"Source: Text/Geometry/Lseries.text";
"Line: 840";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/Lseries.text, line: 840
// Example: H139E17 ()
print "Example: H139E17";
ei := GetEchoInput();
SetEchoInput(true);
//no-test
f := Newforms("G1N16k2A")[1]; f;
B:=BaseRing(f); B;
f1, f2 := Explode(ComplexEmbeddings(f)[1]);
Coefficient(f,2), Coefficient(f1,2), Coefficient(f2,2);
L1 := LSeries(f1);
L2 := LSeries(f2);
CFENew(L1); // new vers of CheckFunctionalEquation
CFENew(L2);
v1 := Evaluate(L1,1); v2 := Evaluate(L2,1); v1,v2;
L := LSeries(f);
C<i> := ComplexField();
L2A := LSeries(f: Embedding:=hom< B -> C | i > );
L2B := LSeries(f: Embedding:=func< x | Conjugates(x)[1] > );
L2C := LSeries(f1: Embedding:=func< x | ComplexConjugate(x) > );
L := LSeries(f1+f2);  // or L:=LSeries(f: Embedding:=func<x|Trace(B!x)>);
Order(DirichletCharacter(f));
assert $1 eq 4;
Evaluate(L,1);
CFENew(L); // new vers of CheckFunctionalEquation
SetEchoInput(ei);
