"Source: Text/RepThy/GalRep.text";
"Line: 1180";
"Date: Fri Sep 26 12:10:12 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/RepThy/GalRep.text, line: 1180
// Example: H58E28 ()
print "Example: H58E28";
ei := GetEchoInput();
SetEchoInput(true);
R<x>:=PolynomialRing(Rationals());
K:=NumberField(x^6-5);
a:=ArtinRepresentations(K)[6];
A:=GaloisRepresentation(a,5); A;
F:=Field(A); F;
DefiningPolynomial(A);
pi:=UniformizingElement(F);
autF:=[* Automorphism(A,g): g in Group(A) *];
[Valuation(sigma(pi)-pi): sigma in autF];
SetEchoInput(ei);
