/* 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([-10, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([121, 11, -11]) primes_array = [ [2, 2, w - 4],\ [2, 2, -w - 3],\ [5, 5, -2*w - 5],\ [5, 5, -2*w + 7],\ [9, 3, 3],\ [23, 23, 2*w - 9],\ [23, 23, -2*w - 7],\ [31, 31, -6*w - 17],\ [31, 31, 6*w - 23],\ [37, 37, 2*w - 3],\ [37, 37, -2*w - 1],\ [41, 41, 2*w - 1],\ [43, 43, -4*w - 9],\ [43, 43, 4*w - 13],\ [49, 7, -7],\ [59, 59, 2*w - 11],\ [59, 59, -2*w - 9],\ [61, 61, -4*w + 17],\ [61, 61, 4*w + 13],\ [73, 73, 8*w + 23],\ [73, 73, -8*w + 31],\ [83, 83, 4*w - 11],\ [83, 83, -4*w - 7],\ [103, 103, 2*w - 13],\ [103, 103, -2*w - 11],\ [107, 107, 14*w + 39],\ [107, 107, -14*w + 53],\ [113, 113, -6*w - 13],\ [113, 113, 6*w - 19],\ [121, 11, -11],\ [127, 127, -8*w - 19],\ [127, 127, -8*w + 27],\ [131, 131, 10*w + 29],\ [131, 131, -10*w + 39],\ [139, 139, 4*w - 7],\ [139, 139, -4*w - 3],\ [163, 163, 4*w - 3],\ [163, 163, 4*w - 1],\ [169, 13, -13],\ [173, 173, 6*w - 17],\ [173, 173, -6*w - 11],\ [197, 197, 4*w - 21],\ [197, 197, -4*w - 17],\ [223, 223, -16*w + 57],\ [223, 223, 16*w + 41],\ [241, 241, 10*w - 33],\ [241, 241, -10*w - 23],\ [251, 251, -12*w - 29],\ [251, 251, -12*w + 41],\ [269, 269, -6*w - 7],\ [269, 269, 6*w - 13],\ [271, 271, -10*w + 41],\ [271, 271, 10*w + 31],\ [277, 277, -4*w - 19],\ [277, 277, 4*w - 23],\ [283, 283, 2*w - 19],\ [283, 283, -2*w - 17],\ [289, 17, -17],\ [307, 307, 6*w + 23],\ [307, 307, 6*w - 29],\ [337, 337, 24*w + 67],\ [337, 337, -24*w + 91],\ [349, 349, -10*w - 21],\ [349, 349, 10*w - 31],\ [353, 353, -6*w - 1],\ [353, 353, 6*w - 7],\ [359, 359, 2*w - 21],\ [359, 359, -2*w - 19],\ [361, 19, -19],\ [367, 367, 8*w - 21],\ [367, 367, -8*w - 13],\ [373, 373, -12*w + 49],\ [373, 373, 12*w + 37],\ [379, 379, -20*w + 71],\ [379, 379, 20*w + 51],\ [389, 389, 20*w + 57],\ [389, 389, -20*w + 77],\ [401, 401, 16*w + 47],\ [401, 401, -16*w + 63],\ [409, 409, -14*w - 33],\ [409, 409, -14*w + 47],\ [419, 419, 10*w + 33],\ [419, 419, -10*w + 43],\ [431, 431, -8*w - 11],\ [431, 431, 8*w - 19],\ [433, 433, 8*w + 29],\ [433, 433, -8*w + 37],\ [443, 443, 2*w - 23],\ [443, 443, -2*w - 21],\ [449, 449, 10*w - 29],\ [449, 449, -10*w - 19],\ [461, 461, -4*w - 23],\ [461, 461, 4*w - 27],\ [467, 467, -26*w + 99],\ [467, 467, 28*w - 101],\ [487, 487, -8*w - 9],\ [487, 487, 8*w - 17],\ [491, 491, -14*w + 57],\ [491, 491, 14*w + 43],\ [523, 523, 18*w + 53],\ [523, 523, -18*w + 71],\ [541, 541, -10*w - 17],\ [541, 541, 10*w - 27],\ [569, 569, -8*w - 31],\ [569, 569, 8*w - 39],\ [599, 599, 16*w - 53],\ [599, 599, -16*w - 37],\ [607, 607, -8*w - 3],\ [607, 607, 8*w - 11],\ [613, 613, -28*w + 107],\ [613, 613, 34*w - 123],\ [617, 617, -18*w + 61],\ [617, 617, -18*w - 43],\ [619, 619, -20*w - 49],\ [619, 619, -20*w + 69],\ [631, 631, -8*w - 1],\ [631, 631, 8*w - 9],\ [647, 647, 8*w - 7],\ [647, 647, 8*w - 1],\ [661, 661, 20*w + 59],\ [661, 661, -20*w + 79],\ [677, 677, -4*w - 27],\ [677, 677, 4*w - 31],\ [701, 701, 10*w - 23],\ [701, 701, -10*w - 13],\ [733, 733, -12*w + 53],\ [733, 733, 12*w + 41],\ [739, 739, 10*w - 47],\ [739, 739, 10*w + 37],\ [743, 743, 2*w - 29],\ [743, 743, -2*w - 27],\ [761, 761, -30*w + 107],\ [761, 761, 30*w + 77],\ [769, 769, -10*w - 11],\ [769, 769, 10*w - 21],\ [787, 787, 6*w - 37],\ [787, 787, -6*w - 31],\ [797, 797, 4*w - 33],\ [797, 797, -4*w - 29],\ [811, 811, -28*w + 99],\ [811, 811, 28*w + 71],\ [821, 821, 18*w - 59],\ [821, 821, -18*w - 41],\ [829, 829, 10*w - 19],\ [829, 829, -10*w - 9],\ [841, 29, -29],\ [853, 853, 14*w - 41],\ [853, 853, 14*w + 27],\ [857, 857, 16*w + 51],\ [857, 857, -16*w + 67],\ [859, 859, 2*w - 31],\ [859, 859, -2*w - 29],\ [863, 863, -24*w - 59],\ [863, 863, -24*w + 83],\ [877, 877, -36*w + 137],\ [877, 877, 38*w - 137],\ [881, 881, -10*w - 7],\ [881, 881, 10*w - 17],\ [907, 907, -14*w + 61],\ [907, 907, 14*w + 47],\ [911, 911, 10*w + 39],\ [911, 911, 10*w - 49],\ [941, 941, -20*w + 81],\ [941, 941, 20*w + 61],\ [947, 947, -12*w - 17],\ [947, 947, 12*w - 29],\ [953, 953, 32*w + 91],\ [953, 953, -32*w + 123],\ [983, 983, 2*w - 33],\ [983, 983, -2*w - 31],\ [1009, 1009, 10*w - 9],\ [1009, 1009, 10*w - 1],\ [1021, 1021, 10*w - 3],\ [1021, 1021, 10*w - 7],\ [1033, 1033, 34*w + 87],\ [1033, 1033, -34*w + 121],\ [1061, 1061, 4*w - 37],\ [1061, 1061, -4*w - 33],\ [1087, 1087, -32*w + 113],\ [1087, 1087, 32*w + 81],\ [1091, 1091, 10*w - 51],\ [1091, 1091, -10*w - 41],\ [1097, 1097, 16*w + 53],\ [1097, 1097, -16*w + 69],\ [1103, 1103, 16*w - 47],\ [1103, 1103, 16*w + 31],\ [1109, 1109, 14*w - 37],\ [1109, 1109, -14*w - 23],\ [1117, 1117, 22*w - 73],\ [1117, 1117, -22*w - 51],\ [1123, 1123, -22*w + 89],\ [1123, 1123, 22*w + 67],\ [1153, 1153, -26*w + 89],\ [1153, 1153, -26*w - 63],\ [1171, 1171, 26*w + 77],\ [1171, 1171, -26*w + 103],\ [1181, 1181, 44*w + 123],\ [1181, 1181, -44*w + 167],\ [1187, 1187, 12*w - 23],\ [1187, 1187, -12*w - 11],\ [1193, 1193, -8*w - 39],\ [1193, 1193, 8*w - 47],\ [1229, 1229, -20*w + 83],\ [1229, 1229, 20*w + 63],\ [1231, 1231, 6*w - 43],\ [1231, 1231, -6*w - 37],\ [1279, 1279, -10*w - 43],\ [1279, 1279, 10*w - 53],\ [1289, 1289, 50*w + 131],\ [1289, 1289, 50*w - 181],\ [1291, 1291, -20*w - 43],\ [1291, 1291, 20*w - 63],\ [1303, 1303, 18*w + 59],\ [1303, 1303, -18*w + 77],\ [1307, 1307, 12*w - 19],\ [1307, 1307, -12*w - 7],\ [1321, 1321, -24*w + 97],\ [1321, 1321, 24*w + 73],\ [1361, 1361, -22*w - 49],\ [1361, 1361, 22*w - 71],\ [1373, 1373, 28*w + 83],\ [1373, 1373, -28*w + 111],\ [1399, 1399, -16*w - 27],\ [1399, 1399, 16*w - 43],\ [1427, 1427, -12*w - 1],\ [1427, 1427, 12*w - 13],\ [1433, 1433, -14*w - 17],\ [1433, 1433, 14*w - 31],\ [1439, 1439, 22*w + 69],\ [1439, 1439, -22*w + 91],\ [1451, 1451, 12*w - 11],\ [1451, 1451, 12*w - 1],\ [1453, 1453, -26*w - 61],\ [1453, 1453, -26*w + 87],\ [1471, 1471, -32*w - 79],\ [1471, 1471, -32*w + 111],\ [1481, 1481, -30*w - 73],\ [1481, 1481, -30*w + 103],\ [1499, 1499, -20*w - 41],\ [1499, 1499, 20*w - 61],\ [1549, 1549, 12*w - 61],\ [1549, 1549, -12*w - 49],\ [1553, 1553, 8*w - 51],\ [1553, 1553, -8*w - 43],\ [1559, 1559, 2*w - 41],\ [1559, 1559, -2*w - 39],\ [1567, 1567, -6*w - 41],\ [1567, 1567, 6*w - 47],\ [1579, 1579, 18*w + 61],\ [1579, 1579, -18*w + 79],\ [1583, 1583, -38*w + 147],\ [1583, 1583, 38*w + 109],\ [1597, 1597, 22*w - 69],\ [1597, 1597, -22*w - 47],\ [1601, 1601, 16*w + 57],\ [1601, 1601, -16*w + 73],\ [1607, 1607, -34*w + 133],\ [1607, 1607, 34*w + 99],\ [1609, 1609, 14*w - 27],\ [1609, 1609, -14*w - 13],\ [1619, 1619, -44*w + 157],\ [1619, 1619, 44*w + 113],\ [1663, 1663, -16*w - 23],\ [1663, 1663, 16*w - 39],\ [1697, 1697, 42*w + 107],\ [1697, 1697, -42*w + 149],\ [1699, 1699, 20*w - 59],\ [1699, 1699, 20*w + 39],\ [1721, 1721, -18*w - 31],\ [1721, 1721, 18*w - 49],\ [1723, 1723, 2*w - 43],\ [1723, 1723, -2*w - 41],\ [1747, 1747, 6*w - 49],\ [1747, 1747, -6*w - 43],\ [1753, 1753, 14*w - 23],\ [1753, 1753, -14*w - 9],\ [1759, 1759, -40*w + 141],\ [1759, 1759, 40*w + 101],\ [1783, 1783, 16*w - 37],\ [1783, 1783, -16*w - 21],\ [1847, 1847, -32*w - 77],\ [1847, 1847, -32*w + 109],\ [1861, 1861, -4*w - 43],\ [1861, 1861, 4*w - 47],\ [1877, 1877, -18*w - 29],\ [1877, 1877, 18*w - 47],\ [1907, 1907, -26*w + 107],\ [1907, 1907, 26*w + 81],\ [1931, 1931, -50*w + 191],\ [1931, 1931, 60*w - 217],\ [1973, 1973, 14*w - 13],\ [1973, 1973, 14*w - 1],\ [1993, 1993, 14*w - 11],\ [1993, 1993, 14*w - 3],\ [1999, 1999, -16*w - 17],\ [1999, 1999, 16*w - 33],\ [2011, 2011, -30*w + 121],\ [2011, 2011, 30*w + 91],\ [2017, 2017, -24*w + 101],\ [2017, 2017, 24*w + 77],\ [2027, 2027, -46*w + 177],\ [2027, 2027, 46*w + 131],\ [2029, 2029, 26*w - 83],\ [2029, 2029, -26*w - 57],\ [2081, 2081, -56*w + 213],\ [2081, 2081, 58*w - 209],\ [2083, 2083, 42*w + 121],\ [2083, 2083, -42*w + 163],\ [2087, 2087, 14*w - 71],\ [2087, 2087, -14*w - 57],\ [2089, 2089, -46*w + 163],\ [2089, 2089, 46*w + 117],\ [2099, 2099, 38*w + 111],\ [2099, 2099, -38*w + 149],\ [2111, 2111, 10*w - 61],\ [2111, 2111, -10*w - 51],\ [2131, 2131, -6*w - 47],\ [2131, 2131, 6*w - 53],\ [2137, 2137, 16*w - 77],\ [2137, 2137, 16*w + 61],\ [2141, 2141, -20*w + 89],\ [2141, 2141, 20*w + 69],\ [2153, 2153, 8*w - 57],\ [2153, 2153, -8*w - 49],\ [2209, 47, -47],\ [2213, 2213, 66*w + 173],\ [2213, 2213, 66*w - 239],\ [2237, 2237, -4*w - 47],\ [2237, 2237, 4*w - 51],\ [2239, 2239, -40*w - 99],\ [2239, 2239, -40*w + 139],\ [2251, 2251, 20*w - 53],\ [2251, 2251, -20*w - 33],\ [2273, 2273, -32*w + 129],\ [2273, 2273, 32*w + 97],\ [2287, 2287, 26*w + 83],\ [2287, 2287, -26*w + 109],\ [2297, 2297, 18*w - 41],\ [2297, 2297, -18*w - 23],\ [2333, 2333, 54*w + 139],\ [2333, 2333, -54*w + 193],\ [2339, 2339, -10*w - 53],\ [2339, 2339, 10*w - 63],\ [2341, 2341, 36*w + 107],\ [2341, 2341, -36*w + 143],\ [2347, 2347, 14*w - 73],\ [2347, 2347, -14*w - 59],\ [2357, 2357, 44*w + 127],\ [2357, 2357, -44*w + 171],\ [2377, 2377, -24*w + 103],\ [2377, 2377, 24*w + 79],\ [2383, 2383, -58*w + 221],\ [2383, 2383, 64*w - 231],\ [2399, 2399, -16*w - 7],\ [2399, 2399, 16*w - 23],\ [2411, 2411, 28*w - 89],\ [2411, 2411, -28*w - 61],\ [2417, 2417, 16*w + 63],\ [2417, 2417, 16*w - 79],\ [2423, 2423, 24*w - 71],\ [2423, 2423, 24*w + 47],\ [2437, 2437, 4*w - 53],\ [2437, 2437, -4*w - 49],\ [2459, 2459, 2*w - 51],\ [2459, 2459, -2*w - 49],\ [2503, 2503, 16*w - 19],\ [2503, 2503, -16*w - 3],\ [2521, 2521, 50*w + 127],\ [2521, 2521, -50*w + 177],\ [2543, 2543, -16*w - 1],\ [2543, 2543, 16*w - 17],\ [2551, 2551, -34*w + 137],\ [2551, 2551, 34*w + 103],\ [2579, 2579, -20*w - 29],\ [2579, 2579, 20*w - 49],\ [2591, 2591, -48*w + 169],\ [2591, 2591, 48*w + 121],\ [2593, 2593, -8*w - 53],\ [2593, 2593, 8*w - 61],\ [2633, 2633, 34*w - 113],\ [2633, 2633, -34*w - 79],\ [2647, 2647, -46*w + 179],\ [2647, 2647, 46*w + 133],\ [2657, 2657, -22*w - 37],\ [2657, 2657, 22*w - 59],\ [2663, 2663, 2*w - 53],\ [2663, 2663, -2*w - 51],\ [2683, 2683, -44*w - 109],\ [2683, 2683, -44*w + 153],\ [2707, 2707, 28*w - 87],\ [2707, 2707, -28*w - 59],\ [2711, 2711, -40*w + 137],\ [2711, 2711, -40*w - 97],\ [2729, 2729, -32*w + 131],\ [2729, 2729, 32*w + 99],\ [2731, 2731, -20*w - 27],\ [2731, 2731, 20*w - 47],\ [2749, 2749, -12*w - 59],\ [2749, 2749, 12*w - 71],\ [2767, 2767, -6*w - 53],\ [2767, 2767, 6*w - 59],\ [2789, 2789, 20*w + 73],\ [2789, 2789, -20*w + 93],\ [2797, 2797, -58*w + 207],\ [2797, 2797, 58*w + 149],\ [2809, 53, -53],\ [2819, 2819, 10*w - 67],\ [2819, 2819, -10*w - 57],\ [2833, 2833, 26*w - 77],\ [2833, 2833, 26*w + 51],\ [2837, 2837, -18*w - 13],\ [2837, 2837, 18*w - 31],\ [2861, 2861, 4*w - 57],\ [2861, 2861, -4*w - 53],\ [2879, 2879, 24*w - 67],\ [2879, 2879, -24*w - 43],\ [2903, 2903, -56*w + 199],\ [2903, 2903, 56*w + 143],\ [2909, 2909, 52*w + 149],\ [2909, 2909, -52*w + 201],\ [2927, 2927, 32*w - 103],\ [2927, 2927, -32*w - 71],\ [2953, 2953, -48*w + 187],\ [2953, 2953, 48*w + 139],\ [2957, 2957, 44*w + 129],\ [2957, 2957, -44*w + 173],\ [3001, 3001, -16*w - 67],\ [3001, 3001, 16*w - 83],\ [3011, 3011, -20*w - 23],\ [3011, 3011, 20*w - 43],\ [3067, 3067, -52*w + 183],\ [3067, 3067, 52*w + 131],\ [3079, 3079, 18*w + 71],\ [3079, 3079, 18*w - 89],\ [3083, 3083, 36*w - 119],\ [3083, 3083, -36*w - 83],\ [3121, 3121, -24*w + 107],\ [3121, 3121, 24*w + 83],\ [3137, 3137, -38*w - 89],\ [3137, 3137, -38*w + 127],\ [3167, 3167, -48*w - 119],\ [3167, 3167, -48*w + 167],\ [3203, 3203, -44*w - 107],\ [3203, 3203, -44*w + 151],\ [3221, 3221, -18*w - 1],\ [3221, 3221, 18*w - 19],\ [3229, 3229, 74*w - 267],\ [3229, 3229, -68*w + 259],\ [3257, 3257, 18*w - 17],\ [3257, 3257, 18*w - 1],\ [3259, 3259, 20*w - 39],\ [3259, 3259, -20*w - 19],\ [3271, 3271, -32*w - 69],\ [3271, 3271, 32*w - 101],\ [3301, 3301, -62*w + 221],\ [3301, 3301, 62*w + 159],\ [3313, 3313, 8*w - 67],\ [3313, 3313, -8*w - 59],\ [3319, 3319, -30*w + 127],\ [3319, 3319, 30*w + 97],\ [3323, 3323, 2*w - 59],\ [3323, 3323, -2*w - 57],\ [3329, 3329, -26*w - 47],\ [3329, 3329, 26*w - 73],\ [3331, 3331, 10*w - 71],\ [3331, 3331, -10*w - 61],\ [3361, 3361, 22*w - 51],\ [3361, 3361, -22*w - 29],\ [3371, 3371, 20*w - 37],\ [3371, 3371, -20*w - 17],\ [3407, 3407, 74*w + 207],\ [3407, 3407, -74*w + 281],\ [3413, 3413, 28*w + 93],\ [3413, 3413, -28*w + 121],\ [3449, 3449, -30*w - 61],\ [3449, 3449, 30*w - 91],\ [3467, 3467, -14*w - 67],\ [3467, 3467, 14*w - 81],\ [3469, 3469, 20*w + 77],\ [3469, 3469, 20*w - 97],\ [3517, 3517, -22*w - 27],\ [3517, 3517, 22*w - 49],\ [3527, 3527, -34*w + 141],\ [3527, 3527, 34*w + 107],\ [3547, 3547, -28*w - 53],\ [3547, 3547, 28*w - 81],\ [3557, 3557, -4*w - 59],\ [3557, 3557, 4*w - 63],\ [3559, 3559, 2*w - 61],\ [3559, 3559, -2*w - 59],\ [3571, 3571, 20*w - 33],\ [3571, 3571, -20*w - 13],\ [3583, 3583, -56*w + 197],\ [3583, 3583, 56*w + 141],\ [3607, 3607, -32*w - 67],\ [3607, 3607, 32*w - 99],\ [3613, 3613, 52*w + 151],\ [3613, 3613, -52*w + 203],\ [3617, 3617, 16*w - 87],\ [3617, 3617, -16*w - 71],\ [3631, 3631, 40*w - 133],\ [3631, 3631, -40*w - 93],\ [3659, 3659, 20*w - 31],\ [3659, 3659, -20*w - 11],\ [3691, 3691, -52*w - 129],\ [3691, 3691, -52*w + 181],\ [3727, 3727, 6*w - 67],\ [3727, 3727, -6*w - 61],\ [3733, 3733, -46*w - 111],\ [3733, 3733, -46*w + 157],\ [3739, 3739, -20*w - 9],\ [3739, 3739, 20*w - 29],\ [3767, 3767, -14*w - 69],\ [3767, 3767, 14*w - 83],\ [3793, 3793, 26*w - 69],\ [3793, 3793, -26*w - 43],\ [3797, 3797, -76*w + 289],\ [3797, 3797, 76*w + 213],\ [3803, 3803, 2*w - 63],\ [3803, 3803, -2*w - 61],\ [3821, 3821, -20*w - 79],\ [3821, 3821, 20*w - 99],\ [3823, 3823, -42*w + 169],\ [3823, 3823, 42*w + 127],\ [3833, 3833, -8*w - 63],\ [3833, 3833, 8*w - 71],\ [3853, 3853, -12*w - 67],\ [3853, 3853, 12*w - 79],\ [3863, 3863, 62*w + 177],\ [3863, 3863, -62*w + 239],\ [3877, 3877, 36*w + 113],\ [3877, 3877, -36*w + 149],\ [3911, 3911, 46*w + 137],\ [3911, 3911, -46*w + 183],\ [3931, 3931, -20*w - 3],\ [3931, 3931, 20*w - 23],\ [3967, 3967, 54*w + 157],\ [3967, 3967, -54*w + 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[9043, 9043, 122*w + 341],\ [9059, 9059, 36*w - 83],\ [9059, 9059, -36*w - 47],\ [9103, 9103, -104*w + 371],\ [9103, 9103, 104*w + 267],\ [9127, 9127, 32*w - 53],\ [9127, 9127, -32*w - 21],\ [9133, 9133, 12*w - 109],\ [9133, 9133, -12*w - 97],\ [9151, 9151, -88*w + 309],\ [9151, 9151, 88*w + 221],\ [9161, 9161, 30*w - 23],\ [9161, 9161, 30*w - 7],\ [9209, 9209, 30*w - 19],\ [9209, 9209, 30*w - 11],\ [9221, 9221, 30*w - 17],\ [9221, 9221, 30*w - 13],\ [9227, 9227, 14*w - 113],\ [9227, 9227, -14*w - 99],\ [9241, 9241, -50*w - 103],\ [9241, 9241, 50*w - 153],\ [9257, 9257, -16*w - 101],\ [9257, 9257, 16*w - 117],\ [9311, 9311, 70*w + 209],\ [9311, 9311, -70*w + 279],\ [9323, 9323, -84*w - 209],\ [9323, 9323, -84*w + 293],\ [9343, 9343, 56*w - 179],\ [9343, 9343, -56*w - 123],\ [9349, 9349, 34*w - 67],\ [9349, 9349, -34*w - 33],\ [9371, 9371, -68*w + 229],\ [9371, 9371, -68*w - 161],\ [9391, 9391, 90*w + 259],\ [9391, 9391, -90*w + 349],\ [9397, 9397, -44*w + 193],\ [9397, 9397, 44*w + 149],\ [9409, 97, -97],\ [9421, 9421, -70*w - 167],\ [9421, 9421, -70*w + 237],\ [9431, 9431, -80*w - 197],\ [9431, 9431, -80*w + 277],\ [9439, 9439, -22*w - 109],\ [9439, 9439, 22*w - 131],\ [9461, 9461, -78*w - 191],\ [9461, 9461, -78*w + 269],\ [9463, 9463, -78*w + 307],\ [9463, 9463, 78*w + 229],\ [9467, 9467, 34*w + 129],\ [9467, 9467, 34*w - 163],\ [9473, 9473, -74*w + 253],\ [9473, 9473, -74*w - 179],\ [9479, 9479, -82*w + 321],\ [9479, 9479, 82*w + 239],\ [9491, 9491, -52*w - 109],\ [9491, 9491, 52*w - 161],\ [9511, 9511, -40*w - 63],\ [9511, 9511, 40*w - 103],\ [9521, 9521, 40*w + 141],\ [9521, 9521, -40*w + 181],\ [9533, 9533, -52*w + 219],\ [9533, 9533, 52*w + 167],\ [9551, 9551, 134*w + 373],\ [9551, 9551, -134*w + 507],\ [9619, 9619, -58*w + 239],\ [9619, 9619, 58*w + 181],\ [9631, 9631, 6*w - 103],\ [9631, 9631, -6*w - 97],\ [9643, 9643, 44*w - 123],\ [9643, 9643, -44*w - 79],\ [9677, 9677, 124*w + 347],\ [9677, 9677, -124*w + 471],\ [9697, 9697, 16*w - 119],\ [9697, 9697, -16*w - 103],\ [9719, 9719, 50*w + 163],\ [9719, 9719, -50*w + 213],\ [9721, 9721, -24*w - 113],\ [9721, 9721, 24*w - 137],\ [9733, 9733, 34*w - 63],\ [9733, 9733, -34*w - 29],\ [9749, 9749, -50*w - 101],\ [9749, 9749, 50*w - 151],\ [9767, 9767, -32*w - 11],\ [9767, 9767, 32*w - 43],\ [9781, 9781, 110*w + 283],\ [9781, 9781, -110*w + 393],\ [9791, 9791, -10*w - 99],\ [9791, 9791, 10*w - 109],\ [9803, 9803, 36*w - 77],\ [9803, 9803, -36*w - 41],\ [9817, 9817, -62*w - 141],\ [9817, 9817, 62*w - 203],\ [9839, 9839, 40*w - 101],\ [9839, 9839, -40*w - 61],\ [9871, 9871, 32*w - 41],\ [9871, 9871, -32*w - 9],\ [9883, 9883, -62*w + 253],\ [9883, 9883, 62*w + 191],\ [9901, 9901, -38*w - 51],\ [9901, 9901, 38*w - 89],\ [9923, 9923, 22*w - 133],\ [9923, 9923, -22*w - 111],\ [9931, 9931, 140*w - 507],\ [9931, 9931, 140*w + 367],\ [9967, 9967, 32*w - 39],\ [9967, 9967, -32*w - 7],\ [9973, 9973, 12*w - 113],\ [9973, 9973, -12*w - 101]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-2, -2, 1, 1, -5, -1, -1, 7, 7, 3, 3, -8, -6, -6, -10, 5, 5, 12, 12, 4, 4, -6, -6, -16, -16, 18, 18, 9, 9, 1, 8, 8, -18, -18, 10, 10, 4, 4, -10, -6, -6, -2, -2, 19, 19, -8, -8, -23, -23, 10, 10, -28, -28, -2, -2, 4, 4, -30, 8, 8, -22, -22, 30, 30, -21, -21, -20, -20, -38, -17, -17, -26, -26, -5, -5, -15, -15, 2, 2, -30, -30, 20, 20, -18, -18, -11, -11, -11, -11, 35, 35, 12, 12, -27, -27, 23, 23, -8, -8, -16, -16, -8, -8, 0, 0, 40, 40, -22, -22, -16, -16, 18, 18, -25, -25, 7, 7, -7, -7, 37, 37, -42, -42, 2, 2, -36, -36, 50, 50, 4, 4, 12, 12, 20, 20, -32, -32, 53, 53, -38, -38, 22, 22, 25, 25, -58, 14, 14, 8, 8, -15, -15, 24, 24, -12, -12, -43, -43, -12, -12, 12, 12, 42, 42, -27, -27, 34, 34, 39, 39, -10, -10, 22, 22, -16, -16, -13, -13, 8, 8, -58, -58, -42, -42, -51, -51, -30, -30, 48, 48, 24, 24, -31, -31, -3, -3, -18, -18, -12, -12, -21, -21, 60, 60, -18, -18, -15, -15, 0, 0, -8, -8, 39, 39, 28, 28, 47, 47, 12, 12, 39, 39, 60, 60, -12, -12, 54, 54, 0, 0, 52, 52, -71, -71, 22, 22, 32, 32, 55, 55, -15, -15, -56, -56, -60, -60, -52, -52, -30, -30, 34, 34, -32, -32, 2, 2, 33, 33, -10, -10, -20, -20, 4, 4, -42, -42, 40, 40, -3, -3, -46, -46, -57, -57, 34, 34, -40, -40, 59, 59, -52, -52, 62, 62, 18, 18, -52, -52, -18, -18, 79, 79, -66, -66, -20, -20, -13, -13, -17, -17, 63, 63, 45, 45, -18, -18, 89, 89, 48, 48, -10, -10, 35, 35, -38, -38, -68, -68, 73, 73, -58, -58, -26, -26, -30, 4, 4, 78, 78, -70, -70, -48, -48, 4, 4, 38, 38, -57, -57, 59, 59, 10, 10, 67, 67, -37, -37, -57, -57, 3, 3, -36, -36, -75, -75, 62, 62, -22, -22, -31, -31, -82, -82, -50, -50, 14, 14, 72, 72, 34, 34, -98, -98, 20, 20, -58, -58, 14, 14, 39, 39, 38, 38, 38, 38, 39, 39, -16, -16, -17, -17, 87, 87, 30, 30, -68, -68, 50, 50, 48, 48, -20, -20, -42, -42, -70, -25, -25, -6, -6, -62, -62, -63, -63, -40, -40, 54, 54, -25, -25, -72, -72, -86, -86, 3, 3, 27, 27, 62, 62, 13, 13, -20, -20, 29, 29, 22, 22, 8, 8, 18, 18, -6, -6, -103, -103, 70, 70, 58, 58, -60, -60, -3, -3, -73, -73, 4, 4, 0, 0, -76, -76, -100, -100, -43, -43, -88, -88, -103, -103, 18, 18, 9, 9, 40, 40, 38, 38, -85, -85, -22, -22, 18, 18, 53, 53, -27, -27, 0, 0, -28, -28, -96, -96, 58, 58, -26, -26, 63, 63, 32, 32, 30, 30, 92, 92, 23, 23, 114, 114, -60, -60, -27, -27, 34, 34, -82, -82, 74, 74, -3, -3, 84, 84, 19, 19, 74, 74, 54, 54, 58, 58, 12, 12, 107, 107, -92, -92, 54, 54, 15, 15, 28, 28, 25, 25, -123, -123, 103, 103, -60, -60, 92, 92, 20, 20, 4, 4, 20, 20, -42, -42, 85, 85, 88, 88, 10, 10, -68, -68, 92, 92, 64, 64, 70, 70, -41, -41, -60, -60, -62, -62, -2, -2, 42, 42, 108, 108, 49, 49, 102, 102, -85, 5, 5, -12, -12, -10, -10, 112, 112, -112, -112, -36, -36, -8, -8, -52, -52, 18, 18, -81, -81, -80, -80, -73, -73, 114, 114, 25, 25, -96, -96, 129, 129, -48, -48, 8, 8, 110, 110, -36, -36, 105, 105, 77, 77, -76, -76, -132, -132, -88, -88, 72, 72, 93, 93, 5, 5, 30, 30, -76, -76, -48, -48, 98, 98, 100, 100, 44, 44, 119, 119, -38, -38, 54, 54, 15, 15, -133, -48, -48, 10, 10, -32, -32, 28, 28, 97, 97, -80, -80, -97, -97, -50, -50, 48, 48, -21, -21, -70, -70, 57, 57, -22, -22, -20, -20, 77, 77, 132, 132, -2, -2, 138, 138, 14, 14, -2, -2, -2, -2, 109, 109, -5, -5, -3, -3, -101, -101, 0, 0, 8, 8, -93, -93, 7, 7, 4, 4, -57, -57, -125, -125, 114, 114, 50, 50, 77, 77, -72, -72, -8, -8, -30, -30, 25, 25, 104, 104, 92, 92, 102, 102, -1, -1, -78, -78, -12, -12, -66, -66, -38, -38, 33, 33, -55, -55, -68, -68, -66, -66, 123, 123, 94, 94, -18, -18, 73, 73, 8, 8, -63, -63, 105, 105, -117, -117, -101, -101, -42, -42, 48, 48, -26, -26, 80, 80, -8, -8, -48, -48, -16, -16, 52, 52, -86, -86, 90, 90, -38, -38, -58, -47, -47, 19, 19, -30, -30, -53, -53, -132, -132, 89, 89, 38, 38, -86, -86, 60, 60, -146, -146, -22, -22, -28, -28, -37, -37, -55, -55, -91, -91, -3, -3, -80, -80, -98, -98, 130, 130, -93, -93, -50, -50, -50, -50, -122, -122, 4, 4, 40, 40, -83, -83, 102, 102, -91, -91, -120, -120, -91, -91, -88, -88, 29, 29, 7, 7, -132, -132, 65, 65, -127, -127, 64, 64, -96, -96, -88, -88, -72, -72, 130, 130, 62, 62, -128, -128, 142, 142, -98, -98, -126, -126, 120, 120, 23, 23, 164, 164, -62, -62, 24, 24, 15, 15, -145, -145, -105, -105, -142, -142, -6, -6, 78, 78, 162, 162, 38, 38, -57, -57, 59, 59, 138, 138, -7, -7, 72, 72, -68, -68, -150, -150, -88, -88, 103, 103, -142, -142, 78, 78, 30, 30, -87, -87, 24, 24, -45, -45, -2, -2, 64, 64, 40, 40, -56, -56, 22, 22, -130, -130, -70, -70, -17, -17, 50, 50, -51, -51, 48, 48, 92, 92, 19, 19, 28, 28, 55, 55, 90, 90, 14, 14, 60, 60, 17, 17, 88, 88, -6, -6, -122, -122, 47, 74, 74, -30, -30, -136, -136, -26, -26, 137, 137, 130, 130, -40, -40, -18, -18, -42, -42, -86, -86, 168, 168, 84, 84, -38, -38, 123, 123, -130, -130, 92, 92, -35, -35, -3, -3, 107, 107, 169, 169, -17, -17, 99, 99, -26, -26, -72, -72, -108, -108, 84, 84, 130, 130, 168, 168, 110, 110, -156, -156, -152, -152, -122, -122, 148, 148, 13, 13, -146, -146, 130, 130, -108, -108, -127, -127, -130, -130, -86, -86, -61, -61, 82, 82, -2, -2, -108, -108, 24, 24, 55, 55, 69, 69, 48, 48, 50, 50, 157, 157, 12, 12, -62, -62, -46, -46, -40, -40, 109, 109, 129, 129, 15, 15, -128, -128, 25, 25, -38, -38, 115, 115, 42, 42, 144, 144, 100, 100, 14, 14, -12, -12, 79, 79, 102, 102, -138, -138, 120, 120, -103, -103, -52, -52, -133, -133, 88, 88, -13, -13, 134, 134, -151, -151, -100, -100, -78, -78, 142, 142, 83, 83, -145, -78, -78, 32, 32, 65, 65, 62, 62, 184, 184, 8, 8, 114, 114, 60, 60, -108, -108, -38, -38, -78, -78, -36, -36, 27, 27, -140, -140, -118, -118, 24, 24, 138, 138, 178, 178, 110, 110, -178, -178, 49, 49, -170, -170, 18, 18, -18, -18, -108, -108, 144, 144, -102, -102, -45, -45, -128, -128, -81, -81, 102, 102, 49, 49, 57, 57, 43, 43, 4, 4] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([121, 11, -11])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]