/*
  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, 1, -7, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([11, 11, -w^3 + w^2 + 6*w + 1])

primes_array = [
[2, 2, w],\
[2, 2, -1/2*w^3 + w^2 + 3/2*w],\
[11, 11, 1/2*w^3 - w^2 - 5/2*w + 4],\
[11, 11, -w^3 + w^2 + 6*w + 1],\
[13, 13, -w^3 + w^2 + 6*w - 3],\
[19, 19, -1/2*w^3 + w^2 + 5/2*w],\
[23, 23, -1/2*w^3 + 2*w^2 - 1/2*w - 2],\
[31, 31, -w^3 + w^2 + 6*w - 1],\
[31, 31, 1/2*w^3 - 7/2*w],\
[43, 43, 1/2*w^3 - w^2 - 9/2*w + 2],\
[67, 67, w^2 - w - 5],\
[67, 67, -1/2*w^3 + 11/2*w + 2],\
[73, 73, w^2 + w + 1],\
[79, 79, 1/2*w^3 + w^2 - 5/2*w - 2],\
[81, 3, -3],\
[83, 83, 2*w^3 - 2*w^2 - 12*w + 5],\
[83, 83, -1/2*w^3 - w^2 + 1/2*w + 2],\
[89, 89, -3/2*w^3 + 2*w^2 + 17/2*w - 2],\
[89, 89, 3/2*w^3 - 2*w^2 - 21/2*w + 2],\
[97, 97, 1/2*w^3 - w^2 - 1/2*w - 2],\
[97, 97, -w^3 + w^2 + 8*w + 1],\
[103, 103, 2*w^3 - 2*w^2 - 14*w + 1],\
[103, 103, w^2 - w - 3],\
[107, 107, -3/2*w^3 + 2*w^2 + 21/2*w - 4],\
[109, 109, 5/2*w^3 - 3*w^2 - 33/2*w + 4],\
[109, 109, -1/2*w^3 + w^2 + 9/2*w - 4],\
[113, 113, -w^3 + w^2 + 8*w - 3],\
[113, 113, 1/2*w^3 - w^2 - 1/2*w + 2],\
[121, 11, 5/2*w^3 - 2*w^2 - 31/2*w + 2],\
[127, 127, -3/2*w^3 + w^2 + 23/2*w],\
[127, 127, -1/2*w^3 + 11/2*w],\
[131, 131, w^2 - 3*w - 3],\
[137, 137, 1/2*w^3 - w^2 - 5/2*w + 6],\
[139, 139, -3/2*w^3 + 2*w^2 + 13/2*w + 2],\
[151, 151, -1/2*w^3 + 2*w^2 + 3/2*w - 10],\
[157, 157, 7/2*w^3 - 5*w^2 - 47/2*w + 10],\
[157, 157, 7/2*w^3 - 4*w^2 - 45/2*w + 4],\
[167, 167, 1/2*w^3 + w^2 - 5/2*w - 4],\
[167, 167, 2*w + 5],\
[173, 173, -w^3 + w^2 + 4*w - 7],\
[181, 181, w^3 - 2*w^2 - 9*w + 1],\
[193, 193, -1/2*w^3 + 2*w^2 + 3/2*w - 8],\
[197, 197, -1/2*w^3 - w^2 + 13/2*w + 2],\
[197, 197, -w^3 + w^2 + 4*w - 1],\
[197, 197, w^3 - 2*w^2 - 7*w + 7],\
[197, 197, -2*w^3 + 3*w^2 + 13*w - 11],\
[199, 199, -2*w^3 + 3*w^2 + 11*w - 5],\
[239, 239, -w^3 + 2*w^2 + 5*w - 1],\
[239, 239, 7/2*w^3 - 4*w^2 - 45/2*w + 6],\
[241, 241, 1/2*w^3 - 2*w^2 - 7/2*w + 8],\
[257, 257, 3/2*w^3 - 2*w^2 - 17/2*w - 4],\
[257, 257, 1/2*w^3 - 7/2*w - 6],\
[257, 257, 7/2*w^3 - 5*w^2 - 43/2*w + 10],\
[257, 257, 3*w^3 - 4*w^2 - 19*w + 7],\
[269, 269, 1/2*w^3 + w^2 + 3/2*w + 2],\
[269, 269, -2*w^3 + 3*w^2 + 11*w - 11],\
[277, 277, 5/2*w^3 - 4*w^2 - 35/2*w + 8],\
[281, 281, -3/2*w^3 + w^2 + 23/2*w - 2],\
[283, 283, -w^3 - w^2 + 8*w + 11],\
[283, 283, -3*w^2 + 3*w + 19],\
[311, 311, 3/2*w^3 - 2*w^2 - 17/2*w - 2],\
[331, 331, -4*w^3 + 7*w^2 + 25*w - 21],\
[337, 337, -5/2*w^3 + 2*w^2 + 35/2*w + 4],\
[337, 337, -2*w^3 + 3*w^2 + 11*w - 9],\
[347, 347, 2*w^3 - 4*w^2 - 12*w + 13],\
[347, 347, 5/2*w^3 - 5*w^2 - 29/2*w + 20],\
[347, 347, -1/2*w^3 - 1/2*w - 6],\
[347, 347, -1/2*w^3 + 3*w^2 + 1/2*w - 16],\
[349, 349, 1/2*w^3 + w^2 - 9/2*w - 4],\
[353, 353, -1/2*w^3 + 2*w^2 + 7/2*w],\
[359, 359, 3/2*w^3 - w^2 - 19/2*w + 2],\
[373, 373, -2*w^3 + 2*w^2 + 12*w + 1],\
[373, 373, -1/2*w^3 + w^2 + 9/2*w - 6],\
[379, 379, w^2 - w - 9],\
[379, 379, -2*w^3 + 3*w^2 + 13*w - 5],\
[383, 383, w^2 + w - 5],\
[389, 389, 9/2*w^3 - 6*w^2 - 59/2*w + 14],\
[397, 397, 2*w^2 - 2*w - 15],\
[401, 401, -1/2*w^3 + 2*w^2 + 3/2*w - 4],\
[419, 419, -3/2*w^3 + w^2 + 15/2*w - 2],\
[419, 419, w^3 + w^2 - 8*w - 15],\
[431, 431, -5/2*w^3 + 4*w^2 + 27/2*w - 16],\
[431, 431, 2*w^3 - 4*w^2 - 10*w + 11],\
[443, 443, 1/2*w^3 - 3*w^2 - 5/2*w + 14],\
[449, 449, 1/2*w^3 + w^2 - 9/2*w - 6],\
[457, 457, -w^3 + 2*w^2 + 7*w - 9],\
[461, 461, 4*w^3 - 5*w^2 - 27*w + 7],\
[487, 487, 2*w^2 - 9],\
[499, 499, 3/2*w^3 - w^2 - 15/2*w - 2],\
[499, 499, 3/2*w^3 - 4*w^2 - 17/2*w + 16],\
[503, 503, -5/2*w^3 + 3*w^2 + 37/2*w],\
[509, 509, -3*w^3 + 3*w^2 + 18*w + 7],\
[521, 521, -1/2*w^3 - 2*w^2 + 11/2*w + 18],\
[521, 521, -5/2*w^3 + 4*w^2 + 31/2*w - 8],\
[523, 523, -1/2*w^3 + 2*w^2 + 11/2*w],\
[523, 523, -1/2*w^3 - w^2 + 9/2*w],\
[547, 547, -7/2*w^3 + 6*w^2 + 45/2*w - 18],\
[547, 547, -w^3 - w^2 + 12*w + 5],\
[547, 547, 3/2*w^3 - w^2 - 19/2*w + 4],\
[547, 547, w^3 - w^2 - 6*w - 5],\
[557, 557, 1/2*w^3 + w^2 - 9/2*w - 12],\
[557, 557, 3/2*w^3 - 2*w^2 - 21/2*w],\
[557, 557, 2*w^3 - 2*w^2 - 12*w + 1],\
[557, 557, w^3 - 3*w^2 - 6*w + 11],\
[569, 569, w^3 - 2*w^2 - 7*w + 1],\
[577, 577, w^3 + w^2 - 6*w - 5],\
[599, 599, -3/2*w^3 + 3*w^2 + 15/2*w - 10],\
[607, 607, -5/2*w^3 + 3*w^2 + 25/2*w + 4],\
[613, 613, w^3 - 9*w + 1],\
[619, 619, 3*w^2 - w - 17],\
[619, 619, w^3 - 3*w^2 - 6*w + 13],\
[625, 5, -5],\
[631, 631, 11/2*w^3 - 7*w^2 - 71/2*w + 16],\
[631, 631, -3/2*w^3 + 2*w^2 + 13/2*w],\
[643, 643, w^2 - 3*w - 5],\
[653, 653, 2*w^2 - 2*w - 11],\
[659, 659, 5*w^3 - 3*w^2 - 36*w - 9],\
[659, 659, -w^3 + 7*w - 1],\
[673, 673, 5/2*w^3 - 2*w^2 - 31/2*w - 4],\
[677, 677, 13/2*w^3 - 6*w^2 - 87/2*w + 2],\
[691, 691, -3/2*w^3 + 2*w^2 + 13/2*w - 2],\
[701, 701, -w^3 + 3*w^2 + 4*w - 13],\
[701, 701, w^3 - 2*w^2 - 9*w + 3],\
[709, 709, -w^2 - 5*w - 1],\
[739, 739, 3/2*w^3 - w^2 - 15/2*w],\
[743, 743, -2*w^3 + w^2 + 15*w + 1],\
[751, 751, -2*w^3 + 4*w^2 + 12*w - 11],\
[757, 757, -6*w^3 + 9*w^2 + 39*w - 23],\
[757, 757, -w^3 - w^2 + 8*w + 3],\
[757, 757, 13/2*w^3 - 8*w^2 - 83/2*w + 16],\
[757, 757, 3*w^3 - 4*w^2 - 17*w + 3],\
[761, 761, 7/2*w^3 - 5*w^2 - 47/2*w + 12],\
[769, 769, -3*w^2 + 7*w + 3],\
[773, 773, -3/2*w^3 - w^2 + 19/2*w + 4],\
[787, 787, -4*w^3 + 5*w^2 + 23*w - 17],\
[787, 787, 1/2*w^3 - w^2 - 9/2*w - 4],\
[809, 809, -2*w^3 + 2*w^2 + 16*w + 3],\
[809, 809, -4*w^3 + 5*w^2 + 25*w - 9],\
[811, 811, 3*w^3 - 3*w^2 - 20*w + 5],\
[811, 811, w^3 - 3*w^2 - 6*w + 17],\
[823, 823, 5/2*w^3 - w^2 - 33/2*w - 10],\
[829, 829, 5/2*w^3 - 3*w^2 - 33/2*w + 2],\
[829, 829, -3*w^3 + 2*w^2 + 23*w - 1],\
[839, 839, -11/2*w^3 + 7*w^2 + 67/2*w - 18],\
[853, 853, -w^3 + 2*w^2 + 3*w - 5],\
[853, 853, -5*w^3 + 7*w^2 + 32*w - 15],\
[857, 857, 3/2*w^3 - 5*w^2 - 15/2*w + 26],\
[859, 859, -w^3 + 3*w^2 + 4*w - 17],\
[863, 863, 4*w^3 - 4*w^2 - 26*w + 3],\
[877, 877, w^3 - 5*w - 5],\
[887, 887, 3/2*w^3 - w^2 - 11/2*w + 8],\
[907, 907, -9/2*w^3 + 7*w^2 + 53/2*w - 24],\
[919, 919, 7/2*w^3 - 6*w^2 - 41/2*w + 22],\
[929, 929, -2*w^3 + 3*w^2 + 11*w - 1],\
[937, 937, 2*w^3 - 4*w^2 - 12*w + 7],\
[947, 947, 9/2*w^3 - 5*w^2 - 61/2*w + 10],\
[953, 953, -1/2*w^3 + 2*w^2 + 3/2*w + 2],\
[961, 31, -1/2*w^3 + 2*w^2 - 1/2*w - 6],\
[977, 977, 5/2*w^3 - 2*w^2 - 31/2*w],\
[983, 983, -5/2*w^3 + 6*w^2 + 27/2*w - 24],\
[983, 983, -3/2*w^3 + 2*w^2 + 21/2*w - 10],\
[983, 983, -w^3 + 4*w^2 + 7*w - 15],\
[983, 983, -1/2*w^3 + 3*w^2 - 3/2*w - 4],\
[997, 997, 1/2*w^3 - w^2 - 5/2*w - 4],\
[997, 997, 1/2*w^3 + w^2 - 17/2*w - 2]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^10 + 4*x^9 - 4*x^8 - 30*x^7 - 7*x^6 + 72*x^5 + 43*x^4 - 54*x^3 - 41*x^2 - 2*x + 1
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e^3 + e^2 - 3*e - 2, e, e^8 + 2*e^7 - 8*e^6 - 14*e^5 + 20*e^4 + 28*e^3 - 13*e^2 - 14*e - 4, 1, -e^9 - 4*e^8 + 5*e^7 + 32*e^6 + e^5 - 82*e^4 - 32*e^3 + 66*e^2 + 35*e - 2, -e^8 - 3*e^7 + 6*e^6 + 19*e^5 - 12*e^4 - 35*e^3 + 8*e^2 + 16*e + 1, -e^6 - 3*e^5 + 4*e^4 + 15*e^3 - e^2 - 16*e - 4, -e^7 - 2*e^6 + 4*e^5 + 8*e^4 - 6*e^2 - 9*e - 2, 2*e^9 + 7*e^8 - 9*e^7 - 48*e^6 - e^5 + 102*e^4 + 40*e^3 - 65*e^2 - 35*e - 3, -3*e^9 - 10*e^8 + 18*e^7 + 76*e^6 - 25*e^5 - 186*e^4 - 17*e^3 + 148*e^2 + 36*e - 9, e^9 + 2*e^8 - 9*e^7 - 16*e^6 + 30*e^5 + 43*e^4 - 42*e^3 - 42*e^2 + 15*e + 10, e^9 + 4*e^8 - 4*e^7 - 28*e^6 - 3*e^5 + 62*e^4 + 26*e^3 - 42*e^2 - 30*e - 6, e^9 + 7*e^8 + 2*e^7 - 52*e^6 - 43*e^5 + 128*e^4 + 98*e^3 - 110*e^2 - 49*e + 10, -5*e^8 - 8*e^7 + 43*e^6 + 56*e^5 - 122*e^4 - 116*e^3 + 113*e^2 + 66*e - 4, 2*e^9 + 6*e^8 - 12*e^7 - 44*e^6 + 16*e^5 + 106*e^4 + 18*e^3 - 91*e^2 - 38*e + 13, 3*e^9 + 12*e^8 - 15*e^7 - 95*e^6 + e^5 + 245*e^4 + 75*e^3 - 209*e^2 - 79*e + 5, 3*e^9 + 6*e^8 - 27*e^7 - 50*e^6 + 78*e^5 + 130*e^4 - 71*e^3 - 103*e^2 + e - 2, -4*e^9 - 12*e^8 + 25*e^7 + 91*e^6 - 33*e^5 - 216*e^4 - 41*e^3 + 155*e^2 + 75*e, 4*e^9 + 12*e^8 - 26*e^7 - 88*e^6 + 50*e^5 + 206*e^4 - 14*e^3 - 150*e^2 - 33*e - 4, 4*e^9 + 13*e^8 - 26*e^7 - 105*e^6 + 38*e^5 + 273*e^4 + 38*e^3 - 230*e^2 - 82*e + 11, 2*e^8 + 6*e^7 - 14*e^6 - 44*e^5 + 34*e^4 + 101*e^3 - 32*e^2 - 71*e - 6, -e^9 - 4*e^8 + 6*e^7 + 36*e^6 - 4*e^5 - 110*e^4 - 26*e^3 + 116*e^2 + 29*e - 12, 3*e^8 + 7*e^7 - 24*e^6 - 49*e^5 + 70*e^4 + 107*e^3 - 74*e^2 - 73*e - 1, -3*e^9 - 10*e^8 + 13*e^7 + 62*e^6 - 110*e^4 - 50*e^3 + 46*e^2 + 45*e + 2, -3*e^9 - 9*e^8 + 17*e^7 + 60*e^6 - 21*e^5 - 119*e^4 - 22*e^3 + 63*e^2 + 41*e + 4, -2*e^9 - 6*e^8 + 14*e^7 + 47*e^6 - 31*e^5 - 120*e^4 + 17*e^3 + 98*e^2 + 15*e - 1, 4*e^9 + 14*e^8 - 21*e^7 - 101*e^6 + 19*e^5 + 232*e^4 + 30*e^3 - 176*e^2 - 28*e + 16, -5*e^9 - 18*e^8 + 25*e^7 + 134*e^6 - 6*e^5 - 321*e^4 - 110*e^3 + 249*e^2 + 126*e - 3, e^9 + e^8 - 10*e^7 - 9*e^6 + 27*e^5 + 22*e^4 - 10*e^3 - 16*e^2 - 18*e - 2, -e^9 + 13*e^7 - 4*e^6 - 64*e^5 + 22*e^4 + 126*e^3 - 30*e^2 - 71*e, -e^9 - 2*e^8 + 7*e^7 + 11*e^6 - 15*e^5 - 13*e^4 + 2*e^3 - 4*e^2 + 20*e - 5, -4*e^8 - 8*e^7 + 27*e^6 + 48*e^5 - 55*e^4 - 82*e^3 + 28*e^2 + 44*e + 3, 2*e^8 - 23*e^6 + e^5 + 81*e^4 - 10*e^3 - 91*e^2 + 15*e + 19, -2*e^9 - 8*e^8 + 9*e^7 + 62*e^6 + 5*e^5 - 156*e^4 - 53*e^3 + 128*e^2 + 37*e - 6, -5*e^9 - 17*e^8 + 28*e^7 + 131*e^6 - 22*e^5 - 325*e^4 - 78*e^3 + 263*e^2 + 90*e - 11, e^9 + 7*e^8 + 5*e^7 - 46*e^6 - 63*e^5 + 99*e^4 + 149*e^3 - 80*e^2 - 98*e + 6, -6*e^9 - 16*e^8 + 44*e^7 + 126*e^6 - 95*e^5 - 319*e^4 + 33*e^3 + 264*e^2 + 56*e - 18, e^9 + e^8 - 10*e^7 - 2*e^6 + 47*e^5 - 10*e^4 - 104*e^3 + 22*e^2 + 71*e - 2, e^9 + 6*e^8 + 5*e^7 - 35*e^6 - 63*e^5 + 58*e^4 + 148*e^3 - 22*e^2 - 95*e - 4, e^8 - 2*e^7 - 15*e^6 + 16*e^5 + 69*e^4 - 36*e^3 - 104*e^2 + 24*e + 21, 3*e^9 + 10*e^8 - 13*e^7 - 65*e^6 - 6*e^5 + 126*e^4 + 80*e^3 - 69*e^2 - 81*e + 1, -7*e^8 - 13*e^7 + 59*e^6 + 96*e^5 - 165*e^4 - 219*e^3 + 150*e^2 + 147*e + 5, e^9 + 4*e^8 - 10*e^7 - 42*e^6 + 30*e^5 + 136*e^4 - 22*e^3 - 138*e^2 - 18*e + 14, 4*e^9 + 11*e^8 - 30*e^7 - 87*e^6 + 71*e^5 + 225*e^4 - 39*e^3 - 191*e^2 - 33*e + 9, -4*e^9 - 16*e^8 + 14*e^7 + 113*e^6 + 28*e^5 - 255*e^4 - 120*e^3 + 189*e^2 + 70*e - 10, 6*e^8 + 14*e^7 - 41*e^6 - 88*e^5 + 95*e^4 + 164*e^3 - 76*e^2 - 90*e - 2, -e^9 - 6*e^8 - e^7 + 40*e^6 + 34*e^5 - 82*e^4 - 77*e^3 + 50*e^2 + 39*e, 5*e^9 + 14*e^8 - 38*e^7 - 112*e^6 + 92*e^5 + 290*e^4 - 61*e^3 - 250*e^2 - 26*e + 18, e^9 + 4*e^8 - 3*e^7 - 22*e^6 + 4*e^5 + 30*e^4 - 39*e^3 - 4*e^2 + 67*e + 8, 6*e^9 + 19*e^8 - 37*e^7 - 143*e^6 + 52*e^5 + 342*e^4 + 48*e^3 - 260*e^2 - 100*e + 16, 2*e^7 + 4*e^6 - 8*e^5 - 17*e^4 - 4*e^3 + 11*e^2 + 28*e + 4, 2*e^8 + 2*e^7 - 21*e^6 - 17*e^5 + 71*e^4 + 40*e^3 - 80*e^2 - 20*e + 8, 3*e^9 + 4*e^8 - 32*e^7 - 36*e^6 + 112*e^5 + 97*e^4 - 139*e^3 - 77*e^2 + 37*e + 3, 7*e^9 + 18*e^8 - 50*e^7 - 134*e^6 + 110*e^5 + 318*e^4 - 62*e^3 - 248*e^2 - 25*e + 26, 6*e^9 + 22*e^8 - 34*e^7 - 178*e^6 + 26*e^5 + 472*e^4 + 112*e^3 - 410*e^2 - 148*e + 12, 3*e^9 + 10*e^8 - 17*e^7 - 72*e^6 + 26*e^5 + 166*e^4 - 17*e^3 - 133*e^2 + 23*e + 20, -3*e^9 - 6*e^8 + 22*e^7 + 38*e^6 - 47*e^5 - 56*e^4 + 17*e^3 - 16*e^2 + 26*e + 24, -6*e^9 - 18*e^8 + 41*e^7 + 140*e^6 - 84*e^5 - 354*e^4 + 41*e^3 + 304*e^2 + 27*e - 36, -8*e^9 - 30*e^8 + 42*e^7 + 234*e^6 - 18*e^5 - 590*e^4 - 164*e^3 + 480*e^2 + 178*e - 16, -2*e^9 - 5*e^8 + 15*e^7 + 39*e^6 - 36*e^5 - 107*e^4 + 23*e^3 + 116*e^2 + 7*e - 19, 3*e^9 + 18*e^8 + 2*e^7 - 132*e^6 - 107*e^5 + 316*e^4 + 269*e^3 - 246*e^2 - 155*e - 4, -e^9 - 3*e^8 + 4*e^7 + 17*e^6 - 2*e^5 - 32*e^4 - e^3 + 24*e^2 - 1, 5*e^9 + 10*e^8 - 44*e^7 - 80*e^6 + 126*e^5 + 201*e^4 - 112*e^3 - 154*e^2 - 8*e - 7, -5*e^9 - 10*e^8 + 45*e^7 + 77*e^6 - 143*e^5 - 184*e^4 + 178*e^3 + 137*e^2 - 56*e - 13, -6*e^9 - 15*e^8 + 48*e^7 + 124*e^6 - 120*e^5 - 335*e^4 + 76*e^3 + 305*e^2 + 40*e - 38, -3*e^9 - 8*e^8 + 23*e^7 + 71*e^6 - 39*e^5 - 199*e^4 - 45*e^3 + 167*e^2 + 101*e + 16, 2*e^9 + 7*e^8 - 10*e^7 - 48*e^6 + 10*e^5 + 101*e^4 + 8*e^3 - 61*e^2 - 18*e + 5, 2*e^9 + 4*e^8 - 14*e^7 - 22*e^6 + 32*e^5 + 23*e^4 - 26*e^3 + 17*e^2 + 2*e - 12, -2*e^9 - 10*e^8 + 6*e^7 + 86*e^6 + 36*e^5 - 245*e^4 - 143*e^3 + 234*e^2 + 107*e - 11, -2*e^9 - 6*e^8 + 10*e^7 + 36*e^6 - 13*e^5 - 64*e^4 + 3*e^3 + 26*e^2 + 4*e + 10, -8*e^8 - 18*e^7 + 56*e^6 + 115*e^5 - 131*e^4 - 217*e^3 + 108*e^2 + 116*e - 12, -8*e^9 - 27*e^8 + 46*e^7 + 207*e^6 - 43*e^5 - 503*e^4 - 110*e^3 + 386*e^2 + 136*e - 13, -2*e^9 - 13*e^8 - 2*e^7 + 103*e^6 + 88*e^5 - 269*e^4 - 254*e^3 + 231*e^2 + 204*e + 2, -4*e^9 - 9*e^8 + 36*e^7 + 75*e^6 - 112*e^5 - 203*e^4 + 124*e^3 + 175*e^2 - 14*e - 6, e^9 + 2*e^8 - 7*e^7 - 16*e^6 + 11*e^5 + 48*e^4 + 11*e^3 - 66*e^2 - 27*e + 20, 6*e^9 + 23*e^8 - 28*e^7 - 171*e^6 - 4*e^5 + 407*e^4 + 148*e^3 - 307*e^2 - 158*e - 2, 2*e^8 - 20*e^6 + 4*e^5 + 62*e^4 - 16*e^3 - 52*e^2 + 8*e - 8, 5*e^9 + 19*e^8 - 20*e^7 - 129*e^6 - 8*e^5 + 276*e^4 + 81*e^3 - 188*e^2 - 50*e + 17, -2*e^8 - 6*e^7 + 18*e^6 + 56*e^5 - 53*e^4 - 160*e^3 + 52*e^2 + 130*e + 6, e^8 - 19*e^6 - 17*e^5 + 83*e^4 + 89*e^3 - 109*e^2 - 105*e + 17, 12*e^9 + 39*e^8 - 68*e^7 - 291*e^6 + 66*e^5 + 705*e^4 + 160*e^3 - 565*e^2 - 206*e + 16, 7*e^9 + 22*e^8 - 45*e^7 - 168*e^6 + 74*e^5 + 408*e^4 + 25*e^3 - 316*e^2 - 94*e + 25, 6*e^9 + 18*e^8 - 38*e^7 - 135*e^6 + 56*e^5 + 318*e^4 + 50*e^3 - 223*e^2 - 110*e - 12, e^9 + 2*e^8 - 7*e^7 - 12*e^6 + 8*e^5 + 16*e^4 + 33*e^3 - 3*e^2 - 57*e + 6, -7*e^9 - 21*e^8 + 46*e^7 + 163*e^6 - 78*e^5 - 413*e^4 - 22*e^3 + 351*e^2 + 82*e - 25, e^8 + 3*e^7 - 4*e^6 - 21*e^5 - 6*e^4 + 45*e^3 + 25*e^2 - 36*e - 12, 13*e^9 + 46*e^8 - 69*e^7 - 352*e^6 + 34*e^5 + 872*e^4 + 259*e^3 - 700*e^2 - 295*e + 8, 14*e^9 + 44*e^8 - 82*e^7 - 323*e^6 + 96*e^5 + 749*e^4 + 142*e^3 - 545*e^2 - 230*e - 1, -7*e^9 - 28*e^8 + 36*e^7 + 228*e^6 - 5*e^5 - 602*e^4 - 169*e^3 + 518*e^2 + 170*e - 32, 8*e^9 + 31*e^8 - 37*e^7 - 237*e^6 - 16*e^5 + 582*e^4 + 222*e^3 - 455*e^2 - 187*e + 13, e^9 + 4*e^8 - 14*e^6 - 19*e^5 - 22*e^4 + 21*e^3 + 86*e^2 + 16*e - 35, e^9 - 4*e^8 - 22*e^7 + 32*e^6 + 123*e^5 - 88*e^4 - 247*e^3 + 86*e^2 + 148*e - 3, -6*e^7 - 13*e^6 + 42*e^5 + 81*e^4 - 88*e^3 - 132*e^2 + 54*e + 31, -4*e^9 - 18*e^8 + 11*e^7 + 130*e^6 + 59*e^5 - 296*e^4 - 230*e^3 + 214*e^2 + 196*e - 4, -5*e^9 - 8*e^8 + 49*e^7 + 58*e^6 - 173*e^5 - 126*e^4 + 240*e^3 + 88*e^2 - 83*e - 30, -7*e^9 - 25*e^8 + 32*e^7 + 175*e^6 + 8*e^5 - 383*e^4 - 183*e^3 + 260*e^2 + 192*e + 10, -9*e^9 - 31*e^8 + 44*e^7 + 218*e^6 - 21*e^5 - 491*e^4 - 125*e^3 + 366*e^2 + 116*e - 21, 7*e^9 + 28*e^8 - 27*e^7 - 204*e^6 - 38*e^5 + 484*e^4 + 216*e^3 - 384*e^2 - 154*e + 2, -2*e^9 - 8*e^8 + 9*e^7 + 64*e^6 + 13*e^5 - 170*e^4 - 113*e^3 + 152*e^2 + 135*e + 2, 4*e^9 + 14*e^8 - 28*e^7 - 126*e^6 + 44*e^5 + 372*e^4 + 48*e^3 - 357*e^2 - 108*e + 9, -6*e^9 - 24*e^8 + 26*e^7 + 177*e^6 + 10*e^5 - 430*e^4 - 150*e^3 + 351*e^2 + 156*e - 14, 6*e^8 + 11*e^7 - 51*e^6 - 76*e^5 + 153*e^4 + 169*e^3 - 150*e^2 - 120*e - 14, -2*e^9 - 9*e^8 + 4*e^7 + 59*e^6 + 27*e^5 - 123*e^4 - 74*e^3 + 88*e^2 + 44*e - 23, -9*e^9 - 34*e^8 + 43*e^7 + 249*e^6 - 9*e^5 - 584*e^4 - 168*e^3 + 441*e^2 + 174*e - 17, -3*e^9 - 4*e^8 + 33*e^7 + 30*e^6 - 136*e^5 - 68*e^4 + 229*e^3 + 40*e^2 - 115*e - 8, 2*e^9 + 8*e^8 - 6*e^7 - 64*e^6 - 46*e^5 + 165*e^4 + 210*e^3 - 141*e^2 - 206*e - 6, -9*e^9 - 26*e^8 + 61*e^7 + 196*e^6 - 118*e^5 - 464*e^4 + 27*e^3 + 335*e^2 + 67*e - 10, 3*e^9 + 17*e^8 - 2*e^7 - 119*e^6 - 73*e^5 + 258*e^4 + 201*e^3 - 147*e^2 - 149*e - 28, -2*e^9 - 2*e^8 + 24*e^7 + 26*e^6 - 93*e^5 - 112*e^4 + 120*e^3 + 168*e^2 - 24*e - 48, -5*e^8 - 11*e^7 + 39*e^6 + 78*e^5 - 97*e^4 - 167*e^3 + 61*e^2 + 102*e + 24, 6*e^9 + 17*e^8 - 32*e^7 - 106*e^6 + 40*e^5 + 200*e^4 + 6*e^3 - 131*e^2 - 6*e + 33, -4*e^9 - 10*e^8 + 24*e^7 + 60*e^6 - 46*e^5 - 105*e^4 + 44*e^3 + 64*e^2 - 40*e - 21, 3*e^9 + 5*e^8 - 23*e^7 - 28*e^6 + 64*e^5 + 40*e^4 - 80*e^3 - 8*e^2 + 48*e - 10, -10*e^9 - 34*e^8 + 61*e^7 + 265*e^6 - 86*e^5 - 675*e^4 - 79*e^3 + 562*e^2 + 182*e - 16, 7*e^9 + 19*e^8 - 52*e^7 - 151*e^6 + 114*e^5 + 386*e^4 - 37*e^3 - 321*e^2 - 79*e + 26, -2*e^9 - 3*e^8 + 21*e^7 + 22*e^6 - 83*e^5 - 45*e^4 + 150*e^3 + 25*e^2 - 119*e - 11, 5*e^9 + 14*e^8 - 33*e^7 - 104*e^6 + 60*e^5 + 252*e^4 + 4*e^3 - 196*e^2 - 53*e - 20, -10*e^9 - 33*e^8 + 59*e^7 + 244*e^6 - 92*e^5 - 593*e^4 - 4*e^3 + 496*e^2 + 68*e - 49, 6*e^9 + 20*e^8 - 28*e^7 - 138*e^6 - 3*e^5 + 302*e^4 + 142*e^3 - 226*e^2 - 133*e + 30, 4*e^9 + 20*e^8 - 5*e^7 - 145*e^6 - 96*e^5 + 339*e^4 + 285*e^3 - 252*e^2 - 198*e - 22, -5*e^9 - 18*e^8 + 27*e^7 + 136*e^6 - 27*e^5 - 342*e^4 - 44*e^3 + 304*e^2 + 45*e - 24, 2*e^9 + 19*e^8 + 11*e^7 - 151*e^6 - 140*e^5 + 401*e^4 + 341*e^3 - 356*e^2 - 245*e + 13, -3*e^9 - 6*e^8 + 25*e^7 + 33*e^6 - 91*e^5 - 39*e^4 + 175*e^3 - 13*e^2 - 147*e - 1, -2*e^9 - 8*e^8 + 19*e^7 + 80*e^6 - 60*e^5 - 256*e^4 + 65*e^3 + 272*e^2 - 2*e - 44, 2*e^9 - 2*e^8 - 30*e^7 + 8*e^6 + 123*e^5 + e^4 - 144*e^3 - 13*e^2 - 3*e - 14, -7*e^9 - 23*e^8 + 36*e^7 + 173*e^6 - 3*e^5 - 426*e^4 - 194*e^3 + 346*e^2 + 196*e, e^9 + e^8 - 12*e^7 - 6*e^6 + 49*e^5 + 5*e^4 - 63*e^3 + 6*e^2 - 4*e + 15, 14*e^9 + 46*e^8 - 78*e^7 - 338*e^6 + 74*e^5 + 796*e^4 + 183*e^3 - 602*e^2 - 244*e + 12, -2*e^9 - 20*e^8 - 18*e^7 + 152*e^6 + 186*e^5 - 390*e^4 - 423*e^3 + 344*e^2 + 274*e + 4, 2*e^8 - 4*e^7 - 30*e^6 + 22*e^5 + 104*e^4 - 34*e^3 - 78*e^2 - 2*e - 24, -10*e^9 - 31*e^8 + 58*e^7 + 227*e^6 - 74*e^5 - 544*e^4 - 75*e^3 + 440*e^2 + 158*e - 31, -e^9 + 6*e^8 + 24*e^7 - 48*e^6 - 118*e^5 + 152*e^4 + 186*e^3 - 180*e^2 - 73*e - 2, -11*e^9 - 35*e^8 + 68*e^7 + 279*e^6 - 69*e^5 - 718*e^4 - 221*e^3 + 595*e^2 + 339*e - 4, -6*e^9 - 15*e^8 + 53*e^7 + 132*e^6 - 149*e^5 - 366*e^4 + 128*e^3 + 311*e^2 + 15*e + 7, 8*e^9 + 26*e^8 - 48*e^7 - 199*e^6 + 57*e^5 + 489*e^4 + 88*e^3 - 385*e^2 - 133*e - 5, -2*e^8 + 2*e^7 + 23*e^6 - 28*e^5 - 92*e^4 + 96*e^3 + 121*e^2 - 82*e - 25, 11*e^9 + 34*e^8 - 66*e^7 - 254*e^6 + 76*e^5 + 594*e^4 + 139*e^3 - 412*e^2 - 214*e - 22, 3*e^9 + 8*e^8 - 29*e^7 - 77*e^6 + 89*e^5 + 229*e^4 - 100*e^3 - 222*e^2 + 38*e + 25, -5*e^9 - 10*e^8 + 38*e^7 + 62*e^6 - 105*e^5 - 110*e^4 + 117*e^3 + 56*e^2 - 26*e - 19, -2*e^9 - 7*e^8 + 9*e^7 + 60*e^6 + 17*e^5 - 183*e^4 - 118*e^3 + 215*e^2 + 119*e - 29, 6*e^9 + 21*e^8 - 43*e^7 - 182*e^6 + 89*e^5 + 515*e^4 - 28*e^3 - 491*e^2 - 61*e + 65, -9*e^9 - 20*e^8 + 66*e^7 + 134*e^6 - 167*e^5 - 278*e^4 + 162*e^3 + 174*e^2 - 49*e + 6, 3*e^9 + 10*e^8 - 16*e^7 - 64*e^6 + 16*e^5 + 106*e^4 + 34*e^3 + 2*e^2 - 49*e - 48, -7*e^8 - 16*e^7 + 51*e^6 + 105*e^5 - 119*e^4 - 181*e^3 + 87*e^2 + 47*e + 3, -8*e^9 - 23*e^8 + 52*e^7 + 168*e^6 - 108*e^5 - 400*e^4 + 86*e^3 + 316*e^2 - 24*e - 25, 8*e^9 + 22*e^8 - 57*e^7 - 175*e^6 + 113*e^5 + 460*e^4 + 3*e^3 - 417*e^2 - 125*e + 48, 2*e^9 + 12*e^8 - 89*e^6 - 61*e^5 + 218*e^4 + 159*e^3 - 182*e^2 - 101*e + 17, 7*e^9 + 20*e^8 - 49*e^7 - 141*e^6 + 125*e^5 + 311*e^4 - 141*e^3 - 215*e^2 + 49*e + 6, -11*e^9 - 46*e^8 + 41*e^7 + 342*e^6 + 76*e^5 - 828*e^4 - 407*e^3 + 658*e^2 + 356*e - 14, 8*e^9 + 23*e^8 - 52*e^7 - 171*e^6 + 92*e^5 + 406*e^4 + 12*e^3 - 287*e^2 - 114*e - 29, -10*e^9 - 27*e^8 + 64*e^7 + 182*e^6 - 126*e^5 - 375*e^4 + 74*e^3 + 231*e^2 - 4*e - 13, -e^9 - 6*e^8 + 13*e^7 + 82*e^6 - 30*e^5 - 309*e^4 - 28*e^3 + 345*e^2 + 92*e - 23, -2*e^9 - 8*e^8 + 8*e^7 + 58*e^6 + 16*e^5 - 128*e^4 - 104*e^3 + 71*e^2 + 113*e + 15, -11*e^9 - 48*e^8 + 43*e^7 + 363*e^6 + 59*e^5 - 883*e^4 - 345*e^3 + 691*e^2 + 269*e - 29, 6*e^9 + 26*e^8 - 25*e^7 - 202*e^6 - 22*e^5 + 526*e^4 + 178*e^3 - 482*e^2 - 152*e + 52, 4*e^8 + 3*e^7 - 46*e^6 - 34*e^5 + 146*e^4 + 92*e^3 - 118*e^2 - 61*e - 28, -8*e^8 - 12*e^7 + 65*e^6 + 81*e^5 - 164*e^4 - 161*e^3 + 123*e^2 + 92*e - 6, -2*e^9 - 11*e^8 + 11*e^7 + 105*e^6 + 8*e^5 - 317*e^4 - 125*e^3 + 277*e^2 + 172*e + 32, 12*e^9 + 45*e^8 - 55*e^7 - 326*e^6 - 2*e^5 + 753*e^4 + 237*e^3 - 545*e^2 - 197*e - 1, 10*e^8 + 12*e^7 - 101*e^6 - 98*e^5 + 332*e^4 + 232*e^3 - 372*e^2 - 142*e + 41, 14*e^9 + 41*e^8 - 92*e^7 - 310*e^6 + 164*e^5 + 753*e^4 + 6*e^3 - 596*e^2 - 172*e + 23, -11*e^9 - 35*e^8 + 66*e^7 + 257*e^6 - 96*e^5 - 592*e^4 - 41*e^3 + 406*e^2 + 110*e + 23, -8*e^9 - 24*e^8 + 54*e^7 + 187*e^6 - 93*e^5 - 457*e^4 - 24*e^3 + 343*e^2 + 103*e + 3, -6*e^9 - 9*e^8 + 63*e^7 + 93*e^6 - 198*e^5 - 294*e^4 + 174*e^3 + 303*e^2 + 27*e - 35, 4*e^9 + 17*e^8 - 10*e^7 - 115*e^6 - 49*e^5 + 239*e^4 + 142*e^3 - 142*e^2 - 62*e - 23]
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^3 + w^2 + 6*w + 1])] = -1

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