/*
  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([5, -1, -7, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([15, 15, w^2 - 2*w - 5])

primes_array = [
[3, 3, -w^3 + 2*w^2 + 5*w - 3],\
[5, 5, w],\
[7, 7, -w^3 + 2*w^2 + 4*w - 3],\
[13, 13, -w^2 + w + 4],\
[13, 13, -w^3 + 2*w^2 + 5*w - 2],\
[16, 2, 2],\
[17, 17, -w + 2],\
[19, 19, -w^3 + 2*w^2 + 3*w - 2],\
[27, 3, w^3 - 3*w^2 - 4*w + 7],\
[31, 31, w^3 - 3*w^2 - 3*w + 7],\
[31, 31, -w^3 + w^2 + 6*w + 1],\
[41, 41, w^2 - w - 1],\
[43, 43, 2*w^3 - 5*w^2 - 6*w + 4],\
[47, 47, -w^3 + 2*w^2 + 5*w - 1],\
[53, 53, -w - 3],\
[53, 53, -w^3 + 3*w^2 + 3*w - 6],\
[59, 59, 2*w^2 - 3*w - 6],\
[59, 59, w^3 - w^2 - 7*w - 3],\
[79, 79, 2*w^3 - 4*w^2 - 8*w + 3],\
[79, 79, w^2 - 2*w - 1],\
[101, 101, 2*w^3 - 4*w^2 - 9*w + 4],\
[103, 103, -w^3 + 3*w^2 + 4*w - 2],\
[103, 103, w^2 - 3*w - 2],\
[107, 107, -w^3 + w^2 + 5*w - 1],\
[109, 109, -w^3 + 2*w^2 + 4*w - 6],\
[121, 11, -w^3 + 2*w^2 + 6*w - 3],\
[121, 11, w^2 - 3*w - 3],\
[125, 5, -w^3 + w^2 + 7*w + 1],\
[127, 127, 2*w^3 - 5*w^2 - 5*w + 7],\
[127, 127, 2*w^3 - 5*w^2 - 7*w + 6],\
[167, 167, -2*w^3 + 5*w^2 + 7*w - 11],\
[169, 13, -w^2 + w + 8],\
[181, 181, -2*w^3 + 5*w^2 + 8*w - 7],\
[193, 193, -w^3 + 3*w^2 + 3*w - 1],\
[197, 197, 2*w^3 - 4*w^2 - 7*w + 8],\
[197, 197, 3*w^3 - 7*w^2 - 10*w + 9],\
[199, 199, w^3 - 2*w^2 - 3*w - 3],\
[211, 211, -w^3 + w^2 + 7*w - 2],\
[211, 211, w^3 - w^2 - 6*w + 1],\
[227, 227, 2*w^3 - 3*w^2 - 9*w + 3],\
[229, 229, 3*w^3 - 6*w^2 - 13*w + 8],\
[239, 239, 2*w^3 - 4*w^2 - 9*w + 3],\
[239, 239, 2*w^3 - 4*w^2 - 6*w + 1],\
[241, 241, 3*w^3 - 7*w^2 - 9*w + 6],\
[241, 241, -2*w^3 + 4*w^2 + 6*w - 3],\
[251, 251, -4*w^3 + 10*w^2 + 15*w - 16],\
[251, 251, -w^3 + 3*w^2 - 3],\
[271, 271, -w^3 + 4*w^2 + 4*w - 11],\
[271, 271, -3*w^3 + 9*w^2 + 6*w - 13],\
[277, 277, -w^3 + 3*w^2 + 2*w - 9],\
[281, 281, -w^3 + 4*w^2 + w - 8],\
[293, 293, 3*w^3 - 7*w^2 - 11*w + 13],\
[293, 293, w^2 - 6],\
[293, 293, -4*w^3 + 11*w^2 + 9*w - 14],\
[293, 293, 3*w^3 - 5*w^2 - 15*w + 6],\
[311, 311, -2*w^3 + 4*w^2 + 7*w - 4],\
[313, 313, -w^3 + 4*w^2 + 3*w - 13],\
[313, 313, -w^3 + w^2 + 6*w - 2],\
[317, 317, w^3 - 4*w^2 - w + 9],\
[337, 337, 3*w^3 - 7*w^2 - 8*w + 7],\
[343, 7, -2*w^3 + 3*w^2 + 9*w + 1],\
[359, 359, -w^3 + 2*w^2 + 4*w - 7],\
[359, 359, 2*w^3 - 3*w^2 - 10*w + 4],\
[367, 367, 2*w^3 - 4*w^2 - 5*w + 2],\
[367, 367, 2*w^3 - 3*w^2 - 11*w - 2],\
[367, 367, 2*w - 7],\
[367, 367, w^3 - 7*w - 4],\
[373, 373, -w^3 + 4*w^2 + w - 14],\
[373, 373, -2*w^3 + 4*w^2 + 10*w - 11],\
[379, 379, w^3 - 2*w^2 - 2*w - 1],\
[383, 383, w^3 - 8*w - 4],\
[397, 397, 4*w^3 - 10*w^2 - 12*w + 7],\
[397, 397, -2*w^3 + 3*w^2 + 9*w - 2],\
[401, 401, -w^3 + 6*w + 8],\
[409, 409, 2*w^3 - 3*w^2 - 11*w + 4],\
[419, 419, 3*w^3 - 6*w^2 - 15*w + 7],\
[419, 419, -w^2 + 4*w + 8],\
[431, 431, 5*w^3 - 15*w^2 - 10*w + 18],\
[431, 431, 3*w^3 - 4*w^2 - 16*w - 2],\
[439, 439, w^3 - w^2 - 4*w - 4],\
[443, 443, -4*w^3 + 9*w^2 + 15*w - 16],\
[461, 461, 2*w^3 - 2*w^2 - 13*w - 1],\
[467, 467, 2*w^3 - 6*w^2 - 2*w + 7],\
[467, 467, 3*w^3 - 3*w^2 - 19*w - 6],\
[479, 479, w^2 - 8],\
[479, 479, -3*w^3 + 7*w^2 + 14*w - 11],\
[491, 491, 3*w^3 - 5*w^2 - 16*w + 2],\
[499, 499, -w^2 + w - 2],\
[509, 509, -w^3 + 5*w^2 - w - 11],\
[509, 509, w^3 - 5*w - 1],\
[521, 521, -w^3 + 4*w^2 + 3*w - 7],\
[521, 521, -w^3 + 2*w^2 + 7*w - 4],\
[541, 541, -2*w^3 + 4*w^2 + 11*w - 6],\
[557, 557, -w^3 + w^2 + 8*w + 3],\
[557, 557, w^3 - 2*w^2 - 2*w - 2],\
[563, 563, 2*w^3 - 2*w^2 - 10*w - 3],\
[563, 563, 3*w^3 - 5*w^2 - 15*w + 1],\
[569, 569, 2*w^2 - 3*w - 4],\
[569, 569, 3*w^3 - 8*w^2 - 9*w + 7],\
[571, 571, -w^3 + 4*w^2 - 11],\
[571, 571, 3*w^3 - 8*w^2 - 11*w + 11],\
[577, 577, 3*w^3 - 8*w^2 - 5*w + 11],\
[577, 577, -4*w^3 + 11*w^2 + 9*w - 9],\
[593, 593, 2*w^3 - 7*w^2 - 2*w + 9],\
[601, 601, -w^3 + 3*w^2 + 5*w - 9],\
[613, 613, 3*w^3 - 5*w^2 - 14*w + 8],\
[613, 613, -w^3 + 2*w^2 + 7*w - 3],\
[617, 617, -2*w^3 + 6*w^2 + 5*w - 4],\
[617, 617, -w^3 + 3*w^2 - w - 6],\
[641, 641, 4*w^3 - 9*w^2 - 17*w + 14],\
[641, 641, -5*w^3 + 12*w^2 + 18*w - 17],\
[643, 643, -3*w^3 + 8*w^2 + 10*w - 13],\
[647, 647, 3*w - 4],\
[647, 647, -w^3 + 4*w^2 + 2*w - 9],\
[653, 653, -w^3 + 2*w^2 + 5*w - 8],\
[661, 661, 2*w^3 - 7*w^2 - 5*w + 21],\
[661, 661, -w^3 + 2*w^2 + 3*w - 8],\
[673, 673, 2*w^3 - 7*w^2 - 5*w + 9],\
[673, 673, w^3 - 2*w^2 - 3*w - 4],\
[677, 677, -w^3 + 4*w^2 + 3*w - 8],\
[683, 683, -3*w^3 + 4*w^2 + 17*w - 1],\
[683, 683, -3*w^3 + 7*w^2 + 8*w - 2],\
[691, 691, w^2 - 4*w - 2],\
[701, 701, 3*w^3 - 6*w^2 - 11*w + 3],\
[709, 709, -w^3 + 4*w^2 + 3*w - 17],\
[709, 709, w^3 + w^2 - 10*w - 8],\
[709, 709, -3*w^3 + 10*w^2 + 2*w - 16],\
[709, 709, w^3 - w^2 - 8*w + 1],\
[727, 727, -w^3 + 5*w^2 - w - 13],\
[727, 727, 2*w^3 - 4*w^2 - 11*w + 2],\
[733, 733, -2*w^3 + 3*w^2 + 10*w - 6],\
[733, 733, 2*w^3 - 5*w^2 - 5*w + 9],\
[739, 739, -3*w^3 + 6*w^2 + 12*w - 8],\
[743, 743, 3*w^3 - 4*w^2 - 17*w - 4],\
[743, 743, 2*w^3 - 3*w^2 - 8*w + 1],\
[743, 743, -3*w^3 + 7*w^2 + 11*w - 7],\
[743, 743, -3*w^3 + 6*w^2 + 11*w - 9],\
[757, 757, 2*w^3 - 5*w^2 - 6*w + 11],\
[757, 757, -w^3 + w^2 + 8*w + 2],\
[761, 761, -5*w^3 + 14*w^2 + 13*w - 12],\
[769, 769, -3*w^2 + 4*w + 13],\
[773, 773, 3*w^3 - 4*w^2 - 18*w + 3],\
[797, 797, 4*w^3 - 7*w^2 - 21*w + 8],\
[797, 797, -3*w^3 + 7*w^2 + 11*w - 16],\
[809, 809, -2*w^2 + 5*w + 11],\
[827, 827, w - 6],\
[829, 829, -w^3 - w^2 + 11*w + 8],\
[841, 29, -3*w^3 + 6*w^2 + 14*w - 6],\
[841, 29, -2*w^3 + 5*w^2 + 8*w - 4],\
[853, 853, 3*w^3 - 6*w^2 - 9*w + 8],\
[857, 857, 2*w^2 - 3*w - 3],\
[859, 859, -w^3 + w^2 + 4*w + 7],\
[863, 863, 2*w^3 - 3*w^2 - 7*w - 2],\
[863, 863, -3*w^3 + 6*w^2 + 10*w - 11],\
[881, 881, -3*w^2 + 4*w + 12],\
[881, 881, w^2 - 2*w + 3],\
[883, 883, 4*w^3 - 13*w^2 - 6*w + 17],\
[883, 883, -2*w^3 + 4*w^2 + 12*w - 3],\
[887, 887, -3*w^3 + 5*w^2 + 16*w - 8],\
[887, 887, 3*w^3 - 5*w^2 - 14*w + 3],\
[911, 911, -w^3 + 10*w + 1],\
[919, 919, 5*w^3 - 13*w^2 - 14*w + 11],\
[929, 929, 2*w^3 - 3*w^2 - 12*w - 4],\
[937, 937, -3*w - 7],\
[941, 941, -w^3 + 3*w^2 + 3*w - 12],\
[947, 947, 2*w^3 - 6*w^2 - 9*w + 8],\
[947, 947, -4*w^3 + 7*w^2 + 19*w - 6],\
[953, 953, 3*w^2 - w - 9],\
[961, 31, 4*w^3 - 12*w^2 - 5*w + 17],\
[971, 971, 3*w^3 - 6*w^2 - 16*w + 12],\
[983, 983, w^3 + w^2 - 7*w - 12],\
[991, 991, -2*w^3 + 7*w^2 + 3*w - 12],\
[991, 991, -2*w^3 + 4*w^2 + 12*w - 9],\
[997, 997, 3*w^3 - 5*w^2 - 14*w + 9],\
[997, 997, -2*w^3 + 3*w^2 + 11*w - 7],\
[1013, 1013, -2*w^3 + 6*w^2 + 3*w - 11],\
[1019, 1019, -w^3 + 5*w^2 + 2*w - 8],\
[1021, 1021, -w^3 + 5*w^2 - w - 17],\
[1021, 1021, 3*w^3 - 6*w^2 - 8*w + 3],\
[1033, 1033, -2*w^3 + 5*w^2 + 6*w - 13],\
[1033, 1033, 3*w^3 - 6*w^2 - 11*w + 4],\
[1051, 1051, 3*w^3 - 7*w^2 - 10*w + 13],\
[1061, 1061, 2*w^2 - 5*w - 13],\
[1063, 1063, -w^3 + w^2 + 5*w + 8],\
[1069, 1069, -5*w^3 + 12*w^2 + 19*w - 18],\
[1069, 1069, w^3 - 5*w^2 - w + 9],\
[1097, 1097, -3*w^3 + 9*w^2 + 8*w - 12],\
[1097, 1097, -2*w^3 + 6*w^2 + 7*w - 12],\
[1103, 1103, -3*w^3 + 4*w^2 + 15*w - 3],\
[1103, 1103, -w^3 + 3*w^2 + 5*w - 11],\
[1109, 1109, 5*w^3 - 11*w^2 - 16*w + 6],\
[1129, 1129, -w^2 + 3*w - 4],\
[1129, 1129, 2*w^3 - 2*w^2 - 10*w - 9],\
[1151, 1151, 4*w^3 - 10*w^2 - 14*w + 13],\
[1153, 1153, -2*w^3 + 5*w^2 + 11*w - 12],\
[1153, 1153, -2*w^3 + 8*w^2 - 13],\
[1153, 1153, -w^3 + 3*w^2 + 5*w - 12],\
[1153, 1153, 2*w^3 - w^2 - 11*w - 4],\
[1163, 1163, -w^3 + w^2 + 9*w - 4],\
[1163, 1163, 2*w^3 - 4*w^2 - 10*w - 1],\
[1171, 1171, 3*w^3 - 4*w^2 - 18*w - 1],\
[1193, 1193, w^3 - 4*w^2 + 2*w + 6],\
[1193, 1193, w^3 - 2*w^2 - 5*w - 4],\
[1201, 1201, 2*w^3 - 4*w^2 - 9*w - 3],\
[1201, 1201, 4*w^3 - 10*w^2 - 13*w + 11],\
[1213, 1213, -4*w^3 + 7*w^2 + 19*w - 11],\
[1217, 1217, -2*w^3 + 8*w^2 + 2*w - 13],\
[1229, 1229, -4*w^3 + 13*w^2 + 6*w - 19],\
[1229, 1229, -4*w^3 + 8*w^2 + 16*w - 13],\
[1229, 1229, -3*w^3 + 9*w^2 + 6*w - 16],\
[1229, 1229, 2*w^3 - 3*w^2 - 6*w - 1],\
[1231, 1231, -3*w^3 + 6*w^2 + 16*w - 8],\
[1231, 1231, -3*w^2 + w + 12],\
[1237, 1237, -2*w^3 + 5*w^2 + 4*w - 9],\
[1237, 1237, -w^2 - 3],\
[1237, 1237, -w^3 + 6*w - 3],\
[1237, 1237, -4*w - 1],\
[1249, 1249, -2*w^3 + 4*w^2 + 5*w - 8],\
[1283, 1283, 3*w - 8],\
[1289, 1289, 2*w^3 - w^2 - 14*w - 6],\
[1289, 1289, 4*w^3 - 9*w^2 - 13*w + 8],\
[1291, 1291, w^3 - w^2 - 3*w - 4],\
[1297, 1297, 4*w^3 - 9*w^2 - 15*w + 9],\
[1303, 1303, -w^3 + 4*w^2 - 13],\
[1321, 1321, 3*w^3 - 6*w^2 - 13*w + 3],\
[1321, 1321, -3*w^3 + 6*w^2 + 11*w - 7],\
[1367, 1367, -2*w^3 + 6*w^2 + 4*w - 13],\
[1369, 37, 2*w^2 - w - 11],\
[1369, 37, w^3 - 2*w^2 - w - 2],\
[1373, 1373, -w^3 + 3*w^2 + 8*w - 6],\
[1381, 1381, -w^3 + 3*w^2 - 9],\
[1381, 1381, 3*w^3 - 8*w^2 - 8*w + 14],\
[1427, 1427, 3*w^3 - 7*w^2 - 9*w + 12],\
[1429, 1429, 4*w^3 - 9*w^2 - 11*w + 8],\
[1433, 1433, -w^3 + 8*w + 12],\
[1447, 1447, -4*w^3 + 10*w^2 + 15*w - 14],\
[1447, 1447, 6*w^3 - 14*w^2 - 21*w + 19],\
[1451, 1451, w^3 - w^2 - 9*w - 4],\
[1459, 1459, 3*w^3 - 7*w^2 - 13*w + 9],\
[1481, 1481, -3*w^2 + 3*w + 19],\
[1481, 1481, -w^3 + 5*w^2 - 3*w - 14],\
[1487, 1487, -2*w^3 + 6*w^2 + w - 6],\
[1489, 1489, -3*w^3 + 3*w^2 + 19*w + 3],\
[1499, 1499, 3*w^2 - 4*w - 7],\
[1511, 1511, 4*w^3 - 6*w^2 - 20*w + 3],\
[1523, 1523, 8*w^3 - 23*w^2 - 17*w + 27],\
[1531, 1531, -w^3 + 2*w^2 + 3*w - 9],\
[1531, 1531, 3*w^3 - 9*w^2 - 8*w + 19],\
[1549, 1549, -5*w^3 + 11*w^2 + 17*w - 18],\
[1553, 1553, 2*w^2 - 9],\
[1567, 1567, 2*w^3 - 7*w^2 - 4*w + 22],\
[1579, 1579, -2*w^3 + 4*w^2 + 8*w + 3],\
[1579, 1579, -3*w^3 + 5*w^2 + 13*w - 1],\
[1607, 1607, w^3 - w^2 - 6*w - 8],\
[1609, 1609, -4*w^3 + 7*w^2 + 19*w - 2],\
[1619, 1619, -5*w^3 + 11*w^2 + 13*w - 9],\
[1627, 1627, 4*w^3 - 9*w^2 - 16*w + 11],\
[1657, 1657, 2*w^3 - 8*w^2 - w + 12],\
[1657, 1657, -4*w^3 + 11*w^2 + 15*w - 17],\
[1667, 1667, -w^3 + 5*w^2 - 6],\
[1667, 1667, -3*w^3 + 6*w^2 + 10*w - 6],\
[1697, 1697, w^3 + w^2 - 9*w - 7],\
[1697, 1697, 3*w^3 - 6*w^2 - 13*w + 2],\
[1697, 1697, w^3 - 6*w + 1],\
[1697, 1697, -5*w^3 + 11*w^2 + 22*w - 17],\
[1709, 1709, w^3 - w^2 - 8*w - 9],\
[1709, 1709, -w^3 + 3*w^2 - 13],\
[1723, 1723, 2*w^3 - 3*w^2 - 7*w - 3],\
[1733, 1733, -w^3 + 4*w^2 + 3*w - 19],\
[1741, 1741, -w^3 + 5*w^2 - 14],\
[1747, 1747, -4*w^3 + 6*w^2 + 22*w + 1],\
[1747, 1747, 2*w^3 - 5*w^2 - 9*w + 2],\
[1753, 1753, -2*w^3 + 5*w^2 + 3*w - 1],\
[1759, 1759, -w^3 + 2*w^2 + 4*w - 9],\
[1783, 1783, -3*w^3 + 8*w^2 + 5*w - 12],\
[1783, 1783, -2*w^3 + 6*w^2 + 3*w - 12],\
[1783, 1783, 2*w^3 - 7*w^2 - 4*w + 17],\
[1783, 1783, 2*w^3 - 6*w^2 - w + 7],\
[1787, 1787, -5*w^3 + 8*w^2 + 25*w - 3],\
[1823, 1823, w^3 - 8*w - 1],\
[1823, 1823, -3*w^3 + 5*w^2 + 14*w + 6],\
[1831, 1831, -3*w^3 + 8*w^2 + 14*w - 18],\
[1847, 1847, w^3 - 3*w^2 - w + 14],\
[1847, 1847, -2*w^3 + 2*w^2 + 11*w + 11],\
[1861, 1861, 2*w^2 - w - 12],\
[1871, 1871, 4*w^3 - 8*w^2 - 19*w + 9],\
[1871, 1871, -w^3 + 5*w^2 - w - 7],\
[1873, 1873, -3*w^3 + 5*w^2 + 13*w - 4],\
[1877, 1877, -4*w^3 + 8*w^2 + 16*w - 7],\
[1877, 1877, 3*w^3 - 5*w^2 - 15*w - 2],\
[1879, 1879, -w^3 + 4*w^2 - w - 12],\
[1907, 1907, w^3 - w^2 - 10*w - 6],\
[1931, 1931, -w^3 + 5*w^2 - w - 19],\
[1931, 1931, -6*w^3 + 17*w^2 + 12*w - 22],\
[1951, 1951, 4*w^3 - 10*w^2 - 14*w + 21],\
[1951, 1951, -2*w^3 + 4*w^2 + 13*w - 13],\
[1993, 1993, 2*w^3 - 2*w^2 - 11*w + 1],\
[1993, 1993, -w^3 + 6*w + 14]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^6 - x^5 - 21*x^4 + 34*x^3 + 23*x^2 - 32*x - 16
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [-1, -1, e, 5/2*e^5 + 1/2*e^4 - 101/2*e^3 + 24*e^2 + 117/2*e + 14, e^5 - 20*e^3 + 14*e^2 + 17*e + 2, 1/4*e^5 + 3/4*e^4 - 21/4*e^3 - 23/2*e^2 + 79/4*e + 12, 7/2*e^5 + 3/2*e^4 - 141/2*e^3 + 18*e^2 + 181/2*e + 32, 1/4*e^5 - 1/4*e^4 - 21/4*e^3 + 17/2*e^2 + 19/4*e - 7, 25/4*e^5 + 15/4*e^4 - 505/4*e^3 + 21/2*e^2 + 727/4*e + 73, -e, -e^4 + 20*e^2 - 12*e - 18, 4*e^5 + 3*e^4 - 81*e^3 - 6*e^2 + 127*e + 64, 25/4*e^5 + 7/4*e^4 - 505/4*e^3 + 101/2*e^2 + 607/4*e + 37, -5*e^5 - 2*e^4 + 101*e^3 - 29*e^2 - 131*e - 36, -3/4*e^5 - 1/4*e^4 + 63/4*e^3 - 9/2*e^2 - 113/4*e - 3, -3/2*e^5 - 5/2*e^4 + 61/2*e^3 + 30*e^2 - 139/2*e - 50, 4*e^5 + 3*e^4 - 81*e^3 - 6*e^2 + 127*e + 58, -3/2*e^5 + 1/2*e^4 + 61/2*e^3 - 30*e^2 - 55/2*e + 4, -4*e^5 - 2*e^4 + 81*e^3 - 14*e^2 - 113*e - 42, 11/4*e^5 + 5/4*e^4 - 223/4*e^3 + 25/2*e^2 + 313/4*e + 29, -7/2*e^5 - 3/2*e^4 + 141/2*e^3 - 18*e^2 - 175/2*e - 38, -1/4*e^5 + 5/4*e^4 + 21/4*e^3 - 57/2*e^2 + 29/4*e + 29, -11/2*e^5 - 7/2*e^4 + 223/2*e^3 - 6*e^2 - 341/2*e - 60, e^5 - 2*e^4 - 20*e^3 + 54*e^2 - 9*e - 30, -4*e^5 - 3*e^4 + 81*e^3 + 5*e^2 - 129*e - 50, -10*e^5 - 7*e^4 + 202*e^3 + 4*e^2 - 301*e - 142, 17/4*e^5 + 7/4*e^4 - 345/4*e^3 + 45/2*e^2 + 471/4*e + 41, -13/2*e^5 - 11/2*e^4 + 263/2*e^3 + 21*e^2 - 431/2*e - 102, -e^5 + e^4 + 20*e^3 - 34*e^2 - 4*e + 20, 3*e^5 + 3*e^4 - 60*e^3 - 19*e^2 + 94*e + 62, -10*e^5 - 4*e^4 + 202*e^3 - 57*e^2 - 261*e - 80, 5/2*e^5 + 5/2*e^4 - 101/2*e^3 - 15*e^2 + 177/2*e + 42, 5/2*e^5 - 3/2*e^4 - 99/2*e^3 + 66*e^2 + 33/2*e - 32, 11/2*e^5 + 5/2*e^4 - 221/2*e^3 + 27*e^2 + 277/2*e + 44, 43/4*e^5 + 21/4*e^4 - 867/4*e^3 + 85/2*e^2 + 1149/4*e + 111, -3*e^5 - e^4 + 60*e^3 - 21*e^2 - 65*e - 24, 5/4*e^5 + 7/4*e^4 - 101/4*e^3 - 37/2*e^2 + 215/4*e + 43, -6*e^5 - 6*e^4 + 121*e^3 + 37*e^2 - 207*e - 108, -7/2*e^5 - 5/2*e^4 + 141/2*e^3 + 2*e^2 - 201/2*e - 42, -29/2*e^5 - 11/2*e^4 + 585/2*e^3 - 90*e^2 - 735/2*e - 118, 19/2*e^5 + 7/2*e^4 - 383/2*e^3 + 59*e^2 + 471/2*e + 80, 13/2*e^5 + 5/2*e^4 - 263/2*e^3 + 40*e^2 + 343/2*e + 52, -15/4*e^5 + 7/4*e^4 + 299/4*e^3 - 175/2*e^2 - 141/4*e + 35, 27/2*e^5 + 9/2*e^4 - 545/2*e^3 + 95*e^2 + 679/2*e + 92, 49/4*e^5 + 15/4*e^4 - 989/4*e^3 + 187/2*e^2 + 1207/4*e + 71, 19/2*e^5 + 17/2*e^4 - 385/2*e^3 - 41*e^2 + 643/2*e + 164, -21/2*e^5 - 9/2*e^4 + 425/2*e^3 - 53*e^2 - 559/2*e - 96, -11*e^5 - 5*e^4 + 222*e^3 - 52*e^2 - 295*e - 100, -8*e^5 - 6*e^4 + 161*e^3 + 9*e^2 - 238*e - 112, -9*e^5 - e^4 + 182*e^3 - 103*e^2 - 198*e - 22, -39/4*e^5 - 17/4*e^4 + 787/4*e^3 - 101/2*e^2 - 1037/4*e - 77, 13/2*e^5 + 9/2*e^4 - 263/2*e^3 - 2*e^2 + 393/2*e + 106, 19*e^5 + 9*e^4 - 384*e^3 + 81*e^2 + 523*e + 178, -9/4*e^5 - 7/4*e^4 + 181/4*e^3 + 9/2*e^2 - 263/4*e - 43, -11/2*e^5 - 5/2*e^4 + 221/2*e^3 - 24*e^2 - 267/2*e - 68, -9*e^5 - 2*e^4 + 182*e^3 - 83*e^2 - 222*e - 46, -12*e^5 - 9*e^4 + 242*e^3 + 16*e^2 - 369*e - 190, 7/2*e^5 - 3/2*e^4 - 141/2*e^3 + 77*e^2 + 91/2*e - 8, -71/4*e^5 - 37/4*e^4 + 1435/4*e^3 - 113/2*e^2 - 1985/4*e - 187, 81/4*e^5 + 39/4*e^4 - 1637/4*e^3 + 169/2*e^2 + 2235/4*e + 175, -4*e^5 + 81*e^3 - 55*e^2 - 88*e - 2, -11*e^5 - 5*e^4 + 221*e^3 - 52*e^2 - 277*e - 104, 45/2*e^5 + 33/2*e^4 - 909/2*e^3 - 21*e^2 + 1389/2*e + 324, -27/2*e^5 - 23/2*e^4 + 545/2*e^3 + 45*e^2 - 877/2*e - 222, -7/2*e^5 - 1/2*e^4 + 143/2*e^3 - 38*e^2 - 179/2*e - 8, -29/2*e^5 - 21/2*e^4 + 587/2*e^3 + 13*e^2 - 913/2*e - 208, -5/2*e^5 - 7/2*e^4 + 101/2*e^3 + 35*e^2 - 195/2*e - 56, -55/4*e^5 - 17/4*e^4 + 1111/4*e^3 - 209/2*e^2 - 1353/4*e - 77, 33/4*e^5 + 15/4*e^4 - 669/4*e^3 + 75/2*e^2 + 927/4*e + 79, -57/4*e^5 - 27/4*e^4 + 1149/4*e^3 - 123/2*e^2 - 1495/4*e - 135, 59/4*e^5 + 33/4*e^4 - 1191/4*e^3 + 75/2*e^2 + 1673/4*e + 173, -1/2*e^5 + 5/2*e^4 + 17/2*e^3 - 59*e^2 + 97/2*e + 46, -61/4*e^5 - 23/4*e^4 + 1233/4*e^3 - 187/2*e^2 - 1591/4*e - 131, -1/2*e^5 + 7/2*e^4 + 21/2*e^3 - 77*e^2 + 63/2*e + 68, -17/2*e^5 - 17/2*e^4 + 343/2*e^3 + 53*e^2 - 571/2*e - 160, 7/2*e^5 + 5/2*e^4 - 139/2*e^3 - e^2 + 171/2*e + 60, -29/4*e^5 - 31/4*e^4 + 585/4*e^3 + 109/2*e^2 - 1031/4*e - 135, 15/2*e^5 + 17/2*e^4 - 303/2*e^3 - 68*e^2 + 549/2*e + 166, 4*e^5 + 3*e^4 - 80*e^3 - 6*e^2 + 106*e + 66, 9/2*e^5 + 5/2*e^4 - 181/2*e^3 + 11*e^2 + 229/2*e + 52, 11/2*e^5 + 1/2*e^4 - 223/2*e^3 + 67*e^2 + 267/2*e - 2, -17/2*e^5 - 1/2*e^4 + 343/2*e^3 - 106*e^2 - 351/2*e - 16, 9*e^5 + 3*e^4 - 182*e^3 + 64*e^2 + 232*e + 48, 8*e^5 + 3*e^4 - 162*e^3 + 49*e^2 + 210*e + 60, 41/2*e^5 + 25/2*e^4 - 829/2*e^3 + 29*e^2 + 1187/2*e + 266, -11/2*e^5 - 1/2*e^4 + 221/2*e^3 - 65*e^2 - 203/2*e - 22, 6*e^4 - e^3 - 121*e^2 + 104*e + 108, 3*e^5 + 3*e^4 - 62*e^3 - 21*e^2 + 130*e + 50, -27*e^5 - 12*e^4 + 546*e^3 - 130*e^2 - 733*e - 238, -3/4*e^5 - 17/4*e^4 + 59/4*e^3 + 145/2*e^2 - 305/4*e - 51, -47/4*e^5 - 41/4*e^4 + 947/4*e^3 + 87/2*e^2 - 1509/4*e - 193, 23/4*e^5 + 5/4*e^4 - 463/4*e^3 + 111/2*e^2 + 537/4*e + 21, -2*e^5 - e^4 + 40*e^3 - 8*e^2 - 42*e - 22, -37/2*e^5 - 21/2*e^4 + 751/2*e^3 - 41*e^2 - 1121/2*e - 192, -8*e^5 - 3*e^4 + 161*e^3 - 47*e^2 - 193*e - 90, 18*e^5 + 8*e^4 - 365*e^3 + 85*e^2 + 500*e + 162, -9*e^5 + e^4 + 181*e^3 - 147*e^2 - 160*e + 20, 33/2*e^5 + 11/2*e^4 - 665/2*e^3 + 116*e^2 + 815/2*e + 132, 2*e^5 + 2*e^4 - 42*e^3 - 13*e^2 + 95*e + 22, 15*e^5 + 2*e^4 - 302*e^3 + 167*e^2 + 318*e + 60, -31*e^5 - 20*e^4 + 627*e^3 - 25*e^2 - 927*e - 388, -26*e^5 - 14*e^4 + 525*e^3 - 77*e^2 - 724*e - 274, -25*e^5 - 10*e^4 + 505*e^3 - 141*e^2 - 655*e - 206, -57/4*e^5 - 23/4*e^4 + 1149/4*e^3 - 163/2*e^2 - 1443/4*e - 101, -19*e^5 - 12*e^4 + 383*e^3 - 21*e^2 - 549*e - 240, 15/2*e^5 + 7/2*e^4 - 303/2*e^3 + 33*e^2 + 423/2*e + 60, 3*e^5 + e^4 - 59*e^3 + 21*e^2 + 46*e + 38, -16*e^5 - 4*e^4 + 323*e^3 - 140*e^2 - 377*e - 86, 39/2*e^5 + 21/2*e^4 - 787/2*e^3 + 57*e^2 + 1089/2*e + 206, -23/2*e^5 - 1/2*e^4 + 463/2*e^3 - 150*e^2 - 457/2*e - 24, -24*e^5 - 13*e^4 + 486*e^3 - 66*e^2 - 692*e - 258, -53/4*e^5 - 31/4*e^4 + 1073/4*e^3 - 55/2*e^2 - 1571/4*e - 153, -101/4*e^5 - 71/4*e^4 + 2041/4*e^3 + 15/2*e^2 - 3075/4*e - 339, -1/2*e^5 - 1/2*e^4 + 21/2*e^3 + 5*e^2 - 53/2*e - 24, -3*e^5 - 3*e^4 + 60*e^3 + 17*e^2 - 97*e - 40, -45/4*e^5 - 31/4*e^4 + 905/4*e^3 + 1/2*e^2 - 1303/4*e - 153, 97/4*e^5 + 71/4*e^4 - 1961/4*e^3 - 45/2*e^2 + 3043/4*e + 333, 17/4*e^5 + 15/4*e^4 - 349/4*e^3 - 33/2*e^2 + 659/4*e + 77, -2*e^5 + 2*e^4 + 40*e^3 - 69*e^2 - 15*e + 54, -47/2*e^5 - 39/2*e^4 + 951/2*e^3 + 71*e^2 - 1537/2*e - 374, -9/2*e^5 - 5/2*e^4 + 179/2*e^3 - 16*e^2 - 207/2*e - 26, -27/2*e^5 - 15/2*e^4 + 547/2*e^3 - 34*e^2 - 779/2*e - 150, 49/4*e^5 + 35/4*e^4 - 993/4*e^3 - 17/2*e^2 + 1519/4*e + 179, 45/4*e^5 - 5/4*e^4 - 909/4*e^3 + 359/2*e^2 + 855/4*e - 5, -21/4*e^5 - 19/4*e^4 + 417/4*e^3 + 47/2*e^2 - 579/4*e - 107, 27/2*e^5 + 17/2*e^4 - 545/2*e^3 + 16*e^2 + 789/2*e + 144, 39/4*e^5 + 1/4*e^4 - 783/4*e^3 + 261/2*e^2 + 705/4*e + 9, -7/2*e^5 - 9/2*e^4 + 143/2*e^3 + 44*e^2 - 295/2*e - 88, 61/4*e^5 + 39/4*e^4 - 1233/4*e^3 + 27/2*e^2 + 1811/4*e + 193, 16*e^5 + 8*e^4 - 322*e^3 + 61*e^2 + 424*e + 168, 9/4*e^5 + 27/4*e^4 - 181/4*e^3 - 207/2*e^2 + 575/4*e + 121, -4*e^5 + e^4 + 80*e^3 - 76*e^2 - 57*e + 30, 39/2*e^5 + 19/2*e^4 - 787/2*e^3 + 77*e^2 + 1063/2*e + 202, -37/2*e^5 - 17/2*e^4 + 747/2*e^3 - 83*e^2 - 981/2*e - 178, -47/2*e^5 - 11/2*e^4 + 949/2*e^3 - 213*e^2 - 1119/2*e - 132, 19*e^5 + 12*e^4 - 385*e^3 + 17*e^2 + 579*e + 232, 20*e^5 + 9*e^4 - 405*e^3 + 93*e^2 + 557*e + 170, -29/2*e^5 - 17/2*e^4 + 583/2*e^3 - 30*e^2 - 773/2*e - 192, 7*e^5 + 3*e^4 - 140*e^3 + 35*e^2 + 154*e + 80, -75/4*e^5 - 25/4*e^4 + 1515/4*e^3 - 265/2*e^2 - 1861/4*e - 131, -11/2*e^5 + 13/2*e^4 + 223/2*e^3 - 206*e^2 - 49/2*e + 96, 75/4*e^5 + 37/4*e^4 - 1515/4*e^3 + 141/2*e^2 + 2045/4*e + 201, -5*e^5 - 7*e^4 + 101*e^3 + 72*e^2 - 196*e - 136, 39/4*e^5 - 3/4*e^4 - 791/4*e^3 + 299/2*e^2 + 805/4*e - 3, -6*e^5 + 2*e^4 + 120*e^3 - 126*e^2 - 74*e + 42, 11/4*e^5 - 3/4*e^4 - 223/4*e^3 + 105/2*e^2 + 197/4*e + 3, 6*e^5 + 2*e^4 - 123*e^3 + 40*e^2 + 187*e + 46, -21*e^5 - 16*e^4 + 424*e^3 + 32*e^2 - 656*e - 314, -23/2*e^5 - 13/2*e^4 + 465/2*e^3 - 25*e^2 - 663/2*e - 162, -69/2*e^5 - 27/2*e^4 + 1393/2*e^3 - 200*e^2 - 1773/2*e - 286, -97/4*e^5 - 47/4*e^4 + 1961/4*e^3 - 195/2*e^2 - 2699/4*e - 219, -87/4*e^5 - 33/4*e^4 + 1755/4*e^3 - 263/2*e^2 - 2205/4*e - 187, 22*e^5 + 14*e^4 - 444*e^3 + 18*e^2 + 635*e + 298, -23/4*e^5 - 17/4*e^4 + 467/4*e^3 + 17/2*e^2 - 737/4*e - 99, 25/2*e^5 + 15/2*e^4 - 507/2*e^3 + 19*e^2 + 741/2*e + 156, -e^5 + e^4 + 22*e^3 - 31*e^2 - 30*e, -20*e^5 - 8*e^4 + 405*e^3 - 115*e^2 - 542*e - 144, 69/2*e^5 + 23/2*e^4 - 1393/2*e^3 + 245*e^2 + 1721/2*e + 234, 28*e^5 + 18*e^4 - 565*e^3 + 26*e^2 + 822*e + 340, 9*e^5 + 6*e^4 - 182*e^3 + 4*e^2 + 274*e + 108, -27/2*e^5 - 15/2*e^4 + 549/2*e^3 - 35*e^2 - 823/2*e - 122, 123/4*e^5 + 45/4*e^4 - 2479/4*e^3 + 395/2*e^2 + 3065/4*e + 239, 87/4*e^5 + 49/4*e^4 - 1755/4*e^3 + 105/2*e^2 + 2417/4*e + 285, -19/2*e^5 - 1/2*e^4 + 385/2*e^3 - 119*e^2 - 441/2*e - 12, 21/2*e^5 + 17/2*e^4 - 423/2*e^3 - 27*e^2 + 637/2*e + 180, -8*e^5 - 4*e^4 + 161*e^3 - 29*e^2 - 210*e - 54, 73/4*e^5 + 7/4*e^4 - 1469/4*e^3 + 433/2*e^2 + 1451/4*e + 47, -3*e^5 + 5*e^4 + 61*e^3 - 142*e^2 + 3*e + 76, 83/2*e^5 + 43/2*e^4 - 1677/2*e^3 + 139*e^2 + 2321/2*e + 422, 20*e^5 + 12*e^4 - 404*e^3 + 35*e^2 + 580*e + 234, 75/4*e^5 + 53/4*e^4 - 1511/4*e^3 - 15/2*e^2 + 2245/4*e + 275, -20*e^5 - 10*e^4 + 406*e^3 - 71*e^2 - 585*e - 196, 8*e^5 + 12*e^4 - 162*e^3 - 129*e^2 + 343*e + 212, -13*e^5 - 4*e^4 + 262*e^3 - 100*e^2 - 321*e - 54, 41/2*e^5 + 39/2*e^4 - 831/2*e^3 - 112*e^2 + 1423/2*e + 372, -3/4*e^5 - 13/4*e^4 + 67/4*e^3 + 115/2*e^2 - 381/4*e - 77, -12*e^5 - 4*e^4 + 241*e^3 - 88*e^2 - 279*e - 56, -25/4*e^5 + 9/4*e^4 + 501/4*e^3 - 267/2*e^2 - 359/4*e + 59, -9*e^5 - 2*e^4 + 182*e^3 - 83*e^2 - 216*e - 42, 6*e^5 + 7*e^4 - 122*e^3 - 62*e^2 + 229*e + 168, -135/4*e^5 - 69/4*e^4 + 2723/4*e^3 - 235/2*e^2 - 3669/4*e - 379, -11*e^5 - 7*e^4 + 223*e^3 - 15*e^2 - 340*e - 88, -43/2*e^5 - 39/2*e^4 + 871/2*e^3 + 97*e^2 - 1451/2*e - 378, 39/4*e^5 + 25/4*e^4 - 787/4*e^3 + 13/2*e^2 + 1125/4*e + 177, 9*e^5 + 10*e^4 - 183*e^3 - 77*e^2 + 343*e + 184, -41/2*e^5 - 27/2*e^4 + 829/2*e^3 - 14*e^2 - 1245/2*e - 238, 81/2*e^5 + 37/2*e^4 - 1635/2*e^3 + 186*e^2 + 2171/2*e + 384, -9*e^5 - 6*e^4 + 184*e^3 - 312*e - 106, -16*e^5 - 5*e^4 + 324*e^3 - 120*e^2 - 407*e - 100, -113/4*e^5 - 55/4*e^4 + 2285/4*e^3 - 225/2*e^2 - 3115/4*e - 247, -63/4*e^5 - 49/4*e^4 + 1271/4*e^3 + 57/2*e^2 - 1961/4*e - 227, -21/2*e^5 - 17/2*e^4 + 425/2*e^3 + 27*e^2 - 689/2*e - 172, -31/2*e^5 - 21/2*e^4 + 629/2*e^3 - 985/2*e - 208, 25/4*e^5 - 1/4*e^4 - 505/4*e^3 + 183/2*e^2 + 515/4*e - 13, 15*e^5 + 8*e^4 - 303*e^3 + 48*e^2 + 432*e + 138, -2*e^5 + e^4 + 42*e^3 - 44*e^2 - 58*e + 26, -5*e^5 + 5*e^4 + 100*e^3 - 169*e^2 - 16*e + 74, 43/4*e^5 + 5/4*e^4 - 867/4*e^3 + 247/2*e^2 + 909/4*e + 51, -e^5 - 4*e^4 + 21*e^3 + 68*e^2 - 88*e - 74, -3/2*e^5 - 3/2*e^4 + 59/2*e^3 + 7*e^2 - 91/2*e - 18, 83/2*e^5 + 41/2*e^4 - 1677/2*e^3 + 159*e^2 + 2301/2*e + 402, 5/2*e^5 - 11/2*e^4 - 105/2*e^3 + 142*e^2 - 3/2*e - 88, 37/2*e^5 + 27/2*e^4 - 745/2*e^3 - 18*e^2 + 1093/2*e + 292, 21*e^5 + 12*e^4 - 426*e^3 + 46*e^2 + 617*e + 232, 53/2*e^5 + 27/2*e^4 - 1071/2*e^3 + 96*e^2 + 1471/2*e + 232, 43/4*e^5 + 45/4*e^4 - 867/4*e^3 - 159/2*e^2 + 1453/4*e + 231, -43/2*e^5 - 17/2*e^4 + 871/2*e^3 - 126*e^2 - 1169/2*e - 166, -25*e^5 - 16*e^4 + 505*e^3 - 26*e^2 - 746*e - 280, 7*e^5 + 7*e^4 - 141*e^3 - 45*e^2 + 228*e + 154, 89/4*e^5 + 59/4*e^4 - 1797/4*e^3 + 21/2*e^2 + 2631/4*e + 263, -6*e^5 - 4*e^4 + 123*e^3 - 2*e^2 - 208*e - 68, -87/4*e^5 - 49/4*e^4 + 1759/4*e^3 - 113/2*e^2 - 2493/4*e - 201, -16*e^5 - 7*e^4 + 321*e^3 - 80*e^2 - 396*e - 162, -3*e^5 - 9*e^4 + 61*e^3 + 141*e^2 - 186*e - 170, -75/2*e^5 - 41/2*e^4 + 1515/2*e^3 - 106*e^2 - 2127/2*e - 404, 20*e^5 + 16*e^4 - 404*e^3 - 46*e^2 + 626*e + 306, -9*e^5 - 4*e^4 + 182*e^3 - 39*e^2 - 240*e - 110, -14*e^5 - 6*e^4 + 283*e^3 - 72*e^2 - 379*e - 102, 55/4*e^5 + 41/4*e^4 - 1111/4*e^3 - 31/2*e^2 + 1725/4*e + 207, e^4 - e^3 - 19*e^2 + 25*e - 12, 27*e^5 + 9*e^4 - 546*e^3 + 192*e^2 + 690*e + 162, -97/4*e^5 - 23/4*e^4 + 1957/4*e^3 - 433/2*e^2 - 2299/4*e - 131, -42*e^5 - 18*e^4 + 847*e^3 - 217*e^2 - 1083*e - 386, -4*e^5 - 6*e^4 + 83*e^3 + 69*e^2 - 205*e - 104, -27/4*e^5 - 17/4*e^4 + 539/4*e^3 - 9/2*e^2 - 677/4*e - 119, e^4 + e^3 - 23*e^2 + 62, -35/4*e^5 - 21/4*e^4 + 711/4*e^3 - 29/2*e^2 - 1053/4*e - 69, 103/4*e^5 + 61/4*e^4 - 2083/4*e^3 + 99/2*e^2 + 3017/4*e + 299, 37*e^5 + 20*e^4 - 749*e^3 + 109*e^2 + 1073*e + 370, -129/4*e^5 - 67/4*e^4 + 2605/4*e^3 - 215/2*e^2 - 3555/4*e - 359, 43/2*e^5 + 19/2*e^4 - 869/2*e^3 + 106*e^2 + 1159/2*e + 196, -5*e^5 - 6*e^4 + 101*e^3 + 53*e^2 - 191*e - 122, -17/4*e^5 - 55/4*e^4 + 341/4*e^3 + 435/2*e^2 - 1099/4*e - 247, -95/4*e^5 - 45/4*e^4 + 1919/4*e^3 - 201/2*e^2 - 2629/4*e - 217, 87/2*e^5 + 63/2*e^4 - 1759/2*e^3 - 33*e^2 + 2697/2*e + 596, 33/2*e^5 + 29/2*e^4 - 667/2*e^3 - 65*e^2 + 1093/2*e + 258, 18*e^5 + 11*e^4 - 362*e^3 + 25*e^2 + 493*e + 240, 53/2*e^5 + 31/2*e^4 - 1073/2*e^3 + 54*e^2 + 1579/2*e + 290, 125/4*e^5 + 47/4*e^4 - 2529/4*e^3 + 389/2*e^2 + 3271/4*e + 205, 45/4*e^5 + 43/4*e^4 - 913/4*e^3 - 129/2*e^2 + 1571/4*e + 229, 147/4*e^5 + 69/4*e^4 - 2971/4*e^3 + 319/2*e^2 + 4001/4*e + 345, 61/4*e^5 + 39/4*e^4 - 1241/4*e^3 + 19/2*e^2 + 1923/4*e + 209, -123/4*e^5 - 49/4*e^4 + 2479/4*e^3 - 351/2*e^2 - 3097/4*e - 265, -15/2*e^5 - 11/2*e^4 + 305/2*e^3 + 10*e^2 - 491/2*e - 114, 35/2*e^5 + 27/2*e^4 - 709/2*e^3 - 31*e^2 + 1125/2*e + 254, 27/4*e^5 - 19/4*e^4 - 543/4*e^3 + 375/2*e^2 + 253/4*e - 57, -43/2*e^5 - 9/2*e^4 + 865/2*e^3 - 205*e^2 - 937/2*e - 110, 97/4*e^5 + 35/4*e^4 - 1961/4*e^3 + 307/2*e^2 + 2475/4*e + 227, -38*e^5 - 20*e^4 + 767*e^3 - 122*e^2 - 1057*e - 396, 24*e^5 + 10*e^4 - 485*e^3 + 131*e^2 + 640*e + 202, 23/2*e^5 + 19/2*e^4 - 465/2*e^3 - 32*e^2 + 737/2*e + 176, -33/2*e^5 - 27/2*e^4 + 673/2*e^3 + 46*e^2 - 1161/2*e - 250, -47*e^5 - 23*e^4 + 949*e^3 - 179*e^2 - 1273*e - 512, 2*e^5 - 10*e^4 - 38*e^3 + 234*e^2 - 138*e - 194, 20*e^5 + 7*e^4 - 403*e^3 + 136*e^2 + 492*e + 136, -22*e^5 - 16*e^4 + 443*e^3 + 15*e^2 - 654*e - 300, 8*e^5 + 7*e^4 - 164*e^3 - 32*e^2 + 301*e + 128, 31*e^5 + 15*e^4 - 627*e^3 + 122*e^2 + 845*e + 342, -55/4*e^5 - 17/4*e^4 + 1107/4*e^3 - 207/2*e^2 - 1237/4*e - 109, -17/2*e^5 - 1/2*e^4 + 345/2*e^3 - 104*e^2 - 371/2*e - 42, 14*e^5 + 4*e^4 - 284*e^3 + 110*e^2 + 351*e + 96, -27/2*e^5 - 15/2*e^4 + 547/2*e^3 - 35*e^2 - 787/2*e - 130, -12*e^5 - 13*e^4 + 243*e^3 + 99*e^2 - 437*e - 282, 4*e^5 - 2*e^4 - 81*e^3 + 93*e^2 + 48*e - 44, -19*e^5 - 3*e^4 + 383*e^3 - 205*e^2 - 422*e - 46, 65/2*e^5 + 51/2*e^4 - 1315/2*e^3 - 68*e^2 + 2071/2*e + 484, -12*e^5 - 3*e^4 + 244*e^3 - 101*e^2 - 317*e - 54, -1/2*e^5 + 17/2*e^4 + 17/2*e^3 - 177*e^2 + 257/2*e + 150, -79/2*e^5 - 55/2*e^4 + 1597/2*e^3 + 5*e^2 - 2417/2*e - 512, -51/2*e^5 - 25/2*e^4 + 1029/2*e^3 - 100*e^2 - 1357/2*e - 258, 22*e^5 + 8*e^4 - 444*e^3 + 138*e^2 + 547*e + 208, 4*e^5 - 3*e^4 - 77*e^3 + 121*e^2 - 23*e - 56, -13*e^5 - 10*e^4 + 262*e^3 + 21*e^2 - 390*e - 208, 9*e^5 + 13*e^4 - 182*e^3 - 135*e^2 + 371*e + 244, 23/4*e^5 - 23/4*e^4 - 455/4*e^3 + 389/2*e^2 - 31/4*e - 107, -13*e^5 - 10*e^4 + 264*e^3 + 25*e^2 - 429*e - 168, -17*e^5 - 7*e^4 + 344*e^3 - 89*e^2 - 453*e - 160, 11/4*e^5 - 7/4*e^4 - 223/4*e^3 + 147/2*e^2 + 161/4*e - 51, -7*e^5 - e^4 + 142*e^3 - 74*e^2 - 167*e - 40, -e^5 - 3*e^4 + 20*e^3 + 51*e^2 - 46*e - 108, 17*e^5 + 8*e^4 - 342*e^3 + 75*e^2 + 450*e + 152, -159/4*e^5 - 97/4*e^4 + 3215/4*e^3 - 109/2*e^2 - 4665/4*e - 499, -79/4*e^5 + 3/4*e^4 + 1587/4*e^3 - 573/2*e^2 - 1429/4*e - 19, -15*e^5 - 6*e^4 + 301*e^3 - 88*e^2 - 364*e - 104, -15/2*e^5 - 3/2*e^4 + 307/2*e^3 - 73*e^2 - 423/2*e - 12, -155/4*e^5 - 93/4*e^4 + 3131/4*e^3 - 133/2*e^2 - 4501/4*e - 459, 89/4*e^5 + 67/4*e^4 - 1793/4*e^3 - 57/2*e^2 + 2647/4*e + 337, 59/2*e^5 + 31/2*e^4 - 1189/2*e^3 + 94*e^2 + 1583/2*e + 334, 49*e^5 + 23*e^4 - 991*e^3 + 216*e^2 + 1352*e + 422, 33/2*e^5 + 17/2*e^4 - 665/2*e^3 + 53*e^2 + 881/2*e + 168, 37*e^5 + 15*e^4 - 747*e^3 + 208*e^2 + 960*e + 344, -8*e^5 + e^4 + 163*e^3 - 129*e^2 - 171*e + 36, -29/2*e^5 - 5/2*e^4 + 587/2*e^3 - 148*e^2 - 677/2*e - 42, 55/4*e^5 - 3/4*e^4 - 1107/4*e^3 + 417/2*e^2 + 1033/4*e - 35, -107/4*e^5 - 13/4*e^4 + 2167/4*e^3 - 601/2*e^2 - 2417/4*e - 95, e^5 - e^4 - 21*e^3 + 31*e^2 + 20*e + 8, -22*e^5 - 19*e^4 + 446*e^3 + 79*e^2 - 755*e - 364, 47*e^5 + 32*e^4 - 950*e^3 + 4*e^2 + 1416*e + 650]
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, -w^3 + 2*w^2 + 5*w - 3])] = 1
AL_eigenvalues[ZF.ideal([5, 5, w])] = 1

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