memo 6/26/2023

? record = 0; for(L=727951332, 100000000000000, omeg = L*0.000001; if(S10(omeg)>0.36, if(S100(omeg)>0.73, print("\n passed S100 ",S100(omeg),"  ",omeg," L="L); if(S1000(omeg)>0.88, print("passed S1000: ", S1000(omeg)); if(S10000(omeg)>0.95, print("passed S10000: ", S10000(omeg)); if(S100000(omeg)>0.98, print("passed S100000: ", S100000(omeg)); print("S1000000(omeg)=", S1000000(omeg))))))))

S10000000(omeg) = {r = 0.0;  for(JJJ=1,10000000,  r = r - exp(I*v2[JJJ]*omeg)/(1/2+I*v2[JJJ]) -exp(-I*v2[JJJ]*omeg)/(1/2-I*v2[JJJ])  ); return(real(r))}
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