default(new_galois_format,1);

tst(n,k)=
{
  P = nflist([n,k],'t); V = List();
  for(a=1,20,
    Q = subst(P,t,a);
    if (polisirreducible(Q),
      if (n > 11 || polgalois(Q)[3] == k, listput(~V,Q))));
  if (!#V, error(k));
  #V;
}

L=[1,1,2,5,5,16,7];
S = vector(#L,i,[1..L[i]]);
for(n=1,#S,print1(n,": ");print([tst(n,k) | k<-S[n]]))

nflist("S25",'t)
nflist("A25",'t)
nflist("A24",'t)
nflist("A23",'t)
nflist("A22",'t)

nflist([47,6],'t)
nflist([47,5],'t)

nflist("C1",'t)
nflist("C2",'t)
nflist("C3",'t)

\\ ERRORS
nflist([4,6])
nflist([18,100000])
