How to reduce the computation time of for loop?

Dear Experts,

I have a query regarding my code below, it takes long time to process the loop, could you please guide how to reduce the processing time.

img = zeros(M,N);
for ii = 3264:64:86610  % sorted for one complete rotation
    dR = sqrt((R0*cos(alpha*pi/180).*cos(Turntable_angle(ii)*pi/180) + x_mat).^2 + (R0*cos(alpha*pi/180).*sin(Turntable_angle(ii)*pi/180) + y_mat).^2 + (z_mat - R0*sin(alpha*pi/180)).^2) - R0;
    for jj = 1:length(Freq_vec)
        S1 = data_matrix; % data
        Sc_win = S1.*repmat(hanning(size(S1,2)).',size(S1,1),1); % apply window
        S = ifftshift(ifft(Sc_win,Nfft,2),2);
        img = img + S(ii,jj).*exp(1j*4*pi*Freq_vec(jj)/c0*dR);
    end
end 

I look forward to receive your valueable suggestions, thank you so much!

Answer 1

[Johan]

You can likely vectorize your code:

i_loop = 3264:64:86610 ;
M = size(i_loop,1);
N = 25;
Freq_vec = rand(N,1);
Turntable_angle = rand(i_loop(end),1);
R0 = 1;
x_mat = 1;
y_mat = 1;
z_mat = 1;
alpha = 1;
c0 = 1;
S1 = rand(i_loop(end),N); % data
% You did not share these function but I assume S is the same size as S1
%           Sc_win = S1.*repmat(hanning(size(S1,2)).',size(S1,1),1); % apply window
%           S = ifftshift(ifft(Sc_win,Nfft,2),2);
tic
dR = sqrt((R0*cos(alpha*pi/180).*cos(Turntable_angle(i_loop)*pi/180) + x_mat).^2 +...
          (R0*cos(alpha*pi/180).*sin(Turntable_angle(i_loop)*pi/180) + y_mat).^2 +...
          (z_mat - R0*sin(alpha*pi/180)).^2) - R0;
imgvec = S1(i_loop,:).*exp(1j*4*pi*dR*Freq_vec'/c0);
toc

Elapsed time is 0.008215 seconds.

imgloop = zeros(size(i_loop,2),N);
tic
for i_row = 3264:64:i_loop(end)  % sorted for one complete rotation
dR = sqrt((R0*cos(alpha*pi/180).*cos(Turntable_angle(i_row)*pi/180) + x_mat).^2 + (R0*cos(alpha*pi/180).*sin(Turntable_angle(i_row)*pi/180) + y_mat).^2 + (z_mat - R0*sin(alpha*pi/180)).^2) - R0;
    for i_col = 1:length(Freq_vec)
        %This make all value of imgloop the same, I don't think this is
        %intended ?
        imgloop = imgloop + S1(i_row,i_col)*exp(1j*4*pi*Freq_vec(i_col)/c0*dR);
    end
end
toc

Elapsed time is 0.665726 seconds.

unique(imgloop)

ans = -7.4497e+02 + 3.1083e+03i

unique(imgvec)

ans = 
   0.0001 + 0.0001i
  -0.0002 + 0.0000i
   0.0002 + 0.0002i
  -0.0000 + 0.0003i
   0.0002 + 0.0002i
   0.0002 + 0.0003i
   0.0002 - 0.0003i
   0.0002 + 0.0003i
  -0.0004 + 0.0000i
  -0.0003 + 0.0002i
  -0.0004 + 0.0001i
   0.0003 - 0.0002i
   0.0003 + 0.0003i
   0.0002 + 0.0004i
  -0.0004 - 0.0003i
   0.0005 + 0.0002i
  -0.0006 + 0.0001i
  -0.0006 + 0.0000i
   0.0006 - 0.0003i
  -0.0000 - 0.0007i
  -0.0007 + 0.0000i
  -0.0008 + 0.0000i
  -0.0005 + 0.0006i
   0.0007 - 0.0004i
   0.0007 - 0.0004i
  -0.0000 - 0.0008i
  -0.0004 + 0.0007i
  -0.0001 + 0.0009i
   0.0007 + 0.0006i
  -0.0008 - 0.0005i
   0.0007 + 0.0006i
  -0.0010 + 0.0001i
   0.0008 + 0.0007i
   0.0008 - 0.0007i
  -0.0009 - 0.0006i
   0.0009 + 0.0007i
   0.0008 - 0.0007i
  -0.0007 + 0.0008i
   0.0009 + 0.0007i
   0.0006 + 0.0010i
   0.0007 + 0.0010i
  -0.0004 - 0.0012i
   0.0009 + 0.0009i
   0.0010 + 0.0008i
   0.0007 + 0.0011i
  -0.0013 - 0.0004i
  -0.0014 - 0.0003i
  -0.0009 + 0.0011i
  -0.0012 - 0.0009i
  -0.0015 - 0.0003i
  -0.0015 - 0.0003i
   0.0013 + 0.0010i
  -0.0014 + 0.0009i
  -0.0017 + 0.0001i
  -0.0009 + 0.0014i
  -0.0002 + 0.0017i
  -0.0002 + 0.0017i
   0.0009 + 0.0015i
  -0.0015 + 0.0009i
   0.0015 - 0.0008i
  -0.0009 + 0.0015i
  -0.0001 - 0.0018i
  -0.0001 - 0.0018i
  -0.0018 + 0.0001i
  -0.0001 - 0.0018i
   0.0009 + 0.0016i
   0.0018 + 0.0006i
   0.0015 + 0.0012i
  -0.0019 + 0.0002i
   0.0019 + 0.0006i
  -0.0013 + 0.0015i
  -0.0017 + 0.0012i
  -0.0017 - 0.0012i
   0.0012 - 0.0017i
   0.0016 + 0.0013i
   0.0017 + 0.0013i
   0.0016 - 0.0014i
  -0.0006 - 0.0020i
  -0.0021 - 0.0005i
  -0.0018 + 0.0012i
  -0.0003 + 0.0023i
   0.0009 - 0.0021i
  -0.0015 + 0.0017i
   0.0022 + 0.0007i
   0.0009 - 0.0022i
   0.0010 - 0.0022i
  -0.0004 + 0.0025i
  -0.0004 + 0.0025i
  -0.0001 - 0.0026i
   0.0021 - 0.0017i
  -0.0027 + 0.0004i
   0.0015 - 0.0023i
  -0.0028 + 0.0005i
  -0.0025 + 0.0016i
   0.0016 - 0.0025i
   0.0029 + 0.0010i
  -0.0030 + 0.0002i
  -0.0026 + 0.0016i
   0.0029 + 0.0010i
  -0.0026 + 0.0016i
   0.0025 + 0.0019i
  -0.0027 + 0.0017i
  -0.0017 + 0.0028i
  -0.0033 + 0.0004i
   0.0017 - 0.0029i
   0.0026 - 0.0022i
   0.0025 + 0.0023i
  -0.0029 + 0.0019i
   0.0019 - 0.0029i
   0.0030 - 0.0017i
  -0.0001 - 0.0035i
  -0.0035 + 0.0002i
  -0.0035 + 0.0004i
   0.0028 + 0.0022i
  -0.0036 + 0.0002i
   0.0028 - 0.0023i
  -0.0005 + 0.0036i
  -0.0005 + 0.0036i
  -0.0036 - 0.0009i
   0.0035 + 0.0011i
  -0.0036 - 0.0010i
   0.0030 + 0.0023i
  -0.0005 + 0.0038i
   0.0031 + 0.0024i
  -0.0038 - 0.0010i
   0.0030 + 0.0025i
   0.0031 + 0.0025i
  -0.0005 + 0.0040i
   0.0031 + 0.0025i
  -0.0033 - 0.0024i
  -0.0040 + 0.0007i
   0.0022 - 0.0035i
   0.0033 + 0.0026i
   0.0023 - 0.0035i
  -0.0002 - 0.0043i
   0.0034 + 0.0026i
   0.0018 - 0.0039i
  -0.0028 + 0.0033i
  -0.0022 + 0.0038i
  -0.0045 + 0.0003i
   0.0036 + 0.0028i
   0.0025 - 0.0038i
  -0.0015 - 0.0043i
   0.0024 + 0.0039i
   0.0037 + 0.0028i
   0.0034 + 0.0032i
   0.0037 + 0.0029i
  -0.0031 + 0.0035i
  -0.0031 + 0.0036i
  -0.0047 + 0.0003i
  -0.0041 + 0.0025i
  -0.0048 - 0.0011i
  -0.0013 - 0.0047i
   0.0022 - 0.0044i
  -0.0049 + 0.0009i
  -0.0042 + 0.0027i
  -0.0042 - 0.0030i
   0.0027 + 0.0043i
  -0.0033 + 0.0039i
  -0.0003 - 0.0052i
  -0.0052 + 0.0003i
  -0.0002 - 0.0053i
   0.0042 + 0.0033i
  -0.0035 + 0.0040i
   0.0047 - 0.0026i
  -0.0029 + 0.0045i
   0.0040 + 0.0037i
  -0.0030 + 0.0046i
   0.0028 + 0.0048i
   0.0053 + 0.0018i
   0.0043 + 0.0035i
   0.0029 + 0.0049i
   0.0045 + 0.0035i
   0.0031 + 0.0048i
  -0.0029 + 0.0049i
  -0.0056 - 0.0013i
   0.0046 + 0.0035i
  -0.0048 + 0.0032i
  -0.0031 + 0.0049i
   0.0051 - 0.0028i
  -0.0049 + 0.0032i
   0.0046 + 0.0036i
  -0.0002 - 0.0059i
  -0.0033 + 0.0049i
   0.0044 - 0.0038i
  -0.0021 - 0.0055i
  -0.0059 + 0.0003i
  -0.0060 + 0.0003i
  -0.0002 - 0.0060i
  -0.0049 - 0.0035i
  -0.0059 + 0.0010i
   0.0032 + 0.0051i
  -0.0051 + 0.0032i
   0.0048 + 0.0037i
  -0.0003 - 0.0061i
  -0.0052 + 0.0032i
  -0.0061 + 0.0003i
  -0.0052 + 0.0032i
  -0.0050 - 0.0035i
   0.0031 - 0.0052i
   0.0048 + 0.0037i
  -0.0052 + 0.0032i
  -0.0021 - 0.0058i
  -0.0007 + 0.0061i
   0.0033 - 0.0053i
  -0.0053 + 0.0033i
  -0.0063 + 0.0004i
  -0.0062 + 0.0012i
  -0.0054 + 0.0033i
   0.0026 - 0.0058i
   0.0047 + 0.0043i
   0.0027 - 0.0058i
  -0.0064 + 0.0004i
   0.0034 - 0.0056i
   0.0051 + 0.0040i
  -0.0056 + 0.0035i
  -0.0066 + 0.0004i
  -0.0057 + 0.0035i
  -0.0044 + 0.0052i
   0.0053 + 0.0043i
   0.0052 - 0.0044i
  -0.0057 + 0.0038i
  -0.0056 - 0.0040i
  -0.0044 + 0.0053i
   0.0028 - 0.0063i
  -0.0068 - 0.0014i
  -0.0060 + 0.0037i
  -0.0036 + 0.0061i
  -0.0071 + 0.0004i
   0.0057 + 0.0044i
   0.0041 + 0.0059i
  -0.0037 + 0.0061i
  -0.0022 - 0.0069i
   0.0055 - 0.0047i
  -0.0011 + 0.0072i
   0.0057 + 0.0046i
  -0.0074 + 0.0004i
  -0.0063 + 0.0040i
   0.0038 - 0.0064i
  -0.0074 + 0.0004i
  -0.0010 + 0.0076i
  -0.0065 + 0.0041i
   0.0032 - 0.0070i
   0.0057 + 0.0053i
   0.0042 + 0.0065i
   0.0074 + 0.0026i
   0.0060 - 0.0051i
  -0.0067 + 0.0042i
   0.0046 + 0.0065i
   0.0047 + 0.0066i
  -0.0052 + 0.0063i
  -0.0043 + 0.0069i
  -0.0081 + 0.0005i
  -0.0023 - 0.0078i
  -0.0023 - 0.0078i
   0.0078 + 0.0025i
  -0.0067 - 0.0048i
   0.0062 - 0.0054i
  -0.0003 - 0.0083i
  -0.0070 + 0.0046i
   0.0066 + 0.0053i
  -0.0085 + 0.0005i
  -0.0011 + 0.0084i
  -0.0085 + 0.0004i
  -0.0083 - 0.0021i
   0.0035 - 0.0078i
   0.0065 - 0.0056i
  -0.0073 + 0.0047i
  -0.0003 - 0.0088i
  -0.0074 + 0.0048i
   0.0064 + 0.0060i
  -0.0045 + 0.0076i
  -0.0088 + 0.0006i
  -0.0073 - 0.0052i
   0.0078 - 0.0043i
   0.0071 + 0.0055i
   0.0066 + 0.0061i
  -0.0015 + 0.0089i
  -0.0048 + 0.0076i
  -0.0090 + 0.0006i
   0.0067 + 0.0062i
  -0.0058 + 0.0070i
  -0.0091 + 0.0013i
   0.0054 + 0.0074i
  -0.0059 + 0.0071i
   0.0053 + 0.0076i
  -0.0075 - 0.0054i
   0.0082 - 0.0044i
   0.0068 + 0.0064i
  -0.0060 + 0.0072i
  -0.0080 + 0.0049i
  -0.0005 - 0.0095i
   0.0075 + 0.0058i
  -0.0093 - 0.0021i
   0.0084 - 0.0046i
  -0.0003 - 0.0095i
   0.0056 + 0.0077i
  -0.0049 + 0.0083i
   0.0045 - 0.0085i
  -0.0053 + 0.0081i
  -0.0003 - 0.0097i
  -0.0095 - 0.0021i
   0.0053 - 0.0081i
   0.0040 - 0.0089i
  -0.0005 - 0.0097i
  -0.0063 + 0.0074i
  -0.0003 - 0.0098i
   0.0078 + 0.0060i
   0.0087 - 0.0049i
   0.0059 + 0.0081i
   0.0059 + 0.0082i
  -0.0015 + 0.0100i
  -0.0015 + 0.0100i
   0.0074 + 0.0069i
   0.0056 + 0.0086i
  -0.0103 + 0.0012i
   0.0090 - 0.0051i
  -0.0089 + 0.0054i
  -0.0067 + 0.0080i
  -0.0089 + 0.0055i
   0.0048 - 0.0094i
  -0.0105 + 0.0018i
   0.0084 + 0.0066i
  -0.0003 - 0.0107i
   0.0083 + 0.0067i
  -0.0016 + 0.0107i
  -0.0017 + 0.0107i
   0.0104 + 0.0034i
  -0.0109 + 0.0006i
  -0.0054 + 0.0095i
   0.0055 + 0.0095i
   0.0088 + 0.0067i
  -0.0014 + 0.0110i
  -0.0003 - 0.0111i
  -0.0015 + 0.0110i
  -0.0058 + 0.0096i
  -0.0095 + 0.0059i
   0.0058 - 0.0097i
   0.0066 + 0.0091i
  -0.0020 + 0.0111i
  -0.0094 + 0.0063i
  -0.0113 + 0.0006i
   0.0045 - 0.0104i
  -0.0005 - 0.0113i
  -0.0074 + 0.0087i
  -0.0114 + 0.0006i
  -0.0115 + 0.0005i
   0.0090 + 0.0073i
   0.0101 - 0.0057i
   0.0101 - 0.0057i
   0.0050 - 0.0105i
  -0.0005 - 0.0117i
   0.0103 - 0.0055i
  -0.0115 + 0.0022i
  -0.0062 + 0.0100i
  -0.0101 + 0.0062i
   0.0104 - 0.0059i
   0.0095 + 0.0073i
  -0.0005 - 0.0120i
   0.0095 + 0.0074i
   0.0068 + 0.0100i
   0.0066 + 0.0101i
  -0.0059 + 0.0106i
  -0.0103 + 0.0065i
   0.0072 + 0.0098i
  -0.0104 + 0.0063i
  -0.0037 - 0.0117i
   0.0090 + 0.0084i
  -0.0079 + 0.0095i
   0.0069 - 0.0103i
   0.0097 + 0.0078i
   0.0091 + 0.0085i
  -0.0122 - 0.0027i
   0.0110 - 0.0060i
  -0.0107 + 0.0066i
  -0.0080 + 0.0097i
  -0.0062 + 0.0109i
   0.0111 - 0.0060i
   0.0093 + 0.0086i
   0.0072 + 0.0106i
   0.0069 - 0.0108i
  -0.0083 + 0.0097i
   0.0113 - 0.0061i
   0.0094 + 0.0088i
  -0.0109 + 0.0067i
  -0.0005 - 0.0128i
  -0.0084 + 0.0098i
   0.0094 + 0.0088i
  -0.0068 + 0.0109i
   0.0067 + 0.0110i
  -0.0125 - 0.0033i
  -0.0006 - 0.0130i
  -0.0130 + 0.0007i
   0.0072 - 0.0109i
   0.0051 - 0.0120i
   0.0103 + 0.0080i
  -0.0131 + 0.0007i
  -0.0067 + 0.0113i
   0.0104 + 0.0080i
  -0.0109 + 0.0073i
   0.0059 - 0.0117i
   0.0072 - 0.0111i
  -0.0039 - 0.0127i
   0.0077 + 0.0108i
   0.0103 + 0.0083i
  -0.0114 + 0.0071i
   0.0106 + 0.0082i
  -0.0109 - 0.0079i
   0.0107 + 0.0082i
   0.0107 + 0.0083i
   0.0063 - 0.0120i
  -0.0134 + 0.0021i
  -0.0131 - 0.0036i
   0.0073 + 0.0115i
  -0.0069 + 0.0117i
  -0.0132 - 0.0033i
   0.0070 - 0.0117i
   0.0107 + 0.0086i
   0.0108 + 0.0084i
   0.0103 - 0.0090i
   0.0056 - 0.0125i
  -0.0067 + 0.0120i
  -0.0069 + 0.0119i
  -0.0117 + 0.0072i
   0.0109 + 0.0084i
  -0.0136 + 0.0022i
   0.0107 + 0.0087i
   0.0073 + 0.0118i
   0.0110 + 0.0084i
  -0.0136 - 0.0028i
  -0.0019 + 0.0138i
  -0.0116 + 0.0078i
   0.0058 - 0.0127i
  -0.0117 + 0.0077i
   0.0070 + 0.0121i
  -0.0140 + 0.0008i
   0.0109 + 0.0088i
   0.0069 + 0.0123i
  -0.0074 + 0.0121i
   0.0112 + 0.0087i
   0.0112 + 0.0086i
  -0.0119 + 0.0078i
   0.0065 - 0.0126i
   0.0075 + 0.0121i
  -0.0117 - 0.0082i
   0.0108 - 0.0094i
  -0.0121 + 0.0075i
   0.0109 - 0.0093i
  -0.0020 + 0.0142i
  -0.0077 + 0.0122i
  -0.0092 + 0.0111i
  -0.0144 + 0.0008i
  -0.0092 + 0.0111i
  -0.0143 + 0.0022i
   0.0080 + 0.0120i
   0.0115 + 0.0089i
   0.0113 + 0.0091i
  -0.0146 + 0.0007i
  -0.0075 + 0.0126i
  -0.0026 + 0.0145i
  -0.0123 + 0.0081i
   0.0084 + 0.0121i
   0.0128 - 0.0073i
  -0.0044 - 0.0141i
  -0.0008 - 0.0149i
   0.0114 - 0.0097i
   0.0065 - 0.0136i
   0.0080 + 0.0129i
  -0.0148 - 0.0032i
  -0.0022 + 0.0151i
  -0.0153 + 0.0009i
  -0.0152 + 0.0022i
  -0.0154 + 0.0008i
   0.0113 + 0.0105i
  -0.0153 + 0.0026i
  -0.0079 + 0.0133i
   0.0085 - 0.0130i
   0.0118 - 0.0102i
   0.0137 - 0.0075i
  -0.0081 + 0.0133i
  -0.0133 + 0.0082i
  -0.0156 + 0.0010i
   0.0120 - 0.0101i
  -0.0134 + 0.0083i
   0.0121 - 0.0101i
   0.0083 - 0.0134i
   0.0140 - 0.0076i
   0.0138 - 0.0079i
  -0.0134 + 0.0086i
  -0.0159 + 0.0018i
   0.0125 + 0.0100i
   0.0084 + 0.0136i
   0.0080 + 0.0139i
  -0.0134 + 0.0088i
  -0.0007 - 0.0161i
   0.0118 + 0.0110i
  -0.0131 - 0.0094i
  -0.0051 - 0.0153i
   0.0128 + 0.0099i
  -0.0057 - 0.0152i
   0.0127 + 0.0102i
  -0.0007 - 0.0163i
  -0.0086 + 0.0138i
  -0.0164 + 0.0007i
  -0.0008 - 0.0164i
  -0.0138 + 0.0089i
  -0.0165 + 0.0008i
   0.0075 - 0.0149i
   0.0094 + 0.0138i
  -0.0006 - 0.0167i
  -0.0165 + 0.0024i
  -0.0008 - 0.0167i
  -0.0082 + 0.0146i
  -0.0137 - 0.0097i
   0.0086 + 0.0144i
  -0.0166 + 0.0024i
  -0.0086 + 0.0144i
  -0.0163 - 0.0040i
  -0.0111 + 0.0127i
  -0.0027 + 0.0167i
   0.0132 + 0.0107i
  -0.0164 - 0.0043i
  -0.0145 + 0.0088i
  -0.0171 + 0.0010i
  -0.0087 + 0.0147i
   0.0097 + 0.0141i
   0.0151 - 0.0082i
   0.0150 - 0.0084i
  -0.0052 - 0.0164i
  -0.0024 + 0.0171i
  -0.0024 + 0.0172i
   0.0092 + 0.0147i
  -0.0094 + 0.0147i
   0.0097 - 0.0145i
  -0.0149 + 0.0092i
   0.0091 + 0.0150i
  -0.0085 + 0.0153i
  -0.0021 + 0.0174i
  -0.0096 + 0.0147i
   0.0069 - 0.0161i
  -0.0149 + 0.0093i
   0.0155 - 0.0084i
   0.0167 + 0.0055i
   0.0097 - 0.0147i
  -0.0176 + 0.0011i
   0.0095 - 0.0149i
  -0.0092 + 0.0151i
   0.0141 + 0.0109i
   0.0070 - 0.0164i
  -0.0030 + 0.0176i
  -0.0116 + 0.0136i
  -0.0094 + 0.0152i
   0.0141 + 0.0110i
  -0.0175 - 0.0038i
  -0.0094 + 0.0154i
  -0.0176 - 0.0045i
  -0.0155 + 0.0095i
   0.0172 + 0.0057i
  -0.0179 + 0.0034i
   0.0160 - 0.0088i
   0.0142 + 0.0115i
   0.0145 + 0.0112i
  -0.0027 + 0.0181i
   0.0145 + 0.0113i
  -0.0029 + 0.0182i
  -0.0118 + 0.0142i
   0.0106 + 0.0151i
   0.0146 + 0.0113i
   0.0144 + 0.0116i
  -0.0090 + 0.0162i
  -0.0122 + 0.0141i
  -0.0151 - 0.0110i
   0.0094 + 0.0162i
   0.0110 + 0.0151i
  -0.0184 + 0.0032i
  -0.0159 + 0.0098i
  -0.0151 - 0.0110i
   0.0104 - 0.0156i
  -0.0100 + 0.0158i
  -0.0186 + 0.0025i
  -0.0025 + 0.0186i
  -0.0188 + 0.0011i
   0.0096 + 0.0162i
   0.0179 + 0.0061i
   0.0104 - 0.0158i
   0.0179 + 0.0060i
   0.0150 + 0.0116i
  -0.0161 + 0.0100i
  -0.0188 + 0.0025i
   0.0167 - 0.0092i
  -0.0191 + 0.0010i
   0.0104 - 0.0161i
   0.0182 + 0.0059i
   0.0144 - 0.0126i
  -0.0123 + 0.0147i
  -0.0164 + 0.0101i
   0.0152 + 0.0118i
   0.0084 - 0.0173i
   0.0099 - 0.0165i
   0.0141 + 0.0132i
   0.0102 - 0.0166i
   0.0142 + 0.0133i
  -0.0025 + 0.0193i
   0.0098 + 0.0170i
   0.0155 + 0.0120i
  -0.0167 + 0.0103i
   0.0105 - 0.0166i
  -0.0060 - 0.0187i
   0.0151 - 0.0127i
   0.0151 - 0.0128i
  -0.0026 + 0.0196i
   0.0187 + 0.0064i
  -0.0160 - 0.0116i
   0.0175 - 0.0095i
  -0.0132 + 0.0150i
  -0.0127 + 0.0154i
   0.0156 + 0.0126i
  -0.0025 + 0.0199i
   0.0091 - 0.0179i
   0.0153 - 0.0131i
  -0.0171 + 0.0106i
   0.0082 - 0.0184i
  -0.0033 + 0.0199i
   0.0161 + 0.0125i
  -0.0071 - 0.0191i
   0.0159 + 0.0128i
  -0.0203 + 0.0026i
  -0.0036 + 0.0201i
   0.0149 + 0.0140i
   0.0180 - 0.0098i
  -0.0203 + 0.0027i
   0.0160 + 0.0129i
   0.0163 + 0.0125i
   0.0101 + 0.0179i
  -0.0105 + 0.0177i
  -0.0206 + 0.0012i
  -0.0172 + 0.0114i
  -0.0207 + 0.0012i
   0.0197 + 0.0066i
   0.0090 - 0.0187i
   0.0196 + 0.0069i
  -0.0207 + 0.0012i
   0.0110 + 0.0176i
   0.0158 - 0.0135i
  -0.0137 + 0.0156i
  -0.0060 - 0.0200i
  -0.0062 - 0.0199i
   0.0089 - 0.0189i
   0.0199 + 0.0068i
  -0.0138 + 0.0158i
   0.0154 + 0.0144i
   0.0155 + 0.0144i
   0.0167 + 0.0129i
   0.0200 + 0.0069i
  -0.0103 + 0.0185i
  -0.0176 + 0.0117i
   0.0093 - 0.0191i
  -0.0209 + 0.0037i
  -0.0136 + 0.0164i
  -0.0138 + 0.0162i
  -0.0139 + 0.0163i
   0.0094 - 0.0192i
   0.0095 - 0.0192i
  -0.0065 - 0.0204i
  -0.0070 - 0.0203i
   0.0170 + 0.0131i
   0.0167 + 0.0135i
  -0.0184 + 0.0112i
  -0.0209 - 0.0053i
  -0.0111 + 0.0185i
  -0.0175 - 0.0127i
  -0.0033 + 0.0214i
   0.0172 + 0.0133i
   0.0127 + 0.0177i
   0.0114 + 0.0186i
   0.0172 + 0.0133i
   0.0173 + 0.0134i
  -0.0215 + 0.0040i
   0.0127 + 0.0179i
   0.0170 + 0.0138i
  -0.0114 + 0.0188i
   0.0161 + 0.0150i
   0.0124 + 0.0182i
  -0.0217 + 0.0040i
   0.0211 + 0.0069i
   0.0175 + 0.0136i
  -0.0111 + 0.0193i
   0.0173 + 0.0140i
   0.0176 + 0.0136i
  -0.0119 + 0.0189i
  -0.0182 - 0.0129i
  -0.0064 - 0.0215i
  -0.0220 + 0.0040i
  -0.0121 + 0.0189i
  -0.0222 + 0.0032i
  -0.0182 - 0.0132i
  -0.0183 - 0.0130i
  -0.0144 + 0.0174i
  -0.0193 + 0.0118i
  -0.0223 + 0.0041i
   0.0216 + 0.0069i
   0.0177 + 0.0142i
   0.0179 + 0.0140i
   0.0180 + 0.0139i
   0.0180 + 0.0140i
   0.0216 + 0.0071i
  -0.0228 + 0.0011i
   0.0171 - 0.0150i
   0.0166 + 0.0156i
  -0.0009 - 0.0228i
  -0.0194 + 0.0120i
  -0.0077 - 0.0216i
  -0.0229 + 0.0013i
  -0.0032 + 0.0227i
   0.0168 + 0.0157i
  -0.0113 + 0.0202i
  -0.0010 - 0.0232i
  -0.0232 + 0.0013i
  -0.0114 + 0.0203i
  -0.0127 + 0.0195i
   0.0182 + 0.0146i
   0.0119 + 0.0202i
   0.0223 + 0.0072i
   0.0120 + 0.0202i
   0.0183 + 0.0148i
   0.0187 + 0.0144i
   0.0173 + 0.0161i
  -0.0132 + 0.0196i
  -0.0156 + 0.0179i
  -0.0237 + 0.0012i
  -0.0237 + 0.0014i
   0.0226 + 0.0076i
  -0.0238 + 0.0016i
   0.0227 + 0.0073i
  -0.0239 + 0.0016i
   0.0183 - 0.0155i
  -0.0202 + 0.0129i
   0.0190 + 0.0146i
   0.0187 + 0.0151i
   0.0228 + 0.0076i
  -0.0027 + 0.0239i
  -0.0034 + 0.0238i
  -0.0008 - 0.0241i
   0.0210 - 0.0119i
   0.0227 + 0.0080i
   0.0129 - 0.0204i
   0.0230 + 0.0074i
  -0.0158 + 0.0182i
   0.0188 + 0.0151i
  -0.0241 + 0.0014i
  -0.0042 + 0.0238i
   0.0128 - 0.0205i
  -0.0043 + 0.0238i
   0.0099 - 0.0221i
   0.0192 + 0.0148i
   0.0192 + 0.0148i
   0.0129 - 0.0206i
  -0.0128 + 0.0207i
  -0.0244 + 0.0014i
  -0.0013 - 0.0245i
  -0.0242 + 0.0040i
  -0.0201 - 0.0141i
  -0.0010 - 0.0246i
  -0.0207 + 0.0135i
   0.0186 - 0.0163i
  -0.0161 + 0.0188i
  -0.0247 + 0.0013i
  -0.0209 + 0.0134i
  -0.0248 + 0.0014i
  -0.0034 + 0.0247i
  -0.0249 + 0.0014i
  -0.0128 + 0.0214i
   0.0139 - 0.0208i
  -0.0242 - 0.0067i
   0.0198 + 0.0154i
  -0.0251 + 0.0014i
   0.0239 + 0.0078i
   0.0239 + 0.0081i
   0.0103 - 0.0230i
  -0.0251 + 0.0030i
   0.0104 - 0.0231i
  -0.0247 - 0.0052i
  -0.0205 - 0.0148i
   0.0136 + 0.0214i
  -0.0217 + 0.0132i
  -0.0248 - 0.0056i
   0.0198 + 0.0160i
   0.0135 - 0.0217i
  -0.0217 + 0.0134i
   0.0203 + 0.0156i
   0.0194 - 0.0168i
  -0.0217 + 0.0139i
  -0.0248 - 0.0069i
   0.0224 - 0.0129i
   0.0202 + 0.0163i
  -0.0259 + 0.0015i
   0.0141 + 0.0218i
   0.0205 + 0.0159i
   0.0137 - 0.0221i
   0.0228 - 0.0126i
  -0.0168 + 0.0199i
  -0.0258 + 0.0034i
   0.0247 + 0.0083i
   0.0207 + 0.0159i
  -0.0217 + 0.0146i
  -0.0261 + 0.0015i
   0.0110 - 0.0239i
  -0.0035 + 0.0260i
  -0.0009 - 0.0263i
   0.0134 + 0.0228i
  -0.0172 + 0.0201i
  -0.0137 + 0.0227i
   0.0108 - 0.0242i
   0.0143 - 0.0223i
  -0.0265 + 0.0014i
  -0.0227 + 0.0138i
  -0.0132 + 0.0231i
  -0.0263 + 0.0044i
  -0.0149 + 0.0222i
   0.0211 + 0.0164i
   0.0212 + 0.0163i
   0.0234 - 0.0131i
  -0.0134 + 0.0232i
  -0.0172 + 0.0207i
   0.0214 + 0.0165i
  -0.0037 + 0.0268i
   0.0145 + 0.0229i
  -0.0041 + 0.0268i
   0.0142 + 0.0231i
  -0.0151 + 0.0226i
   0.0139 - 0.0233i
   0.0216 + 0.0166i
  -0.0012 - 0.0272i
   0.0216 + 0.0167i
  -0.0145 + 0.0233i
  -0.0139 + 0.0236i
   0.0213 + 0.0172i
  -0.0143 + 0.0234i
  -0.0274 + 0.0018i
   0.0260 + 0.0089i
   0.0142 - 0.0235i
  -0.0235 + 0.0144i
   0.0214 + 0.0173i
   0.0209 - 0.0180i
  -0.0134 + 0.0242i
  -0.0012 - 0.0276i
   0.0145 - 0.0236i
   0.0216 + 0.0174i
  -0.0274 + 0.0043i
  -0.0270 - 0.0062i
   0.0216 + 0.0174i
   0.0241 - 0.0138i
  -0.0278 + 0.0015i
   0.0213 - 0.0180i
   0.0221 + 0.0172i
   0.0222 + 0.0171i
  -0.0152 + 0.0235i
   0.0144 + 0.0240i
  -0.0032 + 0.0279i
   0.0222 + 0.0172i
  -0.0014 - 0.0281i
   0.0266 + 0.0091i
  -0.0279 + 0.0039i
   0.0223 + 0.0172i
  -0.0281 + 0.0014i
   0.0140 + 0.0245i
   0.0166 + 0.0228i
  -0.0239 + 0.0151i
   0.0206 + 0.0193i
   0.0207 + 0.0193i
  -0.0274 - 0.0070i
  -0.0281 + 0.0041i
   0.0250 - 0.0135i
  -0.0274 - 0.0075i
  -0.0157 + 0.0237i
  -0.0236 + 0.0158i
   0.0215 - 0.0186i
   0.0163 + 0.0234i
   0.0155 + 0.0239i
  -0.0032 + 0.0284i
   0.0123 - 0.0258i
   0.0271 + 0.0092i
   0.0273 + 0.0087i
   0.0228 + 0.0175i
  -0.0287 + 0.0015i
   0.0272 + 0.0095i
  -0.0288 + 0.0017i
  -0.0243 + 0.0157i
  -0.0040 + 0.0286i
   0.0158 - 0.0243i
   0.0226 + 0.0182i
  -0.0236 - 0.0168i
  -0.0290 + 0.0017i
  -0.0155 + 0.0245i
  -0.0186 + 0.0222i
   0.0222 - 0.0187i
  -0.0290 + 0.0015i
  -0.0290 + 0.0018i
   0.0254 - 0.0142i
   0.0254 - 0.0144i
  -0.0292 + 0.0015i
   0.0224 - 0.0188i
  -0.0239 - 0.0169i
   0.0151 - 0.0250i
  -0.0282 - 0.0077i
   0.0156 + 0.0248i
   0.0228 + 0.0184i
  -0.0085 - 0.0281i
   0.0257 - 0.0143i
  -0.0151 + 0.0252i
   0.0232 + 0.0181i
  -0.0044 + 0.0291i
  -0.0286 - 0.0069i
   0.0158 + 0.0249i
  -0.0291 + 0.0049i
  -0.0040 + 0.0292i
   0.0230 + 0.0185i
  -0.0035 + 0.0293i
  -0.0041 + 0.0293i
   0.0259 - 0.0145i
  -0.0010 - 0.0297i
  -0.0148 + 0.0259i
   0.0125 - 0.0272i
  -0.0242 - 0.0176i
  -0.0012 - 0.0299i
   0.0234 + 0.0188i
   0.0166 - 0.0250i
   0.0237 + 0.0184i
   0.0234 + 0.0189i
  -0.0254 + 0.0164i
  -0.0192 + 0.0233i
  -0.0015 - 0.0302i
  -0.0254 + 0.0165i
  -0.0259 + 0.0159i
   0.0177 + 0.0247i
  -0.0015 - 0.0304i
  -0.0253 + 0.0170i
  -0.0045 + 0.0301i
  -0.0260 + 0.0159i
  -0.0158 + 0.0262i
  -0.0048 + 0.0302i
   0.0161 - 0.0261i
   0.0162 - 0.0260i
   0.0224 + 0.0209i
  -0.0306 + 0.0016i
  -0.0250 - 0.0177i
  -0.0044 + 0.0303i
  -0.0255 + 0.0170i
  -0.0167 + 0.0257i
  -0.0261 + 0.0161i
  -0.0251 - 0.0177i
  -0.0015 - 0.0307i
  -0.0151 + 0.0269i
  -0.0257 + 0.0171i
   0.0245 + 0.0188i
   0.0234 - 0.0202i
   0.0171 - 0.0258i
   0.0159 + 0.0267i
  -0.0300 - 0.0081i
  -0.0303 - 0.0074i
  -0.0203 + 0.0236i
  -0.0306 - 0.0064i
   0.0247 + 0.0191i
  -0.0312 + 0.0015i
   0.0124 - 0.0287i
  -0.0314 + 0.0017i
   0.0240 - 0.0204i
   0.0181 + 0.0257i
   0.0250 + 0.0192i
   0.0274 - 0.0156i
  -0.0268 + 0.0167i
   0.0300 + 0.0096i
  -0.0201 + 0.0244i
   0.0242 - 0.0203i
   0.0168 - 0.0268i
  -0.0108 - 0.0297i
  -0.0036 + 0.0315i
  -0.0042 + 0.0314i
   0.0251 + 0.0194i
  -0.0176 + 0.0266i
   0.0253 + 0.0194i
  -0.0162 + 0.0276i
   0.0234 + 0.0219i
  -0.0315 + 0.0056i
   0.0184 + 0.0262i
   0.0245 - 0.0207i
  -0.0173 + 0.0270i
  -0.0310 - 0.0082i
   0.0235 + 0.0219i
   0.0242 - 0.0213i
  -0.0276 + 0.0168i
  -0.0208 + 0.0248i
  -0.0177 + 0.0271i
  -0.0265 - 0.0188i
  -0.0096 - 0.0311i
   0.0257 + 0.0199i
  -0.0322 + 0.0051i
   0.0251 - 0.0210i
   0.0288 - 0.0155i
  -0.0096 - 0.0313i
   0.0254 + 0.0206i
   0.0151 - 0.0290i
  -0.0322 + 0.0060i
  -0.0324 + 0.0048i
   0.0284 - 0.0163i
  -0.0218 + 0.0246i
  -0.0163 + 0.0286i
  -0.0215 + 0.0249i
  -0.0099 - 0.0314i
  -0.0329 + 0.0020i
   0.0256 + 0.0207i
   0.0130 - 0.0303i
   0.0172 + 0.0281i
  -0.0328 + 0.0041i
  -0.0097 - 0.0315i
  -0.0046 + 0.0327i
   0.0172 - 0.0283i
  -0.0327 + 0.0051i
   0.0180 + 0.0278i
  -0.0283 + 0.0173i
  -0.0321 - 0.0081i
  -0.0333 + 0.0018i
  -0.0272 - 0.0193i
   0.0252 - 0.0219i
  -0.0333 + 0.0015i
   0.0264 + 0.0205i
  -0.0037 + 0.0332i
  -0.0333 + 0.0020i
   0.0182 - 0.0280i
   0.0179 - 0.0283i
   0.0294 - 0.0161i
   0.0260 + 0.0211i
  -0.0273 - 0.0194i
   0.0246 + 0.0228i
   0.0266 + 0.0204i
   0.0320 + 0.0102i
   0.0262 + 0.0211i
  -0.0179 + 0.0285i
   0.0181 - 0.0283i
   0.0173 + 0.0288i
   0.0246 + 0.0229i
   0.0246 + 0.0229i
  -0.0168 + 0.0293i
   0.0268 + 0.0206i
  -0.0338 + 0.0018i
  -0.0054 + 0.0334i
  -0.0017 - 0.0338i
  -0.0094 - 0.0326i
   0.0249 + 0.0231i
  -0.0275 - 0.0199i
  -0.0339 + 0.0017i
   0.0264 + 0.0213i
  -0.0329 - 0.0086i
  -0.0336 + 0.0053i
  -0.0011 - 0.0341i
   0.0265 + 0.0214i
  -0.0042 + 0.0338i
  -0.0340 + 0.0020i
  -0.0014 - 0.0341i
  -0.0341 + 0.0018i
  -0.0057 + 0.0337i
  -0.0171 + 0.0296i
  -0.0342 + 0.0019i
  -0.0041 + 0.0340i
   0.0300 - 0.0165i
   0.0197 + 0.0280i
  -0.0280 - 0.0198i
   0.0251 + 0.0235i
   0.0272 + 0.0210i
   0.0174 + 0.0296i
  -0.0294 + 0.0179i
  -0.0339 + 0.0062i
  -0.0294 + 0.0180i
   0.0189 + 0.0290i
  -0.0048 + 0.0343i
  -0.0010 - 0.0346i
   0.0192 - 0.0289i
  -0.0103 - 0.0331i
  -0.0344 + 0.0049i
  -0.0347 + 0.0020i
  -0.0293 + 0.0189i
  -0.0336 - 0.0093i
  -0.0186 + 0.0295i
   0.0329 + 0.0115i
   0.0331 + 0.0111i
  -0.0040 + 0.0347i
  -0.0345 + 0.0056i
  -0.0349 + 0.0017i
  -0.0045 + 0.0347i
  -0.0350 + 0.0018i
   0.0263 - 0.0231i
   0.0267 - 0.0227i
  -0.0177 + 0.0303i
  -0.0285 - 0.0204i
   0.0257 + 0.0240i
   0.0257 + 0.0240i
  -0.0011 - 0.0352i
   0.0279 + 0.0215i
   0.0279 + 0.0216i
  -0.0293 + 0.0197i
  -0.0353 + 0.0017i
  -0.0050 + 0.0350i
  -0.0302 + 0.0184i
  -0.0057 + 0.0349i
  -0.0188 + 0.0300i
  -0.0018 - 0.0354i
   0.0195 + 0.0296i
  -0.0287 - 0.0209i
  -0.0288 - 0.0207i
  -0.0053 + 0.0351i
   0.0193 - 0.0297i
   0.0206 + 0.0289i
   0.0209 + 0.0288i
  -0.0101 - 0.0341i
  -0.0351 + 0.0066i
   0.0272 - 0.0232i
   0.0194 - 0.0302i
   0.0280 + 0.0225i
  -0.0292 - 0.0210i
   0.0275 - 0.0232i
   0.0286 + 0.0220i
  -0.0360 + 0.0019i
  -0.0048 + 0.0358i
  -0.0229 + 0.0279i
   0.0159 - 0.0324i
  -0.0356 + 0.0062i
   0.0315 - 0.0179i
   0.0343 + 0.0117i
   0.0274 - 0.0238i
   0.0288 + 0.0221i
   0.0316 - 0.0179i
  -0.0309 + 0.0189i
  -0.0058 + 0.0358i
  -0.0360 + 0.0047i
   0.0315 - 0.0181i
   0.0278 - 0.0234i
  -0.0358 + 0.0065i
  -0.0234 + 0.0278i
   0.0283 + 0.0228i
   0.0266 + 0.0249i
   0.0276 - 0.0237i
  -0.0295 - 0.0213i
  -0.0017 - 0.0365i
  -0.0307 + 0.0198i
   0.0198 + 0.0307i
   0.0290 + 0.0223i
  -0.0303 + 0.0204i
   0.0285 + 0.0230i
  -0.0366 + 0.0021i
   0.0349 + 0.0111i
  -0.0236 + 0.0280i
   0.0279 - 0.0238i
   0.0195 - 0.0311i
   0.0178 + 0.0322i
  -0.0042 + 0.0365i
  -0.0046 + 0.0365i
   0.0291 + 0.0226i
   0.0350 + 0.0116i
   0.0287 + 0.0231i
  -0.0116 - 0.0350i
  -0.0193 + 0.0315i
  -0.0363 + 0.0068i
  -0.0314 + 0.0194i
  -0.0057 + 0.0365i
  -0.0314 + 0.0195i
   0.0161 - 0.0333i
   0.0190 + 0.0317i
   0.0159 - 0.0334i
  -0.0370 + 0.0019i
   0.0293 + 0.0227i
   0.0192 - 0.0317i
  -0.0051 + 0.0367i
  -0.0302 - 0.0215i
   0.0353 + 0.0113i
  -0.0065 + 0.0365i
   0.0295 + 0.0226i
  -0.0016 - 0.0371i
  -0.0363 - 0.0078i
  -0.0371 + 0.0021i
  -0.0016 - 0.0372i
  -0.0018 - 0.0373i
  -0.0368 + 0.0062i
   0.0189 + 0.0322i
   0.0203 + 0.0314i
  -0.0017 - 0.0373i
  -0.0311 + 0.0208i
  -0.0193 + 0.0321i
  -0.0246 + 0.0282i
   0.0287 - 0.0241i
  -0.0305 - 0.0218i
   0.0329 - 0.0180i
   0.0198 - 0.0319i
   0.0298 + 0.0229i
   0.0189 + 0.0325i
   0.0297 + 0.0231i
   0.0327 - 0.0186i
   0.0329 - 0.0184i
  -0.0376 + 0.0022i
  -0.0374 + 0.0052i
  -0.0367 - 0.0088i
   0.0286 - 0.0247i
  -0.0306 - 0.0222i
   0.0201 + 0.0320i
  -0.0196 + 0.0323i
   0.0358 + 0.0120i
  -0.0365 - 0.0099i
  -0.0316 + 0.0208i
   0.0221 + 0.0307i
   0.0333 - 0.0180i
   0.0278 + 0.0259i
  -0.0374 + 0.0066i
  -0.0374 + 0.0067i
  -0.0370 - 0.0086i
  -0.0016 - 0.0380i
  -0.0380 + 0.0022i
   0.0361 + 0.0123i
   0.0172 - 0.0340i
  -0.0196 + 0.0327i
   0.0149 - 0.0352i
  -0.0198 + 0.0327i
  -0.0054 + 0.0378i
  -0.0325 + 0.0202i
   0.0291 - 0.0250i
  -0.0373 - 0.0090i
  -0.0326 + 0.0201i
  -0.0313 - 0.0222i
   0.0304 + 0.0236i
  -0.0327 + 0.0202i
  -0.0210 + 0.0323i
   0.0195 + 0.0333i
   0.0306 + 0.0235i
   0.0306 + 0.0236i
   0.0198 + 0.0332i
  -0.0387 + 0.0018i
   0.0306 + 0.0237i
  -0.0387 + 0.0023i
   0.0302 + 0.0243i
  -0.0326 + 0.0211i
  -0.0059 + 0.0385i
   0.0369 + 0.0127i
  -0.0389 + 0.0026i
  -0.0121 - 0.0372i
  -0.0383 - 0.0082i
   0.0211 + 0.0330i
  -0.0046 + 0.0389i
  -0.0384 - 0.0079i
  -0.0208 + 0.0333i
  -0.0056 + 0.0388i
   0.0297 - 0.0258i
  -0.0327 + 0.0219i
  -0.0386 - 0.0076i
  -0.0201 + 0.0338i
  -0.0215 + 0.0330i
  -0.0052 + 0.0390i
   0.0164 - 0.0358i
  -0.0019 - 0.0394i
   0.0183 - 0.0350i
   0.0219 + 0.0329i
  -0.0395 + 0.0023i
  -0.0111 - 0.0380i
   0.0375 + 0.0126i
  -0.0215 + 0.0333i
  -0.0109 - 0.0382i
  -0.0058 + 0.0393i
  -0.0213 + 0.0336i
  -0.0258 + 0.0303i
   0.0215 + 0.0335i
   0.0207 - 0.0342i
  -0.0054 + 0.0396i
   0.0311 + 0.0251i
  -0.0202 + 0.0345i
  -0.0394 + 0.0068i
  -0.0386 - 0.0106i
   0.0352 - 0.0192i
  -0.0342 + 0.0209i
  -0.0389 - 0.0098i
  -0.0401 + 0.0018i
  -0.0327 - 0.0234i
  -0.0218 + 0.0338i
  -0.0340 + 0.0215i
  -0.0053 + 0.0399i
   0.0295 + 0.0275i
   0.0212 - 0.0344i
   0.0315 + 0.0253i
   0.0321 + 0.0246i
   0.0221 - 0.0339i
  -0.0224 + 0.0337i
   0.0206 + 0.0349i
  -0.0341 + 0.0219i
  -0.0125 - 0.0386i
  -0.0406 + 0.0025i
   0.0355 - 0.0198i
   0.0198 + 0.0355i
  -0.0047 + 0.0405i
   0.0323 + 0.0249i
  -0.0347 + 0.0215i
  -0.0342 + 0.0224i
   0.0319 + 0.0256i
   0.0225 + 0.0342i
  -0.0349 + 0.0215i
  -0.0399 - 0.0092i
   0.0324 + 0.0251i
  -0.0348 + 0.0217i
   0.0229 - 0.0341i
  -0.0017 - 0.0410i
  -0.0123 - 0.0392i
  -0.0054 + 0.0407i
  -0.0411 + 0.0020i
   0.0326 + 0.0252i
   0.0325 + 0.0253i
  -0.0337 - 0.0238i
   0.0359 - 0.0205i
   0.0174 - 0.0376i
   0.0207 + 0.0360i
   0.0323 + 0.0261i
  -0.0405 - 0.0095i
  -0.0411 + 0.0061i
  -0.0203 + 0.0363i
   0.0224 - 0.0351i
   0.0396 + 0.0129i
  -0.0415 + 0.0025i
   0.0181 - 0.0375i
  -0.0401 - 0.0112i
  -0.0049 + 0.0414i
   0.0331 + 0.0254i
  -0.0404 - 0.0105i
  -0.0418 + 0.0020i
  -0.0352 + 0.0227i
  -0.0343 - 0.0241i
  -0.0128 - 0.0399i
   0.0333 + 0.0256i
   0.0332 + 0.0258i
  -0.0065 + 0.0416i
  -0.0206 + 0.0368i
  -0.0360 + 0.0219i
   0.0234 - 0.0351i
  -0.0409 - 0.0105i
   0.0329 + 0.0266i
  -0.0130 - 0.0403i
   0.0322 - 0.0275i
  -0.0411 - 0.0103i
  -0.0227 + 0.0358i
  -0.0019 - 0.0424i
   0.0404 + 0.0131i
   0.0336 + 0.0261i
   0.0402 + 0.0140i
  -0.0426 + 0.0022i
  -0.0425 + 0.0027i
   0.0184 - 0.0385i
  -0.0412 - 0.0113i
   0.0321 - 0.0281i
   0.0338 + 0.0260i
  -0.0363 + 0.0225i
  -0.0355 + 0.0238i
   0.0241 + 0.0353i
   0.0339 + 0.0262i
  -0.0146 - 0.0402i
   0.0340 + 0.0261i
  -0.0277 + 0.0327i
  -0.0240 + 0.0356i
  -0.0357 + 0.0239i
   0.0230 - 0.0364i
   0.0217 + 0.0372i
  -0.0053 + 0.0428i
   0.0380 - 0.0205i
   0.0329 - 0.0280i
  -0.0132 - 0.0412i
  -0.0064 + 0.0429i
  -0.0354 - 0.0251i
  -0.0370 + 0.0227i
   0.0411 + 0.0141i
   0.0239 + 0.0363i
   0.0241 - 0.0363i
  -0.0221 + 0.0375i
  -0.0354 - 0.0253i
   0.0240 - 0.0364i
  -0.0373 + 0.0227i
   0.0319 + 0.0298i
  -0.0062 + 0.0432i
  -0.0014 - 0.0437i
  -0.0238 + 0.0367i
   0.0382 - 0.0213i
  -0.0373 + 0.0228i
   0.0213 + 0.0382i
   0.0345 + 0.0269i
  -0.0437 + 0.0021i
  -0.0437 + 0.0023i
   0.0341 + 0.0275i
  -0.0438 + 0.0023i
   0.0321 + 0.0299i
  -0.0432 + 0.0080i
  -0.0125 - 0.0421i
   0.0225 - 0.0378i
  -0.0375 + 0.0231i
   0.0349 + 0.0269i
   0.0337 - 0.0284i
  -0.0376 + 0.0231i
  -0.0377 + 0.0230i
  -0.0428 - 0.0112i
   0.0324 + 0.0302i
   0.0334 - 0.0291i
   0.0420 + 0.0140i
  -0.0375 + 0.0236i
   0.0247 - 0.0369i
  -0.0018 - 0.0444i
   0.0227 + 0.0382i
  -0.0021 - 0.0444i
  -0.0073 + 0.0438i
  -0.0442 + 0.0052i
   0.0422 + 0.0142i
   0.0183 - 0.0405i
   0.0353 + 0.0273i
  -0.0381 + 0.0232i
  -0.0155 - 0.0420i
   0.0349 + 0.0281i
   0.0327 + 0.0306i
  -0.0444 + 0.0061i
   0.0243 + 0.0376i
   0.0424 + 0.0145i
  -0.0373 + 0.0250i
  -0.0245 + 0.0376i
  -0.0235 + 0.0383i
   0.0175 - 0.0414i
  -0.0436 - 0.0111i
  -0.0063 + 0.0446i
  -0.0235 + 0.0385i
   0.0330 + 0.0308i
  -0.0451 + 0.0025i
   0.0330 + 0.0308i
  -0.0446 + 0.0075i
   0.0343 - 0.0295i
  -0.0381 + 0.0244i
   0.0258 + 0.0372i
   0.0352 + 0.0284i
  -0.0446 + 0.0080i
  -0.0367 - 0.0266i
  -0.0366 - 0.0267i
   0.0254 + 0.0376i
   0.0360 + 0.0277i
  -0.0225 + 0.0395i
   0.0343 - 0.0300i
   0.0398 - 0.0223i
  -0.0302 + 0.0342i
  -0.0126 - 0.0438i
   0.0262 + 0.0374i
  -0.0450 + 0.0076i
   0.0362 + 0.0279i
   0.0345 - 0.0301i
   0.0363 + 0.0279i
  -0.0057 + 0.0455i
   0.0190 - 0.0418i
  -0.0066 + 0.0455i
   0.0401 - 0.0226i
  -0.0063 + 0.0456i
  -0.0160 - 0.0431i
  -0.0374 - 0.0269i
  -0.0153 - 0.0435i
   0.0365 + 0.0282i
   0.0273 + 0.0373i
   0.0360 + 0.0290i
   0.0360 + 0.0291i
  -0.0067 + 0.0458i
   0.0351 - 0.0302i
  -0.0455 - 0.0092i
  -0.0232 + 0.0402i
   0.0361 + 0.0292i
  -0.0020 - 0.0464i
  -0.0380 - 0.0268i
  -0.0465 + 0.0030i
  -0.0377 - 0.0274i
  -0.0460 + 0.0075i
   0.0369 + 0.0286i
  -0.0457 - 0.0094i
  -0.0462 + 0.0064i
   0.0257 - 0.0390i
   0.0245 - 0.0398i
  -0.0382 - 0.0270i
  -0.0467 + 0.0023i
   0.0370 + 0.0287i
   0.0365 + 0.0294i
   0.0354 - 0.0308i
  -0.0023 - 0.0469i
   0.0409 - 0.0231i
  -0.0462 + 0.0083i
   0.0344 + 0.0320i
  -0.0398 + 0.0251i
  -0.0392 + 0.0261i
  -0.0238 + 0.0408i
  -0.0314 + 0.0354i
  -0.0016 - 0.0473i
  -0.0460 - 0.0110i
  -0.0068 + 0.0468i
   0.0361 - 0.0306i
  -0.0462 - 0.0104i
   0.0375 + 0.0290i
  -0.0473 + 0.0025i
   0.0376 + 0.0290i
  -0.0470 + 0.0063i
  -0.0388 - 0.0274i
   0.0376 + 0.0289i
  -0.0023 - 0.0474i
  -0.0132 - 0.0456i
   0.0376 + 0.0290i
   0.0347 + 0.0325i
  -0.0077 + 0.0470i
   0.0378 + 0.0291i
  -0.0257 + 0.0402i
  -0.0311 + 0.0363i
  -0.0467 - 0.0103i
   0.0451 + 0.0157i
  -0.0054 + 0.0475i
  -0.0408 + 0.0249i
  -0.0246 + 0.0410i
   0.0374 + 0.0301i
  -0.0408 + 0.0255i
  -0.0253 + 0.0409i
   0.0374 + 0.0303i
  -0.0320 + 0.0360i
   0.0382 + 0.0295i
   0.0458 + 0.0152i
  -0.0472 - 0.0102i
  -0.0238 + 0.0421i
  -0.0404 + 0.0265i
   0.0259 - 0.0408i
  -0.0474 - 0.0097i
  -0.0068 + 0.0479i
   0.0354 + 0.0330i
   0.0195 - 0.0444i
  -0.0475 - 0.0095i
   0.0423 - 0.0238i
  -0.0259 + 0.0410i
  -0.0485 + 0.0023i
  -0.0405 + 0.0267i
  -0.0070 + 0.0481i
  -0.0145 - 0.0464i
  -0.0245 + 0.0421i
  -0.0054 + 0.0484i
   0.0368 - 0.0320i
   0.0429 - 0.0232i
  -0.0408 + 0.0267i
   0.0254 - 0.0418i
  -0.0399 - 0.0282i
  -0.0084 + 0.0482i
  -0.0479 - 0.0098i
  -0.0253 + 0.0418i
  -0.0395 - 0.0288i
  -0.0476 - 0.0112i
   0.0261 + 0.0415i
   0.0467 + 0.0149i
   0.0264 + 0.0413i
  -0.0490 + 0.0028i
   0.0359 + 0.0335i
   0.0256 - 0.0421i
   0.0273 - 0.0410i
   0.0391 + 0.0301i
  -0.0087 + 0.0486i
   0.0385 + 0.0310i
   0.0431 - 0.0242i
   0.0252 + 0.0425i
   0.0385 + 0.0311i
   0.0192 - 0.0456i
  -0.0326 + 0.0373i
  -0.0076 + 0.0490i
  -0.0486 - 0.0103i
  -0.0250 + 0.0429i
  -0.0266 + 0.0419i
  -0.0423 + 0.0261i
  -0.0407 - 0.0286i
  -0.0247 + 0.0432i
  -0.0023 - 0.0498i
  -0.0498 + 0.0028i
   0.0212 - 0.0451i
  -0.0254 + 0.0430i
   0.0366 + 0.0340i
  -0.0014 - 0.0499i
   0.0388 + 0.0314i
   0.0395 + 0.0306i
  -0.0083 + 0.0493i
  -0.0019 - 0.0500i
  -0.0256 + 0.0430i
  -0.0072 + 0.0495i
  -0.0330 + 0.0377i
  -0.0495 + 0.0079i
   0.0224 - 0.0448i
   0.0382 - 0.0325i
   0.0258 - 0.0430i
   0.0390 + 0.0315i
   0.0397 + 0.0306i
  -0.0491 - 0.0103i
   0.0397 + 0.0308i
  -0.0502 + 0.0024i
  -0.0332 + 0.0377i
   0.0443 - 0.0238i
   0.0391 + 0.0317i
  -0.0144 - 0.0482i
  -0.0256 + 0.0433i
   0.0392 + 0.0317i
   0.0399 + 0.0308i
   0.0392 + 0.0317i
   0.0284 + 0.0418i
  -0.0164 - 0.0478i
   0.0401 + 0.0309i
  -0.0073 + 0.0501i
  -0.0423 + 0.0278i
  -0.0428 + 0.0271i
   0.0272 - 0.0428i
   0.0444 - 0.0246i
  -0.0061 + 0.0504i
  -0.0066 + 0.0504i
   0.0446 - 0.0245i
  -0.0432 + 0.0268i
  -0.0492 - 0.0129i
  -0.0148 - 0.0487i
  -0.0082 + 0.0502i
  -0.0069 + 0.0505i
  -0.0413 - 0.0298i
  -0.0083 + 0.0503i
   0.0272 - 0.0431i
   0.0403 + 0.0313i
  -0.0510 + 0.0027i
   0.0405 + 0.0313i
  -0.0265 + 0.0438i
  -0.0511 + 0.0026i
  -0.0427 + 0.0283i
  -0.0505 + 0.0085i
  -0.0270 + 0.0435i
  -0.0277 + 0.0431i
  -0.0436 + 0.0271i
  -0.0513 + 0.0029i
  -0.0513 + 0.0033i
   0.0274 + 0.0435i
   0.0400 + 0.0324i
  -0.0440 + 0.0267i
   0.0446 - 0.0257i
   0.0401 + 0.0323i
   0.0407 + 0.0316i
  -0.0421 - 0.0298i
  -0.0024 - 0.0515i
   0.0491 + 0.0158i
  -0.0017 - 0.0516i
   0.0209 - 0.0472i
  -0.0084 + 0.0510i
   0.0493 + 0.0158i
  -0.0087 + 0.0510i
   0.0451 - 0.0255i
  -0.0507 - 0.0106i
  -0.0016 - 0.0518i
  -0.0066 + 0.0515i
   0.0490 + 0.0172i
  -0.0511 + 0.0090i
  -0.0021 - 0.0519i
  -0.0444 + 0.0270i
  -0.0519 + 0.0029i
  -0.0508 - 0.0111i
  -0.0516 + 0.0069i
  -0.0515 + 0.0081i
   0.0492 + 0.0172i
  -0.0333 + 0.0402i
  -0.0521 + 0.0027i
   0.0267 - 0.0450i
  -0.0443 + 0.0279i
  -0.0343 + 0.0395i
  -0.0511 - 0.0118i
   0.0234 - 0.0469i
   0.0289 + 0.0437i
  -0.0518 + 0.0079i
  -0.0436 + 0.0291i
  -0.0269 + 0.0450i
   0.0416 + 0.0320i
  -0.0441 + 0.0285i
   0.0238 - 0.0468i
  -0.0524 + 0.0028i
  -0.0158 - 0.0501i
   0.0501 + 0.0160i
   0.0282 + 0.0444i
   0.0416 + 0.0322i
  -0.0274 + 0.0450i
   0.0499 + 0.0169i
  -0.0526 + 0.0031i
   0.0457 - 0.0262i
  -0.0076 + 0.0522i
   0.0398 - 0.0347i
  -0.0157 - 0.0504i
  -0.0522 + 0.0084i
   0.0412 + 0.0332i
   0.0387 + 0.0361i
  -0.0516 - 0.0122i
  -0.0512 - 0.0136i
   0.0413 + 0.0333i
  -0.0077 + 0.0525i
   0.0504 + 0.0165i
  -0.0448 + 0.0286i
  -0.0276 + 0.0454i
  -0.0531 + 0.0032i
   0.0291 + 0.0446i
  -0.0096 + 0.0524i
  -0.0343 + 0.0408i
   0.0293 + 0.0445i
   0.0421 + 0.0327i
   0.0408 - 0.0343i
  -0.0340 + 0.0411i
   0.0298 + 0.0443i
   0.0416 + 0.0335i
  -0.0078 + 0.0529i
  -0.0093 + 0.0527i
  -0.0088 + 0.0528i
  -0.0438 - 0.0307i
  -0.0277 + 0.0458i
   0.0392 + 0.0365i
   0.0406 - 0.0349i
   0.0423 + 0.0328i
   0.0230 - 0.0485i
   0.0424 + 0.0329i
   0.0426 + 0.0327i
   0.0273 + 0.0463i
  -0.0521 - 0.0133i
   0.0409 - 0.0350i
   0.0394 + 0.0368i
  -0.0436 - 0.0317i
   0.0394 + 0.0368i
   0.0298 - 0.0450i
   0.0470 - 0.0265i
  -0.0539 + 0.0029i
  -0.0540 + 0.0026i
   0.0428 + 0.0331i
  -0.0441 - 0.0313i
   0.0395 + 0.0370i
  -0.0156 - 0.0518i
  -0.0289 + 0.0458i
  -0.0067 + 0.0538i
  -0.0064 + 0.0538i
   0.0428 + 0.0332i
   0.0515 + 0.0170i
   0.0281 - 0.0464i
  -0.0016 - 0.0543i
   0.0313 + 0.0444i
  -0.0461 + 0.0287i
  -0.0286 + 0.0462i
  -0.0283 + 0.0464i
  -0.0275 + 0.0469i
   0.0431 + 0.0332i
  -0.0273 + 0.0471i
  -0.0167 - 0.0519i
   0.0282 + 0.0466i
   0.0398 + 0.0372i
   0.0304 - 0.0453i
   0.0399 + 0.0372i
   0.0284 + 0.0466i
   0.0313 + 0.0447i
  -0.0442 - 0.0322i
  -0.0445 - 0.0318i
   0.0416 - 0.0357i
   0.0401 + 0.0375i
   0.0479 - 0.0268i
  -0.0448 - 0.0317i
   0.0435 + 0.0338i
  -0.0539 - 0.0113i
   0.0485 - 0.0262i
   0.0429 + 0.0346i
  -0.0531 - 0.0146i
  -0.0543 + 0.0096i
   0.0480 - 0.0271i
   0.0278 + 0.0477i
  -0.0153 - 0.0531i
   0.0319 + 0.0452i
   0.0240 - 0.0499i
  -0.0300 + 0.0465i
   0.0431 + 0.0349i
  -0.0548 + 0.0086i
   0.0441 + 0.0339i
  -0.0172 - 0.0529i
  -0.0542 - 0.0125i
  -0.0096 + 0.0548i
   0.0529 + 0.0172i
  -0.0556 + 0.0033i
  -0.0271 + 0.0487i
  -0.0366 + 0.0420i
  -0.0474 + 0.0293i
   0.0310 - 0.0464i
  -0.0281 + 0.0482i
  -0.0356 + 0.0431i
   0.0419 - 0.0370i
   0.0485 - 0.0279i
  -0.0476 + 0.0294i
  -0.0559 + 0.0032i
  -0.0471 + 0.0304i
   0.0303 - 0.0471i
  -0.0280 + 0.0485i
  -0.0552 + 0.0095i
   0.0410 + 0.0382i
  -0.0479 + 0.0292i
   0.0410 + 0.0383i
  -0.0557 + 0.0075i
   0.0535 + 0.0174i
   0.0412 + 0.0384i
   0.0447 + 0.0343i
  -0.0563 + 0.0035i
  -0.0559 + 0.0072i
   0.0533 + 0.0186i
  -0.0082 + 0.0558i
   0.0440 + 0.0354i
   0.0536 + 0.0179i
  -0.0480 + 0.0298i
   0.0537 + 0.0176i
  -0.0077 + 0.0560i
   0.0449 + 0.0345i
   0.0449 + 0.0346i
  -0.0461 - 0.0330i
  -0.0308 + 0.0476i
  -0.0550 - 0.0140i
  -0.0071 + 0.0564i
  -0.0567 + 0.0035i
   0.0500 - 0.0271i
   0.0449 + 0.0349i
   0.0449 + 0.0350i
   0.0416 + 0.0388i
   0.0292 + 0.0490i
  -0.0097 + 0.0562i
  -0.0024 - 0.0570i
  -0.0486 + 0.0300i
   0.0540 + 0.0188i
   0.0300 + 0.0486i
   0.0306 + 0.0483i
  -0.0170 - 0.0546i
  -0.0571 + 0.0032i
   0.0497 - 0.0284i
  -0.0087 + 0.0566i
  -0.0569 + 0.0068i
  -0.0468 - 0.0331i
   0.0455 + 0.0350i
  -0.0019 - 0.0574i
   0.0455 + 0.0350i
   0.0454 + 0.0352i
  -0.0570 + 0.0068i
   0.0500 - 0.0283i
   0.0318 - 0.0479i
   0.0317 + 0.0480i
   0.0545 + 0.0184i
   0.0239 - 0.0523i
   0.0260 - 0.0514i
   0.0455 + 0.0353i
   0.0546 + 0.0181i
  -0.0491 + 0.0302i
   0.0549 + 0.0175i
   0.0331 + 0.0472i
   0.0436 - 0.0377i
  -0.0490 + 0.0304i
  -0.0286 + 0.0500i
   0.0438 - 0.0375i
  -0.0486 + 0.0311i
  -0.0321 + 0.0479i
  -0.0090 + 0.0570i
   0.0439 - 0.0375i
   0.0450 + 0.0362i
  -0.0491 + 0.0305i
  -0.0494 + 0.0300i
  -0.0319 + 0.0482i
   0.0450 + 0.0363i
   0.0318 - 0.0483i
  -0.0298 + 0.0496i
   0.0325 + 0.0479i
  -0.0103 + 0.0570i
  -0.0019 - 0.0579i
  -0.0578 + 0.0034i
   0.0451 + 0.0363i
   0.0242 - 0.0526i
  -0.0186 - 0.0549i
   0.0232 - 0.0532i
  -0.0576 + 0.0069i
   0.0452 + 0.0365i
  -0.0080 + 0.0576i
  -0.0581 + 0.0029i
  -0.0312 + 0.0491i
  -0.0565 - 0.0139i
   0.0330 + 0.0479i
  -0.0023 - 0.0581i
   0.0255 - 0.0523i
   0.0427 + 0.0396i
  -0.0574 + 0.0097i
   0.0554 + 0.0181i
  -0.0475 - 0.0337i
  -0.0382 + 0.0440i
   0.0556 + 0.0176i
   0.0462 + 0.0356i
   0.0313 - 0.0492i
   0.0427 + 0.0399i
  -0.0583 + 0.0036i
  -0.0185 - 0.0554i
  -0.0583 + 0.0029i
   0.0241 - 0.0532i
   0.0445 - 0.0380i
   0.0455 + 0.0368i
  -0.0287 + 0.0510i
  -0.0501 + 0.0304i
   0.0512 - 0.0287i
  -0.0501 + 0.0306i
  -0.0586 + 0.0033i
  -0.0092 + 0.0580i
   0.0458 + 0.0369i
  -0.0587 + 0.0034i
  -0.0569 - 0.0148i
  -0.0587 + 0.0037i
  -0.0477 - 0.0345i
  -0.0375 + 0.0455i
   0.0313 + 0.0500i
   0.0467 + 0.0360i
   0.0322 + 0.0495i
  -0.0590 + 0.0036i
  -0.0068 + 0.0587i
   0.0449 - 0.0384i
   0.0468 + 0.0361i
  -0.0069 + 0.0587i
  -0.0103 + 0.0583i
  -0.0087 + 0.0586i
  -0.0387 + 0.0449i
   0.0348 + 0.0479i
  -0.0592 + 0.0036i
   0.0469 + 0.0364i
  -0.0504 + 0.0314i
   0.0470 + 0.0364i
  -0.0505 + 0.0314i
   0.0516 - 0.0296i
   0.0565 + 0.0187i
  -0.0508 + 0.0310i
   0.0567 + 0.0181i
   0.0464 + 0.0375i
   0.0471 + 0.0365i
   0.0437 + 0.0406i
   0.0437 + 0.0406i
   0.0472 + 0.0366i
   0.0437 + 0.0407i
  -0.0081 + 0.0593i
   0.0439 + 0.0408i
   0.0522 - 0.0296i
  -0.0093 + 0.0593i
  -0.0076 + 0.0596i
  -0.0075 + 0.0596i
   0.0529 - 0.0287i
  -0.0322 + 0.0508i
   0.0468 + 0.0378i
  -0.0094 + 0.0595i
   0.0344 + 0.0494i
  -0.0594 + 0.0104i
  -0.0099 + 0.0595i
  -0.0383 + 0.0466i
   0.0471 + 0.0379i
  -0.0594 + 0.0113i
   0.0321 - 0.0513i
   0.0575 + 0.0188i
  -0.0517 + 0.0316i
  -0.0186 - 0.0577i
   0.0259 - 0.0548i
   0.0350 + 0.0495i
   0.0330 - 0.0510i
   0.0573 + 0.0201i
   0.0316 + 0.0519i
  -0.0089 + 0.0601i
   0.0324 - 0.0515i
   0.0445 + 0.0415i
  -0.0306 + 0.0526i
   0.0576 + 0.0197i
   0.0467 - 0.0391i
   0.0533 - 0.0294i
  -0.0520 + 0.0317i
  -0.0306 + 0.0527i
  -0.0080 + 0.0605i
   0.0309 + 0.0527i
  -0.0596 - 0.0134i
  -0.0610 + 0.0039i
  -0.0333 + 0.0513i
   0.0476 + 0.0384i
   0.0448 + 0.0418i
   0.0534 - 0.0301i
  -0.0339 + 0.0511i
  -0.0327 + 0.0519i
   0.0342 + 0.0509i
   0.0335 + 0.0514i
   0.0487 + 0.0375i
  -0.0176 - 0.0589i
   0.0268 - 0.0554i
   0.0488 + 0.0377i
   0.0535 - 0.0306i
  -0.0299 + 0.0539i
  -0.0335 + 0.0517i
  -0.0616 + 0.0034i
   0.0320 - 0.0527i
   0.0489 + 0.0376i
   0.0468 - 0.0403i
  -0.0519 + 0.0334i
  -0.0616 + 0.0039i
  -0.0501 - 0.0360i
   0.0451 + 0.0422i
   0.0471 - 0.0400i
  -0.0312 + 0.0533i
   0.0452 + 0.0422i
   0.0321 - 0.0528i
   0.0474 - 0.0397i
  -0.0410 + 0.0463i
  -0.0526 + 0.0325i
  -0.0027 - 0.0618i
  -0.0328 + 0.0525i
  -0.0527 + 0.0325i
  -0.0315 + 0.0534i
  -0.0412 + 0.0463i
   0.0454 + 0.0423i
   0.0251 - 0.0567i
  -0.0505 - 0.0361i
   0.0484 + 0.0390i
   0.0587 + 0.0204i
   0.0455 + 0.0423i
  -0.0313 + 0.0537i
   0.0324 + 0.0531i
  -0.0523 + 0.0336i
  -0.0106 + 0.0613i
  -0.0504 - 0.0366i
  -0.0622 + 0.0037i
  -0.0519 + 0.0346i
   0.0495 + 0.0380i
   0.0328 - 0.0531i
   0.0337 + 0.0526i
  -0.0027 - 0.0624i
   0.0320 - 0.0536i
  -0.0080 + 0.0619i
  -0.0624 + 0.0039i
   0.0351 + 0.0517i
   0.0496 + 0.0381i
  -0.0340 + 0.0525i
  -0.0104 + 0.0617i
   0.0543 - 0.0311i
  -0.0625 + 0.0030i
   0.0497 + 0.0381i
  -0.0026 - 0.0626i
  -0.0530 + 0.0335i
   0.0344 + 0.0524i
   0.0266 - 0.0568i
  -0.0407 + 0.0477i
  -0.0205 - 0.0593i
  -0.0627 + 0.0036i
   0.0489 + 0.0395i
  -0.0616 - 0.0128i
  -0.0628 + 0.0040i
  -0.0620 + 0.0110i
   0.0461 + 0.0429i
  -0.0523 + 0.0350i
   0.0553 - 0.0302i
  -0.0220 - 0.0591i
   0.0461 + 0.0430i
   0.0462 + 0.0430i
  -0.0112 + 0.0622i
   0.0464 + 0.0431i
  -0.0348 + 0.0529i
   0.0339 - 0.0535i
   0.0350 - 0.0528i
  -0.0538 + 0.0335i
   0.0353 - 0.0528i
   0.0494 + 0.0399i
   0.0477 - 0.0419i
   0.0604 + 0.0196i
   0.0340 + 0.0537i
  -0.0213 - 0.0599i
  -0.0077 + 0.0631i
   0.0605 + 0.0195i
  -0.0326 + 0.0547i
  -0.0541 + 0.0335i
  -0.0543 + 0.0334i
  -0.0108 + 0.0628i
   0.0467 + 0.0435i
   0.0466 + 0.0436i
   0.0485 - 0.0415i
   0.0498 + 0.0401i
   0.0506 + 0.0391i
  -0.0639 + 0.0029i
  -0.0533 + 0.0354i
  -0.0029 - 0.0640i
   0.0358 + 0.0531i
   0.0276 - 0.0579i
  -0.0641 + 0.0034i
   0.0484 - 0.0423i
  -0.0548 + 0.0335i
  -0.0547 + 0.0338i
   0.0336 - 0.0549i
  -0.0329 + 0.0553i
  -0.0353 + 0.0538i
   0.0500 + 0.0405i
   0.0508 + 0.0395i
   0.0471 + 0.0438i
   0.0490 - 0.0418i
  -0.0644 + 0.0031i
  -0.0540 + 0.0352i
   0.0343 - 0.0547i
   0.0566 - 0.0311i
  -0.0627 - 0.0155i
  -0.0645 + 0.0030i
  -0.0424 + 0.0487i
  -0.0411 + 0.0498i
  -0.0318 + 0.0562i
  -0.0550 + 0.0340i
  -0.0331 + 0.0555i
   0.0375 + 0.0527i
   0.0488 - 0.0425i
  -0.0647 + 0.0030i
   0.0340 - 0.0551i
   0.0505 + 0.0406i
  -0.0647 + 0.0033i
   0.0513 + 0.0396i
   0.0348 + 0.0547i
   0.0356 - 0.0542i
   0.0512 + 0.0398i
  -0.0648 + 0.0039i
  -0.0635 - 0.0137i
  -0.0649 + 0.0033i
   0.0615 + 0.0210i
  -0.0649 + 0.0042i
  -0.0101 + 0.0643i
   0.0323 + 0.0567i
   0.0270 - 0.0595i
  -0.0530 - 0.0383i
  -0.0653 + 0.0039i
  -0.0366 + 0.0542i
   0.0574 - 0.0315i
  -0.0081 + 0.0649i
   0.0278 - 0.0593i
   0.0345 + 0.0557i
  -0.0646 + 0.0107i
  -0.0556 + 0.0347i
   0.0377 + 0.0537i
  -0.0210 - 0.0622i
  -0.0425 + 0.0502i
   0.0350 + 0.0557i
  -0.0336 + 0.0566i
  -0.0561 + 0.0346i
  -0.0560 + 0.0347i
  -0.0652 + 0.0094i
   0.0372 + 0.0544i
  -0.0557 + 0.0352i
  -0.0029 - 0.0659i
   0.0321 + 0.0576i
  -0.0561 + 0.0347i
   0.0495 - 0.0436i
  -0.0551 + 0.0365i
   0.0328 + 0.0574i
   0.0345 - 0.0565i
  -0.0195 - 0.0633i
   0.0523 + 0.0407i
  -0.0539 - 0.0386i
  -0.0662 + 0.0039i
   0.0632 + 0.0201i
  -0.0539 - 0.0386i
  -0.0196 - 0.0635i
   0.0350 - 0.0565i
   0.0352 - 0.0563i
   0.0526 + 0.0406i
  -0.0025 - 0.0664i
  -0.0648 - 0.0145i
   0.0526 + 0.0406i
  -0.0650 - 0.0141i
  -0.0568 + 0.0347i
   0.0519 + 0.0417i
  -0.0655 + 0.0117i
   0.0275 - 0.0606i
   0.0505 - 0.0434i
   0.0382 + 0.0546i
  -0.0079 + 0.0662i
   0.0310 - 0.0590i
  -0.0034 - 0.0667i
   0.0263 - 0.0615i
  -0.0440 + 0.0504i
  -0.0668 + 0.0032i
   0.0531 + 0.0408i
  -0.0668 + 0.0040i
  -0.0650 - 0.0162i
   0.0363 + 0.0563i
  -0.0212 - 0.0636i
   0.0638 + 0.0208i
  -0.0232 - 0.0629i
   0.0515 - 0.0430i
   0.0364 + 0.0564i
  -0.0358 + 0.0568i
  -0.0371 + 0.0560i
  -0.0544 - 0.0394i
  -0.0108 + 0.0664i
  -0.0672 + 0.0041i
   0.0532 + 0.0412i
  -0.0658 - 0.0141i
  -0.0338 + 0.0582i
  -0.0189 - 0.0646i
  -0.0219 - 0.0637i
   0.0512 - 0.0438i
  -0.0350 + 0.0576i
  -0.0664 + 0.0118i
  -0.0549 - 0.0391i
  -0.0550 - 0.0391i
   0.0512 - 0.0439i
  -0.0566 + 0.0367i
  -0.0576 + 0.0352i
   0.0533 + 0.0414i
  -0.0439 + 0.0512i
   0.0289 - 0.0611i
  -0.0675 + 0.0043i
   0.0290 - 0.0611i
   0.0359 + 0.0574i
   0.0346 - 0.0582i
  -0.0085 + 0.0672i
   0.0310 - 0.0603i
  -0.0349 + 0.0581i
  -0.0096 + 0.0672i
   0.0357 + 0.0578i
   0.0591 - 0.0336i
  -0.0372 + 0.0570i
   0.0517 - 0.0442i
   0.0539 + 0.0416i
  -0.0680 + 0.0032i
  -0.0451 + 0.0511i
   0.0531 + 0.0428i
   0.0334 + 0.0594i
   0.0645 + 0.0223i
  -0.0682 + 0.0035i
  -0.0555 - 0.0398i
   0.0500 + 0.0467i
  -0.0021 - 0.0684i
   0.0356 + 0.0585i
   0.0602 - 0.0326i
  -0.0455 + 0.0512i
   0.0542 + 0.0419i
   0.0501 + 0.0468i
  -0.0033 - 0.0685i
  -0.0685 + 0.0039i
  -0.0120 + 0.0676i
   0.0379 + 0.0572i
  -0.0686 + 0.0032i
   0.0518 - 0.0452i
   0.0536 + 0.0431i
  -0.0561 - 0.0399i
  -0.0359 + 0.0587i
  -0.0083 + 0.0683i
  -0.0678 + 0.0120i
   0.0604 - 0.0331i
  -0.0452 + 0.0520i
  -0.0688 + 0.0042i
   0.0536 + 0.0433i
  -0.0683 + 0.0094i
  -0.0449 + 0.0523i
  -0.0575 + 0.0380i
   0.0546 + 0.0422i
   0.0538 + 0.0433i
   0.0546 + 0.0423i
   0.0538 + 0.0434i
   0.0349 + 0.0597i
   0.0549 + 0.0421i
  -0.0683 + 0.0114i
  -0.0588 + 0.0367i
  -0.0685 + 0.0106i
  -0.0214 - 0.0659i
  -0.0208 - 0.0662i
   0.0540 + 0.0436i
  -0.0589 + 0.0368i
  -0.0451 + 0.0528i
   0.0607 - 0.0339i
   0.0551 + 0.0425i
  -0.0080 + 0.0691i
   0.0524 - 0.0458i
  -0.0103 + 0.0689i
   0.0550 + 0.0428i
   0.0386 + 0.0580i
   0.0367 + 0.0593i
   0.0319 - 0.0620i
  -0.0691 + 0.0094i
   0.0288 - 0.0636i
  -0.0353 + 0.0603i
  -0.0697 + 0.0042i
  -0.0594 + 0.0367i
  -0.0698 + 0.0039i
   0.0615 - 0.0333i
  -0.0380 + 0.0588i
   0.0554 + 0.0429i
   0.0554 + 0.0429i
  -0.0374 + 0.0593i
   0.0556 + 0.0428i
  -0.0585 + 0.0388i
  -0.0348 + 0.0609i
   0.0555 + 0.0430i
   0.0556 + 0.0428i
   0.0536 - 0.0454i
  -0.0375 + 0.0594i
   0.0359 - 0.0605i
   0.0370 - 0.0599i
  -0.0034 - 0.0703i
  -0.0384 + 0.0590i
  -0.0601 + 0.0369i
   0.0559 + 0.0430i
   0.0347 + 0.0615i
  -0.0021 - 0.0706i
  -0.0698 + 0.0108i
  -0.0121 + 0.0695i
  -0.0122 + 0.0695i
  -0.0027 - 0.0706i
  -0.0207 - 0.0676i
   0.0551 + 0.0443i
  -0.0462 + 0.0535i
  -0.0706 + 0.0042i
   0.0314 - 0.0633i
   0.0407 + 0.0579i
  -0.0460 + 0.0538i
   0.0668 + 0.0233i
   0.0673 + 0.0217i
   0.0533 - 0.0465i
  -0.0383 + 0.0595i
  -0.0703 + 0.0084i
   0.0622 - 0.0338i
  -0.0374 + 0.0602i
   0.0371 + 0.0604i
   0.0365 + 0.0608i
  -0.0455 + 0.0545i
   0.0536 - 0.0465i
   0.0376 + 0.0603i
   0.0301 - 0.0644i
  -0.0375 + 0.0604i
  -0.0205 - 0.0681i
   0.0676 + 0.0222i
   0.0313 - 0.0640i
   0.0324 - 0.0634i
   0.0680 + 0.0215i
  -0.0712 + 0.0036i
   0.0545 - 0.0460i
  -0.0608 + 0.0373i
  -0.0361 + 0.0616i
   0.0283 - 0.0655i
  -0.0235 - 0.0674i
  -0.0713 + 0.0039i
   0.0564 + 0.0439i
  -0.0025 - 0.0714i
  -0.0207 - 0.0684i
  -0.0465 + 0.0544i
  -0.0715 + 0.0035i
  -0.0032 - 0.0715i
  -0.0714 + 0.0044i
   0.0389 - 0.0601i
  -0.0709 + 0.0105i
  -0.0715 + 0.0040i
  -0.0381 + 0.0607i
   0.0626 - 0.0348i
   0.0284 - 0.0658i
   0.0566 + 0.0439i
  -0.0600 + 0.0394i
  -0.0123 + 0.0707i
  -0.0614 + 0.0374i
  -0.0718 + 0.0045i
   0.0559 + 0.0452i
  -0.0117 + 0.0710i
  -0.0604 + 0.0391i
  -0.0612 + 0.0380i
   0.0632 - 0.0345i
  -0.0719 + 0.0039i
  -0.0709 + 0.0127i
   0.0526 + 0.0492i
   0.0628 - 0.0353i
  -0.0590 - 0.0414i
  -0.0115 + 0.0712i
  -0.0360 + 0.0625i
  -0.0462 + 0.0554i
  -0.0720 + 0.0039i
   0.0528 + 0.0492i
   0.0292 - 0.0660i
  -0.0199 - 0.0694i
  -0.0705 - 0.0154i
  -0.0588 - 0.0419i
   0.0631 - 0.0353i
  -0.0371 + 0.0620i
   0.0529 + 0.0493i
   0.0628 - 0.0360i
   0.0389 - 0.0611i
  -0.0719 + 0.0092i
   0.0337 - 0.0642i
  -0.0589 - 0.0423i
  -0.0115 + 0.0716i
  -0.0462 + 0.0560i
   0.0573 + 0.0446i
  -0.0701 - 0.0192i
  -0.0726 + 0.0037i
  -0.0726 + 0.0043i
  -0.0102 + 0.0720i
   0.0691 + 0.0227i
  -0.0231 - 0.0691i
  -0.0613 + 0.0394i
   0.0534 + 0.0497i
   0.0557 - 0.0472i
   0.0534 + 0.0498i
  -0.0032 - 0.0730i
   0.0325 - 0.0654i
  -0.0124 + 0.0720i
  -0.0486 + 0.0547i
   0.0329 - 0.0654i
   0.0635 - 0.0364i
   0.0696 + 0.0228i
   0.0579 + 0.0449i
  -0.0380 + 0.0626i
   0.0696 + 0.0229i
  -0.0029 - 0.0732i
  -0.0362 + 0.0638i
  -0.0083 + 0.0729i
   0.0644 - 0.0351i
   0.0582 + 0.0447i
  -0.0712 - 0.0181i
  -0.0734 + 0.0040i
  -0.0613 + 0.0405i
   0.0304 - 0.0669i
  -0.0626 + 0.0385i
  -0.0734 + 0.0048i
  -0.0378 + 0.0632i
  -0.0736 + 0.0041i
  -0.0107 + 0.0729i
   0.0583 + 0.0452i
  -0.0399 + 0.0622i
   0.0646 - 0.0360i
   0.0408 - 0.0617i
   0.0420 + 0.0609i
   0.0541 + 0.0505i
   0.0643 - 0.0366i
  -0.0739 + 0.0046i
  -0.0630 + 0.0388i
  -0.0631 + 0.0388i
   0.0644 - 0.0365i
   0.0367 + 0.0643i
  -0.0723 - 0.0160i
  -0.0471 + 0.0573i
  -0.0718 - 0.0186i
   0.0701 + 0.0241i
  -0.0387 + 0.0633i
  -0.0373 + 0.0643i
  -0.0633 + 0.0391i
   0.0328 - 0.0668i
  -0.0086 + 0.0739i
  -0.0111 + 0.0736i
  -0.0633 + 0.0392i
  -0.0718 - 0.0197i
   0.0414 + 0.0619i
  -0.0366 + 0.0649i
  -0.0120 + 0.0736i
  -0.0398 + 0.0630i
   0.0591 + 0.0454i
  -0.0634 + 0.0394i
  -0.0746 + 0.0034i
   0.0563 - 0.0491i
  -0.0023 - 0.0747i
   0.0591 + 0.0457i
   0.0570 - 0.0484i
  -0.0027 - 0.0747i
  -0.0097 + 0.0741i
   0.0711 + 0.0231i
   0.0582 + 0.0470i
   0.0386 + 0.0641i
   0.0583 + 0.0469i
  -0.0208 - 0.0719i
  -0.0743 + 0.0096i
  -0.0124 + 0.0739i
   0.0415 - 0.0624i
   0.0389 - 0.0642i
   0.0298 - 0.0689i
  -0.0639 + 0.0397i
  -0.0484 + 0.0576i
   0.0551 + 0.0513i
   0.0569 - 0.0493i
   0.0712 + 0.0246i
  -0.0752 + 0.0034i
   0.0595 + 0.0463i
   0.0598 + 0.0459i
   0.0349 - 0.0669i
  -0.0129 + 0.0744i
  -0.0754 + 0.0046i
  -0.0611 - 0.0445i
  -0.0755 + 0.0044i
  -0.0503 + 0.0566i
  -0.0644 + 0.0398i
   0.0579 - 0.0488i
  -0.0746 + 0.0133i
   0.0662 - 0.0369i
  -0.0757 + 0.0040i
   0.0403 + 0.0642i
  -0.0483 + 0.0584i
   0.0555 + 0.0517i
  -0.0413 + 0.0637i
  -0.0383 + 0.0655i
   0.0665 - 0.0367i
  -0.0751 + 0.0115i
  -0.0759 + 0.0045i
   0.0659 - 0.0379i
   0.0431 + 0.0627i
   0.0603 + 0.0464i
  -0.0650 + 0.0395i
  -0.0760 + 0.0044i
  -0.0622 - 0.0438i
   0.0602 + 0.0466i
   0.0404 + 0.0646i
  -0.0099 + 0.0756i
   0.0593 + 0.0479i
  -0.0761 + 0.0048i
   0.0664 - 0.0375i
   0.0406 + 0.0646i
   0.0422 - 0.0636i
   0.0595 + 0.0479i
   0.0603 + 0.0468i
  -0.0034 - 0.0763i
   0.0606 + 0.0465i
   0.0595 + 0.0480i
   0.0579 - 0.0500i
  -0.0023 - 0.0765i
  -0.0103 + 0.0758i
   0.0726 + 0.0243i
  -0.0383 + 0.0663i
  -0.0025 - 0.0766i
  -0.0120 + 0.0757i
   0.0669 - 0.0375i
   0.0383 + 0.0665i
   0.0317 - 0.0699i
   0.0606 + 0.0471i
  -0.0220 - 0.0736i
   0.0339 - 0.0690i
  -0.0768 + 0.0041i
   0.0607 + 0.0473i
  -0.0125 + 0.0759i
  -0.0507 + 0.0579i
   0.0672 - 0.0376i
   0.0427 + 0.0641i
   0.0610 + 0.0471i
   0.0421 + 0.0646i
   0.0339 - 0.0692i
  -0.0659 + 0.0401i
  -0.0036 - 0.0771i
   0.0392 + 0.0665i
  -0.0103 + 0.0765i
  -0.0040 - 0.0772i
  -0.0029 - 0.0772i
  -0.0392 + 0.0667i
  -0.0433 + 0.0641i
   0.0603 + 0.0486i
   0.0455 + 0.0627i
   0.0382 + 0.0673i
  -0.0774 + 0.0038i
   0.0594 - 0.0497i
  -0.0774 + 0.0037i
  -0.0493 + 0.0598i
   0.0734 + 0.0249i
  -0.0774 + 0.0043i
   0.0614 + 0.0473i
   0.0612 + 0.0475i
  -0.0659 + 0.0408i
   0.0410 - 0.0660i
  -0.0753 - 0.0192i
   0.0679 - 0.0380i
   0.0614 + 0.0478i
  -0.0770 + 0.0113i
  -0.0410 + 0.0662i
  -0.0662 + 0.0409i
   0.0405 - 0.0666i
   0.0618 + 0.0476i
  -0.0500 + 0.0599i
   0.0442 + 0.0644i
   0.0619 + 0.0477i
  -0.0758 - 0.0192i
   0.0609 + 0.0490i
  -0.0657 + 0.0423i
   0.0573 + 0.0533i
   0.0400 + 0.0672i
  -0.0265 - 0.0736i
  -0.0417 + 0.0662i
  -0.0263 - 0.0738i
  -0.0218 - 0.0753i
   0.0599 - 0.0507i
   0.0403 + 0.0673i
  -0.0270 - 0.0737i
   0.0600 - 0.0506i
   0.0436 - 0.0653i
  -0.0397 + 0.0678i
   0.0575 + 0.0536i
   0.0687 - 0.0382i
  -0.0638 - 0.0459i
   0.0624 + 0.0480i
  -0.0036 - 0.0786i
  -0.0382 + 0.0688i
  -0.0393 + 0.0682i
   0.0691 - 0.0378i
   0.0624 + 0.0481i
  -0.0671 + 0.0414i
  -0.0787 + 0.0049i
  -0.0432 + 0.0659i
  -0.0036 - 0.0788i
  -0.0639 - 0.0461i
  -0.0787 + 0.0046i
  -0.0039 - 0.0788i
   0.0425 - 0.0665i
   0.0624 + 0.0484i
   0.0626 + 0.0481i
   0.0437 - 0.0658i
  -0.0789 + 0.0047i
   0.0578 + 0.0540i
  -0.0790 + 0.0042i
  -0.0779 + 0.0135i
   0.0441 - 0.0657i
   0.0404 + 0.0681i
  -0.0644 - 0.0461i
   0.0597 - 0.0519i
   0.0578 + 0.0541i
  -0.0675 + 0.0416i
   0.0626 + 0.0487i
  -0.0218 - 0.0763i
   0.0750 + 0.0259i
   0.0581 + 0.0540i
   0.0413 + 0.0679i
   0.0696 - 0.0383i
  -0.0523 + 0.0598i
  -0.0793 + 0.0046i
   0.0583 + 0.0542i
   0.0599 - 0.0523i
  -0.0676 + 0.0421i
  -0.0507 + 0.0614i
   0.0598 - 0.0525i
   0.0444 - 0.0662i
  -0.0796 + 0.0036i
   0.0757 + 0.0251i
   0.0630 + 0.0489i
  -0.0785 + 0.0143i
   0.0693 - 0.0395i
   0.0631 + 0.0490i
  -0.0653 - 0.0460i
  -0.0109 + 0.0791i
   0.0418 + 0.0681i
  -0.0776 - 0.0193i
  -0.0683 + 0.0417i
  -0.0404 + 0.0690i
   0.0634 + 0.0488i
   0.0757 + 0.0261i
  -0.0418 + 0.0683i
  -0.0107 + 0.0794i
   0.0633 + 0.0492i
   0.0635 + 0.0489i
   0.0588 + 0.0546i
  -0.0249 - 0.0763i
  -0.0802 + 0.0040i
  -0.0249 - 0.0763i
  -0.0036 - 0.0802i
  -0.0683 + 0.0423i
  -0.0408 + 0.0693i
  -0.0227 - 0.0772i
  -0.0804 + 0.0042i
   0.0627 + 0.0505i
  -0.0804 + 0.0044i
   0.0765 + 0.0254i
  -0.0805 + 0.0042i
  -0.0783 - 0.0191i
  -0.0416 + 0.0692i
   0.0591 + 0.0550i
   0.0638 + 0.0496i
   0.0708 - 0.0388i
  -0.0113 + 0.0800i
  -0.0033 - 0.0808i
  -0.0660 - 0.0467i
  -0.0269 - 0.0763i
   0.0591 + 0.0553i
  -0.0689 + 0.0426i
  -0.0028 - 0.0809i
  -0.0809 + 0.0049i
  -0.0805 + 0.0092i
   0.0477 + 0.0655i
   0.0641 + 0.0496i
  -0.0413 + 0.0698i
  -0.0678 + 0.0444i
   0.0443 + 0.0679i
  -0.0689 + 0.0427i
  -0.0661 - 0.0471i
  -0.0679 + 0.0445i
  -0.0690 + 0.0427i
  -0.0438 + 0.0683i
  -0.0041 - 0.0811i
  -0.0107 + 0.0806i
  -0.0811 + 0.0046i
  -0.0802 + 0.0132i
  -0.0139 + 0.0801i
  -0.0424 + 0.0694i
  -0.0693 + 0.0427i
  -0.0801 + 0.0144i
  -0.0804 + 0.0131i
  -0.0695 + 0.0425i
   0.0644 + 0.0500i
   0.0646 + 0.0497i
  -0.0660 - 0.0478i
   0.0429 - 0.0694i
  -0.0143 + 0.0803i
  -0.0271 - 0.0770i
  -0.0801 - 0.0162i
  -0.0037 - 0.0817i
   0.0620 - 0.0533i
  -0.0816 + 0.0045i
   0.0711 - 0.0406i
  -0.0122 + 0.0810i
   0.0718 - 0.0395i
  -0.0698 + 0.0429i
   0.0419 + 0.0705i
   0.0430 - 0.0698i
   0.0715 - 0.0403i
  -0.0143 + 0.0808i
   0.0780 + 0.0254i
  -0.0800 - 0.0185i
   0.0340 - 0.0748i
  -0.0798 - 0.0194i
  -0.0803 - 0.0179i
   0.0617 - 0.0544i
  -0.0821 + 0.0047i
   0.0650 + 0.0505i
   0.0333 - 0.0753i
  -0.0808 + 0.0155i
  -0.0531 + 0.0631i
   0.0651 + 0.0506i
   0.0437 + 0.0699i
  -0.0427 + 0.0706i
  -0.0459 + 0.0686i
  -0.0702 + 0.0436i
   0.0471 + 0.0678i
  -0.0437 + 0.0701i
  -0.0672 - 0.0481i
  -0.0695 + 0.0447i
   0.0366 - 0.0741i
  -0.0451 + 0.0693i
   0.0783 + 0.0264i
   0.0721 - 0.0405i
   0.0606 + 0.0565i
   0.0415 + 0.0716i
   0.0645 + 0.0519i
  -0.0142 + 0.0816i
  -0.0433 + 0.0707i
  -0.0111 + 0.0822i
   0.0424 + 0.0713i
  -0.0409 + 0.0722i
  -0.0450 + 0.0698i
   0.0656 + 0.0509i
   0.0636 - 0.0535i
  -0.0024 - 0.0833i
   0.0350 - 0.0756i
   0.0660 + 0.0508i
   0.0661 + 0.0508i
   0.0338 - 0.0762i
  -0.0833 + 0.0045i
  -0.0833 + 0.0052i
   0.0484 + 0.0680i
   0.0381 - 0.0742i
   0.0327 - 0.0768i
  -0.0555 + 0.0624i
  -0.0106 + 0.0828i
   0.0407 + 0.0731i
  -0.0430 + 0.0717i
  -0.0100 + 0.0831i
  -0.0836 + 0.0044i
  -0.0548 + 0.0632i
   0.0796 + 0.0259i
   0.0443 - 0.0712i
  -0.0556 + 0.0629i
  -0.0839 + 0.0043i
  -0.0714 + 0.0442i
   0.0737 - 0.0404i
  -0.0687 - 0.0485i
   0.0474 + 0.0695i
  -0.0106 + 0.0835i
   0.0477 + 0.0693i
  -0.0689 - 0.0484i
  -0.0558 + 0.0631i
   0.0666 + 0.0516i
   0.0668 + 0.0515i
   0.0666 + 0.0517i
   0.0800 + 0.0266i
   0.0419 + 0.0732i
   0.0616 + 0.0576i
   0.0667 + 0.0518i
  -0.0237 - 0.0811i
  -0.0815 - 0.0222i
  -0.0539 + 0.0652i
  -0.0556 + 0.0637i
   0.0648 - 0.0543i
  -0.0689 - 0.0491i
  -0.0845 + 0.0045i
  -0.0272 - 0.0803i
   0.0740 - 0.0416i
  -0.0563 + 0.0636i
   0.0671 + 0.0522i
  -0.0103 + 0.0844i
  -0.0727 + 0.0442i
   0.0662 + 0.0534i
  -0.0850 + 0.0039i
   0.0672 + 0.0521i
  -0.0542 + 0.0656i
  -0.0850 + 0.0045i
   0.0644 - 0.0558i
  -0.0851 + 0.0048i
   0.0665 + 0.0535i
   0.0624 + 0.0582i
   0.0664 + 0.0537i
  -0.0831 - 0.0199i
   0.0449 + 0.0727i
   0.0810 + 0.0276i
   0.0678 + 0.0521i
   0.0666 + 0.0538i
  -0.0273 - 0.0812i
  -0.0848 + 0.0121i
  -0.0728 + 0.0451i
  -0.0856 + 0.0051i
  -0.0733 + 0.0446i
   0.0679 + 0.0524i
  -0.0734 + 0.0445i
  -0.0729 + 0.0453i
  -0.0732 + 0.0448i
  -0.0039 - 0.0859i
  -0.0859 + 0.0047i
   0.0679 + 0.0529i
   0.0369 - 0.0778i
   0.0671 + 0.0540i
   0.0451 + 0.0734i
  -0.0861 + 0.0047i
  -0.0729 + 0.0461i
   0.0660 - 0.0556i
  -0.0141 + 0.0851i
  -0.0441 + 0.0742i
   0.0474 - 0.0724i
   0.0502 + 0.0706i
   0.0674 + 0.0544i
   0.0421 + 0.0758i
   0.0508 + 0.0703i
  -0.0438 + 0.0749i
  -0.0851 - 0.0171i
   0.0381 - 0.0780i
   0.0505 + 0.0707i
  -0.0859 + 0.0133i
  -0.0433 + 0.0754i
  -0.0154 + 0.0856i
  -0.0475 + 0.0729i
  -0.0852 - 0.0180i
  -0.0566 + 0.0661i
  -0.0870 + 0.0044i
   0.0690 + 0.0533i
  -0.0117 + 0.0864i
  -0.0095 + 0.0867i
   0.0469 + 0.0736i
  -0.0867 + 0.0101i
  -0.0871 + 0.0057i
  -0.0269 - 0.0831i
  -0.0715 - 0.0504i
  -0.0864 + 0.0135i
  -0.0727 + 0.0486i
  -0.0266 - 0.0834i
   0.0454 - 0.0748i
  -0.0140 + 0.0864i
  -0.0742 + 0.0465i
  -0.0862 + 0.0158i
   0.0344 - 0.0807i
   0.0768 - 0.0425i
  -0.0033 - 0.0877i
  -0.0869 + 0.0126i
  -0.0868 + 0.0133i
   0.0693 + 0.0539i
  -0.0458 + 0.0749i
  -0.0096 + 0.0873i
  -0.0869 + 0.0131i
  -0.0449 + 0.0755i
  -0.0751 + 0.0457i
  -0.0742 + 0.0471i
   0.0661 - 0.0579i
  -0.0028 - 0.0880i
   0.0483 - 0.0736i
   0.0769 - 0.0429i
   0.0686 + 0.0552i
  -0.0879 + 0.0051i
  -0.0044 - 0.0880i
   0.0775 - 0.0420i
  -0.0271 - 0.0839i
   0.0504 + 0.0724i
   0.0451 - 0.0759i
  -0.0753 + 0.0462i
   0.0699 + 0.0540i
  -0.0755 + 0.0459i
  -0.0871 + 0.0154i
  -0.0874 + 0.0132i
   0.0509 + 0.0723i
  -0.0492 + 0.0735i
   0.0464 - 0.0754i
  -0.0138 + 0.0874i
  -0.0430 + 0.0774i
  -0.0743 + 0.0482i
  -0.0479 + 0.0745i
  -0.0145 + 0.0875i
   0.0441 + 0.0769i
  -0.0244 - 0.0853i
  -0.0886 + 0.0048i
  -0.0100 + 0.0882i
  -0.0723 - 0.0515i
  -0.0131 + 0.0878i
  -0.0452 + 0.0765i
  -0.0587 + 0.0667i
  -0.0568 + 0.0683i
   0.0670 - 0.0583i
  -0.0757 + 0.0467i
  -0.0267 - 0.0848i
  -0.0584 + 0.0671i
  -0.0159 + 0.0875i
  -0.0869 - 0.0191i
   0.0694 + 0.0558i
   0.0651 + 0.0609i
  -0.0129 + 0.0882i
  -0.0890 + 0.0049i
  -0.0871 - 0.0192i
  -0.0488 + 0.0747i
   0.0671 - 0.0588i
  -0.0883 + 0.0131i
  -0.0130 + 0.0884i
   0.0654 + 0.0609i
   0.0654 + 0.0610i
   0.0849 + 0.0282i
  -0.0106 + 0.0888i
  -0.0280 - 0.0850i
  -0.0478 + 0.0757i
   0.0679 - 0.0586i
  -0.0488 + 0.0753i
  -0.0767 + 0.0466i
  -0.0875 - 0.0199i
   0.0657 + 0.0612i
  -0.0869 - 0.0230i
   0.0699 + 0.0564i
  -0.0154 + 0.0885i
   0.0713 + 0.0548i
  -0.0276 - 0.0857i
  -0.0299 - 0.0849i
  -0.0755 + 0.0492i
  -0.0475 + 0.0767i
   0.0713 + 0.0552i
   0.0659 + 0.0616i
   0.0685 - 0.0587i
  -0.0876 - 0.0215i
   0.0452 + 0.0781i
  -0.0901 + 0.0051i
   0.0689 - 0.0583i
  -0.0481 + 0.0764i
   0.0704 + 0.0566i
   0.0714 + 0.0553i
  -0.0763 + 0.0484i
  -0.0438 + 0.0790i
   0.0661 + 0.0616i
   0.0497 + 0.0755i
  -0.0871 - 0.0241i
   0.0463 - 0.0778i
   0.0787 - 0.0448i
   0.0683 - 0.0595i
  -0.0873 - 0.0241i
   0.0485 + 0.0765i
  -0.0892 + 0.0157i
  -0.0773 + 0.0472i
   0.0531 + 0.0734i
  -0.0109 + 0.0900i
  -0.0905 + 0.0054i
  -0.0034 - 0.0906i
  -0.0152 + 0.0894i
  -0.0496 + 0.0759i
   0.0665 + 0.0618i
  -0.0740 - 0.0526i
  -0.0508 + 0.0753i
   0.0414 - 0.0809i
   0.0720 + 0.0555i
  -0.0147 + 0.0897i
  -0.0902 + 0.0121i
   0.0689 - 0.0595i
  -0.0909 + 0.0049i
  -0.0255 - 0.0875i
   0.0471 - 0.0780i
  -0.0745 - 0.0526i
  -0.0489 + 0.0771i
  -0.0901 + 0.0149i
  -0.0149 + 0.0901i
   0.0712 + 0.0573i
   0.0696 - 0.0593i
   0.0491 + 0.0772i
  -0.0914 + 0.0048i
   0.0712 + 0.0575i
   0.0467 + 0.0788i
  -0.0746 - 0.0531i
  -0.0131 + 0.0908i
  -0.0894 - 0.0209i
  -0.0268 - 0.0878i
   0.0868 + 0.0297i
  -0.0307 - 0.0865i
  -0.0487 + 0.0778i
  -0.0900 - 0.0183i
  -0.0917 + 0.0060i
   0.0408 - 0.0824i
  -0.0135 + 0.0909i
  -0.0918 + 0.0053i
   0.0672 + 0.0627i
  -0.0784 + 0.0482i
   0.0470 + 0.0792i
  -0.0600 + 0.0699i
  -0.0303 - 0.0870i
   0.0675 + 0.0628i
   0.0717 + 0.0579i
  -0.0466 + 0.0796i
  -0.0922 + 0.0044i
  -0.0296 - 0.0874i

[Amjad Iqbal]

@Johan

Thank you for your quick code, I need little integration to your code, since x_mat, y_mat, z_mat are 2D matrices given below,

x_vect = -6:0.02:6;

y_vect = -6:0.02:6;

z_vect = 0;

%x,y,z grid

[x_mat,y_mat, z_mat] = meshgrid(x_vect,y_vect, z_vect);

freq_vec = rand(235,1);

R0 = 135;

alpha = 3;

S1 = rand(88821,235);

Ndeg = 86610-3263;

Turntable_angle = linspace(-180,180, Ndeg);

could you please check with 2D x_mat, y_mat, z_mat?

Answer 2

[Jon]

With the code you show, it appears that the values of S1, Sc_win, and S do not change as a function of any of the loop variables. If this is really the case (and not just due to some simplification in how you presented your example), then these variables can just be computed once before entering the first loop.

So

img = zeros(M,N);
% the following three lines were moved out of the loop as they do not
% change
S1 = data_matrix; % data
Sc_win = S1.*repmat(hanning(size(S1,2)).',size(S1,1),1); % apply window
S = ifftshift(ifft(Sc_win,Nfft,2),2);
for ii = 3264:64:86610  % sorted for one complete rotation
dR = sqrt((R0*cos(alpha*pi/180).*cos(Turntable_angle(ii)*pi/180) + x_mat).^2 + (R0*cos(alpha*pi/180).*sin(Turntable_angle(ii)*pi/180) + y_mat).^2 + (z_mat - R0*sin(alpha*pi/180)).^2) - R0;
    for jj = 1:length(Freq_vec)

        img = img + S(ii,jj).*exp(1j*4*pi*Freq_vec(jj)/c0*dR);
    end
end 

[Amjad Iqbal]

Yes dear @Jon I'm aware of that, since S, Sc_win, S1, are not associated to the loop. However, ii runs for 3264:64:86610 which is very time consuming, that's why I was curious how can I reduce. could you please advise how can I reduce this time consumption particulalry.

[Jon]

I don't know enough about your problem to know how to modify your whole approach to somehow make it more efficient, I am just looking at the code you have. Assuming that the number of iterations (numel(3264:64:86610)*numel(Freq_vec) )can't be changed, to make it run faster,you need to do as little as possible inside of the loops. So moving unecessary calculations outside of the loop, as I suggested is how you can make it run faster.

[Steven Lord]

A couple more small optimizations:

img = zeros(M,N);
% the following three lines were moved out of the loop as they do not
% change
S1 = data_matrix; % data
Sc_win = S1.*repmat(hanning(size(S1,2)).',size(S1,1),1); % apply window
S = ifftshift(ifft(Sc_win,Nfft,2),2);

Since Turntable_angle doesn't change inside the loop, compute the trig functions on the vector all at once. In addition, since those angles are in degrees use cosd instead of multiplying the angle by the "magic number" pi/180. Do the same for the alpha variable (which I would consider renaming since alpha has a meaning in MATLAB already.)

cTA = cosd(Turntable_angle);
sTA = sind(Turntable_angle);
cA = cosd(alpha);
sA = sind(alpha);

Now dR has no dependency on ii so pull it out of the loop as well.

dR = sqrt((R0*cA.*cTA + x_mat).^2 + (R0*cA.*sTA + y_mat).^2 + (z_mat - R0*sA).^2) - R0;

Looking at the inner loop, since the only dependency on jj in the exp call is to operate on individual elements of Freq_vec, compute that quantity outside the jj loop. In addition, since it doesn't depend on jj, we can pull that outside the outer loop as well.

I suspect you can probably eliminate the loops entirely with a sum call, perhaps combined with reshape and/or permute, but to be certain of that I'd want to see the sizes of each of the variables in your code.

E = exp(4j*pi*Freq_vec./c0.*dR);
for ii = 3264:64:86610  % sorted for one complete rotation
    for jj = 1:length(Freq_vec)
        img = img + S(ii,jj).*E;
    end
end 

[Amjad Iqbal]

@Steven Lord

one more thing to integrate for this line:

since x_mat, y_mat, z_mat are 2D matrices

dR = sqrt((R0*cA.*cTA + x_mat).^2 + (R0*cA.*sTA + y_mat).^2 + (z_mat - R0*sA).^2) - R0;

x_vect = -6:0.05:6;

y_vect = -6:0.05:6;

z_vect = 0;

% x,y,z grid

[x_mat,y_mat, z_mat] = meshgrid(x_vect,y_vect, z_vect);

I believe this will be much faster, however, still facing an issue >> Arrays have incompatible sizes for this operation