%RUN_SCONJ_LAG

tic
global dig a ab0 ab1
dig=32, digits(dig);
a=vpa(0);
ab0=sr_laguerre(dig,75); ab1=sr_laguerre(dig,75,a);
n=45;
[U,d1]=sConj_lag(n); errd=1;
while errd > .5e-6
  dig=dig+16
  d0=d1; d00=d0;
  for j=1:n
    if imag(double(d00(j)))<0, d00(j)=conj(d00(j)); end
  end
  [U,d1]=sConj_lag(n); d11=d1;
  for j=1:n
    if imag(double(d11(j)))<0, d11(j)=conj(d11(j)); end
  end
  err=abs((d00-d11)./d11);
  errd=max(double(err))
end
dig
d=double(d1)
for k=1:n
  if imag(d(k))==0
    d(k)=d(k)+(1e-20)*i; break
  end
end
%  plot(d,'k*','MarkerSize',16);set(gca,'FontSize',24) 
semilogx(d,'k*','MarkerSize',16);set(gca,'FontSize',24)
axis([10^(-100) 10^(20) -.15 .15])
for i=1:n
  if real(d(i))<=0, error('conjecture is false'); end
end
%n
disp('conjecture is true')
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