Borrar filtros
Borrar filtros

Trapz error in calculating 2D integrals: ORDER contains an invalid permutation index

4 visualizaciones (últimos 30 días)
Hi all, I am very new to matlab and I need to use trapz or cumtrapz to calculate a double integral. Part I of the code calculates the the eigenvalue and eigenvectors of a given Hamiltonian matrix at each point of x and y, and stores them into a harsh map container, this parts run perfectly fine. Part II uses the result I stored in the container to calculate the Berry curvature using the complicated formula. So now at each point of x and y in the grid, I have MBerry("1,1") , MBerry("1,2") ,MBerry("1,3") etc MBerry("2,1") ,MBerry("2,2") etc up to M("98,98") values. And I would like to calculate the trapz Integral of this 3D plot. However I get an error :
Error using permute
ORDER contains an invalid permutation index.
I should get an answer of I is equal around 25.
%q =4 case
%Part I of the code
a=0.25;
N=100;
q=1;
Eigenvector=[];
M = containers.Map();
ChernNumber = 0;
for u=0:99
for v= 0:99
disp(u);
disp(v);
x=(2*pi*u)/(q*N);
y=(2*pi*v)/(q*N);
%K is the Hamiltonian matrix
K=[-2*cos(2*pi*a-y) -exp(i*x) 0 -exp(-i*x); -exp(-i*x) -2*cos(2*pi*2*a-y) -exp(i*x) 0; 0 -exp(-i*x) -2*cos(2*pi*3*a-y) -exp(i*x); -exp(i*x) 0 -exp(-i*x) -2*cos(2*pi*4*a-y)];
%find eigenvalue
e=eig(K)
%find eigenvector
[V,D]=eig(K);
%Store eigenvector in a container hash map
keySet = sprintf("%u,%u", u, v)
Eigenvector=V(:,1)
valueSet = Eigenvector
M(keySet) = valueSet
end
end
%The above part runs perfectly fine
%Part II of the code
%This part calculates the Berry curvature using the eigenvectors calculated
%in the above code
%Define an empty container MBerry
MBerry = containers.Map();
for u=0:98
for v=0:98
keySet = sprintf("%d,%d", u, v)
%Calculation of Berry Curvature for each point of the momentum
%space grid
BerryCurvature=...
log((dot(M(sprintf('%d,%d',u,v)),M(sprintf('%d,%d',u+1,v)))/abs(dot(M(sprintf('%d,%d',u,v)),M(sprintf('%d,%d',u+1,v)))))*...
(dot(M(sprintf('%d,%d',u+1,v)),M(sprintf('%d,%d',u+1,v+1)))/abs(dot(M(sprintf('%d,%d',u+1,v)),M(sprintf('%d,%d',u+1,v+1)))))*...
(dot(M(sprintf('%d,%d',u+1,v+1)),M(sprintf('%d,%d',u,v+1)))/abs(dot(M(sprintf('%d,%d',u+1,v+1)),M(sprintf('%d,%d',u,v+1)))))*...
(dot(M(sprintf('%d,%d',u,v+1)),M(sprintf('%d,%d',u,v)))/abs(dot(M(sprintf('%d,%d',u,v+1)),M(sprintf('%d,%d',u,v))))))
MBerry(keySet) = BerryCurvature
%Calucation of the Chern number
ChernNumber= ChernNumber + sum(MBerry(keySet))
%All of the above code work fine
%Using cumtrapz to calculate the Chern Number
x=(2*pi*u)/(q*N);
y=(2*pi*v)/(q*N);
MBerry(keySet);
I = cumtrapz(y,cumtrapz(x,MBerry(keySet),2))
end
end

Respuesta aceptada

Torsten
Torsten el 25 de Ag. de 2022
Editada: Torsten el 25 de Ag. de 2022
Although I have no idea of what you are doing in your code ...
%q =4 case
%Part I of the code
a=0.25;
N=100;
q=1;
Eigenvector=[];
M = cell(100); %containers.Map();
ChernNumber = 0;
for u=0:99
for v= 0:99
%disp(u);
%disp(v);
x=(2*pi*u)/(q*N);
y=(2*pi*v)/(q*N);
%K is the Hamiltonian matrix
K=[-2*cos(2*pi*a-y) -exp(i*x) 0 -exp(-i*x); -exp(-i*x) -2*cos(2*pi*2*a-y) -exp(i*x) 0; 0 -exp(-i*x) -2*cos(2*pi*3*a-y) -exp(i*x); -exp(i*x) 0 -exp(-i*x) -2*cos(2*pi*4*a-y)];
%find eigenvalue
e=eig(K);
%find eigenvector
[V,D]=eig(K);
%Store eigenvector in a container hash map
%keySet = sprintf("%u,%u", u, v);
Eigenvector=V(:,1);
valueSet = Eigenvector;
%M(keySet) = valueSet;
M{u+1,v+1} = valueSet;
%M(keySet)
end
end
%class(M)
%size(M)
%M
%The above part runs perfectly fine
%Part II of the code
%This part calculates the Berry curvature using the eigenvectors calculated
%in the above code
%Define an empty container MBerry
%MBerry = containers.Map();
MBerry = zeros(99);
for u=0:98
for v=0:98
%keySet = sprintf("%d,%d", u, v)
%Calculation of Berry Curvature for each point of the momentum
%space grid
%BerryCurvature=...
%log((dot(M(sprintf('%d,%d',u,v)),M(sprintf('%d,%d',u+1,v)))/abs(dot(M(sprintf('%d,%d',u,v)),M(sprintf('%d,%d',u+1,v)))))*...
%(dot(M(sprintf('%d,%d',u+1,v)),M(sprintf('%d,%d',u+1,v+1)))/abs(dot(M(sprintf('%d,%d',u+1,v)),M(sprintf('%d,%d',u+1,v+1)))))*...
%(dot(M(sprintf('%d,%d',u+1,v+1)),M(sprintf('%d,%d',u,v+1)))/abs(dot(M(sprintf('%d,%d',u+1,v+1)),M(sprintf('%d,%d',u,v+1)))))*...
%(dot(M(sprintf('%d,%d',u,v+1)),M(sprintf('%d,%d',u,v)))/abs(dot(M(sprintf('%d,%d',u,v+1)),M(sprintf('%d,%d',u,v))))))
BerryCurvature = ...
log((dot(M{u+1,v+1},M{u+2,v+1})/abs(dot(M{u+1,v+1},M{u+2,v+1})))*...
(dot(M{u+2,v+1},M{u+2,v+2})/abs(dot(M{u+2,v+1},M{u+2,v+2})))*...
(dot(M{u+2,v+2},M{u+1,v+2})/abs(dot(M{u+2,v+2},M{u+1,v+2})))*...
(dot(M{u+1,v+2},M{u+1,v+1})/abs(dot(M{u+1,v+2},M{u+1,v+1}))));
MBerry(u+1,v+1) = BerryCurvature;
%Calucation of the Chern number
%ChernNumber= ChernNumber + sum(MBerry(keySet))
%All of the above code work fine
%Using cumtrapz to calculate the Chern Number
%x=(2*pi*u)/(q*N);
%y=(2*pi*v)/(q*N);
%MBerry(keySet);
%I = cumtrapz(y,cumtrapz(x,MBerry(keySet),2))
end
end
x = (2*pi*(0:98))/(q*N);
y = (2*pi*(0:98))/(q*N);
I = cumtrapz(y,cumtrapz(x,MBerry,2))
I =
0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 + 0.0001i -0.0000 + 0.0001i -0.0000 + 0.0001i -0.0000 + 0.0001i -0.0000 + 0.0001i -0.0000 + 0.0001i -0.0000 + 0.0001i -0.0000 + 0.0001i -0.0000 + 0.0001i -0.0000 + 0.0001i -0.0000 + 0.0001i -0.0000 + 0.0001i -0.0000 + 0.0001i -0.0000 + 0.0001i -0.0000 + 0.0001i -0.0000 + 0.0002i -0.0000 + 0.0002i -0.0000 + 0.0002i -0.0000 + 0.0002i -0.0000 + 0.0002i -0.0000 + 0.0002i -0.0000 + 0.0002i -0.0000 + 0.0002i -0.0000 + 0.0002i -0.0000 + 0.0002i -0.0000 + 0.0002i -0.0000 + 0.0002i -0.0000 + 0.0002i -0.0000 + 0.0002i -0.0000 + 0.0002i -0.0000 + 0.0003i -0.0000 + 0.0003i -0.0000 + 0.0003i -0.0000 + 0.0003i -0.0000 + 0.0003i -0.0000 + 0.0003i -0.0000 + 0.0003i -0.0000 + 0.0003i -0.0000 + 0.0003i -0.0000 + 0.0003i -0.0000 + 0.0003i -0.0000 + 0.0003i -0.0000 + 0.0003i -0.0000 + 0.0003i -0.0000 + 0.0003i -0.0000 + 0.0003i -0.0000 + 0.0003i -0.0000 + 0.0003i -0.0000 + 0.0004i -0.0000 + 0.0004i -0.0000 + 0.0004i -0.0000 + 0.0004i -0.0000 + 0.0004i -0.0000 + 0.0004i -0.0000 + 0.0004i -0.0000 + 0.0004i -0.0000 + 0.0004i -0.0000 + 0.0004i -0.0000 + 0.0004i -0.0000 + 0.0004i -0.0000 + 0.0004i -0.0000 + 0.0005i -0.0000 + 0.0005i -0.0000 + 0.0005i -0.0000 + 0.0005i -0.0000 + 0.0005i -0.0000 + 0.0005i -0.0000 + 0.0005i -0.0000 + 0.0005i -0.0000 + 0.0005i -0.0000 + 0.0005i -0.0000 + 0.0005i -0.0000 + 0.0005i -0.0000 + 0.0005i -0.0000 + 0.0005i -0.0000 + 0.0005i -0.0000 + 0.0005i -0.0000 + 0.0005i -0.0000 + 0.0005i -0.0000 + 0.0006i -0.0000 + 0.0006i -0.0000 + 0.0006i -0.0000 + 0.0006i -0.0000 + 0.0006i -0.0000 + 0.0006i -0.0000 + 0.0006i -0.0000 + 0.0006i -0.0000 + 0.0006i -0.0000 + 0.0006i -0.0000 + 0.0006i 0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 + 0.0001i -0.0000 + 0.0001i -0.0000 + 0.0001i -0.0000 + 0.0001i -0.0000 + 0.0001i -0.0000 + 0.0001i -0.0000 + 0.0002i -0.0000 + 0.0002i 0.0000 + 0.0002i 0.0000 + 0.0002i 0.0000 + 0.0002i 0.0000 + 0.0002i -0.0000 + 0.0003i -0.0000 + 0.0003i -0.0000 + 0.0003i -0.0000 + 0.0003i -0.0000 + 0.0003i -0.0000 + 0.0003i -0.0000 + 0.0003i -0.0000 + 0.0003i -0.0000 + 0.0003i -0.0000 + 0.0003i -0.0000 + 0.0003i -0.0000 + 0.0004i -0.0000 + 0.0004i -0.0000 + 0.0004i -0.0000 + 0.0004i -0.0000 + 0.0004i -0.0000 + 0.0004i -0.0000 + 0.0004i -0.0000 + 0.0005i -0.0000 + 0.0005i -0.0000 + 0.0005i -0.0000 + 0.0005i -0.0000 + 0.0005i -0.0000 + 0.0005i -0.0000 + 0.0006i -0.0000 + 0.0006i -0.0000 + 0.0006i -0.0000 + 0.0006i -0.0000 + 0.0006i -0.0000 + 0.0006i -0.0000 + 0.0006i -0.0000 + 0.0006i -0.0000 + 0.0006i -0.0000 + 0.0007i -0.0000 + 0.0007i -0.0000 + 0.0007i -0.0000 + 0.0007i -0.0000 + 0.0007i -0.0000 + 0.0007i -0.0000 + 0.0007i -0.0000 + 0.0007i -0.0000 + 0.0007i -0.0000 + 0.0008i -0.0000 + 0.0008i -0.0000 + 0.0008i -0.0000 + 0.0008i -0.0000 + 0.0008i -0.0000 + 0.0009i -0.0000 + 0.0009i -0.0000 + 0.0009i -0.0000 + 0.0009i -0.0000 + 0.0009i -0.0000 + 0.0009i -0.0000 + 0.0009i -0.0000 + 0.0009i -0.0000 + 0.0009i -0.0000 + 0.0010i -0.0000 + 0.0010i -0.0000 + 0.0010i -0.0000 + 0.0010i -0.0000 + 0.0010i -0.0000 + 0.0010i -0.0000 + 0.0010i -0.0000 + 0.0010i -0.0000 + 0.0010i -0.0000 + 0.0011i -0.0000 + 0.0011i -0.0000 + 0.0011i -0.0000 + 0.0011i -0.0000 + 0.0011i -0.0000 + 0.0011i -0.0000 + 0.0012i -0.0000 + 0.0012i -0.0000 + 0.0012i -0.0000 + 0.0012i -0.0000 + 0.0012i -0.0000 + 0.0012i -0.0000 + 0.0012i -0.0000 + 0.0013i -0.0000 + 0.0013i -0.0000 + 0.0013i 0.0000 + 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0001i 0.0000 + 0.0001i -0.0000 + 0.0001i -0.0000 + 0.0001i -0.0000 + 0.0001i -0.0000 + 0.0002i -0.0000 + 0.0002i -0.0000 + 0.0002i -0.0000 + 0.0002i 0.0000 + 0.0003i 0.0000 + 0.0003i 0.0000 + 0.0003i 0.0000 + 0.0003i 0.0000 + 0.0004i 0.0000 + 0.0004i -0.0000 + 0.0004i -0.0000 + 0.0004i -0.0000 + 0.0004i -0.0000 + 0.0005i -0.0000 + 0.0005i -0.0000 + 0.0005i -0.0000 + 0.0005i -0.0000 + 0.0005i -0.0000 + 0.0005i -0.0000 + 0.0005i -0.0000 + 0.0006i -0.0000 + 0.0006i -0.0000 + 0.0006i -0.0000 + 0.0006i -0.0000 + 0.0006i -0.0000 + 0.0007i -0.0000 + 0.0007i -0.0000 + 0.0007i -0.0000 + 0.0007i -0.0000 + 0.0008i -0.0000 + 0.0008i -0.0000 + 0.0008i -0.0000 + 0.0008i -0.0000 + 0.0009i -0.0000 + 0.0009i -0.0000 + 0.0009i -0.0000 + 0.0009i -0.0000 + 0.0009i -0.0000 + 0.0010i -0.0000 + 0.0010i -0.0000 + 0.0010i -0.0000 + 0.0010i -0.0000 + 0.0010i -0.0000 + 0.0010i -0.0000 + 0.0010i -0.0000 + 0.0010i -0.0000 + 0.0011i -0.0000 + 0.0011i -0.0000 + 0.0011i -0.0000 + 0.0011i -0.0000 + 0.0011i -0.0000 + 0.0012i -0.0000 + 0.0012i -0.0000 + 0.0012i -0.0000 + 0.0013i -0.0000 + 0.0013i -0.0000 + 0.0013i -0.0000 + 0.0013i -0.0000 + 0.0014i -0.0000 + 0.0014i -0.0000 + 0.0014i -0.0000 + 0.0014i -0.0000 + 0.0014i -0.0000 + 0.0014i -0.0000 + 0.0015i -0.0000 + 0.0015i -0.0000 + 0.0015i -0.0000 + 0.0015i -0.0000 + 0.0015i -0.0000 + 0.0015i -0.0000 + 0.0015i -0.0000 + 0.0016i -0.0000 + 0.0016i -0.0000 + 0.0016i -0.0000 + 0.0016i -0.0000 + 0.0016i -0.0000 + 0.0017i -0.0000 + 0.0017i -0.0000 + 0.0017i -0.0000 + 0.0018i -0.0000 + 0.0018i -0.0000 + 0.0018i -0.0000 + 0.0018i -0.0000 + 0.0019i -0.0000 + 0.0019i -0.0000 + 0.0019i -0.0000 + 0.0019i -0.0000 + 0.0019i -0.0000 + 0.0019i -0.0000 + 0.0020i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0001i 0.0000 + 0.0001i 0.0000 + 0.0001i -0.0000 + 0.0001i -0.0000 + 0.0002i -0.0000 + 0.0002i -0.0000 + 0.0002i -0.0000 + 0.0003i -0.0000 + 0.0003i -0.0000 + 0.0003i -0.0000 + 0.0004i 0.0000 + 0.0004i 0.0000 + 0.0004i 0.0000 + 0.0005i 0.0000 + 0.0005i 0.0000 + 0.0005i 0.0000 + 0.0006i 0.0000 + 0.0006i -0.0000 + 0.0006i -0.0000 + 0.0006i -0.0000 + 0.0006i -0.0000 + 0.0007i -0.0000 + 0.0007i -0.0000 + 0.0007i -0.0000 + 0.0007i -0.0000 + 0.0007i -0.0000 + 0.0008i -0.0000 + 0.0008i -0.0000 + 0.0008i -0.0000 + 0.0008i -0.0000 + 0.0009i -0.0000 + 0.0009i -0.0000 + 0.0009i -0.0000 + 0.0010i -0.0000 + 0.0010i -0.0000 + 0.0011i -0.0000 + 0.0011i -0.0000 + 0.0011i -0.0000 + 0.0012i -0.0000 + 0.0012i -0.0000 + 0.0012i -0.0000 + 0.0013i -0.0000 + 0.0013i -0.0000 + 0.0013i -0.0000 + 0.0013i -0.0000 + 0.0013i -0.0000 + 0.0014i -0.0000 + 0.0014i -0.0000 + 0.0014i -0.0000 + 0.0014i -0.0000 + 0.0014i -0.0000 + 0.0014i -0.0000 + 0.0015i -0.0000 + 0.0015i -0.0000 + 0.0015i -0.0000 + 0.0016i -0.0000 + 0.0016i -0.0000 + 0.0016i -0.0000 + 0.0017i -0.0000 + 0.0017i -0.0000 + 0.0017i -0.0000 + 0.0018i -0.0000 + 0.0018i -0.0000 + 0.0019i -0.0000 + 0.0019i -0.0000 + 0.0019i -0.0000 + 0.0019i -0.0000 + 0.0020i -0.0000 + 0.0020i -0.0000 + 0.0020i -0.0000 + 0.0020i -0.0000 + 0.0020i -0.0000 + 0.0021i -0.0000 + 0.0021i -0.0000 + 0.0021i -0.0000 + 0.0021i -0.0000 + 0.0021i -0.0000 + 0.0022i -0.0000 + 0.0022i -0.0000 + 0.0022i -0.0000 + 0.0022i -0.0000 + 0.0023i -0.0000 + 0.0023i -0.0000 + 0.0023i -0.0000 + 0.0024i -0.0000 + 0.0024i -0.0000 + 0.0025i -0.0000 + 0.0025i -0.0000 + 0.0025i -0.0000 + 0.0026i -0.0000 + 0.0026i -0.0000 + 0.0026i -0.0000 + 0.0026i -0.0000 + 0.0027i -0.0000 + 0.0027i -0.0000 + 0.0027i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0001i 0.0000 + 0.0001i 0.0000 + 0.0001i -0.0000 + 0.0002i -0.0000 + 0.0002i -0.0000 + 0.0002i -0.0000 + 0.0003i -0.0000 + 0.0003i -0.0000 + 0.0004i -0.0000 + 0.0004i -0.0000 + 0.0005i -0.0000 + 0.0005i 0.0000 + 0.0006i 0.0000 + 0.0006i 0.0000 + 0.0007i 0.0000 + 0.0007i 0.0000 + 0.0007i 0.0000 + 0.0008i 0.0000 + 0.0008i 0.0000 + 0.0008i -0.0000 + 0.0008i 0.0000 + 0.0009i 0.0000 + 0.0009i -0.0000 + 0.0009i -0.0000 + 0.0009i -0.0000 + 0.0010i -0.0000 + 0.0010i -0.0000 + 0.0010i -0.0000 + 0.0011i -0.0000 + 0.0011i -0.0000 + 0.0011i -0.0000 + 0.0012i -0.0000 + 0.0012i -0.0000 + 0.0013i -0.0000 + 0.0013i -0.0000 + 0.0014i -0.0000 + 0.0014i -0.0000 + 0.0015i -0.0000 + 0.0015i -0.0000 + 0.0016i -0.0000 + 0.0016i -0.0000 + 0.0016i -0.0000 + 0.0017i -0.0000 + 0.0017i -0.0000 + 0.0017i -0.0000 + 0.0017i -0.0000 + 0.0018i -0.0000 + 0.0018i -0.0000 + 0.0018i -0.0000 + 0.0018i -0.0000 + 0.0019i -0.0000 + 0.0019i -0.0000 + 0.0019i -0.0000 + 0.0019i -0.0000 + 0.0020i -0.0000 + 0.0020i -0.0000 + 0.0021i -0.0000 + 0.0021i -0.0000 + 0.0022i -0.0000 + 0.0022i -0.0000 + 0.0023i -0.0000 + 0.0023i -0.0000 + 0.0024i -0.0000 + 0.0024i -0.0000 + 0.0025i -0.0000 + 0.0025i -0.0000 + 0.0025i -0.0000 + 0.0026i -0.0000 + 0.0026i -0.0000 + 0.0026i -0.0000 + 0.0026i -0.0000 + 0.0027i -0.0000 + 0.0027i -0.0000 + 0.0027i -0.0000 + 0.0027i -0.0000 + 0.0027i -0.0000 + 0.0028i -0.0000 + 0.0028i -0.0000 + 0.0028i -0.0000 + 0.0029i -0.0000 + 0.0029i -0.0000 + 0.0030i -0.0000 + 0.0030i -0.0000 + 0.0031i -0.0000 + 0.0031i -0.0000 + 0.0032i -0.0000 + 0.0032i -0.0000 + 0.0033i -0.0000 + 0.0033i -0.0000 + 0.0033i -0.0000 + 0.0034i -0.0000 + 0.0034i -0.0000 + 0.0034i -0.0000 + 0.0035i -0.0000 + 0.0035i -0.0000 + 0.0035i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0001i 0.0000 + 0.0001i 0.0000 + 0.0001i 0.0000 + 0.0002i -0.0000 + 0.0002i -0.0000 + 0.0003i -0.0000 + 0.0003i -0.0000 + 0.0004i -0.0000 + 0.0004i -0.0000 + 0.0005i -0.0000 + 0.0005i -0.0000 + 0.0006i 0.0000 + 0.0007i 0.0000 + 0.0007i 0.0000 + 0.0008i 0.0000 + 0.0008i 0.0000 + 0.0009i 0.0000 + 0.0009i 0.0000 + 0.0010i 0.0000 + 0.0010i 0.0000 + 0.0010i 0.0000 + 0.0011i 0.0000 + 0.0011i 0.0000 + 0.0011i 0.0000 + 0.0012i -0.0000 + 0.0012i -0.0000 + 0.0012i -0.0000 + 0.0012i -0.0000 + 0.0013i -0.0000 + 0.0013i -0.0000 + 0.0014i -0.0000 + 0.0014i -0.0000 + 0.0015i -0.0000 + 0.0015i -0.0000 + 0.0016i -0.0000 + 0.0017i -0.0000 + 0.0017i -0.0000 + 0.0018i -0.0000 + 0.0019i -0.0000 + 0.0019i -0.0000 + 0.0020i -0.0000 + 0.0020i -0.0000 + 0.0021i -0.0000 + 0.0021i -0.0000 + 0.0021i -0.0000 + 0.0022i -0.0000 + 0.0022i -0.0000 + 0.0022i -0.0000 + 0.0022i -0.0000 + 0.0023i -0.0000 + 0.0023i -0.0000 + 0.0023i -0.0000 + 0.0024i -0.0000 + 0.0024i -0.0000 + 0.0024i -0.0000 + 0.0025i -0.0000 + 0.0025i -0.0000 + 0.0026i -0.0000 + 0.0027i -0.0000 + 0.0027i -0.0000 + 0.0028i -0.0000 + 0.0029i -0.0000 + 0.0029i -0.0000 + 0.0030i -0.0000 + 0.0030i -0.0000 + 0.0031i -0.0000 + 0.0031i -0.0000 + 0.0032i -0.0000 + 0.0032i -0.0000 + 0.0032i -0.0000 + 0.0033i -0.0000 + 0.0033i -0.0000 + 0.0033i -0.0000 + 0.0034i -0.0000 + 0.0034i -0.0000 + 0.0034i -0.0000 + 0.0035i -0.0000 + 0.0035i -0.0000 + 0.0035i -0.0000 + 0.0036i -0.0000 + 0.0036i -0.0000 + 0.0037i -0.0000 + 0.0037i -0.0000 + 0.0038i -0.0000 + 0.0038i -0.0000 + 0.0039i -0.0000 + 0.0040i -0.0000 + 0.0040i -0.0000 + 0.0041i -0.0000 + 0.0042i -0.0000 + 0.0042i -0.0000 + 0.0043i -0.0000 + 0.0043i -0.0000 + 0.0043i -0.0000 + 0.0044i -0.0000 + 0.0044i -0.0000 + 0.0044i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0001i 0.0000 + 0.0001i 0.0000 + 0.0002i 0.0000 + 0.0002i -0.0000 + 0.0003i -0.0000 + 0.0003i -0.0000 + 0.0004i -0.0000 + 0.0004i -0.0000 + 0.0005i -0.0000 + 0.0006i -0.0000 + 0.0007i -0.0000 + 0.0008i 0.0000 + 0.0008i 0.0000 + 0.0009i 0.0000 + 0.0010i 0.0000 + 0.0010i 0.0000 + 0.0011i 0.0000 + 0.0011i 0.0000 + 0.0012i 0.0000 + 0.0012i 0.0000 + 0.0013i 0.0000 + 0.0013i 0.0000 + 0.0013i 0.0000 + 0.0014i 0.0000 + 0.0014i -0.0000 + 0.0014i -0.0000 + 0.0015i -0.0000 + 0.0015i -0.0000 + 0.0016i -0.0000 + 0.0016i -0.0000 + 0.0017i -0.0000 + 0.0017i -0.0000 + 0.0018i -0.0000 + 0.0019i -0.0000 + 0.0020i -0.0000 + 0.0020i -0.0000 + 0.0021i -0.0000 + 0.0022i -0.0000 + 0.0023i -0.0000 + 0.0023i -0.0000 + 0.0024i -0.0000 + 0.0025i -0.0000 + 0.0025i -0.0000 + 0.0026i -0.0000 + 0.0026i -0.0000 + 0.0026i -0.0000 + 0.0027i -0.0000 + 0.0027i -0.0000 + 0.0028i -0.0000 + 0.0028i -0.0000 + 0.0028i -0.0000 + 0.0029i -0.0000 + 0.0029i -0.0000 + 0.0030i -0.0000 + 0.0030i -0.0000 + 0.0031i -0.0000 + 0.0031i -0.0000 + 0.0032i -0.0000 + 0.0033i -0.0000 + 0.0033i -0.0000 + 0.0034i -0.0000 + 0.0035i -0.0000 + 0.0036i -0.0000 + 0.0037i -0.0000 + 0.0037i -0.0000 + 0.0038i -0.0000 + 0.0038i -0.0000 + 0.0039i -0.0000 + 0.0039i -0.0000 + 0.0040i -0.0000 + 0.0040i -0.0000 + 0.0041i -0.0000 + 0.0041i -0.0000 + 0.0041i -0.0000 + 0.0042i -0.0000 + 0.0042i -0.0000 + 0.0042i -0.0000 + 0.0043i -0.0000 + 0.0043i -0.0000 + 0.0044i -0.0000 + 0.0044i -0.0000 + 0.0045i -0.0000 + 0.0046i -0.0000 + 0.0046i -0.0000 + 0.0047i -0.0000 + 0.0048i -0.0000 + 0.0049i -0.0000 + 0.0050i -0.0000 + 0.0050i -0.0000 + 0.0051i -0.0000 + 0.0052i -0.0000 + 0.0052i -0.0000 + 0.0053i -0.0000 + 0.0053i -0.0000 + 0.0054i -0.0000 + 0.0054i -0.0000 + 0.0054i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0001i 0.0000 + 0.0001i 0.0000 + 0.0002i 0.0000 + 0.0002i -0.0000 + 0.0003i -0.0000 + 0.0004i -0.0000 + 0.0004i -0.0000 + 0.0005i -0.0000 + 0.0006i -0.0000 + 0.0007i -0.0000 + 0.0008i 0.0000 + 0.0009i 0.0000 + 0.0010i 0.0000 + 0.0011i 0.0000 + 0.0012i 0.0000 + 0.0012i 0.0000 + 0.0013i 0.0000 + 0.0014i 0.0000 + 0.0014i 0.0000 + 0.0015i 0.0000 + 0.0015i 0.0000 + 0.0016i 0.0000 + 0.0016i 0.0000 + 0.0017i 0.0000 + 0.0017i 0.0000 + 0.0017i 0.0000 + 0.0018i -0.0000 + 0.0018i -0.0000 + 0.0019i -0.0000 + 0.0020i -0.0000 + 0.0020i -0.0000 + 0.0021i -0.0000 + 0.0022i -0.0000 + 0.0023i -0.0000 + 0.0024i -0.0000 + 0.0025i -0.0000 + 0.0026i -0.0000 + 0.0027i -0.0000 + 0.0027i -0.0000 + 0.0028i -0.0000 + 0.0029i -0.0000 + 0.0030i -0.0000 + 0.0030i -0.0000 + 0.0031i -0.0000 + 0.0031i -0.0000 + 0.0032i -0.0000 + 0.0032i -0.0000 + 0.0033i -0.0000 + 0.0033i -0.0000 + 0.0034i -0.0000 + 0.0034i -0.0000 + 0.0035i -0.0000 + 0.0035i -0.0000 + 0.0036i -0.0000 + 0.0036i -0.0000 + 0.0037i -0.0000 + 0.0038i -0.0000 + 0.0039i -0.0000 + 0.0039i -0.0000 + 0.0040i -0.0000 + 0.0041i -0.0000 + 0.0042i -0.0000 + 0.0043i -0.0000 + 0.0044i -0.0000 + 0.0045i -0.0000 + 0.0046i -0.0000 + 0.0046i -0.0000 + 0.0047i -0.0000 + 0.0048i -0.0000 + 0.0048i -0.0000 + 0.0049i -0.0000 + 0.0049i -0.0000 + 0.0049i -0.0000 + 0.0050i -0.0000 + 0.0050i -0.0000 + 0.0051i -0.0000 + 0.0051i -0.0000 + 0.0052i -0.0000 + 0.0052i -0.0000 + 0.0053i -0.0000 + 0.0054i -0.0000 + 0.0054i -0.0000 + 0.0055i -0.0000 + 0.0056i -0.0000 + 0.0057i -0.0000 + 0.0058i -0.0000 + 0.0059i -0.0000 + 0.0060i -0.0000 + 0.0061i -0.0000 + 0.0062i -0.0000 + 0.0062i -0.0000 + 0.0063i -0.0000 + 0.0064i -0.0000 + 0.0064i -0.0000 + 0.0065i -0.0000 + 0.0065i -0.0000 + 0.0066i 0.0000 + 0.0000i 0.0000 + 0.0001i 0.0000 + 0.0001i 0.0000 + 0.0002i 0.0000 + 0.0002i 0.0000 + 0.0003i -0.0000 + 0.0004i -0.0000 + 0.0004i -0.0000 + 0.0005i -0.0000 + 0.0006i -0.0000 + 0.0007i -0.0000 + 0.0008i -0.0000 + 0.0010i 0.0000 + 0.0011i 0.0000 + 0.0012i 0.0000 + 0.0013i 0.0000 + 0.0014i 0.0000 + 0.0015i 0.0000 + 0.0016i 0.0000 + 0.0016i 0.0000 + 0.0017i 0.0000 + 0.0018i 0.0000 + 0.0018i 0.0000 + 0.0019i 0.0000 + 0.0019i 0.0000 + 0.0020i 0.0000 + 0.0020i 0.0000 + 0.0021i 0.0000 + 0.0021i -0.0000 + 0.0022i -0.0000 + 0.0023i -0.0000 + 0.0023i -0.0000 + 0.0024i -0.0000 + 0.0025i -0.0000 + 0.0026i -0.0000 + 0.0027i -0.0000 + 0.0028i -0.0000 + 0.0029i -0.0000 + 0.0030i -0.0000 + 0.0032i -0.0000 + 0.0033i -0.0000 + 0.0034i -0.0000 + 0.0035i -0.0000 + 0.0035i -0.0000 + 0.0036i -0.0000 + 0.0037i -0.0000 + 0.0037i -0.0000 + 0.0038i -0.0000 + 0.0038i -0.0000 + 0.0039i -0.0000 + 0.0039i -0.0000 + 0.0040i -0.0000 + 0.0040i -0.0000 + 0.0041i -0.0000 + 0.0042i -0.0000 + 0.0042i -0.0000 + 0.0043i -0.0000 + 0.0044i -0.0000 + 0.0045i -0.0000 + 0.0046i -0.0000 + 0.0047i -0.0000 + 0.0048i -0.0000 + 0.0049i -0.0000 + 0.0050i -0.0000 + 0.0051i -0.0000 + 0.0052i -0.0000 + 0.0053i -0.0000 + 0.0054i -0.0000 + 0.0055i -0.0000 + 0.0056i -0.0000 + 0.0056i -0.0000 + 0.0057i -0.0000 + 0.0058i -0.0000 + 0.0058i -0.0000 + 0.0059i -0.0000 + 0.0059i -0.0000 + 0.0060i -0.0000 + 0.0060i -0.0000 + 0.0061i -0.0000 + 0.0061i -0.0000 + 0.0062i -0.0000 + 0.0063i -0.0000 + 0.0064i -0.0000 + 0.0064i -0.0000 + 0.0065i -0.0000 + 0.0066i -0.0000 + 0.0068i -0.0000 + 0.0069i -0.0000 + 0.0070i -0.0000 + 0.0071i -0.0000 + 0.0072i -0.0000 + 0.0073i -0.0000 + 0.0074i -0.0000 + 0.0075i -0.0000 + 0.0076i -0.0000 + 0.0076i -0.0000 + 0.0077i -0.0000 + 0.0077i -0.0000 + 0.0078i 0.0000 + 0.0000i 0.0000 + 0.0001i 0.0000 + 0.0001i 0.0000 + 0.0002i 0.0000 + 0.0003i 0.0000 + 0.0003i -0.0000 + 0.0004i -0.0000 + 0.0005i -0.0000 + 0.0006i -0.0000 + 0.0007i -0.0000 + 0.0009i -0.0000 + 0.0010i 0.0000 + 0.0011i 0.0000 + 0.0013i 0.0000 + 0.0014i 0.0000 + 0.0015i 0.0000 + 0.0016i 0.0000 + 0.0017i 0.0000 + 0.0018i 0.0000 + 0.0019i 0.0000 + 0.0020i 0.0000 + 0.0021i 0.0000 + 0.0021i 0.0000 + 0.0022i 0.0000 + 0.0022i 0.0000 + 0.0023i 0.0000 + 0.0024i 0.0000 + 0.0024i -0.0000 + 0.0025i -0.0000 + 0.0026i -0.0000 + 0.0026i -0.0000 + 0.0027i -0.0000 + 0.0028i -0.0000 + 0.0029i -0.0000 + 0.0030i -0.0000 + 0.0032i -0.0000 + 0.0033i -0.0000 + 0.0034i -0.0000 + 0.0036i -0.0000 + 0.0037i -0.0000 + 0.0038i -0.0000 + 0.0039i -0.0000 + 0.0040i -0.0000 + 0.0041i -0.0000 + 0.0042i -0.0000 + 0.0043i -0.0000 + 0.0044i -0.0000 + 0.0044i -0.0000 + 0.0045i -0.0000 + 0.0046i -0.0000 + 0.0046i -0.0000 + 0.0047i -0.0000 + 0.0047i -0.0000 + 0.0048i -0.0000 + 0.0049i -0.0000 + 0.0049i -0.0000 + 0.0050i -0.0000 + 0.0051i -0.0000 + 0.0052i -0.0000 + 0.0053i -0.0000 + 0.0055i -0.0000 + 0.0056i -0.0000 + 0.0057i -0.0000 + 0.0059i -0.0000 + 0.0060i -0.0000 + 0.0061i -0.0000 + 0.0062i -0.0000 + 0.0063i -0.0000 + 0.0064i -0.0000 + 0.0065i -0.0000 + 0.0066i -0.0000 + 0.0067i -0.0000 + 0.0067i -0.0000 + 0.0068i -0.0000 + 0.0069i -0.0000 + 0.0069i -0.0000 + 0.0070i -0.0000 + 0.0070i -0.0000 + 0.0071i -0.0000 + 0.0072i -0.0000 + 0.0073i -0.0000 + 0.0073i -0.0000 + 0.0074i -0.0000 + 0.0075i -0.0000 + 0.0077i -0.0000 + 0.0078i -0.0000 + 0.0079i -0.0000 + 0.0080i -0.0000 + 0.0082i -0.0000 + 0.0083i -0.0000 + 0.0084i -0.0000 + 0.0085i -0.0000 + 0.0087i -0.0000 + 0.0087i -0.0000 + 0.0088i -0.0000 + 0.0089i -0.0000 + 0.0090i -0.0000 + 0.0090i -0.0000 + 0.0091i 0.0000 + 0.0000i 0.0000 + 0.0001i 0.0000 + 0.0001i 0.0000 + 0.0002i 0.0000 + 0.0003i 0.0000 + 0.0004i -0.0000 + 0.0005i -0.0000 + 0.0006i 0.0000 + 0.0007i 0.0000 + 0.0008i -0.0000 + 0.0010i -0.0000 + 0.0011i 0.0000 + 0.0013i 0.0000 + 0.0015i 0.0000 + 0.0016i 0.0000 + 0.0017i 0.0000 + 0.0019i 0.0000 + 0.0020i 0.0000 + 0.0021i 0.0000 + 0.0022i 0.0000 + 0.0023i 0.0000 + 0.0024i 0.0000 + 0.0025i 0.0000 + 0.0025i 0.0000 + 0.0026i 0.0000 + 0.0027i 0.0000 + 0.0027i 0.0000 + 0.0028i -0.0000 + 0.0029i -0.0000 + 0.0030i -0.0000 + 0.0030i -0.0000 + 0.0031i -0.0000 + 0.0033i -0.0000 + 0.0034i -0.0000 + 0.0035i -0.0000 + 0.0036i -0.0000 + 0.0038i -0.0000 + 0.0040i -0.0000 + 0.0041i -0.0000 + 0.0043i -0.0000 + 0.0044i -0.0000 + 0.0045i -0.0000 + 0.0047i -0.0000 + 0.0048i -0.0000 + 0.0049i -0.0000 + 0.0050i -0.0000 + 0.0050i -0.0000 + 0.0051i -0.0000 + 0.0052i -0.0000 + 0.0053i -0.0000 + 0.0053i -0.0000 + 0.0054i -0.0000 + 0.0055i -0.0000 + 0.0055i -0.0000 + 0.0056i -0.0000 + 0.0057i -0.0000 + 0.0058i -0.0000 + 0.0059i -0.0000 + 0.0060i -0.0000 + 0.0062i -0.0000 + 0.0063i -0.0000 + 0.0065i -0.0000 + 0.0066i -0.0000 + 0.0068i -0.0000 + 0.0069i -0.0000 + 0.0071i -0.0000 + 0.0072i -0.0000 + 0.0073i -0.0000 + 0.0074i -0.0000 + 0.0075i -0.0000 + 0.0076i -0.0000 + 0.0077i -0.0000 + 0.0078i -0.0000 + 0.0078i -0.0000 + 0.0079i -0.0000 + 0.0080i -0.0000 + 0.0080i -0.0000 + 0.0081i -0.0000 + 0.0082i -0.0000 + 0.0083i -0.0000 + 0.0084i -0.0000 + 0.0085i -0.0000 + 0.0086i -0.0000 + 0.0087i -0.0000 + 0.0088i -0.0000 + 0.0090i -0.0000 + 0.0091i -0.0000 + 0.0093i -0.0000 + 0.0094i -0.0000 + 0.0096i -0.0000 + 0.0097i -0.0000 + 0.0099i -0.0000 + 0.0100i -0.0000 + 0.0101i -0.0000 + 0.0102i -0.0000 + 0.0103i -0.0000 + 0.0104i -0.0000 + 0.0104i -0.0000 + 0.0105i 0.0000 + 0.0000i 0.0000 + 0.0001i 0.0000 + 0.0002i 0.0000 + 0.0002i 0.0000 + 0.0003i 0.0000 + 0.0004i 0.0000 + 0.0005i 0.0000 + 0.0007i 0.0000 + 0.0008i 0.0000 + 0.0010i 0.0000 + 0.0011i 0.0000 + 0.0013i 0.0000 + 0.0015i 0.0000 + 0.0017i 0.0000 + 0.0018i 0.0000 + 0.0020i 0.0000 + 0.0021i 0.0000 + 0.0023i 0.0000 + 0.0024i 0.0000 + 0.0025i 0.0000 + 0.0026i 0.0000 + 0.0027i 0.0000 + 0.0028i 0.0000 + 0.0029i 0.0000 + 0.0029i 0.0000 + 0.0030i 0.0000 + 0.0031i 0.0000 + 0.0032i 0.0000 + 0.0033i 0.0000 + 0.0034i 0.0000 + 0.0035i 0.0000 + 0.0036i -0.0000 + 0.0037i -0.0000 + 0.0038i -0.0000 + 0.0040i -0.0000 + 0.0041i -0.0000 + 0.0043i -0.0000 + 0.0045i -0.0000 + 0.0047i -0.0000 + 0.0048i -0.0000 + 0.0050i -0.0000 + 0.0052i -0.0000 + 0.0053i -0.0000 + 0.0054i -0.0000 + 0.0055i -0.0000 + 0.0056i -0.0000 + 0.0057i -0.0000 + 0.0058i -0.0000 + 0.0059i -0.0000 + 0.0060i -0.0000 + 0.0060i -0.0000 + 0.0061i -0.0000 + 0.0062i -0.0000 + 0.0063i -0.0000 + 0.0064i -0.0000 + 0.0065i -0.0000 + 0.0066i -0.0000 + 0.0067i -0.0000 + 0.0069i -0.0000 + 0.0070i -0.0000 + 0.0072i -0.0000 + 0.0073i -0.0000 + 0.0075i -0.0000 + 0.0077i -0.0000 + 0.0079i -0.0000 + 0.0080i -0.0000 + 0.0082i -0.0000 + 0.0083i -0.0000 + 0.0084i -0.0000 + 0.0086i -0.0000 + 0.0087i -0.0000 + 0.0088i -0.0000 + 0.0088i -0.0000 + 0.0089i -0.0000 + 0.0090i -0.0000 + 0.0091i -0.0000 + 0.0091i -0.0000 + 0.0092i -0.0000 + 0.0093i -0.0000 + 0.0094i -0.0000 + 0.0095i -0.0000 + 0.0096i -0.0000 + 0.0097i -0.0000 + 0.0099i -0.0000 + 0.0100i -0.0000 + 0.0102i -0.0000 + 0.0104i -0.0000 + 0.0105i -0.0000 + 0.0107i -0.0000 + 0.0109i -0.0000 + 0.0111i -0.0000 + 0.0112i -0.0000 + 0.0113i -0.0000 + 0.0115i -0.0000 + 0.0116i -0.0000 + 0.0117i -0.0000 + 0.0118i -0.0000 + 0.0119i -0.0000 + 0.0119i 0.0000 + 0.0000i -0.0000 + 0.0001i 0.0000 + 0.0002i 0.0000 + 0.0003i 0.0000 + 0.0004i 0.0000 + 0.0005i 0.0000 + 0.0006i 0.0000 + 0.0008i 0.0000 + 0.0009i 0.0000 + 0.0011i 0.0000 + 0.0013i 0.0000 + 0.0015i 0.0000 + 0.0017i 0.0000 + 0.0018i 0.0000 + 0.0020i 0.0000 + 0.0022i 0.0000 + 0.0024i 0.0000 + 0.0026i 0.0000 + 0.0027i 0.0000 + 0.0028i 0.0000 + 0.0029i 0.0000 + 0.0030i 0.0000 + 0.0031i 0.0000 + 0.0032i 0.0000 + 0.0033i 0.0000 + 0.0034i 0.0000 + 0.0035i 0.0000 + 0.0036i 0.0000 + 0.0037i 0.0000 + 0.0038i 0.0000 + 0.0039i 0.0000 + 0.0040i 0.0000 + 0.0041i 0.0000 + 0.0043i 0.0000 + 0.0045i 0.0000 + 0.0046i 0.0000 + 0.0048i -0.0000 + 0.0050i -0.0000 + 0.0052i -0.0000 + 0.0054i -0.0000 + 0.0056i -0.0000 + 0.0058i -0.0000 + 0.0059i -0.0000 + 0.0061i -0.0000 + 0.0062i -0.0000 + 0.0063i -0.0000 + 0.0064i -0.0000 + 0.0065i -0.0000 + 0.0066i -0.0000 + 0.0067i -0.0000 + 0.0068i -0.0000 + 0.0069i -0.0000 + 0.0069i -0.0000 + 0.0070i -0.0000 + 0.0071i -0.0000 + 0.0073i -0.0000 + 0.0074i -0.0000 + 0.0075i -0.0000 + 0.0077i -0.0000 + 0.0078i -0.0000 + 0.0080i -0.0000 + 0.0082i -0.0000 + 0.0084i -0.0000 + 0.0086i -0.0000 + 0.0088i -0.0000 + 0.0090i -0.0000 + 0.0092i -0.0000 + 0.0093i -0.0000 + 0.0095i -0.0000 + 0.0096i -0.0000 + 0.0097i -0.0000 + 0.0098i -0.0000 + 0.0099i -0.0000 + 0.0100i -0.0000 + 0.0101i -0.0000 + 0.0102i -0.0000 + 0.0102i -0.0000 + 0.0103i -0.0000 + 0.0104i -0.0000 + 0.0105i -0.0000 + 0.0106i -0.0000 + 0.0108i -0.0000 + 0.0109i -0.0000 + 0.0111i -0.0000 + 0.0112i -0.0000 + 0.0114i -0.0000 + 0.0116i -0.0000 + 0.0118i -0.0000 + 0.0120i -0.0000 + 0.0122i -0.0000 + 0.0124i -0.0000 + 0.0126i -0.0000 + 0.0127i -0.0000 + 0.0128i -0.0000 + 0.0130i -0.0000 + 0.0131i -0.0000 + 0.0132i -0.0000 + 0.0133i -0.0000 + 0.0134i 0.0000 + 0.0000i 0.0000 + 0.0001i 0.0000 + 0.0002i 0.0000 + 0.0003i 0.0000 + 0.0004i 0.0000 + 0.0005i 0.0000 + 0.0007i 0.0000 + 0.0008i 0.0000 + 0.0010i 0.0000 + 0.0012i 0.0000 + 0.0014i 0.0000 + 0.0016i 0.0000 + 0.0018i 0.0000 + 0.0020i 0.0000 + 0.0023i 0.0000 + 0.0025i 0.0000 + 0.0026i 0.0000 + 0.0028i 0.0000 + 0.0030i 0.0000 + 0.0031i 0.0000 + 0.0032i 0.0000 + 0.0033i 0.0000 + 0.0035i 0.0000 + 0.0036i 0.0000 + 0.0036i 0.0000 + 0.0037i 0.0000 + 0.0038i 0.0000 + 0.0039i 0.0000 + 0.0040i 0.0000 + 0.0042i 0.0000 + 0.0043i 0.0000 + 0.0044i 0.0000 + 0.0046i 0.0000 + 0.0047i 0.0000 + 0.0049i 0.0000 + 0.0051i 0.0000 + 0.0053i 0.0000 + 0.0056i -0.0000 + 0.0058i -0.0000 + 0.0060i -0.0000 + 0.0062i -0.0000 + 0.0064i -0.0000 + 0.0066i -0.0000 + 0.0067i 0.0000 + 0.0068i -0.0000 + 0.0070i -0.0000 + 0.0071i -0.0000 + 0.0072i -0.0000 + 0.0073i -0.0000 + 0.0074i -0.0000 + 0.0075i -0.0000 + 0.0076i -0.0000 + 0.0077i 0.0000 + 0.0078i -0.0000 + 0.0079i -0.0000 + 0.0080i -0.0000 + 0.0082i -0.0000 + 0.0083i -0.0000 + 0.0085i -0.0000 + 0.0087i -0.0000 + 0.0089i -0.0000 + 0.0091i -0.0000 + 0.0093i -0.0000 + 0.0095i -0.0000 + 0.0097i -0.0000 + 0.0099i -0.0000 + 0.0101i -0.0000 + 0.0103i -0.0000 + 0.0104i -0.0000 + 0.0106i -0.0000 + 0.0107i -0.0000 + 0.0108i -0.0000 + 0.0109i -0.0000 + 0.0110i -0.0000 + 0.0111i -0.0000 + 0.0112i -0.0000 + 0.0113i -0.0000 + 0.0114i -0.0000 + 0.0115i -0.0000 + 0.0116i -0.0000 + 0.0118i -0.0000 + 0.0119i -0.0000 + 0.0120i -0.0000 + 0.0122i -0.0000 + 0.0124i -0.0000 + 0.0126i -0.0000 + 0.0128i -0.0000 + 0.0130i -0.0000 + 0.0133i -0.0000 + 0.0135i -0.0000 + 0.0137i -0.0000 + 0.0139i -0.0000 + 0.0140i -0.0000 + 0.0142i -0.0000 + 0.0143i -0.0000 + 0.0145i -0.0000 + 0.0146i -0.0000 + 0.0147i -0.0000 + 0.0148i 0.0000 + 0.0000i 0.0000 + 0.0001i 0.0000 + 0.0002i 0.0000 + 0.0003i 0.0000 + 0.0004i 0.0000 + 0.0006i 0.0000 + 0.0007i 0.0000 + 0.0009i 0.0000 + 0.0011i 0.0000 + 0.0013i 0.0000 + 0.0015i 0.0000 + 0.0017i 0.0000 + 0.0020i 0.0000 + 0.0022i 0.0000 + 0.0025i 0.0000 + 0.0027i 0.0000 + 0.0029i 0.0000 + 0.0031i 0.0000 + 0.0032i 0.0000 + 0.0034i 0.0000 + 0.0035i 0.0000 + 0.0036i 0.0000 + 0.0038i 0.0000 + 0.0039i 0.0000 + 0.0040i 0.0000 + 0.0041i 0.0000 + 0.0042i 0.0000 + 0.0043i 0.0000 + 0.0044i 0.0000 + 0.0045i 0.0000 + 0.0047i 0.0000 + 0.0048i 0.0000 + 0.0050i 0.0000 + 0.0052i 0.0000 + 0.0054i 0.0000 + 0.0056i -0.0000 + 0.0058i -0.0000 + 0.0061i -0.0000 + 0.0063i -0.0000 + 0.0065i -0.0000 + 0.0068i -0.0000 + 0.0070i -0.0000 + 0.0071i -0.0000 + 0.0073i -0.0000 + 0.0075i -0.0000 + 0.0076i -0.0000 + 0.0077i -0.0000 + 0.0078i -0.0000 + 0.0079i -0.0000 + 0.0080i -0.0000 + 0.0081i -0.0000 + 0.0083i -0.0000 + 0.0084i -0.0000 + 0.0085i -0.0000 + 0.0086i -0.0000 + 0.0087i -0.0000 + 0.0089i -0.0000 + 0.0091i -0.0000 + 0.0092i -0.0000 + 0.0094i -0.0000 + 0.0097i -0.0000 + 0.0099i -0.0000 + 0.0101i -0.0000 + 0.0104i -0.0000 + 0.0106i -0.0000 + 0.0108i -0.0000 + 0.0110i -0.0000 + 0.0112i -0.0000 + 0.0114i -0.0000 + 0.0115i -0.0000 + 0.0117i -0.0000 + 0.0118i -0.0000 + 0.0119i -0.0000 + 0.0120i -0.0000 + 0.0121i -0.0000 + 0.0122i -0.0000 + 0.0123i -0.0000 + 0.0124i -0.0000 + 0.0125i -0.0000 + 0.0127i -0.0000 + 0.0128i -0.0000 + 0.0130i -0.0000 + 0.0131i -0.0000 + 0.0133i -0.0000 + 0.0135i -0.0000 + 0.0137i -0.0000 + 0.0140i -0.0000 + 0.0142i -0.0000 + 0.0144i -0.0000 + 0.0147i -0.0000 + 0.0149i -0.0000 + 0.0151i -0.0000 + 0.0153i -0.0000 + 0.0155i -0.0000 + 0.0156i -0.0000 + 0.0157i -0.0000 + 0.0159i -0.0000 + 0.0160i -0.0000 + 0.0161i 0.0000 + 0.0000i -0.0000 + 0.0001i 0.0000 + 0.0002i 0.0000 + 0.0003i 0.0000 + 0.0005i 0.0000 + 0.0006i 0.0000 + 0.0008i 0.0000 + 0.0010i 0.0000 + 0.0012i 0.0000 + 0.0014i 0.0000 + 0.0016i 0.0000 + 0.0019i 0.0000 + 0.0021i 0.0000 + 0.0024i 0.0000 + 0.0026i 0.0000 + 0.0029i 0.0000 + 0.0031i 0.0000 + 0.0033i 0.0000 + 0.0035i 0.0000 + 0.0036i 0.0000 + 0.0038i 0.0000 + 0.0039i 0.0000 + 0.0040i 0.0000 + 0.0042i 0.0000 + 0.0043i 0.0000 + 0.0044i 0.0000 + 0.0045i 0.0000 + 0.0046i 0.0000 + 0.0047i 0.0000 + 0.0049i 0.0000 + 0.0050i 0.0000 + 0.0052i 0.0000 + 0.0054i 0.0000 + 0.0056i 0.0000 + 0.0058i 0.0000 + 0.0060i 0.0000 + 0.0063i 0.0000 + 0.0065i -0.0000 + 0.0068i -0.0000 + 0.0070i -0.0000 + 0.0073i -0.0000 + 0.0075i -0.0000 + 0.0077i 0.0000 + 0.0079i 0.0000 + 0.0080i 0.0000 + 0.0082i 0.0000 + 0.0083i -0.0000 + 0.0084i 0.0000 + 0.0085i 0.0000 + 0.0087i -0.0000 + 0.0088i -0.0000 + 0.0089i -0.0000 + 0.0090i 0.0000 + 0.0091i -0.0000 + 0.0093i -0.0000 + 0.0094i -0.0000 + 0.0096i -0.0000 + 0.0097i -0.0000 + 0.0099i -0.0000 + 0.0102i -0.0000 + 0.0104i -0.0000 + 0.0106i -0.0000 + 0.0109i -0.0000 + 0.0112i -0.0000 + 0.0114i -0.0000 + 0.0117i -0.0000 + 0.0119i -0.0000 + 0.0121i -0.0000 + 0.0123i -0.0000 + 0.0124i -0.0000 + 0.0126i -0.0000 + 0.0127i -0.0000 + 0.0128i -0.0000 + 0.0129i -0.0000 + 0.0130i -0.0000 + 0.0132i -0.0000 + 0.0133i -0.0000 + 0.0134i -0.0000 + 0.0135i -0.0000 + 0.0136i -0.0000 + 0.0138i -0.0000 + 0.0139i -0.0000 + 0.0141i -0.0000 + 0.0143i -0.0000 + 0.0145i -0.0000 + 0.0148i -0.0000 + 0.0150i -0.0000 + 0.0153i -0.0000 + 0.0155i -0.0000 + 0.0158i -0.0000 + 0.0160i -0.0000 + 0.0163i -0.0000 + 0.0165i -0.0000 + 0.0166i -0.0000 + 0.0168i -0.0000 + 0.0169i -0.0000 + 0.0171i -0.0000 + 0.0172i -0.0000 + 0.0173i 0.0000 + 0.0000i -0.0000 + 0.0001i 0.0000 + 0.0002i 0.0000 + 0.0004i 0.0000 + 0.0005i 0.0000 + 0.0007i 0.0000 + 0.0008i 0.0000 + 0.0010i 0.0000 + 0.0012i 0.0000 + 0.0015i 0.0000 + 0.0017i 0.0000 + 0.0020i 0.0000 + 0.0023i 0.0000 + 0.0026i 0.0000 + 0.0028i 0.0000 + 0.0031i 0.0000 + 0.0033i 0.0000 + 0.0035i 0.0000 + 0.0037i 0.0000 + 0.0039i 0.0000 + 0.0040i 0.0000 + 0.0042i 0.0000 + 0.0043i 0.0000 + 0.0044i 0.0000 + 0.0046i 0.0000 + 0.0047i 0.0000 + 0.0048i 0.0000 + 0.0049i 0.0000 + 0.0050i 0.0000 + 0.0052i 0.0000 + 0.0053i 0.0000 + 0.0055i 0.0000 + 0.0057i 0.0000 + 0.0059i 0.0000 + 0.0061i 0.0000 + 0.0064i 0.0000 + 0.0067i 0.0000 + 0.0069i 0.0000 + 0.0072i -0.0000 + 0.0075i -0.0000 + 0.0077i -0.0000 + 0.0080i 0.0000 + 0.0082i 0.0000 + 0.0084i 0.0000 + 0.0085i 0.0000 + 0.0087i 0.0000 + 0.0088i 0.0000 + 0.0090i 0.0000 + 0.0091i 0.0000 + 0.0092i 0.0000 + 0.0093i 0.0000 + 0.0095i 0.0000 + 0.0096i 0.0000 + 0.0097i 0.0000 + 0.0098i -0.0000 + 0.0100i -0.0000 + 0.0102i 0.0000 + 0.0104i 0.0000 + 0.0106i 0.0000 + 0.0108i -0.0000 + 0.0111i -0.0000 + 0.0113i -0.0000 + 0.0116i -0.0000 + 0.0119i -0.0000 + 0.0122i -0.0000 + 0.0124i -0.0000 + 0.0126i -0.0000 + 0.0129i -0.0000 + 0.0130i -0.0000 + 0.0132i -0.0000 + 0.0134i -0.0000 + 0.0135i -0.0000 + 0.0136i -0.0000 + 0.0138i -0.0000 + 0.0139i -0.0000 + 0.0140i -0.0000 + 0.0141i -0.0000 + 0.0142i -0.0000 + 0.0144i -0.0000 + 0.0145i -0.0000 + 0.0147i -0.0000 + 0.0148i -0.0000 + 0.0150i -0.0000 + 0.0153i -0.0000 + 0.0155i -0.0000 + 0.0157i -0.0000 + 0.0160i -0.0000 + 0.0163i -0.0000 + 0.0166i -0.0000 + 0.0168i -0.0000 + 0.0171i -0.0000 + 0.0173i -0.0000 + 0.0175i -0.0000 + 0.0177i -0.0000 + 0.0179i -0.0000 + 0.0180i -0.0000 + 0.0182i -0.0000 + 0.0183i -0.0000 + 0.0184i 0.0000 + 0.0000i -0.0000 + 0.0001i -0.0000 + 0.0003i 0.0000 + 0.0004i 0.0000 + 0.0005i 0.0000 + 0.0007i 0.0000 + 0.0009i 0.0000 + 0.0011i 0.0000 + 0.0013i 0.0000 + 0.0016i 0.0000 + 0.0018i 0.0000 + 0.0021i 0.0000 + 0.0024i 0.0000 + 0.0027i 0.0000 + 0.0030i 0.0000 + 0.0032i 0.0000 + 0.0035i 0.0000 + 0.0037i 0.0000 + 0.0039i 0.0000 + 0.0041i 0.0000 + 0.0043i 0.0000 + 0.0044i 0.0000 + 0.0045i 0.0000 + 0.0047i 0.0000 + 0.0048i 0.0000 + 0.0049i 0.0000 + 0.0050i 0.0000 + 0.0052i 0.0000 + 0.0053i 0.0000 + 0.0055i 0.0000 + 0.0056i 0.0000 + 0.0058i 0.0000 + 0.0060i 0.0000 + 0.0062i 0.0000 + 0.0065i 0.0000 + 0.0068i 0.0000 + 0.0070i 0.0000 + 0.0073i -0.0000 + 0.0076i -0.0000 + 0.0079i -0.0000 + 0.0082i -0.0000 + 0.0084i -0.0000 + 0.0086i 0.0000 + 0.0088i 0.0000 + 0.0090i 0.0000 + 0.0092i 0.0000 + 0.0093i 0.0000 + 0.0095i 0.0000 + 0.0096i 0.0000 + 0.0097i -0.0000 + 0.0098i -0.0000 + 0.0100i -0.0000 + 0.0101i -0.0000 + 0.0102i -0.0000 + 0.0104i -0.0000 + 0.0106i -0.0000 + 0.0107i -0.0000 + 0.0109i -0.0000 + 0.0112i -0.0000 + 0.0114i -0.0000 + 0.0117i -0.0000 + 0.0120i -0.0000 + 0.0122i -0.0000 + 0.0125i -0.0000 + 0.0128i -0.0000 + 0.0131i -0.0000 + 0.0133i -0.0000 + 0.0136i -0.0000 + 0.0138i -0.0000 + 0.0139i -0.0000 + 0.0141i -0.0000 + 0.0143i -0.0000 + 0.0144i -0.0000 + 0.0145i -0.0000 + 0.0146i -0.0000 + 0.0148i -0.0000 + 0.0149i -0.0000 + 0.0150i -0.0000 + 0.0152i -0.0000 + 0.0153i -0.0000 + 0.0155i -0.0000 + 0.0157i -0.0000 + 0.0159i -0.0000 + 0.0161i -0.0000 + 0.0163i -0.0000 + 0.0166i -0.0000 + 0.0169i -0.0000 + 0.0172i -0.0000 + 0.0175i -0.0000 + 0.0177i -0.0000 + 0.0180i -0.0000 + 0.0183i -0.0000 + 0.0185i -0.0000 + 0.0187i -0.0000 + 0.0189i -0.0000 + 0.0190i -0.0000 + 0.0192i -0.0000 + 0.0193i -0.0000 + 0.0194i 0.0000 + 0.0000i -0.0000 + 0.0001i -0.0000 + 0.0003i 0.0000 + 0.0004i 0.0000 + 0.0006i 0.0000 + 0.0007i 0.0000 + 0.0009i 0.0000 + 0.0011i 0.0000 + 0.0014i 0.0000 + 0.0016i 0.0000 + 0.0019i 0.0000 + 0.0022i 0.0000 + 0.0025i 0.0000 + 0.0028i 0.0000 + 0.0031i 0.0000 + 0.0034i 0.0000 + 0.0036i 0.0000 + 0.0039i 0.0000 + 0.0041i 0.0000 + 0.0043i 0.0000 + 0.0045i 0.0000 + 0.0046i 0.0000 + 0.0048i 0.0000 + 0.0049i 0.0000 + 0.0050i 0.0000 + 0.0052i 0.0000 + 0.0053i 0.0000 + 0.0054i 0.0000 + 0.0056i 0.0000 + 0.0057i 0.0000 + 0.0059i 0.0000 + 0.0061i 0.0000 + 0.0063i 0.0000 + 0.0065i 0.0000 + 0.0068i 0.0000 + 0.0071i 0.0000 + 0.0074i 0.0000 + 0.0077i -0.0000 + 0.0080i -0.0000 + 0.0083i -0.0000 + 0.0085i -0.0000 + 0.0088i -0.0000 + 0.0090i 0.0000 + 0.0092i 0.0000 + 0.0094i 0.0000 + 0.0096i 0.0000 + 0.0098i -0.0000 + 0.0099i -0.0000 + 0.0100i -0.0000 + 0.0102i -0.0000 + 0.0103i -0.0000 + 0.0104i -0.0000 + 0.0106i -0.0000 + 0.0107i -0.0000 + 0.0109i -0.0000 + 0.0110i -0.0000 + 0.0112i -0.0000 + 0.0115i -0.0000 + 0.0117i -0.0000 + 0.0119i -0.0000 + 0.0122i -0.0000 + 0.0125i -0.0000 + 0.0128i -0.0000 + 0.0131i -0.0000 + 0.0134i -0.0000 + 0.0137i -0.0000 + 0.0140i -0.0000 + 0.0142i -0.0000 + 0.0144i -0.0000 + 0.0146i -0.0000 + 0.0148i -0.0000 + 0.0149i -0.0000 + 0.0151i -0.0000 + 0.0152i -0.0000 + 0.0153i -0.0000 + 0.0155i -0.0000 + 0.0156i -0.0000 + 0.0157i -0.0000 + 0.0159i -0.0000 + 0.0160i -0.0000 + 0.0162i -0.0000 + 0.0164i -0.0000 + 0.0166i -0.0000 + 0.0168i -0.0000 + 0.0171i -0.0000 + 0.0174i -0.0000 + 0.0177i -0.0000 + 0.0180i -0.0000 + 0.0183i -0.0000 + 0.0186i -0.0000 + 0.0188i -0.0000 + 0.0191i -0.0000 + 0.0193i -0.0000 + 0.0196i -0.0000 + 0.0197i -0.0000 + 0.0199i -0.0000 + 0.0201i -0.0000 + 0.0202i -0.0000 + 0.0204i 0.0000 + 0.0000i -0.0000 + 0.0001i -0.0000 + 0.0003i 0.0000 + 0.0004i 0.0000 + 0.0006i 0.0000 + 0.0008i 0.0000 + 0.0010i 0.0000 + 0.0012i 0.0000 + 0.0014i 0.0000 + 0.0017i 0.0000 + 0.0020i 0.0000 + 0.0023i 0.0000 + 0.0026i 0.0000 + 0.0029i 0.0000 + 0.0032i 0.0000 + 0.0035i 0.0000 + 0.0038i 0.0000 + 0.0040i 0.0000 + 0.0043i 0.0000 + 0.0045i 0.0000 + 0.0046i 0.0000 + 0.0048i 0.0000 + 0.0049i 0.0000 + 0.0051i 0.0000 + 0.0052i 0.0000 + 0.0054i 0.0000 + 0.0055i 0.0000 + 0.0056i 0.0000 + 0.0058i 0.0000 + 0.0060i 0.0000 + 0.0061i 0.0000 + 0.0063i 0.0000 + 0.0066i 0.0000 + 0.0068i 0.0000 + 0.0071i 0.0000 + 0.0074i 0.0000 + 0.0077i 0.0000 + 0.0080i -0.0000 + 0.0083i -0.0000 + 0.0086i -0.0000 + 0.0089i -0.0000 + 0.0092i -0.0000 + 0.0094i -0.0000 + 0.0096i 0.0000 + 0.0098i 0.0000 + 0.0100i -0.0000 + 0.0102i -0.0000 + 0.0103i -0.0000 + 0.0105i -0.0000 + 0.0106i -0.0000 + 0.0107i -0.0000 + 0.0109i -0.0000 + 0.0110i -0.0000 + 0.0112i -0.0000 + 0.0113i -0.0000 + 0.0115i -0.0000 + 0.0117i -0.0000 + 0.0119i -0.0000 + 0.0122i -0.0000 + 0.0124i -0.0000 + 0.0127i -0.0000 + 0.0130i -0.0000 + 0.0133i -0.0000 + 0.0137i -0.0000 + 0.0140i -0.0000 + 0.0142i -0.0000 + 0.0145i -0.0000 + 0.0148i -0.0000 + 0.0150i -0.0000 + 0.0152i -0.0000 + 0.0154i -0.0000 + 0.0155i -0.0000 + 0.0157i -0.0000 + 0.0158i -0.0000 + 0.0159i -0.0000 + 0.0161i -0.0000 + 0.0162i -0.0000 + 0.0164i -0.0000 + 0.0165i -0.0000 + 0.0167i -0.0000 + 0.0169i -0.0000 + 0.0171i -0.0000 + 0.0173i -0.0000 + 0.0175i -0.0000 + 0.0178i -0.0000 + 0.0181i -0.0000 + 0.0184i -0.0000 + 0.0187i -0.0000 + 0.0190i -0.0000 + 0.0193i -0.0000 + 0.0196i -0.0000 + 0.0199i -0.0000 + 0.0201i -0.0000 + 0.0203i -0.0000 + 0.0205i -0.0000 + 0.0207i -0.0000 + 0.0209i -0.0000 + 0.0210i -0.0000 + 0.0212i 0.0000 + 0.0000i -0.0000 + 0.0001i -0.0000 + 0.0003i 0.0000 + 0.0004i 0.0000 + 0.0006i 0.0000 + 0.0008i 0.0000 + 0.0010i 0.0000 + 0.0012i 0.0000 + 0.0015i 0.0000 + 0.0018i 0.0000 + 0.0021i 0.0000 + 0.0024i 0.0000 + 0.0027i 0.0000 + 0.0030i 0.0000 + 0.0033i 0.0000 + 0.0036i 0.0000 + 0.0039i 0.0000 + 0.0042i 0.0000 + 0.0044i 0.0000 + 0.0046i 0.0000 + 0.0048i 0.0000 + 0.0050i 0.0000 + 0.0051i 0.0000 + 0.0053i 0.0000 + 0.0054i 0.0000 + 0.0056i 0.0000 + 0.0057i 0.0000 + 0.0058i 0.0000 + 0.0060i 0.0000 + 0.0062i 0.0000 + 0.0063i 0.0000 + 0.0066i 0.0000 + 0.0068i 0.0000 + 0.0070i 0.0000 + 0.0073i 0.0000 + 0.0076i 0.0000 + 0.0079i -0.0000 + 0.0083i -0.0000 + 0.0086i -0.0000 + 0.0089i -0.0000 + 0.0092i -0.0000 + 0.0095i -0.0000 + 0.0097i -0.0000 + 0.0100i -0.0000 + 0.0102i -0.0000 + 0.0103i -0.0000 + 0.0105i -0.0000 + 0.0107i -0.0000 + 0.0108i -0.0000 + 0.0110i -0.0000 + 0.0111i -0.0000 + 0.0112i -0.0000 + 0.0114i -0.0000 + 0.0115i -0.0000 + 0.0117i -0.0000 + 0.0119i -0.0000 + 0.0121i -0.0000 + 0.0123i -0.0000 + 0.0126i -0.0000 + 0.0129i -0.0000 + 0.0132i -0.0000 + 0.0135i -0.0000 + 0.0138i -0.0000 + 0.0141i -0.0000 + 0.0144i -0.0000 + 0.0147i -0.0000 + 0.0150i -0.0000 + 0.0153i -0.0000 + 0.0155i -0.0000 + 0.0157i -0.0000 + 0.0159i -0.0000 + 0.0161i -0.0000 + 0.0162i -0.0000 + 0.0164i -0.0000 + 0.0165i -0.0000 + 0.0167i -0.0000 + 0.0168i -0.0000 + 0.0169i -0.0000 + 0.0171i -0.0000 + 0.0173i -0.0000 + 0.0174i -0.0000 + 0.0177i -0.0000 + 0.0179i -0.0000 + 0.0181i -0.0000 + 0.0184i -0.0000 + 0.0187i -0.0000 + 0.0190i -0.0000 + 0.0194i -0.0000 + 0.0197i -0.0000 + 0.0200i -0.0000 + 0.0203i -0.0000 + 0.0206i -0.0000 + 0.0208i -0.0000 + 0.0211i -0.0000 + 0.0213i -0.0000 + 0.0214i -0.0000 + 0.0216i -0.0000 + 0.0218i -0.0000 + 0.0219i 0.0000 + 0.0000i -0.0000 + 0.0001i 0.0000 + 0.0003i 0.0000 + 0.0005i 0.0000 + 0.0006i 0.0000 + 0.0008i 0.0000 + 0.0010i 0.0000 + 0.0013i 0.0000 + 0.0015i 0.0000 + 0.0018i 0.0000 + 0.0021i 0.0000 + 0.0025i 0.0000 + 0.0028i 0.0000 + 0.0031i 0.0000 + 0.0035i 0.0000 + 0.0038i 0.0000 + 0.0040i 0.0000 + 0.0043i 0.0000 + 0.0045i 0.0000 + 0.0048i 0.0000 + 0.0049i 0.0000 + 0.0051i 0.0000 + 0.0053i 0.0000 + 0.0054i 0.0000 + 0.0056i 0.0000 + 0.0057i 0.0000 + 0.0059i 0.0000 + 0.0060i 0.0000 + 0.0062i 0.0000 + 0.0064i 0.0000 + 0.0065i 0.0000 + 0.0068i 0.0000 + 0.0070i 0.0000 + 0.0073i 0.0000 + 0.0075i 0.0000 + 0.0079i -0.0000 + 0.0082i -0.0000 + 0.0085i -0.0000 + 0.0089i -0.0000 + 0.0092i -0.0000 + 0.0095i -0.0000 + 0.0098i -0.0000 + 0.0100i -0.0000 + 0.0103i -0.0000 + 0.0105i -0.0000 + 0.0107i -0.0000 + 0.0108i -0.0000 + 0.0110i -0.0000 + 0.0112i -0.0000 + 0.0113i -0.0000 + 0.0114i -0.0000 + 0.0116i -0.0000 + 0.0117i -0.0000 + 0.0119i -0.0000 + 0.0121i -0.0000 + 0.0123i -0.0000 + 0.0125i -0.0000 + 0.0127i -0.0000 + 0.0130i -0.0000 + 0.0133i -0.0000 + 0.0136i -0.0000 + 0.0139i -0.0000 + 0.0142i -0.0000 + 0.0146i -0.0000 + 0.0149i -0.0000 + 0.0152i -0.0000 + 0.0155i -0.0000 + 0.0158i -0.0000 + 0.0160i -0.0000 + 0.0162i -0.0000 + 0.0164i -0.0000 + 0.0166i -0.0000 + 0.0167i -0.0000 + 0.0169i -0.0000 + 0.0170i -0.0000 + 0.0172i -0.0000 + 0.0173i -0.0000 + 0.0175i -0.0000 + 0.0176i -0.0000 + 0.0178i -0.0000 + 0.0180i -0.0000 + 0.0182i -0.0000 + 0.0184i -0.0000 + 0.0187i -0.0000 + 0.0190i -0.0000 + 0.0193i -0.0000 + 0.0196i -0.0000 + 0.0200i -0.0000 + 0.0203i -0.0000 + 0.0206i -0.0000 + 0.0209i -0.0000 + 0.0212i -0.0000 + 0.0215i -0.0000 + 0.0217i -0.0000 + 0.0219i -0.0000 + 0.0221i -0.0000 + 0.0223i -0.0000 + 0.0225i -0.0000 + 0.0226i 0.0000 + 0.0000i -0.0000 + 0.0001i 0.0000 + 0.0003i 0.0000 + 0.0005i 0.0000 + 0.0006i 0.0000 + 0.0008i -0.0000 + 0.0011i -0.0000 + 0.0013i 0.0000 + 0.0016i 0.0000 + 0.0019i 0.0000 + 0.0022i 0.0000 + 0.0025i 0.0000 + 0.0029i 0.0000 + 0.0032i 0.0000 + 0.0036i 0.0000 + 0.0039i 0.0000 + 0.0042i 0.0000 + 0.0044i 0.0000 + 0.0047i 0.0000 + 0.0049i 0.0000 + 0.0051i 0.0000 + 0.0053i 0.0000 + 0.0054i 0.0000 + 0.0056i 0.0000 + 0.0057i 0.0000 + 0.0059i 0.0000 + 0.0060i 0.0000 + 0.0062i 0.0000 + 0.0064i 0.0000 + 0.0065i 0.0000 + 0.0067i 0.0000 + 0.0070i 0.0000 + 0.0072i 0.0000 + 0.0075i 0.0000 + 0.0078i 0.0000 + 0.0081i -0.0000 + 0.0084i -0.0000 + 0.0088i -0.0000 + 0.0091i -0.0000 + 0.0094i -0.0000 + 0.0098i -0.0000 + 0.0101i -0.0000 + 0.0103i -0.0000 + 0.0106i -0.0000 + 0.0108i -0.0000 + 0.0110i -0.0000 + 0.0112i -0.0000 + 0.0113i -0.0000 + 0.0115i -0.0000 + 0.0116i -0.0000 + 0.0118i -0.0000 + 0.0119i -0.0000 + 0.0121i -0.0000 + 0.0122i -0.0000 + 0.0124i -0.0000 + 0.0126i -0.0000 + 0.0128i -0.0000 + 0.0131i -0.0000 + 0.0134i -0.0000 + 0.0136i -0.0000 + 0.0140i -0.0000 + 0.0143i -0.0000 + 0.0146i -0.0000 + 0.0150i -0.0000 + 0.0153i -0.0000 + 0.0156i -0.0000 + 0.0159i -0.0000 + 0.0162i -0.0000 + 0.0165i -0.0000 + 0.0167i -0.0000 + 0.0169i -0.0000 + 0.0170i -0.0000 + 0.0172i -0.0000 + 0.0174i -0.0000 + 0.0175i -0.0000 + 0.0177i -0.0000 + 0.0178i -0.0000 + 0.0180i -0.0000 + 0.0181i -0.0000 + 0.0183i -0.0000 + 0.0185i -0.0000 + 0.0187i -0.0000 + 0.0190i -0.0000 + 0.0192i -0.0000 + 0.0195i -0.0000 + 0.0199i -0.0000 + 0.0202i -0.0000 + 0.0205i -0.0000 + 0.0209i -0.0000 + 0.0212i -0.0000 + 0.0215i -0.0000 + 0.0218i -0.0000 + 0.0221i -0.0000 + 0.0223i -0.0000 + 0.0226i -0.0000 + 0.0228i -0.0000 + 0.0229i -0.0000 + 0.0231i -0.0000 + 0.0233i 0.0000 + 0.0000i -0.0000 + 0.0002i 0.0000 + 0.0003i 0.0000 + 0.0005i 0.0000 + 0.0007i 0.0000 + 0.0009i -0.0000 + 0.0011i -0.0000 + 0.0013i 0.0000 + 0.0016i 0.0000 + 0.0019i 0.0000 + 0.0022i 0.0000 + 0.0026i 0.0000 + 0.0029i 0.0000 + 0.0033i 0.0000 + 0.0036i 0.0000 + 0.0040i 0.0000 + 0.0043i 0.0000 + 0.0046i 0.0000 + 0.0048i 0.0000 + 0.0050i 0.0000 + 0.0052i 0.0000 + 0.0054i 0.0000 + 0.0056i 0.0000 + 0.0057i 0.0000 + 0.0059i 0.0000 + 0.0060i 0.0000 + 0.0062i 0.0000 + 0.0064i 0.0000 + 0.0065i 0.0000 + 0.0067i 0.0000 + 0.0069i 0.0000 + 0.0071i 0.0000 + 0.0074i 0.0000 + 0.0077i 0.0000 + 0.0080i -0.0000 + 0.0083i -0.0000 + 0.0086i -0.0000 + 0.0090i -0.0000 + 0.0093i -0.0000 + 0.0097i -0.0000 + 0.0100i -0.0000 + 0.0103i -0.0000 + 0.0106i -0.0000 + 0.0108i -0.0000 + 0.0111i -0.0000 + 0.0113i -0.0000 + 0.0115i -0.0000 + 0.0116i -0.0000 + 0.0118i -0.0000 + 0.0119i -0.0000 + 0.0121i -0.0000 + 0.0122i -0.0000 + 0.0124i -0.0000 + 0.0126i -0.0000 + 0.0128i -0.0000 + 0.0130i -0.0000 + 0.0132i -0.0000 + 0.0134i -0.0000 + 0.0137i -0.0000 + 0.0140i -0.0000 + 0.0143i -0.0000 + 0.0147i -0.0000 + 0.0150i -0.0000 + 0.0154i -0.0000 + 0.0157i -0.0000 + 0.0161i -0.0000 + 0.0164i -0.0000 + 0.0166i -0.0000 + 0.0169i -0.0000 + 0.0171i -0.0000 + 0.0173i -0.0000 + 0.0175i -0.0000 + 0.0177i -0.0000 + 0.0178i -0.0000 + 0.0180i -0.0000 + 0.0181i -0.0000 + 0.0183i -0.0000 + 0.0185i -0.0000 + 0.0186i -0.0000 + 0.0188i -0.0000 + 0.0190i -0.0000 + 0.0192i -0.0000 + 0.0195i -0.0000 + 0.0198i -0.0000 + 0.0201i -0.0000 + 0.0204i -0.0000 + 0.0207i -0.0000 + 0.0211i -0.0000 + 0.0214i -0.0000 + 0.0218i -0.0000 + 0.0221i -0.0000 + 0.0224i -0.0000 + 0.0227i -0.0000 + 0.0229i -0.0000 + 0.0232i -0.0000 + 0.0234i -0.0000 + 0.0235i -0.0000 + 0.0237i -0.0000 + 0.0239i 0.0000 + 0.0000i -0.0000 + 0.0002i 0.0000 + 0.0003i 0.0000 + 0.0005i 0.0000 + 0.0007i 0.0000 + 0.0009i -0.0000 + 0.0011i -0.0000 + 0.0014i 0.0000 + 0.0017i 0.0000 + 0.0020i 0.0000 + 0.0023i 0.0000 + 0.0027i 0.0000 + 0.0030i 0.0000 + 0.0034i 0.0000 + 0.0037i 0.0000 + 0.0041i 0.0000 + 0.0044i 0.0000 + 0.0047i 0.0000 + 0.0049i 0.0000 + 0.0052i 0.0000 + 0.0054i 0.0000 + 0.0056i 0.0000 + 0.0057i 0.0000 + 0.0059i 0.0000 + 0.0060i 0.0000 + 0.0062i 0.0000 + 0.0064i 0.0000 + 0.0065i 0.0000 + 0.0067i 0.0000 + 0.0069i 0.0000 + 0.0071i 0.0000 + 0.0073i 0.0000 + 0.0076i 0.0000 + 0.0079i 0.0000 + 0.0082i -0.0000 + 0.0085i -0.0000 + 0.0089i -0.0000 + 0.0092i -0.0000 + 0.0096i -0.0000 + 0.0099i -0.0000 + 0.0103i -0.0000 + 0.0106i -0.0000 + 0.0109i -0.0000 + 0.0111i -0.0000 + 0.0114i -0.0000 + 0.0116i -0.0000 + 0.0118i -0.0000 + 0.0119i -0.0000 + 0.0121i -0.0000 + 0.0122i -0.0000 + 0.0124i -0.0000 + 0.0126i -0.0000 + 0.0127i -0.0000 + 0.0129i -0.0000 + 0.0131i -0.0000 + 0.0133i -0.0000 + 0.0135i -0.0000 + 0.0138i -0.0000 + 0.0141i -0.0000 + 0.0144i -0.0000 + 0.0147i -0.0000 + 0.0151i -0.0000 + 0.0154i -0.0000 + 0.0158i -0.0000 + 0.0161i -0.0000 + 0.0165i -0.0000 + 0.0168i -0.0000 + 0.0171i -0.0000 + 0.0173i -0.0000 + 0.0176i -0.0000 + 0.0178i -0.0000 + 0.0180i -0.0000 + 0.0181i -0.0000 + 0.0183i -0.0000 + 0.0184i -0.0000 + 0.0186i -0.0000 + 0.0188i -0.0000 + 0.0189i -0.0000 + 0.0191i -0.0000 + 0.0193i -0.0000 + 0.0195i -0.0000 + 0.0197i -0.0000 + 0.0200i -0.0000 + 0.0203i -0.0000 + 0.0206i -0.0000 + 0.0209i -0.0000 + 0.0213i -0.0000 + 0.0216i -0.0000 + 0.0220i -0.0000 + 0.0223i -0.0000 + 0.0227i -0.0000 + 0.0230i -0.0000 + 0.0233i -0.0000 + 0.0235i -0.0000 + 0.0238i -0.0000 + 0.0240i -0.0000 + 0.0242i -0.0000 + 0.0243i -0.0000 + 0.0245i 0.0000 + 0.0000i -0.0000 + 0.0002i -0.0000 + 0.0003i 0.0000 + 0.0005i 0.0000 + 0.0007i 0.0000 + 0.0009i -0.0000 + 0.0012i -0.0000 + 0.0014i 0.0000 + 0.0017i 0.0000 + 0.0020i 0.0000 + 0.0024i 0.0000 + 0.0027i 0.0000 + 0.0031i 0.0000 + 0.0035i 0.0000 + 0.0038i 0.0000 + 0.0042i 0.0000 + 0.0045i 0.0000 + 0.0048i 0.0000 + 0.0050i 0.0000 + 0.0053i 0.0000 + 0.0055i 0.0000 + 0.0057i 0.0000 + 0.0059i 0.0000 + 0.0060i 0.0000 + 0.0062i 0.0000 + 0.0064i 0.0000 + 0.0065i 0.0000 + 0.0067i 0.0000 + 0.0069i 0.0000 + 0.0071i 0.0000 + 0.0073i 0.0000 + 0.0075i -0.0000 + 0.0078i -0.0000 + 0.0081i -0.0000 + 0.0084i -0.0000 + 0.0087i -0.0000 + 0.0091i -0.0000 + 0.0095i -0.0000 + 0.0098i -0.0000 + 0.0102i -0.0000 + 0.0105i -0.0000 + 0.0109i -0.0000 + 0.0111i -0.0000 + 0.0114i -0.0000 + 0.0116i -0.0000 + 0.0119i -0.0000 + 0.0120i -0.0000 + 0.0122i -0.0000 + 0.0124i -0.0000 + 0.0126i -0.0000 + 0.0127i -0.0000 + 0.0129i -0.0000 + 0.0130i -0.0000 + 0.0132i -0.0000 + 0.0134i -0.0000 + 0.0136i -0.0000 + 0.0139i -0.0000 + 0.0141i -0.0000 + 0.0144i -0.0000 + 0.0147i -0.0000 + 0.0151i -0.0000 + 0.0154i -0.0000 + 0.0158i -0.0000 + 0.0162i -0.0000 + 0.0166i -0.0000 + 0.0169i -0.0000 + 0.0172i -0.0000 + 0.0175i -0.0000 + 0.0178i -0.0000 + 0.0180i -0.0000 + 0.0182i -0.0000 + 0.0184i -0.0000 + 0.0186i -0.0000 + 0.0188i -0.0000 + 0.0189i -0.0000 + 0.0191i -0.0000 + 0.0192i -0.0000 + 0.0194i -0.0000 + 0.0196i -0.0000 + 0.0198i -0.0000 + 0.0200i -0.0000 + 0.0202i -0.0000 + 0.0205i -0.0000 + 0.0208i -0.0000 + 0.0211i -0.0000 + 0.0214i -0.0000 + 0.0218i -0.0000 + 0.0222i -0.0000 + 0.0225i -0.0000 + 0.0229i -0.0000 + 0.0233i -0.0000 + 0.0236i -0.0000 + 0.0239i -0.0000 + 0.0241i -0.0000 + 0.0244i -0.0000 + 0.0246i -0.0000 + 0.0248i -0.0000 + 0.0249i -0.0000 + 0.0251i 0.0000 + 0.0000i -0.0000 + 0.0002i -0.0000 + 0.0003i 0.0000 + 0.0005i 0.0000 + 0.0007i 0.0000 + 0.0009i -0.0000 + 0.0012i -0.0000 + 0.0014i 0.0000 + 0.0017i 0.0000 + 0.0021i 0.0000 + 0.0024i 0.0000 + 0.0028i 0.0000 + 0.0032i 0.0000 + 0.0036i 0.0000 + 0.0039i 0.0000 + 0.0043i 0.0000 + 0.0046i 0.0000 + 0.0049i 0.0000 + 0.0052i 0.0000 + 0.0054i 0.0000 + 0.0056i 0.0000 + 0.0058i 0.0000 + 0.0060i 0.0000 + 0.0062i 0.0000 + 0.0064i 0.0000 + 0.0065i 0.0000 + 0.0067i 0.0000 + 0.0069i 0.0000 + 0.0070i 0.0000 + 0.0072i 0.0000 + 0.0075i 0.0000 + 0.0077i -0.0000 + 0.0080i -0.0000 + 0.0083i -0.0000 + 0.0086i -0.0000 + 0.0089i -0.0000 + 0.0093i -0.0000 + 0.0097i -0.0000 + 0.0101i -0.0000 + 0.0105i -0.0000 + 0.0108i -0.0000 + 0.0111i -0.0000 + 0.0114i -0.0000 + 0.0117i -0.0000 + 0.0119i -0.0000 + 0.0122i -0.0000 + 0.0124i -0.0000 + 0.0125i -0.0000 + 0.0127i -0.0000 + 0.0129i -0.0000 + 0.0130i -0.0000 + 0.0132i -0.0000 + 0.0134i -0.0000 + 0.0136i -0.0000 + 0.0138i -0.0000 + 0.0140i -0.0000 + 0.0142i -0.0000 + 0.0145i -0.0000 + 0.0148i -0.0000 + 0.0151i -0.0000 + 0.0155i -0.0000 + 0.0158i -0.0000 + 0.0162i -0.0000 + 0.0166i -0.0000 + 0.0170i -0.0000 + 0.0173i -0.0000 + 0.0177i -0.0000 + 0.0180i -0.0000 + 0.0182i -0.0000 + 0.0185i -0.0000 + 0.0187i -0.0000 + 0.0189i -0.0000 + 0.0191i -0.0000 + 0.0192i -0.0000 + 0.0194i -0.0000 + 0.0196i -0.0000 + 0.0197i -0.0000 + 0.0199i -0.0000 + 0.0201i -0.0000 + 0.0203i -0.0000 + 0.0205i -0.0000 + 0.0207i -0.0000 + 0.0210i -0.0000 + 0.0213i -0.0000 + 0.0216i -0.0000 + 0.0220i -0.0000 + 0.0224i -0.0000 + 0.0227i -0.0000 + 0.0231i -0.0000 + 0.0235i -0.0000 + 0.0239i -0.0000 + 0.0242i -0.0000 + 0.0245i -0.0000 + 0.0247i -0.0000 + 0.0250i -0.0000 + 0.0252i -0.0000 + 0.0254i -0.0000 + 0.0256i -0.0000 + 0.0258i 0.0000 + 0.0000i -0.0000 + 0.0002i 0.0000 + 0.0003i 0.0000 + 0.0005i 0.0000 + 0.0007i 0.0000 + 0.0010i -0.0000 + 0.0012i -0.0000 + 0.0015i 0.0000 + 0.0018i 0.0000 + 0.0021i 0.0000 + 0.0025i 0.0000 + 0.0029i 0.0000 + 0.0033i 0.0000 + 0.0037i 0.0000 + 0.0040i 0.0000 + 0.0044i 0.0000 + 0.0047i 0.0000 + 0.0050i 0.0000 + 0.0053i 0.0000 + 0.0056i 0.0000 + 0.0058i 0.0000 + 0.0060i 0.0000 + 0.0062i 0.0000 + 0.0064i 0.0000 + 0.0065i 0.0000 + 0.0067i 0.0000 + 0.0069i 0.0000 + 0.0070i 0.0000 + 0.0072i 0.0000 + 0.0074i 0.0000 + 0.0077i 0.0000 + 0.0079i -0.0000 + 0.0082i -0.0000 + 0.0085i -0.0000 + 0.0088i -0.0000 + 0.0092i -0.0000 + 0.0096i -0.0000 + 0.0100i -0.0000 + 0.0104i -0.0000 + 0.0107i -0.0000 + 0.0111i -0.0000 + 0.0114i -0.0000 + 0.0117i -0.0000 + 0.0120i -0.0000 + 0.0123i -0.0000 + 0.0125i -0.0000 + 0.0127i -0.0000 + 0.0129i -0.0000 + 0.0131i -0.0000 + 0.0132i -0.0000 + 0.0134i -0.0000 + 0.0136i -0.0000 + 0.0137i -0.0000 + 0.0139i -0.0000 + 0.0141i -0.0000 + 0.0144i -0.0000 + 0.0146i -0.0000 + 0.0149i -0.0000 + 0.0152i -0.0000 + 0.0155i -0.0000 + 0.0159i -0.0000 + 0.0163i -0.0000 + 0.0167i -0.0000 + 0.0170i -0.0000 + 0.0174i -0.0000 + 0.0178i -0.0000 + 0.0181i -0.0000 + 0.0184i -0.0000 + 0.0187i -0.0000 + 0.0190i -0.0000 + 0.0192i -0.0000 + 0.0194i -0.0000 + 0.0196i -0.0000 + 0.0198i -0.0000 + 0.0199i -0.0000 + 0.0201i -0.0000 + 0.0203i -0.0000 + 0.0204i -0.0000 + 0.0206i -0.0000 + 0.0208i -0.0000 + 0.0211i -0.0000 + 0.0213i -0.0000 + 0.0216i -0.0000 + 0.0219i -0.0000 + 0.0222i -0.0000 + 0.0226i -0.0000 + 0.0230i -0.0000 + 0.0234i -0.0000 + 0.0237i -0.0000 + 0.0241i -0.0000 + 0.0245i -0.0000 + 0.0248i -0.0000 + 0.0251i -0.0000 + 0.0254i -0.0000 + 0.0257i -0.0000 + 0.0259i -0.0000 + 0.0261i -0.0000 + 0.0263i -0.0000 + 0.0264i 0.0000 + 0.0000i -0.0000 + 0.0002i 0.0000 + 0.0004i 0.0000 + 0.0006i 0.0000 + 0.0008i 0.0000 + 0.0010i -0.0000 + 0.0012i -0.0000 + 0.0015i 0.0000 + 0.0018i 0.0000 + 0.0022i 0.0000 + 0.0026i 0.0000 + 0.0030i 0.0000 + 0.0034i 0.0000 + 0.0038i 0.0000 + 0.0042i 0.0000 + 0.0045i 0.0000 + 0.0049i 0.0000 + 0.0052i 0.0000 + 0.0055i 0.0000 + 0.0057i 0.0000 + 0.0060i 0.0000 + 0.0062i 0.0000 + 0.0064i 0.0000 + 0.0065i 0.0000 + 0.0067i 0.0000 + 0.0069i 0.0000 + 0.0071i 0.0000 + 0.0072i 0.0000 + 0.0074i 0.0000 + 0.0076i 0.0000 + 0.0079i 0.0000 + 0.0081i -0.0000 + 0.0084i -0.0000 + 0.0087i -0.0000 + 0.0091i -0.0000 + 0.0094i -0.0000 + 0.0098i -0.0000 + 0.0102i -0.0000 + 0.0106i -0.0000 + 0.0110i -0.0000 + 0.0114i -0.0000 + 0.0118i -0.0000 + 0.0121i -0.0000 + 0.0124i -0.0000 + 0.0126i -0.0000 + 0.0128i -0.0000 + 0.0130i -0.0000 + 0.0132i -0.0000 + 0.0134i -0.0000 + 0.0136i -0.0000 + 0.0138i -0.0000 + 0.0139i -0.0000 + 0.0141i -0.0000 + 0.0143i -0.0000 + 0.0145i -0.0000 + 0.0148i -0.0000 + 0.0150i -0.0000 + 0.0153i -0.0000 + 0.0156i -0.0000 + 0.0160i -0.0000 + 0.0163i -0.0000 + 0.0167i -0.0000 + 0.0171i -0.0000 + 0.0175i -0.0000 + 0.0179i -0.0000 + 0.0183i -0.0000 + 0.0186i -0.0000 + 0.0190i -0.0000 + 0.0192i -0.0000 + 0.0195i -0.0000 + 0.0197i -0.0000 + 0.0199i -0.0000 + 0.0201i -0.0000 + 0.0203i -0.0000 + 0.0205i -0.0000 + 0.0207i -0.0000 + 0.0208i -0.0000 + 0.0210i -0.0000 + 0.0212i -0.0000 + 0.0214i -0.0000 + 0.0216i -0.0000 + 0.0219i -0.0000 + 0.0222i -0.0000 + 0.0225i -0.0000 + 0.0228i -0.0000 + 0.0232i -0.0000 + 0.0236i -0.0000 + 0.0240i -0.0000 + 0.0244i -0.0000 + 0.0248i -0.0000 + 0.0252i -0.0000 + 0.0255i -0.0000 + 0.0258i -0.0000 + 0.0261i -0.0000 + 0.0264i -0.0000 + 0.0266i -0.0000 + 0.0268i -0.0000 + 0.0270i -0.0000 + 0.0272i 0.0000 + 0.0000i -0.0000 + 0.0002i 0.0000 + 0.0004i 0.0000 + 0.0006i 0.0000 + 0.0008i 0.0000 + 0.0010i -0.0000 + 0.0013i -0.0000 + 0.0016i 0.0000 + 0.0019i 0.0000 + 0.0023i 0.0000 + 0.0026i 0.0000 + 0.0030i 0.0000 + 0.0035i 0.0000 + 0.0039i 0.0000 + 0.0043i 0.0000 + 0.0047i 0.0000 + 0.0050i 0.0000 + 0.0053i 0.0000 + 0.0056i 0.0000 + 0.0059i 0.0000 + 0.0061i 0.0000 + 0.0063i 0.0000 + 0.0065i 0.0000 + 0.0067i 0.0000 + 0.0069i 0.0000 + 0.0071i 0.0000 + 0.0073i 0.0000 + 0.0075i 0.0000 + 0.0077i 0.0000 + 0.0079i 0.0000 + 0.0081i 0.0000 + 0.0084i -0.0000 + 0.0087i -0.0000 + 0.0090i -0.0000 + 0.0094i -0.0000 + 0.0097i -0.0000 + 0.0101i -0.0000 + 0.0106i -0.0000 + 0.0110i -0.0000 + 0.0114i -0.0000 + 0.0118i -0.0000 + 0.0121i -0.0000 + 0.0124i -0.0000 + 0.0127i -0.0000 + 0.0130i -0.0000 + 0.0132i -0.0000 + 0.0134i -0.0000 + 0.0136i -0.0000 + 0.0138i -0.0000 + 0.0140i -0.0000 + 0.0142i -0.0000 + 0.0144i -0.0000 + 0.0146i -0.0000 + 0.0148i -0.0000 + 0.0150i -0.0000 + 0.0152i -0.0000 + 0.0155i -0.0000 + 0.0158i -0.0000 + 0.0161i -0.0000 + 0.0164i -0.0000 + 0.0168i -0.0000 + 0.0172i -0.0000 + 0.0176i -0.0000 + 0.0181i -0.0000 + 0.0185i -0.0000 + 0.0188i -0.0000 + 0.0192i -0.0000 + 0.0195i -0.0000 + 0.0198i -0.0000 + 0.0201i -0.0000 + 0.0203i -0.0000 + 0.0205i -0.0000 + 0.0207i -0.0000 + 0.0209i -0.0000 + 0.0211i -0.0000 + 0.0213i -0.0000 + 0.0215i -0.0000 + 0.0216i -0.0000 + 0.0218i -0.0000 + 0.0221i -0.0000 + 0.0223i -0.0000 + 0.0226i -0.0000 + 0.0229i -0.0000 + 0.0232i -0.0000 + 0.0235i -0.0000 + 0.0239i -0.0000 + 0.0243i -0.0000 + 0.0247i -0.0000 + 0.0252i -0.0000 + 0.0256i -0.0000 + 0.0259i -0.0000 + 0.0263i -0.0000 + 0.0266i -0.0000 + 0.0269i -0.0000 + 0.0272i -0.0000 + 0.0274i -0.0000 + 0.0276i -0.0000 + 0.0278i -0.0000 + 0.0280i

Más respuestas (1)

Christine Tobler
Christine Tobler el 25 de Ag. de 2022
Replace the line
I = cumtrapz(y,cumtrapz(x,MBerry(keySet),2));
with
I = cumtrapz(y,cumtrapz(x,MBerry(keySet),2), 1);
Here's what happens to cause the error: MBerry(keySet) in one iteration returns a scalar, and then the above line becomes
x = 1.234; % Just using some scalars here, the values don't matter
y = 2.345;
MBerry_keySet = 3.456;
tmp = cumtrapz(x, MBerry_keySet, 2)
tmp = 0
I = cumtrapz(y, tmp)
Error using permute
ORDER contains an invalid permutation index.

Error in cumtrapz (line 56)
y = permute(y,perm);
This last call takes two scalars, and in this case CUMTRAPZ goes into the cumtrapz(y, dim) syntax instead of the cumtrapz(x, y) branch. The error message is because 0 is not a valid dimension input.
It's not great of course that we have two overlapping syntaxes like this here. The best workaround is to just use the three-input syntax which has no ambiguity as to which input is treated how.
I'll make a note to improve the error message here so it mentions the DIM argument.
  1 comentario
Tsz Tsun
Tsz Tsun el 25 de Ag. de 2022
Do you mean like this ?
%q =4 case
%Part I of the code
a=0.25;
N=100;
q=1;
Eigenvector=[];
M = containers.Map();
ChernNumber = 0;
for u=0:99
for v= 0:999
disp(u);
disp(v);
x=(2*pi*u)/(q*N);
y=(2*pi*v)/(q*N);
%K is the Hamiltonian matrix
K=[-2*cos(2*pi*a-y) -exp(i*x) 0 -exp(-i*x); -exp(-i*x) -2*cos(2*pi*2*a-y) -exp(i*x) 0; 0 -exp(-i*x) -2*cos(2*pi*3*a-y) -exp(i*x); -exp(i*x) 0 -exp(-i*x) -2*cos(2*pi*4*a-y)];
%find eigenvalue
e=eig(K)
%find eigenvector
[V,D]=eig(K);
%Store eigenvector in a container hash map
keySet = sprintf("%u,%u", u, v)
Eigenvector=V(:,1)
valueSet = Eigenvector
M(keySet) = valueSet
end
end
%The above part runs perfectly fine
%Part II of the code
%This part calculates the Berry curvature using the eigenvectors calculated
%in the above code
%Define an empty container MBerry
MBerry = containers.Map();
for u=0:98
for v=0:98
keySet = sprintf("%d,%d", u, v)
%Calculation of Berry Curvature for each point of the momentum
%space grid
BerryCurvature=...
log((dot(M(sprintf('%d,%d',u,v)),M(sprintf('%d,%d',u+1,v)))/abs(dot(M(sprintf('%d,%d',u,v)),M(sprintf('%d,%d',u+1,v)))))*...
(dot(M(sprintf('%d,%d',u+1,v)),M(sprintf('%d,%d',u+1,v+1)))/abs(dot(M(sprintf('%d,%d',u+1,v)),M(sprintf('%d,%d',u+1,v+1)))))*...
(dot(M(sprintf('%d,%d',u+1,v+1)),M(sprintf('%d,%d',u,v+1)))/abs(dot(M(sprintf('%d,%d',u+1,v+1)),M(sprintf('%d,%d',u,v+1)))))*...
(dot(M(sprintf('%d,%d',u,v+1)),M(sprintf('%d,%d',u,v)))/abs(dot(M(sprintf('%d,%d',u,v+1)),M(sprintf('%d,%d',u,v))))))
MBerry(keySet) = BerryCurvature
%Calucation of the Chern number
ChernNumber= ChernNumber + sum(MBerry(keySet))
%All of the above code work fine
%Using cumtrapz to calculate the Chern Number
x=(2*pi*u)/(q*N);
y=(2*pi*v)/(q*N);
MBerry(keySet);
I = cumtrapz(y,cumtrapz(x,MBerry(keySet),2), 1)
end
end
The error messages go away, however, I obtain I = 0 for all entries when I run it. I should obtain a value close to ChernNumber (i.e. around 25) as above.

Iniciar sesión para comentar.

Categorías

Más información sobre Particle & Nuclear Physics en Help Center y File Exchange.

Etiquetas

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by