"Source: Text/Ring/Char.text";
"Line: 641";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/Char.text, line: 641
// Example: H43E4 ()
print "Example: H43E4";
ei := GetEchoInput();
SetEchoInput(true);
K := NumberField(Polynomial([4,3,-1,1])); // x^3-x^2+3*x+4
f7 := Factorization(7*Integers(K))[1][1];
G:= DirichletGroup(f7^2,[1]);
chi := G.1*G.2*G.3;
cc := CentralCharacter(chi); Conductor(cc);
cc := CentralCharacter(chi^14); Conductor(cc);
////////////////
K := NumberField(Polynomial([-10,-9,-10,1]));
#ClassGroup(K); // C7 class group
assert $1 eq 7;
f5 := Factorization(5*Integers(K))[1][1];
H := HeckeCharacterGroup(f5,[1]);
cc:=CentralCharacter(H.1); Conductor(cc);
Order(H.1), Order(cc);
IsTrivial(CentralCharacter(H.1^4));
assert $1;
SetEchoInput(ei);
