/*
  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([36, 6, -13, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([16,4,-1/6*w^3 + 1/6*w^2 + 1/6*w + 1])

primes_array = [
[4, 2, 1/3*w^3 - 4/3*w^2 - 4/3*w + 6],\
[4, 2, -1/3*w^3 - 2/3*w^2 + 10/3*w + 7],\
[9, 3, -1/2*w^3 + 3/2*w^2 + 7/2*w - 9],\
[9, 3, 1/3*w^3 + 2/3*w^2 - 7/3*w - 5],\
[11, 11, -1/6*w^3 + 1/6*w^2 + 1/6*w],\
[19, 19, w + 1],\
[19, 19, 1/6*w^3 - 1/6*w^2 - 13/6*w + 2],\
[25, 5, -1/3*w^3 + 1/3*w^2 + 7/3*w - 1],\
[29, 29, -1/6*w^3 + 1/6*w^2 + 13/6*w],\
[29, 29, w - 1],\
[31, 31, 1/3*w^3 - 1/3*w^2 - 10/3*w + 3],\
[31, 31, 1/6*w^3 - 1/6*w^2 - 1/6*w + 2],\
[41, 41, -1/2*w^3 - 1/2*w^2 + 9/2*w + 5],\
[41, 41, -1/2*w^3 + 3/2*w^2 + 5/2*w - 8],\
[59, 59, 1/3*w^3 - 1/3*w^2 - 10/3*w - 1],\
[59, 59, -1/3*w^3 + 4/3*w^2 + 7/3*w - 7],\
[59, 59, 1/2*w^3 - 1/2*w^2 - 5/2*w + 2],\
[79, 79, w^2 - 11],\
[79, 79, 1/6*w^3 - 7/6*w^2 - 7/6*w + 3],\
[89, 89, -1/6*w^3 + 1/6*w^2 + 19/6*w - 5],\
[89, 89, 1/6*w^3 - 1/6*w^2 - 19/6*w - 3],\
[109, 109, -1/6*w^3 + 7/6*w^2 + 1/6*w - 9],\
[109, 109, -7/6*w^3 + 19/6*w^2 + 49/6*w - 20],\
[109, 109, -5/6*w^3 + 17/6*w^2 + 23/6*w - 12],\
[109, 109, 1/6*w^3 + 5/6*w^2 - 13/6*w - 4],\
[121, 11, 1/6*w^3 - 1/6*w^2 - 7/6*w - 3],\
[139, 139, 1/3*w^3 - 4/3*w^2 + 5/3*w - 1],\
[139, 139, -5/3*w^3 - 7/3*w^2 + 50/3*w + 29],\
[169, 13, w^3 + w^2 - 10*w - 13],\
[169, 13, -5/6*w^3 + 17/6*w^2 + 17/6*w - 12],\
[179, 179, -1/3*w^3 + 4/3*w^2 + 1/3*w - 7],\
[179, 179, -2/3*w^3 + 2/3*w^2 + 17/3*w - 5],\
[181, 181, -w^3 + 3*w^2 + 4*w - 13],\
[181, 181, -1/6*w^3 + 7/6*w^2 + 1/6*w - 11],\
[181, 181, 7/6*w^3 + 11/6*w^2 - 79/6*w - 25],\
[181, 181, 1/6*w^3 + 5/6*w^2 - 13/6*w - 2],\
[191, 191, -5/6*w^3 - 1/6*w^2 + 53/6*w + 7],\
[191, 191, 1/6*w^3 + 11/6*w^2 - 19/6*w - 16],\
[211, 211, -1/6*w^3 + 1/6*w^2 - 5/6*w - 2],\
[211, 211, -1/2*w^3 + 1/2*w^2 + 9/2*w + 2],\
[211, 211, 1/3*w^3 - 1/3*w^2 - 4/3*w - 3],\
[211, 211, -1/2*w^3 + 1/2*w^2 + 11/2*w - 4],\
[229, 229, 5/6*w^3 + 1/6*w^2 - 53/6*w - 9],\
[229, 229, 1/2*w^3 - 3/2*w^2 - 1/2*w + 2],\
[239, 239, 5/6*w^3 + 7/6*w^2 - 59/6*w - 19],\
[239, 239, 1/2*w^3 - 5/2*w^2 + 1/2*w + 5],\
[241, 241, 1/6*w^3 - 1/6*w^2 - 13/6*w - 4],\
[241, 241, w - 5],\
[269, 269, -1/6*w^3 + 7/6*w^2 + 1/6*w - 2],\
[269, 269, 1/3*w^3 - 7/3*w^2 - 1/3*w + 7],\
[271, 271, 5/3*w^3 + 7/3*w^2 - 47/3*w - 25],\
[271, 271, -5/3*w^3 + 17/3*w^2 + 23/3*w - 27],\
[281, 281, 1/6*w^3 + 5/6*w^2 - 1/6*w - 7],\
[281, 281, -1/2*w^3 + 3/2*w^2 + 9/2*w - 8],\
[311, 311, 11/6*w^3 + 7/6*w^2 - 113/6*w - 23],\
[311, 311, -4/3*w^3 + 13/3*w^2 + 10/3*w - 13],\
[311, 311, -2/3*w^3 + 5/3*w^2 + 20/3*w - 17],\
[311, 311, 1/6*w^3 + 5/6*w^2 + 5/6*w + 1],\
[349, 349, -1/2*w^3 + 1/2*w^2 + 11/2*w - 1],\
[349, 349, -5/6*w^3 + 17/6*w^2 + 29/6*w - 14],\
[349, 349, 1/6*w^3 - 1/6*w^2 + 5/6*w - 1],\
[349, 349, -2/3*w^3 - 4/3*w^2 + 17/3*w + 13],\
[359, 359, -1/6*w^3 + 13/6*w^2 + 7/6*w - 18],\
[359, 359, -1/6*w^3 - 11/6*w^2 + 13/6*w + 18],\
[361, 19, 2/3*w^3 - 2/3*w^2 - 14/3*w + 1],\
[379, 379, 1/2*w^3 + 1/2*w^2 - 7/2*w - 7],\
[379, 379, -5/6*w^3 + 11/6*w^2 + 23/6*w - 7],\
[379, 379, w^3 - 9*w - 5],\
[379, 379, -2/3*w^3 + 5/3*w^2 + 14/3*w - 7],\
[401, 401, -1/3*w^3 + 7/3*w^2 + 4/3*w - 17],\
[401, 401, -4/3*w^3 - 8/3*w^2 + 43/3*w + 31],\
[419, 419, 1/6*w^3 - 1/6*w^2 + 5/6*w],\
[419, 419, 1/2*w^3 - 1/2*w^2 - 11/2*w + 2],\
[421, 421, -5/6*w^3 - 7/6*w^2 + 47/6*w + 11],\
[421, 421, 1/3*w^3 - 1/3*w^2 - 19/3*w - 7],\
[431, 431, 5/6*w^3 + 1/6*w^2 - 41/6*w - 6],\
[431, 431, 2/3*w^3 - 8/3*w^2 - 8/3*w + 15],\
[431, 431, 5/6*w^3 - 11/6*w^2 - 29/6*w + 7],\
[431, 431, 1/2*w^3 - 5/2*w^2 + 5/2*w + 2],\
[439, 439, 5/6*w^3 + 1/6*w^2 - 41/6*w - 4],\
[439, 439, 1/2*w^3 - 1/2*w^2 - 9/2*w + 8],\
[449, 449, 5/6*w^3 - 17/6*w^2 - 29/6*w + 18],\
[449, 449, 11/6*w^3 - 41/6*w^2 - 41/6*w + 29],\
[449, 449, -7/6*w^3 + 31/6*w^2 + 7/6*w - 16],\
[449, 449, 5/3*w^3 + 7/3*w^2 - 56/3*w - 33],\
[461, 461, -1/6*w^3 + 1/6*w^2 + 19/6*w - 3],\
[461, 461, 1/6*w^3 - 1/6*w^2 - 19/6*w - 1],\
[479, 479, -2*w - 1],\
[479, 479, 1/3*w^3 - 1/3*w^2 - 13/3*w + 3],\
[491, 491, 2/3*w^3 + 1/3*w^2 - 14/3*w - 7],\
[491, 491, 5/6*w^3 - 11/6*w^2 - 35/6*w + 7],\
[509, 509, 5/6*w^3 - 11/6*w^2 - 29/6*w + 8],\
[509, 509, 5/6*w^3 + 1/6*w^2 - 41/6*w - 5],\
[521, 521, -1/6*w^3 + 7/6*w^2 - 17/6*w + 1],\
[521, 521, -1/6*w^3 + 7/6*w^2 - 11/6*w - 3],\
[521, 521, -1/6*w^3 + 7/6*w^2 + 19/6*w - 5],\
[521, 521, 2/3*w^3 + 1/3*w^2 - 26/3*w - 11],\
[541, 541, 1/6*w^3 + 5/6*w^2 - 31/6*w - 17],\
[541, 541, 5/6*w^3 - 17/6*w^2 - 47/6*w + 23],\
[541, 541, 3*w^3 + 3*w^2 - 32*w - 47],\
[541, 541, 2/3*w^3 + 4/3*w^2 - 14/3*w - 11],\
[571, 571, -1/3*w^3 + 1/3*w^2 + 13/3*w - 1],\
[571, 571, 2*w - 1],\
[571, 571, -1/3*w^3 + 4/3*w^2 + 7/3*w - 1],\
[571, 571, 1/6*w^3 + 5/6*w^2 - 7/6*w - 13],\
[599, 599, 1/2*w^3 + 1/2*w^2 - 9/2*w - 2],\
[599, 599, -1/6*w^3 + 1/6*w^2 + 19/6*w - 2],\
[599, 599, 1/6*w^3 - 1/6*w^2 - 19/6*w],\
[599, 599, 1/2*w^3 - 3/2*w^2 - 5/2*w + 11],\
[601, 601, 1/6*w^3 + 11/6*w^2 - 7/6*w - 15],\
[601, 601, -1/3*w^3 + 7/3*w^2 - 5/3*w - 5],\
[601, 601, 2/3*w^3 + 4/3*w^2 - 26/3*w - 19],\
[601, 601, 1/2*w^3 - 5/2*w^2 - 7/2*w + 13],\
[659, 659, w^2 - 13],\
[659, 659, -5/6*w^3 + 11/6*w^2 + 29/6*w - 12],\
[659, 659, -1/6*w^3 + 7/6*w^2 + 7/6*w - 1],\
[659, 659, 5/6*w^3 + 1/6*w^2 - 41/6*w - 1],\
[691, 691, 1/2*w^3 - 1/2*w^2 - 11/2*w + 10],\
[691, 691, -1/6*w^3 + 1/6*w^2 - 5/6*w - 8],\
[701, 701, -2*w^2 + w + 11],\
[701, 701, -1/6*w^3 + 13/6*w^2 + 7/6*w - 9],\
[701, 701, -1/6*w^3 + 13/6*w^2 + 1/6*w - 16],\
[701, 701, -w^3 + w^2 + 9*w - 1],\
[709, 709, -2/3*w^3 + 11/3*w^2 + 14/3*w - 21],\
[709, 709, 1/3*w^3 + 5/3*w^2 + 2/3*w - 5],\
[709, 709, 7/6*w^3 - 25/6*w^2 - 43/6*w + 25],\
[709, 709, 2/3*w^3 - 2/3*w^2 - 23/3*w - 1],\
[719, 719, 2*w^2 - 2*w - 19],\
[719, 719, -2*w^2 + 2*w + 7],\
[739, 739, 5/6*w^3 - 5/6*w^2 - 29/6*w + 4],\
[739, 739, -5/6*w^3 + 11/6*w^2 + 53/6*w - 17],\
[739, 739, -1/6*w^3 - 5/6*w^2 - 11/6*w],\
[739, 739, -w^3 + w^2 + 8*w - 5],\
[751, 751, -1/6*w^3 + 1/6*w^2 + 25/6*w + 8],\
[751, 751, -1/3*w^3 + 1/3*w^2 + 16/3*w - 11],\
[761, 761, -2/3*w^3 + 5/3*w^2 + 8/3*w - 9],\
[761, 761, 5/6*w^3 + 1/6*w^2 - 47/6*w - 3],\
[769, 769, 1/3*w^3 - 7/3*w^2 - 7/3*w + 11],\
[769, 769, -4/3*w^3 - 8/3*w^2 + 46/3*w + 33],\
[769, 769, -1/2*w^3 + 5/2*w^2 + 5/2*w - 20],\
[769, 769, 2*w^2 - 17],\
[809, 809, 1/6*w^3 + 11/6*w^2 - 31/6*w - 15],\
[809, 809, -5/6*w^3 - 1/6*w^2 + 35/6*w + 3],\
[809, 809, 1/6*w^3 + 11/6*w^2 - 31/6*w - 9],\
[809, 809, w^3 - 2*w^2 - 7*w + 11],\
[811, 811, -1/6*w^3 - 5/6*w^2 + 25/6*w + 7],\
[811, 811, 1/6*w^3 + 5/6*w^2 - 25/6*w - 15],\
[811, 811, -1/6*w^3 - 5/6*w^2 + 25/6*w - 4],\
[811, 811, 1/6*w^3 + 5/6*w^2 - 25/6*w - 4],\
[821, 821, -1/2*w^3 - 5/2*w^2 + 13/2*w + 16],\
[821, 821, 1/6*w^3 - 13/6*w^2 - 7/6*w + 21],\
[821, 821, 3/2*w^3 + 1/2*w^2 - 35/2*w - 20],\
[821, 821, -1/6*w^3 + 13/6*w^2 + 7/6*w - 7],\
[829, 829, -1/6*w^3 + 19/6*w^2 - 11/6*w - 23],\
[829, 829, 5/6*w^3 - 17/6*w^2 - 5/6*w + 8],\
[829, 829, -4/3*w^3 - 2/3*w^2 + 43/3*w + 15],\
[829, 829, -1/6*w^3 - 17/6*w^2 + 25/6*w + 16],\
[839, 839, 1/3*w^3 - 7/3*w^2 + 2/3*w + 5],\
[839, 839, 1/2*w^3 + 3/2*w^2 - 13/2*w - 20],\
[841, 29, -5/6*w^3 + 5/6*w^2 + 35/6*w - 4],\
[859, 859, 1/6*w^3 + 5/6*w^2 - 37/6*w + 7],\
[859, 859, 13/6*w^3 + 17/6*w^2 - 127/6*w - 33],\
[881, 881, -2/3*w^3 + 2/3*w^2 + 20/3*w + 5],\
[881, 881, 17/6*w^3 + 19/6*w^2 - 167/6*w - 42],\
[911, 911, -1/6*w^3 + 13/6*w^2 - 11/6*w - 6],\
[911, 911, 3/2*w^3 + 1/2*w^2 - 33/2*w - 17],\
[911, 911, 5/6*w^3 - 17/6*w^2 + 1/6*w + 5],\
[911, 911, 7/6*w^3 - 1/6*w^2 - 61/6*w - 1],\
[929, 929, -7/6*w^3 - 11/6*w^2 + 67/6*w + 22],\
[929, 929, -1/6*w^3 + 1/6*w^2 - 11/6*w + 6],\
[941, 941, 11/6*w^3 + 19/6*w^2 - 107/6*w - 34],\
[941, 941, 4/3*w^3 - 10/3*w^2 - 25/3*w + 19],\
[941, 941, -11/6*w^3 + 41/6*w^2 + 47/6*w - 31],\
[941, 941, 1/2*w^3 + 1/2*w^2 - 13/2*w - 13],\
[961, 31, -1/3*w^3 + 1/3*w^2 + 7/3*w + 5],\
[991, 991, -1/6*w^3 - 5/6*w^2 + 25/6*w + 6],\
[991, 991, 1/6*w^3 + 5/6*w^2 - 25/6*w - 5]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^8 - 11*x^6 + 22*x^4 - 9*x^2 + 1
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, 0, -2, e^6 - 11*e^4 + 21*e^2 - 5, -7*e^7 + 75*e^5 - 133*e^3 + 29*e, -11*e^7 + 119*e^5 - 220*e^3 + 56*e, -e^7 + 11*e^5 - 21*e^3 + 3*e, 4*e^6 - 43*e^4 + 76*e^2 - 15, e^7 - 12*e^5 + 32*e^3 - 23*e, 4*e^7 - 42*e^5 + 67*e^3 - 3*e, 18*e^7 - 193*e^5 + 343*e^3 - 72*e, -6*e^7 + 64*e^5 - 111*e^3 + 17*e, 7*e^7 - 75*e^5 + 133*e^3 - 31*e, 23*e^7 - 248*e^5 + 452*e^3 - 105*e, -3*e^6 + 33*e^4 - 65*e^2 + 11, -9*e^6 + 97*e^4 - 177*e^2 + 37, e^6 - 11*e^4 + 23*e^2 - 9, 2*e^6 - 22*e^4 + 46*e^2 - 22, e^6 - 9*e^4 + 3*e^2 + 9, 6*e^7 - 63*e^5 + 100*e^3 - e, 11*e^7 - 120*e^5 + 229*e^3 - 62*e, -23*e^7 + 249*e^5 - 462*e^3 + 118*e, -16*e^6 + 173*e^4 - 318*e^2 + 71, -5*e^6 + 52*e^4 - 81*e^2 + 8, 9*e^7 - 98*e^5 + 189*e^3 - 74*e, -9*e^6 + 98*e^4 - 185*e^2 + 46, -e^6 + 13*e^4 - 39*e^2 + 19, -e^6 + 10*e^4 - 11*e^2 + 2, -26*e^7 + 278*e^5 - 489*e^3 + 99*e, -35*e^7 + 376*e^5 - 674*e^3 + 151*e, 21*e^7 - 227*e^5 + 416*e^3 - 90*e, 20*e^7 - 213*e^5 + 366*e^3 - 65*e, 11*e^7 - 117*e^5 + 197*e^3 - 9*e, 39*e^7 - 421*e^5 + 768*e^3 - 168*e, -5*e^7 + 54*e^5 - 101*e^3 + 34*e, -51*e^7 + 548*e^5 - 982*e^3 + 211*e, -15*e^7 + 163*e^5 - 308*e^3 + 92*e, 31*e^7 - 334*e^5 + 605*e^3 - 134*e, 3*e^7 - 33*e^5 + 68*e^3 - 38*e, -17*e^6 + 183*e^4 - 331*e^2 + 73, 16*e^6 - 171*e^4 + 300*e^2 - 69, -6*e^7 + 64*e^5 - 111*e^3 + 13*e, 29*e^6 - 313*e^4 + 569*e^2 - 127, 6*e^6 - 64*e^4 + 116*e^2 - 36, 17*e^6 - 185*e^4 + 345*e^2 - 69, -17*e^6 + 183*e^4 - 327*e^2 + 69, -25*e^6 + 267*e^4 - 469*e^2 + 97, 4*e^6 - 39*e^4 + 36*e^2 + 21, 20*e^6 - 216*e^4 + 398*e^2 - 96, -18*e^6 + 192*e^4 - 332*e^2 + 56, 38*e^7 - 411*e^5 + 760*e^3 - 191*e, 9*e^7 - 97*e^5 + 177*e^3 - 41*e, e^6 - 14*e^4 + 51*e^2 - 32, 14*e^6 - 151*e^4 + 276*e^2 - 65, -3*e^6 + 36*e^4 - 91*e^2 + 30, -15*e^6 + 162*e^4 - 297*e^2 + 50, 8*e^6 - 88*e^4 + 172*e^2 - 44, 16*e^6 - 174*e^4 + 324*e^2 - 82, 8*e^7 - 85*e^5 + 142*e^3 + 5*e, 31*e^6 - 330*e^4 + 569*e^2 - 116, 32*e^7 - 345*e^5 + 630*e^3 - 167*e, 10*e^6 - 108*e^4 + 198*e^2 - 46, -10*e^6 + 104*e^4 - 158*e^2 + 12, -5*e^6 + 55*e^4 - 111*e^2 + 25, 4*e^6 - 44*e^4 + 90*e^2 - 36, 20*e^6 - 216*e^4 + 400*e^2 - 100, -e^6 + 13*e^4 - 39*e^2 + 7, -20*e^6 + 216*e^4 - 394*e^2 + 90, -9*e^6 + 97*e^4 - 179*e^2 + 35, -23*e^7 + 249*e^5 - 459*e^3 + 95*e, -30*e^7 + 323*e^5 - 586*e^3 + 159*e, 26*e^7 - 280*e^5 + 511*e^3 - 137*e, 41*e^7 - 446*e^5 + 844*e^3 - 235*e, -26*e^7 + 281*e^5 - 517*e^3 + 124*e, 16*e^7 - 173*e^5 + 322*e^3 - 107*e, -9*e^6 + 100*e^4 - 201*e^2 + 54, 22*e^7 - 237*e^5 + 434*e^3 - 131*e, -3*e^4 + 22*e^2 - 3, 7*e^7 - 73*e^5 + 114*e^3 - 12*e, 6*e^6 - 67*e^4 + 134*e^2 - 25, -44*e^6 + 476*e^4 - 872*e^2 + 192, -70*e^7 + 753*e^5 - 1360*e^3 + 315*e, 14*e^7 - 153*e^5 + 297*e^3 - 108*e, 32*e^7 - 346*e^5 + 636*e^3 - 136*e, -52*e^7 + 559*e^5 - 1005*e^3 + 228*e, 12*e^7 - 131*e^5 + 257*e^3 - 108*e, 15*e^7 - 159*e^5 + 268*e^3 - 42*e, 5*e^7 - 50*e^5 + 59*e^3 + 18*e, 38*e^7 - 408*e^5 + 729*e^3 - 147*e, -37*e^6 + 398*e^4 - 717*e^2 + 168, 38*e^6 - 407*e^4 + 726*e^2 - 169, 36*e^6 - 389*e^4 + 712*e^2 - 165, 16*e^6 - 177*e^4 + 352*e^2 - 101, -5*e^7 + 53*e^5 - 87*e^3 - 19*e, -46*e^7 + 495*e^5 - 894*e^3 + 207*e, -96*e^7 + 1034*e^5 - 1872*e^3 + 420*e, 3*e^7 - 30*e^5 + 33*e^3 + 44*e, -68*e^7 + 732*e^5 - 1326*e^3 + 320*e, 23*e^6 - 244*e^4 + 419*e^2 - 100, -22*e^7 + 237*e^5 - 428*e^3 + 91*e, -23*e^6 + 246*e^4 - 431*e^2 + 90, -4*e^7 + 46*e^5 - 112*e^3 + 86*e, 73*e^7 - 787*e^5 + 1432*e^3 - 334*e, 16*e^6 - 172*e^4 + 312*e^2 - 60, 31*e^6 - 336*e^4 + 625*e^2 - 148, -41*e^7 + 440*e^5 - 782*e^3 + 135*e, 53*e^7 - 575*e^5 + 1075*e^3 - 281*e, 16*e^7 - 169*e^5 + 278*e^3 - 33*e, 63*e^7 - 675*e^5 + 1195*e^3 - 251*e, -36*e^6 + 385*e^4 - 680*e^2 + 145, 17*e^7 - 185*e^5 + 354*e^3 - 124*e, -40*e^7 + 437*e^5 - 840*e^3 + 241*e, -7*e^6 + 68*e^4 - 67*e^2 - 32, -21*e^6 + 225*e^4 - 399*e^2 + 103, -78*e^7 + 838*e^5 - 1503*e^3 + 343*e, -41*e^6 + 443*e^4 - 807*e^2 + 177, -19*e^7 + 205*e^5 - 372*e^3 + 58*e, 9*e^6 - 97*e^4 + 175*e^2 - 55, 5*e^6 - 57*e^4 + 125*e^2 - 37, -17*e^7 + 182*e^5 - 320*e^3 + 65*e, -34*e^6 + 367*e^4 - 672*e^2 + 145, 36*e^7 - 383*e^5 + 660*e^3 - 127*e, -4*e^6 + 44*e^4 - 82*e^2 - 4, 23*e^7 - 244*e^5 + 413*e^3 - 58*e, 91*e^7 - 981*e^5 + 1781*e^3 - 393*e, 54*e^7 - 584*e^5 + 1080*e^3 - 284*e, 18*e^7 - 193*e^5 + 342*e^3 - 73*e, -68*e^7 + 729*e^5 - 1298*e^3 + 285*e, -78*e^7 + 840*e^5 - 1525*e^3 + 375*e, -33*e^6 + 355*e^4 - 639*e^2 + 141, -23*e^7 + 246*e^5 - 431*e^3 + 88*e, -16*e^7 + 166*e^5 - 246*e^3 - 36*e, 15*e^6 - 158*e^4 + 261*e^2 - 54, -33*e^6 + 355*e^4 - 641*e^2 + 119, -22*e^6 + 234*e^4 - 398*e^2 + 78, -107*e^7 + 1150*e^5 - 2063*e^3 + 446*e, 20*e^7 - 219*e^5 + 424*e^3 - 119*e, 44*e^6 - 470*e^4 + 826*e^2 - 194, 46*e^7 - 494*e^5 + 880*e^3 - 170*e, -84*e^7 + 906*e^5 - 1650*e^3 + 378*e, 38*e^6 - 405*e^4 + 698*e^2 - 149, -80*e^7 + 862*e^5 - 1571*e^3 + 403*e, 17*e^6 - 181*e^4 + 309*e^2 - 59, -34*e^7 + 368*e^5 - 685*e^3 + 189*e, -22*e^6 + 242*e^4 - 482*e^2 + 128, 37*e^7 - 396*e^5 + 692*e^3 - 97*e, 5*e^6 - 51*e^4 + 63*e^2 + 15, 31*e^6 - 336*e^4 + 627*e^2 - 158, -8*e^7 + 90*e^5 - 198*e^3 + 100*e, 55*e^7 - 593*e^5 + 1082*e^3 - 262*e, -5*e^6 + 55*e^4 - 103*e^2 - 17, -9*e^7 + 92*e^5 - 127*e^3 - 26*e, 27*e^6 - 295*e^4 + 559*e^2 - 137, 54*e^7 - 580*e^5 + 1034*e^3 - 198*e, 48*e^7 - 516*e^5 + 929*e^3 - 227*e, -12*e^7 + 130*e^5 - 238*e^3 + 38*e, 34*e^7 - 367*e^5 + 671*e^3 - 172*e, 19*e^6 - 207*e^4 + 393*e^2 - 113, 12*e^6 - 132*e^4 + 258*e^2 - 54, -2*e^6 + 17*e^4 - 21, 7*e^7 - 79*e^5 + 172*e^3 - 60*e, 45*e^7 - 476*e^5 + 794*e^3 - 111*e, -31*e^6 + 332*e^4 - 589*e^2 + 102, -23*e^6 + 247*e^4 - 439*e^2 + 93, -58*e^7 + 628*e^5 - 1165*e^3 + 303*e, 5*e^7 - 63*e^5 + 190*e^3 - 136*e, -14*e^7 + 144*e^5 - 207*e^3 - 15*e, 69*e^7 - 740*e^5 + 1315*e^3 - 260*e, -2*e^6 + 20*e^4 - 24*e^2 - 12, -41*e^6 + 438*e^4 - 769*e^2 + 142, -154*e^7 + 1655*e^5 - 2973*e^3 + 654*e, 35*e^6 - 376*e^4 + 681*e^2 - 170, 25*e^7 - 274*e^5 + 536*e^3 - 177*e, 29*e^6 - 316*e^4 + 601*e^2 - 140, 46*e^6 - 492*e^4 + 864*e^2 - 176, -74*e^7 + 793*e^5 - 1405*e^3 + 278*e, -72*e^7 + 775*e^5 - 1399*e^3 + 280*e]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([4,2,1/3*w^3 + 2/3*w^2 - 10/3*w - 7])] = -1

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