/* 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([-13, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([900, 30, -30]) primes_array = [ [4, 2, 2],\ [7, 7, w + 2],\ [7, 7, w - 3],\ [9, 3, 3],\ [11, 11, w + 1],\ [11, 11, w - 2],\ [13, 13, w],\ [13, 13, w - 1],\ [17, 17, -w - 5],\ [17, 17, w - 6],\ [25, 5, -5],\ [29, 29, -w - 6],\ [29, 29, w - 7],\ [37, 37, 2*w - 5],\ [37, 37, -2*w - 3],\ [43, 43, -w - 7],\ [43, 43, w - 8],\ [47, 47, 3*w + 7],\ [47, 47, 3*w - 10],\ [53, 53, 2*w - 1],\ [59, 59, -w - 8],\ [59, 59, w - 9],\ [89, 89, -3*w - 4],\ [89, 89, 3*w - 7],\ [97, 97, -w - 10],\ [97, 97, w - 11],\ [107, 107, 3*w - 5],\ [107, 107, -3*w - 2],\ [113, 113, -3*w - 1],\ [113, 113, 3*w - 4],\ [131, 131, 4*w - 11],\ [131, 131, -4*w - 7],\ [149, 149, 4*w - 21],\ [149, 149, -4*w - 17],\ [163, 163, -4*w - 5],\ [163, 163, 4*w - 9],\ [197, 197, -w - 14],\ [197, 197, w - 15],\ [199, 199, 5*w - 14],\ [199, 199, -5*w - 9],\ [211, 211, 4*w - 3],\ [211, 211, 4*w - 1],\ [223, 223, -3*w - 17],\ [223, 223, 3*w - 20],\ [227, 227, -w - 15],\ [227, 227, w - 16],\ [229, 229, -4*w - 19],\ [229, 229, 4*w - 23],\ [241, 241, 5*w - 12],\ [241, 241, -5*w - 7],\ [269, 269, -5*w - 22],\ [269, 269, 5*w - 27],\ [271, 271, 2*w - 19],\ [271, 271, -2*w - 17],\ [281, 281, 6*w - 17],\ [281, 281, -6*w - 11],\ [293, 293, -w - 17],\ [293, 293, w - 18],\ [307, 307, -7*w - 15],\ [307, 307, 7*w - 22],\ [311, 311, 5*w - 7],\ [311, 311, -5*w - 2],\ [317, 317, 4*w - 25],\ [317, 317, -4*w - 21],\ [331, 331, 5*w - 2],\ [331, 331, 5*w - 3],\ [347, 347, 2*w - 21],\ [347, 347, -2*w - 19],\ [361, 19, -19],\ [367, 367, -w - 19],\ [367, 367, w - 20],\ [409, 409, -7*w - 12],\ [409, 409, 7*w - 19],\ [431, 431, 2*w - 23],\ [431, 431, -2*w - 21],\ [433, 433, 3*w - 25],\ [433, 433, -3*w - 22],\ [439, 439, -7*w - 11],\ [439, 439, 7*w - 18],\ [449, 449, -w - 21],\ [449, 449, w - 22],\ [461, 461, -6*w - 1],\ [461, 461, 6*w - 7],\ [467, 467, 7*w - 17],\ [467, 467, -7*w - 10],\ [487, 487, 8*w - 23],\ [487, 487, -8*w - 15],\ [521, 521, -9*w - 19],\ [521, 521, 9*w - 28],\ [523, 523, 2*w - 25],\ [523, 523, -2*w - 23],\ [529, 23, -23],\ [541, 541, 10*w - 33],\ [541, 541, 10*w + 23],\ [547, 547, -6*w - 29],\ [547, 547, 6*w - 35],\ [577, 577, -7*w - 5],\ [577, 577, 7*w - 12],\ [587, 587, -w - 24],\ [587, 587, w - 25],\ [593, 593, -7*w - 4],\ [593, 593, 7*w - 11],\ [599, 599, 5*w - 33],\ [599, 599, -5*w - 28],\ [607, 607, 7*w - 10],\ [607, 607, -7*w - 3],\ [619, 619, 7*w - 9],\ [619, 619, -7*w - 2],\ [643, 643, 7*w - 6],\ [643, 643, 7*w - 1],\ [647, 647, 7*w - 2],\ [647, 647, 7*w - 5],\ [653, 653, -9*w - 16],\ [653, 653, 9*w - 25],\ [661, 661, -5*w - 29],\ [661, 661, 5*w - 34],\ [673, 673, 8*w - 43],\ [673, 673, -8*w - 35],\ [683, 683, 7*w - 40],\ [683, 683, -7*w - 33],\ [727, 727, 8*w - 15],\ [727, 727, -8*w - 7],\ [733, 733, -9*w - 38],\ [733, 733, 9*w - 47],\ [743, 743, -w - 27],\ [743, 743, w - 28],\ [751, 751, 3*w - 31],\ [751, 751, -3*w - 28],\ [757, 757, -7*w - 34],\ [757, 757, 7*w - 41],\ [811, 811, -3*w - 29],\ [811, 811, 3*w - 32],\ [823, 823, -8*w - 1],\ [823, 823, 8*w - 9],\ [839, 839, 8*w - 7],\ [839, 839, 8*w - 1],\ [857, 857, -w - 29],\ [857, 857, w - 30],\ [859, 859, -5*w - 32],\ [859, 859, 5*w - 37],\ [863, 863, -9*w - 10],\ [863, 863, 9*w - 19],\ [877, 877, -4*w - 31],\ [877, 877, 4*w - 35],\ [907, 907, 13*w - 43],\ [907, 907, 13*w + 30],\ [911, 911, 7*w - 43],\ [911, 911, -7*w - 36],\ [929, 929, 5*w - 38],\ [929, 929, -5*w - 33],\ [937, 937, 3*w - 34],\ [937, 937, -3*w - 31],\ [941, 941, -9*w - 7],\ [941, 941, 9*w - 16],\ [947, 947, -12*w - 25],\ [947, 947, 12*w - 37],\ [953, 953, -11*w - 20],\ [953, 953, 11*w - 31],\ [961, 31, -31],\ [967, 967, -6*w - 35],\ [967, 967, 6*w - 41],\ [971, 971, 2*w - 33],\ [971, 971, -2*w - 31],\ [983, 983, -9*w - 5],\ [983, 983, 9*w - 14],\ [991, 991, -7*w - 37],\ [991, 991, 7*w - 44],\ [997, 997, 9*w - 50],\ [997, 997, -9*w - 41],\ [1013, 1013, 4*w - 37],\ [1013, 1013, -4*w - 33],\ [1031, 1031, 9*w - 11],\ [1031, 1031, -9*w - 2],\ [1049, 1049, 13*w - 41],\ [1049, 1049, -13*w - 28],\ [1051, 1051, 11*w - 29],\ [1051, 1051, -11*w - 18],\ [1061, 1061, 9*w - 8],\ [1061, 1061, 9*w - 1],\ [1069, 1069, -10*w - 11],\ [1069, 1069, 10*w - 21],\ [1097, 1097, -11*w - 17],\ [1097, 1097, 11*w - 28],\ [1103, 1103, 2*w - 35],\ [1103, 1103, -2*w - 33],\ [1109, 1109, -w - 33],\ [1109, 1109, w - 34],\ [1117, 1117, -13*w - 27],\ [1117, 1117, 13*w - 40],\ [1123, 1123, 6*w - 43],\ [1123, 1123, -6*w - 37],\ [1129, 1129, 10*w - 19],\ [1129, 1129, -10*w - 9],\ [1151, 1151, 5*w - 41],\ [1151, 1151, -5*w - 36],\ [1153, 1153, -14*w - 31],\ [1153, 1153, 14*w - 45],\ [1181, 1181, -10*w - 7],\ [1181, 1181, 10*w - 17],\ [1213, 1213, -3*w - 35],\ [1213, 1213, 3*w - 38],\ [1223, 1223, -11*w - 14],\ [1223, 1223, 11*w - 25],\ [1229, 1229, -5*w - 37],\ [1229, 1229, 5*w - 42],\ [1259, 1259, 15*w + 34],\ [1259, 1259, 15*w - 49],\ [1279, 1279, -9*w - 44],\ [1279, 1279, 9*w - 53],\ [1283, 1283, 12*w - 31],\ [1283, 1283, -12*w - 19],\ [1289, 1289, -10*w - 1],\ [1289, 1289, 10*w - 11],\ [1297, 1297, -11*w - 12],\ [1297, 1297, 11*w - 23],\ [1301, 1301, -14*w - 29],\ [1301, 1301, 14*w - 43],\ [1319, 1319, -w - 36],\ [1319, 1319, w - 37],\ [1321, 1321, 10*w - 3],\ [1321, 1321, 10*w - 7],\ [1361, 1361, 8*w - 51],\ [1361, 1361, -8*w - 43],\ [1367, 1367, -11*w - 49],\ [1367, 1367, 11*w - 60],\ [1427, 1427, -13*w - 22],\ [1427, 1427, 13*w - 35],\ [1447, 1447, 11*w - 18],\ [1447, 1447, -11*w - 7],\ [1459, 1459, -6*w - 41],\ [1459, 1459, 6*w - 47],\ [1471, 1471, -11*w - 6],\ [1471, 1471, 11*w - 17],\ [1483, 1483, -13*w - 21],\ [1483, 1483, 13*w - 34],\ [1493, 1493, 11*w - 16],\ [1493, 1493, -11*w - 5],\ [1499, 1499, -15*w - 31],\ [1499, 1499, 15*w - 46],\ [1531, 1531, -11*w - 3],\ [1531, 1531, 11*w - 14],\ [1543, 1543, -13*w - 55],\ [1543, 1543, 13*w - 68],\ [1553, 1553, -8*w - 45],\ [1553, 1553, 8*w - 53],\ [1579, 1579, -9*w - 47],\ [1579, 1579, 9*w - 56],\ [1583, 1583, 11*w - 10],\ [1583, 1583, 11*w - 1],\ [1597, 1597, 11*w - 8],\ [1597, 1597, 11*w - 3],\ [1601, 1601, 11*w - 7],\ [1601, 1601, 11*w - 4],\ [1607, 1607, -7*w - 44],\ [1607, 1607, 7*w - 51],\ [1619, 1619, 12*w - 23],\ [1619, 1619, -12*w - 11],\ [1627, 1627, -w - 40],\ [1627, 1627, w - 41],\ [1637, 1637, 4*w - 45],\ [1637, 1637, -4*w - 41],\ [1667, 1667, -13*w - 56],\ [1667, 1667, 13*w - 69],\ [1681, 41, -41],\ [1697, 1697, 14*w - 37],\ [1697, 1697, -14*w - 23],\ [1709, 1709, -w - 41],\ [1709, 1709, w - 42],\ [1721, 1721, -15*w - 28],\ [1721, 1721, 15*w - 43],\ [1733, 1733, 13*w - 29],\ [1733, 1733, -13*w - 16],\ [1753, 1753, -8*w - 47],\ [1753, 1753, 8*w - 55],\ [1759, 1759, -17*w - 37],\ [1759, 1759, 17*w - 54],\ [1777, 1777, 13*w - 28],\ [1777, 1777, -13*w - 15],\ [1787, 1787, -12*w - 5],\ [1787, 1787, 12*w - 17],\ [1789, 1789, -9*w - 49],\ [1789, 1789, 9*w - 58],\ [1801, 1801, 7*w - 53],\ [1801, 1801, -7*w - 46],\ [1811, 1811, 10*w - 61],\ [1811, 1811, -10*w - 51],\ [1831, 1831, -5*w - 44],\ [1831, 1831, 5*w - 49],\ [1861, 1861, 3*w - 46],\ [1861, 1861, -3*w - 43],\ [1871, 1871, 16*w - 47],\ [1871, 1871, -16*w - 31],\ [1879, 1879, -w - 43],\ [1879, 1879, w - 44],\ [1901, 1901, 7*w - 54],\ [1901, 1901, -7*w - 47],\ [1907, 1907, 12*w - 7],\ [1907, 1907, 12*w - 5],\ [1933, 1933, -13*w - 11],\ [1933, 1933, 13*w - 24],\ [1951, 1951, -3*w - 44],\ [1951, 1951, 3*w - 47],\ [1997, 1997, 4*w - 49],\ [1997, 1997, -4*w - 45],\ [1999, 1999, -13*w - 9],\ [1999, 1999, 13*w - 22],\ [2003, 2003, -7*w - 48],\ [2003, 2003, 7*w - 55],\ [2027, 2027, 19*w + 43],\ [2027, 2027, 19*w - 62],\ [2029, 2029, -13*w - 8],\ [2029, 2029, 13*w - 21],\ [2039, 2039, -10*w - 53],\ [2039, 2039, 10*w - 63],\ [2063, 2063, 2*w - 47],\ [2063, 2063, -2*w - 45],\ [2083, 2083, 13*w - 19],\ [2083, 2083, -13*w - 6],\ [2111, 2111, 15*w - 37],\ [2111, 2111, -15*w - 22],\ [2113, 2113, -14*w - 15],\ [2113, 2113, 14*w - 29],\ [2129, 2129, 13*w - 17],\ [2129, 2129, -13*w - 4],\ [2131, 2131, 15*w - 79],\ [2131, 2131, -15*w - 64],\ [2137, 2137, 3*w - 49],\ [2137, 2137, -3*w - 46],\ [2179, 2179, 11*w - 67],\ [2179, 2179, -11*w - 56],\ [2213, 2213, 7*w - 57],\ [2213, 2213, -7*w - 50],\ [2237, 2237, 13*w - 5],\ [2237, 2237, 13*w - 8],\ [2239, 2239, 13*w - 6],\ [2239, 2239, 13*w - 7],\ [2243, 2243, -w - 47],\ [2243, 2243, w - 48],\ [2251, 2251, 2*w - 49],\ [2251, 2251, -2*w - 47],\ [2269, 2269, 17*w - 48],\ [2269, 2269, -17*w - 31],\ [2273, 2273, 14*w - 25],\ [2273, 2273, -14*w - 11],\ [2333, 2333, 19*w - 59],\ [2333, 2333, -19*w - 40],\ [2339, 2339, -w - 48],\ [2339, 2339, w - 49],\ [2341, 2341, 14*w - 23],\ [2341, 2341, -14*w - 9],\ [2347, 2347, -17*w - 30],\ [2347, 2347, 17*w - 47],\ [2357, 2357, 18*w - 53],\ [2357, 2357, -18*w - 35],\ [2381, 2381, 15*w - 32],\ [2381, 2381, -15*w - 17],\ [2389, 2389, 4*w - 53],\ [2389, 2389, -4*w - 49],\ [2423, 2423, 17*w - 46],\ [2423, 2423, -17*w - 29],\ [2437, 2437, -w - 49],\ [2437, 2437, w - 50],\ [2447, 2447, 2*w - 51],\ [2447, 2447, -2*w - 49],\ [2467, 2467, 9*w - 64],\ [2467, 2467, -9*w - 55],\ [2531, 2531, 5*w - 56],\ [2531, 2531, -5*w - 51],\ [2543, 2543, 7*w - 60],\ [2543, 2543, -7*w - 53],\ [2551, 2551, 16*w - 37],\ [2551, 2551, -16*w - 21],\ [2557, 2557, 11*w - 70],\ [2557, 2557, -11*w - 59],\ [2591, 2591, 13*w - 76],\ [2591, 2591, -13*w - 63],\ [2593, 2593, 14*w - 9],\ [2593, 2593, 14*w - 5],\ [2621, 2621, 19*w - 56],\ [2621, 2621, -19*w - 37],\ [2633, 2633, -8*w - 55],\ [2633, 2633, 8*w - 63],\ [2657, 2657, 7*w - 61],\ [2657, 2657, -7*w - 54],\ [2659, 2659, -6*w - 53],\ [2659, 2659, 6*w - 59],\ [2663, 2663, 16*w - 35],\ [2663, 2663, -16*w - 19],\ [2687, 2687, -11*w - 60],\ [2687, 2687, 11*w - 71],\ [2693, 2693, -18*w - 31],\ [2693, 2693, 18*w - 49],\ [2699, 2699, -20*w - 41],\ [2699, 2699, 20*w - 61],\ [2707, 2707, 17*w - 42],\ [2707, 2707, -17*w - 25],\ [2713, 2713, -19*w - 36],\ [2713, 2713, 19*w - 55],\ [2719, 2719, 15*w - 83],\ [2719, 2719, -15*w - 68],\ [2731, 2731, -13*w - 64],\ [2731, 2731, 13*w - 77],\ [2741, 2741, -15*w - 8],\ [2741, 2741, 15*w - 23],\ [2749, 2749, 5*w - 58],\ [2749, 2749, -5*w - 53],\ [2767, 2767, -16*w - 17],\ [2767, 2767, 16*w - 33],\ [2803, 2803, -19*w - 35],\ [2803, 2803, 19*w - 54],\ [2819, 2819, 11*w - 72],\ [2819, 2819, -11*w - 61],\ [2833, 2833, -9*w - 58],\ [2833, 2833, 9*w - 67],\ [2837, 2837, -17*w - 23],\ [2837, 2837, 17*w - 40],\ [2851, 2851, -3*w - 53],\ [2851, 2851, 3*w - 56],\ [2861, 2861, -5*w - 54],\ [2861, 2861, 5*w - 59],\ [2879, 2879, -14*w - 67],\ [2879, 2879, 14*w - 81],\ [2887, 2887, 6*w - 61],\ [2887, 2887, -6*w - 55],\ [2909, 2909, -15*w - 1],\ [2909, 2909, 15*w - 16],\ [2939, 2939, 15*w - 14],\ [2939, 2939, 15*w - 1],\ [2953, 2953, -11*w - 62],\ [2953, 2953, 11*w - 73],\ [2957, 2957, -w - 54],\ [2957, 2957, w - 55],\ [2969, 2969, 15*w - 11],\ [2969, 2969, 15*w - 4],\ [3011, 3011, 7*w - 64],\ [3011, 3011, -7*w - 57],\ [3037, 3037, -4*w - 55],\ [3037, 3037, 4*w - 59],\ [3049, 3049, 22*w - 69],\ [3049, 3049, -22*w - 47],\ [3061, 3061, -19*w - 32],\ [3061, 3061, 19*w - 51],\ [3067, 3067, -w - 55],\ [3067, 3067, w - 56],\ [3083, 3083, 2*w - 57],\ [3083, 3083, -2*w - 55],\ [3089, 3089, -11*w - 63],\ [3089, 3089, 11*w - 74],\ [3121, 3121, 8*w - 67],\ [3121, 3121, -8*w - 59],\ [3137, 3137, 18*w - 43],\ [3137, 3137, -18*w - 25],\ [3163, 3163, -13*w - 67],\ [3163, 3163, 13*w - 80],\ [3167, 3167, -16*w - 7],\ [3167, 3167, 16*w - 23],\ [3169, 3169, -16*w - 73],\ [3169, 3169, 16*w - 89],\ [3181, 3181, -15*w - 71],\ [3181, 3181, 15*w - 86],\ [3187, 3187, -3*w - 56],\ [3187, 3187, 3*w - 59],\ [3191, 3191, 21*w - 62],\ [3191, 3191, -21*w - 41],\ [3209, 3209, -5*w - 57],\ [3209, 3209, 5*w - 62],\ [3217, 3217, 9*w - 70],\ [3217, 3217, -9*w - 61],\ [3229, 3229, 17*w - 33],\ [3229, 3229, -17*w - 16],\ [3257, 3257, -7*w - 59],\ [3257, 3257, 7*w - 66],\ [3271, 3271, 16*w - 19],\ [3271, 3271, -16*w - 3],\ [3299, 3299, -10*w - 63],\ [3299, 3299, 10*w - 73],\ [3301, 3301, -19*w - 29],\ [3301, 3301, 19*w - 48],\ [3323, 3323, 17*w - 31],\ [3323, 3323, -17*w - 14],\ [3329, 3329, 5*w - 63],\ [3329, 3329, -5*w - 58],\ [3343, 3343, 16*w - 15],\ [3343, 3343, 16*w - 1],\ [3391, 3391, 16*w - 9],\ [3391, 3391, 16*w - 7],\ [3407, 3407, 19*w - 100],\ [3407, 3407, -19*w - 81],\ [3449, 3449, 17*w - 28],\ [3449, 3449, -17*w - 11],\ [3461, 3461, -13*w - 69],\ [3461, 3461, 13*w - 82],\ [3469, 3469, 23*w - 71],\ [3469, 3469, -23*w - 48],\ [3491, 3491, -21*w - 38],\ [3491, 3491, 21*w - 59],\ [3499, 3499, 15*w - 88],\ [3499, 3499, -15*w - 73],\ [3511, 3511, 7*w - 68],\ [3511, 3511, -7*w - 61],\ [3527, 3527, -w - 59],\ [3527, 3527, w - 60],\ [3541, 3541, -3*w - 59],\ [3541, 3541, 3*w - 62],\ [3547, 3547, 2*w - 61],\ [3547, 3547, -2*w - 59],\ [3557, 3557, 17*w - 25],\ [3557, 3557, -17*w - 8],\ [3593, 3593, 19*w - 44],\ [3593, 3593, -19*w - 25],\ [3613, 3613, -13*w - 70],\ [3613, 3613, 13*w - 83],\ [3617, 3617, 18*w - 35],\ [3617, 3617, -18*w - 17],\ [3673, 3673, 17*w - 21],\ [3673, 3673, -17*w - 4],\ [3697, 3697, -17*w - 3],\ 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46],\ [8963, 8963, -22*w - 113],\ [8963, 8963, 22*w - 135],\ [8999, 8999, -26*w - 121],\ [8999, 8999, 26*w - 147],\ [9001, 9001, 3*w - 97],\ [9001, 9001, -3*w - 94],\ [9011, 9011, 25*w - 144],\ [9011, 9011, -25*w - 119],\ [9059, 9059, -27*w - 11],\ [9059, 9059, 27*w - 38],\ [9067, 9067, 14*w - 115],\ [9067, 9067, -14*w - 101],\ [9091, 9091, 35*w - 102],\ [9091, 9091, -35*w - 67],\ [9103, 9103, 13*w - 113],\ [9103, 9103, -13*w - 100],\ [9109, 9109, -11*w - 98],\ [9109, 9109, 11*w - 109],\ [9127, 9127, -6*w - 95],\ [9127, 9127, 6*w - 101],\ [9133, 9133, 38*w - 119],\ [9133, 9133, -38*w - 81],\ [9173, 9173, 33*w - 89],\ [9173, 9173, -33*w - 56],\ [9209, 9209, 37*w - 113],\ [9209, 9209, -37*w - 76],\ [9221, 9221, -30*w - 37],\ [9221, 9221, 30*w - 67],\ [9239, 9239, -27*w - 7],\ [9239, 9239, 27*w - 34],\ [9281, 9281, -17*w - 106],\ [9281, 9281, 17*w - 123],\ [9311, 9311, -31*w - 43],\ [9311, 9311, 31*w - 74],\ [9319, 9319, 31*w - 164],\ [9319, 9319, -31*w - 133],\ [9337, 9337, 29*w - 57],\ [9337, 9337, -29*w - 28],\ [9341, 9341, -20*w - 111],\ [9341, 9341, 20*w - 131],\ [9343, 9343, 32*w - 81],\ [9343, 9343, -32*w - 49],\ [9371, 9371, 5*w - 101],\ [9371, 9371, -5*w - 96],\ [9377, 9377, -16*w - 105],\ [9377, 9377, 16*w - 121],\ [9391, 9391, 41*w + 93],\ [9391, 9391, 41*w - 134],\ [9397, 9397, -37*w - 75],\ [9397, 9397, 37*w - 112],\ [9419, 9419, 27*w - 29],\ [9419, 9419, -27*w - 2],\ [9421, 9421, -29*w - 27],\ [9421, 9421, 29*w - 56],\ [9433, 9433, -9*w - 98],\ [9433, 9433, 9*w - 107],\ [9463, 9463, 22*w - 137],\ [9463, 9463, -22*w - 115],\ [9491, 9491, -10*w - 99],\ [9491, 9491, 10*w - 109],\ [9497, 9497, -19*w - 110],\ [9497, 9497, 19*w - 129],\ [9511, 9511, 17*w - 124],\ [9511, 9511, -17*w - 107],\ [9533, 9533, 13*w - 115],\ [9533, 9533, -13*w - 102],\ [9539, 9539, 26*w - 149],\ [9539, 9539, -26*w - 123],\ [9547, 9547, 28*w - 43],\ [9547, 9547, -28*w - 15],\ [9551, 9551, 2*w - 99],\ [9551, 9551, -2*w - 97],\ [9587, 9587, 27*w - 22],\ [9587, 9587, 27*w - 5],\ [9629, 9629, 27*w - 8],\ [9629, 9629, 27*w - 19],\ [9631, 9631, 18*w - 127],\ [9631, 9631, -18*w - 109],\ [9661, 9661, 29*w - 53],\ [9661, 9661, -29*w - 24],\ [9689, 9689, -w - 98],\ [9689, 9689, w - 99],\ [9739, 9739, -11*w - 101],\ [9739, 9739, 11*w - 112],\ [9743, 9743, 17*w - 125],\ [9743, 9743, -17*w - 108],\ [9767, 9767, 37*w - 110],\ [9767, 9767, -37*w - 73],\ [9769, 9769, 5*w - 103],\ [9769, 9769, -5*w - 98],\ [9781, 9781, -3*w - 98],\ [9781, 9781, 3*w - 101],\ [9811, 9811, -29*w - 22],\ [9811, 9811, 29*w - 51],\ [9829, 9829, -20*w - 113],\ [9829, 9829, 20*w - 133],\ [9833, 9833, 16*w - 123],\ [9833, 9833, -16*w - 107],\ [9851, 9851, -39*w - 82],\ [9851, 9851, 39*w - 121],\ [9857, 9857, 7*w - 106],\ [9857, 9857, -7*w - 99],\ [9859, 9859, 28*w - 37],\ [9859, 9859, -28*w - 9],\ [9871, 9871, -31*w - 38],\ [9871, 9871, 31*w - 69],\ [9883, 9883, 29*w - 50],\ [9883, 9883, -29*w - 21],\ [9887, 9887, -w - 99],\ [9887, 9887, w - 100],\ [9901, 9901, 15*w - 121],\ [9901, 9901, -15*w - 106],\ [9907, 9907, -21*w - 115],\ [9907, 9907, 21*w - 136],\ [9949, 9949, -37*w - 72],\ [9949, 9949, 37*w - 109],\ [9973, 9973, -12*w - 103],\ [9973, 9973, 12*w - 115]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [1, -4, -4, 1, 0, 0, 2, 2, 6, 6, 1, -6, -6, 2, 2, -4, -4, 0, 0, -6, 0, 0, 18, 18, 2, 2, -12, -12, -18, -18, 0, 0, -6, -6, -4, -4, -6, -6, 8, 8, 20, 20, 20, 20, -12, -12, -10, -10, 2, 2, -6, -6, -16, -16, 18, 18, -6, -6, 20, 20, 0, 0, 18, 18, -28, -28, 12, 12, -22, -28, -28, 26, 26, 0, 0, 26, 26, 8, 8, -6, -6, -30, -30, -36, -36, -28, -28, 18, 18, 20, 20, -46, -10, -10, -28, -28, 2, 2, -12, -12, 30, 30, -24, -24, -4, -4, 44, 44, -4, -4, 24, 24, 18, 18, 14, 14, 26, 26, -12, -12, -28, -28, -22, -22, -24, -24, -40, -40, 2, 2, -4, -4, 20, 20, 24, 24, -18, -18, -4, -4, 24, 24, 2, 2, 44, 44, -48, -48, -6, -6, 26, 26, 18, 18, 36, 36, 6, 6, 2, -4, -4, 24, 24, -24, -24, -16, -16, 26, 26, -54, -54, 24, 24, 18, 18, -52, -52, 42, 42, 14, 14, 6, 6, 0, 0, -6, -6, 2, 2, -52, -52, 26, 26, -24, -24, -22, -22, -30, -30, -46, -46, -24, -24, 18, 18, 0, 0, -40, -40, -12, -12, -30, -30, -22, -22, 42, 42, -48, -48, 26, 26, -6, -6, 24, 24, 12, 12, 20, 20, 20, 20, -16, -16, -28, -28, -54, -54, 48, 48, 20, 20, 68, 68, 6, 6, -28, -28, -24, -24, -22, -22, 66, 66, -48, -48, -48, -48, -28, -28, 42, 42, -12, -12, -46, -18, -18, -30, -30, 42, 42, -6, -6, -46, -46, -40, -40, 26, 26, -36, -36, 38, 38, -22, -22, 0, 0, -40, -40, -10, -10, 24, 24, 8, 8, -30, -30, 60, 60, 26, 26, 56, 56, -78, -78, 80, 80, 12, 12, -12, -12, 14, 14, 48, 48, 72, 72, -28, -28, 24, 24, -70, -70, -30, -30, 44, 44, 2, 2, 20, 20, -6, -6, 66, 66, -88, -88, 60, 60, -52, -52, -34, -34, -42, -42, 18, 18, 24, 24, 38, 38, -4, -4, 42, 42, 42, 42, 14, 14, -48, -48, -70, -70, 0, 0, 92, 92, -24, -24, -48, -48, -40, -40, -22, -22, 48, 48, -46, -46, 18, 18, 6, 6, -42, -42, 68, 68, -48, -48, -24, -24, -6, -6, -48, -48, -52, -52, -22, -22, 32, 32, 20, 20, -54, -54, 14, 14, -28, -28, -4, -4, -48, -48, 2, 2, -54, -54, 44, 44, -6, -6, -96, -96, 92, 92, -78, -78, -72, -72, 2, 2, -78, -78, -6, -6, 24, 24, -22, -22, 26, 26, -34, -34, -28, -28, -36, -36, 42, 42, 2, 2, 102, 102, -52, -52, -72, -72, -46, -46, 14, 14, -52, -52, 96, 96, 66, 66, -22, -22, -10, -10, -90, -90, -16, -16, -24, -24, 38, 38, -36, -36, -30, -30, -76, -76, 56, 56, -48, -48, 90, 90, 18, 18, 62, 62, -48, -48, -28, -28, 80, 80, -48, -48, 14, 14, -28, -28, 90, 90, -18, -18, -94, -94, -42, -42, -22, -22, 26, 26, -30, -30, 62, 62, 72, 72, -22, -4, -4, 68, 68, 24, 24, -70, -70, 48, 48, 84, 84, -28, -28, 30, 30, 74, 74, 24, 24, -124, -124, -24, -24, -84, -84, -54, -54, -100, -100, -108, -108, 68, 68, 18, 18, 48, 48, 62, 62, -28, -28, -118, -118, 96, 96, -48, -48, -102, -102, -16, -16, 74, 74, -72, -72, -78, -78, 80, 80, 18, 18, 66, 66, 108, 108, -6, -6, -22, -22, 54, 54, 92, 92, 74, 74, -4, -4, -6, -6, -28, -28, 74, 74, -48, -48, -96, -96, 90, 90, -118, 60, 60, 14, 14, -28, -28, 96, 96, 62, 62, -16, -16, -6, -6, -4, -4, -22, -22, -52, -52, -114, -114, -24, -24, -54, -54, 68, 68, -78, -78, 32, 32, 68, 68, 84, 84, 72, 72, -46, -46, -18, -18, -58, -58, -126, -126, 18, 18, -24, -24, -70, -70, -118, -118, 0, 0, -70, -70, 114, 114, 26, 26, 80, 80, 44, 44, 72, 72, -142, 96, 96, -124, -124, 74, 74, 42, 42, 72, 72, -48, -48, -10, -10, 74, 74, -84, -84, -76, -76, 74, 74, 48, 48, -102, -102, -102, -102, -142, 68, 68, -6, -6, 102, 102, -24, -24, 44, 44, 74, 74, 54, 54, -100, -100, -88, -88, -100, -100, -118, -118, 36, 36, 138, 138, -28, -28, -72, -72, 50, 50, -52, -52, 98, 98, 86, 86, -148, -148, 120, 120, 42, 42, -94, -94, -6, -6, 14, 14, 120, 120, 42, 42, -54, -54, -130, -130, 80, 80, 84, 84, 12, 12, 0, 0, 116, 116, -72, -72, 50, 50, 66, 66, -4, -4, 90, 90, 92, 92, 32, 32, 42, 42, 44, 44, -102, -102, 120, 120, 98, 98, 44, 44, -126, -126, -54, -54, 92, 92, -70, -70, -106, -106, -94, -124, -124, -96, -96, 18, 18, 8, 8, -34, -34, 120, 120, -78, -78, -108, -108, 92, 92, -66, -66, -144, -144, 122, 122, -100, -100, 74, 74, 42, 42, -142, -142, 66, 66, 44, 44, -66, -66, 2, 2, -96, -96, 50, 50, -4, -4, 108, 108, -76, -76, -78, -78, 44, 44, 66, 66, 62, 62, 152, 152, -78, -78, 44, 44, 44, 44, -66, -66, -72, -72, -22, -22, 108, 108, -42, -42, 122, 122, -28, -28, -22, -72, -72, 68, 68, 108, 108, -10, -10, 0, 0, 92, 92, 24, 24, -144, -144, 2, 2, -102, -102, -16, -16, -36, -36, -120, -120, -102, -102, -72, -72, 48, 48, -16, -16, 54, 54, 68, 68, 164, 164, -70, -70, 98, 98, 108, 108, -118, -118, -168, -168, 8, 8, 20, 20, -42, -42, 6, 6, -22, -22, -94, -94, 162, 162, 122, 122, -6, -6, -94, -94, -24, -24, -6, -6, -100, -100, 72, 72, 134, 134, 8, 8, -156, -156, -126, -126, 110, 110, 50, 50, 0, 0, 164, 164, 72, 72, 98, 98, 138, 138, 114, 114, 2, 2, 114, 114, -132, -132, 146, 146, 54, 54, 138, 138, -40, -40, -28, -28, 74, 74, -54, -54, -48, -48, -6, -6, -126, -126, 66, 66, 12, 12, -46, -46, 96, 96, -76, -76, 128, 128, -94, -94, 144, 144, 14, 14, 168, 168, 180, 180, -34, -34, 146, 146, -114, -114, 8, 8, 2, 2, -108, -108, -84, -84, -154, -154, -48, -48, 32, 32, 116, 116, 68, 68, 68, 68, -90, -90, -28, -28, -168, -168, -30, -30, 90, 90, 32, 32, -4, -4, 134, 134, -120, -120, 146, 146, -78, -78, 138, 138, -72, -72, -148, -148, -126, -126, 170, 170, 120, 120, 72, 72, 90, 90, 12, 12, -28, -28, -70, -70, 146, 146, 42, 42, -130, -130, -48, -48, 12, 12, 72, 72, -70, -70, -96, -96, -48, -48, 92, 92, 164, 164, -76, -76, -34, -34, -52, -52, -46, -46, -54, -54, -150, -150, 18, 18, 96, 96, 90, 90, -72, -72, 128, 128, 122, 122, -30, -30, -124, -124, 96, 96, 174, 174, -88, -88, 50, 50, 120, 120, 62, 62, 74, 74, -4, -4, 120, 120, -90, -90, 80, 80, -30, -30, -168, -168, 20, 20, -24, -24, 108, 108, 42, 42, 80, 80, 134, 134, -6, -6, 44, 44, 168, 168, 48, 48, 74, 74, -58, -58, 140, 140, -10, -10, 126, 126, 0, 0, 30, 30, 140, 140, -88, -88, -4, -4, 168, 168, -106, -106, -52, -52, -130, -130, 74, 74] 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([9, 3, 3])] = -1 AL_eigenvalues[ZF.ideal([25, 5, -5])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]