "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]], "Output",
+ CellChangeTimes->{3.508838200700156*^9, 3.5088386861861067`*^9,
+ 3.509970046004353*^9, 3.510030292369396*^9, 3.510325625486863*^9}]
+}, Open ]]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell["Sectors", "Subsection",
+ CellChangeTimes->{{3.50908051097156*^9, 3.5090805120273943`*^9}}],
+
+Cell[CellGroupData[{
+
+Cell["N = 0", "Subsubsection",
+ CellChangeTimes->{{3.509080572847994*^9, 3.5090805744030046`*^9}}],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"FHN0Basis", " ", "=", " ",
+ RowBox[{"FHBasis", "[",
+ RowBox[{"[",
+ RowBox[{"{", "1", "}"}], "]"}], "]"}]}]], "Input",
+ CellChangeTimes->{{3.509080606595818*^9, 3.5090806092362127`*^9}, {
+ 3.509080644988741*^9, 3.509080654707156*^9}}],
+
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{"{",
+ RowBox[{"0", ",", "0", ",", "0", ",", "0"}], "}"}], "}"}]], "Output",
+ CellChangeTimes->{3.5090806558336973`*^9, 3.509970046254805*^9,
+ 3.51003029270404*^9, 3.510325625543804*^9}]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[{
+ RowBox[{
+ RowBox[{"HFHN0matrix", " ", "=", " ",
+ RowBox[{"Table", "[", " ",
+ RowBox[{
+ RowBox[{"HFH", "[",
+ RowBox[{"f", ",", "i"}], "]"}], ",", " ",
+ RowBox[{"{",
+ RowBox[{"f", ",", "FHN0Basis"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"i", ",", "FHN0Basis"}], "}"}]}], " ", "]"}]}],
+ ";"}], "\[IndentingNewLine]",
+ RowBox[{"HFHN0matrix", "//", "MatrixForm"}]}], "Input",
+ CellChangeTimes->{{3.509080658962317*^9, 3.509080699734676*^9}}],
+
+Cell[BoxData[
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {"0"}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
+ "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]], "Output",
+ CellChangeTimes->{3.5090807030335493`*^9, 3.509970046343501*^9,
+ 3.510030292808241*^9, 3.5103256255938673`*^9}]
+}, Open ]]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[TextData[{
+ "N = 1, ",
+ Cell[BoxData[
+ FormBox[
+ RowBox[{
+ SubscriptBox["S", "z"], "=",
+ RowBox[{
+ RowBox[{"-", "1"}], "/", "2"}]}], TraditionalForm]]]
+}], "Subsubsection",
+ CellChangeTimes->{{3.509080572847994*^9, 3.5090805744030046`*^9}, {
+ 3.509080723461989*^9, 3.509080739915999*^9}}],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"FHN1SdownBasis", " ", "=", " ",
+ RowBox[{"FHBasis", "[",
+ RowBox[{"[",
+ RowBox[{"{",
+ RowBox[{"2", ",", "5"}], "}"}], "]"}], "]"}]}]], "Input",
+ CellChangeTimes->{{3.509080606595818*^9, 3.5090806092362127`*^9}, {
+ 3.509080644988741*^9, 3.509080654707156*^9}, {3.509080752222481*^9,
+ 3.5090807863471317`*^9}}],
+
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"0", ",", "0", ",", "0", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"0", ",", "1", ",", "0", ",", "0"}], "}"}]}], "}"}]], "Output",
+ CellChangeTimes->{3.5090806558336973`*^9, 3.509080787703191*^9,
+ 3.509970046459276*^9, 3.510030293543831*^9, 3.5103256256437387`*^9}]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[{
+ RowBox[{
+ RowBox[{"HFHN1Sdownmatrix", " ", "=", " ",
+ RowBox[{"Table", "[", " ",
+ RowBox[{
+ RowBox[{"HFH", "[",
+ RowBox[{"f", ",", "i"}], "]"}], ",", " ",
+ RowBox[{"{",
+ RowBox[{"f", ",", "FHN1SdownBasis"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"i", ",",
+ StyleBox["FHN1SdownBasis",
+ FontWeight->"Plain"]}], "}"}]}], " ", "]"}]}],
+ ";"}], "\[IndentingNewLine]",
+ RowBox[{"HFHN1Sdownmatrix", "//", "MatrixForm"}]}], "Input",
+ CellChangeTimes->{{3.509080658962317*^9, 3.509080699734676*^9}, {
+ 3.5090808101811743`*^9, 3.5090808368693*^9}}],
+
+Cell[BoxData[
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {"0",
+ RowBox[{"-", "t"}]},
+ {
+ RowBox[{"-", "t"}], "0"}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
+ "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]], "Output",
+ CellChangeTimes->{3.5090807030335493`*^9, 3.50908083835019*^9,
+ 3.509970046609377*^9, 3.510030293827169*^9, 3.5103256256935463`*^9}]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"Eigensystem", "[", "HFHN1Sdownmatrix", "]"}]], "Input",
+ CellChangeTimes->{{3.509080847171867*^9, 3.509080852594387*^9}}],
+
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "t"}], ",", "t"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"1", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "}"}]}], "}"}]], "Output",
+ CellChangeTimes->{3.509080853122671*^9, 3.509970046760251*^9,
+ 3.51003029389473*^9, 3.5103256257434397`*^9}]
+}, Open ]]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[TextData[{
+ "N = 1, ",
+ Cell[BoxData[
+ FormBox[
+ RowBox[{
+ SubscriptBox["S", "z"], "=",
+ RowBox[{
+ RowBox[{"+", "1"}], "/", "2"}]}], TraditionalForm]]]
+}], "Subsubsection",
+ CellChangeTimes->{{3.509080572847994*^9, 3.5090805744030046`*^9}, {
+ 3.509080723461989*^9, 3.509080739915999*^9}, {3.50908087568501*^9,
+ 3.509080875986874*^9}}],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"FHN1SupBasis", " ", "=", " ",
+ RowBox[{"FHBasis", "[",
+ RowBox[{"[",
+ RowBox[{"{",
+ RowBox[{"3", ",", "9"}], "}"}], "]"}], "]"}]}]], "Input",
+ CellChangeTimes->{{3.509080606595818*^9, 3.5090806092362127`*^9}, {
+ 3.509080644988741*^9, 3.509080654707156*^9}, {3.509080752222481*^9,
+ 3.5090807863471317`*^9}, {3.509080881136285*^9, 3.509080904169484*^9}}],
+
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"0", ",", "0", ",", "1", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}]], "Output",
+ CellChangeTimes->{3.5090806558336973`*^9, 3.509080787703191*^9,
+ 3.509080905301075*^9, 3.509970046855816*^9, 3.51003029395993*^9,
+ 3.510325625793338*^9}]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[{
+ RowBox[{
+ RowBox[{"HFHN1Supmatrix", " ", "=", " ",
+ RowBox[{"Table", "[", " ",
+ RowBox[{
+ RowBox[{"HFH", "[",
+ RowBox[{"f", ",", "i"}], "]"}], ",", " ",
+ RowBox[{"{",
+ RowBox[{"f", ",", "FHN1SupBasis"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"i", ",",
+ StyleBox["FHN1SupBasis",
+ FontWeight->"Plain"]}], "}"}]}], " ", "]"}]}],
+ ";"}], "\[IndentingNewLine]",
+ RowBox[{"HFHN1Supmatrix", "//", "MatrixForm"}]}], "Input",
+ CellChangeTimes->{{3.509080658962317*^9, 3.509080699734676*^9}, {
+ 3.5090808101811743`*^9, 3.5090808368693*^9}, {3.5090809139129343`*^9,
+ 3.50908092707698*^9}}],
+
+Cell[BoxData[
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {"0",
+ RowBox[{"-", "t"}]},
+ {
+ RowBox[{"-", "t"}], "0"}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
+ "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]], "Output",
+ CellChangeTimes->{3.5090807030335493`*^9, 3.50908083835019*^9,
+ 3.5090809290251207`*^9, 3.509970046990045*^9, 3.5100302940613613`*^9,
+ 3.510325625844454*^9}]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"Eigensystem", "[", "HFHN1Supmatrix", "]"}]], "Input",
+ CellChangeTimes->{{3.509080847171867*^9, 3.509080852594387*^9},
+ 3.5090809341805077`*^9}],
+
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "t"}], ",", "t"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"1", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "}"}]}], "}"}]], "Output",
+ CellChangeTimes->{3.509080853122671*^9, 3.509080934856102*^9,
+ 3.5099700470439663`*^9, 3.510030294149268*^9, 3.510325625894435*^9}]
+}, Open ]]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[TextData[{
+ "N = 2, ",
+ Cell[BoxData[
+ FormBox[
+ RowBox[{
+ SubscriptBox["S", "z"], "=",
+ RowBox[{"-", "1"}]}], TraditionalForm]]]
+}], "Subsubsection",
+ CellChangeTimes->{{3.509080572847994*^9, 3.5090805744030046`*^9}, {
+ 3.509080723461989*^9, 3.509080739915999*^9}, {3.50908087568501*^9,
+ 3.509080875986874*^9}, {3.509080954377675*^9, 3.509080960909334*^9}}],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"FHN2SdownBasis", " ", "=", " ",
+ RowBox[{"FHBasis", "[",
+ RowBox[{"[",
+ RowBox[{"{", "6", "}"}], "]"}], "]"}]}]], "Input",
+ CellChangeTimes->{{3.509080606595818*^9, 3.5090806092362127`*^9}, {
+ 3.509080644988741*^9, 3.509080654707156*^9}, {3.509080752222481*^9,
+ 3.5090807863471317`*^9}, {3.509080881136285*^9, 3.509080904169484*^9}, {
+ 3.509080965235941*^9, 3.509081008387887*^9}}],
+
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{"{",
+ RowBox[{"0", ",", "1", ",", "0", ",", "1"}], "}"}], "}"}]], "Output",
+ CellChangeTimes->{3.5090806558336973`*^9, 3.509080787703191*^9,
+ 3.509080905301075*^9, 3.5090810101669073`*^9, 3.509970047077467*^9,
+ 3.510030294228916*^9, 3.5103256259446163`*^9}]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[{
+ RowBox[{
+ RowBox[{"HFHN2Sdownmatrix", " ", "=", " ",
+ RowBox[{"Table", "[", " ",
+ RowBox[{
+ RowBox[{"HFH", "[",
+ RowBox[{"f", ",", "i"}], "]"}], ",", " ",
+ RowBox[{"{",
+ RowBox[{"f", ",", "FHN2SdownBasis"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"i", ",",
+ StyleBox["FHN2SdownBasis",
+ FontWeight->"Plain"]}], "}"}]}], " ", "]"}]}],
+ ";"}], "\[IndentingNewLine]",
+ RowBox[{"HFHN2Sdownmatrix", "//", "MatrixForm"}]}], "Input",
+ CellChangeTimes->{{3.509080658962317*^9, 3.509080699734676*^9}, {
+ 3.5090808101811743`*^9, 3.5090808368693*^9}, {3.5090809139129343`*^9,
+ 3.50908092707698*^9}, {3.509081018447012*^9, 3.509081032983221*^9}}],
+
+Cell[BoxData[
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {"0"}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
+ "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]], "Output",
+ CellChangeTimes->{3.5090807030335493`*^9, 3.50908083835019*^9,
+ 3.5090809290251207`*^9, 3.509081035395775*^9, 3.509970047135475*^9,
+ 3.510030294312437*^9, 3.510325626092774*^9}]
+}, Open ]]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[TextData[{
+ "N = 2, ",
+ Cell[BoxData[
+ FormBox[
+ RowBox[{
+ SubscriptBox["S", "z"], "=", "0"}], TraditionalForm]]]
+}], "Subsubsection",
+ CellChangeTimes->{{3.509080572847994*^9, 3.5090805744030046`*^9}, {
+ 3.509080723461989*^9, 3.509080739915999*^9}, {3.50908087568501*^9,
+ 3.509080875986874*^9}, {3.509081065308095*^9, 3.5090810741553288`*^9}}],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"FHN2S0Basis", " ", "=", " ",
+ RowBox[{"FHBasis", "[",
+ RowBox[{"[",
+ RowBox[{"{",
+ RowBox[{"4", ",", "7", ",", "10", ",", "13"}], "}"}], "]"}],
+ "]"}]}]], "Input",
+ CellChangeTimes->{{3.509080606595818*^9, 3.5090806092362127`*^9}, {
+ 3.509080644988741*^9, 3.509080654707156*^9}, {3.509080752222481*^9,
+ 3.5090807863471317`*^9}, {3.509080881136285*^9, 3.509080904169484*^9}, {
+ 3.509081077427451*^9, 3.509081140669469*^9}}],
+
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"0", ",", "0", ",", "1", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"0", ",", "1", ",", "1", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "0", ",", "0", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "1", ",", "0", ",", "0"}], "}"}]}], "}"}]], "Output",
+ CellChangeTimes->{
+ 3.5090806558336973`*^9, 3.509080787703191*^9, 3.509080905301075*^9, {
+ 3.509081114764721*^9, 3.509081141232716*^9}, 3.5090811729164743`*^9,
+ 3.509970047174118*^9, 3.510030294396461*^9, 3.510325626144672*^9}]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[{
+ RowBox[{
+ RowBox[{"HFHN2S0matrix", " ", "=", " ",
+ RowBox[{"Table", "[", " ",
+ RowBox[{
+ RowBox[{"HFH", "[",
+ RowBox[{"f", ",", "i"}], "]"}], ",", " ",
+ RowBox[{"{",
+ RowBox[{"f", ",", "FHN2S0Basis"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"i", ",",
+ StyleBox["FHN2S0Basis",
+ FontWeight->"Plain"]}], "}"}]}], " ", "]"}]}],
+ ";"}], "\[IndentingNewLine]",
+ RowBox[{"HFHN2S0matrix", "//", "MatrixForm"}]}], "Input",
+ CellChangeTimes->{{3.509080658962317*^9, 3.509080699734676*^9}, {
+ 3.5090808101811743`*^9, 3.5090808368693*^9}, {3.5090809139129343`*^9,
+ 3.50908092707698*^9}, {3.509081148135426*^9, 3.509081161875668*^9}}],
+
+Cell[BoxData[
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {"U",
+ RowBox[{"-", "t"}],
+ RowBox[{"-", "t"}], "0"},
+ {
+ RowBox[{"-", "t"}], "0", "0",
+ RowBox[{"-", "t"}]},
+ {
+ RowBox[{"-", "t"}], "0", "0",
+ RowBox[{"-", "t"}]},
+ {"0",
+ RowBox[{"-", "t"}],
+ RowBox[{"-", "t"}], "U"}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
+ "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]], "Output",
+ CellChangeTimes->{3.5090807030335493`*^9, 3.50908083835019*^9,
+ 3.5090809290251207`*^9, 3.509081173102688*^9, 3.5099700472406263`*^9,
+ 3.510030294481472*^9, 3.5103256261953077`*^9}]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"Eigensystem", "[", "HFHN2S0matrix", "]"}]], "Input",
+ CellChangeTimes->{{3.509080847171867*^9, 3.509080852594387*^9},
+ 3.5090809341805077`*^9, 3.509081165471714*^9}],
+
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"0", ",", "U", ",",
+ RowBox[{
+ FractionBox["1", "2"], " ",
+ RowBox[{"(",
+ RowBox[{"U", "-",
+ SqrtBox[
+ RowBox[{
+ RowBox[{"16", " ",
+ SuperscriptBox["t", "2"]}], "+",
+ SuperscriptBox["U", "2"]}]]}], ")"}]}], ",",
+ RowBox[{
+ FractionBox["1", "2"], " ",
+ RowBox[{"(",
+ RowBox[{"U", "+",
+ SqrtBox[
+ RowBox[{
+ RowBox[{"16", " ",
+ SuperscriptBox["t", "2"]}], "+",
+ SuperscriptBox["U", "2"]}]]}], ")"}]}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"0", ",",
+ RowBox[{"-", "1"}], ",", "1", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "1"}], ",", "0", ",", "0", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",",
+ RowBox[{"-",
+ FractionBox[
+ RowBox[{
+ RowBox[{"-", "U"}], "-",
+ SqrtBox[
+ RowBox[{
+ RowBox[{"16", " ",
+ SuperscriptBox["t", "2"]}], "+",
+ SuperscriptBox["U", "2"]}]]}],
+ RowBox[{"4", " ", "t"}]]}], ",",
+ RowBox[{"-",
+ FractionBox[
+ RowBox[{
+ RowBox[{"-", "U"}], "-",
+ SqrtBox[
+ RowBox[{
+ RowBox[{"16", " ",
+ SuperscriptBox["t", "2"]}], "+",
+ SuperscriptBox["U", "2"]}]]}],
+ RowBox[{"4", " ", "t"}]]}], ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",",
+ RowBox[{"-",
+ FractionBox[
+ RowBox[{
+ RowBox[{"-", "U"}], "+",
+ SqrtBox[
+ RowBox[{
+ RowBox[{"16", " ",
+ SuperscriptBox["t", "2"]}], "+",
+ SuperscriptBox["U", "2"]}]]}],
+ RowBox[{"4", " ", "t"}]]}], ",",
+ RowBox[{"-",
+ FractionBox[
+ RowBox[{
+ RowBox[{"-", "U"}], "+",
+ SqrtBox[
+ RowBox[{
+ RowBox[{"16", " ",
+ SuperscriptBox["t", "2"]}], "+",
+ SuperscriptBox["U", "2"]}]]}],
+ RowBox[{"4", " ", "t"}]]}], ",", "1"}], "}"}]}], "}"}]}],
+ "}"}]], "Output",
+ CellChangeTimes->{3.509080853122671*^9, 3.509080934856102*^9,
+ 3.509081173216898*^9, 3.5099700473346043`*^9, 3.5100302946148157`*^9,
+ 3.5103256262953653`*^9}]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"N", "[",
+ RowBox[{"%", "/.",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"t", "\[Rule]", "1"}], ",",
+ RowBox[{"U", "\[Rule]", "1"}]}], "}"}]}], "]"}]], "Input",
+ CellChangeTimes->{{3.509081185051283*^9, 3.509081227527027*^9}}],
+
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"0.`", ",", "1.`", ",",
+ RowBox[{"-", "1.5615528128088303`"}], ",", "2.5615528128088303`"}],
+ "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"0.`", ",",
+ RowBox[{"-", "1.`"}], ",", "1.`", ",", "0.`"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "1.`"}], ",", "0.`", ",", "0.`", ",", "1.`"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ "1.`", ",", "1.2807764064044151`", ",", "1.2807764064044151`", ",",
+ "1.`"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1.`", ",",
+ RowBox[{"-", "0.7807764064044151`"}], ",",
+ RowBox[{"-", "0.7807764064044151`"}], ",", "1.`"}], "}"}]}], "}"}]}],
+ "}"}]], "Output",
+ CellChangeTimes->{{3.5090811985980186`*^9, 3.509081228573151*^9},
+ 3.5099700474079323`*^9, 3.510030294838773*^9, 3.510325626346389*^9}]
+}, Open ]]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[TextData[{
+ "N = 2, ",
+ Cell[BoxData[
+ FormBox[
+ RowBox[{
+ SubscriptBox["S", "z"], "=",
+ RowBox[{"+", "1"}]}], TraditionalForm]]]
+}], "Subsubsection",
+ CellChangeTimes->{{3.509080572847994*^9, 3.5090805744030046`*^9}, {
+ 3.509080723461989*^9, 3.509080739915999*^9}, {3.50908087568501*^9,
+ 3.509080875986874*^9}, {3.509080954377675*^9, 3.509080960909334*^9}, {
+ 3.509081309203281*^9, 3.5090813094907713`*^9}}],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"FHN2SupBasis", " ", "=", " ",
+ RowBox[{"FHBasis", "[",
+ RowBox[{"[",
+ RowBox[{"{", "11", "}"}], "]"}], "]"}]}]], "Input",
+ CellChangeTimes->{{3.509080606595818*^9, 3.5090806092362127`*^9}, {
+ 3.509080644988741*^9, 3.509080654707156*^9}, {3.509080752222481*^9,
+ 3.5090807863471317`*^9}, {3.509080881136285*^9, 3.509080904169484*^9}, {
+ 3.509080965235941*^9, 3.509081008387887*^9}, {3.509081315975029*^9,
+ 3.509081316039914*^9}, {3.509081346455505*^9, 3.509081346840076*^9}}],
+
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{"{",
+ RowBox[{"1", ",", "0", ",", "1", ",", "0"}], "}"}], "}"}]], "Output",
+ CellChangeTimes->{3.5090806558336973`*^9, 3.509080787703191*^9,
+ 3.509080905301075*^9, 3.5090810101669073`*^9, 3.509081349455768*^9,
+ 3.509970047473996*^9, 3.510030294904725*^9, 3.5103256263952312`*^9}]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[{
+ RowBox[{
+ RowBox[{"HFHN2Supmatrix", " ", "=", " ",
+ RowBox[{"Table", "[", " ",
+ RowBox[{
+ RowBox[{"HFH", "[",
+ RowBox[{"f", ",", "i"}], "]"}], ",", " ",
+ RowBox[{"{",
+ RowBox[{"f", ",", "FHN2SupBasis"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"i", ",",
+ StyleBox["FHN2SupBasis",
+ FontWeight->"Plain"]}], "}"}]}], " ", "]"}]}],
+ ";"}], "\[IndentingNewLine]",
+ RowBox[{"HFHN2Supmatrix", "//", "MatrixForm"}]}], "Input",
+ CellChangeTimes->{{3.509080658962317*^9, 3.509080699734676*^9}, {
+ 3.5090808101811743`*^9, 3.5090808368693*^9}, {3.5090809139129343`*^9,
+ 3.50908092707698*^9}, {3.509081018447012*^9, 3.509081032983221*^9}, {
+ 3.509081355866563*^9, 3.5090813687676783`*^9}}],
+
+Cell[BoxData[
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {"0"}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
+ "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]], "Output",
+ CellChangeTimes->{3.5090807030335493`*^9, 3.50908083835019*^9,
+ 3.5090809290251207`*^9, 3.509081035395775*^9, 3.509081374969657*^9,
+ 3.509970047541456*^9, 3.510030294971818*^9, 3.51032562644627*^9}]
+}, Open ]]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[TextData[{
+ "N = 3, ",
+ Cell[BoxData[
+ FormBox[
+ RowBox[{
+ SubscriptBox["S", "z"], "=",
+ RowBox[{
+ RowBox[{"-", "1"}], "/", "2"}]}], TraditionalForm]]]
+}], "Subsubsection",
+ CellChangeTimes->{{3.509080572847994*^9, 3.5090805744030046`*^9}, {
+ 3.509080723461989*^9, 3.509080739915999*^9}, {3.50908087568501*^9,
+ 3.509080875986874*^9}, {3.509081065308095*^9, 3.5090810741553288`*^9}, {
+ 3.509081433906945*^9, 3.5090814576806498`*^9}, {3.5090814895165443`*^9,
+ 3.509081489565625*^9}}],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"FHN3SdownBasis", " ", "=", " ",
+ RowBox[{"FHBasis", "[",
+ RowBox[{"[",
+ RowBox[{"{",
+ RowBox[{"8", ",", "14"}], "}"}], "]"}], "]"}]}]], "Input",
+ CellChangeTimes->{{3.509080606595818*^9, 3.5090806092362127`*^9}, {
+ 3.509080644988741*^9, 3.509080654707156*^9}, {3.509080752222481*^9,
+ 3.5090807863471317`*^9}, {3.509080881136285*^9, 3.509080904169484*^9}, {
+ 3.509081077427451*^9, 3.509081140669469*^9}, {3.509081462627431*^9,
+ 3.509081464496978*^9}, {3.5090814948262863`*^9, 3.509081532871961*^9}}],
+
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"0", ",", "1", ",", "1", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "1", ",", "0", ",", "1"}], "}"}]}], "}"}]], "Output",
+ CellChangeTimes->{
+ 3.5090806558336973`*^9, 3.509080787703191*^9, 3.509080905301075*^9, {
+ 3.509081114764721*^9, 3.509081141232716*^9}, 3.5090811729164743`*^9,
+ 3.509081534964801*^9, 3.509970047607524*^9, 3.510030295053656*^9,
+ 3.510325626495886*^9}]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[{
+ RowBox[{
+ RowBox[{"HFHN3Sdownmatrix", " ", "=", " ",
+ RowBox[{"Table", "[", " ",
+ RowBox[{
+ RowBox[{"HFH", "[",
+ RowBox[{"f", ",", "i"}], "]"}], ",", " ",
+ RowBox[{"{",
+ RowBox[{"f", ",", "FHN3SdownBasis"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"i", ",",
+ StyleBox["FHN3SdownBasis",
+ FontWeight->"Plain"]}], "}"}]}], " ", "]"}]}],
+ ";"}], "\[IndentingNewLine]",
+ RowBox[{"HFHN3Sdownmatrix", "//", "MatrixForm"}]}], "Input",
+ CellChangeTimes->{{3.509080658962317*^9, 3.509080699734676*^9}, {
+ 3.5090808101811743`*^9, 3.5090808368693*^9}, {3.5090809139129343`*^9,
+ 3.50908092707698*^9}, {3.509081148135426*^9, 3.509081161875668*^9}, {
+ 3.509081544645392*^9, 3.509081560035411*^9}}],
+
+Cell[BoxData[
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {"U",
+ RowBox[{"-", "t"}]},
+ {
+ RowBox[{"-", "t"}], "U"}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
+ "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]], "Output",
+ CellChangeTimes->{3.5090807030335493`*^9, 3.50908083835019*^9,
+ 3.5090809290251207`*^9, 3.509081173102688*^9, 3.509081564168229*^9,
+ 3.509970047675343*^9, 3.51003029513037*^9, 3.5103256265464*^9}]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"Eigensystem", "[", "HFHN3Sdownmatrix", "]"}]], "Input",
+ CellChangeTimes->{{3.509080847171867*^9, 3.509080852594387*^9},
+ 3.5090809341805077`*^9, 3.509081165471714*^9, 3.5090815670737553`*^9}],
+
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{
+ RowBox[{"-", "t"}], "+", "U"}], ",",
+ RowBox[{"t", "+", "U"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"1", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "}"}]}], "}"}]], "Output",
+ CellChangeTimes->{3.509080853122671*^9, 3.509080934856102*^9,
+ 3.509081173216898*^9, 3.509081567945903*^9, 3.5099700477413607`*^9,
+ 3.5100302952192383`*^9, 3.510325626595799*^9}]
+}, Open ]]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[TextData[{
+ "N = 3, ",
+ Cell[BoxData[
+ FormBox[
+ RowBox[{
+ SubscriptBox["S", "z"], "=",
+ RowBox[{
+ RowBox[{"+", "1"}], "/", "2"}]}], TraditionalForm]]]
+}], "Subsubsection",
+ CellChangeTimes->{{3.509080572847994*^9, 3.5090805744030046`*^9}, {
+ 3.509080723461989*^9, 3.509080739915999*^9}, {3.50908087568501*^9,
+ 3.509080875986874*^9}, {3.509081065308095*^9, 3.5090810741553288`*^9}, {
+ 3.509081433906945*^9, 3.5090814576806498`*^9}, {3.5090814895165443`*^9,
+ 3.509081489565625*^9}, 3.5090815926501493`*^9}],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"FHN3SupBasis", " ", "=", " ",
+ RowBox[{"FHBasis", "[",
+ RowBox[{"[",
+ RowBox[{"{",
+ RowBox[{"12", ",", "15"}], "}"}], "]"}], "]"}]}]], "Input",
+ CellChangeTimes->{{3.509080606595818*^9, 3.5090806092362127`*^9}, {
+ 3.509080644988741*^9, 3.509080654707156*^9}, {3.509080752222481*^9,
+ 3.5090807863471317`*^9}, {3.509080881136285*^9, 3.509080904169484*^9}, {
+ 3.509081077427451*^9, 3.509081140669469*^9}, {3.509081462627431*^9,
+ 3.509081464496978*^9}, {3.5090814948262863`*^9, 3.509081532871961*^9}, {
+ 3.509081601474731*^9, 3.509081630665339*^9}}],
+
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"1", ",", "0", ",", "1", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "1", ",", "1", ",", "0"}], "}"}]}], "}"}]], "Output",
+ CellChangeTimes->{
+ 3.5090806558336973`*^9, 3.509080787703191*^9, 3.509080905301075*^9, {
+ 3.509081114764721*^9, 3.509081141232716*^9}, 3.5090811729164743`*^9,
+ 3.509081534964801*^9, 3.509081632937151*^9, 3.509970047808132*^9,
+ 3.510030295297756*^9, 3.510325626646489*^9}]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[{
+ RowBox[{
+ RowBox[{"HFHN3Supmatrix", " ", "=", " ",
+ RowBox[{"Table", "[", " ",
+ RowBox[{
+ RowBox[{"HFH", "[",
+ RowBox[{"f", ",", "i"}], "]"}], ",", " ",
+ RowBox[{"{",
+ RowBox[{"f", ",", "FHN3SupBasis"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"i", ",",
+ StyleBox["FHN3SupBasis",
+ FontWeight->"Plain"]}], "}"}]}], " ", "]"}]}],
+ ";"}], "\[IndentingNewLine]",
+ RowBox[{"HFHN3Supmatrix", "//", "MatrixForm"}]}], "Input",
+ CellChangeTimes->{{3.509080658962317*^9, 3.509080699734676*^9}, {
+ 3.5090808101811743`*^9, 3.5090808368693*^9}, {3.5090809139129343`*^9,
+ 3.50908092707698*^9}, {3.509081148135426*^9, 3.509081161875668*^9}, {
+ 3.509081544645392*^9, 3.509081560035411*^9}, {3.509081641999453*^9,
+ 3.509081654472526*^9}}],
+
+Cell[BoxData[
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {"U",
+ RowBox[{"-", "t"}]},
+ {
+ RowBox[{"-", "t"}], "U"}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
+ "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]], "Output",
+ CellChangeTimes->{3.5090807030335493`*^9, 3.50908083835019*^9,
+ 3.5090809290251207`*^9, 3.509081173102688*^9, 3.509081564168229*^9,
+ 3.509081660633189*^9, 3.5099700478753853`*^9, 3.510030295365656*^9,
+ 3.5103256266968517`*^9}]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"Eigensystem", "[", "HFHN3Supmatrix", "]"}]], "Input",
+ CellChangeTimes->{{3.509080847171867*^9, 3.509080852594387*^9},
+ 3.5090809341805077`*^9, 3.509081165471714*^9, 3.5090815670737553`*^9, {
+ 3.509081664937511*^9, 3.509081674443981*^9}}],
+
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{
+ RowBox[{"-", "t"}], "+", "U"}], ",",
+ RowBox[{"t", "+", "U"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"1", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "}"}]}], "}"}]], "Output",
+ CellChangeTimes->{3.509080853122671*^9, 3.509080934856102*^9,
+ 3.509081173216898*^9, 3.509081567945903*^9, 3.509081675524811*^9,
+ 3.509970048046549*^9, 3.510030295458765*^9, 3.5103256267427063`*^9}]
+}, Open ]]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[TextData[{
+ "N = 4, ",
+ Cell[BoxData[
+ FormBox[
+ RowBox[{
+ SubscriptBox["S", "z"], "=", "0"}], TraditionalForm]]]
+}], "Subsubsection",
+ CellChangeTimes->{{3.509080572847994*^9, 3.5090805744030046`*^9}, {
+ 3.509080723461989*^9, 3.509080739915999*^9}, {3.50908087568501*^9,
+ 3.509080875986874*^9}, {3.509081065308095*^9, 3.5090810741553288`*^9}, {
+ 3.509081433906945*^9, 3.5090814576806498`*^9}, {3.5090814895165443`*^9,
+ 3.509081489565625*^9}, 3.5090815926501493`*^9, {3.5090816973051367`*^9,
+ 3.509081702350813*^9}}],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"FHN4S0Basis", " ", "=", " ",
+ RowBox[{"FHBasis", "[",
+ RowBox[{"[",
+ RowBox[{"{", "16", "}"}], "]"}], "]"}]}]], "Input",
+ CellChangeTimes->{{3.509080606595818*^9, 3.5090806092362127`*^9}, {
+ 3.509080644988741*^9, 3.509080654707156*^9}, {3.509080752222481*^9,
+ 3.5090807863471317`*^9}, {3.509080881136285*^9, 3.509080904169484*^9}, {
+ 3.509081077427451*^9, 3.509081140669469*^9}, {3.509081462627431*^9,
+ 3.509081464496978*^9}, {3.5090814948262863`*^9, 3.509081532871961*^9}, {
+ 3.509081601474731*^9, 3.509081630665339*^9}, {3.509081707635148*^9,
+ 3.509081726210595*^9}}],
+
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{"{",
+ RowBox[{"1", ",", "1", ",", "1", ",", "1"}], "}"}], "}"}]], "Output",
+ CellChangeTimes->{
+ 3.5090806558336973`*^9, 3.509080787703191*^9, 3.509080905301075*^9, {
+ 3.509081114764721*^9, 3.509081141232716*^9}, 3.5090811729164743`*^9,
+ 3.509081534964801*^9, 3.509081632937151*^9, 3.509081728714408*^9,
+ 3.509970048109439*^9, 3.510030295537692*^9, 3.510325626796653*^9}]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[{
+ RowBox[{
+ RowBox[{"HFHN4S0matrix", " ", "=", " ",
+ RowBox[{"Table", "[", " ",
+ RowBox[{
+ RowBox[{"HFH", "[",
+ RowBox[{"f", ",", "i"}], "]"}], ",", " ",
+ RowBox[{"{",
+ RowBox[{"f", ",", "FHN4S0Basis"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"i", ",",
+ StyleBox["FHN4S0Basis",
+ FontWeight->"Plain"]}], "}"}]}], " ", "]"}]}],
+ ";"}], "\[IndentingNewLine]",
+ RowBox[{"HFHN4S0matrix", "//", "MatrixForm"}]}], "Input",
+ CellChangeTimes->{{3.509080658962317*^9, 3.509080699734676*^9}, {
+ 3.5090808101811743`*^9, 3.5090808368693*^9}, {3.5090809139129343`*^9,
+ 3.50908092707698*^9}, {3.509081148135426*^9, 3.509081161875668*^9}, {
+ 3.509081544645392*^9, 3.509081560035411*^9}, {3.509081641999453*^9,
+ 3.509081654472526*^9}, {3.509081734734194*^9, 3.509081749114333*^9}}],
+
+Cell[BoxData[
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {
+ RowBox[{"2", " ", "U"}]}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
+ "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]], "Output",
+ CellChangeTimes->{3.5090807030335493`*^9, 3.50908083835019*^9,
+ 3.5090809290251207`*^9, 3.509081173102688*^9, 3.509081564168229*^9,
+ 3.509081660633189*^9, 3.5090817507359343`*^9, 3.509970048175845*^9,
+ 3.510030295620113*^9, 3.5103256268467484`*^9}]
+}, Open ]]
+}, Open ]]
+}, Open ]]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell["t - J model", "Section",
+ CellChangeTimes->{{3.508787678198584*^9, 3.508787682796872*^9}}],
+
+Cell[BoxData[
+ RowBox[{
+ SubscriptBox["H", "tJ"], " ", "=",
+ RowBox[{
+ RowBox[{
+ RowBox[{"-", "t"}],
+ RowBox[{
+ SubscriptBox["\[Sum]", "\[Sigma]"],
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{
+ SubsuperscriptBox["c",
+ RowBox[{"1", ",", "\[Sigma]"}], "\[Dagger]"],
+ SubscriptBox["c",
+ RowBox[{"2", ",", "\[Sigma]"}]]}], "+",
+ RowBox[{
+ SubsuperscriptBox["c",
+ RowBox[{"2", ",", "\[Sigma]"}], "\[Dagger]"],
+ SubscriptBox["c",
+ RowBox[{"1", ",", "\[Sigma]"}]]}]}], ")"}]}]}], "+", " ",
+ RowBox[{"J", " ",
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{
+ SubscriptBox["S", "1"], ".",
+ SubscriptBox["S", "2"]}], "-",
+ RowBox[{
+ SubscriptBox["n", "1"],
+ RowBox[{
+ SubscriptBox["n", "2"], "/", "4"}]}]}], ")"}]}]}]}]], "Text",
+ CellChangeTimes->{{3.508787698583405*^9, 3.508787703684375*^9}, {
+ 3.50878774000204*^9, 3.5087877991075373`*^9}, {3.508787845628374*^9,
+ 3.508787924934188*^9}, 3.5098732576715527`*^9, {3.6041459732061234`*^9,
+ 3.604145989694685*^9}}],
+
+Cell[CellGroupData[{
+
+Cell["Basis", "Subsection",
+ CellChangeTimes->{{3.5090794061916933`*^9, 3.509079406904153*^9}}],
+
+Cell["\<\
+For each basis state, the first two elements are either a spinor for the \
+particle on site 1 or 0 for no particle and the last two elements likewise \
+for the second site.\
+\>", "Text",
+ CellChangeTimes->{{3.5103255121690903`*^9, 3.510325606566979*^9},
+ 3.5411607660955963`*^9}],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"tJBasis", " ", "=", " ",
+ RowBox[{"Flatten", "[", " ",
+ RowBox[{
+ RowBox[{"Table", "[", " ",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"k", ",", "l", ",", "m", ",", "n"}], "}"}], ",", " ",
+ RowBox[{"{",
+ RowBox[{"k", ",", "0", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"l", ",", "0", ",",
+ RowBox[{"1", "-", "k"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"m", ",", "0", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"n", ",", "0", ",",
+ RowBox[{"1", "-", "m"}]}], "}"}]}], "]"}], ",", " ", "3"}],
+ "]"}]}]], "Input",
+ CellChangeTimes->{{3.508783880127376*^9, 3.508783991254715*^9}, {
+ 3.508784023788666*^9, 3.508784071702196*^9}, {3.508837729976532*^9,
+ 3.508837730106048*^9}, {3.508837770902673*^9, 3.508837837983169*^9}, {
+ 3.508840464198662*^9, 3.508840464461895*^9}, {3.5088405270837297`*^9,
+ 3.508840555634008*^9}, {3.5088406193841267`*^9, 3.508840677205818*^9}, {
+ 3.509078854415884*^9, 3.509078927477874*^9}}],
+
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"0", ",", "0", ",", "0", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"0", ",", "0", ",", "0", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"0", ",", "0", ",", "1", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"0", ",", "1", ",", "0", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"0", ",", "1", ",", "0", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"0", ",", "1", ",", "1", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "0", ",", "0", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "0", ",", "0", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "0", ",", "1", ",", "0"}], "}"}]}], "}"}]], "Output",
+ CellChangeTimes->{
+ 3.5088405566060343`*^9, 3.508840625450501*^9, {3.5088406677031403`*^9,
+ 3.50884067823619*^9}, {3.509078923267597*^9, 3.50907892809859*^9},
+ 3.509873004146297*^9, 3.509874184303581*^9, 3.509970051351584*^9,
+ 3.5100302957051363`*^9, 3.510325626897502*^9}]
+}, Open ]]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell["Hamiltonian", "Subsection",
+ CellChangeTimes->{{3.509079420532467*^9, 3.50907942309033*^9}}],
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{"HtJ", "[",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"kf_", ",", "lf_", ",", "mf_", ",", "nf_"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"ki_", ",", "li_", ",", "mi_", ",", "ni_"}], "}"}]}], "]"}], " ",
+ ":=", " ", "\[IndentingNewLine]",
+ RowBox[{
+ RowBox[{
+ RowBox[{"-", "t"}], " ",
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{"DiscreteDelta", "[",
+ RowBox[{
+ RowBox[{"kf", "-", "ki", "-", "1"}], ",",
+ RowBox[{"mf", "-", "mi", "+", "1"}], ",",
+ RowBox[{"lf", "-", "li"}], ",",
+ RowBox[{"nf", "-", "ni"}]}], "]"}], "+",
+ RowBox[{"DiscreteDelta", "[",
+ RowBox[{
+ RowBox[{"kf", "-", "ki", "+", "1"}], ",",
+ RowBox[{"mf", "-", "mi", "-", "1"}], ",",
+ RowBox[{"lf", "-", "li"}], ",",
+ RowBox[{"nf", "-", "ni"}]}], "]"}], "+", "\[IndentingNewLine]",
+ RowBox[{"DiscreteDelta", "[",
+ RowBox[{
+ RowBox[{"kf", "-", "ki"}], ",",
+ RowBox[{"mf", "-", "mi"}], ",",
+ RowBox[{"lf", "-", "li", "-", "1"}], ",",
+ RowBox[{"nf", "-", "ni", "+", "1"}]}], "]"}], "+",
+ RowBox[{"DiscreteDelta", "[",
+ RowBox[{
+ RowBox[{"kf", "-", "ki"}], ",",
+ RowBox[{"mf", "-", "mi"}], ",",
+ RowBox[{"lf", "-", "li", "+", "1"}], ",",
+ RowBox[{"nf", "-", "ni", "-", "1"}]}], "]"}]}], ")"}]}], " ", "+",
+ "\[IndentingNewLine]",
+ RowBox[{
+ FractionBox["J", "4"],
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{"Sum", "[", " ",
+ RowBox[{
+ RowBox[{
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"kf", ",", "lf"}], "}"}], ".",
+ RowBox[{"PauliMatrix", "[", "\[Alpha]", "]"}], ".",
+ RowBox[{"{",
+ RowBox[{"ki", ",", "li"}], "}"}]}], "*",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"mf", ",", "nf"}], "}"}], ".",
+ RowBox[{"PauliMatrix", "[", "\[Alpha]", "]"}], ".",
+ RowBox[{"{",
+ RowBox[{"mi", ",", "ni"}], "}"}]}]}], ",", " ",
+ RowBox[{"{",
+ RowBox[{"\[Alpha]", ",", "3"}], "}"}]}], " ", "]"}], " ", "-", " ",
+ RowBox[{
+ RowBox[{"(",
+ RowBox[{"ki", "+", "li"}], ")"}],
+ RowBox[{"(",
+ RowBox[{"mi", "+", "ni"}], ")"}],
+ RowBox[{"DiscreteDelta", "[",
+ RowBox[{
+ RowBox[{"kf", "-", "ki"}], ",",
+ RowBox[{"mf", "-", "mi"}], ",",
+ RowBox[{"lf", "-", "li"}], ",",
+ RowBox[{"nf", "-", "ni"}]}], "]"}]}]}], ")"}]}]}]}]], "Input",
+ CellChangeTimes->{{3.5087832565532103`*^9, 3.508783258500182*^9}, {
+ 3.508783348190814*^9, 3.5087836326748962`*^9}, {3.508783843170176*^9,
+ 3.508783850313211*^9}, {3.508785074190639*^9, 3.508785080524797*^9}, {
+ 3.508837185610881*^9, 3.508837187974235*^9}, {3.5088377114253597`*^9,
+ 3.5088377115681562`*^9}, {3.5088378907530746`*^9, 3.508837918838941*^9}, {
+ 3.50883796354082*^9, 3.508837969300885*^9}, {3.508838011485293*^9,
+ 3.508838143990327*^9}, {3.508840697248144*^9, 3.508840697591522*^9}, {
+ 3.5090785040742826`*^9, 3.509078536676858*^9}, {3.509078571853326*^9,
+ 3.509078620164332*^9}, {3.509079045831913*^9, 3.50907904657579*^9}, {
+ 3.5098740553726187`*^9, 3.509874156469371*^9}}],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[{
+ RowBox[{
+ RowBox[{"HtJmatrix", " ", "=", " ",
+ RowBox[{"Table", "[", " ",
+ RowBox[{
+ RowBox[{"HtJ", "[",
+ RowBox[{"f", ",", "i"}], "]"}], ",", " ",
+ RowBox[{"{",
+ RowBox[{"f", ",", "tJBasis"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"i", ",", "tJBasis"}], "}"}]}], " ", "]"}]}],
+ ";"}], "\[IndentingNewLine]",
+ RowBox[{"HtJmatrix", "//", "MatrixForm"}]}], "Input",
+ CellChangeTimes->{{3.508783670539372*^9, 3.508783704346925*^9}, {
+ 3.5087837778192*^9, 3.5087837828681717`*^9}, {3.508784092387499*^9,
+ 3.508784122553347*^9}, 3.508784221180039*^9, {3.508838154137784*^9,
+ 3.508838167857397*^9}, {3.508838199737981*^9, 3.5088382000263166`*^9}, {
+ 3.5088386843965683`*^9, 3.508838684823778*^9}, {3.509078643533945*^9,
+ 3.509078672053007*^9}}],
+
+Cell[BoxData[
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {"0", "0", "0", "0", "0", "0", "0", "0", "0"},
+ {"0", "0", "0",
+ RowBox[{"-", "t"}], "0", "0", "0", "0", "0"},
+ {"0", "0", "0", "0", "0", "0",
+ RowBox[{"-", "t"}], "0", "0"},
+ {"0",
+ RowBox[{"-", "t"}], "0", "0", "0", "0", "0", "0", "0"},
+ {"0", "0", "0", "0", "0", "0", "0", "0", "0"},
+ {"0", "0", "0", "0", "0",
+ RowBox[{"-",
+ FractionBox["J", "2"]}], "0",
+ FractionBox["J", "2"], "0"},
+ {"0", "0",
+ RowBox[{"-", "t"}], "0", "0", "0", "0", "0", "0"},
+ {"0", "0", "0", "0", "0",
+ FractionBox["J", "2"], "0",
+ RowBox[{"-",
+ FractionBox["J", "2"]}], "0"},
+ {"0", "0", "0", "0", "0", "0", "0", "0", "0"}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
+ "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]], "Output",
+ CellChangeTimes->{
+ 3.5090786743176003`*^9, 3.5090790110265493`*^9, 3.509873004530007*^9, {
+ 3.5098741695820513`*^9, 3.509874184454855*^9}, 3.50997005153472*^9,
+ 3.510030295936781*^9, 3.510325626973976*^9}]
+}, Open ]]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell["Sectors", "Subsection",
+ CellChangeTimes->{{3.5090794532933083`*^9, 3.509079454551938*^9}}],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{"N", "=", "0"}], ",", " ",
+ RowBox[{
+ SubscriptBox["S", "z"], "=", "0"}]}]], "Subsubsection",
+ CellChangeTimes->{{3.509079942612878*^9, 3.509079951079707*^9}}],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"tJN0Basis", " ", "=", " ",
+ RowBox[{"tJBasis", "[",
+ RowBox[{"[",
+ RowBox[{"{", "1", "}"}], "]"}], "]"}]}]], "Input",
+ CellChangeTimes->{{3.509079714800024*^9, 3.509079765089875*^9}}],
+
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{"{",
+ RowBox[{"0", ",", "0", ",", "0", ",", "0"}], "}"}], "}"}]], "Output",
+ CellChangeTimes->{{3.50907973069385*^9, 3.50907973607672*^9},
+ 3.5090797663366823`*^9, 3.5098730046858273`*^9, 3.509874184555613*^9,
+ 3.509970051684512*^9, 3.510030296073934*^9, 3.5103256271116953`*^9}]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[{
+ RowBox[{
+ RowBox[{"HtJN0", " ", "=", " ",
+ RowBox[{"Table", "[", " ",
+ RowBox[{
+ RowBox[{"HtJ", "[",
+ RowBox[{"f", ",", "i"}], "]"}], ",", " ",
+ RowBox[{"{",
+ RowBox[{"f", ",", "tJN0Basis"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"i", ",", "tJN0Basis"}], "}"}]}], " ", "]"}]}],
+ ";"}], "\[IndentingNewLine]",
+ RowBox[{"HtJN0", " ", "//", "MatrixForm"}]}], "Input",
+ CellChangeTimes->{{3.509079510184618*^9, 3.509079524894363*^9}, {
+ 3.509079591799148*^9, 3.5090795932955713`*^9}, {3.509079748970049*^9,
+ 3.509079779450526*^9}}],
+
+Cell[BoxData[
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {"0"}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
+ "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]], "Output",
+ CellChangeTimes->{3.509079780962462*^9, 3.509873004748386*^9,
+ 3.5098741846222553`*^9, 3.509970051718769*^9, 3.510030296158188*^9,
+ 3.510325627164168*^9}]
+}, Open ]]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{"N", "=", "1"}], ",", " ",
+ RowBox[{
+ SubscriptBox["S", "z"], "=",
+ RowBox[{
+ RowBox[{"-", "1"}], "/", "2"}]}]}]], "Subsubsection",
+ CellChangeTimes->{{3.509079942612878*^9, 3.509079968638932*^9}}],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"tJN1SdownBasis", " ", "=", " ",
+ RowBox[{"tJBasis", "[",
+ RowBox[{"[",
+ RowBox[{"{",
+ RowBox[{"2", ",", "4"}], "}"}], "]"}], "]"}]}]], "Input",
+ CellChangeTimes->{{3.509079812636983*^9, 3.5090798593901653`*^9}}],
+
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"0", ",", "0", ",", "0", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"0", ",", "1", ",", "0", ",", "0"}], "}"}]}], "}"}]], "Output",
+ CellChangeTimes->{3.509079860013033*^9, 3.509873004814958*^9,
+ 3.509874184688035*^9, 3.509970051773518*^9, 3.5100302962420883`*^9,
+ 3.510325627214677*^9}]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[{
+ RowBox[{
+ RowBox[{"HtJN1Sdown", " ", "=", " ",
+ RowBox[{"Table", "[", " ",
+ RowBox[{
+ RowBox[{"HtJ", "[",
+ RowBox[{"f", ",", "i"}], "]"}], ",", " ",
+ RowBox[{"{",
+ RowBox[{"f", ",", "tJN1SdownBasis"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"i", ",", "tJN1SdownBasis"}], "}"}]}], " ", "]"}]}],
+ ";"}], "\[IndentingNewLine]",
+ RowBox[{"HtJN1Sdown", " ", "//", "MatrixForm"}]}], "Input",
+ CellChangeTimes->{{3.509079510184618*^9, 3.509079524894363*^9}, {
+ 3.509079591799148*^9, 3.5090795932955713`*^9}, {3.509079748970049*^9,
+ 3.509079779450526*^9}, {3.5090798768892097`*^9, 3.5090799011830387`*^9}}],
+
+Cell[BoxData[
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {"0",
+ RowBox[{"-", "t"}]},
+ {
+ RowBox[{"-", "t"}], "0"}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
+ "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]], "Output",
+ CellChangeTimes->{3.5090799021483192`*^9, 3.509873004882298*^9,
+ 3.509874184755988*^9, 3.5099700518231773`*^9, 3.510030296325145*^9,
+ 3.510325627264242*^9}]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"Eigensystem", "[", "HtJN1Sdown", "]"}]], "Input",
+ CellChangeTimes->{{3.509079906937154*^9, 3.509079918011222*^9}}],
+
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "t"}], ",", "t"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"1", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "}"}]}], "}"}]], "Output",
+ CellChangeTimes->{3.5090799187559566`*^9, 3.509873004975389*^9,
+ 3.509874184822618*^9, 3.50997005187321*^9, 3.510030296409807*^9,
+ 3.510325627315303*^9}]
+}, Open ]]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{"N", "=", "1"}], ",", " ",
+ RowBox[{
+ SubscriptBox["S", "z"], "=",
+ RowBox[{
+ RowBox[{"+", "1"}], "/", "2"}]}]}]], "Subsubsection",
+ CellChangeTimes->{{3.509079942612878*^9, 3.509079987671603*^9}}],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"tJN1SupBasis", " ", "=", " ",
+ RowBox[{"tJBasis", "[",
+ RowBox[{"[",
+ RowBox[{"{",
+ RowBox[{"3", ",", "7"}], "}"}], "]"}], "]"}]}]], "Input",
+ CellChangeTimes->{{3.509079812636983*^9, 3.5090798593901653`*^9}, {
+ 3.509079992698197*^9, 3.5090800180903187`*^9}}],
+
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"0", ",", "0", ",", "1", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}]], "Output",
+ CellChangeTimes->{3.509079860013033*^9, 3.5090800190574627`*^9,
+ 3.50987300501471*^9, 3.5098741848889513`*^9, 3.5099700519236717`*^9,
+ 3.510030296493371*^9, 3.510325627365245*^9}]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[{
+ RowBox[{
+ RowBox[{"HtJN1Sup", " ", "=", " ",
+ RowBox[{"Table", "[", " ",
+ RowBox[{
+ RowBox[{"HtJ", "[",
+ RowBox[{"f", ",", "i"}], "]"}], ",", " ",
+ RowBox[{"{",
+ RowBox[{"f", ",", "tJN1SupBasis"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"i", ",", "tJN1SupBasis"}], "}"}]}], " ", "]"}]}],
+ ";"}], "\[IndentingNewLine]",
+ RowBox[{"HtJN1Sup", " ", "//", "MatrixForm"}]}], "Input",
+ CellChangeTimes->{{3.509079510184618*^9, 3.509079524894363*^9}, {
+ 3.509079591799148*^9, 3.5090795932955713`*^9}, {3.509079748970049*^9,
+ 3.509079779450526*^9}, {3.5090798768892097`*^9, 3.5090799011830387`*^9}, {
+ 3.509080024877133*^9, 3.5090800412428102`*^9}}],
+
+Cell[BoxData[
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {"0",
+ RowBox[{"-", "t"}]},
+ {
+ RowBox[{"-", "t"}], "0"}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
+ "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]], "Output",
+ CellChangeTimes->{3.5090799021483192`*^9, 3.509080044133542*^9,
+ 3.509873005082075*^9, 3.509874184956231*^9, 3.509970051973385*^9,
+ 3.510030296581338*^9, 3.5103256274147053`*^9}]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"Eigensystem", "[", "HtJN1Sup", "]"}]], "Input",
+ CellChangeTimes->{{3.509079906937154*^9, 3.509079918011222*^9}, {
+ 3.509080048319892*^9, 3.5090800497919607`*^9}}],
+
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "t"}], ",", "t"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"1", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "}"}]}], "}"}]], "Output",
+ CellChangeTimes->{3.5090799187559566`*^9, 3.5090800512318707`*^9,
+ 3.509873005149672*^9, 3.509874185023218*^9, 3.509970052023752*^9,
+ 3.5100302966608562`*^9, 3.5103256274652576`*^9}]
+}, Open ]]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{"N", "=", "2"}], ",", " ",
+ RowBox[{
+ SubscriptBox["S", "z"], "=", "0"}]}]], "Subsubsection",
+ CellChangeTimes->{{3.509079942612878*^9, 3.509079987671603*^9}, {
+ 3.5090800757135487`*^9, 3.5090800810425262`*^9}}],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"tJN2S0Basis", " ", "=", " ",
+ RowBox[{"tJBasis", "[",
+ RowBox[{"[",
+ RowBox[{"{",
+ RowBox[{"6", ",", "8"}], "}"}], "]"}], "]"}]}]], "Input",
+ CellChangeTimes->{{3.509079812636983*^9, 3.5090798593901653`*^9}, {
+ 3.509079992698197*^9, 3.5090800180903187`*^9}, {3.5090800890822287`*^9,
+ 3.5090800928165913`*^9}, {3.5090801228255587`*^9, 3.509080123174704*^9}}],
+
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"0", ",", "1", ",", "1", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1", ",", "0", ",", "0", ",", "1"}], "}"}]}], "}"}]], "Output",
+ CellChangeTimes->{3.509079860013033*^9, 3.5090800190574627`*^9,
+ 3.509080124699259*^9, 3.509080186784032*^9, 3.5098730053534737`*^9,
+ 3.509874185090362*^9, 3.509970052073296*^9, 3.510030296745442*^9,
+ 3.5103256275148582`*^9}]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[{
+ RowBox[{
+ RowBox[{"HtJN2S0", " ", "=", " ",
+ RowBox[{"Table", "[", " ",
+ RowBox[{
+ RowBox[{"HtJ", "[",
+ RowBox[{"f", ",", "i"}], "]"}], ",", " ",
+ RowBox[{"{",
+ RowBox[{"f", ",", "tJN2S0Basis"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"i", ",", "tJN2S0Basis"}], "}"}]}], " ", "]"}]}],
+ ";"}], "\[IndentingNewLine]",
+ RowBox[{"HtJN2S0", " ", "//", "MatrixForm"}]}], "Input",
+ CellChangeTimes->{{3.509079510184618*^9, 3.509079524894363*^9}, {
+ 3.509079591799148*^9, 3.5090795932955713`*^9}, {3.509079748970049*^9,
+ 3.509079779450526*^9}, {3.5090798768892097`*^9, 3.5090799011830387`*^9}, {
+ 3.509080024877133*^9, 3.5090800412428102`*^9}, {3.509080145433753*^9,
+ 3.509080159129292*^9}}],
+
+Cell[BoxData[
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {
+ RowBox[{"-",
+ FractionBox["J", "2"]}],
+ FractionBox["J", "2"]},
+ {
+ FractionBox["J", "2"],
+ RowBox[{"-",
+ FractionBox["J", "2"]}]}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
+ "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]], "Output",
+ CellChangeTimes->{3.5090799021483192`*^9, 3.509080044133542*^9,
+ 3.5090801869273252`*^9, 3.509873005417053*^9, 3.5098741851562157`*^9,
+ 3.5099700521239557`*^9, 3.510030296965186*^9, 3.510325627565387*^9}]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"Eigensystem", "[", "HtJN2S0", "]"}]], "Input",
+ CellChangeTimes->{{3.509079906937154*^9, 3.509079918011222*^9}, {
+ 3.509080048319892*^9, 3.5090800497919607`*^9}, 3.509080170049466*^9}],
+
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"0", ",",
+ RowBox[{"-", "J"}]}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"1", ",", "1"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "1"}], ",", "1"}], "}"}]}], "}"}]}], "}"}]], "Output",
+ CellChangeTimes->{3.5090799187559566`*^9, 3.5090800512318707`*^9,
+ 3.509080186986652*^9, 3.509873005483986*^9, 3.5098741852237053`*^9,
+ 3.509970052174533*^9, 3.510030297030752*^9, 3.510325627615778*^9}]
+}, Open ]]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{"N", "=", "2"}], ",", " ",
+ RowBox[{
+ SubscriptBox["S", "z"], "=",
+ RowBox[{"-", "1"}]}]}]], "Subsubsection",
+ CellChangeTimes->{{3.509079942612878*^9, 3.509079987671603*^9}, {
+ 3.5090800757135487`*^9, 3.5090800810425262`*^9}, {3.509080217102944*^9,
+ 3.509080217190887*^9}, 3.509080301415887*^9}],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"tJN2SdownBasis", " ", "=", " ",
+ RowBox[{"tJBasis", "[",
+ RowBox[{"[",
+ RowBox[{"{", "5", "}"}], "]"}], "]"}]}]], "Input",
+ CellChangeTimes->{{3.509079812636983*^9, 3.5090798593901653`*^9}, {
+ 3.509079992698197*^9, 3.5090800180903187`*^9}, {3.5090800890822287`*^9,
+ 3.5090800928165913`*^9}, {3.5090801228255587`*^9, 3.509080123174704*^9}, {
+ 3.509080225633051*^9, 3.509080225720783*^9}, {3.5090803065633593`*^9,
+ 3.509080318618063*^9}}],
+
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{"{",
+ RowBox[{"0", ",", "1", ",", "0", ",", "1"}], "}"}], "}"}]], "Output",
+ CellChangeTimes->{3.509079860013033*^9, 3.5090800190574627`*^9,
+ 3.509080124699259*^9, 3.509080186784032*^9, 3.509080319431724*^9,
+ 3.509873005550837*^9, 3.5098741852903147`*^9, 3.5099700522238407`*^9,
+ 3.510030297105237*^9, 3.51032562766639*^9}]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[{
+ RowBox[{
+ RowBox[{"HtJN2Sdown", " ", "=", " ",
+ RowBox[{"Table", "[", " ",
+ RowBox[{
+ RowBox[{"HtJ", "[",
+ RowBox[{"f", ",", "i"}], "]"}], ",", " ",
+ RowBox[{"{",
+ RowBox[{"f", ",", "tJN2SdownBasis"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"i", ",", "tJN2SdownBasis"}], "}"}]}], " ", "]"}]}],
+ ";"}], "\[IndentingNewLine]",
+ RowBox[{"HtJN2Sdown", " ", "//", "MatrixForm"}]}], "Input",
+ CellChangeTimes->{{3.509079510184618*^9, 3.509079524894363*^9}, {
+ 3.509079591799148*^9, 3.5090795932955713`*^9}, {3.509079748970049*^9,
+ 3.509079779450526*^9}, {3.5090798768892097`*^9, 3.5090799011830387`*^9}, {
+ 3.509080024877133*^9, 3.5090800412428102`*^9}, {3.509080145433753*^9,
+ 3.509080159129292*^9}, {3.509080328717297*^9, 3.509080339783039*^9}}],
+
+Cell[BoxData[
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {"0"}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
+ "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]], "Output",
+ CellChangeTimes->{3.5090799021483192`*^9, 3.509080044133542*^9,
+ 3.5090801869273252`*^9, 3.5090803417903633`*^9, 3.509873005617288*^9,
+ 3.509874185462298*^9, 3.509970052286819*^9, 3.5100302971769*^9,
+ 3.51032562771595*^9}]
+}, Open ]]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{"N", "=", "2"}], ",", " ",
+ RowBox[{
+ SubscriptBox["S", "z"], "=",
+ RowBox[{"+", "1"}]}]}]], "Subsubsection",
+ CellChangeTimes->{{3.509079942612878*^9, 3.509079987671603*^9}, {
+ 3.5090800757135487`*^9, 3.5090800810425262`*^9}, {3.509080217102944*^9,
+ 3.509080217190887*^9}, 3.509080301415887*^9, 3.509080364434093*^9}],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"tJN2SupBasis", " ", "=", " ",
+ RowBox[{"tJBasis", "[",
+ RowBox[{"[",
+ RowBox[{"{", "9", "}"}], "]"}], "]"}]}]], "Input",
+ CellChangeTimes->{{3.509079812636983*^9, 3.5090798593901653`*^9}, {
+ 3.509079992698197*^9, 3.5090800180903187`*^9}, {3.5090800890822287`*^9,
+ 3.5090800928165913`*^9}, {3.5090801228255587`*^9, 3.509080123174704*^9}, {
+ 3.509080225633051*^9, 3.509080225720783*^9}, {3.5090803065633593`*^9,
+ 3.509080318618063*^9}, {3.5090803691319313`*^9, 3.509080374180279*^9}}],
+
+Cell[BoxData[
+ RowBox[{"{",
+ RowBox[{"{",
+ RowBox[{"1", ",", "0", ",", "1", ",", "0"}], "}"}], "}"}]], "Output",
+ CellChangeTimes->{3.509079860013033*^9, 3.5090800190574627`*^9,
+ 3.509080124699259*^9, 3.509080186784032*^9, 3.509080319431724*^9,
+ 3.5090803943765373`*^9, 3.5098730056841087`*^9, 3.509874185524622*^9,
+ 3.509970052318865*^9, 3.5100302972652063`*^9, 3.510325627763411*^9}]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[{
+ RowBox[{
+ RowBox[{"HtJN2Sup", " ", "=", " ",
+ RowBox[{"Table", "[", " ",
+ RowBox[{
+ RowBox[{"HtJ", "[",
+ RowBox[{"f", ",", "i"}], "]"}], ",", " ",
+ RowBox[{"{",
+ RowBox[{"f", ",", "tJN2SupBasis"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"i", ",", "tJN2SupBasis"}], "}"}]}], " ", "]"}]}],
+ ";"}], "\[IndentingNewLine]",
+ RowBox[{"HtJN2Sup", " ", "//", "MatrixForm"}]}], "Input",
+ CellChangeTimes->{{3.509079510184618*^9, 3.509079524894363*^9}, {
+ 3.509079591799148*^9, 3.5090795932955713`*^9}, {3.509079748970049*^9,
+ 3.509079779450526*^9}, {3.5090798768892097`*^9, 3.5090799011830387`*^9}, {
+ 3.509080024877133*^9, 3.5090800412428102`*^9}, {3.509080145433753*^9,
+ 3.509080159129292*^9}, {3.509080328717297*^9, 3.509080339783039*^9}, {
+ 3.509080379877461*^9, 3.509080390317148*^9}}],
+
+Cell[BoxData[
+ TagBox[
+ RowBox[{"(", "\[NoBreak]", GridBox[{
+ {"0"}
+ },
+ GridBoxAlignment->{
+ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
+ "RowsIndexed" -> {}},
+ GridBoxSpacings->{"Columns" -> {
+ Offset[0.27999999999999997`], {
+ Offset[0.7]},
+ Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+ Offset[0.2], {
+ Offset[0.4]},
+ Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+ Function[BoxForm`e$,
+ MatrixForm[BoxForm`e$]]]], "Output",
+ CellChangeTimes->{3.5090799021483192`*^9, 3.509080044133542*^9,
+ 3.5090801869273252`*^9, 3.5090803417903633`*^9, 3.509080394526349*^9,
+ 3.509873005750936*^9, 3.509874185590584*^9, 3.509970052375643*^9,
+ 3.510030297352895*^9, 3.5103256278157883`*^9}]
+}, Open ]]
+}, Open ]]
+}, Open ]]
+}, Open ]]
+},
+WindowSize->{2552, 1396},
+WindowMargins->{{0, Automatic}, {Automatic, 0}},
+CellContext->Notebook,
+FrontEndVersion->"8.0 for Mac OS X x86 (32-bit, 64-bit Kernel) (October 5, \
+2011)",
+StyleDefinitions->"Default.nb"
+]
+(* End of Notebook Content *)
+
+(* Internal cache information *)
+(*CellTagsOutline
+CellTagsIndex->{}
+*)
+(*CellTagsIndex
+CellTagsIndex->{}
+*)
+(*NotebookFileOutline
+Notebook[{
+Cell[CellGroupData[{
+Cell[567, 22, 159, 2, 67, "Section"],
+Cell[729, 26, 366, 12, 38, "Text"],
+Cell[1098, 40, 207, 4, 26, "Text"],
+Cell[1308, 46, 1104, 32, 43, "Input"],
+Cell[CellGroupData[{
+Cell[2437, 82, 1281, 37, 78, "Input"],
+Cell[3721, 121, 996, 29, 113, "Output"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[4754, 155, 97, 1, 34, "Subsection"],
+Cell[4854, 158, 581, 15, 31, "Text"],
+Cell[CellGroupData[{
+Cell[5460, 177, 3613, 91, 193, "Input"],
+Cell[CellGroupData[{
+Cell[9098, 272, 463, 10, 20, "Print"],
+Cell[9564, 284, 547, 15, 20, "Print"],
+Cell[10114, 301, 975, 26, 31, "Print"],
+Cell[11092, 329, 237, 4, 20, "Print"],
+Cell[11332, 335, 486, 11, 38, "Print"],
+Cell[11821, 348, 443, 9, 20, "Print"],
+Cell[12267, 359, 763, 22, 20, "Print"],
+Cell[13033, 383, 1237, 34, 56, "Print"],
+Cell[14273, 419, 237, 4, 20, "Print"],
+Cell[14513, 425, 585, 15, 39, "Print"],
+Cell[15101, 442, 514, 12, 38, "Print"],
+Cell[15618, 456, 443, 9, 20, "Print"],
+Cell[16064, 467, 547, 15, 20, "Print"],
+Cell[16614, 484, 973, 26, 31, "Print"],
+Cell[17590, 512, 235, 4, 20, "Print"],
+Cell[17828, 518, 486, 11, 38, "Print"]
+}, Open ]]
+}, Open ]],
+Cell[18341, 533, 917, 22, 45, "Text"]
+}, Open ]]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[19307, 561, 108, 1, 67, "Section"],
+Cell[19418, 564, 485, 12, 28, "Text"],
+Cell[CellGroupData[{
+Cell[19928, 580, 508, 15, 27, "Input"],
+Cell[20439, 597, 842, 28, 27, "Output"]
+}, Open ]],
+Cell[21296, 628, 417, 13, 33, "Input"],
+Cell[21716, 643, 417, 13, 33, "Input"],
+Cell[22136, 658, 300, 8, 27, "Input"],
+Cell[22439, 668, 348, 10, 27, "Input"],
+Cell[22790, 680, 276, 7, 27, "Input"],
+Cell[23069, 689, 927, 28, 27, "Input"],
+Cell[23999, 719, 409, 11, 27, "Input"],
+Cell[CellGroupData[{
+Cell[24433, 734, 133, 2, 27, "Input"],
+Cell[24569, 738, 1180, 28, 157, "Output"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[25786, 771, 97, 1, 34, "Subsection"],
+Cell[25886, 774, 712, 19, 31, "Text"],
+Cell[CellGroupData[{
+Cell[26623, 797, 1873, 49, 178, "Input"],
+Cell[CellGroupData[{
+Cell[28521, 850, 374, 8, 20, "Print"],
+Cell[28898, 860, 374, 11, 20, "Print"],
+Cell[29275, 873, 860, 23, 20, "Print"],
+Cell[30138, 898, 410, 11, 20, "Print"],
+Cell[30551, 911, 372, 8, 20, "Print"],
+Cell[30926, 921, 464, 14, 20, "Print"],
+Cell[31393, 937, 906, 24, 38, "Print"],
+Cell[32302, 963, 633, 19, 20, "Print"],
+Cell[32938, 984, 354, 7, 20, "Print"],
+Cell[33295, 993, 535, 16, 20, "Print"],
+Cell[33833, 1011, 1066, 28, 54, "Print"],
+Cell[34902, 1041, 856, 25, 20, "Print"],
+Cell[35761, 1068, 352, 7, 20, "Print"],
+Cell[36116, 1077, 418, 12, 20, "Print"],
+Cell[36537, 1091, 906, 24, 38, "Print"],
+Cell[37446, 1117, 633, 19, 20, "Print"],
+Cell[38082, 1138, 354, 7, 20, "Print"],
+Cell[38439, 1147, 328, 9, 20, "Print"],
+Cell[38770, 1158, 858, 23, 20, "Print"],
+Cell[39631, 1183, 410, 11, 20, "Print"]
+}, Open ]]
+}, Open ]]
+}, Open ]]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[40114, 1202, 103, 1, 67, "Section"],
+Cell[40220, 1205, 719, 24, 44, "Text"],
+Cell[CellGroupData[{
+Cell[40964, 1233, 93, 1, 34, "Subsection"],
+Cell[41060, 1236, 522, 10, 42, "Text"],
+Cell[41585, 1248, 335, 9, 27, "Input"],
+Cell[CellGroupData[{
+Cell[41945, 1261, 554, 15, 27, "Input"],
+Cell[42502, 1278, 1171, 36, 27, "Output"]
+}, Open ]]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[43722, 1320, 103, 1, 34, "Subsection"],
+Cell[43828, 1323, 115, 1, 26, "Text"],
+Cell[43946, 1326, 656, 21, 71, "Input"],
+Cell[CellGroupData[{
+Cell[44627, 1351, 1857, 54, 78, "Input"],
+Cell[46487, 1407, 3354, 96, 303, "Output"]
+}, Open ]]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[49890, 1509, 95, 1, 34, "Subsection"],
+Cell[49988, 1512, 197, 4, 26, "Text"],
+Cell[50188, 1518, 3280, 82, 208, "Input"],
+Cell[CellGroupData[{
+Cell[53493, 1604, 336, 8, 27, "Input"],
+Cell[CellGroupData[{
+Cell[53854, 1616, 468, 9, 20, "Print"],
+Cell[54325, 1627, 520, 11, 20, "Print"],
+Cell[54848, 1640, 1035, 25, 20, "Print"],
+Cell[55886, 1667, 485, 9, 20, "Print"],
+Cell[56374, 1678, 532, 10, 20, "Print"],
+Cell[56909, 1690, 469, 9, 20, "Print"],
+Cell[57381, 1701, 532, 10, 20, "Print"],
+Cell[57916, 1713, 469, 9, 20, "Print"],
+Cell[58388, 1724, 532, 10, 20, "Print"],
+Cell[58923, 1736, 468, 9, 20, "Print"],
+Cell[59394, 1747, 608, 14, 20, "Print"],
+Cell[60005, 1763, 1148, 28, 38, "Print"],
+Cell[61156, 1793, 485, 9, 20, "Print"],
+Cell[61644, 1804, 702, 15, 20, "Print"],
+Cell[62349, 1821, 663, 14, 20, "Print"],
+Cell[63015, 1837, 469, 9, 20, "Print"],
+Cell[63487, 1848, 700, 15, 20, "Print"],
+Cell[64190, 1865, 662, 14, 20, "Print"],
+Cell[64855, 1881, 469, 9, 20, "Print"],
+Cell[65327, 1892, 700, 15, 20, "Print"],
+Cell[66030, 1909, 663, 14, 20, "Print"],
+Cell[66696, 1925, 468, 9, 20, "Print"],
+Cell[67167, 1936, 677, 16, 20, "Print"],
+Cell[67847, 1954, 1587, 42, 68, "Print"],
+Cell[69437, 1998, 485, 9, 20, "Print"],
+Cell[69925, 2009, 752, 16, 20, "Print"],
+Cell[70680, 2027, 751, 15, 20, "Print"],
+Cell[71434, 2044, 792, 16, 26, "Print"],
+Cell[72229, 2062, 471, 9, 20, "Print"],
+Cell[72703, 2073, 763, 15, 20, "Print"],
+Cell[73469, 2090, 755, 16, 20, "Print"],
+Cell[74227, 2108, 773, 15, 26, "Print"],
+Cell[75003, 2125, 469, 9, 20, "Print"],
+Cell[75475, 2136, 743, 15, 20, "Print"],
+Cell[76221, 2153, 770, 15, 26, "Print"],
+Cell[76994, 2170, 754, 16, 20, "Print"],
+Cell[77751, 2188, 467, 9, 20, "Print"],
+Cell[78221, 2199, 750, 18, 20, "Print"],
+Cell[78974, 2219, 1908, 52, 90, "Print"],
+Cell[80885, 2273, 485, 9, 20, "Print"],
+Cell[81373, 2284, 797, 16, 20, "Print"],
+Cell[82173, 2302, 836, 16, 20, "Print"],
+Cell[83012, 2320, 817, 16, 20, "Print"],
+Cell[83832, 2338, 847, 18, 20, "Print"],
+Cell[84682, 2358, 471, 9, 20, "Print"],
+Cell[85156, 2369, 810, 15, 20, "Print"],
+Cell[85969, 2386, 825, 17, 20, "Print"],
+Cell[86797, 2405, 800, 16, 20, "Print"],
+Cell[87600, 2423, 826, 17, 20, "Print"],
+Cell[88429, 2442, 469, 9, 20, "Print"],
+Cell[88901, 2453, 819, 16, 20, "Print"],
+Cell[89723, 2471, 825, 17, 20, "Print"],
+Cell[90551, 2490, 811, 15, 20, "Print"],
+Cell[91365, 2507, 782, 15, 20, "Print"],
+Cell[92150, 2524, 470, 9, 20, "Print"],
+Cell[92623, 2535, 819, 20, 20, "Print"],
+Cell[93445, 2557, 2244, 61, 100, "Print"],
+Cell[95692, 2620, 485, 9, 20, "Print"],
+Cell[96180, 2631, 861, 18, 20, "Print"],
+Cell[97044, 2651, 889, 19, 26, "Print"],
+Cell[97936, 2672, 894, 18, 20, "Print"],
+Cell[98833, 2692, 904, 18, 26, "Print"],
+Cell[99740, 2712, 881, 17, 20, "Print"],
+Cell[100624, 2731, 469, 9, 20, "Print"],
+Cell[101096, 2742, 881, 18, 20, "Print"],
+Cell[101980, 2762, 868, 18, 26, "Print"],
+Cell[102851, 2782, 912, 18, 20, "Print"],
+Cell[103766, 2802, 904, 18, 26, "Print"],
+Cell[104673, 2822, 867, 18, 20, "Print"],
+Cell[105543, 2842, 471, 9, 20, "Print"],
+Cell[106017, 2853, 875, 17, 20, "Print"],
+Cell[106895, 2872, 903, 18, 26, "Print"],
+Cell[107801, 2892, 852, 16, 20, "Print"],
+Cell[108656, 2910, 902, 18, 26, "Print"],
+Cell[109561, 2930, 843, 17, 20, "Print"]
+}, Open ]]
+}, Open ]],
+Cell[110431, 2951, 981, 15, 56, "Text"]
+}, Open ]]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[111461, 2972, 155, 2, 67, "Section"],
+Cell[111619, 2976, 1075, 31, 36, "Text"],
+Cell[CellGroupData[{
+Cell[112719, 3011, 97, 1, 34, "Subsection"],
+Cell[112819, 3014, 309, 7, 41, "Text"],
+Cell[CellGroupData[{
+Cell[113153, 3025, 792, 19, 27, "Input"],
+Cell[113948, 3046, 1550, 38, 27, "Output"]
+}, Open ]]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[115547, 3090, 101, 1, 34, "Subsection"],
+Cell[115651, 3093, 2535, 66, 73, "Input"],
+Cell[CellGroupData[{
+Cell[118211, 3163, 757, 17, 43, "Input"],
+Cell[118971, 3182, 2506, 57, 269, "Output"]
+}, Open ]]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[121526, 3245, 96, 1, 34, "Subsection"],
+Cell[CellGroupData[{
+Cell[121647, 3250, 98, 1, 24, "Subsubsection"],
+Cell[CellGroupData[{
+Cell[121770, 3255, 267, 6, 27, "Input"],
+Cell[122040, 3263, 229, 5, 27, "Output"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[122306, 3273, 493, 13, 43, "Input"],
+Cell[122802, 3288, 678, 18, 27, "Output"]
+}, Open ]]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[123529, 3312, 308, 10, 26, "Subsubsection"],
+Cell[CellGroupData[{
+Cell[123862, 3326, 349, 8, 27, "Input"],
+Cell[124214, 3336, 348, 8, 27, "Output"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[124599, 3349, 609, 16, 43, "Input"],
+Cell[125211, 3367, 765, 21, 45, "Output"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[126013, 3393, 145, 2, 27, "Input"],
+Cell[126161, 3397, 433, 14, 27, "Output"]
+}, Open ]]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[126643, 3417, 356, 11, 26, "Subsubsection"],
+Cell[CellGroupData[{
+Cell[127024, 3432, 393, 8, 27, "Input"],
+Cell[127420, 3442, 370, 9, 27, "Output"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[127827, 3456, 651, 17, 43, "Input"],
+Cell[128481, 3475, 792, 22, 45, "Output"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[129310, 3502, 171, 3, 27, "Input"],
+Cell[129484, 3507, 456, 14, 27, "Output"]
+}, Open ]]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[129989, 3527, 376, 10, 26, "Subsubsection"],
+Cell[CellGroupData[{
+Cell[130390, 3541, 418, 8, 27, "Input"],
+Cell[130811, 3551, 303, 6, 27, "Output"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[131151, 3562, 705, 17, 43, "Input"],
+Cell[131859, 3581, 746, 19, 27, "Output"]
+}, Open ]]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[132654, 3606, 358, 9, 26, "Subsubsection"],
+Cell[CellGroupData[{
+Cell[133037, 3619, 467, 10, 27, "Input"],
+Cell[133507, 3631, 604, 14, 27, "Output"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[134148, 3650, 693, 17, 43, "Input"],
+Cell[134844, 3669, 1022, 30, 77, "Output"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[135903, 3704, 192, 3, 27, "Input"],
+Cell[136098, 3709, 2382, 78, 55, "Output"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[138517, 3792, 257, 7, 27, "Input"],
+Cell[138777, 3801, 915, 25, 27, "Output"]
+}, Open ]]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[139741, 3832, 427, 11, 26, "Subsubsection"],
+Cell[CellGroupData[{
+Cell[140193, 3847, 512, 9, 27, "Input"],
+Cell[140708, 3858, 325, 6, 27, "Output"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[141070, 3869, 748, 18, 43, "Input"],
+Cell[141821, 3889, 767, 19, 27, "Output"]
+}, Open ]]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[142637, 3914, 506, 13, 26, "Subsubsection"],
+Cell[CellGroupData[{
+Cell[143168, 3931, 542, 10, 27, "Input"],
+Cell[143713, 3943, 472, 11, 27, "Output"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[144222, 3959, 754, 18, 43, "Input"],
+Cell[144979, 3979, 831, 22, 43, "Output"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[145847, 4006, 219, 3, 27, "Input"],
+Cell[146069, 4011, 558, 17, 27, "Output"]
+}, Open ]]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[146676, 4034, 534, 13, 26, "Subsubsection"],
+Cell[CellGroupData[{
+Cell[147235, 4051, 590, 11, 27, "Input"],
+Cell[147828, 4064, 494, 11, 27, "Output"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[148359, 4080, 795, 19, 43, "Input"],
+Cell[149157, 4101, 863, 23, 43, "Output"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[150057, 4129, 267, 4, 27, "Input"],
+Cell[150327, 4135, 578, 17, 27, "Output"]
+}, Open ]]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[150954, 4158, 540, 12, 26, "Subsubsection"],
+Cell[CellGroupData[{
+Cell[151519, 4174, 611, 11, 27, "Input"],
+Cell[152133, 4187, 422, 8, 27, "Output"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[152592, 4200, 837, 19, 43, "Input"],
+Cell[153432, 4221, 846, 21, 27, "Output"]
+}, Open ]]
+}, Open ]]
+}, Open ]]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[154351, 4250, 96, 1, 67, "Section"],
+Cell[154450, 4253, 1099, 33, 36, "Text"],
+Cell[CellGroupData[{
+Cell[155574, 4290, 95, 1, 34, "Subsection"],
+Cell[155672, 4293, 292, 6, 26, "Text"],
+Cell[CellGroupData[{
+Cell[155989, 4303, 1037, 24, 27, "Input"],
+Cell[157029, 4329, 1049, 25, 27, "Output"]
+}, Open ]]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[158127, 4360, 98, 1, 34, "Subsection"],
+Cell[158228, 4363, 3226, 80, 91, "Input"],
+Cell[CellGroupData[{
+Cell[161479, 4447, 807, 18, 43, "Input"],
+Cell[162289, 4467, 1467, 38, 175, "Output"]
+}, Open ]]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[163805, 4511, 97, 1, 34, "Subsection"],
+Cell[CellGroupData[{
+Cell[163927, 4516, 197, 5, 25, "Subsubsection"],
+Cell[CellGroupData[{
+Cell[164149, 4525, 216, 5, 27, "Input"],
+Cell[164368, 4532, 327, 6, 27, "Output"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[164732, 4543, 586, 15, 43, "Input"],
+Cell[165321, 4560, 723, 19, 27, "Output"]
+}, Open ]]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[166093, 4585, 241, 7, 25, "Subsubsection"],
+Cell[CellGroupData[{
+Cell[166359, 4596, 249, 6, 27, "Input"],
+Cell[166611, 4604, 371, 9, 27, "Output"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[167019, 4618, 656, 15, 43, "Input"],
+Cell[167678, 4635, 791, 22, 45, "Output"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[168506, 4662, 139, 2, 27, "Input"],
+Cell[168648, 4666, 480, 15, 27, "Output"]
+}, Open ]]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[169177, 4687, 241, 7, 25, "Subsubsection"],
+Cell[CellGroupData[{
+Cell[169443, 4698, 298, 7, 27, "Input"],
+Cell[169744, 4707, 396, 9, 27, "Output"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[170177, 4721, 699, 16, 43, "Input"],
+Cell[170879, 4739, 813, 22, 45, "Output"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[171729, 4766, 188, 3, 27, "Input"],
+Cell[171920, 4771, 509, 15, 27, "Output"]
+}, Open ]]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[172478, 4792, 250, 6, 25, "Subsubsection"],
+Cell[CellGroupData[{
+Cell[172753, 4802, 398, 8, 27, "Input"],
+Cell[173154, 4812, 444, 10, 27, "Output"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[173635, 4827, 744, 17, 43, "Input"],
+Cell[174382, 4846, 941, 26, 63, "Output"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[175360, 4877, 210, 3, 27, "Input"],
+Cell[175573, 4882, 529, 15, 27, "Output"]
+}, Open ]]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[176151, 4903, 342, 8, 25, "Subsubsection"],
+Cell[CellGroupData[{
+Cell[176518, 4915, 475, 9, 27, "Input"],
+Cell[176996, 4926, 371, 7, 27, "Output"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[177404, 4938, 802, 17, 43, "Input"],
+Cell[178209, 4957, 793, 20, 27, "Output"]
+}, Open ]]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[179051, 4983, 364, 8, 25, "Subsubsection"],
+Cell[CellGroupData[{
+Cell[179440, 4995, 521, 9, 27, "Input"],
+Cell[179964, 5006, 396, 7, 27, "Output"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[180397, 5018, 843, 18, 43, "Input"],
+Cell[181243, 5038, 820, 20, 27, "Output"]
+}, Open ]]
+}, Open ]]
+}, Open ]]
+}, Open ]]
+}
+]
+*)
+
+(* End of internal cache information *)
diff --git a/exercises/ex07_solution/tightBinding.pdf b/exercises/ex07_solution/tightBinding.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..62acba3a34f788d96ce0c1c11a8704315b7a24bf
Binary files /dev/null and b/exercises/ex07_solution/tightBinding.pdf differ
diff --git a/exercises/ex07_solution/tightBindingPlots.nb b/exercises/ex07_solution/tightBindingPlots.nb
new file mode 100644
index 0000000000000000000000000000000000000000..94bce9328328c8295e4a7bddb421dae65aec40cf
--- /dev/null
+++ b/exercises/ex07_solution/tightBindingPlots.nb
@@ -0,0 +1,4716 @@
+(* Content-type: application/vnd.wolfram.mathematica *)
+
+(*** Wolfram Notebook File ***)
+(* http://www.wolfram.com/nb *)
+
+(* CreatedBy='Mathematica 8.0' *)
+
+(*CacheID: 234*)
+(* Internal cache information:
+NotebookFileLineBreakTest
+NotebookFileLineBreakTest
+NotebookDataPosition[ 157, 7]
+NotebookDataLength[ 277757, 4707]
+NotebookOptionsPosition[ 277182, 4683]
+NotebookOutlinePosition[ 277535, 4699]
+CellTagsIndexPosition[ 277492, 4696]
+WindowFrame->Normal*)
+
+(* Beginning of Notebook Content *)
+Notebook[{
+Cell[BoxData[
+ RowBox[{
+ RowBox[{"SetDirectory", "[",
+ RowBox[{"NotebookDirectory", "[", "]"}], "]"}], ";"}]], "Input",
+ CellChangeTimes->{{3.603693394888689*^9, 3.6036934082878933`*^9}}],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"tightBinding3D", "=",
+ RowBox[{"Plot3D", "[",
+ RowBox[{
+ RowBox[{
+ RowBox[{"-", "2"}],
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{"Cos", "[", "kx", "]"}], " ", "+", " ",
+ RowBox[{"Cos", "[", "ky", "]"}]}], ")"}]}], ",",
+ RowBox[{"{",
+ RowBox[{"kx", ",",
+ RowBox[{"-", "\[Pi]"}], ",", "\[Pi]"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"ky", ",",
+ RowBox[{"-", "\[Pi]"}], ",", "\[Pi]"}], "}"}], ",",
+ RowBox[{"Ticks", "\[Rule]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "\[Pi]"}], ",",
+ RowBox[{
+ RowBox[{"-", "\[Pi]"}], "/", "2"}], ",", "0", ",",
+ RowBox[{"\[Pi]", "/", "2"}], ",", "\[Pi]"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "\[Pi]"}], ",",
+ RowBox[{
+ RowBox[{"-", "\[Pi]"}], "/", "2"}], ",", "0", ",",
+ RowBox[{"\[Pi]", "/", "2"}], ",", "\[Pi]"}], "}"}]}], "}"}]}], ",",
+ RowBox[{"AxesLabel", "\[Rule]",
+ RowBox[{"{",
+ RowBox[{
+ "\"\<\!\(\*SubscriptBox[\(k\), \(x\)]\)\>\"", ",",
+ "\"\<\!\(\*SubscriptBox[\(k\), \(y\)]\)\>\"", ",",
+ "\"\<\[Epsilon](k)\>\""}], "}"}]}]}], "]"}]}]], "Input",
+ CellChangeTimes->{{3.603692837892145*^9, 3.60369285026022*^9}, {
+ 3.60369289370977*^9, 3.6036929373472*^9}, {3.603693044502232*^9,
+ 3.603693051752363*^9}, {3.6036930940048637`*^9, 3.60369309706608*^9}, {
+ 3.6036931326646547`*^9, 3.603693194773513*^9}, {3.603693268790053*^9,
+ 3.603693272352414*^9}, {3.6036937656772537`*^9, 3.6036937955583467`*^9},
+ 3.604372717555108*^9}],
+
+Cell[BoxData[
+ Graphics3DBox[GraphicsComplex3DBox[CompressedData["
+1:eJx1nXecl8Xxx0/ggEMpdiIW1GjsMcQedFdFothR0GgsGDFYoom9FzDBBvjL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+ "], {{
+ {EdgeForm[None], GraphicsGroup3DBox[{Polygon3DBox[CompressedData["
+1:eJxFnHf8V+P7x9/vsw9RsrK3IqJtpaGSlR0VIWW27JmMQlIps6yKUGaIkNE0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+ "]],
+ Polygon3DBox[CompressedData["
+1:eJw1nAn8F9P3xufz+czMnU8lKaGUVkuyZN/JkpKlTWhTllS0KHuRSGlFkV0k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+ "]], Polygon3DBox[CompressedData["
+1:eJwl12e0VcUZxvED7MO9l25QowETUQIKKioEUGKkg4j0Ioi0AGIWoSpE6b2D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=
+
+ "]], Polygon3DBox[CompressedData["
+1:eJwl0TkvRFEYxvEThhEUiEoh0fsAtqDRKISpVLYPYBS0tHaFXU1HIrGEimQU
+KhIKWhr7voXK72SKf/Lc//vk3PfcW9WXTvXnhBDKkY+yZAjNiRC+8FoQwiK5
+hD2+Ji+Es9wQzlEr73MZnTbdIy6DSn6VL0I9f49bnXFnTGCQv+CmdKdxKQ9x
+U2aTuNd95J7wIBebNcSMu4JsJ3Y35RJuwBlprMmturt8hTzCDWNLTvEnaLfb
+FXeNDvmUO9bvTGTvFO9Wza/zM94xjUfzl/gt4k5yqVmT/IkXz/M6CyjhG7kP
+PPOz3BwK+bq4O274UW4MXfxBIrtj3PVQ7uY2dJJyL9eDUbk2mf0H8V+8mX9z
+P3iXV7hlfMi/3F/cTT5Ei7zjjG0k3WvOOf8PUkup
+ "]]}]}, {}, {}, {}, {}}, {
+ {GrayLevel[0], Line3DBox[CompressedData["
+1:eJwl0r1L1WEYxvFbj56yU1qZ0aQ0SYNRRJtGg1KY9iKZ+TLVIAoVRJD+AWIt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+ "]]}, {
+ Line3DBox[CompressedData["
+1:eJwVzksyQ1EYReFfpQrpEQzAHAhCJoERGIAMxCOeyQRSHslglFI6EiTkIRGk
+n47vNFbtvde55967elDaPZyJiD2sz0ZszUcU0JqLOJLTTERTP9ZP8KrfZCN6
+ns1jzX7DLde3N5K333HHDexNPLibs9v8V/oOHrkl7oM71YdcR1/gXlDmPu0z
+OXJWl23+XF6g5+xSNtDku/aVfo2+fs99u1fAtj1AnRunjWL6FzS4H3sHT+4u
+20P+Nz2DZ24lvYur6H/cSF/kWqhyY3tfTpzV5D+inTh9
+ "]],
+ Line3DBox[{1598, 1842, 2220, 2407, 1856, 1843, 1028, 1599, 1845, 2326,
+ 1777, 1600, 1847, 2327, 1778, 1601, 2256, 2328, 1779, 1602, 2258, 2329,
+ 1780, 1857, 2409, 1848, 1781, 1858, 2410, 1849, 2221, 2408, 1859,
+ 1850, 1032, 1603, 1852, 2330, 1782, 1604, 1854, 2331, 1783, 1605, 2260,
+ 2332, 1784, 1606, 2262, 2333, 1785, 1860, 2411, 1855, 1786, 1861}],
+ Line3DBox[{1607, 1862, 2222, 2412, 2029, 1863, 2223, 2413, 1608, 1037,
+ 1609, 2334, 1787, 1610, 2335, 1788, 1611, 2414, 1864, 1789, 2030, 2476,
+ 1865, 1790, 2031, 2477, 1866, 2224, 2415, 2032, 1867, 2225, 2416,
+ 1612, 2226, 2362, 1613, 2336, 1791, 1614, 2337, 1792, 1615, 2417, 1868,
+ 1793, 2033, 2478, 1869, 1794, 1616}],
+ Line3DBox[{1617, 1870, 2227, 2418, 2034, 1871, 2228, 2419, 1618, 2229,
+ 2363, 1619, 1048, 1620, 2338, 1795, 1621, 2420, 1872, 1796, 2035, 2479,
+ 1873, 1797, 2036, 2480, 1874, 2230, 2421, 2037, 1875, 2231, 2422,
+ 1622, 2232, 2364, 1623, 2233, 2365, 1624, 2339, 1798, 1625, 2423, 1876,
+ 1799, 2038, 2481, 1877, 1800, 1626}],
+ Line3DBox[{1628, 1878, 1879, 2482, 1627, 1880, 1881, 2424, 1629, 2234,
+ 2366, 1630, 2235, 2367, 1631, 1059, 1632, 2425, 1882, 1883, 1633, 2426,
+ 1884, 1885, 1634, 2427, 1886, 1887, 2483, 1635, 1888, 1889, 2428,
+ 1636, 2236, 2368, 1637, 2237, 2369, 1638, 2238, 2370, 1639, 2429, 1890,
+ 1891, 1640, 2430, 1892, 1893, 1641}],
+ Line3DBox[{1655, 1921, 1920, 2436, 1654, 1919, 1918, 2435, 1653, 1916,
+ 2376, 2276, 1652, 2274, 2375, 1914, 1651, 2272, 2374, 1912, 1650, 2434,
+ 1911, 1910, 1649, 2487, 1909, 1908, 2433, 1648, 1907, 1906, 2432,
+ 1647, 1905, 1234, 1646, 1903, 2373, 2268, 1645, 2266, 2372, 1901, 1644,
+ 2264, 2371, 1899, 1643, 2431, 1897, 1896, 1642, 2484, 1895, 1894,
+ 1898}], Line3DBox[CompressedData["
+1:eJwVzksuw2EYhfH371LEKmyEGpW6DCp1r0trKGWodStaO7EEorYh0oggTcMW
+UNefwZNzzvN+g2+kuJMrJxExh0YqIjMYMYE+bOFmKGIYdbeiXUIvmtyrPOMP
+ByJ69GvuRZ5yHTlrJ3Lf/YRr6zNcyApX4571ae7X3tQ3cMyfc2v6On7cxmUa
+d/yR+6g+hm+3grzt9w9+RV/FF3/l7ZN+wO/an7jkHv//xD3IKbvLl1Hl7rks
+92Fvo8K1uEnu3V7UF7DHN7i8Po83t2W5hAv8AQSBL8o=
+ "]],
+ Line3DBox[CompressedData["
+1:eJwV0EsuQ2EchvG/RGjpzaXudUmKVVgBo9qBBBPUpQkxbcS1ESEiNqC7QKt7
+YGQB0olYgN8ZPHnf9znfl5NzFjaqlb2eiFjHeV/EaipiDSPYxGs6It0fcYMt
+exujeOMHuEt36rLIvXOD+jV3Jse4FpfRG9yPXbbHZZa75br6Ijchd5Dj75Dh
+PrHLTaKKPP8iv/l9eYApHGKlN+Le8yO9hmm0nStwD95zIWe4D25If+SuZInr
+cMP6E/drL9mzyT/gnrk/fZmbk8fJ9ydnkeO+cMLN4xRFvin/AST7JK0=
+ "]],
+ Line3DBox[CompressedData["
+1:eJwV0LdKg2EUBuDjkPLH7h14HepiAwUxRnfByQJxUnAViRWxIFETO3gTls07
+EDddLYgFb8DnHx7ec97zJYR0Ts2Xyg0RMUk9GzGUj7himA6WOOEliWil5s2A
+/ZJB2rnX/8kjt81cRJv5Tvcrq7ofOZF+Xq67H+i+zeO6Frmq29d9mUu6ZrlI
+nQX23Ar6Jy7s/TQxQo2HTMSuN73mc/popMwxz+l3suNNt/2MHgrc6j/ltlvF
+70jMN7oPuaV7l2P2vFxx39C9mYu6nFzWrelezaO6rJxJ/wumqbgl+kdO7V1k
+mOOQWa75Bzp1MY8=
+ "]],
+ Line3DBox[{1693, 1933, 2239, 2439, 1946, 1934, 2344, 1814, 1694, 1935,
+ 2345, 1815, 1695, 1936, 2346, 1816, 1696, 2293, 2347, 1817, 1697, 2294,
+ 2348, 1818, 1947, 2441, 1938, 1819, 1948, 2442, 1940, 2240, 2440,
+ 1949, 1941, 1094, 1698, 1942, 2349, 1820, 1699, 1943, 2350, 1821, 1700,
+ 2295, 2351, 1822, 1701, 2296, 2352, 1823, 1950, 2443, 1945, 1824,
+ 1951}], Line3DBox[{1702, 1952, 2241, 2444, 2081, 1953, 2242, 2445,
+ 1703, 2353, 1825, 1704, 2354, 1826, 1705, 2355, 1827, 1706, 2446, 1954,
+ 1828, 2082, 2502, 1955, 1829, 2083, 2503, 1956, 2243, 2447, 2084,
+ 1957, 2244, 2448, 1707, 1104, 1708, 2356, 1830, 1709, 2357, 1831, 1710,
+ 2449, 1958, 1832, 2085, 2504, 1959, 1833, 1711}],
+ Line3DBox[{1712, 1960, 2245, 2450, 2086, 1961, 2246, 2451, 1713, 2247,
+ 2389, 1714, 2358, 1834, 1715, 2359, 1835, 1716, 2452, 1962, 1836, 2087,
+ 2505, 1963, 1837, 2088, 2506, 1964, 2248, 2453, 2089, 1965, 2249,
+ 2454, 1717, 2250, 2390, 1718, 1115, 1719, 2360, 1838, 1720, 2455, 1966,
+ 1839, 2090, 2507, 1967, 1840, 1721}],
+ Line3DBox[{1723, 1968, 1969, 2508, 1722, 1970, 1971, 2456, 1724, 2251,
+ 2391, 1725, 2252, 2392, 1726, 2361, 1841, 1727, 2457, 1972, 1973, 1728,
+ 2458, 1974, 1975, 1729, 2459, 1976, 1977, 2509, 1730, 1978, 1979,
+ 2460, 1731, 2253, 2393, 1732, 2254, 2394, 1733, 1126, 1734, 2461, 1980,
+ 1981, 1735, 2462, 1982, 1983, 1736}],
+ Line3DBox[{1750, 2010, 2009, 2467, 1749, 2008, 1372, 1748, 2006, 2400,
+ 2310, 1747, 2308, 2399, 2004, 1746, 2306, 2398, 2002, 1745, 2466, 2001,
+ 2000, 1744, 2513, 1999, 1998, 2465, 1743, 1997, 1996, 2464, 1742,
+ 1995, 1355, 1741, 1993, 2397, 2302, 1740, 2300, 2396, 1991, 1739, 2298,
+ 2395, 1989, 1738, 2463, 1987, 1986, 1737, 2510, 1985, 1984, 1988}],
+ Line3DBox[CompressedData["
+1:eJwVzksuQ2EYgOHvRKrtMozrWtdVULUCLYYsgJbqxWUdOrARkU4IkbpXMTVu
+RISngyff97//OTlnrLRT3E4iosjnqJmJWGOJUwapiA/92H7CIrfZiAzvejcd
+saDdOKfpaylzi3n9zv2bNuK8ydzwfa2nJc4bzGpHtHjV21rD3iTPKgW6+ov7
+ZfsKM9T58o/Pes1+yDTXng2e9I7vTWlXzn/mo/Zrlp0nzUv3D9qPvaRNmBfa
+vfZtX9fGzSqV4X/oZ9qufY8cB+xzzj8MgjCD
+ "]]}, {
+ Line3DBox[{840, 1146, 1021, 2471, 841, 1147, 1029, 2326, 859, 1037, 874,
+ 2363, 1047, 889, 2366, 1057, 904, 2371, 1226, 1067, 919, 2378, 1227,
+ 1075, 927, 2384, 1258, 1083, 2497, 935, 1277, 1091, 2345, 943, 1099,
+ 2353, 958, 2389, 1109, 973, 2391, 1119, 988, 2395, 1347, 1129, 1003,
+ 2402, 1348, 1137, 1011}],
+ Line3DBox[{842, 1148, 1022, 2472, 843, 1149, 1030, 2327, 860, 1038,
+ 2334, 875, 1048, 890, 2367, 1058, 905, 2372, 1228, 1068, 920, 2379,
+ 1229, 1076, 928, 2385, 1259, 1084, 2498, 936, 1278, 1092, 2346, 944,
+ 1100, 2354, 959, 1110, 2358, 974, 2392, 1120, 989, 2396, 1349, 1130,
+ 1004, 2403, 1350, 1138, 1012}],
+ Line3DBox[{844, 1150, 1151, 2322, 1385, 1152, 1153, 2328, 861, 1039,
+ 2335, 876, 1049, 2338, 891, 1059, 906, 2373, 1230, 1231, 1412, 2485,
+ 1232, 1233, 1423, 2491, 1260, 1261, 2340, 1427, 1279, 1280, 2347, 945,
+ 1101, 2355, 960, 1111, 2359, 975, 1121, 2361, 990, 2397, 1351, 1352,
+ 1450, 2511, 1353, 1354, 1013}],
+ Line3DBox[{845, 1154, 1155, 2323, 1387, 1156, 1157, 2329, 862, 1183,
+ 2414, 1184, 877, 1197, 2420, 1198, 892, 1211, 2425, 1212, 907, 1234,
+ 1235, 1414, 2486, 1237, 1238, 1424, 2492, 1263, 1264, 2341, 1428, 1282,
+ 1283, 2348, 946, 1304, 2446, 1305, 961, 1318, 2452, 1319, 976, 1332,
+ 2457, 1333, 991, 1355, 1356, 1452, 2512, 1358, 1359, 1379}],
+ Line3DBox[CompressedData["
+1:eJwVzrEuQ1EcgPH/TXslJiKW1kQXXoCnYOgLSLpp0nbq0kRqISRWAxYkJqIS
+YWMwSDqWDo0ENZcmnkB/d/jy/c93zj3nLlYa5XoSEWVs5CLu04gHVBFTEf/8
+Ph1R45x1Hsf5iC1tjzd9c85N+9fahbmudbildbRb87b2mDXrtv5kPtT6vKPt
+arPunsG++Q19jO2/cg/z9j6cHZq/keALnxjoR1xwpog584GW8p13inyKF22B
+n7VlPkNXW8ne0Fb5xPqS1zDU1rNz2hWX3L2EG/Nv9n+o4Acj/GECwq4wCg==
+
+ "]], Line3DBox[CompressedData["
+1:eJwVzc8qhFEYgPF3GGTBRnaSWWEIYSE3QW6AZCX5djZKrGjK1gIbid3UiKIo
+JvkTOzVm6d8FoFyA31k8Pe/7nHO+rzCfzSznImIWU40R500Rvc0RF7yEBvMo
+3lsjcpxpl+gzX/FuPmLR2RbPeX/IK3pZOzJn2gmvahXt1LymXadmX9er5m2t
+zhvaptbu+2NoQ8l+g5qzfnvV/OvuKw/Za9zJd1zke87jC8P2N+8+zTt4wID2
+yB0oOWvhM//v4v10R+vmW63IB3jSBvlFm+A9+zFP4kObTve0Mhd8fxw9qKS3
+qKf39mfzAn4wYv/mP/wDbts0/g==
+ "]],
+ Line3DBox[{850, 1163, 1025, 2474, 851, 1164, 1033, 2330, 867, 2362,
+ 1042, 882, 2364, 1052, 897, 2368, 1062, 912, 2374, 1243, 1071, 923,
+ 2381, 1244, 1079, 931, 2387, 1268, 1087, 2500, 939, 1289, 1095, 2349,
+ 951, 1104, 966, 2390, 1114, 981, 2393, 1124, 996, 2398, 1364, 1133,
+ 1007, 2405, 1365, 1141, 1016}],
+ Line3DBox[{852, 1165, 1026, 2475, 853, 1166, 1034, 2331, 868, 1043,
+ 2336, 883, 2365, 1053, 898, 2369, 1063, 913, 2375, 1245, 1072, 924,
+ 2382, 1246, 1080, 932, 2388, 1269, 1088, 2501, 940, 1290, 1096, 2350,
+ 952, 1105, 2356, 967, 1115, 982, 2394, 1125, 997, 2399, 1366, 1134,
+ 1008, 2406, 1367, 1142, 1017}],
+ Line3DBox[{854, 1167, 1168, 2324, 1392, 1169, 1170, 2332, 869, 1044,
+ 2337, 884, 1054, 2339, 899, 2370, 1064, 914, 2376, 1247, 1248, 1419,
+ 2488, 1249, 1250, 1425, 2493, 1270, 1271, 2342, 1431, 1291, 1292, 2351,
+ 953, 1106, 2357, 968, 1116, 2360, 983, 1126, 998, 2400, 1368, 1369,
+ 1457, 2514, 1370, 1371, 1018}],
+ Line3DBox[{855, 1171, 1172, 2325, 1394, 1173, 1174, 2333, 870, 1191,
+ 2417, 1192, 885, 1205, 2423, 1206, 900, 1219, 2429, 1220, 915, 1251,
+ 2435, 1252, 1421, 2489, 1254, 1255, 1426, 2494, 1273, 1274, 2343, 1432,
+ 1294, 1295, 2352, 954, 1312, 2449, 1313, 969, 1326, 2455, 1327, 984,
+ 1340, 2461, 1341, 999, 1372, 1373, 1459, 2515, 1375, 1376, 1383}],
+ Line3DBox[CompressedData["
+1:eJwVzr8ug2EYhvFH0CiRNBU2khJmToBzqMVk6MAgIdJELAzCpOkkkSaNxaIG
+CZFomUnDEaCxFSfg3+b3Dlfu+72e53vfr1DaKK73RMQilnojWv0Rt9hENhMx
+gE42ouw8qA+h3hexxh3LVd805Lb5BXeub3E3coe75Jr6AXcvd533+Af9iOvK
+fa7Cjbg7j2r6B+5VdvBr50U+Y8z8zexD/8Qw3tFNc74mx+1MYFQ/5HLyzluT
+8gRtbko+crPyFE/cXLqDm097zmdyIb3DLac97krOuHsa1/pP+j+s4Btf+MM/
+xjMx3Q==
+ "]], Line3DBox[CompressedData["
+1:eJwVzi1Ig2EUBtArU0FmWfCnDcFi3NqaFsHqksGgZQviQASxrIxtxSQMxmBY
+ZhCxiGWgLooo02Aa2J3N6qZ4DA/PvefC+31Lu6XN/YmIyMtXIqI0GfE4FbEj
+n9KZiRjqoVvBLT0dcWHv81U94Nu8Y35mWf3E8uzUfmZfllu2wU5Yyz4vV2yN
+1VnKvujtBTnnPZZze+cj3dP38sbb7hl2Z//Qr7rKX3TDbYXNeqdiv+EP9hpP
+6zK7Zl3zEZvTB/ZjfmkusqTeY4esbd5iCV1gTf3Lf2Sdj2RsLv7/p3xLxrf/
+AMEaMQA=
+ "]],
+ Line3DBox[{1010, 1136, 1346, 2401, 1002, 1128, 2463, 1345, 987, 1118,
+ 2456, 1331, 972, 1108, 2451, 1317, 957, 1098, 2445, 1303, 942, 2344,
+ 1090, 1276, 934, 2496, 1082, 1257, 2383, 926, 1074, 1225, 2377, 918,
+ 1066, 2431, 1224, 903, 1056, 2424, 1210, 888, 1046, 2419, 1196, 873,
+ 1036, 2413, 1182, 858, 1028, 1145, 839, 2470, 1020, 1143, 1144}],
+ Line3DBox[CompressedData["
+1:eJwV0C9IQ1EcBeCf6HvDpmDyTxDWZNGwYLSK24rVwUAQNkHEIsiKaHHJIGKY
+TGRJUMaq6KIKIujAJlbLBKt+C4dzz3ffbth8uVasjkRESX5HI7bHIh6TiIr8
+yOV4xEB/u9t0l00jru0XXtCfvMyvnJ9YXr+yNXZiX9gL0mMrrMHO7TnpsGV2
+yKbsWW/PSJsv8S+WDn8rD/Lmu6a7RXf39kD39QF/16fucmzSG0d2l/ftY57V
+dXbL7pz32bTesff4jfMWm9A1tstazussozfYmc54O5VV/icfPLGrvn8e/geS
+s/8BpYYucA==
+ "]],
+ Line3DBox[{1015, 1140, 1363, 2404, 1006, 1132, 2466, 1362, 995, 1123,
+ 2460, 1339, 980, 1113, 2454, 1325, 965, 1103, 2448, 1311, 950, 1094,
+ 1288, 938, 2499, 1086, 1267, 2386, 930, 1078, 1242, 2380, 922, 1070,
+ 2434, 1241, 911, 1061, 2428, 1218, 896, 1051, 2422, 1204, 881, 1041,
+ 2416, 1190, 866, 1032, 1162, 849, 2473, 1024, 1159, 1161}]}, {}, {}}},
+ VertexNormals->CompressedData["
+1:eJyVfWV8VkfzdnB3SpHiWrw4AbJ40FCkuBV3d0pxd2lx9+JeINyDFSheQkiA
+EEgCJLg7Ie9Zdq7zNPPvfnj75f5l2c7Ozs7OzuzONSdnh76NOsf18vK6k8TL
+K57zO6742k1+2bb74HdTRIzz3zOVcu0/b9J/uKu+K7PLrydt8IlfamaqCoWi
+VL0VJ+L8/Oah2v2oV+V03qt80r34/MeiSmGq19lGJ2oMf6wm+cyvknHUUp9c
+eRrsOVTqluoQN9dB3b5vyscuuj1qTfKbuj3u6lNX2jt0LpdZMFHTGeY95LWm
+U6TOcW89bt4bwyL1uNvr3dmlx/Uy/40JrmT4vPrC8Mn9SfZn+iTpMz8k+WH+
+SfLP8yU5X5YPSfmwHD1SnugHuaJ/yN1+nWdMC3N/TyUPKhFQ5q4q1D3ls+s9
+o1Rw4R3xkmS5qSZ1yzK8R8XbamLy0Qm8hz9U4TMuHqk/J0jdCh4UOT7/TTVj
+QO535Z32um8mXtftp4Z0TjTBaf+1z5Vdmk7nNSM6aDqLTze/r+msvvT7+unO
+eH/lu3FAj7sr96W5elzIueUmw2d2b8Mn9yfZn+mTpM/8kOSH+SfJP8+X5HxZ
+LiTlw/L0SHlinaCnWC/QhVxBP/3nUg2SrLjr/ubKUqRUSNsbKjzKt/G0IpHq
+2rcXdzX5PVz9GVD+fM5TQWpI2+aVdftwnznHdfuQXJvDdHuQOp9Q//85Eywe
+p3/71Y8arOm8Db23MZEzbqb8M0recMYdfH/fZT0u5HxiteGzzivDJ/cn2Z/p
+k6TP/JDkh/knyT/Pk+R8WT4k5cPy9Eh5Yp9g32O/YF2hp1hf8AG5gp/b0aEj
+FtW45/5mDGowd+0/gSr56aFd9N9/DE84Xf9e3xq2WrePvnm9q6ZTZn3FcZrO
+b7s7ftZ0TlxuNLqeM+6Orksr6XH/Xho3p9Y3yDnpBcPnlXyGT+5Psj/TJ0mf
++SHJD/NNkn+eL8n5snxIyofl6ZHyhJ2CHYW9wr7Cvsf+cvWA9RT6AL4hV5f/
+qiuHfJU//9K4gbt1e664y4ZpOu8y1++r6VyNE5Aml0OnULmkS7Wcs1xUxTT/
+v3q/qvxvOcdNYPhcvN7wyf1J9mf6JOkzHyT5Yf5J8s/zJTlflg9J+bA8PVKe
+OCdwLuG8gF2DHYV9wz7Evsd+hN5AT6E/mCfkivkWrV3cW///+N08du0BTSew
+4a6EiZ1xVxT58a0eN2vtV5V6/stuDF9n+NxR0fDJ/Un2Z7ok6TM/JPlh/kny
+z/MlOV+WD0n5sDw9Up44p3HO47zGuYJzCecL7CDsKOwh9i32PfYv9Ax6Cn2D
+XCBXyCd5Gq/3ejz8XlOnn//7HBzRwPD5dyPDJ/cj2Z/pk6TP/JDkh/knyT/P
+l+R8WT4k5cPy9Eh5wk/CPOAv4VxHO853nENox3kEu4l22E/sc7Rjv0Mv0Q79
+hBzRDnni79i/z9GfZH+mT5I+8+O2gx/m32137b+Zr9uO+bJ83HbIh+XpkfIU
++kwWfSaLPpNFn8miz2TRZ7LoM1n0mSz6TBZ9Jos+k0WfyaLPZNFnsuizK09h
+n8lin8lin8lin8lin8lin8lin8lin8lin8lin8lin8lin8lin8lin8lin115
+Cn+DLP4GWfwNsvgbZPE3yOJvkMXfIIu/QRZ/gyz+Bln8DbL4G2TxN8jib5DF
+33DlKfxnsvjPZPGfyeI/k8V/Jov/TBb/mSz+M1n8Z7L4z2Txn8niP5PFfyaL
+/0wW/9mVp4gHyRIPkiUeJEs8SJZ4kCzxIFniQbLEg2SJB8kSD5IlHiRLPEiW
+eJAs8SBZ4kFXnuJ+gyz3G2S53yDL/QZZ7jfIcr9BlvsNstxvkOV+gyz3G2S5
+3yDL/QZZ7jfIcr9BlvsNEvdLuK/zWO7rPJb7Oo/lvs5jua/zWO7rPJb7Oo/l
+vs5jua/zWO7rPJb7Oo/lvs5jua/zWO7rPJb7Oleeb6Y/Wp8iS7D7mzK6V8PM
+3zxSa2snfrAheZQK++nx3/MK/qPups0dpGpHuH/j39G+58dSr0tO2OJTdWTh
+ahsS3FCbyj5NX6viE/Vnnow1At9GqUtTqw7cFbTGJ2BEs5rJE9xVSfZGBNza
+HuH+Dqv8w4d9c2+reWV/vjKuxSMVOLTps6fxz6kcnSvH/bZVqGo74kCR5s8j
+1euJK0a9nHNH/bm6GL2ce0Ndee3ZUCLtY5UgWZxWTT6fUYvf6L9D1MqiUzM0
+jXH8xrqnugUXuq1+LKb/DlZdhm44oOlHLI0s88yh/+j9xkaa/pRroxJp+uV+
+r7hS00+8PfMbTf/bCmUn6Xn+VH5Y3vnOvCPjRFeq7Mx3292xn5I68hre0z9D
+Sud3V93Cl7XcXhxq1V7PZ/+JkplDnd9xGd913+/M69S8dUPWOnLx7K0xrZQj
+pw872+3V8mE6JOm0mdXaf44zXmCD73JtdMaf6/Ugvh6X6ZCkw3yS5JPpkKSz
+98G1qKtvo6hv6qm39boM2vnzQb0uzD9J/lluZJEbSbnxupBlXUiuC687Wdad
+5Lqz/pHUT9ZjkvrMekZS31hfCfoLveW/PVKfeTyS+t+9a4F2SaaGqiUJXzWa
+/Pyeigw8uSPzojBX77EPoP/1l3V7msjpP6p1ktW6f5nAjk91f9iT5N+b/nV/
+jdWfZH8elyzjeuS4kC/2GeQM+WKfQc41wrMn0+2F09TtodtLHOsZ95XTPrHX
+vqWPHDpP4v32UdP5tfftopoOt5NsZzok6fC4JMdlPknyCX3CvodeQZ+w76FX
+ofl8pwQ57bcqT/LT7bOq6N9g5Zswf9WGDp2THxOd1XRmfNK/IWgn2c50SNLh
+cUmOy3yS5BP7B3YI+wj7B3YI+6jeyyOFdfuT3mmq6/asl5qW03L7fUrNCC3/
+vtVv3NZ0tsb1Ha3pcDvJdqZDkg6PS3Jc5pMkn7AvsIuwM7AXsH+wG7BrsJew
+b7A7bIcU7A/sFOwf7BX0BvoI/YGeQR+hb1gnrD/WC+uK9cf6Qi6QN+QDOULe
+kOe7s1s26Hnit+Yb/xt6vvO6RX071+H7aNW6pOUz4OXxnpp//I1/Rzv/TbJ/
+8OFGvZI58sKv7+pHflkcufF4JMflfiT7M12S4/J8yTJfkvNleZJFniTlyetF
+lvUiuV6sPyT1h/WNpL6xnpDUE9Yrj9Qr1kOSenjl5iP/GmERKk94o3N5O11V
+7Q4PnXMm6r7UW0J/nLs4z3H+Cr0l8CP0kzBfoYcEuQl9I8g/YaOUX6o7fFb9
+s13NfA6f75bsz/y3w6fQK8L64hzptMzwefqw4VPoFUFPmD5J+kKvyKJX7rhC
+f1z+hZ648xX64MqH14Xkuoh1d+XM6+KR6yLWnSzrTqAv7BtB38S6E+gLu0fQ
+W2GvCPov7BJhHwn7Q9iPYt0J6yLsD8EOiHUnrLuwS+56iXV36Qu75PYX9scd
+V9gTl39hN9z5Cvvgykesu7suwj64chbr7q6LsBvuOi5quv2+9tPatyh8b9Lz
+e/S4wM1o7S+J84hgN25OeTo4sdO//86qJR3/in4pNKJiln/5aYmfmv6P98Tq
+T7I/j0uWcT1yXOEnkMVPIIufQBY/gSx+Aln8BLL4CWTxE1w+hZ9GFj+NLH4a
+Wfw0svhpZPHTyOKnkcVP+x+fsf1ksvjJZPGTyeInk8VPJoufTBY/mSx+ssun
+iNMJcYqIuwlxkLgHIMRNIn4hxBHifsClL+J0l08R17t8ijjdXRcR17vrIuJ0
+Vw9FXO/qoYjHXbsh4mv3HBHxPlniaLe/uAcgcQ9AclwR77v9Rfzujiviazlf
+kvMV8bWUJ0l5ivharhfJ9RJxtKs/Ii529UHE6W67iE9dvRLxu6uHr8Y0H6HP
+68LND+Uv4JwLEbWomj4XEJ8jXhfxO+6jyHIf5cG449+OOKzP2YblT6/R9FPk
+/nJB04cfCTsN+wz7f2eCoT+kqqEv7nk8OI+YPkn64j7H7S/uZ9xxWQ4k5QA5
+ynmJewxXDuLewyPalbwPEfJXGBd/49/RjvsI3IvgXiJpk+8TTfn7gcrh9evS
+ateC1YHJG9vnXRmizl1o53tx+0M1aWmXurPyB6kpF/Xfjt96oP39yU7/W9k+
+Bur+4dlTrNP9xbq491diHRXkzOeue/7j/BXrqLCO8DvhJ8IPEevo0oe/Ivvj
+vJfj8rxIzovlQFIOLDeSchPr7t6vCj2R60JyXaBPch0xHtYN487rtK5hVad9
+fu3warp9cE7Dv+sXtR664sHHR2rOjgbdKqS8jf4k+zN9kvQxf+gF5BCR6Xjq
+mU779FqfRun22rX17w133F1P6K+8Kx+rX57q3xD0J9mf6ZOkj/WA3mFdWo3N
+MUPPN9f2TLk1n6MOD4j893yLbp8/Sc83a2BXj54v9yfZn+mTpC/8UldPoGfQ
+a+gb7gFxj4j7QMgX6wM5Y/6QH+QA/jA/8Cn8XgU/Fn/j3y3+sII/jHgScQzi
+C+Enu3QQh8j+8KfluMw/Sf55viTny/IhKR/hn7vyZzmTlDPsuFwX2BHIA/YE
+97lox70u9gnasV+gx2iHPkPP0A59g9zRDvkj/kc74kHEh7Id8Yykw+OSHJf5
+dNvBJ8/Lbce8WA5uO+SAc1TKTeg/WfSfLPpPFv0ni/4T9EfoOQn9dONm6KfQ
+W7LoLVn0lix6Sxa9decl9JMs+unKTdg3stg3stg3stg3stg3l76w52Sx52Sx
+52Sx52Sx5y59cX6R5fwiy/lFlvOLLOeXS1+8B5E4Z93z2eIvkcVfIou/RBZ/
+yZW/eG9y9UT4RST9IuxX7FPhF7n3M+J9yqUv/CKy+EVk8YvI4heRxS+S8icp
+f+H/yHUhuS7rr44e8FPjc+5v01TT1ZGxT1WvtgEzuo87rV5/Wby+RdMwtT+s
+SrNv1EM1emXSFc2dv/epRjl7OP/eakzSaN3e9dG6tX7O/198wp9/aTr1Uw9a
+pulwO8n2fr+FTm/3/hw1znQlzYeO23zulb/ml9D7GcYjjI9xmT+SfE7p9zg4
+btcTqkXHqWtmJY9UXQvUG1Nv8z20k2y/1n3HeT2fCVtOrOjo0O95utc8TV+0
+E9rBN+YH/jeUWJ1V013SY0bDeM74v7R6l7C+Q1+0E9rfdK9aspMz3qckOf7S
+8uvXo3S5DA59bifZXmLKrbd6PPz+nr7NBz2uaCe08/9PGAd0RDuhneVCkB/k
+I9oJ7bzehPXHurN8SMpHtBPaoTdMh0AH85HzYv3wQF+gJ5A7y9uVM+Qu26HH
+rFck9MrVL+gV9IP1wtUH6IdsF/rvzhfzhPwwX/ABfbfoucvPoYpJ9r539kmL
+ZmdGd3l/TmXp98OjBI4czm6ol+X0xr/VD+cuHBv663V1Kc2ljN3WPcb+UnJ/
+3a/m/WWQ02/BiUWr9f/39NiR7bq/4NNdX+5Psj/zQeAL/DAfBL7Aj5ivu6+5
+H0n+h8QN2LXsbqhK/ShlpiXOb/VBJ/zrd4hUrcqPyElT7qjxxTL+OMb3mpoR
+9cOMgEQP3P0v9bnA1sr5HvrcU1kHbgz4p/0N1b/vmfYD30VIPXTni3lCTpjv
+zl7hCx84dFKsjW57xaFzYXjls5rOUPV+TBm/+2rA9vxbZ2+6ovb0W5K/59u7
+7j6X+7FwlVd79Hzw+/fBOCX8nHkJ/Xf3e9xOcUodc/ipNmpL1cEOP7W2rfmk
++eF2ku1MlyT9+Ue3fueZcocaTPzmspbbuz7RWa46csM+kXaM50tyvixPkvIs
+6tcpaVm/+5Tj0ASl5XD4u5nbejhywD6R9pbXl+T6iv2uoLe8LiTXRegJgY5Y
+dwKfQk9c+ybsvLt/hT6QRR8I8hHrS5C/0AcS9t+105ZzwW0X+kAWfSCLPrj8
+iPV1+Rf64NpPse6uPMU6uvIX6+7aSXGOkNh3JOXcd9PTDHp9+ZfWlZ7oq+lP
+3t/+tqPPKnp6nGvjfK/R9Jc5Cmg7sKVs3tF6ffPX9D+XyOG/74gk7fT6rk2+
+MFivl/eg4D8CHP4rXDv37Vd9YHvKdswj7Jhrn4QdU9JuCzvs9o85V66OHjdy
+c9EyV51x04ZUG6vHTZaw0seZDp/T2rSuntjhM8OWvfc0n8K/cuWDfQJ5Q87C
+v3L1NkWXfduOOvwUSaISDnP46fd+T2fND7eTbK+1wPd5/rVhauuRPJv759zs
+eXAw2eE2ex7K88JdF6y35OeGz/wbRxw7U+vxl5/GO+tSbsDjA3pdeL4k58vy
+ISkf4R96xPlFkh9eX5Lry/pAUh+En+muI/RM6hv0A+eeOH9Jrnvbl+PeF1gb
+RtV33Ir/VZ6NxybX8hTno9tf+Cfu+Sj00D0fxb5Q4FPouRJywL5QkAPvH3c/
+YR+hH/4/9AddjAP6Qp+VWF/ov8L6Cn1WQn8U64+C/gh/TFn8Mbdd6L+y6L/b
+Dn8C/gX8CpxzOE9g93DO8bnnnndiX7jzEnquhB0gKTfmhyz8kORH6LkSdo+k
+Pgg9V8KuEvQC+gA7K/UE+03qA/ab1B/MH3oBOWD+0CPIAXoAvYA+CP9fWfx/
+tx1+DM5tnHfwh9g/cv0inIuyP/t5BL8P/h7TIUkH9k7OC/ZOygF2U843X0dz
+TuHeotYoY3+gx9B36LNod+18gv2Jak1tGOnS2Ttk2tvsD++pg4uN/Ud73uPG
+/sO/hN8Bv0K0u/5GpdXGboNOWl9jt+GXWOiQpJN91seTUxpGunSSP/k8NofD
+58V3xq66fLY2dhXnmUUOJOUg9Mo9p4Qeklgvdx9jvYT+kNAf188S+oO4gSz6
+I+mQpCP0xOVf6BWJ/UVyXsKek9i/rl2xnBeu3yXuYchyD+O2C7vq+pPCDpPF
+7pGww4T4A3ZY2E+XjrBLJM41knIQds+dr/Ab3fiXz3sfPv8Vzn3hX/nAv4Ie
+Y39jXwv/wQd0hB/i3gOADvY39jXvFyX3C+4FZJzF+07JfYe/YSdgH3i/u/+O
+/c79/rdPuT/z57aDT/idkBPkw3Jx+0M+kCP3JylP2CHwg3bYFcwL6yT9NHHf
+QlLOsEOQp7hvcf1V8Cf9aoyHdca44l7FjUcEHR8LHVff4JfIeFzIzZUzzi15
+PyDkqSBP2C9574H9Ju9nxL2Nux8Fn+7+Ffrp3vuJ+xbXfgr+SfIPfYQeivsQ
+t7+Yl0tf3G+4fIr5uvMS+uzq54W2189p/ktnOzxgrkOneIFTAzQdYTdcfSC/
+3lV1/9fftb2t++cdFvBY9xd+smv/hT0h7BemQ5IO80OSH+EHunZP7BfXLol4
+3PUPxXwV6ONv/DvaxXwV+BT7TmHfiXjT9ZfEfF064rxw94WQg+STJJ+gC34l
+n7CjsDPi3Hf3C9ZD0hH03fUS/idZ6Lj9hZzd9RXnBcEOi7jG1XMhB5dOyPvc
+3bovua0ynSt96UrFcLWx7ctU1ePfU4F3mqRcUzZS1cuz/8KpWyFqxuhKJx+t
+vqNav3q1vOOzR2rJ6Qrb9v283Mdry7UDK8reVk/qPr7749sHavfuIbV+nxis
+CofXDy1cNUR17+Lt0TjWVRE1m2ic/eSIIqc1PtSWT+UzsORkTb9Zy/APmv6m
+3L5JVjr0P4VP9F4R80B9zjhqQYPZq32+X/5+ZL5N4Wrd1ll5DjePUEuGzku+
+KHqjT/7Wg4bVGuXYgWKf+r5se9pf1qnr8fH87q5LblO0z6IcAc58Vy093FvP
+t17vawdXl42kUo9HVD3tzNe7/8REj535KsMPNWV+NjI/BfI/OOPMl5qm7zVS
+z/di7kSZivxvvrTyv+f7f/KmWJ60jOUZl+X5Of+zX5350vgiJ7z1fFdsXfud
+nm+hpw0T+DePoL7H4vRa6Mx3+rabF3yd+Xrdu+2f+12QqucpmLxqTJTaVjHB
+idfvb6uYFT03V/8QrjoWaFG23b57KuLzyTN5Tt5Un7+vNvSsuq+2N/Np6tM+
+Qs3avvzHjmeC1bbcl2trHP33hYod0vUJMo58cU3j05tN69VQ9y+2Nf1g3T9F
+VMphuv/sk9dra/oNT64eoOmXWLQofV6HfoZLxevkcvgZX658Xc2PT8Wt6d44
+/KRotTy/14b9/ie5zk1dxtfnNP1pHPevwP3nGfrUgOkXZ/rNDT8EfpIzP9sN
+/wT+MzH/n8x8aQfPdzbP94uRD3Vi+dxl+by/+1We5Mfy3MHynD4maeW6p6+q
+jDHjfuv29KEK+SPls30rb6qeDw89P/LxjvK9lLrF+FxRql+ieou7HgtWbTbl
+nRBR5666tTdpxeLx76tGSdN/m+u3a2pohy39dF2I04dfjtO/n44tWqzrLXxu
+vrK17l9+dXhz3f/ojc2ldP9Jt0LnafoVrjWfqekXqPz4oqZf7nSGF7UdfnKk
++eOM5sdvzKTc+x1+3p68P7rtzj3+yblu0FWuF1HV9Kfs3L8+959q6FN5pp+X
+6X8x/FA5wc8wwz+dYv4/Mv+tzXwplOfbmOfb3ciHarF8+rN8Jhh5UiYhz1bz
+7zTXch48M/0U3V4hy7HUms97baO9PI4c3nm189V0yqXbtUvTOZp87gItN79v
+ixbQ4wbEnfC9Hrdm6JUxmr/3E6b30b8XFxb8Q/PZ9UjS3rr/sXgJa+j+0wMy
++er+kQ1zrtVyLpR440hNf2a9hpGafkjw4yR1HH5CV1Y4rPnp/aJcDc1P8T6p
+Fmo5x+M6TEu4/sk9059ucf8e3P+hoU8FBf1uhh8CP9OYH1/DP70T/JOZL8n5
+3jXyofcsn/Isn6ZGnjSE5VmJ5RncYVraPM4+Xdwu4ZUqjp7vq7C2nN53q36c
+H6L39cvKp1+0dfZF+ZLjM+h998+Adxu1HRjT/XRyvY82zx4yWe+jjHdODtN2
+I+Cpdz+978q2zJJI13XpHpBjnO7/nWd5Id2/7NnI7br/90PijNL0B95KVUTv
+u2T/NO2g6Y+vfXOlthsxN9Kn0ftui0+dqV/tRssrQ7TdQF2rnVzPZ5bpT9Hc
+fzP3L2zoU3+mn4Tp9zT8UBbBTybDP11h/ssw/5fNfGksz/cPnu8KIx96zfLx
+ZvlcNvKkpSzPP1me679Jk6CHc85uq9c8lT5nS20dMFKfO6nT72+mz9lCjYK6
+/OWcO2XGTPigz9n7ZX/J0dA5Twul6RLnN+d8aTm8QnZ9vszgPLG7nJdUh/OL
+nqc71KCbc671Pnqovabv/7TCdU3fs7psPIc+tft22U1Nv/+g8xX1uRaUbnh8
+hz6l69+qlKa/wP91i3/RJ0l/3quv5w78Dq/De825E17o6znltg/cYc6pHbd7
+fyqfxc0P9Gpy6sKHdYtCZd6gF/KmUu7+eo4jTvRq2tGc42H3v577bnv0SnPu
+Z5qRJdKh77Y/WDm8+vr/0SdJX8ifLPIni/zJIn+yyJ8s8ieL/Mkif5e+2Kdk
+2adk2adk2adk2adk2adk2adk2adk2adk2adk2adk2adk2adk2adk2aeEfSrO
+HbKcO2Q5d8hy7pDl3CHLuUOWc4cs5w5Zzh2ynDtkOXfIcu6Q5dwhy7lDlnOH
+cO4IP4osfhRZ/Ciy+FFk8aPI4keRxY8iix9FFj+KLH4UWfwosvhRZPGjyOJH
+kcWPcuUp4gKyxAVkiQvIEheQJS4gS1xAlriALHEBWeICssQFZIkLyBIXkCUu
+IEtcQJa4gBAXiDiaLHE0IY4W8TIhXrblzYq4lSxxKyFuFfEpIT615akWM3Gl
+6mXiSs8UjiujTRyqxpo41LOM41BxD+DBPYCI9z2If0Vc70Fcv9nE77TQxO+e
+3By/R5t4nz6YeN+Tj+N9EY97EI+LuNsdV8TXHsTXoc/zzv9+yh33t1qqOlX6
+XHfO66fDAge1iFLnc6f7Y0Sla6pMxc+tjk8JU3vaRNHuko8UDd88bV/qy6pu
+601ZM6y55eJAk4k6QldbZt5bYModCs2Q466mP7/mma2afoI11SY59GlJtVOJ
+Rzr0c05+tUXTT/6T2uTQpy+1p23V9PeEFuzwL/qUVtCfOTk0Iue+YPXq7vTU
+Xj2iVM53fa6GL7yj4nbNWe1yobvu74aJoUu+xISowM8Xljc5EamKvv5x1ov0
+YWp6mQcn40ZcVysY3xok6h0tbd6odY59wTT16KAmmv7iFjXiRjj0+wUNv3ep
+0F3q3X/wGE2/z/2LrzX9wuuq/+LQpx0HN27R9JecW/byX/QpmOk3YPovn6Wn
+uFkCVfgvzcOqnnio3r/O9Xe5RCFqycP8TX0Xhqn1Zyd/c2V+pPozceb1lX+4
+rgY/rrt1ZNJ77m/GD6NeH58WpNrvG1jkdJX7qlXB+G0av4lQo+e8WeB39Zo6
+8zBVkUmz76l2w39dVLfbXZXqhfqyJyJIFTpxqXOcLIH0oX1AhmrOuKWu3PIq
+74z7unaD9zUXhtHKLy/r6nFXzxl9W487c+eOCc54NPlJnLN6XL9XYd+ecMaN
+utlZj0vXxy1rrcftmPz33/W4w7rfbuSMS6Uy9hmhx22/ckSIHvd8oRypc4Rc
+VRVWTryy5PVDtbTl/iIHh95U4Z3DPY++C1OXxj/MFD9HlCq662HlPr2CVajP
+kln6/Iq/b30xHd/9VDAwp7b/7XPQMH3e4fcJ6jfm+72D7j8vXs+Gun/vPc0r
+6v7jzpw/ki3kKmXdMCThUmdcn3nHOuhxK8SU6OCMSz3KVvXT487ce3uwHnfa
+s3Rd9bnTc/WoeppO+MceStPpYMYj/lV3eNyqQ76bpvsX/nZ+Kd0/MPx4Nt3/
+UOWtKbcFBKlFtQp/eOz7QK35sdvxVoVvq4NHb6eZtDFcfW67u2qXlvdV0/Sv
+rnvPvqGSTVw1TK9XqVW7amq5Xbn7Nv5eR2791xTz0+ub5n3volrOk3eU/VPL
+ec+uzmv0euC37tMaFfS6XN/UesWWgCCq/fx82SfOuIMfHU/d2hm36thE+yZu
+DKebNT+M1OPO+u591grOuFMT/vN1vcbEOd5Jj5ujrH8+Pe69kZX0uLR6ZeDX
+cceXXLhfjzvJ6AGxXqiGrA/PfX4/tOBGqMp+oX+P7cMi1IHlO5M6+0QtCJg1
+qXTZ+2rfroCog0fuqC1ZFi7atOa2KjD6RKq5a6NU00kLTx2/EqrWdF2ZP+Dv
+/9XfCOF6A7O5PkCXxqdSzr8RSuMrbDqs6Q8Ii2in6ddLuL+YQ5/Ovj6Z95BD
+v1K2ack2O/QHNc/yfM7aKGq2+63XCYd+zkRPmmv6oVx34Iagf3D2sR3FfSNU
+wJp9A+JvPqBCtjYbP7/tA7W1/Iqgh6ceqAy1cnZa3uKY2rNu86kRg8PV/oxL
+2lU4+kgVTlBxT7WWJ9WMCXOffykRqv7iujFVuC7CTK57cGdol0vFfCOoz6TM
+yRI49BccXlpogUO/oNc/cx36lDig+glN/0qPGblGOvRLf95e26FP2b7d/0DT
+77HmddmY/9Enb6Y/i+mHsJ29wnb3N7a3O/fW+HawY89T+l19M6zSNdqb/8U0
+bW+37+3zRNvzXr+0+rQn9WXKkO6jn7a34N+P6zeA/1Wj0ydw6BN+M06ombGv
+Q79H99RntD1/1XVyk+EO/UyDo25o+lu3/hWo7Xn/2hWz7nXon/39l/maPupB
+NBF1Zgq+ylAtl2PPC1aYczamexR1HPb6W21vYWdhd/uyvX0+bViQtudxO5fP
+59hbmnDhYbx4jr0NYf25I+qZvKVph7U9z5ZxeErHnlPCW2draPqFwy/kcugT
+fmfWIb8Yh/6xEs/2aXveuOCcapr+vY4rfvgXfQpj+jOZflLfxyHanndIHHHJ
+seeUKlOLN9qe+8yu3Ffb86tBp97/Mz+Szj9ff1bbVdhT2NcGvI/umn2n1ph9
+R+N43002+1SNM/uUsE+nZdw4Xtvzj4/bJHDsOdV5l66ItufDn3ZN44xLhZOX
+KObYczo6PFmCKs64bC8Iv7XZbvQzdobSGjtDk9jOJDF2icoYu0SwS536PPqY
+3bHnn7vfCnHsOf3Qv+w32q72+Lbgfm3Pz/31LJdjV6lKkgOltV2tZuykKmTs
+JF1lOwl7CvsKuzrV2GHFdpgi2A6HJVu0SdvzBf0upnbsOVXYVLWOHvfozhEt
+tD2vO9y3mR63RfKtPfS4d8y5QHPNuUA4F/j8IPw+5nFvmXOH+NwhnDvJcoT6
+b3XsebXFSws7dpV2Nvympbbnvd60v+/YVVUlW7Hhjl2l7b4Hlml7PsKcg6qE
+OQcJ5+ADc26qYHNuUic+N2ewPYV9/ZH1ofz0WfW0PQ9SFXvqcbs86LtJjxu1
+b8pUbc83JBiyW4+bys//jh73b3PuUxtz7hPO/Z+Nn0AtjZ9AY9hPYH+C8JuJ
+/YrUjTLn0PZ8SaGMaXYMi6C8De6tu+jsw2E19vloex53Y/7hjr2lbTGRxbU9
+H3LSO8Cxtyr71VHHHHtLQ66svXfFsbeoHxLA9S4asv8T1L3OoHmOPZ+/2K+D
+ph8yM+NHTb/+0JDIUo49n/Yw435N/0r0jbWafonl8/Zoe+7xuvVJ05/c70UG
+bc9XsX/1j6BfZdvyZdqeL/JunSf15gOUoni1Ltqe39ra/bC251/qzp2wusUx
+KlwwesdXe57Kp4q255N3Tk/j2/IkBay5fVHb8wD2b2OSmrocS9j/nPVbVX9t
+zwt2P+av6c+qODmltucbBiwbrO35jgd7IzT9O09vJ9P23P9lo0Lanv/9d4Ja
+mv52qpoh5n/06T3TX8r0BZ8KfIp4xAfxiFgXhXUR81KYl1gvhfUS81VLRL1W
+XkcFOR8281J3zLzUDp4X+/PqDfvz+9ifL27WUZ0y66gm8ToWMf6z2s7+8zL2
+n9cZeapzRp4qnOUZ38QRah7HEXk4jqhj9EfNNvqjAlh/+PxQPfk86c/nyHzj
+5yv4+cvYzxfrqLCOz85Erb6zw98f36mox3G6iNd8EK8JfVbQZ6EPCvog9FxB
+z4WeKOiJ0H93XXjdaYVY970mjqMDHMfV5zhuoNEHyif04ZqJm6gwx00zOW4K
+MfpJqevF1s8jJn6k0xw/luf4cYjRT0og9DOOidOIf9VmjtemmPiOEN/l5viu
+yu6+o883uqmuTvz7Va7599XSLen6jc0crgruuxh51mkfcPGGT26n/ZdDNbfq
+9qe8XrJeaynTn/py/xHcv4KhT9eY/nKmL+y/sth/Bft/19hntdnYZwX7/NLE
+WWoVx1nrOc4qauy8um7svOrMdj63idfUR47XynK8lih1pYBJ8//3jow67eK8
+UDgv0F++h4pzxOWzh5kXVRPzWmTiU0J8eojj0/hGPlSD5bOL5fPIxLmEOPcD
+x7nCf1AW/0HBf/CY813VM+e7asnne1kTx6meHMfN4jguyPgJ6jfjJ6iK7CcM
+M/Ggys7xYGWOB4vNLLZm8p29/0c+wt9Q8DfQX757Cj9EwQ/pZuZF58W87pj4
+ly6L+LeNkQ9FC/mcNnE0IY5exnG08D+Vxf9U8D+HGv9QsX+oTrB/6GPiRBUq
+4sTxxs9Un4yfqeqzn3nRxJuqHsebgzje3DE+SarJjr5J+Qh/VcFfRf8R4ntS
+wo9V8GMrmXkR5nWR53XAxNcUzfF1M46vExj5EOSTmuWz28TptITj9FUcp4t4
+RFniEYV4RMRZCnGWiFMU4hQRfynEXyJ+ceu4irjMjSs5TlGNTJyiIjlOGWDi
+X9WO498cHP9yXKa6m7hMXeC4rJSJN1Upjjd7crxZyMRF7u88jo9qm7hbXeK4
+24fj7qcmzlJZTZylknCc1d3EieqhiRPVdxwnFjDxr8rL8e9Vjn8fpr3nHebY
+bbx372J9EHGcssRxCnGciE8V4lMR3ynEdyJuVYhbRdynZor6uk1Efd0XZt3J
+i9d9Eq97PnPvQW353mM133vsMPpAnVgfMrM+7DP3DFSN7xlm8j1DL6OHBD2E
+PzPP3LfQQb5v2cb3LXmMPhP0uTPrM+stJWa93cd6+4e596CCfO+xl+89Vt7y
+nzPcJ1z1ybF07MP2gepFkTT5T8aPkvckZLknIcs9iXvPIPSQoIdCbwl6O9Vr
+1o5hDj9hP273euTwE7IucJ/mR+gVQa+EHhL08GbVvBdO9f3LvzPX4znD9XZm
+GfoUyvSDmb64tyHLvQ1Z7m0I9zZifQnrK/SBoA/LjPypH8v/FctfrBdhvcT6
+EtZXrCNhHcV9HVnu68hyX0e4TxP2h2B/hL0i2CuxjoR1FHaGYGeEXSLYJbGO
+hHUUdolgl8T6EtZX2B+C/RH3jWS5byTLfaMrH2EHCHZA2A2C3RDrTlh3sd8J
++13YB4J9EHaAYAe8s66J1n51qrbZpzp+L+X8NPQv7fe+yBKnyzmnPf6m4ld1
+e/0UW+KMc9ofsHxkfd3Ppj/F5f71uH9JQ59SM/1cTF/ck5PlnpxwTy78E4J/
+IvwZgj8j/BOCfyL8Gar/336I+900ca9Og//bz3HzEMR9u8un8E8I/onwZwj+
+jPBPCP6J8GcI/ox4ZyHLOwvBzxT+M8F/Fv42wd8W/jPBfxb+NlX8bz/ZlY94
+lyGf//bD3XwD8V5DeK8R/rM7L+Fvu/eQwn8m+M/C33bvM8U7HVne6QjvdCK+
+I8R3Ih507+tEfEeI70Q8SJ3/O45z5SPe9ajUf8eJ7ve8xHsf4b1PxHeE+E7E
+g+49p4jvCPGdiAcJ8aB4tyXLuy3h3Va8RxPeo8V7LuE9V7xTE96pxTvv/6lj
+nEzU3RX3UYT7KHF/Rbi/EvddhPsucT9GuB8T91GufRb3V4T7K3FPRbinEvdg
+hHswcW9G4f99f0W4vxLv3WR57ya8d4t3fMI7vngHJ7yDi/d9wvu+eB+nBqIe
+clqxLuI+inAfJe6v3Ptncd9FuO8S92Pufa+4jyLcR4n7K/feW9xTEe6pxD0Y
+4R5M3Ju598/5bmb30/5YnMqhrx4753u/uA0unnDOd/XleS/tFzUb+WLAE6e9
+6MB0bfS5L/AgHuBBli982lr7P7LucXVDh5ownUJMJ7cZl+LzuAN5XIG/8AB/
+IfhU4DO/ybdx4m2DB7nM+TaCfwX+65i8HVWW8SYVOW9H8O/W+21j8n9UDONW
+1nD+j5iXwry2b7sTcSLJMf9W/J3hHPx9vccm74j2Mk6nKOcdCTkoyCHA5C8R
+cEAzOX/pqsl3osyMG9rM+U47D86JXpjumhqxpN/wGtUeqnwtFnernu+WKnlt
+3NLfnfZPZRrv1u3JV/lv1O2wz0m5zug8rmdYwfSnj9w/KfffYujTL0y/ANO/
++HPV9OlmXFXJfnqVo3qWR+rs19+b6lKtRyfTOO0v4p9trNt3JdC/N1VRPmdl
+Pd4g05+ecf8d3P+MoU/Jmf45pj92XGiJRc68tgUPbKn5WVcvcofmZ+ayy5f1
+fGMGN52v23/6Lekz3b6d/SVZj3eh6U/R3L8x9x9h6NN2pr+e6Qt/VcFfvWby
+ilV6zuv+jfOKhR+r4Mf6m/xk9TPnhw/k/GTh37r1cu+ZPGfVl/PMifOchd+r
+4PeWW72rzklHD0eK73ffM/nVVJjz21tzfrXwkxX85JQmT5uKcJ58Oc7TXm7y
+umk759WX4bxuzg9388wfcX74HZNP7rZ7rTJ2Y7vJV3fzxn/ifPUwk9/utg/i
+/HYhZ4KchTwJ8hRyI8hNyIcs8iHIR8iBLHIgyEHoJ1n0kyz6SRb9JIt+EvRT
+7Eey7Eey7Eey7Eey7EfCfhT2hyz2hyz2hyz2hyz2h2B/xLsM4V1GnAuEc0G8
+1xDea8S5QDgXxDuOW+9UnAuEc0G87xDed8S5QJZzgXAuiPcgwnuQOBfIci4Q
+zoUp5r1YjTDvxWouvxeXbp0vY6Jd4SpB24xJ4+W9rG7VXdHz7Y4odSn0WeaE
+gaf8n8/9Egu/ifYgPh+H8flYybx30yXz3q1S8Xv3gBnLPzr06f6+X9bHdegH
+tl1y+Y2mP25uVOUyR/3b8PmYjeVwkduT8ntZPZZz/8Q1fkjs8DksbZaPMXku
+q9PhLzNoPkXeFCFvSvQn9L+dLed6WnfCfxjbw/O839Hei+/fTvG9TefgC36a
+/zJb97f1cvh/c/XtLk1H5FMR8qlEf0L/4d7D22u54ddYs+due2u+LzrL417b
+1ap+FUcOv7BdOs18BnF7Ir73eMrnwhAjZ/XcyJn+YTlv6ZDiez2v5qxvuVnO
+f3B7JPtpg3gdyxt9oPRGHyiI9UHkGyjkG4j+Cv1FPphCPtj+y7PKlzkZpvbu
+y7vh8NnrKnD6lHKFakWqG0aeijg/bRHL82cjT5Wf5f+J5bnc5IG5v1k5H6z+
+mMctSzv0300pXcrfoR9zNv1hTV/Iv6JF/gryF/lmCvlmTQx9usv0vzD9/UYP
+Kclak793m/Wwj9FD6sN6e4718IaRD11m+Sxm+ew28qFjQj5CboR2IQeyyIEg
+ByFnssiZIGexX8iyXwj7RciHIB8xX7LM152XkCdZ5EmQp8gnJ+ST30hW8LmW
+w4FSeQOPOPQDOhwMLOjQF/aQLPaQYA//4XXCPBYx/3H9J6fR9IenKt3R49Cf
+t7RGc82/sJ8ei/0k2E+Bo/cARy/y2Al57EnMuNSNx53L4wrcvTuusM9ksc8E
++3yT5YhfX5bnNSNPOsHyvMryFLh4D3DxIg9KIQ9K2CsFeyXWS2G9RD6YQj5Y
+1rXTppT/NUTFm0pH/1pxT41scuBl1IVwuV7Ksl4K6yXspLLYSQU7edrkj6nF
+Jn9M3eT8sdmLX90t6/CzJaJHqlMOP0eTlCn7wOFHrJfCeok8NIU8tN8MHdrK
+dPyZjlgXZVkXhXVJaORGK4TcvjVyI8htFMutw61Dab0d/tMWelNVt5+P/uKn
+xxXnkbKcRwrnUTOTL62mcr50f86X3nYpd99yDv1nk1bN1fTjHhg1X9Pfa9oJ
+7dH7TXuUyeumPCKvu43hk9Iwn5eYzyQGx+rGFy0Zx9q4vNkXXrH+e65mGVyt
+G194GFcr8skJ4wr5EOQj5kuW+RLmK/LJCfnkQg5kkQNZ5ECQg9gXhH0h/C6y
++F0Ev0voOVn0nKDnQm8Jeiv0kCx6SNBD2ElZ1wt8yjpdoXweyfpaw/h8r8j1
+rNJw/SXobQ6uZ5WC68xgv8v6VAIn5QOclKCvQF/w49ZNEvNy6wsJ/JcP8F+C
+H7duj+BfgX8hH7cuDehiHNBHvRLgFIFPRH0N4ESBZ0Q9COB0gc9F/QLgpIGP
+Bl5atgPfK+kAjyrHBX5S8ok8VOSlIh8V9VaAswS+EvVBgHMFvhX1LIAzBr4Y
+9ReA8wa+G3hv2Q58sqQDPK0cF/hPySfq+wDnB3wf6sUAJwp8KOqbAKcLfC7q
+UwAnDbww6kcApw58OvDqsh14Y0kHeGA5LvCrkk/gFeW8UJ8I+EXgB1FHBvhX
+4F5RtwX4Y+COUWcE+G/gplEXA/h74O6Bw5ftwI1LOsA5y3GBa5V8Aocp54V7
+atxP4F4CdZeA1wROE3V2gPcFzhd1aoC3Bq4ZdUyAdwfOHXVAUG8AuH7cV+Je
+DfdpOBdxn4d7PNy7yf6oXyDpA98u+QE+XPIP/LCcL+5xLHLzSLnhfh/3OrjP
+Qb0k4KSBj0Z9H+DUgU9HPRrUCQB+H/VTUKcB9Rlwn4v7SNxDQp7uPSjff+K+
+UvZH3QdJH3UKJD/A1Uv+gQOX88U9l5QP3nXwzoP3Hbx/4N4L912oMwV8OXDl
+qIsEfD9w/ajjg/oKqKuAujOob4G6Frjvxj0u7m8hT/h98Pdwzyv7o16GpI/6
+DpIf1COQ/AM/L+eLe0ApH8R1iPMQ3+F9CPeCuA+EnwG/A/4G8q2B1wdOH3W7
+gNcHTh/5xKijgPd61J9CHQXUT0C+LOpbIF8CdZRQ3wJ1LZAfibojqDeCekCo
+O4J6I3iHwL077tuxjrH99OfoT7I/8qIs45IcF/kflnmRnBfyGyxyIyk35DdY
+1oXkuuD+V6474nbE8YjfgesAzgP4DtRlQz0G1GFAHTHUw0AdDNS9Qj0S2A3U
+aUI9GNSBQV0Y2Y46JpIO6m7IcVEnQvKJun6oK7BRnHeoJ4E6EqiDhnoe8rxD
+PRXUUUGdKdSzwXmEujayHeeUpIO6IXJcnFOST9RHkPNaGdvPIennoE4G6mOg
+vhvqlKA+CeqRoU4M/BPUz0KdHtTnQb0e2Y76MpIO6qHIceHnSD5XxvZz3Hnh
+nRvvG3jXWBbbvyXUhUB9QNQFQT0Q1LNDXZbGwr9FXRz4pagXhrpEqEeE9068
+7+FdD/YH75B4f8T7n+yPOkeSPvxkyQ/qyEj+UfdEzhfvQBa5eaTckB+AdyG8
+B6GuIuqpoI4K6gCing3q2KBuHeoJoY4Q6qyhnhPqOOE9GO+ieA+FPPF+i3db
+vJvK/qgPJemjnpHkB/V3JP+oFyPni3cyKR/klyDfBHkmyKvAexre0VCPEnVo
+UH8G9RNRBwhxK+r9oQ4T6i+hPh3qYKH+Fd7R8Z6Md2TIE/dVuKfCe7Psj7pa
+kj7qQEl+ULdI8o86O3K+eF+U8sH9L+6DcQ88dniJaR+7R6lmH7dk3rLHiYcL
+DxkwZNEd1b5CwaE/n3ioUj7KcP5epkDV60W28UsShbh1Oi5wPinySFHPAnm7
+yNdF3Qfc2+F+DPUU8E6I98Hfi/xQ3eGHkqcJHK758fspyX7NT9SAPZ0dfmjP
+oqcPND/eZ1ru0PwAZw7cGPIzgccGPg+4POCWcW+N+y7ggXEvjvvwLweH5Qia
+H6lujR/xovzCMPWsxbHCjX+47tYlCeP8WeSXon4H8pSRn4w6F8ijR/486kcA
+JwF8xJLsB+I549LpOAuSejvjVp5cv5EeF/h54OGQvwqcOXCHyMMEHhs4YOSn
+AecMPDHyzQa3e922imO38x5PG/e8E/fV+bnG8ZKOPdy5PjimUPe76tbpd5l2
+zrqnKu3d+uBgRJBbpwM4AOT/o/4FcB7Ad6Q+ENrRoU89Wi6KPufQ/7yrBGn6
+Z9KMKFm4+13y+63u6x0O/fuTSx3T9F3cOOOSkb8HPDZwzMjTS/cwWXSPNxHq
+m3Kpu+6vcl9Vr3jp50pXr7l1Q4BLQL496nEAdwK8iSpQulDPNxF0+HXtmppO
+v5I/VNZ0gFcH7hm4WuDAgZMGPvo2v3ME8nsR3omOxs18Ue8734bh8zbvCaY8
+lVqt0npe88L6rXrfJRy5e8DdTIGUsu3tQ1rPUacG+dHIi0Y9F+ShI/8c9VBw
+n417bNQZwTs53seL/5lxit53hzome6n5+anb0wjNj1+CYkv1vnuRb9oczc/N
+0lkiNT+oswAcJPK6UY8AeFPgTIHnx7sK3lNcnDy/Y+P9Wtb3QH5p9wd3m+r9
+OKzgyvnOfqQxO7/vqvcF6vUgHxz56qhrg7x75NujLgxwG8BroN4KcDzA73Rq
+kNtb78eqm/7cqse9Gbpvhh4XdSWA7wSuE/UXgKNFXjfqFwD/Ddw36gIAXw5c
+uawHgjpLte9eGqn36d/lJt9w9hE9Cwu9rfdR1fExWZ19pO5uTqn3EcV7ODTZ
+IWcfod4N8CjAoaCODPBJwCWFVzg0Ru/TmMvJr2n620ucD9H0yz1b1VDv0/xD
+O1zU9FMeiQnX+xT1F4BTBz4ddQ2Aawee3VbfQ8UM+bp/L6TPovcv7elStL3e
+d6jLA9wM9q937P3r4qfaVFr1df8O+aeJ3r8U3WaOj6aDehDAx2P/vo+9f916
+C7L+Buoaof6CtJ+osyDtLfDh8jwCPlzabeCf5bkG/LO0//vK5hv43uea8v/5
+Yu/xLaLUuZLx45SeEqbSMe4L58tuPl+A45LnEfA28hwH3kaea8BLnBf+APAk
+4eJ8jJiUL/9Hn2v0bOaXQprPJye/u1LK4RN+MuoCoh4g6v+iHm0Z4ceizi7q
+66JerewPP1PSR/0++U6BuhjyfHHrYojzqNb1jIe+pA9Ts47OTPHjiUiVq8qx
+48/Dr6vUo5N3D05zWb1rX6rkypKP1MAr74seXX3LxT3ifJzO5yNwdPI8jb++
+SK6Y9GGUIuvdgAYO/dldjo/X9Mtc8H5/Pc1l2lNkWwJNP1vCLdHk0EedDnke
+oU6HPL/uiPMR+GI/y/kIfKZsB95PnrOBvO+W87h+PC7wFcBbIJ8fdUOAkwA+
+4lirLJlvOPIc8EuCpyuc+Xp9yF9VyxN1Q4DDAP5i3azxypGbWtG11W4tt/G7
+B+/Scjt4vE+QXq/FyRI81u09Zg16rtuBiwZOEfjEDkmfTNPr2HLnjCxazqtO
+DR6oxwUuGvhU4FJLMs6ztGhnOgQ6K5kO8JByXOaTJJ88L5LzAv5EyuG4kRtJ
+uQF/IuWMuirAiwAnsjLgwURn/6oqYy+FjHP27ySvRLm0nUFdFeBUgE9hvKHq
+y7iWgXyO43sV8h4bdTGAi8K5ifoXwD8B94S6D8ClAY+G+g7An8E/Qf0C4AXh
+D6BOAXCBwAMCxw68KXCm03998I+2t2Obrsym7VhI/6c/ajkArw6cMfDF+RgP
+LNuZDkk6wLXKcSWeHfhW4B4t8yI5L+D6gPODvwT8HvB8wPEBn2ZZF5LrInHo
+A3jdgV+SerLK6BVBryayXgGnJPUQ9+3IUwZ+DfVNpP+J+3bgCHFvjPod8GNR
+x8OtN8F538B7uvhP0Q78p/TDcb+NcXG/DXyj9OdxXy3nhe+yoN4t6tyiDpH0
+G1FXSPqZqOci/VLUJZF+LOrmo4476rcviK3/dJ31FnXeZX/g4aVfDby09MOB
+j5V+O3Ce8POB90T9XymfTaxXlY1e0TjWK3zPBnWCUR8Y3wNAffr+4n0QdfdR
+bx/162V/1B2W9FG3V74XoN6T9JNR70n61Yf5/FpozgXqyudCDz6nWpjzhZbx
++fIdn0dl2M/vzucRcOkyLtjA58tyc77QWD5fzvI50t+cIxT93pwj72P7G67/
+jPpT0t9GvQzUz0DdDNTLQP0M+BXesf0N188Hfl7GBcANAkcI/GDa2P6GW7dt
+RWx/z8X9FTX+lWL/inKwf4V6WMAXwg+MZ/w0xX4azWE/rSb7h3OMf0h52T9E
+vQ/g/oH3Txzbb3ToG78R9T5QHwJ1IVAnAu24b0lk6JCkg/oCclzmk2Yzn3mY
+z3ix/U93XsBVSjkUje2XunJbEfvexpUz6oUBB4l4KtTEC4rjBXrG8QLqhQF/
+iThL4oX/YJwmvhcl75NRxwo4ZsRfqFcFvDJwyqjTBBw54i/UYwJeHPEa6g0B
+3w9cP+oKAccP/D7qs6B+A+o27OT47rCJ7+g8x3eow4I6H6jvkZ/jPrTjXnG7
+oUMcJ9IFpoM6EXJcifPFOY46BZZ5kZwXcPjA5SMeRPwI/D1w98CTW9aF5LoA
+fyv1ITR2vOnqD3C2Ut/wvTfUrUe9euBagXMFvhX15oBzAr4JOE/groC3Ag4T
+ODDgv4CTBC4NeDR8FwffacH3WYBvBN4ROEfU30EdF9RvwfddJB3UeZH9Ue9D
+0gdeTvIJPJucF/BmUg74HoCUM3BiUp7AP0v547t6+G4AvheA7wPhezUtxXsi
+vsOD7+/gezayP75DIOnje3X4LgG+F4DvA+F7OPhODcaVuFp8z0b2x3cIJH3g
+pYGfBm4a9Q2BnwNuDrhi4PyA7wPuF7hD4A2BywUOEvhH4GOBlwVOFvWVUKcH
+9XlQr0e2o16MpAO8pRwXeEjJJ/CKcl7ADUo5ACcv5QY8OfDlwJWjLiTwhcAV
+Ao8N/xy4SKwr8JpYX+CZgR8FbhT4YeCJgSNGnSnUK0KdItQtku2osyPpAKcq
+xwWOVPIJnKecF3CVUg6oIyDlBrw98PfA3aOeJvCXwF0Cxw5cKfCkwJkD5wp8
+K3DgwN0Cbwt8NfDWwFmjPhfqOaGOE+o6yXbUJ5J0gO+V4wJ/K/kEPlbOC7hT
+KQfUX5Byw3c08d0SfK8E3yfD97IW/HdeKOH7X/ieluyP76BI+sK+kcW+kcW+
+kcW+kcW+ufRRZwF1F1BvAXVXgbsF3hb1DoA/Bu4Y9QiAhwYOGvUCgM8GLhu4
+euDsga9HPTXU2UJ9LdTbku2oYyXpAAcuxwVOW/IJHLWcF/DGUg6o0yHlBnyX
+fNcGvgt4L+C8gKcCvgG4KuCLgDcCzgj4IuAegDMCXhS4RuAZgRcFrhF4xsOM
+e0T/hbH7k+wPvKjE7QIvinbgRoGHBD4SuEjgbYC/Ae4GeBvgNoC7AS4ROEXg
+E4FLBE4R+ETgDIEvQd4gcIZoB97QxfGK91DgeIHrBZ4X+GQ5X+Bdgdd0cZqM
+dwVeEzjNGMZpo39o7P4k+wOvCPwicIvAKwK/CNwi8M9S327y+/g/Am8LHCBw
+gcADAtcH/BNwT8D1Af8E3BNw9Zb1UnK9gIsDbgx4MeDfgBsDXgx4ZuB6gecF
+7hc44GyM/wXuV/YHPs0yLslxgfuyyIGkHICDlfIE7hE4SOAfgXuU7/XAPQJP
+BhwZ6gVY9pGS+wj1Cyz7Qsl9AfkDhwf8HfDewDcD14x6AXK/o14A6gGgDkBf
+tj8yLwL1AmR/4KjluMANyrwLrKPkH3UELHaVpF0Ffk/KH3hjuY6oIyDtOeoI
+SHsSwvhV/qWajGMFfhV4VuBYgV8FjhD5VMCvAkfo4gf5PLLYDSXtBvClwFki
+fwz4UuAsga8EPh/4deDWL3H+zXXGay9hOwN8u+wPPKdlXJLjAj9pkQNJOQCn
+LeUJfDXw1sBZA18t89YgZ+BKgScFThi4WOBhUd8BdQswX9TvQH0O1OU4z+fC
+IZGnh/odsj/qIEj6wOvKPEDgdSWfkJucF+oFSPkAjwq7Afwm8KiwP8BdAo8K
+PChwoMCjAj8K3CjwqNiPLq6T8ajYX8CBAhcq24ELlXSAU5XjAqcq+QSOVM4L
++FUpB3y/UOJMGf/iI/EvjHfwkXgH+Pn4LjG+R4zvFEpcDOed+si8U9DB95Px
+3WR8pwp1Sn7nfRoR+x7YzRvZE/s+0817KRv73t7Ni0gQ+35ezeR77FSx78nd
+PA3O6yDkdeTk+3D5/Tt8pwnfO5T5DJz/oGT+Q1uTp6Q4T0khT8nPkl9xR+RX
+IE+jssmbovMmb0ohb8r2fTpvk8el8po8LoU8Ls77UtEm70sh76u6ySujcJNX
+ppBXVsfkodEZk4emnnMemvweHL5btCl2/oD7Hjef38HHifdEfm9SeG/6wu9N
+G2LndbjvU905v0K+f/F7Gcn3srSx18t9D8J3GeX7UWWTF6oOmbxQ6st5ofhu
+mXy3wvfA5DtXepOnSulNniohT/WsyYNV9UweLCEPlvNmVXeTN0vIm91l8nLp
+psnLJeTlDjF5vJTH5PES8ng5j1rt5Tzq8pxHzfnGCvnGVTjfmPOxVQrOx67P
++dj9+V3fze/gd4F2Jm+ckDfek/PGOY+akEf9nPOoOf+cfuL889qcf473G7zn
+bOR3HOTNKpM3q/Jz3izyQoeYvFA1lvNCfTmf9suIr/m0Ki3n0+K7IDL/IRvn
+2Q7n/AfF7/KdTf6nqmzyP1Uo5382MPmx6qHJj1W3OT+W82nVHpNPq1pwPi3y
+bHdze3NuZ/oE+rdj06coph/K9FF/2ZL3QjLvheVDg/9bPhQj5MNyJilnfN+o
+1ZteZ8Z88fdHnVjkV9ScqLJu27rfP5DzK4BblPkPaPda9byF7r+U2znfWL3k
+fOMQni/wjKcK9ug61hkXddchZ5m3DBziSdEf+RhyXOAKZX4I2n3FvDhPm5Cn
+nYrlhvq5rYV8IM+aIt+b84oV8opDeN2R34N8n1mc54N1HMr5z6N5HfE+1x/v
+dbwfge9oaPYX1eH9JXAN9JL3I3Afic3+pd68f/EdGrzfFYv9fqfk+91Stien
+jD0h2BPYn+3G/lAFtj+wM4mNnaEGbGeAB0nE7T9yO/ARoF81Nn3ayvSBE0G9
+b8u7Lcl32xi2VzdZPi9iy4eSCPnAjjVgOddlOaNu0eT1SyMT/HXCH/WLULer
+fecXXRI67ajfxfchhPsQ1EdazfcI/EuZ+D4B9fJ+FnRQl+qqwB2g3pzkJ4DH
+g9+1gPujbhfqeFXneHDLjOCGh/o8VGW+TzQ+mpxzJMnAup1Ph6hPgSpnrSuR
+KmutyC3fLrquDqnvUzR17NPJ0FK9nP404MTAn3T/gDrJU+j+/osfDnD6U3S3
+zVV0/0nzfjjxk9Pff033nBV9I9WRXw5NWhYSpkY2Wrz152nX1cU8vbNpPdzg
+M+mQtnvlbv1YQa/jq23DvlRw+l+otHad7r/m4Y/Buj/yDl08Ae8L7k/nuf9q
+7s/0SdJnfgj8/ML8ePE5FY/PqU18Ti3x7fOzPq97x/sco/2i082yH9Xn76hP
+u3cuTH1PFX8yZcOHVPfUhjnDp2T7OUg9uthJ96fcmXZ87T/6cPNjun/qlqWD
+nP40pfezKbp/tSItu+n+RYdt66TrMsTr8dxP4ywHNR7to3GLs0+XnKFxjEtG
+ZSyh26+Ne5BDt8/ZvWiqXq/0BY/k/kyBNG1Qtila/p37Lu+q1ytx717ZMiy6
+TsOeBiq9Xq/ivVmr12vyqe/ffnL6r9x7oLbuf+qHWgf1ehWfV3TvN07/fT6h
+b/R62b7HGnZ/XnO9jgkmZPrekRvdLNXjgZZbq+CTjfQ6fgm61kbvx0F3avTT
+cv715erSun9M9bi+un+Vizm/6eD0/57tYVG2h3PYHo4x/emL6N/a0CfQH8j0
+mR8CP7eYH9RbH8j8Q09s32Pteb72r3p9U47oF6z9sS7Bf97S65Vsd6uLen3n
+ln412lkvKrRu1Sa9XkcbV9b96c/Zub/2L1PxZajuPyZ16Gu9vuf2teig+9et
+PParPtjwERVWfP667p+93+t1p1stq1fS6zv3ybiv677QL4ded2o6bXt23W77
+fqjt+91MR/1u6KgmTKeiGZc+mXFVCI9riy/GmXmpv828FObFclAsB1WW5ZDc
+yI3mGLkpyK2XkTOlMHJWXVnOtu9NR7C+xTXrq0J4fVkf1GejD2ow6wPrj4o2
++qOqs/6MZb36zO3VuL0N69UnpgO9DWe9isfjQq/Omv2i8pj9ovbzfnlj9pca
+ZfaXWsH7y/Yu393sU/rU6+s+Vdin882+piRmXyvsa9u7OfASLdk/AW4C+RA1
+2M9BXoTtXRt5kCfYv0I+ZGZ+d4R/9ZDfH23vznOMvVKLjb2iQLZXxYx9o7jG
+vhHsW1pjD9VEYw8J9vCxsZ8ql7GfNIbt52hjb6mosbcEe8v2mXoa+0yn2D4f
+4XPnsLHzhHPnEp876825QOX5XHjN5845c47QWj5HuJ3QjvOI6ZCkw+OSP4+L
+84XM+ajemvORJvL5eMqcp6q7OU8J5ynePf8W74kx5lymNOZcpoN8Lm8z5zgV
+Nec4leNz3PYueS5w5PnFi6+rHq1et3jyT6R68F2ZBNUdOnnyKLVo8XW6cL7u
+Kt2+ZFpoWd2e0bSry9y+lNuf9ay9reMhf3+J3zlh6FNPQT93Vd9mZY8FqvPJ
+ym2Y6My7Rf8UC8s7fHYZX/jFGme/Tegc/2J+Zx063F8TsNiRW5P7M+fr9sJD
+CiUo4LS39AxOvcRpTxwv6/vSxwJp2ZG3tzSdPtkOBGg6TU1/+p77N+P+nQx9
+msj0OzJ9W139jew3wE/B+sLusP1QQ9hu2Orqx/C5hXMSdgZ6c0nQz94zbaq1
+znyHT0u7RfN5+HKnGM3nhwsDd2k5TFpaPly3v9xctqKeV/27u/KWceT5qdbi
+E1oOzRdmS+vtyCFg1ZNnWRbs95d1pT4bOjSR6TxnOtnMuDSCx/XncdflDZng
+rBcN/f3GdE3/SNSgQC3nPuwn9BHfp9v8bPxmrSf+BZf76XX3qRU4Vq/7/CbP
+fTs5eiLrMhVjP6Ag+wXwB2zfv1u0/miZJY5evT9QI7Gm/yWocANNn/1khXq/
+C9nvXct+9lL2u7Owv73c0FEfDB36zHR2Gf7piOGfKjD/G3heHm6vJOYl88l/
+Yz4/Cvp/GHmqIUaedIjlyfJXLH86JNZ9ilkvwro3NetOH82600+87p9iry89
+4/5ZeX1HMn3ola2OvdB/gv+M87Itn58W/XfzZ+C3wY+z6L9LvyvbgfFmnxL2
+6U9sBwqafU2teF97GTuglhs7QP3ZDpz5O85erf+y3kgztg8FmE5zptOZ7QPb
+H+rE42Yz9oouGHtFrdheIU5A3IB7rSxsJy8ZO0nL2E4+ZTuJeh2D2U4OYD/V
+1XfW81NsP9k+0yO2n7c5frvB8VwNjuOCOT4M4ngR+u/hc+cLx2UT+Nz5i8+d
+vhzHXeFzB3bwksj//MLnTkaOB//kc2crnzulOH4sy+cO9EnSiYkba71UP7Fe
+8F8a83pB/hf5vID8/3+/e2L7vsmW2PtR+fN+bB57f6lmvL9Wsd14x/Ynmvf1
+XI7LkrL/NoP9ty4cl31mf28E+3t72M4cYjtZke0J+5P0K/uTq9ifPMPxWl72
+Pw+w/3lD3DMg7yIzvg/C/ttj8X2Qv9jfgx1mubv3Y01Z/nyuu/dg0Nuboh4C
+7hmYT1WM48q9zOdr9pMncRy6nOeF8/Ia24+dvI5d2U9OwPHsUJYby5nScvw7
+leUMuyPp4HyMZjuJ8/EKn4/wc6NYPmtjn3d0mPXh//e7Hrbvd+SN7f+49iRJ
+bH+G+vK+OM9+Wje2A/CjeN+p4uzvefO+i+Z7mwzsH+LeJj/7defZLsF/YztA
+vdj/vMp24Ajf57xmf3Uy2w28803ieye89zWOe6vJjB0n/BOLOoF4X2zH91p4
+Z4w+kSNoutN/NtfbOcJ0cE7j3M7M5zXsWhDrG94TOR/APf/RDr1EfXJ8HwF2
+8w7bUeRFoL4h7vHAP+oBYb6oC9SE55tKvJ9iXpDTIe7//wDRamMN
+ "]],
+ Axes->True,
+ AxesLabel->{
+ FormBox[
+ "\"\\!\\(\\*SubscriptBox[\\(k\\), \\(x\\)]\\)\"", TraditionalForm],
+ FormBox[
+ "\"\\!\\(\\*SubscriptBox[\\(k\\), \\(y\\)]\\)\"", TraditionalForm],
+ FormBox["\"\[Epsilon](k)\"", TraditionalForm]},
+ BoxRatios->{1, 1, 0.4},
+ Method->{"RotationControl" -> "Globe"},
+ PlotRange->
+ NCache[{{-Pi, Pi}, {-Pi, Pi}, {-4.,
+ 3.999999999999597}}, {{-3.141592653589793,
+ 3.141592653589793}, {-3.141592653589793, 3.141592653589793}, {-4.,
+ 3.999999999999597}}],
+ PlotRangePadding->{
+ Scaled[0.02],
+ Scaled[0.02],
+ Scaled[0.02]},
+ Ticks->{{{
+ NCache[-Pi, -3.141592653589793],
+ FormBox[
+ RowBox[{"-", "\[Pi]"}], TraditionalForm]}, {
+ NCache[Rational[-1, 2] Pi, -1.5707963267948966`],
+ FormBox[
+ RowBox[{"-",
+ FractionBox["\[Pi]", "2"]}], TraditionalForm]}, {0,
+ FormBox["0", TraditionalForm]}, {
+ NCache[Rational[1, 2] Pi, 1.5707963267948966`],
+ FormBox[
+ FractionBox["\[Pi]", "2"], TraditionalForm]}, {
+ NCache[Pi, 3.141592653589793],
+ FormBox["\[Pi]", TraditionalForm]}}, {{
+ NCache[-Pi, -3.141592653589793],
+ FormBox[
+ RowBox[{"-", "\[Pi]"}], TraditionalForm]}, {
+ NCache[Rational[-1, 2] Pi, -1.5707963267948966`],
+ FormBox[
+ RowBox[{"-",
+ FractionBox["\[Pi]", "2"]}], TraditionalForm]}, {0,
+ FormBox["0", TraditionalForm]}, {
+ NCache[Rational[1, 2] Pi, 1.5707963267948966`],
+ FormBox[
+ FractionBox["\[Pi]", "2"], TraditionalForm]}, {
+ NCache[Pi, 3.141592653589793],
+ FormBox["\[Pi]", TraditionalForm]}}}]], "Output",
+ CellChangeTimes->{{3.603692920199164*^9, 3.603692937797933*^9},
+ 3.60369305267076*^9, 3.603693097387198*^9, 3.603693134109413*^9, {
+ 3.603693185830611*^9, 3.6036932042918997`*^9}, 3.6036932796152773`*^9, {
+ 3.6036933649289017`*^9, 3.6036933790478354`*^9}, {3.603693411692937*^9,
+ 3.603693416866695*^9}, 3.603693797047988*^9, {3.6036938280653973`*^9,
+ 3.60369383217148*^9}, {3.604372726742483*^9, 3.6043727470831327`*^9}},
+ ImageCache->GraphicsData["CompressedBitmap", "\<\
+eJysvQWYXcl5p9/bLWk05Bl77BkzxHHiOMZ4s951nE02u//YcUgttZiZmZlb
+LLWYmUcMI6YRMzMzY5O6W1LX//2qvjr33NunZzR+ouepVsO9B+r83o8K7r/X
+bteofvPa7RrXrf3937ep3apR47ptv//PLdvwq5T/lpT03xrRvvn9JPneJCX5
+L/ZfY/miP+j3Ofa/Eubp06fG/+P7luG/ljT/8A//YI4dO2bu3r1rPvzwQ/Pq
+1aukFvEHePz4senZs6d5+PCh6d69ux4g1/6XYrp162YP3aFDh6SW8W+8cuWK
+WbRokTl8+LBp27Zt3F9LmcuXL5tKlSqZn/3sZ+bHP/6x+c1vfmNu3brVvOid
+2O/fjb6dSkVeEn1PFSMOlXBj4UO9oXcnl96yZUtpScn2a0kzYsQI+5rwnYff
+y9uC52LP435XUFBgL57GoeRrSZOVlZXYS/5QL+U/eyTe635lj5n01mf3XwX3
+2g3aF3PnzjW/+93vTFpamvmP//gPk52dnfTb4ND+2ho0aBAcv747wEa9+M2b
+N8th7SXk5OT8T/k/WV6cHHGvycUfb5P+adSoUebJkyf2p78NLqSkni10sOBv
+CQc4e/as6dWrl/3p18HVvBnrrhL29ME1JSXVC3dJCXP06FH7l/Pnz5t/+Zd/
++VXwzi/pCz777Tdv3jTVq1c3v/71r82yZct+EVzCl7XLw2/XQyTVDXdqiiks
+LDT5+fn2p58G5/8g1HuJPRru5VruYHeDM3/4xd54Kzjj1yPemBLxxprujdeD
+N34r4o0lIt5Yw73xanCp3/1ib7SdbmXxveDc3484RMmIQ1R3h7gQnPuHEW8s
+FfHGaqFzc3ECqf/H998MLuRHf9rx/vVf/9Xcu3fPTJ8+3fTo0ePrwfX9OOJ4
+b0Qcr2r88TIzMy1VS5YsMcePH/9acH0/iThe6YjjVYk/3vPnz83AgQPtNU6c
+OPGD4Pp+9sWO11n/pEI3L1++TPrf9nclLYOVK1e2IP393/+99EXSe8GF//I1
+T1TZnaiTHlTIHDZsmL3wP/7xj3KSpP8IDvrriIO+GXHQSuGDljB5eXn29wsX
+LhTz/O9Bb/yPL3a89va/N8Ti2GOKFxHPIuqaP3++GTp0aNIfg4v9nxEHfyvi
+4BXDBy9t7eLOnTvN3/3d30l3mzt37ljLv337dtOnT5/fBxf/dxHHfzvi+BXC
+x08xW7ZsMb/97W9N165dk/4luNi//1MOVsLk5uaa//zP/zSrV682V69e/efg
+4qJMV9QFvxPxuvLuHB30HL///e+tt5G3IYd/Cq45ymD89k85R4rp3Lmz2bVr
+l/3p/wQ3EaXXqBO8G/G6tPgTCNz9+vWzP/3v4A5+H3GwL0UcrFz8wSTYkdAh
+6FT76j9+sYOtDG7z3yPe+F7EG71zjIpHfucOuiy4mv+MOOj7xR60SIyixxuo
+7/AEy09/Flx42dc8x1dCD8HHLXqCdD29dGmrVq3M1q1bzejRo78f3EdaxDm+
+XOx9xIc2cecoacaPH2/Wr19vX9+iRQtz8ODBpO8EN1Mx4kRfiTiRj3ASQqC/
+jz9XlSpVzMWLF+0rBg0aJKYqKeb1Kn/BcyXESwnn+tGPfmT7T/6JQ+TekmIe
+sfoXOld8XBV3ohTzT//0T+bSpUv2p2QzcuTImJ+sGXGWDyLO8u/xl07cb5Un
+//AMZu/eve7i7Lvq/CkHLWHu379v2rRpY581CcaXg66oH3G8r0Yc79/c8bz4
+xZn7P70bXFzDiIN9LeJgPhYsmgalBGmQy1ACN5A0LrjkJl/wLEUzpJRw8JX0
+j+4Eo4PbaBZxgg8jTvCmdm5CJKcX7CzBZ6RK9mZaFncu+9e39AwJsZ2eoZz+
+NcFO/Sa4kdYRB/8g+GtCAujvJiHu03N5m1Mkz7LX2S7iRD4JCPfYG3qOhFgw
+4Rxhe/U3weVGue+oG/xGxOtK6bOIig9/F35cRWzYL4PzR4XgrV7z/L+PP0eC
+7fp50I/dIo73zYjj/bM7Xjn9U9g+/XVwwT0iDvatiIP9f+5gPYOr6P3F3tgt
+OGPfiDd+O+KN/8+9sUtwxvQv9sZ/1T+9lv34QXB5g17zLP83/iyfZz9izn9o
+xAm+E3GCf3In8HJIsB/fDi54+J92vARr8Y3geCMjjvfdiOP9n/jjJViEj4L7
+HRNxvO9FHO8f44+XQP9Xg+sb96ccL5rqmIebGHHQ70cc9B/cQesHVzM54o0/
+iHijSz5dLcaecdoXe2Ot4IwzIt74ZxFvVHtZIzjj7Ig3/jDijb4zb9++LbGK
+hEhqX1z2b1899zUP5m9J3M+LFy/sT87ou2DOvnp+xMH+POJg/olISjlkyJDw
+wSoEB4uqIc2JOMGPIl7nQC8VDtttVi9JMs5Tz1UuOFdUhSSqm6PO5VzAm5FJ
+ufxLTU219nrPnj3+JlPlP/ssl0ec5C8iTvJ1PUlici4nlEdSrZotEJnWrVv7
+k8SqFisjTvKXESf5SH8XztCdxXARob3iNa95xe5gRTJ0Z9FUFUUq8THzve41
+r9mnyOEE7R09eELi/u3wqaMr/N8NbnNjxPl/HHF+X3ROyN98Rh7O6xNuPWHk
+IOYINn+hU0endb7kEE779fzeB7zusMQ3gz7ZFnFhfxVxYSX0wqJyQH9h4RJC
+woW97iDHR0GPbY+4sJ9EXFiKXlhUwvjT8NMpdmQklpvt+kLnjMgd9YSx7GBv
+xBH/OuKIyXoXUbmjHjSWFez/Qgctkju6cm0o+D9U3G3HVcTCGaNeUiy2PxJx
+iB8HJ4gy+79yh/hl8KLjEYf4WfFv/FlwbpvtfWh8fcgeQVMjPVbSzyOO44rJ
+ruPsBdhRxVI27vzQtF/NA8DItsKaN19qTJPFxjT62Jj6C4ypM8+YWriS6jON
+qYrLr0y8UGGKMWmTjD1DKmFQGUKrMqNohGxlALAMoWCZYaa0vOD/BZcZHmfz
+1xV1rb9w12p7tIQpmvrVCzoDsQ8CnXS47rvFmF6bjOm+wZgu692L232CP1ll
+TEtuqxm31ZjbasBt1eO2anNbNfHG1WYZU4XbqsRtlZ/q3leWICx1PG0stzFa
+bysjuC1Thsi5zGAaIXqZge49ZUgKyvRzPfp3wS2XjrjlqMccvuViY4casQ75
+uhkNFxkAN2y3MYNBecAOY/p9akyfrcb0BKlu2P/O2g9t6YdW9EOLFcY0Xcaj
+XcKjXWRM3YU8WkKeGsRQVXnElXnEFafzaKc6jRCWpk4w8U84Q5+w74Yhkd1g
+ypBclelD6y1klunlOuZv4rVg7yVKFVFd5JTiXGiyqiL8ntqxP/zSzICvqceM
+mQyqEw4bM/agMaPosRH7jBm6B2NOj6XTY31RTy/U0x31dEU9nTa422hDkNAS
+KJoBRRPU0xD11EM9dVBPTXqsOj1WhR6rRI9VQD1pqKfsFAVC1VMmrB4Phe+y
+wQld1j+u25Kl30oE3faT+G5z0i9hppL6T+dGZ54wYdP1eR2pFtHHw+JG/u3f
+/k1/KvryZDlgjdh5/8bMP+MufNZJzs+5p9DRk7iW8XT0GMzryAPGDKejhyDP
+gciz/05kSUf3pKO70dFdkGfHje4YrdciS+TZlI5uTEc3oKPr0tG16egaYFoN
+TCuDaUUwLU9nl0OeZadGdHSUPn1HD9KOHmDC+kyWnk6RnrYC1dvmO/uT/d0b
+xmfkthesiylpe6G0GYOcxh108pp0xPXCNHpjxknzRWStT+N79r+S5sSJE+bQ
+oUM2gpXk8MKFC8U8laKHrxwj4DdmBY566QVjFp83ZuE5Y+addZ0w8xSXySVO
+RjgTuORxXPpobiGDWxnGLQ3moQ2AkH4Q0htCemBTumFTOvPQOuhDa+UfGjal
+ETalPjalLjalFjalOjalKoRUhpAKs/WhQUjqNH0IuI0yGJUy3qhEERL10GKE
+JNknV8LaFn1ovY0+Qr4m6x+s+elr35VkPdGHIYykk75kHcdAlDl4pzOkI7jx
+kSh3NAoei5InHHHKnnLcddqMU1/o2Wrg4EtsRePVUjZelWIAmYqkPjawmzFj
+RtQjT4k4a4XYI/+GWXvVmE+uGLOSoHQ5j38JgesiJLAACcw957pzxmkMI3cy
+CaWO5/GP4e5G8fhH8PiHcteDuPt0eqEvj78XvdKD3ulKL3WC2/abpOvlXG+a
+5hjIJhjIhnBbH27rwG1NuK0Ot1XgttI8/9qvmrLy+Kfr45zMA4HbMmED6bkd
+Hs+tfT1GMkECyQG8b9kn/Vb4SdsXBm8cpFoaYnX1gfFOw1myD0wXkrRuOMke
+CLs3Au+L0Psj+IE7nFMVVyGWbCRgjKaHxtJT4+mxieJaTrienH7aqD1+PVH8
+dbwoissV9u/fb5M7CWcxz+7wycXZ+XIxHXzbbLlpzMYbxqy/bsyaa8asRhcr
+0MUydLEYXSxEF/PRxBzVhNzBFJQ9kTsah9JHc4cjUf5wCBiCJgZy9/0xC30g
+pCea6I4muqCJjvRWu80uykt621SD/irQXxH6y0N/OegvOzPi0U+Q9CTJFi28
+P7R/1zBCH7dQHn7YJdUn9pGCRfC0+3/mE3dyGq7WZaRKDatTFutTDiuUxvVU
+4Loq4burYKGqca01ZtqA1/UwyWNj7qsp1q3FMhcgt0Hy7bF+Hde6CKsbMUMP
+YodeINKXbulP9wygmwbRXUP3OgFl0I2j6M4xdOs4uncC3TzppOv2aWeKNSo/
+LV4/vgIl4zVSoA80Epljxx+2TEwtXzI77hjz6W1jtt4yZjNtA+pZh3o+QT2r
+UM9y1LMU9SxCPQtQzjwsyuzzxhuCydzBBO5kLHc0CiwyuMNhYDIYXAaIcPbp
+jDaEqYIxrTe5J9YM/BrTkw0wJPXo1dr0bk0MSTUMSRUMSUUMSXkCgHIEAGUJ
+AFJn6JPmaQV+pHhDUlK5jHMfKqnSGmb1lcG4QElhNX2WkjJUTaPduSUIkZyh
+HNdUnmurONWr57um1hyXQknOIbmH5CBNucfm3GtLfGcbfGg7jGlH+qLzBheF
+dqePetFXfTBF/TBF6ZiiQXtcQCU+Woz1SPp4NH09lj4fD7gTxaeLcXdqinIW
+UdboJ/FqkjLfmDFjilVTqYjDxiYDJX1k9t03Zs89Y3beNWY7bRvq2oK6NqKs
+9bS1KGs1ylqBspahrCUo62OUNR+7NBdlzcIuTVe7NInbGc9tjeH2Rh7zMipt
++gFUb7qjB93Sle7pDHAdAK/tFistdynfMY3XqLLo4dr0dE34rQ7HVeC5Enaq
+PHaqHHYqFTuVCvNlpkeoa5xXVyFPnJZBG04bWhhlt5J06M+rzIcnzj/Bonz9
+cpzlstbudS1XTG+qrx+YilitynBRlTuozp3U5I5qc2f1uMMGi1yu14Q7byZ6
+g7HWn7ir7rDeZTtdNrnsR4Lz3nRkXyxXOpZrIB08eJ8LCsQRZKC3UViuMRIz
+nnDMT/yCrs+V2oLMQwZCypZ1wyJRw6VRybMb5bL1D3P4obuV/Q+M2YvudtN2
+oL1P0d1W2ma0twHtrUN3n2DVVqG95WhvKdpbhPYWor156G42Vm0m2pt2zvjA
+cCTWbDh3O4S7Hsjdp9MLfemNXhDYg97pSi91EtlBaFtIbQ2xLTYGHrjBJyo7
+OrwmHV8d4KsAfiUMQHkMQTkMQhkMQxmMWpmw9CYnSG9MYUx6I14hildWeva1
+g/ndINrAQrSWLl/6u+tPEZmVsHFvSlhnIsyB0q1xWitq15y0/tzl/pNcYptG
+zlVhukt4q3DV1bj6mtxFbe6mrlSKFrskWZLlZsDWgrtvvcbdVfv1Lt+TvE9S
+CUkpesFtHzqxH505YK+LOyXWGEZnj6DTR9L5o4879schtQmn44trn+clVWpu
+OKqEzDMwoX/2tW9GHOoPMVv2NXPskTFHaIceufvYh972oLWd6Gw7bRta24LO
+NqKz9bS1aG01WluJzpahsyXo7GN0tgCdzb1sdaY27HtmLG5zNPeVwT0OE6Ed
+cULrj2nvu1+FBoJdsXGddoSEBqotQLaZFioaEoTUQ2116O9a9Ht1UK8K8pVA
+v8JCp7a0sAudKWZIruHdmMJGicJeqcJeorBXqjB+HsTPA2kDaOkvRUL9X4mB
+KywZmDqJwMPWrHiL5pWVYMxsJi9ntEqTQhwGrSJKq4xBq4ZBq4FBq8Xd1OGu
+6i1xSpNqgVQNmmPiW6nS2tErHTa5bKUrvdWdXutJ7/WmF/vudlGsBCWDUNoQ
+ensYvT7iqD7wEmYMD2ScxDPOh0bl2FFmzQ1tRI4hvRVxCDcb4mv2daeeGHOC
+duwxUqMdoh1Que1BbrtoO5Dcp8htK3LbRNuA5NYhtzXIbRVyW4FpW4rkFl/X
+s3PsmZi06Zi0KbjTSZr5j8Vaj+IOR4jksOKDRXKHQ5IDwe4iOTqqM2h2pOPa
+0YFt6MhWW7xs3ja1kVoNpFZNpVZZ/amP1tJEas6nJvmeLTMZKU1EQuNpY196
+T15m+AuntCEFSIU2iDaQNoCWXiBieyE2rN9L97J+r6ziQrZOjj0wVC0Y7Co1
+ST+MDtbGxDRXRjWXOtVVlazmIKQSl1+V26iO5mpyW7UXueJGg2Wu2NGE22+G
+5lqo5tpusJmx6YjmOkuFiy7rQdf1QnN9pJCy1z+W0tadWM3R/eJi5HGMQXBj
+T38hwf1l8YJ7O+IQ/zdm1D4wZ54ac5p2knYc5R2lHaYdRHn7H7tb2o0Cd6K8
+7ShvG20z6tuI8tajvLUobzXKW3nLP93S5mOM3QIM3VwM3WwM3Qyc6jRV38Rz
+QapgxYc9H6riG6Di63PAia/HXm8fS5o226zorK1riu9ovN6f7h1Th96vpSKs
+vqwQERaayotf4V1fIcJXpsK8lySgL0lAX5KAvvCdX2YSopqQjwZpY/MQBG0k
+LYM2PK+kT0kHPEd7/Cqdl/WXVqDie2Gt30vrVJFz/0Jxu/K7Ac6wuev7bsyl
+euWNCqlvnHp3P3oihWPUl4a1K4/6KqK+yqivGjDVwK/WkqIz6quH+hpwv425
+76bY++Zr3fvb0Dft6KMOW5SHd00v+O2DoZMwWeKWAXTxoMPOxYirEf4zJKTm
+cYx2Ba1I5UW51c9Q3jsRh/jHsPIuPDPmHO0s7TTtFO0EKjxGO0I7hAoP0Pap
+Cnehwh2o8FPaVlS4CRVuQIXr7saksAL7txT7txj7txAVzlcVzlIVTsUOTnYq
+NOPOBIbeqpBuGEx3DDyihe13RICmG73XZZezfu2J8Npuc063JcFL85gYTcN1
+wdHEINbEE1XHI1VdWvie/TUiGZPDo6dl5CT5AYsyQ/h5EG1gtv6OnCA9FzE9
+dyLrnyeis0IrcN4S4Q6wUV7MyIVThBHmTXscfLBICSNWDimlYX8rzLFlOFN1
+gSvLSXmu9lId8/vAtOJG2nBD7ba47KkTdqsLN91tpwtxe2G7+iChfvsdpQMO
+ORlJnwnBw447mjNOmuD25J8fhYwyXH8Rko99z5ciROPmGX3VvvFKljGXaBdp
+5zPRD+0M7RTtBPo5TjtKO4x+DtL2o5+9T1w37UQ/22nb0M/mB/q03jdrMGKr
+MWIrMWLLkc8S5LNI5TOPiG0O8pmJfKaLfDBik5DPBJEPbnTMadXKe2bwMSsd
+k0639KV7etNNPfeGPGhYQ+JFvUHbLPNKnd5qrSzEiL0y1Za/RDgvTJUlL/Cm
+BXjTAgxZPoYsz5Sfk8fTfM5TzfVjoWUmZmHEMlV96gSHZKIP2oBntKzkoNSZ
+9HdOVN6ipYt3feFiukEa5w3RhHaYJreS5CZ4zDLqMW2GIgnyNFeOkQKfFPrK
+yxiNjNUgtqqIrfpiV8qpg92qh91qIEMF2K0meE0p+7TAa1oFglW7rapAqSui
+vm67XOwrMXBvFNgXI9bvoOtq8RmDjhRVodyH3O0vig3Coqc2u4nSblqU7bT3
+IxTp5tx+2R70WrYxV2iXs50qL9DO0c7STtNOoszjtKO0IyjzEO0AytxH2/PE
+O7j3zSYs2nos2los2idIchWSXIEklyHJxUjyYyS5AEnOxaLNDktSLNqFYAR0
+DKHqqMCIOz87iL4ZQB/199Kk/3pKcEd/dt1jzZtGJG8587a10LTcUoh5K8S8
+FZomGwoxcYWm0bpCzFyhqb/2VWn1oZUXo86PUedC1Dk/n9Qij9TiOanFc+K9
+3NIx2SHJAU9oT53EBmT50cMy6epfB+S7eG+wBndDNb8drpnISM1MJP8dG+85
+y+hQq+TNUrqRzEYyHAk/pfxcWQahFrlyTy0UWGe5KzBKOaiRjFyo9yRlN61Q
+YJstqsJPnQol/JXMS2AWpyDRiQDulUjPeustnT3kmHMnDdyC30jT5wKzIrPf
+w/pLeEeUEv9XzKF+2VxHgiLHqyrHS7QLtPO0s9lOjqdoJ2jHRI6ZKkfafuS4
+96nXwXtmK0ZyE22jynINslyNLFciy+XIcqnKciGynC+yxFLOvmplqbp7I2Yp
+0eTo006XeAcz/IQ/T4qL+Q6F9fqW02ac2Sw0HbYXmvafFpKAFFqNYj59aNgs
+JFGRZ4O1hUneNIoblrDQgeDF+JY3nAPEQGI80733/TESzFMjiFEc+jImvwyV
+oMhvTGERI2jfgxEsM8OVcaSKKNVEqSpWRH6VMYJVF7vSj1QepQJZFyNYHyPY
+SOUnSbxIUGILiTHkRtt/6vxGp522M1L0VqSPeqHAPvsT7OER54bcLKCkpMip
+UT4pCK+G+Azh6WRkDukWYH5k/3orx5ibtOu0a7SrtCu0S7SLtPM5TnVnaKdo
+J2jHUd5R2mGUd5C2/5kmGKhvJ9ex/bFXz9tWfRtQ3zrU9wnqW4X6VqC+Zahv
+CepbdDPw0cF7ZmAUpzmDaEO88Wednx6rChyJAkeoAn18762iZB29Ne1V6xhY
+RVGhPIAO6sBFhW22FVpLKU68pXPkJfThNNJ5Nr6FA8JqSwvx668Cq5g29xWm
+6pVJnYW+ZrwKAkNJTkhMnJlVn47xtJIdiGQH57izfQd1vnDlmsA4FsaMY1id
+07W4KLn4HFd0lHKQVecil7tLuUgKlFKo9OpsqOpsusFFvKgzMBNSD5AOCSnU
+YttNDWVPNZTSudLJIlOxX+mH9RhREwx9kSS8kCZOnvE7IvC9X/0WNo3/PWYa
+3ze3chEr7QbtGu0q7Qrtcm5MrOdoZ3KcWE+KWLNVrFl6mFJmH3rdg1Z30Xag
+109JTbY+Mt7grSveUAYSlZDS+2+RqvjvKRdiWcmEs85gEloG1ZIMTZQluCHI
+SZZoh7uVuEclpg+klLUFYSX3cCFosjwRckF5NmFldgwErRHp1vjMpskGvQon
+1zejCz2YuApzXZJRbmbM/peZghAnIszxr6TIg9lE06Pw8hnPNeQthZYJCgY9
+cwIdRiI04rkk4D6+8BbVh5Vpc51Tr+B0+6bKUBIwLhVX4C4dFi2Xrbc6Iyq3
+J+x2VIl22R3INEi7RDtiUQO5HlAbEWUSS6sOE5ZbfRRSqX3DVyOE+auYML9t
+7iLAO7mxhyICvZ4oUNoF2rlcJ9DTtJM5TqDHst17D2FND9ASFYpFNdtoW0h8
+Nj4MwsSQQQ2UGTKoNukRlfq8WSLNaTGlBsoUpUqxSuoGI09yzxknpHNErMOP
+x+5KAqIhR12Ujmp9vhMIdb+zFDbfdgFpUHEM1Lk1PFXnXVNXij7i3a1NRYz4
+1oo6nFI2PJzix4gnGxcBaNbtwSnllTYcw5qRjSXNdZWgsVIZeuGqlJPULn+T
+HKcQMRai9UJynEJSskL0X0iEiVlfVIiLL7QmvsayQlNzhbvE2lxqXR1ma4Ax
+bbTOlQwEsGaq1paqVoGQ9FBX/HfYLsmhxD+ddxZaEYlqu8eMa5Kf+yeGNQR2
+1IIXv3oxYfmeatatJShpZs2aZb773e+aX/ziF+YnP/mJ/Bw58uuXrIaV7ZKt
+r9jXPXhuzH3aXdod2m3azefuIq/z/1XaFdpl2sXnTuDnaWdzncBP5ahY3zVH
+MMKHskL6pgURw5OYvoOI4UHMc4dj1Y81q19wzYncp1KI3HejrY+rFR4v9SFb
+JBp7OqhZitBHObHboplX+nD//QkPx7s2Hw0b24Fa45Q4rd/BonY6yT5zsbNW
+lPL0YwX3zbb26VltSNJSD1nVWfnZ49hlZsaqssUOJGbYJCuoJgwEgAHZEhgr
+MF91patxWOYJgDEp3wE19YVJnf5CKqqm3KwXJm3OS0wzbf5LU2HhS1t9lSqs
+VGOrQYMEPxIE1VoVWKH6a2IOzAf/YsYl6WxG8tlik0tEJcyScKutRhtBbbW0
+NRXWkisXUnLppRacyM4+16jlcn4sObz2VEn4jnIie5s8e/bMvv7KlStRU/D8
++qKiBfof2Nc9RNhRINyi3VAYroVAuCQgPI+BcEY9w4kcZ+mPZMdI2E/b60l4
+6kjQeMRsdjQkBTWue/FKlKLCkgQq5isR8ncp2s+MFe6ThYsUMfzeWU6MMeJ9
+ACeTmKWkH7wI2mj7N6Cho0ZqCihFQp8CDolhomHGWzatCcIXrcD6YU9JzCVB
+bxnCAetan3C1zgqX3wsOUnWqhDOoED9hKCgVWxyC2cJ+1FPH1SXpC0Y9X0hd
+4h2PR8aT4Gp9ZbfqUqnZvZLaXRCI1f3klam3xmajNitttN5mqT5/a7nZ2fPW
+WwqtzbcRyva4IDroIJ/bYT/c76IWvbpJFMFC/89aCyWaz8jIsOvDokx71P5X
+Lo10Ja9HKDSs7Hui7DyUTbtFu0G7nuceahFlP4/Zx1Oo2yv7aLYNtF1WGFJ2
+ONLeFmSHpVxdgrY2PuQuoaGniNrrz44BXHUxzaxLQvbMS4GQp190Q1NTdXhq
+8jk5By6A65OQ3B9Evpd6xkQfpvvs8ozLLse4/8PB8ldtvD4kNLJqDf8Bl7T7
+mSNS3OwsoanYtq2uANpK51U3lWABK19fsrHl5i1vyOMmIpnQchRbtw1SSDsZ
+RIbqC2T8ID1fwu30vDg2y6RbQ19a7USZsZm+kqw2nj9Py4GbXOx8LiH4c1zL
+c1vmKz8/DzufT9CVbyotLiCpLSipNrzO6ldx+pfCoQ94RFQa7HgfLZrv4pNG
+rWv0dfbb1XePatqTlBS5fvz78dIvbgat/ycL+EgrI6XvZ+FGr+SCgsdo+BHa
+fkh7QLtPu5cXr/+bqv9rysBl/r+U5/QvP5997iy76N/G8Tkh/SfEObtCcY68
+11r3UF1uXahkvDq+bKwVjpI23hEIpM2TdiUWFNhA/7JrYGEt/oyL7n+PSbKt
+6pWMSwQsLxekqyQdcPGKdJpvyoY30D5cklBpqCQCCfOoeks4u9sONmm54834
+aeTENVWkkjbXDYuWc/OIk97xSARz7mQQ9pVMTZG5Anawtkz//JIeiQE5LrYZ
+lJ0U/G50FvafNi5LLe6X0D0x0HTajOcmdVaeKTs7D91LeTufBKMA3b8wFRe9
+QPcvTZWlL9X4F5ZSwyYdYCsloRTUV0nEuEuw0mNvnNADYz/CLRexyovatULF
+/j390x/+8Idg9XpyINSojQjdWNv79mBPUODjPNe+iJqv5im074oht0I+rUI+
+ERJyOEzZFzPmQYwXhCkq5A1ezPecMf/EDcl5QyaDusvdwC6HWHJD7mxxzMAH
+Og/0rY2fg1qE/d0193vvDDT252gzL+tUpC+5kCehLuMzgiSdNSMTtUaecNM2
+ZPrGkMPGT2mW+fDd/Hz4LW4sXt7Wcq2bJdIYU95QRh+WupkkNRB2tfluTVMF
+hJ0mxY7w0pjE6czxS2P84qNgSrNMQrCTEV6GZsnYiTP5b3jBD9c5DiPzNIIp
+ZSoveoUBjw/Ua/tAvbQMblstSX3F11a8qAnLvNftq4GKFKbE7wntI52eI3cq
+sRbY3oKW93wSeuDAARulyD9JQgm/k6Li7yidh7dneIpmn+SJClA6xuIRgf5D
+2gPafdpd2h3abdot2k3addo12tV81fq3zbnX1LoPXOTUO33xBZ3LYMpmN+ps
+x/k2oPX195zhluFneb0MQa+6bYehk0XxPBTR/LKbrsmkBnnZ0htcVVEE7JWW
+kHFrvg3y3Oty58T1Ohtl/nUpgfjMd04s+7WWf/rFIApSav7STn4LhwvDj7h5
+cjJfLl3mAuxxc+l6ooNu6KHzFjffTl4bXsnXCEnVJyavu8jN26tOTF5FpiPM
+cvOsynnF+5VAYxIjGxO30DbJeiUMfmzSYRD19Hvp1N/fTs9JL7AprU4lG1yg
+xoJIaBTeYTRtLG0cbUKozvO+q/PM0jqPLF2b77IJGcaRmbvVtFheQ2s8Uo6S
+dFaUSArr58Z1Cg0cSj7Tx0+eOOyiQpl3J35xlJ80EWXyvxuGw+1nU6NGDTt0
+Xbdu3agw5tsRXPipr/K6Z3ChbIBGvmxOGEbjXjFo3FA0fFBzUYKavNjCrqig
+JpGPpPjhHvPpoxgjW5SRjfctI/6RrgWRNXesS+CnVQLIyls+NAGVEkKK+gkP
+RLJUfnxJQ9JdKQKJhU9WOy8vXKJpsE+FFyUUifzsIQmOZrnAKEXjQJnqPl5m
+6p0ILXPx66P8mjkefi/I6AEZXbGanTSsDxYTy/wtNNQQPdX72M2dDi+9lvnV
+abq2NYj5o/3AZ62Rs1C4vnDTc9+JuYl0bQNf2dkfMsM3KRh7B4gRtIyXX9Pn
+q+PZpnlojLLdNpe4dg5N1JBJGpLnpOtMM4n47BTHE25643hXIYjaGky17jNc
+2WvF/ylqSUDUxsnfVyfihW7Fjmqf5FtHkC9prFf7/c9RuxwDRxAL4fOMj3yC
+gYMItSf5xVR7Q6XKHY8jFP/AKV7O473Curs8rDVW65/cCZv41beNyl9IKBG4
+DdvkTcRNoYmH79oKv4xD+bZCk4PlOq9kqZ/uhN4/vmbnbOqV/8LMQe+zcAcz
+NAmWtUQTT7m1RbLGaJRMW5Up0wd0jbBf2C1TrLeihc1u/ZK81+83IGucmhD4
+NMIN1Jfp2/Njey7ImhVZu1Ler5qfEJXgmiL7LVi5xi8IFeveN3AN/aUkF5uD
+rosl/BSnYHIJbfQrVwgKTyxJHDud5UYWyiaMnYo7qLHMTbn346ZhWlptcjWr
+9hIW6rSm7qFJdf3FbBx060tkTmbGcX3Athaj3t3Z74Tt1rRo+cPgdd+LQCJc
+MMoUJCwKQIGLAguBwjwuIBegPaDdp92j3aXdod2m3SqIrfbV+CgKC+8Ekvwk
+Sqney3l9VrsXHHaDwy7azseKxSPFIjZCJbM7N7oZnjAmczyd4MUZrHXzjpND
+lIh/WOsngpaQTELedd/lFT4pXf9A7UKy1I0IWNeGEw7NnmUeIJAk+flJi0Kr
+NmR10BxdlSYXMw0oJsvCp+NuGecYWanCYxy+3y31DLaV+NQtB+2+KbQZCR6g
+9Qq3jFSWk8r+Kg1k9cy82P4qVZBdpaluSaq8p6yPjaJ23ojagCS2SL6UXSnr
+rGKwPlpXw5fURxU3oXSYiU3+C88s8HNeJumj+rodYpNZV+EpLzIQUUVnXPnp
+LrICSmZceTBkzp8s/WyrM05l3Z6fbSrr+WTC8oAD6nJLmlF08lhZ+oMVmuxW
+ZLhRqNBCoNJh72D/JewmGMYlMrOO2DfSX0BmviXHOhPrUCwRcMNlPPwMcuQk
+NwpimcWVzyDndCx8CqoRYXL2FEOPnGObdyj37eToEjJHX6OkDfLd+rt8EZJS
+rJ/Z4AYF+GmjxFok4n7zoM0Pw25n8yNJGzbrhDD5/caIvB2UkrwgVodWoiy7
+4RbYLQahj0FowSW3ZHiOIjTdb0Ag+08cdUvqRx1wO7MM2+O2YhiAMPptdUvy
+e2wwX/NJb2ivGTHwVroxxadE7grRxy57s2vI49bDuazAaSq8Mtx6g4R5XrKC
+XWYkyKoWWd0iQwyVQhNday11UwylbmsTgjWxKdEyxbr9FhMqXLwZLD+S9EoW
+uo057ha6TjoVrN/VymRRfUftbhmtb7/MMqzvb4RipWxkmaXNhdDPCiSVeFpg
+pR44iCipe5nf5H+RuncQcVJ35X+bTYelLu+zg1syzJsZBO0ybdsq/XGs87Y/
+dNO3tz6Q320R2W65X8hz41t7HJG+yl/WRiU7BDbd9zaCDMOJvKRNNrZqKGbp
+eSyd8+ljLoBv/R4aPm1XHMJBml368gkyX3XTrfFbjsyXIvPFpAsfI/MFF2L7
+bNhtVgidJhM6TTzidorRLZtUBl8zPWXzAJ1s1V6WgmM3WyKnZrJMHJvaENta
+D8nVxt7WIFSqSqhUWdeNlJcNDGQjg/gl70lB0cfvv9RHHGniHjcCRm/dR0VW
+DiTspuCjJ/va2DrRr+qxvT13opGv78n6E7f6abvbI0L2iugPzgPAerCu65Sc
+SfaWkD0mZK+JKTpv2eUFb8RJPWHT1aTP0PmfRej8Iw2D5HU5aDLQOlrNVO2i
+dqf1F2id9oj2kPaAdv+F0/odfS3BkNV6qFhkrqjOL4a17gZxvX7tjJ0sK3V6
+CrHzu4M6A3ffU6+EElbnssxlm1twlcKXwqS3nEwfFNrVL9K2qNrlf/s7Z5+T
+JZbSfU34Trh5HM6MSUb43U5NS3baSejy9aNgxpBXu2Ut5FU26nJDu7rVr6Im
+eVgp+0Jg3Jei/EUXSaAx7vO1YGp3hfLhLE52JEoYjiKGyL4qGPX+GMQ+RAI9
+UX43vxhdttUgcmhFBNEcw9oEA9sQ5dfD6NZG+TVQfjWUX3mCqh/ll0P5qRG7
+xiRkw284QyDiL2nK9FRR9zKuBRD8KhIC+9pBJrbiJryqS9evFnEW09yGR2mz
+3AZIlea6oQwZ0qi5yK3mkqGOhuosZCedVuvUCvi1q9vczjuyAZPsxCPVhUG6
+GF+SMNmxZ6xuIyL70EwrhqSorYY/LJ6kH7roiqv6MOR9ctG6Zyi7IMYQ/Did
+/3mxCN194e5L84lio6KLOlpsC686B+JUeNabziOWGex2LnFoFrssrJDX70HH
+u2k7H+mONKXAqjCMlf1++0PvG2zivFNMP0GVQ8KGWfZgzwCKZL6k+44oLMnu
+HhS8QNqOR8Z5KEFRsJQFurIe/HZsrwu7i4rffwcfsRgf8fE5H+v92MzgKU6V
+HcTwD+PxD2NkByqe+HCe/hBUMJAQqD8JZR8U0lOnz3TGV3Qg5GiLmlqhqubQ
+0oSwpCGKq0eoUpsMogZqrIYqq4xXYlBrOVSbmkjLoBAtugFdkk8ZYl7Dg+PM
+lbqYnia8W1pvC1F4J6b+CRANNuFla0WjrtCySBkSkaER2T2s4my3m5gMm9RI
+WJArAMkuZFJ4bq2uVLYa6KxbDfSUHRGBqP8ut6PFECAafsAlbWN0M6dJuOip
+sY3bInfE/2YIGisfvwIy7HTcrORSATQBOA6aZKEGpp4BxdMXzu/ISxOg8Tup
+3FFmbIil4xTe7RQJsZQZnUgXzL1P5EZWf8BOEF/tk+VyjwvhphDruOuRLqSA
+oULfSoZg2fMEFojReO1uzU388Mf+TAkkyFw0ARHv9p6N6fYoMbt0UXGwnB1S
+tuBXNt2O7Tlkd6uClJWX/DX+zCzCryzQcYnZPKoZRBFTsYGToWUCOfdYHu0o
+HvEIaBmK7RzI4+9PZNUHWnquVmKQSgciq7bIpxUyag4tTaClIRKrBy21oaUm
+tFSDlipjlRjkWQ6ZpiLX1NejxeHQ0xakemhg+99jnPQ2PiUpfu+q8I4cGSZu
+owTvaOT15bjoNFCvMNMNqlSd4xas+00SZPClofLRHD5ahXd92ejK0z0kw9Id
+hgbQiYPhY5jsVaWbnY077EJX2dhQtpmc5fiIwsP9LnLz97+MAOW9ACP+8DxG
+Cs8cVvhdyMVI3eqFpCXex8jBPS7y/T31M7dDvESGabEZSfZ9Z5SVk9kJvLiV
+Usnm8DOfKcnK0gNPC83+J4Vm32OZ87X38StweKzTv+Q7s/uRrAWXrylCkjAV
+GoBICZalxqLmEtZ3Saa/3/kz3yWH3CoEczhbbv9ItiklP+q5LMeZ8gch+R27
+uHB/aNm0bBuxW3cpCXbDue329tp0Q4sbPzWrCNtWELYtBa9F5OQLdR7CbJ74
+TPCahpWcDF4TCN/GopBRKGUEeA0lRBmIivpjbfuAV8+VihiK60Di0hYVtsJa
+N8dqNwGvhljyeoRvtVFuTRRcbZx7fUWUnQZeZRWvVPBKHVgUL6HF9ljMEcGW
+KdPdxnPdg5Smu/29RtQ/LeKIknzZOOyIwtsrhSBLDUFWnsuvOKPonjcyftMA
+i9J4qU5xArI2CllHuqfLxtg2XlINlKqgVAeH0p0j9rrNaGVT2gmH7Ca19iai
+xke+XjxZUR+U6HZtd0ZcwFK4ki1db8WFb5avkCsKxW9+By2PVqgkHLiiawmu
+6GIIrWBOt6IlCxAT8BK67GsPwdVB2oEnwpfs77HvCWzte/zKexL5Dt58Hr9f
+OTrw1C2shRuXVfml0Ed0euFRt1wi2RzL4W9SYPuKDSZ9+HYsFFj61bpyVYdk
+LbnsRaBA7dVtf3b7bc38TJVfmc1EdxuI7taRB60BqNUAtQKglgLUYoBaqGsi
+ZvOUZwLUNMzrZBQwgXxoLKoYhTpGANQQ8qGBANUfBfUBqJ7L3fs6obL2qK0N
+QLUEqGaY+8YosiFA1SNUqk3IVBOgqo1RqHAZaai6bAioVFSfmgCUuCFLRE8b
+uvWwZAlB3WyTikG3oHjczbi/KWHJ8i5XOfuz2DhLYmznfZfGdqk+cZtiYjuW
+gVQNkKoFUnW5yfrcbCPdHU803YqOaOsd+Hq3z2JPSR6xQv23uY1bh9CRw3cH
+j14iaYmoZx8r1lV9BlB/FQGUWzr5RiJQJhcUcgpsbEePwBR0qceyREVQZY8R
+BHjfiHNYkQHe89AUwtz4tWpxVIVWm8cT9cri4p0U3ylh+4UwtxxRsBPXplAk
+S4iYLD4mWSjlnUeUEOeZ7EtOyFKNk7ZgfVJnAMgAUHJsGMgnb/yOq6UT/bXK
+yvhjsmeD7PnxxO13dFALcrqNmzrHvzU7cFifEhhuBbLNQLYRyNaTQq0hhVp9
+DtDOkFIB2WKFbB4PfzaQzQSyacQyk9HGeDQyBshGYoqHo58hpFEDgaw/2uqj
+kHUlXuqE/tqjwzZA1hLImqHRxmi1AZDVRbu10XANtFxttIIGZGnovSy6LxuC
+LNVDpsGgQha4rBTBCb/VNfBbSlyy/NmhWCIWMTonFqzKUKBSdfNSeb/sxC8j
+RjJyJCNINbmBOlI3lPrhQreTv/VPfuNSBarrOmX4TZOBWxpNf42j3ybSf1Nw
+S9Ppy1lEAnOPFZ8TaUnOz2AJf35JbHf3KKbeDOVJEUy5IPBL4SCwOEflkQp7
+Kj9jPOyoruZpHPg8mAgeXlynVIm0swR2q9LMmKc4/KxQqRKiDjx5qT3Bd/qT
+h+mVvMbSZ0k5bH3TEQX0qK0CHrOR3HGF2EWDDiaB5lSu/539ciZXOurM89jS
+kMAaSJXxjJB4OluyylO694TdFUV21ZG9nR67DewO+2HW/2n24cT2knXtBq6d
+wLUduLaRdW0h69oIXOuBaw1wrQauFWRdy4Br8VEFDGHMRiQzEMtU4JoEXOOB
+awxwjQSu4cA1BLgGEAv1Q2+9l6rW0GFH4GqHsW+DRlui1WZotjFwNUDHddFz
+bXRdY5R7fRUcSEUcSZrCVRa4yoY9WCzTcgz1MN57pQhaANQl8F5djPzKNc+Z
+7H3Xw8QnZn30WP1i1b+EWDFY/hFV/+7OvfeiD/oS96XTH4Pol6ESMkvoDGBj
+97hsVbLWaQddiD3nSLhqFw+XVum+oTglfDhPyYh3+IX/YdLeCL1OSeOKcwUS
+QENZxQSEyQIaHs2jJu8P1/TCAeFNj9zbAWaXdSJ8sMZPV1qf1q0BTmZ51kpZ
+1uS1sovPETg7DD+Hnr4sSQj2UgPZ0DzzZPvrkpayQzQhU15yxBY1jorbOuYO
+m+X4Emd5SgedTueiD8vNWbED5577SPlcLHZNlm9S5KqTZYF40o/sngayucsZ
+2eAl021bJZunybZ9xzVEPKIjRgcJD/dD117yrd3QtRO6tuO6tkHXFujaCF3r
+oWsNdK2GrhUniBWha9FhJQy6ZqOUGShmKnRNIswZj5pGo6oMFDZsDWn6Kt3/
+FDuaSIOoOsiGulnVJ1ka4KJz4HIEiS4Wha7icrrJp8NodBfnegIetJAXFeil
+SpUEp5imVZOK5E6VJ7uxquo40VoEenUI9OrDfiN8UhOpVy5yPqmtVGXcZh12
+JKAHEXBvAr1+3O0A7nowDA2DoZEwNEacOZHzJBiaQi9Nx1HNgqO5h4uN9OIQ
+iv6Qqai5lH7bszBHYd4iOCoZcJQFHJkvLEdauPhSXOEiDJL1WaFpA+E48Jqf
+eP+eS6xyY9sVyP4aIZBcaKUQHQOHo89emSOCxlPhB5R0ZOjQk5fJ8mPS+5ax
+I0rOUfV1xzRCO5EAzumcWAQqPvOcxUP4uSCTSS/mGZ2Cc1F+dzFXfJHssHAh
+x21Ec97vjyQ7dz2zew/6APg4idUxyDmig7kHIWc/5OyFnN2QsxNytkPONsjZ
+AjkbIWc95KyBnFWQswJylio5C7CrcyFnFuRMh5wpkDNxix+F+tAMQmfp+KO+
+i93ru6PFzmiyA9pshz9qjT9qgW6bot9G+KP6+KO6+KNaJDI1hrv3VCarqoBP
+SBN/1N8Ge29obcLGcxaszrbJ7zoLdZ28jdE/yIvc638Vy6xC3CUlhabr+JEo
+z92QGHdl4S6N6yuvmZ+MjFXFn1aHu5pwV0cqm1Lh5B4b43ubEeC2/Nhx1x7u
+Oil33eGuF9z1BYx0/NegTa6KKtXUUfTjWLibQJ9O3uOy15n08xy4m3+o+MDw
+a/HgRX2IWtTkfv9RUGHwwq+LAK+EBS/7RQBesiXvg7hYMSlUY4/izjqx/FAO
+pl5M3oeodajm7Xj4smLwWfAyHXhHn70EPpmJfvjpCz+9xoaQXNFh/4dkhfOI
+fUehHoGLB0D5DJgsh59H8ExObPKpIHheE0NpF+107EtiLvC6qrXLMR9cQlZj
+EgfIvhKX/W49oa3Lzmf6Y39kzuDRThMunoTLE3B5TLk8DJcHiRcPwOU+uNwN
+lztJxrbD5Ta43AyXG+FyHVyugctVcLkcLpfoHgXz98RGgydg28eitVF4shHE
+iUPR4SD0mA6XfT5WX4BmO6PdDmi4LVy2gsvmcNkELhui93rovg5c1lIuq8JF
+JbisAJdpMFMOn1UWhsriGVN7mXB8aJMOiyUQdgw8YidjSbXQyhZl8UFjHKT2
+9b1DxUUPqFbv7XABF1aOCyyvAW0lLrzKBDeELQNzMkBXF6PTgJtsxM02BdAW
+C9QpLnaDe100O5UhDBnK6C+Zq2SwADocQEcC6Bic43ic4yQJF3COM/a6AH3e
+AfveqLjyq/FsRn2OYBSbv9A4NMSm/NOCgOcxWVCU1ZfqBdUTWj/oQsqvxtEY
+nmkR5wnz4zyhJVLeJxWRi7kxd0hc6ZLYEnjAV3i/lx5Aj96Rp26DYWHS/sRL
+BUX5/VH78lfJwRHU+Tn6ksXB8muh3g9JO7dnw0bxype09HlZfOAVqbJezfcd
+p1knty1fXS5yVbfBsM0WTK7kyNCi3U5QN7q0YTNu8jwR5jmiy7PweJrncwoe
+T5C7HdflQ4fh8dANmITHvfC4Gx53YmO3w+NWeNx82pgNJ2GS/O0TeFx5WAOK
+vzDzUctsTPsMFDSVMGsSSI5HXWNQ2UjUNhwkh4DkQJTYX5HsMdeYrqi1E0i2
+x720QcUtQbLZeNwLSDZA6fVQfG2UX3OopnEQUQkky4NkGqSUCyGZGkPSUua8
+qA1RLYwdjT4VZ/XKdFDwOrq/xWD9VQzW4kDtY+KyutRBOuAg5Rsp44RArTLO
+jQHW4NZqcYt1ALU+oDYka20yGys0140fWi9K93TSDLfHSiJXuq4fXTiArhyM
+hRsmMbvE7kSx4wB1okQleNPpgDoLbzoXUOfvL96LKqml9E+ywD/RK8rn6OoH
+VQabaBX5lM6UANRfJjhYl7+KSy1lay9y9hyta+a8sH41WVhO+kqY5M8auy46
+iTy0tuJ6XrCryuXnsV2O/FZcfu+4M9mF5nSWjkTHtgAqYY5Cb2kl94WF/Vim
+W75yQtE9maXYlrZO+owzEcHo+AXdeuaSXIjzluLnr2rd9ZoQfD0gWA0QP123
+BF8PbWZjmyX4Wo6UlK+FhhUuQ+8l6L2IN70Awech+CwEn8GbnoLgkxB8/LZS
+DMGHrhH1QvBeCN4NwTvPQ/FZKIbgTRC8/niwGH0FDnXZPvfWhVA8D0nNhuIZ
+yGwKcpuI7MYhwdFIMQOKh0HxYGQ6AIr7zteAD4q7QHFHKG5HsNgaqbdA8k1J
+4BqBQQNwqAsWtZXiauBSGWwqQnF5MEpTisv2DFHc1ca1sTjX4dnRWHLdkNyv
+PbjhSDgO3CRfK+0Vgza1v9ZWB7kBjbJcVTmurjxXWVGhrcqVVx/vBvBlIF8G
+9BsCbWOp40o9F2hbK7QdST27LHHv60UP9SUESScEHkQIPJTeG0EvjqI3x+Jh
+J9Czk+nhaTtcQj4bcOftLb5k84FjKlldq3y4tf/3ySefyOfxBnlkdna2adeu
+nax5DXanjfow3ChXbCn2C3XDpVM/JGExDuP7vf8qfAMvZnf4UH4v5IQZLrT8
+nslyQe2pLN34sCS8FuiNHHtmN1QPpqqe5MUSS5+yFVipZpaKQ/d8buD9Pwfb
+GwUBhvx0Uxb03hTWb/oo3u5IdcOCeyPHfwbDdc59DQtyFXCvAO5lwL0EuBcA
+9zxu9xzgngHc04TBJwH3uC7NPQy4B68AL+DuBdzdgLvjrM8Xfm7W43bXkCat
+IhpbDrVL92iqiqbmoq1ZPOvp6G0yupsAtWOhdhSaHAG1Q6F2ENSmo9s+czUs
+htrOUNsBatui9VZovgXabzoacuGhPlzUhY9aQ5QLuKkMPxXgqDw8lQtRmxqi
+VlgMouCOEhh3kNUj7YPouL2RX6kz/vnrsds3xO5AHScZ6gYnK2To9XHd1ce6
+WQEykFlXysHcWyPusSn32mKWm0kg3HZYyL0v0oiY/ulDP/WD3QGwO5i+G4bT
+zSA6Hk10PA52J+J0p+B0p8PuLJzu3N0OmShuv6K+8D1z+vRp07hxY/sJWNu2
+bTO3b982tWrVsi+TDXTkA9evXr1qP2x96tSp9vcyF3/VqlWKcZGPn46qMPlg
+OpTUukF6CIaKkPu1Lwmlt0kuv33ni0KcLDDwthue4Tzdgyq026DjuNCcg1/H
+8SsfRZ/k1Ceg9jgMl7Bf3Q0d19+lBF95XeZLXv9K6X7DmgVPsM9Nr+T54Pia
+c7BqYm7YwdSbBb7DbrnsnJ9uC8u3Jcu9/TzYkJaj3tLq1E0YvgHD12nX4Pgq
+DF+B4cswfAnnexGOz8PxOZzvGTg+Rfh8Ujk+CseH4fggQdP+C7EVkTtwwNtw
+wJsJoTccIZSG5U9geSUsL4flJbs0vYXlOWhuJixPg+XJ6HE8LI9BoyPR6nBY
+HgLLA8nw+ivLPdB3V3TeCb23h+U2MNAKFprDRJOR+C84qQcvdZTl6nBUhQC2
+EixXgK80WC4Hb2WV5dR4lpN8diuBs+W3vZ2U1i6oRrULfq+8y7v+PBZA+2GR
+vm5MU4Zf7FAMfrgc11SeLLfSCI0QuOYaXHstguc6cFx/kpug0IT7a859toTj
+NnMcxzLO2lU57iXlOLLcdILnQfTXUCkJwPEoOB5LX07YHKwNmaddLdxExcoe
+4bftZ6iuW7cu8LyrV6826enp9vt9+/aZevXq2eovOAcLjDdu3Gh69uxpf/Jb
+JYc//734YlUxDKeEGU5Kdp7YPhWh923zlMjgycvXopf3wC+e3rrhCHwvOYTJ
+S3MKwe189isIfhWMmZzOemlOge/JTNkK4cSzfL0QvksRpuWX9s8vxVnbo0vw
+nSxunNs7KwbBNkux3zZRAbZZ7nW5a+jlSDe1mnarIFghRF/YMdk7+dJbss/M
+3VhLkU3y8MLhDVFvE0rfguabkHwTkm/gka9D8zVovgrNV6D5EjRfxCOfh+az
+eOQz0HyKUPrEdXecI1diFO8jGd59hrD6FGH1CcLqY4TV0LwBmtdC82poXgHN
+y3ZqXA3N8/DMs1HgDGiegionos5x0DwamjOIHodB82CUPGAeXmi2xtWovQuq
+74j620FzG4hoCRnNoLkxpDSA5nqQU1vXXFZDk1UgqyI0l4e0NPRXDvLKdgto
+Fopj9eMOxtOcIviWMGXaBn9raxzR7YRmRVoGfnzE7bx1Kc01bWCd7sZVy3E5
+5Ye48dbKCnQNLrsWSX0dgK43wU2CkMkQMimiBUC3nuXGckVfnemGblok6APQ
+/QF64MrYbtuT6MqpW1yxYRYOeS7Bz4KdxQfRX1aS3zKpqanmj3/8o6VVhj2H
+Dh1qFixYEJD805/+VD7FwcNJeG0qVqxof3q/WGDjK8kp8ZUrFy1/M4iW5aVf
+ANX4zQRC0XI8qoXmIkBBq581IC87w5lPZxaAakFJc/JZvl4o39mfku3XEkIt
+3xVYok9lvvTjrrhqXPYr67qFVnHj59W1X9K0NeZz5T1vWn8rFxrmVW7kjt74
+XWvHuMUU2TAhWbaJSpbd/8BV9v+7p8jeVQd8B2Rvg+wtkL0FsjdpN8D2Othe
+A9mrIHsFB3wJbC/igM+D7Vkc8GmwPXU9NunnMIH0QQLp/WTAe8F2N9juANtP
+wXYL2G4C2/VguwZsV5GQLUdLS7erI0Zrc8B2JthOA9vJYDsBbMeC7SiwHYFO
+hyKgQWCbrtj2nI5+0XZnNN4BbNuCbSv03wJsm8JDI7hoAB914aS2LomrCj+V
+wbYC2JYH2zSwLQe2ZcE2tYsJV7AsiMkaTFtE29omv2srILcJouzYH5RiWZjX
+wcSnzT7J7ubcdKqE873dB1snTEzwy/EHSx2ASDmDSHk0We44yTbwsJMlWqHD
+ZhIpzwHO+a4TP4vJt21g3KxZs8C7Ll++3AwbNixgUtYZjRs3Tj7YIvCuO3bs
+MF26dImBaQ/udk0tmeg/rfuMGtvJEjwlAk6JJbIvvWy+8l+FZoruxnvOwvQy
+Ds3Tmfklgc6jyXf2p2RzCjQttPZ39qVZLzQKg8qkd+3hziuXEmZf1DNefh7z
+51Ln9nHwzfzYEg3P5d0Xxk8KsnMI79suknW5soOPtmTZ1S1FNupM+jd75Puc
+Tdo9LVDdBdE7IHobPG+B5y3wvIlXvQ6i18DzKnhexqteAtELeNXzIHpWverJ
+Kxovg+ghED0AovuIkfeA6C4Q3Q6i20B0M4huANF1e4mXQXQliC5TRBeiuHko
+bzYqnAGiU0F0EgodD6JjQHQkseFwEB0CogNxMf1nabwMol1BtBPuqD1uqQ2I
+tgTRZiDaBP01BNH6IFpHEa0OolVBtBKIVgCS8sCSBjTlQLQsWkxVRIPCsnWa
+Fry2UrWKYdnG2J/sH+xLZLJEe1METfviUEZs0ezlBqLKEUWXk4EpnG4FrrAS
+2XAVra/VkIEsGdDijupjfBpihJqQETSXCjspZhsMVPuZztl2IXvornW8vvRU
++hI3eCaDaMNhfOQnroov1fxJ9PDUja42OHuLqzgs+LRYxt9Xxt+TXWLNpEmT
+zPDhw+0nJsmH1dSvXz8ugn706JGpU6dOsB2+vH7ZsmVqKaLmU8Qi5dxgSrqf
+6lcibupEMIpb0mW56nx1KlLARYhyfnfHrqz6HMp9Onsh55WPk4PDxRywwFwU
+8xT79Q2xAvZ1Zxzi1kqct3jLsSQGfzcO7yuK+DXdVTFwu/lxbjfJR9b31Yg9
+cAYtRVbfJ8vWRfxNNjGS3Rtt8zMZv2wecqqHMP4Axu/jhu/rZJC7MH4Hxm/D
++G0YvwXjN3HD1+H8GpxfhfHLuOFLwSc5/tacuYpLhvMTlzSSJno+BOcH4Hwf
+ufBucuGdPPNPDxNJH8Qd78cdw/kaOF8N5yvgfOlWrXOhvrmocBaKnA7nk8nz
+JqDWsah2FOrNWIhnQs2D4XyAct4LxXeH8y5w3hHO2xGGtobzFnDeDM4bQ01D
+6KkHRXV07VR16KoC5xUhrgKcl4fANEgsF815gLn1vgTJrYMwurXxvNsXCOmx
+PDmOePvyLvG0l02gvTzXV5HrrKzbdMk0klrcRx3upx60N4D2xtDebKKbeiJT
+UGQqSgelvZvWCvrQT/3prwH022D6bxghdsZKV+WXav9EvPqU9a6WOHOTq0XM
+d8/gWxE8vudIL6lYdu7c2dy9e9ej7cNp2WNUPH1+fn4k1eGPGVKik+wqE4u0
+mxGfEmZak9/ScaWriDXDvrIdeO8Q06EStP98Eo2lw0zbl5wl71Wm8efF8fy+
+5flMVlGe5XhyXInXLcu5juWrfhTIsewKa6XsFQaeusDNMbkfZP0PbdzySOej
+PH6h28jYzclS7FaV7jMUZLPhx5zoETQ/hOaH0Pwg0xF9X2f334XoOxB9B6Jv
+Q/QtiL4Bzdfx2tf8ypTvm4s47fPXcN7AfOYyMTZO+8QFhZq4+iBA7wfovQC9
+C6B3APQ2gN4M0BsBeh1Af7ID543LWIaYlmx2752H0GYjuhmIbyoinIQgxyPM
+MQh0JEIdDtBD52pE+papAB/lhUU8ZFm4SYWfVK1JJfk6lHWsiiLftQp4bGUc
+k63dCxyUv4hB2SEUZ4eK0rYg1sMBKUVvAVLmhVQAyMoAWVWBrCnDXABZFyAb
+SBFdiunj3VwTmXMic0/aA2QnBbK7AtmX+0wnlxi0mHsl5x0BkKNWugL+eFzw
+JICcKgEOYfbsTa6csGBr8TlvKUVRNrH2//i+ZDyo8hHmMkVj5MiRYVBlaElq
+0rFAPWJRi654zxG5BXiWcLN+Ndl9Jmp9amf9hgvLnxFY+x2M/eBQsNgxWYj5
+TDZfvCabBQlsvvpMNv3+2+L6bwqbt6zbTODSxs96xodxQUUJi6fcvWx/80Tu
+UPYQfEO2zbTbZ8pbZCvlJ5zwMYw+tiNWj7Kklx/C6AMYfaDbEdyD0bswegdG
+b8PobbzuTTi9oVv8XSW6vkzyewlQL/D4zgHqWbzuaUA9eV4jbUA9THR9gOh6
+H9H1bkDdCajbAXUroG7ag/fdhfcF1NWAugKRLVVQFyDAuYA6C1FOR5yTl/mi
+zAdmMMnvgBnudb0Rene8bRe8bUe8bXti0TbEpK2AoznetgmwNCKybjAAUHQh
+ZQ2gqorHq9RD94hwZKY47+mIlVkbluQyLU2M5lYCcWs7baNNkAy/FtBlQ0Cn
+AXQFrqWS1NA04q/BtdYmQqgL0PWlgi6VdKmoj3czVWTGSjuA7gjQXWbGNiXr
+Q6bRn4xjIEAPAejhAJ0B0KOJqccRU08E6CkAPZ2YetYGV2CY7/o40r2W1K8y
+VnTs2DHrW2W8KPbhC8FnkYR4D21s9leheNluueGa9aspwT4CyQGwbmLVO3EV
+qtcY0/XLKeVtfjjXZsE5hRrIlioO2uKZfSdg9mwEsxfDzDpf6r29IlvUjxao
+H30QMPsoYPaxTRK8tbIlgQK/ZvyZ9NizYEbkU073lNM+lQUzT7Jld/THONfH
+QPsIaB/yIB7iWB/o2tJ7gHsXcO8A7W2gvaWzrm4A7TVS4itAewnvehFoz192
+4J7Bu54C3BO6D84RwD0IuPsBdy9p8S7S4h2kxdv2GbMFcDcC7jrA/QRwVwLu
+ckS1ZKPOlviemYRTHY9THYuzGYVTHYHzGQq3g+A2XbdP7omuu8FtZ7jtALft
+4LY13LaEg2ZkxE3gtiHc1ldua8FOdbitAkuV8MwV4Ks8nKXhmcuqZ05tr3Yi
+RWi1+PpUGJDlJ+eiS4bDZU+xlrr+2r0+VH1ODVFcrpcbvyrf180qqQzFVZVi
+Gbuuw9XXk4q5VM6lgj7WzVCRmSptobgDFHee7gjuoXlDPygesMCNmcvY+QjJ
+MSTXgOIJq1wpcKqELWtd7WEeJC/cVDzFfvPNx48f26EhmSPZvXt3dcnfj3jH
+X4awzcoLdlYrEdv5o0TcSraA3FJFJikHkfA9G0SHIuGkcM3Yzox0kzFcZb9k
+AOsZC2uB9bA2m7Wcubz2q0H+WpTRQmXUhBkNx7tFIL1XoA61pE9Zg1t57Gd9
+urgiJaipP7O3lZlv/ObbmZzkGSd8luPaU2Lfp+D5BDwfg+dj8HwkDTwf4lcf
+6IrRe/jVu37f6K+bWySzN6HzOm71KoRexq1egtAL0HkOt3oWQk+T0J48o+6V
++PcQ8e8B3Oo+3OpuCN0JoZ9C6FYI3UwMvIGkdi2Ert4azJ9cgIbmoqdZeNXp
+eIopeIyJkDoOUkdDagakDkOXgyF1gJLaG+32QMNdIbUTpHZA223ReGu03gLN
+N4PUxpDaEBbq9dPwFE6qwUsVSK0EQxUgtTw8pcFVWUeq9ZxJrkxlHasnt0Ww
+/s1B61orC2hrG0O3MeFho1hAngBt2e5uWCqtlxumqtDXTSqpqsl3TcKD2lIf
+50bqS718pJuQ0nysm6DShhtvP9kNdHeZFnO7fUn60+e5QXEZHB8u+YPkEZJP
+AO1EOneKhC6431l0+Bzc7/wNn+d2U2TKhf1Fhw4d9HfBBrlFaY1tkJtkg5gs
+m8uF18OF1p9aFadYZEsXh6x3tslu0FNYfTeuGhV8+Fds5DYIk22FWMtSdu83
+52dLx9WbAl5zAl5duP1+XHoa50/zi/jTgFW/uO+xWiONKJ55m+Xma4d2iXS2
+jbNkceWZ0oRZeH0Gr0/h9Sm8PpEGr4/h9RG8PoJXmWT+4EHAKlGRuQOvt285
+Zm/A6zU86hVhFo96EWbPw+tZPOoZPOopmD2huwAdhtmDMLsfZvcQCu+C2e0w
+u02Yxatu3GH85kGrcKrLidiWrHdvnY+k5iCtmXA7DW4nI7sJcDsWbkfB7Qi4
+HQq3g5Bquu5M3RMZd0POXZB1R+TdHpm3Qe6tkH1zuG2K72oEDg2U29qgUgNk
+qqLEymBUCW4rglR50ErrEMmu86WtjHpb8PW7WbfwIbSGz0EyLJtctw0dJFSc
+kjEoGYsq192NTZXv5caqKkmhDHarKbu1YbeuFM6lgD7CTTxpJoV1brY1N91u
+ghvO7kxHdAux23+OG/qWIfBhdF7GIje+JuNsE5a7Qt80nO4M2J0Nu/Ngd+Fn
+sJuirvPKlStm0aJFdqpz27ZtPwPfv1DmPb6yU2+mE6h4lihnm+LkLU7pjSD3
+i0BXXexXihSSXxPdBP9bZMzIxbsu3Tyv40JxIL/7p4Dsh4aKIuxy/TcDfm1a
+wUGzOUF2ruM4C4azbC6baRcgPYNj+SBEyU+ewvATuyXr40cyOP4otlewuQ/E
+98hn7wLxbSC+heO9CcjXgfgqjvcyIF/C8V4A5HM43rOAfPo0DhiQj59wxzmk
+IO8F5N3ktDsA+dM9CvAvzXp871qi49WAvAKQlyrICwB5Ljqbhd6mo70paHAi
+WhwHyKMBOQOQhwHyYHQ7QEHujaZ7oO2uaLwTWu+A5tui/dYw0AKQmwFyY9ho
+CMj1df1rTfipBshVujiYKwJzhTDMgJwaDbLAC7vNTXIAtOS98SzHOeIwyFK5
+lpEqGbFK6+5GsCr0cvNFKgNyNR/TSyV8sJtb0mCYm2vSVCrmRBmtiDbakh90
+AOROgNyVjuihIPelg9LnuMHwoZJfLHSjbzIKN14iGolsJMIB5FmAPIfoef46
+h1jUZ/u44d5Sdh5GpUqVzM9+9jPz4x//2PzmN7+RIaSU4mH+8yD1FenluT23
+g1YQG/IJ0eyknuL8loMpzPL9F8HnO4Xrx685MUOca7J1w/GTM4oZAS6hg0bx
+w0I2pNYdpt+Lxjkhz43wyTbacOFzCVeli8UlvsZuR8nz/f5pri9yOF1OrmvZ
+kvJmZ9t1WfjoLNjOhO1M2H72xB79sXD9BB/9RNl+SNr7QFPee7cd33fg+zZs
+38RJ34Dva7B9BSd9GbYv4qTPw/c5nPQZ+D5FYH1C+T5M6nsAvvfB9579+rT+
+xmwlrt60nfh6G3xvIQsmGVuJj1iGxJasUWeN/OYgw5nIcRrSnIxEJyDVsfA9
+ilR4BHwPRc6DkHX/Seqs4bsbfHcBgY6g0A4k2oBGSxBpDipN4bsRfDdQvmuB
+VQ34rto13llXUL7LwXdZ0Extq3jG811K+Pb5cXP7q6QQ7n8d4G1foCWuVMVb
+BqhkoKp8dzdwVbGXm1dSFbyrK94yoF1vsJuDInNRmnBPzbm3llKmG+MGwztK
++W6Sm8cS+OhZbgBdBtJlQD2DGHu0JCngPUECHwmAiLNngPds8J7ntyyPctBv
+h+C1SIQ/W+ipFkefygShp1JYemr971OV8RMn42TH6qMX/n0hXnV7yTs24Ez8
+SJbrrwOs+t7XnLPhilXvRgzmvkr0yfEF5mA18JuvE1XrmscU2xVaY08KOWW3
+H5udKur4tReRy/3mqrmwDAu/OdnyeQU58JsNv1nwm/XUMZyJf35GjP0Mfp8q
+v4/h99E9rgXf/ECXGt2D3zs3HMO34Pcm/vk6DF+96Bi+BL8XzjqGz+KfT8Pw
+SQLtY24HIHPwkLL7P8yuvcTb5MbbYHizMrxOGV4Fw8theKkyvACG56K1WWhu
++mJcCjqcCMPjYHg0DGfMxE9Px0+j3QHKcG803QOGu6LzTui9A7pvi/5bw0EL
+eGgGw41huCGs1NM18zVhqHpX9dMwXEkZLg9vaXBXrniGHbjNZNpHPMvNLcvq
+vyUsV9ftPJV8/b5luayyLANdFbiOilJe47qqcH0yOF1TWa7Ltdcf7CaryKQV
+mbwi88xac6/tsFsdpJQ3wU106aEs95vhBsdlkHwYLI+A5VGSsCyy427+Qy3n
+a3cLlnaCtL2Ndxy3H2q0/Lof9R6mW4Y+tNnRkGQdFwnGNh9Zhfu6jyvTuhqV
+r1tp4dkNx7wZ54SL4TqyAB3iuvgCdKmIAV3LtDvim8WPGcVi7CT/GZLFJcsx
+p+xiEjvCHewD5zxyTuCRc/ODPYGVbNvc/En+bJcr5kJ2DmTnQHa2NMjOguws
+yM58pOR9zTwF7CeA/Rjn/Ai4H3q4AfsuYN/BOd8WuAH7Bs75GnBfwTlfBu6L
+gH3+tIP7DM75FHAfP+rv9jfmAFn0XoLv3WTRO8iiP91hzBai701E3+uJvtcS
+fa+G7pXQvQy5LdGdxOZD9xzongnd06B7MgqdAN1joXsUdI+A7iFT8Uaouv8E
+9dJ4ru54sC4ZeK/hqH8o3gwyWkJIc+huAt2NoKe+0l0LqmpAV1Uoq6J0V4S8
+CtBdXukuC92pbZTweLpl6UOzRLRtaC6fKtIiVCHTgNy+rp1N0x1hH5qK3e14
+l6kiVTkurYZu/VtH6usD3awUmZ3SdJibrdJKKnyA3R6wO5F4dJnILU82doaL
+gJ1O1wyaHXyg5wR6b7LEOeTQM/DLs/HL8+jhhQ7sr4cS3vA/ebN654+U2oSP
+sY8C/AchwO2cgzzbUnQ+QoEPrB8Fgy6CQGwz21Jxe2gUWWdUKs5v+zL1FRnt
++a8YGC5V3MCwY7xEIuN+Q7hi0mifefjpGZbwlz7LeGa7QAi3s1ALYnsU58Tm
+sgVx9/M8+eQKbbIo43mOLL+UQz6H8OcQniuNp5MD4dkQng3hWVrPznyAHwfx
+ZyD+FMSfgPgjEH9I/P1AVyvdA/E7IH4b/30LzG+C+HX891XBHP99CcwvgPm5
+kxZzvbT/ZY7pRjkHD8g0PmJxMN8J5tvBfCuYbwbzDWC+Dif+CZivAvPliG+p
+bmq7AFHORaCzEOp0MJ8C5hNxSONwTKPRcgaYD0Pbg9H4gInqyMG8B5h3BfPO
+YN4BPtrCSSt4aQHmTcG8MSw1gKl6PdWRE4xXV8wrg3klMK+omKeBZDkwL1sM
+5m+EMW9mnXqS8+pvu9e0ikdcEndJ4Mt1cFV1GQdL66xb/Se9H55PbcfMh3Gv
+GfPceJyMy42nHybRH1MJqqcD7qwVrigx35nGb7nElqPEIZpiP+pW1hPGxoSj
+P7lHfvfI8SmeVgh9JIQ+KnBwJrspgrFdZnQbRJ0Q+WHc9jaJm2rE+d7nUTWt
+YuEsns2PPmMAuDBqANi+5vrnFLnip2mk2EUZT2Px9As/1cymwsEE8hSL5/N8
+H4sDp13YZdGUluT4/K55rrOjhU/b4DMXPnPhMwc+s5XPLPjMhM9M+HwGn0/v
+OEYfw+cj+Hx4I8boXRi9A5+3LjlGb8DnNdzwFWX04im1PL8zpwmxTx7FGyui
+h/Ybs58Yey8x9i5i7B0gug1Et4DoJhBdD6JrQXQ1iK5cizcG0cWr1BsjwzlI
+cibSnAaik5HrBGQ7lhhyFIgOB9EhIDoIRNPHu/f0AtHuINoFRDuCaDsQbQOi
+LUG0GYg2AdGGvXFzimitbs4bVwPRKiBTWRGtAErlQSpNEU1trZjGx9mE002l
+MBaFajM7NtXcxMpk/hhtXZ1N8nHJy6X+JoNhMihWkWup1N0Na1fHlNTU3L5e
+fzdtRaavyDQWmc7Skntszb22lfqf1AGlHih1QfpDpsII8gPop0GYtKH02XD6
+biTRzBjJWcTkiemTSAfkZy5z9Yl5IL/QIe8Q90jKP91sQ9cHqyNPsRti9erV
+S38qagK+FyuKpVgb8PC5/dh2mU0oduBhvpsbTOigvjlo99WJqTHw7i+83XDI
+FiSLMdDIIsEUJPmg2S0LdqbgbFDifmnXOZzSSdN2HURywljz119jrPmLm4MH
+Gos/fuE3IAqZgBd+0aVbQ2I3RoiZgWSTZ+eE5HGqvFxtkmDnEYZXM3k46Tyd
+Pi1G4DlG4DlGIBcjkKNGIBsjkIURyMIIZN4NGYLb8YbgwTX3+rtXnCG4jRG4
+dSFmCK5iBC6fdq+5QDx+jnj8DFbg1BFjTmAJjunuWQexBPuwBHtw1juxBNux
+BFuxBJvJuDdgCdZhCdZgCVZhCZZjCZaqJViAOuei0lkodjrKnYIlmIiax6Hq
+0WSVGdNwaCh+MMofoJagN0T0gIyuBLCdCWQ7kKm2hZ5WUNQCmpoS9DbGEjRQ
+S1AHS1AT+qpDYVW1BJWgsyKUVlBLUA5LUDbaEpQSSyCJdTPjDUG8EWhR1BBI
+El82wRBIUb6iFO+kANDdjZrL6HltNQQNpOg3wM2HkXkxLYa6eTJtMQTtpVAo
+BUMpHNINPTV2EZIGTnOj+DKanzHbDSyMFYMqhpVunUoSPoMunr3MFTkWuM9C
+cFv36L4XDu3wnnZu+lewjvkPf/iDnW1tfBHdajr8Ca4PEOsD+wHED2Ti8wMp
+tD2wk0Hk44zlY/nuW6fnZkTf0+nH99QM2P1aX8R/rmuKZrh+f+TwJltqAAR+
+u533eb8EOLtQFzSVhGi/VDi8urjousUU/9UGCXZhVJL/cIHiLEHiLOvXtAT2
+9RIY+IzcOmy1CLIUO6cg2Drweb7PfmTPatskTcAYiGnIMWINXJMNhfLsPuh5
+Ov/6ua2ZP3/sx8ZzHnJoTEJ22CRgDp5hDp5iDp5gDh5jDh5ddybh/lV9LJdC
+JgFzcP2sWup/MJcI3a1FIC44i0U4jTU4eYj44IDGB1iE/ViEvViE3ViEHViE
+T7cRH2ARNmER1mMR1q4nPsAirMQiLMMiLNb9HueJXEW2hK9TkfIkLMJ45D0G
+mY9C7iOm4PfI1AeRqaeP0/gARLpjEbpgETqCTzswagNOLbEIzfu6+KARuNXX
+3Wdrg2ENcKyGRagCnpXBtJJahPJtY1bBxwep3io0syF802D+d1PjW4lirIJ9
+WRuX/EsRwFsEGaITqyDzZipL4UAKCBitWvrBB/X7ubk2TQa6uTcyB6eVDBVg
+FdpLUYKQqLOUIMe6eTu9Q1ZB5gbIHIERhAgjsQpjsArjxbgucOVNKXPOpJvn
+YBXm0+0LnUF2Cy/sFnqli7cKvlZ34MABmybIP6nVkclHxgnfCf1O1uTes3bi
+nt2j7j4U3csLWrIs5PWhiZ8Vejf0Kc/BYsnoSMFu1lFCLYf9cIJct7WH2/2n
+0G4WcDY7tnnAab8LkN0S5IVsOlBg1zDr9cpqZveTfP16sLL5dOYLDTFiy5qD
+knwxc9New0oE2cOLwEgkuSXf7nLijAQBk4QMeVqUFxuRL03sRL61E/ncdX62
+NrET+YGdyCNsyHvizezfmlxsRC42IgcbkY2NyMJGZGEjMrERz7ART2+G7AQ2
+4iE24sEVtRPYiDvYiFuEDTfPadpG2HDlFB2BkbhA2HAOI3H2iDMUpzAUJzAU
+x/Zr+ECevw9DsQdDsRNDsR1DsQ1DsRlDsRFDsQ5D8QmGYhWGYjlKXaKGYgEK
+nouhmIWhmE7wOwWVT0Tt41D96Ol+C+q3LdgVIa9CWwd32N2nht298/RNBOWm
+QeTv6E5yv/uFywQiEPdOXyr5UtGXyr6M0slonYzaVZEYBMRralxSr6+bjiOj
++TI9R6bptBzipu20k0JEhpuGJzMBuoN4r/Ehp48FHDLNzR6QWQQySiEjjjLy
+KLXNqSA+A8RnLyXyB/EFrsNcsd3i9c7n4V3CfopvjRo1zO9+9ztTt27dqCLA
+t8IZgOyQcVeaxfuuhAF2/wwH8538oBKnqb8zoB7kW+L07D7tN2x5LnD7+bHd
+bgHKb8hld+CjnbIbgbjfncx8Zbf2Of7sBdapuC2AvmW3CTrpdicIGD6jOwqd
+053C/BLo8PpIP7/08yasJbn6e6g691ZQnfOeXl4jcf/zAhOGOFkI5uJhWBB2
+zUEsf/MIf93kg3A+COc/sRg7A0D0/xyMn4NxLhjngHE2GGeDcRYYZ4Lxs5sO
+5adg/AR3/9ijTPR/XxdUgrLr0u+a6yQAV6H4Cu7+EhRfwN2fF5Kh+AwUnyIB
+OAnJx5XkQ5B8AJL3QvLu7bh9SP4UkrdA8qaNuH1IXgvJqyF5BSQvQ5iLl6nb
+h+TZkDxjvvE7Yo+aigsj/h+KaxuE/tPHqreHje4w0oUguSNZczv4aQNHLfs5
+b98UF9oIzhrotl+14a8mHFaDySp+J6FSJtWjGwv3BfJSYgIS6C9pv/68CP32
+7WHnrvRL5V9GAGScT8b7qkm8wdXUUvrr93VzeJqkuzk9MrdHJuvJXB+ZvNdR
+ypHQ303Kk8Q4vUP0D5rq5hTI3IKREhdJfAT9k8QEiilc5EqgMuIx323R+2YA
+/nvFg+/z/lwZ+NE/Rfnzb6qBkN/J5la33DhRCdn3yg+s3c5zjGhLtvsEpVjS
+7dtCu2j5D1y9nu932yoREK+f1ODr33ZT3dzYhzWc8dvxvevyednA74fhLb40
+AyhUvnXDPs94rtt6JLz+OXHyS3F8+1VYIUedGMnrPhHONnknnW/LI4GLLhlz
+0Vna7GbX4I38PeD5IcBtfA/gzwE8F8BzATwHwLMBPAvAM286yJ8B+FMAfwLg
+jwH80ZUAcndN3za3cdU3Afw6rvqaQH7CQX4RwM/jqs8B+VkgP+0h32fM0b3q
+soF8H5DvAfJdQL4dyLcB+WYg3wjk69bKjpK4bCBfDuRLlhu/vfY04tDJSHYi
+0h2HhEcj5Qwc2jAgH4zMByjkvQnpe4BCV5DoBBodQKQtIX1rQvoW4NOMkL4J
+IX1DDenrgFgtcKsOelVBsAooVgbJiqBZAUTL09JaB8PRluwmtgndMeJjvytK
+fKsY8VLkl2K/FP0rJBAvY4DVpe6g9qee1CP6ulk9MrtHZvnIbB+Z9SOzf2SW
+n8z26ypVTojvpVlN/4mubCZjkzIDIUO6a5Yb0Jgg3Qjx08RkiukkGJoH8QuW
+K40+kv9K8cR/p1i6dX9ZxHnT7ux+M9cX4MJlvJu2XH0rL1jHaIv4GpZbd3ZD
+PLrb+dJ/2OVVyzlkcxXhT+aTgycAHnxwUNx29i5iP55ZCO92R+1Ssu+uNQFJ
+P4ij/EJuzIt7wsOrRMLT2/5EwhM9eJjwAttpBVxIARdVkKXNEl7wTKbRFkB4
+QYjwfAjPw4Xn6Ye1PIfw5xCeC+E5EJ5t90HIuimdkgnhzyD86bV4yh/ixh9c
+NMFHuJ11lN+A8Gu48SsQfvmYo/wClJ9Xys9A+Snc+AkoP6aUH4Ly/VC+l6B8
+N5TvgPJPNxuzFco3Qfl6KF+7xicRf2UW617T84g/ZxOHzkCjU9HqJDQ7Hu2O
+AfWRoD6c7H0I2fsgdJ6unw7REwa6wUIXmOgI6u0HOJ/eSnw6qDcF9cZhnw5n
+NeGtGuxVVdQrwWTFNg53UDflQg4+tbmv4Dv8iwBfwn79pTMMUW6+tRsyEPBl
+CEGGEmRIQUb/ZBRQRgOtmwf8WmqT6gN+Qyk/9HdTgmRqUCvAb0vg0n6Ym/4n
+0wBlOmBP7Yh+E9w0IwFs6FQ3OUEmKYwhyB8vnSmdusCNcM5a5Aqo8zWG8l7+
+w89h3t7518PRu2wPfT3HtiSd62atCA6xhNtFwPJcHMpvBSiHP8dWLinsr0/7
+PetLB59MEfXRMEefvSwpm2hrlf6I3VRbtsIX3oV7ebHdjjfLfdTFmWyN6T4K
+9ikK7x2WsOPB5yKe5cboEhEPnHm+liELbKaTQHl2IuUfBpQXhCjPh/J8KM/T
+D7AQyp9Dee7tgHSTjR/PgvJMKH92zZH+FMqfQPnjywHh98+7Q9yG8lunlXR8
++VUl/RKkX1TSzwnp+PLTkH4S0o9D+tHd7v0HIH0fpO+B9J2Qvh3St0H65vX+
+1n9uPlltzMqVsqsWPl1FNx8RzsELzRRvRBw6GaFOgPax0D4a2jMQ8zBEPRja
+B6jIexPf9iCC7woInQGiA2C0S3fOvaU4d8BpAu2NFKS6eNRaQFYD4KoBXhUA
+rAyIlYR2wCxPS4P2sh7WWDgvWMN7Y+f5XXD/i8+kXOoDaUq5DBPIcIEMG1jC
+u7iBxVretWOWGnCxjSXtkGLjADdFSKYKyZShDtxk5xFuoqBMGOyl0U36BHXt
+Yg7FLE53cxTG0XkT57pBURkclUHS2Yuda1/oOjwoy7+mR/8o9LsrSPNKVoD4
+NdlxKJgyasG55ja9FZ9+Le6jIq5ZAtzHR1zJN/4TXJLsR7skfRBAH/4Aa/+Z
+oKFPMIx9IJSS7z/FUD5lRj5tRj53pqT9IJr4j6VJ0a9HntrPxBBjkOTXZuvO
++vYcidvqEwSU0OrH9ZBRCFaHvoj5/gSj4LeDkdnsxdiEWNKeYpN2axbsyESB
+hC8v7Jz2F1zZC+7yxTNtT+UFL57IAin7BuxBgdqDfOxBHl4/T+e2e5uQiz3I
+wR5kYw+ysAeZ15xNeIY9eIo9eHLZvf7RRW7lArdEcH9Xl3nfwiDcwPVfxyhc
+wyhcwShcVqNwAaNwHtd/NmQUTpDFH1OjcBCjsF+Nwi6Mwo7N3hj80mxcRwiw
+xpg1BPqrCfRXEOgvVaOwQDwTRmEWRmEGep6Krieh7/HofAxebSRp/XDC2yFE
+/AOViT4w0hNeusFNF/jppGFAW7hqBV8tCAOaSRiAUWio/NWRMAA2q8NpVXit
+okahIhxXaOWMQrmQUUiNGYU3xCjoBzeIUfh5EaNg39TKFQvT2rjioXf71iBg
+kap2dpOBZFJQbb0omRMoM3+biCWTdEXSlkFuYlF7bq7TcDevsLvc8GiN9ce7
+SUkC9TCMwgiMwiixonTaBOk86cT5blRExkvnYhTmu3jrmxH24I3i7UFsHwe1
+ApezLdPwciXXNlno9ty/5EqwQ4FQr83tcp/ivH2e/4wn+dyZ0hZ++bhC/5kW
+CQbAfapiSvC5wMcyY5419umKsil/8HFw7vr5Tn+Sr18RQ2E/Rc5/PJUYE//x
+cInGILzFt835dTTxul/h/V54F0NrFLxB8IN3QaRQYP5/1t4DPKorSxetkUSw
+255ud5zpnr4Teron9sx8d+J79+s7893w3n13wiMYcG5ng23AYJNssk0wNsEk
+gzE52iaKDBJBCEWEhHLOOecAnj7v//da+5xTpSoZTz++b0mi6tSpqr3X/6+1
+914hlBF0P/4Bywj+vXh6CaQE8/g9s5j6KlaQUNx7ygp3lRWGmnjQ12i2/bVA
+C0mhH6TQB1LorWbIfpWDhX03OKELnNCpnNAOTmgDJ7TCUWgGJzQVeLxQC16o
+UV6oBC9UgBPKwAmlGcILReCFAvBCXorHC5lahzgdvJByTQfwr53r8BWuXsLK
+ALRwCbRwHrRwFrQQC1o4AVo4pk0tDkODD0CT90Kjd0Gzd1DDQQtbQAsbQQvr
+gYK1QMMa0MIqRccymNDFcJjfwepgAZA0d5X4C7OxOpgJpE23/oIi8AWg8tl5
+6i+AFp4Ech8Hgh8DkqcA0ZNIDaCFiRblQP14uyMwzSwGpjIKaJp70DfNsTJK
+fSE/WwT0KGEC6WaWuA+TQ92H+RKPZNyHheo+LJHQQoYYMtRw+gqJZJiN7/gW
+V0JrJSxx4QYJU1ym/hPjot5XtmC81Ee75HyUkROMoOBRyC6OMccaVMwz1c+E
+LcJ5DyOwxXd9u3123V/MRnAl3I0uNQ2o2LHNFmcpo7ktM4d7Zb4QemMnTQ84
+UsUYdmZ0PQU/YRT2e6GqljRyRKT33Fi3mXiWOg63AZ7bndr+uOPfpS2rfAn8
+pf/jz9HSj7XzV25nSd4qu1sp6WHpZtcrbOXvykPGKB8Mqidu/Qj9sA+6sQxf
+QRkSmjvaDc0NYQyzc4DhIWFwSQHCEDLAp1LCIEl0kWxAGKQL911JGPeUMO4K
+YdA3MYwxCMYY1Ej8ATBGPxijj4zRW8Utnx4wRneFd6sOMEY7GKMNjNEKT6JF
+WaNRg4HqwBg1YIxqMEZVlrBGOVijDKxRYlkDnkQ+WCMXrJEN1shKdOxhY/JV
+rDCwukhQxohXxrhwRhjjNBjjJBjjuO4nHKG9gzO8D07xbmo3tRza/jG1Hrby
+I6ww1sGh/gArjNWKkOUbgp2JeXDK5yhjGGcCjPHaEnEmXlY0PgeE/lJXGNaZ
+eNznTEwagTHGkDHsloIQBfcQLV38zKMG60i8JSEHDD1gCAKDk+hIPAt6eF5p
+jEFMU5dJ+ALDHBnuOGu1BDwx8Gn+WgmEYmjkUu01tIKDoKsLBk9t2GlOQ50t
+GLBt+yScgmEVe46Yk9Po/wAnfNvdaMAT+Z3SNbXQqGYRWaGYYC3pI9hNc3D/
+0sDuC5S4Dkax7XT8EJse287hRvIVgGwxmdsnTMC25MZ34DuBA/BB2b08U4Nf
+MvBbGqH/is3OwzZDjzI/f9tths7rb+vrbbPZcI1mC3ycYLvr2T4/tjByyNpC
++eFhNzvH5YW7YVyJYFLQUMAH3ONAPytYRuBn+dJlhWg/K/CxNvMYWOGesAJX
+JuCFn5AXnCFlhUH4EQMavN9fbZiBxOD0ghZ6lBa6yvCZQQsdoIV20EI7aKEN
+tNACWmgGLTRq5Yt6UEMtqKFGqaES1FCh1FAKaiiGM1Go1JAHashJsvuH/+Ck
+YZGRAm64CW64AW64Bm64Am64DG64CG/iHLjhDLjhFLjhBLjhqHbKPQxVPgCV
+3gvV3rUvvEfxIS0mPIqV6lEsBTcsAje8w4XGavEouNCYpdzAhcarXGgoNzw/
+XzwKLjSe8nGD61GAGx4FN0y03gC4Yfyr6jRMhbzC7D2PIqaah5m9N1W2J2QV
+4vcq5LD7R4YlnuA25zwJY/wlWOI5/VgMaHplqYQ8MvRxBukNLPEm6W6NBEsz
+KGohWGIJlhvL9esznHKNsgQDqhhYtXm3rb8X7RwA5R4+Gnm/wc8ORsW/5XJC
+FHuOsxNAh3QhZzfyfBrZAiK20Cw27A59kYnfK+pXBpCxKRJ/IKBN0PkRHnAK
+BjxKoOT1Oy4t8EU55iwwm8xzx6wvsgAOQwwGHIC3OjGGGAw5/GqUk9bx77rL
+iL9AQHjQXJChbJCpfkYoI6iXYI/SbNs+2znIdRLueoTQqA5CxEOGkcnAxgB6
+h4fR7qbjPfPd75mu8l+qV/QlRt5Ih25SkArGulRwr1mcBJCBc1epYKieK4w6
+EnEQGygT9CoTdIMJusAEnWCCDmGCKFIB1lCtSgZNIIPGXPUVQAa1IINqkEGV
+kkE5ySBdyKAIZFCQ4tV3zr6JIb+hKwwQQioIIQmEkAhCuA5CuApCiFNCOK+E
+EHsSDsNxb4lxBG7vQbi/++AG78YS41MQwnYQwlbaQtpEEMI6IOADEMJqRcRy
+IoRI0SXGPC4xVviWGEvFYeAS4+V31GEIWWI84SOEySCESTNCHAYAfLwQwmgy
+Ag8ipjqWEAJCEN8QzlAuMC9TTuHuJs80eLbBM44pb/JqDttYE/fAaEdGPTL6
+cS7Av4D8Bp5bvEG9kIeC8oV4+rptr2zY7jxoIi/Msc1BYP+IYP+3IkM/XIWN
+h30kID78behbJhzTrHaAqIM+fKfhBuArt1t28PN69KAv2jjeBX22nXRBvz12
+KOA+ZT7/m2c7/Ix1cnBhdp/ntN4BEgzoBfjAPH8AyUDFLbzfLS17mo7facB5
+Kgkgtf3f9TvgL/2f/AQhmMvAFQG71U4nwaUE3cO0DoLtQm/bX1sHoXzQbQIo
+pxJ3vVMJXu8/eGx3HYYHgmpphHKC8gEdhOFscNdlgzFmg+HLLmECwwq6Xviy
+zVzTyrGxdHCvyaODuyzTDD5gwgGcg0HQwQCWDAPaZ6HPRwc9oIPu0mGU4LTD
+OWgDH5ATWsAJzT5OqFdOqAEnVIMTKsEHFXAOysAJJcoJvC4fDkIu1g7khDvg
+hNvaoyENnJCsnJCgnBAPTrgETrgATjgXi0XESXEUjh/zHIVD0O799H3pA9NR
+IAJg+bbQAmIRsR4W8UP4z+9jEbFyY7Cj8LY6ClxEvEkru9y3iPBxwkiOwuSv
+dhQsLxhOeMX4DcoL33N5YbzyguGEGbLByY1OnoLw/JPnoDwPZQgEQyGeni/x
+T8/rR3x5scRHvbpMi+MGHnGWYAmxXL/y6q3iHKzVY0jGYcE5MGe4PMv9FISx
++6Cc+PDk57B0V/q6bPGgt4z4TXlEkZwKbUzTI/BbII8MkMdtSCa0NwuafKfL
+CVq6R8u+Ym6ffQc6BXlmJyHX7GaatYMnUeSNKBKGdXdu4W6GI7r4ovQuPJvW
+6cYdpeB9U9p/5SRDktog7b/Ca5Jd6sBf5n9R5uef8nlzPRjGUIj5HlyXcKei
+WymkJ5hC8pQ+uPwp0nVS2DWGz6Xg9f7zi9B9B2OtLX0MBdPHADcbBo3PNWij
+DA3r3jVbOnft7qTsUEaRQexwgDycL1sdvy9BMmniwlDJwwj4wxlS9hhU9hjQ
+lKM+yx7ljscgYI9OsEcHHQrQB8xJKIE0gUAatWxPHQkE5FENh6JKCaQ83RLo
+f3UKscIoAIHkgUBylEAyfQSSAgK5GYeVBgjkGgjkynmsNEAgF8/AsYhVx+KE
+OhZH79+xiLR3udC/d6krjZlcaSwJXmlw7/KrHItwBKKOxZgwBBLNn2apwX3L
+aXq9j0XopHA/lPuik5VFeL7Kc1bDIPMk2oKRlGbZsUgCr6YtlUAsBmS9sUIi
+NhiNOU+9D0Z0MIiLwVx8HSM4Gcn5oS49GA2yCWO3FWO4na4I2GXXAYkc2X9Y
+jpCOSDPGH3w9chnjc0Ucr3jXDejlTehoEgxdMmgmtcWzuOmgmFsd3D7ghqJs
+KVhrr3ANGNYwLxgjf2XxRyZ/3O6xMVJkE3CIkwZJ7VIfLcZJbPtVlPsXvIlE
+4Oim0kqKGmawjnFQwtEFdz7scqdA9kqNp2GoQj2NiqGg1Yd+t4e8QMa7XqGQ
+9rtSRt5uRRg8Dmkp74D5irZagJuM2OcPSAZJkCq6fQcZZIkvOxx7MEua+LLF
+CfIx7jX6fIy79XRByBJDyhI+ppC7THF6fSTRDZLoAkl0FhmicDrgZrQXqKsB
+lmgFSzSDJZrAEo3ZyhRwM2rBFDXKFJWat1gKV6MErkaRMkU+mCIXTJENpsgC
+U9yWZkROKpgiCUyRCKa4fhHuxnl1N85EcDe0feihw8Huxidh9iyHuRtAzCIw
+xdvve+7GbHU3zBJkcfAS5Hnds/QfgIZzNyaEdzcCEfyNVwxTTHU8tvD5G6FM
+Yf0NxmExHuuZeRKK+byyhWGKJRKXzVguxmkbplglYZ0M72QkCGO6GdvN16zA
+mNAP4QHxWj3p2PipRJXwEJmHyTxU5n4w94UPwLXjyVIEN2S0nyli/EzhGAfA
+kkW0RxbfdeKhklehmtdgyBKgsTegvTehxUnQ5mRodooG5KaBONI7FLg+8GZ0
+C4Bvyz7dWP4R7WQYnriFx9K7fT6P2b1L7sQFyR2kryTcMKmdDCEXkS1uQBJa
+Cb3rrW5LvVv6Dlk9Fu4/kN1KH0WEXYx4wdjBRf5IEZC2EHpg9dIeNwxqtNOn
+tYJsuQI3UXnIrOWGguIduTn5oLs56VuGGIowf3sUEUWOILPQkahXqeOda7k5
+YVjC50v0w5fo07POHqWIblBEV5GhiShyBDjYsES+CFmiBSzRrCzRoCXElCX0
+O/6U/oRT5mOJQmWJvET4FGCJO2CJTGWJtCvQCLDETSxKblz0fIo4n09xVn2K
+E8c8nyJ09/JTsMR2aPlW2kawxAZ64vTIgYhVGx34yvxs3xzxfDOSj2BRH85J
+iDE//zIY9XjdBJ+PQDYhq/BE5DG/jwDkPz1XfASGZJhVxiKJ32LkpkH9uxLf
+9SaQP2e1RHky2pM+whKfj8AYMUaG0kdYr8hnyMjWXXLqw9Mfnhvz/JjsykXd
+EV2BhHMS/NC3Pcz4zxfJHO0995BzHovbC1CvS1CzODBAPLTvKjTxGhjgOhjg
+BpQ0Ecp6E4qb1Ga3KFJMMl0q9xY6jeUP6PEGQD7WSesm5lO7jT9gvmUSrrpp
+EnUTO7AMSWznpNxo8wgBCHeu4m2uUJp586stXHZc04XRNeO54DH+4LfkE3xR
+gt6ExAECiTJ8Eu2k4A1T9aNF634GPQquiUgX+SEeRZl6E3bhYeBxNyRoOpQu
+cF3nkJRFDaaLh03Bz/4Bt7KJm8TsZj90G65gzGRIPMTYIK74Ur//l547gcsa
+iAvlCZFacSmGMItDmM1BJYsBkEU/yKJPs516mO0Etgj8lfBFoUhHgeMRRl4w
+YTT5CKMuU35Xq1tR4SOMYpBFIcgi/6ZHGNkgjCwQRsa14a5Fgs+1uGxdi1Pq
+WmARchyE8YXfteCeHffuYAo/2a0hsA87Kz4a7klwM3MO/fN3vc1MrjmmLjSe
+hNSbBkFPCfEajMXXk86v3qRwnYbxPvow1DFdbsfbkp5IU6QrOit0Wnjgyigu
+HsC+oE4DqYMhHQwFZeQXA8F5QMOIMFIHw0bpNDCMdOl6XV5skmgyHgTTudqg
+Gxg8COKBEB0wOmJ0yLiE41JOnYYRmON7+hQ7bPzLv/yLuhCeI+EjkhjPfXjE
+OQYbdAL26BTU7TTU7ixU8DxU8QLU8hJU9DLUNR7EcgXEchWafA0afb3FWHjD
+BIltXmRUknfQL27CWCeZy/IkuyyPdm7gkgRg/no7P/n1Nhrc62pcSSTxuH0c
+5DLeKo7S/Cvz//hm192XS+RhXsL/k3+uuquksYZebuBtEtsNgYmfAl5JEW6x
+3d2yej0qoxh60WCPksFgeuHzQZmVkCYIa0ewbWwrpH0ohF40uISFwvv0TLlf
+qWXAlksZ4zLLkDILY7HVC3HH1gZO3DPfkrsZsozjQgXEIlJvFjx1Zo8D83e3
+xqOWIR+1DGCu+0EtfZj33hLdgoEedBc5Hr8UGH6JctrzOVOGXnKD6aXxjnu2
+VItFC9mliuwCZikDs5SmeOxSoOySq+xyB+ySeS28S3KdLsk5cUku2W2Okz6X
+5AtlkR8GbYuGeCCyq8FzBT0/XcDzU7stas9PdVs09Pz0mTlBHstoNchfk2DG
+hRDMBB/BGP9ESYb7JnwnviN9JX6CF9Q/YQgpoz940stPzE8+e4XElTEefb76
+J9z8ZSTJ8g2ef8L9HZ4ou/7Jp7Ky414Q94Ssf3JA/ZORCeY75tcoJycnx8nI
+yHCuXLni/OIXv3BKSkoCuiDBq0b7lyaHoUOfQZ+OQseOQ99OQu9OwXE5DV08
+C508Bx29AI65CI65BP2Ngy7HNxlPwpABnYVr0PnrbcZh8HNIogg+j/FM8JDy
+HIjFuYbrr7bh4avm7OBKqxCERfll3P5SE1ypi434gb/0pfhLhMYaz+EbXGoS
+OorXl+OG/k9kqMzwjOUXdZzc5Q4I5o7u6eb1u9/Axy/uasiNzYjAL22WXwal
+TnSXcgubiLAJAWscazVUcospxqa1VwKSkT3KJZe7w+IvxgQduvp3QfSaerZF
+tD5LJHIZrBRyGSgbTjA9QjDMNi9k4xglGPKL057nuAzTCnZpgTTrvkhDlrp1
+oJdq0EtVulBMuY9iipRi8pVi/KuejKueE5N82XNiroVzYmQnVV3Pn7i7qD4H
+xvmY5ww7HOejrzietR5N6PGsz6Mxr7nPeC4JuA1HOTHevunPIzo1kyM4NdyR
+4bvzU7xonZpF4tTw0/JTz/I7NavlkInfkPvFy3xODXeIXKdGOWerOjU7fE4N
+10Mc2SPi1ATCJYKFkM7jjz/uvPPOO86sWbOcn/70p86ePXsCMS7pyA6r9H49
+BNt1BKr2OdTuKFTwGNTxBNTyFFQ0Fqp6Bip7Fmp8HpxzAZwDnBPw4nDQo2ix
+iyXQRpTsiFwzzsrVdo9CrgD78QBMXKsTIy+5bCzyJc2Uuoi7XcBdzzdS4c81
+gGfON7gezHk+0yByrsFcZa6+2OR5MHEtwjokL8M6bco6wjZ2OziNZ0I9YcnG
+ejOqzQ978eSaQ17H/HdIo9a2aYa0DEpfbJay7XDZKca0FmOLE7Y66SOR9ffZ
+GHBWZLUF34wXQ/8KDMPTXnUI77knuQ8E77Iqx9zTWHGwjHPPpI+CYejEYLLu
+VgdzzBAmc9DnxPSDY/ow2b2Y9B7NMjOODBShq8A4MlFORz6rgRqayfXRjFJM
+EyimAWukei0cWaM0U+mjmRKlmULQTEFisDfDtdJt683ED/dmrlpv5rSdjD83
+nozdgh0WGnYfJ75+12a+dW38oWFf4dp8zdCwGMHE13N4JoY6PJZ8RnJ4ForD
+wxNr1+F5Tx2eVXI49Y46PEv9Ds8mcXjWqsOzUVdVdHi4oqLDs9s6PFxRicPz
+ldwT46SlpZkOpM3NzVxZjQnzCilP903zQfZD7w5CDw9DJz+Dfn4BPT0GnT0O
+/T0BPT4FnY6F/TwNEjpb7xKAu2N5AZi4SA+FAqxcbjE0Y0Z9FP9Sb+VyqzyH
+a2L4gii+Elecb/Jo6hywdbaB3+hMvZ04/KX/488f8nlz3XlN5rLvf1nI0JAQ
+qe6KklBCu7c3RHfHz0CZ4RmI/o7o/be/koBafQTEt2HH0a4B6ZFmCKhPWzmw
+4PtoQz7G88CnYMkorTkTRerx5ajcCz4JloPg0d7iqV7EXF7LV9eYrRqlHZd6
+KoR6Bq2LA+rpL/Hop7fIEZh0F7L6v2EfeDcdlDzHpZ+2HKEf3rL5jmPopzGE
+fqp99FOm9FOcFOzp5NHTCVlMpWMxlQr6SbKezgUd+b90LujWrjo5ZqeGLxnp
+uPh+HB03Dm1lGEcnJA7tl18Vhxb+uFh8nBjPAxq+AeweEo/g8DwV4vDwen46
+4/DoIss4PO+qw7Pyqx2eD9Xh+egTz+HZrg7PLp/D498A/l5k0vmuPnXw4EGn
+traWhOP2OR7GODatYz/07iB08BD08Qh083Po6BegnKPQ2+PQ4ROgnJO1jrXl
+p6HxZyhkB651zjVhrXS+2TbLw1+4ijxyzgqvMpfidco/p4GXWJEY51QdHz5Z
+51EP/paHHzJXna73njqrbOMyncdydKzkY37DXVMlywG1OYjKsCTTG0QySp7f
+kT1hTZ3jWxmmwf9rIfWQhgFT2s+U9GMl4DbdlGE3cvY1ZvdUdmLsMVEm7Pb0
+kOkWw74Stqq1oRutTmcq3yghaoZslNmiGR20hvLxTJRxcEaRZuRV6uLcrfK+
+xZByjBHwzADmdaBEuabY45qeInV3ChyXbDrzlGxyDdnoPf/V+DotPrJpANnU
+ZegoKdlUKNmUJofxd0A2uQk+f+eq5+9wWXXzkvzfv3tz8bS3e3NKd29+HZ8n
+KBz+/fDh8NPuMxz+PqLchGtsLY779nKCllgjeTmLfF7O8pG9HL5mxUZJHLJe
+zoYwXs5O9XL2WS9Hllj3QThDQ0PO5s2bDeE8EOlyG6CyFwq4H8p4EMp5CEp6
+pMI6tjHOUSj0MSj3ccgJnoeepNKfanBGO7EN7g7IqQZvq3iU/sSFQRRyopZ3
+xX2inWM1jkal4C886HsDtxDuKdKMUhsphsR1oVmdGaUX3vaabD+bbaSb5Jcw
+jgyXUtm+wH1z5tTvuPyiZTMDlqsi8Qtf247XdfSbnunsykz3wESvsYtcb4/0
+q+lnkOBAF/dhBjUKdtBHLUNCLVwXGW7xB8W7wWwcZu79PuBuzxh+EW5xl07K
+LYzKZZUtUAvsiyGXYiGXviIll0KXXKKcLrMJbLglV7iFTxlHJhtPg1igY80R
+qKUK1FIJailP8ejF+DI3hV7cXZtQX8ZN4/8bJ/Gi8WXk6OmsF9Xid2j+I/Fv
+QZl41qHRTDzr0Lyhubs2sJ7X8wDouflfP/5tnD/+Lca/knI9HHakHelkO8Sx
+edLn2JBino/k2CwLdmzm+xwbfvPl672FlHVs1qtjQzeQZODuHO8T4raOTSDC
+Skpbz1r6ycrKciZMmGD+94C7ezPWY5aHnN3FHv73g10OgF0OQmUPQ3WPQI0/
+gzp/DvkC6v0FXZqj/HHMuB9HwR1Ha93XR/EivOvnNXp5DdXpKOkEf/5QieiM
+xxQumuNl/9gwRUJH8O6uYQlvd9c9OTbpuJYl+oNYwrS8rVE28LFEwJ7BteH6
+dry+g9IrfdvZB7q7R/pMsledYYku6adhy+kbmmi3W7RDrYbHNbHWS6Mb46cI
+7/hZOILXVLusHJ4gosgPgT8MZohCYYieAvkYIAinK89xKcIQH+ihDW5H6x1x
+PVrAD83ghybwQwP4oR7rnFqNcqtWjqhQnjAuSJLwhN8FIUdkgyOybEr/37sb
+u/RAbujGLj2Qy+qBnAv1QCLE2X8SzgMJTchjHqum+Ad5ILrucRPyfJU/rAcy
+UuAbrw1zhB058E2OpP54xANrd6kTyfFY6nM8Vsgizjoei32Ox0p1PD7wOR7k
+0S3aWy/cgfWRyI6HkoLliz6s5u1TD4a5fIxHD2OdT6F+u2CsdsMj3gN62AvZ
+D4o4AKU9UInLDvLHoSq+y2HQxaEqj07wFJQaV5qrcMGhSrnAlUpvF4Y35I33
+6pvso7CcFR5U3sZ/zSX7CBNcg8+9Tz/KwUrv4Naylks/6r6ckBWR+k0/dS5y
+FQQXJV6JJ8hFCVkC8e3v9Hox+bZ6SInWN2DHrkpIFaQGUqvnQg36uxnXtkBa
+IW24RzukA/fthLBpdXe3IR4ugUxKIptssYkPSWeg3bGDZKsA2ppAQ5KcE0XC
+oZcSnnIM47Cq6IheiZDOT5yBYnFN+os84uktCEM8SjodIJ32bI94WrOCiadR
+iafORzzWQamgg5LskU+REk++rH0CtgdYZsher91sua4Oiv/k2gbTfS0H5ZOv
+LkbmOihajMx1UHzFyEIdlP9/gu9GhQu+0w7NPw7e2w3nkiwM75LM9bkki8K4
+JGt8LsnGYJdE3nsEqvnDME8ZryNaFfkTKNYOKNmnoJadFNDLLurgbgPrPeXe
+YiWGT+AnGQjPGhbaYxjAFruLMbcgU+2Q20bxP1F81ALHPAkx71vkWFqzSYP7
+SD7CaKQSQ1SHLY3UutYayynnNPdwmuzqa7Q5mLpmmUPdllQb8PITk3Z4x5ce
+7JYd6mPDMhAHhDWWqvqk0mItpE7XQI343YTXtEBaIW24TzukA2TR2e243e7Z
+FZtdddl7s69DOn/160JmQGuHiscyaM7MyBom0V8zfEEbAYm5f9hPG95hkG83
+1nhAuksyWGp2SjAUAxzpAY45WAPj2Vfo4w3wRbdWCCFvmA8C0sBC2NDGHR9t
+ZAbThvVZ6tJ91OHzWQx10GfhuibRsW3JfC6Lu2tifJY48VnCHkbfZ26gv1rZ
+sCICm4N9Fn/R0je1aOkMX9FS67OYoqVhfJZfO+zuwRHD7nzrGkn3+2ZEZ2WO
+z1lZqM7KMp+zguVLwDYEJeZD92JZpkUdlO9GZo2fhnnqQY81op2tUKmPRQL2
+sW1F8ti2QirxNgZ2by/CKz4pdjdP+PRWaOKWfJGt+bwUj1gM2yc35+kFBeae
+FvY+osLrlI2UifaL82HdJa6GjgNC3FmJ1R3fc03ulohc9m3X1bCeUpokGZq0
+gCwtKsBiZSxUxtLFxZBSSBmkAqJ1We1SqF6j6prwkmZIC6QVt2mDtEM6cOtO
+SFentN7uMWFuveaQ3XYHY6sP2ydAuKKJSB708YRWA/C7F3JwE+2nCS6MKtw2
+RR5NeCzBfqNF4mAYJ4MjDabACtVwRZ43LvQx6F90ZDuWLHB7UEXg34Qsbou4
+hOHzM2pAFtU+P6Pc52fweZ+fETFCLskfIRcStG8TAU/4KgwcjlCSaKsteroj
+QkVz9TPmrwlT0XxZSEXzt6XoqaloPidM0VNbxOxrZRK/wmijX/dIGW5H4Fuq
+k2bT1Oc+cO3ysbYQ/jT8pulI3PAzd/fCVBMw2hXtfJTnjHI25tF5+sinNpSP
+oDrroTrrs6ky+AtatyFHHgvY/Qo+PMpZB81amy1PbcDLPnJ38R9wNpMzQAeW
+erZRoLSgF+N10F+xWykHAYAj3C6pcYYRgTmC8YiAB7zysj8xXkNyh4Thp2uO
+UKbkMZtqCPlAcyGkCFICKesx1VqdSkV9Df6ug9RDGnSt0ozXtUBaca82SDuk
+A/fvhHThvbo7pEU3G/jaJqFsCMZmP+wSwkYCA3quPWjOygcbOFSsC2QTeDU9
+j3ivMfWIqsMf3A5qTH2wqwBr4yeB/kJDBE4fxro3X7wGvqhbVxmdmJvObGUC
+wwJtWTwxbs0Ut6EllAkiuA6VKcZ1kLH/J/EcQk53jetwfbjrEBqMH7Qjal0H
+1h9SMjj0mWSruoVOw9Q7ZzZLUL1zLDoWrovQw2S5yc03Ofov+XqYPDM/fL3z
+r6hmGIkMIiX8/EfPe196x3H9CsbI2NMXhgWb895VErpnt0Xtee+qjSHnvdtl
+DWLPe0kSodui9rz3O5GJ5I/DPGXqDPzYvHKMsy7HxwQgFdCLYYGtrtPxkFh/
+7kSI9TdrBT/q7cmIot4WE72qgayWo5jey7ygDE0rZgUD1kDJA3ILIEWQEkip
+Wwz1W04V/l8DqYXUQRogjRoE24zfLbhXK6Qd9+6AdFKA9C5ItxfSy2ag7OrV
+Z3Yt+/kZBxqtKpjqXya0fVDz6wTjMaEYjzJ7CNHumanc20I8msiOIrSjiGuM
+W6+iugdjOgzZdwyyiWunDYgGsqMI7SjiOvDPkW18qth4/r883F7CfUbBX7vg
+28U8o1WEYqVQKcsOHtOyg+EKmzNJncnqTFo3XUs+kVIZq7b6bPx6r2vJHLXx
+b6iNf225JM2/7OtawtIc/q4lj72lbQzUxrO8xwQftMd50JYCQtG/ZvDYfR2r
+vqMLhsVe9Cqzibi76R6rrgne3TTHqpuCdzeth8DtYCLT7G7uH5aOMwKu/yTM
+U3/Kn2PUIdlSoBZctx526o4mtxBdDEO9eZx6QjCsoPtLE116WaPSGY3OXJyb
+CuRUTfO9rWVIsjulwFk+qx9CihWcZfhdAamCVENqIXWQelzbAGnUY8gW3KcV
+0ob7tkM6IJ14ry59v258BvbzZt9O9uRjQ6++Run5w44gtgzwQJ0p4UcQ15pj
+Tn/4eDCMA4Lj0V7sg8Y/mPsMQzP4sr9ATHWfD9A9uQLqLvWwXFBnuaCOIqrZ
++Xlkiy00+/vWWJt1vv9swrXWYcJBh2XlswjQeS0CdEarBcZ6ZckjdidhY429
+rJPPz/IN5/E5vqZBs0boKxBa9TPIrA5H3q912hhua++94NPGsFt7W0JOG9U3
+d83qfjGrvjyVcK65ZLsJykKe+itv2T7W+Myuv1wqW/vctOcR4+e2nsMDTmyd
+iZM0QdoMEo/TxBQmv91gVm2rBeQoU/snU4qHmYqCeW7i1vedEgCpDFIOqYRU
+QWogtbiuHtIAaYQ06RZZC363AlztkA5Ip4YtdOF9u/H+3U2mQW4U2+ZFsa1W
+FGvv40MMaOjEgNbBGjRL4UF7uhcTGlbk22aPNtvs5sXFxgBzy8IYSiAr8KDT
+r7jqJa4stnJ82LpjsBVFcEURWUxEtK5wJu9Io/mHYTfg/UbTvwFfHMloJgQb
+TZbYMkZTEcZanHHntbr3Ga3VGxumG8jnetz+A1N11nb4Gta0d6NUrn0b5mL+
+h1KvcvZqqXI7/T2vaS+r4BoXeKHUvmTT3ifn2X2oMaYk3ngFqPbxdO3jaI1x
+NM9NdaxEwmiodfxaZ3+Lg91eG3Q00nbaapvX4Tv78+d1EGlh8jrCWUfF6J+5
+y+e/9m+ocRt8d4ndtuHPPyYinWOwDyc1bPqs5m0wXyxec1ITAIubLHcBSVW4
+3GY9P0i2wiofvwshxYBaKaQMUgGpwmPVkFpIHaQe0oDXNUKa1Ma14p5tkHa9
+dyfer4tCGHY3mq2iBulhyRZ3bI3TV+e4le/7a+xXGqg2MctVXqb3YKW7Mg05
++5JlqbC2LksDPlCOcUHZB0ASmL25LjCZZJVt4587YOwowwzfTyIaPr5s2C53
+SvDJfNEI1s9NHFd8JsZJCbxrF6WO9uXz0pSD1fdNU45Y2xH592x7TVPs0Vi9
+fVI1ntXj17Gn7CdSOpr3X75ZCsaycOyCtVJummWnZ0GbZ6yQYrMsOsvq9S+q
+M8vS1SxQy1LWLGntb7z76OzhrffEf53mRIcpjCuP/aVY1QiW9CszPkMsqX/T
+25+BZX1YWlL6sMMyPsMkQNiMz08UpUG7XEciL04Vpj8P89RfC3T5ykecPQDs
+vlKJAzxSIUHHzHM4CcCehtaf0+TOy0wg1+oUrE+TBPCkSP08XcQ+4uQAbHmQ
+AkgRpARSBimHVEKqIDWQWkg9pAFgbIQ0KShbfOnf7XiPDkgn3q+rURrJdzdI
+o+gexsmxR903TK8atqUgQPu1amR/ldRsGahUgyhbR4HQtSW3jwxOoxWn/RqM
+2292/i1OrTdBz7RPQWqACsvZDY+0i3LH8kNHVgQbelttqNzuR8MMaFWqL8Qu
+2UsXGJatFFoO5iom4orUrr0BkNr2GKbYPUB64Zwd1D+xLTLFgB41BtS0bmAL
+hx0HpQEMG8FshFlYz/avO6T9A9tAGEu6SZrJvL1eWkbM+UBaSMxcJQ1o2Ijm
+FYD1JbWkbD/BNhRsR8G2FKxBz1YVrEnvdsgOtqpibWMUtH6kjvLVlQutTnnf
+tjRMjmSklIEF95kywG14N2Vgb7At9W0hfTsySP8izFN/Y36avW9nT5HE6jI5
+4DN4fkeh0Mc1IfIMlP58jRR6iGMFGch14CQRmEluUrv8W04WoJoN25oLyYcU
+QooBuxJIGaQCUgmpxuM1kDpIPaQB0ojXNmlWZAsg2Qppw+07GgWenXRgu4jJ
+boPJnlrpKcceUn3SAMIUd+63dZQ8XBJ/JhpnwL9OVPMZ7R0AR1tcWmwW2McU
+lXiMP8cKOnM8dHbfEXR2CkINQPFSnyUNiCn9sXv+w9uOtOvrurn+QFh/Ug9r
+sCSGKe8GpCZf0bLzcabpnVLnX7C9pXPmjHSrPn5KrmcjlUNA6f7PpR0T2zKx
+PdPHQOnmvdLLbS0Ub80OaenE1yzbIv3f2AeO/eDmQnnfhBK/8b60h2LvOPaQ
+Yy+5FxWlbCnFjhDsO8cGMo8pStmXjg1m2E3C9rB2e9jL4jRK2tirvZ2m10wz
+9eatvfUQO86HWFPfLdwpUMjekCnV4qukYFenoYmFBrEjhNzT+3X3hnY4w0q1
+EHv79GBZ94ZGQOxfRkKsjT9lPs8hpg9Cn48yfxmQja2U2iwXgIfLwAXLvl1z
+o99/6CQDtmnA0y1N48sCznIgecBeAaQQUgwphZRDKiBVkGpILaQOUo/rG/SY
+pUnv04r7tkHaQQ0dhGmnWWx21UkLZ7ZyZpPXHhPd1lttIvrwMVl8uc9GwUWx
+mFEUs3VpJ70NnUAIUmU7R+qacEunX2O8AFPeNs8cEKsBNTDNdmEaRZwqqtXh
+DYQ1pWJouRz9QfByNEJQR1AujMUpJFdx6i/Ymq6tIZKu2Hn5z9KcEhaVfehs
+w+lYYPUklqTHFKtskXbgqPRRZD9FtkzeBqxu2S9dVddD1dhl9X2o3krFKns0
+LtooLdrmrZM+juznyL6O7OL66nvS3o1t3ow1XSTWlG2faU3ZEZYt4tgqji2i
+jTWd5bWPDsHqKOlQGTAJeNNYaSBc7XdT43mmbAgHVV/zW9J5XvU1f7IvA9hm
+hiT7muoma6Q/Dn3dZSG+rq1uwkZ9DIH52F997YDgkmdeh/REdwRQ/pW7JP07
+84DU8zoAo3FYqwkcK5UKJqySdK5SjeN3nOtAwA1IEhCRApCkQzJ00/MOQJQD
+yYMUQIogJZAygKwcvyshVZAaSG2jd3TbiNc3QZo1a64Vv9tw/3ZIB6STUus2
+UY9i91VmlFR5LVF69RNGsYgYQzhLvXzV/pLgJabv5DNgMWix58egMZNRhCCP
+bBSEvWa5CSjiRd3qzfpsphrN0X6jacBoHAJ7nvK9oPOUer9nG5I8YjxbPx4h
+eTe1JGqi15Xh1nUveUR7QjrX43xtoYHH88DjGeDxFPB4/LTazZPSx5T9TPd8
+Ll2M2c2YXY3Z1pztzddCzdZ8Kh2Qjd2EeVi8WVqjz98g/VTZPZldlNlNme3U
+p0GtX16ue0SLpQMzOzEbuzlfWrOzRTtbtbN7M7s4s8+rweJMx8Pja87okMbQ
+YkDNUBOafxHUoiWoLcPM4SVRTWHEt6T8iCmJ6qtu9orPybXVzWb7CoGY6mbq
+5A6rbvax9M7coE4uS6Ky4S6LJ/P42ZjMw0HFkx+JjM7/PLLJjHaOAKhfAKjH
+S+y0/75zHkC9BCjEARJXYTYTIImwVclATSrkFlB0WzdNs4GwXEg+UFcIKYaU
+QsogFZBKSLWiug7X1UMaII14fZPeowX3bIW0QdohHSYaobOGZMIm6GyFypao
+bH3Y4+ta1Evj2Ftmp7RXCloQbSUGiZqcNWClSLdoDVSjjTsb43dnPZTG+FHq
+9DJVywOqdW7DLT9lUIctP0Gg/uSNYX6tzR8lTlMUp8m+gqRJWuTcBkf+nWnP
+mAqzmXTV188ZMI0HTC/DbF4ATM8Cpqfh4p4ETI8pTA8DpgcA072A6S7AdAdg
+ug0w3QKYboSKrYeqfQiVWw3VW6EwXQKYLgRMFwCm8wDTtwDT2YDpTKjxdKjz
+q4DpK1DxlxSmbJD+9EIxmY8Dpo8BGpMBkUlz1WQCPuNnK0TfcPwm0+wfxYRp
+4G58Xtlj+jNz8Xg9MzUtU96Qw5zJs33tEd4KLlz6XLjCpcuCC5f6C4PZwqXL
+beHSLRJXzvjy9RgYlitmCIhpm7DXa5tApJm2CV9ENp3RAs6/DvPU3/KnmMjv
+OSegtbHQ4rPQ7AtYq12CFY2H8l8DCG4AEDchKQBIGsB5C3Jbk7hy8DsP4CqA
+FEGKIaWQctfvfcSpxv9rIXWQelzfAGmENGn+Ywt+t0LaIO2QDrxPZ7X0Kdfe
+xMzIrLATpbX+adJKXUSWmDJW9EGNp+o/fYx2d3k86xhNuEWH4i28YZR3CF5N
+fucrowndtEqbtc0qNamKupSgYuFu1kJWolrGBOmWnELYQRIBveuA3hXALg6w
+uwjYnYeFPAPYnQLsTpxRywhv9RBgtx+w2wPY7QTsPgHstgJ2mwC7DYDdWmjR
+GmjTqk/VMkLLFkPb3oFVmA8NnAvYvQnYzQLsZgB2r0FTp0FjX35PLSO0+Rlo
+9VOA3ROA3WPQ9inzxTI+SssINEzww25mEOzonL4WCrlRCkNrETkasur8I3+T
+IhPRwGNVt0D4fC0QrvUr/AXCTSuB97wC4abW5wderU/rqDKQigFVH2yTACt/
+K4HQrkaEzyGg7YgEbIU1h4q4v4mEOIDNTBWMwFE4bidhFU8DfOegwBcAvssA
+3xUo+HWA7wYkCQBMAQjSIRkARaZuguYAKPmQAkhRrRftU47/V0CqINWQWkgd
+pB7SgNc2Qpr0Hi343Yr7tkHaIR08Wu2spFHqwlt3aU5FN888uk0QM0ti95S4
+VZyiWOdAMGcyf/qs3YuOZPcEhIq/GA9/Y8LZO7NMFBzC5EFLrGM63Or9s9OU
+ESZlMd1XJSpNKuoaDEKKIWztweu0gaDpD+R2JYaXmgocJgOHN4HBBGDwGjAY
+DwxeAgYvAINngcHTwOBJYPDYWXndEWDw4AmYPejILujKDjD0NujOFujQRmBw
+PTD4ITD4PjC4UjG4BLq3EKy/ABicBwy+BWswG1ZhJnR1OjD4KjA4FXr8kmLw
+WWDwaViXJ6D3jwODUxb4zB6wMQE4Gf+mz+yNhMHXjCeqzcvHDGtebvdusfJU
+TP6+waDbFGieRB7Zlh7G6i2RCOTXtUi/sXqrJIqJEcsMVmSR/rDNgrZL1DOb
+BW3ZbUIqzCHTpxi73Yf0PV5+WRR+BAD+bUQA/qG5x+dwu45BI08BhGcAwnPQ
+34vQ4zio91UAMQFATAQCkiGpQMMtAPE2JEt3OXPxO1+BVIzfJfh/KaQcUgmp
+gtRAaiF1kHpII6RJd0db8LsV0sZcgPZKTkoH3qazwmu43SUd8qLY0SbaFJcW
+MPVo/n8vgdYXFAgQ7Z052tWgRaDnZo7xcBftx5wbLGHPIofvon4zrN2rz/Cd
+dWhpJIO7dB/u0uz9f8E+fW5PX+LujkbY3wL20oC7FOAuCbi7AdxdB+6uAHdx
+wN1F4O4ccHcGuDsF3J04p3YPLuch4G4/cLcHuNsJ3H0C3H0M3G2CzmyA7qwF
+7tYAd6t2qd0D1y+Cvr0N3M0D7uYAd7OBuzeAu+mwE69BV6cCdy+vVLsHm/IM
+9PpJ6PfjwN1jPtw9ChxMHBl3tG7qdA4H3mumW59vSWhe5AEvqOHvlLdsKt93
+nOcX+gzfUgkLZAe/r9VDh8Wjdth7jnL2HlFDd9Tt9S1dOcPj7O9CdmWkxNoX
+YPPj0LhTQNhZIOw8EHYJKhsPhF0DwhIgN4GyZKh4GuQWVP52ud0v/65TAGQU
+QoohJZAySDmkElIFqYHUQuohDYBMI6RJF2st+N0KaYO0QzrKrffXWUor0qmt
+X1wxVouFT0PgRRPWV6hn+na7M2BLRPqWcu6Wp3FFc8w5hQ9hnmWzm612Gcey
+zcNtmhwjAly4T4OFV4YPXre0jHO6LtL+0bSgsS1xia48oguSDYRlWXTBuqUB
+YclA2E2gKwHougp0xQNdl4CuC0DXWaArFug6CXQdU3QdAboOAF17ga5dUIgd
+UIxt8Cy3QFE2Al3rga4PwdDvg6lX7laLBnQtBLoWQMnmAl1vQunegPLNgBK+
+BnRNA7pehkV4cYVc/0ug6ymg6wmg6zGgazLQNRne3SRF1wSga/xbiizdA1V0
+0Wa9HgqqUebnN4MsWRCgZnvds3kWwjMRtzfufBMfFJDGKN8wMUfsaxu28/Xn
+ApYjXw2Uf4i0QRJ42Hyso1CRE1CVWOjRWejUBejXZejcFejedajjDahqEiQF
+6ptmFz6BHzo5gE8e4FMAKYQUQ0ohZZAKSCWkGlIDqYPUQxogjZAmtTQt+N2K
++7Rp5kU7fndol2Y2YuzkoqqTlqbLwKRbT9J7pMZElGJFDNCwI4GYoCOBAOuh
+WXjYwDfr8ZkwNQuOUUG7ka1BkWp/6jTh/423pZaNrcvHCsQ1GVLonP83vdxu
+SZNY0xCSEIHkAyZ5kBxA5I46gRmASTogkgKIJAEiN2CErgMiVwCRy4DIRUDk
+HCByBhA5BYicuKDGBzA5hAXY/lioBBZfO6EK2wGRrVCNTZ85xt0PPORMhlZP
+gr2YBO16FFo2cSStns4dxNfdgLPXHStiLH4+ol7zTI9ne5NVr/2d4Z95WzrD
+83qG2zAmzvR8Xi6xcoyZs61f530gITtML1kMT22ZemqMUWf8HePw2POZYT8M
+/9nK3DXmsDGX7YiclfDMRHvFjoSN/yMiNh40b3kMc30SqnEa+DgHHboIXYoD
+Rq4CI9ehg4k29/JHTjrUNQOSqdHIuVDjfEgBpAhSDNUuhZRBKiCVkGpILaQO
+Ug9pwHWNkp3gNON3i/7dht/tlBLTvBwfuMMcXndqRf6uQls8O4YFJgUiUglB
+EhZjgmKg8TvcmZluBPKSB/gHCK4nW5diw0+8/dYk2g+WgE2GyDRxnZla+SnT
+hxb9bXqZZWjr1FvaXx2IKYIUEC2QXEg2EJOlaLkFw5IGtCQDLYlASwLQchVo
+iQNaLgEtF+IxU0DMacgpoOb4RTUmQMvBM7q/9j1nI7y09fDSPsTq6H3YkBV7
+1X5Ar96Bfs2HgzIHNmQ2bMhM2JDpsCGvQienQjdfgo6+sEqufwZOz5PQ48eX
+2FXKWGcidH4CdH/8HEUYsOGibAahNN2J9tsOgZh4agwZC1kJWZxxz597/9xc
+fFRxxnM6gzXFmemv/o6vv/oS6a/OWNTX35XQN4bAMRSOIXGMW2WLZcaxLlWc
+rdgqYXQMp1vLXFDWntgtETyM5GFED2MGeAayX3F2RKJ/YPkiYu3/jIg1k/jg
+HIdWnIKWnIF+nYe+XYI6xrkJjt93bkKDkyGpUPB0yG0of5bGJucCGPmQQkgR
+pARSCimHVECqINWQWkgdpB7SAGkscS1BC/7bitu1iUSxCTADOgqlR1+HgVin
+OQCz9aO71OJ0G+9MwJYfccc99FysN9vdRMx2FG/8qc5g+ANstVO6MxETaqii
+WNAkiuXWcL2p55hloOfGArCFoGk4elugx07mZZASQg9SSOhB8tIVemlqpAC/
+dEAvBdC7CejdAPSuA3pX4M/FAX6XIBcAwbOA4Ol4Dd34T87+s1ATuHE74cZt
+hxu3FYukTVgkbQD81kKF1kCVVu2Xt1gKOl8EdXsbajcP8HsL8JsF+M0A/F6D
+ik6Fqr6MNcULUN3nFH5PQaWfAPymQM0nw4WbBLWf+LZjywYGIU+9tlG6KvIj
+b5T5+fMgxNnT7vE+xPEEjvuNUxRxPC1/coGcnj+riGP0C4NKpy6XINPpQNwb
+qySejRHi81ilBV9nIau2AHHLNKFy1TaJiWNsHGPkGIXDaBxG5TA651MM124M
+2z4GqB/zrNsIiPsv7hJJcCaadRRTewJTHXtbd+F/4MRD0a5BMW9AQW9CZ1Og
+u2mQW1DwTLUnOYBbHiQfUggpgpRAyiDlkErgpgpSDamB1ELqi70y8U24phnS
+AmnlDnkbXbd2GlDTTMYUY+8ynlyXTak1Wwk9LqR6NZw5AqRiwkBqlPn5gPtY
+T3ZQbEgEg2Zydk36frQpYPhjKcasvmJ9lpqxTG3gmyl4qoCUQ0qJJ0gRpBAD
+nX9L8JQDuaN4ugU8pQJPyXD+bgJTCcDUNcgV4CoOuLrknlH/zDkFTB2PUzMG
+c3YQa6R9ANYuAGsHgLUNwNoCjdgIzVgPDfkAmrIaGrNCgbUYwHoHwJoPYM0B
+sGYDWDMBrNehgdOgiS9DI1+EZj7/vlz/NDT2CWjuYwDWZGjzJADrUQGWMx4a
+Px6aP26u1BmLci2a9RmnO1bEnv1FRFRxt5679tw5nKSoYuwJz7x59v0U3o8x
+ZM9pCjHjVRi3wmhQRoUy7mzWatgy1iJgTQLWJtggkaRLtSrbCnzf1UDVBzsk
+pm0DULWJOZD7JY6G8TS7mCOJsduPMTx0wkVWOGBFCbB+EeYpcw5twyJPY8rP
+YfovQB0uQ12uQHWuQ+USoapJUNkUSDo0OQOanqnangOw5QFsBZBCSDGkBFIG
+qYBUQqog1dbnHOvU4b/1is9G/G7CLZoLpOV0Gy9rM22aCgRj0awCDCPjg5db
+w6JHoEWzlOsunHJcGRUGWjFqs3yPuRBTeAXCma5oRRgNWyue/R2pAKiepvkq
+d3wN6jB6tZAaSBWAVgkph5RhZEsgxZBCjHQBJB+Si5HP1i3BDIAtHb5jKsCW
+BLAlQhKSHBsbeRE4Owf7dRq26yQwdixeXnYYGNsPjO0BxnYCY58AYx/Dv9mE
+BdYG+DtroS9roDcroT/vKsYWAmMLgLG5wNibYPI3gLHp0MFXoYuvQC9fgn6+
+AD19VjH2JPT3cejxZGBsEjD2KHR8InR9gmJsHDFm/UfgxGfJol3c0WPUGA4C
+cLT5+fMgrI3TOBHuDk7wYc1YsXlycE2s8SDbWDHF2otLJSaFMZ2M7ZzOHODV
+Ekc250OJK2Mc6EJ8vyX4nsu0RgjjRRmLxpg0xqYxRm0zUzWYssHUDYzdbmBt
+3zE5reCpBXfVRwDbf40ENt1QP47ZPYlZPg16PYeZvwgtiIOGXIXGJECLEiHJ
+0K5UqHI61DoDkqlqnwsI5EMKIEWQYkgpwFMGqYBUqodXjd81kFpIHa6pVwg1
+4nczpEVAZwDH1VC+Ni8yBqwjn+Yt32wB5jm2tJRAMI+X9wyPx9DN8hDIhXMa
+oyIdZnX6DrM6DArbjSljHStTAk+F1xB97Kpkerdl+9B3R5BXTfRBKhR9pZmC
+viKiD5IPycO450Du6B7ILcxHGhCY4m7A/41zHQi8CpMXD5N3CebuPMzdGUDw
+FCB44oqaOKzaDgKC+y5AVbBq+/QMqDoWJg4Q3AgIrgMEP8DSYzWW+iv0YGYx
+1OwdqNt8QHAOIDgbEJyJZczrUM1pUNGXoaovQG2fW6N+I9T5Caj1FKj3JEDw
+UUBwIlR/AiA4HlAYN9+YOIEWIDMO0AmBISHmZgTNcI2eYJJWbwQUcs/eRaKi
+kGEkPNdm5Ncz+CjPaVISQ06m4mO+io/7+iqJ4py1RqLIGE02f71EZS/CV12q
+KFwBFK4GCj8ACtdhWDZgeDYBhVuBwu2H5WyQZ4Q8KzxwQs4w1Or9ZmQg/mNE
+IH7fvOsJTG4swHgWk34Bk38JYIyHMlyDctyAwtyEAiVDodIgt6BktzVFNBuK
+nwvJBzAKIUWQEkhpvmOjHivx3ypINaQGUgupUxw14ndTnuIw33RRNwgEpGwD
+sQ6RKOJP4dOVa52+bp4K9+QYbzLHCVmMhWItwChXeWK4nYvx7JxINGtBcZWW
+La09+HRrDldppqqc6ZaY4/V5r8fvWiIOUgWpxICVQ8ogJRjAYkghpACSD8mD
+5Oheyu0MHay/dZIx9jcxBzdAitcxH1cwL3EA3UUA7hwAdxp27yQAd+yq2jv4
+lgcuQRsAuJ2we5/A7n0Mu7cJWrEB2rEWgHsfgFsJwL2rgFsIjVoAzZoLDXsT
+mvYGADcdgHsVWvgKtPFFaOXza+G/faD2Dpr7GDR48kiAmxcRcLR3bxhs2ZOt
+GTo3o8yfPw+C2jgNAeEWp4WbhRpDRhg6wuPrJ9+RKK5nfVB7hXmBzA9cJQGa
+DNRkJNgcfJl5+FJvM6cQX3IJoLZM05dWYQDWMK0JA7KeaU775didx4A8DuSx
+II8H92EwD2JQj8SK0RsBa//kLt0EYT8xb3QMM3gSM3kaM3oOM3sRs3wZs30F
+SLsOpN2AMiRBKVIgaVCaW5DbSuU5ULQ8SD4UvxBSrMdGpfhdBimHVEAqIVW4
+rhpSi7/rcj2YNUNajJfYmkeQEVLt/NGRa4PzWQjNFlztMvsc3QZaPTnu4stu
+wxsX1jVeo8NGYnTy6Y5sIinHAszUls81EsWuo4FHXCQ1KMjqcKsaSDWkEreq
+gJRBSokkSDGkCFKIx/LxOzfL2qi/dzIwiOkYzFRIMgb2JgY4AQN9DXCKx6Bf
+wgSch/06i8mIBZxOaIj/Z7Bfh+BC7oP92g379SmgtA1Q2gIobcSsr8PsfwAt
+WA1teO+I2q0D0Kh90CxozlvQoFnQpBmA0muA0tTNcBuhbS9A655dqzCC+/g4
+NHMKNHQSNPVRQGkioDQBUBoPTR6nUDIwmuuEQokwmmUcRbshMtPbXgSORqln
+HA5MvI0B1Bw5GeMJGU/KpiiYGBPC2KxfAkzPaWYBY7emKpimvy/hlIzvYnjl
+3PUS98X4r0X4qks1q34lhmA1huIDDMk6ZiMxKwlg2gowbQeYPsXw7T4mp4I8
+HTyM4f3srOMWXAuPp/8W5ikT16+9AY9jIk9hUs9wcoGui5joOEz6VU4+lCAR
+ypAESYFypAFdGZBM3QfIgZLl2SOlbzrF0MESSCkeLoOUQyqoh9kCqhpInepp
+I9S4CdKcGwwsanZ7rpu1wsJDBkudOa79EutDfLnWyJqpsWFM19hQq5VtU8F1
+dea+R0eOG+WrnWK0WwzwFvgWP6b5uPzYjQr0enJFjkCuSr9q+R35+hyGEkgx
+pMiO0j84OXj6jg4gBzMNA5uig5yIAU/AwF/FBMSlymScw6ScwQSdAuqOayD/
+YRiwA0DdXhiwXTBgn8CAfQyPcRM8xg3g2LXwGN+Hx7gSKvPuZ2q4gLgFQNzc
+PTBcULOZULfXgbhpUL+XoYYvQiWfg2r+UhH3BNR2CtR3EtT4USBuIhA3AYgb
+v9iHuAXDEBdFyBFo1mH07UKK1ZpJBbTbIVbM5W/6ADdHjhJ4pMADvMkMenxb
+AkGeXCgBkc8q2BikxWCtV5k0+74EURJsDKqcs14CvN7eJHHOSxRsK5jix1Q/
+gG0twLaBaUVML2KaEUZsB0ZuJ8C2B2DbzwAzgO2IBpwBSg9FBtx/jwi43xRn
+MUHYk3N6HqC7lCzsSpbl3CemC/uShdOhGxl2t/LbTj5UpwBSBCmGlJDYleCp
+dST8KjUAtZB6C7YcH9iIMGNA2gzMrHfWbiHAM7ZsqfclbmKX8eRon7q9fcSx
+riXzjpYBNQOwnJBCKDmuYRR7GWPgZfvbGlsK8Af+RRCmTq1FGK1wjVrlSkgF
+pBxSRqLBcyV6XSH+X6CWPkfdSnoA9ATS1DNIoj+OYb2O4b2CYb5Mfx3DfhbD
+H4upOHFTDRqm6BD8xP2A2G4Ytk9h2LbDsG2BYdsIJVgHZfgAEFsNiK04qgYN
+ivM2FGgeIPYWIDZrFxQRSvYaViRToXQvQfme3wil1SjYJ+EfPgZlnQylfRQQ
+mwiITfBBbFwoxGTv0W/YooxlG+VBzKapzTSPvuEYoyem7Y+c8Tz+5jH4fDkW
+Z8AHAz8eZ9INk2+Apuc0yv9lfKCpqyQki+GQDIucvU7CJOcCTfOZEIsvtAhf
+bKkm361kMh7Q9CHQtA5o+giDsRmD8jHQtB1o+hRo2s0wTaDpAAbwsIemwAhw
++h8R4fSQeflJLKJjMV9nAakLmL/LSeL3E05cB3A9wHVB6i3HhjplQxVyM8X/
+KciSlUVRpvhHpbryqMgSOFXrqqROVaqB+wTqc9H3aqHNaPUMB+HEMrjt2Qok
+LKfsfoR173xQCjr5svuIAXsMHe0mXve4DuUotyqfLuR0adfhuqRtXD1iLRj4
+hlkVElCNumLkypGubU2urCi5suQKsyLPaxlVogtRusr5ukDNVijfxqdLx6dP
+5c4SRugmRi2BO04AVjxAdQkDfR4DfgYDfwqTcFwDoY5gcg5govbCbu0CoD4B
+oD6G3doMu7XhHP1Yvve3nMehZ1Ogb49C9yb6QDF+qQ8UGkxhF07DbE9MkO2R
+bYo3uFU/SxAjV0W7Ky6+tT22Y8zIY4zzZZoL3vSXCghGTTF6ilFUrzE1hpls
+6yR+8a2PJJ5xAQCxEIBYooBYAUCsBiDWABBrAYgNAMQmxiUzPplxyoybZPzk
+KTfhe1hZ7ZDHfkMw8T/dNdJf6aVmjXRFVrenr8tql6tern6vYiK4/XTD1lT9
+vpOGebqle8VZGbKWztPdrALd3eKam2vvskxBRKXuhBENXKvX3fEQ0SS7aLK8
+l5HlBlubcbXa+EQ79wS4GTfK3SrwQUGSJUfpwZUfC4oH8eIMHqK4a2g2Lxjp
+p4rdZRTYRYK0FzV7kO35LiQKuHHKzZImSINuZHJTsxZSA6mGVOnj3AQtLzB7
+MWZztEg3S/Nw9xx910xuqnJzFZKKD5qkm67XefCBYYvDMF7kgQiG+zRgcRJ2
+5liyvPYQZmd/grLzI846eG8fwHtbDe/tPZiWZZLw4LwNZZl3CL4MvLc3oEjT
+YVZe/RSr9U/gsWEV/hxW47+E8j39kZ5IgDqIlnGhaFkQhBauh94yVsJuNcx2
+4RIwUIn2oDLWGBwLF96BB2ETgL8JC8zh2BiF70tAyCvMXgFCXv9QYg8Zg8hY
+xDmwffOBkLe3ShTw0h1qNhiZzwj9A3qb0c5ehj/COhzWeC/+g65/IzIg/u8w
+T0kNEDml4Q5rLLjnLKBxAcbiMgY/PtFy3u84NzApSZicFPBWGuSWHlbeweTl
+3JIdXp6x8LylSM9fSm/LjnCFns1U61lNrfr23EnmeY5iwzzWkq3N4VrvyEEQ
+c4DveKHf3LF262rIAZLfWIQ7542OdEAVpQlXZpMvzwbkdumWvLT/jubpGI/J
+KAHZxB9rDtFa9ECtUc8B6rn/X4hvZ8/gfmCO5Cr1iI5HdSW4pBhSCCngkR4k
+R1/Oo74MoCZNjwBv8sydZ+/4dvH40pcwgOcxuGcw2KfSbUTRj5294LFdmLAd
+4LWPMYmbseDZAE9sLTyx96EiK6Eqy7X+zkJ4YvMBlzng2NmAywxo1Wvg36ng
+4ZcAl+ehdc9C+57RuIPH4YlNgYY+Ck9sArR2ApYQ496z1elGu95XiKER5ES7
+yNGLFSzy7MPeEdZcefF4RcuEd+RImUfLU4DRx4HVp2BknnnXWsGHnbUMoGeo
+L0N+YSi2gQs+OSGxJIwp2c/4R2Djs0ueBzUCOP5XmKekipW4HccwpidhlE9f
+VQ/pt534G3IonwCHKhEmJAmSAoykAyMZWsg3O13OHPMgBbcEG8UaAFCmAQGV
+t+XsksECDBqos9hwd52iTYBBi0hAzkWjTaeRNhFbsaIja0TbEe6AKCJcosSO
+SCCFWyrO9YFGBTdEyTfxTgETqBEtIRsmeKOt0IHH0ArNbymUCI8mDdJt0N91
++F0DqS6SCJFKjRgp1QiSIo0oYWRJrr4miwFeQE063jYVkoyPlgjEJECu4kvE
+4VtftOnIP3VOYrSPacrxYczOfszUHszcTszgdrDdVrDeRkzueujKB9CZ1dCd
+92Bnlp1S+wLQzIWevQnQvAEHZTpAM42V0QCaF0DRzwE0zwA0TyloHgNoJsPx
+mUjQwBmaAMofD+doHDy1cfDUxi2x4I32A4f2Jhg6BhxvqgmKUu8NhunPgmDD
+W3CXnLDhKTFPixmZMQWweQKwYRgUr38O2H1xtYRJMVLxtbUSuTgTH3c2LM8c
+fPx5+Bpv4+ssAhcs3anWByb1fUbTA3LrALmPMBSbv5BwLYZtfYph2o3h2scg
+Sgzf4UtBJmkkJ+3/iQQ7G0Z+Bnx2HtNzEdx2GVMVD567BknA1CUyJBrgS8V0
+3tIAUEbQ5DAwFNOdny6gK9LotVKNZqvIENAx0o0Rb7WZbphfgwbFMTiumd5Y
+i4mjI9QYQ8dYujYvrNVniYJMkd3J9jaxQxYvQfCSdKhoN/62141rinablUkM
+ocQ/AWEmrFdiDjsKBWoMSy+S+ETGKbZAmt34qu+ZcMZ6DW+s1XDHKg1/LNdw
+yGINjyxguCRen6Phk5m4bwbeMA2SgjdPwge9kW9D/f/MuYBvdBZfOxajcwLj
+eVSd5oMgwX0gxF2Ynx2Yq48xb5sxjxswp2uxuHkfNmolbNRy6M6SWHnNfOjU
+HOjWLOjZDEDtNawJpgJqL8Glex5Q+yXWDU/DpXtCzzKnwGt6FFCbAE9qPPR6
+fCjU1M0zeFmo8xBl0BbjbhMozEa7AJML/szbU1CEjX9HzqR4NsUzqsm4+2NA
+2JN4t6c1Z+R5IOxFgP4V5pOsleDEGUDYLCDsTSBsLhC2YJvEES9WhL23VwId
+GfDIwEcGQDJei3FbjN/agdHZiVHaA4TtB8IOAWGfxQWj7IHIKPvfEY3b74jn
+x/Qa3O4sOPA8cwoglwG6eEzWteuSc8CwToZ3pmMyM9Q9v5MqYMtLE7AVanR2
+iUZrM8eBYaSM5FawWeNRr0HfDP42YDOAarEVRiVkXD0+TXgfE86wmcd6TBBf
+iB2TKNoIGJM0xF7aqh43G7hbYuUpJpZX4uh/xFBfxtWb+Po2xgH7YvD5mzH5
+jM2vh9RBaiHVkEpIBaQMUsoYf0ihxvznQXL09bdx71uQ1CKv+lMCPsdVYC0e
+lu0SrNp5+IJn8LVO4Wsz7cCYMgzvAQz9HkzDTkzJdkzPVvDiRkzZekzfB5jS
+1Zja96Axy+AHLtISGHOPQxOhXTOhZa+D06ex4BE08AX4gc9i2fQ0NPNJPbyc
+gmXTJGBsIuzEeIsxaPg48QOdccsFYwYpvuWU+oWulbOenpi2t5xoD2Z/6h3t
+zldn0ge1CYvlDGsS3mTycgmLelKh9uxqifd9CVB7BR/u1XUStjgTUJsNqL0F
+qM3bJjHDjB1euls3HfZLCCRDIddhED7CYGwC1LbCSd4eKzEljC1hjMlBDODh
+eF1tDIfR6Mio+2d3A0Kw9kNxJHHPkyC+WCZqgwTPM4EU94+7IpkK1zF5iQmS
+wZCKCb2lu0PMcMhm+pzmCBVozhAzIkogZemSKVF5y7HNAms01KZOU5GYltSU
+iaFn7sUok9ZnM5jUsAVGsmyKNO+M1qLNjVkPAzRJTeyzmSbRbv9fuXM3odbF
+DK5Ok8HFrC6T3VViUlrkm3zXJIG1QJo1EaxRk8XqNXmMSWRVmlRWrklmJZAi
+TT7Lh+TqazPLHBtvlFoiuWuJxZLLxpw25rYxx+0cgBebI7lvR3UX5yAGdB/G
+eDfGfQfmYhvmZjPmaQPmay3m7n3M40rM6XLM7xJNU5wPfXoLFD4LPuQMOE6v
+QudeAeBehA/5HPTxGZiAp2DYntDKxJOht48CcBMIOJiPcdDtce+HAG6ZD3CL
+XNBFETw+l1KG2NCtBVsUnwj8uXcK7EPb+EUe2iYCbZOWSwQUI6GesunGjLDH
+J3qZyS5A22tA23Sg7Q186jeBtjnbJJCYAcWLFW3vAW2rmEjDhBom1nwhkVqM
+2GLk1g6gbSdGaw8DKy/LKflnV4OM29jIKPvXME+ZKuGBPzB3OM5CCMDc6YuS
+pH0BeLscL+ml1zBnN1hIAfOXckMyhzL0eONOsuThMV2VeXkFkKJUSWdl3l65
+ricqNeuV2a8WcMyMbbCAo81jauAok0MbArrhCzcb2hC0cBvr2+k2kMsdEW6m
+sEwfDRjQBiLo0WUT8yMpXUUmxTiKCZSB3zKZx52lIryso1wylJmpzIxlZi7z
+cWYyM6OZmc11FZLpXKOZzxWaCV2qmdFFEGZL59uegj92MnHbjHJJrE4pk0Tr
+GyWSeB2PT3QJ6DvPsgf5kqB9HF/2c7XwBzBcezCqOzHq2zELWzE7GzFT6zFr
+H2AGV0Nf3sPMLsMMLzqvZi7WmtPfdl6Hzk1jBjn08AXo47NwKZ+GS/kEkPeY
+bkU/Ch2eCF0eD+SN8yMPLuU461LqVjdWcKHmLhAOfp67KciLdm2cgJOv+5m5
+C9HH3XsebfEU+dHlEsPBsKgnFH2/ZBg+PtWL+HQvA33TNkgM4wzmwjAnZruE
+GDPUeCHQt0TT1lbgW69mPs1nEq61AejbBPRtBfq2n5FYFMakMDblALBx+OrI
+9u43+NBvyF8GhP8W5so/NT8l9u/oWamKEHtBqiScvySJq3F4s6tXpJpCIqYx
+GUBMxZSma7WTTK3CkIPpZjUUVmcoFCDakqfEYYUWdWBxB4PDWz4cZkgxiCa3
+KMvXt3z+Nd0Yd/Gm+SXGnXRLAcf4oUgxWfqBaGkKJyn89DyLLN5Zs6Zbpcss
+2LpKOGxdQEeXmixW3mAVjg4Aql2Kc5giHS1atIPFOxq0mEedFveo1mIfFZAy
+LQJSbJuU/MDJw3+ztWYI64ewjgjribCuCOuLXC+TeiOsO8L6I6xDchpf4QS+
+3VGA8zNlon0Yrt3gtR0Y8m0Y/s0pWgHTKI85fWS+OxR1HBR2HJy0cVDicdaD
+VEfOv1LzGbRhsNL1WMCAyWJrgXEhtc6LedVCuYuB01I5HJu4XAI0JjOyHu/8
+5Gp1IT+QSERGJL6yQSIUpzMDhpkwgNMcEMQ8mOi3AadFCqd3AaeVgNP7gNOH
+gNM6wOkjwGkz4PQxNP0TwGkntHzPZTkdPwQzcyQhIqRGhYXU/xsRUt8RP/Ks
+FPg5fUEK/rDwz2XWv4uXgkA3rko5BRYtYfGSWxoVk8Vyl4BUbpKBVMD2Xi3W
+AkRlWpSoIs2HKbV1dVpisyEUT5EMmyYjSPRrSHDEqFAg9bkxt5GBpOULTXUZ
+FnnyYahExZTX7y6zizqWi+qEYnfSEHVUcdu5XYtLtWqdnCYtQMVCVPVamKpG
+C1VVSuGqgPVEi/H/Qi1ylauV4lj8ikWwWAyLRbFYHItFsq5B4vH2l4Cj8/ho
+Z/AxTwFHx1lyEl/ucJ6cbH2f0yob6r8ZBA+j0LrAci1OMDysLRlNfBAlGgnh
++n5RZtvjZwKIJXJKbAEx8T2JXJqC93oc7/mUxr8znpBxhS8BEFMBiNeYrgJA
+vLFdwnkZ1jsfgHgHgFisKS7vARCr4N+uYQoMU2GYEoMF5xbo6TYAYgd0dBf0
+cy908wAAcVgAER1GzWPCAmKcu5zyu3cnzkqtuTMXpPYca9CxFt3VeKlNxxp1
+SayuDCikaSgma2nduSk1fvj//GSpeVekNfBKtC5eearCQKvJ+mHgMyuCggfD
+WRVz+QhnVtaoeGdRmulBLGh6sGIoBAH9dN/6TO0l4MAUGjRIYMYy6w+OZi1C
+qwmsUii10wiCToDg9005w3Ytb8gyhy2qzCx/2KjlEFkWkeURayBVWqu0HL/L
+ICVaWpElFllqMUefZwnGW7VSkjGZdVNZP5V1VFlPFR/hIgBxDh/tdKki9Hc9
+7Y8J3baLotryYZ/Cy3pmgWOcpyg+TLVfGKL2gZ+ae4xnsNC7oukMIJoETX8M
+mv6Eajrj+BjP9wKzQJgNAk1/DZo+Y7tE2zLqdi40fQE0faFq+nJmljDDhJkm
+zDg5BfqHpm9mYDw0fTtU8FNo+m6o3z6o3kEw75GbltvuV90nhLnyj81PiZA7
+Br/t5Fmpb3oWyn/hotQ9Zf3Ta1D+BJb8h/In4xOkQvnTExy3YcpNqaiarxVW
+WWm1WCuvsgpruVZkpd5Xp3096pcvGWZNE/4wKvIOXX++u5KRon3UeladftDU
+tGVt2z4VU2VT1y69UK3ecgVaTwVDUlkxl5VzTdFOW8SzxlTZNdV227T6bosW
+D2VVXlbnbZBqvbbXeZUW8y3XAr/FWvCXhX9zISwEzJdn4Hc6S3pDkljiG291
+DW8ZX2WKCpvb/VGQzvuZfZEjhK2RN2+LDzTKqPlo17MZt8i3AbBEcm0DP3Im
+Y7XyGDT7yQ+Vx5lmwXQLpl1As6dBs1/fLlGts6HZc6DZ86DZb0OzF2nqxrtM
+5TgG5+YEnBto9vrTEs63BTq2Dfq1g9G0VxW74dg7Oqw6T4yozhKhdhzqfApv
+cwbqfA4gugh1jrskVbdZfZtVuFmNO+Wauyl0G7hiaVIW785VlWZRbxb3LtJi
+3yzCb1Q6RQoNk8ZrlMbrw9G4tzjgJeEWBwHZhA5ya2zeeBiNHhXkxwS8Nbpf
+qbWouimv3sdtrz67SQU3p8Kty06VBnn/Lqu2s3y7EZZz79Ty7izzznLvraqL
+LAPPkvANtgC1lIt3qpswHJCKJikpXwIpghQ0Scl5lp6/o30cbuG1aZBk3Cux
+TjXTxI0In4zyFHixq5miq0LfD3oHMEuU2ZfpPta7urJeaQ5uxqgL9BJU9RWo
+6qtQ1enMHoKqzoaqzoGqzoeqvqOquoypElDVVVDVNaccWyluF2PoGEsHPTgs
+x4JhFTUqrKI+GuZKA1cbQBYrhW1joaxnz0lrhksXpVUDWzYkxLkBZOzowDLV
+xue4YapXm84PVFZ2gmBHCKOsSVKdnspKRSX3spOEy73pQdzrp14+HWE7aXQ4
+6lXiHUFDVUsDUa6zEZA6/1pFPGD6ImMZPGD7ApSpgHX7K1wXvtKQeZX2Fag2
+umv6Snbb9gOmFjObgsQ4HdCv9gbpF9LSoIr1LdNSpF5bjNQ0S9uRSkh5CwYL
+Utwi7UnyIbmQbEimtiFJ13bVf+NRbbSfZkm8hmwX00ZQM42G+rXzPU87uQfE
+k3yGwUyGz/D4ern+GQYrb3KMSQaTMTiNQWofgSw3M3yTYZzQgk+hBbsx8/sw
+0wcxw0fSIq4Gw2vlJNf5FdLUmjix0rrnNHTxHN724nnTosDd9WK7H7b9Yfsf
+tgEy/tl1aQ/ENkE52jbIKiMVkW2FLGtWKGtaRaz1KaK3pyJwD+f9urr4gGVN
+Tx+zJWbXHB6IwxuIuJmJuerXOgbabSLax5rSuMl0QCw37Uwr9FLdHemvMreu
+No27a6RJFJtF9YAouyFd9dLnrbNBGku1N0qjqVav4Tn7UDW2SG+qulZwKKQa
+UtUqPazYy4o9rYogBZA8SA7kjm0tZ6obxajvupg71C4X2sMzy4d+rVstO5AT
+GO3LqN91cu1TGyVA61kQ5QsgypcYPs8wehDlDBDlrL0SCzkXRLkA3urCL9Rz
+BVGugE1fDTX9APqyDmr6EdR0M3TkY+jHJ9CLndCHPdCB/Zj3Q+n3zZ6BwJQw
+F/1UHVy++VG88QkobOxpxfePnLgL0jSOzeOoq2wmx6ZyaaqrbDZ3R3WVTeiM
+riZKc7piJc2yZJ91h9SEkGZjhqWk+9qEH+OxZranpT1SB+2r9visgkov3CAN
+xYvYANDtolthYw0HqtzGRdXaUBDSZ2pn97JrfY9pm8QmhKYhIaQTFNfR7FWy
+b21Rx7VVGhuyCykbHda1SeNDdiqthJRDSiHF7dLRlJ1Nc9tkeP7JNehRVM0o
+6iUJ0540vWs23d7jlFo+tNrJfXKGX0yCdk7RxA1GQjEi6llo5wvQzpehndN2
+SqjhDGjnLGjnW9DOedDOt1U7l0I734WSrIR2vg/t/BDasf6yRGZtgUZsS5Aw
+kl2Y8b2Y6f2Y4UMZfg0d5Vc+84+BEaqfj0XST9HG33VOg0nPnTWtC02fUbYy
+vHpR+o8mXva0M121M0u1M0e1k5ppWPSm9Dl1zXlKsDm3LMq/g3emv4JFH/RY
+VDOIXN3M0+2CfCfMboFqpjXgPqUc5SklSHOw0kJlkBvFA6Yn14DuC/Qbjew3
+DiD71LJfbW+DMeuNzFZnd+muJmlvy+s7WqXtLTtSt7SpgkLhGtulVW5dh3Sy
+roZUdkhLXbbWLYEUdQg6/ofLmrTWSpBGHVdQQ1cyVN3VxDV6YgNNnAhNnMTA
+1Y2qjQxoZRz4donXY9zeNGji69DEmdDE2dDEt6CJ87D2eVtjypdCE9+FJq48
+J4FKH0ID1kMDNmI9vQWzvg2zvYPBTZjZvZjRA6KJMcp4fkX0OPLxMDr4h+bn
+j4UjAYETeOPYWGlvyzbUF8+KOrI99TVVR7atTgZhpmpRDDaNv3Nd2uhaoiwI
+Q5QVwUTphpdaoryvTV2txO0m7GTbzsE9UnPL08MwihjcLtxVxNFBijiklnuI
+ajhYbfS0RnqTD+gifcB4j+xf/gOnH9zYB+kFN/Y2mSbnTg/UsFt5kY3QO9uk
+MXobVK8V0tyhAMTvhk6oJKQWUtOF0YFUQMq6dIT+t6eHf+QpnKU/n+KNZ9An
+FG+SKt7jDAqF4j0DxXsOivciFO9lKN40KN7rWMnMhOLNhuLNgeLNV8VbjLlf
+hnl/D4q3CnO+BnO9Foq3AXO8CfO7FfO6HXO5A3O4C4q3F/N0IMtPg5G07wnX
+iRS7/CNZ0JyQFudsdX5Wde4SdC4O73/lvLRGv6E6l4LPkX4l2DjnJEgbZ2uY
+Q+mvUujPDRsO70RS5x6ORH+mYIarb5o5yQyvnjxPh/t08eJvo2v3jMyaRfRG
+mgeW0ieNoHLOEAzxEHRt0Oz7D9by9YNwFAfqrFYPNBi9g771Q9f6IL3Qt17o
+W4/qXDd0rQvSCV3rgI61QVohLdCx5k7VPehYPaSuG3oHqYZUdst7jPOWLT+R
+Y7O1coQ2foOcUk+yAfpQryehXs9AvZ7dKUFcDOaatl+Cu2ZCvWZDveYw8P+E
+qhhjm89JYNgqTOuaeIlfYRzLpkQ5Xecp+w5M1S5M0V5MwYHs8L6gz8I+FYbd
+/kB/GnY77jjH8RFOUdvAcuegcRdU2+Lxca5C2xKgbYmXhN3S4j12y/Kz2w1h
+t6KbvuWKshuvj+QGumvnbw0nNyraHa3Mkm1y3WUac70iaL35Qmx9w/YkZUks
+bu4glsSqWFHOUIV92KdXeLiWvEbnbtAsfwd1e2YACjXAVUd/MxMd+lSXKD3Q
+pW7oUhekE3rUAR1qh7RBf1ogzV2qU9Cfhh7oFKS2R9Ex2eOvHznjGc23CQsK
+jaB9HMrzJJTnaSjPs1CeF6A8L0N5ph2EAkF5ZkJ5ZkN55mDm5mtA/GLM1jIo
+z3tQnlWYpTVwidZidjZgVjZhRrakmtNg+e4xLu2onjwdUU9+IIwEJjyBd4uF
+npxRPbkIPbl8VhnpgjBSUigjqRUMYqREl5ECtqV2ZUrk/ZWIoQJZrpIETMkR
+3IdKYvNLzRxBOagkvQWOsJEwUYQdlG+YHRSjMspDQxF4aMi4XkPUlyHuRw8a
+9hnU/TkojDMA9hmAtvS3ymN90JZeaEoPpBva0gXphLZ0QEvaIW3QklZIC7Sk
+uUde09ALrekVkBsk2+04xsk8u1fiZhg/M+0wFANKMRNKMQuQnqNK8Q6UYvEF
+icF5L16240xQsn+V+EzEuf+ubGlg7k/ipqcx92dx4wuwSJfOCD9cU364GYkf
+ILkJLj/YCJHSpLDOTzh60Gl/KHja7yg3gBe01oY77eSGnnzHLaNd6EhThiLT
+bc9HDjLbZqb1XC7SbN81s33XONp34WQPNRihBjQytmIQ8z2oTjbnfEDnvB9z
+3dfOj9LBpUIPprsb0oXp7sRUd0DaMdVtkBZMczOkqU8G6UVOgNnD+mbofP3S
+Ba/M0h8Jk2PqT2CWYk8IQs8rQuN8CE1UhKbGhUdorp7G+hDqLubvY+PJdHox
+nSmy3Gmif2qQ2ZHjKzNka1jmm4rnJgC1zyIzKnQfCbMTGGPQaOZF5+cu5ucu
+5ueu8Qg4Q6M4Q2Z+7mJ+7gKLQ6YN61AT520I8zOIuRlstazzTWcA89PfIdKH
+iemF9GByujExXZBOTEwHpB0T09aH7wRp6RM8LhECxyxowv9zYWD0e+bnt4bB
+6JzC6LIPRjfCwQgknmWPV74f0cr6N1sinA4ywNibmzsKISb859htj6482ylX
+K9HbeTFBUtq1MvzEEDiWcodPTEzoxODhJgbN3MWccF6GMC9DwMygLkoHMS8D
+mJMBzEc/pA9z0ov56IF0Yz66IJ2Ykw5IO+ajrV/ndBHH20yBBIEHng8zKb9r
+fv7mMNScVdRcUtRcDUFNClET79idXBc0ERxt/26t/4zLDVXQSWnOkjxCMyky
+IbJaz7Wp4aNMLp/N62Okdq8BS58xY2ZiSpzwbrRvboY0tOy+5ibGzM3dFhHM
+TZRankFdpHFqBjAt/ZiSPgqmpBfSgynphnRhWjr7MUX95vp3XLRITkzghYgT
+842waLmoaLkSjBZNePqpRUqowXGhEnqYE3qQbmekyT8jUgrAXMPKLx2slAbq
+6mRmJWekwDcjRdrYrtixM/KVs2GRIguY4bNxj7Nxr4l2+B5m4x5nAyi5qygZ
+AkqGMB2DmIpB9TUHMBUDmIZ+SB+moRfSg6noDp6O+e50SAUuMTch0/GfzM8H
+RsRJvOAkYBPSfTiJ7P/dDGGwSIfBGb5cpDvelPA5U66Ep2UdhrQ6JdfVzIht
+p2EaMxU72ubTPR8LWmF6k8EJqOY1d3Vz7R4mwggm455MRkBm4wF3Nu5hNu7p
+bNztkNkYktngKrXbjt4AZqEf0tens4FZ6IJ0Dsjkz3Gn4xGZjpdcEy+YGB0J
+E5aMggzI5RADEmEXKuwZp4brmvG/rflgMv4Ba4Vac6TGmC2GxJoVdgKYq+X2
+M7ETUKKdyjH6AxHW9xj7KMNKY4gDM/BmErzBN0MfxaHHfIcb/LudMvhDXY4d
++wH1o/v7ZOx7MeY9kG6Me5eO/Wx37L8nY/9KGCj8jj7mg0LA7lH7YOAkhJqL
+EZZBw073Ur0IT05BrWYu2Cng36zD0MJiijm2xBsmAI6MmYICETMFGHqbYWCn
+oE8PhgeCh58Okmk4f1ccXREubO7V25WyDj8HP4pjj4f9o3+Pe8MYfri4GHxn
+CBw02CNCzR/o0xVQv87AgKjtG66x/m0Z+amRRt42Ab8PgzDyLoX/sCpZo6tS
+JbjWDrubMKLxJuwh0GyH3Qx5mxny9nzHG/ZCb9i7dTe11zfkPIfnEejg/Q35
+Pd17CBryR0KH3LnXKUp/V8d8SMd8UMd8AGPd36+fRrV9hqvtotKBaWHG/Efm
+588iLitCHaSwC3//SYw9z9YoIA57qW/Yq3TYbZchk/F9R+tU5UrpUFNxLd+R
+sjgdBWatXyhpM3bUe3Q/sa/MVfSATSIftOt2GXFZzI0xltbwi8cx5hZfmkPi
+L1s5G18GD3kUx5trDR3xoV4Z8cE+Y/D7jUuG0bYj/po74rIYCLzqcrtMwQ/v
+a3Xg34RL9am3exbLuAHfGBf7xrhCxjhax8IUeMmWUmBSVS+PRTXN6EKZWVmF
+/XPs8HYVhxleXYwNQKEHQd+D3raIDO0jnhPjG1razS91B43D+mV7sDbf6xJt
+5tjeNTtlGF0eRECbB6HJAxhTjm3foHndVHdo5cAm8HoYZRZu+bmnzMdGXiP7
+99XTfMrsBmfoIBf6BrlMB5nXVt8OLhliR5o1DDHQLHDmDrVtVdRZ5BtqDHMP
+eKO3zAvk4DAP6DAPyjDL3hMGmVqsy13/MNNCUn9l0sc4X/qG+F63O8RmgDHM
+feZAB0M8OKDDLEMsnkiMF+USmB5xjL8/TJFDd4tCd5PdszKSxQ1fJJZvfEts
+XtHvmLx1k7Oe6atWpHXttB6rDG+Bb3iLdHiZyyO5CCYMWwNSTUQKh3ZAh3ZQ
+hlZ29TCwHF47rMFDSw228fxfdnL87Nje65GxveuObbQzpGM7OKgvet4d2D+X
+gZ0RZmB/y/z8bpDynqLyntQt2NPeFuw1y8RxIWfiCSHxmMk6oH9uEpTdggC+
+gbUl0mz9Tf/AthX6BtY3qN0Y1B4d1D717DioAzXDBtZV2Lsho3pPRlX4AQr7
+pZ7KfCkDG8WR5YSAbu+CEjimvnE1X+o516mQEnOBmS7dipb+wtzxmGpprGrp
++dO+M48LeqIbJ2FabuhLgsYL6kDyMfYFZ5oO00/ZEK9CR7I6wkiaetz+kSzS
+tpklpoFz0CgywpQj2a8L9wEdxUEdxSHfKHK1Hm5VoqNIFe2yywiq571exx3G
+u/3cxR4wR2oyimagnnYV9K9lJGeFUVCTJ6MbXFTQ48dVQXlGcFpOys2pJcb0
+OoM2NKSIoW82DjPL7gt/T9I+UiSrt0SHtDzDV48pK6RArO0igOFkQaM2LQvB
+XHUd0oDtSNBTIUG7DIDs1zSjAR3OQQwnT3yGuGkowyle16hwXheXIWY073Xr
+4xjJe30jjuYT7mj+vYzm7Iij+bCnoSfkVI5nwDyVu3xOQmCuYSRvXJZAQka0
+pl2zX/MP3CyaPB1KW5CgVIfSlH3L0gKh2V5h64Y8qS/YbIdSq2t0lHhZyN3Q
+TDuMjCHt0/AoGwHgG0bZdh3rbiOFc17vcaWGMeQoq06axZyMYiDcME5xh/G/
+yDC+GWYYZSEn+0hH7cHVKd9ROobRxrklYBgT4+3w/Zw5GaKUNicvWXLN3boO
+tkqYDiO7PrBmPYtpu4X3OYyF0jjNDCOGr0OPGJj7xtQfZj/0SBiu08cIMwxh
+v656BzCEPErisQK1cchuxYUfw4AM4gPuIFpVNIvrgWB+nOQO4D/KAL7l8qNo
+n+wAmzNhDJkJwGLEiw7ZlUuOTVdNktB/L4XrpiYGp3jVMIp0xFhzkPU43eq0
+2VIcudaOGJSuqVBKJLWWuGa1s4Jfq4vJIhiqHgxVrwTiOX0Yqn5o20CDXVEN
+urv8QzJUbhSC3Ry4a4bqrhkqNc+ia9aUDKgW61BNdE2JlMYOzA2ja98xPyVa
+0B8qdPaM9b1+T2LQNVnC5v64uZ86Yqwhwu6pbD9nqtHd9iqYshcCy2NX50of
+FdvLiGXbWtQrZz9mFghgTnKnZtYwJaGHh9u9tWQVd8waRcx39e2+G+zBIx8+
+XqODx6vfHa8o489EW3iasfg3V8P+Lxm2eZGGTY6/f9sfJy3JJRirxCuaJAjt
+StexYuq5rbfiFhLLkI5i7G9kyolnS7ltjhVLo9ZBsxqKvM0rlixp02IKzN3u
+1AykbihWt0Yh92KgGE/HICY9/5fBkuMjwVW7t91ndpywAqf+6YpwyKwGMUpY
+bw158KP8qzs+UgNKNmNDxufb5qeUgjp6UqN0gcOzZ33pDUwrYx4O08quSaa+
+SSu25TJStBRUuq/QYaaWi7ZDlSvFlM1Q2RKZ33KaSqW4S2u5ZLZ3VHk5WkwU
+6NZYbUYcMsyrT8Nu9NDbXXXf7yBF+wdJqvSYEZIiBoEFLkcJ3GQ1x7SPkzbU
+3pefdCVO80wxJkm2eoGOiSnZY2vRZWjR4ExpL2LGJEd6qrCabo0tIVps2s6a
+v5vLpfYGB6UdA9Kh2T5mUDAgPRiQHo17YwxSv0YBDPj4aNDbs9dd4mh338Y/
+JH7a/l/ukEgSohyohCiNbB5LwMaJ05oPg4E5D+K+xDzEOCntkHBN8tCTtb7K
+LVs7LM1XNfa21BdnuX7TFyPXX237t5zaIu3JW+obGNZAYCK3f2A0mp/B0j0a
+DNiHQenzhUYM6HGfwRhc/UG6+oPG1dedFVmahrj6/9Mdk8kyJgvDjMm3zM8/
+EYU57eVnnrsgicnMz7/CujNXpe5M0g2tqYYxydDgJXYnzM2QDk6FWdIYg/1C
+yvQYu6pASmWaBqocEyCnUZ14d0xqJLORKWGdmt3Q3SiBkRqo5obj9fuOPwe6
+XAP3lQPy312D9YQMyKKIAyIFC0zSlM3UxmBcsvU/rmrRKwxGcmg1x1tadjtT
+ezrYooqBH0oDvv+vrivpbasKo2aQWLSFllKpSAhUMYgFC1Q2sEDiz/APWCOG
+ikHMVFBQgQULJFra1M3sDG7cOqkTN7PjeKhdO4mHOIkzkSzNOfd8vo6CvYnS
+ynn3G+59fu/eMyxbMTJSXqNLOhVqqvZOWCuK3ExeXL0kigcR9AQr76630Hr7
+mw47ofN5K8Shnrcf57Yyt0Vsk/PQ9iwOVYf3/LwQqinwYZsyOFRF4KLmRU9L
+t6GPug1DpkcUltZepKm1hzJMUknWtnrmWYZZlYH/pkETZbdzVgZKp65kzCw+
+J5GeSrMMK2K4khq4VRLLpYnVboJk9wwytG/whAM7bz20jfWAHW0c8JXjwHbV
+3/XZC5AgoIK7eZ62zF3rkW+w36RfhkzvLCx76DEKeUblwBmjqrTlO+dtqV9y
+lhXO9m3J/E5TMhSmyN7qQ4kRlZFrBXO/akdqG6RClkQrq5M0gVx3joAzCY3a
+qwuGsb/TOld2R2d2fKa18O/h8aeOd3za7yvtj9s0/ZT9dE2nWAcKcHtQom+0
+oQ+hACMowJ27khCOTkhae2qqmfjZxvyc8w5qJBflfUfl6Oyy9HGdcXlW2mcs
+AMVfykUVYN0e7jfKojJtVVuvpkSl7hgubNcwKMQ6EPPAQ3We4u7b+dW+9flt
+n7C28AOfdExYh5BU3Qoi2R4k24dkB8MyLg5jZo+NN59WLzTiuNNN2+EHLcic
+/Ri6nEqafTS6nKOUIrpczEtyao1SHaZSULVEa+Jrud/JOqgb9HbbwG87REMZ
+2GbPkAM8HN1zr357/+vwWz5hbUEGPm2T8En3U4whJ+uHu1o37mp9uMUPUK82
+0qz6OfoKNMbxlXc/boY1tqVI0wiq5VM139n6pqTFSs3IPFXtkPQKJX2KkmMo
+k5yOaV0tN699wvF/NjeEb68b3phov+0dIYuIYCFMYtd93++67/vdw9Z77kV/
+K9euS+CSX8WnLG3XU6QXHG727mXn0knbhEjMDETi8mmimcyMHZ3TBGAJvUxS
+yBm9zFAKE73MIa1H6GWxKKmVtVXHtfdE5aoB3GrGICFsnxDqLQMx1g0wtS30
+BwFFB5qqb/rOfaBkPmvTuRNKkHm82ugeldHvIBbicFTGKGMxeQyNx2XqNYWc
+HlhO82jV4rJZnWck60mxwYd5qS0VkFMR+ayiVSXLh0xWEgir9hRSQz41QsIN
+wrtl6DyCjOoun+2D43PyDZ+ZHuIDn7fJTFrL59UwzEW6g/dgLvZj8YWQ3AiS
+C8dkohTF4puYMcfNhZbt7QKSS6SlA5xCs9I56brlCtLDKax5YmQJeZXRqzJy
+q6BPVTtkIcSdsGSCTAk23TRgGwFUBguRSp/LR89SgS865iPUoTMoQC69yGUA
+N5Ih5DKKXMam5FjkvA3n5DRBHf1Ze6ZeRC5LWSlBptCkDCWx0KS87SQV0aQV
+MuPXxfAsG4eOVKWqPSoSX10zxOyGIfQ2LZHXfSIfKZEv/fpR+NpT99YjCL8P
+rRickH+ZM5HDHLs3a07EuAfGlyRw7uYb2pBAG5IUs0Qb0kUPkMpjyRSMz0+C
+NLmpZP6RYFVG5BXb067uCudL4GfNQJ+v+VV/SVF/1ab8El48o+mE2IN3zZML
+sYcm5WfjDFwRe3RetgWTiD2OKTRth9MLiD2Rb96uTjfSKHt2TUIa+YpY3UWU
+fYXEWmOGkY5TRsnLtulZEVqVv7/iq635H/i6Y9zmJYaYbyPmXsQ8gJiHEPPo
+tAxIaK/gHNeXJG9NGd6Zpu7oqUYCsyS5IqGbDGqdRbg56iaQiE4OMBmWWyKy
+kT205t6ySnu6wAUfqUob+KZjpNo/vIUou/FF0TcpSxRao4Qxoccwoe9hQo8n
+j4oEn3aKiq7CCDOxKi2eFKqaQZhZ48mTnkzyZ4FcOyM4kWyyakG+6IP8TkF+
+6yevQtMX+o2onFno0OJstKelsh9GaBH/qvask1SNo+HTWGezdpawiNASqF6y
+LJWJNELLkjW9KU4qqX+PEFqBHBihaF7wUV1WVN+3KZ1gl9oOo813cFLeGP0z
+zS+pM05HOYqmTmD9xxBXHHFNW1zzlC0qSfGCyhfLNTG4M4grSzoiYso1OWDP
++4iuKKIfOkWknabnGv0oTwjlGcHcuoMwImlpXlJiL0bJPcqG2dPqXFmiG4sI
+Y6kmEnlqyzEhG2kt4vN+vV5VAD92LInuN10PJMlOafYBzPEQ4hhBHHcQRyQr
+mb8Jyv5RugwtemDPUrMVKSksII7EpqMJuwqc8xX4QwFc9jNFw8ork+rvXRj2
+NobtXZSYLqU9R9JSFIxQYRDDjmPY+xSKQgfi9jU5s+448264s364PzXcT23y
+Fd1SbxnXMWjXnFR7ezFoPwYNYdBhDBqmpCFl2TBoFINOINcYBp1qPhif8aP9
+pdF+7jiaBGuuz0mhlEqlPRipDyMNYqQhjDT6SJI/kRUnmeIGeMYPcE0DXOk4
+gFbcNVz8Bi5+C4u+G48avVSRwwwOYQYPFyzsp/2kuKmr/tLxqlonf6Mj/6A4
+N3HFYMbWyUkfW1BX+dV39skj1wsEjghsnfB/06u/uWqjtKNgtz48qA//ZoEd
+Iyo+5T83os/9fiwdXuwJ/6ExfchNRzdwVP8ReOw/yPm0Mw==\
+\>"]]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"tightBindingContour", "=",
+ RowBox[{"ContourPlot", "[",
+ RowBox[{
+ RowBox[{
+ RowBox[{"-", "2"}],
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{"Cos", "[", "kx", "]"}], " ", "+", " ",
+ RowBox[{"Cos", "[", "ky", "]"}]}], ")"}]}], ",",
+ RowBox[{"{",
+ RowBox[{"kx", ",",
+ RowBox[{"-", "\[Pi]"}], ",", "\[Pi]"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"ky", ",",
+ RowBox[{"-", "\[Pi]"}], ",", "\[Pi]"}], "}"}], ",",
+ RowBox[{"FrameTicks", "\[Rule]",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "\[Pi]"}], ",",
+ RowBox[{
+ RowBox[{"-", "\[Pi]"}], "/", "2"}], ",", "0", ",",
+ RowBox[{"\[Pi]", "/", "2"}], ",", "\[Pi]"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "\[Pi]"}], ",",
+ RowBox[{
+ RowBox[{"-", "\[Pi]"}], "/", "2"}], ",", "0", ",",
+ RowBox[{"\[Pi]", "/", "2"}], ",", "\[Pi]"}], "}"}]}], "}"}]}], ",",
+ RowBox[{"FrameLabel", "\[Rule]",
+ RowBox[{"{",
+ RowBox[{
+ "\"\<\!\(\*SubscriptBox[\(k\), \(x\)]\)\>\"", ",",
+ "\"\<\!\(\*SubscriptBox[\(k\), \(y\)]\)\>\""}], "}"}]}]}],
+ "]"}]}]], "Input",
+ CellChangeTimes->{{3.603692983787211*^9, 3.603693039687956*^9}, {
+ 3.603693200358313*^9, 3.6036932006040773`*^9}, {3.603693253948852*^9,
+ 3.6036932863186903`*^9}, {3.603693809725132*^9, 3.6036938189928617`*^9},
+ 3.604372720535181*^9}],
+
+Cell[BoxData[
+ GraphicsBox[GraphicsComplexBox[CompressedData["
+1:eJyNnXmYV8Wx92eAEfAqGq9rXFHjEsU1btFYrZLEaNyXa0xck2jcFRNRExXX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+ "], {{
+ {RGBColor[0.293416, 0.0574044, 0.529412], EdgeForm[None],
+ GraphicsGroupBox[{PolygonBox[CompressedData["
+1:eJxFmFtwlWcVhv+9dxKanX3KBmcKCj05WnW0CA2gJIHiVSChI8SZ9oaSEwQa
+EsALD4EcmarTGelF8XRVnNGE1plaOzp2oI6ltnWmpUC9aiv0gkNINYGOpok4
+Et+H9WZ68c+/9vrX933r+K717Xva+7b1ppMk+VsqSTJ6V+jHhJ5B0d+qSpKb
+1UmyvSJJluSSpFXPYj3bTT8s/l7JbtCzWusf0HNJT5vWnhHvqukG0+1JrL8i
+ervo8crYi32WLdK54reK3yjetqrgn00HvyP55OxV7KVnk74dFH+RFH/INLrO
+Suev6vt9mZBB9p2aJDlfE98qxF8v/n7J70oHjfzjejfqqRP951KSnNRer+WT
+JCf5jeIfkPy+dJyFzFt6X7NdVZnwAzK/zCbJcT3PyYb307G2WXLPar+H9f62
+ZOol/2Y6fIHs9erw3ah4VXqGJfOh3pWmB00Pif59VciMiJ7Rmn/Krj78o30+
+peeUzvmR/PSUeL8oJslp0Q9K7jHRW9IRY/Y5oH2Kkn9J8r36nhP9Y/Fz5SQp
+iH41Hz5ADpnX5JODoscLcQ40Zx0qRLz69b6YDp9v1X73a59viv898XvS4Tv8
+1qX3ZefGR9Uhs1X7fFnya7TvaDn2+45z4GU931CuHJX8g/r+jH6v0fpnpM8x
+0f+qlf6y7X7l0EG98+WQr9G5Q/b/TsnfLZ/Xi94h+qbW/Ednvygb79K6yVT4
+6ILjOyu6Lx18zjonH5+tiThddq6j/xvap1U6/CAfcST225zbf6qMfL5T/p/z
+PofTkRPkA37Ehyf0/nUh/HxaNj0pGzr1vUfv885J8qxOe6+1/U3i/d16bvSe
+H6diP/xFXKjja3raUhHfCdP4Fd3w7dvidbs+W11f1FmD8xP+uXTUITq853rn
+LOqG/KN2Zu0X6N3iv+v6Omwa+T3WmRrB15Ou68pMYAR1hC/BHeq4x2ciM1QI
+/qDencWIWbfer+vcR8R/tCLiWu9z56ojvjtdI/A3GwfmzGfdiYpYC87NGete
+yUV824uRb+jZKfkXSrFmtBA2vme7HnJut4gek19frgx822AZsHGqIvjkOTY1
+2l4wBCwAB/YVo7ZvFKJO+1IRL3Kgx7VDHB9LBT4TuwbvD1bsx1epeJezQeez
+UcvU9SHXPmvHcuGDQ3ovLwZWXda5GX1fe0f4at0dQQ9YT3Rc5RzY7XOJZ5Nj
+Snwft54t2rc5F9hEfVKnv1GNrMB38sOjet+ojvrHJxOuP2LNudM1cTbxqasM
+fGsydlB3P5XOv5POU9qnQ/Ry5UNbMXKwy3jeXQobsZX6vbFwVj7i8XnhxH7j
+Bvjx19o4a1Ehao3YE/fb2JCN+iUmzenwLT0OzF6pZ6YQPv6hzuovR53+Ix/+
+wC9bUtHX6KP4Al3AErBiWSZk8OGMdH5COvxb76WZqE38TO6MOX+o3XHX71RN
++Jh4kbvYja/w3ZT55OFe63DB+tS5V6PDSttXZ2z5Sjb0Q7c/gGvi/bc29mtx
+TMl1cpJ4oSf5QHzAi27HqLMy1rLnpyXT6xohh1+sijxudM6g22guetrPFYsT
+pVj/Gfl1JBe+xcf4FT570gOpF7Dy9Xzg3qul0BFdqeth5yf9aK/rhbP2uaZa
+jFkz9hvzQJdtwWb0Hy/FzFBvvHvFswEzAlj6tPH0XdcFmDAv/yXZsOeDdNhO
+D0hl4xuzwCLPJ2B4lWcM1lKLl9xj6Ml512/RNL2Yh2/gA32feqffL8nGb+j5
+2tDhpXx8X+zZAL9nFnCgMuqaHBhzD6IXkV8TrvexbORTxvi9xzpTx9iDLbeq
+wy7sZcaZ85yzy1gNZpM3YAJ+ZpZp9hxCj9ri3rTGeUjdgQFgAXGk1+xyXJrc
+Y8D5mxWhBzo8Vw4ajOEc8oC1XV57e8ZTzL6mPXtKgS3NloG3zliXz4Q+6DaQ
+C97PpP+ZXPiuXvTZQpx9PR95eMu2/zEf+z5fCiyhn2Hvgo/wDXMoeAVWkafT
+ztXxbPgaXGPddq+lBsj5FaXoUbPuU/SdC67lncWYoXfoPUDf9owx6Tmmw/6c
+Mq7ek4l+sMOxIj/Bt89mYgZlZqZm+8zn3Hc8P3+9GH7AH9TXoOcr8rF3oWfV
+hDz42+e+xPy2w3oeM+7SqzqNqRszIbdk4Z4h+Sfy4QvmLPCWuQSMIWcX+y5w
+zPcT5B9xXIgP8WQ+wLdt7hF7StErOYscbDUmg6Vri1Fz9P/pitiXPVl33rZg
+PzSxAyPPeSakdofs8wHT+ORIOnyKPzdLp3nFsakQ/j9seXDjsPOZuB0y/4VC
+9AJ6wkg67jPssywXfOqL+B1yLTOfog89YpPlt/r7Vfd+dLs3E7m9NBezKViK
+LzhjOIk67/ee2VLMsF8sR68lN9cXYzYkFivdQzgbGqwdtu3YhJ3oiC4jxuFR
++4RauN1rZcv/aiOPhi2zwvi/vBBnMSO1e4ZhT/xD7Z5wjXDH4B7x/UL4B9vA
+bs4hBpzV73vK8VLgB31rtfsVdJNrhbynL7RbV3zSa/4a91N69sLMA01PAQdG
+fRaYz7ncSZ831vyW3MsHxnHXAS9vuReQs7yJKbhLjTAPMZPRD9YVI8eqfC71
+knccyUVylNwFE+grs45FzvJbLE8tbrIMum20DPGih837zgJu3MbtJPy41HnC
+Q87gh93F0PG0a6jRdcS9i/tXQTZOupa+UI65mfn5iN7P5mPO+Fw5cu1u5wnx
+afSMVG/+Zs+xOfe+k+5/Rz1j45OPPUtUOk8aTBOXX+VilvluLuYD5oS/6P1G
+PvplyffFk94TTAKbnnKNkE/E5ZTvokd9p1tqPnoyH1C/4Ncpy6w3f8YYe6fl
+pwsx/1zXe9L4Sc4PujaJBe9B96B+4zT1iD/4jU/AMPKA2mU/sJc5gXter+Xb
+PLOiz8pyzAPMBSPliO1PipEX7NPnHAaPyXkwZpnriBln3nfaL5WDBs/InSbX
+O318wjhDfNp8LrYMWIbcHneONRRD72njCrhDX+Hcm66FsmeWDmMpNUnejphG
+zyv5iC9xni5FvpF32LHfMk8X40zwjPsVc+NHhaiFi55n8Pek/Ukfph8POB8+
+NA4c8N38Sf+Xcs32jngtccSn+LarGDFiLfpjC3uRV9jLGRnPUxesA/dv/ENf
+437CPeWq7yvT7kfcBaZM08vHrGeL+zj+AQuR2er/Ci5aN75/YJkjpueM4cf9
+3wV4A33JGE7ukdv8pge3JYHH3AmpNTCsyrgH/rSkPtmfveG/7x5HnU7aX/i5
+z/LMJ3f5bsgcR38f8z36qvtWhe1osq+4R/O/RId7H/L0IOquyTrDO+ueOOR9
+6B0LvZD64j8yYtJXDMwAR8AN7iEj4j9QDozfYH6398cPzLTUN/VIXWZcm8yL
+xGQ4FzryHwoxBZe4h6w2zR1+4T+WtywzYbtW+ay3LY/cm/b5FdPYyz2G/wjw
+Bz35jPmN5i/8V3nOMv8HVoa2hg==
+ "]], PolygonBox[CompressedData["
+1:eJwlk7tPFWEQxWfN5fq63+7eVRsTQmwMPqIWIvhqtLL0BhOsJHgVVBShgShB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=
+
+ "]]}]},
+ {RGBColor[0.4455187332341498, 0.32186997546921486`, 0.7432107918860154],
+ EdgeForm[None], GraphicsGroupBox[{PolygonBox[CompressedData["
+1:eJxNmXmsVdUVxg99073v3jOqrdYBnk20juBUjVpNqiagjfqcJ6SgDxEEHBCN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+
+ "]], PolygonBox[CompressedData["
+1:eJwtlmds12UQx5/Kv5P/b/ybOAjQ8UIQsQzBEcCYKCaABEpBLAhUQApChyC0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+ "]]}]},
+ {RGBColor[0.5469205553902498, 0.49818035911535813`, 0.8857433198100256],
+ EdgeForm[None], GraphicsGroupBox[{PolygonBox[CompressedData["
+1:eJxFmgmwVdWVhs+Dd+993HfPvfdcFLVNg0MlorwgWsYwimLUbmMUnFrUWNEW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+ "]], PolygonBox[CompressedData["
+1:eJwll3lwVfUVx29C8l5eePfedx+I4MI6Y9VEpVaxbCoNS8W2EoQpCDpCAatg
+ACuyWGVagWhYq1YkAWSRRYuE1bTsso2A2A4u7Ywtlt0SpB3UoFPb6efb7x9n
+7jn3rL/f+Z3zO78OI8cPrCoMgqBFQRAU8X07FwTLS4JgGbAVPIiCYFBpELyS
+DoKLcRAMSYLgRLMgGJcJggfAjyCzDdln0f8gGwQzkR9YYBsN8G4HyouD4DT6
+XcCnZo13TwXBWGQ3868W2Up0DsP7LvR1yA/FZ/889rPmLUFmC7xD0P2gX4Ze
+D/1bZP6EbCP/zsN7Cfow9IfQ56CrkOmO7HH8tSP+ncB4/E8ExoVBMAz50chX
+wH8K+mbWdAdrW8EaR6N7LOu1NWDjEPQfgT3g0/n3Ebxy6Lls3FDky8DvyTv2
+bth7BHsfZi27E52j8BfC/wj+J8j/C/4E/vWE9ynyHYitN3Qn7BXyrw94TdZ4
+AP8N8O78q4P/KPrdwF8HZsH/kpibiH0A8DD4n+H/BHyPYsT/88isQXY/dDfo
+BdC/g74baIO9b9iPXuBLiO888R1EfwF0O2w8BH8K9LXE+zL8o/APQZ+GLiGH
+D0PPR/8c8V+Bzm7wQ0AH8GH8y4O3BKLQOVFuzuC/Ef48YAz4aGCu1hOad541
+NOL7K+gfYL8XcBu+6/CXK7DOfOSvR+YA8f2aeL6D7BBkehU7p8PBZ2S9Nq1h
+LfiPkB+G7WPI9wefg71ZBfZxO/JfYPMCtqey3xvgfQN9CbqEIvkc/e9BZ7G1
+EBuz0S9BJ639wsdO/FejM7vYNTAL/H1gIbZKgcHgj6PfrcRnUmfzGDpF6L4B
+/Je9KgPOInsOKAe/DZkTafuU74uhY5NN2b4APQX8FeA96JbQ1yBfD/2PyDWh
+2pBMPfSt2Diedo2p1joDn0AXYf8W8ALWNBPZl+AH4G+iPwLeRta7FXoC9nvC
+Wwm9FPoC/BnQc9E5gP2D0D0K/K9r7H/i5YBGePu0P+AxcAp6P/Qc8KeRPwvd
+kv1cn3FOj+BrPDH1KHGNqFa6IP8i8heR7yF/wLyU9/yf6PeOHbty+hfod3Ou
+3Tbk6D3sdQI6s94J+BhO/FdCT+QsPIrOY+h+H/lz8Fvg/w7wlfBfKPIenUd+
+O/5mqJcAV8HLILMF3sf4+wx/Mf+ugF4N/2/IbgOeAx+B/0Gs7Un4T8GfBOzD
+3+7YvWgVMfwQ2Z/DT+PvF/x7J3YPUS8ZB7wGvyP/nmvmnHQCvwZ+ObKdWM+1
+iWtMtaYedpPqh5haF/qMVSL/GTbWyxb0VmQ/hV4DvRj6LcUOdEy7Ru5Fv2PO
+tTyd/RmA/iDtebF7yD5sNyC/osh79i3yp+C/ib1anWl4O1Vf0NXALvCQfy3S
+7gnqDZeBFeDN2Z+98g3cAl2G/+uwN0XnHfp16GXQl4inscQ1qlpVT1RvXK2e
+nThGxToSuA/8/sj4jcS7W7UAvQH5JdjchO29yDwJvo49vQu6DdA25Rwr11qD
+1qKYh8fOuXKvHnsf/mqJYRKxtMb+tqxrWLX8b2T6gLfLuTdUs74O2Gsf+awV
+Qz/DeegH/R/oWuzNx17/0L13Gv/OYO8s/LdSztm5yDEr9gnArtg5VC6XAl9B
+74JennZPUm9STpXbOuCL2D1UvbQCaIL3ZWzdjdi/gP3B/Psr/mvwfxH/bWPf
+nQ3ApchnVmd3ss4wsncCa5C/FfkaeO1j32XbgSbkl0U+u6pZ1W5f4FtkF7De
+Z1nvGeh18J7A3uPYSrFfm9KuqVOhY1JsOpM6m21D30WKsT3614fu/aeBG6Bb
+hL4bFdPVie8U3S1/x9+S0D1IvegD+JXQ70L3JXfVxPRTfK3O+a5sQn4j/Ms5
+81TDX4Onc861YiwBPxq596omVBtas9auHqNeoxlKs1Qz9nsH9Cb41ZpfkN8M
+fkJnLOWaORl5z7X36mnqbc0Sy6qGihKfCZ0N9Uz1zt2Ra2sA/8ZEzpFypTM9
+EX9b1JPwN1k1oH4cO3evsb5XsXc6a556snrzq8T7BPFeic4f4O2JnRv1JPWm
+U4n3UjOhZsPxoXuVzqjO6oXEd7dsyFZF4llhIP/6gP8Y6Iq/j/UP3d6JeeqZ
+/++deffqPD0rG/lM6WxppmiFvYHIj8q456n3jck71nHoPAL+deLcneBfMfqV
+iWct6dwPPjTx7Koeo16jnq3erZlGs01x3rVZz3qbgU9PfFaLoZ/WWoC9Gd9x
+v8L+Yej9Gc+kNYqHGNfiryv/OsM7COzKeAabGTpHytUZZIap1yWW1Z2tu/vB
+xHfTSfHlO3FvCPE/RziwLOOZTbOber56v2aKq9ULEt/NbeHXJe6h6qXqsR3g
+nww922pG1qxcFnkW0gytWVoztmbtQugC6NVA9+ZeU0p3BfSd0AXkJwMd5C2r
+GWk7tsfGzq3u1Na6i/C/FHwIkIbeiPwi9KugW6neoVOlnik0WxwFrir1jP0+
+sUSaaQr9r1XeOVFupJPOu6eqt6pnj4icc+VeMSv2dTnXunzK90M6g7rr0RkF
+/bO8cc08O9SvoIPmvmNvCD3zafbTzK7ZvTTybK090F6sVT9t7jdRqFqGrmju
+mBV7HDmX+ieezrTOtnSk2y/2WZBP+S4J/ZbQDK5ZfGXiu60ja14OvgZYm/Eb
+QW+FtxPPZmXQW8AfCN0LtUatVTOIZhHd8cfBU6FzoZmmBfweOedCd3hP8BdC
+z/LzgLPEVqUej+6DxDOAeG6OPatpBt/K3lzGxqKM3yQbkH0n8qyrnrpHvR+4
+C3oU+kPztinbqqHnke8b+65UT5wbeWbV7Ko7+jx4Yd69U28MvTUeQ6cq7Z6p
+3nlT7FlZPa428h2uu1wzw0F4Y0PflXrz6e13t954KdfQosQzl2Yv2dwB//PE
+s6XedKuQHQm/POUZfDLrrVDNppyD1cguDv021syu2V1vWr1tNWNPyvpNqbdl
+PfKbEudQuVwDvSrxTKPZRjPuZM06ec8qetNNy7vmVfva43ngvwHqMs6JclOT
++C2iGUKzhGZWza6SeRHe4LxnT/Vc9V69EfVW1AxVj/7mxLHdiE49+Gz+Hci4
+p6m3qcZV6/p3ROcr71zqjaW3VnniWV413hXdyrzPit78evv/Ev78jPdQe9kl
+79lDM6lm08XwV2R8RnRW1LPUu/RvifYm8V4pZ8pdA/SmjHOgXOjM6+zr3+8T
+r0Fr0RtiY+I3jd42c6GnJZ4xNWtqBt8fu6ertyvGZxLfibobNUM1wZ+aWFcz
+i2aXS7FnKc0sml3+B1bASbI=
+ "]]}]},
+ {RGBColor[0.6259490281195165, 0.6273881033512626, 0.9109150720273521],
+ EdgeForm[None], GraphicsGroupBox[{PolygonBox[CompressedData["
+1:eJxNm3fcVsWVxy/vC2992n0siIICUiyAawGxJBaaHTBgAYxGTUxiipqNYoum
+IEbTbRExiogaNZbEgr2nbEw2ZI2Iq0FRibsaARHEKGZ/3/f345P9435mnrlz
+Z86cOXPO75wzz6ATv3rkV1qKopjfuyhaVd7SVhRHdBfFX/sUxcGVojhIzw76
+PbxRFH9oL4phKh/p0u/OojilV1FMrRbF2yrfUr8/q32JnkUaa6zK0zTwO3rX
+v6Mo1qr+Hxr/BI3xM439nib777IontM4S1Veq7b5elar/Qr1fU/PPH27VmOd
+pParVX6g53Oq36TyYtHZ3ebfr+hZTqn+GzV+f72/VHOdrTH+ome12q/QHPM1
+12UqPxLN16jte/WieE3fPaA+T+n3vS2ur9K3V6r8qZ75rFHlVXruVH2x+j+o
++pbqM1Dr2q7D9E5OH2ieHPqHpG1yvh2j8qHMNV78Ok90DtU4s0XXWXoebvHY
+9Fmr9m/0dp9hhcvz03+9ngvSPqiP+1Ef32o+X6Xxh6o+XvXPq95P+/ee+DJD
+9ZWad4nKp2tF8Ubqh4gfx4qXd2icmXrG6dt39e3vNeZ+ev+RnjNV78iY/GZt
+a9JnfYv7X632+1Q+o7JvZAk5Gpq1P5X2E1Q/Xs+B+r2V1r2PymMK7/EOqh+n
++sd6v5ueJ/X78Zr3+wmVr/fxnrEPx1bML3j1Xe3r5Rprjsou0TlJ7Rv17QQ9
+a/R8SX1eUNtnWvz7en1/lur/VL1F/feKnLwmXq3Qc0aXaVkeepCjvdPnFZVn
+ZPwfaM4/ibcLNMYBomf/ivl9k8pZ+u5clc93+cx06puX1Pdj6NO7afq+S21z
+VN+85v58t1oytUrPzeLHdI01Tc8/9N3v9WwUH14S7SNaLaMv6pspkVVkbID2
+cqho2k582FJjbVExXzlHlKylb8Xv5un3EI29vZ6Vqt/f4jOA/I9Q28569lV7
+RWP11phdKmdUzHfkd9cWf0P/F3SWvi36nlf5imhYrbY71ed9vb8m52jTGUMG
+xor+x1ssy/dmHPb6q5rjO5rrVJULtc4b+vg8H90U3zT+gdI/s1Q/Sfw8RuVi
+9btL/e9R+T96/2a7ZeueTgS2KO7WPB1t1iHwYKroa1V9XcV6Y2148liLZffd
+wt8jo8N6WUaRmVPV3qnxBqr/raoPF2+G6VmDrkt/+l4rOhZo7mtKy9CJLd7X
+vq2u7xB5/EzqHb3MA87v6FbTAH/Yk8F6OvX+26J5idZQVfmExt1cdEwVH36t
+8b+p+Yer/+2cs5zB21TfPnqgVN+Gnt3Vb1/J2HV6N0blcO3RSNG5g8Z7U2N/
+oc1jMf9jOcPomAujW77fcP0HDeupx8Kre0XjEV3ey7005hiNOUJj3lH1mb68
+tBztpGdQi+e4IDRzvhdn3zkjs3r7LKCDfxW5ulH7dITKM1UexXnobV00Rb/3
+0fMn/R6gcpnGX6L6033Mi8+q/kQf8+LkrGtxaL5e/YeoPFXlmD4elzFntFkP
+Qgdnc2baJ1U87ymF380MnYsjM9DfrvU2tPbNtd5b1P8yvf9OxXt6b/q8Idks
+9e1BhW0ge7EnZ0f9PtC847W/B4sP61q8l5NjQ9Cx79St6wvt3Qvd3t+H4VUf
+26JT1L69xhmsZ2S3dTj6mX7nl9ZT55a2xZxp9mLvisuHCtuxtZnvJPXbKnZp
+jPb7NdE9WuUoPUtVH6ny3orlZlTdcgFtyMmO4sNHar9eZ3MzjTlH635Q7Vvq
+m0n69pLoiZXqf49o/Fvde9BRs/2hDs8/0rcf6unNb9HzXdFyhsrTNP6W6tem
+8QeobbXGWtVunfiUnn6i/2DN1a5vD1I5Uf2mi6cHqvyx+q+I/n1cbRvU57d6
+pjR8TiarPFn9Tle/T2uunfR7ifrvqPLndWOXm1X2Vt+jxePWDp9pdA5n/Bx9
+97LaP1/4Pf3u0FyXileXq61shna1z9Pvn3R4DdCPruqlZwE8BH91Gzt9UnOv
+0/v9GsZUjA+uGp5xrlH/fp22o5y3IZ2mC/nbRmvYRr83q7pve+Z9u93tO8YO
+LtWYW2i8rbtdxyZynpAzZOxkjXORyvMz9pBgv1F6v7zbsnqX1rhBfV6tWu+j
+/7v13cxur411IYuMiY4alzPLOeXcLstcA1W+pKe9l9cLH9br/V2tHueuwjiR
+PmBFzgs0dPbx/rGPJ4rPcyte65dr1pXozCMbto3QD38e6jLfONef0ru+6jNN
+5Qka73j0b4fPKGe1rbd19guxBdjQOX2MK36qMZ4XT29s9RrXRPee3uK9+pTq
+qyq2/78WPe+kPl28uqvmcdY2PCf2cpieDRrvfT2/0JhHqt8szXF4aTszNrYJ
+e4QcIAPgzKnBn9iUPWNbwZJjgpGeSTv2pVer26kvbTH+Gaf3z4gnT3cZa4Kz
+JwQ7wW/4zr6Mrlk/oCfAX/Ojgy7V71dE8+4N8wu+jS2M9X8WXUffa9MfPbc+
+Ngvd2IWdLyxP69LOHlB/tjDGXB/+HNVmPwO9DP55PxgDm7i4y7gWTP14bNmA
+YLyjwXt9jAGQN37vlT0F04HtzorvsDQ8eS+6GN7+oPR+f680HVOinxut7kOd
+/Xk+e/TT9IG2n+iblVrnnuLPihZj1KN6GVePy7xg14mqzy6sD3pkvtU4fnz6
+7BXaVgeb0469wr95J3zcWLUeGtU0vh2bNT4oGqoa87CG8ezzGWcyuEjfTlF5
+fNV79qL6fqu03rxQ5SEa62X12RV9WFq/TVR9bvgGHsYm7hY7i91YEZvHWlek
+D+t7Vc8BOSOsHT9jssafob07tOkxV4Q/0Lh3+IlfAO7syH69mjFn52yCrbD7
+Ldlf8AA25BFMp9bxrOipqc/9Ddv6OTXbf+QJWcK+046Nxzb0iw37fJvPBH7Y
+qzoLr/w/3NMZDNfa6bHBFthS/LEh4fHY8Bl7gU8B9kOex0VngCWHdvvd2VWf
+6+PFh6NE59aiYbrKL9aMHb4p3n+1Zhx6WcXy3qa5S/Ae+kz9n2u3j4SvBO4+
+qts2CXuErCKT+AtHV4yRroqPhl5Af0DTbeEheIxxwGT4E2tCPz7I1IwzqWb9
+d0lp/cfaGRNceWEw342iayEbp/ffqBqTPp7+8IGzc0W34w3o5bubtpG3N2wj
+kW18xSP1/nA9b+n3SVXb8wnqe4FoO0djLBCtl+j9dt3eE+gHg8GHUyrWPegg
+MOzD0Q/oyQfTp3/dvusrrKlm/+MMzXO82s5rszz1b7X8odv/GTwJrhwtOj6t
+Pt/Td7+quf8vVda1znbRUlU5Uf0mVEzf/MQT0Ku/1xxbaS83b5rfr4fnfMf+
+bojfj6yBn6EJ2o5q2s5h775fcSwEvxv7/oWq9cER6nNqzX7n2epzStU6+mC1
+n1m1XzNT9etqbuf9l2q2LfNLz4mcM+/9OYNgWvy4PcPDr1R91n9c+pysjV9D
+iUwNi92hf4+Mqd8OWteg0jj29fj182o+byPrxvJP5/ziO0MbNoW+D4Q/W0ZH
+gg2Oz/6AK2b2sv94SWEch59+vfrN6jYuqXRY96B/0aPgxycz1+NayxfUtm23
+1/px1ovuQkejczjjg2Lr3w3Wxma9qTH+lrE4Z43I9qR8i24Hs4wKbmH/F+ec
+Hqe2Y7q9Js7fEzmD54hHL4r+XRqOKYA38Xdb0gcfBx+ROR/VuxvUZzeVp1WM
+o5/Kut4MTr44doO1Y1PYB2J6rBmZgm/E0J7MWhhzIfEN5K5iLIRPix5A3ltC
+A2O/2edf372ZufD70AXI795aw985yw3bio+jz/Fb+I7Y3EU1+2Nza7Z32DDs
+1/dr3uOJdfs6t2dd2GjicEOia+m/OngHmQPnfLNmPf+70rStzLp6R8aQmWMq
+1on4RltH/1/Zy/psTcYnloZsXRL/a3HwDLYWm7tXl/m3MLL318QniTNMbHed
+s3lg6EdmVoZf8OrYyABtM+OL4m/ie4EzF4qWYXouajEumBwZQw8fEd3InGBs
+5gBz7564Ef5RS7tjH8RLlyd+Cm3rg7vANRNrjmmdXXpPXwpt7wfP0Gdo5jku
+ehs/5BOxI5zvtcGNA4PVOWunR2cu0riL1H9Bab+kLVj2BPGwS/VDGtaxXwtO
+OC3fghOeKo3Vwey3q36rxrlV5YSGMdN4lU+0mX/QjM+Eb8YYxIfxwdCVMytu
+Y0z8b+SYeALYEJ+Ec4ePSBs+MnSfEQwG7jgjtBFHxI/C9lyquf6r3bZ4ZtV8
+/5x4eW3F8W9ixsSsbw6+xi6NjnzODj5FzvHDto5fxvrwBbDds4NxwOVzWhw/
+nBY/bkFo2LbVNDHWnqLhWv3+SmkdR1/863HZB9ayX8U+H2Mu1pz3h19g5jOD
+gQt9/w98VOx1u8dnrgMa9lX2bzjuxT7CX3w2ZOHvmr9de9pbZ6K16d+0/0Zz
+7qxv/qJvRzTsAxHfx9fYLPGq23KW8AMZbytim+p/at14kJjsFwvzG7yKf4G+
+HgDv1P+QLvuH6NhfdDoOhp2DT/AL3u7RtO5aVzXenBs8eXfpb+4sHXuF1/jA
+YMRFiQWxf+zjueHhTalzZu9I7OixquPuz+r9vQ2339fw+Z0bfEusfk728YPI
+BXx4pHQc86HSaz07692vZt2yZ824e25kctvIB/sIFp4dzI/ffl6n9cU/I689
+cfF27y9yQix5RHTI1NSJLfPdnOiZuSmZi7FYA/Qvj109oLBNYT2s5cOqdSex
+5Dlp5/uja87d/LbiverfbTmemzHpc1jNsdsH0BMa5y3R8XfVl7VbnncnntBu
+PYsu5kwxJvuBz3VlcOnT7Y7/Euc9tOYzdIvGmV4zr/+o8jXR8Z/olZr3d7+c
+kccq/vZTah+NzmyzXvlhw7bsmppjj9gjbAcxSXQIdpCcDBgGHAS/2Rt4Thx6
+XmLx2E/sKHHjw8SDQ7u9PnJp5NSe0fh7N+37IsuzMw77RS7u2fDi4S7HMvhm
+D/Fp906vZ8uq8TM4+q3YjcmFfRDmZt5ZFetBYpwn14yhHhZ/ti4TVyqtK9Ad
+8OXEmvf5vNJxrxND/9iUpyaecHb8nZV1+1ffxR+tGbvdorYHEtcivrVP1fLz
+9dL2GkwJ3ty3apovLh0H2jGxoMfTB8xJ3BPbe53o/3nFcaZLKtbPE3OW9686
+jnJjad2GXUH3TVV9SrflF4yBvkPXnZk6fJ5Sc5zyydKxLTA4ORN0P+Og/++L
+DgcfgimZ6wbwWdW5L3IFJ9Xcdhv8rBqv3l/aJzsqscSd65ab+VX/JsZG3PAu
+/V6HDShtF9BdnGP8b/pdntgINhmcOahivQkWwc+YkXzNNrEp6KMJddu4j+ve
+e2SA/R2avAZ0L+1yXJ5Y1SOpg0OOzZj4LGDXY1MHR4AtOGu7VIxj7izs0zIu
+OIH88J8jq7yfkT74QvhsxA2373AMjtjPitDDGGC3NYn70DY8dPZLHBcbTV4H
++z2maR8SXxJd/ZMu23hs+Y7xMbFDf4weeKdqLAAfiLsSC+nBSar/LuMTBxhd
+95yPVvxQZ5978pyhZ6+66fx1xb4N2Hpo6ZjB9snpUCJHyNPgtG8IJpkVGsBc
+5PvAMOTfLok/i2+Pj9+DMbrtz6AriQ8SJ5ze9HnoyQtUHEOamT7kz8ijjWs4
+f0YebUbT8SziWj8KtjouPsjkbmPKW4JjwDOPgWeapqGjajxMzhPbx36yr+jJ
+j6IvoX9kcgezS/uyg7Pe/rHX+B3QfmPiA8ja0uSE0ENXdP9rP6/I3nE/gb2E
+V4wJ9oInGzM3867PftMfnECfHQrr8hmhsxrfvCztf+BH4YNsk7OCDR+Rs8kZ
+vaYSv6Fhn6l/6Ce2Af3YI+wZ7ZwXcg3IUN8W5xLwRU8vfbdiVnTvfskdc653
+LT0ePij53w/bjWeI2Y9N3B4dv0fiTf9L7lP1hepf73Qd+7i+tK25seHcCTmU
+fy/tH4yo2CYckzwaNqs1toMxL65ab6O/mR/sM0f93iudZyC/d37iLZ9sOmbM
+t0ML+6j4qv/WcD5wj9ijLZJ3BttcWLFv1NV0DrG74pgyNgF54h3lutxbIBdF
+H2K68Jl3yBsY5t3gGGwqc+CTgqHg6YTYxNFZF/mijzodZ14TmqDno9Lt91eN
+VcB87OH+2Rvmgg//CC+w6cyNjbiptD5Hr0MLPIE3nJuRFfP70dLnD1xzb2md
+d2tyCH2Ti9+UkyOesE98UHTazck93Vb32UK3booRkPvelBsBK2K/h+WuzudK
+6/t+kWP6jqp47gEd9kfmZSzaGQ+ZRraXaq4hrLXLcQD6oBOwhdDKPl6dsm94
+iL58OvofPqwJL35W2icgd1dNLrtWtw/AuexX2r/Bz8FG/qI0TgOvfRw79Wf8
+hob3b1+VN5S29dh8aN8l6/plaYxPTIuYIf3Za/T+PuEnfgDYHv8Ce40fis3m
+TLBf5JuJkc9KjAhfFJ/00IbveMBTzumPunxXA8zJfY3V0V13Vs0jzt/a+Dbv
+qtyl23qF+0cb9HuN+r+v8jddzluQsyA/hL19J3Fd2om5vdQwln45ax2Vfds0
+N/KJDlyc/sS6wJP48Izxm9wVIKaJLh9T9zlaFZqXpT8xI2zdhthTbA62Z3Xs
+FHMwfqO0/ibvt7HbepV3xDsv63JMBb9/YuKc9EHHonvZh2Mi39xtmR5/rTV+
+Yh+VH4QGdCZ+5wepo//Rm9j0g6I7qV/UtP4gN/VwzX1PahrPTwq2AQOBVYhL
+jMldiOtrxs5LgknQ0+jrTTygzljos8OCzx/NfR7w2aIO+6TofPLq3HXgHH8x
+56dv1XG+XRLrQ0bWhOeM8WjwFVif+d+u2KfBt+HcoVPRrehP2oaknTm3z7zI
+7IjKv+I+lNgIzhTYkrMEXfhhyBB3MXZOfe/EuzbpnCmxBcROjsl5x6ehnTN0
+dPaOPsjilfHzsKPoJr57IDk4bDExzKPTn3U8k7Xw/oHIPHadPSC2jwweFrnF
+tj4SzLkkPg57fX7GwtbQ9nC+xddZlRwBuRnsCjJBLAPcD+ZHJrcLzjw39yIu
+UPmjhvEMuOb53FF4sW4MSl4WbE3sizr3mQ5Nrurwpu0mY0LPlOTRBjeMS3cK
+n5EJ6pyph+LXP1baji0MZliV/AhnmXMDreDqQd2JoRWe/4TQgH/5RvJSYErO
+5/BgMPBNj41JfOwOldvX3T64bsy1bXBLJfgQfYpuA/cQG5kWbIYd3DMxh0U1
+x3qI+cwrTRf0Ed/bqW567qk4Bkcs7ub4XMSViOWBjxZlvQfmbsb4pnOK5BZ3
+a2S8wvfIuKtAvgesglwfGdnmTI2MPoXGadEhj9Yc43ykZj9hSWSG+47I2huJ
+h3O/hH7ENj9MvXfqxJPBgYxPnXs1zEdeGr9nQvwd/L/7s66t4i+vK40T0Glg
+BfwzzuBl8cUm5ltiFdgP9De6Df+E8wW+QW7xcYn14p+SVwNL9GDx6ITWYC2w
+LTgYvQjmJU7BWWTuadk7cvL4uvi5xDg4f69XrJNGhYcjg1cYv3fGHxIde3D8
+kQ3Rw9C5PLTtXxjDHpQ+6H54Cy8pN4a39J2atfQu3d6q8oXSNuGspu8MsYZJ
+9eRpg2PPKh0HIB6AXePMHhAbB5bGZuETge+JAXKnmDrjEl98Lu1f63LehLuW
+6Jk/5VvWAjYmBsFDO+MTy+y5y1d4vOcS1/1a6XUvTOyHGBAY5fym8dJAbFDV
+sT5ifpuVxuVtVePQRrBoT5n6tKZtwoM134XiHlRL0/EV7hHi/3JHAp1DPo/v
+6uEPMW3sJhjrsKZzxOSKuXMBbiTmMqXp3Bw5OnAcPh66nfuu8IV7jMQMiB1s
+umdEnRgCsQfyNcSO0K3kYfEBrixNCznGQQ37yls0/H5+7iMN5J6E6tuqz9Wl
+cRbxmB+WlgXyxthRdD1xDMZ7J5iNezrDcteIs4B/Cg3fKG0fyFFw53dEMBtx
+480TOyYuhgzBH2w2d0ppA8dxb4bcObkRciTE7uDHlrlfxF2kAWkn/gCP1iTm
+sCL10bkXN7Xp/WMuzgvlH1Jn3+jP3n2ptKyRlzuttJwR91qaO/DLsEEV419i
+RVdWTAsxOXAoePTu3I3nrh55qLWpg+PJK01KvAJMT9s+Tdsl9A66grt39Plk
+1X4k36BLj2s698K9gysqvq+3bdO5oYkZE0zdCN8oy9R3TztY+jNN/ya3D23c
+NRyUEn8DfMT+sE/MAe0DQz9x1m91OT5K3/5p544++ulbdeemsMfYYmJE1J/F
+v6i43LdpPcK5r4mf53ba7mD/z2l6/LOb/nbTd9hSfmNPJ3cZN4AZiHNw35oY
+DLqYdmzsvonHEpclH4394v4Bcd7xwZbc0eQ+5Gulz9YZ0TvQTz6C78n/Usem
+jGv6jBIfBSP0C/Y+tmndQx5+TuJcD8Y3wWYjK8gyMRz2h/dbpw9jH5K56NOV
+/Bp9+c24n0i+krtCt9adQ+HuD74FvmJP/Cf8AF9z74Xf3BXfr2k/mLuB+P/4
+edy/QObYN/Jd66vOrZBjQQbHRw7RyWXiWD+sWI64z4IfxroW5AxyNsldcoeI
+O0jotRGdlh/kDZuCXkAXT889mZcb9kXwN5AD/g+Ajphb2g6DibHFX6/4LgR3
+ItBJtMNPfJSNm3yZTudOWCd7DT7h/gEY5O2cHf5Pgq67qnQsg7jFRRXne/C5
+Fzd8Hw4bvIfKIYnt7Bqfd0PoQb++HR1LnIU54TE6nztj6G7y3WCRHhzS5Xfw
+BDlHxtlL5PGl6HzifNgGcp07ar5R+F9V525YG3kW8ip/iX3kfio6eHDpGMh5
+Wfu5GRt54c74iPjOxGPAKpv+u0JJTJ4zxzfgInT5quhz9DR7sSkX8XzWS4zl
+gMS+2G/08tXR+Uuzv+TJD4xO7rHFnZZX9Pqy2HHiHPsnVgONrJdzg23cGL+J
+84g+50wiRyPSB/9uWezFtVXfWeLOO/8FIM9BbgMaBof/4GRoZk7u7IwMT5bV
+bVfJG4Af6Q+GxC/CpyC28tnStojcLHSxT9y5YI9XZE+RhbfCH0r4Bs8uKm3r
+uBfPfwzAJ9eV9plYA3aR+4XIzNiG7/mhLw5X+e3Suoo7U5xjzvMRsfnY+x67
+32754Wz8NW3gOv6PAa+/XJrG19KH8Vakju/M3Wn8ZeLZxLvRFdgSdNLVFcfY
+kVV8MWh8I7JBrBQMgK8Hv7nbgs6kbYdgA+4akvOY1PD9bOaaUfUdAnTHwtIy
+SawQnQW25byMDC2vhp47k9v9VWlMytkEi5xVMe4jxwUeXB7ZOyj3yT/ddN/l
+wYcX5m7kd0rzkTmwEfwXBf15n8r/Axk48Vk=
+ "]], PolygonBox[CompressedData["
+
+1:eJwll3mwl2MUx59776+79Vve54fSgrbrhjSUUpJlqAil1I2ElC2hooXG1r5p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+ "]]}]},
+ {RGBColor[0.7005028309634165, 0.7471753197051194, 0.9126146691033419],
+ EdgeForm[None], GraphicsGroupBox[{PolygonBox[CompressedData["
+1:eJxFm3vclWO6x5/1rvew1nrXWs96luTQGMd2FKNIEfI2JCIqe1NDRSnFjBBt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+ "]], PolygonBox[CompressedData["
+1:eJwlmHeUV9URx9/C7u+3v+VX3ltIaBbKopQgICJHQFh67wlIpIQiCkS6K5wE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+
+ "]]}]},
+ {RGBColor[0.7737900624999999, 0.85071925, 0.90903175], EdgeForm[None],
+ GraphicsGroupBox[{PolygonBox[CompressedData["
+1:eJxFmgm4VeV1hjfce898zt7nKCCoT9MKKhBFBhGTgkOVQRqMQ0yjCGodEBlU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+ "]], PolygonBox[CompressedData["
+1:eJwtmHmQVNUVxt/QM9PdY3e/9xqU1YIUaCAmIoKKlGGz2EwiCZQkskNQwGIR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+ "]]}]},
+ {RGBColor[0.8407444374999999, 0.87304675, 0.87903625], EdgeForm[None],
+ GraphicsGroupBox[{PolygonBox[CompressedData["
+1:eJxFmXmQVNUVxrunZ+mZ7tevu4m4YZSEGJcqDRijkYCCiEQHUyXLGIyyiYos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+ "]], PolygonBox[CompressedData["
+1:eJwtlllslVUQxw90b+93v/tdZIsQWSqC0ahFZQsgtZStLQlQioAsVaKALUtb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+ "]]}]},
+ {RGBColor[0.9076988125000001, 0.8953742499999999, 0.84904075], EdgeForm[
+ None], GraphicsGroupBox[{PolygonBox[CompressedData["
+1:eJxNmFtwlVcVx/c5J0nJ5ZzvEBXHSZNQaIGOgQiFUdSn1miHCs4UiHUgHcc6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+ "]], PolygonBox[CompressedData["
+1:eJwlk8tLVHEUx49htxxm5t4ZyCij0pGZgla1qKBVRQU9FkZpVBAWpGWGlRgZ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+ "]]}]}}, {{},
+ TagBox[
+ TooltipBox[
+ {GrayLevel[0], Opacity[0.4],
+ LineBox[{3322, 4574, 3478, 4231, 4232, 4233, 3700, 3701, 3460, 4183,
+ 4184, 4185, 3176, 3985, 3180, 4744, 3984, 3799, 3879, 3878, 3251,
+ 3880, 3881, 3800, 3801, 3181, 3804, 3185, 4581, 3487, 4580, 3488,
+ 3741, 3740, 4243, 4242, 4241, 3489, 4582, 3643}],
+ LineBox[{3332, 4576, 3481, 4234, 4235, 4236, 3736, 3737, 3483, 4577,
+ 3482, 4578, 3182, 3986, 3925, 3926, 3924, 3928, 3927, 3976, 3922,
+ 3923, 3795, 3796, 3177, 3983, 4643, 4644, 4563, 3474, 4562, 3475,
+ 3733, 3732, 4216, 4215, 4214, 3607, 4723, 3640}],
+ LineBox[{3373, 4722, 3606, 4720, 3605, 4721, 3726, 3727, 3541, 4634,
+ 3540, 4663, 3575, 3243, 3224, 4748, 3876, 3851, 3916, 3915, 3296,
+ 3974, 3975, 3973, 4213, 4212, 3244, 3228, 4642, 3549, 4641, 3550,
+ 3731, 3730, 3472, 4560, 3473, 4561, 3653}],
+ LineBox[{3378, 4635, 3543, 4309, 4310, 4311, 3618, 4128, 3619, 4734,
+ 3577, 4664, 3576, 4665, 4741, 4740, 3997, 3966, 3967, 3965, 3969,
+ 3968, 3289, 3963, 3964, 3962, 3996, 3995, 4111, 4658, 4659, 3663,
+ 3662, 3787, 3572, 3723, 3722, 4307, 4306, 4305, 3536, 4633, 3650}]},
+ "3"],
+ Annotation[#, 3, "Tooltip"]& ],
+ TagBox[
+ TooltipBox[
+ {GrayLevel[0], Opacity[0.4],
+ LineBox[{3321, 4572, 4573, 4229, 4230, 3250, 3699, 3458, 4548, 3459,
+ 4549, 3582, 4771, 3583, 3401, 4413, 4415, 4414, 3331, 3767, 3330,
+ 3680, 3610, 4125, 4791, 3479, 4575, 3480, 4077, 4455, 4019, 3429,
+ 4017, 3428, 4018, 3486, 4079, 4783, 3337, 4374, 3338, 4423, 4424,
+ 4422, 3405, 3588, 4773, 3587, 4591, 3495, 4251, 4252, 3259, 3745,
+ 3260, 4254, 4253, 4593, 4592, 3645}],
+ LineBox[{3339, 4583, 4584, 4244, 4245, 3255, 3742, 3256, 4247, 4246,
+ 3490, 4585, 3585, 4772, 3586, 3403, 4416, 4418, 4417, 3333, 3802,
+ 3864, 3865, 4192, 4191, 4789, 3425, 4456, 3426, 4001, 3381, 3998,
+ 3422, 3797, 3861, 3862, 4187, 4186, 4781, 3323, 4360, 3324, 4409,
+ 4410, 4408, 3398, 3551, 4752, 3297, 4323, 3476, 4564, 4565, 4219,
+ 3246, 3734, 3245, 4218, 4217, 4725, 4724, 3641}],
+ LineBox[{3372, 4718, 4719, 4715, 4717, 4716, 3721, 3286, 4304, 4632,
+ 4631, 3535, 4350, 3316, 4763, 3571, 4657, 4209, 4405, 4404, 3371,
+ 3960, 3370, 3961, 3539, 3850, 3849, 3848, 3455, 4066, 3666, 4069,
+ 3457, 4067, 3456, 4068, 3548, 3860, 3859, 3858, 3377, 4406, 4407,
+ 4210, 4211, 3601, 4778, 3600, 4640, 3547, 4321, 4322, 3295, 3729,
+ 3471, 4557, 4559, 4558, 3652}],
+ LineBox[{3379, 4636, 4637, 4312, 4313, 3291, 4735, 3290, 3674, 3793,
+ 3792, 3578, 3764, 3318, 4764, 3635, 3420, 4447, 4449, 4448, 3374,
+ 3852, 4095, 4096, 3542, 3843, 3842, 3841, 3453, 4051, 3450, 4048,
+ 3452, 3839, 4092, 4093, 3537, 3834, 3833, 3832, 3366, 4438, 4439,
+ 4437, 3415, 3570, 4762, 3315, 4110, 3569, 4107, 4109, 4108, 3720,
+ 3281, 4295, 4294, 4627, 4626, 3649}]},
+ "2"],
+ Annotation[#, 2, "Tooltip"]& ],
+ TagBox[
+ TooltipBox[
+ {GrayLevel[0], Opacity[0.4], LineBox[CompressedData["
+1:eJwVzbsuhGEQBuBXKVlniYRKIaFyShQkWhUJHUFiaWxhUSkcShcgWmeisdUS
+lcJFbKMTh4ZCpyEexZP5552Z7+8ulmfW6pJM811Iai3JYUOy3ZzssMt6Y7LB
+Jj28yt5451H/7O7Fd7U1mXA75o09/WxT8iD7Na+X/agV/bzZAouUZPuyDrs1
+b52ox4x451y94IyS+1VO7Zfpdftk/8rsklH7t+odVYrmS6ywTJeskzkKdo/8
+c+j/X2bD6pTsQG3Xt3Hv7U/1g0l5n77CDVsMygbo59rtlzou/wP2iy+5
+ "]],
+ LineBox[CompressedData["
+1:eJwVz7suRHEUxeE1vcs5R4HQKCjUKlFQoSEZNSYKMQo60Ujc3kFPonIZhcsQ
+72OGMN7Ap/hl7b32Xvt/zsTWfn2vlmQFVX+yWyVDA8kOrWiTHtH3vmRmMJlW
+/xRJD79o6+t21rBcJqtuXPKvsG6/1A/zC9qy0+Ndq795L+o2nvGGV2yblbIV
+CizJLKLpnVvzO9yghXs07H/SL3QxLjOGQ5lRmQ3EzhOt0U16bn72f1s/5zsW
+7M7j0azL7+ADU/pJNx/8+4X6lHeCY4zoD2Rm6R+qsyrS
+ "]],
+ LineBox[CompressedData["
+1:eJwNzr0uA2AYxfFTlEh8L2xYLV3MOpgYSBqxWXoBNXR0CWhE7ILb8BFTEYkQ
+EsEF1CYhabSV+A3/nOec5zx53/nqdqVWSLKO2dFkeCq5pucTyQUucTaWPIwk
+S+NJydyV9fCHJv9l1zGfut10uzGZXPFl/WPZnKxu/tb9wR3f4ffc7dr/mtvy
+G9pE3X7a/Qy68h4aujV6SNfk0XvCI3b0n+kLBlDEkV6/3qtdHy1gwb9K/Ik3
+V3TeZW/YklXt2m5uvTFkHkQRi/yq7ofdgfletq/fkjXoJ12W/wNBGjIa
+ "]],
+ LineBox[CompressedData["
+1:eJwVz70uhFEUheGlQIOZ0dGIzOgnuIAxKKegZRqJlgY1iZZEJW7BlRj/0fn7
+ZlwClUSI5yvevGvvs/c5ObNbu+s7Q0k6WBxPZiaTZy6qSR8DHOkdohhLNiaS
+Bp6wiW5Zm6ljCtM4rSSr7jjhFT7mJle4ihpe1MNmC7mPd3xggDV3vvIbRjCK
+c29v69/Kd7jBA+7R0e/xNX7lP5yZ/ynPvbPPDd7jOT7gJZ6vJW1e4E/zV/a+
++MJfm3LL3KP6Ul6W2+Ueena+uaX/D60SLh4=
+ "]]},
+ "1"],
+ Annotation[#, 1, "Tooltip"]& ],
+ TagBox[
+ TooltipBox[
+ {GrayLevel[0], Opacity[0.4], LineBox[CompressedData["
+1:eJwl1FtMz2EYB/DXaVQqGZtjK4cacxhbTEVTCIUKuSLkHKIIM2eFYWyUyZmc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+ "]]},
+ "0"],
+ Annotation[#, 0, "Tooltip"]& ],
+ TagBox[
+ TooltipBox[
+ {GrayLevel[0], Opacity[0.4], LineBox[CompressedData["
+1:eJwl1FdsjmEYxvFX1TiwWyWxWiItalcpKsQoEqO1RxwghAoSKzUjsVpdHIjR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+ "]]},
+ RowBox[{"-", "1"}]],
+ Annotation[#, -1, "Tooltip"]& ],
+ TagBox[
+ TooltipBox[
+ {GrayLevel[0], Opacity[0.4], LineBox[CompressedData["
+1:eJwl099PzXEcx/FPNimrk5DNzxzGjfnxH7jAZhipLkQu2CpDHTbkwlzY3HCJ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+ "]]},
+ RowBox[{"-", "2"}]],
+ Annotation[#, -2, "Tooltip"]& ],
+ TagBox[
+ TooltipBox[
+ {GrayLevel[0], Opacity[0.4], LineBox[CompressedData["
+1:eJwl0jtPlEEUh/GxMpE7NWhoEFSinUThA0BphQ0oCCIiqBUKEdwlyMUSRay0
+gN1lSZRoDFC5XFxCYvwSgoIRvFGIEfhtKJ48c/4z58zkzVvS2Hmp40gI4QWS
+OSHczw3hHsoKQ1hXn+QvXM4b2SFs5Ycwrf5doMf6Jbqd78FX+SrXoBan9ZzC
+MWdG80J4gnpcQQMWzLvOrbiGFjTjKSL6oqjAprln+Bt3c7HZx80s4gTH8c97
+3tn/Y72DGXvb6k9ch8uZHiT1n+B5e3t65nifz8nPYtzdUe/66cwP3FK3YwR3
+cBcduI1OPMeQ8/l602bl8Qon9Max7C1LWMQHea79LHkOL6vfy1NYwKQ8hiV5
+lv1FzuZB83fkEd7mLVS7twofZRf4Ir7Lx3hYz0P5M+sH3G72TbThsZn9zkUx
+o36NV5iV//cdjspX+JE6zQPcK+vDW+u/sje8yz1mx9Cq/wauuq8JjUjJz3Ml
+Pustznwn7+qST2DNjFL1FP8qOPz3DgAg+GMt
+ "]]},
+ RowBox[{"-", "3"}]],
+ Annotation[#, -3, "Tooltip"]& ], {}, {}}}],
+ AspectRatio->1,
+ Frame->True,
+ FrameLabel->{
+ FormBox[
+ "\"\\!\\(\\*SubscriptBox[\\(k\\), \\(x\\)]\\)\"", TraditionalForm],
+ FormBox[
+ "\"\\!\\(\\*SubscriptBox[\\(k\\), \\(y\\)]\\)\"", TraditionalForm]},
+ FrameTicks->{{{
+ NCache[-Pi, -3.141592653589793],
+ FormBox[
+ RowBox[{"-", "\[Pi]"}], TraditionalForm]}, {
+ NCache[Rational[-1, 2] Pi, -1.5707963267948966`],
+ FormBox[
+ RowBox[{"-",
+ FractionBox["\[Pi]", "2"]}], TraditionalForm]}, {0,
+ FormBox["0", TraditionalForm]}, {
+ NCache[Rational[1, 2] Pi, 1.5707963267948966`],
+ FormBox[
+ FractionBox["\[Pi]", "2"], TraditionalForm]}, {
+ NCache[Pi, 3.141592653589793],
+ FormBox["\[Pi]", TraditionalForm]}}, {{
+ NCache[-Pi, -3.141592653589793],
+ FormBox[
+ RowBox[{"-", "\[Pi]"}], TraditionalForm]}, {
+ NCache[Rational[-1, 2] Pi, -1.5707963267948966`],
+ FormBox[
+ RowBox[{"-",
+ FractionBox["\[Pi]", "2"]}], TraditionalForm]}, {0,
+ FormBox["0", TraditionalForm]}, {
+ NCache[Rational[1, 2] Pi, 1.5707963267948966`],
+ FormBox[
+ FractionBox["\[Pi]", "2"], TraditionalForm]}, {
+ NCache[Pi, 3.141592653589793],
+ FormBox["\[Pi]", TraditionalForm]}}},
+ PlotRange->
+ NCache[{{-Pi, Pi}, {-Pi, Pi}}, {{-3.141592653589793,
+ 3.141592653589793}, {-3.141592653589793, 3.141592653589793}}],
+ PlotRangeClipping->True,
+ PlotRangePadding->{
+ Scaled[0.02],
+ Scaled[0.02]}]], "Output",
+ CellChangeTimes->{{3.6036930100783863`*^9, 3.6036930408832607`*^9},
+ 3.603693201247554*^9, 3.6036932551432533`*^9, 3.603693287881331*^9, {
+ 3.6036933651562653`*^9, 3.603693379271288*^9}, {3.603693411824589*^9,
+ 3.603693417017581*^9}, {3.60369381980022*^9, 3.603693832337619*^9}, {
+ 3.604372727053968*^9, 3.604372747249778*^9}}]
+}, Open ]],
+
+Cell[BoxData[{
+ RowBox[{
+ RowBox[{"Export", "[",
+ RowBox[{"\"\<tightBinding3D.pdf\>\"", ",", "tightBinding3D"}], "]"}],
+ ";"}], "\[IndentingNewLine]",
+ RowBox[{
+ RowBox[{"Export", "[",
+ RowBox[{"\"\<tightBindingContour.pdf\>\"", ",", "tightBindingContour"}],
+ "]"}], ";"}]}], "Input",
+ CellChangeTimes->{{3.603693290438525*^9, 3.6036933278694*^9}, {
+ 3.6036933742679167`*^9, 3.60369337622892*^9}}]
+},
+WindowSize->{740, 867},
+WindowMargins->{{4, Automatic}, {Automatic, 4}},
+FrontEndVersion->"8.0 for Mac OS X x86 (32-bit, 64-bit Kernel) (October 5, \
+2011)",
+StyleDefinitions->"Default.nb"
+]
+(* End of Notebook Content *)
+
+(* Internal cache information *)
+(*CellTagsOutline
+CellTagsIndex->{}
+*)
+(*CellTagsIndex
+CellTagsIndex->{}
+*)
+(*NotebookFileOutline
+Notebook[{
+Cell[557, 20, 191, 4, 27, "Input"],
+Cell[CellGroupData[{
+Cell[773, 28, 1639, 42, 53, "Input"],
+Cell[2415, 72, 170255, 2813, 297, 93340, 1552, "CachedBoxData", "BoxData", \
+"Output"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[172707, 2890, 1478, 40, 53, "Input"],
+Cell[174188, 2932, 102563, 1736, 386, "Output"]
+}, Open ]],
+Cell[276766, 4671, 412, 10, 43, "Input"]
+}
+]
+*)
+
+(* End of internal cache information *)