/*
  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, 1, -6, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([17, 17, 1/2*w^3 - w^2 - w + 3/2])

primes_array = [
[4, 2, -1/2*w^3 + 3*w + 5/2],\
[4, 2, w^3 - w^2 - 6*w],\
[13, 13, -1/2*w^3 + w^2 + 3*w - 1/2],\
[13, 13, 1/2*w^3 - w^2 - 3*w + 7/2],\
[13, 13, -1/2*w^3 + 4*w - 1/2],\
[13, 13, -1/2*w^3 + 4*w + 5/2],\
[17, 17, 1/2*w^3 - w^2 - w + 3/2],\
[47, 47, -w^2 + 2],\
[47, 47, -w^3 + 2*w^2 + 5*w - 5],\
[47, 47, -3/2*w^3 + w^2 + 10*w + 3/2],\
[47, 47, -1/2*w^3 + 5*w - 1/2],\
[67, 67, 3/2*w^3 - 2*w^2 - 8*w + 3/2],\
[67, 67, 1/2*w^3 - 2*w - 5/2],\
[67, 67, -1/2*w^3 + w^2 + w - 5/2],\
[67, 67, -3/2*w^3 + w^2 + 9*w - 1/2],\
[81, 3, -3],\
[89, 89, w^2 - 2*w - 4],\
[89, 89, 3/2*w^3 - 2*w^2 - 9*w + 3/2],\
[89, 89, -1/2*w^3 + w^2 + 4*w - 7/2],\
[89, 89, -w^3 + 7*w + 1],\
[101, 101, -1/2*w^3 + 3*w - 5/2],\
[101, 101, -1/2*w^3 + w^2 + 2*w - 11/2],\
[101, 101, -w^3 + w^2 + 6*w + 3],\
[101, 101, w - 4],\
[103, 103, 3/2*w^3 - 3*w^2 - 7*w + 7/2],\
[103, 103, -w^2 + 8],\
[103, 103, -1/2*w^3 - w^2 + 3*w + 11/2],\
[103, 103, -1/2*w^3 - w^2 + 3*w + 13/2],\
[137, 137, 1/2*w^3 - 2*w - 7/2],\
[137, 137, -1/2*w^3 + w^2 + w - 7/2],\
[137, 137, 3/2*w^3 - 2*w^2 - 8*w + 1/2],\
[137, 137, -3/2*w^3 + w^2 + 9*w - 3/2],\
[149, 149, 3/2*w^3 - 9*w - 13/2],\
[149, 149, 7/2*w^3 - 3*w^2 - 21*w - 3/2],\
[149, 149, 2*w^3 - 2*w^2 - 12*w - 1],\
[149, 149, -w^2 + 6],\
[157, 157, -5/2*w^3 + 3*w^2 + 13*w - 9/2],\
[157, 157, -2*w^3 + 3*w^2 + 12*w - 4],\
[157, 157, 1/2*w^3 - 2*w^2 - 2*w + 15/2],\
[157, 157, 5/2*w^3 - 2*w^2 - 14*w - 3/2],\
[191, 191, 3/2*w^3 - 2*w^2 - 8*w - 1/2],\
[191, 191, -3/2*w^3 + w^2 + 9*w - 5/2],\
[191, 191, 1/2*w^3 - 2*w - 9/2],\
[191, 191, -1/2*w^3 + w^2 + w - 9/2],\
[239, 239, -5/2*w^3 + 2*w^2 + 16*w + 1/2],\
[239, 239, 2*w^3 - 13*w - 8],\
[239, 239, -7/2*w^3 + 3*w^2 + 20*w - 1/2],\
[239, 239, -1/2*w^3 + 4*w + 11/2],\
[251, 251, -5/2*w^3 + 3*w^2 + 13*w - 1/2],\
[251, 251, -2*w^3 + w^2 + 14*w + 2],\
[251, 251, 3/2*w^3 - w^2 - 7*w - 7/2],\
[251, 251, -w^3 + 9*w + 1],\
[271, 271, -w^3 + 7*w - 1],\
[271, 271, -3/2*w^3 + 2*w^2 + 9*w + 1/2],\
[271, 271, w^2 - 2*w - 6],\
[271, 271, -1/2*w^3 + w^2 + 4*w - 11/2],\
[293, 293, -1/2*w^3 + 2*w^2 + 2*w - 13/2],\
[293, 293, -3/2*w^3 + w^2 + 11*w - 3/2],\
[293, 293, -1/2*w^3 + 2*w^2 + 2*w - 7/2],\
[293, 293, -3/2*w^3 + w^2 + 11*w + 3/2],\
[307, 307, w^3 - w^2 - 8*w + 1],\
[307, 307, 2*w^3 - 2*w^2 - 13*w + 2],\
[307, 307, -1/2*w^3 + 2*w^2 + w - 9/2],\
[307, 307, -1/2*w^3 - w^2 + 4*w + 9/2],\
[353, 353, -3/2*w^3 + 2*w^2 + 8*w - 15/2],\
[353, 353, 11/2*w^3 - 4*w^2 - 34*w - 7/2],\
[353, 353, 6*w^3 - 4*w^2 - 36*w - 7],\
[353, 353, 9/2*w^3 - 3*w^2 - 26*w - 5/2],\
[361, 19, 1/2*w^3 + w^2 - 3*w - 15/2],\
[361, 19, -2*w^3 + 2*w^2 + 10*w - 7],\
[373, 373, -1/2*w^3 + 2*w^2 + 2*w - 9/2],\
[373, 373, -3/2*w^3 + w^2 + 11*w + 1/2],\
[373, 373, -1/2*w^3 + 2*w^2 + 2*w - 11/2],\
[373, 373, 3/2*w^3 - w^2 - 11*w + 1/2],\
[409, 409, 2*w^3 - 3*w^2 - 10*w + 2],\
[409, 409, -w^3 + 5*w + 5],\
[409, 409, -1/2*w^3 + w^2 - 7/2],\
[409, 409, 5/2*w^3 - 2*w^2 - 15*w + 5/2],\
[421, 421, -2*w^3 + w^2 + 12*w],\
[421, 421, 5/2*w^3 - 3*w^2 - 14*w + 3/2],\
[421, 421, -w^3 + 2*w^2 + 3*w - 5],\
[421, 421, 1/2*w^3 - w - 7/2],\
[443, 443, 5/2*w^3 - 3*w^2 - 15*w + 3/2],\
[443, 443, 1/2*w^3 - w^2 - 5*w + 9/2],\
[443, 443, -1/2*w^3 + 2*w^2 - 13/2],\
[443, 443, -3/2*w^3 + 10*w + 3/2],\
[463, 463, 4*w^3 - 4*w^2 - 22*w + 5],\
[463, 463, 3*w^3 - 4*w^2 - 14*w + 2],\
[463, 463, -5/2*w^3 + 2*w^2 + 14*w - 7/2],\
[463, 463, 3/2*w^3 - w^2 - 7*w - 9/2],\
[509, 509, -7/2*w^3 + 2*w^2 + 20*w + 3/2],\
[509, 509, 5/2*w^3 - w^2 - 16*w - 5/2],\
[509, 509, -5/2*w^3 + 4*w^2 + 10*w - 13/2],\
[509, 509, 9/2*w^3 - 5*w^2 - 25*w + 7/2],\
[523, 523, 3*w^3 - 3*w^2 - 16*w + 3],\
[523, 523, 2*w^3 - 2*w^2 - 9*w + 2],\
[523, 523, 5/2*w^3 - 3*w^2 - 12*w + 3/2],\
[523, 523, -5/2*w^3 + 2*w^2 + 13*w + 3/2],\
[557, 557, 3*w^3 - 3*w^2 - 16*w + 1],\
[557, 557, 5/2*w^3 - 2*w^2 - 13*w + 1/2],\
[557, 557, -2*w^3 + 2*w^2 + 9*w],\
[557, 557, -5/2*w^3 + 3*w^2 + 12*w - 7/2],\
[577, 577, -w^3 - w^2 + 6*w + 9],\
[577, 577, 7/2*w^3 - 3*w^2 - 21*w - 7/2],\
[577, 577, 1/2*w^3 - 2*w^2 - 3*w + 17/2],\
[577, 577, -5/2*w^3 + 3*w^2 + 13*w - 19/2],\
[599, 599, -4*w^3 + 4*w^2 + 22*w - 1],\
[599, 599, w^3 + w^2 - 8*w - 7],\
[599, 599, -5/2*w^3 + 3*w^2 + 16*w - 11/2],\
[599, 599, 3/2*w^3 - w^2 - 7*w - 13/2],\
[613, 613, w^3 - 5*w - 9],\
[613, 613, -2*w^3 + 3*w^2 + 10*w + 2],\
[613, 613, -1/2*w^3 + w^2 - 15/2],\
[613, 613, -5/2*w^3 + 2*w^2 + 15*w - 13/2],\
[625, 5, -5],\
[647, 647, 2*w^3 - 3*w^2 - 8*w + 6],\
[647, 647, -3*w^3 + 2*w^2 + 17*w - 1],\
[647, 647, 3/2*w^3 - w^2 - 6*w - 7/2],\
[647, 647, -7/2*w^3 + 4*w^2 + 19*w - 3/2],\
[659, 659, w^3 + w^2 - 6*w - 5],\
[659, 659, -2*w^3 + 4*w^2 + 9*w - 8],\
[659, 659, -7/2*w^3 + 3*w^2 + 22*w - 1/2],\
[659, 659, 1/2*w^3 - 7*w + 1/2],\
[701, 701, 3*w^3 - 2*w^2 - 18*w - 8],\
[701, 701, 7/2*w^3 - 3*w^2 - 21*w - 9/2],\
[701, 701, -1/2*w^3 - 2*w^2 + 3*w + 19/2],\
[701, 701, 15/2*w^3 - 5*w^2 - 45*w - 19/2],\
[727, 727, 2*w^3 - 3*w^2 - 12*w + 2],\
[727, 727, w^3 - 2*w^2 - 7*w + 7],\
[727, 727, 1/2*w^3 + w^2 - 6*w - 13/2],\
[727, 727, 3/2*w^3 - 11*w - 1/2],\
[761, 761, 3*w^3 - 4*w^2 - 18*w + 4],\
[761, 761, -w^3 + 2*w^2 + 8*w - 6],\
[761, 761, 2*w^2 - 4*w - 7],\
[761, 761, -2*w^3 + 14*w + 3],\
[769, 769, 5/2*w^3 - 3*w^2 - 15*w + 1/2],\
[769, 769, -1/2*w^3 + w^2 + 5*w - 11/2],\
[769, 769, 3/2*w^3 - 10*w - 1/2],\
[769, 769, -1/2*w^3 + 2*w^2 - 15/2],\
[829, 829, 7/2*w^3 - 4*w^2 - 20*w + 5/2],\
[829, 829, -5/2*w^3 + 4*w^2 + 12*w - 7/2],\
[829, 829, 7/2*w^3 - 3*w^2 - 21*w + 7/2],\
[829, 829, 3/2*w^3 - 3*w^2 - 5*w + 13/2],\
[863, 863, 3*w^3 - 2*w^2 - 19*w + 1],\
[863, 863, w^2 - 4*w - 4],\
[863, 863, -5/2*w^3 + 4*w^2 + 13*w - 9/2],\
[863, 863, 1/2*w^3 + w^2 - 2*w - 13/2],\
[883, 883, -4*w^3 + 4*w^2 + 22*w - 3],\
[883, 883, 3*w^3 - 2*w^2 - 16*w - 2],\
[883, 883, -3*w^3 + 4*w^2 + 14*w - 4],\
[883, 883, 2*w^3 - 2*w^2 - 8*w + 1],\
[919, 919, 1/2*w^3 - w - 11/2],\
[919, 919, -5/2*w^3 + 3*w^2 + 14*w + 1/2],\
[919, 919, w^3 - 2*w^2 - 3*w + 7],\
[919, 919, -2*w^3 + w^2 + 12*w - 2],\
[953, 953, 7/2*w^3 - 3*w^2 - 19*w + 3/2],\
[953, 953, 5/2*w^3 - 2*w^2 - 12*w - 3/2],\
[953, 953, 7/2*w^3 - 4*w^2 - 18*w + 5/2],\
[953, 953, -5/2*w^3 + 3*w^2 + 11*w - 7/2]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [-3, -3, -2, -2, -2, -2, 1, 0, 0, 0, 0, 4, 4, 4, 4, 18, 10, 10, 10, 10, -10, -10, -10, -10, 8, 8, 8, 8, -6, -6, -6, -6, -10, -10, -10, -10, -2, -2, -2, -2, -16, -16, -16, -16, -16, -16, -16, -16, 12, 12, 12, 12, -16, -16, -16, -16, 6, 6, 6, 6, -12, -12, -12, -12, -30, -30, -30, -30, -22, -22, 6, 6, 6, 6, 26, 26, 26, 26, 22, 22, 22, 22, 28, 28, 28, 28, 32, 32, 32, 32, -2, -2, -2, -2, -36, -36, -36, -36, 30, 30, 30, 30, -14, -14, -14, -14, -24, -24, -24, -24, -26, -26, -26, -26, -14, 8, 8, 8, 8, 4, 4, 4, 4, -18, -18, -18, -18, 40, 40, 40, 40, -22, -22, -22, -22, -14, -14, -14, -14, -34, -34, -34, -34, 16, 16, 16, 16, -12, -12, -12, -12, 24, 24, 24, 24, -22, -22, -22, -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([17, 17, 1/2*w^3 - w^2 - w + 3/2])] = -1

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