"Source: Text/Geometry/Lseries.text";
"Line: 2585";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/Lseries.text, line: 2585
// Example: H139E29 ()
print "Example: H139E29";
ei := GetEchoInput();
SetEchoInput(true);
K<s> := QuadraticField(-3);
I := Factorization(3 * IntegerRing(K))[1][1];
H := HeckeCharacterGroup(I^2);
G := Grossencharacter(H.0, [[1, 0]]); // canonical character
E := EllipticCurve([1, (3+s)/2, 0, (1+s)/2, 0]);
Norm(Conductor(E));
assert $1 eq 73;
LG := LSeries(G);
LE := LSeries(E);
TP := TensorProduct(LE, LG, [<I, 5>], K); // ensure 3-part correct
LSetPrecision(TP, 9); // there is another factor of 3 from K
LCfRequired(TP); // approx for old CheckFunctionalEquation
CFENew(TP);
SetEchoInput(ei);
