/* 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([-15, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([75, 15, 5*w]) primes_array = [ [2, 2, w + 1],\ [3, 3, w],\ [5, 5, w],\ [7, 7, w + 1],\ [7, 7, w + 6],\ [11, 11, -w - 2],\ [11, 11, w - 2],\ [17, 17, w + 7],\ [17, 17, w + 10],\ [43, 43, w + 12],\ [43, 43, w + 31],\ [53, 53, w + 11],\ [53, 53, w + 42],\ [59, 59, 2*w - 1],\ [59, 59, -2*w - 1],\ [61, 61, 2*w - 11],\ [61, 61, -2*w - 11],\ [67, 67, w + 22],\ [67, 67, w + 45],\ [71, 71, 3*w - 8],\ [71, 71, -3*w - 8],\ [103, 103, w + 18],\ [103, 103, w + 85],\ [109, 109, 2*w - 13],\ [109, 109, -2*w - 13],\ [113, 113, w + 44],\ [113, 113, w + 69],\ [127, 127, w + 53],\ [127, 127, w + 74],\ [131, 131, 3*w - 2],\ [131, 131, -3*w - 2],\ [137, 137, w + 17],\ [137, 137, w + 120],\ [163, 163, w + 34],\ [163, 163, w + 129],\ [169, 13, -13],\ [173, 173, w + 19],\ [173, 173, w + 154],\ [179, 179, 5*w - 14],\ [179, 179, -5*w - 14],\ [181, 181, -w - 14],\ [181, 181, w - 14],\ [191, 191, 4*w - 7],\ [191, 191, -4*w - 7],\ [197, 197, w + 58],\ [197, 197, w + 139],\ [223, 223, w + 98],\ [223, 223, w + 125],\ [229, 229, 2*w - 17],\ [229, 229, -2*w - 17],\ [233, 233, w + 99],\ [233, 233, w + 134],\ [239, 239, -4*w - 1],\ [239, 239, 4*w - 1],\ [241, 241, -w - 16],\ [241, 241, w - 16],\ [251, 251, 6*w - 17],\ [251, 251, -6*w - 17],\ [257, 257, w + 23],\ [257, 257, w + 234],\ [283, 283, w + 79],\ [283, 283, w + 204],\ [293, 293, w + 111],\ [293, 293, w + 182],\ [307, 307, w + 130],\ [307, 307, w + 177],\ [311, 311, -5*w - 8],\ [311, 311, 5*w - 8],\ [317, 317, w + 40],\ [317, 317, w + 277],\ [349, 349, 3*w - 22],\ [349, 349, -3*w - 22],\ [353, 353, w + 108],\ [353, 353, w + 245],\ [359, 359, 5*w - 4],\ [359, 359, -5*w - 4],\ [361, 19, -19],\ [367, 367, w + 105],\ [367, 367, w + 262],\ [409, 409, 5*w - 28],\ [409, 409, -5*w - 28],\ [419, 419, 6*w - 11],\ [419, 419, -6*w - 11],\ [421, 421, 6*w - 31],\ [421, 421, -6*w - 31],\ [431, 431, 8*w - 23],\ [431, 431, -8*w - 23],\ [463, 463, w + 101],\ [463, 463, w + 362],\ [479, 479, 7*w - 16],\ [479, 479, -7*w - 16],\ [487, 487, w + 224],\ [487, 487, w + 263],\ [491, 491, -6*w - 7],\ [491, 491, 6*w - 7],\ [523, 523, w + 231],\ [523, 523, w + 292],\ [529, 23, -23],\ [541, 541, -3*w - 26],\ [541, 541, 3*w - 26],\ [547, 547, w + 62],\ [547, 547, w + 485],\ [557, 557, w + 153],\ [557, 557, w + 404],\ [593, 593, w + 269],\ [593, 593, w + 324],\ [599, 599, -8*w - 19],\ [599, 599, 8*w - 19],\ [601, 601, 4*w - 29],\ [601, 601, -4*w - 29],\ [607, 607, w + 135],\ [607, 607, w + 472],\ [617, 617, w + 218],\ [617, 617, w + 399],\ [643, 643, w + 119],\ [643, 643, w + 524],\ [653, 653, w + 253],\ [653, 653, w + 400],\ [659, 659, 10*w - 29],\ [659, 659, -10*w - 29],\ [661, 661, -w - 26],\ [661, 661, w - 26],\ [677, 677, w + 37],\ [677, 677, w + 640],\ [709, 709, -7*w - 38],\ [709, 709, 7*w - 38],\ [719, 719, -7*w - 4],\ [719, 719, 7*w - 4],\ [727, 727, w + 200],\ [727, 727, w + 527],\ [769, 769, -w - 28],\ [769, 769, w - 28],\ [773, 773, w + 244],\ [773, 773, w + 529],\ [787, 787, w + 184],\ [787, 787, w + 603],\ [797, 797, w + 183],\ [797, 797, w + 614],\ [823, 823, w + 76],\ [823, 823, w + 747],\ [829, 829, 6*w - 37],\ [829, 829, -6*w - 37],\ [839, 839, -8*w - 11],\ [839, 839, 8*w - 11],\ [841, 29, -29],\ [857, 857, w + 300],\ [857, 857, w + 557],\ [883, 883, w + 402],\ [883, 883, w + 481],\ [907, 907, w + 165],\ [907, 907, w + 742],\ [911, 911, 8*w - 7],\ [911, 911, -8*w - 7],\ [953, 953, w + 341],\ [953, 953, w + 612],\ [961, 31, -31],\ [967, 967, w + 54],\ [967, 967, w + 913],\ [971, 971, 10*w - 23],\ [971, 971, -10*w - 23],\ [977, 977, w + 70],\ [977, 977, w + 907],\ [1009, 1009, -w - 32],\ [1009, 1009, w - 32],\ [1013, 1013, w + 415],\ [1013, 1013, w + 598],\ [1019, 1019, -9*w - 14],\ [1019, 1019, 9*w - 14],\ [1021, 1021, 3*w - 34],\ [1021, 1021, -3*w - 34],\ [1031, 1031, -11*w - 28],\ [1031, 1031, 11*w - 28],\ [1063, 1063, w + 503],\ [1063, 1063, w + 560],\ [1069, 1069, 5*w - 38],\ [1069, 1069, -5*w - 38],\ [1087, 1087, w + 333],\ [1087, 1087, w + 754],\ [1091, 1091, 13*w - 38],\ [1091, 1091, -13*w - 38],\ [1097, 1097, w + 47],\ [1097, 1097, w + 1050],\ [1123, 1123, w + 517],\ [1123, 1123, w + 606],\ [1129, 1129, 4*w - 37],\ [1129, 1129, -4*w - 37],\ [1151, 1151, 9*w - 8],\ [1151, 1151, -9*w - 8],\ [1193, 1193, w + 49],\ [1193, 1193, w + 1144],\ [1201, 1201, -7*w - 44],\ [1201, 1201, 7*w - 44],\ [1217, 1217, w + 254],\ [1217, 1217, w + 963],\ [1249, 1249, -8*w - 47],\ [1249, 1249, 8*w - 47],\ [1259, 1259, 14*w - 41],\ [1259, 1259, -14*w - 41],\ [1277, 1277, w + 80],\ [1277, 1277, w + 1197],\ [1303, 1303, w + 620],\ [1303, 1303, w + 683],\ [1319, 1319, -12*w - 29],\ [1319, 1319, 12*w - 29],\ [1321, 1321, 11*w - 56],\ [1321, 1321, -11*w - 56],\ [1327, 1327, w + 544],\ [1327, 1327, w + 783],\ [1369, 37, -37],\ [1373, 1373, w + 580],\ [1373, 1373, w + 793],\ [1381, 1381, 7*w - 46],\ [1381, 1381, -7*w - 46],\ [1423, 1423, w + 381],\ [1423, 1423, w + 1042],\ [1429, 1429, -w - 38],\ [1429, 1429, w - 38],\ [1433, 1433, w + 674],\ [1433, 1433, w + 759],\ [1439, 1439, 15*w - 44],\ [1439, 1439, -15*w - 44],\ [1447, 1447, w + 66],\ [1447, 1447, w + 1381],\ [1451, 1451, -10*w - 7],\ [1451, 1451, 10*w - 7],\ [1483, 1483, w + 434],\ [1483, 1483, w + 1049],\ [1489, 1489, 9*w - 52],\ [1489, 1489, -9*w - 52],\ [1493, 1493, w + 222],\ [1493, 1493, w + 1271],\ [1499, 1499, -10*w - 1],\ [1499, 1499, 10*w - 1],\ [1511, 1511, 13*w - 32],\ [1511, 1511, -13*w - 32],\ [1543, 1543, w + 104],\ [1543, 1543, w + 1439],\ [1549, 1549, 11*w - 58],\ [1549, 1549, -11*w - 58],\ [1553, 1553, w + 633],\ [1553, 1553, w + 920],\ [1559, 1559, 11*w - 16],\ [1559, 1559, -11*w - 16],\ [1567, 1567, w + 749],\ [1567, 1567, w + 818],\ [1571, 1571, 14*w - 37],\ [1571, 1571, -14*w - 37],\ [1609, 1609, -4*w - 43],\ [1609, 1609, 4*w - 43],\ [1613, 1613, w + 593],\ [1613, 1613, w + 1020],\ [1619, 1619, -11*w - 14],\ [1619, 1619, 11*w - 14],\ [1621, 1621, 2*w - 41],\ [1621, 1621, -2*w - 41],\ [1627, 1627, w + 760],\ [1627, 1627, w + 867],\ [1637, 1637, w + 735],\ [1637, 1637, w + 902],\ [1663, 1663, w + 443],\ [1663, 1663, w + 1220],\ [1669, 1669, -6*w - 47],\ [1669, 1669, 6*w - 47],\ [1681, 41, -41],\ [1697, 1697, w + 267],\ [1697, 1697, w + 1430],\ [1723, 1723, w + 72],\ [1723, 1723, w + 1651],\ [1733, 1733, w + 59],\ [1733, 1733, w + 1674],\ [1741, 1741, 5*w - 46],\ [1741, 1741, -5*w - 46],\ [1747, 1747, w + 310],\ [1747, 1747, w + 1437],\ [1783, 1783, w + 753],\ [1783, 1783, w + 1030],\ [1789, 1789, 2*w - 43],\ [1789, 1789, -2*w - 43],\ [1801, 1801, -3*w - 44],\ [1801, 1801, 3*w - 44],\ [1811, 1811, 11*w - 2],\ [1811, 1811, -11*w - 2],\ [1861, 1861, 6*w - 49],\ [1861, 1861, -6*w - 49],\ [1867, 1867, w + 690],\ [1867, 1867, w + 1177],\ [1871, 1871, -12*w - 17],\ [1871, 1871, 12*w - 17],\ [1877, 1877, w + 814],\ [1877, 1877, w + 1063],\ [1913, 1913, w + 433],\ [1913, 1913, w + 1480],\ [1931, 1931, -15*w - 38],\ [1931, 1931, 15*w - 38],\ [1973, 1973, w + 691],\ [1973, 1973, w + 1282],\ [1979, 1979, -14*w - 31],\ [1979, 1979, 14*w - 31],\ [1987, 1987, w + 118],\ [1987, 1987, w + 1869],\ [1997, 1997, w + 100],\ [1997, 1997, w + 1897],\ [2029, 2029, -11*w - 62],\ [2029, 2029, 11*w - 62],\ [2039, 2039, 12*w - 11],\ [2039, 2039, -12*w - 11],\ [2083, 2083, w + 981],\ [2083, 2083, w + 1102],\ [2089, 2089, -13*w - 68],\ [2089, 2089, 13*w - 68],\ [2099, 2099, -14*w - 29],\ [2099, 2099, 14*w - 29],\ [2111, 2111, 12*w - 7],\ [2111, 2111, -12*w - 7],\ [2143, 2143, w + 882],\ [2143, 2143, w + 1261],\ [2153, 2153, w + 605],\ [2153, 2153, w + 1548],\ [2161, 2161, 4*w - 49],\ [2161, 2161, -4*w - 49],\ [2203, 2203, w + 837],\ [2203, 2203, w + 1366],\ [2209, 47, -47],\ [2213, 2213, w + 194],\ [2213, 2213, w + 2019],\ [2221, 2221, 10*w - 61],\ [2221, 2221, -10*w - 61],\ [2237, 2237, w + 67],\ [2237, 2237, w + 2170],\ [2269, 2269, -6*w - 53],\ [2269, 2269, 6*w - 53],\ [2273, 2273, w + 309],\ [2273, 2273, w + 1964],\ [2281, 2281, 11*w - 64],\ [2281, 2281, -11*w - 64],\ [2287, 2287, w + 483],\ [2287, 2287, w + 1804],\ [2297, 2297, w + 974],\ [2297, 2297, w + 1323],\ [2333, 2333, w + 919],\ [2333, 2333, w + 1414],\ [2339, 2339, -13*w - 14],\ [2339, 2339, 13*w - 14],\ [2341, 2341, 2*w - 49],\ [2341, 2341, -2*w - 49],\ [2347, 2347, w + 84],\ [2347, 2347, w + 2263],\ [2351, 2351, 15*w - 32],\ [2351, 2351, -15*w - 32],\ [2357, 2357, w + 1039],\ [2357, 2357, w + 1318],\ [2383, 2383, w + 229],\ [2383, 2383, w + 2154],\ [2389, 2389, 14*w - 73],\ [2389, 2389, -14*w - 73],\ [2393, 2393, w + 761],\ [2393, 2393, w + 1632],\ [2399, 2399, 17*w - 44],\ [2399, 2399, -17*w - 44],\ [2411, 2411, 14*w - 23],\ [2411, 2411, -14*w - 23],\ [2417, 2417, w + 110],\ [2417, 2417, w + 2307],\ [2459, 2459, -18*w - 49],\ [2459, 2459, 18*w - 49],\ [2467, 2467, w + 233],\ [2467, 2467, w + 2234],\ [2477, 2477, w + 510],\ [2477, 2477, w + 1967],\ [2503, 2503, w + 1208],\ [2503, 2503, w + 1295],\ [2521, 2521, 8*w - 59],\ [2521, 2521, -8*w - 59],\ [2531, 2531, 13*w - 2],\ [2531, 2531, -13*w - 2],\ [2579, 2579, -14*w - 19],\ [2579, 2579, 14*w - 19],\ [2591, 2591, -15*w - 28],\ [2591, 2591, 15*w - 28],\ [2633, 2633, w + 1259],\ [2633, 2633, w + 1374],\ [2647, 2647, w + 696],\ [2647, 2647, w + 1951],\ [2657, 2657, w + 73],\ [2657, 2657, w + 2584],\ [2683, 2683, w + 424],\ [2683, 2683, w + 2259],\ [2689, 2689, -w - 52],\ [2689, 2689, w - 52],\ [2693, 2693, w + 214],\ [2693, 2693, w + 2479],\ [2699, 2699, 15*w - 26],\ [2699, 2699, -15*w - 26],\ [2707, 2707, w + 285],\ [2707, 2707, w + 2422],\ [2711, 2711, 19*w - 52],\ [2711, 2711, -19*w - 52],\ [2749, 2749, 2*w - 53],\ [2749, 2749, -2*w - 53],\ [2753, 2753, w + 382],\ [2753, 2753, w + 2371],\ [2767, 2767, w + 840],\ [2767, 2767, w + 1927],\ [2777, 2777, w + 540],\ [2777, 2777, w + 2237],\ [2803, 2803, w + 724],\ [2803, 2803, w + 2079],\ [2819, 2819, 14*w - 11],\ [2819, 2819, -14*w - 11],\ [2837, 2837, w + 306],\ [2837, 2837, w + 2531],\ [2879, 2879, 16*w - 31],\ [2879, 2879, -16*w - 31],\ [2887, 2887, w + 686],\ [2887, 2887, w + 2201],\ [2897, 2897, w + 940],\ [2897, 2897, w + 1957],\ [2939, 2939, -14*w - 1],\ [2939, 2939, 14*w - 1],\ [2957, 2957, w + 77],\ [2957, 2957, w + 2880],\ [2999, 2999, -16*w - 29],\ [2999, 2999, 16*w - 29],\ [3001, 3001, -3*w - 56],\ [3001, 3001, 3*w - 56],\ [3011, 3011, 18*w - 43],\ [3011, 3011, -18*w - 43],\ [3049, 3049, -16*w - 83],\ [3049, 3049, 16*w - 83],\ [3061, 3061, 17*w - 86],\ [3061, 3061, -17*w - 86],\ [3067, 3067, w + 96],\ [3067, 3067, w + 2971],\ [3109, 3109, -7*w - 62],\ [3109, 3109, 7*w - 62],\ [3119, 3119, -15*w - 16],\ [3119, 3119, 15*w - 16],\ [3121, 3121, -w - 56],\ [3121, 3121, w - 56],\ [3137, 3137, w + 363],\ [3137, 3137, w + 2774],\ [3163, 3163, w + 1507],\ [3163, 3163, w + 1656],\ [3169, 3169, 12*w - 73],\ [3169, 3169, -12*w - 73],\ [3181, 3181, 6*w - 61],\ [3181, 3181, -6*w - 61],\ [3187, 3187, w + 772],\ [3187, 3187, w + 2415],\ [3191, 3191, 20*w - 53],\ [3191, 3191, -20*w - 53],\ [3229, 3229, 3*w - 58],\ [3229, 3229, -3*w - 58],\ [3251, 3251, -21*w - 58],\ [3251, 3251, 21*w - 58],\ [3257, 3257, w + 668],\ [3257, 3257, w + 2589],\ [3299, 3299, 19*w - 46],\ [3299, 3299, -19*w - 46],\ [3301, 3301, -14*w - 79],\ [3301, 3301, 14*w - 79],\ [3307, 3307, w + 315],\ [3307, 3307, w + 2992],\ [3343, 3343, w + 689],\ [3343, 3343, w + 2654],\ [3359, 3359, -15*w - 4],\ [3359, 3359, 15*w - 4],\ [3361, 3361, 7*w - 64],\ [3361, 3361, -7*w - 64],\ [3371, 3371, 15*w - 2],\ [3371, 3371, -15*w - 2],\ [3413, 3413, w + 1586],\ [3413, 3413, w + 1827],\ [3463, 3463, w + 102],\ [3463, 3463, w + 3361],\ [3469, 3469, -5*w - 62],\ [3469, 3469, 5*w - 62],\ [3491, 3491, -18*w - 37],\ [3491, 3491, 18*w - 37],\ [3529, 3529, 8*w - 67],\ [3529, 3529, -8*w - 67],\ [3533, 3533, w + 775],\ [3533, 3533, w + 2758],\ [3539, 3539, 22*w - 61],\ [3539, 3539, -22*w - 61],\ [3541, 3541, 10*w - 71],\ [3541, 3541, -10*w - 71],\ [3547, 3547, w + 1235],\ [3547, 3547, w + 2312],\ [3557, 3557, w + 634],\ [3557, 3557, w + 2923],\ [3583, 3583, w + 1288],\ [3583, 3583, w + 2295],\ [3593, 3593, w + 526],\ [3593, 3593, w + 3067],\ [3607, 3607, w + 1071],\ [3607, 3607, w + 2536],\ [3617, 3617, w + 248],\ [3617, 3617, w + 3369],\ [3643, 3643, w + 505],\ [3643, 3643, w + 3138],\ [3659, 3659, -17*w - 26],\ [3659, 3659, 17*w - 26],\ [3671, 3671, -16*w - 13],\ [3671, 3671, 16*w - 13],\ [3677, 3677, w + 393],\ [3677, 3677, w + 3284],\ [3709, 3709, -3*w - 62],\ [3709, 3709, 3*w - 62],\ [3719, 3719, -16*w - 11],\ [3719, 3719, 16*w - 11],\ [3727, 3727, w + 688],\ [3727, 3727, w + 3039],\ [3769, 3769, 12*w - 77],\ [3769, 3769, -12*w - 77],\ [3779, 3779, -22*w - 59],\ [3779, 3779, 22*w - 59],\ [3797, 3797, w + 354],\ [3797, 3797, w + 3443],\ [3823, 3823, w + 1329],\ [3823, 3823, w + 2494],\ [3833, 3833, w + 1482],\ [3833, 3833, w + 2351],\ [3847, 3847, w + 460],\ [3847, 3847, w + 3387],\ [3851, 3851, -17*w - 22],\ [3851, 3851, 17*w - 22],\ [3889, 3889, 7*w - 68],\ [3889, 3889, -7*w - 68],\ [3907, 3907, w + 679],\ [3907, 3907, w + 3228],\ [3911, 3911, 21*w - 52],\ [3911, 3911, -21*w - 52],\ [3917, 3917, w + 140],\ [3917, 3917, w + 3777],\ [3943, 3943, w + 514],\ [3943, 3943, w + 3429],\ [3967, 3967, w + 345],\ [3967, 3967, w + 3622],\ [4003, 4003, w + 639],\ [4003, 4003, w + 3364],\ [4013, 4013, w + 1523],\ [4013, 4013, w + 2490],\ [4019, 4019, -18*w - 29],\ [4019, 4019, 18*w - 29],\ [4021, 4021, -15*w - 86],\ [4021, 4021, 15*w - 86],\ [4027, 4027, w + 979],\ [4027, 4027, w + 3048],\ [4073, 4073, w + 1388],\ [4073, 4073, w + 2685],\ [4079, 4079, 17*w - 16],\ [4079, 4079, -17*w - 16],\ [4091, 4091, 23*w - 62],\ [4091, 4091, -23*w - 62],\ [4129, 4129, 17*w - 92],\ [4129, 4129, -17*w - 92],\ [4133, 4133, w + 91],\ [4133, 4133, w + 4042],\ [4139, 4139, 17*w - 14],\ [4139, 4139, -17*w - 14],\ [4157, 4157, w + 1003],\ [4157, 4157, w + 3154],\ [4201, 4201, 20*w - 101],\ [4201, 4201, -20*w - 101],\ [4211, 4211, 26*w - 77],\ [4211, 4211, -26*w - 77],\ [4217, 4217, w + 1495],\ [4217, 4217, w + 2722],\ [4243, 4243, w + 545],\ [4243, 4243, w + 3698],\ [4253, 4253, w + 1992],\ [4253, 4253, w + 2261],\ [4259, 4259, 19*w - 34],\ [4259, 4259, -19*w - 34],\ [4261, 4261, -9*w - 74],\ [4261, 4261, 9*w - 74],\ [4271, 4271, 17*w - 8],\ [4271, 4271, -17*w - 8],\ [4327, 4327, w + 114],\ [4327, 4327, w + 4213],\ [4337, 4337, w + 1253],\ [4337, 4337, w + 3084],\ [4363, 4363, w + 1291],\ [4363, 4363, w + 3072],\ [4373, 4373, w + 1835],\ [4373, 4373, w + 2538],\ [4391, 4391, -19*w - 32],\ [4391, 4391, 19*w - 32],\ [4397, 4397, w + 2008],\ [4397, 4397, w + 2389],\ [4423, 4423, w + 176],\ [4423, 4423, w + 4247],\ [4441, 4441, 16*w - 91],\ [4441, 4441, -16*w - 91],\ [4447, 4447, w + 1378],\ [4447, 4447, w + 3069],\ [4451, 4451, -22*w - 53],\ [4451, 4451, 22*w - 53],\ [4457, 4457, w + 1706],\ [4457, 4457, w + 2751],\ [4483, 4483, w + 1150],\ [4483, 4483, w + 3333],\ [4493, 4493, w + 488],\ [4493, 4493, w + 4005],\ [4507, 4507, w + 1443],\ [4507, 4507, w + 3064],\ [4517, 4517, w + 884],\ [4517, 4517, w + 3633],\ [4549, 4549, -18*w - 97],\ [4549, 4549, 18*w - 97],\ [4561, 4561, -9*w - 76],\ [4561, 4561, 9*w - 76],\ [4567, 4567, w + 317],\ [4567, 4567, w + 4250],\ [4603, 4603, w + 737],\ [4603, 4603, w + 3866],\ [4621, 4621, 21*w - 106],\ [4621, 4621, -21*w - 106],\ [4637, 4637, w + 1578],\ [4637, 4637, w + 3059],\ [4663, 4663, w + 2052],\ [4663, 4663, w + 2611],\ [4673, 4673, w + 1070],\ [4673, 4673, w + 3603],\ [4679, 4679, 21*w - 44],\ [4679, 4679, -21*w - 44],\ [4691, 4691, -18*w - 13],\ [4691, 4691, 18*w - 13],\ [4723, 4723, w + 575],\ [4723, 4723, w + 4148],\ [4729, 4729, -12*w - 83],\ [4729, 4729, 12*w - 83],\ [4733, 4733, w + 2014],\ [4733, 4733, w + 2719],\ [4751, 4751, -25*w - 68],\ [4751, 4751, 25*w - 68],\ [4783, 4783, w + 1950],\ [4783, 4783, w + 2833],\ [4789, 4789, 6*w - 73],\ [4789, 4789, -6*w - 73],\ [4793, 4793, w + 2319],\ [4793, 4793, w + 2474],\ [4799, 4799, -23*w - 56],\ [4799, 4799, 23*w - 56],\ [4801, 4801, -4*w - 71],\ [4801, 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[8923, 8923, w + 1529],\ [8923, 8923, w + 7394],\ [8929, 8929, 16*w - 113],\ [8929, 8929, -16*w - 113],\ [8933, 8933, w + 4195],\ [8933, 8933, w + 4738],\ [8941, 8941, -14*w - 109],\ [8941, 8941, 14*w - 109],\ [8951, 8951, -28*w - 53],\ [8951, 8951, 28*w - 53],\ [8999, 8999, -27*w - 44],\ [8999, 8999, 27*w - 44],\ [9001, 9001, -11*w - 104],\ [9001, 9001, 11*w - 104],\ [9007, 9007, w + 3346],\ [9007, 9007, w + 5661],\ [9011, 9011, -30*w - 67],\ [9011, 9011, 30*w - 67],\ [9043, 9043, w + 1033],\ [9043, 9043, w + 8010],\ [9049, 9049, -24*w - 133],\ [9049, 9049, 24*w - 133],\ [9059, 9059, -34*w - 91],\ [9059, 9059, 34*w - 91],\ [9067, 9067, w + 1469],\ [9067, 9067, w + 7598],\ [9103, 9103, w + 4161],\ [9103, 9103, w + 4942],\ [9109, 9109, -10*w - 103],\ [9109, 9109, 10*w - 103],\ [9127, 9127, w + 782],\ [9127, 9127, w + 8345],\ [9137, 9137, w + 1487],\ [9137, 9137, w + 7650],\ [9173, 9173, w + 3545],\ [9173, 9173, w + 5628],\ [9181, 9181, 26*w - 139],\ [9181, 9181, -26*w - 139],\ [9187, 9187, w + 525],\ [9187, 9187, w + 8662],\ [9239, 9239, -36*w - 101],\ [9239, 9239, 36*w - 101],\ [9241, 9241, -8*w - 101],\ [9241, 9241, 8*w - 101],\ [9257, 9257, w + 2215],\ [9257, 9257, w + 7042],\ [9283, 9283, w + 1823],\ [9283, 9283, w + 7460],\ [9293, 9293, w + 2675],\ [9293, 9293, w + 6618],\ [9311, 9311, 25*w - 8],\ [9311, 9311, -25*w - 8],\ [9343, 9343, w + 3029],\ [9343, 9343, w + 6314],\ [9349, 9349, 2*w - 97],\ [9349, 9349, -2*w - 97],\ [9371, 9371, 25*w - 2],\ [9371, 9371, -25*w - 2],\ [9377, 9377, w + 137],\ [9377, 9377, w + 9240],\ [9403, 9403, w + 168],\ [9403, 9403, w + 9235],\ [9409, 97, -97],\ [9413, 9413, w + 1265],\ [9413, 9413, w + 8148],\ [9419, 9419, -34*w - 89],\ [9419, 9419, 34*w - 89],\ [9421, 9421, -11*w - 106],\ [9421, 9421, 11*w - 106],\ [9431, 9431, -32*w - 77],\ [9431, 9431, 32*w - 77],\ [9437, 9437, w + 1073],\ [9437, 9437, w + 8364],\ [9463, 9463, w + 3367],\ [9463, 9463, w + 6096],\ [9473, 9473, w + 3817],\ [9473, 9473, w + 5656],\ [9479, 9479, -29*w - 56],\ [9479, 9479, 29*w - 56],\ [9491, 9491, -27*w - 38],\ [9491, 9491, 27*w - 38],\ [9497, 9497, w + 3511],\ [9497, 9497, w + 5986],\ [9533, 9533, w + 4117],\ [9533, 9533, w + 5416],\ [9539, 9539, 35*w - 94],\ [9539, 9539, -35*w - 94],\ [9547, 9547, w + 1712],\ [9547, 9547, w + 7835],\ [9551, 9551, -28*w - 47],\ [9551, 9551, 28*w - 47],\ [9601, 9601, 9*w - 104],\ [9601, 9601, -9*w - 104],\ [9643, 9643, w + 3765],\ [9643, 9643, w + 5878],\ [9649, 9649, -8*w - 103],\ [9649, 9649, 8*w - 103],\ [9661, 9661, -6*w - 101],\ [9661, 9661, 6*w - 101],\ [9677, 9677, w + 220],\ [9677, 9677, w + 9457],\ [9719, 9719, 37*w - 104],\ [9719, 9719, -37*w - 104],\ [9721, 9721, 12*w - 109],\ [9721, 9721, -12*w - 109],\ [9769, 9769, -21*w - 128],\ [9769, 9769, 21*w - 128],\ [9781, 9781, 18*w - 121],\ [9781, 9781, -18*w - 121],\ [9787, 9787, w + 3175],\ [9787, 9787, w + 6612],\ [9791, 9791, 31*w - 68],\ [9791, 9791, -31*w - 68],\ [9829, 9829, 14*w - 113],\ [9829, 9829, -14*w - 113],\ [9833, 9833, w + 3037],\ [9833, 9833, w + 6796],\ [9839, 9839, 40*w - 119],\ [9839, 9839, -40*w - 119],\ [9851, 9851, 26*w - 17],\ [9851, 9851, -26*w - 17],\ [9857, 9857, w + 4204],\ [9857, 9857, w + 5653],\ [9883, 9883, w + 3077],\ [9883, 9883, w + 6806],\ [9901, 9901, -22*w - 131],\ [9901, 9901, 22*w - 131],\ [9907, 9907, w + 3458],\ [9907, 9907, w + 6449],\ [9949, 9949, 10*w - 107],\ [9949, 9949, -10*w - 107],\ [9967, 9967, w + 3952],\ [9967, 9967, w + 6015]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-2, -1, 0, -3, -3, -2, -2, -2, -2, 1, 1, 4, 4, 10, 10, 7, 7, -3, -3, 8, 8, -4, -4, 5, 5, 4, 4, -8, -8, -12, -12, 18, 18, 11, 11, -25, -6, -6, 10, 10, 17, 17, -22, -22, 18, 18, -19, -19, -15, -15, 24, 24, -20, -20, -23, -23, -12, -12, -12, -12, -9, -9, -6, -6, 7, 7, 18, 18, 8, 8, 10, 10, -6, -6, 0, 0, -13, 27, 27, 5, 5, 20, 20, 22, 22, 18, 18, -24, -24, -30, -30, -13, -13, 8, 8, 31, 31, -10, -3, -3, -8, -8, -42, -42, -16, -16, 20, 20, -13, -13, -8, -8, -12, -12, 36, 36, 14, 14, 40, 40, -38, -38, -42, -42, 25, 25, -30, -30, -43, -43, 35, 35, 24, 24, 7, 7, -52, -52, 41, 41, -30, -30, -10, -10, 42, 28, 28, 41, 41, 12, 12, 58, 58, -56, -56, -53, 32, 32, -42, -42, -2, -2, 5, 5, 14, 14, 30, 30, -53, -53, 18, 18, -19, -19, -5, -5, 17, 17, 8, 8, 38, 38, -29, -29, 5, 5, -2, -2, -46, -46, 22, 22, -42, -42, 10, 10, -60, -60, -42, -42, -39, -39, 30, 30, -58, -58, 37, 37, -70, -6, -6, 37, 37, 16, 16, 35, 35, 54, 54, -10, -10, -53, -53, -42, -42, -4, -4, -30, -30, 44, 44, 30, 30, -12, -12, -29, -29, 15, 15, -6, -6, 10, 10, -73, -73, -2, -2, 45, 45, 14, 14, 60, 60, 37, 37, -28, -28, -12, -12, 1, 1, -10, -10, -18, -42, -42, -4, -4, -26, -26, -13, -13, -8, -8, 41, 41, 75, 75, -33, -33, 48, 48, -33, -33, -33, -33, 78, 78, 48, 48, 84, 84, -72, -72, 24, 24, 30, 30, -28, -28, 28, 28, 5, 5, -60, -60, -19, -19, 25, 25, 30, 30, -12, -12, 61, 61, -66, -66, -38, -38, -29, -29, -90, -56, -56, -3, -3, -62, -62, -25, -25, 44, 44, -43, -43, -48, -48, 8, 8, -86, -86, -30, -30, 77, 77, -53, -53, -12, -12, 68, 68, -89, -89, -45, -45, -6, -6, -40, -40, 78, 78, -42, -42, -80, -80, 92, 92, -72, -72, -84, -84, 47, 47, -12, -12, -80, -80, -42, -42, -6, -6, -8, -8, 8, 8, 36, 36, 45, 45, 64, 64, -20, -20, 77, 77, -2, -2, 10, 10, -36, -36, 67, 67, 68, 68, -69, -69, -60, -60, -12, -12, -10, -10, 67, 67, -72, -72, 70, 70, -32, -32, -50, -50, -23, -23, 68, 68, -10, -10, -58, -58, -73, -73, 10, 10, 90, 90, 17, 17, 38, 38, -19, -19, 15, 15, -23, -23, -28, -28, -92, -92, -50, -50, 48, 48, 18, 18, 0, 0, -13, -13, -83, -83, 61, 61, 0, 0, -83, -83, 48, 48, 64, 64, 91, 91, 65, 65, -72, -72, -5, -5, 84, 84, 20, 20, 82, 82, 117, 117, 28, 28, 56, 56, 14, 14, 7, 7, -92, -92, 71, 71, -60, -60, 88, 88, -52, -52, 35, 35, 30, 30, -73, -73, 95, 95, -70, -70, -22, -22, -64, -64, -36, -36, 77, 77, 48, 48, -65, -65, 77, 77, -92, -92, -2, -2, -99, -99, 37, 37, 1, 1, 64, 64, -110, -110, 22, 22, -123, -123, -56, -56, 60, 60, 48, 48, -85, -85, -66, -66, 90, 90, 18, 18, 77, 77, -42, -42, -12, -12, -89, -89, -56, -56, -120, -120, 7, 7, 8, 8, 97, 97, 68, 68, 71, 71, 4, 4, 108, 108, 78, 78, -39, -39, -33, -33, -83, -83, 18, 18, 18, 18, -64, -64, 54, 54, -28, -28, 18, 18, -110, -110, 47, 47, -103, -103, 51, 51, -53, -53, -52, -52, -64, -64, -76, -76, -110, -110, -42, -42, -79, -79, -115, -115, -126, -126, 98, 98, -49, -49, -70, -70, -36, -36, -30, -30, 2, 2, -32, -32, 17, 17, -22, -22, 38, 38, 56, 56, 70, 70, 30, 30, -22, -22, 108, 108, -10, -10, 104, 104, 27, 27, -64, -64, -30, -30, -112, -112, 140, 140, 82, 82, -63, -63, -6, -6, 17, 17, -32, -32, 35, 35, -73, -73, -52, -52, -62, -62, -126, -126, 120, 120, 107, 107, 118, 118, -49, -49, 50, 14, 14, 87, 87, 98, 98, 114, 114, 0, 0, -8, -8, -42, -42, 96, 96, -45, -45, -12, -12, 128, 128, 121, 121, 90, 90, -73, -73, -53, -53, -132, -132, -79, -79, -55, -55, -76, -76, 87, 87, -92, -92, 11, 11, -10, -10, 42, 42, 72, 72, -22, -22, -102, -102, -19, -19, 50, 50, 84, 84, 37, 37, 98, 98, 68, 68, -59, -59, 105, 105, 144, 144, 137, 137, -133, -133, -35, -35, 50, 50, 57, 57, 78, 78, 21, 21, 30, 30, 107, 107, 138, 138, 31, 31, 84, 84, -33, -33, 114, 114, -23, -23, -12, -12, 116, 116, -96, -96, -2, -2, 90, 90, -158, -73, -73, 38, 38, -90, -90, -23, -23, -62, -62, 48, 48, 101, 101, 14, 14, -130, -130, -23, -23, 107, 107, 22, 22, 32, 32, -75, -75, -126, -126, 82, 82, -42, -42, -90, -90, 12, 12, 58, 58, -30, -30, -128, -128, -76, -76, 60, 60, 97, 97, 31, 31, -5, -5, 20, 20, 38, 38, -84, -84, -60, -60, -3, -3, -72, -72, -29, -29, 155, 155, -6, -6, -83, -83, -22, -22, -99, -99, -130, 100, 100, -28, -28, -72, -72, -132, -132, 105, 105, -120, -120, 17, 17, -43, -43, -82, -82, -2, -2, -66, -66, -50, -50, 112, 112, -15, -15, -110, -110, 130, 130, 88, 88, 24, 24, 107, 107, -12, -12, -59, -59, -126, -126, 55, 55, -33, -33, -32, -32, -65, -65, 114, 114, -102, -102, -132, -132, 65, 65, 0, 0, -93, -93, 28, 28, -150, -150, -100, -100, -83, -83, -32, -32, 156, 156, 62, 62, 70, 70, -36, -36, -33, -33, -43, -43, -2, -2, -44, -44, 62, 62, 48, 48, 110, 110, 34, 34, -12, -12, 44, 44, 47, 47, -102, -102, -90, -90, -178, -3, -3, -2, -2, 61, 61, 50, 50, -130, -130, -86, -86, -73, -73, -82, -82, 48, 48, 17, 17, -28, -28, -122, -122, -5, -5, -120, -120, -158, -158, 138, 138, 28, 28, -29, -29, 115, 115, -126, -126, 17, 17, 88, 88, -112, -112, 165, 165, 35, 35, 131, 131, -118, -118, -153, -153, 144, 144, -18, -18, -68, -68, -2, -2, 41, 41, -66, -66, 82, 82, -132, -132, -149, -149, -70, -70, 7, 7, 37, 37, 125, 125, -16, -16, 10, 10, 77, 77, 144, 144, 157, 157, -164, -164, 30, 30, -113, -113, 168, 168, 18, 18, -29, -29, -43, -43, -84, -84, -125, -125, -46, -46, -118, -118, -42, -42, -100, -100, 57, 57, -88, -88, 138, 138, -139, -139, -155, -155, -40, -40, -73, -73, -39, -39, 55, 55, -68, -68, 8, 8, 164, 164, 122, 122, 17, 17, 30, 30, -33, -33, 8, 8, 116, 116, 54, 54, -152, -152, -119, -119, 150, 150, -22, -22, 188, 188, 56, 56, 95, -36, -36, -60, -60, 97, 97, 68, 68, -82, -82, 176, 176, -86, -86, 0, 0, 168, 168, 38, 38, -66, -66, 120, 120, 67, 67, 18, 18, 47, 47, 121, 121, 45, 45, 37, 37, 158, 158, -40, -40, 157, 157, 5, 5, -113, -113, -173, -173, 68, 68, -155, -155, -126, -126, -80, -80, -2, -2, 8, 8, -149, -149, -98, -98, 47, 47, -85, -85, 17, 17] 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])] = 1 AL_eigenvalues[ZF.ideal([5, 5, w])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]