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It defines the Pauli matrices and provides \ tools to visualize pure and mixed states of a qubit. This package is part of \ the VQM packages which can be obtained here: ", ButtonBox["http://www.uni-graz.at/imawww/vqm/software.html", ButtonData:>{ URL[ "http://www.uni-graz.at/imawww/vqm/software.html"], None}, ButtonStyle->"Hyperlink"], " (free download). The VQM packages are part of the Visual Quantum \ Mechanics project, see ", ButtonBox["http://www.uni-graz.at/imawww/vqm/", ButtonData:>{ URL[ "http://www.uni-graz.at/imawww/vqm/"], None}, ButtonStyle->"Hyperlink"], ". In particular, these packages are distributed with the book ", StyleBox["Advanced Visual Quantum Mechanics", FontSlant->"Italic"], ", Springer-Verlag New York, 2004." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Load package", "Section"], Cell["<"Italic"], " or in other third-party packages." }], "Text"], Cell[TextData[{ "The package also defines ", StyleBox["QSpinBasis", "InlineInput"], " as a default basis for some basis-dependent commands. It is initially \ equal to ", StyleBox["$QSpinBasis", "InlineInput"], ", but can be changed with the command ", StyleBox["QSetSpinBasis[{", "InlineInput"], "basespinor1", StyleBox[",", "InlineInput"], "basespinor2", StyleBox["}]", "InlineInput"], ". This influences how the components of spinors are calculated." }], "Text"], Cell[CellGroupData[{ Cell["\<\ QSetSpinBasis[QxBasis]; QSpinBasis\ \>", "Input"], Cell[BoxData[ \({{1\/\@2, 1\/\@2}, {\(-\(1\/\@2\)\), 1\/\@2}}\)], "Output"] }, Open ]], Cell[TextData[{ "An example of an operation that depends on the chosen basis is the \ calculation of the components of a spinor with respect to that basis. This is \ done with the command ", StyleBox["QSpinorToComponents", "InlineInput"], ". The spinor psi is given with respect to the reference basis ", StyleBox["$QSpinBasis", "InlineInput"], ". ", StyleBox["QSpinorToComponents[", "InlineInput"], "psi", StyleBox["]", "InlineInput"], " calculates the components of psi with respect to the basis ", StyleBox["QSpinBasis", "InlineInput"], ". This gives the components of the spinor {1,0} with respect to the \ previously set ", StyleBox["QSpinBasis", "InlineInput"], ":" }], "Text"], Cell[CellGroupData[{ Cell["components = QSpinorToComponents[{1,0}]", "Input"], Cell[BoxData[ \({1\/\@2, \(-\(1\/\@2\)\)}\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["components.QSpinBasis", "InlineInput"], " returns the original spinor. More generally, ", StyleBox["QComponentsToSpinor", "InlineInput"], " takes two complex coefficients and forms the corresponding linear \ combination of the basis vectors in ", StyleBox["QSpinBasis", "InlineInput"], ". The result is the spinor in the canonical standard basis." }], "Text"], Cell[CellGroupData[{ Cell["QComponentsToSpinor[components]", "Input"], Cell[BoxData[ \({1, 0}\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["QProjectUp[", "InlineInput"], "psi", StyleBox["]", "InlineInput"], " projects a spinor psi into the direction of the first basis vector of ", StyleBox["QSpinBasis", "InlineInput"], ", " }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(QProjectUp[{1, 0}]\)], "Input"], Cell[BoxData[ \({1\/2, 1\/2}\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["QProjectDown[", "InlineInput"], "psi", StyleBox["]", "InlineInput"], " gives the part proportional to the second basis vector. The sum of the \ two projections is the identity, that is," }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(sp\ = \ {1, I};\)\), "\[IndentingNewLine]", \(QProjectUp[sp] + QProjectDown[sp]\ \[Equal] \ sp\)}], "Input"], Cell[BoxData[ \(True\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["QProbabilityUp[", "InlineInput"], "psi", StyleBox["]", "InlineInput"], " gives the probability that the spinor has spin-up with respect to the ", StyleBox["QSpinBasis", "InlineInput"], ", ", StyleBox["QProbabilityDown[", "InlineInput"], "psi", StyleBox["]", "InlineInput"], " gives the probability for spin down." }], "Text"], Cell["\<\ A natural method for the visualization of a spinor is to represent \ its components with respect to a basis by a bar diagram. 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00?o0000omWIfOoIfMT04ooIfMV6oono00oofMWIQ_l0oclFomWIf@03o`000?oIfMWofMWI007ofMWI 000MomWIf@03o`000?oIfMWofMWI01?ofMWIQ_oo_`0?omWIfHKo0?lo5_oIfMT00ol0003ofMWIomWI f@01omWIf@007OoIfMT00ol0003ofMWIomWIf@0ComWIfHKookl03ooIfMV6o`3o?aKofMWI00?o0000 omWIfOoIfMT00OoIfMT001gofMWI00?o0000omWIfOoIfMT04ooIfMV6oono00oofMWIQ_l0oclFomWI f@03o`000?oIfMWofMWI007ofMWI000MomWIf@03o`000?oIfMWofMWI01?ofMWIQ_oo_`0?omWIfHKo 0?lo5_oIfMT00ol0003ofMWIomWIf@01omWIf@004_oIfMT4o`000003o`h>3_oIfMWofMWI00CofMWI 00?o0000omWIfOoIfMT04ooIfMV6oono00oofMWIQ_l0oclFomWIf@03o`000?oIfMWofMWI007ofMWI 000DomWIf@03o`000?oIfMWofMWI00KofMWI00?o0000omWIfOoIfMT04ooIfMV6oono00oofMWIQ_l0 oclFomWIf@03o`000?oIfMWofMWI007ofMWI000DomWIf@03o`000?oIfMWofMWI00KofMWI00?o0000 omWIfOoIfMT04ooIfMV6oono00oofMWIQ_l0oclFomWIf@03o`000?oIfMWofMWI007ofMWI000DomWI f@03o`000?oIfMWofMWI00KofMWI0ol0000;omWIfOoo0000;?l0000"], ImageRangeCache->{{{0, 359}, {221.375, 0}} -> {-0.295379, -0.213261, \ 0.00840207, 0.00741536}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell["You can compute the norm of a spinor with", "Text"], Cell[CellGroupData[{ Cell["Norm[{2,-I}]", "Input"], Cell[BoxData[ \(\@5\)], "Output"] }, Open ]], Cell[TextData[{ "and ", StyleBox["QNormalize", "InlineInput"], " returns a spinor with norm 1" }], "Text"], Cell[CellGroupData[{ Cell["QNormalize[{2,-I}]", "Input"], Cell[BoxData[ \({2\/\@5, \(-\(\[ImaginaryI]\/\@5\)\)}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["Norm[%]", "Input"], Cell[BoxData[ \(1\)], "Output"] }, Open ]], Cell[TextData[{ " The function ", StyleBox["QNormalize", "InlineInput"], " can also be used to normalize arbitrary vectors" }], "Text"], Cell[CellGroupData[{ Cell["QNormalize[{1,2,3}]", "Input"], Cell[BoxData[ \({1\/\@14, \@\(2\/7\), 3\/\@14}\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Some matrices", "Section"], Cell[TextData[{ "The package \"", StyleBox["VQM`Spinors", "InlineInput"], "\" also defines the some important operators. First of all, we have the \ Pauli spin matrices ", StyleBox["QPauliSigma1", "InlineInput"], ", ", StyleBox["QPauliSigma2", "InlineInput"], ", and ", StyleBox["QPauliSigma3", "InlineInput"], ". Moreover, ", StyleBox["QPauliSigmaV", "InlineInput"], " is a vector with the three Pauli matrices as components" }], "Text"], Cell[CellGroupData[{ Cell["QPauliSigma2//MatrixForm", "Input"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"0", \(-\[ImaginaryI]\)}, {"\[ImaginaryI]", "0"} }, RowSpacings->1, ColumnSpacings->1, ColumnAlignments->{Left}], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["QPauliSigmaV", "Input"], Cell[BoxData[ \({{{0, 1}, {1, 0}}, {{0, \(-\[ImaginaryI]\)}, {\[ImaginaryI], 0}}, {{1, 0}, {0, \(-1\)}}}\)], "Output"] }, Open ]], Cell[TextData[{ "The two-by-two identity matrix is ", StyleBox["QIdentity2", "InlineInput"], ". The Pauli sigma matrices are the quantum-mechanical observables for the \ spin measured with respect to the x-, y-, and z-axis of the reference \ coordinate system in ", Cell[BoxData[ \(TraditionalForm\`\[DoubleStruckCapitalR]\^3\)]], ". The spin-observable with respect to an arbitrary axis (represented by a \ vector ", StyleBox["kv", "InlineInput"], ") is ", StyleBox["QSpinHamiltonian[kv]", "InlineInput"], ". This matrix is obtained as\n ", StyleBox["QPauliSigma1.kv[[1]]+QPauliSigma2.kv[[2]]+QPauliSigma3.kv[[3]]", "InlineInput"] }], "Text"], Cell["This is a three-dimensional vector with symbolic components", "Text"], Cell["\<\ Clear[k0, k1, k2, k3, kv]; kv = {k1,k2,k3};\ \>", "Input"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"hs", "=", StyleBox[\(QSpinHamiltonian[kv]\), "InlineInput"]}]], "Input"], Cell[BoxData[ \({{k3, k1 - \[ImaginaryI]\ k2}, {k1 + \[ImaginaryI]\ k2, \(-k3\)}}\)], \ "Output"] }, Open ]], Cell[TextData[{ "A density matrix is a hermitian matrix with trace 1. It is also determined \ by a vector in ", Cell[BoxData[ \(TraditionalForm\`\[DoubleStruckCapitalR]\^3\)]], ":" }], "Text"], Cell[TextData[{ "This is the density matrix describing spin in the direction of ", StyleBox["kv", "InlineInput"] }], "Text"], Cell[CellGroupData[{ Cell["ma = QVectorToDensityMatrix[kv]", "Input"], Cell[BoxData[ \({{\(1 + k3\)\/2, 1\/2\ \((k1 - \[ImaginaryI]\ k2)\)}, {1\/2\ \((k1 + \[ImaginaryI]\ \ k2)\), \(1 - k3\)\/2}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(ma // MatrixForm\)], "Input"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {\(\(1 + k3\)\/2\), \(1\/2\ \((k1 - \[ImaginaryI]\ k2)\)\)}, {\(1\/2\ \((k1 + \[ImaginaryI]\ k2)\)\), \(\(1 - k3\)\/2\)} }, RowSpacings->1, ColumnSpacings->1, ColumnAlignments->{Left}], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output"] }, Open ]], Cell["\<\ A four-vector {k0,k1,k2,k3} can be converted into a Hermitian \ matrix by:\ \>", "Text"], Cell[CellGroupData[{ Cell["QVectorToHermitianMatrix[{k0,k1,k2,k3}]", "Input"], Cell[BoxData[ \({{k0 + k3, k1 - \[ImaginaryI]\ k2}, {k1 + \[ImaginaryI]\ k2, k0 - k3}}\)], "Output"] }, Open ]], Cell["and a three-vector {k1,k2,k3} by", "Text"], Cell[CellGroupData[{ Cell["QVectorToHermitianMatrix[{k1,k2,k3}]", "Input"], Cell[BoxData[ \({{k3, k1 - \[ImaginaryI]\ k2}, {k1 + \[ImaginaryI]\ k2, \(-k3\)}}\)], \ "Output"] }, Open ]], Cell["which is the same as QSpinHamiltonian[{k1,k2,k3}]", "Text"], Cell["\<\ There is also an inverse operation which determines the vector from \ a Hermitian matrix:\ \>", "Text"], Cell[TextData[{ StyleBox["QHermitianMatrixToVector", "InlineInput"], " is inverse to ", StyleBox["QVectorToHermitianMatrix", "InlineInput"], ":" }], "Text"], Cell[TextData[{ StyleBox["QDensityMatrixToVector", "InlineInput"], " is inverse to ", StyleBox["QVectorToDensityMatrix", "InlineInput"], ":" }], "Text"], Cell[CellGroupData[{ Cell["\<\ QHermitianMatrixToVector[QVectorToHermitianMatrix[{k0,k1,k2,k3}]] \ // Simplify\ \>", "Input"], Cell[BoxData[ \({k0, k1, k2, k3}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ QDensityMatrixToVector[QVectorToDensityMatrix[{k1,k2,k3}]] // \ Simplify\ \>", "Input"], Cell[BoxData[ \({k1, k2, k3}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ ma == QVectorToDensityMatrix[QDensityMatrixToVector[ma]] //Simplify\ \ \>", "Input"], Cell[BoxData[ \(True\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["The spinors QSpinorUp and QSpinorDown", "Section"], Cell[TextData[{ "The package defines two basis spinors for each direction in ", Cell[BoxData[ \(TraditionalForm\`\[DoubleStruckCapitalR]\^3\)]], ". These spinors are ", StyleBox["QSpinorUp[", "InlineInput"], "vector", StyleBox["]", "InlineInput"], " and ", StyleBox["QSpinorDown[", "InlineInput"], "vector", StyleBox["]", "InlineInput"], ". Here 'vector ' defines the direction. These spinors are eigenvectors of \ the matrix ", StyleBox["QVectorToMatrix[", "InlineInput"], "vector", StyleBox["]", "InlineInput"], "." }], "Text"], Cell["Clear[k1, k2, k3, kv]; kv = {k1,k2,k3};", "Input"], Cell[CellGroupData[{ Cell["\<\ QVectorToDensityMatrix[kv].QSpinorUp[kv] == Sqrt[kv.kv] \ QSpinorUp[kv]//Simplify\ \>", "Input"], Cell[BoxData[ \({\(-\(\(k1\^2 + k2\^2 + \((\(-1\) + k3)\)\ \((k3 + \@\(k1\^2 + k2\^2 + k3\^2\))\)\)\/\(2\ \ \@2\ \@\(k1\^2 + k2\^2 + k3\ \((k3 + \@\(k1\^2 + k2\^2 + k3\^2\))\)\)\)\)\), \ \(-\(\(\((k1 + \[ImaginaryI]\ k2)\)\ \((\(-1\) + \@\(k1\^2 + k2\^2 + k3\^2\))\ \)\)\/\(2\ \@2\ \@\(k1\^2 + k2\^2 + k3\ \((k3 + \@\(k1\^2 + k2\^2 + \ k3\^2\))\)\)\)\)\)} \[Equal] {0, 0}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ QVectorToHermitianMatrix[kv].QSpinorDown[kv] == -Sqrt[kv.kv] \ QSpinorDown[kv]//Simplify\ \>", "Input"], Cell[BoxData[ \(True\)], "Output"] }, Open ]], Cell[TextData[{ "Hence, for example, ", StyleBox["QSpinorUp[", "InlineInput"], "vector", StyleBox["]", "InlineInput"], " is the state with spin-up in the direction of 'vector'. The two spinors \ form an orthonormal basis in ", Cell[BoxData[ \(TraditionalForm\`\[DoubleStruckCapitalC]\^2\)]], ". For example," }], "Text"], Cell[CellGroupData[{ Cell["QConjSpinorUp[kv].QSpinorUp[kv]//Simplify", "Input"], Cell[BoxData[ \(1\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["QConjSpinorDown[kv].QSpinorUp[kv]//Simplify", "Input"], Cell[BoxData[ \(0\)], "Output"] }, Open ]], Cell[TextData[{ "The conjugate comples spinors ", StyleBox["QConjSpinorUp[kv]", "InlineInput"], " and ", StyleBox["QConjSpinorDown[kv]", "InlineInput"], " have been defined for convenience." }], "Text"], Cell[TextData[{ "We also note that ", StyleBox["QSpinorUp[kv]", "InlineInput"], " has a phase discontinuity on the negative z-axis, and ", StyleBox["QSpinorDown", "InlineInput"], StyleBox["[kv]", "InlineInput"], " has a phase discontinuity on the positive z-axis." }], "Text"], Cell[CellGroupData[{ Cell["QSpinorUp[{0,0,-1}]", "Input"], Cell[BoxData[ \({0, 1}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["Limit[QSpinorUp[{eps,0,-1}],eps->0]", "Input"], Cell[BoxData[ \({0, 1}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["Limit[QSpinorUp[{-eps,0,-1}],eps->0]", "Input"], Cell[BoxData[ \({0, \(-1\)}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["Limit[QSpinorUp[{0,eps,-1}],eps->0]", "Input"], Cell[BoxData[ \({0, \[ImaginaryI]}\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Spinors and Vectors", "Section"], Cell["Consider the unit vector in three-dimensional space", "Text"], Cell[CellGroupData[{ Cell["vec = {-4/9,8/9,-1/9}", "Input"], Cell[BoxData[ \({\(-\(4\/9\)\), 8\/9, \(-\(1\/9\)\)}\)], "Output"] }, Open ]], Cell["\<\ It defines a direction in space. The state which is \"spin-up\" \ with respect to this direction is\ \>", "Text"], Cell[CellGroupData[{ Cell["sp = QSpinorUp[vec]", "Input"], Cell[BoxData[ \({2\/3, \(-\(1\/3\)\) + \(2\ \[ImaginaryI]\)\/3}\)], "Output"] }, Open ]], Cell["We can convert this spinor back to the vector", "Text"], Cell[CellGroupData[{ Cell["QSpinorToVector[sp]", "Input"], Cell[BoxData[ \({\(-\(4\/9\)\), 8\/9, \(-\(1\/9\)\)}\)], "Output"] }, Open ]], Cell[TextData[{ "The norm (length) of the three-dimensional real vector ", StyleBox["QSpinorToVector[", "InlineInput"], "spinor", StyleBox["]", "InlineInput"], " is equal to ", StyleBox["Norm[", "InlineInput"], "spinor", StyleBox["]^2", "InlineInput"], ", that is" }], "Text"], Cell[CellGroupData[{ Cell["Norm[QSpinorToVector[{3,2}]] == Norm[{3,2}]^2", "Input"], Cell[BoxData[ \(True\)], "Output"] }, Open ]], Cell[TextData[{ "The command ", StyleBox["QSpinorToVector", "InlineInput"], " accepts the option ", StyleBox["QVectorLength", "InlineInput"] }], "Text"], Cell[TextData[{ StyleBox["QSpinorToVector[psi, QVectorLength->", "InlineInput"], "n", StyleBox["]", "InlineInput"], " with", StyleBox["\n", "Input"], "n=1\t\t\tgenerates a unit vector\nn=2\t\t\tgenerates a vector with norm \ Norm[psi]^2 (default)\nn=3\t\t\tgenerates a vector with norm Norm[psi]" }], "Text"], Cell["\<\ There is also an inverse command QVectorToSpinor that accepts the \ same option.\ \>", "Text"], Cell[TextData[{ StyleBox["QVectorToSpinor[vec, QVectorLength->", "InlineInput"], "n", StyleBox["]", "InlineInput"], " with the option", StyleBox["\n", "Input"], "n=1\t\t\tgenerates a unit spinor\nn=2\t\t\tgenerates a vector with norm \ Norm[vec]^1/2 (default)\nn=3\t\t\tgenerates a vector with norm Norm[vec]" }], "Text"], Cell[TextData[{ "We have ", StyleBox["QVectorToSpinor[", "InlineInput"], "vec", StyleBox[", QVectorLength->1] == QSpinorUp[", "InlineInput"], "vec", StyleBox["]", "InlineInput"], "." }], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["QExtractPhase", "Section"], Cell["\<\ Note that the relation between spinors and vectors is not \ one-to-one. Here is another normalized spinor that gives the same vector than \ the spinor sp above:\ \>", "Text"], Cell[CellGroupData[{ Cell["sp2 = {2/3,2 I/3-1/3}", "Input"], Cell[BoxData[ \({2\/3, \(-\(1\/3\)\) + \(2\ \[ImaginaryI]\)\/3}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["QSpinorToVector[sp2]", "Input"], Cell[BoxData[ \({\(-\(4\/9\)\), 8\/9, \(-\(1\/9\)\)}\)], "Output"] }, Open ]], Cell["\<\ Generally, two spinors differing by a phase, sp1=Exp[I phi] sp2, \ lead to the same vector. \ \>", "Text"], Cell[TextData[{ StyleBox["QExtractPhase[", "InlineInput"], "psi", StyleBox["]", "InlineInput"], " returns a real number for any nonzero psi={z1,z2}. This number is a phase \ determined from comparison with ", StyleBox["QSpinorUp", "InlineInput"], ", where ", StyleBox["QSpinorUp", "InlineInput"], " is taken with respect to the spin-up direction defined by psi. Let us \ illustrate this with an example:" }], "Text"], Cell[CellGroupData[{ Cell["psi = QNormalize[{-2 I,1}]", "Input"], Cell[BoxData[ \({\(-\(\(2\ \[ImaginaryI]\)\/\@5\)\), 1\/\@5}\)], "Output"] }, Open ]], Cell["This spinor has the spin-up direction (unit vector)", "Text"], Cell[CellGroupData[{ Cell["dir = QSpinorToVector[psi]", "Input"], Cell[BoxData[ \({0, 4\/5, 3\/5}\)], "Output"] }, Open ]], Cell[TextData[{ "Note, however, that ", StyleBox["QSpinorUp[", "InlineInput"], "dir", StyleBox["]", "InlineInput"], " is different from ", StyleBox["psi", "InlineInput"] }], "Text"], Cell[CellGroupData[{ Cell["QSpinorUp[dir]", "Input"], Cell[BoxData[ \({2\/\@5, \[ImaginaryI]\/\@5}\)], "Output"] }, Open ]], Cell[TextData[{ "but the difference is only a phase factor. The phase can be obtained with \ ", StyleBox["QExtractPhase", "InlineInput"], ":" }], "Text"], Cell[CellGroupData[{ Cell["ph = QExtractPhase[psi]", "Input"], Cell[BoxData[ \(\(-\(\[Pi]\/2\)\)\)], "Output"] }, Open ]], Cell[TextData[{ "psi can now be recovered by multiplying ", StyleBox["QSpinorUp[", "InlineInput"], "dir", StyleBox["]", "InlineInput"], " with the appropriate phase factor" }], "Text"], Cell[CellGroupData[{ Cell["Exp[I ph] QSpinorUp[dir]", "Input"], Cell[BoxData[ \({\(-\(\(2\ \[ImaginaryI]\)\/\@5\)\), 1\/\@5}\)], "Output"] }, Open ]], Cell["\<\ Any spinor psi is thus uniquely determined by a three-dimensional \ vector together with phase factor.\ \>", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Rotations", "Section"], Cell[TextData[{ StyleBox["QRotationSO3[", "InlineInput"], "vector", StyleBox["]", "InlineInput"], " and ", StyleBox["QRotationSU2[", "InlineInput"], "vector", StyleBox["]", "InlineInput"], " define rotations around the axis given by vector through an angle given \ by ", StyleBox["Norm[", "InlineInput"], "vector", StyleBox["]", "InlineInput"], ". The matrix ", StyleBox["QRotationSO3[", "InlineInput"], "vector", StyleBox["]", "InlineInput"], " is an orthogonal 3x3-matrix. ", StyleBox["QRotationSU2[", "InlineInput"], "vector", StyleBox["]", "InlineInput"], " is a unitary 2x2 matrix realizing the 'spinor representation' of the \ rotation group." }], "Text"], Cell["For example,", "Text"], Cell[CellGroupData[{ Cell["QRotationSU2[{2 Pi,0,0}]//MatrixForm", "Input"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {\(-1\), "0"}, {"0", \(-1\)} }, RowSpacings->1, ColumnSpacings->1, ColumnAlignments->{Left}], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["QRotationSU2[{1,1,1}]//MatrixForm", "Input"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {\(Cos[\@3\/2] - \(\[ImaginaryI]\ Sin[\@3\/2]\)\/\@3\), \ \(-\(\(\((1 + \[ImaginaryI])\)\ Sin[\@3\/2]\)\/\@3\)\)}, {\(\(\((1 - \[ImaginaryI])\)\ Sin[\@3\/2]\)\/\@3\), \(Cos[\@3\/2] \ + \(\[ImaginaryI]\ Sin[\@3\/2]\)\/\@3\)} }, RowSpacings->1, ColumnSpacings->1, ColumnAlignments->{Left}], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output"] }, Open ]], Cell["\<\ The textbook-form of the SU(2)-rotation matrix can be obtained as \ follows. Let us first define a unit vector with symbolic components.\ \>", \ "Text"], Cell["\<\ Clear[nv,n1,n2,n3]; nv = {n1,n2,n3}; (* should be a unit vector *)\ \>", "Input"], Cell[CellGroupData[{ Cell["QRotationSU2[phi nv] // Simplify[#,{phi>0,nv.nv==1}]&", "Input"], Cell[BoxData[ \({{Cos[ phi\/2] - \[ImaginaryI]\ n3\ Sin[ phi\/2], \(-\[ImaginaryI]\)\ \((n1 - \[ImaginaryI]\ n2)\)\ Sin[ phi\/2]}, {\((\(-\[ImaginaryI]\)\ n1 + n2)\)\ Sin[phi\/2], Cos[phi\/2] + \[ImaginaryI]\ n3\ Sin[phi\/2]}}\)], "Output"] }, Open ]], Cell["This matrix is the same as the following:", "Text"], Cell[CellGroupData[{ Cell["\<\ MatrixExp[-I phi/2 QVectorToHermitianMatrix[nv]] // ExpToTrig // \ Simplify[#,{phi>0,nv.nv==1}]&\ \>", "Input"], Cell[BoxData[ \({{Cos[ phi\/2] - \[ImaginaryI]\ n3\ Sin[ phi\/2], \(-\[ImaginaryI]\)\ \((n1 - \[ImaginaryI]\ n2)\)\ Sin[ phi\/2]}, {\((\(-\[ImaginaryI]\)\ n1 + n2)\)\ Sin[phi\/2], Cos[phi\/2] + \[ImaginaryI]\ n3\ Sin[phi\/2]}}\)], "Output"] }, Open ]], Cell["\<\ Any unitary 2x2-matrix may be considered a SU(2) rotation. The \ following example shows the connection with a basis transformation\ \>", \ "Text"], Cell[CellGroupData[{ Cell["\<\ Clear[a,b]; T=QRotationSU2[{1,1,1}]; newBasis={T.QzBasis[[1]], T.QzBasis[[2]]}; QSpinorToComponents[{a,b},QUseBasis->newBasis] == Inverse[T].{a,b} // \ Simplify\ \>", "Input"], Cell[BoxData[ \(True\)], "Output"] }, Open ]], Cell["\<\ The connection between rotations in SO(3) and rotations in SU(2) is \ the following:\ \>", "Text"], Cell["\<\ rotV = {1, 0.5, -1}; R = QRotationSO3[rotV]; T = QRotationSU2[rotV];\ \>", "Input"], Cell[CellGroupData[{ Cell["\<\ QVectorToSpinor[ R . {1,0,0} ] == T . \ QVectorToSpinor[{1,0,0}]\ \>", "Input"], Cell[BoxData[ \(True\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ QVectorToHermitianMatrix[ R . {1,0,0} ] == Chop[T . \ QVectorToHermitianMatrix[{1,0,0}] . 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These commands \ are also used by ", StyleBox["VQM`Spinors", "InlineInput"], " for the visualization of spinors and Hermitian matrices.. " }], "Text"], Cell[TextData[{ "The commands ", StyleBox["QVectorToArrow", "InlineInput"], " and ", StyleBox["QSpinorToArrow", "InlineInput"], " return a 3D-graphics primitive describing an arrow whose properties are \ determined by the following options" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Options[QVectorToArrow]\)], "Input"], Cell[BoxData[ \({QArrowHead \[Rule] True, QArrowShaft \[Rule] False, QLinePointSize \[Rule] 0.001`, QMinLength \[Rule] 0.1`, QArrowShape \[Rule] Automatic, QHeadColor \[Rule] GrayLevel[0], QArrowScale \[Rule] 1, QShaftColor \[Rule] GrayLevel[0], QNeedleStyle \[Rule] False}\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["QArrowHead->True", "InlineInput"], " (default) causes the vector to be drawn with an arrow head.", StyleBox[" QArrowHead->Automatic", "InlineInput"], " draws the vector with a point of size ", StyleBox["2*QLinePointSize", "InlineInput"], " instead of the ", StyleBox["QArrowHead", "InlineInput"], ". Otherwise the vector is just represented by a line segment." }], "Text"], Cell[TextData[{ StyleBox["QMinLength", "InlineInput"], StyleBox["->0.1", "InlineInput"], " (default) specifies that vectors of length less than 0.1 are to be drawn \ as points of size QLinePointSize." }], "Text"], Cell[TextData[{ StyleBox["QArrowShape->{", "InlineInput"], StyleBox["n", FontSlant->"Italic"], ",", StyleBox["k", FontSlant->"Italic"], StyleBox["}", "InlineInput"], ": The head of the arrow is a cone with half height ", StyleBox["h", FontSlant->"Italic"], " = ", StyleBox["k", FontSlant->"Italic"], " * ", StyleBox["Norm[", "InlineInput"], "vector", StyleBox["]", "InlineInput"], " and radius ", StyleBox["r ", FontSlant->"Italic"], "= ", StyleBox["h", FontSlant->"Italic"], StyleBox["/(2 GoldenRatio)", "InlineInput"], " drawn using ", StyleBox["n", FontSlant->"Italic"], " polygons. If ", StyleBox["k", FontSlant->"Italic"], " is negative, then ", StyleBox["h", FontSlant->"Italic"], " = -", StyleBox["k", FontSlant->"Italic"], ". Default is (1,1/6)" }], "Text"], Cell[TextData[{ StyleBox["QArrowScale", "InlineInput"], StyleBox["-> ", "InlineInput"], StyleBox["k", FontSlant->"Italic"], " scales the length of the arrow by the factor ", StyleBox["k", FontSlant->"Italic"], "." }], "Text"], Cell[TextData[{ StyleBox["QHeadColor", "InlineInput"], StyleBox["->", "InlineInput"], StyleBox["colordirective", FontSlant->"Italic"], ": The arrow appears in the color specified by colordirective. Turn \ Lighting off to see the effect." }], "Text"], Cell[TextData[{ StyleBox["QLinePointSize", "InlineInput"], StyleBox["->", "InlineInput"], StyleBox["pt", FontSlant->"Italic"], " causes the shaft of the arrow to be drawn with relative pointsize ", StyleBox["pt", FontSlant->"Italic"], ". 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.68876 m .76004 .69289 L s .37705 .37227 m .37699 .36913 L s .75249 .45029 m .7506 .45482 L s .29223 .69267 m .28586 .68853 L s .30192 .45458 m .30005 .45004 L s .56749 .327 m .56845 .32789 L s .48424 .32784 m .4852 .32695 L s .72534 .75351 m .71796 .75678 L s .33427 .75661 m .32689 .75333 L s .64232 .81692 m .63405 .81871 L s .41813 .81862 m .40986 .81682 L s .6256 .3417 m .62622 .34382 L s .777 .50182 m .77407 .50669 L s .56649 .32612 m .56749 .327 L s .42644 .34371 m .42707 .34158 L s .4852 .32695 m .4862 .32607 L s .2784 .50643 m .27548 .50155 L s 0 0 1 r .26686 .56772 m .25882 .55771 L s .5 g .56545 .32527 m .56649 .32612 L s .4862 .32607 m .48724 .32522 L s .78791 .622 m .78271 .62671 L s .26964 .62646 m .26445 .62174 L s .71883 .40242 m .71807 .40639 L s .56437 .32443 m .56545 .32527 L s .67556 .36615 m .67564 .3693 L s .48724 .32522 m .48832 .32439 L s .37699 .36913 m .37708 .36598 L s .33452 .40617 m .33377 .4022 L s .62488 .33958 m .6256 .3417 L s .79056 .55836 m .78656 .56332 L s .42707 .34158 m .42779 .33947 L s .65052 .81499 m .64232 .81692 L s .40986 .81682 m .40167 .81488 L s 0 0 1 r .79489 .55625 m .78698 .56631 L s .5 g .26585 .56305 m .26186 .55808 L s .56325 .32362 m .56437 .32443 L s .48832 .32439 m .48945 .32358 L s .56209 .32284 m .56325 .32362 L s .73258 .75011 m .72534 .75351 L s .48945 .32358 m .49061 .3228 L s .32689 .75333 m .31966 .74992 L s .75415 .44571 m .75249 .45029 L s .77263 .6845 m .76643 .68876 L s .30005 .45004 m .29839 .44546 L s .28586 .68853 m .27967 .68426 L s .56089 .32208 m .56209 .32284 L s .62406 .33748 m .62488 .33958 L s .49061 .3228 m .4918 .32204 L s .42779 .33947 m .42862 .33737 L s .65862 .81293 m .65052 .81499 L s .40167 .81488 m .39357 .81281 L s .55966 .32135 m .56089 .32208 L s .4918 .32204 m .49304 .32131 L s .67533 .363 m .67556 .36615 L s 0 0 1 r .78988 .53117 m .78092 .516 L s .5 g .37708 .36598 m .37732 .36283 L s .77971 .49688 m .777 .50182 L s .27548 .50155 m .27278 .49661 L s .5584 .32064 m .55966 .32135 L s .49304 .32131 m .49431 .3206 L s .71939 .39843 m .71883 .40242 L s .33377 .4022 m .33321 .39821 L s .62314 .3354 m .62406 .33748 L s .5571 .31996 m .5584 .32064 L s .49431 .3206 m .49561 .31993 L s .42862 .33737 m .42955 .33528 L s .79289 .61718 m .78791 .622 L s .26445 .62174 m .25948 .61691 L s .55577 .31931 m .5571 .31996 L s .49561 .31993 m .49694 .31928 L s .66663 .81074 m .65862 .81293 L s .39357 .81281 m .38557 .81061 L s .5544 .31869 m .55577 .31931 L s .49694 .31928 m .4983 .31866 L s .79433 .55331 m .79056 .55836 L s .73965 .74659 m .73258 .75011 L s .31966 .74992 m .31259 .74639 L s .26186 .55808 m .2581 .55303 L s .67495 .35986 m .67533 .363 L s .55301 .3181 m .5544 .31869 L s .4983 .31866 m .4997 .31806 L s .37732 .36283 m .37771 .35968 L s .62212 .33333 m .62314 .3354 L s .42955 .33528 m .43057 .33322 L s .7556 .44109 m .75415 .44571 L s .29839 .44546 m .29696 .44083 L s .55159 .31753 m .55301 .3181 L s .4997 .31806 m .50112 .3175 L s .77863 .68012 m .77263 .6845 L s .27967 .68426 m .27368 .67988 L s .55015 .317 m .55159 .31753 L s .50112 .3175 m .50257 .31697 L s .54868 .3165 m .55015 .317 L s .50257 .31697 m .50404 .31648 L s .71977 .39442 m .71939 .39843 L s .33321 .39821 m .33285 .3942 L s .621 .33129 m .62212 .33333 L s .67453 .80841 m .66663 .81074 L s .54718 .31603 m .54868 .3165 L s .50404 .31648 m .50553 .31601 L s .43057 .33322 m .4317 .33117 L s .38557 .81061 m .37767 .80828 L s .78218 .49187 m .77971 .49688 L s .54566 .3156 m .54718 .31603 L s .50553 .31601 m .50705 .31558 L s .27278 .49661 m .27032 .4916 L s .54413 .3152 m .54566 .3156 L s .67441 .35671 m .67495 .35986 L s .50705 .31558 m .50859 .31518 L s .37771 .35968 m .37825 .35654 L s .54257 .31483 m .54413 .3152 L s .50859 .31518 m .51014 .31481 L s 0 0 1 r .79787 .54666 m .78988 .53117 L s .25882 .55771 m .25173 .54736 L s .5 g .541 .31449 m .54257 .31483 L s .51014 .31481 m .51172 .31447 L s .79764 .61226 m .79289 .61718 L s .74657 .74293 m .73965 .74659 L s .53941 .31419 m .541 .31449 L s .51172 .31447 m .5133 .31418 L s .61978 .32926 m .621 .33129 L s .25948 .61691 m .25473 .61198 L s .31259 .74639 m .30569 .74273 L s .4317 .33117 m .43292 .32915 L s .53781 .31392 m .53941 .31419 L s .5133 .31418 m .51491 .31391 L s .5362 .31369 m .53781 .31392 L s .51491 .31391 m .51652 .31368 L s .53458 .3135 m .5362 .31369 L s .51652 .31368 m .51815 .31349 L s .79786 .54817 m .79433 .55331 L s .53294 .31333 m .53458 .3135 L s .75683 .43642 m .7556 .44109 L s .51815 .31349 m .51978 .31333 L s .68232 .80595 m .67453 .80841 L s .5313 .31321 m .53294 .31333 L s .51978 .31333 m .52142 .3132 L s .37767 .80828 m .36988 .80582 L s .29696 .44083 m .29574 .43617 L s .52966 .31312 m .5313 .31321 L s .52142 .3132 m .52306 .31311 L s .2581 .55303 m .25458 .54789 L s .52801 .31306 m .52966 .31312 L s .52306 .31311 m .52471 .31306 L s .52636 .31304 m .52801 .31306 L s .52471 .31306 m .52636 .31304 L s .71995 .39039 m .71977 .39442 L s .78443 .67563 m .77863 .68012 L s .33285 .3942 m .33268 .39017 L s .61846 .32727 m .61978 .32926 L s .67373 .35358 m .67441 .35671 L s .43292 .32915 m .43424 .32716 L s .27368 .67988 m .26789 .67538 L s .37825 .35654 m .37894 .35341 L s .78442 .48681 m .78218 .49187 L s .27032 .4916 m .2681 .48653 L s .61705 .3253 m .61846 .32727 L s .43424 .32716 m .43566 .32519 L s .69 .80337 m .68232 .80595 L s .75331 .73916 m .74657 .74293 L s .36988 .80582 m .36221 .80322 L s .30569 .74273 m .29896 .73895 L s .67289 .35045 m .67373 .35358 L s .37894 .35341 m .37979 .35028 L s .80217 .60723 m .79764 .61226 L s .25473 .61198 m .25022 .60695 L s .71994 .38635 m .71995 .39039 L s .75784 .43173 m .75683 .43642 L s .61554 .32336 m .61705 .3253 L s .33268 .39017 m .3327 .38613 L s .43566 .32519 m .43717 .32325 L s .29574 .43617 m .29474 .43147 L s .25458 .54789 m .2513 .54267 L s .79001 .67103 m .78443 .67563 L s .26789 .67538 m .26232 .67077 L s .69756 .80065 m .69 .80337 L s .61394 .32145 m .61554 .32336 L s .36221 .80322 m .35466 .8005 L s .43717 .32325 m .43878 .32134 L s .67191 .34734 m .67289 .35045 L s .37979 .35028 m .38078 .34717 L s 0 .667 .167 r .79935 .54978 m .65394 .58788 L .67198 .60442 L closepath p F P 0 g s 0 .667 .167 r .79935 .54978 m .64874 .54993 L .65394 .58788 L closepath p F P 0 g s 0 .667 .167 r .79935 .54978 m .66141 .5275 L .64874 .54993 L closepath p F P 0 g s 0 .667 .167 r .79935 .54978 m .68515 .5824 L .67979 .54342 L closepath p F P 0 g s .5 g .79786 .54817 m .79887 .54658 L s 0 0 1 r .79489 .55625 m .79915 .54987 L s 0 .667 .167 r .79935 .54978 m .67198 .60442 L .68515 .5824 L closepath p F P 0 g s 0 0 1 r .79927 .54981 m .79928 .54983 L s .79928 .54983 m .80488 .56241 L s .4 g .005 w .5631 .62318 m .66477 .73412 L s .5 Mabswid 0 .667 .167 r .79935 .54978 m .67979 .54342 L .66141 .5275 L closepath p F P 0 g s 0 0 1 r .02 w .79935 .54978 Mdot .5 Mabswid .79923 .54976 m .79925 .54973 L s .79922 .54976 m .79923 .54976 L s .79925 .54973 m .80184 .54584 L s .5 g .79887 .54658 m .80115 .54296 L s 0 0 1 r .79787 .54666 m .79925 .54976 L s .79925 .54976 m .79925 .54977 L s .5 g .78642 .48168 m .78442 .48681 L s .75988 .73526 m .75331 .73916 L s .2681 .48653 m .26611 .4814 L s .29896 .73895 m .2924 .73504 L s .61225 .31957 m .61394 .32145 L s .43878 .32134 m .44048 .31947 L s .71974 .38231 m .71994 .38635 L s .3327 .38613 m .33291 .38209 L s .75862 .427 m .75784 .43173 L s .29474 .43147 m .29397 .42674 L s 0 0 1 r .25173 .54736 m .24563 .53668 L s .5 g .53023 .85992 m .52195 .85991 L s .5385 .85979 m .53023 .85992 L s .52195 .85991 m .51368 .85978 L s .80646 .60211 m .80217 .60723 L s .70499 .79781 m .69756 .80065 L s .54676 .85954 m .5385 .85979 L s .51368 .85978 m .50542 .85952 L s .67077 .34425 m .67191 .34734 L s .35466 .8005 m .34724 .79765 L s .61047 .31773 m .61225 .31957 L s .25022 .60695 m .24594 .60183 L s .38078 .34717 m .38193 .34408 L s .44048 .31947 m .44226 .31763 L s .555 .85916 m .54676 .85954 L s .50542 .85952 m .49718 .85913 L s .56323 .85865 m .555 .85916 L s .49718 .85913 m .48895 .85861 L s .8042 .53767 m .80115 .54296 L s .2513 .54267 m .24827 .53738 L s .79538 .66631 m .79001 .67103 L s 0 0 1 r .8078 .53512 m .80184 .54584 L s .5 g .57143 .85801 m .56323 .85865 L s .48895 .85861 m .48076 .85797 L s .26232 .67077 m .25696 .66605 L s .6086 .31593 m .61047 .31773 L s .44226 .31763 m .44414 .31583 L s .57959 .85724 m .57143 .85801 L s .48076 .85797 m .47259 .85719 L s .71934 .37827 m .71974 .38231 L s .76626 .73124 m .75988 .73526 L s .33291 .38209 m .33332 .37804 L s .2924 .73504 m .28603 .73101 L s .66949 .34118 m .67077 .34425 L s .78817 .47651 m .78642 .48168 L s .38193 .34408 m .38322 .34101 L s 0 0 1 r .81085 .57839 m .80488 .56241 L s .5 g .58772 .85635 m .57959 .85724 L s .26611 .4814 m .26438 .47622 L s .47259 .85719 m .46446 .85629 L s .71229 .79485 m .70499 .79781 L s .60663 .31417 m .6086 .31593 L s .34724 .79765 m .33995 .79468 L s .44414 .31583 m .44611 .31407 L s .75918 .42224 m .75862 .427 L s .29397 .42674 m .29343 .42198 L s .4 g .005 w .25961 .66843 m .35813 .63688 L s .5 g .5 Mabswid .59581 .85532 m .58772 .85635 L s .46446 .85629 m .45638 .85527 L s .60459 .31245 m .60663 .31417 L s .44611 .31407 m .44816 .31236 L s .81051 .5969 m .80646 .60211 L s .24594 .60183 m .24191 .59661 L s .60384 .85418 m .59581 .85532 L s .66805 .33813 m .66949 .34118 L s .45638 .85527 m .44835 .85411 L s .38322 .34101 m .38467 .33797 L s .71874 .37422 m .71934 .37827 L s .33332 .37804 m .33393 .374 L s .80699 .53231 m .8042 .53767 L s .80053 .66149 m .79538 .66631 L s .60246 .31077 m .60459 .31245 L s .44816 .31236 m .45029 .31068 L s .24827 .53738 m .2455 .53201 L s .25696 .66605 m .25183 .66122 L s .71944 .79175 m .71229 .79485 L s .33995 .79468 m .3328 .79158 L s .61182 .8529 m .60384 .85418 L s .77245 .7271 m .76626 .73124 L s .44835 .85411 m .44038 .85283 L s .28603 .73101 m .27985 .72687 L s .78967 .47129 m .78817 .47651 L s .60025 .30914 m .60246 .31077 L s .45029 .31068 m .45251 .30906 L s .26438 .47622 m .26289 .471 L s .66646 .33511 m .66805 .33813 L s .7595 .41747 m .75918 .42224 L s .38467 .33797 m .38626 .33495 L s .61973 .8515 m .61182 .8529 L s .44038 .85283 m .43247 .85142 L s .29343 .42198 m .29312 .41721 L s .59796 .30756 m .60025 .30914 L s .45251 .30906 m .4548 .30748 L s .71795 .37018 m .71874 .37422 L s .33393 .374 m .33473 .36996 L s .62758 .84998 m .61973 .8515 L s .43247 .85142 m .42463 .84989 L s .72645 .78854 m .71944 .79175 L s 0 0 1 r .24563 .53668 m .24057 .52572 L s .5 g .3328 .79158 m .32581 .78836 L s .81431 .59159 m .81051 .5969 L s 0 0 1 r .81576 .59452 m .81085 .57839 L s .5 g .59559 .30603 m .59796 .30756 L s .4548 .30748 m .45717 .30595 L s .24191 .59661 m .23812 .5913 L s .66473 .33212 m .66646 .33511 L s .38626 .33495 m .388 .33196 L s .77845 .72285 m .77245 .7271 L s .80545 .65656 m .80053 .66149 L s .80952 .52688 m .80699 .53231 L s .27985 .72687 m .27386 .72261 L s .25183 .66122 m .24692 .65629 L s .2455 .53201 m .24298 .52658 L s .63535 .84833 m .62758 .84998 L s 0 0 1 r .81271 .52413 m .8078 .53512 L s .5 g .59315 .30455 m .59559 .30603 L s .42463 .84989 m .41686 .84824 L s .45717 .30595 m .45962 .30447 L s .7596 .41268 m .7595 .41747 L s .79092 .46602 m .78967 .47129 L s .29312 .41721 m .29304 .41241 L s .26289 .471 m .26165 .46573 L s .59064 .30312 m .59315 .30455 L s .71696 .36616 m .71795 .37018 L s .45962 .30447 m .46213 .30304 L s .33473 .36996 m .33573 .36594 L s .66285 .32917 m .66473 .33212 L s .388 .33196 m .38989 .32901 L s .64304 .84656 m .63535 .84833 L s .7333 .78521 m .72645 .78854 L s .41686 .84824 m .40917 .84646 L s .32581 .78836 m .31896 .78502 L s .58805 .30174 m .59064 .30312 L s .46213 .30304 m .46472 .30167 L s .5854 .30042 m .58805 .30174 L s .46472 .30167 m .46738 .30035 L s .81785 .5862 m .81431 .59159 L s .65064 .84466 m .64304 .84656 L s .66082 .32625 m .66285 .32917 L s .40917 .84646 m .40158 .84456 L s .78424 .71848 m .77845 .72285 L s .23812 .5913 m .23459 .58591 L s .38989 .32901 m .39192 .32609 L s .27386 .72261 m .26808 .71824 L s .81013 .65153 m .80545 .65656 L s .81179 .52138 m .80952 .52688 L s .58269 .29916 m .5854 .30042 L s .71577 .36214 m .71696 .36616 L s .46738 .30035 m .47009 .2991 L s .24692 .65629 m .24225 .65125 L s .75945 .40787 m .7596 .41268 L s .33573 .36594 m .33693 .36192 L s .24298 .52658 m .24072 .52108 L s .29304 .41241 m .29319 .40761 L s .79191 .46072 m .79092 .46602 L s .73999 .78176 m .7333 .78521 L s .57991 .29796 m .58269 .29916 L s .47009 .2991 m .47287 .2979 L s .31896 .78502 m .31228 .78156 L s .26165 .46573 m .26067 .46043 L s .65815 .84265 m .65064 .84466 L s 0 0 1 r .81957 .61076 m .81576 .59452 L s .5 g .40158 .84456 m .39407 .84253 L s .65865 .32338 m .66082 .32625 L s .39192 .32609 m .3941 .32322 L s .57708 .29682 m .57991 .29796 L s .47287 .2979 m .47571 .29676 L s .57419 .29574 m .57708 .29682 L s .47571 .29676 m .47861 .29568 L s .71438 .35815 m .71577 .36214 L s .33693 .36192 m .33833 .35793 L s .66557 .84051 m .65815 .84265 L s .39407 .84253 m .38666 .84039 L s .57124 .29473 m .57419 .29574 L s .47861 .29568 m .48155 .29467 L s .78982 .714 m .78424 .71848 L s 0 0 1 r .24057 .52572 m .23658 .51452 L s .5 g .65634 .32054 m .65865 .32338 L s .26808 .71824 m .26251 .71376 L s .3941 .32322 m .39642 .32039 L s .82113 .58073 m .81785 .5862 L s .75908 .40306 m .75945 .40787 L s 0 .872 .872 r .52632 .58304 m .64874 .54993 L .65394 .58788 L closepath p F P 0 g s 0 .872 .872 r .52632 .58304 m .66141 .5275 L .64874 .54993 L closepath p F P 0 g s .5 g .23459 .58591 m .23133 .58043 L s .29319 .40761 m .29358 .4028 L s .56825 .29377 m .57124 .29473 L s .74652 .77819 m .73999 .78176 L s .48155 .29467 m .48455 .29372 L s .31228 .78156 m .30576 .77799 L s .81457 .64641 m .81013 .65153 L s .8138 .51583 m .81179 .52138 L s .24225 .65125 m .23783 .64612 L s 0 .872 .872 r .52632 .58304 m .65394 .58788 L .67198 .60442 L closepath p F P 0 g s .5 g .24072 .52108 m .23873 .51552 L s .56521 .29289 m .56825 .29377 L s .48455 .29372 m .48759 .29284 L s 0 0 1 r .81654 .51289 m .81271 .52413 L s .5 g .79265 .45538 m .79191 .46072 L s .26067 .46043 m .25995 .45509 L s .67287 .83825 m .66557 .84051 L s .56213 .29207 m .56521 .29289 L s .48759 .29284 m .49067 .29203 L s .38666 .84039 m .37936 .83813 L s .65389 .31776 m .65634 .32054 L s .39642 .32039 m .39888 .31761 L s .7128 .35418 m .71438 .35815 L s .55901 .29132 m .56213 .29207 L s .49067 .29203 m .49379 .29128 L s .33833 .35793 m .33993 .35396 L s .55585 .29064 m .55901 .29132 L s .49379 .29128 m .49695 .2906 L s .55267 .29002 m .55585 .29064 L s .49695 .2906 m .50014 .28999 L s .54945 .28948 m .55267 .29002 L s .50014 .28999 m .50336 .28945 L s .75846 .39825 m .75908 .40306 L s .75287 .7745 m .74652 .77819 L s .79519 .70942 m .78982 .714 L s .68007 .83588 m .67287 .83825 L s .30576 .77799 m .29942 .7743 L s .6513 .31502 m .65389 .31776 L s .29358 .4028 m .29421 .39798 L s .37936 .83813 m .37217 .83575 L s .26251 .71376 m .25715 .70917 L s .39888 .31761 m .40148 .31488 L s .5462 .28901 m .54945 .28948 L s .50336 .28945 m .50661 .28898 L s 0 0 1 r .82226 .62706 m .81957 .61076 L s .5 g .54294 .28861 m .5462 .28901 L s .50661 .28898 m .50987 .28859 L s .82415 .57519 m .82113 .58073 L s .53965 .28828 m .54294 .28861 L s .50987 .28859 m .51316 .28826 L s .23133 .58043 m .22832 .57488 L s .53636 .28802 m .53965 .28828 L s .51316 .28826 m .51646 .28801 L s .81876 .64118 m .81457 .64641 L s .53305 .28784 m .53636 .28802 L s .51646 .28801 m .51977 .28783 L s .71101 .35023 m .7128 .35418 L s .81553 .51022 m .8138 .51583 L s .52973 .28773 m .53305 .28784 L s .51977 .28783 m .52309 .28772 L s .23783 .64612 m .23365 .6409 L s .33993 .35396 m .34172 .35002 L s .52641 .28769 m .52973 .28773 L s .52309 .28772 m .52641 .28769 L s .79312 .45002 m .79265 .45538 L s .23873 .51552 m .23702 .50991 L s .25995 .45509 m .2595 .44972 L s .64858 .31234 m .6513 .31502 L s .40148 .31488 m .40421 .3122 L s .68715 .83339 m .68007 .83588 L s .37217 .83575 m .36509 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.81914 .46403 m .81972 .46988 L s .68991 .85272 m .68391 .85523 L s .23294 .46956 m .23353 .46371 L s .36839 .85509 m .36239 .85258 L s .66619 .30037 m .67055 .30347 L s .38232 .30329 m .38669 .3002 L s .73586 .34662 m .7391 .35112 L s .7608 .7949 m .7556 .79867 L s .3137 .35087 m .31696 .34638 L s .29675 .79847 m .29155 .79469 L s .8381 .5286 m .83739 .53459 L s .78517 .40136 m .78715 .40674 L s .80547 .73184 m .80119 .73654 L s .84263 .59651 m .84064 .60233 L s .26558 .40644 m .26758 .40107 L s .2512 .73629 m .24694 .73158 L s .21519 .53426 m .2145 .52827 L s .21188 .60201 m .20991 .59618 L s .83269 .66385 m .82956 .66926 L s .2229 .66896 m .21978 .66356 L s .66167 .29736 m .66619 .30037 L s .69579 .85011 m .68991 .85272 L s .38669 .3002 m .39122 .2972 L s .36239 .85258 m .35652 .84997 L s .73237 .34219 m .73586 .34662 L s 0 0 1 r .23206 .46804 m .23393 .45624 L s .5 g .31696 .34638 m .32046 .34195 L s .76581 .79104 m .7608 .7949 L s .81826 .45817 m .81914 .46403 L s .29155 .79469 m 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.34641 m .57764 .3475 L s .29228 .52516 m .28849 .5206 L s .67303 .38796 m .67209 .39101 L s .47499 .34744 m .47503 .34635 L s .38049 .39084 m .37956 .38779 L s .7398 .70455 m .73272 .70818 L s .76586 .64018 m .75985 .64444 L s .74372 .4681 m .74102 .47241 L s .31952 .70798 m .31244 .70435 L s .29245 .64421 m .28645 .63995 L s .31146 .47217 m .30877 .46786 L s .62751 .36101 m .62721 .36314 L s .77323 .57763 m .76836 .5822 L s .4254 .36303 m .42511 .36089 L s .57752 .34532 m .57761 .34641 L s 0 0 1 r .77816 .57599 m .76848 .58527 L s .5 g .47503 .34635 m .47512 .34526 L s .68704 .76853 m .67901 .77112 L s .284 .58195 m .27914 .57737 L s .37318 .77098 m .36515 .76838 L s .71321 .42198 m .71154 .42578 L s .57739 .34423 m .57752 .34532 L s .34099 .42557 m .33934 .42177 L s .47512 .34526 m .47526 .34417 L s 0 0 1 r .74875 .47285 m .7364 .4594 L s .5 g .6277 .35886 m .62751 .36101 L s .67383 .38489 m .67303 .38796 L s .42511 .36089 m .42492 .35875 L s .5772 .34314 m .57739 .34423 L s .37956 .38779 m .37876 .38472 L s .47526 .34417 m .47544 .34308 L s .57696 .34205 m .5772 .34314 L s .47544 .34308 m .47569 .34199 L s .69497 .76579 m .68704 .76853 L s .36515 .76838 m .35724 .76564 L s .76753 .51621 m .76394 .52085 L s .74672 .70079 m .7398 .70455 L s .31244 .70435 m .30553 .70058 L s .28849 .5206 m .28491 .51595 L s .74622 .46373 m .74372 .4681 L s .62779 .35671 m .6277 .35886 L s .42492 .35875 m .42483 .3566 L s .30877 .46786 m .30628 .46349 L s .57667 .34097 m .57696 .34205 L s .77168 .63581 m .76586 .64018 L s .47569 .34199 m .47598 .34092 L s .53047 .82952 m .52168 .82952 L s .53927 .82938 m .53047 .82952 L s .52168 .82952 m .51288 .82937 L s .28645 .63995 m .28064 .63557 L s .54805 .82911 m .53927 .82938 L s .51288 .82937 m .5041 .82909 L s .7147 .41813 m .71321 .42198 L s .33934 .42177 m .33786 .41792 L s .77789 .57295 m .77323 .57763 L s .67448 .3818 m .67383 .38489 L s .55682 .82869 m .54805 .82911 L s .5041 .82909 m .49533 .82867 L s .37876 .38472 m .37812 .38163 L s .27914 .57737 m .27449 .5727 L s .57633 .3399 m .57667 .34097 L s .47598 .34092 m .47632 .33984 L s .56557 .82814 m .55682 .82869 L s .49533 .82867 m .48658 .8281 L s .62779 .35456 m .62779 .35671 L s .42483 .3566 m .42485 .35444 L s .57429 .82744 m .56557 .82814 L s .57594 .33884 m .57633 .3399 L s 0 0 1 r .76032 .48679 m .74875 .47285 L s .5 g .48658 .8281 m .47786 .8274 L s .47632 .33984 m .47671 .33878 L s .70276 .76292 m .69497 .76579 L s .35724 .76564 m .34945 .76276 L s .58298 .82661 m .57429 .82744 L s .47786 .8274 m .46918 .82656 L s .5755 .33778 m .57594 .33884 L s .47671 .33878 m .47715 .33772 L s .75347 .6969 m .74672 .70079 L s .67499 .37869 m .67448 .3818 L s .62768 .35241 m .62779 .35456 L s .37812 .38163 m .37761 .37852 L s .59163 .82564 m .58298 .82661 L s .42485 .35444 m .42496 .35229 L s .30553 .70058 m .2988 .69669 L s .46918 .82656 m .46053 .82558 L s .57501 .33673 m .5755 .33778 L s .74851 .45931 m .74622 .46373 L s .47715 .33772 m .47765 .33667 L s .77091 .51149 m .76753 .51621 L s .716 .41425 m .7147 .41813 L s .30628 .46349 m .304 .45906 L s .28491 .51595 m .28154 .51123 L s .33786 .41792 m .33656 .41404 L s 0 0 1 r .27581 .57735 m .26686 .56772 L s .5 g .77729 .63132 m .77168 .63581 L s .57447 .33569 m .57501 .33673 L s .47765 .33667 m .47819 .33564 L s .28064 .63557 m .27504 .63107 L s .60023 .82453 m .59163 .82564 L s .46053 .82558 m .45193 .82446 L s .78234 .56818 m .77789 .57295 L s .62746 .35026 m .62768 .35241 L s 0 0 1 r .78698 .56631 m .77816 .57599 L s .5 g .71043 .75992 m .70276 .76292 L s .57388 .33467 m .57447 .33569 L s .42496 .35229 m .42518 .35014 L s .27449 .5727 m .27006 .56792 L s .47819 .33564 m .47878 .33461 L s .34945 .76276 m .34179 .75975 L s .60878 .82328 m .60023 .82453 L s .45193 .82446 m .44339 .82321 L s .67536 .37557 m .67499 .37869 L s .37761 .37852 m .37726 .3754 L s .57325 .33365 m .57388 .33467 L s .47878 .33461 m .47942 .3336 L s 0 0 1 r .77106 .50119 m .76032 .48679 L s .5 g .57256 .33265 m .57325 .33365 L s .62715 .34811 m .62746 .35026 L s .47942 .3336 m .48011 .3326 L s .71713 .41033 m .716 .41425 L s .42518 .35014 m .4255 .34799 L s .61727 .82189 m .60878 .82328 L s .44339 .82321 m .4349 .82181 L s .76004 .69289 m .75347 .6969 L s .33656 .41404 m .33545 .41012 L s .2988 .69669 m .29223 .69267 L s .7506 .45482 m .74851 .45931 L s .304 .45906 m .30192 .45458 L s .57183 .33167 m .57256 .33265 L s .48011 .3326 m .48084 .33161 L s .77407 .50669 m .77091 .51149 L s .28154 .51123 m .2784 .50643 L s .71796 .75678 m .71043 .75992 L s .67557 .37244 m .67536 .37557 L s .57105 .3307 m .57183 .33167 L s .34179 .75975 m .33427 .75661 L s .48084 .33161 m .48162 .33064 L s .78271 .62671 m .77729 .63132 L s .62569 .82037 m .61727 .82189 L s .37726 .3754 m .37705 .37227 L s .62674 .34596 m .62715 .34811 L s .4349 .82181 m .42648 .82028 L s .4255 .34799 m .42592 .34584 L s .27504 .63107 m .26964 .62646 L s .57023 .32974 m .57105 .3307 L s .48162 .33064 m .48245 .32969 L s .78656 .56332 m .78234 .56818 L s .27006 .56792 m .26585 .56305 L s .56936 .32881 m .57023 .32974 L s .48245 .32969 m .48332 .32876 L s .63405 .81871 m .62569 .82037 L s .71807 .40639 m .71713 .41033 L s .42648 .82028 m .41813 .81862 L s .62622 .34382 m .62674 .34596 L s .33545 .41012 m .33452 .40617 L s .42592 .34584 m .42644 .34371 L s .56845 .32789 m .56936 .32881 L s .48332 .32876 m .48424 .32784 L s 0 0 1 r .78092 .516 m .77106 .50119 L s .5 g .67564 .3693 m .67557 .37244 L s .76643 .68876 m .76004 .69289 L s .37705 .37227 m .37699 .36913 L s .75249 .45029 m .7506 .45482 L s .29223 .69267 m .28586 .68853 L s .30192 .45458 m .30005 .45004 L s .56749 .327 m .56845 .32789 L s .48424 .32784 m .4852 .32695 L s .72534 .75351 m .71796 .75678 L s .33427 .75661 m .32689 .75333 L s .64232 .81692 m .63405 .81871 L s .41813 .81862 m .40986 .81682 L s .6256 .3417 m .62622 .34382 L s .777 .50182 m .77407 .50669 L s .56649 .32612 m .56749 .327 L s .42644 .34371 m .42707 .34158 L s .4852 .32695 m .4862 .32607 L s .2784 .50643 m .27548 .50155 L s 0 0 1 r .26686 .56772 m .25882 .55771 L s .5 g .56545 .32527 m .56649 .32612 L s .4862 .32607 m .48724 .32522 L s .78791 .622 m .78271 .62671 L s .26964 .62646 m .26445 .62174 L s .71883 .40242 m .71807 .40639 L s .56437 .32443 m .56545 .32527 L s .67556 .36615 m .67564 .3693 L s .48724 .32522 m .48832 .32439 L s .37699 .36913 m .37708 .36598 L s .33452 .40617 m .33377 .4022 L s .62488 .33958 m .6256 .3417 L s .79056 .55836 m .78656 .56332 L s .42707 .34158 m .42779 .33947 L s .65052 .81499 m .64232 .81692 L s .40986 .81682 m .40167 .81488 L s 0 0 1 r .79489 .55625 m .78698 .56631 L s .5 g .26585 .56305 m .26186 .55808 L s .56325 .32362 m .56437 .32443 L s .48832 .32439 m .48945 .32358 L s .56209 .32284 m .56325 .32362 L s .73258 .75011 m .72534 .75351 L s .48945 .32358 m .49061 .3228 L s .32689 .75333 m .31966 .74992 L s .75415 .44571 m .75249 .45029 L s .77263 .6845 m .76643 .68876 L s .30005 .45004 m .29839 .44546 L s .28586 .68853 m .27967 .68426 L s .56089 .32208 m .56209 .32284 L s .62406 .33748 m .62488 .33958 L s .49061 .3228 m .4918 .32204 L s .42779 .33947 m .42862 .33737 L s .65862 .81293 m .65052 .81499 L s .40167 .81488 m .39357 .81281 L s .55966 .32135 m .56089 .32208 L s .4918 .32204 m .49304 .32131 L s .67533 .363 m .67556 .36615 L s 0 0 1 r .78988 .53117 m .78092 .516 L s .5 g .37708 .36598 m .37732 .36283 L s .77971 .49688 m .777 .50182 L s .27548 .50155 m .27278 .49661 L s .5584 .32064 m .55966 .32135 L s .49304 .32131 m .49431 .3206 L s .71939 .39843 m .71883 .40242 L s .33377 .4022 m .33321 .39821 L s .62314 .3354 m .62406 .33748 L s .5571 .31996 m .5584 .32064 L s .49431 .3206 m .49561 .31993 L s .42862 .33737 m .42955 .33528 L s .79289 .61718 m .78791 .622 L s .26445 .62174 m .25948 .61691 L s .55577 .31931 m .5571 .31996 L s .49561 .31993 m .49694 .31928 L s .66663 .81074 m .65862 .81293 L s .39357 .81281 m .38557 .81061 L s .5544 .31869 m .55577 .31931 L s .49694 .31928 m .4983 .31866 L s .79433 .55331 m .79056 .55836 L s .73965 .74659 m .73258 .75011 L s .31966 .74992 m .31259 .74639 L s .26186 .55808 m .2581 .55303 L s .67495 .35986 m .67533 .363 L s .55301 .3181 m .5544 .31869 L s .4983 .31866 m .4997 .31806 L s .37732 .36283 m .37771 .35968 L s .62212 .33333 m .62314 .3354 L s .42955 .33528 m .43057 .33322 L s .7556 .44109 m .75415 .44571 L s .29839 .44546 m .29696 .44083 L s .55159 .31753 m .55301 .3181 L s .4997 .31806 m .50112 .3175 L s .77863 .68012 m .77263 .6845 L s .27967 .68426 m .27368 .67988 L s .55015 .317 m .55159 .31753 L s .50112 .3175 m .50257 .31697 L s .54868 .3165 m .55015 .317 L s .50257 .31697 m .50404 .31648 L s .71977 .39442 m .71939 .39843 L s .33321 .39821 m .33285 .3942 L s .621 .33129 m .62212 .33333 L s .67453 .80841 m .66663 .81074 L s .54718 .31603 m .54868 .3165 L s .50404 .31648 m .50553 .31601 L s .43057 .33322 m .4317 .33117 L s .38557 .81061 m .37767 .80828 L s .78218 .49187 m .77971 .49688 L s .54566 .3156 m .54718 .31603 L s .50553 .31601 m .50705 .31558 L s .27278 .49661 m .27032 .4916 L s .54413 .3152 m .54566 .3156 L s .67441 .35671 m .67495 .35986 L s .50705 .31558 m .50859 .31518 L s .37771 .35968 m .37825 .35654 L s .54257 .31483 m .54413 .3152 L s .50859 .31518 m .51014 .31481 L s 0 0 1 r .79787 .54666 m .78988 .53117 L s .25882 .55771 m .25173 .54736 L s .5 g .541 .31449 m .54257 .31483 L s .51014 .31481 m .51172 .31447 L s .79764 .61226 m .79289 .61718 L s .74657 .74293 m .73965 .74659 L s .53941 .31419 m .541 .31449 L s .51172 .31447 m .5133 .31418 L s .61978 .32926 m .621 .33129 L s .25948 .61691 m .25473 .61198 L s .31259 .74639 m .30569 .74273 L s .4317 .33117 m .43292 .32915 L s .53781 .31392 m .53941 .31419 L s .5133 .31418 m .51491 .31391 L s .5362 .31369 m .53781 .31392 L s .51491 .31391 m .51652 .31368 L s .53458 .3135 m .5362 .31369 L s .51652 .31368 m .51815 .31349 L s .79786 .54817 m .79433 .55331 L s .53294 .31333 m .53458 .3135 L s .75683 .43642 m .7556 .44109 L s .51815 .31349 m .51978 .31333 L s .68232 .80595 m .67453 .80841 L s .5313 .31321 m .53294 .31333 L s .51978 .31333 m .52142 .3132 L s .37767 .80828 m .36988 .80582 L s .29696 .44083 m .29574 .43617 L s .52966 .31312 m .5313 .31321 L s .52142 .3132 m .52306 .31311 L s .2581 .55303 m .25458 .54789 L s .52801 .31306 m .52966 .31312 L s .52306 .31311 m .52471 .31306 L s .52636 .31304 m .52801 .31306 L s .52471 .31306 m .52636 .31304 L s .71995 .39039 m .71977 .39442 L s .78443 .67563 m .77863 .68012 L s .33285 .3942 m .33268 .39017 L s .61846 .32727 m .61978 .32926 L s .67373 .35358 m .67441 .35671 L s .43292 .32915 m .43424 .32716 L s .27368 .67988 m .26789 .67538 L s .37825 .35654 m .37894 .35341 L s .78442 .48681 m .78218 .49187 L s .27032 .4916 m .2681 .48653 L s .61705 .3253 m .61846 .32727 L s .43424 .32716 m .43566 .32519 L s .69 .80337 m .68232 .80595 L s .75331 .73916 m .74657 .74293 L s .36988 .80582 m .36221 .80322 L s .30569 .74273 m .29896 .73895 L s .67289 .35045 m .67373 .35358 L s .37894 .35341 m .37979 .35028 L s .80217 .60723 m .79764 .61226 L s .25473 .61198 m .25022 .60695 L s .71994 .38635 m .71995 .39039 L s .75784 .43173 m .75683 .43642 L s .61554 .32336 m .61705 .3253 L s .33268 .39017 m .3327 .38613 L s .43566 .32519 m .43717 .32325 L s .29574 .43617 m .29474 .43147 L s .25458 .54789 m .2513 .54267 L s .79001 .67103 m .78443 .67563 L s .26789 .67538 m .26232 .67077 L s .69756 .80065 m .69 .80337 L s .61394 .32145 m .61554 .32336 L s .36221 .80322 m .35466 .8005 L s .43717 .32325 m .43878 .32134 L s .67191 .34734 m .67289 .35045 L s .37979 .35028 m .38078 .34717 L s 0 .667 .167 r .79935 .54978 m .7256 .57125 L .73719 .58119 L closepath p F P 0 g s 0 .667 .167 r .79935 .54978 m .72239 .54801 L .7256 .57125 L closepath p F P 0 g s 0 .667 .167 r .79935 .54978 m .73071 .53432 L .72239 .54801 L closepath p F P 0 g s 0 .667 .167 r .79935 .54978 m .7457 .56765 L .74243 .54403 L closepath p F P 0 g s .5 g .79886 .54659 m .79887 .54658 L s .79786 .54817 m .79886 .54659 L s 0 0 1 r .79489 .55625 m .79914 .54989 L s 0 .667 .167 r .79935 .54978 m .73719 .58119 L .7457 .56765 L closepath p F P 0 g s 0 0 1 r .79928 .54981 m .79929 .54984 L s .79929 .54984 m .80488 .56241 L s 0 .667 .167 r .79935 .54978 m .74243 .54403 L .73071 .53432 L closepath p F P 0 g s 0 0 1 r .02 w .79935 .54978 Mdot .5 Mabswid .79923 .54975 m .79925 .54972 L s .79923 .54975 m .79923 .54975 L s .79925 .54972 m .80184 .54584 L s .5 g .79887 .54658 m .80115 .54296 L s 0 0 1 r .79787 .54666 m .79925 .54975 L s .79925 .54975 m .79925 .54976 L s 0 g .001 w .52632 .58304 m .74416 .5565 L s .5 g .5 Mabswid .78642 .48168 m .78442 .48681 L s .75988 .73526 m .75331 .73916 L s .2681 .48653 m .26611 .4814 L s .29896 .73895 m .2924 .73504 L s .61225 .31957 m .61394 .32145 L s .43878 .32134 m .44048 .31947 L s .71974 .38231 m .71994 .38635 L s .3327 .38613 m .33291 .38209 L s .75862 .427 m .75784 .43173 L s .29474 .43147 m .29397 .42674 L s 0 0 1 r .25173 .54736 m .24563 .53668 L s .5 g .53023 .85992 m .52195 .85991 L s .5385 .85979 m .53023 .85992 L s .52195 .85991 m .51368 .85978 L s .80646 .60211 m .80217 .60723 L s .70499 .79781 m .69756 .80065 L s .54676 .85954 m .5385 .85979 L s .51368 .85978 m .50542 .85952 L s .67077 .34425 m .67191 .34734 L s .35466 .8005 m .34724 .79765 L s .61047 .31773 m .61225 .31957 L s .25022 .60695 m .24594 .60183 L s .38078 .34717 m .38193 .34408 L s .44048 .31947 m .44226 .31763 L s .555 .85916 m .54676 .85954 L s .50542 .85952 m .49718 .85913 L s .56323 .85865 m .555 .85916 L s .49718 .85913 m .48895 .85861 L s .8042 .53767 m .80115 .54296 L s .2513 .54267 m .24827 .53738 L s .79538 .66631 m .79001 .67103 L s 0 0 1 r .8078 .53512 m .80184 .54584 L s .5 g .57143 .85801 m .56323 .85865 L s .48895 .85861 m .48076 .85797 L s .26232 .67077 m .25696 .66605 L s .6086 .31593 m .61047 .31773 L s .44226 .31763 m .44414 .31583 L s .57959 .85724 m .57143 .85801 L s .48076 .85797 m .47259 .85719 L s .71934 .37827 m .71974 .38231 L s .76626 .73124 m .75988 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.36594 L s .66285 .32917 m .66473 .33212 L s .388 .33196 m .38989 .32901 L s .64304 .84656 m .63535 .84833 L s .7333 .78521 m .72645 .78854 L s .41686 .84824 m .40917 .84646 L s .32581 .78836 m .31896 .78502 L s .58805 .30174 m .59064 .30312 L s .46213 .30304 m .46472 .30167 L s .5854 .30042 m .58805 .30174 L s .46472 .30167 m .46738 .30035 L s .81785 .5862 m .81431 .59159 L s .65064 .84466 m .64304 .84656 L s .66082 .32625 m .66285 .32917 L s .40917 .84646 m .40158 .84456 L s .78424 .71848 m .77845 .72285 L s .23812 .5913 m .23459 .58591 L s .38989 .32901 m .39192 .32609 L s .27386 .72261 m .26808 .71824 L s .81013 .65153 m .80545 .65656 L s .81179 .52138 m .80952 .52688 L s .58269 .29916 m .5854 .30042 L s .71577 .36214 m .71696 .36616 L s .46738 .30035 m .47009 .2991 L s .24692 .65629 m .24225 .65125 L s .75945 .40787 m .7596 .41268 L s .33573 .36594 m .33693 .36192 L s .24298 .52658 m .24072 .52108 L s .29304 .41241 m .29319 .40761 L s .79191 .46072 m .79092 .46602 L s .73999 .78176 m .7333 .78521 L s .57991 .29796 m .58269 .29916 L s .47009 .2991 m .47287 .2979 L s .31896 .78502 m .31228 .78156 L s .26165 .46573 m .26067 .46043 L s .65815 .84265 m .65064 .84466 L s 0 0 1 r .81957 .61076 m .81576 .59452 L s .5 g .40158 .84456 m .39407 .84253 L s .65865 .32338 m .66082 .32625 L s .39192 .32609 m .3941 .32322 L s .57708 .29682 m .57991 .29796 L s .47287 .2979 m .47571 .29676 L s .57419 .29574 m .57708 .29682 L s .47571 .29676 m .47861 .29568 L s .71438 .35815 m .71577 .36214 L s .33693 .36192 m .33833 .35793 L s .66557 .84051 m .65815 .84265 L s .39407 .84253 m .38666 .84039 L s .57124 .29473 m .57419 .29574 L s .47861 .29568 m .48155 .29467 L s .78982 .714 m .78424 .71848 L s 0 0 1 r .24057 .52572 m .23658 .51452 L s .5 g .65634 .32054 m .65865 .32338 L s .26808 .71824 m .26251 .71376 L s .3941 .32322 m .39642 .32039 L s .82113 .58073 m .81785 .5862 L s .75908 .40306 m .75945 .40787 L s .23459 .58591 m .23133 .58043 L s .29319 .40761 m .29358 .4028 L s .56825 .29377 m .57124 .29473 L s .74652 .77819 m .73999 .78176 L s .48155 .29467 m .48455 .29372 L s .31228 .78156 m .30576 .77799 L s .81457 .64641 m .81013 .65153 L s .8138 .51583 m .81179 .52138 L s .24225 .65125 m .23783 .64612 L s .24072 .52108 m .23873 .51552 L s .56521 .29289 m .56825 .29377 L s .48455 .29372 m .48759 .29284 L s 0 0 1 r .81654 .51289 m .81271 .52413 L s .5 g .79265 .45538 m .79191 .46072 L s .26067 .46043 m .25995 .45509 L s .67287 .83825 m .66557 .84051 L s .56213 .29207 m .56521 .29289 L s .48759 .29284 m .49067 .29203 L s .38666 .84039 m .37936 .83813 L s .65389 .31776 m .65634 .32054 L s .39642 .32039 m .39888 .31761 L s .7128 .35418 m .71438 .35815 L s .55901 .29132 m .56213 .29207 L s .49067 .29203 m .49379 .29128 L s .33833 .35793 m .33993 .35396 L s .55585 .29064 m .55901 .29132 L s .49379 .29128 m .49695 .2906 L s .55267 .29002 m .55585 .29064 L s .49695 .2906 m .50014 .28999 L s .54945 .28948 m .55267 .29002 L s .50014 .28999 m .50336 .28945 L s .75846 .39825 m .75908 .40306 L s .75287 .7745 m .74652 .77819 L s .79519 .70942 m .78982 .714 L s .68007 .83588 m .67287 .83825 L s .30576 .77799 m .29942 .7743 L s .6513 .31502 m .65389 .31776 L s .29358 .4028 m .29421 .39798 L s .37936 .83813 m .37217 .83575 L s .26251 .71376 m .25715 .70917 L s .39888 .31761 m .40148 .31488 L s .5462 .28901 m .54945 .28948 L s .50336 .28945 m .50661 .28898 L s 0 0 1 r .82226 .62706 m .81957 .61076 L s .5 g .54294 .28861 m .5462 .28901 L s .50661 .28898 m .50987 .28859 L s .82415 .57519 m .82113 .58073 L s .53965 .28828 m .54294 .28861 L s .50987 .28859 m .51316 .28826 L s .23133 .58043 m .22832 .57488 L s .53636 .28802 m .53965 .28828 L s .51316 .28826 m .51646 .28801 L s .81876 .64118 m .81457 .64641 L s .53305 .28784 m .53636 .28802 L s .51646 .28801 m .51977 .28783 L s .71101 .35023 m .7128 .35418 L s .81553 .51022 m .8138 .51583 L s .52973 .28773 m .53305 .28784 L s .51977 .28783 m .52309 .28772 L s .23783 .64612 m .23365 .6409 L s .33993 .35396 m .34172 .35002 L s .52641 .28769 m .52973 .28773 L s .52309 .28772 m .52641 .28769 L s .79312 .45002 m .79265 .45538 L s .23873 .51552 m .23702 .50991 L s .25995 .45509 m .2595 .44972 L s .64858 .31234 m .6513 .31502 L s .40148 .31488 m .40421 .3122 L s .68715 .83339 m .68007 .83588 L s .37217 .83575 m .36509 .83325 L s .75904 .7707 m .75287 .7745 L s .75761 .39344 m .75846 .39825 L s .29942 .7743 m .29326 .77049 L s .29421 .39798 m .29508 .39317 L s .64572 .30972 m .64858 .31234 L s .40421 .3122 m .40708 .30958 L s .80033 .70473 m .79519 .70942 L s .70904 .34632 m .71101 .35023 L s .25715 .70917 m .25202 .70447 L s .34172 .35002 m .34371 .34611 L s .69411 .83078 m .68715 .83339 L s .36509 .83325 m .35814 .83063 L s 0 0 1 r .23658 .51452 m .2337 .5031 L s .5 g .8269 .56957 m .82415 .57519 L s .22832 .57488 m .22559 .56926 L s .79332 .44463 m .79312 .45002 L s .8227 .63587 m .81876 .64118 L s .81699 .50456 m .81553 .51022 L s .64273 .30716 m .64572 .30972 L s .2595 .44972 m .2593 .44433 L s .40708 .30958 m .41007 .30702 L s .23365 .6409 m .22973 .63558 L s .23702 .50991 m .23557 .50425 L s 0 0 1 r .81925 .50145 m .81654 .51289 L s .5 g .76503 .76679 m .75904 .7707 L s .70686 .34244 m .70904 .34632 L s .75651 .38863 m .75761 .39344 L s .29326 .77049 m .28728 .76658 L s .34371 .34611 m .34589 .34223 L s .29508 .39317 m .29619 .38837 L s 0 0 1 r .82379 .64334 m .82226 .62706 L s .5 g .70094 .82806 m .69411 .83078 L s .35814 .83063 m .35132 .82791 L s .63961 .30466 m .64273 .30716 L s .41007 .30702 m .4132 .30452 L s .80525 .69994 m .80033 .70473 L s .25202 .70447 m .24712 .69968 L s .52985 .88349 m .52237 .88349 L s .53733 .88338 m .52985 .88349 L s .52237 .88349 m .51489 .88337 L s .5448 .88315 m .53733 .88338 L s .51489 .88337 m .50742 .88314 L s .63636 .30222 m .63961 .30466 L s .4132 .30452 m .41645 .30209 L s .55226 .88281 m .5448 .88315 L s .50742 .88314 m .49996 .88279 L s .79326 .43923 m .79332 .44463 L s .70449 .33861 m .70686 .34244 L s .70763 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s .24712 .69968 m .24246 .69478 L s .62951 .29756 m .633 .29986 L s .34464 .82506 m .33809 .82211 L s .41982 .29973 m .42331 .29744 L s .5964 .87839 m .58915 .87941 L s .46309 .87936 m .45583 .87833 L s .79293 .43381 m .79326 .43923 L s 0 0 1 r .2337 .5031 m .23197 .49152 L s .5 g .25938 .43893 m .25973 .43351 L s .7536 .37907 m .75518 .38384 L s .77642 .75865 m .77082 .76278 L s .29753 .38358 m .29912 .37881 L s 0 0 1 r .82415 .65955 m .82379 .64334 L s .5 g .60361 .87726 m .5964 .87839 L s .62591 .29535 m .62951 .29756 L s .2815 .76255 m .27591 .75843 L s .45583 .87833 m .44863 .87719 L s .42331 .29744 m .42692 .29523 L s .83156 .55813 m .82937 .56388 L s .81906 .49312 m .81816 .49886 L s .82978 .62499 m .82637 .63047 L s .22314 .56357 m .22096 .55781 L s .23441 .49855 m .23353 .49281 L s .22606 .63018 m .22267 .62469 L s .69918 .33108 m .70193 .33482 L s 0 0 1 r .82081 .48985 m .81925 .50145 L s .5 g .35085 .33461 m .35361 .33088 L s .72059 .81922 m .71419 .82228 L s .61075 .87601 m .60361 .87726 L s .44863 .87719 m .44149 .87594 L s .33809 .82211 m .33169 .81905 L s .6222 .2932 m .62591 .29535 L s .42692 .29523 m .43064 .29309 L s .61784 .87466 m .61075 .87601 L s .81436 .69007 m .80992 .69505 L s .44149 .87594 m .43441 .87458 L s .24246 .69478 m .23804 .68979 L s .61838 .29114 m .6222 .2932 L s .43064 .29309 m .43446 .29103 L s .75179 .37432 m .7536 .37907 L s .29912 .37881 m .30095 .37406 L s .79233 .42838 m .79293 .43381 L s .69624 .32739 m .69918 .33108 L s .78181 .75443 m .77642 .75865 L s .35361 .33088 m .35656 .32719 L s .62485 .8732 m .61784 .87466 L s .25973 .43351 m .26035 .42809 L s .43441 .87458 m .4274 .87311 L s .27591 .75843 m .27053 .75419 L s .72684 .81605 m .72059 .81922 L s .33169 .81905 m .32545 .81588 L s .61446 .28917 m .61838 .29114 L s .43446 .29103 m .43839 .28906 L s .81966 .48735 m .81906 .49312 L s .83346 .55232 m .83156 .55813 L s .83292 .61943 m .82978 .62499 L s .23353 .49281 m .23295 .48703 L s .22096 .55781 m .21908 .552 L s 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s .81998 .48155 m .81966 .48735 L s .83507 .54645 m .83346 .55232 L s .23295 .48703 m .23265 .48123 L s .59781 .28213 m .60211 .28376 L s .83578 .6138 m .83292 .61943 L s .45076 .28366 m .45506 .28205 L s .21908 .552 m .21749 .54613 L s .21955 .61913 m .21671 .61349 L s 0 0 1 r .8212 .47813 m .82081 .48985 L s .5 g .74743 .36492 m .74973 .3696 L s .73886 .80941 m .73294 .81278 L s .65209 .86626 m .64541 .86816 L s .40685 .86805 m .40018 .86615 L s .30302 .36935 m .30533 .36466 L s .31937 .8126 m .31345 .80922 L s .59343 .28061 m .59781 .28213 L s .45506 .28205 m .45944 .28053 L s .82248 .67983 m .81855 .68499 L s .68629 .3167 m .68979 .3202 L s .36303 .32001 m .36653 .31651 L s .79195 .74568 m .78699 .7501 L s .23386 .68471 m .22994 .67955 L s .79029 .41754 m .79145 .42296 L s .26537 .74986 m .26042 .74543 L s .58898 .27917 m .59343 .28061 L s .26124 .42266 m .26241 .41724 L s .45944 .28053 m .4639 .2791 L s .65867 .86426 m .65209 .86626 L s .40018 .86615 m .3936 .86415 L s .58445 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s .57705 .30248 m .57949 .30361 L s .47327 .30355 m .47572 .30242 L s .24425 .54584 m .24142 .54042 L s .77334 .4349 m .77272 .4399 L s .57455 .3014 m .57705 .30248 L s .27987 .43963 m .27926 .43462 L s .47572 .30242 m .47822 .30134 L s .80545 .65656 m .80053 .66149 L s .25182 .66122 m .24692 .65629 L s .74183 .77431 m .73508 .77781 L s .69739 .35173 m .69869 .35538 L s .31718 .77763 m .31043 .77412 L s .35401 .35518 m .35531 .35153 L s .57199 .30038 m .57455 .3014 L s .47822 .30134 m .48078 .30032 L s .56939 .29941 m .57199 .30038 L s .48078 .30032 m .48338 .29936 L s .56674 .29849 m .56939 .29941 L s .48338 .29936 m .48604 .29845 L s .56404 .29764 m .56674 .29849 L s .48604 .29845 m .48873 .2976 L s .69592 .34811 m .69739 .35173 L s .35531 .35153 m .3568 .34791 L s .81364 .53524 m .81106 .54072 L s .56131 .29685 m .56404 .29764 L s .48873 .2976 m .49147 .2968 L s .77373 .42986 m .77334 .4349 L s .24142 .54042 m .23885 .53493 L s .74842 .7707 m .74183 .77431 L s .27926 .43462 m .27889 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m .45193 .27439 L s .82268 .46583 m .82356 .47175 L s .59561 .27289 m .60099 .27448 L s .22911 .47142 m .23 .4655 L s .45193 .27439 m .45732 .2728 L s .73776 .82118 m .73252 .82451 L s .31982 .82433 m .31459 .82099 L s .81942 .70889 m .81585 .71391 L s .59014 .27141 m .59561 .27289 L s .23658 .71364 m .23302 .70862 L s .45732 .2728 m .46279 .27133 L s .74916 .35503 m .75258 .35979 L s .30022 .35952 m .30366 .35477 L s .8457 .58469 m .84432 .59062 L s .5846 .27006 m .59014 .27141 L s .46279 .27133 m .46834 .26999 L s .20823 .5903 m .20686 .58437 L s .57898 .26883 m .5846 .27006 L s .46834 .26999 m .47395 .26876 L s .74282 .81775 m .73776 .82118 L s .31459 .82099 m .30953 .81756 L s .57331 .26772 m .57898 .26883 L s .47395 .26876 m .47963 .26767 L s .8215 .45991 m .82268 .46583 L s .23 .4655 m .23121 .45959 L s .56758 .26674 m .57331 .26772 L s .47963 .26767 m .48536 .26669 L s .74549 .35033 m .74916 .35503 L s .30366 .35477 m .30735 .35008 L s .5618 .26589 m .56758 .26674 L s .82272 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.90266 L s .51132 .90265 m .50541 .90238 L s .5528 .90204 m .5469 .9024 L s .50541 .90238 m .49951 .90202 L s .82576 .69863 m .82272 .7038 L s .55868 .9016 m .5528 .90204 L s .7524 .81063 m .74771 .81423 L s .49951 .90202 m .49363 .90157 L s .22973 .70352 m .22671 .69835 L s .30466 .81404 m .29997 .81044 L s .56453 .90107 m .55868 .9016 L s .49363 .90157 m .48778 .90103 L s .57035 .90044 m .56453 .90107 L s .48778 .90103 m .48196 .90041 L s .73741 .34115 m .74157 .3457 L s .57614 .89974 m .57035 .90044 L s .31128 .34545 m .31546 .34091 L s .48196 .90041 m .47618 .89969 L s .84754 .5727 m .84678 .57872 L s .2058 .57839 m .20505 .57237 L s .58188 .89894 m .57614 .89974 L s .47618 .89969 m .47043 .89889 L s .58758 .89805 m .58188 .89894 L s .47043 .89889 m .46473 .898 L s .81819 .4481 m .82 .454 L s .75691 .80695 m .7524 .81063 L s .23272 .45368 m .23455 .44778 L s .29997 .81044 m .29548 .80675 L s .59324 .89708 m .58758 .89805 L s .46473 .898 m .45908 .89703 L s .82853 .6934 m .82576 .69863 L s .22671 .69835 m .22395 .69311 L s .733 .33668 m .73741 .34115 L s .31546 .34091 m .31988 .33644 L s .59883 .89603 m .59324 .89708 L s .45908 .89703 m .45349 .89597 L s .60437 .89489 m .59883 .89603 L s .45349 .89597 m .44795 .89482 L s .84799 .56665 m .84754 .5727 L s .65 .466 .622 r .78207 .78016 m .72353 .72355 L .70836 .74293 L closepath p F P 0 g s .412 .44 .779 r .78207 .78016 m .73235 .71055 L .72353 .72355 L closepath p F P 0 g s .5 g .76122 .80319 m .75691 .80695 L s .20505 .57237 m .20463 .56632 L s .29548 .80675 m .29118 .80298 L s .60985 .89366 m .60437 .89489 L s .44795 .89482 m .44248 .89359 L s .81607 .44222 m .81819 .4481 L s .72836 .3323 m .733 .33668 L s .23455 .44778 m .23669 .4419 L s .31988 .33644 m .32453 .33206 L s .61526 .89235 m .60985 .89366 L s .44248 .89359 m .43708 .89228 L s .83102 .6881 m .82853 .6934 L s .691 .22 .127 r .78207 .78016 m .70836 .74293 L .70175 .74966 L closepath p F P 0 g s .5 g .22395 .69311 m .22148 .68781 L s .62059 .89096 m .61526 .89235 L s .43708 .89228 m .43175 .89088 L s .76532 .79934 m .76122 .80319 L s .29118 .80298 m .28708 .79913 L s .72348 .32801 m .72836 .3323 L s .62585 .88948 m .62059 .89096 L s .32453 .33206 m .32943 .32778 L s .43175 .89088 m .42649 .8894 L s .84811 .56058 m .84799 .56665 L s .20463 .56632 m .20452 .56025 L s .81363 .43637 m .81607 .44222 L s .23669 .4419 m .23914 .43605 L s .63103 .88793 m .62585 .88948 L s .42649 .8894 m .42132 .88784 L s .83322 .68275 m .83102 .6881 L s .22148 .68781 m .21929 .68245 L s .71836 .32382 m .72348 .32801 L s .76922 .79543 m .76532 .79934 L s .63612 .88629 m .63103 .88793 L s .32943 .32778 m .33455 .32359 L s .28708 .79913 m .2832 .79521 L s .42132 .88784 m .41624 .8862 L s .64112 .88458 m .63612 .88629 L s .41624 .8862 m .41124 .88448 L s .84791 .55448 m .84811 .56058 L s .81088 .43056 m .81363 .43637 L s .20452 .56025 m .20474 .55415 L s .23914 .43605 m .24191 .43024 L s .71303 .31973 m .71836 .32382 L s .33455 .32359 m .3399 .31951 L s .64602 .88278 m .64112 .88458 L s .41124 .88448 m .40634 .88268 L s .77291 .79144 m .76922 .79543 L s .2832 .79521 m .27952 .79121 L s .83514 .67734 m .83322 .68275 L s .892 .503 .284 r .78207 .78016 m .72593 .71699 L .73235 .71055 L closepath p F P 0 g s .5 g .21929 .68245 m .21739 .67704 L s .65082 .88091 m .64602 .88278 L s .40634 .88268 m .40155 .88081 L s .70747 .31575 m .71303 .31973 L s .3399 .31951 m .34547 .31553 L s .80781 .42478 m .81088 .43056 L s .65552 .87897 m .65082 .88091 L s .24191 .43024 m .24499 .42447 L s .40155 .88081 m .39685 .87886 L s .84738 .54837 m .84791 .55448 L s .77638 .78738 m .77291 .79144 L s .27952 .79121 m .27607 .78715 L s .20474 .55415 m .20529 .54804 L s .7017 .31188 m .70747 .31575 L s .552 .637 .888 r .78207 .78016 m .70175 .74966 L .71049 .73673 L closepath p F P 0 g s .5 g .34547 .31553 m .35125 .31167 L s .83677 .67188 m .83514 .67734 L s .66011 .87695 m .65552 .87897 L s .21739 .67704 m .21578 .67157 L s .39685 .87886 m .39227 .87684 L s .66459 .87486 m .66011 .87695 L s .39227 .87684 m .3878 .87474 L s .77962 .78325 m .77638 .78738 L s .80443 .41906 m .80781 .42478 L s .69571 .30814 m .7017 .31188 L s .27607 .78715 m .27284 .78302 L s .24499 .42447 m .24839 .41874 L s .35125 .31167 m .35725 .30793 L s .84651 .54225 m .84738 .54837 L s .20529 .54804 m .20617 .54192 L s .66895 .87269 m .66459 .87486 L s .3878 .87474 m .38345 .87257 L s .83809 .66637 m .83677 .67188 L s .21578 .67157 m .21447 .66607 L s .744 .599 .696 r .78207 .78016 m .71049 .73673 L .72593 .71699 L closepath p F P 0 g s 0 .6 .4 r .70259 .68831 m .78207 .78016 L s .7701 .62588 m .78207 .78016 L s .61339 .82554 m .78207 .78016 L s 0 g .001 w .52631 .58304 m .71622 .72941 L s .5 g .5 Mabswid .68953 .30452 m .69571 .30814 L s .35725 .30793 m .36345 .30432 L s .78088 .78149 m .78264 .77906 L s .77962 .78325 m .78088 .78149 L s .27284 .78302 m .26983 .77883 L s .67318 .87046 m .66895 .87269 L s .38345 .87257 m .37922 .87034 L s .80074 .41338 m .80443 .41906 L s .24839 .41874 m .2521 .41307 L s .68314 .30103 m .68953 .30452 L s .36345 .30432 m .36984 .30084 L s .84532 .53613 m .84651 .54225 L s .20617 .54192 m .20739 .5358 L s .67729 .86816 m .67318 .87046 L s .37922 .87034 m .37511 .86803 L s .83912 .66082 m .83809 .66637 L s .21447 .66607 m .21346 .66052 L s .78542 .77481 m .78264 .77906 L s .67656 .29767 m .68314 .30103 L s .36984 .30084 m .37643 .29749 L s .26983 .77883 m .26706 .77458 L s .79673 .40777 m .80074 .41338 L s .68127 .86579 m .67729 .86816 L s .37511 .86803 m .37114 .86566 L s .2521 .41307 m .25612 .40747 L s .6698 .29446 m .67656 .29767 L s .37643 .29749 m .3832 .29429 L s .84378 .53001 m .84532 .53613 L s .68512 .86336 m .68127 .86579 L s .37114 .86566 m .3673 .86322 L s .20739 .5358 m .20894 .52968 L s .78797 .7705 m .78542 .77481 L s .26706 .77458 m .26453 .77027 L s .83983 .65524 m .83912 .66082 L s .21346 .66052 m .21276 .65493 L s .66287 .29139 m .6698 .29446 L s .3832 .29429 m .39015 .29123 L s .79242 .40223 m .79673 .40777 L s .25612 .40747 m .26045 .40193 L s .68883 .86086 m .68512 .86336 L s .3673 .86322 m .3636 .86072 L s .65576 .28847 m .66287 .29139 L s .39015 .29123 m .39726 .28832 L s .79027 .76614 m .78797 .7705 L s .84191 .52391 m .84378 .53001 L s .69239 .8583 m .68883 .86086 L s .26453 .77027 m .26223 .7659 L s .3636 .86072 m .36005 .85816 L s .20894 .52968 m .21083 .52357 L s 0 .6 .4 r .69385 .5294 m .70259 .68831 L s .5 g .64849 .28571 m .65576 .28847 L s .39726 .28832 m .40454 .28556 L s .84024 .64963 m .83983 .65524 L s .7878 .39676 m .79242 .40223 L s .21276 .65493 m .21237 .64932 L s .26045 .40193 m .26509 .39647 L s .69581 .85569 m .69239 .8583 L s .36005 .85816 m .35664 .85554 L s .64108 .2831 m .64849 .28571 L s .40454 .28556 m .41196 .28296 L s .79233 .76174 m .79027 .76614 L s .26223 .7659 m .26019 .76149 L s .63351 .28065 m .64108 .2831 L s .41196 .28296 m .41953 .28052 L s .8397 .51782 m .84191 .52391 L s .78287 .39138 m .7878 .39676 L s .21083 .52357 m .21306 .51748 L s .69908 .85302 m .69581 .85569 L s .35664 .85554 m .35338 .85287 L s .26509 .39647 m .27004 .39109 L s .84033 .64399 m .84024 .64963 L s .21237 .64932 m .2123 .64369 L s .62582 .27837 m .63351 .28065 L s .41953 .28052 m .42724 .27825 L s .70219 .85029 m .69908 .85302 L s .618 .27626 m .62582 .27837 L s .35338 .85287 m .35027 .85014 L s .42724 .27825 m .43506 .27615 L s .79414 .75728 m .79233 .76174 L s .26019 .76149 m .25839 .75704 L s .77764 .38609 m .78287 .39138 L s .27004 .39109 m .27528 .3858 L s .61006 .27432 m .618 .27626 L s .43506 .27615 m .44301 .27422 L s .83715 .51175 m .8397 .51782 L s .21306 .51748 m .21563 .51142 L s .70514 .84751 m .70219 .85029 L s .35027 .85014 m .34733 .84735 L s .84011 .63834 m .84033 .64399 L s .60202 .27255 m .61006 .27432 L s .44301 .27422 m .45106 .27246 L s .2123 .64369 m .21254 .63803 L s .59388 .27097 m .60202 .27255 L s .45106 .27246 m .4592 .27089 L s .7957 .75279 m .79414 .75728 L s .25839 .75704 m .25685 .75254 L s .77211 .38089 m .77764 .38609 L s .58565 .26956 m .59388 .27097 L s .4592 .27089 m .46743 .26949 L s .70794 .84467 m .70514 .84751 L s .27528 .3858 m .28082 .38061 L s .34733 .84735 m .34454 .84452 L s .57735 .26834 m .58565 .26956 L s .46743 .26949 m .47574 .26828 L s .83425 .50572 m .83715 .51175 L s .21563 .51142 m .21855 .50539 L s .56898 .2673 m .57735 .26834 L s .47574 .26828 m .48411 .26725 L s .83956 .63267 m .84011 .63834 L s .56056 .26644 m .56898 .2673 L s .48411 .26725 m .49253 .2664 L s .21254 .63803 m .2131 .63236 L s .71057 .84179 m .70794 .84467 L s .34454 .84452 m .34192 .84163 L s .5521 .26578 m .56056 .26644 L s .49253 .2664 m .501 .26574 L s .79699 .74825 m .7957 .75279 L s .25685 .75254 m .25557 .74801 L s .5436 .2653 m .5521 .26578 L s .501 .26574 m .5095 .26528 L s .76629 .3758 m .77211 .38089 L s .53508 .26501 m .5436 .2653 L s .5095 .26528 m .51802 .265 L s .28082 .38061 m .28666 .37553 L s .52655 .26491 m .53508 .26501 L s .51802 .265 m .52655 .26491 L s .52786 .90069 m .52459 .90069 L s .53112 .90064 m .52786 .90069 L s .71302 .83887 m .71057 .84179 L s .52459 .90069 m .52133 .90063 L s .53438 .90054 m .53112 .90064 L s .52133 .90063 m .51807 .90053 L s .53763 .9004 m .53438 .90054 L s .51807 .90053 m .51482 .90039 L s .34192 .84163 m .33947 .8387 L s .54087 .9002 m .53763 .9004 L s .51482 .90039 m .51159 .90019 L s .54409 .89996 m .54087 .9002 L s .83101 .49973 m .83425 .50572 L s .51159 .90019 m .50836 .89994 L s .5473 .89966 m .54409 .89996 L s .50836 .89994 m .50515 .89965 L s .21855 .50539 m .2218 .4994 L s .5505 .89932 m .5473 .89966 L s .50515 .89965 m .50196 .8993 L s .55367 .89893 m .5505 .89932 L s .50196 .8993 m .49879 .89891 L s .83869 .627 m .83956 .63267 L s .79803 .74369 m .79699 .74825 L s .76018 .37082 m .76629 .3758 L s .55682 .89849 m .55367 .89893 L s .2131 .63236 m .21399 .62669 L s .49879 .89891 m .49564 .89847 L s .25557 .74801 m .25455 .74344 L s .28666 .37553 m .29279 .37055 L s .55993 .89801 m .55682 .89849 L s .49564 .89847 m .49252 .89798 L s .56302 .89748 m .55993 .89801 L s .49252 .89798 m .48944 .89745 L s .71531 .8359 m .71302 .83887 L s .33947 .8387 m .3372 .83573 L s .56608 .8969 m .56302 .89748 L s .48944 .89745 m .48638 .89686 L s .5691 .89627 m .56608 .8969 L s .48638 .89686 m .48336 .89624 L s .57209 .8956 m .5691 .89627 L s .48336 .89624 m .48038 .89556 L s .57503 .89489 m .57209 .8956 L s .48038 .89556 m .47744 .89484 L s .82743 .49378 m .83101 .49973 L s .75379 .36596 m .76018 .37082 L s .2218 .4994 m .2254 .49346 L s .29279 .37055 m .2992 .3657 L s 0 .6 .4 r .70259 .68831 m .52631 .73944 L s .5 g .71742 .83288 m .71531 .8359 L s .7988 .73909 m .79803 .74369 L s .57793 .89412 m .57503 .89489 L s .3372 .83573 m .33509 .83272 L s .47744 .89484 m .47454 .89408 L s .25455 .74344 m .2538 .73884 L s .8375 .62132 m .83869 .627 L s .21399 .62669 m .2152 .62101 L s .58078 .89332 m .57793 .89412 L s .47454 .89408 m .4717 .89327 L s .58358 .89247 m .58078 .89332 L s .4717 .89327 m .4689 .89242 L s .58633 .89158 m .58358 .89247 L s .4689 .89242 m .46615 .89153 L s .71936 .82983 m .71742 .83288 L s .33509 .83272 m .33317 .82967 L s .74712 .36123 m .75379 .36596 L s .2992 .3657 m .30588 .36097 L s .58903 .89065 m .58633 .89158 L s .46615 .89153 m .46346 .89059 L s .82351 .48789 m .82743 .49378 L s .7993 .73447 m .7988 .73909 L s .2254 .49346 m .22934 .48757 L s .59167 .88967 m .58903 .89065 L s .46346 .89059 m .46082 .88962 L s .2538 .73884 m .25331 .73422 L s .83598 .61565 m .8375 .62132 L s .59425 .88866 m .59167 .88967 L s .46082 .88962 m .45824 .8886 L s .2152 .62101 m .21674 .61534 L s .72111 .82675 m .71936 .82983 L s .33317 .82967 m .33143 .82658 L s .59676 .8876 m .59425 .88866 L s .45824 .8886 m .45573 .88754 L s .74018 .35662 m .74712 .36123 L s .30588 .36097 m .31284 .35638 L s .59922 .88651 m .59676 .8876 L s .45573 .88754 m .45328 .88645 L s .79953 .72983 m .7993 .73447 L s .6016 .88538 m .59922 .88651 L s .45328 .88645 m .45089 .88531 L s .25331 .73422 m .25309 .72958 L s .81925 .48206 m .82351 .48789 L s .72268 .82363 m .72111 .82675 L s .22934 .48757 m .23363 .48174 L s .33143 .82658 m .32987 .82346 L s .60392 .88421 m .6016 .88538 L s .45089 .88531 m .44858 .88414 L s .73297 .35216 m .74018 .35662 L s .83412 .61 m .83598 .61565 L s .31284 .35638 m .32006 .35192 L s .21674 .61534 m .21862 .60969 L s .60617 .883 m .60392 .88421 L s .44858 .88414 m .44634 .88294 L s .72406 .82048 m .72268 .82363 L s .32987 .82346 m .3285 .82031 L s .60834 .88177 m .60617 .883 L s .44634 .88294 m .44417 .8817 L s .79948 .72518 m .79953 .72983 L s .25309 .72958 m .25315 .72492 L s .7255 .34784 m .73297 .35216 L s .81464 .4763 m .81925 .48206 L s .61044 .88049 m .60834 .88177 L s .32006 .35192 m .32754 .34761 L s .44417 .8817 m .44208 .88042 L s .23363 .48174 m .23825 .47598 L s .61246 .87919 m .61044 .88049 L s .44208 .88042 m .44006 .87911 L s .72525 .8173 m .72406 .82048 L s .83194 .60435 m .83412 .61 L s .3285 .82031 m .32732 .81713 L s .21862 .60969 m .22082 .60405 L s .61439 .87785 m .61246 .87919 L s .44006 .87911 m .43813 .87778 L s .71778 .34368 m .7255 .34784 L s .32754 .34761 m .33527 .34346 L s .79916 .72051 m .79948 .72518 L s .25315 .72492 m .25349 .72025 L s .61625 .87648 m .61439 .87785 L s .43813 .87778 m .43628 .87641 L s .80971 .47061 m .81464 .4763 L s .72625 .8141 m .72525 .8173 L s .23825 .47598 m .2432 .4703 L s .32732 .81713 m .32633 .81392 L s .61802 .87509 m .61625 .87648 L s .43628 .87641 m .43451 .87501 L s .70982 .33967 m .71778 .34368 L s .33527 .34346 m .34325 .33946 L s .82942 .59874 m .83194 .60435 L s .22082 .60405 m .22335 .59843 L s .61971 .87366 m .61802 .87509 L s .43451 .87501 m .43283 .87358 L s .72706 .81088 m .72625 .8141 L s .79856 .71584 m .79916 .72051 L s .32633 .81392 m .32553 .8107 L s .25349 .72025 m .2541 .71558 L s .62131 .87221 m .61971 .87366 L s .43283 .87358 m .43124 .87213 L s .80443 .46501 m .80971 .47061 L s .70163 .33583 m .70982 .33967 L s .2432 .4703 m .24849 .4647 L s .34325 .33946 m .35145 .33563 L s .62281 .87073 m .62131 .87221 L s .43124 .87213 m .42973 .87065 L s .72766 .80763 m .72706 .81088 L s .32553 .8107 m .32494 .80746 L s .82657 .59315 m .82942 .59874 L s .62423 .86923 m .62281 .87073 L s .42973 .87065 m .42832 .86915 L s .22335 .59843 m .22622 .59285 L s .69321 .33216 m .70163 .33583 L s .35145 .33563 m .35988 .33196 L s .79768 .71116 m .79856 .71584 L s .2541 .71558 m .255 .7109 L s .62555 .86771 m .62423 .86923 L s .42832 .86915 m .42701 .86762 L s .79883 .4595 m .80443 .46501 L s .24849 .4647 m .25411 .4592 L s .72808 .80438 m .72766 .80763 L s .32494 .80746 m .32454 .8042 L s .62678 .86616 m .62555 .86771 L s .42701 .86762 m .42578 .86607 L s .68458 .32866 m .69321 .33216 L s .35988 .33196 m .36853 .32848 L s .82339 .5876 m .82657 .59315 L s .62791 .86459 m .62678 .86616 L s .42578 .86607 m .42466 .86451 L s .22622 .59285 m .22942 .5873 L s .79652 .70649 m .79768 .71116 L s .255 .7109 m .25618 .70623 L s .67574 .32535 m .68458 .32866 L s .72829 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L s .24719 .43241 m .25202 .42677 L s .58943 .89353 m .58633 .89447 L s 0 0 1 r .67351 .86218 m .66818 .86669 L s .5 g .46613 .89442 m .46304 .89348 L s .67735 .86068 m .67472 .86301 L s .59246 .89255 m .58943 .89353 L s .37777 .86288 m .37514 .86055 L s .46304 .89348 m .46 .89249 L s .65086 .29251 m .65889 .29532 L s .39417 .29517 m .40222 .29236 L s .59544 .89152 m .59246 .89255 L s .46 .89249 m .45703 .89146 L s .74364 .35478 m .75021 .35946 L s .30277 .3592 m .30936 .35453 L s .8167 .70399 m .8164 .709 L s .73826 .81601 m .73631 .81939 L s .23621 .70873 m .23592 .70371 L s .59835 .89045 m .59544 .89152 L s .45703 .89146 m .45412 .89039 L s .7839 .76367 m .78271 .76794 L s .31621 .81921 m .31427 .81582 L s .64266 .28987 m .65086 .29251 L s .40222 .29236 m .41042 .28973 L s .67984 .85831 m .67735 .86068 L s .26985 .76771 m .26867 .76344 L s .37514 .86055 m .37266 .85818 L s .83576 .63656 m .83664 .64215 L s .82743 .49378 m .83101 .49973 L s 0 0 1 r .37986 .86284 m .37499 .85818 L s 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.30191 .38532 m .30948 .38071 L s .26755 .73293 m .26844 .72853 L s .25412 .4592 m .26007 .45379 L s .64166 .85746 m .64072 .85925 L s .64615 .31068 m .65538 .31338 L s .41186 .85915 m .41093 .85736 L s .39775 .31323 m .407 .31054 L s .5742 .87725 m .57302 .87798 L s .47954 .87794 m .47837 .87721 L s .69848 .82448 m .69802 .82722 L s .35458 .82707 m .35413 .82433 L s .74631 .78063 m .74647 .78425 L s .30616 .78405 m .30634 .78043 L s .57533 .87651 m .5742 .87725 L s .82053 .59777 m .8237 .60323 L s .47837 .87721 m .47725 .87647 L s .2291 .60293 m .23228 .59747 L s .64248 .85565 m .64166 .85746 L s .41093 .85736 m .41011 .85555 L s .63675 .30818 m .64615 .31068 L s .57641 .87575 m .57533 .87651 L s .47725 .87647 m .47617 .8757 L s .407 .31054 m .4164 .30805 L s .81441 .52473 m .81901 .53034 L s .23387 .53003 m .23848 .52443 L s .57744 .87497 m .57641 .87575 L s .47617 .8757 m .47514 .87492 L s .80842 .66361 m .81052 .66864 L s .73575 .37649 m .74357 .38096 L s .24222 .66836 m .24433 .66334 L s 0 0 1 r .35834 .8275 m .35782 .82211 L s .5 g .30948 .38071 m .31732 .37625 L s .69878 .82173 m .69848 .82448 L s .35413 .82433 m .35384 .82158 L s .5 0 0 r .62775 .75261 m .58972 .72154 L .5609 .71044 L closepath p F P 0 g s .4 g .005 w .63993 .70702 m .66477 .73412 L s .5 Mabswid .307 0 .174 r .62775 .75261 m .61965 .70251 L .58972 .72154 L closepath p F P 0 g s .4 g .005 w .35716 .39846 m .56976 .63044 L s .56976 .63044 m .63993 .70702 L s .5 g .5 Mabswid .57843 .87417 m .57744 .87497 L s .47514 .87492 m .47415 .87413 L s .64319 .85383 m .64248 .85565 L s .78311 .72439 m .78425 .72877 L s .41011 .85555 m .4094 .85373 L s .62721 .30588 m .63675 .30818 L s .4164 .30805 m .42595 .30576 L s .78665 .44878 m .7929 .45409 L s .26844 .72853 m .26959 .72415 L s 0 0 .15 r .62775 .75261 m .62121 .67208 L .61965 .70251 L closepath p F P 0 g s 0 0 1 r .69483 .82133 m .69441 .82673 L s .5 g .26007 .45379 m .26634 .44849 L s 0 0 1 r .72273 .37252 m .71896 .35852 L s .5 g .57936 .87336 m .57843 .87417 L s .47415 .87413 m .47322 .87332 L s .74592 .77701 m .74631 .78063 L s .30634 .78043 m .30674 .77682 L s .58024 .87254 m .57936 .87336 L s .47322 .87332 m .47234 .87249 L s .61754 .30378 m .62721 .30588 L s .64379 .852 m .64319 .85383 L s .42595 .30576 m .43563 .30368 L s .4094 .85373 m .40881 .8519 L s .81704 .59235 m .82053 .59777 L s .58107 .8717 m .58024 .87254 L s .6989 .81897 m .69878 .82173 L s .47234 .87249 m .47152 .87165 L s .23228 .59747 m .23579 .59205 L s .35384 .82158 m .35373 .81882 L s .72766 .37217 m .73575 .37649 L s .31732 .37625 m .32543 .37194 L s .80947 .51921 m .81441 .52473 L s .58185 .87085 m .58107 .8717 L s .60774 .3019 m .61754 .30378 L s .47152 .87165 m .47074 .8708 L s .23848 .52443 m .24344 .51891 L s .43563 .30368 m .44543 .30181 L s .64427 .85016 m .64379 .852 L s .40881 .8519 m .40834 .85005 L s .80603 .65862 m .80842 .66361 L s .24433 .66334 m .24674 .65834 L s .7817 .72001 m .78311 .72439 L s .58257 .86999 m .58185 .87085 L s .47074 .8708 m .47002 .86994 L s .7453 .77339 m .74592 .77701 L s .26959 .72415 m .27102 .71977 L s .78008 .44359 m .78665 .44878 L s .30674 .77682 m .30737 .77319 L s .26634 .44849 m .27292 .44331 L s .59784 .30023 m .60774 .3019 L s .44543 .30181 m .45534 .30015 L s 0 0 1 r .35782 .82211 m .35798 .81668 L s .5 g .58324 .86911 m .58257 .86999 L s .47002 .86994 m .46935 .86906 L s .69885 .8162 m .6989 .81897 L s .35373 .81882 m .35379 .81605 L s .64464 .8483 m .64427 .85016 L s .40834 .85005 m .40798 .8482 L s 0 0 1 r .69457 .8159 m .69483 .82133 L s .5 g .58784 .29878 m .59784 .30023 L s .58385 .86823 m .58324 .86911 L s .45534 .30015 m .46534 .29871 L s .46935 .86906 m .46874 .86818 L s .71931 .36802 m .72766 .37217 L s .32543 .37194 m .33379 .3678 L s .58441 .86733 m .58385 .86823 L s .46874 .86818 m .46819 .86728 L s .81322 .58698 m .81704 .59235 L s .57776 .29755 m .58784 .29878 L s .46534 .29871 m .47543 .29748 L s .23579 .59205 m .23963 .58669 L s .64489 .84644 m .64464 .8483 L s .40798 .8482 m .40773 .84634 L s .80421 .51376 m .80947 .51921 L s .58491 .86643 m .58441 .86733 L s .74447 .76978 m .7453 .77339 L s .46819 .86728 m .46769 .86638 L s .56761 .29653 m .57776 .29755 L s .24344 .51891 m .24872 .51347 L s .69863 .81343 m .69885 .8162 L s .47543 .29748 m .48558 .29648 L s .30737 .77319 m .30822 .76958 L s .35379 .81605 m .35402 .81328 L s .78001 .71564 m .7817 .72001 L s .80332 .65365 m .80603 .65862 L s .27102 .71977 m .27272 .7154 L s .77319 .43852 m .78008 .44359 L s .24674 .65834 m .24946 .65338 L s .55741 .29574 m .56761 .29653 L s .48558 .29648 m .49579 .2957 L s .58535 .86552 m .58491 .86643 L s .27292 .44331 m .27982 .43824 L s .46769 .86638 m .46726 .86547 L s .54716 .29517 m .55741 .29574 L s .49579 .2957 m .50603 .29515 L s .71071 .36404 m .71931 .36802 L s .64502 .84458 m .64489 .84644 L s .33379 .3678 m .3424 .36383 L s .40773 .84634 m .40761 .84448 L s .53689 .29483 m .54716 .29517 L s .50603 .29515 m .51631 .29482 L s .58574 .8646 m .58535 .86552 L s .46726 .86547 m .46687 .86455 L s .5266 .29471 m .53689 .29483 L s .51631 .29482 m .5266 .29471 L s .247 .281 .7 r .62775 .75261 m .5609 .71044 L .56203 .67985 L closepath p F P 0 g s 0 0 1 r .35798 .81668 m .35883 .81126 L s .72567 .38766 m .72273 .37252 L s .5 g .58606 .86367 m .58574 .8646 L s .46687 .86455 m .46655 .86362 L s .69823 .81066 m .69863 .81343 L s .35402 .81328 m .35443 .81051 L s .838 .468 .352 r .62775 .75261 m .5924 .66052 L .62121 .67208 L closepath p F P 0 g s 0 0 1 r .69362 .81048 m .69457 .8159 L s .5 g .64503 .84271 m .64502 .84458 L s .7434 .76617 m .74447 .76978 L s .40761 .84448 m .4076 .84261 L s .30822 .76958 m .30929 .76597 L s .80908 .58167 m .81322 .58698 L s .58633 .86275 m .58606 .86367 L s .46655 .86362 m .46629 .86269 L s .23963 .58669 m .24379 .58138 L s .79861 .50841 m .80421 .51376 L s .70187 .36024 m .71071 .36404 L s .77806 .71129 m .78001 .71564 L s .24872 .51347 m .25434 .50812 L s .3424 .36383 m .35125 .36003 L s .58654 .86181 m .58633 .86275 L s .76601 .43358 m .77319 .43852 L s .27272 .7154 m .27469 .71106 L s .46629 .86269 m .46608 .86176 L s .27982 .43824 m .28703 .43331 L s .80032 .64872 m .80332 .65365 L s .24946 .65338 m .25249 .64845 L s .64493 .84084 m .64503 .84271 L s .4076 .84261 m .40771 .84074 L s .69766 .80789 m .69823 .81066 L s .58669 .86087 m .58654 .86181 L s .46608 .86176 m .46594 .86082 L s .35443 .81051 m .35501 .80774 L s .58677 .85993 m .58669 .86087 L s .46594 .86082 m .46586 .85988 L s .74211 .76257 m .7434 .76617 L s .30929 .76597 m .3106 .76237 L s .6447 .83897 m .64493 .84084 L s .40771 .84074 m .40794 .83887 L s .69281 .35661 m .70187 .36024 L s .35125 .36003 m .36033 .35642 L s .5868 .85899 m .58677 .85993 L s .46586 .85988 m .46583 .85894 L s 0 0 1 r .35883 .81126 m .36037 .80585 L s .5 g .8046 .57642 m .80908 .58167 L s .69691 .80513 m .69766 .80789 L s .35501 .80774 m .35576 .80498 L s .77584 .70697 m .77806 .71129 L s .24379 .58138 m .24828 .57614 L s .58677 .85805 m .5868 .85899 L s .75852 .42877 m .76601 .43358 L s .46583 .85894 m .46587 .858 L s 0 0 1 r .69199 .80507 m .69362 .81048 L s .5 g .79268 .50315 m .79861 .50841 L s .27469 .71106 m .27693 .70673 L s .28703 .43331 m .29453 .42851 L s .25434 .50812 m .26028 .50286 L s .64436 .8371 m .6447 .83897 L s .40794 .83887 m .4083 .837 L s .797 .64383 m .80032 .64872 L s .58668 .85711 m .58677 .85805 L s .25249 .64845 m .25582 .64356 L s .46587 .858 m .46596 .85706 L s 0 0 1 r .52632 .86433 m .53921 .85465 L s .5 g .68353 .35318 m .69281 .35661 L s .36033 .35642 m .36962 .353 L s .7406 .75898 m .74211 .76257 L s .58652 .85617 m .58668 .85711 L s .46596 .85706 m .46612 .85612 L s .3106 .76237 m .31213 .75879 L s .6439 .83524 m .64436 .8371 L s .69599 .80237 m .69691 .80513 L s .4083 .837 m .40877 .83513 L s .35576 .80498 m .35669 .80222 L s .58631 .85523 m .58652 .85617 L s .46612 .85612 m .46634 .85518 L s 0 0 1 r .72775 .40387 m .72567 .38766 L s .5 g .75073 .42411 m .75852 .42877 L s .58603 .8543 m .58631 .85523 L s .46634 .85518 m .46662 .85425 L s .77334 .70267 m .77584 .70697 L s .29453 .42851 m .30233 .42386 L s .67404 .34994 m .68353 .35318 L s .27693 .70673 m .27943 .70244 L s .79981 .57124 m .8046 .57642 L s .36962 .353 m .37912 .34977 L s .64331 .83338 m .6439 .83524 L s .40877 .83513 m .40935 .83328 L s .24828 .57614 m .2531 .57096 L s .78643 .49799 m .79268 .50315 L s .575 .34 .522 r .62775 .75261 m .56203 .67985 L .5924 .66052 L closepath p F P 0 g s .01 w .52632 .58304 m .5781 .66962 L s .5 g .5 Mabswid .26028 .50286 m .26655 .49771 L s 0 0 1 r .36037 .80585 m .3626 .80048 L s .5 g .5857 .85337 m .58603 .8543 L s .46662 .85425 m .46695 .85332 L s .79339 .63899 m .797 .64383 L s .69489 .79963 m .69599 .80237 L s .73885 .75541 m .7406 .75898 L s .25582 .64356 m .25945 .63872 L s .35669 .80222 m .3578 .79948 L s .31213 .75879 m .31388 .75522 L s 0 0 1 r .68966 .79971 m .69199 .80507 L s .5 g .5853 .85244 m .5857 .85337 L s .46695 .85332 m .46735 .85239 L s .64261 .83153 m .64331 .83338 L s .40935 .83328 m .41006 .83143 L s .66435 .34689 m .67404 .34994 L s .37912 .34977 m .38881 .34673 L s .58485 .85152 m .5853 .85244 L s .46735 .85239 m .46781 .85147 L s .74267 .4196 m .75073 .42411 L s .58434 .85061 m .58485 .85152 L s .30233 .42386 m .31041 .41936 L s .46781 .85147 m .46832 .85056 L s .77058 .69841 m .77334 .70267 L s .69362 .7969 m .69489 .79963 L s .64179 .82969 m .64261 .83153 L s .3578 .79948 m .35909 .79675 L s .41006 .83143 m .41089 .82958 L s .27943 .70244 m .28221 .69818 L s .58376 .8497 m .58434 .85061 L s .79469 .56614 m .79981 .57124 L s .46832 .85056 m .4689 .84966 L s .77987 .49295 m .78643 .49799 L s .73688 .75187 m .73885 .75541 L s .65449 .34406 m .66435 .34689 L s .2531 .57096 m .25823 .56587 L s .31388 .75522 m .31586 .75168 L s .26655 .49771 m .27313 .49267 L s .38881 .34673 m .39869 .34391 L s .78947 .6342 m .79339 .63899 L s .58313 .84881 m .58376 .8497 L s .4689 .84966 m .46953 .84876 L s .25945 .63872 m .26339 .63394 L s .64085 .82786 m .64179 .82969 L s .41089 .82958 m .41184 .82776 L s 0 0 1 r .3626 .80048 m .36552 .79518 L s .53921 .85465 m .5522 .84361 L s .5 g .58244 .84792 m .58313 .84881 L s .46953 .84876 m .47023 .84787 L s .69217 .79419 m .69362 .7969 L s .35909 .79675 m .36054 .79404 L s 0 0 1 r .68664 .79442 m .68966 .79971 L s .5 g .64445 .34143 m .65449 .34406 L s .73433 .41524 m .74267 .4196 L s .39869 .34391 m .40874 .34129 L s .31041 .41936 m .31877 .41501 L s .5817 .84705 m .58244 .84792 L s .47023 .84787 m .47098 .847 L s .63979 .82604 m .64085 .82786 L s .41184 .82776 m .4129 .82594 L s .76754 .69419 m .77058 .69841 L s .28221 .69818 m .28526 .69396 L s .73469 .74835 m .73688 .75187 L s .5809 .84618 m .5817 .84705 L s .47098 .847 m .47178 .84614 L s .31586 .75168 m .31807 .74816 L s 0 0 1 r .72894 .42109 m .72775 .40387 L s .5 g .77299 .48802 m .77987 .49295 L s .63425 .33901 m .64445 .34143 L s .78925 .56113 m .79469 .56614 L s .40874 .34129 m .41894 .33888 L s .27313 .49267 m .28003 .48775 L s .58004 .84533 m .5809 .84618 L s .47178 .84614 m .47264 .84529 L s .25823 .56587 m .26368 .56086 L s .69055 .7915 m .69217 .79419 L s .36054 .79404 m .36218 .79135 L s .63861 .82424 m .63979 .82604 L s .78525 .62947 m .78947 .6342 L s .4129 .82594 m .41409 .82414 L s .26339 .63394 m .26762 .62921 L s .57912 .8445 m .58004 .84533 L s .47264 .84529 m .47356 .84445 L s .72571 .41105 m .73433 .41524 L s .31877 .41501 m .3274 .41083 L s .62391 .33681 m .63425 .33901 L s .57816 .84367 m .57912 .8445 L s .41894 .33888 m .42929 .33669 L s .47356 .84445 m .47453 .84363 L s 0 0 1 r .36552 .79518 m .36912 .78996 L s .5 g .63732 .82246 m .63861 .82424 L s .73227 .74487 m .73469 .74835 L s .41409 .82414 m .41538 .82236 L s .31807 .74816 m .3205 .74468 L s .57713 .84286 m .57816 .84367 L s .47453 .84363 m .47556 .84282 L s .76424 .69001 m .76754 .69419 L s .68875 .78883 m .69055 .7915 L s .28526 .69396 m .28858 .68979 L s 0 0 1 r .68294 .78922 m .68664 .79442 L s .5 g .36218 .79135 m .36398 .78868 L s .61344 .33483 m .62391 .33681 L s .42929 .33669 m .43977 .33473 L s .57606 .84207 m .57713 .84286 L s .47556 .84282 m .47663 .84203 L s .76581 .48322 m .77299 .48802 L s .28003 .48775 m .28723 .48296 L s .63591 .82069 m .63732 .82246 L s .7835 .5562 m .78925 .56113 L s .41538 .82236 m .4168 .8206 L s .57493 .8413 m .57606 .84207 L s .47663 .84203 m .47776 .84125 L s .26368 .56086 m .26945 .55594 L s .71685 .40703 m .72571 .41105 L s .3274 .41083 m .33628 .40682 L s .78073 .62481 m .78525 .62947 L s .60285 .33307 m .61344 .33483 L s .43977 .33473 m .45037 .33298 L s .57376 .84054 m .57493 .8413 L s .26762 .62921 m .27216 .62455 L s .47776 .84125 m .47894 .8405 L s .68678 .78619 m .68875 .78883 L s .36398 .78868 m .36596 .78604 L s .72962 .74142 m .73227 .74487 L s 0 0 1 r .5522 .84361 m .56523 .83126 L s .5 g .57253 .8398 m .57376 .84054 L s .47894 .8405 m .48017 .83976 L s .63439 .81895 m .63591 .82069 L s .3205 .74468 m .32316 .74123 L s .4168 .8206 m .41833 .81886 L s .59215 .33154 m .60285 .33307 L s .45037 .33298 m .46107 .33147 L s .57126 .83908 m .57253 .8398 L s .76068 .68588 m .76424 .69001 L s .48017 .83976 m .48144 .83904 L s .28858 .68979 m .29216 .68566 L s .58137 .33024 m .59215 .33154 L s .56994 .83838 m .57126 .83908 L s .48144 .83904 m .48277 .83834 L s .46107 .33147 m .47186 .33018 L s 0 0 1 r .36912 .78996 m .3734 .78486 L s .5 g .63275 .81723 m .63439 .81895 L s .75832 .47855 m .76581 .48322 L s 0 0 1 r .72922 .43925 m .72894 .42109 L s .5 g .70773 .40319 m .71685 .40703 L s .41833 .81886 m .41997 .81714 L s .28723 .48296 m .29473 .47829 L s .33628 .40682 m .34541 .40299 L s .56857 .8377 m .56994 .83838 L s .48277 .83834 m .48413 .83767 L s 0 0 1 r .67856 .78413 m .68294 .78922 L s .5 g .68464 .78357 m .68678 .78619 L s .57051 .32918 m .58137 .33024 L s .36596 .78604 m .36811 .78343 L s .47186 .33018 m .48272 .32913 L s .77745 .55138 m .7835 .5562 L s .26945 .55594 m .27553 .55111 L s .56717 .83704 m .56857 .8377 L s .48413 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L s .538 .82978 m .53991 .82998 L s .51283 .82997 m .51474 .82977 L s .28191 .5464 m .28858 .54179 L s .53608 .82961 m .538 .82978 L s .51474 .82977 m .51666 .8296 L s .53415 .82947 m .53608 .82961 L s .51666 .8296 m .51859 .82946 L s .76542 .61127 m .77081 .6157 L s .53221 .82936 m .53415 .82947 L s .51859 .82946 m .52052 .82935 L s .53027 .82928 m .53221 .82936 L s .52052 .82935 m .52247 .82928 L s .28211 .61545 m .28752 .61103 L s .52832 .82923 m .53027 .82928 L s .52247 .82928 m .52442 .82923 L s 0 0 1 r .37835 .77989 m .38395 .77508 L s .5 g .52637 .82922 m .52832 .82923 L s .52442 .82923 m .52637 .82922 L s .62063 .80751 m .62291 .80905 L s .42984 .80896 m .43213 .80743 L s .7484 .67384 m .75275 .67779 L s 0 0 1 r .66783 .7744 m .67352 .77919 L s .5 g .30011 .67757 m .30448 .67362 L s .6744 .77346 m .67721 .77593 L s .37557 .7758 m .37839 .77333 L s .71684 .72804 m .72036 .73131 L s .73415 .4654 m .74249 .46963 L s .33246 .73113 m .33599 .72786 L s .66899 .38972 m .67899 .39279 L 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L s .705 .71856 m .70915 .72166 L s .7427 .52894 m .75022 .53318 L s .3437 .72149 m .34787 .7184 L s 0 0 1 r .5911 .8028 m .6038 .78681 L s .5 g .30281 .53295 m .31035 .52872 L s .74755 .59854 m .75378 .60268 L s .73381 .66242 m .73893 .66615 L s .70757 .45369 m .71668 .45742 L s .29919 .60245 m .30544 .59832 L s .31398 .66594 m .3191 .66222 L s .33644 .45721 m .34556 .45349 L s .59889 .79663 m .60192 .79783 L s .45088 .79777 m .45391 .79656 L s .61638 .37752 m .62721 .37952 L s .42602 .37941 m .43685 .37742 L s 0 0 1 r .72443 .49846 m .72697 .47803 L s .5 g .65796 .76183 m .66156 .76406 L s .39127 .76393 m .39487 .76171 L s .59578 .79547 m .59889 .79663 L s .45391 .79656 m .45702 .79541 L s .60543 .37575 m .61638 .37752 L s .70063 .71554 m .705 .71856 L s .43685 .37742 m .4478 .37566 L s 0 0 1 r .39701 .76602 m .40443 .76182 L s .5 g .34787 .7184 m .35224 .71537 L s .5926 .79437 m .59578 .79547 L s .45702 .79541 m .46021 .79431 L s .7349 .52485 m .7427 .52894 L s 0 0 1 r .64709 .76124 m .65459 .7654 L s .5 g .31035 .52872 m .31816 .52462 L s .69823 .45013 m .70757 .45369 L s .34556 .45349 m .35492 .44994 L s .72846 .65877 m .73381 .66242 L s .65422 .75967 m .65796 .76183 L s .59438 .3742 m .60543 .37575 L s .3191 .66222 m .32447 .65858 L s .39487 .76171 m .39862 .75955 L s .74104 .59451 m .74755 .59854 L s .4478 .37566 m .45886 .37413 L s .58934 .79331 m .5926 .79437 L s .30544 .59832 m .31195 .59429 L s .46021 .79431 m .46347 .79326 L s .58323 .37289 m .59438 .3742 L s .45886 .37413 m .47001 .37283 L s .58601 .79231 m .58934 .79331 L s .46347 .79326 m .4668 .79226 L s .69607 .71258 m .70063 .71554 L s .35224 .71537 m .35681 .71242 L s .65033 .75757 m .65422 .75967 L s 0 0 1 r .6038 .78681 m .61623 .76975 L s .5 g .39862 .75955 m .40252 .75745 L s .57201 .37181 m .58323 .37289 L s .47001 .37283 m .48124 .37176 L s .58262 .79136 m .58601 .79231 L s .4668 .79226 m .4702 .79131 L s .68865 .44676 m .69823 .45013 L s .35492 .44994 m .36451 .44658 L s .72684 .52089 m 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m .57208 .78886 L s .48075 .78882 m .48438 .7881 L s .64214 .75355 m .6463 .75553 L s .71852 .51708 m .72684 .52089 L s .40656 .75542 m .41073 .75345 L s .32624 .52068 m .33457 .51688 L s .56479 .78748 m .56846 .78814 L s .71703 .65176 m .72286 .65522 L s .48438 .7881 m .48805 .78745 L s .33008 .65503 m .33592 .65157 L s 0 0 1 r .41241 .75786 m .42091 .75418 L s .5 g .72725 .58678 m .73428 .59058 L s .56107 .78688 m .56479 .78748 L s .68637 .70689 m .69132 .70969 L s .48805 .78745 m .49176 .78685 L s .31873 .59037 m .32577 .58658 L s .36158 .70954 m .36654 .70674 L s 0 0 1 r .63046 .75367 m .63903 .75732 L s .62774 .75259 m .62774 .75258 L s .62774 .75258 m .62834 .7517 L s .62772 .75261 m .62773 .7526 L s .61623 .76975 m .62772 .75261 L s .5 g .55732 .78634 m .56107 .78688 L s .49176 .78685 m .49551 .78632 L s .66887 .44059 m .67886 .44358 L s .37431 .44341 m .38432 .44043 L s .63784 .75165 m .64214 .75355 L s .41073 .75345 m .41503 .75155 L s .55354 .78587 m .55732 .78634 L s .49551 .78632 m .4993 .78584 L s 0 0 1 r .71655 .54086 m .72096 .51945 L s .5 g .54972 .78545 m .55354 .78587 L s .4993 .78584 m .50312 .78543 L s .54588 .7851 m .54972 .78545 L s .50312 .78543 m .50696 .78508 L s .70996 .51343 m .71852 .51708 L s .54201 .78481 m .54588 .7851 L s .50696 .78508 m .51083 .7848 L s .33457 .51688 m .34315 .51324 L s .71098 .6484 m .71703 .65176 L s .53813 .78458 m .54201 .78481 L s .68123 .70417 m .68637 .70689 L s .33592 .65157 m .34199 .64821 L s .51083 .7848 m .51471 .78457 L s .63342 .74981 m .63784 .75165 L s .36654 .70674 m .37169 .70402 L s .41503 .75155 m .41946 .74972 L s .53424 .78442 m .53813 .78458 L s .51471 .78457 m .51861 .78442 L s .53033 .78433 m .53424 .78442 L s .65869 .4378 m .66887 .44059 L s .51861 .78442 m .52251 .78432 L s .52642 .78429 m .53033 .78433 L s .52251 .78432 m .52642 .78429 L s .38432 .44043 m .39451 .43766 L s 0 0 1 r .42091 .75418 m .4299 .75078 L s .5 g .71998 .5831 m .72725 .58678 L s .32577 .58658 m .33306 .58291 L s 0 0 1 r .62141 .75031 m .62766 .75263 L s .62766 .75263 m .62768 .75264 L s .62768 .75264 m .63046 .75367 L s .5 g .62887 .74805 m .63342 .74981 L s .41946 .74972 m .42402 .74796 L s 0 0 1 r .02 w .62775 .75261 Mdot .5 Mabswid .62834 .7517 m .64003 .73275 L s .5 g .67591 .70153 m .68123 .70417 L s .64832 .43522 m .65869 .4378 L s .70116 .50994 m .70996 .51343 L s .37169 .70402 m .37702 .70139 L s .39451 .43766 m .40488 .43509 L s .34315 .51324 m .35196 .50976 L s .70469 .64514 m .71098 .6484 L s .34199 .64821 m .34829 .64496 L s 0 0 1 r .71123 .5626 m .71655 .54086 L s .5 g .6242 .74637 m .62887 .74805 L s .42402 .74796 m .42869 .74628 L s .71247 .57955 m .71998 .5831 L s 0 0 1 r .4299 .75078 m .43933 .74768 L s .5 g .33306 .58291 m .34058 .57936 L s 0 0 1 r .61191 .74726 m .62141 .75031 L s .5 g .6378 .43285 m .64832 .43522 L s .40488 .43509 m .41542 .43272 L s .67041 .69898 m .67591 .70153 L s .37702 .70139 m .38252 .69884 L s .61942 .74476 m .6242 .74637 L s .42869 .74628 m .43347 .74467 L s .69213 .50662 m .70116 .50994 L s .35196 .50976 m .361 .50645 L s .6982 .64199 m .70469 .64514 L s .34829 .64496 m .3548 .64182 L s 0 0 1 r .64003 .73275 m .65125 .71302 L s .5 g .62712 .43069 m .6378 .43285 L s .41542 .43272 m .4261 .43058 L s .61454 .74323 m .61942 .74476 L s .43347 .74467 m .43837 .74315 L s 0 0 1 r .43933 .74768 m .44917 .7449 L s .5 g .70472 .57614 m .71247 .57955 L s 0 0 1 r .70502 .58453 m .71123 .5626 L s .5 g .34058 .57936 m .34835 .57596 L s 0 0 1 r .60201 .74453 m .61191 .74726 L s .5 g .66475 .69653 m .67041 .69898 L s .38252 .69884 m .3882 .69639 L s .60955 .74178 m .61454 .74323 L s .6163 .42874 m .62712 .43069 L s .43837 .74315 m .44336 .74171 L s .68288 .50347 m .69213 .50662 L s .4261 .43058 m .43692 .42864 L s .361 .50645 m .37026 .50331 L s .69149 .63895 m .6982 .64199 L s .3548 .64182 m .36152 .63879 L s 0 0 1 r .65125 .71302 m .66193 .6926 L s .44917 .7449 m .45938 .74246 L s .5 g .60446 .74042 m .60955 .74178 L s .44336 .74171 m .44845 .74035 L s .65891 .69417 m .66475 .69653 L s 0 0 1 r .69795 .60652 m .70502 .58453 L s .5 g .3882 .69639 m .39404 .69404 L s .60537 .42702 m .6163 .42874 L s .69674 .57287 m .70472 .57614 L s .43692 .42864 m .44787 .42693 L s 0 0 1 r .59176 .74214 m .60201 .74453 L s .5 g .34835 .57596 m .35633 .5727 L s .59928 .73914 m .60446 .74042 L s .67343 .5005 m .68288 .50347 L s .44845 .74035 m .45364 .73908 L s .37026 .50331 m .37972 .50034 L s .59432 .42552 m .60537 .42702 L s .44787 .42693 m .45892 .42544 L s .68457 .63603 m .69149 .63895 L s 0 0 1 r .66193 .6926 m .67199 .67162 L s .5 g .36152 .63879 m .36844 .63588 L s 0 0 1 r .69006 .62845 m .69795 .60652 L s .5 g .65292 .69191 m .65891 .69417 L s 0 0 1 r .45938 .74246 m .4699 .74036 L s .5 g .39404 .69404 m .40004 .69179 L s .59402 .73795 m .59928 .73914 L s .45364 .73908 m .4589 .73789 L s 0 0 1 r .5812 .74009 m .59176 .74214 L s .5 g .58318 .42424 m .59432 .42552 L s .45892 .42544 m .47006 .42418 L s .68855 .56974 m .69674 .57287 L s 0 0 1 r 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