/*
  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([44, 2, -15, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([16, 4, w^3 - 3*w^2 - 8*w + 16])

primes_array = [
[4, 2, w + 2],\
[4, 2, -1/2*w^3 + 3/2*w^2 + 9/2*w - 10],\
[9, 3, 1/2*w^3 - 5/2*w^2 - 5/2*w + 17],\
[9, 3, 3/2*w^3 - 11/2*w^2 - 19/2*w + 28],\
[11, 11, 1/2*w^3 - 3/2*w^2 - 9/2*w + 11],\
[11, 11, -w - 3],\
[25, 5, w^3 - 3*w^2 - 7*w + 15],\
[29, 29, w + 1],\
[29, 29, 1/2*w^3 - 3/2*w^2 - 9/2*w + 9],\
[31, 31, -1/2*w^3 + 5/2*w^2 + 5/2*w - 16],\
[31, 31, 1/2*w^3 - 3/2*w^2 - 9/2*w + 5],\
[31, 31, -w + 3],\
[31, 31, 3/2*w^3 - 11/2*w^2 - 19/2*w + 29],\
[59, 59, 2*w^2 - w - 13],\
[59, 59, 9/2*w^3 - 31/2*w^2 - 61/2*w + 85],\
[61, 61, 2*w^3 - 6*w^2 - 15*w + 31],\
[61, 61, -3/2*w^3 + 11/2*w^2 + 21/2*w - 34],\
[71, 71, 3/2*w^3 - 11/2*w^2 - 19/2*w + 32],\
[71, 71, -1/2*w^3 + 5/2*w^2 + 5/2*w - 13],\
[79, 79, -3*w^3 + 10*w^2 + 19*w - 51],\
[79, 79, 15/2*w^3 - 51/2*w^2 - 103/2*w + 139],\
[101, 101, -2*w^3 + 7*w^2 + 14*w - 37],\
[101, 101, -1/2*w^3 + 5/2*w^2 + 7/2*w - 16],\
[109, 109, w^3 - 3*w^2 - 6*w + 19],\
[109, 109, -w^3 + 4*w^2 + 5*w - 19],\
[121, 11, -3/2*w^3 + 9/2*w^2 + 21/2*w - 23],\
[139, 139, -w^3 + 4*w^2 + 7*w - 25],\
[139, 139, -5/2*w^3 + 17/2*w^2 + 33/2*w - 41],\
[149, 149, 1/2*w^3 + 1/2*w^2 - 11/2*w - 8],\
[149, 149, 5/2*w^3 - 19/2*w^2 - 35/2*w + 50],\
[149, 149, -9/2*w^3 + 31/2*w^2 + 59/2*w - 82],\
[149, 149, -5/2*w^3 + 19/2*w^2 + 35/2*w - 56],\
[151, 151, -1/2*w^3 + 3/2*w^2 + 3/2*w - 12],\
[151, 151, 3/2*w^3 - 9/2*w^2 - 25/2*w + 28],\
[179, 179, -1/2*w^3 + 3/2*w^2 + 9/2*w - 3],\
[179, 179, w - 5],\
[229, 229, -15/2*w^3 + 51/2*w^2 + 105/2*w - 142],\
[229, 229, 1/2*w^3 - 7/2*w^2 - 7/2*w + 19],\
[229, 229, -17/2*w^3 + 57/2*w^2 + 119/2*w - 156],\
[229, 229, -9/2*w^3 + 33/2*w^2 + 55/2*w - 82],\
[239, 239, -9*w^3 + 31*w^2 + 59*w - 161],\
[239, 239, w^3 + w^2 - 11*w - 19],\
[241, 241, 5/2*w^3 - 15/2*w^2 - 37/2*w + 37],\
[241, 241, -2*w^3 + 6*w^2 + 13*w - 29],\
[251, 251, -7/2*w^3 + 25/2*w^2 + 45/2*w - 67],\
[251, 251, 1/2*w^3 - 5/2*w^2 - 13/2*w + 7],\
[251, 251, -1/2*w^3 + 1/2*w^2 + 13/2*w + 4],\
[251, 251, -1/2*w^3 + 7/2*w^2 + 3/2*w - 23],\
[271, 271, -w^3 + 4*w^2 + 5*w - 25],\
[271, 271, -5/2*w^3 + 17/2*w^2 + 33/2*w - 47],\
[281, 281, 5/2*w^3 - 15/2*w^2 - 39/2*w + 41],\
[281, 281, 3/2*w^3 - 7/2*w^2 - 27/2*w + 14],\
[289, 17, -7/2*w^3 + 25/2*w^2 + 45/2*w - 62],\
[289, 17, 5/2*w^3 - 15/2*w^2 - 39/2*w + 37],\
[311, 311, -19/2*w^3 + 65/2*w^2 + 129/2*w - 175],\
[311, 311, -7/2*w^3 + 25/2*w^2 + 47/2*w - 71],\
[311, 311, 7/2*w^3 - 25/2*w^2 - 49/2*w + 67],\
[311, 311, -3/2*w^3 + 11/2*w^2 + 15/2*w - 31],\
[331, 331, 19/2*w^3 - 65/2*w^2 - 127/2*w + 173],\
[331, 331, -w^3 - w^2 + 10*w + 15],\
[349, 349, -5/2*w^3 + 15/2*w^2 + 33/2*w - 35],\
[349, 349, 3/2*w^3 - 11/2*w^2 - 21/2*w + 36],\
[361, 19, 2*w^3 - 6*w^2 - 14*w + 29],\
[361, 19, 2*w^3 - 6*w^2 - 14*w + 31],\
[379, 379, 1/2*w^3 - 5/2*w^2 - 1/2*w + 20],\
[379, 379, -1/2*w^3 + 5/2*w^2 + 1/2*w - 9],\
[401, 401, -7/2*w^3 + 25/2*w^2 + 45/2*w - 69],\
[401, 401, w^3 - 3*w^2 - 5*w + 19],\
[409, 409, 3/2*w^3 - 7/2*w^2 - 23/2*w + 13],\
[409, 409, -11/2*w^3 + 37/2*w^2 + 77/2*w - 100],\
[409, 409, 7/2*w^3 - 23/2*w^2 - 47/2*w + 58],\
[409, 409, -w^3 + 3*w^2 + 9*w - 9],\
[419, 419, 3/2*w^3 - 13/2*w^2 - 17/2*w + 36],\
[419, 419, -5/2*w^3 + 19/2*w^2 + 31/2*w - 54],\
[421, 421, -w^3 + 4*w^2 + 5*w - 27],\
[421, 421, 7/2*w^3 - 23/2*w^2 - 47/2*w + 63],\
[439, 439, 2*w^3 - 7*w^2 - 14*w + 35],\
[439, 439, -1/2*w^3 + 5/2*w^2 + 7/2*w - 18],\
[461, 461, -5/2*w^3 + 17/2*w^2 + 33/2*w - 48],\
[461, 461, -13/2*w^3 + 45/2*w^2 + 85/2*w - 119],\
[461, 461, -1/2*w^3 + 3/2*w^2 + 1/2*w - 15],\
[461, 461, 3/2*w^3 - 11/2*w^2 - 17/2*w + 32],\
[479, 479, -3*w^3 + 10*w^2 + 19*w - 53],\
[479, 479, 5/2*w^3 - 17/2*w^2 - 33/2*w + 51],\
[491, 491, 3*w^2 - 2*w - 23],\
[491, 491, 13/2*w^3 - 45/2*w^2 - 87/2*w + 120],\
[499, 499, -3*w^3 + 11*w^2 + 21*w - 63],\
[499, 499, -5/2*w^3 + 19/2*w^2 + 31/2*w - 50],\
[499, 499, 11/2*w^3 - 37/2*w^2 - 75/2*w + 101],\
[499, 499, 9*w^3 - 31*w^2 - 58*w + 159],\
[509, 509, 3/2*w^3 - 9/2*w^2 - 23/2*w + 29],\
[509, 509, w^3 - 3*w^2 - 6*w + 21],\
[521, 521, 2*w^3 - 8*w^2 - 12*w + 43],\
[521, 521, -3/2*w^3 + 11/2*w^2 + 19/2*w - 36],\
[521, 521, 2*w^3 - 8*w^2 - 12*w + 47],\
[521, 521, -7/2*w^3 + 23/2*w^2 + 45/2*w - 58],\
[541, 541, -1/2*w^3 + 5/2*w^2 + 13/2*w - 6],\
[541, 541, 9/2*w^3 - 33/2*w^2 - 55/2*w + 80],\
[541, 541, -15/2*w^3 + 51/2*w^2 + 101/2*w - 134],\
[541, 541, w^3 - w^2 - 7*w + 1],\
[571, 571, 13/2*w^3 - 47/2*w^2 - 79/2*w + 116],\
[571, 571, -5/2*w^3 + 11/2*w^2 + 43/2*w - 21],\
[599, 599, -3*w^3 + 9*w^2 + 19*w - 47],\
[599, 599, -15/2*w^3 + 51/2*w^2 + 103/2*w - 137],\
[599, 599, -w^3 + 2*w^2 + 11*w + 1],\
[599, 599, 5/2*w^3 - 17/2*w^2 - 35/2*w + 38],\
[601, 601, -1/2*w^3 + 11/2*w^2 - 5/2*w - 47],\
[601, 601, -3/2*w^3 + 13/2*w^2 + 17/2*w - 30],\
[619, 619, -w^3 + 5*w^2 + 5*w - 27],\
[619, 619, -1/2*w^3 + 1/2*w^2 + 11/2*w - 2],\
[619, 619, -2*w^3 + 7*w^2 + 12*w - 39],\
[619, 619, -3*w^3 + 11*w^2 + 19*w - 63],\
[631, 631, -3/2*w^3 + 13/2*w^2 + 17/2*w - 37],\
[631, 631, 5/2*w^3 - 19/2*w^2 - 31/2*w + 53],\
[641, 641, 5*w^3 - 16*w^2 - 35*w + 79],\
[641, 641, -2*w^3 + 8*w^2 + 12*w - 53],\
[641, 641, 3/2*w^3 - 11/2*w^2 - 23/2*w + 34],\
[641, 641, 3/2*w^3 - 11/2*w^2 - 23/2*w + 27],\
[659, 659, -5/2*w^3 + 19/2*w^2 + 31/2*w - 51],\
[659, 659, -3/2*w^3 + 13/2*w^2 + 17/2*w - 39],\
[661, 661, -5/2*w^3 + 17/2*w^2 + 33/2*w - 50],\
[661, 661, 5*w^3 - 17*w^2 - 30*w + 83],\
[661, 661, 5/2*w^3 - 17/2*w^2 - 31/2*w + 46],\
[661, 661, 3/2*w^3 - 5/2*w^2 - 21/2*w + 9],\
[691, 691, -3/2*w^3 + 13/2*w^2 + 19/2*w - 35],\
[691, 691, 3*w^3 - 11*w^2 - 20*w + 63],\
[709, 709, 19/2*w^3 - 65/2*w^2 - 127/2*w + 171],\
[709, 709, 4*w^3 - 14*w^2 - 28*w + 75],\
[709, 709, 1/2*w^3 - 5/2*w^2 - 15/2*w + 4],\
[709, 709, -w^3 + 5*w^2 + 7*w - 31],\
[739, 739, 11/2*w^3 - 37/2*w^2 - 73/2*w + 95],\
[739, 739, -3/2*w^3 + 5/2*w^2 + 25/2*w - 5],\
[739, 739, 27/2*w^3 - 91/2*w^2 - 187/2*w + 247],\
[739, 739, 4*w^3 - 15*w^2 - 24*w + 73],\
[751, 751, -5/2*w^3 + 19/2*w^2 + 35/2*w - 49],\
[751, 751, -2*w^2 + 2*w + 21],\
[751, 751, -9*w^3 + 31*w^2 + 61*w - 169],\
[751, 751, 17/2*w^3 - 57/2*w^2 - 117/2*w + 152],\
[761, 761, 5/2*w^3 - 15/2*w^2 - 33/2*w + 39],\
[761, 761, -3*w^3 + 9*w^2 + 22*w - 47],\
[761, 761, 9/2*w^3 - 29/2*w^2 - 61/2*w + 80],\
[761, 761, 25/2*w^3 - 85/2*w^2 - 169/2*w + 227],\
[769, 769, 2*w^3 - 8*w^2 - 12*w + 45],\
[811, 811, 5/2*w^3 - 19/2*w^2 - 27/2*w + 45],\
[811, 811, 1/2*w^3 - 7/2*w^2 + 1/2*w + 29],\
[821, 821, 25/2*w^3 - 85/2*w^2 - 173/2*w + 233],\
[821, 821, 19/2*w^3 - 63/2*w^2 - 135/2*w + 173],\
[829, 829, -7/2*w^3 + 27/2*w^2 + 43/2*w - 79],\
[829, 829, 10*w^3 - 34*w^2 - 67*w + 179],\
[829, 829, -3/2*w^3 + 1/2*w^2 + 27/2*w + 9],\
[829, 829, 5/2*w^3 - 13/2*w^2 - 41/2*w + 31],\
[839, 839, -3/2*w^3 + 11/2*w^2 + 25/2*w - 26],\
[839, 839, 2*w^3 - 7*w^2 - 16*w + 43],\
[841, 29, 5/2*w^3 - 15/2*w^2 - 35/2*w + 39],\
[881, 881, -8*w^3 + 27*w^2 + 56*w - 151],\
[881, 881, -w^3 + 3*w^2 + 4*w - 21],\
[911, 911, 5/2*w^3 - 19/2*w^2 - 33/2*w + 51],\
[911, 911, 2*w^3 - 8*w^2 - 13*w + 47],\
[919, 919, 3/2*w^3 - 9/2*w^2 - 27/2*w + 29],\
[919, 919, -3*w - 5],\
[919, 919, 1/2*w^3 - 7/2*w^2 - 5/2*w + 17],\
[919, 919, -4*w^3 + 14*w^2 + 27*w - 81],\
[929, 929, 7/2*w^3 - 23/2*w^2 - 49/2*w + 58],\
[929, 929, 13*w^3 - 44*w^2 - 89*w + 237],\
[929, 929, 9/2*w^3 - 29/2*w^2 - 59/2*w + 78],\
[929, 929, -w^3 + 2*w^2 + 7*w - 5],\
[941, 941, 5/2*w^3 - 19/2*w^2 - 31/2*w + 59],\
[941, 941, -3/2*w^3 + 13/2*w^2 + 17/2*w - 31],\
[941, 941, w^3 - 3*w^2 - 10*w + 7],\
[941, 941, -8*w^3 + 27*w^2 + 56*w - 147],\
[971, 971, -9/2*w^3 + 29/2*w^2 + 73/2*w - 92],\
[971, 971, -1/2*w^3 + 5/2*w^2 + 17/2*w - 1],\
[991, 991, w^3 - 4*w^2 - 3*w + 15],\
[991, 991, -1/2*w^3 + 1/2*w^2 + 15/2*w + 6],\
[1019, 1019, 3*w^3 - 9*w^2 - 19*w + 45],\
[1019, 1019, 3*w^3 - 11*w^2 - 20*w + 53],\
[1019, 1019, -1/2*w^3 + 1/2*w^2 + 17/2*w + 9],\
[1019, 1019, -1/2*w^3 + 5/2*w^2 - 3/2*w - 4],\
[1021, 1021, -3/2*w^3 + 13/2*w^2 + 19/2*w - 37],\
[1021, 1021, 3*w^3 - 11*w^2 - 20*w + 61],\
[1049, 1049, w^3 - 4*w^2 - 9*w + 15],\
[1049, 1049, 5/2*w^3 - 17/2*w^2 - 39/2*w + 54],\
[1051, 1051, 3/2*w^3 - 11/2*w^2 - 15/2*w + 21],\
[1051, 1051, -1/2*w^3 + 7/2*w^2 + 7/2*w - 23],\
[1051, 1051, 9/2*w^3 - 31/2*w^2 - 63/2*w + 83],\
[1051, 1051, -1/2*w^3 + 1/2*w^2 + 13/2*w + 8],\
[1061, 1061, 2*w^3 - 5*w^2 - 14*w + 19],\
[1061, 1061, 9/2*w^3 - 29/2*w^2 - 63/2*w + 72],\
[1091, 1091, 3/2*w^3 - 5/2*w^2 - 21/2*w + 10],\
[1091, 1091, 3/2*w^3 - 3/2*w^2 - 19/2*w + 7],\
[1091, 1091, -13/2*w^3 + 43/2*w^2 + 91/2*w - 116],\
[1091, 1091, 19/2*w^3 - 63/2*w^2 - 135/2*w + 174],\
[1109, 1109, -5/2*w^3 + 17/2*w^2 + 33/2*w - 53],\
[1109, 1109, 4*w^3 - 13*w^2 - 26*w + 67],\
[1109, 1109, -3/2*w^3 + 11/2*w^2 + 23/2*w - 25],\
[1109, 1109, 4*w^3 - 13*w^2 - 28*w + 65],\
[1171, 1171, 1/2*w^3 - 1/2*w^2 + 3/2*w + 12],\
[1171, 1171, 11/2*w^3 - 35/2*w^2 - 87/2*w + 105],\
[1181, 1181, 2*w^3 - 8*w^2 - 13*w + 45],\
[1181, 1181, -5/2*w^3 + 19/2*w^2 + 33/2*w - 53],\
[1201, 1201, -5/2*w^3 + 15/2*w^2 + 39/2*w - 45],\
[1201, 1201, -1/2*w^3 + 3/2*w^2 + 13/2*w - 3],\
[1201, 1201, -w^3 + 3*w^2 + 10*w - 21],\
[1201, 1201, 3/2*w^3 - 9/2*w^2 - 17/2*w + 29],\
[1229, 1229, -5*w^3 + 17*w^2 + 35*w - 91],\
[1229, 1229, 3/2*w^3 - 9/2*w^2 - 25/2*w + 17],\
[1249, 1249, 5/2*w^3 - 17/2*w^2 - 35/2*w + 40],\
[1249, 1249, 3/2*w^3 - 3/2*w^2 - 21/2*w + 4],\
[1249, 1249, w^2 - 13],\
[1249, 1249, 9*w^3 - 30*w^2 - 63*w + 163],\
[1289, 1289, 3/2*w^3 - 1/2*w^2 - 23/2*w - 3],\
[1289, 1289, 11*w^3 - 37*w^2 - 76*w + 201],\
[1291, 1291, -1/2*w^3 - 7/2*w^2 + 13/2*w + 29],\
[1291, 1291, 23/2*w^3 - 79/2*w^2 - 155/2*w + 212],\
[1301, 1301, 11*w^3 - 38*w^2 - 73*w + 201],\
[1301, 1301, 1/2*w^3 - 5/2*w^2 - 17/2*w + 3],\
[1319, 1319, 12*w^3 - 40*w^2 - 85*w + 219],\
[1319, 1319, 3/2*w^3 - 1/2*w^2 - 19/2*w - 1],\
[1321, 1321, -1/2*w^3 - 1/2*w^2 - 1/2*w - 7],\
[1321, 1321, -3*w^3 + 11*w^2 + 15*w - 45],\
[1361, 1361, -3*w^3 + 11*w^2 + 21*w - 57],\
[1361, 1361, 5/2*w^3 - 15/2*w^2 - 39/2*w + 35],\
[1381, 1381, -3*w^3 + 9*w^2 + 23*w - 43],\
[1381, 1381, 2*w^3 - 6*w^2 - 12*w + 27],\
[1381, 1381, -1/2*w^3 + 3/2*w^2 + 9/2*w - 1],\
[1381, 1381, w - 7],\
[1399, 1399, 9/2*w^3 - 33/2*w^2 - 57/2*w + 85],\
[1399, 1399, -5/2*w^3 + 15/2*w^2 + 41/2*w - 37],\
[1409, 1409, 3/2*w^3 - 1/2*w^2 - 21/2*w - 1],\
[1409, 1409, -23/2*w^3 + 77/2*w^2 + 161/2*w - 211],\
[1409, 1409, 11/2*w^3 - 39/2*w^2 - 71/2*w + 98],\
[1409, 1409, 1/2*w^3 - 9/2*w^2 - 1/2*w + 37],\
[1429, 1429, 3/2*w^3 - 5/2*w^2 - 33/2*w - 5],\
[1429, 1429, 7/2*w^3 - 25/2*w^2 - 37/2*w + 53],\
[1439, 1439, -7*w^3 + 23*w^2 + 52*w - 135],\
[1439, 1439, -1/2*w^3 - 1/2*w^2 + 1/2*w - 5],\
[1451, 1451, 1/2*w^3 + 3/2*w^2 - 13/2*w - 15],\
[1451, 1451, -13/2*w^3 + 45/2*w^2 + 85/2*w - 120],\
[1459, 1459, -7/2*w^3 + 27/2*w^2 + 43/2*w - 70],\
[1459, 1459, 5/2*w^3 - 21/2*w^2 - 29/2*w + 65],\
[1471, 1471, 5/2*w^3 - 17/2*w^2 - 37/2*w + 43],\
[1471, 1471, -3*w^3 + 10*w^2 + 21*w - 49],\
[1481, 1481, -6*w^3 + 21*w^2 + 40*w - 113],\
[1481, 1481, -16*w^3 + 54*w^2 + 112*w - 299],\
[1481, 1481, 9*w^3 - 30*w^2 - 63*w + 161],\
[1481, 1481, 1/2*w^3 - 9/2*w^2 - 3/2*w + 30],\
[1489, 1489, -8*w^3 + 26*w^2 + 60*w - 151],\
[1489, 1489, -w^3 + 5*w^2 + 6*w - 35],\
[1489, 1489, 7/2*w^3 - 25/2*w^2 - 47/2*w + 63],\
[1489, 1489, -w^3 + w^2 + 3*w - 13],\
[1499, 1499, 3*w^3 - 10*w^2 - 21*w + 45],\
[1499, 1499, 9/2*w^3 - 29/2*w^2 - 65/2*w + 75],\
[1511, 1511, -11/2*w^3 + 35/2*w^2 + 79/2*w - 91],\
[1511, 1511, -5/2*w^3 + 21/2*w^2 + 33/2*w - 54],\
[1511, 1511, 7/2*w^3 - 19/2*w^2 - 57/2*w + 42],\
[1511, 1511, 5/2*w^3 - 15/2*w^2 - 29/2*w + 41],\
[1531, 1531, -4*w^2 + 2*w + 29],\
[1531, 1531, 9*w^3 - 31*w^2 - 61*w + 167],\
[1549, 1549, -1/2*w^3 + 1/2*w^2 + 13/2*w - 5],\
[1549, 1549, -3/2*w^3 + 11/2*w^2 + 15/2*w - 34],\
[1559, 1559, 9/2*w^3 - 29/2*w^2 - 63/2*w + 76],\
[1559, 1559, 2*w^3 - 5*w^2 - 14*w + 23],\
[1571, 1571, 3*w^3 - 9*w^2 - 20*w + 43],\
[1571, 1571, 2*w^3 - 7*w^2 - 14*w + 45],\
[1601, 1601, -27/2*w^3 + 93/2*w^2 + 179/2*w - 247],\
[1601, 1601, 1/2*w^3 - 1/2*w^2 + 5/2*w + 16],\
[1609, 1609, -1/2*w^3 + 7/2*w^2 + 1/2*w - 31],\
[1609, 1609, 3/2*w^3 - 7/2*w^2 - 23/2*w + 25],\
[1621, 1621, 7/2*w^3 - 25/2*w^2 - 45/2*w + 71],\
[1621, 1621, -1/2*w^3 + 7/2*w^2 + 3/2*w - 19],\
[1681, 41, -3*w^3 + 9*w^2 + 21*w - 43],\
[1681, 41, 3*w^3 - 9*w^2 - 21*w + 47],\
[1721, 1721, -1/2*w^3 - 3/2*w^2 + 21/2*w + 25],\
[1721, 1721, -9/2*w^3 + 33/2*w^2 + 49/2*w - 78],\
[1759, 1759, 4*w^3 - 14*w^2 - 25*w + 75],\
[1759, 1759, 2*w^3 - 7*w^2 - 12*w + 43],\
[1831, 1831, -3/2*w^3 + 7/2*w^2 + 29/2*w - 6],\
[1831, 1831, 15/2*w^3 - 51/2*w^2 - 103/2*w + 136],\
[1849, 43, -1/2*w^3 + 7/2*w^2 - 3/2*w - 31],\
[1849, 43, 15/2*w^3 - 51/2*w^2 - 101/2*w + 138],\
[1871, 1871, 3*w^3 - 9*w^2 - 18*w + 43],\
[1871, 1871, -7/2*w^3 + 21/2*w^2 + 45/2*w - 51],\
[1879, 1879, 21/2*w^3 - 71/2*w^2 - 145/2*w + 195],\
[1879, 1879, -w^3 - w^2 + 8*w + 9],\
[1889, 1889, 2*w^3 - 4*w^2 - 16*w + 15],\
[1889, 1889, -6*w^3 + 20*w^2 + 40*w - 105],\
[1901, 1901, 2*w^2 - 7*w - 29],\
[1901, 1901, -19/2*w^3 + 65/2*w^2 + 133/2*w - 182],\
[1901, 1901, 1/2*w^3 - 11/2*w^2 - 7/2*w + 30],\
[1901, 1901, -1/2*w^3 + 5/2*w^2 + 1/2*w - 24],\
[1931, 1931, -1/2*w^3 + 9/2*w^2 + 3/2*w - 34],\
[1931, 1931, -5/2*w^3 + 19/2*w^2 + 35/2*w - 59],\
[1931, 1931, -5/2*w^3 + 19/2*w^2 + 35/2*w - 47],\
[1931, 1931, 6*w^3 - 21*w^2 - 40*w + 109],\
[1949, 1949, -3/2*w^3 + 15/2*w^2 + 19/2*w - 46],\
[1949, 1949, -11/2*w^3 + 39/2*w^2 + 75/2*w - 105],\
[1979, 1979, -7/2*w^3 + 21/2*w^2 + 55/2*w - 51],\
[1979, 1979, 3/2*w^3 - 5/2*w^2 - 29/2*w + 7],\
[1979, 1979, 9/2*w^3 - 31/2*w^2 - 55/2*w + 81],\
[1979, 1979, -2*w^3 + 6*w^2 + 11*w - 27]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^5 - x^4 - 13*x^3 + 25*x^2 - 2*x - 12
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [0, e, e^4 + e^3 - 12*e^2 + 2*e + 11, -3/2*e^4 - 1/2*e^3 + 37/2*e^2 - 25/2*e - 10, -e^4 + 13*e^2 - 12*e - 8, 3*e^4 + e^3 - 38*e^2 + 25*e + 27, 4*e^4 + e^3 - 51*e^2 + 35*e + 35, -3/2*e^4 - 1/2*e^3 + 39/2*e^2 - 23/2*e - 16, 4*e^4 + e^3 - 51*e^2 + 35*e + 36, 3/2*e^4 + 1/2*e^3 - 37/2*e^2 + 27/2*e + 16, -5*e^4 - 2*e^3 + 62*e^2 - 38*e - 37, -2*e + 2, -13/2*e^4 - 5/2*e^3 + 161/2*e^2 - 99/2*e - 55, -10*e^4 - 4*e^3 + 125*e^2 - 76*e - 89, -e^4 + 13*e^2 - 10*e, -3*e^4 - 2*e^3 + 37*e^2 - 14*e - 29, 7/2*e^4 + 3/2*e^3 - 87/2*e^2 + 49/2*e + 36, 21/2*e^4 + 9/2*e^3 - 259/2*e^2 + 155/2*e + 88, 7/2*e^4 + 1/2*e^3 - 91/2*e^2 + 63/2*e + 41, -1/2*e^4 + 1/2*e^3 + 15/2*e^2 - 21/2*e - 2, -19/2*e^4 - 9/2*e^3 + 233/2*e^2 - 131/2*e - 80, 13/2*e^4 + 5/2*e^3 - 157/2*e^2 + 109/2*e + 43, -21/2*e^4 - 7/2*e^3 + 263/2*e^2 - 179/2*e - 88, -11*e^4 - 4*e^3 + 136*e^2 - 92*e - 80, 3*e^4 + 2*e^3 - 36*e^2 + 18*e + 28, 13*e^4 + 5*e^3 - 161*e^2 + 104*e + 106, 31/2*e^4 + 11/2*e^3 - 385/2*e^2 + 257/2*e + 124, -21/2*e^4 - 7/2*e^3 + 261/2*e^2 - 177/2*e - 81, 15/2*e^4 + 5/2*e^3 - 187/2*e^2 + 131/2*e + 66, -27/2*e^4 - 13/2*e^3 + 335/2*e^2 - 181/2*e - 121, 3*e^4 + e^3 - 37*e^2 + 29*e + 23, 39/2*e^4 + 17/2*e^3 - 487/2*e^2 + 281/2*e + 179, 16*e^4 + 6*e^3 - 201*e^2 + 124*e + 141, -23/2*e^4 - 9/2*e^3 + 285/2*e^2 - 175/2*e - 98, -13*e^4 - 5*e^3 + 162*e^2 - 101*e - 113, 22*e^4 + 10*e^3 - 271*e^2 + 156*e + 199, 8*e^4 + e^3 - 100*e^2 + 85*e + 57, 21*e^4 + 9*e^3 - 257*e^2 + 158*e + 168, 7*e^4 + 2*e^3 - 91*e^2 + 56*e + 75, 3*e^4 + 2*e^3 - 36*e^2 + 15*e + 33, 7/2*e^4 + 7/2*e^3 - 79/2*e^2 + 17/2*e + 21, 17/2*e^4 + 7/2*e^3 - 211/2*e^2 + 125/2*e + 68, 2*e^4 + e^3 - 27*e^2 + 13*e + 32, -19/2*e^4 - 9/2*e^3 + 235/2*e^2 - 131/2*e - 98, -2*e^4 - 2*e^3 + 25*e^2 + 2*e - 17, -5*e^4 - 2*e^3 + 65*e^2 - 34*e - 68, -4*e^4 + 51*e^2 - 46*e - 33, -23*e^4 - 10*e^3 + 283*e^2 - 168*e - 196, 13/2*e^4 + 5/2*e^3 - 159/2*e^2 + 103/2*e + 52, -18*e^4 - 8*e^3 + 222*e^2 - 130*e - 166, -12*e^4 - 6*e^3 + 147*e^2 - 84*e - 105, 7/2*e^4 + 3/2*e^3 - 87/2*e^2 + 57/2*e + 41, 12*e^4 + 3*e^3 - 150*e^2 + 110*e + 96, -57/2*e^4 - 23/2*e^3 + 703/2*e^2 - 447/2*e - 234, 1/2*e^4 - 5/2*e^3 - 13/2*e^2 + 65/2*e - 13, 45/2*e^4 + 21/2*e^3 - 555/2*e^2 + 315/2*e + 210, -33/2*e^4 - 13/2*e^3 + 419/2*e^2 - 243/2*e - 166, 25/2*e^4 + 13/2*e^3 - 307/2*e^2 + 171/2*e + 108, -15/2*e^4 - 9/2*e^3 + 189/2*e^2 - 79/2*e - 84, -3/2*e^4 + 3/2*e^3 + 41/2*e^2 - 59/2*e - 4, 7*e^4 + e^3 - 89*e^2 + 70*e + 56, -6*e^4 - 5*e^3 + 73*e^2 - 26*e - 71, -37/2*e^4 - 17/2*e^3 + 457/2*e^2 - 255/2*e - 155, -13*e^4 - 5*e^3 + 164*e^2 - 98*e - 127, -5*e^4 + 67*e^2 - 48*e - 56, -21/2*e^4 - 11/2*e^3 + 263/2*e^2 - 125/2*e - 106, -13*e^4 - 6*e^3 + 164*e^2 - 87*e - 141, -3/2*e^4 - 1/2*e^3 + 43/2*e^2 - 1/2*e - 31, 21/2*e^4 + 11/2*e^3 - 255/2*e^2 + 129/2*e + 94, 4*e^4 + e^3 - 52*e^2 + 33*e + 43, -3/2*e^4 + 3/2*e^3 + 37/2*e^2 - 79/2*e + 4, e^4 - e^3 - 10*e^2 + 25*e - 16, 21*e^4 + 9*e^3 - 261*e^2 + 147*e + 202, -11*e^4 - 5*e^3 + 133*e^2 - 79*e - 76, 5*e^4 + 2*e^3 - 61*e^2 + 42*e + 36, 12*e^4 + 7*e^3 - 146*e^2 + 73*e + 112, -33*e^4 - 14*e^3 + 412*e^2 - 242*e - 299, 6*e^4 + 2*e^3 - 76*e^2 + 48*e + 76, -13/2*e^4 + 1/2*e^3 + 167/2*e^2 - 161/2*e - 56, 33*e^4 + 13*e^3 - 408*e^2 + 259*e + 276, 7/2*e^4 + 5/2*e^3 - 93/2*e^2 + 23/2*e + 53, 11*e^4 + 4*e^3 - 137*e^2 + 88*e + 106, -47/2*e^4 - 15/2*e^3 + 589/2*e^2 - 381/2*e - 190, -43/2*e^4 - 21/2*e^3 + 527/2*e^2 - 299/2*e - 193, 17*e^4 + 6*e^3 - 216*e^2 + 126*e + 181, e^4 + 2*e^3 - 4*e^2 - 2*e - 27, -4*e^4 - 3*e^3 + 43*e^2 - 19*e - 3, 15*e^4 + 6*e^3 - 184*e^2 + 120*e + 111, 5*e^4 + 3*e^3 - 61*e^2 + 35*e + 34, -23/2*e^4 - 13/2*e^3 + 283/2*e^2 - 123/2*e - 109, -31*e^4 - 11*e^3 + 383*e^2 - 257*e - 245, 23/2*e^4 + 15/2*e^3 - 277/2*e^2 + 121/2*e + 111, 17*e^4 + 9*e^3 - 209*e^2 + 111*e + 163, -2*e^3 + 33*e - 16, -3*e^4 - 3*e^3 + 35*e^2 - 5*e - 29, 7*e^4 + 2*e^3 - 88*e^2 + 63*e + 47, 81/2*e^4 + 29/2*e^3 - 1013/2*e^2 + 639/2*e + 341, -12*e^4 - 4*e^3 + 151*e^2 - 95*e - 103, 5*e^4 + 3*e^3 - 62*e^2 + 19*e + 49, 7/2*e^4 + 5/2*e^3 - 85/2*e^2 + 9/2*e + 30, -7*e^4 - 2*e^3 + 86*e^2 - 58*e - 53, 7/2*e^4 + 1/2*e^3 - 95/2*e^2 + 63/2*e + 59, 9/2*e^4 + 3/2*e^3 - 117/2*e^2 + 73/2*e + 57, -2*e^4 + e^3 + 29*e^2 - 33*e - 39, 18*e^4 + 7*e^3 - 221*e^2 + 149*e + 123, 35*e^4 + 14*e^3 - 434*e^2 + 272*e + 291, -25/2*e^4 - 13/2*e^3 + 299/2*e^2 - 169/2*e - 86, -43/2*e^4 - 19/2*e^3 + 537/2*e^2 - 303/2*e - 190, -5*e^4 - 5*e^3 + 58*e^2 - 13*e - 25, -39/2*e^4 - 13/2*e^3 + 483/2*e^2 - 335/2*e - 137, 5/2*e^4 + 5/2*e^3 - 59/2*e^2 + 11/2*e + 24, 69/2*e^4 + 29/2*e^3 - 865/2*e^2 + 487/2*e + 325, 5*e^4 + 2*e^3 - 61*e^2 + 36*e + 18, -65/2*e^4 - 17/2*e^3 + 821/2*e^2 - 575/2*e - 263, -5/2*e^4 - 7/2*e^3 + 59/2*e^2 + 15/2*e - 35, -e^4 - e^3 + 16*e^2 + 7*e - 34, 20*e^4 + 4*e^3 - 252*e^2 + 196*e + 151, -e^4 - 2*e^3 + 8*e^2 - 4, -3*e^4 + e^3 + 39*e^2 - 45*e - 8, 3/2*e^4 + 1/2*e^3 - 35/2*e^2 + 51/2*e + 9, -3*e^4 - 2*e^3 + 35*e^2 - 18*e - 25, -15*e^4 - 10*e^3 + 179*e^2 - 80*e - 119, -87/2*e^4 - 29/2*e^3 + 1093/2*e^2 - 715/2*e - 363, 53/2*e^4 + 17/2*e^3 - 661/2*e^2 + 439/2*e + 194, -31*e^4 - 13*e^3 + 388*e^2 - 229*e - 287, 29*e^4 + 13*e^3 - 360*e^2 + 201*e + 277, -15*e^4 - 3*e^3 + 188*e^2 - 157*e - 106, 1/2*e^4 + 11/2*e^3 + 5/2*e^2 - 79/2*e - 6, -13*e^4 - 3*e^3 + 164*e^2 - 121*e - 116, -7*e^4 - 2*e^3 + 83*e^2 - 64*e - 34, -3/2*e^4 + 1/2*e^3 + 35/2*e^2 - 49/2*e - 17, 3/2*e^4 + 1/2*e^3 - 37/2*e^2 + 35/2*e - 2, -12*e^4 - 6*e^3 + 144*e^2 - 80*e - 96, -11*e^4 - 2*e^3 + 140*e^2 - 98*e - 87, 3*e^4 + 3*e^3 - 32*e^2 + 11*e + 11, -26*e^4 - 10*e^3 + 323*e^2 - 196*e - 221, 6*e^4 - 81*e^2 + 58*e + 77, 28*e^4 + 9*e^3 - 354*e^2 + 223*e + 252, 21*e^4 + 7*e^3 - 258*e^2 + 179*e + 161, 20*e^4 + 5*e^3 - 256*e^2 + 179*e + 174, 39/2*e^4 + 7/2*e^3 - 495/2*e^2 + 375/2*e + 159, 20*e^4 + 6*e^3 - 253*e^2 + 165*e + 193, -1/2*e^4 - 1/2*e^3 + 3/2*e^2 - 23/2*e + 16, 12*e^4 + 5*e^3 - 149*e^2 + 95*e + 111, 37/2*e^4 + 9/2*e^3 - 475/2*e^2 + 339/2*e + 162, -23/2*e^4 - 11/2*e^3 + 281/2*e^2 - 183/2*e - 94, -7*e^4 - 7*e^3 + 81*e^2 - 16*e - 54, -45/2*e^4 - 17/2*e^3 + 565/2*e^2 - 339/2*e - 179, 15*e^4 + 7*e^3 - 183*e^2 + 111*e + 86, -23*e^4 - 6*e^3 + 288*e^2 - 214*e - 175, -25/2*e^4 - 1/2*e^3 + 321/2*e^2 - 267/2*e - 111, 45/2*e^4 + 11/2*e^3 - 577/2*e^2 + 397/2*e + 213, -34*e^4 - 13*e^3 + 421*e^2 - 267*e - 261, -27/2*e^4 - 11/2*e^3 + 341/2*e^2 - 213/2*e - 138, 23/2*e^4 + 11/2*e^3 - 281/2*e^2 + 161/2*e + 104, -41/2*e^4 - 9/2*e^3 + 515/2*e^2 - 395/2*e - 150, -48*e^4 - 21*e^3 + 594*e^2 - 355*e - 408, -30*e^4 - 9*e^3 + 378*e^2 - 247*e - 258, 17*e^4 + 13*e^3 - 205*e^2 + 77*e + 158, -11/2*e^4 - 5/2*e^3 + 143/2*e^2 - 59/2*e - 89, -5*e^4 - 6*e^3 + 51*e^2 - 14*e, -20*e^4 - 10*e^3 + 243*e^2 - 144*e - 151, -15*e^4 - 11*e^3 + 176*e^2 - 71*e - 121, -30*e^4 - 12*e^3 + 380*e^2 - 220*e - 297, -17/2*e^4 - 11/2*e^3 + 209/2*e^2 - 81/2*e - 82, 28*e^4 + 12*e^3 - 351*e^2 + 202*e + 265, 35/2*e^4 + 9/2*e^3 - 437/2*e^2 + 329/2*e + 132, 11/2*e^4 + 3/2*e^3 - 147/2*e^2 + 91/2*e + 95, 37/2*e^4 + 5/2*e^3 - 469/2*e^2 + 375/2*e + 127, 19*e^4 + 9*e^3 - 236*e^2 + 137*e + 173, -15*e^4 - 4*e^3 + 190*e^2 - 128*e - 123, 13/2*e^4 + 15/2*e^3 - 141/2*e^2 + 17/2*e + 31, -15*e^4 - 5*e^3 + 182*e^2 - 141*e - 101, 5*e^4 + 2*e^3 - 61*e^2 + 46*e + 22, 43/2*e^4 + 15/2*e^3 - 543/2*e^2 + 361/2*e + 195, -11*e^4 - 8*e^3 + 129*e^2 - 66*e - 66, -9/2*e^4 - 5/2*e^3 + 101/2*e^2 - 63/2*e - 9, 4*e^3 + 7*e^2 - 34*e - 1, 34*e^4 + 10*e^3 - 428*e^2 + 294*e + 268, 7/2*e^4 + 1/2*e^3 - 75/2*e^2 + 99/2*e - 5, 21/2*e^4 + 9/2*e^3 - 263/2*e^2 + 127/2*e + 104, -9/2*e^4 - 3/2*e^3 + 109/2*e^2 - 65/2*e - 25, 24*e^4 + 10*e^3 - 301*e^2 + 180*e + 227, -37/2*e^4 - 13/2*e^3 + 463/2*e^2 - 315/2*e - 136, -3*e^4 - 5*e^3 + 29*e^2 + 9*e - 14, -17*e^4 - 5*e^3 + 214*e^2 - 157*e - 125, -65/2*e^4 - 21/2*e^3 + 817/2*e^2 - 543/2*e - 266, -2*e^4 - 5*e^3 + 22*e^2 + 33*e - 49, -13/2*e^4 - 1/2*e^3 + 165/2*e^2 - 155/2*e - 39, -7*e^4 - 8*e^3 + 78*e^2 - 6*e - 63, -7*e^4 - 5*e^3 + 86*e^2 - 17*e - 67, 17/2*e^4 - 3/2*e^3 - 215/2*e^2 + 227/2*e + 38, -75/2*e^4 - 35/2*e^3 + 919/2*e^2 - 523/2*e - 313, 24*e^4 + 11*e^3 - 296*e^2 + 168*e + 228, 12*e^4 + 5*e^3 - 149*e^2 + 98*e + 125, 36*e^4 + 17*e^3 - 449*e^2 + 242*e + 329, -22*e^4 - 8*e^3 + 281*e^2 - 166*e - 245, 33*e^4 + 15*e^3 - 404*e^2 + 243*e + 251, -35*e^4 - 14*e^3 + 437*e^2 - 258*e - 342, -15/2*e^4 - 13/2*e^3 + 181/2*e^2 - 51/2*e - 52, 10*e^4 + 3*e^3 - 127*e^2 + 78*e + 95, -33*e^4 - 18*e^3 + 402*e^2 - 203*e - 297, -21/2*e^4 - 3/2*e^3 + 265/2*e^2 - 243/2*e - 77, -47/2*e^4 - 23/2*e^3 + 585/2*e^2 - 279/2*e - 230, -34*e^4 - 15*e^3 + 415*e^2 - 259*e - 255, -37*e^4 - 14*e^3 + 460*e^2 - 300*e - 287, 89/2*e^4 + 31/2*e^3 - 1113/2*e^2 + 721/2*e + 394, 19/2*e^4 + 3/2*e^3 - 253/2*e^2 + 161/2*e + 127, -25*e^4 - 11*e^3 + 305*e^2 - 183*e - 205, -14*e^4 - 5*e^3 + 179*e^2 - 111*e - 150, 9*e^4 + 6*e^3 - 108*e^2 + 53*e + 95, 39*e^4 + 12*e^3 - 494*e^2 + 327*e + 343, -21*e^4 - 6*e^3 + 267*e^2 - 184*e - 210, 19*e^4 + 6*e^3 - 237*e^2 + 164*e + 130, -73/2*e^4 - 27/2*e^3 + 905/2*e^2 - 595/2*e - 301, 87/2*e^4 + 33/2*e^3 - 1095/2*e^2 + 645/2*e + 395, 73/2*e^4 + 23/2*e^3 - 905/2*e^2 + 649/2*e + 289, -3/2*e^4 - 5/2*e^3 + 43/2*e^2 + 45/2*e - 63, 26*e^4 + 9*e^3 - 325*e^2 + 216*e + 185, 39*e^4 + 11*e^3 - 489*e^2 + 330*e + 310, 43*e^4 + 14*e^3 - 538*e^2 + 346*e + 350, e^4 + e^3 - 15*e^2 + e + 9, -17*e^4 - 7*e^3 + 205*e^2 - 137*e - 128, 19/2*e^4 + 9/2*e^3 - 223/2*e^2 + 139/2*e + 39, 5*e^4 + e^3 - 69*e^2 + 30*e + 98, 12*e^4 + 8*e^3 - 144*e^2 + 61*e + 100, 47/2*e^4 + 27/2*e^3 - 577/2*e^2 + 293/2*e + 222, -32*e^4 - 9*e^3 + 405*e^2 - 273*e - 275, 69/2*e^4 + 21/2*e^3 - 869/2*e^2 + 577/2*e + 301, -109/2*e^4 - 39/2*e^3 + 1367/2*e^2 - 871/2*e - 474, 13/2*e^4 + 15/2*e^3 - 151/2*e^2 - 23/2*e + 84, -25*e^4 - 11*e^3 + 314*e^2 - 167*e - 237, -103/2*e^4 - 49/2*e^3 + 1269/2*e^2 - 737/2*e - 456, 36*e^4 + 13*e^3 - 452*e^2 + 276*e + 346, 22*e^4 + 7*e^3 - 273*e^2 + 175*e + 147, 85/2*e^4 + 31/2*e^3 - 1057/2*e^2 + 669/2*e + 367, -20*e^4 - 9*e^3 + 245*e^2 - 157*e - 127, 21/2*e^4 + 13/2*e^3 - 263/2*e^2 + 107/2*e + 108, -23/2*e^4 - 7/2*e^3 + 297/2*e^2 - 201/2*e - 144, -7*e^4 - 2*e^3 + 90*e^2 - 48*e - 45, 37/2*e^4 + 7/2*e^3 - 463/2*e^2 + 365/2*e + 128, 62*e^4 + 24*e^3 - 777*e^2 + 472*e + 541, -28*e^4 - 13*e^3 + 339*e^2 - 209*e - 201, 19/2*e^4 + 15/2*e^3 - 227/2*e^2 + 85/2*e + 92, -65*e^4 - 27*e^3 + 804*e^2 - 483*e - 570, -41/2*e^4 - 29/2*e^3 + 499/2*e^2 - 195/2*e - 200, -12*e^4 - 6*e^3 + 155*e^2 - 73*e - 119, -55/2*e^4 - 23/2*e^3 + 681/2*e^2 - 381/2*e - 220, 113/2*e^4 + 45/2*e^3 - 1411/2*e^2 + 847/2*e + 518, 49*e^4 + 15*e^3 - 616*e^2 + 404*e + 413, -97/2*e^4 - 33/2*e^3 + 1213/2*e^2 - 791/2*e - 425, 27*e^4 + 7*e^3 - 340*e^2 + 237*e + 205, -33*e^4 - 15*e^3 + 410*e^2 - 241*e - 291, -53*e^4 - 19*e^3 + 667*e^2 - 423*e - 464, 8*e^4 + e^3 - 98*e^2 + 89*e + 58, 5/2*e^4 - 7/2*e^3 - 67/2*e^2 + 163/2*e, -33/2*e^4 - 17/2*e^3 + 419/2*e^2 - 191/2*e - 184, -27/2*e^4 - 23/2*e^3 + 317/2*e^2 - 89/2*e - 130, -29*e^4 - 9*e^3 + 366*e^2 - 257*e - 266, 51*e^4 + 21*e^3 - 636*e^2 + 373*e + 468, -5/2*e^4 - 5/2*e^3 + 75/2*e^2 + 13/2*e - 70, -8*e^4 + e^3 + 105*e^2 - 95*e - 39, -14*e^4 - 10*e^3 + 167*e^2 - 64*e - 143, 59/2*e^4 + 27/2*e^3 - 735/2*e^2 + 425/2*e + 271, 19/2*e^4 + 7/2*e^3 - 231/2*e^2 + 189/2*e + 87, -13*e^4 - 10*e^3 + 159*e^2 - 42*e - 126, -4*e^4 - 2*e^3 + 51*e^2 - 26*e - 12, -83/2*e^4 - 41/2*e^3 + 1017/2*e^2 - 539/2*e - 365, 145/2*e^4 + 57/2*e^3 - 1789/2*e^2 + 1131/2*e + 600, -16*e^4 - 4*e^3 + 209*e^2 - 138*e - 200, -32*e^4 - 18*e^3 + 390*e^2 - 198*e - 312, 65/2*e^4 + 31/2*e^3 - 785/2*e^2 + 461/2*e + 251, 43*e^4 + 18*e^3 - 540*e^2 + 295*e + 429, 69*e^4 + 26*e^3 - 856*e^2 + 539*e + 587, -34*e^4 - 12*e^3 + 423*e^2 - 280*e - 287, -41/2*e^4 - 29/2*e^3 + 489/2*e^2 - 187/2*e - 207, 11*e^4 + 5*e^3 - 134*e^2 + 85*e + 127, -61/2*e^4 - 23/2*e^3 + 763/2*e^2 - 449/2*e - 298, -20*e^4 - 7*e^3 + 249*e^2 - 167*e - 191, -21*e^4 - 10*e^3 + 262*e^2 - 136*e - 217, 7*e^4 - e^3 - 93*e^2 + 91*e + 84, -30*e^4 - 10*e^3 + 370*e^2 - 268*e - 212, -1/2*e^4 + 1/2*e^3 + 1/2*e^2 - 25/2*e + 49, 29*e^4 + 3*e^3 - 373*e^2 + 311*e + 228, -27/2*e^4 - 11/2*e^3 + 335/2*e^2 - 189/2*e - 129, 3*e^4 + 5*e^3 - 32*e^2 - 33*e + 15, 50*e^4 + 21*e^3 - 616*e^2 + 382*e + 402, 23/2*e^4 + 3/2*e^3 - 309/2*e^2 + 217/2*e + 135, 91/2*e^4 + 25/2*e^3 - 1155/2*e^2 + 767/2*e + 414, -73/2*e^4 - 25/2*e^3 + 925/2*e^2 - 593/2*e - 315, -125/2*e^4 - 41/2*e^3 + 1569/2*e^2 - 1031/2*e - 513, -119/2*e^4 - 45/2*e^3 + 1485/2*e^2 - 923/2*e - 534, 35*e^4 + 13*e^3 - 438*e^2 + 273*e + 313, -41*e^4 - 15*e^3 + 508*e^2 - 329*e - 307, 16*e^4 + 16*e^3 - 184*e^2 + 28*e + 149, 121/2*e^4 + 51/2*e^3 - 1497/2*e^2 + 905/2*e + 520, -11/2*e^4 - 3/2*e^3 + 135/2*e^2 - 69/2*e - 15, -59/2*e^4 - 29/2*e^3 + 707/2*e^2 - 451/2*e - 165, 30*e^4 + 12*e^3 - 380*e^2 + 206*e + 296, 66*e^4 + 25*e^3 - 826*e^2 + 501*e + 570]
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, w + 2])] = 1

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