"Source: Text/Ring/Char.text";
"Line: 1299";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/Char.text, line: 1299
// Example: H43E15 ()
print "Example: H43E15";
ei := GetEchoInput();
SetEchoInput(true);
G := Grossencharacter(EllipticCurve("27a")); G;
K := NumberField(Order(Modulus(G)));
I := Ideal(Decomposition(K,3)[1][1]);
RootNumber(G,I);
RootNumber(G,InfinitePlaces(K)[1]);
RootNumber(G); // product of the two previous
// over Q, the root numbers get induced to -1 and -1
RootNumber(G,3); // at the rational prime 3
RootNumber(HodgeStructure(G)); // at oo
for k in [1..12] do k,Real(RootNumber(G^k)); end for;
SetEchoInput(ei);
