/*
  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([29, 11, -10, -2, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([11,11,w^2 - 2*w - 4])

primes_array = [
[11, 11, -w - 1],\
[11, 11, w^2 - 5],\
[11, 11, -w^2 + 2*w + 4],\
[11, 11, w - 2],\
[16, 2, 2],\
[19, 19, w^2 - 2*w - 5],\
[19, 19, -w^2 + 6],\
[25, 5, -2*w^2 + 2*w + 11],\
[29, 29, w],\
[29, 29, 2*w^2 - w - 10],\
[29, 29, -2*w^2 + 3*w + 9],\
[29, 29, w - 1],\
[31, 31, w^3 - 6*w - 6],\
[31, 31, -w^3 + 3*w^2 + 3*w - 11],\
[41, 41, w^3 - 4*w^2 - 2*w + 16],\
[41, 41, w^3 - 5*w^2 - 2*w + 24],\
[59, 59, w^3 - w^2 - 5*w - 2],\
[59, 59, 2*w^2 - w - 13],\
[61, 61, w^3 - w^2 - 6*w + 3],\
[61, 61, -w^3 + 2*w^2 + 5*w - 3],\
[71, 71, 2*w^2 - w - 16],\
[71, 71, -w^3 + 3*w^2 + 4*w - 10],\
[71, 71, -w^3 + 7*w + 4],\
[71, 71, w^3 - 5*w^2 - 2*w + 23],\
[79, 79, -w^3 + 4*w^2 + 3*w - 16],\
[79, 79, w^3 + w^2 - 8*w - 10],\
[81, 3, -3],\
[131, 131, 4*w^2 - 5*w - 24],\
[131, 131, 4*w^2 - 3*w - 25],\
[139, 139, w^2 + w - 9],\
[139, 139, -w^3 + w^2 + 6*w - 5],\
[149, 149, w^3 - w^2 - 4*w + 2],\
[149, 149, w^3 - 2*w^2 - 3*w + 2],\
[151, 151, -w^3 + 7*w + 3],\
[151, 151, -w^3 + 3*w^2 + 4*w - 9],\
[179, 179, -w^3 - 2*w^2 + 10*w + 16],\
[179, 179, -w^3 + 3*w^2 + 3*w - 6],\
[179, 179, w^3 - 6*w - 1],\
[179, 179, w^3 - 5*w^2 - 3*w + 23],\
[191, 191, w^3 - 6*w^2 - w + 27],\
[191, 191, w^3 + 3*w^2 - 10*w - 21],\
[199, 199, -w^3 + 2*w^2 + 6*w - 4],\
[199, 199, -4*w^2 + 3*w + 22],\
[199, 199, 4*w^2 - 5*w - 21],\
[199, 199, 3*w^2 - 4*w - 12],\
[239, 239, -w^3 + w^2 + 4*w - 6],\
[239, 239, 2*w^3 - 5*w^2 - 9*w + 17],\
[239, 239, 2*w^3 - w^2 - 13*w - 5],\
[239, 239, w^3 - 8*w^2 + 2*w + 41],\
[241, 241, -w^3 + 5*w^2 + 4*w - 25],\
[241, 241, w^3 - 6*w - 8],\
[241, 241, -w^3 + 3*w^2 + 3*w - 13],\
[241, 241, w^3 - 5*w^2 + w + 19],\
[269, 269, w^2 - 2*w - 10],\
[269, 269, w^2 - 11],\
[271, 271, w^3 + 2*w^2 - 8*w - 18],\
[271, 271, 2*w^3 - 13*w - 10],\
[271, 271, 2*w^3 + w^2 - 15*w - 16],\
[271, 271, w^3 - 5*w^2 - w + 23],\
[289, 17, 2*w^2 - 11],\
[289, 17, -2*w^2 + 4*w + 9],\
[311, 311, w^3 - 4*w^2 - 3*w + 10],\
[311, 311, w^3 - 7*w^2 - w + 34],\
[331, 331, w^3 - w^2 - 7*w + 4],\
[331, 331, w^3 - 2*w^2 - 6*w + 3],\
[349, 349, w^3 + w^2 - 6*w - 12],\
[349, 349, -w^3 + 4*w^2 + w - 16],\
[361, 19, 4*w^2 - 4*w - 21],\
[379, 379, w^3 - 3*w^2 - 3*w + 15],\
[379, 379, 2*w^3 - 2*w^2 - 12*w + 1],\
[379, 379, -2*w^3 + 4*w^2 + 10*w - 11],\
[379, 379, w^3 - 6*w - 10],\
[401, 401, -2*w^3 + 7*w^2 + 8*w - 30],\
[401, 401, -w^3 + 2*w^2 + 6*w - 2],\
[419, 419, 5*w^2 - 4*w - 26],\
[419, 419, 5*w^2 - 6*w - 25],\
[421, 421, 3*w^2 - w - 20],\
[421, 421, -2*w^3 + 2*w^2 + 10*w + 3],\
[431, 431, w^2 - 3*w - 5],\
[431, 431, w^2 + w - 7],\
[449, 449, 2*w^3 - 13*w - 7],\
[449, 449, -2*w^3 + 6*w^2 + 7*w - 18],\
[461, 461, w^3 - w^2 - 8*w + 3],\
[461, 461, -w^3 + 2*w^2 + 7*w - 5],\
[491, 491, w^3 - 3*w^2 - 6*w + 15],\
[491, 491, w^3 - 9*w - 7],\
[499, 499, 4*w^2 - 6*w - 23],\
[499, 499, -4*w^2 + 2*w + 25],\
[509, 509, 2*w^3 - 3*w^2 - 11*w + 6],\
[521, 521, -w^3 + 3*w^2 + 2*w - 12],\
[521, 521, -w^3 + 4*w^2 + 2*w - 19],\
[529, 23, w^3 - 7*w^2 - w + 35],\
[529, 23, -w^3 + 3*w^2 + 4*w - 5],\
[541, 541, 2*w^3 - w^2 - 12*w - 5],\
[541, 541, w^3 - 2*w^2 - 7*w + 9],\
[569, 569, w^3 - 8*w - 2],\
[569, 569, -w^3 + 3*w^2 + 5*w - 9],\
[599, 599, -w^3 - 4*w^2 + 10*w + 25],\
[599, 599, -w^3 + 7*w^2 - 36],\
[601, 601, 5*w^2 - 6*w - 26],\
[601, 601, -2*w^3 + 8*w^2 + 6*w - 33],\
[601, 601, -2*w^3 - 2*w^2 + 16*w + 21],\
[601, 601, 5*w^2 - 4*w - 27],\
[619, 619, w^3 + 4*w^2 - 11*w - 26],\
[619, 619, w^3 - 3*w^2 - 5*w + 18],\
[641, 641, -w^3 + 3*w^2 + 6*w - 14],\
[641, 641, -w^3 + 9*w + 6],\
[659, 659, -w^3 - 4*w^2 + 10*w + 28],\
[659, 659, -w^3 + 6*w^2 - w - 27],\
[659, 659, -w^3 - 3*w^2 + 8*w + 23],\
[659, 659, -w^3 + 7*w^2 - w - 33],\
[691, 691, w^3 - w^2 - 8*w + 2],\
[691, 691, 2*w^3 - 2*w^2 - 11*w + 1],\
[701, 701, -w^3 - w^2 + 7*w + 15],\
[701, 701, -w^3 + 4*w^2 + 2*w - 20],\
[709, 709, -2*w^3 - w^2 + 15*w + 15],\
[709, 709, 2*w^3 - 7*w^2 - 7*w + 27],\
[719, 719, -w^3 - 4*w^2 + 13*w + 26],\
[719, 719, w^3 - 7*w^2 - 2*w + 34],\
[739, 739, 2*w^3 + 2*w^2 - 15*w - 24],\
[739, 739, -2*w^3 + 8*w^2 + 5*w - 35],\
[751, 751, -w^3 - 3*w^2 + 9*w + 25],\
[751, 751, -w^3 + 6*w^2 - 30],\
[761, 761, 3*w^3 - 2*w^2 - 16*w - 8],\
[761, 761, -3*w^3 + 7*w^2 + 11*w - 23],\
[769, 769, -2*w^3 + 4*w^2 + 11*w - 10],\
[769, 769, w^3 + 2*w^2 - 9*w - 12],\
[809, 809, -3*w^3 + 3*w^2 + 16*w + 4],\
[809, 809, w^3 + 5*w^2 - 12*w - 30],\
[811, 811, -w^3 - 4*w^2 + 10*w + 27],\
[811, 811, -2*w^3 + 5*w^2 + 9*w - 14],\
[811, 811, -2*w^3 + w^2 + 13*w + 2],\
[811, 811, -w^3 + 7*w^2 - w - 32],\
[821, 821, 2*w^3 - 8*w^2 - 7*w + 35],\
[821, 821, -2*w^3 - 2*w^2 + 17*w + 22],\
[829, 829, -3*w^3 + 20*w + 13],\
[829, 829, -w^3 + 7*w^2 - w - 36],\
[829, 829, w^3 + 4*w^2 - 10*w - 31],\
[829, 829, 2*w^3 - 3*w^2 - 11*w + 14],\
[859, 859, -w^3 + 7*w^2 - 3*w - 31],\
[859, 859, 7*w^2 - 9*w - 39],\
[859, 859, 7*w^2 - 5*w - 41],\
[859, 859, 3*w^3 - 4*w^2 - 17*w + 2],\
[929, 929, w^3 + 5*w^2 - 14*w - 31],\
[929, 929, -2*w^3 + 4*w^2 + 10*w - 5],\
[929, 929, w^3 - 9*w^2 + 4*w + 44],\
[929, 929, -w^3 + 8*w^2 + w - 39],\
[941, 941, -w^3 + 7*w^2 - 34],\
[941, 941, w^3 + 4*w^2 - 11*w - 28],\
[961, 31, -5*w^2 + 5*w + 28],\
[971, 971, -3*w^3 + w^2 + 19*w + 14],\
[971, 971, -3*w^3 + 8*w^2 + 12*w - 31],\
[991, 991, -w^3 - 5*w^2 + 11*w + 35],\
[991, 991, w^3 - 8*w^2 + 2*w + 40]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^2 - 9*x + 19
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [2*e - 12, 3*e - 15, -1, e, -4*e + 19, -4*e + 16, -2*e + 14, 3*e - 18, e - 3, -e + 10, -4*e + 24, -e + 10, 5*e - 25, -3*e + 16, -2*e + 12, -4*e + 14, 5*e - 31, 4*e - 8, -3*e + 23, 2*e - 4, 5*e - 32, -5*e + 18, 7*e - 27, -8*e + 36, 5*e - 19, -10*e + 40, 6*e - 32, -4*e + 4, -4*e + 26, 15*e - 67, 13*e - 65, 14*e - 62, -4*e + 22, -12*e + 60, -8*e + 34, 3*e - 21, 2*e + 12, -12*e + 48, 6*e - 24, -10*e + 46, -4*e + 18, 6*e - 30, 4*e - 8, -3*e + 10, 4*e - 28, 8*e - 16, 14*e - 58, 9*e - 42, -14*e + 72, -10*e + 28, 7*e - 26, -3*e + 28, 12*e - 38, 13*e - 52, -4*e + 20, 10, 3*e - 33, 15*e - 67, 22*e - 100, 10*e - 44, 13*e - 47, 15*e - 54, -22*e + 104, -21*e + 99, 12, 6*e - 50, -10*e + 32, 6*e - 24, 3*e + 19, -24*e + 108, 16*e - 64, 18*e - 84, -2*e + 2, 21*e - 87, -12*e + 48, 8*e - 60, 2*e - 40, 10*e - 70, -16*e + 72, -e - 9, -2*e + 4, -16*e + 62, -23*e + 102, -4*e + 28, -12*e + 54, 23*e - 91, -3*e + 18, 5*e - 1, -5*e + 22, -13*e + 36, 2*e - 12, 20*e - 80, 27*e - 109, -18*e + 90, 18*e - 56, 8*e - 8, -25*e + 113, -32*e + 144, -14*e + 60, 3*e + 22, 18*e - 54, -18*e + 92, 14*e - 44, -3*e + 1, 9*e - 33, -15*e + 78, -13*e + 65, -32*e + 156, 11*e - 60, -17*e + 78, 11*e - 63, 10, 15*e - 38, 19*e - 72, 35*e - 165, -21*e + 81, -16*e + 98, -4*e + 10, -17*e + 89, -27*e + 125, 29*e - 140, 31*e - 145, -e + 19, 8*e - 74, -32*e + 142, 21*e - 116, -22*e + 92, -31*e + 123, -32*e + 124, -2*e + 34, -6*e + 20, 17*e - 80, -16*e + 92, -11*e + 25, 23*e - 108, -8, -27*e + 110, 7*e - 23, -24*e + 104, -7*e + 38, 13*e - 55, -39*e + 162, -16*e + 58, 29*e - 129, 9*e - 63, 12, 4*e - 16, -14*e + 30, -31*e + 157, 36*e - 164, 2*e + 18, 19*e - 76, -24*e + 132, -2]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([11,11,w^2 - 2*w - 4])] = 1

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