/* 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. = PolynomialRing(QQ) g = P([2, 4, -5, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([16, 2, 2]) primes_array = [ [2, 2, w],\ [4, 2, -w^3 + 4*w + 1],\ [5, 5, w + 1],\ [13, 13, -w^2 + 3],\ [17, 17, -w^3 + w^2 + 3*w - 1],\ [19, 19, -w^3 + 3*w - 1],\ [23, 23, -w + 3],\ [31, 31, -w^2 - 2*w + 1],\ [41, 41, w^3 + w^2 - 5*w - 3],\ [43, 43, 2*w - 1],\ [53, 53, -w - 3],\ [53, 53, w^3 - w^2 - 4*w + 1],\ [61, 61, w^3 - 3*w - 5],\ [67, 67, w^3 + w^2 - 5*w - 1],\ [81, 3, -3],\ [83, 83, -w^3 + 5*w - 3],\ [89, 89, w^2 + 1],\ [97, 97, w^3 - w^2 - 5*w + 1],\ [97, 97, 3*w^3 - 5*w^2 - 14*w + 21],\ [97, 97, w^3 - 3*w - 3],\ [97, 97, w^3 - 7*w - 3],\ [103, 103, w^3 - w^2 - 3*w + 5],\ [107, 107, -2*w^3 + 2*w^2 + 8*w - 7],\ [109, 109, 3*w^3 - 3*w^2 - 13*w + 11],\ [113, 113, 2*w^3 - 2*w^2 - 10*w + 7],\ [113, 113, w^3 + w^2 - 5*w - 7],\ [121, 11, 2*w^2 - w - 9],\ [121, 11, 2*w^2 - w - 7],\ [125, 5, -w^3 + 2*w^2 + 3*w - 7],\ [131, 131, 4*w^3 - 5*w^2 - 18*w + 19],\ [137, 137, w^3 + w^2 - 6*w - 5],\ [137, 137, 3*w^3 - 13*w - 3],\ [139, 139, 3*w^3 - 5*w^2 - 13*w + 19],\ [149, 149, 2*w^3 - 9*w + 1],\ [163, 163, -2*w^2 + 11],\ [163, 163, -w^3 + w^2 + 6*w - 3],\ [163, 163, w^3 - 2*w^2 - 5*w + 5],\ [163, 163, 3*w^3 - 3*w^2 - 14*w + 15],\ [173, 173, 2*w^3 - 10*w + 1],\ [173, 173, 2*w^3 - 3*w^2 - 8*w + 13],\ [179, 179, 2*w^3 + w^2 - 8*w - 1],\ [181, 181, 2*w^3 - 4*w^2 - 9*w + 15],\ [193, 193, w^2 - 7],\ [199, 199, 2*w^2 - 5],\ [211, 211, -2*w^3 + 8*w - 3],\ [211, 211, -2*w^3 + w^2 + 8*w - 3],\ [223, 223, 3*w - 1],\ [223, 223, -2*w^3 - w^2 + 8*w + 5],\ [229, 229, -w^3 + 3*w^2 + 4*w - 11],\ [233, 233, -w^3 + 3*w^2 - 5],\ [233, 233, w^3 + 2*w^2 - 5*w - 3],\ [239, 239, 2*w^3 - 7*w - 1],\ [241, 241, w^3 - 2*w^2 - 3*w + 11],\ [251, 251, 2*w^2 - w - 5],\ [251, 251, 2*w^2 + 2*w - 7],\ [271, 271, -2*w^3 + 2*w^2 + 7*w - 9],\ [283, 283, 6*w^3 - 6*w^2 - 28*w + 23],\ [293, 293, 4*w^3 - 4*w^2 - 17*w + 17],\ [293, 293, 2*w^3 - 2*w^2 - 7*w + 5],\ [307, 307, 6*w^3 - 7*w^2 - 28*w + 29],\ [311, 311, w^3 - 2*w^2 - 3*w + 1],\ [311, 311, 2*w^2 - 2*w - 7],\ [311, 311, 2*w^3 - 4*w^2 - 8*w + 17],\ [311, 311, -w^3 + 3*w^2 + 4*w - 9],\ [347, 347, -w^3 - w^2 + 6*w - 1],\ [347, 347, -3*w^3 + 5*w^2 + 15*w - 21],\ [349, 349, 2*w^3 + 2*w^2 - 11*w - 7],\ [349, 349, 3*w^3 - w^2 - 15*w + 3],\ [353, 353, w^3 + w^2 - 3*w - 5],\ [353, 353, -4*w^3 + 16*w + 5],\ [361, 19, 6*w^3 - 8*w^2 - 27*w + 31],\ [367, 367, 3*w^3 - 3*w^2 - 13*w + 9],\ [367, 367, -2*w^2 - w + 9],\ [373, 373, -2*w^3 + w^2 + 10*w - 7],\ [379, 379, w^3 + 2*w^2 - 7*w - 7],\ [383, 383, -w^3 + 2*w^2 + 3*w - 9],\ [389, 389, -2*w^3 + 3*w^2 + 10*w - 9],\ [389, 389, w^2 - 2*w - 5],\ [397, 397, 2*w^3 - w^2 - 10*w - 1],\ [397, 397, w - 5],\ [409, 409, w^3 - w^2 - 6*w - 3],\ [419, 419, w^3 - 7*w + 1],\ [419, 419, -3*w^3 + 2*w^2 + 13*w - 11],\ [421, 421, w^3 + w^2 - 4*w + 3],\ [421, 421, 3*w^3 + w^2 - 14*w - 3],\ [431, 431, w^2 + 2*w - 7],\ [449, 449, w^3 + w^2 - 3*w - 9],\ [457, 457, -2*w^3 + w^2 + 8*w - 9],\ [457, 457, 2*w^3 - 2*w^2 - 7*w + 11],\ [463, 463, -w^3 - w^2 + 8*w - 3],\ [463, 463, 3*w^3 - 3*w^2 - 15*w + 13],\ [487, 487, 2*w^3 - 2*w^2 - 7*w + 1],\ [487, 487, w^2 - 2*w - 7],\ [499, 499, 3*w^3 - 3*w^2 - 12*w + 11],\ [503, 503, -3*w^3 + w^2 + 13*w + 5],\ [509, 509, -w^3 - w^2 + 7*w + 5],\ [521, 521, 2*w^3 + 2*w^2 - 9*w - 5],\ [523, 523, -2*w^2 - 1],\ [541, 541, 2*w^3 - 2*w^2 - 8*w + 3],\ [541, 541, w^3 - 2*w^2 - 7*w + 5],\ [547, 547, 3*w^3 - 4*w^2 - 13*w + 13],\ [563, 563, w^3 + 3*w^2 - 3*w - 11],\ [571, 571, -w^3 + w - 3],\ [571, 571, 2*w^3 + w^2 - 10*w - 1],\ [587, 587, 3*w^3 - 15*w + 1],\ [587, 587, 3*w^3 - w^2 - 14*w - 1],\ [593, 593, 3*w^3 - 2*w^2 - 15*w + 7],\ [593, 593, -2*w^3 + w^2 + 6*w - 1],\ [599, 599, -w^3 + w^2 + 4*w + 3],\ [599, 599, 2*w^3 + 2*w^2 - 11*w - 3],\ [607, 607, -w - 5],\ [607, 607, -w^3 + 4*w^2 + 5*w - 19],\ [613, 613, 2*w^3 + w^2 - 8*w + 1],\ [617, 617, 3*w^3 - w^2 - 12*w + 5],\ [617, 617, -2*w^3 + 12*w - 3],\ [619, 619, w^2 - 4*w - 3],\ [631, 631, -3*w^2 - 4*w + 7],\ [631, 631, -6*w^3 + 4*w^2 + 27*w - 15],\ [643, 643, -w^3 + 2*w^2 + 7*w - 7],\ [643, 643, 3*w^2 - 11],\ [647, 647, 4*w^3 - 4*w^2 - 17*w + 15],\ [653, 653, -2*w^3 - 2*w^2 + 10*w + 7],\ [653, 653, w^3 - 3*w^2 - 6*w + 7],\ [659, 659, -3*w^3 + 2*w^2 + 15*w - 11],\ [673, 673, w^3 + w^2 - 3*w - 7],\ [677, 677, w^3 - 3*w^2 - 3*w + 13],\ [677, 677, 2*w^3 - 2*w^2 - 11*w + 9],\ [709, 709, w^3 + w^2 - 2*w - 5],\ [751, 751, w^3 - 5*w^2 - 4*w + 21],\ [757, 757, -2*w^3 + 2*w^2 + 12*w - 1],\ [757, 757, -w^3 + w^2 + 2*w - 7],\ [761, 761, 4*w^3 - w^2 - 20*w + 3],\ [787, 787, 4*w + 3],\ [797, 797, 5*w^3 - 4*w^2 - 23*w + 17],\ [809, 809, -2*w^3 + 9*w - 5],\ [821, 821, 3*w^2 - 2*w - 9],\ [823, 823, -w^2 - 3],\ [863, 863, -w^3 + w^2 + 5*w - 9],\ [881, 881, -4*w^3 + 5*w^2 + 16*w - 21],\ [881, 881, -5*w^3 + 4*w^2 + 23*w - 13],\ [887, 887, 2*w^3 - 2*w^2 - 11*w + 7],\ [907, 907, -3*w^3 + 2*w^2 + 13*w - 3],\ [907, 907, 2*w^2 + 2*w - 9],\ [911, 911, -3*w^3 + w^2 + 15*w + 3],\ [919, 919, 3*w^2 - 7],\ [919, 919, 2*w^3 - 7*w + 7],\ [937, 937, 4*w^3 - 4*w^2 - 18*w + 13],\ [937, 937, 3*w^3 - w^2 - 13*w + 7],\ [977, 977, -4*w^3 + 2*w^2 + 19*w - 9],\ [983, 983, -w^3 + 4*w^2 + 5*w - 13],\ [983, 983, -2*w^3 + 2*w^2 + 9*w - 3],\ [991, 991, -w^3 + 4*w^2 + 3*w - 19],\ [991, 991, 2*w - 7],\ [1019, 1019, -5*w^3 + 5*w^2 + 23*w - 23],\ [1031, 1031, -2*w^3 + 4*w + 3],\ [1039, 1039, -3*w^3 + w^2 + 12*w - 3],\ [1051, 1051, -4*w^3 - 2*w^2 + 23*w + 9],\ [1051, 1051, 5*w^3 - 5*w^2 - 21*w + 21],\ [1051, 1051, 4*w^3 - 6*w^2 - 20*w + 23],\ [1051, 1051, 4*w^2 + 2*w - 11],\ [1061, 1061, -w^3 + 3*w^2 + 8*w - 7],\ [1061, 1061, 5*w^3 - 3*w^2 - 24*w + 13],\ [1063, 1063, -w^3 - w^2 + 8*w + 5],\ [1069, 1069, 2*w^2 - 4*w - 5],\ [1087, 1087, 2*w^3 - 2*w^2 - 10*w + 3],\ [1091, 1091, 3*w^3 - 17*w + 3],\ [1091, 1091, 3*w^3 + w^2 - 12*w - 7],\ [1093, 1093, 6*w^3 - 8*w^2 - 26*w + 29],\ [1093, 1093, 6*w^3 - 6*w^2 - 26*w + 25],\ [1093, 1093, -w^3 + 3*w^2 + 6*w - 15],\ [1093, 1093, 2*w^3 - 4*w^2 - 6*w + 13],\ [1117, 1117, 2*w^3 + w^2 - 12*w - 7],\ [1129, 1129, -w^3 + 3*w^2 + 7*w - 13],\ [1129, 1129, 2*w^2 - 3*w + 3],\ [1163, 1163, 2*w^3 + 3*w^2 - 10*w - 13],\ [1163, 1163, -2*w^3 + 2*w^2 + 6*w - 9],\ [1171, 1171, 3*w^2 - 2*w - 7],\ [1171, 1171, -3*w^3 + 11*w + 1],\ [1181, 1181, -5*w^3 + 6*w^2 + 23*w - 29],\ [1187, 1187, 4*w^3 - 2*w^2 - 20*w + 5],\ [1187, 1187, 2*w^3 - 3*w^2 - 10*w + 17],\ [1201, 1201, 5*w^3 - 3*w^2 - 22*w + 9],\ [1213, 1213, 2*w^3 + 2*w^2 - 13*w - 7],\ [1213, 1213, 3*w^3 - 11*w + 1],\ [1217, 1217, -2*w^3 + 4*w^2 + 11*w - 11],\ [1223, 1223, 2*w^3 - w^2 - 12*w + 7],\ [1223, 1223, w^3 + 2*w^2 - 5*w - 13],\ [1229, 1229, 2*w^3 - 6*w - 5],\ [1229, 1229, 3*w^3 + 2*w^2 - 11*w - 7],\ [1237, 1237, -w^3 + w^2 + w - 5],\ [1237, 1237, -2*w^3 + 10*w - 5],\ [1249, 1249, -3*w^3 + 3*w^2 + 13*w - 17],\ [1249, 1249, 2*w^3 - 12*w + 1],\ [1249, 1249, 4*w^3 - 5*w^2 - 18*w + 17],\ [1249, 1249, 4*w^3 - 3*w^2 - 18*w + 15],\ [1277, 1277, -3*w^3 + 2*w^2 + 11*w - 3],\ [1279, 1279, w^3 + w^2 - 3*w - 11],\ [1279, 1279, w^2 - 6*w - 1],\ [1279, 1279, -3*w^3 + 4*w^2 + 11*w - 9],\ [1279, 1279, 2*w^3 - 11*w + 5],\ [1283, 1283, 2*w^3 + 2*w^2 - 9*w - 1],\ [1283, 1283, -2*w^3 + 13*w - 5],\ [1291, 1291, 3*w^3 - 5*w^2 - 16*w + 19],\ [1291, 1291, -2*w^3 + 13*w + 3],\ [1301, 1301, -w^3 + 3*w^2 + 2*w - 11],\ [1301, 1301, w^3 + 3*w^2 - 7*w - 5],\ [1319, 1319, 2*w^3 - 2*w^2 - 8*w + 13],\ [1321, 1321, w^3 + 2*w^2 - 7*w - 9],\ [1321, 1321, -6*w^3 + 8*w^2 + 28*w - 37],\ [1361, 1361, -w^3 + w + 7],\ [1361, 1361, -4*w^3 + 2*w^2 + 17*w - 5],\ [1367, 1367, -w^3 + w^2 + 8*w - 1],\ [1381, 1381, 3*w^3 - w^2 - 11*w + 5],\ [1427, 1427, w^3 + 3*w^2 - 5*w - 5],\ [1427, 1427, -w^3 + 4*w^2 + 3*w - 13],\ [1427, 1427, 6*w^3 - 7*w^2 - 26*w + 33],\ [1427, 1427, -4*w^3 + w^2 + 18*w + 7],\ [1429, 1429, 3*w^3 - 3*w^2 - 17*w + 17],\ [1433, 1433, -w^3 + 5*w - 7],\ [1451, 1451, -3*w^3 + w^2 + 15*w - 7],\ [1451, 1451, -w^3 + 5*w^2 + 5*w - 19],\ [1459, 1459, -5*w + 9],\ [1471, 1471, -4*w^3 + 8*w^2 + 19*w - 29],\ [1483, 1483, w^3 + 3*w^2 - 6*w - 5],\ [1483, 1483, -3*w^3 - w^2 + 12*w - 1],\ [1487, 1487, -2*w^3 + 2*w^2 + 11*w - 15],\ [1489, 1489, 2*w^3 - 5*w^2 - 10*w + 23],\ [1493, 1493, 3*w^3 - 5*w^2 - 12*w + 25],\ [1493, 1493, 3*w^3 - 6*w^2 - 15*w + 25],\ [1499, 1499, 2*w^2 + 2*w - 13],\ [1499, 1499, w^3 + 3*w^2 - 5*w - 11],\ [1523, 1523, -w^3 + 3*w^2 + 5*w - 5],\ [1523, 1523, 4*w^3 - w^2 - 14*w + 9],\ [1523, 1523, -3*w^3 + w^2 + 14*w - 7],\ [1523, 1523, -2*w^3 + 3*w^2 + 6*w - 11],\ [1543, 1543, -w^3 + 3*w^2 + w - 9],\ [1543, 1543, -4*w^3 + 7*w^2 + 20*w - 29],\ [1559, 1559, 2*w^2 - 13],\ [1559, 1559, -4*w^2 - w + 17],\ [1571, 1571, 5*w - 3],\ [1579, 1579, 2*w^2 + 2*w - 11],\ [1579, 1579, w^3 + w^2 - 7*w - 11],\ [1583, 1583, 2*w^3 - 3*w^2 - 10*w + 7],\ [1597, 1597, -3*w^3 + w^2 + 7*w + 1],\ [1601, 1601, -5*w^3 + 3*w^2 + 23*w - 13],\ [1601, 1601, 5*w^3 - w^2 - 20*w + 9],\ [1607, 1607, 2*w^3 - w^2 - 10*w - 5],\ [1609, 1609, 3*w^3 - 8*w^2 - 13*w + 37],\ [1609, 1609, 3*w^3 - 2*w^2 - 11*w + 7],\ [1613, 1613, 2*w^3 - 4*w^2 - 12*w + 13],\ [1621, 1621, 5*w - 1],\ [1621, 1621, -2*w^3 + 5*w^2 + 8*w - 17],\ [1627, 1627, 3*w^3 + w^2 - 14*w - 1],\ [1627, 1627, -2*w^3 + 2*w^2 + 9*w + 1],\ [1637, 1637, 7*w^3 - 12*w^2 - 31*w + 49],\ [1657, 1657, -2*w^3 + 2*w^2 + 9*w - 1],\ [1657, 1657, -5*w^3 + w^2 + 21*w - 7],\ [1663, 1663, 9*w^3 - 11*w^2 - 39*w + 45],\ [1667, 1667, -4*w^3 + 3*w^2 + 16*w - 7],\ [1669, 1669, -w^3 - w^2 - w - 3],\ [1693, 1693, -3*w^3 + w^2 + 11*w - 1],\ [1693, 1693, w^3 + 2*w^2 - 11*w - 5],\ [1709, 1709, 3*w^3 + 3*w^2 - 16*w - 5],\ [1721, 1721, w^3 - 4*w^2 - 3*w + 11],\ [1747, 1747, 2*w^3 - 2*w^2 - 11*w + 1],\ [1747, 1747, w^3 + 3*w^2 - 4*w - 7],\ [1753, 1753, -6*w^3 + 6*w^2 + 28*w - 21],\ [1787, 1787, w^3 + 3*w^2 - 7*w - 13],\ [1787, 1787, -w^3 + w^2 + 8*w - 5],\ [1789, 1789, 2*w^3 + 3*w^2 - 12*w - 7],\ [1789, 1789, 4*w^2 - 15],\ [1801, 1801, w^3 + 3*w^2 - 7*w - 7],\ [1811, 1811, -3*w^3 + 2*w^2 + 11*w - 5],\ [1823, 1823, -w^3 + 3*w^2 + 6*w - 5],\ [1831, 1831, 5*w^3 - 4*w^2 - 21*w + 17],\ [1867, 1867, 3*w^3 - w^2 - 10*w + 5],\ [1871, 1871, 2*w^3 + 2*w^2 - 6*w - 7],\ [1873, 1873, -3*w^3 + 3*w^2 + 10*w - 7],\ [1879, 1879, 2*w^3 - 4*w^2 - 7*w + 17],\ [1889, 1889, 3*w^3 - 17*w - 3],\ [1907, 1907, -4*w^3 - 2*w^2 + 19*w + 5],\ [1907, 1907, 6*w^3 - 8*w^2 - 29*w + 33],\ [1913, 1913, -w^3 + w^2 + 8*w - 3],\ [1913, 1913, w^3 + 2*w^2 - 9*w + 3],\ [1933, 1933, w^2 + 4*w - 9],\ [1933, 1933, 6*w^3 - 6*w^2 - 26*w + 23],\ [1951, 1951, w^3 + 2*w^2 - 3*w - 11],\ [1951, 1951, -2*w^3 + 2*w^2 + 10*w - 1],\ [1973, 1973, -5*w^3 + 7*w^2 + 23*w - 25],\ [1979, 1979, -3*w^3 + 5*w^2 + 11*w - 19],\ [1987, 1987, 2*w^3 - 2*w^2 - 6*w + 11],\ [1993, 1993, -w^3 + 3*w - 7],\ [1993, 1993, w^3 + w^2 - 2*w - 9],\ [1997, 1997, 5*w^3 - w^2 - 19*w - 5],\ [1999, 1999, -3*w^3 + 3*w^2 + 15*w - 19],\ [2011, 2011, 5*w^3 - 6*w^2 - 23*w + 21],\ [2039, 2039, -2*w^3 + 4*w^2 + 8*w - 9],\ [2039, 2039, -3*w^3 + 4*w^2 + 11*w - 17],\ [2053, 2053, -2*w^3 + 3*w^2 + 8*w - 5],\ [2069, 2069, 5*w^3 - 6*w^2 - 21*w + 19],\ [2069, 2069, w^3 - 2*w^2 - 5*w - 3],\ [2069, 2069, 5*w^3 - 10*w^2 - 23*w + 43],\ [2069, 2069, 3*w^3 - 2*w^2 - 13*w + 1],\ [2081, 2081, 7*w^3 - 10*w^2 - 31*w + 37],\ [2081, 2081, -3*w^3 + 2*w^2 + 11*w - 15],\ [2099, 2099, -4*w^3 + 5*w^2 + 14*w - 13],\ [2111, 2111, w^3 + 3*w^2 - 6*w - 9],\ [2129, 2129, 4*w^3 - 4*w^2 - 20*w + 15],\ [2129, 2129, 4*w^2 - 3*w - 15],\ [2141, 2141, -w^3 + w^2 + w - 7],\ [2153, 2153, 7*w^3 - 11*w^2 - 30*w + 45],\ [2153, 2153, -4*w^3 + 8*w^2 + 17*w - 37],\ [2153, 2153, 4*w^3 + w^2 - 14*w - 3],\ [2153, 2153, -3*w^3 + 4*w^2 + 13*w - 11],\ [2161, 2161, 3*w^3 - 7*w^2 - 11*w + 27],\ [2179, 2179, w^3 + 3*w^2 - 5*w - 9],\ [2179, 2179, -2*w^3 + 14*w - 7],\ [2197, 13, w^3 + 3*w^2 - 6*w - 7],\ [2203, 2203, 6*w^3 - 9*w^2 - 28*w + 33],\ [2203, 2203, 3*w^3 + 3*w^2 - 13*w - 7],\ [2207, 2207, -4*w^3 + 16*w - 5],\ [2221, 2221, 5*w^3 - 3*w^2 - 21*w + 13],\ [2221, 2221, -3*w^3 + 3*w^2 + 16*w - 13],\ [2237, 2237, w^3 - w^2 - 3*w - 5],\ [2239, 2239, 3*w^3 - w^2 - 16*w + 9],\ [2239, 2239, -4*w^3 + 8*w^2 + 18*w - 31],\ [2243, 2243, -2*w^3 + 2*w^2 + 12*w - 5],\ [2251, 2251, 3*w^3 + 3*w^2 - 14*w - 7],\ [2251, 2251, 4*w^3 + 2*w^2 - 15*w - 1],\ [2267, 2267, w^3 - 5*w^2 + 15],\ [2269, 2269, 3*w^3 - 3*w^2 - 11*w + 3],\ [2273, 2273, -w^3 + 5*w^2 + 2*w - 17],\ [2281, 2281, -3*w^3 - w^2 + 11*w + 7],\ [2287, 2287, -3*w^3 + 4*w^2 + 17*w - 19],\ [2287, 2287, 4*w^2 + w - 11],\ [2287, 2287, w^3 - 5*w - 7],\ [2287, 2287, -5*w^3 + 21*w - 3],\ [2293, 2293, w^3 + w^2 - 8*w - 7],\ [2293, 2293, -2*w^3 - 2*w^2 + 7*w + 9],\ [2293, 2293, -4*w^3 + 6*w^2 + 16*w - 25],\ [2293, 2293, -5*w^3 + w^2 + 20*w - 7],\ [2309, 2309, 2*w^3 + 2*w^2 - 12*w - 1],\ [2311, 2311, -2*w^3 - w^2 + 10*w - 3],\ [2333, 2333, -5*w^3 + 7*w^2 + 25*w - 29],\ [2341, 2341, 6*w^3 - 7*w^2 - 24*w + 27],\ [2341, 2341, -w^3 + 5*w^2 + 6*w - 11],\ [2347, 2347, -5*w^3 + 7*w^2 + 23*w - 33],\ [2347, 2347, 4*w^3 - 2*w^2 - 16*w + 3],\ [2347, 2347, -6*w^3 + 8*w^2 + 26*w - 37],\ [2347, 2347, -w^3 - w^2 + 4*w - 5],\ [2351, 2351, -3*w^2 - 2*w + 13],\ [2357, 2357, 6*w^3 - 4*w^2 - 29*w + 15],\ [2357, 2357, 3*w^3 - 4*w^2 - 13*w + 21],\ [2371, 2371, 3*w^3 - 13*w + 9],\ [2371, 2371, -7*w^3 + 29*w + 9],\ [2377, 2377, w^3 - 3*w^2 - 7*w + 15],\ [2377, 2377, 4*w^3 - 6*w^2 - 21*w + 25],\ [2399, 2399, -3*w^3 + w^2 + 10*w - 1],\ [2401, 7, -7],\ [2411, 2411, 4*w^3 + w^2 - 16*w + 1],\ [2417, 2417, 3*w^3 + 2*w^2 - 15*w - 3],\ [2423, 2423, 5*w^3 + w^2 - 20*w - 3],\ [2437, 2437, -2*w^3 + 3*w^2 + 12*w - 11],\ [2437, 2437, 7*w^3 - 13*w^2 - 32*w + 55],\ [2437, 2437, -3*w^3 + w^2 + 14*w - 9],\ [2437, 2437, 3*w^3 - 3*w^2 - 9*w + 5],\ [2459, 2459, 5*w^2 - 2*w - 23],\ [2459, 2459, 5*w^3 - 4*w^2 - 23*w + 19],\ [2467, 2467, 4*w^3 + 4*w^2 - 15*w - 11],\ [2473, 2473, -w - 7],\ [2503, 2503, -4*w^3 + w^2 + 16*w - 11],\ [2521, 2521, 3*w^3 - 7*w^2 - 16*w + 27],\ [2531, 2531, -2*w^2 + w - 3],\ [2539, 2539, w^3 - 3*w^2 - 2*w + 13],\ [2543, 2543, -w^3 + 3*w^2 + 5*w - 3],\ [2549, 2549, 3*w^3 - 9*w - 5],\ [2549, 2549, -3*w^3 + w^2 + 10*w - 3],\ [2551, 2551, 2*w^3 - 4*w^2 - 9*w + 21],\ [2557, 2557, 3*w^3 - 4*w^2 - 15*w + 11],\ [2579, 2579, 6*w^3 - 8*w^2 - 27*w + 29],\ [2591, 2591, 2*w^3 - 6*w^2 - 8*w + 23],\ [2609, 2609, 6*w^3 - 5*w^2 - 26*w + 17],\ [2617, 2617, 7*w^3 - 7*w^2 - 32*w + 31],\ [2633, 2633, -5*w^3 + 3*w^2 + 22*w - 15],\ [2659, 2659, -6*w^3 - w^2 + 26*w + 13],\ [2659, 2659, w^3 + 3*w^2 - 7*w - 17],\ [2663, 2663, 2*w^3 - 2*w^2 - 12*w - 5],\ [2683, 2683, 4*w^3 - 3*w^2 - 22*w + 21],\ [2683, 2683, -w^3 + 3*w^2 + 5*w - 1],\ [2687, 2687, -w^3 - w^2 + 3*w - 5],\ [2687, 2687, -2*w^3 - w^2 + 12*w - 3],\ [2687, 2687, -3*w^3 + 5*w^2 + 15*w - 15],\ [2687, 2687, 3*w^3 + 3*w^2 - 16*w - 9],\ [2693, 2693, 2*w^3 + 3*w^2 - 10*w - 7],\ [2711, 2711, 6*w^3 - 8*w^2 - 28*w + 29],\ [2719, 2719, w^3 - 5*w^2 + w + 13],\ [2729, 2729, 4*w^3 - 3*w^2 - 16*w + 9],\ [2729, 2729, 2*w^2 + 5*w - 5],\ [2741, 2741, 3*w^3 + w^2 - 12*w + 3],\ [2741, 2741, w^3 - 9*w + 3],\ [2749, 2749, w^3 - w^2 - 4*w - 5],\ [2749, 2749, -2*w^3 + 13*w - 3],\ [2789, 2789, -3*w^3 + 4*w^2 + 11*w - 19],\ [2789, 2789, 3*w^3 - w^2 - 17*w + 11],\ [2791, 2791, 2*w^3 + 2*w^2 - 9*w - 15],\ [2791, 2791, w^3 - 9*w + 1],\ [2791, 2791, 7*w^3 - 11*w^2 - 33*w + 47],\ [2791, 2791, 3*w^3 - 17*w - 1],\ [2801, 2801, 2*w^2 - 4*w - 7],\ [2801, 2801, 3*w^3 - w^2 - 7*w + 1],\ [2803, 2803, -w^3 + 2*w^2 - w - 5],\ [2809, 53, -2*w^3 + 4*w^2 + 7*w - 7],\ [2819, 2819, 4*w^2 - 2*w - 13],\ [2833, 2833, 2*w^3 + w^2 - 6*w - 7],\ [2843, 2843, 6*w^3 - 8*w^2 - 25*w + 35],\ [2843, 2843, 4*w^3 - 2*w^2 - 19*w + 11],\ [2861, 2861, 8*w^3 - 11*w^2 - 36*w + 49],\ [2879, 2879, w^3 - w^2 - 5*w - 5],\ [2879, 2879, w^3 + w^2 - w - 13],\ [2887, 2887, 7*w^3 + 2*w^2 - 35*w - 9],\ [2887, 2887, -4*w^3 + 5*w^2 + 20*w - 15],\ [2939, 2939, 4*w^3 - 2*w^2 - 18*w + 1],\ [2939, 2939, -w^3 + w^2 + 9*w - 7],\ [2953, 2953, -5*w^3 + 9*w^2 + 22*w - 33],\ [2963, 2963, w^3 - 5*w^2 - 5*w + 17],\ [3001, 3001, 4*w^2 + w - 19],\ [3037, 3037, w^3 + w^2 - 7],\ [3037, 3037, w^3 + 4*w^2 - 9*w - 9],\ [3041, 3041, -5*w^3 + 7*w^2 + 22*w - 33],\ [3041, 3041, -4*w^3 - w^2 + 16*w + 9],\ [3041, 3041, -2*w^3 - 4*w^2 + 14*w + 13],\ [3041, 3041, -2*w^3 + 3*w^2 + 6*w - 13],\ [3049, 3049, -w^3 + 3*w^2 + 7*w - 3],\ [3067, 3067, w^3 + w^2 - 4*w - 11],\ [3067, 3067, -3*w^3 + 6*w^2 + 13*w - 29],\ [3079, 3079, 2*w^3 + 5*w^2 - 6*w - 17],\ [3079, 3079, 2*w^3 + 3*w^2 - 10*w - 9],\ [3079, 3079, w^3 + 3*w^2 - 7*w - 15],\ [3079, 3079, -5*w^3 + w^2 + 21*w + 9],\ [3089, 3089, -4*w^3 + w^2 + 16*w - 3],\ [3089, 3089, 5*w^3 - 2*w^2 - 25*w + 5],\ [3109, 3109, -w^2 - 5],\ [3109, 3109, w^2 - 2*w - 11],\ [3119, 3119, 5*w^3 - 9*w^2 - 24*w + 31],\ [3119, 3119, 2*w^3 - 4*w - 5],\ [3137, 3137, -w^3 + 3*w^2 + 2*w - 15],\ [3167, 3167, -2*w^3 - 2*w^2 + 15*w + 7],\ [3167, 3167, 4*w^3 - 4*w^2 - 21*w + 19],\ [3169, 3169, -5*w^2 - 4*w + 9],\ [3181, 3181, -3*w^3 + 2*w^2 + 9*w - 3],\ [3187, 3187, -4*w^3 + 2*w^2 + 16*w - 7],\ [3187, 3187, 2*w^3 + 2*w^2 - 10*w + 1],\ [3191, 3191, -5*w^3 + 4*w^2 + 23*w - 23],\ [3191, 3191, 5*w^3 + w^2 - 18*w - 5],\ [3203, 3203, -2*w^3 + 6*w^2 + 10*w - 27],\ [3229, 3229, 4*w^3 + w^2 - 18*w - 1],\ [3229, 3229, 7*w^3 - 5*w^2 - 31*w + 17],\ [3257, 3257, 5*w^3 - 11*w^2 - 23*w + 47],\ [3271, 3271, 6*w^3 - 11*w^2 - 30*w + 43],\ [3271, 3271, 6*w - 1],\ [3271, 3271, -5*w^3 - w^2 + 21*w + 11],\ [3271, 3271, 2*w^3 - 13*w + 1],\ [3299, 3299, -w^3 + 3*w^2 + 8*w - 15],\ [3299, 3299, -2*w^2 + 6*w + 5],\ [3301, 3301, -8*w^3 - w^2 + 34*w + 13],\ [3307, 3307, -w^3 + 2*w^2 + 9*w - 3],\ [3307, 3307, -8*w^3 + 6*w^2 + 35*w - 25],\ [3313, 3313, 6*w^3 - 6*w^2 - 25*w + 31],\ [3323, 3323, -6*w^3 + w^2 + 26*w - 3],\ [3323, 3323, -2*w^2 - 3*w + 15],\ [3347, 3347, 2*w^3 - 6*w^2 - 5*w + 17],\ [3373, 3373, 4*w^3 - 4*w^2 - 18*w + 11],\ [3373, 3373, 4*w^3 - 6*w^2 - 20*w + 19],\ [3389, 3389, 4*w^2 - 11],\ [3389, 3389, 3*w^3 - 7*w^2 - 15*w + 21],\ [3391, 3391, 4*w^3 - 15*w + 1],\ [3391, 3391, 4*w^3 - 7*w^2 - 16*w + 29],\ [3433, 3433, -5*w^2 + 2*w + 19],\ [3433, 3433, -w^3 + 4*w^2 + 7*w - 17],\ [3449, 3449, 2*w^2 - 3*w - 11],\ [3449, 3449, 3*w^3 - w^2 - 15*w - 7],\ [3463, 3463, 4*w^2 - w - 13],\ [3463, 3463, -5*w^3 - 3*w^2 + 23*w + 7],\ [3467, 3467, 3*w^3 + 2*w^2 - 13*w - 1],\ [3469, 3469, 4*w^2 - 3*w - 9],\ [3491, 3491, w^3 - 5*w^2 - 7*w + 11],\ [3499, 3499, 5*w^3 - 2*w^2 - 23*w + 1],\ [3499, 3499, -8*w^3 + 9*w^2 + 34*w - 37],\ [3511, 3511, w^3 - 5*w^2 - 8*w + 11],\ [3511, 3511, -2*w^3 + 6*w^2 + 4*w - 13],\ [3517, 3517, w^3 + 4*w^2 - 3*w - 9],\ [3527, 3527, w^2 - 4*w - 7],\ [3529, 3529, -8*w^3 + 10*w^2 + 38*w - 39],\ [3529, 3529, 2*w^3 - 5*w - 7],\ [3539, 3539, 6*w^3 - 4*w^2 - 28*w + 11],\ [3539, 3539, 4*w^2 - w - 9],\ [3541, 3541, 6*w^3 - 23*w - 9],\ [3547, 3547, -3*w^3 - 2*w^2 + 11*w + 9],\ [3557, 3557, -3*w^3 + 2*w^2 + 15*w + 3],\ [3571, 3571, 3*w^3 - w^2 - 15*w + 11],\ [3581, 3581, 6*w^3 - 2*w^2 - 28*w + 1],\ [3593, 3593, 5*w^3 - w^2 - 24*w + 5],\ [3593, 3593, -2*w^3 + 3*w^2 + 4*w - 9],\ [3607, 3607, 3*w^3 - 4*w^2 - 17*w + 11],\ [3607, 3607, -w^3 - 5*w^2 + 6*w + 21],\ [3617, 3617, 2*w^3 + 4*w^2 - 7*w - 7],\ [3617, 3617, 2*w^2 + 4*w - 11],\ [3623, 3623, -5*w^3 + 4*w^2 + 25*w - 17],\ [3631, 3631, 8*w^3 - 14*w^2 - 36*w + 57],\ [3631, 3631, -2*w^3 + 4*w^2 + 13*w - 7],\ [3637, 3637, 6*w^3 - 3*w^2 - 26*w + 7],\ [3637, 3637, w^3 + 2*w^2 - w - 9],\ [3659, 3659, 4*w^3 - 4*w^2 - 14*w + 13],\ [3677, 3677, -w^3 + w^2 + 3*w - 11],\ [3691, 3691, -4*w^3 + 5*w^2 + 14*w - 19],\ [3697, 3697, -4*w^3 + 18*w - 3],\ [3719, 3719, w^3 + 5*w^2 - 2*w - 9],\ [3733, 3733, 3*w^2 + 2*w - 15],\ [3733, 3733, -5*w^3 + 5*w^2 + 22*w - 15],\ [3767, 3767, w^3 + w^2 - w - 9],\ [3767, 3767, -3*w^3 + 3*w^2 + 13*w - 5],\ [3793, 3793, 2*w^2 + 3*w - 13],\ [3793, 3793, 5*w^3 - 3*w^2 - 25*w + 9],\ [3797, 3797, -9*w^3 - w^2 + 39*w + 15],\ [3797, 3797, 4*w^3 - 6*w^2 - 21*w + 21],\ [3803, 3803, -6*w^3 + 4*w^2 + 26*w - 15],\ [3803, 3803, 2*w - 9],\ [3823, 3823, -5*w^3 + 10*w^2 + 23*w - 39],\ [3833, 3833, w^3 + w^2 - 5*w - 11],\ [3847, 3847, 3*w^3 - 5*w^2 - 11*w + 21],\ [3851, 3851, 4*w^2 - 2*w - 9],\ [3851, 3851, -2*w^3 + 6*w^2 + 9*w - 21],\ [3853, 3853, -w^3 + w^2 + 7*w - 13],\ [3863, 3863, 4*w^3 - 6*w^2 - 18*w + 19],\ [3881, 3881, -4*w^3 + 14*w + 7],\ [3889, 3889, -3*w^3 + w^2 + 12*w - 13],\ [3889, 3889, -4*w^3 + 2*w^2 + 21*w - 9],\ [3889, 3889, 5*w^3 - 6*w^2 - 25*w + 25],\ [3889, 3889, 3*w^3 - 7*w^2 - 12*w + 21],\ [3907, 3907, -3*w^3 + 9*w^2 + 14*w - 39],\ [3917, 3917, 3*w^3 + 3*w^2 - 13*w - 17],\ [3917, 3917, 9*w^3 - 11*w^2 - 40*w + 41],\ [3917, 3917, -w^3 + w^2 + 4*w - 11],\ [3917, 3917, 3*w^3 - 3*w^2 - 11*w - 1],\ [3923, 3923, -2*w^3 + 4*w^2 + 12*w - 21],\ [3923, 3923, w^3 + 3*w^2 - 11*w - 7],\ [3931, 3931, -3*w^3 + 19*w - 7],\ [3947, 3947, -4*w^3 + 4*w^2 + 22*w - 9],\ [3947, 3947, -5*w^3 - w^2 + 17*w + 7],\ [3947, 3947, -w^3 - 4*w^2 + 3*w + 17],\ [3947, 3947, -2*w^3 - 4*w^2 + 12*w + 3]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [0, -1, -1, 1, -3, -4, -6, 2, 7, -6, -3, 13, 11, 2, -5, 18, -14, -11, -5, 13, 6, -6, 4, -5, -6, 1, 10, -14, 7, 6, -7, 11, -16, -21, 2, -12, -10, 12, -7, -21, 2, -15, -3, -18, -2, 18, -10, 14, 2, -18, 3, -4, 5, 14, -26, -4, -18, -6, -15, 0, 26, -10, -10, -18, 0, 6, -7, -1, -14, 21, -25, 18, 0, -17, 6, -4, -39, 33, 17, -2, -35, -34, 30, -38, 29, 0, -1, 33, -18, -34, -22, 24, 28, 6, -40, 26, 3, -6, 22, 13, 2, -18, 30, 14, 36, -2, 21, -39, 24, -10, 22, -36, 17, 18, -1, 18, -20, -38, 28, -8, 40, -39, -45, -30, -30, 6, 51, -23, -18, 6, 39, -3, -12, -6, -43, -30, 16, 56, -18, 7, 30, 38, 36, -2, 46, 6, -42, -38, -2, 14, -36, -32, 6, 32, 42, 30, 28, 0, 22, -36, -11, -30, 16, -3, -16, -12, -10, 58, 9, 13, 6, -13, -14, -41, 60, 24, 32, 40, 21, -18, 28, -1, -19, 27, -45, 18, -50, 33, -50, 34, 49, 1, -65, -13, -11, -27, -42, -18, -16, 26, -38, 60, -60, -10, -62, -22, -36, -27, 46, 38, -59, -62, 34, -48, -32, 42, -30, 19, -6, 28, -20, -70, -4, 8, -68, -38, -67, -27, 66, 36, 0, -24, -72, 44, 22, -28, 40, -54, 30, -18, 10, 38, -4, -55, -14, -15, 6, 13, -49, -3, -22, 45, -44, -48, -57, -25, -59, 72, 22, -1, 11, -37, -41, 19, -62, -54, -53, -76, 60, -51, -9, 5, -14, 74, -22, -38, -80, -25, 10, -35, 36, -78, -45, -7, 61, 33, 52, 52, 57, -58, 82, 6, -21, 6, 64, -52, -4, 28, 23, 26, -10, -75, -33, -77, 45, -72, -32, -74, -51, 54, -58, 75, 5, 19, 30, 74, -4, -23, -62, 6, 18, 17, 46, -33, 44, -16, 88, -28, 38, 78, 79, -18, 65, -16, 72, 18, -76, -10, -33, -11, 74, -33, 36, -13, 25, -25, -48, 28, -16, 18, 48, -54, 3, -6, 4, -26, -58, 70, 3, 60, -43, 12, -37, 50, -66, 13, -52, -14, 42, 78, -86, -47, -36, 50, 16, -53, -3, -70, 27, -28, -42, 33, -7, -85, -6, 38, 66, -56, -60, 24, 54, -30, 28, -13, 82, 20, -10, 55, -81, 10, -30, 62, 82, 67, 84, 2, 22, -78, -18, 74, -4, -10, -50, -31, 38, -94, 15, 50, -16, -22, -46, -96, -84, -69, -60, 46, 7, 11, 10, 47, 93, -98, -11, 50, -42, 48, 40, 44, 44, 54, 58, 75, 22, 18, 108, 66, 54, -12, -98, 3, -70, 88, -6, 44, 30, -25, 79, -17, -74, -8, 60, 86, 60, 22, 19, 44, 86, -19, -6, -48, -4, -82, 57, -30, -27, -66, 90, 17, -7, -27, -77, -64, -32, 66, -14, -68, 60, 46, 70, 28, 29, -86, -7, -35, 50, 100, -38, -60, 33, 24, 61, 66, 61, -116, -10, 27, 17, 20, -20, -52, 63, -46, -40, -78, -40, 34, -54, 39, 111, 30, 36, 19, -79, -17, 69, 84, 56, -64, 6, 120, 62, 98, -31, 58, 75, 11, 87, -2, -86, 0, -30, 13, 82, -37, 4, -104, 16, -6, 32, -74, 42] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([2, 2, w])] = -1 AL_eigenvalues[ZF.ideal([4, 2, -w^3 + 4*w + 1])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]