/*
  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([25, 5, w^3 - 3*w^2 - 7*w + 15])

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^6 - 4*x^5 - 11*x^4 + 42*x^3 + 39*x^2 - 99*x - 27
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, 1/3*e^3 - 2/3*e^2 - 3*e + 3, -1/3*e^4 + e^3 + 4/3*e^2 - 4*e + 4, e^2 - e - 5, 1/3*e^3 + 1/3*e^2 - 4*e - 2, -1/3*e^4 + e^3 + 4/3*e^2 - 3*e + 4, -1, 1/3*e^4 - 13/3*e^2 - 2*e + 9, 1/3*e^4 - 1/3*e^3 - 11/3*e^2 + 2*e + 6, 2/3*e^3 - 1/3*e^2 - 6*e - 1, e + 1, 1/3*e^3 - 2/3*e^2 - 3*e + 4, -1/3*e^4 + 4/3*e^3 + 2/3*e^2 - 5*e + 5, 2*e^2 - 3*e - 8, -2/3*e^4 + 5/3*e^3 + 10/3*e^2 - 5*e + 7, 1/3*e^5 - 1/3*e^4 - 14/3*e^3 + e^2 + 16*e + 1, -1/3*e^5 + 2*e^4 - 40/3*e^2 + 7*e + 10, 2/3*e^4 - 3*e^3 - 5/3*e^2 + 15*e - 6, 1/3*e^4 - 2*e^3 - 4/3*e^2 + 12*e + 3, -e^4 + 2*e^3 + 8*e^2 - 7*e - 10, -2/3*e^4 + 4/3*e^3 + 7*e^2 - 8*e - 16, -1/3*e^4 + 4/3*e^3 + 5/3*e^2 - 6*e - 3, -1/3*e^4 + 5/3*e^3 + e^2 - 10*e, -2/3*e^5 + 4/3*e^4 + 6*e^3 - 4*e^2 - 11*e - 14, 2/3*e^5 - 10/3*e^4 - 7/3*e^3 + 68/3*e^2 - 5*e - 23, 5/3*e^4 - 6*e^3 - 29/3*e^2 + 31*e + 1, -1/3*e^5 + 1/3*e^4 + 4*e^3 - 5/3*e^2 - 8*e - 1, 1/3*e^5 - 4/3*e^4 - 2*e^3 + 32/3*e^2 - e - 22, -2*e^4 + 20/3*e^3 + 35/3*e^2 - 31*e - 6, -1/3*e^5 + 1/3*e^4 + 10/3*e^3 + 8/3*e^2 - 9*e - 10, -5/3*e^4 + 19/3*e^3 + 10*e^2 - 36*e - 9, 1/3*e^5 - 7/3*e^4 - 1/3*e^3 + 52/3*e^2 - 3*e - 10, -2/3*e^5 + 8/3*e^4 + 11/3*e^3 - 56/3*e^2 + 22, 2/3*e^5 - 4/3*e^4 - 7*e^3 + 8*e^2 + 16*e - 8, -2/3*e^5 + 3*e^4 + 7/3*e^3 - 49/3*e^2 + 5*e + 1, 2/3*e^5 - 7/3*e^4 - 11/3*e^3 + 31/3*e^2 + e + 13, -1/3*e^5 + 4/3*e^4 - 11/3*e^2 + 11*e - 7, -4/3*e^4 + 6*e^3 + 10/3*e^2 - 33*e + 11, 1/3*e^5 - 4/3*e^4 - 8/3*e^3 + 9*e^2 + 5*e + 2, -2/3*e^4 + 3*e^3 + 14/3*e^2 - 15*e - 16, 1/3*e^5 - e^4 - 2*e^3 + 13/3*e^2 - e + 1, -1/3*e^5 + 4/3*e^4 + 5/3*e^3 - 8*e^2 + 2*e + 1, e^5 - 8/3*e^4 - 31/3*e^3 + 64/3*e^2 + 24*e - 24, -e^5 + 3*e^4 + 20/3*e^3 - 55/3*e^2 - 3*e + 30, 1/3*e^5 - 7*e^3 + 4/3*e^2 + 30*e - 11, 2/3*e^5 - 3*e^4 - 3*e^3 + 59/3*e^2 + 6*e - 12, -2/3*e^5 + 5/3*e^4 + 8*e^3 - 37/3*e^2 - 32*e + 21, -1/3*e^5 + 7/3*e^4 - 2*e^3 - 41/3*e^2 + 17*e + 1, -e^5 + 14/3*e^4 + 4/3*e^3 - 79/3*e^2 + 21*e + 14, e^5 - 2*e^4 - 38/3*e^3 + 43/3*e^2 + 39*e - 13, 2/3*e^5 - 14/3*e^4 + 1/3*e^3 + 101/3*e^2 - 10*e - 25, -2/3*e^5 + 1/3*e^4 + 29/3*e^3 + 8/3*e^2 - 37*e - 7, 1/3*e^5 - 10/3*e^4 + 4*e^3 + 56/3*e^2 - 23*e + 12, -1/3*e^5 + 1/3*e^4 + 14/3*e^3 + 3*e^2 - 20*e - 15, -1/3*e^5 + e^4 + 13/3*e^3 - 10*e^2 - 10*e + 14, -e^4 + 10/3*e^3 + 7/3*e^2 - 6*e + 19, 1/3*e^5 - e^4 + 1/3*e^3 + 2/3*e^2 - 18*e + 11, 1/3*e^4 + 5/3*e^3 - 11/3*e^2 - 22*e + 4, 2/3*e^4 - 5/3*e^3 - 13/3*e^2 + 7*e + 22, 1/3*e^4 - 2/3*e^3 - 4*e^2 + 4*e + 31, 2/3*e^5 - 4/3*e^4 - 17/3*e^3 + 7/3*e^2 + 12*e + 11, -2/3*e^5 + 11/3*e^4 + 7/3*e^3 - 26*e^2 + e + 17, -2/3*e^3 + 4/3*e^2 + 4*e - 5, 5/3*e^4 - 20/3*e^3 - 25/3*e^2 + 35*e - 2, 1/3*e^5 + 4/3*e^4 - 29/3*e^3 - 23/3*e^2 + 40*e - 5, -1/3*e^5 + 8/3*e^4 - 4/3*e^3 - 67/3*e^2 + 14*e + 37, -7/3*e^4 + 22/3*e^3 + 32/3*e^2 - 34*e + 14, -2/3*e^4 + 5/3*e^3 + 31/3*e^2 - 11*e - 37, -1/3*e^5 + e^4 + 4/3*e^3 - 3*e^2 - 9, 1/3*e^5 - 7/3*e^4 - 5/3*e^3 + 21*e^2 + 3*e - 27, 1/3*e^5 - 4/3*e^4 - 4*e^3 + 38/3*e^2 + 17*e - 24, -1/3*e^5 + 8/3*e^3 + 22/3*e^2 - 2*e - 21, 1/3*e^5 - 8/3*e^4 + 4/3*e^3 + 64/3*e^2 - 18*e - 44, -1/3*e^5 - e^4 + 7*e^3 + 29/3*e^2 - 21*e - 26, 1/3*e^5 - 8/3*e^4 - e^3 + 22*e^2 + 4*e - 19, -1/3*e^5 + 1/3*e^4 + 2*e^3 + 19/3*e^2 - 3*e - 25, e^5 - 10/3*e^4 - 28/3*e^3 + 22*e^2 + 25*e - 17, -e^5 + 13/3*e^4 + 4/3*e^3 - 19*e^2 + 20*e - 20, 1/3*e^5 + 4/3*e^4 - 28/3*e^3 - 37/3*e^2 + 40*e + 18, 2/3*e^5 - 2/3*e^4 - 34/3*e^3 + 6*e^2 + 36*e + 7, -2/3*e^5 + 4*e^4 - 14/3*e^3 - 52/3*e^2 + 50*e + 1, -1/3*e^5 + 4*e^4 - 17/3*e^3 - 27*e^2 + 34*e + 18, -1/3*e^5 + 10/3*e^4 - 5*e^3 - 68/3*e^2 + 40*e + 35, 1/3*e^5 + 5/3*e^4 - 10*e^3 - 37/3*e^2 + 35*e + 23, 2/3*e^5 - 4/3*e^4 - 7/3*e^3 - 4/3*e^2 - 22*e + 26, -2/3*e^5 + 8/3*e^4 + 5*e^3 - 64/3*e^2 + 2*e + 26, -1/3*e^5 + 3*e^4 - 13/3*e^3 - 50/3*e^2 + 34*e + 17, 1/3*e^5 + 1/3*e^4 - 19/3*e^3 - 16/3*e^2 + 20*e + 32, 2/3*e^5 - 7/3*e^4 - 14/3*e^3 + 55/3*e^2 - 3*e - 17, -2/3*e^5 + e^4 + 6*e^3 - 11/3*e^2 - e + 13, e^5 - 3*e^4 - 11/3*e^3 + 19/3*e^2 - 10*e + 37, -e^5 + 14/3*e^4 + 7*e^3 - 104/3*e^2 - 15*e + 34, e^5 - 4*e^4 - 13/3*e^3 + 83/3*e^2 - 12*e - 47, 3*e^4 - 28/3*e^3 - 52/3*e^2 + 49*e - 6, -e^5 + 4/3*e^4 + 38/3*e^3 - 29/3*e^2 - 30*e + 7, 2*e^4 - 14/3*e^3 - 59/3*e^2 + 20*e + 36, -2/3*e^4 + 4/3*e^3 + 3*e^2 + 1, 1/3*e^5 - 2/3*e^4 + 5/3*e^3 - 16/3*e^2 - 33*e + 22, 1/3*e^4 - 2/3*e^3 - 3*e - 17, -1/3*e^5 + e^4 + 5*e^3 - 37/3*e^2 - 8*e + 19, -1/3*e^4 + 1/3*e^3 + 8/3*e^2 + 10*e + 10, 8/3*e^3 - 13/3*e^2 - 27*e + 31, -1/3*e^5 + 7/3*e^4 + e^3 - 53/3*e^2 - 7*e + 3, 7/3*e^4 - 8*e^3 - 46/3*e^2 + 36*e + 18, 8/3*e^4 - 11*e^3 - 35/3*e^2 + 63*e - 9, 1/3*e^5 - 2/3*e^4 - 10/3*e^3 + 2/3*e^2 + 16*e - 3, 4*e^3 - 6*e^2 - 27*e + 17, -2/3*e^4 + 17/3*e^3 - 14/3*e^2 - 29*e + 32, -e^5 + 13/3*e^4 + 5/3*e^3 - 56/3*e^2 + 12*e - 22, -1/3*e^5 - e^4 + 34/3*e^3 - e^2 - 46*e + 19, 1/3*e^5 - 2*e^4 + 10/3*e^3 + 32/3*e^2 - 33*e - 20, e^5 - 11/3*e^4 - 29/3*e^3 + 26*e^2 + 34*e - 25, e^5 - 7*e^4 + 4/3*e^3 + 151/3*e^2 - 19*e - 45, -e^5 + 53/3*e^3 + 8/3*e^2 - 74*e + 3, -1/3*e^5 + 5/3*e^4 - 10*e^2 + 6*e - 3, 1/3*e^5 - 1/3*e^4 - 20/3*e^3 + 6*e^2 + 30*e - 30, 1/3*e^5 - 10/3*e^3 - 6*e^2 - 4*e + 33, -1/3*e^5 + 7/3*e^4 - 7/3*e^3 - 13*e^2 + 31*e + 9, -5/3*e^5 + 14/3*e^4 + 49/3*e^3 - 35*e^2 - 35*e + 36, 5/3*e^5 - 16/3*e^4 - 29/3*e^3 + 91/3*e^2 - 3*e - 33, 2/3*e^5 - 7/3*e^4 - 8/3*e^3 + 46/3*e^2 - 18*e - 20, -17/3*e^4 + 16*e^3 + 116/3*e^2 - 75*e - 32, -2/3*e^5 + 2/3*e^4 + 25/3*e^3 - 5*e^2 - 11*e + 13, -14/3*e^4 + 40/3*e^3 + 37*e^2 - 70*e - 56, -e^5 + 13/3*e^4 + 8/3*e^3 - 92/3*e^2 + 25*e + 52, e^5 - 1/3*e^4 - 47/3*e^3 + 14/3*e^2 + 41*e - 14, 2/3*e^5 - 10/3*e^4 - 4*e^3 + 24*e^2 + 7*e - 7, -11/3*e^4 + 9*e^3 + 80/3*e^2 - 42*e - 14, -2/3*e^5 + 2*e^4 + 7/3*e^3 - 10/3*e^2 + 7*e - 16, -8/3*e^4 + 16/3*e^3 + 27*e^2 - 25*e - 47, -11/3*e^4 + 12*e^3 + 68/3*e^2 - 62*e - 15, -10/3*e^4 + 31/3*e^3 + 71/3*e^2 - 51*e - 30, 1/3*e^5 - 2/3*e^4 - 19/3*e^3 + 38/3*e^2 + 14*e - 30, -1/3*e^5 + 1/3*e^4 - 2/3*e^3 + 17/3*e^2 + 29*e - 12, -e^4 + 5/3*e^3 + 35/3*e^2 - 11*e - 11, -5/3*e^4 + 3*e^3 + 41/3*e^2 - 9*e + 1, -e^5 + 7/3*e^4 + 10*e^3 - 37/3*e^2 - 17*e - 11, e^5 - 14/3*e^4 - 1/3*e^3 + 70/3*e^2 - 34*e - 5, 2/3*e^5 - 11/3*e^4 - 4*e^3 + 94/3*e^2 + 19*e - 38, -2/3*e^5 + 2/3*e^4 + 10*e^3 - 13/3*e^2 - 46*e + 22, 8/3*e^4 - 9*e^3 - 41/3*e^2 + 47*e + 11, 5/3*e^4 - 14/3*e^3 - 46/3*e^2 + 22*e + 50, 2*e^4 - 8*e^3 - 10*e^2 + 42*e + 5, -2/3*e^4 + 5*e^3 + 14/3*e^2 - 41*e - 14, -8/3*e^4 + 26/3*e^3 + 34/3*e^2 - 31*e + 19, 11/3*e^4 - 32/3*e^3 - 88/3*e^2 + 54*e + 33, 14/3*e^4 - 43/3*e^3 - 29*e^2 + 71*e, -e^5 + 4*e^4 + 3*e^3 - 21*e^2 + 14*e - 2, -1/3*e^5 + 8/3*e^4 - 4*e^3 - 17*e^2 + 31*e + 22, 1/3*e^5 + 4/3*e^4 - 12*e^3 - 3*e^2 + 53*e - 17, e^5 - 8/3*e^4 - 32/3*e^3 + 19*e^2 + 28*e - 26, -1/3*e^5 - 2/3*e^4 + 25/3*e^3 + 20/3*e^2 - 42*e - 28, 1/3*e^5 - 11/3*e^4 + 4*e^3 + 25*e^2 - 19*e - 34, 4/3*e^4 + 7/3*e^3 - 22*e^2 - 18*e + 31, -2/3*e^5 - e^4 + 11*e^3 + 37/3*e^2 - 30*e + 6, 2/3*e^5 - 13/3*e^4 - 4/3*e^3 + 113/3*e^2 - 12*e - 39, 4/3*e^5 - 10/3*e^4 - 37/3*e^3 + 52/3*e^2 + 32*e - 12, -4/3*e^5 + 6*e^4 + 19/3*e^3 - 40*e^2 - 4*e + 24, -2/3*e^5 + 2/3*e^4 + 14/3*e^3 + 4/3*e^2 + 13*e - 4, 2/3*e^5 - 2*e^4 - 7*e^3 + 62/3*e^2 + 5*e - 43, 5/3*e^5 - 23/3*e^4 - 5*e^3 + 130/3*e^2 - 19*e - 13, -5/3*e^5 + 5*e^4 + 12*e^3 - 68/3*e^2 - 15*e - 25, 5/3*e^5 - 5*e^4 - 40/3*e^3 + 100/3*e^2 + 15*e - 30, -2/3*e^5 + 4*e^4 + 13/3*e^3 - 100/3*e^2 - 15*e + 31, 2/3*e^5 - 4/3*e^4 - 10/3*e^3 - 10/3*e^2 + e + 28, -5/3*e^5 + 5*e^4 + 35/3*e^3 - 30*e^2 - 5*e + 30, 1/3*e^5 - 5/3*e^4 - 5/3*e^3 + 61/3*e^2 - 2*e - 48, -1/3*e^5 - 2*e^4 + 37/3*e^3 + 6*e^2 - 51*e + 45, 1/3*e^5 + 5/3*e^4 - 26/3*e^3 - 13*e^2 + 20*e + 13, -1/3*e^5 + 8/3*e^4 - 10/3*e^3 - 58/3*e^2 + 39*e + 28, 5/3*e^5 - 4*e^4 - 43/3*e^3 + 61/3*e^2 + 16*e, -5/3*e^5 + 20/3*e^4 + 22/3*e^3 - 41*e^2 + 18*e + 30, 1/3*e^5 - 5*e^4 + 13/3*e^3 + 128/3*e^2 - 15*e - 53, -1/3*e^5 - 7/3*e^4 + 32/3*e^3 + 68/3*e^2 - 53*e - 29, -2*e^5 + 10/3*e^4 + 22*e^3 - 40/3*e^2 - 52*e - 23, 2*e^5 - 10*e^4 - 14/3*e^3 + 196/3*e^2 - 32*e - 65, e^5 - 8/3*e^4 - 26/3*e^3 + 6*e^2 + 25*e + 39, -e^5 + 7*e^4 - 4*e^3 - 37*e^2 + 38*e - 18, 2/3*e^5 + 1/3*e^4 - 38/3*e^3 - 34/3*e^2 + 54*e + 46, -2/3*e^5 + 22/3*e^4 - 11*e^3 - 41*e^2 + 65*e - 5, 4/3*e^5 - 3*e^4 - 29/3*e^3 + 29/3*e^2 - 4*e + 22, -4/3*e^5 + 17/3*e^4 + 16/3*e^3 - 107/3*e^2 + 22*e + 25, 4/3*e^5 - 26/3*e^4 + 7/3*e^3 + 142/3*e^2 - 34*e + 14, 1/3*e^5 - 7/3*e^4 + 5*e^3 + 20/3*e^2 - 33*e + 23, -1/3*e^5 + 1/3*e^4 + 28/3*e^3 - 28/3*e^2 - 47*e + 29, -4/3*e^5 + 4*e^4 + 29/3*e^3 - 32/3*e^2 - 24*e - 52, -2/3*e^5 + 4/3*e^4 + 26/3*e^3 - 37/3*e^2 - 19*e + 5, 2/3*e^5 - 7/3*e^4 - e^3 + 10*e^2 - 24*e - 16, -2/3*e^5 + 2*e^4 - 2/3*e^3 + 2/3*e^2 + 30*e - 44, -1/3*e^5 + 4/3*e^4 - 5/3*e^3 + 2/3*e^2 + 21*e + 10, 2/3*e^5 - 8/3*e^4 - 8*e^3 + 76/3*e^2 + 24*e - 44, 1/3*e^5 - 5/3*e^4 - 3*e^3 + 13*e^2 + 8*e + 31, -e^5 + 14/3*e^4 - 4*e^3 - 50/3*e^2 + 59*e - 14, e^5 - 5/3*e^4 - 52/3*e^3 + 61/3*e^2 + 60*e - 35, 5/3*e^5 - 17/3*e^4 - 38/3*e^3 + 125/3*e^2 + 19*e - 60, -5/3*e^5 + 4*e^4 + 47/3*e^3 - 26*e^2 - 32*e + 30, -e^5 + 2/3*e^4 + 38/3*e^3 + 3*e^2 - 28*e - 38, e^5 - 6*e^4 + e^3 + 39*e^2 - 38*e - 44, -1/3*e^5 + 2*e^4 - 4/3*e^3 - 35/3*e^2 + 23*e - 28, 1/3*e^5 - 14/3*e^3 - 7/3*e^2 + 7*e - 25, -e^5 + 11/3*e^4 + 6*e^3 - 65/3*e^2 + e - 19, 1/3*e^5 - 13/3*e^4 + 122/3*e^2 + 9*e - 61, -1/3*e^5 - e^4 + 11/3*e^3 + 64/3*e^2 - 15*e - 61, e^5 - 10/3*e^4 - 5*e^3 + 46/3*e^2 - 8*e - 19, -2*e^4 + 13/3*e^3 + 16/3*e^2 - 4*e + 47, 2*e^4 - 19/3*e^3 - 4/3*e^2 + 16*e - 49, e^5 - 10/3*e^4 - 9*e^3 + 76/3*e^2 + 24*e + 11, -10/3*e^4 + 19/3*e^3 + 77/3*e^2 - 23*e - 17, -e^5 + 3*e^4 + 22/3*e^3 - 53/3*e^2 - 13*e + 59, -5/3*e^4 + 4/3*e^3 + 24*e^2 - 8*e - 62, 5/3*e^5 - 4*e^4 - 56/3*e^3 + 21*e^2 + 63*e - 10, -5/3*e^5 + 28/3*e^4 - 2/3*e^3 - 155/3*e^2 + 37*e - 13, 7/3*e^4 - 17/3*e^3 - 12*e^2 + 21*e - 5, 5/3*e^3 - 31/3*e^2 - 4*e + 61, 2*e^5 - 13/3*e^4 - 58/3*e^3 + 20*e^2 + 42*e + 32, -2*e^5 + 28/3*e^4 + 7*e^3 - 181/3*e^2 + 17*e + 71, 2/3*e^5 - 2*e^4 + 2/3*e^2 - 21*e - 1, -2/3*e^5 + 8/3*e^4 + 9*e^3 - 82/3*e^2 - 35*e + 14, 1/3*e^5 - 7/3*e^4 + 14/3*e^3 + 10/3*e^2 - 45*e + 47, -1/3*e^5 + 5/3*e^4 - e^3 - 2*e^2 + 25*e - 37, -5/3*e^5 + 17/3*e^4 + 20/3*e^3 - 95/3*e^2 + 36*e + 36, 5/3*e^5 - 10/3*e^4 - 18*e^3 + 24*e^2 + 25*e - 21, 2/3*e^5 + 1/3*e^4 - 7/3*e^3 - 23*e^2 - 24*e + 58, -2/3*e^5 + 13/3*e^4 + 6*e^3 - 45*e^2 - 12*e + 67, -1/3*e^5 - 5/3*e^4 + 6*e^3 + 46/3*e^2 - 11*e + 17, 1/3*e^5 - 5/3*e^4 - 17/3*e^3 + 82/3*e^2 + 19*e - 55, -4/3*e^5 + 26/3*e^4 - 4*e^3 - 51*e^2 + 46*e + 10, 4/3*e^5 - 5/3*e^4 - 20*e^3 + 8*e^2 + 77*e - 2, 1/3*e^5 + 1/3*e^4 - 16/3*e^3 - 37/3*e^2 + 36*e + 50, -1/3*e^5 + 14/3*e^4 - 8/3*e^3 - 110/3*e^2 - 3*e + 41, -7/3*e^5 + 11*e^4 + 29/3*e^3 - 215/3*e^2 - 8*e + 41, 7/3*e^5 - 6*e^4 - 23*e^3 + 100/3*e^2 + 73*e - 22, e^5 - 25/3*e^4 + 1/3*e^3 + 209/3*e^2 - 19*e - 77, -e^5 - 4/3*e^4 + 40/3*e^3 + 86/3*e^2 - 34*e - 59, 2/3*e^5 - 5*e^3 - 49/3*e^2 + 8*e + 39, -2/3*e^5 + 5*e^4 + 13/3*e^3 - 142/3*e^2 - 19*e + 57, e^5 - 2*e^4 - 9*e^3 - 3*e^2 + 23*e + 51, -e^5 + 8*e^4 - 19/3*e^3 - 133/3*e^2 + 51*e - 24, 1/3*e^5 - 2*e^4 - 2/3*e^3 + 62/3*e^2 - 7*e - 45, -1/3*e^5 - 5/3*e^4 + 32/3*e^3 + 7*e^2 - 42*e + 24, -e^4 + 20/3*e^3 + 5/3*e^2 - 47*e + 34, -5/3*e^4 + 6*e^3 + 23/3*e^2 - 21*e + 28, e^5 - 20/3*e^4 + 1/3*e^3 + 50*e^2 - 25*e - 57, 2/3*e^5 + 4/3*e^4 - 15*e^3 - 35/3*e^2 + 59*e + 42, -2/3*e^5 + 17/3*e^4 - 14/3*e^3 - 40*e^2 + 38*e + 69, -e^5 - 1/3*e^4 + 47/3*e^3 + 9*e^2 - 50*e - 18, -e^5 + 10/3*e^4 + 19/3*e^3 - 14*e^2 - 8*e + 8, -1/3*e^5 + 11/3*e^4 - 35/3*e^3 - 35/3*e^2 + 75*e - 41, 1/3*e^5 + 4/3*e^4 - 46/3*e^3 + 2/3*e^2 + 72*e - 41, e^5 - 5*e^4 - 2*e^3 + 27*e^2 - 13*e + 32, 1/3*e^4 + 8/3*e^3 - 26/3*e^2 - 34*e + 44, -5/3*e^3 + 7/3*e^2 + 27*e + 5, -5/3*e^5 + 23/3*e^4 + 11*e^3 - 163/3*e^2 - 15*e + 21, -5/3*e^5 + 16/3*e^4 + 34/3*e^3 - 89/3*e^2 - 14*e + 28, 5/3*e^5 - 16/3*e^4 - 4*e^3 + 10*e^2 - 34*e + 51, 5/3*e^5 - 6*e^4 - 35/3*e^3 + 39*e^2 + 18*e - 14, 2/3*e^5 - e^4 - 20/3*e^3 - 5*e^2 + 11*e + 48, -2/3*e^5 + 17/3*e^4 - 22/3*e^3 - 83/3*e^2 + 59*e - 24, 1/3*e^5 + 2*e^4 - 41/3*e^3 - 40/3*e^2 + 67*e + 15, -1/3*e^5 + 5*e^4 - 31/3*e^3 - 89/3*e^2 + 56*e + 12, 2/3*e^5 + 2/3*e^4 - 38/3*e^3 - 11/3*e^2 + 46*e - 11, -2/3*e^5 + 11/3*e^4 + 8/3*e^3 - 98/3*e^2 + e + 61, 7/3*e^5 - 5*e^4 - 25*e^3 + 85/3*e^2 + 71*e - 9, -7/3*e^5 + 32/3*e^4 + 28/3*e^3 - 212/3*e^2 + 6*e + 69, 8/3*e^5 - 7*e^4 - 80/3*e^3 + 47*e^2 + 65*e - 33, -8/3*e^5 + 31/3*e^4 + 12*e^3 - 61*e^2 + 13*e + 51, 2*e^5 - 7/3*e^4 - 28*e^3 + 52/3*e^2 + 86*e - 21, -2*e^5 + 28/3*e^4 + 17/3*e^3 - 191/3*e^2 + 27*e + 84, -5/3*e^5 + 12*e^4 - e^3 - 263/3*e^2 + 24*e + 89, 5/3*e^5 - 2/3*e^4 - 24*e^3 - 29/3*e^2 + 92*e + 47, 4/3*e^3 - 8/3*e^2 - 8*e - 39, -2/3*e^4 + 3*e^3 + 8/3*e^2 - 16*e - 14, 5/3*e^5 - 23/3*e^4 - 7/3*e^3 + 39*e^2 - 39*e + 6, -5/3*e^5 + 14/3*e^4 + 44/3*e^3 - 74/3*e^2 - 26*e - 6, 2/3*e^5 + e^4 - 43/3*e^3 - 32/3*e^2 + 54*e + 21, -2/3*e^5 + 6*e^4 - 22/3*e^3 - 37*e^2 + 55*e + 18, 2/3*e^5 - e^4 - 23/3*e^3 + 7*e^2 + 6*e - 5, -2/3*e^5 + 7/3*e^4 + 4/3*e^3 - 35/3*e^2 + 28*e + 10, 2/3*e^5 + e^4 - 32/3*e^3 - 8*e^2 + 19*e - 20, -2/3*e^5 + 8/3*e^4 + 16/3*e^3 - 29*e^2 + 2*e + 58, -4/3*e^5 + 20/3*e^4 - 4*e^3 - 27*e^2 + 66*e - 21, 4/3*e^5 - 3*e^4 - 18*e^3 + 70/3*e^2 + 55*e - 15, -e^5 + 5*e^4 + 14/3*e^3 - 121/3*e^2 + 12*e + 34, e^5 - 2/3*e^4 - 28/3*e^3 - 20/3*e^2 + 3*e + 7, -1/3*e^5 + 4/3*e^4 - 11/3*e^3 + 20/3*e^2 + 33*e - 24, 1/3*e^5 - 7/3*e^4 - 7/3*e^3 + 55/3*e^2 + 6*e + 21, -4/3*e^5 + 9*e^4 - 16/3*e^3 - 185/3*e^2 + 71*e + 70, -2/3*e^5 + 2/3*e^4 + e^3 + 41/3*e^2 + 34*e - 69, 2/3*e^5 - 11/3*e^4 - 13/3*e^3 + 32*e^2 - 5*e - 51, 4/3*e^5 + 5/3*e^4 - 82/3*e^3 - 35/3*e^2 + 93*e + 4, 1/3*e^5 + e^4 - 41/3*e^3 - 1/3*e^2 + 60*e - 25, -4/3*e^5 + 8*e^4 - 11/3*e^3 - 47*e^2 + 64*e + 45, 4/3*e^5 - e^4 - 19*e^3 + 4/3*e^2 + 51*e + 39, -1/3*e^5 + 4*e^4 - 41/3*e^3 - 10*e^2 + 89*e - 58, -4/3*e^5 + 29/3*e^4 - 20/3*e^3 - 182/3*e^2 + 68*e + 54, 4/3*e^5 - 67/3*e^3 - 7*e^2 + 77*e + 45, -1/3*e^5 + 6*e^4 - 26/3*e^3 - 36*e^2 + 35*e - 18, 2/3*e^5 - 10/3*e^4 - 11/3*e^3 + 76/3*e^2 - e - 9, -2/3*e^5 + 4/3*e^4 + 10/3*e^3 + 4/3*e^2 + 9*e - 12, 1/3*e^5 - 1/3*e^4 - 4/3*e^3 - 53/3*e^2 + 8*e + 81]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([25, 5, w^3 - 3*w^2 - 7*w + 15])] = 1

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