/* 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, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([784, 28, 28]) primes_array = [ [2, 2, -w],\ [7, 7, -2*w + 1],\ [7, 7, -2*w - 1],\ [9, 3, 3],\ [17, 17, 3*w + 1],\ [17, 17, 3*w - 1],\ [23, 23, w + 5],\ [23, 23, -w + 5],\ [25, 5, 5],\ [31, 31, 4*w + 1],\ [31, 31, -4*w + 1],\ [41, 41, 2*w - 7],\ [41, 41, -2*w - 7],\ [47, 47, -w - 7],\ [47, 47, w - 7],\ [71, 71, -6*w - 1],\ [71, 71, 6*w - 1],\ [73, 73, -7*w - 5],\ [73, 73, 7*w - 5],\ [79, 79, -w - 9],\ [79, 79, w - 9],\ [89, 89, -4*w - 11],\ [89, 89, 4*w - 11],\ [97, 97, -7*w - 1],\ [97, 97, 7*w - 1],\ [103, 103, -3*w - 11],\ [103, 103, 3*w - 11],\ [113, 113, 2*w - 11],\ [113, 113, -2*w - 11],\ [121, 11, -11],\ [127, 127, -8*w - 1],\ [127, 127, 8*w - 1],\ [137, 137, 4*w - 13],\ [137, 137, -4*w - 13],\ [151, 151, 3*w - 13],\ [151, 151, -3*w - 13],\ [167, 167, -w - 13],\ [167, 167, w - 13],\ [169, 13, -13],\ [191, 191, 10*w - 3],\ [191, 191, -10*w - 3],\ [193, 193, -4*w - 15],\ [193, 193, 4*w - 15],\ [199, 199, -10*w - 1],\ [199, 199, 10*w - 1],\ [223, 223, -w - 15],\ [223, 223, w - 15],\ [233, 233, -11*w - 3],\ [233, 233, 11*w - 3],\ [239, 239, -5*w - 17],\ [239, 239, 5*w - 17],\ [241, 241, -11*w - 1],\ [241, 241, 11*w - 1],\ [257, 257, 4*w - 17],\ [257, 257, -4*w - 17],\ [263, 263, 7*w - 19],\ [263, 263, -7*w - 19],\ [271, 271, -3*w - 17],\ [271, 271, 3*w - 17],\ [281, 281, 2*w - 17],\ [281, 281, -2*w - 17],\ [311, 311, -5*w - 19],\ [311, 311, 5*w - 19],\ [313, 313, -8*w - 21],\ [313, 313, 8*w - 21],\ [337, 337, -13*w - 1],\ [337, 337, 13*w - 1],\ [353, 353, 2*w - 19],\ [353, 353, -2*w - 19],\ [359, 359, -w - 19],\ [359, 359, w - 19],\ [361, 19, -19],\ [367, 367, 9*w - 23],\ [367, 367, -9*w - 23],\ [383, 383, -14*w - 3],\ [383, 383, 14*w - 3],\ [401, 401, -8*w - 23],\ [401, 401, 8*w - 23],\ [409, 409, -17*w - 13],\ [409, 409, 17*w - 13],\ [431, 431, -7*w - 23],\ [431, 431, 7*w - 23],\ [433, 433, 2*w - 21],\ [433, 433, -2*w - 21],\ [439, 439, -w - 21],\ [439, 439, w - 21],\ [449, 449, -15*w - 1],\ [449, 449, 15*w - 1],\ [457, 457, -6*w - 23],\ [457, 457, 6*w - 23],\ [463, 463, 9*w - 25],\ [463, 463, -9*w - 25],\ [479, 479, -18*w - 13],\ [479, 479, 18*w - 13],\ [487, 487, 16*w - 5],\ [487, 487, -16*w - 5],\ [503, 503, 16*w - 3],\ [503, 503, -16*w - 3],\ [521, 521, 2*w - 23],\ [521, 521, -2*w - 23],\ [569, 569, -17*w - 3],\ [569, 569, 17*w - 3],\ [577, 577, -17*w - 1],\ [577, 577, 17*w - 1],\ [593, 593, 4*w - 25],\ [593, 593, -4*w - 25],\ [599, 599, -11*w - 29],\ [599, 599, 11*w - 29],\ [601, 601, 8*w - 27],\ [601, 601, -8*w - 27],\ [607, 607, 3*w - 25],\ [607, 607, -3*w - 25],\ [617, 617, 2*w - 25],\ [617, 617, -2*w - 25],\ [631, 631, -7*w - 27],\ [631, 631, 7*w - 27],\ [641, 641, -10*w - 29],\ [641, 641, 10*w - 29],\ [647, 647, -18*w - 1],\ [647, 647, 18*w - 1],\ [673, 673, -12*w - 31],\ [673, 673, 12*w - 31],\ [719, 719, 11*w - 31],\ [719, 719, -11*w - 31],\ [727, 727, -w - 27],\ [727, 727, w - 27],\ [743, 743, 7*w - 29],\ [743, 743, -7*w - 29],\ [751, 751, 13*w - 33],\ [751, 751, -13*w - 33],\ [761, 761, 10*w - 31],\ [761, 761, -10*w - 31],\ [769, 769, 23*w - 17],\ [769, 769, -23*w - 17],\ [809, 809, 4*w - 29],\ [809, 809, -4*w - 29],\ [823, 823, -3*w - 29],\ [823, 823, 3*w - 29],\ [839, 839, -w - 29],\ [839, 839, w - 29],\ [841, 29, -29],\ [857, 857, 21*w - 5],\ [857, 857, -21*w - 5],\ [863, 863, 24*w - 17],\ [863, 863, -24*w - 17],\ [881, 881, -21*w - 1],\ [881, 881, 21*w - 1],\ [887, 887, 13*w - 35],\ [887, 887, -13*w - 35],\ [911, 911, 26*w + 21],\ [911, 911, -26*w + 21],\ [919, 919, 22*w - 7],\ [919, 919, -22*w - 7],\ [929, 929, -4*w - 31],\ [929, 929, 4*w - 31],\ [937, 937, -12*w - 35],\ [937, 937, 12*w - 35],\ [953, 953, 2*w - 31],\ [953, 953, -2*w - 31],\ [967, 967, -22*w - 1],\ [967, 967, 22*w - 1],\ [977, 977, -14*w - 37],\ [977, 977, 14*w - 37],\ [983, 983, -11*w - 35],\ [983, 983, 11*w - 35],\ [991, 991, -26*w - 19],\ [991, 991, 26*w - 19],\ [1009, 1009, -23*w - 7],\ [1009, 1009, 23*w - 7],\ [1031, 1031, 13*w - 37],\ [1031, 1031, -13*w - 37],\ [1033, 1033, 23*w - 5],\ [1033, 1033, -23*w - 5],\ [1039, 1039, 5*w - 33],\ [1039, 1039, -5*w - 33],\ [1049, 1049, -23*w - 3],\ [1049, 1049, 23*w - 3],\ [1063, 1063, -9*w - 35],\ [1063, 1063, 9*w - 35],\ [1087, 1087, -w - 33],\ [1087, 1087, w - 33],\ [1097, 1097, -27*w - 19],\ [1097, 1097, 27*w - 19],\ [1103, 1103, -24*w - 7],\ [1103, 1103, 24*w - 7],\ [1129, 1129, -14*w - 39],\ [1129, 1129, 14*w - 39],\ [1151, 1151, -24*w - 1],\ [1151, 1151, 24*w - 1],\ [1153, 1153, -6*w - 35],\ [1153, 1153, 6*w - 35],\ [1193, 1193, -4*w - 35],\ [1193, 1193, 4*w - 35],\ [1201, 1201, 25*w - 7],\ [1201, 1201, -25*w - 7],\ [1217, 1217, 2*w - 35],\ [1217, 1217, -2*w - 35],\ [1223, 1223, -w - 35],\ [1223, 1223, w - 35],\ [1231, 1231, -15*w - 41],\ [1231, 1231, 15*w - 41],\ [1249, 1249, -25*w - 1],\ [1249, 1249, 25*w - 1],\ [1279, 1279, 11*w - 39],\ [1279, 1279, -11*w - 39],\ [1289, 1289, -14*w - 41],\ [1289, 1289, 14*w - 41],\ [1297, 1297, 31*w + 25],\ [1297, 1297, -31*w + 25],\ [1303, 1303, 26*w - 7],\ [1303, 1303, -26*w - 7],\ [1319, 1319, -5*w - 37],\ [1319, 1319, 5*w - 37],\ [1321, 1321, -10*w - 39],\ [1321, 1321, 10*w - 39],\ [1327, 1327, 26*w - 5],\ [1327, 1327, -26*w - 5],\ [1361, 1361, 2*w - 37],\ [1361, 1361, -2*w - 37],\ [1367, 1367, -w - 37],\ [1367, 1367, w - 37],\ [1369, 37, -37],\ [1399, 1399, 15*w - 43],\ [1399, 1399, -15*w - 43],\ [1409, 1409, -27*w - 7],\ [1409, 1409, 27*w - 7],\ [1423, 1423, -32*w - 25],\ [1423, 1423, 32*w - 25],\ [1433, 1433, -27*w - 5],\ [1433, 1433, 27*w - 5],\ [1439, 1439, -11*w - 41],\ [1439, 1439, 11*w - 41],\ [1447, 1447, -17*w - 45],\ [1447, 1447, 17*w - 45],\ [1471, 1471, -5*w - 39],\ [1471, 1471, 5*w - 39],\ [1481, 1481, 10*w - 41],\ [1481, 1481, -10*w - 41],\ [1487, 1487, 28*w - 9],\ [1487, 1487, -28*w - 9],\ [1489, 1489, -4*w - 39],\ [1489, 1489, 4*w - 39],\ [1511, 1511, -13*w - 43],\ [1511, 1511, 13*w - 43],\ [1543, 1543, 28*w - 5],\ [1543, 1543, -28*w - 5],\ [1553, 1553, -33*w - 25],\ [1553, 1553, 33*w - 25],\ [1559, 1559, 28*w - 3],\ [1559, 1559, -28*w - 3],\ [1567, 1567, -28*w - 1],\ [1567, 1567, 28*w - 1],\ [1583, 1583, -34*w + 27],\ [1583, 1583, 34*w + 27],\ [1601, 1601, -29*w - 9],\ [1601, 1601, 29*w - 9],\ [1607, 1607, -11*w - 43],\ [1607, 1607, 11*w - 43],\ [1609, 1609, -6*w - 41],\ [1609, 1609, 6*w - 41],\ [1657, 1657, -29*w - 5],\ [1657, 1657, 29*w - 5],\ [1663, 1663, -3*w - 41],\ [1663, 1663, 3*w - 41],\ [1697, 1697, -16*w - 47],\ [1697, 1697, 16*w - 47],\ [1721, 1721, -35*w - 27],\ [1721, 1721, 35*w - 27],\ [1753, 1753, 18*w - 49],\ [1753, 1753, -18*w - 49],\ [1759, 1759, -15*w - 47],\ [1759, 1759, 15*w - 47],\ [1777, 1777, 6*w - 43],\ [1777, 1777, -6*w - 43],\ [1783, 1783, 11*w - 45],\ [1783, 1783, -11*w - 45],\ [1801, 1801, -20*w - 51],\ [1801, 1801, 20*w - 51],\ [1823, 1823, 17*w - 49],\ [1823, 1823, -17*w - 49],\ [1831, 1831, 3*w - 43],\ [1831, 1831, -3*w - 43],\ [1847, 1847, -w - 43],\ [1847, 1847, w - 43],\ [1849, 43, -43],\ [1871, 1871, 13*w - 47],\ [1871, 1871, -13*w - 47],\ [1873, 1873, -31*w - 7],\ [1873, 1873, 31*w - 7],\ [1879, 1879, 19*w - 51],\ [1879, 1879, -19*w - 51],\ [1889, 1889, 16*w - 49],\ [1889, 1889, -16*w - 49],\ [1913, 1913, 31*w - 3],\ [1913, 1913, -31*w - 3],\ [1951, 1951, 15*w - 49],\ [1951, 1951, -15*w - 49],\ [1993, 1993, 4*w - 45],\ [1993, 1993, -4*w - 45],\ [1999, 1999, 32*w - 7],\ [1999, 1999, -32*w - 7],\ [2017, 2017, 2*w - 45],\ [2017, 2017, -2*w - 45],\ [2039, 2039, -32*w - 3],\ [2039, 2039, 32*w - 3],\ [2063, 2063, 13*w - 49],\ [2063, 2063, -13*w - 49],\ [2081, 2081, -39*w + 31],\ [2081, 2081, 39*w + 31],\ [2087, 2087, -19*w - 53],\ [2087, 2087, 19*w - 53],\ [2089, 2089, -16*w - 51],\ [2089, 2089, 16*w - 51],\ [2111, 2111, 7*w - 47],\ [2111, 2111, -7*w - 47],\ [2113, 2113, 12*w - 49],\ [2113, 2113, -12*w - 49],\ [2129, 2129, 33*w - 7],\ [2129, 2129, -33*w - 7],\ [2137, 2137, -6*w - 47],\ [2137, 2137, 6*w - 47],\ [2143, 2143, -21*w - 55],\ [2143, 2143, 21*w - 55],\ [2153, 2153, 33*w - 5],\ [2153, 2153, -33*w - 5],\ [2161, 2161, -18*w - 53],\ [2161, 2161, 18*w - 53],\ [2207, 2207, -w - 47],\ [2207, 2207, w - 47],\ [2239, 2239, 40*w - 31],\ [2239, 2239, -40*w - 31],\ [2273, 2273, 8*w - 49],\ [2273, 2273, -8*w - 49],\ [2281, 2281, -22*w - 57],\ [2281, 2281, 22*w - 57],\ [2287, 2287, -34*w - 5],\ [2287, 2287, 34*w - 5],\ [2297, 2297, -16*w - 53],\ [2297, 2297, 16*w - 53],\ [2311, 2311, -34*w - 1],\ [2311, 2311, 34*w - 1],\ [2351, 2351, -5*w - 49],\ [2351, 2351, 5*w - 49],\ [2377, 2377, 18*w - 55],\ [2377, 2377, -18*w - 55],\ [2383, 2383, 3*w - 49],\ [2383, 2383, -3*w - 49],\ [2393, 2393, 2*w - 49],\ [2393, 2393, -2*w - 49],\ [2399, 2399, -w - 49],\ [2399, 2399, w - 49],\ [2417, 2417, -14*w - 53],\ [2417, 2417, 14*w - 53],\ [2423, 2423, -23*w - 59],\ [2423, 2423, 23*w - 59],\ [2441, 2441, -35*w - 3],\ [2441, 2441, 35*w - 3],\ [2447, 2447, -17*w - 55],\ [2447, 2447, 17*w - 55],\ [2473, 2473, 8*w - 51],\ [2473, 2473, -8*w - 51],\ [2503, 2503, -7*w - 51],\ [2503, 2503, 7*w - 51],\ [2521, 2521, -41*w - 29],\ [2521, 2521, 41*w - 29],\ [2543, 2543, 36*w - 7],\ [2543, 2543, -36*w - 7],\ [2551, 2551, 5*w - 51],\ [2551, 2551, -5*w - 51],\ [2591, 2591, -36*w - 1],\ [2591, 2591, 36*w - 1],\ [2593, 2593, 2*w - 51],\ [2593, 2593, -2*w - 51],\ [2609, 2609, 43*w - 33],\ [2609, 2609, -43*w - 33],\ [2617, 2617, 37*w - 11],\ [2617, 2617, -37*w - 11],\ [2633, 2633, -14*w - 55],\ [2633, 2633, 14*w - 55],\ [2647, 2647, -44*w + 35],\ [2647, 2647, 44*w + 35],\ [2657, 2657, 37*w - 9],\ [2657, 2657, -37*w - 9],\ [2663, 2663, -23*w - 61],\ [2663, 2663, 23*w - 61],\ [2671, 2671, 17*w - 57],\ [2671, 2671, -17*w - 57],\ [2687, 2687, -13*w - 55],\ [2687, 2687, 13*w - 55],\ [2689, 2689, -37*w - 7],\ [2689, 2689, 37*w - 7],\ [2711, 2711, 7*w - 53],\ [2711, 2711, -7*w - 53],\ [2713, 2713, -37*w - 5],\ [2713, 2713, 37*w - 5],\ [2719, 2719, 25*w - 63],\ [2719, 2719, -25*w - 63],\ [2729, 2729, 37*w - 3],\ [2729, 2729, -37*w - 3],\ [2753, 2753, -22*w - 61],\ [2753, 2753, 22*w - 61],\ [2767, 2767, -38*w - 11],\ [2767, 2767, 38*w - 11],\ [2777, 2777, 4*w - 53],\ [2777, 2777, -4*w - 53],\ [2791, 2791, -3*w - 53],\ [2791, 2791, 3*w - 53],\ [2801, 2801, 2*w - 53],\ [2801, 2801, -2*w - 53],\ [2809, 53, -53],\ [2833, 2833, -18*w - 59],\ [2833, 2833, 18*w - 59],\ [2857, 2857, 14*w - 57],\ [2857, 2857, -14*w - 57],\ [2879, 2879, -38*w - 3],\ [2879, 2879, 38*w - 3],\ [2887, 2887, -38*w - 1],\ [2887, 2887, 38*w - 1],\ [2897, 2897, -8*w - 55],\ [2897, 2897, 8*w - 55],\ [2903, 2903, -17*w - 59],\ [2903, 2903, 17*w - 59],\ [2927, 2927, -7*w - 55],\ [2927, 2927, 7*w - 55],\ [2953, 2953, 6*w - 55],\ [2953, 2953, -6*w - 55],\ [2969, 2969, 16*w - 59],\ [2969, 2969, -16*w - 59],\ [2999, 2999, 19*w - 61],\ [2999, 2999, -19*w - 61],\ [3001, 3001, 22*w - 63],\ [3001, 3001, -22*w - 63],\ [3023, 3023, -w - 55],\ [3023, 3023, w - 55],\ [3041, 3041, -39*w - 1],\ [3041, 3041, 39*w - 1],\ [3049, 3049, -47*w - 37],\ [3049, 3049, 47*w - 37],\ [3079, 3079, -40*w - 11],\ [3079, 3079, 40*w - 11],\ [3089, 3089, 14*w - 59],\ [3089, 3089, -14*w - 59],\ [3119, 3119, -40*w - 9],\ [3119, 3119, 40*w - 9],\ [3121, 3121, 8*w - 57],\ [3121, 3121, -8*w - 57],\ [3137, 3137, 26*w - 67],\ [3137, 3137, -26*w - 67],\ [3167, 3167, -23*w - 65],\ [3167, 3167, 23*w - 65],\ [3169, 3169, 20*w - 63],\ [3169, 3169, -20*w - 63],\ [3191, 3191, 40*w - 3],\ [3191, 3191, -40*w - 3],\ [3209, 3209, 16*w - 61],\ [3209, 3209, -16*w - 61],\ [3217, 3217, 4*w - 57],\ [3217, 3217, -4*w - 57],\ [3257, 3257, -22*w - 65],\ [3257, 3257, 22*w - 65],\ [3271, 3271, 15*w - 61],\ [3271, 3271, -15*w - 61],\ [3313, 3313, -41*w - 7],\ [3313, 3313, 41*w - 7],\ [3319, 3319, 9*w - 59],\ [3319, 3319, -9*w - 59],\ [3329, 3329, -47*w - 33],\ [3329, 3329, 47*w - 33],\ [3343, 3343, -21*w - 65],\ [3343, 3343, 21*w - 65],\ [3359, 3359, -42*w - 13],\ [3359, 3359, 42*w - 13],\ [3361, 3361, -41*w - 1],\ [3361, 3361, 41*w - 1],\ [3391, 3391, -17*w - 63],\ [3391, 3391, 17*w - 63],\ [3407, 3407, 42*w - 11],\ [3407, 3407, -42*w - 11],\ [3433, 3433, -49*w - 37],\ [3433, 3433, 49*w - 37],\ [3449, 3449, -4*w - 59],\ [3449, 3449, 4*w - 59],\ [3457, 3457, -16*w - 63],\ [3457, 3457, 16*w - 63],\ [3463, 3463, -3*w - 59],\ [3463, 3463, 3*w - 59],\ [3481, 59, -59],\ [3511, 3511, 25*w - 69],\ [3511, 3511, -25*w - 69],\ [3527, 3527, -42*w - 1],\ [3527, 3527, 42*w - 1],\ [3529, 3529, -43*w - 13],\ [3529, 3529, 43*w - 13],\ [3559, 3559, 9*w - 61],\ [3559, 3559, -9*w - 61],\ [3583, 3583, 27*w - 71],\ [3583, 3583, -27*w - 71],\ [3593, 3593, -8*w - 61],\ [3593, 3593, 8*w - 61],\ [3607, 3607, -21*w - 67],\ [3607, 3607, 21*w - 67],\ [3617, 3617, 43*w - 9],\ [3617, 3617, -43*w - 9],\ [3623, 3623, 7*w - 61],\ [3623, 3623, -7*w - 61],\ [3631, 3631, -50*w - 37],\ [3631, 3631, 50*w - 37],\ [3671, 3671, 5*w - 61],\ [3671, 3671, -5*w - 61],\ [3673, 3673, 43*w - 5],\ [3673, 3673, -43*w - 5],\ [3697, 3697, -43*w - 1],\ [3697, 3697, 43*w - 1],\ [3719, 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113],\ [8719, 8719, -45*w - 113],\ [8737, 8737, -12*w - 95],\ [8737, 8737, 12*w - 95],\ [8753, 8753, -67*w - 15],\ [8753, 8753, 67*w - 15],\ [8761, 8761, 79*w - 61],\ [8761, 8761, -79*w - 61],\ [8783, 8783, -11*w - 95],\ [8783, 8783, 11*w - 95],\ [8807, 8807, -68*w - 21],\ [8807, 8807, 68*w - 21],\ [8831, 8831, 80*w - 63],\ [8831, 8831, -80*w - 63],\ [8839, 8839, -39*w - 109],\ [8839, 8839, 39*w - 109],\ [8849, 8849, -26*w - 101],\ [8849, 8849, 26*w - 101],\ [8863, 8863, 9*w - 95],\ [8863, 8863, -9*w - 95],\ [8887, 8887, 68*w - 19],\ [8887, 8887, -68*w - 19],\ [8929, 8929, 67*w - 7],\ [8929, 8929, -67*w - 7],\ [8951, 8951, 25*w - 101],\ [8951, 8951, -25*w - 101],\ [8969, 8969, 67*w - 3],\ [8969, 8969, -67*w - 3],\ [8999, 8999, -35*w - 107],\ [8999, 8999, 35*w - 107],\ [9001, 9001, 79*w - 59],\ [9001, 9001, -79*w - 59],\ [9007, 9007, -3*w - 95],\ [9007, 9007, 3*w - 95],\ [9041, 9041, 28*w - 103],\ [9041, 9041, -28*w - 103],\ [9049, 9049, 24*w - 101],\ [9049, 9049, -24*w - 101],\ [9103, 9103, 31*w - 105],\ [9103, 9103, -31*w - 105],\ [9127, 9127, -68*w - 11],\ [9127, 9127, 68*w - 11],\ [9137, 9137, 34*w - 107],\ [9137, 9137, -34*w - 107],\ [9151, 9151, -27*w - 103],\ [9151, 9151, 27*w - 103],\ [9161, 9161, 69*w - 19],\ [9161, 9161, -69*w - 19],\ [9199, 9199, 68*w - 7],\ [9199, 9199, -68*w - 7],\ [9209, 9209, 10*w - 97],\ [9209, 9209, -10*w - 97],\ [9239, 9239, -68*w - 3],\ [9239, 9239, 68*w - 3],\ [9241, 9241, -42*w - 113],\ [9241, 9241, 42*w - 113],\ [9257, 9257, -26*w - 103],\ [9257, 9257, 26*w - 103],\ [9281, 9281, 8*w - 97],\ [9281, 9281, -8*w - 97],\ [9311, 9311, -7*w - 97],\ [9311, 9311, 7*w - 97],\ [9319, 9319, -80*w - 59],\ [9319, 9319, 80*w - 59],\ [9337, 9337, 6*w - 97],\ [9337, 9337, -6*w - 97],\ [9343, 9343, -29*w - 105],\ [9343, 9343, 29*w - 105],\ [9377, 9377, 4*w - 97],\ [9377, 9377, -4*w - 97],\ [9391, 9391, 3*w - 97],\ [9391, 9391, -3*w - 97],\ [9431, 9431, 35*w - 109],\ [9431, 9431, -35*w - 109],\ [9433, 9433, -38*w - 111],\ [9433, 9433, 38*w - 111],\ [9439, 9439, 70*w - 19],\ [9439, 9439, -70*w - 19],\ [9463, 9463, 13*w - 99],\ [9463, 9463, -13*w - 99],\ [9473, 9473, -69*w - 7],\ [9473, 9473, 69*w - 7],\ [9479, 9479, 82*w - 63],\ [9479, 9479, -82*w - 63],\ [9497, 9497, -69*w - 5],\ [9497, 9497, 69*w - 5],\ [9511, 9511, -70*w - 17],\ [9511, 9511, 70*w - 17],\ [9521, 9521, -69*w - 1],\ [9521, 9521, 69*w - 1],\ [9551, 9551, 80*w - 57],\ [9551, 9551, -80*w - 57],\ [9601, 9601, -10*w - 99],\ [9601, 9601, 10*w - 99],\ [9623, 9623, -84*w + 67],\ [9623, 9623, 84*w + 67],\ [9631, 9631, -70*w - 13],\ [9631, 9631, 70*w - 13],\ [9649, 9649, -30*w - 107],\ [9649, 9649, 30*w - 107],\ [9679, 9679, 70*w - 11],\ [9679, 9679, -70*w - 11],\ [9689, 9689, -16*w - 101],\ [9689, 9689, 16*w - 101],\ [9697, 9697, 42*w - 115],\ [9697, 9697, -42*w - 115],\ [9719, 9719, 70*w - 9],\ [9719, 9719, -70*w - 9],\ [9721, 9721, -71*w - 19],\ [9721, 9721, 71*w - 19],\ [9743, 9743, -47*w - 119],\ [9743, 9743, 47*w - 119],\ [9767, 9767, -29*w - 107],\ [9767, 9767, 29*w - 107],\ [9769, 9769, -4*w - 99],\ [9769, 9769, 4*w - 99],\ [9791, 9791, 70*w - 3],\ [9791, 9791, -70*w - 3],\ [9817, 9817, -44*w - 117],\ [9817, 9817, 44*w - 117],\ [9833, 9833, 32*w - 109],\ [9833, 9833, -32*w - 109],\ [9839, 9839, -49*w - 121],\ [9839, 9839, 49*w - 121],\ [9857, 9857, -71*w - 15],\ [9857, 9857, 71*w - 15],\ [9871, 9871, 35*w - 111],\ [9871, 9871, -35*w - 111],\ [9887, 9887, 84*w - 65],\ [9887, 9887, -84*w - 65],\ [9929, 9929, -46*w - 119],\ [9929, 9929, 46*w - 119],\ [9967, 9967, 82*w - 59],\ [9967, 9967, -82*w - 59]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [0, 1, 1, -6, -6, -6, 0, 0, -6, -8, -8, 2, 2, 8, 8, 8, 8, 10, 10, -16, -16, -6, -6, -6, -6, 16, 16, 2, 2, -6, 8, 8, -6, -6, 0, 0, -16, -16, -22, 16, 16, -14, -14, 0, 0, 0, 0, -22, -22, -8, -8, 10, 10, 2, 2, -24, -24, 0, 0, -6, -6, -8, -8, -14, -14, 2, 2, -14, -14, 0, 0, 26, -16, -16, 24, 24, 18, 18, -14, -14, 8, 8, 10, 10, -24, -24, 34, 34, -38, -38, 16, 16, 24, 24, 16, 16, -40, -40, 18, 18, 26, 26, -14, -14, 34, 34, 24, 24, 26, 26, -32, -32, -38, -38, -24, -24, -30, -30, 32, 32, -14, -14, -8, -8, -16, -16, -32, -32, 8, 8, -30, -30, -22, -22, 26, 26, -24, -24, 48, 48, -22, 18, 18, -16, -16, 18, 18, 16, 16, -24, -24, 40, 40, 10, 10, 10, 10, -6, -6, 16, 16, 2, 2, 0, 0, 16, 16, 2, 2, -24, -24, -22, -22, -40, -40, 42, 42, 24, 24, 56, 56, -6, -6, 40, 40, -38, -38, 40, 40, 50, 50, -6, -6, 2, 2, 2, 2, 24, 24, -8, -8, -30, -30, -24, -24, -6, -6, 50, 50, 64, 64, 24, 24, -46, -46, -48, -48, -6, -6, 24, 24, -70, 8, 8, -62, -62, -72, -72, -6, -6, -56, -56, 8, 8, 64, 64, 10, 10, 64, 64, 26, 26, -8, -8, -56, -56, 18, 18, 48, 48, -32, -32, 0, 0, 18, 18, -40, -40, -22, -22, 18, 18, 8, 8, 58, 58, -70, -70, 74, 74, 8, 8, 18, 18, -56, -56, 58, 58, 0, 0, -40, -40, -16, -16, -70, 40, 40, -46, -46, 16, 16, 82, 82, 10, 10, -16, -16, 66, 66, 16, 16, -14, -14, -48, -48, -48, -48, -46, -46, 24, 24, 10, 10, 0, 0, 34, 34, 50, 50, -86, -86, -64, -64, -38, -38, -86, -86, -72, -72, -40, -40, -78, -78, -38, -38, -8, -8, -6, -6, 56, 56, 16, 16, 42, 42, 24, 24, -86, -86, -40, -40, 18, 18, 32, 32, -22, -22, -40, -40, 90, 90, -16, -16, 42, 42, 32, 32, -8, -8, -24, -24, 66, 66, 42, 42, -14, -14, -6, -6, -24, -24, -30, -30, 24, 24, -16, -16, -88, -88, -46, -46, 32, 32, -54, -54, 88, 88, -14, -14, -30, -30, 48, 48, 82, 82, -16, -16, -30, -30, -70, -46, -46, 74, 74, 32, 32, 32, 32, 42, 42, -72, -72, -96, -96, -30, -30, 90, 90, 96, 96, -14, -14, 32, 32, 42, 42, 26, 26, 48, 48, -30, -30, 16, 16, -30, -30, 18, 18, -56, -56, -102, -102, 40, 40, 66, 66, -94, -94, 42, 42, -80, -80, 18, 18, -80, -80, 2, 2, 8, 8, 48, 48, -14, -14, 32, 32, 96, 96, -14, -14, -102, -102, 10, 10, -64, -64, -118, 0, 0, -24, -24, 10, 10, 16, 16, 32, 32, 10, 10, 80, 80, -6, -6, 120, 120, 112, 112, -104, -104, 74, 74, 82, 82, -80, -80, -86, 64, 64, 66, 66, 104, 104, -14, -14, 74, 74, 96, 96, 90, 90, -80, -80, -56, -56, 2, 2, -46, -46, 24, 24, 112, 112, 42, 42, -32, -32, -88, -88, -30, -30, -72, -72, -78, -78, -86, -86, 2, 2, -48, -48, -40, -40, -8, -8, -102, -102, 106, 106, -72, -72, 50, 50, -6, -6, 10, 10, 32, 32, 42, 42, 72, 72, 82, 82, 114, 114, 42, 42, 104, 104, -30, -30, -96, -96, -70, -70, 88, 88, 2, 2, 16, 16, -70, -70, -48, -48, 50, 50, -118, -94, -94, -16, -16, -30, -30, -88, -88, 112, 112, 56, 56, 64, 64, -6, -6, -14, -14, 40, 40, -94, -94, -56, -56, -72, -72, -14, -14, 10, 10, 40, 40, 0, 0, 64, 64, -126, -126, 32, 32, -14, -14, -46, -46, -8, -8, -48, -48, -126, -126, 80, 80, 64, 64, -70, -70, 72, 72, -40, -40, 0, 0, -62, -62, 2, 2, -16, -16, -30, -30, 16, 16, 112, 112, 58, 58, 72, 72, 42, 42, -96, -96, 66, 66, -24, -24, 106, 106, -48, -48, 2, 2, -54, -54, -24, -24, 106, 106, 18, 18, 136, 136, -48, -48, -30, -30, -120, -120, -120, -120, -142, -142, -32, -32, -30, -30, 2, 2, 128, 128, -64, -64, 64, 64, -48, -48, 122, 122, 88, 88, -110, -110, -64, -64, 96, 96, 128, 128, 146, 146, -80, -80, -86, -86, -38, -38, 120, 120, 106, 106, -72, -72, -96, -96, -32, -32, 18, 18, -112, -112, 80, 80, -6, -6, -54, -54, 96, 96, -86, -86, 34, 34, -96, -96, 8, 8, -70, -70, -8, -8, -24, -24, -54, -54, 112, 112, 42, 42, -142, -142, -70, -70, -72, -72, -40, -40, -16, -16, -22, -22, 104, 104, -102, -102, -112, -112, -96, -96, 48, 48, -96, -96, -102, -102, 2, 2, 16, 16, -62, -62, -104, -104, -6, -6, 152, 152, 2, 2, -78, -78, -110, -110, 90, 90, 130, 130, 56, 56, 106, 106, -38, -38, -46, -46, -24, -24, -8, -8, -62, -62, -88, -88, 34, 34, 56, 56, 0, 0, -22, -22, 154, 154, -72, -72, 154, 154, -24, -24, -62, -62, 42, 42, -54, -54, 72, 72, -32, -32, -102, 40, 40, -48, -48, 122, 122, -136, -136, 122, 122, 72, 72, -136, -136, -6, -6, -96, -96, -110, -110, -144, -144, -144, -144, 82, 82, -48, -48, -54, -54, 128, 128, -104, -104, -70, -70, -70, -70, -24, -24, 120, 120, -118, -118, -62, -62, -32, -32, 50, 50, 66, 66, 106, 106, -14, -14, 114, 114, -150, -150, 24, 24, -158, -158, 90, 90, -86, -86, -104, -104, 122, 122, 74, 74, 56, 56, -40, -40, 48, 48, 112, 112, -150, -150, -86, -86, 18, 18, -120, -120, -64, -64, 16, 16, 26, 26, 80, 80, 114, 114, -134, -134, 0, 0, -142, -142, 106, 106, -24, -24, -152, -152, -32, -32, -54, -54, -32, -32, -166, -166, -70, -70, 82, 82, -160, -160, 18, 18, -72, -72, -22, -22, 88, 88, -46, -46, 48, 48, -104, -104, -30, -30, 48, 48, 106, 106, 88, 88, -30, -30, 40, 40, 74, 74, 8, 8, 66, 66, 34, 34, 18, 18, 2, 2, -24, -24, 56, 56, -40, -40, 114, 114, 106, 106, -176, -176, 10, 10, -120, -120, 40, 40, -30, -30, 24, 24, 170, 170, -72, -72, 16, 16, 122, 122, 34, 34, 106, 106, -64, -64, 50, 50, -118, -118, 58, 58, 104, 104, -32, -32, 136, 136, -40, -40, -30, -30, -80, -80, -40, -40, 2, 2, 112, 112, 138, 138, -128, -128, -6, -6, -64, -64, -174, -174, 66, 66, -152, -152, 112, 112, -30, -30, -24, -24, 34, 34, -8, -8, 90, 90, -168, -168, -6, -6, 82, 82, 2, 2, -96, -96, 24, 24, -86, -86, 136, 136, 34, 34, 88, 88, -144, -144, -102, -102, 40, 40, -24, -24, 34, 34, 96, 96, 34, 34, 80, 80, -62, -62, 72, 72, -110, -110, 104, 104, 48, 48, 146, 146, 32, 32, -70, -70, -78, -78, -168, -168, -182, -182, 24, 24, 88, 88, -6, -6, 72, 72, 66, 66, -142, -142, -40, -40, 114, 114, 160, 160, 112, 112, -78, -78, 96, 96] 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([7, 7, -2*w + 1])] = -1 AL_eigenvalues[ZF.ideal([7, 7, -2*w - 1])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]