"Source: Text/Ring/Char.text";
"Line: 968";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/Char.text, line: 968
// Example: H43E9 ()
print "Example: H43E9";
ei := GetEchoInput();
SetEchoInput(true);
K := QuadraticField(-59);
I := Factorization(59*IntegerRing(K))[1][1];
H := HeckeCharacterGroup(I);
DG := DirichletGroup(I);
GR := Grossencharacter(H.0, DG.1^29, [[3,0]]); // cube of canonical char
L := LSeries(GR);
CFENew(L);
Sign(L);
CentralValue(L);
LSetPrecision(L, 9);
LTaylor(L, 2, 3); // first 3 terms of Taylor series about s=2
GR3 := Grossencharacter(H.0, DG.1^29, [[1,0]])^3;
CentralValue(LSeries(GR3));
SetEchoInput(ei);
