ex-tau2

read("computel");              /* for Steve Finch */
default(realprecision,40);

coefgrow(n) = 2*n^20;
tau(n)      = (5*sigma(n,3)+7*sigma(n,5))*n/12\
              -35*sum(k=1,n-1,(6*k-4*(n-k))*sigma(k,3)*sigma(n-k,5));
tau2(n)      = tau(n)^2;

conductor = 1;
gammaV    = [0,1,-10];
weight    = 23;
Lpoles    = [];
Lresidues = automatic;

len=cflength();
v1=vector(len,n,tau2(n));
v2=vector(len,n,n^11);
v3=vector(len,n,if(issquare(n),n^11,0));
cfs=concat(dirdiv(dirmul(v1,v3),v2),vector(1000,k,0));

initLdata("cfs[k]");

{
forstep(s0=12.5,22.0,0.5,
  s0=round(2*s0)/2;
  print("  L       = ",lval = L(s0));
  print("  (check) = ",lval2 = L(s0,1.1),"  (err=",errprint(lval-lval2),")");
  print("f(",s0,") = ",lval/zeta(2*s0-22)*zeta(s0-11));
);
}