/*
  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([8, -12, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([3, 3, -1/2*w^2 + 1/2*w + 7])

primes_array = [
[2, 2, -1/2*w^2 - 1/2*w + 4],\
[2, 2, -w^2 + 11],\
[3, 3, -1/2*w^2 + 1/2*w + 7],\
[5, 5, -3/2*w^2 - 1/2*w + 15],\
[9, 3, -1/2*w^2 + 5/2*w - 1],\
[25, 5, 7/2*w^2 - 31/2*w + 9],\
[29, 29, -5/2*w^2 + 1/2*w + 29],\
[41, 41, -w^2 + 3*w - 1],\
[41, 41, -1/2*w^2 - 3/2*w + 3],\
[41, 41, 2*w + 7],\
[43, 43, -7/2*w^2 - 1/2*w + 37],\
[43, 43, 1/2*w^2 - 9/2*w + 3],\
[43, 43, 1/2*w^2 - 1/2*w + 1],\
[47, 47, -w^2 + w + 15],\
[53, 53, -2*w^2 + 2*w + 29],\
[59, 59, w^2 - w - 13],\
[67, 67, -1/2*w^2 + 1/2*w + 9],\
[71, 71, 2*w - 3],\
[73, 73, 3/2*w^2 - 11/2*w + 1],\
[79, 79, -3/2*w^2 + 15/2*w - 5],\
[97, 97, 3*w^2 - w - 35],\
[101, 101, 2*w - 5],\
[103, 103, 5/2*w^2 + 3/2*w - 23],\
[107, 107, 1/2*w^2 - 5/2*w - 1],\
[109, 109, -2*w - 1],\
[109, 109, -4*w^2 + 16*w - 9],\
[109, 109, 5*w^2 - 21*w + 11],\
[131, 131, w^2 + w - 5],\
[137, 137, 7*w^2 - 31*w + 17],\
[137, 137, 3*w^2 + 3*w - 23],\
[137, 137, 2*w^2 - 25],\
[139, 139, 2*w^2 - 21],\
[151, 151, w^2 - w - 7],\
[157, 157, 14*w^2 - 60*w + 33],\
[163, 163, -2*w - 3],\
[167, 167, 3/2*w^2 + 1/2*w - 17],\
[173, 173, -1/2*w^2 + 5/2*w - 5],\
[181, 181, -5/2*w^2 + 21/2*w - 7],\
[181, 181, w^2 + 3*w + 1],\
[181, 181, w^2 + 5*w + 5],\
[191, 191, 1/2*w^2 - 5/2*w - 13],\
[193, 193, -w^2 + 3*w - 3],\
[197, 197, 1/2*w^2 + 3/2*w - 7],\
[197, 197, -2*w^2 + 10*w - 5],\
[197, 197, -9/2*w^2 + 1/2*w + 51],\
[199, 199, 2*w - 9],\
[199, 199, 3/2*w^2 - 3/2*w - 13],\
[199, 199, w^2 + w - 11],\
[227, 227, -1/2*w^2 - 3/2*w - 3],\
[233, 233, -1/2*w^2 + 1/2*w - 3],\
[233, 233, -10*w^2 + 44*w - 25],\
[233, 233, 5*w^2 - 21*w + 9],\
[241, 241, 7/2*w^2 - 27/2*w + 3],\
[251, 251, w^2 - w - 3],\
[251, 251, 9/2*w^2 - 37/2*w + 9],\
[251, 251, -9/2*w^2 + 9/2*w + 65],\
[257, 257, 1/2*w^2 - 1/2*w - 11],\
[263, 263, -3*w^2 + 13*w - 9],\
[269, 269, 3/2*w^2 - 3/2*w - 23],\
[271, 271, 4*w^2 - 45],\
[277, 277, -1/2*w^2 + 9/2*w - 5],\
[307, 307, -w^2 + 5*w - 7],\
[311, 311, 13/2*w^2 - 57/2*w + 15],\
[313, 313, -9/2*w^2 + 41/2*w - 13],\
[317, 317, 4*w - 1],\
[331, 331, -w^2 - w - 1],\
[337, 337, 5/2*w^2 - 21/2*w + 3],\
[343, 7, -7],\
[347, 347, 3*w^2 - 11*w + 5],\
[353, 353, -21/2*w^2 + 89/2*w - 25],\
[359, 359, 9/2*w^2 - 5/2*w - 57],\
[367, 367, 9/2*w^2 - 5/2*w - 59],\
[379, 379, 4*w^2 - 18*w + 9],\
[379, 379, -9/2*w^2 + 37/2*w - 11],\
[379, 379, -3/2*w^2 + 3/2*w + 1],\
[383, 383, 5*w^2 - w - 61],\
[397, 397, -5/2*w^2 + 25/2*w - 13],\
[401, 401, -9*w^2 + 39*w - 23],\
[419, 419, 11*w^2 - 7*w - 145],\
[421, 421, -3*w^2 - w + 31],\
[433, 433, 7/2*w^2 - 31/2*w + 7],\
[439, 439, 3*w^2 - w - 33],\
[439, 439, -3/2*w^2 + 7/2*w - 3],\
[439, 439, 3/2*w^2 + 1/2*w - 11],\
[443, 443, -2*w^2 + 10*w - 11],\
[443, 443, 13*w^2 - 57*w + 33],\
[449, 449, 3/2*w^2 - 3/2*w - 11],\
[457, 457, 2*w^2 - 19],\
[457, 457, 5/2*w^2 - 17/2*w - 1],\
[457, 457, 3/2*w^2 + 9/2*w + 1],\
[461, 461, 3/2*w^2 - 7/2*w - 1],\
[463, 463, 2*w^2 - 6*w - 3],\
[463, 463, 5/2*w^2 - 5/2*w - 37],\
[463, 463, 3/2*w^2 + 1/2*w - 3],\
[479, 479, -11/2*w^2 + 51/2*w - 15],\
[491, 491, 6*w^2 - 67],\
[499, 499, -7/2*w^2 + 3/2*w + 39],\
[521, 521, 7*w^2 - 29*w + 13],\
[541, 541, 5*w^2 + 3*w - 45],\
[547, 547, 7/2*w^2 - 27/2*w + 5],\
[547, 547, 15/2*w^2 - 3/2*w - 89],\
[547, 547, 1/2*w^2 + 3/2*w - 15],\
[563, 563, 3/2*w^2 - 11/2*w - 3],\
[577, 577, 2*w^2 + 2*w - 13],\
[587, 587, 5/2*w^2 + 3/2*w - 21],\
[593, 593, -1/2*w^2 - 3/2*w - 5],\
[599, 599, 5/2*w^2 - 1/2*w - 35],\
[601, 601, 24*w^2 - 104*w + 57],\
[607, 607, w^2 + 3*w + 3],\
[619, 619, -w^2 + w - 3],\
[619, 619, 10*w^2 - 111],\
[619, 619, -5*w^2 + 23*w - 15],\
[631, 631, 4*w^2 - 4*w - 57],\
[647, 647, -7*w^2 + 33*w - 19],\
[653, 653, 3*w^2 - 11*w + 3],\
[661, 661, 2*w^2 - 6*w - 1],\
[673, 673, 2*w^2 - 8*w + 7],\
[677, 677, -w^2 + 7*w - 9],\
[683, 683, 9/2*w^2 + 11/2*w - 31],\
[683, 683, -4*w^2 + 2*w + 53],\
[683, 683, 8*w + 27],\
[691, 691, 15/2*w^2 + 1/2*w - 81],\
[709, 709, 3/2*w^2 - 7/2*w - 27],\
[727, 727, 9/2*w^2 - 1/2*w - 55],\
[733, 733, -15/2*w^2 + 7/2*w + 93],\
[743, 743, 1/2*w^2 + 7/2*w - 7],\
[751, 751, 3*w^2 - w - 41],\
[769, 769, 17/2*w^2 - 77/2*w + 21],\
[773, 773, 33/2*w^2 - 13/2*w - 205],\
[787, 787, 13*w^2 - 57*w + 31],\
[797, 797, -5*w^2 + 19*w - 11],\
[809, 809, -4*w - 11],\
[811, 811, w^2 + 3*w - 9],\
[811, 811, w^2 - w - 19],\
[811, 811, 4*w - 9],\
[823, 823, 19/2*w^2 - 79/2*w + 21],\
[829, 829, 3/2*w^2 - 3/2*w - 7],\
[829, 829, w^2 - 3*w - 9],\
[829, 829, 3/2*w^2 + 5/2*w - 13],\
[841, 29, -7/2*w^2 + 23/2*w - 5],\
[853, 853, 4*w^2 - 47],\
[853, 853, 5/2*w^2 - 5/2*w - 33],\
[853, 853, -8*w^2 + 36*w - 23],\
[863, 863, 3/2*w^2 - 3/2*w - 5],\
[877, 877, -3/2*w^2 + 15/2*w - 1],\
[883, 883, 3/2*w^2 - 3/2*w - 25],\
[883, 883, 15/2*w^2 - 7/2*w - 91],\
[883, 883, -11/2*w^2 + 47/2*w - 15],\
[887, 887, 1/2*w^2 + 23/2*w + 33],\
[911, 911, -6*w - 19],\
[929, 929, 9/2*w^2 - 33/2*w + 1],\
[947, 947, 1/2*w^2 - 9/2*w - 19],\
[967, 967, 8*w^2 + 4*w - 75],\
[971, 971, 9/2*w^2 + 7/2*w - 39],\
[971, 971, -5*w^2 + 3*w + 63],\
[971, 971, 37/2*w^2 - 157/2*w + 43],\
[977, 977, -w^2 + 3*w + 23],\
[991, 991, 2*w^2 - 2*w - 15]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^10 + 2*x^9 - 14*x^8 - 25*x^7 + 66*x^6 + 100*x^5 - 114*x^4 - 136*x^3 + 40*x^2 + 32*x - 8
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, 1/4*e^8 + 1/2*e^7 - 3*e^6 - 21/4*e^5 + 23/2*e^4 + 31/2*e^3 - 31/2*e^2 - 11*e + 4, 1, 1/4*e^9 + 1/2*e^8 - 7/2*e^7 - 27/4*e^6 + 31/2*e^5 + 30*e^4 - 20*e^3 - 46*e^2 - 6*e + 8, -1/4*e^9 - 1/2*e^8 + 7/2*e^7 + 23/4*e^6 - 33/2*e^5 - 19*e^4 + 28*e^3 + 15*e^2 - 6*e + 2, 1/4*e^9 + 1/2*e^8 - 4*e^7 - 27/4*e^6 + 43/2*e^5 + 57/2*e^4 - 41*e^3 - 38*e^2 + 13*e + 6, -1/4*e^9 + 9/2*e^7 - 1/4*e^6 - 27*e^5 + 3*e^4 + 58*e^3 - 10*e^2 - 26*e + 10, -3/4*e^9 - 3/2*e^8 + 10*e^7 + 69/4*e^6 - 89/2*e^5 - 119/2*e^4 + 70*e^3 + 58*e^2 - 11*e - 2, -1/4*e^9 - 1/2*e^8 + 3*e^7 + 19/4*e^6 - 25/2*e^5 - 21/2*e^4 + 25*e^3 - 23*e - 2, 1/4*e^9 + 1/2*e^8 - 7/2*e^7 - 23/4*e^6 + 35/2*e^5 + 20*e^4 - 36*e^3 - 19*e^2 + 20*e - 2, e^9 + 2*e^8 - 13*e^7 - 23*e^6 + 55*e^5 + 81*e^4 - 79*e^3 - 90*e^2 + 10*e + 12, 1/2*e^9 + e^8 - 7*e^7 - 25/2*e^6 + 32*e^5 + 50*e^4 - 46*e^3 - 68*e^2 - 10*e + 12, -1/2*e^9 - e^8 + 13/2*e^7 + 25/2*e^6 - 27*e^5 - 101/2*e^4 + 37*e^3 + 70*e^2 - 5*e - 14, e^9 + 3/2*e^8 - 14*e^7 - 17*e^6 + 131/2*e^5 + 57*e^4 - 111*e^3 - 53*e^2 + 34*e, -3/4*e^9 - 2*e^8 + 19/2*e^7 + 97/4*e^6 - 39*e^5 - 92*e^4 + 54*e^3 + 114*e^2 - 2*e - 18, -e^9 - 2*e^8 + 27/2*e^7 + 24*e^6 - 60*e^5 - 179/2*e^4 + 92*e^3 + 104*e^2 - 15*e - 10, 1/2*e^9 + e^8 - 13/2*e^7 - 23/2*e^6 + 28*e^5 + 83/2*e^4 - 44*e^3 - 52*e^2 + 13*e + 10, -e^6 - 2*e^5 + 9*e^4 + 16*e^3 - 18*e^2 - 28*e, -1/2*e^9 - e^8 + 7*e^7 + 27/2*e^6 - 31*e^5 - 59*e^4 + 39*e^3 + 86*e^2 + 18*e - 10, -3/2*e^9 - 3*e^8 + 21*e^7 + 73/2*e^6 - 98*e^5 - 137*e^4 + 158*e^3 + 158*e^2 - 18*e - 16, -1/2*e^8 - 1/2*e^7 + 7*e^6 + 11/2*e^5 - 63/2*e^4 - 20*e^3 + 49*e^2 + 27*e - 18, 5/4*e^9 + 3/2*e^8 - 37/2*e^7 - 71/4*e^6 + 183/2*e^5 + 65*e^4 - 162*e^3 - 73*e^2 + 54*e + 6, -e^9 - 2*e^8 + 27/2*e^7 + 25*e^6 - 59*e^5 - 201/2*e^4 + 83*e^3 + 136*e^2 + 3*e - 22, e^9 + 3/2*e^8 - 15*e^7 - 18*e^6 + 153/2*e^5 + 64*e^4 - 143*e^3 - 61*e^2 + 50*e + 4, 1/4*e^9 + 3/2*e^8 - e^7 - 67/4*e^6 - 17/2*e^5 + 113/2*e^4 + 37*e^3 - 60*e^2 - 19*e + 10, 1/4*e^9 + 3/2*e^8 - 3/2*e^7 - 79/4*e^6 - 11/2*e^5 + 87*e^4 + 43*e^3 - 139*e^2 - 56*e + 38, 3/4*e^9 + 1/2*e^8 - 23/2*e^7 - 17/4*e^6 + 121/2*e^5 + 6*e^4 - 122*e^3 + 12*e^2 + 66*e - 8, 1/2*e^9 - 8*e^7 + 5/2*e^6 + 45*e^5 - 24*e^4 - 100*e^3 + 58*e^2 + 62*e - 12, 11/4*e^9 + 11/2*e^8 - 37*e^7 - 265/4*e^6 + 327/2*e^5 + 497/2*e^4 - 246*e^3 - 296*e^2 + 23*e + 34, -1/2*e^9 - 3/2*e^8 + 6*e^7 + 35/2*e^6 - 45/2*e^5 - 62*e^4 + 24*e^3 + 67*e^2 + 10*e - 12, 1/4*e^9 + 1/2*e^8 - 7/2*e^7 - 27/4*e^6 + 31/2*e^5 + 31*e^4 - 20*e^3 - 55*e^2 - 8*e + 22, 1/2*e^7 + 2*e^6 - 3*e^5 - 39/2*e^4 - 3*e^3 + 52*e^2 + 21*e - 26, 3/2*e^9 + 3*e^8 - 21*e^7 - 73/2*e^6 + 98*e^5 + 137*e^4 - 158*e^3 - 158*e^2 + 14*e + 12, -1/2*e^9 - 3/2*e^8 + 11/2*e^7 + 39/2*e^6 - 29/2*e^5 - 167/2*e^4 - 9*e^3 + 129*e^2 + 39*e - 34, -e^9 - 2*e^8 + 13*e^7 + 24*e^6 - 54*e^5 - 90*e^4 + 70*e^3 + 106*e^2 + 10*e - 8, -e^9 - 3*e^8 + 25/2*e^7 + 37*e^6 - 50*e^5 - 289/2*e^4 + 60*e^3 + 188*e^2 + 23*e - 38, -7/4*e^9 - 5/2*e^8 + 26*e^7 + 113/4*e^6 - 263/2*e^5 - 187/2*e^4 + 242*e^3 + 80*e^2 - 77*e + 10, -1/2*e^8 - 1/2*e^7 + 7*e^6 + 9/2*e^5 - 65/2*e^4 - 10*e^3 + 51*e^2 + e - 6, -5/4*e^9 - 5/2*e^8 + 33/2*e^7 + 111/4*e^6 - 145/2*e^5 - 90*e^4 + 113*e^3 + 81*e^2 - 18*e - 6, 5/4*e^9 + 5/2*e^8 - 35/2*e^7 - 131/4*e^6 + 161/2*e^5 + 140*e^4 - 124*e^3 - 202*e^2 + 4*e + 24, 1/2*e^9 + 2*e^8 - 5*e^7 - 51/2*e^6 + 10*e^5 + 104*e^4 + 22*e^3 - 144*e^2 - 60*e + 36, 1/4*e^9 + 1/2*e^8 - 9/2*e^7 - 31/4*e^6 + 53/2*e^5 + 38*e^4 - 52*e^3 - 63*e^2 + 8*e + 22, 3/2*e^9 + 7/2*e^8 - 21*e^7 - 97/2*e^6 + 189/2*e^5 + 219*e^4 - 132*e^3 - 331*e^2 - 24*e + 52, 3/4*e^9 + 3/2*e^8 - 19/2*e^7 - 61/4*e^6 + 81/2*e^5 + 40*e^4 - 68*e^3 - 14*e^2 + 36*e - 4, -5/4*e^9 - 7/2*e^8 + 33/2*e^7 + 179/4*e^6 - 143/2*e^5 - 184*e^4 + 102*e^3 + 255*e^2 + 8*e - 46, 1/2*e^9 + e^8 - 8*e^7 - 29/2*e^6 + 42*e^5 + 68*e^4 - 69*e^3 - 106*e^2 - 10*e + 20, 1/2*e^9 + e^8 - 7*e^7 - 29/2*e^6 + 30*e^5 + 71*e^4 - 31*e^3 - 124*e^2 - 34*e + 24, -5/2*e^9 - 9/2*e^8 + 34*e^7 + 107/2*e^6 - 305/2*e^5 - 198*e^4 + 239*e^3 + 233*e^2 - 50*e - 24, 1/2*e^7 - 2*e^6 - 9*e^5 + 45/2*e^4 + 45*e^3 - 62*e^2 - 57*e + 6, 5/4*e^9 + 7/2*e^8 - 29/2*e^7 - 171/4*e^6 + 97/2*e^5 + 166*e^4 - 26*e^3 - 216*e^2 - 72*e + 40, -3/4*e^9 + 1/2*e^8 + 27/2*e^7 - 31/4*e^6 - 163/2*e^5 + 40*e^4 + 185*e^3 - 73*e^2 - 114*e + 22, -1/2*e^9 - 1/2*e^8 + 8*e^7 + 11/2*e^6 - 83/2*e^5 - 14*e^4 + 70*e^3 - 7*e^2 - 6*e + 20, -5/4*e^9 - 7/2*e^8 + 31/2*e^7 + 171/4*e^6 - 121/2*e^5 - 165*e^4 + 71*e^3 + 211*e^2 + 12*e - 30, 5/2*e^9 + 5*e^8 - 71/2*e^7 - 123/2*e^6 + 169*e^5 + 467/2*e^4 - 282*e^3 - 272*e^2 + 43*e + 26, 2*e^6 + 3*e^5 - 21*e^4 - 24*e^3 + 54*e^2 + 42*e - 12, 3/2*e^9 + 3*e^8 - 41/2*e^7 - 71/2*e^6 + 93*e^5 + 257/2*e^4 - 147*e^3 - 140*e^2 + 19*e - 2, -5/4*e^9 - 3/2*e^8 + 39/2*e^7 + 79/4*e^6 - 203/2*e^5 - 83*e^4 + 182*e^3 + 108*e^2 - 38*e + 4, -3/2*e^9 - 9/2*e^8 + 18*e^7 + 115/2*e^6 - 129/2*e^5 - 239*e^4 + 49*e^3 + 343*e^2 + 74*e - 64, -5/4*e^9 - 7/2*e^8 + 16*e^7 + 175/4*e^6 - 135/2*e^5 - 349/2*e^4 + 96*e^3 + 230*e^2 + 7*e - 30, 3/2*e^9 + 5/2*e^8 - 20*e^7 - 51/2*e^6 + 179/2*e^5 + 68*e^4 - 151*e^3 - 27*e^2 + 66*e - 12, -5/4*e^9 - 5/2*e^8 + 16*e^7 + 115/4*e^6 - 133/2*e^5 - 203/2*e^4 + 96*e^3 + 114*e^2 - 13*e - 18, e^9 + 3/2*e^8 - 14*e^7 - 17*e^6 + 133/2*e^5 + 60*e^4 - 115*e^3 - 73*e^2 + 26*e + 24, -e^7 - e^6 + 10*e^5 + 6*e^4 - 22*e^3 - 8*e, -1/2*e^9 + 1/2*e^8 + 9*e^7 - 15/2*e^6 - 105/2*e^5 + 38*e^4 + 110*e^3 - 69*e^2 - 54*e + 28, -1/4*e^9 - 5/2*e^8 + 5/2*e^7 + 151/4*e^6 - 5/2*e^5 - 187*e^4 - 38*e^3 + 318*e^2 + 100*e - 68, 1/2*e^9 + 3/2*e^8 - 6*e^7 - 31/2*e^6 + 51/2*e^5 + 42*e^4 - 47*e^3 - 19*e^2 + 22*e + 8, 3/2*e^9 + 3*e^8 - 20*e^7 - 75/2*e^6 + 84*e^5 + 152*e^4 - 103*e^3 - 212*e^2 - 24*e + 42, e^9 + 3/2*e^8 - 15*e^7 - 20*e^6 + 151/2*e^5 + 85*e^4 - 137*e^3 - 113*e^2 + 42*e + 12, 1/2*e^9 + 2*e^8 - 3*e^7 - 47/2*e^6 - 10*e^5 + 92*e^4 + 72*e^3 - 138*e^2 - 64*e + 40, -3/4*e^9 - 5/2*e^8 + 8*e^7 + 117/4*e^6 - 47/2*e^5 - 209/2*e^4 + 9*e^3 + 110*e^2 + 25*e + 2, 3*e^9 + 4*e^8 - 44*e^7 - 48*e^6 + 216*e^5 + 180*e^4 - 375*e^3 - 210*e^2 + 94*e + 4, 1/2*e^9 - 7*e^7 + 13/2*e^6 + 36*e^5 - 66*e^4 - 84*e^3 + 176*e^2 + 70*e - 64, -e^9 - 4*e^8 + 21/2*e^7 + 53*e^6 - 24*e^5 - 459/2*e^4 - 36*e^3 + 346*e^2 + 111*e - 74, 3/2*e^9 + 3*e^8 - 21*e^7 - 69/2*e^6 + 102*e^5 + 119*e^4 - 194*e^3 - 120*e^2 + 96*e + 24, e^9 + e^8 - 15*e^7 - 14*e^6 + 73*e^5 + 65*e^4 - 115*e^3 - 98*e^2 - 2*e - 4, 3/2*e^9 + 2*e^8 - 20*e^7 - 35/2*e^6 + 92*e^5 + 28*e^4 - 174*e^3 + 38*e^2 + 114*e - 20, -1/2*e^9 - 1/2*e^8 + 6*e^7 + 5/2*e^6 - 43/2*e^5 + 13*e^4 + 22*e^3 - 67*e^2 - 4*e + 40, -2*e^9 - 3*e^8 + 30*e^7 + 38*e^6 - 150*e^5 - 151*e^4 + 264*e^3 + 192*e^2 - 70*e - 26, -3/2*e^9 - e^8 + 23*e^7 + 19/2*e^6 - 119*e^5 - 21*e^4 + 224*e^3 - 6*e^2 - 80*e + 20, -3*e^9 - 11/2*e^8 + 44*e^7 + 69*e^6 - 433/2*e^5 - 271*e^4 + 370*e^3 + 331*e^2 - 58*e - 26, -7/4*e^9 - 3*e^8 + 51/2*e^7 + 149/4*e^6 - 123*e^5 - 147*e^4 + 202*e^3 + 194*e^2 - 34*e - 34, e^8 + 3*e^7 - 9*e^6 - 29*e^5 + 16*e^4 + 72*e^3 + 18*e^2 - 36*e - 12, -3/2*e^9 - 4*e^8 + 37/2*e^7 + 99/2*e^6 - 71*e^5 - 395/2*e^4 + 77*e^3 + 276*e^2 + 31*e - 50, -e^9 - 3*e^8 + 13*e^7 + 38*e^6 - 53*e^5 - 154*e^4 + 54*e^3 + 214*e^2 + 60*e - 56, 3/2*e^9 + 3*e^8 - 21*e^7 - 79/2*e^6 + 95*e^5 + 166*e^4 - 139*e^3 - 228*e^2 + 2*e + 32, 1/2*e^9 - e^8 - 10*e^7 + 27/2*e^6 + 63*e^5 - 61*e^4 - 137*e^3 + 110*e^2 + 66*e - 60, -2*e^9 - 7/2*e^8 + 29*e^7 + 47*e^6 - 277/2*e^5 - 205*e^4 + 224*e^3 + 299*e^2 - 22*e - 46, 3/4*e^9 + 1/2*e^8 - 25/2*e^7 - 13/4*e^6 + 143/2*e^5 - 11*e^4 - 154*e^3 + 80*e^2 + 84*e - 44, 9/4*e^9 + 2*e^8 - 71/2*e^7 - 99/4*e^6 + 187*e^5 + 93*e^4 - 350*e^3 - 98*e^2 + 110*e - 10, -1/2*e^9 - 1/2*e^8 + 9*e^7 + 25/2*e^6 - 97/2*e^5 - 85*e^4 + 72*e^3 + 175*e^2 + 32*e - 36, -15/4*e^9 - 13/2*e^8 + 103/2*e^7 + 313/4*e^6 - 465/2*e^5 - 298*e^4 + 356*e^3 + 373*e^2 - 40*e - 50, -1/2*e^9 - e^8 + 13/2*e^7 + 19/2*e^6 - 31*e^5 - 41/2*e^4 + 64*e^3 - 8*e^2 - 29*e + 2, -3/2*e^9 - 2*e^8 + 43/2*e^7 + 47/2*e^6 - 102*e^5 - 169/2*e^4 + 166*e^3 + 86*e^2 - 29*e + 26, 7/2*e^9 + 7*e^8 - 47*e^7 - 167/2*e^6 + 208*e^5 + 308*e^4 - 316*e^3 - 356*e^2 + 36*e + 44, -5/2*e^9 - 5*e^8 + 69/2*e^7 + 125/2*e^6 - 156*e^5 - 493/2*e^4 + 234*e^3 + 318*e^2 - e - 54, 5/2*e^9 + 3*e^8 - 38*e^7 - 71/2*e^6 + 195*e^5 + 125*e^4 - 360*e^3 - 116*e^2 + 112*e - 16, -2*e^9 - 4*e^8 + 26*e^7 + 44*e^6 - 111*e^5 - 142*e^4 + 163*e^3 + 126*e^2 - 20*e + 4, 1/4*e^9 + 3/2*e^8 - 5/2*e^7 - 91/4*e^6 + 5/2*e^5 + 111*e^4 + 32*e^3 - 180*e^2 - 74*e + 44, 5/4*e^9 + 5/2*e^8 - 17*e^7 - 107/4*e^6 + 161/2*e^5 + 155/2*e^4 - 149*e^3 - 40*e^2 + 57*e - 2, e^9 + 3/2*e^8 - 16*e^7 - 21*e^6 + 167/2*e^5 + 93*e^4 - 135*e^3 - 125*e^2 - 30*e + 4, 2*e^7 + 4*e^6 - 20*e^5 - 38*e^4 + 52*e^3 + 98*e^2 - 18*e - 44, -1/2*e^9 - 2*e^8 + 7*e^7 + 59/2*e^6 - 33*e^5 - 143*e^4 + 52*e^3 + 234*e^2 + 4*e - 44, e^9 + 3*e^8 - 11*e^7 - 37*e^6 + 33*e^5 + 146*e^4 - 9*e^3 - 196*e^2 - 62*e + 32, 11/4*e^9 + 7/2*e^8 - 40*e^7 - 165/4*e^6 + 391/2*e^5 + 309/2*e^4 - 340*e^3 - 192*e^2 + 87*e + 18, -5*e^9 - 19/2*e^8 + 68*e^7 + 114*e^6 - 609/2*e^5 - 425*e^4 + 465*e^3 + 499*e^2 - 38*e - 52, 1/2*e^9 - 1/2*e^8 - 7*e^7 + 31/2*e^6 + 79/2*e^5 - 113*e^4 - 116*e^3 + 239*e^2 + 144*e - 56, 1/2*e^7 + 2*e^6 - 3*e^5 - 37/2*e^4 - 8*e^3 + 34*e^2 + 51*e + 2, 5/4*e^9 + 3/2*e^8 - 41/2*e^7 - 71/4*e^6 + 233/2*e^5 + 61*e^4 - 248*e^3 - 48*e^2 + 114*e - 8, -1/2*e^9 - 2*e^8 + 4*e^7 + 47/2*e^6 - 2*e^5 - 89*e^4 - 28*e^3 + 118*e^2 + 16*e - 20, 5*e^6 + 6*e^5 - 51*e^4 - 46*e^3 + 134*e^2 + 76*e - 48, e^9 + 4*e^8 - 9*e^7 - 49*e^6 + 12*e^5 + 191*e^4 + 52*e^3 - 254*e^2 - 92*e + 60, 2*e^9 + 4*e^8 - 29*e^7 - 54*e^6 + 138*e^5 + 238*e^4 - 215*e^3 - 354*e^2 + 2*e + 48, 1/2*e^9 + 2*e^8 - 6*e^7 - 49/2*e^6 + 25*e^5 + 95*e^4 - 38*e^3 - 124*e^2 - 2*e + 36, 1/2*e^9 + 1/2*e^8 - 7*e^7 - 9/2*e^6 + 71/2*e^5 + 7*e^4 - 81*e^3 + 19*e^2 + 66*e - 20, 7/2*e^9 + 15/2*e^8 - 89/2*e^7 - 177/2*e^6 + 363/2*e^5 + 655/2*e^4 - 241*e^3 - 399*e^2 + e + 70, -7/4*e^9 - 5/2*e^8 + 53/2*e^7 + 125/4*e^6 - 269/2*e^5 - 121*e^4 + 240*e^3 + 140*e^2 - 62*e - 16, 7/4*e^9 + 5/2*e^8 - 53/2*e^7 - 125/4*e^6 + 265/2*e^5 + 123*e^4 - 221*e^3 - 155*e^2 + 16*e + 10, -7/4*e^9 - 4*e^8 + 43/2*e^7 + 189/4*e^6 - 80*e^5 - 173*e^4 + 76*e^3 + 198*e^2 + 42*e - 14, -e^9 - e^8 + 14*e^7 + 9*e^6 - 66*e^5 - 17*e^4 + 108*e^3 - 22*e^2 + 44, 1/2*e^9 + e^8 - 5*e^7 - 23/2*e^6 + 7*e^5 + 40*e^4 + 42*e^3 - 44*e^2 - 86*e + 8, e^9 - 1/2*e^8 - 18*e^7 + 10*e^6 + 223/2*e^5 - 60*e^4 - 263*e^3 + 117*e^2 + 162*e - 36, e^8 - 16*e^6 - 2*e^5 + 79*e^4 + 16*e^3 - 122*e^2 - 28*e + 12, 5/4*e^9 + 7/2*e^8 - 29/2*e^7 - 171/4*e^6 + 99/2*e^5 + 170*e^4 - 38*e^3 - 239*e^2 - 32*e + 50, -2*e^9 - 5*e^8 + 25*e^7 + 62*e^6 - 98*e^5 - 246*e^4 + 112*e^3 + 324*e^2 + 48*e - 44, -1/2*e^8 + 8*e^6 + 1/2*e^5 - 39*e^4 + 57*e^2 - 22*e - 2, -3/2*e^9 - 2*e^8 + 43/2*e^7 + 45/2*e^6 - 105*e^5 - 155/2*e^4 + 193*e^3 + 90*e^2 - 83*e - 26, -1/2*e^9 - e^8 + 6*e^7 + 13/2*e^6 - 27*e^5 + 12*e^4 + 58*e^3 - 94*e^2 - 36*e + 24, -3/2*e^8 - e^7 + 24*e^6 + 25/2*e^5 - 129*e^4 - 48*e^3 + 245*e^2 + 54*e - 62, -1/2*e^9 - 5/2*e^8 + 5/2*e^7 + 53/2*e^6 + 27/2*e^5 - 161/2*e^4 - 81*e^3 + 65*e^2 + 93*e + 6, 3/2*e^9 + 3*e^8 - 23*e^7 - 83/2*e^6 + 120*e^5 + 188*e^4 - 226*e^3 - 288*e^2 + 66*e + 56, 3/2*e^9 + 5*e^8 - 19*e^7 - 131/2*e^6 + 76*e^5 + 277*e^4 - 81*e^3 - 400*e^2 - 74*e + 98, -7/4*e^9 - 3/2*e^8 + 49/2*e^7 + 65/4*e^6 - 223/2*e^5 - 56*e^4 + 170*e^3 + 70*e^2 - 22*e - 8, -3/2*e^9 - 11/2*e^8 + 18*e^7 + 143/2*e^6 - 135/2*e^5 - 301*e^4 + 71*e^3 + 425*e^2 + 42*e - 72, -3/2*e^9 - 4*e^8 + 20*e^7 + 103/2*e^6 - 87*e^5 - 216*e^4 + 119*e^3 + 314*e^2 + 40*e - 68, 7/2*e^9 + 6*e^8 - 49*e^7 - 137/2*e^6 + 231*e^5 + 233*e^4 - 392*e^3 - 224*e^2 + 100*e, 2*e^9 + 2*e^8 - 34*e^7 - 26*e^6 + 195*e^5 + 103*e^4 - 402*e^3 - 116*e^2 + 160*e + 4, 1/4*e^9 + 1/2*e^8 - 13/2*e^7 - 35/4*e^6 + 101/2*e^5 + 45*e^4 - 130*e^3 - 71*e^2 + 54*e + 38, 3/4*e^9 - 1/2*e^8 - 14*e^7 + 27/4*e^6 + 169/2*e^5 - 67/2*e^4 - 177*e^3 + 74*e^2 + 65*e - 50, -21/4*e^9 - 17/2*e^8 + 145/2*e^7 + 399/4*e^6 - 659/2*e^5 - 359*e^4 + 514*e^3 + 390*e^2 - 86*e - 16, 1/4*e^9 + 5/2*e^8 - 3/2*e^7 - 151/4*e^6 - 15/2*e^5 + 188*e^4 + 61*e^3 - 325*e^2 - 102*e + 94, -1/4*e^9 - 5/2*e^8 + 1/2*e^7 + 143/4*e^6 + 41/2*e^5 - 172*e^4 - 105*e^3 + 303*e^2 + 110*e - 78, -15/4*e^9 - 13/2*e^8 + 107/2*e^7 + 329/4*e^6 - 499/2*e^5 - 329*e^4 + 386*e^3 + 421*e^2 - 28*e - 34, 9/2*e^9 + 9*e^8 - 60*e^7 - 203/2*e^6 + 270*e^5 + 341*e^4 - 449*e^3 - 332*e^2 + 134*e + 42, -e^9 - 3/2*e^8 + 14*e^7 + 21*e^6 - 127/2*e^5 - 101*e^4 + 101*e^3 + 181*e^2 - 38*e - 44, -1/2*e^9 + e^8 + 12*e^7 - 11/2*e^6 - 82*e^5 - 20*e^4 + 187*e^3 + 104*e^2 - 96*e - 26, -e^9 + 17*e^7 - 3*e^6 - 97*e^5 + 32*e^4 + 210*e^3 - 86*e^2 - 140*e + 32, -1/2*e^9 + 11*e^7 + 15/2*e^6 - 71*e^5 - 71*e^4 + 140*e^3 + 150*e^2 - 10*e + 4, 2*e^9 + 4*e^8 - 53/2*e^7 - 44*e^6 + 119*e^5 + 281/2*e^4 - 204*e^3 - 128*e^2 + 75*e + 30, 2*e^9 + 4*e^8 - 28*e^7 - 49*e^6 + 133*e^5 + 188*e^4 - 232*e^3 - 226*e^2 + 72*e + 24, -5/2*e^9 - 4*e^8 + 38*e^7 + 93/2*e^6 - 200*e^5 - 158*e^4 + 394*e^3 + 132*e^2 - 158*e + 12, -e^9 - 3*e^8 + 13*e^7 + 37*e^6 - 56*e^5 - 144*e^4 + 82*e^3 + 180*e^2 + 6, 5/2*e^9 + 7*e^8 - 31*e^7 - 175/2*e^6 + 120*e^5 + 350*e^4 - 129*e^3 - 472*e^2 - 76*e + 92, -5/2*e^9 - 7*e^8 + 29*e^7 + 163/2*e^6 - 102*e^5 - 289*e^4 + 102*e^3 + 320*e^2 + 32*e - 48, 2*e^9 + 5*e^8 - 26*e^7 - 62*e^6 + 108*e^5 + 241*e^4 - 134*e^3 - 300*e^2 - 62*e + 32, 3*e^9 + 4*e^8 - 45*e^7 - 49*e^6 + 226*e^5 + 187*e^4 - 400*e^3 - 220*e^2 + 106*e + 24, -e^9 - 2*e^8 + 14*e^7 + 24*e^6 - 68*e^5 - 94*e^4 + 123*e^3 + 124*e^2 - 32*e + 4, -7/4*e^9 - 1/2*e^8 + 55/2*e^7 - 3/4*e^6 - 299/2*e^5 + 42*e^4 + 312*e^3 - 131*e^2 - 160*e + 46, -3*e^9 - 8*e^8 + 38*e^7 + 99*e^6 - 151*e^5 - 391*e^4 + 168*e^3 + 522*e^2 + 78*e - 96]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

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

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