"Source: Text/Geometry/HypGeomMot.text";
"Line: 1010";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/HypGeomMot.text, line: 1010
// Example: H138E8 ()
print "Example: H138E8";
ei := GetEchoInput();
SetEchoInput(true);
H := HypergeometricData([1/2,1/2,1/2,1/2],[0,0,0,0]);
Lf := LSeries(Newforms(ModularForms(8,4))[1][1]);
T := PolynomialRing(Integers()).1; // dummy variable
f3 := EulerFactor(Lf,3 : Integral)*(1-3*T); // make it a poly
f5 := EulerFactor(Lf,5 : Integral)*(1-5*T); // via Integral
f17 := EulerFactor(Lf,17 : Integral)*(1-17*T);
f2 := 1+T+6*T^2+8*T^3+64*T^4; // determined by Tornaria
BP := [<2,0,f2>,<3,1,f3>,<5,1,f5>,<17,1,f17>];
L := LSeries(H,256 : BadPrimes:=BP);
Conductor(L);
assert $1 eq 255;
assert Abs(CFENew(L)) lt 10^(-28);
H := HypergeometricData([1/2,1/2,1/2,1/2],[0,0,0,0]);
MValue(H);
assert $1 eq 256;
t := 1/2^8; // makes v_2(Mt)=0
f2 := EulerFactor(H,t,2 : Fake);
f2;
L := LSeries(H,t : BadPrimes:=[<2,0,f2>]);
Conductor(L);
assert $1 eq 255;
assert Abs(CFENew(L)) lt 10^(-28);
SetEchoInput(ei);
