{
factsig(f)=
     local(v,i);
     v=vector(length(f~),i,poldegree(lift(f[i,][1])));
     return(vecsort(v));
}


{
splitting(nf,p) = factsig(factormod(nf.pol,p))
}





























\\{
\\for(j=1,37,
\\  v=[];
\\  y=[];
\\  for(i=1,1000,
\\    p=prime(i);
\\    if(p!=j,
\\      fs=factsig(factormod(f,p)); 
\\      if(fs==[1,1,1],
\\        v=concat(v,[lift(Mod(p,j))]));
\\      if(fs==[3],
\\        y=concat(y,[lift(Mod(p,j))]));
\\    );
\\  );
\\  v=uniq(vecsort(v));
\\  y=uniq(vecsort(y));
\\  print(j": "length(v)"  "length(y));
\\)
\\}