"Source: Text/RepThy/ArtRep.text";
"Line: 517";
"Date: Tue Jul  3 23:00:01 2018";
"Main: Thu May 25 10:02:38 2023";
// original file: Text/RepThy/ArtRep.text, line: 517
// Example: H47E5 ()
print "Example: H47E5";
ei := GetEchoInput();
SetEchoInput(true);
SetEchoInput(false);
load galpols;
SetEchoInput(true);
f := PolynomialWithGaloisGroup(8,46); // order 576
K := NumberField(f); // octic field
A := ArtinRepresentations(K);
[Degree(a) : a in A];
[Order(Character(Determinant(a))) : a in A];
chi := DirichletCharacter(A[3]); // order 4
Conductor(chi), Conductor(chi^2);
Minimize(ArtinRepresentation(chi)); // disc = N(chi)^2*N(chi^2)
Factorization(Discriminant(Integers(Field($1))));
SetEchoInput(ei);
