%RUN_UCONJ_HERM

tic
global mu ab1 abhrh abj
mu=5; 
ab1=r_hermite(100,mu); abj=r_jacobi01(100,0,2*mu);
abhrh=loadvpa('coeffhrghermite0.txt',9,32,100,2);
for n=5
  dig=16; [U,d1]=Uconj_herm(dig,n); errd=1;
  while errd > .5e-6
    dig=dig+4;
    d0=d1; d00=d0;
    for j=1:n
      if imag(d00(j))<0, d00(j)=conj(d00(j)); end
    end
    [U,d1]=Uconj_herm(dig,n); d11=d1;
    for j=1:n
      if imag(d11(j))<0, d11(j)=conj(d11(j)); end
    end
%    d11(n)
    err=abs((d00-d11)./d11);
    errd=max(err);
  end
  d=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^-(30) 10^5 -.2 .2])
  for i=1:n
    if real(d(i))<=0, error('conjecture is false'); end
  end
%  n
  disp('conjecture is true')
end
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