/* 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, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([196, 14, -14]) primes_array = [ [3, 3, -w - 3],\ [3, 3, -w + 4],\ [4, 2, 2],\ [5, 5, w - 5],\ [5, 5, -w - 4],\ [13, 13, -w - 1],\ [13, 13, w - 2],\ [19, 19, 3*w - 14],\ [19, 19, -3*w - 11],\ [41, 41, -w - 7],\ [41, 41, w - 8],\ [47, 47, 3*w - 11],\ [47, 47, -3*w - 8],\ [49, 7, -7],\ [61, 61, 2*w - 1],\ [73, 73, -3*w + 16],\ [73, 73, 3*w + 13],\ [83, 83, 2*w - 13],\ [83, 83, -2*w - 11],\ [97, 97, 7*w + 22],\ [97, 97, 7*w - 29],\ [103, 103, -3*w - 14],\ [103, 103, 3*w - 17],\ [107, 107, -3*w - 4],\ [107, 107, 3*w - 7],\ [109, 109, 5*w - 19],\ [109, 109, 5*w + 14],\ [113, 113, 9*w - 38],\ [113, 113, 9*w + 29],\ [121, 11, -11],\ [127, 127, -6*w - 23],\ [127, 127, 6*w - 29],\ [131, 131, -3*w - 1],\ [131, 131, 3*w - 4],\ [137, 137, 3*w - 2],\ [137, 137, 3*w - 1],\ [149, 149, 6*w - 23],\ [149, 149, 6*w + 17],\ [163, 163, 4*w - 11],\ [163, 163, -4*w - 7],\ [167, 167, -w - 13],\ [167, 167, w - 14],\ [179, 179, 9*w + 28],\ [179, 179, 9*w - 37],\ [197, 197, -4*w - 19],\ [197, 197, 4*w - 23],\ [199, 199, -5*w - 11],\ [199, 199, 5*w - 16],\ [229, 229, 10*w + 31],\ [229, 229, 10*w - 41],\ [239, 239, 10*w - 47],\ [239, 239, 10*w + 37],\ [241, 241, 7*w + 19],\ [241, 241, 7*w - 26],\ [257, 257, -w - 16],\ [257, 257, w - 17],\ [263, 263, 2*w - 19],\ [263, 263, -2*w - 17],\ [269, 269, -5*w + 28],\ [269, 269, 5*w + 23],\ [271, 271, -5*w - 8],\ [271, 271, 5*w - 13],\ [283, 283, 3*w - 22],\ [283, 283, -3*w - 19],\ [289, 17, -17],\ [293, 293, -6*w - 13],\ [293, 293, 6*w - 19],\ [317, 317, 11*w + 41],\ [317, 317, 11*w - 52],\ [347, 347, 12*w + 37],\ [347, 347, 12*w - 49],\ [353, 353, 6*w - 17],\ [353, 353, -6*w - 11],\ [367, 367, 7*w - 23],\ [367, 367, -7*w - 16],\ [379, 379, 5*w - 4],\ [379, 379, 5*w - 1],\ [431, 431, 5*w - 31],\ [431, 431, -5*w - 26],\ [439, 439, 11*w - 43],\ [439, 439, 11*w + 32],\ [443, 443, -7*w - 31],\ [443, 443, -7*w + 38],\ [449, 449, -6*w - 7],\ [449, 449, 6*w - 13],\ [461, 461, 15*w - 62],\ [461, 461, 15*w + 47],\ [463, 463, -3*w - 23],\ [463, 463, 3*w - 26],\ [479, 479, 9*w + 23],\ [479, 479, 9*w - 32],\ [487, 487, -9*w + 46],\ [487, 487, -9*w - 37],\ [491, 491, -w - 22],\ [491, 491, w - 23],\ [503, 503, 13*w - 62],\ [503, 503, -13*w - 49],\ [529, 23, -23],\ [563, 563, 17*w + 62],\ [563, 563, 17*w - 79],\ [569, 569, 15*w + 46],\ [569, 569, 15*w - 61],\ [571, 571, -9*w - 38],\ [571, 571, -9*w + 47],\ [601, 601, 15*w + 56],\ [601, 601, 15*w - 71],\ [607, 607, 6*w - 37],\ [607, 607, -6*w - 31],\ [613, 613, -12*w - 47],\ [613, 613, 12*w - 59],\ [619, 619, -3*w - 26],\ [619, 619, 3*w - 29],\ [659, 659, -7*w - 34],\ [659, 659, 7*w - 41],\ [683, 683, -9*w - 19],\ [683, 683, 9*w - 28],\ [691, 691, -7*w - 4],\ [691, 691, 7*w - 11],\ [719, 719, 21*w - 88],\ [719, 719, 21*w + 67],\ [727, 727, -7*w - 1],\ [727, 727, 7*w - 8],\ [733, 733, 3*w - 31],\ [733, 733, -3*w - 28],\ [751, 751, -8*w - 11],\ [751, 751, 8*w - 19],\ [757, 757, 21*w + 76],\ [757, 757, 21*w - 97],\ [773, 773, 9*w - 26],\ [773, 773, -9*w - 17],\ [797, 797, -w - 28],\ [797, 797, w - 29],\ [809, 809, -5*w - 32],\ [809, 809, 5*w - 37],\ [827, 827, 12*w - 43],\ [827, 827, 12*w + 31],\ [829, 829, -12*w + 61],\ [829, 829, -12*w - 49],\ [839, 839, 2*w - 31],\ [839, 839, -2*w - 29],\ [841, 29, -29],\ [853, 853, -11*w - 26],\ [853, 853, 11*w - 37],\ [857, 857, 16*w - 77],\ [857, 857, -16*w - 61],\ [859, 859, 15*w - 73],\ [859, 859, -15*w - 58],\ [863, 863, 24*w + 77],\ [863, 863, 24*w - 101],\ [881, 881, 15*w + 43],\ [881, 881, 15*w - 58],\ [911, 911, -11*w + 58],\ [911, 911, -11*w - 47],\ [919, 919, 3*w - 34],\ [919, 919, -3*w - 31],\ [929, 929, 9*w - 22],\ [929, 929, -9*w - 13],\ [937, 937, 13*w + 34],\ [937, 937, 13*w - 47],\ [961, 31, -31],\ [967, 967, 8*w - 7],\ [967, 967, 8*w - 1],\ [971, 971, -12*w - 29],\ [971, 971, 12*w - 41],\ [977, 977, -w - 31],\ [977, 977, w - 32],\ [991, 991, -15*w - 59],\ [991, 991, 15*w - 74],\ [1021, 1021, 9*w - 52],\ [1021, 1021, -9*w - 43],\ [1033, 1033, -11*w - 23],\ [1033, 1033, 11*w - 34],\ [1049, 1049, 8*w - 49],\ [1049, 1049, -8*w - 41],\ [1051, 1051, 6*w - 43],\ [1051, 1051, -6*w - 37],\ [1093, 1093, 26*w - 109],\ [1093, 1093, 26*w + 83],\ [1097, 1097, 18*w - 71],\ [1097, 1097, 18*w + 53],\ [1103, 1103, -9*w - 7],\ [1103, 1103, 9*w - 16],\ [1117, 1117, -9*w - 44],\ [1117, 1117, 9*w - 53],\ [1123, 1123, 3*w - 37],\ [1123, 1123, -3*w - 34],\ [1163, 1163, 9*w - 13],\ [1163, 1163, -9*w - 4],\ [1171, 1171, 13*w - 44],\ [1171, 1171, -13*w - 31],\ [1181, 1181, 25*w - 116],\ [1181, 1181, 25*w + 91],\ [1193, 1193, 9*w - 11],\ [1193, 1193, -9*w - 2],\ [1201, 1201, 10*w - 23],\ [1201, 1201, -10*w - 13],\ [1217, 1217, 27*w + 86],\ [1217, 1217, 27*w - 113],\ [1223, 1223, 9*w - 8],\ [1223, 1223, 9*w - 1],\ [1229, 1229, 9*w - 2],\ [1229, 1229, 9*w - 7],\ [1259, 1259, 5*w - 43],\ [1259, 1259, -5*w - 38],\ [1277, 1277, 4*w - 41],\ [1277, 1277, -4*w - 37],\ [1297, 1297, 22*w + 67],\ [1297, 1297, 22*w - 89],\ [1301, 1301, 19*w - 92],\ [1301, 1301, -19*w - 73],\ [1303, 1303, 16*w + 43],\ [1303, 1303, 16*w - 59],\ [1327, 1327, 17*w + 47],\ [1327, 1327, 17*w - 64],\ [1361, 1361, 15*w + 38],\ [1361, 1361, 15*w - 53],\ [1367, 1367, -14*w + 73],\ [1367, 1367, -14*w - 59],\ [1369, 37, -37],\ [1381, 1381, -10*w - 7],\ [1381, 1381, 10*w - 17],\ [1399, 1399, -15*w - 62],\ [1399, 1399, -15*w + 77],\ [1423, 1423, -3*w - 38],\ [1423, 1423, 3*w - 41],\ [1439, 1439, 23*w + 86],\ [1439, 1439, 23*w - 109],\ [1451, 1451, 15*w - 52],\ [1451, 1451, -15*w - 37],\ [1459, 1459, -18*w - 71],\ [1459, 1459, 18*w - 89],\ [1483, 1483, 29*w + 92],\ [1483, 1483, 29*w - 121],\ [1489, 1489, -10*w - 1],\ [1489, 1489, 10*w - 11],\ [1511, 1511, 5*w - 46],\ [1511, 1511, -5*w - 41],\ [1559, 1559, 24*w + 73],\ [1559, 1559, 24*w - 97],\ [1567, 1567, 6*w - 49],\ [1567, 1567, -6*w - 43],\ [1571, 1571, 12*w - 31],\ [1571, 1571, -12*w - 19],\ [1583, 1583, 13*w + 58],\ [1583, 1583, -13*w + 71],\ [1601, 1601, 33*w - 139],\ [1601, 1601, 33*w + 106],\ [1613, 1613, 21*w + 61],\ [1613, 1613, 21*w - 82],\ [1627, 1627, -9*w - 49],\ [1627, 1627, 9*w - 58],\ [1663, 1663, 11*w - 19],\ [1663, 1663, -11*w - 8],\ [1667, 1667, -12*w - 17],\ [1667, 1667, 12*w - 29],\ [1669, 1669, -3*w - 41],\ [1669, 1669, 3*w - 44],\ [1693, 1693, -14*w - 29],\ [1693, 1693, 14*w - 43],\ [1699, 1699, 25*w + 76],\ [1699, 1699, 25*w - 101],\ [1709, 1709, -15*w - 34],\ [1709, 1709, 15*w - 49],\ [1721, 1721, -16*w - 67],\ [1721, 1721, -16*w + 83],\ [1723, 1723, 19*w - 71],\ [1723, 1723, 19*w + 52],\ [1733, 1733, 28*w - 131],\ [1733, 1733, 28*w + 103],\ [1747, 1747, 23*w - 91],\ [1747, 1747, 23*w + 68],\ [1753, 1753, 34*w + 109],\ [1753, 1753, 34*w - 143],\ [1783, 1783, -18*w + 91],\ [1783, 1783, -18*w - 73],\ [1789, 1789, 11*w - 13],\ [1789, 1789, -11*w - 2],\ [1811, 1811, 25*w - 119],\ [1811, 1811, -25*w - 94],\ [1831, 1831, 21*w - 103],\ [1831, 1831, -21*w - 82],\ [1849, 43, -43],\ [1871, 1871, 15*w - 47],\ [1871, 1871, -15*w - 32],\ [1877, 1877, -w - 43],\ [1877, 1877, w - 44],\ [1879, 1879, 16*w - 53],\ [1879, 1879, -16*w - 37],\ [1907, 1907, 12*w - 23],\ [1907, 1907, -12*w - 11],\ [1913, 1913, -17*w + 88],\ [1913, 1913, -17*w - 71],\ [1933, 1933, -3*w - 44],\ [1933, 1933, 3*w - 47],\ [1949, 1949, -15*w - 31],\ [1949, 1949, 15*w - 46],\ [1951, 1951, -6*w - 47],\ [1951, 1951, 6*w - 53],\ [1979, 1979, 13*w - 74],\ [1979, 1979, -13*w - 61],\ [1993, 1993, 27*w + 101],\ [1993, 1993, 27*w - 128],\ [1997, 1997, 27*w + 82],\ [1997, 1997, 27*w - 109],\ [1999, 1999, 31*w + 97],\ [1999, 1999, 31*w - 128],\ [2017, 2017, -21*w - 83],\ [2017, 2017, 21*w - 104],\ [2027, 2027, 12*w - 19],\ [2027, 2027, -12*w - 7],\ [2029, 2029, -12*w - 59],\ [2029, 2029, 12*w - 71],\ [2069, 2069, -5*w - 47],\ [2069, 2069, 5*w - 52],\ [2083, 2083, 19*w + 49],\ [2083, 2083, 19*w - 68],\ [2087, 2087, 33*w - 137],\ [2087, 2087, 33*w + 104],\ [2089, 2089, 14*w - 37],\ [2089, 2089, -14*w - 23],\ [2099, 2099, 15*w - 44],\ [2099, 2099, -15*w - 29],\ [2113, 2113, 29*w - 118],\ [2113, 2113, 29*w + 89],\ [2131, 2131, 20*w - 73],\ [2131, 2131, 20*w + 53],\ [2221, 2221, 25*w + 73],\ [2221, 2221, 25*w - 98],\ [2237, 2237, 18*w - 61],\ [2237, 2237, -18*w - 43],\ [2243, 2243, 2*w - 49],\ [2243, 2243, -2*w - 47],\ [2269, 2269, -15*w + 83],\ [2269, 2269, 15*w + 68],\ [2273, 2273, -8*w - 53],\ [2273, 2273, 8*w - 61],\ [2293, 2293, 12*w - 73],\ [2293, 2293, -12*w - 61],\ [2309, 2309, 15*w - 41],\ [2309, 2309, -15*w - 26],\ [2333, 2333, -7*w - 52],\ [2333, 2333, 7*w - 59],\ [2357, 2357, 4*w - 53],\ [2357, 2357, -4*w - 49],\ [2383, 2383, 16*w - 47],\ [2383, 2383, -16*w - 31],\ [2393, 2393, -13*w - 64],\ [2393, 2393, 13*w - 77],\ [2399, 2399, -17*w + 91],\ [2399, 2399, -17*w - 74],\ [2437, 2437, 36*w - 167],\ [2437, 2437, 36*w + 131],\ [2441, 2441, 18*w - 59],\ [2441, 2441, -18*w - 41],\ [2459, 2459, 25*w - 122],\ [2459, 2459, -25*w - 97],\ [2467, 2467, 13*w - 17],\ [2467, 2467, -13*w - 4],\ [2521, 2521, -13*w - 1],\ [2521, 2521, 13*w - 14],\ [2543, 2543, 24*w - 91],\ [2543, 2543, 24*w + 67],\ [2549, 2549, -20*w + 103],\ [2549, 2549, -20*w - 83],\ [2557, 2557, 13*w - 2],\ [2557, 2557, 13*w - 11],\ [2609, 2609, 32*w - 151],\ [2609, 2609, 32*w + 119],\ [2657, 2657, 16*w + 73],\ [2657, 2657, -16*w + 89],\ [2659, 2659, -30*w - 113],\ [2659, 2659, 30*w - 143],\ [2671, 2671, -9*w - 58],\ [2671, 2671, 9*w - 67],\ [2683, 2683, 41*w - 172],\ [2683, 2683, 41*w + 131],\ [2687, 2687, -26*w - 101],\ [2687, 2687, 26*w - 127],\ [2689, 2689, -27*w - 104],\ [2689, 2689, 27*w - 131],\ [2693, 2693, 21*w + 53],\ [2693, 2693, 21*w - 74],\ [2699, 2699, 5*w - 58],\ [2699, 2699, -5*w - 53],\ [2711, 2711, -11*w - 62],\ [2711, 2711, 11*w - 73],\ [2729, 2729, -15*w - 19],\ [2729, 2729, 15*w - 34],\ [2731, 2731, -15*w - 71],\ [2731, 2731, 15*w - 86],\ [2741, 2741, -w - 52],\ [2741, 2741, w - 53],\ [2749, 2749, -19*w - 43],\ [2749, 2749, 19*w - 62],\ [2767, 2767, -17*w - 32],\ [2767, 2767, 17*w - 49],\ [2791, 2791, 40*w - 167],\ [2791, 2791, 40*w + 127],\ [2797, 2797, 9*w - 68],\ [2797, 2797, -9*w - 59],\ [2801, 2801, 33*w - 134],\ [2801, 2801, 33*w + 101],\ [2803, 2803, -18*w - 79],\ [2803, 2803, -18*w + 97],\ [2809, 53, -53],\ [2819, 2819, 21*w - 73],\ [2819, 2819, -21*w - 52],\ [2833, 2833, -3*w - 53],\ [2833, 2833, 3*w - 56],\ [2851, 2851, -20*w - 47],\ [2851, 2851, 20*w - 67],\ [2879, 2879, -15*w - 16],\ [2879, 2879, 15*w - 31],\ [2887, 2887, 39*w + 142],\ [2887, 2887, 39*w - 181],\ [2903, 2903, -17*w + 94],\ [2903, 2903, 17*w + 77],\ [2909, 2909, 30*w - 119],\ [2909, 2909, 30*w + 89],\ [2927, 2927, 27*w - 104],\ [2927, 2927, 27*w + 77],\ [2953, 2953, 14*w - 13],\ [2953, 2953, 14*w - 1],\ [2969, 2969, 15*w - 29],\ [2969, 2969, -15*w - 14],\ [3001, 3001, 17*w - 46],\ [3001, 3001, -17*w - 29],\ [3011, 3011, -15*w - 13],\ [3011, 3011, 15*w - 28],\ [3023, 3023, -22*w - 91],\ [3023, 3023, -22*w + 113],\ [3037, 3037, 36*w - 169],\ [3037, 3037, 36*w + 133],\ [3041, 3041, 5*w - 61],\ [3041, 3041, -5*w - 56],\ [3049, 3049, 15*w - 88],\ [3049, 3049, -15*w - 73],\ [3089, 3089, 15*w - 26],\ [3089, 3089, -15*w - 11],\ [3163, 3163, 27*w - 133],\ [3163, 3163, -27*w - 106],\ [3167, 3167, 31*w - 149],\ [3167, 3167, -31*w - 118],\ [3169, 3169, -3*w - 56],\ [3169, 3169, 3*w - 59],\ [3181, 3181, 35*w - 142],\ [3181, 3181, 35*w + 107],\ [3187, 3187, -9*w - 62],\ [3187, 3187, 9*w - 71],\ [3191, 3191, -15*w - 8],\ [3191, 3191, 15*w - 23],\ [3217, 3217, -17*w - 26],\ [3217, 3217, 17*w - 43],\ [3221, 3221, 15*w - 22],\ [3221, 3221, -15*w - 7],\ [3229, 3229, 34*w + 103],\ [3229, 3229, 34*w - 137],\ [3253, 3253, 26*w + 71],\ [3253, 3253, 26*w - 97],\ [3299, 3299, -15*w - 4],\ [3299, 3299, 15*w - 19],\ [3307, 3307, 28*w + 79],\ [3307, 3307, 28*w - 107],\ [3313, 3313, 31*w + 91],\ [3313, 3313, 31*w - 122],\ [3319, 3319, 29*w + 83],\ [3319, 3319, 29*w - 112],\ [3343, 3343, 19*w - 56],\ [3343, 3343, -19*w - 37],\ [3359, 3359, -15*w - 1],\ [3359, 3359, 15*w - 16],\ [3371, 3371, 35*w + 131],\ [3371, 3371, 35*w - 166],\ [3389, 3389, 15*w - 14],\ [3389, 3389, 15*w - 1],\ [3391, 3391, 43*w - 179],\ [3391, 3391, 43*w + 136],\ [3407, 3407, -w - 58],\ [3407, 3407, w - 59],\ [3413, 3413, 7*w - 68],\ [3413, 3413, -7*w - 61],\ [3457, 3457, 9*w - 73],\ [3457, 3457, -9*w - 64],\ [3461, 3461, 27*w - 101],\ [3461, 3461, 27*w + 74],\ [3463, 3463, -16*w - 13],\ [3463, 3463, 16*w - 29],\ [3481, 59, -59],\ [3491, 3491, 45*w + 143],\ [3491, 3491, 45*w - 188],\ [3499, 3499, -20*w - 41],\ [3499, 3499, 20*w - 61],\ [3511, 3511, -23*w - 56],\ [3511, 3511, 23*w - 79],\ [3529, 3529, 45*w + 163],\ [3529, 3529, 45*w - 208],\ [3533, 3533, 21*w - 67],\ [3533, 3533, -21*w - 46],\ [3539, 3539, 2*w - 61],\ [3539, 3539, -2*w - 59],\ [3541, 3541, 15*w - 91],\ [3541, 3541, -15*w - 76],\ [3547, 3547, 6*w - 67],\ [3547, 3547, -6*w - 61],\ [3557, 3557, -11*w - 68],\ [3557, 3557, 11*w - 79],\ [3583, 3583, 41*w - 169],\ [3583, 3583, 41*w + 128],\ [3613, 3613, 19*w - 53],\ [3613, 3613, -19*w - 34],\ [3659, 3659, 10*w - 77],\ [3659, 3659, -10*w - 67],\ [3673, 3673, 49*w + 157],\ [3673, 3673, 49*w - 206],\ [3701, 3701, -20*w + 109],\ [3701, 3701, 20*w + 89],\ [3709, 3709, -15*w - 77],\ [3709, 3709, 15*w - 92],\ [3733, 3733, -12*w - 71],\ [3733, 3733, 12*w - 83],\ [3767, 3767, -w - 61],\ [3767, 3767, w - 62],\ [3769, 3769, 3*w - 64],\ [3769, 3769, -3*w - 61],\ [3779, 3779, -5*w - 62],\ [3779, 3779, 5*w - 67],\ [3797, 3797, 42*w + 131],\ [3797, 3797, 42*w - 173],\ [3821, 3821, 45*w + 142],\ [3821, 3821, 45*w - 187],\ [3823, 3823, -16*w - 1],\ [3823, 3823, 16*w - 17],\ [3847, 3847, 37*w + 112],\ [3847, 3847, 37*w - 149],\ [3863, 3863, -21*w - 43],\ [3863, 3863, 21*w - 64],\ [3877, 3877, -9*w - 67],\ [3877, 3877, 9*w - 76],\ [3889, 3889, -27*w + 136],\ [3889, 3889, -27*w - 109],\ [3907, 3907, -23*w - 53],\ [3907, 3907, 23*w - 76],\ [3917, 3917, 18*w - 41],\ [3917, 3917, -18*w - 23],\ [3919, 3919, 35*w - 139],\ [3919, 3919, 35*w + 104],\ [3923, 3923, 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76],\ [4231, 4231, -30*w - 119],\ [4231, 4231, 30*w - 149],\ [4243, 4243, 44*w + 137],\ [4243, 4243, 44*w - 181],\ [4261, 4261, 36*w - 173],\ [4261, 4261, -36*w - 137],\ [4271, 4271, -35*w - 134],\ [4271, 4271, 35*w - 169],\ [4273, 4273, 33*w - 161],\ [4273, 4273, -33*w - 128],\ [4283, 4283, -22*w + 119],\ [4283, 4283, -22*w - 97],\ [4289, 4289, 39*w + 118],\ [4289, 4289, 39*w - 157],\ [4297, 4297, 17*w - 19],\ [4297, 4297, -17*w - 2],\ [4327, 4327, 43*w + 133],\ [4327, 4327, 43*w - 176],\ [4373, 4373, -21*w - 38],\ [4373, 4373, 21*w - 59],\ [4391, 4391, 49*w - 227],\ [4391, 4391, 49*w + 178],\ [4397, 4397, 33*w + 94],\ [4397, 4397, 33*w - 127],\ [4441, 4441, -24*w + 127],\ [4441, 4441, -24*w - 103],\ [4457, 4457, -18*w - 13],\ [4457, 4457, 18*w - 31],\ [4489, 67, -67],\ [4513, 4513, 19*w - 41],\ [4513, 4513, -19*w - 22],\ [4517, 4517, -4*w - 67],\ [4517, 4517, 4*w - 71],\ [4519, 4519, 40*w + 121],\ [4519, 4519, 40*w - 161],\ [4523, 4523, 17*w - 103],\ [4523, 4523, -17*w - 86],\ [4561, 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[8707, 8707, 28*w - 71],\ [8707, 8707, -28*w - 43],\ [8719, 8719, -25*w - 16],\ [8719, 8719, 25*w - 41],\ [8737, 8737, 43*w - 161],\ [8737, 8737, 43*w + 118],\ [8779, 8779, 15*w - 118],\ [8779, 8779, -15*w - 103],\ [8783, 8783, 24*w - 13],\ [8783, 8783, 24*w - 11],\ [8803, 8803, 31*w - 92],\ [8803, 8803, -31*w - 61],\ [8831, 8831, 72*w - 301],\ [8831, 8831, 72*w + 229],\ [8849, 8849, 69*w - 287],\ [8849, 8849, 69*w + 218],\ [8861, 8861, -27*w - 34],\ [8861, 8861, 27*w - 61],\ [8867, 8867, -11*w - 98],\ [8867, 8867, 11*w - 109],\ [8887, 8887, 37*w - 128],\ [8887, 8887, -37*w - 91],\ [8893, 8893, 49*w - 191],\ [8893, 8893, 49*w + 142],\ [8933, 8933, 17*w - 124],\ [8933, 8933, -17*w - 107],\ [8951, 8951, 33*w - 104],\ [8951, 8951, -33*w - 71],\ [8963, 8963, 23*w - 142],\ [8963, 8963, -23*w - 119],\ [8971, 8971, 65*w - 268],\ [8971, 8971, 65*w + 203],\ [9001, 9001, -15*w - 104],\ [9001, 9001, 15*w - 119],\ [9013, 9013, 26*w - 49],\ [9013, 9013, -26*w - 23],\ [9029, 9029, -20*w - 113],\ [9029, 9029, 20*w - 133],\ [9041, 9041, -35*w + 184],\ [9041, 9041, -35*w - 149],\ [9043, 9043, 29*w - 76],\ [9043, 9043, -29*w - 47],\ [9067, 9067, 9*w - 106],\ [9067, 9067, -9*w - 97],\ [9103, 9103, 64*w - 263],\ [9103, 9103, 64*w + 199],\ [9109, 9109, 60*w - 283],\ [9109, 9109, 60*w + 223],\ [9137, 9137, -27*w - 31],\ [9137, 9137, 27*w - 58],\ [9151, 9151, 25*w - 32],\ [9151, 9151, -25*w - 7],\ [9199, 9199, -42*w + 211],\ [9199, 9199, -42*w - 169],\ [9227, 9227, -29*w - 134],\ [9227, 9227, 29*w - 163],\ [9257, 9257, 19*w - 131],\ [9257, 9257, -19*w - 112],\ [9277, 9277, 21*w - 137],\ [9277, 9277, -21*w - 116],\ [9281, 9281, 65*w + 239],\ [9281, 9281, 65*w - 304],\ [9311, 9311, 27*w - 56],\ [9311, 9311, -27*w - 29],\ [9319, 9319, 45*w - 223],\ [9319, 9319, -45*w - 178],\ [9337, 9337, 62*w + 191],\ [9337, 9337, 62*w - 253],\ [9349, 9349, -25*w - 1],\ [9349, 9349, 25*w - 26],\ [9391, 9391, 75*w - 346],\ [9391, 9391, 75*w + 271],\ [9397, 9397, 51*w - 247],\ [9397, 9397, -51*w - 196],\ [9403, 9403, -29*w - 44],\ [9403, 9403, 29*w - 73],\ [9413, 9413, -13*w - 103],\ [9413, 9413, 13*w - 116],\ [9419, 9419, 45*w + 124],\ [9419, 9419, 45*w - 169],\ [9421, 9421, 25*w - 2],\ [9421, 9421, 25*w - 23],\ [9433, 9433, 63*w + 233],\ [9433, 9433, 63*w - 296],\ [9439, 9439, 61*w - 248],\ [9439, 9439, 61*w + 187],\ [9467, 9467, 33*w - 101],\ [9467, 9467, -33*w - 68],\ [9491, 9491, -w - 97],\ [9491, 9491, w - 98],\ [9497, 9497, -11*w - 101],\ [9497, 9497, 11*w - 112],\ [9511, 9511, 25*w - 8],\ [9511, 9511, 25*w - 17],\ [9521, 9521, -41*w + 208],\ [9521, 9521, -41*w - 167],\ [9613, 9613, 59*w - 238],\ [9613, 9613, 59*w + 179],\ [9619, 9619, 79*w + 253],\ [9619, 9619, 79*w - 332],\ [9623, 9623, 39*w - 136],\ [9623, 9623, -39*w - 97],\ [9629, 9629, 30*w - 79],\ [9629, 9629, -30*w - 49],\ [9643, 9643, 44*w - 163],\ [9643, 9643, 44*w + 119],\ [9677, 9677, 63*w - 257],\ [9677, 9677, 63*w + 194],\ [9679, 9679, -15*w - 107],\ [9679, 9679, 15*w - 122],\ [9719, 9719, 5*w - 103],\ [9719, 9719, -5*w - 98],\ [9721, 9721, -45*w - 179],\ [9721, 9721, 45*w - 224],\ [9733, 9733, 26*w - 37],\ [9733, 9733, -26*w - 11],\ [9769, 9769, 46*w - 173],\ [9769, 9769, 46*w + 127],\ [9787, 9787, -21*w - 118],\ [9787, 9787, 21*w - 139],\ [9817, 9817, 47*w + 131],\ [9817, 9817, 47*w - 178],\ [9833, 9833, -53*w - 203],\ [9833, 9833, 53*w - 256],\ [9857, 9857, 27*w - 49],\ [9857, 9857, -27*w - 22],\ [9883, 9883, 49*w + 139],\ [9883, 9883, 49*w - 188],\ [9887, 9887, 72*w - 299],\ [9887, 9887, 72*w + 227],\ [9901, 9901, 50*w + 143],\ [9901, 9901, 50*w - 193],\ [9907, 9907, 52*w - 203],\ [9907, 9907, 52*w + 151],\ [9923, 9923, -37*w - 157],\ [9923, 9923, -37*w + 194],\ [9929, 9929, -25*w - 127],\ [9929, 9929, 25*w - 152],\ [9931, 9931, 28*w - 59],\ [9931, 9931, -28*w - 31]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-2, -2, 1, 0, 0, -4, -4, 2, 2, 6, 6, -12, -12, 1, 8, 2, 2, -6, -6, -10, -10, -4, -4, 12, 12, 2, 2, 6, 6, -22, -16, -16, 18, 18, 18, 18, -18, -18, -16, -16, -12, -12, -12, -12, -18, -18, 20, 20, -4, -4, 24, 24, -10, -10, 18, 18, 0, 0, -12, -12, -16, -16, -22, -22, 2, 24, 24, 6, 6, -24, -24, 18, 18, 8, 8, -16, -16, 24, 24, 8, 8, -12, -12, 18, 18, 12, 12, 32, 32, -36, -36, -16, -16, -12, -12, 0, 0, -46, 30, 30, 6, 6, 32, 32, 26, 26, 32, 32, 2, 2, 26, 26, -24, -24, -12, -12, -46, -46, 12, 12, 44, 44, -40, -40, -40, -40, 2, 2, 24, 24, -12, -12, 6, 6, -36, -36, 56, 56, 12, 12, -22, 44, 44, -18, -18, 14, 14, -24, -24, -54, -54, 48, 48, 56, 56, 6, 6, 2, 2, -46, 32, 32, -6, -6, -6, -6, -16, -16, -4, -4, 26, 26, -30, -30, 44, 44, -22, -22, -6, -6, 48, 48, -34, -34, -46, -46, -60, -60, 20, 20, 60, 60, 66, 66, 14, 14, -6, -6, -24, -24, 30, 30, 18, 18, 24, 24, -34, -34, -48, -48, 8, 8, 32, 32, -18, -18, -24, -24, -70, -22, -22, -40, -40, 56, 56, 24, 24, -48, -48, 38, 38, -46, -46, -58, -58, 0, 0, -12, -12, -16, -16, 66, 66, 0, 0, 66, 66, -72, -72, -10, -10, 8, 8, 48, 48, 32, 32, 56, 56, -10, -10, 54, 54, -6, -6, -4, -4, -6, -6, 56, 56, -46, -46, -16, -16, -10, -10, 42, 42, -40, -40, -22, 48, 48, 78, 78, 44, 44, 42, 42, 54, 54, 62, 62, 84, 84, -64, -64, 30, 30, 14, 14, -78, -78, -16, -16, -70, -70, -72, -72, 32, 32, -30, -30, 32, 32, 0, 0, -70, -70, 30, 30, 26, 26, -10, -10, -10, -10, -78, -78, 54, 54, 2, 2, 18, 18, -82, -82, -12, -12, -30, -30, -24, -24, -28, -28, 18, 18, -36, -36, 62, 62, -30, -30, 60, 60, 2, 2, 38, 38, 0, 0, 30, 30, 38, 38, -42, -42, 18, 18, 14, 14, 8, 8, 20, 20, -12, -12, 62, 62, -48, -48, 60, 60, 24, 24, -42, -42, -4, -4, 66, 66, -40, -40, 32, 32, 92, 92, 62, 62, 30, 30, 86, 86, -70, -66, -66, 26, 26, 44, 44, -24, -24, 44, 44, 0, 0, 18, 18, -96, -96, 38, 38, -54, -54, -58, -58, 24, 24, 0, 0, -40, -40, 78, 78, -10, -10, -66, -66, -22, -22, 60, 60, -34, -34, -40, -40, -16, -16, 24, 24, 86, 86, -18, -18, -46, -46, 32, 32, 72, 72, 14, 14, 2, 2, 80, 80, -40, -40, -96, -96, -24, -24, 42, 42, 80, 80, 72, 72, -18, -18, -34, -34, 48, 48, -100, -100, -82, 102, 102, 98, 98, -16, -16, 74, 74, 108, 108, 36, 36, -4, -4, -34, -34, -42, -42, -88, -88, -58, -58, 90, 90, 74, 74, -12, -12, -16, -16, -46, -46, 96, 96, -10, -10, 54, 54, -12, -12, 96, 96, -64, -64, -40, -40, -24, -24, 44, 44, 110, 110, 20, 20, -18, -18, 32, 32, -66, -66, -90, -90, 8, 8, 56, 56, -78, -78, 72, 72, -78, -78, 44, 44, -112, -112, 38, 38, 6, 6, -42, -42, -4, -4, -82, -82, 108, 108, -60, -60, 86, 86, 72, 72, -126, -126, -52, -52, 32, 32, -4, -4, -48, -48, -46, -46, 18, 18, 90, 90, -22, -22, -64, -64, -24, -24, 48, 48, 42, 42, -58, -58, -102, -102, -118, -94, -94, -114, -114, -16, -16, 24, 24, -118, -118, -52, -52, -28, -28, -22, -22, -108, -108, 104, 104, -30, -30, 98, 98, -16, -16, 18, 18, 116, 116, 104, 104, -72, -72, 80, 80, 20, 20, -60, -60, 12, 12, 126, 126, 36, 36, 54, 54, -10, -10, -70, -70, -46, -46, -40, -40, -42, -42, -118, -118, 102, 102, -142, -36, -36, -34, -34, -70, -70, -78, -78, -64, -64, -54, -54, 54, 54, 32, 32, 98, 98, -48, -48, -58, -58, -18, -18, 102, 102, 102, 102, 72, 72, 86, 86, -24, -24, 48, 48, -54, -54, -28, -28, 86, 86, 54, 54, -18, -18, -100, -100, 14, 14, -48, -48, 12, 12, -40, -40, 60, 60, 38, 38, -78, -78, 120, 120, 12, 12, 74, 74, 114, 114, -46, -46, 72, 72, 2, 2, -54, -54, -22, -22, -52, -52, -46, -46, 128, 128, -48, -48, 32, 32, -72, -72, 6, 6, 110, 110, -82, -82, -66, -66, 20, 20, -58, -58, -18, -18, -24, -24, 6, 6, -130, -130, -24, -24, -48, -48, 104, 104, -108, -108, -10, -10, 116, 116, -30, -30, 78, 78, -108, -108, 18, 18, -24, -24, 26, 26, 96, 96, -94, 56, 56, 156, 156, -114, -114, 8, 8, -48, -48, 126, 126, -12, -12, -6, -6, 8, 8, -66, -66, -24, -24, -24, -24, -130, -130, 20, 20, -100, -100, 134, 134, -70, -70, -156, -156, 140, 140, 144, 144, 42, 42, -52, -52, 50, 50, -72, -72, 2, 2, -22, -22, -18, -18, -4, -4, 96, 96, -42, -42, -120, -120, -46, -46, 56, 56, 108, 108, -10, -10, 138, 138, -34, -34, 42, 42, -40, -40, -58, -58, -160, -160, 48, 48, 56, 56, 90, 90, -114, -114, -154, -154, 2, 2, -72, -72, 96, 96, -30, -30, -24, -24, -112, -112, -90, -90, 152, 152, 12, 12, -4, -4, -16, -16, 62, 62, 96, 96, 54, 54, 158, 158, 134, 134, -10, -10, 50, 50, 38, 38, 54, 54, -102, -102, 90, 90, -30, -30, 24, 24, 74, 74, -120, -120, 74, 74, -60, -60, -78, -78, 14, 14, -100, -100, -144, -144, 146, 146, 68, 68, -30, -30, -72, -72, -78, -78, -40, -40, 44, 44, 8, 8, -64, -64, -138, -138, -130, -130, 128, 128, -162, -162, 86, 86, -120, -120, 128, 128, 68, 68, 66, 66, 18, 18, 0, 0, -120, -120, 62, 62, 36, 36, -142, -28, -28, -166, -166, -90, -90, 74, 74, -108, -108, 116, 116, 138, 138, -70, -70, 6, 6, -6, -6, 170, 170, -24, -24, -118, -118, -24, -24, -112, -112, 60, 60, -46, -46, 44, 44, -126, -126, 104, 104, -150, -150, 176, 176, 146, 146, -30, -30, -82, -82, 86, 86, -24, -24, -28, -28, 164, 164, -172, -172, 12, 12, 126, 126, -10, -10, 104, 104, 30, 30, -118, -118, -108, -108, -4, -4, 138, 138, -124, -124, 8, 8, -24, -24, -142, -142, -138, -138, 122, 122, -22, -22, -64, -64, -82, -82, -4, -4, 84, 84, -124, -124, 144, 144, -150, -150, 132, 132, 42, 42, 32, 32, -124, -124, -30, -30, -108, -108, 42, 42, -28, -28, -70, -70, -166, -166, 120, 120, 30, 30, -118, -118, -40, -40, 68, 68, -70, -70, -66, -66, -136, -136, 128, 128, 120, 120, -186, -186, 62, 62, 138, 138, -192, -192, -112, -112, 50, 50, -46, -46, 104, 104, -124, -124, -136, -136, -132, -132, -60, -60, -28, -28, 74, 74, 188, 188, 78, 78, 78, 78, 150, 150, -28, -28, -162, -162, 38, 38, 116, 116, 24, 24, 78, 78, 32, 32, 108, 108, -184, -184, 24, 24, 2, 2, -40, -40, -58, -58, -148, -148, -154, -154, 126, 126, 138, 138, 146, 146, -96, -96, 164, 164, -28, -28, -24, -24, 54, 54, -22, -22] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([4, 2, 2])] = -1 AL_eigenvalues[ZF.ideal([49, 7, -7])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]