restart:N:=8:
a:=1: #0.0001 to 10f:=array(0..N-1):for n from 0 to N-1 do f[n]:=(1+a^2)/(1+a*n^2);od:W:=evalf(exp(-2*Pi*I/N)):for a1 from 0 to 1 dofor a0 from 0 to 1 dofor b0 from 0 to 1 doadd(f[4*a2+2*a1+a0]*W^(4*a2*b0),a2=0..1);X0[4*a1+2*a0+b0]:=%;od: od: od:
for i from 1 to N-1 do X0[i] od:for a0 from 0 to 1 dofor b0 from 0 to 1 dofor b1 from 0 to 1 doadd(X0[4*a1+2*a0+b0]*W^(2*a1*(2*b1+b0)),a1=0..1);X1[4*a0+2*b0+b1]:=%;od: od: od: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for b2 from 0 to 1 dofor b1 from 0 to 1 dofor b0 from 0 to 1 doadd(X1[4*a0+2*b0+b1]*W^(a0*(4*b2+2*b1+b0)),a0=0..1);F[4*b2+2*b1+b0]:=%;od: od: od:
for i to N-1 do F[i] od:for j from 0 to N-1 do
add(F[k]*W^(-j*k),k=0..N-1);inv[j]:=%/N; od:for i to N-1 do inv[i] od:u:=[seq([i,abs(f[i])],i=0..N-1)]:
v:=[seq([i,abs(inv[i])],i=0..N-1)]:plot([u,v],colour=[blue,white],thickness=[6,2]);LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=