/*
  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, 14, -13, -2, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([5, 5, -1/2*w^3 + 2*w^2 + 7/2*w - 14])

primes_array = [
[4, 2, w^2 - 2*w - 6],\
[4, 2, -w^2 + 7],\
[5, 5, -1/2*w^3 + 2*w^2 + 7/2*w - 14],\
[5, 5, 1/2*w^3 + 1/2*w^2 - 6*w - 9],\
[11, 11, 1/2*w^3 - 2*w^2 - 5/2*w + 11],\
[11, 11, 1/2*w^3 + 1/2*w^2 - 5*w - 7],\
[31, 31, 1/2*w^2 + 1/2*w - 4],\
[31, 31, -1/2*w^2 + 3/2*w + 3],\
[41, 41, 1/2*w^2 + 1/2*w - 6],\
[41, 41, 2*w^3 - 15/2*w^2 - 25/2*w + 50],\
[41, 41, 5/2*w^2 - 1/2*w - 17],\
[41, 41, 1/2*w^2 - 3/2*w - 5],\
[61, 61, -1/2*w^3 + w^2 + 7/2*w - 1],\
[61, 61, -1/2*w^3 + 1/2*w^2 + 4*w - 3],\
[71, 71, 1/2*w^3 + w^2 - 11/2*w - 13],\
[71, 71, -1/2*w^3 + 5/2*w^2 + 2*w - 17],\
[81, 3, -3],\
[89, 89, -w^3 + 3/2*w^2 + 13/2*w - 9],\
[89, 89, w^3 - 7/2*w^2 - 11/2*w + 20],\
[89, 89, -w^3 - 1/2*w^2 + 19/2*w + 12],\
[89, 89, 1/2*w^3 + 2*w^2 - 17/2*w - 19],\
[109, 109, 1/2*w^3 + 3/2*w^2 - 7*w - 15],\
[109, 109, -1/2*w^3 + 1/2*w^2 + 4*w - 5],\
[121, 11, -3/2*w^2 + 3/2*w + 10],\
[131, 131, 3/2*w^3 - 13/2*w^2 - 9*w + 43],\
[131, 131, -3/2*w^3 - 2*w^2 + 35/2*w + 29],\
[139, 139, -3/2*w^3 + 11/2*w^2 + 10*w - 39],\
[139, 139, 1/2*w^3 + w^2 - 11/2*w - 9],\
[139, 139, -1/2*w^3 + 5/2*w^2 + 2*w - 13],\
[139, 139, -3/2*w^3 - w^2 + 33/2*w + 25],\
[151, 151, -1/2*w^3 + 3/2*w^2 + 3*w - 5],\
[151, 151, -1/2*w^3 + 9/2*w + 1],\
[179, 179, 5/2*w^2 - 3/2*w - 20],\
[179, 179, -w^3 + 5/2*w^2 + 11/2*w - 5],\
[179, 179, -w^3 + 1/2*w^2 + 15/2*w - 2],\
[179, 179, w^3 + 1/2*w^2 - 19/2*w - 10],\
[181, 181, 1/2*w^2 - 3/2*w - 8],\
[181, 181, 3/2*w^2 - 1/2*w - 13],\
[181, 181, -3/2*w^2 + 5/2*w + 12],\
[181, 181, 1/2*w^2 + 1/2*w - 9],\
[191, 191, w^3 + 1/2*w^2 - 17/2*w - 9],\
[191, 191, 1/2*w^3 - w^2 - 5/2*w + 8],\
[199, 199, -1/2*w^3 + 7/2*w^2 + 3*w - 23],\
[199, 199, -1/2*w^3 - 2*w^2 + 17/2*w + 17],\
[211, 211, w^3 - 5/2*w^2 - 9/2*w + 3],\
[211, 211, -w^3 + 1/2*w^2 + 13/2*w - 3],\
[229, 229, 3/2*w^3 - 2*w^2 - 21/2*w - 6],\
[229, 229, -w^3 + 3*w^2 + 8*w - 23],\
[239, 239, -w^3 + 3*w^2 + 4*w - 9],\
[239, 239, w^3 - 9*w - 7],\
[239, 239, 1/2*w^3 - 3/2*w^2 - 2*w + 13],\
[239, 239, -w^3 + 7*w + 3],\
[241, 241, 1/2*w^3 + 2*w^2 - 15/2*w - 16],\
[241, 241, -1/2*w^3 + 7/2*w^2 + 2*w - 21],\
[251, 251, w^3 - 5/2*w^2 - 9/2*w + 10],\
[251, 251, w^3 - 9*w - 9],\
[269, 269, w^3 - 1/2*w^2 - 17/2*w - 10],\
[269, 269, w^3 - 5/2*w^2 - 13/2*w + 18],\
[281, 281, -1/2*w^3 + 3*w^2 + 3/2*w - 19],\
[281, 281, 1/2*w^3 + 3/2*w^2 - 6*w - 15],\
[289, 17, w^3 - 3/2*w^2 - 15/2*w - 1],\
[289, 17, -w^3 + 3/2*w^2 + 15/2*w - 9],\
[331, 331, 3/2*w^2 - 1/2*w - 14],\
[331, 331, -3/2*w^2 + 5/2*w + 13],\
[349, 349, -w^3 + 3/2*w^2 + 11/2*w - 1],\
[349, 349, w^3 - 5/2*w^2 - 13/2*w + 14],\
[359, 359, -w^3 + 5/2*w^2 + 11/2*w - 14],\
[359, 359, w^3 - 1/2*w^2 - 15/2*w - 7],\
[361, 19, 2*w^2 - 2*w - 15],\
[361, 19, -2*w^2 + 2*w + 13],\
[379, 379, 5/2*w^2 - 3/2*w - 16],\
[379, 379, 5/2*w^2 - 7/2*w - 15],\
[389, 389, 7/2*w^2 - 1/2*w - 26],\
[389, 389, 1/2*w^3 - 3/2*w^2 - 5*w + 5],\
[389, 389, 1/2*w^3 + 2*w^2 - 11/2*w - 18],\
[389, 389, 3/2*w^3 - 1/2*w^2 - 13*w - 15],\
[409, 409, -w^3 + 7/2*w^2 + 9/2*w - 19],\
[409, 409, w^3 + 1/2*w^2 - 17/2*w - 12],\
[439, 439, -1/2*w^3 + 5/2*w^2 + w - 15],\
[439, 439, 1/2*w^3 + w^2 - 9/2*w - 12],\
[461, 461, 1/2*w^3 + 2*w^2 - 15/2*w - 18],\
[461, 461, -1/2*w^3 + 7/2*w^2 + 2*w - 23],\
[479, 479, -1/2*w^3 + 2*w^2 + 7/2*w - 10],\
[479, 479, 1/2*w^3 - 2*w^2 - 5/2*w + 7],\
[491, 491, -2*w^3 + 1/2*w^2 + 29/2*w - 1],\
[491, 491, 2*w^3 - 11/2*w^2 - 19/2*w + 12],\
[499, 499, -w^3 + 5/2*w^2 + 13/2*w - 13],\
[499, 499, w^3 - 1/2*w^2 - 17/2*w - 5],\
[509, 509, -w^3 + 3/2*w^2 + 15/2*w - 2],\
[509, 509, w^3 - 3/2*w^2 - 15/2*w + 6],\
[521, 521, -1/2*w^3 + 2*w^2 + 9/2*w - 15],\
[521, 521, 1/2*w^3 + 1/2*w^2 - 7*w - 9],\
[529, 23, -w^3 + 2*w^2 + 5*w - 9],\
[529, 23, -3/2*w^2 + 7/2*w + 12],\
[541, 541, 3/2*w^3 + 1/2*w^2 - 14*w - 17],\
[541, 541, -3/2*w^3 + 5*w^2 + 17/2*w - 29],\
[569, 569, -2*w^3 + 1/2*w^2 + 35/2*w + 18],\
[569, 569, -w^3 - 5/2*w^2 + 27/2*w + 27],\
[571, 571, -w^3 + w^2 + 8*w + 7],\
[571, 571, -1/2*w^3 + 2*w^2 + 3/2*w - 4],\
[571, 571, 1/2*w^3 + 1/2*w^2 - 4*w - 1],\
[571, 571, -4*w^3 - 7/2*w^2 + 91/2*w + 68],\
[599, 599, -1/2*w^3 - 5/2*w^2 + 10*w + 21],\
[599, 599, 2*w^3 + 5/2*w^2 - 47/2*w - 37],\
[599, 599, 2*w^3 - 17/2*w^2 - 25/2*w + 56],\
[599, 599, -1/2*w^3 + 4*w^2 + 7/2*w - 28],\
[601, 601, -w^3 - 3/2*w^2 + 23/2*w + 18],\
[601, 601, 1/2*w^3 + 7/2*w^2 - 5*w - 27],\
[601, 601, 1/2*w^3 - 5*w^2 + 7/2*w + 28],\
[601, 601, 2*w^3 - 3*w^2 - 13*w + 21],\
[619, 619, -w^3 + 5/2*w^2 + 9/2*w - 8],\
[619, 619, w^3 - 1/2*w^2 - 13/2*w - 2],\
[631, 631, -5/2*w^3 + 1/2*w^2 + 18*w - 1],\
[631, 631, -5/2*w^3 + 7*w^2 + 23/2*w - 15],\
[641, 641, 5/2*w^2 - 1/2*w - 20],\
[641, 641, -5/2*w^2 + 9/2*w + 18],\
[659, 659, w^3 - 7/2*w^2 - 15/2*w + 28],\
[659, 659, w^3 + 2*w^2 - 11*w - 21],\
[661, 661, -w^3 + 15/2*w^2 + 11/2*w - 52],\
[661, 661, -3/2*w^3 + 1/2*w^2 + 13*w + 5],\
[661, 661, 3/2*w^3 - 4*w^2 - 19/2*w + 17],\
[661, 661, -w^3 - 9/2*w^2 + 35/2*w + 40],\
[691, 691, 2*w^3 - 9/2*w^2 - 21/2*w + 5],\
[691, 691, -5/2*w^3 - w^2 + 55/2*w + 37],\
[701, 701, w^3 - 2*w^2 - 7*w + 3],\
[701, 701, w^3 - w^2 - 8*w + 5],\
[709, 709, -11/2*w^2 + 3/2*w + 40],\
[709, 709, -3/2*w^3 - 3/2*w^2 + 16*w + 23],\
[739, 739, 1/2*w^3 - 9/2*w^2 + 3*w + 25],\
[739, 739, 1/2*w^3 + 3*w^2 - 9/2*w - 24],\
[751, 751, -7/2*w^3 + 12*w^2 + 47/2*w - 83],\
[751, 751, -3/2*w^3 + 23/2*w + 3],\
[751, 751, -3/2*w^3 + 9/2*w^2 + 7*w - 13],\
[751, 751, 7/2*w^3 + 3/2*w^2 - 37*w - 51],\
[761, 761, -3/2*w^3 - 1/2*w^2 + 14*w + 19],\
[761, 761, -w^3 + 3/2*w^2 + 15/2*w - 4],\
[761, 761, -3/2*w^3 + 5*w^2 + 17/2*w - 31],\
[769, 769, -3*w^3 - 5/2*w^2 + 69/2*w + 51],\
[769, 769, -1/2*w^3 - 4*w^2 + 9/2*w + 27],\
[769, 769, -w^3 - 5/2*w^2 + 29/2*w + 25],\
[769, 769, 3*w^3 - 23/2*w^2 - 41/2*w + 80],\
[809, 809, 1/2*w^3 + 2*w^2 - 13/2*w - 17],\
[809, 809, 1/2*w^3 - 7/2*w^2 - w + 21],\
[821, 821, 1/2*w^3 - 1/2*w^2 - 6*w + 3],\
[821, 821, -1/2*w^3 + w^2 + 11/2*w - 3],\
[829, 829, -3/2*w^3 + 3*w^2 + 23/2*w - 10],\
[829, 829, -w^3 + 2*w^2 + 5*w + 1],\
[829, 829, 7/2*w^2 - 3/2*w - 28],\
[829, 829, 3/2*w^3 - 3/2*w^2 - 13*w + 3],\
[839, 839, -w^3 - 7/2*w^2 + 17/2*w + 27],\
[839, 839, 2*w^3 + 1/2*w^2 - 43/2*w - 27],\
[839, 839, 2*w^3 - 13/2*w^2 - 29/2*w + 46],\
[839, 839, -w^3 - 3/2*w^2 + 19/2*w + 14],\
[841, 29, 5/2*w^2 - 5/2*w - 19],\
[841, 29, 5/2*w^2 - 5/2*w - 16],\
[859, 859, 1/2*w^3 + w^2 - 5/2*w - 12],\
[859, 859, w^3 + 3/2*w^2 - 19/2*w - 19],\
[859, 859, -w^3 + 9/2*w^2 + 7/2*w - 26],\
[859, 859, 1/2*w^3 - 5/2*w^2 + w + 13],\
[881, 881, -1/2*w^3 + 1/2*w^2 + 6*w + 1],\
[881, 881, 1/2*w^3 - w^2 - 11/2*w + 7],\
[911, 911, -1/2*w^3 + 5/2*w^2 + 3*w - 13],\
[911, 911, 1/2*w^3 + w^2 - 13/2*w - 8],\
[941, 941, -2*w^3 + 7/2*w^2 + 27/2*w - 21],\
[941, 941, 3/2*w^3 - 7*w^2 - 21/2*w + 51],\
[941, 941, 3/2*w^3 + 5/2*w^2 - 20*w - 35],\
[941, 941, -2*w^3 + 13/2*w^2 + 29/2*w - 48],\
[961, 31, -w^2 + w + 13],\
[1009, 1009, -5/2*w^2 - 1/2*w + 18],\
[1009, 1009, 3/2*w^3 - 3/2*w^2 - 12*w - 5],\
[1021, 1021, w^3 + w^2 - 10*w - 19],\
[1021, 1021, w^3 - 5/2*w^2 - 9/2*w + 12],\
[1031, 1031, -1/2*w^3 + 3/2*w^2 + 5*w - 9],\
[1031, 1031, -w^3 + 3/2*w^2 + 13/2*w - 2],\
[1049, 1049, -3/2*w^3 - 1/2*w^2 + 16*w + 23],\
[1049, 1049, -2*w^3 + 9/2*w^2 + 23/2*w - 6],\
[1049, 1049, -2*w^3 + 3/2*w^2 + 29/2*w - 8],\
[1049, 1049, 3/2*w^3 - 5*w^2 - 21/2*w + 37],\
[1051, 1051, -2*w^3 + 11/2*w^2 + 17/2*w - 10],\
[1051, 1051, -3*w^3 - 1/2*w^2 + 59/2*w + 36],\
[1051, 1051, -3*w^3 + 19/2*w^2 + 39/2*w - 62],\
[1051, 1051, 2*w^3 - 1/2*w^2 - 27/2*w + 2],\
[1061, 1061, 11/2*w^2 - 3/2*w - 38],\
[1061, 1061, 11/2*w^2 - 19/2*w - 34],\
[1069, 1069, 1/2*w^3 - 4*w^2 - 5/2*w + 25],\
[1069, 1069, 2*w^3 - 20*w - 25],\
[1069, 1069, -2*w^3 + 6*w^2 + 14*w - 43],\
[1069, 1069, 1/2*w^3 + 5/2*w^2 - 9*w - 19],\
[1109, 1109, -5/2*w^3 + 13/2*w^2 + 12*w - 13],\
[1109, 1109, -5/2*w^3 + w^2 + 35/2*w - 3],\
[1151, 1151, 13/2*w^2 - 3/2*w - 46],\
[1151, 1151, 1/2*w^3 + 3/2*w^2 - 5*w - 17],\
[1151, 1151, 1/2*w^3 - 3*w^2 - 1/2*w + 20],\
[1151, 1151, 13/2*w^2 - 23/2*w - 41],\
[1171, 1171, w^3 - 3/2*w^2 - 13/2*w + 12],\
[1171, 1171, 1/2*w^3 - 1/2*w^2 - 6*w + 1],\
[1171, 1171, -1/2*w^3 + w^2 + 11/2*w - 5],\
[1171, 1171, -1/2*w^3 + 5*w^2 - 7/2*w - 26],\
[1201, 1201, 1/2*w^3 + 1/2*w^2 - 6*w - 3],\
[1201, 1201, -1/2*w^3 + 2*w^2 + 7/2*w - 8],\
[1229, 1229, 1/2*w^3 + 5/2*w^2 - 8*w - 21],\
[1229, 1229, -1/2*w^3 + 4*w^2 + 3/2*w - 26],\
[1249, 1249, -w^3 + 7/2*w^2 + 9/2*w - 12],\
[1249, 1249, w^3 + 1/2*w^2 - 17/2*w - 5],\
[1279, 1279, 1/2*w^3 + 3/2*w^2 - 3*w - 15],\
[1279, 1279, -1/2*w^3 + 3*w^2 - 3/2*w - 16],\
[1289, 1289, 5/2*w^2 - 9/2*w - 19],\
[1289, 1289, w^3 - 9/2*w^2 - 15/2*w + 32],\
[1289, 1289, -w^3 - 3/2*w^2 + 27/2*w + 21],\
[1289, 1289, 5/2*w^2 - 1/2*w - 21],\
[1291, 1291, -1/2*w^3 + 5*w^2 - 9/2*w - 23],\
[1291, 1291, 1/2*w^3 + 7/2*w^2 - 4*w - 23],\
[1301, 1301, -3/2*w^3 + 2*w^2 + 21/2*w - 10],\
[1301, 1301, -3/2*w^3 + 5/2*w^2 + 10*w - 1],\
[1319, 1319, 4*w^3 - 29/2*w^2 - 49/2*w + 93],\
[1319, 1319, -4*w^3 - 5/2*w^2 + 83/2*w + 58],\
[1321, 1321, -17/2*w^2 + 31/2*w + 52],\
[1321, 1321, 17/2*w^2 - 3/2*w - 59],\
[1361, 1361, -3*w^3 - 7/2*w^2 + 71/2*w + 58],\
[1361, 1361, -3/2*w^3 - 3*w^2 + 39/2*w + 34],\
[1369, 37, 3/2*w^3 - 1/2*w^2 - 13*w - 17],\
[1369, 37, 3/2*w^3 + 1/2*w^2 - 11*w - 3],\
[1381, 1381, w^3 - 5*w^2 - 2*w + 27],\
[1381, 1381, w^3 + 2*w^2 - 9*w - 21],\
[1399, 1399, w^3 + 5/2*w^2 - 19/2*w - 25],\
[1399, 1399, w^3 - 11/2*w^2 - 3/2*w + 31],\
[1439, 1439, -2*w^3 + 13/2*w^2 + 23/2*w - 40],\
[1439, 1439, 4*w^3 + 3*w^2 - 43*w - 65],\
[1451, 1451, 1/2*w^3 + 9/2*w^2 - 5*w - 35],\
[1451, 1451, -1/2*w^3 + 6*w^2 - 11/2*w - 35],\
[1459, 1459, -3/2*w^3 + 9/2*w^2 + 9*w - 25],\
[1459, 1459, -3/2*w^3 + 1/2*w^2 + 10*w + 7],\
[1471, 1471, 3/2*w^3 - 11/2*w^2 - 7*w + 31],\
[1471, 1471, -3/2*w^3 - w^2 + 27/2*w + 20],\
[1489, 1489, -3*w^3 - 3*w^2 + 34*w + 51],\
[1489, 1489, 1/2*w^3 + 5/2*w^2 - 6*w - 25],\
[1489, 1489, -1/2*w^3 + 4*w^2 - 1/2*w - 28],\
[1489, 1489, 3*w^3 - 12*w^2 - 19*w + 79],\
[1499, 1499, 1/2*w^3 - 7/2*w^2 + 2*w + 19],\
[1499, 1499, 1/2*w^3 + 5/2*w^2 - 6*w - 21],\
[1499, 1499, -1/2*w^3 + 4*w^2 - 1/2*w - 24],\
[1499, 1499, -w^3 + 5/2*w^2 + 11/2*w - 17],\
[1511, 1511, -2*w^3 + 15/2*w^2 + 17/2*w - 37],\
[1511, 1511, -2*w^3 - 3/2*w^2 + 35/2*w + 23],\
[1531, 1531, 1/2*w^3 - 3*w^2 - 9/2*w + 16],\
[1531, 1531, -2*w^3 + 9/2*w^2 + 23/2*w - 8],\
[1531, 1531, -2*w^3 + 3/2*w^2 + 29/2*w - 6],\
[1531, 1531, w^3 + 5/2*w^2 - 21/2*w - 25],\
[1549, 1549, -1/2*w^3 + 1/2*w^2 + 3*w - 7],\
[1549, 1549, 1/2*w^3 - w^2 - 5/2*w - 4],\
[1579, 1579, w^3 + 3/2*w^2 - 19/2*w - 13],\
[1579, 1579, -w^3 + 9/2*w^2 + 7/2*w - 20],\
[1609, 1609, -11/2*w^2 + 1/2*w + 37],\
[1609, 1609, 11/2*w^2 - 21/2*w - 32],\
[1619, 1619, 1/2*w^3 - 3/2*w^2 - w + 15],\
[1619, 1619, w^3 - 3/2*w^2 - 21/2*w + 1],\
[1621, 1621, -2*w^3 + 15/2*w^2 + 23/2*w - 49],\
[1621, 1621, 1/2*w^3 + 3/2*w^2 - 9*w - 19],\
[1669, 1669, 1/2*w^3 + 5/2*w^2 - 7*w - 23],\
[1669, 1669, 1/2*w^3 - 4*w^2 - 1/2*w + 27],\
[1699, 1699, -w^3 + 1/2*w^2 + 17/2*w - 2],\
[1699, 1699, -w^3 + 5/2*w^2 + 13/2*w - 6],\
[1709, 1709, 1/2*w^3 + 3/2*w^2 - 2*w - 15],\
[1709, 1709, -1/2*w^3 + 3*w^2 - 5/2*w - 15],\
[1721, 1721, 5/2*w^3 - w^2 - 45/2*w - 20],\
[1721, 1721, -5/2*w^3 + 13/2*w^2 + 17*w - 41],\
[1741, 1741, -w^3 + 5/2*w^2 + 13/2*w - 3],\
[1741, 1741, -5/2*w^3 - 3*w^2 + 61/2*w + 48],\
[1741, 1741, -5*w^3 + 35/2*w^2 + 65/2*w - 116],\
[1741, 1741, -w^3 + 5*w^2 + 6*w - 31],\
[1759, 1759, 4*w^3 - 16*w^2 - 26*w + 111],\
[1759, 1759, 3*w^3 + 3/2*w^2 - 61/2*w - 43],\
[1789, 1789, w^3 + 1/2*w^2 - 17/2*w - 14],\
[1789, 1789, -w^3 + 7/2*w^2 + 9/2*w - 21],\
[1801, 1801, w^3 + 5/2*w^2 - 23/2*w - 24],\
[1801, 1801, w^3 + 11/2*w^2 - 15/2*w - 38],\
[1831, 1831, 13/2*w^2 - 1/2*w - 46],\
[1831, 1831, -3/2*w^3 + 8*w^2 + 19/2*w - 53],\
[1831, 1831, 9/2*w^3 - 33/2*w^2 - 28*w + 109],\
[1831, 1831, -13/2*w^2 + 25/2*w + 40],\
[1861, 1861, 5/2*w^2 - 9/2*w - 8],\
[1861, 1861, 5/2*w^2 - 1/2*w - 10],\
[1871, 1871, -1/2*w^3 - 1/2*w^2 + 7*w + 15],\
[1871, 1871, -1/2*w^3 - 4*w^2 + 7/2*w + 26],\
[1879, 1879, 1/2*w^3 - 9/2*w^2 - w + 25],\
[1879, 1879, -w^3 - 5/2*w^2 + 23/2*w + 27],\
[1879, 1879, w^3 - 11/2*w^2 - 7/2*w + 35],\
[1879, 1879, 1/2*w^3 + 3*w^2 - 17/2*w - 20],\
[1889, 1889, w^3 + 5/2*w^2 - 25/2*w - 27],\
[1889, 1889, -w^3 + 11/2*w^2 + 9/2*w - 36],\
[1901, 1901, -3*w^3 - w^2 + 32*w + 41],\
[1901, 1901, 3*w^3 - 10*w^2 - 21*w + 69],\
[1931, 1931, 2*w^3 - 15/2*w^2 - 13/2*w + 26],\
[1931, 1931, -w^3 + 11/2*w^2 + 5/2*w - 31],\
[1951, 1951, -w^3 + 1/2*w^2 + 13/2*w + 7],\
[1951, 1951, 2*w^2 - 19],\
[1979, 1979, -1/2*w^3 + 4*w^2 + 1/2*w - 25],\
[1979, 1979, 7/2*w^3 + w^2 - 73/2*w - 47],\
[1979, 1979, 7/2*w^3 - 23/2*w^2 - 24*w + 79],\
[1979, 1979, 1/2*w^3 + 5/2*w^2 - 7*w - 21],\
[1999, 1999, -w^3 + 15/2*w^2 + 11/2*w - 54],\
[1999, 1999, -w^3 + 15/2*w^2 - 9/2*w - 37]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^2 - 3*x + 1
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, -2, 1, e - 3, -3*e + 5, 2*e - 7, 5*e - 13, -6*e + 9, e + 1, -2*e + 4, 2*e + 1, -9*e + 14, -8*e + 14, -e + 6, 6*e - 9, -2*e + 8, -1, -7, 6*e - 13, -4*e, 5*e - 8, 5*e - 14, 2*e - 9, -8*e + 9, 15*e - 27, -9*e + 2, 5*e - 10, 7*e - 21, -8*e + 15, e - 7, e - 12, 3*e + 3, -15*e + 17, 5*e + 1, -3*e + 18, -9*e + 18, 15*e - 28, -6*e + 9, -8*e + 16, -10*e + 21, -7*e + 3, 4*e + 14, 11*e - 25, 13*e - 21, -4*e + 8, -18*e + 24, -16*e + 15, 12*e - 28, -10*e + 33, -11*e + 6, -8*e + 12, 12*e - 33, -8*e + 9, -9*e + 18, e - 17, -19, 8*e - 33, 17*e - 15, 11*e - 5, -10*e + 30, 2*e + 12, 11*e - 3, -3*e - 11, -13*e + 13, 11*e - 3, 8*e - 31, -6*e + 13, -6*e + 13, 3*e - 28, 22*e - 41, 14*e - 7, 16*e - 36, e, 10*e + 5, 19*e - 32, -11*e + 9, 23*e - 43, -20*e + 25, 15*e - 22, -9*e + 7, 5*e - 5, -16*e + 19, 34*e - 47, -18*e + 25, -4*e + 9, 13*e - 23, 9*e - 9, 6*e - 26, -20*e + 12, 30, -24*e + 43, -15*e - 5, 4*e - 44, 22*e - 52, 12*e - 33, -7*e - 5, -8*e - 7, -35, -21*e + 25, -4*e - 11, -e + 6, 10*e - 1, -20*e + 33, -20*e + 46, -2*e - 17, -8*e + 13, 22*e - 44, -6*e + 23, 11*e - 20, -2*e + 7, 6*e + 24, 2*e - 39, -10*e - 17, 11*e - 41, -e - 3, -6*e + 9, 2*e - 4, -9*e + 18, 28*e - 27, 29*e - 61, 3*e + 19, -28, 17*e - 30, 7*e - 28, 8*e - 27, -18*e + 31, -29*e + 37, -17*e + 28, -6*e - 26, 4*e + 16, 16*e - 16, 32*e - 55, -5*e + 25, -32*e + 53, 12*e - 28, -4*e - 7, 11*e + 14, -e + 19, 14*e - 40, 15*e - 49, -2*e - 5, 5*e + 14, -8*e + 10, 10*e + 24, 40*e - 70, 2*e - 18, 25*e - 35, 3*e - 35, 2*e + 26, -14*e + 35, e + 48, 2*e + 39, -6*e + 18, 4*e + 27, -18*e + 31, -16*e + 23, 9*e - 34, -4*e + 39, 3*e - 16, 10*e - 25, -14*e + 15, 7*e - 8, 2*e - 40, -24*e + 22, -34*e + 55, -24*e + 53, -24*e + 66, -35*e + 37, 5*e + 21, -4*e + 25, 13, 6*e - 8, 16*e - 33, 9*e + 8, -11*e - 1, -12*e + 53, 12*e - 64, -14*e + 4, -8*e + 17, -26*e + 29, 33*e - 62, -16*e + 1, 35*e - 37, 36, 4*e - 15, 15*e - 66, 34*e - 50, -24*e + 6, -6*e + 16, 5*e + 5, 12*e - 53, 5*e - 43, 15*e - 45, 43*e - 57, -24*e + 41, 42*e - 77, 32*e - 42, -12*e + 10, 3*e - 27, 9*e - 26, -3*e + 49, 37*e - 58, 3*e - 30, -6*e + 29, 2*e + 3, -29*e + 73, -7*e - 1, 4*e + 23, -10*e + 50, 47*e - 58, -32*e + 20, 6*e + 30, 4*e + 14, -38, -5*e + 3, -11*e + 24, 11*e + 17, -25*e + 77, 24*e - 49, -24*e + 31, 35*e - 53, -13*e - 17, 6*e + 6, -9*e - 24, -31*e + 13, 38*e - 69, 37*e - 49, -9*e + 46, 49*e - 82, -30*e + 35, 44*e - 58, -20*e + 34, 25*e - 48, 5*e + 11, 37*e - 52, 13*e - 65, 14*e - 30, -7*e + 3, -12*e - 44, -52*e + 67, 15*e + 3, 31*e - 57, 21*e - 14, 54*e - 69, -4*e + 23, 20*e + 14, -44*e + 51, 20*e - 39, 6*e - 4, 55*e - 71, 46*e - 89, -38*e + 40, 22*e - 82, -17*e + 38, 28*e - 63, -16*e + 58, 24*e - 65, 22*e - 3, 4*e - 71, -16*e - 1, -28*e + 71, 31*e - 9, -22*e + 19, 42*e - 62, 10*e + 3, -36*e + 65, 4*e + 44, 22*e - 78, 18*e - 53, -20*e - 15, -48*e + 56, -38*e + 65, 14*e - 65, -12*e + 15, 19*e - 33, 3*e - 32, -9*e + 50, 30*e - 59, -20*e + 61, 19*e - 48, -16*e + 10, -51*e + 94, -16*e + 19, 18*e + 10, 57*e - 70, -23*e + 7, 52*e - 96, -6*e - 20, 30*e - 55, 34*e - 69, -24*e + 72, 20*e - 5, -42*e + 81, -43*e + 46, -32*e + 27, -76*e + 115, 35*e - 62, -18*e - 21, -22*e + 15, -e - 46, 28*e - 45, 16*e - 14]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([5, 5, -1/2*w^3 + 2*w^2 + 7/2*w - 14])] = -1

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