"Source: Text/Geometry/Lseries.text";
"Line: 3041";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/Lseries.text, line: 3041
// Example: H139E37 ()
print "Example: H139E37";
ei := GetEchoInput();
SetEchoInput(true);
x := PolynomialRing(Integers()).1;
H := HypergeometricData([4,4],[1,1,2,2]);
L := LSeries(H,2 : Precision:=10);
assert IsSymplectic(L); // degree 4 weight 1
L`parent;
S := Symmetrization(L,[1,1] : BadPrimes:=[<2,16,1-2*x>]);
Degree(S);
CFENew(S);
Factorization(S)[2];
S := SymplecticSymmetrization(L,[1,1] :  BadPrimes:=[<2,16,1>]);
Degree(S);
CFENew(S);
H := HypergeometricData([4,2,2,2,2],[1,1,1,1,1,1]);
L := LSeries(H,1 : Precision:=10); // t=1 degeneration
Conductor(L); // degree 4, conductor 2^8, motivic wt 5
S := SymplecticSymmetrization(L,[1,1] : BadPrimes:=[<2,8,1>]);
time CFENew(S);
K<zeta5> := CyclotomicField(5);
p5 := Factorization(5*Integers(K))[1][1];
psi := HeckeCharacterGroup(p5^2).0;
GR := Grossencharacter(psi,[[3,0],[1,2]]);
L := LSeries(GR :  Precision:=15);
S := SymplecticSymmetrization(L,[1,1] : BadPrimes:=[<5,6,1>]);
CFENew(S); // S is imprimitive
Q := S/Translate(LSeries(KroneckerCharacter(5)),3);
CFENew(Q);
SetEchoInput(ei);
