/*
  This code can be loaded, or copied and paste using cpaste, into Sage.
  It will load the data associated to the HMF, including
  the field, level, and Hecke and Atkin-Lehner eigenvalue data.
*/

P.<x> = PolynomialRing(QQ)
g = P([-1, -3, 6, 4, -5, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([79,79,-w^3 + w^2 + 4*w - 1])

primes_array = [
[13, 13, w^5 - 5*w^3 + 4*w],\
[25, 5, w^5 - 5*w^3 + 6*w - 1],\
[25, 5, -w^3 + w^2 + 3*w - 1],\
[25, 5, w^5 - 4*w^3 - w^2 + 3*w + 2],\
[27, 3, w^4 - w^3 - 4*w^2 + 2*w + 2],\
[27, 3, w^4 - w^3 - 4*w^2 + 2*w + 3],\
[53, 53, -w^4 + w^3 + 3*w^2 - 2*w + 1],\
[53, 53, -w^4 + w^3 + 4*w^2 - 3*w - 4],\
[53, 53, -w^5 + w^4 + 4*w^3 - 4*w^2 - 3*w + 1],\
[53, 53, w^3 - 2*w - 2],\
[53, 53, w^5 - 5*w^3 - w^2 + 5*w],\
[53, 53, -w^4 + 4*w^2 + w - 4],\
[64, 2, -2],\
[79, 79, -2*w^5 + w^4 + 9*w^3 - 3*w^2 - 9*w + 2],\
[79, 79, -w^5 - w^4 + 5*w^3 + 4*w^2 - 6*w - 1],\
[79, 79, w^3 - w^2 - 4*w + 1],\
[79, 79, -2*w^5 + 2*w^4 + 9*w^3 - 7*w^2 - 9*w + 3],\
[79, 79, -2*w^4 + w^3 + 7*w^2 - 3*w - 3],\
[79, 79, -w^5 + 6*w^3 - w^2 - 8*w + 1],\
[103, 103, 2*w^4 - 7*w^2 - w + 3],\
[103, 103, w^5 - w^4 - 4*w^3 + 5*w^2 + 2*w - 4],\
[103, 103, -w^5 - w^4 + 4*w^3 + 4*w^2 - 2*w - 3],\
[103, 103, w^5 - 2*w^4 - 4*w^3 + 6*w^2 + 4*w - 1],\
[103, 103, -w^4 + w^3 + 5*w^2 - 3*w - 4],\
[103, 103, 2*w^5 - w^4 - 10*w^3 + 3*w^2 + 10*w - 1],\
[131, 131, w^5 - w^4 - 5*w^3 + 3*w^2 + 4*w - 1],\
[131, 131, -w^5 + 2*w^4 + 4*w^3 - 6*w^2 - 4*w + 2],\
[131, 131, w^5 - w^4 - 4*w^3 + 5*w^2 + 2*w - 5],\
[131, 131, 2*w^4 - 7*w^2 - w + 2],\
[131, 131, -2*w^5 + w^4 + 9*w^3 - 2*w^2 - 8*w],\
[131, 131, 2*w^5 - w^4 - 10*w^3 + 3*w^2 + 10*w],\
[157, 157, -w^5 - w^4 + 5*w^3 + 5*w^2 - 6*w - 3],\
[157, 157, -2*w^3 + w^2 + 5*w - 2],\
[157, 157, -w^5 - w^4 + 4*w^3 + 5*w^2 - 3*w - 3],\
[157, 157, -w^5 + 5*w^3 - 7*w],\
[157, 157, -2*w^5 + w^4 + 8*w^3 - 3*w^2 - 6*w + 2],\
[157, 157, -w^5 + w^4 + 5*w^3 - 4*w^2 - 7*w + 2],\
[181, 181, w^2 - 2*w - 2],\
[181, 181, 2*w^5 - 9*w^3 + 7*w],\
[181, 181, -w^5 + 2*w^4 + 5*w^3 - 8*w^2 - 5*w + 4],\
[181, 181, -w^5 + w^4 + 6*w^3 - 3*w^2 - 9*w + 1],\
[181, 181, 2*w^5 - 2*w^4 - 8*w^3 + 6*w^2 + 5*w - 2],\
[181, 181, w^4 - 2*w^2 - 2],\
[233, 233, 2*w^3 - w^2 - 5*w + 1],\
[233, 233, -w^5 - w^4 + 6*w^3 + 3*w^2 - 8*w],\
[233, 233, w^5 - w^4 - 5*w^3 + 4*w^2 + 7*w - 3],\
[233, 233, w^5 + w^4 - 5*w^3 - 5*w^2 + 6*w + 4],\
[233, 233, -w^5 + 4*w^3 + 2*w^2 - 2*w - 3],\
[233, 233, 2*w^5 - w^4 - 8*w^3 + 3*w^2 + 6*w - 1],\
[311, 311, 2*w^5 - 2*w^4 - 9*w^3 + 6*w^2 + 8*w - 2],\
[311, 311, w^4 + w^3 - 3*w^2 - 4*w + 1],\
[311, 311, -w^5 + 2*w^4 + 5*w^3 - 7*w^2 - 5*w + 2],\
[311, 311, w^5 - w^4 - 4*w^3 + 4*w^2 + w - 3],\
[311, 311, w^4 - 2*w^2 - w - 2],\
[311, 311, -2*w^5 + w^4 + 9*w^3 - 4*w^2 - 7*w + 2],\
[313, 313, -w^5 + 5*w^3 + w^2 - 4*w - 3],\
[313, 313, -w^5 + 6*w^3 - 7*w + 1],\
[313, 313, -w^4 + w^3 + 5*w^2 - 3*w - 3],\
[313, 313, -w^5 + w^4 + 3*w^3 - 4*w^2 + 4],\
[313, 313, -w^5 + 2*w^4 + 4*w^3 - 7*w^2 - 4*w + 2],\
[313, 313, -2*w^4 + w^3 + 7*w^2 - 2*w - 4],\
[337, 337, 2*w^5 - w^4 - 7*w^3 + 2*w^2 + 2*w + 2],\
[337, 337, w^5 - 2*w^4 - 3*w^3 + 7*w^2 + 2*w - 3],\
[337, 337, 2*w^5 - w^4 - 9*w^3 + 2*w^2 + 10*w - 1],\
[337, 337, -2*w^5 - w^4 + 9*w^3 + 4*w^2 - 8*w],\
[337, 337, 3*w^5 - 2*w^4 - 13*w^3 + 7*w^2 + 11*w - 5],\
[337, 337, w^4 - w^3 - 2*w^2 + 4*w],\
[389, 389, 2*w^5 - w^4 - 9*w^3 + 4*w^2 + 7*w],\
[389, 389, -2*w^5 + 3*w^4 + 8*w^3 - 9*w^2 - 7*w + 3],\
[389, 389, -w^5 + 2*w^4 + 5*w^3 - 7*w^2 - 5*w],\
[389, 389, -2*w^5 + 3*w^4 + 9*w^3 - 10*w^2 - 8*w + 2],\
[389, 389, -3*w^5 + w^4 + 14*w^3 - 2*w^2 - 12*w],\
[389, 389, -w^5 + w^4 + 5*w^3 - 3*w^2 - 3*w + 1],\
[443, 443, -2*w^5 + w^4 + 8*w^3 - w^2 - 7*w - 3],\
[443, 443, 2*w^5 - w^4 - 9*w^3 + 4*w^2 + 8*w],\
[443, 443, w^5 - 3*w^4 - 4*w^3 + 11*w^2 + 2*w - 4],\
[443, 443, 2*w^5 - w^4 - 9*w^3 + 2*w^2 + 8*w - 2],\
[443, 443, -2*w^4 + 2*w^3 + 7*w^2 - 4*w - 3],\
[443, 443, -3*w^5 + w^4 + 15*w^3 - 3*w^2 - 17*w + 2],\
[467, 467, 2*w^5 - 2*w^4 - 9*w^3 + 6*w^2 + 10*w - 1],\
[467, 467, w^5 + w^4 - 5*w^3 - 6*w^2 + 6*w + 5],\
[467, 467, -w^5 - 2*w^4 + 5*w^3 + 7*w^2 - 5*w - 3],\
[467, 467, -2*w^5 + w^4 + 11*w^3 - 4*w^2 - 13*w + 3],\
[467, 467, 3*w^5 - 2*w^4 - 13*w^3 + 6*w^2 + 11*w - 1],\
[467, 467, -2*w^5 + w^4 + 9*w^3 - w^2 - 8*w - 3],\
[521, 521, w^5 + 2*w^4 - 6*w^3 - 7*w^2 + 7*w + 3],\
[521, 521, 2*w^5 - 2*w^4 - 8*w^3 + 6*w^2 + 7*w - 1],\
[521, 521, -w^5 + w^4 + 6*w^3 - 4*w^2 - 10*w + 3],\
[521, 521, 2*w^5 - 3*w^4 - 9*w^3 + 10*w^2 + 9*w - 3],\
[521, 521, -2*w^5 + 11*w^3 - 13*w + 1],\
[521, 521, 3*w^5 - w^4 - 13*w^3 + 3*w^2 + 11*w - 1],\
[547, 547, w^4 + w^3 - 5*w^2 - 3*w + 1],\
[547, 547, -2*w^5 + 3*w^4 + 9*w^3 - 11*w^2 - 10*w + 6],\
[547, 547, w^4 - w^3 - w^2 + 3*w - 3],\
[547, 547, 2*w^4 + w^3 - 9*w^2 - 2*w + 6],\
[547, 547, 3*w^5 - w^4 - 13*w^3 + 3*w^2 + 11*w - 2],\
[547, 547, -w^5 + w^4 + 6*w^3 - 4*w^2 - 10*w + 2],\
[571, 571, -w^5 + 4*w^3 + 3*w^2 - 3*w - 4],\
[571, 571, -w^5 - w^4 + 3*w^3 + 6*w^2 - 5],\
[571, 571, w^5 - 6*w^3 + 2*w^2 + 9*w - 4],\
[571, 571, 2*w^5 - 9*w^3 - w^2 + 10*w + 1],\
[571, 571, 2*w^5 - 11*w^3 + w^2 + 13*w - 3],\
[571, 571, -w^5 + 7*w^3 - w^2 - 12*w + 2],\
[599, 599, -2*w^5 + w^4 + 8*w^3 - 5*w^2 - 5*w + 5],\
[599, 599, w^5 - w^4 - 6*w^3 + 4*w^2 + 6*w - 2],\
[599, 599, w^4 - 2*w^3 - 5*w^2 + 7*w + 4],\
[599, 599, -2*w^5 + 10*w^3 - w^2 - 11*w + 3],\
[599, 599, w^5 - 3*w^4 - 5*w^3 + 11*w^2 + 7*w - 5],\
[599, 599, -w^5 + w^4 + 6*w^3 - 3*w^2 - 8*w + 3],\
[677, 677, -w^5 - 2*w^4 + 6*w^3 + 8*w^2 - 9*w - 4],\
[677, 677, -3*w^5 + 2*w^4 + 13*w^3 - 7*w^2 - 12*w + 4],\
[677, 677, w^4 + w^3 - 5*w^2 - 5*w + 4],\
[677, 677, -2*w^5 + 9*w^3 - w^2 - 7*w + 1],\
[677, 677, w^5 - 5*w^3 + 2*w^2 + 5*w - 5],\
[677, 677, -w^5 - w^4 + 7*w^3 + 2*w^2 - 10*w + 1],\
[701, 701, w^5 - 3*w^4 - 3*w^3 + 11*w^2 + 2*w - 6],\
[701, 701, w^5 + w^4 - 6*w^3 - 5*w^2 + 6*w + 4],\
[701, 701, -w^5 - w^4 + 3*w^3 + 4*w^2 + 2*w - 2],\
[701, 701, 3*w^5 - 2*w^4 - 14*w^3 + 5*w^2 + 14*w],\
[701, 701, 3*w^5 - 2*w^4 - 14*w^3 + 8*w^2 + 13*w - 5],\
[701, 701, -w^5 + 2*w^4 + 3*w^3 - 7*w^2 + 2*w + 3],\
[727, 727, w^5 + 2*w^4 - 5*w^3 - 8*w^2 + 6*w + 3],\
[727, 727, -w^5 + 4*w^3 + 3*w^2 - 3*w - 6],\
[727, 727, -w^5 - w^4 + 5*w^3 + 2*w^2 - 4*w + 2],\
[727, 727, 3*w^5 - 2*w^4 - 13*w^3 + 6*w^2 + 12*w - 3],\
[727, 727, -2*w^5 + 11*w^3 - w^2 - 13*w + 1],\
[727, 727, w^5 - 3*w^4 - 4*w^3 + 10*w^2 + 5*w - 4],\
[857, 857, -w^5 + 3*w^4 + 5*w^3 - 11*w^2 - 5*w + 5],\
[857, 857, -w^5 - 2*w^4 + 4*w^3 + 9*w^2 - 3*w - 7],\
[857, 857, 2*w^5 + w^4 - 9*w^3 - 4*w^2 + 6*w + 3],\
[857, 857, 2*w^5 - 3*w^4 - 7*w^3 + 10*w^2 + 2*w - 5],\
[857, 857, -w^5 + 6*w^3 - 2*w^2 - 8*w + 2],\
[857, 857, -3*w^3 + w^2 + 9*w],\
[859, 859, 2*w^4 - 2*w^3 - 5*w^2 + 5*w - 2],\
[859, 859, -2*w^5 + 9*w^3 - 6*w - 2],\
[859, 859, -w^4 - w^3 + 2*w^2 + 3*w + 4],\
[859, 859, -w^5 - 2*w^4 + 6*w^3 + 9*w^2 - 7*w - 7],\
[859, 859, -2*w^5 - w^4 + 10*w^3 + 4*w^2 - 9*w - 4],\
[859, 859, -w^5 - w^4 + 4*w^3 + 4*w^2 - 3*w + 1],\
[883, 883, 2*w^5 + w^4 - 10*w^3 - 4*w^2 + 11*w],\
[883, 883, -2*w^5 + w^4 + 9*w^3 - 3*w^2 - 10*w + 3],\
[883, 883, 3*w^5 - w^4 - 13*w^3 + 2*w^2 + 12*w + 1],\
[883, 883, 3*w^5 - 2*w^4 - 12*w^3 + 6*w^2 + 8*w - 3],\
[883, 883, w^5 - 6*w^3 + w^2 + 10*w - 3],\
[883, 883, -2*w^5 + 11*w^3 - w^2 - 14*w + 3],\
[911, 911, -3*w^5 + 15*w^3 - 15*w + 1],\
[911, 911, -2*w^5 + 2*w^4 + 8*w^3 - 8*w^2 - 6*w + 3],\
[911, 911, -2*w^5 + 11*w^3 - 13*w + 2],\
[911, 911, -2*w^5 + 10*w^3 + 2*w^2 - 10*w - 1],\
[911, 911, 2*w^4 - 2*w^3 - 8*w^2 + 6*w + 7],\
[911, 911, -3*w^4 + 12*w^2 - 7],\
[937, 937, 3*w^4 - w^3 - 10*w^2 + 2*w + 4],\
[937, 937, -w^5 + 2*w^4 + 5*w^3 - 9*w^2 - 6*w + 5],\
[937, 937, -w^5 + 2*w^4 + 2*w^3 - 6*w^2 + 3*w + 3],\
[937, 937, 2*w^5 - w^4 - 11*w^3 + 4*w^2 + 12*w - 3],\
[937, 937, -2*w^5 + 11*w^3 + w^2 - 14*w],\
[937, 937, 2*w^5 + w^4 - 9*w^3 - 5*w^2 + 7*w + 5],\
[961, 31, -3*w^5 + w^4 + 12*w^3 - 3*w^2 - 8*w + 2],\
[961, 31, -2*w^5 + 2*w^4 + 10*w^3 - 7*w^2 - 13*w + 3],\
[961, 31, -w^5 + w^4 + 7*w^3 - 5*w^2 - 10*w + 4]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [0, -6, -4, -6, 8, -8, -10, -2, -6, 0, 6, -6, -3, 8, -8, 1, 8, 0, -14, -4, 0, -8, -10, -4, 2, 10, 18, -16, -20, 4, -2, 6, 2, -18, -14, -16, -22, 12, 10, 10, 10, -16, -26, 10, 18, -10, 18, 0, -6, 24, 24, 24, -20, 16, -14, 6, -2, 26, 22, -26, -4, -26, 32, -8, 30, 4, 6, 2, 34, -10, 30, 18, -12, -24, -12, -26, 4, 26, 24, -12, 18, -12, 40, 26, -36, -18, 10, 24, 4, -26, -30, 10, -28, -26, 36, 28, -38, -8, 20, -30, -20, -26, -44, 8, -22, -16, 48, -28, 24, 22, 26, -38, -28, -42, 16, -30, -12, 34, -18, -20, 46, -24, 2, 28, -8, -16, -28, -18, 18, 4, -18, 30, 6, -24, -36, 6, 36, -4, -14, 36, -6, 44, 28, 32, 44, -32, -2, -20, -8, 18, -48, 2, 32, 48, -10, -58, -20, -12, -6, -22]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([79,79,-w^3 + w^2 + 4*w - 1])] = -1

# EXAMPLE:
# pp = ZF.ideal(2).factor()[0][0]
# hecke_eigenvalues[pp]