"Source: Text/Geometry/HypGeomMot.text";
"Line: 1758";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/HypGeomMot.text, line: 1758
// Example: H138E17 ()
print "Example: H138E17";
ei := GetEchoInput();
SetEchoInput(true);
J := JacketMotive([], [], 2, 1/3, 0); J; // twist by 2^(1/3)
GR := Grossencharacter(J); GR;
ef := func<G,p | EulerFactor(G,p : Integral)>;
P := PrimesUpTo(100);
&and[ef(GR,p) eq ef(GR2,p) where GR2:=GR^2 : p in P]; // same over Q
p7 := Ideal(Decomposition(Field(J),7)[1][1]); // norm 7, degree 1
GR(p7);
(GR^2)(p7);
ComplexEvaluation(J,p7); // same as GR, not GR^2
PK := [p : p in PrimesUpTo(100,Field(J)) | Norm(p) ne 3];
Max([Norm(GR(p)-ComplexEvaluation(J,p)) : p in PK | Degree(p) eq 1]);
J := JacobiMotive([3/4,1/8,5/8],[1/2]); // scaling by 5
psi := Grossencharacter(J); psi;
G := HeckeCharacterGroup(64*Integers(J`K));
TG := TargetRestriction(G,CyclotomicField(1));
P := [p : p in PrimesUpTo(1000) | p mod 8 eq 5];
A := [EulerFactor(psi,p : Integral) : p in P];
tw := psi*TG.2;
B := [EulerFactor(tw,p : Integral) : p in P];
assert A eq B; // same L-function over Q
// but they are different over primes that are 5 mod 8
(TG.2)(Factorization(5*Integers(J`K))[1][1]);
SetEchoInput(ei);
