/*
  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([-2, -8, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([8, 4, 3*w^2 - 4*w - 22])

primes_array = [
[2, 2, -w],\
[2, 2, w^2 - 2*w - 5],\
[5, 5, w^2 + 3*w + 1],\
[7, 7, -2*w^2 + 2*w + 17],\
[7, 7, -w^2 + w + 9],\
[13, 13, 2*w + 1],\
[25, 5, -3*w^2 + 5*w + 19],\
[27, 3, 3],\
[29, 29, w^2 + w - 1],\
[31, 31, w^2 - w - 1],\
[37, 37, 2*w^2 + 6*w + 3],\
[41, 41, -6*w^2 - 14*w - 3],\
[53, 53, -4*w^2 + 6*w + 27],\
[59, 59, 2*w^2 - 4*w - 11],\
[61, 61, w^2 - w - 3],\
[61, 61, -2*w^2 + 2*w + 13],\
[73, 73, w^2 + 3*w + 3],\
[97, 97, w^2 + w - 15],\
[101, 101, w^2 + 3*w - 1],\
[101, 101, w^2 - w - 11],\
[101, 101, 2*w - 5],\
[103, 103, 3*w^2 - 3*w - 23],\
[103, 103, -w^2 + w - 1],\
[103, 103, 2*w - 3],\
[107, 107, 5*w^2 - 7*w - 37],\
[127, 127, w^2 + w - 5],\
[139, 139, -4*w^2 + 10*w + 13],\
[149, 149, 5*w^2 + 13*w + 5],\
[149, 149, w^2 - 3*w - 7],\
[149, 149, 5*w^2 + 11*w + 3],\
[151, 151, w^2 - 3*w - 9],\
[151, 151, 5*w^2 - 7*w - 35],\
[151, 151, 6*w + 1],\
[163, 163, -2*w^2 + 2*w + 19],\
[169, 13, 4*w^2 - 6*w - 29],\
[173, 173, 3*w^2 - w - 33],\
[173, 173, 2*w^2 - 4*w - 17],\
[173, 173, -6*w^2 - 14*w - 1],\
[179, 179, -4*w^2 - 8*w - 1],\
[181, 181, -2*w^2 - 2*w + 1],\
[181, 181, w^2 + 5*w + 3],\
[181, 181, -4*w^2 - 8*w + 1],\
[191, 191, 3*w^2 + 7*w + 3],\
[191, 191, 4*w^2 - 6*w - 31],\
[191, 191, 4*w^2 - 4*w - 33],\
[193, 193, -4*w - 3],\
[223, 223, -2*w^2 - 2*w + 3],\
[227, 227, 7*w^2 + 19*w + 5],\
[229, 229, -w^2 + 7*w + 1],\
[233, 233, -2*w - 7],\
[239, 239, 2*w^2 - 4*w - 15],\
[241, 241, -3*w^2 + 5*w + 17],\
[251, 251, -6*w^2 + 12*w + 31],\
[257, 257, 4*w^2 - 4*w - 31],\
[263, 263, 9*w^2 - 11*w - 67],\
[269, 269, 2*w^2 + 6*w + 5],\
[271, 271, 2*w^2 - 4*w - 5],\
[271, 271, -4*w + 13],\
[271, 271, -2*w^2 - 8*w - 7],\
[277, 277, -3*w^2 + 3*w + 19],\
[281, 281, -6*w^2 + 10*w + 37],\
[283, 283, 2*w^2 + 4*w - 3],\
[283, 283, 2*w^2 + 8*w + 3],\
[283, 283, -3*w^2 - 7*w + 1],\
[293, 293, w^2 - 7*w - 3],\
[307, 307, -2*w^2 - 1],\
[311, 311, 7*w^2 - 9*w - 51],\
[317, 317, -w^2 - 3*w + 23],\
[317, 317, 2*w^2 - 6*w - 7],\
[317, 317, 7*w^2 + 19*w + 7],\
[331, 331, -3*w^2 - 9*w - 1],\
[331, 331, w^2 - w - 13],\
[331, 331, 2*w^2 - 23],\
[337, 337, 2*w^2 + 4*w + 3],\
[347, 347, 2*w^2 + 8*w + 1],\
[353, 353, 2*w^2 - 2*w - 9],\
[373, 373, w^2 - 7*w + 13],\
[379, 379, w^2 + w - 9],\
[383, 383, w^2 + 3*w + 5],\
[389, 389, -w^2 + w - 3],\
[401, 401, -4*w^2 - 8*w + 3],\
[409, 409, 2*w^2 - 3],\
[409, 409, w^2 - 5*w - 5],\
[409, 409, 5*w^2 - 5*w - 41],\
[419, 419, 6*w^2 - 8*w - 49],\
[421, 421, w^2 + w - 11],\
[431, 431, 4*w^2 - 8*w - 19],\
[443, 443, 2*w^2 - 5],\
[457, 457, -2*w^2 + 2*w - 1],\
[461, 461, 2*w^2 - 13],\
[463, 463, 2*w^2 - 2*w - 7],\
[467, 467, 2*w^2 + 8*w + 9],\
[479, 479, -2*w^2 - 6*w + 1],\
[479, 479, 3*w^2 - w - 15],\
[479, 479, 12*w^2 - 14*w - 95],\
[487, 487, -6*w^2 + 14*w + 23],\
[491, 491, 11*w^2 - 13*w - 85],\
[521, 521, -5*w^2 + 11*w + 21],\
[521, 521, 4*w - 3],\
[521, 521, 8*w + 1],\
[523, 523, -10*w^2 + 14*w + 73],\
[541, 541, 3*w^2 - w - 19],\
[547, 547, 11*w^2 + 25*w + 1],\
[547, 547, 3*w^2 - 5*w - 15],\
[547, 547, 7*w^2 - 7*w - 59],\
[557, 557, -3*w^2 + 7*w + 7],\
[571, 571, 4*w^2 + 10*w + 5],\
[587, 587, 2*w^2 - 6*w - 9],\
[599, 599, -9*w^2 + 17*w + 49],\
[599, 599, -3*w^2 + 3*w + 17],\
[599, 599, 8*w^2 + 18*w + 5],\
[601, 601, 19*w^2 - 25*w - 143],\
[617, 617, 7*w^2 - 9*w - 57],\
[619, 619, 3*w^2 - 7*w - 15],\
[619, 619, w^2 - 5*w - 7],\
[619, 619, -2*w - 9],\
[641, 641, -w^2 + 3*w - 5],\
[643, 643, 7*w^2 - 7*w - 61],\
[647, 647, -7*w^2 + 11*w + 45],\
[653, 653, -8*w^2 - 16*w - 3],\
[659, 659, w^2 - 3*w - 15],\
[673, 673, w^2 + 3*w - 5],\
[683, 683, -7*w^2 - 15*w - 1],\
[701, 701, 3*w^2 + 3*w - 5],\
[709, 709, -3*w^2 - 5*w - 3],\
[733, 733, -6*w - 5],\
[743, 743, -2*w^2 - 2*w - 3],\
[743, 743, 4*w - 5],\
[743, 743, 6*w^2 - 6*w - 49],\
[751, 751, -6*w^2 - 12*w + 1],\
[757, 757, w^2 - 5*w - 9],\
[757, 757, -w^2 - w - 5],\
[757, 757, 4*w^2 - 8*w - 23],\
[773, 773, -8*w^2 + 14*w + 47],\
[787, 787, 8*w^2 - 10*w - 65],\
[797, 797, 9*w^2 - 13*w - 65],\
[811, 811, 6*w^2 - 8*w - 41],\
[821, 821, 6*w^2 - 6*w - 53],\
[823, 823, -4*w^2 - 6*w + 1],\
[823, 823, 9*w^2 + 19*w + 5],\
[823, 823, w^2 - 7*w - 5],\
[827, 827, -3*w^2 - 3*w + 47],\
[829, 829, -4*w^2 + 4*w + 37],\
[841, 29, 5*w^2 - 9*w - 27],\
[853, 853, 11*w^2 - 15*w - 79],\
[857, 857, -9*w^2 + 21*w + 35],\
[863, 863, 3*w^2 + 11*w + 5],\
[877, 877, 4*w - 7],\
[881, 881, -3*w^2 + w - 1],\
[887, 887, 2*w^2 - 19],\
[911, 911, -8*w^2 + 6*w + 75],\
[919, 919, 10*w^2 + 22*w - 1],\
[929, 929, -4*w^2 - 6*w + 3],\
[937, 937, 3*w^2 + 11*w + 7],\
[947, 947, -6*w - 7],\
[947, 947, 10*w^2 - 12*w - 81],\
[947, 947, 2*w^2 - 10*w - 5],\
[953, 953, 3*w^2 - w - 13],\
[961, 31, 7*w^2 - 9*w - 49],\
[967, 967, 6*w^2 - 14*w - 25],\
[983, 983, -10*w^2 - 22*w - 1],\
[991, 991, 3*w^2 - w - 21],\
[997, 997, 3*w^2 - 5*w - 5],\
[997, 997, -2*w^2 - 10*w - 1],\
[997, 997, -8*w + 27]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^7 - x^6 - 10*x^5 + 8*x^4 + 24*x^3 - 15*x^2 - 13*x + 8
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [0, e, 4*e^6 - e^5 - 41*e^4 + 2*e^3 + 100*e^2 + 9*e - 48, 5*e^6 - e^5 - 52*e^4 + 130*e^2 + 17*e - 65, -2*e^6 + e^5 + 20*e^4 - 5*e^3 - 47*e^2 + 23, -e^6 + e^5 + 10*e^4 - 7*e^3 - 23*e^2 + 7*e + 10, 5*e^6 - e^5 - 51*e^4 - e^3 + 123*e^2 + 22*e - 60, -10*e^6 + 3*e^5 + 102*e^4 - 9*e^3 - 245*e^2 - 20*e + 113, e^6 - 10*e^4 - 3*e^3 + 23*e^2 + 13*e - 11, -11*e^6 + 4*e^5 + 111*e^4 - 16*e^3 - 262*e^2 - 12*e + 120, 8*e^6 - 3*e^5 - 81*e^4 + 11*e^3 + 193*e^2 + 15*e - 90, e^6 - e^5 - 8*e^4 + 6*e^3 + 8*e^2 - 5*e + 5, 15*e^6 - 6*e^5 - 151*e^4 + 25*e^3 + 355*e^2 + 16*e - 157, 10*e^6 - 3*e^5 - 103*e^4 + 8*e^3 + 254*e^2 + 25*e - 125, 12*e^6 - 4*e^5 - 123*e^4 + 13*e^3 + 299*e^2 + 25*e - 135, 17*e^6 - 4*e^5 - 175*e^4 + 7*e^3 + 427*e^2 + 44*e - 199, 13*e^6 - 4*e^5 - 133*e^4 + 11*e^3 + 323*e^2 + 38*e - 157, -14*e^6 + 5*e^5 + 141*e^4 - 19*e^3 - 329*e^2 - 19*e + 144, 6*e^6 - 2*e^5 - 62*e^4 + 6*e^3 + 152*e^2 + 16*e - 68, e^5 - e^4 - 9*e^3 + 5*e^2 + 13*e - 2, -4*e^6 + 2*e^5 + 41*e^4 - 11*e^3 - 99*e^2 + 7*e + 41, -e^6 - 2*e^5 + 12*e^4 + 19*e^3 - 37*e^2 - 31*e + 22, -24*e^6 + 8*e^5 + 244*e^4 - 28*e^3 - 582*e^2 - 42*e + 262, 6*e^6 - e^5 - 63*e^4 + 160*e^2 + 17*e - 77, -11*e^6 + 4*e^5 + 112*e^4 - 15*e^3 - 269*e^2 - 15*e + 118, 5*e^6 - e^5 - 54*e^4 + 144*e^2 + 21*e - 77, -24*e^6 + 7*e^5 + 245*e^4 - 20*e^3 - 586*e^2 - 45*e + 261, -18*e^6 + 4*e^5 + 185*e^4 - 4*e^3 - 452*e^2 - 55*e + 219, 22*e^6 - 6*e^5 - 226*e^4 + 14*e^3 + 548*e^2 + 52*e - 250, -23*e^6 + 9*e^5 + 232*e^4 - 39*e^3 - 545*e^2 - 21*e + 242, -18*e^6 + 4*e^5 + 184*e^4 - 4*e^3 - 442*e^2 - 52*e + 206, 22*e^6 - 6*e^5 - 226*e^4 + 16*e^3 + 548*e^2 + 46*e - 248, 18*e^6 - 4*e^5 - 186*e^4 + 2*e^3 + 460*e^2 + 62*e - 224, -3*e^6 + 29*e^4 + 6*e^3 - 56*e^2 - 22*e + 14, 6*e^6 - e^5 - 63*e^4 - e^3 + 159*e^2 + 25*e - 84, -36*e^6 + 9*e^5 + 371*e^4 - 15*e^3 - 909*e^2 - 105*e + 438, -24*e^6 + 6*e^5 + 246*e^4 - 9*e^3 - 595*e^2 - 74*e + 285, -30*e^6 + 9*e^5 + 307*e^4 - 26*e^3 - 742*e^2 - 67*e + 346, 6*e^6 - 4*e^5 - 58*e^4 + 24*e^3 + 126*e^2 - 20*e - 50, -14*e^6 + 3*e^5 + 144*e^4 - e^3 - 353*e^2 - 48*e + 173, 3*e^6 + e^5 - 35*e^4 - 13*e^3 + 105*e^2 + 32*e - 64, 37*e^6 - 11*e^5 - 377*e^4 + 32*e^3 + 902*e^2 + 74*e - 420, 27*e^6 - 7*e^5 - 278*e^4 + 14*e^3 + 680*e^2 + 71*e - 331, 20*e^6 - 6*e^5 - 204*e^4 + 16*e^3 + 492*e^2 + 50*e - 236, -34*e^6 + 10*e^5 + 346*e^4 - 26*e^3 - 828*e^2 - 80*e + 390, -16*e^6 + 5*e^5 + 163*e^4 - 15*e^3 - 389*e^2 - 37*e + 178, -4*e^6 + e^5 + 39*e^4 - 2*e^3 - 80*e^2 - 3*e + 13, -16*e^6 + 8*e^5 + 162*e^4 - 42*e^3 - 386*e^2 + 2*e + 182, -29*e^6 + 8*e^5 + 298*e^4 - 19*e^3 - 727*e^2 - 75*e + 334, -4*e^6 + e^5 + 42*e^4 - 3*e^3 - 107*e^2 + 2*e + 54, -37*e^6 + 13*e^5 + 378*e^4 - 50*e^3 - 912*e^2 - 51*e + 417, 30*e^6 - 10*e^5 - 306*e^4 + 34*e^3 + 734*e^2 + 60*e - 328, 19*e^6 - 5*e^5 - 194*e^4 + 10*e^3 + 464*e^2 + 55*e - 219, 21*e^6 - 5*e^5 - 213*e^4 + 7*e^3 + 505*e^2 + 58*e - 224, 18*e^6 - 4*e^5 - 184*e^4 + 4*e^3 + 442*e^2 + 60*e - 198, -16*e^6 + 4*e^5 + 164*e^4 - 8*e^3 - 396*e^2 - 36*e + 190, -15*e^6 + 4*e^5 + 150*e^4 - 9*e^3 - 345*e^2 - 39*e + 154, -9*e^6 + 4*e^5 + 91*e^4 - 18*e^3 - 220*e^2 - 2*e + 118, 5*e^6 - e^5 - 50*e^4 + 116*e^2 + 11*e - 49, 7*e^6 - 3*e^5 - 73*e^4 + 15*e^3 + 181*e^2 - 70, 24*e^6 - 7*e^5 - 243*e^4 + 17*e^3 + 573*e^2 + 65*e - 266, 3*e^6 + 2*e^5 - 33*e^4 - 20*e^3 + 86*e^2 + 34*e - 34, 33*e^6 - 8*e^5 - 340*e^4 + 13*e^3 + 831*e^2 + 93*e - 404, 7*e^6 - 2*e^5 - 70*e^4 + 3*e^3 + 159*e^2 + 31*e - 60, -14*e^6 + 3*e^5 + 144*e^4 - 3*e^3 - 353*e^2 - 38*e + 171, 23*e^6 - 9*e^5 - 232*e^4 + 38*e^3 + 544*e^2 + 15*e - 247, 4*e^6 - e^5 - 39*e^4 - 2*e^3 + 86*e^2 + 31*e - 31, -7*e^6 + 2*e^5 + 69*e^4 - 2*e^3 - 154*e^2 - 32*e + 66, 19*e^6 - 3*e^5 - 195*e^4 - 6*e^3 + 472*e^2 + 74*e - 230, 10*e^6 - 6*e^5 - 99*e^4 + 35*e^3 + 223*e^2 - 27*e - 91, -41*e^6 + 14*e^5 + 416*e^4 - 49*e^3 - 993*e^2 - 71*e + 454, 25*e^6 - 9*e^5 - 252*e^4 + 34*e^3 + 588*e^2 + 33*e - 259, -16*e^6 + 2*e^5 + 166*e^4 + 8*e^3 - 410*e^2 - 54*e + 202, 36*e^6 - 10*e^5 - 367*e^4 + 25*e^3 + 879*e^2 + 87*e - 407, -46*e^6 + 14*e^5 + 470*e^4 - 40*e^3 - 1134*e^2 - 106*e + 532, 29*e^6 - 9*e^5 - 293*e^4 + 30*e^3 + 686*e^2 + 44*e - 302, 32*e^6 - 11*e^5 - 325*e^4 + 40*e^3 + 778*e^2 + 47*e - 365, -e^6 + e^5 + 8*e^4 - 8*e^3 - 10*e^2 + 9*e + 17, -20*e^6 + 8*e^5 + 204*e^4 - 36*e^3 - 492*e^2 - 4*e + 228, -18*e^6 + 4*e^5 + 187*e^4 - 4*e^3 - 464*e^2 - 53*e + 217, -23*e^6 + 5*e^5 + 235*e^4 - 5*e^3 - 563*e^2 - 72*e + 250, 10*e^6 - 4*e^5 - 102*e^4 + 18*e^3 + 246*e^2 + 6*e - 114, 11*e^6 - 4*e^5 - 110*e^4 + 15*e^3 + 253*e^2 + 23*e - 97, 26*e^6 - 7*e^5 - 263*e^4 + 13*e^3 + 619*e^2 + 71*e - 276, -14*e^6 + 6*e^5 + 140*e^4 - 26*e^3 - 326*e^2 - 16*e + 144, 15*e^6 - e^5 - 155*e^4 - 20*e^3 + 382*e^2 + 90*e - 176, -5*e^6 + 53*e^4 + 10*e^3 - 134*e^2 - 32*e + 64, 23*e^6 - 4*e^5 - 238*e^4 - 3*e^3 + 581*e^2 + 75*e - 278, -17*e^6 + 2*e^5 + 182*e^4 + 11*e^3 - 481*e^2 - 71*e + 262, -e^6 + e^5 + 11*e^4 - 11*e^3 - 29*e^2 + 34*e + 20, 6*e^6 - 4*e^5 - 60*e^4 + 26*e^3 + 142*e^2 - 26*e - 64, 52*e^6 - 18*e^5 - 530*e^4 + 64*e^3 + 1272*e^2 + 98*e - 588, 30*e^6 - 12*e^5 - 298*e^4 + 50*e^3 + 678*e^2 + 30*e - 284, -3*e^6 - e^5 + 30*e^4 + 16*e^3 - 62*e^2 - 31*e - 1, -41*e^6 + 13*e^5 + 416*e^4 - 44*e^3 - 988*e^2 - 65*e + 449, -13*e^6 + 5*e^5 + 132*e^4 - 20*e^3 - 318*e^2 - 15*e + 149, 8*e^6 - 6*e^5 - 80*e^4 + 38*e^3 + 188*e^2 - 22*e - 100, -15*e^6 + 9*e^5 + 151*e^4 - 51*e^3 - 353*e^2 + 20*e + 146, 25*e^6 - 7*e^5 - 257*e^4 + 19*e^3 + 629*e^2 + 64*e - 306, 15*e^6 - 4*e^5 - 153*e^4 + 4*e^3 + 370*e^2 + 56*e - 176, 32*e^6 - 14*e^5 - 322*e^4 + 64*e^3 + 756*e^2 + 18*e - 330, -23*e^6 + 5*e^5 + 236*e^4 - 2*e^3 - 568*e^2 - 87*e + 265, -19*e^6 + 8*e^5 + 191*e^4 - 34*e^3 - 438*e^2 - 24*e + 168, -21*e^6 + 11*e^5 + 208*e^4 - 58*e^3 - 474*e^2 + 19*e + 207, -36*e^6 + 8*e^5 + 372*e^4 - 8*e^3 - 922*e^2 - 108*e + 462, 18*e^6 - 6*e^5 - 184*e^4 + 22*e^3 + 446*e^2 + 12*e - 226, -9*e^6 + 2*e^5 + 90*e^4 - e^3 - 203*e^2 - 35*e + 102, -24*e^6 + 6*e^5 + 244*e^4 - 6*e^3 - 580*e^2 - 84*e + 264, -47*e^6 + 14*e^5 + 480*e^4 - 41*e^3 - 1151*e^2 - 99*e + 524, 39*e^6 - 15*e^5 - 392*e^4 + 62*e^3 + 912*e^2 + 45*e - 407, -9*e^6 + 4*e^5 + 91*e^4 - 22*e^3 - 208*e^2 + 18*e + 74, -29*e^6 + 6*e^5 + 298*e^4 - 5*e^3 - 721*e^2 - 75*e + 326, -9*e^6 + 2*e^5 + 93*e^4 - 3*e^3 - 219*e^2 - 24*e + 81, -e^6 - 2*e^5 + 13*e^4 + 18*e^3 - 50*e^2 - 20*e + 44, 36*e^6 - 14*e^5 - 364*e^4 + 56*e^3 + 860*e^2 + 42*e - 370, 2*e^5 - 16*e^3 - 8*e^2 + 10*e + 34, -37*e^6 + 16*e^5 + 371*e^4 - 72*e^3 - 866*e^2 - 28*e + 386, -17*e^6 + 4*e^5 + 173*e^4 - 4*e^3 - 416*e^2 - 56*e + 218, -33*e^6 + 8*e^5 + 337*e^4 - 8*e^3 - 812*e^2 - 112*e + 392, -64*e^6 + 19*e^5 + 655*e^4 - 49*e^3 - 1587*e^2 - 179*e + 758, -39*e^6 + 14*e^5 + 391*e^4 - 48*e^3 - 906*e^2 - 76*e + 396, 17*e^6 - 5*e^5 - 175*e^4 + 14*e^3 + 420*e^2 + 36*e - 164, -7*e^6 + 5*e^5 + 72*e^4 - 30*e^3 - 184*e^2 + 21*e + 95, 8*e^6 - 3*e^5 - 78*e^4 + 5*e^3 + 173*e^2 + 42*e - 70, -10*e^6 + 2*e^5 + 106*e^4 + 2*e^3 - 280*e^2 - 56*e + 156, -16*e^6 + 4*e^5 + 164*e^4 - 10*e^3 - 398*e^2 - 26*e + 198, 27*e^6 - 10*e^5 - 278*e^4 + 39*e^3 + 685*e^2 + 33*e - 322, 47*e^6 - 14*e^5 - 480*e^4 + 37*e^3 + 1159*e^2 + 111*e - 540, 73*e^6 - 23*e^5 - 744*e^4 + 66*e^3 + 1788*e^2 + 177*e - 841, -12*e^6 + 6*e^5 + 122*e^4 - 30*e^3 - 296*e^2 + 4*e + 146, 30*e^6 - 8*e^5 - 307*e^4 + 15*e^3 + 741*e^2 + 103*e - 341, 6*e^6 - 4*e^5 - 62*e^4 + 25*e^3 + 163*e^2 - 24*e - 107, -79*e^6 + 27*e^5 + 804*e^4 - 94*e^3 - 1926*e^2 - 137*e + 883, -18*e^6 + 8*e^5 + 183*e^4 - 44*e^3 - 436*e^2 + 19*e + 201, -34*e^6 + 12*e^5 + 348*e^4 - 48*e^3 - 846*e^2 - 32*e + 402, -12*e^6 + 2*e^5 + 128*e^4 + 4*e^3 - 336*e^2 - 46*e + 178, -30*e^6 + 6*e^5 + 308*e^4 - 6*e^3 - 750*e^2 - 78*e + 384, 23*e^6 - 7*e^5 - 235*e^4 + 23*e^3 + 563*e^2 + 44*e - 248, -51*e^6 + 19*e^5 + 516*e^4 - 76*e^3 - 1226*e^2 - 51*e + 559, -22*e^6 + 4*e^5 + 222*e^4 + 6*e^3 - 522*e^2 - 92*e + 250, -25*e^6 + 2*e^5 + 261*e^4 + 26*e^3 - 660*e^2 - 116*e + 352, -6*e^6 + 2*e^5 + 64*e^4 - 12*e^3 - 160*e^2 + 8*e + 50, 2*e^6 - 2*e^5 - 21*e^4 + 15*e^3 + 57*e^2 - 3*e - 41, -34*e^6 + 12*e^5 + 343*e^4 - 41*e^3 - 805*e^2 - 65*e + 359, -9*e^6 + 3*e^5 + 97*e^4 - 17*e^3 - 257*e^2 + 10*e + 132, 26*e^6 - 16*e^5 - 259*e^4 + 93*e^3 + 605*e^2 - 47*e - 273, -27*e^6 + 8*e^5 + 270*e^4 - 21*e^3 - 623*e^2 - 61*e + 272, 39*e^6 - 16*e^5 - 394*e^4 + 69*e^3 + 937*e^2 + 29*e - 428, -23*e^6 + 5*e^5 + 232*e^4 + e^3 - 551*e^2 - 89*e + 282, 11*e^6 - 6*e^5 - 110*e^4 + 35*e^3 + 253*e^2 - 15*e - 118, 41*e^6 - 16*e^5 - 418*e^4 + 69*e^3 + 1001*e^2 + 37*e - 448, 63*e^6 - 19*e^5 - 642*e^4 + 54*e^3 + 1546*e^2 + 137*e - 705, -e^6 - 2*e^5 + 7*e^4 + 23*e^3 + 3*e^2 - 42*e - 11, -81*e^6 + 29*e^5 + 823*e^4 - 109*e^3 - 1961*e^2 - 122*e + 886, -2*e^6 + 2*e^5 + 18*e^4 - 14*e^3 - 28*e^2 + 22*e - 16, 13*e^6 + 3*e^5 - 140*e^4 - 48*e^3 + 360*e^2 + 125*e - 165, 77*e^6 - 22*e^5 - 783*e^4 + 54*e^3 + 1874*e^2 + 182*e - 874, -e^5 - e^4 + 10*e^3 + 8*e^2 - 19*e - 16, 25*e^6 - 13*e^5 - 249*e^4 + 67*e^3 + 563*e^2 - 2*e - 216, -42*e^6 + 16*e^5 + 428*e^4 - 64*e^3 - 1032*e^2 - 54*e + 474, 17*e^6 - e^5 - 178*e^4 - 26*e^3 + 452*e^2 + 113*e - 229, -54*e^6 + 18*e^5 + 544*e^4 - 58*e^3 - 1278*e^2 - 108*e + 580, 10*e^6 - e^5 - 103*e^4 - 6*e^3 + 252*e^2 + 29*e - 122, -10*e^6 + 4*e^5 + 99*e^4 - 15*e^3 - 221*e^2 - 19*e + 91, -19*e^6 + 3*e^5 + 199*e^4 + 7*e^3 - 511*e^2 - 74*e + 276]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

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

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