/* 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([-8, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([33, 33, -2*w + 1]) primes_array = [ [2, 2, -w - 2],\ [2, 2, -w + 3],\ [3, 3, 2*w - 7],\ [11, 11, 4*w - 13],\ [17, 17, -2*w + 5],\ [17, 17, 2*w + 3],\ [25, 5, 5],\ [29, 29, -2*w + 3],\ [29, 29, 2*w + 1],\ [31, 31, -2*w + 9],\ [31, 31, 2*w + 7],\ [37, 37, -4*w - 11],\ [37, 37, 4*w - 15],\ [41, 41, -10*w + 33],\ [41, 41, 6*w - 19],\ [49, 7, -7],\ [67, 67, 2*w - 11],\ [67, 67, -2*w - 9],\ [83, 83, 4*w + 5],\ [83, 83, 4*w - 9],\ [97, 97, 8*w + 21],\ [97, 97, 8*w - 29],\ [101, 101, 6*w - 17],\ [101, 101, 6*w + 11],\ [103, 103, -6*w - 17],\ [103, 103, 6*w - 23],\ [107, 107, 4*w - 7],\ [107, 107, -4*w - 3],\ [131, 131, 4*w - 3],\ [131, 131, 4*w - 1],\ [149, 149, 10*w + 21],\ [149, 149, 10*w - 31],\ [157, 157, 4*w + 15],\ [157, 157, 4*w - 19],\ [163, 163, 2*w - 15],\ [163, 163, -2*w - 13],\ [167, 167, 8*w - 23],\ [167, 167, 8*w + 15],\ [169, 13, -13],\ [173, 173, 14*w + 31],\ [173, 173, 14*w - 45],\ [181, 181, -20*w + 69],\ [181, 181, -12*w + 43],\ [197, 197, -6*w - 7],\ [197, 197, 6*w - 13],\ [199, 199, 10*w - 37],\ [199, 199, -10*w - 27],\ [223, 223, 2*w - 17],\ [223, 223, -2*w - 15],\ [227, 227, 12*w + 25],\ [227, 227, 12*w - 37],\ [229, 229, -4*w + 21],\ [229, 229, -4*w - 17],\ [233, 233, 6*w - 11],\ [233, 233, -6*w - 5],\ [239, 239, -8*w + 21],\ [239, 239, 8*w + 13],\ [263, 263, 16*w - 51],\ [263, 263, 16*w + 35],\ [281, 281, -6*w - 1],\ [281, 281, 6*w - 7],\ [293, 293, 6*w - 5],\ [293, 293, 6*w - 1],\ [313, 313, -8*w + 33],\ [313, 313, -8*w - 25],\ [331, 331, -10*w - 29],\ [331, 331, 10*w - 39],\ [347, 347, 12*w - 35],\ [347, 347, 12*w + 23],\ [359, 359, -8*w - 9],\ [359, 359, 8*w - 17],\ [361, 19, -19],\ [367, 367, 2*w - 21],\ [367, 367, -2*w - 19],\ [379, 379, 6*w + 23],\ [379, 379, 6*w - 29],\ [397, 397, 4*w - 25],\ [397, 397, -4*w - 21],\ [421, 421, -28*w + 97],\ [421, 421, -20*w + 71],\ [431, 431, 16*w + 33],\ [431, 431, 16*w - 49],\ [433, 433, 8*w - 35],\ [433, 433, -8*w - 27],\ [461, 461, 14*w - 41],\ [461, 461, 14*w + 27],\ [463, 463, -18*w + 65],\ [463, 463, -34*w + 117],\ [479, 479, -8*w - 3],\ [479, 479, 8*w - 11],\ [487, 487, -6*w + 31],\ [487, 487, -6*w - 25],\ [491, 491, 36*w - 119],\ [491, 491, 20*w - 63],\ [499, 499, -14*w - 39],\ [499, 499, 14*w - 53],\ [503, 503, -8*w - 1],\ [503, 503, 8*w - 9],\ [529, 23, -23],\ [557, 557, 18*w + 37],\ [557, 557, 18*w - 55],\ [563, 563, -12*w + 31],\ [563, 563, 12*w + 19],\ [569, 569, -10*w - 11],\ [569, 569, 10*w - 21],\ [577, 577, -32*w + 111],\ [577, 577, -24*w + 85],\ [593, 593, 14*w - 39],\ [593, 593, 14*w + 25],\ [619, 619, -10*w - 33],\ [619, 619, 10*w - 43],\ [631, 631, -38*w + 131],\ [631, 631, -22*w + 79],\ [643, 643, 2*w - 27],\ [643, 643, -2*w - 25],\ [659, 659, 12*w + 17],\ [659, 659, 12*w - 29],\ [661, 661, -12*w + 49],\ [661, 661, -12*w - 37],\ [677, 677, 26*w - 83],\ [677, 677, 26*w + 57],\ [691, 691, 18*w - 67],\ [691, 691, -18*w - 49],\ [701, 701, 30*w + 67],\ [701, 701, 30*w - 97],\ [709, 709, -4*w - 27],\ [709, 709, 4*w - 31],\ [727, 727, -6*w - 29],\ [727, 727, 6*w - 35],\ [743, 743, 16*w + 29],\ [743, 743, 16*w - 45],\ [751, 751, 2*w - 29],\ [751, 751, -2*w - 27],\ [757, 757, -36*w + 125],\ [757, 757, -28*w + 99],\ [761, 761, 10*w - 13],\ [761, 761, -10*w - 3],\ [809, 809, 10*w - 9],\ [809, 809, 10*w - 1],\ [821, 821, 10*w - 3],\ [821, 821, 10*w - 7],\ [823, 823, -26*w + 93],\ [823, 823, -42*w + 145],\ [827, 827, -12*w - 13],\ [827, 827, 12*w - 25],\ [829, 829, 4*w - 33],\ [829, 829, -4*w - 29],\ [857, 857, 22*w + 45],\ [857, 857, 22*w - 67],\ [859, 859, 6*w - 37],\ [859, 859, -6*w - 31],\ [883, 883, -14*w + 57],\ [883, 883, -14*w - 43],\ [887, 887, 16*w + 27],\ [887, 887, 16*w - 43],\ [907, 907, 22*w - 81],\ [907, 907, -22*w - 59],\ [941, 941, 14*w + 19],\ [941, 941, 14*w - 33],\ [953, 953, 26*w + 55],\ [953, 953, 26*w - 81],\ [991, 991, 2*w - 33],\ [991, 991, -2*w - 31],\ [1019, 1019, 12*w - 19],\ [1019, 1019, -12*w - 7],\ [1021, 1021, 12*w - 53],\ [1021, 1021, -12*w - 41],\ [1031, 1031, 24*w + 49],\ [1031, 1031, 24*w - 73],\ [1039, 1039, -46*w + 159],\ [1039, 1039, -30*w + 107],\ [1087, 1087, -14*w + 59],\ [1087, 1087, -14*w - 45],\ [1091, 1091, 20*w - 57],\ [1091, 1091, 20*w + 37],\ [1093, 1093, 4*w - 37],\ [1093, 1093, -4*w - 33],\ [1097, 1097, 42*w - 137],\ [1097, 1097, 38*w - 123],\ [1123, 1123, 2*w - 35],\ [1123, 1123, -2*w - 33],\ [1151, 1151, 16*w + 23],\ [1151, 1151, 16*w - 39],\ [1153, 1153, -8*w - 37],\ [1153, 1153, 8*w - 45],\ [1163, 1163, 12*w - 11],\ [1163, 1163, 12*w - 1],\ [1171, 1171, -18*w - 53],\ [1171, 1171, 18*w - 71],\ [1187, 1187, 12*w - 7],\ [1187, 1187, 12*w - 5],\ [1213, 1213, -12*w - 43],\ [1213, 1213, 12*w - 55],\ [1217, 1217, 14*w - 27],\ [1217, 1217, -14*w - 13],\ [1223, 1223, 56*w - 185],\ [1223, 1223, 32*w - 101],\ [1229, 1229, 18*w + 29],\ [1229, 1229, -18*w + 47],\ [1237, 1237, -4*w - 35],\ [1237, 1237, 4*w - 39],\ [1279, 1279, -34*w + 121],\ [1279, 1279, -50*w + 173],\ [1283, 1283, 36*w - 115],\ [1283, 1283, 36*w + 79],\ [1289, 1289, 22*w + 41],\ [1289, 1289, 22*w - 63],\ [1291, 1291, -10*w + 51],\ [1291, 1291, -10*w - 41],\ [1303, 1303, 6*w - 43],\ [1303, 1303, -6*w - 37],\ [1319, 1319, 40*w + 89],\ [1319, 1319, 40*w - 129],\ [1321, 1321, -8*w - 39],\ [1321, 1321, 8*w - 47],\ [1361, 1361, 14*w - 23],\ [1361, 1361, -14*w - 9],\ [1423, 1423, -18*w + 73],\ [1423, 1423, -18*w - 55],\ [1427, 1427, 28*w + 57],\ [1427, 1427, 28*w - 85],\ [1451, 1451, -20*w + 53],\ [1451, 1451, -20*w - 33],\ [1453, 1453, 28*w - 103],\ [1453, 1453, -28*w - 75],\ [1481, 1481, 26*w - 77],\ [1481, 1481, 26*w + 51],\ [1483, 1483, 22*w - 85],\ [1483, 1483, -22*w - 63],\ [1487, 1487, -16*w - 17],\ [1487, 1487, 16*w - 33],\ [1489, 1489, -24*w - 67],\ [1489, 1489, 24*w - 91],\ [1493, 1493, 22*w - 61],\ [1493, 1493, 22*w + 39],\ [1543, 1543, -54*w + 187],\ [1543, 1543, -38*w + 135],\ [1549, 1549, -4*w - 39],\ [1549, 1549, 4*w - 43],\ [1553, 1553, -14*w - 1],\ [1553, 1553, 14*w - 15],\ [1559, 1559, 32*w + 67],\ [1559, 1559, 32*w - 99],\ [1567, 1567, 2*w - 41],\ [1567, 1567, -2*w - 39],\ [1583, 1583, 16*w - 31],\ [1583, 1583, -16*w - 15],\ [1601, 1601, 14*w - 11],\ [1601, 1601, 14*w - 3],\ [1609, 1609, -16*w - 53],\ [1609, 1609, 16*w - 69],\ [1613, 1613, 14*w - 9],\ [1613, 1613, 14*w - 5],\ [1619, 1619, -20*w + 51],\ [1619, 1619, 20*w + 31],\ [1621, 1621, 12*w + 47],\ [1621, 1621, -12*w + 59],\ [1667, 1667, 36*w - 113],\ [1667, 1667, 68*w - 225],\ [1699, 1699, -34*w + 123],\ [1699, 1699, -66*w + 227],\ [1733, 1733, 26*w - 75],\ [1733, 1733, 26*w + 49],\ [1741, 1741, -20*w + 81],\ [1741, 1741, -20*w - 61],\ [1747, 1747, 14*w + 51],\ [1747, 1747, 14*w - 65],\ [1753, 1753, 32*w + 85],\ [1753, 1753, 32*w - 117],\ [1783, 1783, -22*w - 65],\ [1783, 1783, 22*w - 87],\ [1811, 1811, 44*w + 97],\ [1811, 1811, 44*w - 141],\ [1823, 1823, 16*w - 25],\ [1823, 1823, -16*w - 9],\ [1831, 1831, -42*w + 149],\ [1831, 1831, -58*w + 201],\ [1847, 1847, 48*w - 155],\ [1847, 1847, 48*w + 107],\ [1849, 43, -43],\ [1873, 1873, -8*w - 45],\ [1873, 1873, 8*w - 53],\ [1877, 1877, -22*w + 57],\ [1877, 1877, 22*w + 35],\ [1879, 1879, 10*w - 57],\ [1879, 1879, -10*w - 47],\ [1889, 1889, -18*w - 19],\ [1889, 1889, 18*w - 37],\ [1913, 1913, 38*w - 119],\ [1913, 1913, 74*w - 245],\ [1931, 1931, 20*w + 27],\ [1931, 1931, 20*w - 47],\ [1949, 1949, 30*w - 89],\ [1949, 1949, 30*w + 59],\ [1951, 1951, -18*w - 59],\ [1951, 1951, 18*w - 77],\ [1979, 1979, 28*w + 53],\ [1979, 1979, 28*w - 81],\ [1997, 1997, 18*w - 35],\ [1997, 1997, -18*w - 17],\ [2011, 2011, -38*w + 137],\ [2011, 2011, -70*w + 241],\ [2017, 2017, -56*w + 195],\ [2017, 2017, -48*w + 169],\ [2029, 2029, -20*w + 83],\ [2029, 2029, -20*w - 63],\ [2063, 2063, 16*w - 15],\ [2063, 2063, 16*w - 1],\ [2081, 2081, 46*w - 147],\ [2081, 2081, 46*w + 101],\ [2083, 2083, 2*w - 47],\ [2083, 2083, -2*w - 45],\ [2087, 2087, 16*w - 3],\ [2087, 2087, 16*w - 13],\ [2111, 2111, 16*w - 9],\ [2111, 2111, 16*w - 7],\ [2113, 2113, -16*w - 57],\ [2113, 2113, 16*w - 73],\ [2129, 2129, 50*w - 161],\ [2129, 2129, 50*w + 111],\ [2137, 2137, -24*w - 71],\ [2137, 2137, 24*w - 95],\ [2141, 2141, 34*w + 69],\ [2141, 2141, 34*w - 103],\ [2143, 2143, -62*w + 215],\ [2143, 2143, -46*w + 163],\ [2153, 2153, 58*w - 189],\ [2153, 2153, 54*w - 175],\ [2161, 2161, 32*w - 119],\ [2161, 2161, -32*w - 87],\ [2179, 2179, -30*w - 83],\ [2179, 2179, 30*w - 113],\ [2203, 2203, -6*w - 47],\ [2203, 2203, 6*w - 53],\ [2207, 2207, 32*w - 95],\ [2207, 2207, 32*w + 63],\ [2209, 47, -47],\ [2213, 2213, 26*w + 45],\ [2213, 2213, 26*w - 71],\ [2243, 2243, 28*w + 51],\ [2243, 2243, 28*w - 79],\ [2269, 2269, -4*w - 47],\ [2269, 2269, 4*w - 51],\ [2273, 2273, -18*w - 11],\ [2273, 2273, 18*w - 29],\ [2281, 2281, 8*w - 57],\ [2281, 2281, -8*w - 49],\ [2293, 2293, 12*w - 65],\ [2293, 2293, -12*w - 53],\ [2309, 2309, 38*w + 79],\ [2309, 2309, 38*w - 117],\ [2311, 2311, 10*w - 61],\ [2311, 2311, -10*w - 51],\ [2339, 2339, -20*w - 21],\ [2339, 2339, 20*w - 41],\ [2341, 2341, -60*w + 209],\ [2341, 2341, -52*w + 183],\ [2347, 2347, -74*w + 255],\ [2347, 2347, -42*w + 151],\ [2351, 2351, -24*w + 61],\ [2351, 2351, 24*w + 37],\ [2377, 2377, 16*w - 75],\ [2377, 2377, 16*w + 59],\ [2393, 2393, 22*w - 51],\ [2393, 2393, 22*w + 29],\ [2411, 2411, 36*w + 73],\ [2411, 2411, 36*w - 109],\ [2417, 2417, 18*w - 25],\ [2417, 2417, -18*w - 7],\ [2441, 2441, -26*w + 69],\ [2441, 2441, 26*w + 43],\ [2459, 2459, 20*w - 39],\ [2459, 2459, -20*w - 19],\ [2467, 2467, 2*w - 51],\ [2467, 2467, -2*w - 49],\ [2473, 2473, -24*w + 97],\ [2473, 2473, -24*w - 73],\ [2477, 2477, 18*w - 23],\ [2477, 2477, -18*w - 5],\ [2539, 2539, -10*w - 53],\ [2539, 2539, 10*w - 63],\ [2543, 2543, 24*w + 35],\ [2543, 2543, 24*w - 59],\ [2549, 2549, 22*w + 27],\ [2549, 2549, 22*w - 49],\ [2557, 2557, 28*w - 109],\ [2557, 2557, -28*w - 81],\ [2591, 2591, 40*w - 123],\ [2591, 2591, 40*w + 83],\ [2609, 2609, 18*w - 17],\ [2609, 2609, 18*w - 1],\ [2657, 2657, 18*w - 5],\ [2657, 2657, 18*w - 13],\ [2671, 2671, 2*w - 53],\ [2671, 2671, -2*w - 51],\ [2677, 2677, -4*w - 51],\ [2677, 2677, 4*w - 55],\ [2689, 2689, -64*w + 223],\ [2689, 2689, -56*w + 197],\ [2707, 2707, -78*w + 269],\ [2707, 2707, -46*w + 165],\ [2731, 2731, 22*w - 93],\ [2731, 2731, -22*w - 71],\ [2741, 2741, 54*w + 119],\ [2741, 2741, 54*w - 173],\ [2789, 2789, 58*w + 129],\ [2789, 2789, 58*w - 187],\ [2797, 2797, -84*w + 289],\ [2797, 2797, -44*w + 159],\ [2801, 2801, 30*w - 83],\ [2801, 2801, 30*w + 53],\ [2803, 2803, 18*w - 83],\ [2803, 2803, 18*w + 65],\ [2809, 53, -53],\ [2837, 2837, -22*w - 23],\ [2837, 2837, 22*w - 45],\ [2879, 2879, 88*w - 291],\ [2879, 2879, 48*w - 151],\ [2887, 2887, -26*w + 105],\ [2887, 2887, -26*w - 79],\ [2903, 2903, 24*w + 31],\ [2903, 2903, 24*w - 55],\ [2939, 2939, -20*w - 9],\ [2939, 2939, 20*w - 29],\ [2953, 2953, -8*w - 55],\ [2953, 2953, 8*w - 63],\ [2969, 2969, 22*w - 43],\ [2969, 2969, -22*w - 21],\ [2971, 2971, -38*w - 103],\ [2971, 2971, 38*w - 141],\ [2999, 2999, 40*w + 81],\ [2999, 2999, 40*w - 121],\ [3001, 3001, -32*w - 91],\ [3001, 3001, 32*w - 123],\ [3011, 3011, -20*w - 7],\ [3011, 3011, 20*w - 27],\ [3019, 3019, 10*w - 67],\ [3019, 3019, -10*w - 57],\ [3037, 3037, -12*w - 59],\ [3037, 3037, 12*w - 71],\ [3061, 3061, -68*w + 237],\ [3061, 3061, -60*w + 211],\ [3067, 3067, 6*w - 61],\ [3067, 3067, -6*w - 55],\ [3119, 3119, 32*w + 57],\ [3119, 3119, 32*w - 89],\ [3137, 3137, 34*w - 97],\ [3137, 3137, 34*w + 63],\ [3167, 3167, 64*w - 207],\ [3167, 3167, 72*w - 235],\ [3169, 3169, -24*w + 101],\ [3169, 3169, -24*w - 77],\ [3203, 3203, 44*w + 91],\ [3203, 3203, 44*w - 135],\ [3209, 3209, 22*w - 39],\ [3209, 3209, -22*w - 17],\ [3217, 3217, -16*w + 81],\ [3217, 3217, -16*w - 65],\ [3251, 3251, 20*w - 17],\ [3251, 3251, 20*w - 3],\ [3259, 3259, -26*w + 107],\ [3259, 3259, -26*w - 81],\ [3271, 3271, -10*w - 59],\ [3271, 3271, 10*w - 69],\ [3299, 3299, 20*w - 11],\ [3299, 3299, 20*w - 9],\ [3301, 3301, 12*w - 73],\ [3301, 3301, -12*w - 61],\ [3329, 3329, -30*w + 79],\ [3329, 3329, 30*w + 49],\ [3331, 3331, 2*w - 59],\ [3331, 3331, -2*w - 57],\ [3391, 3391, -30*w - 89],\ [3391, 3391, 30*w - 119],\ [3407, 3407, 32*w + 55],\ [3407, 3407, 32*w - 87],\ [3433, 3433, -32*w - 93],\ [3433, 3433, 32*w - 125],\ [3449, 3449, 38*w - 111],\ [3449, 3449, 38*w + 73],\ [3457, 3457, -72*w + 251],\ [3457, 3457, -64*w + 225],\ [3461, 3461, 26*w - 59],\ [3461, 3461, 26*w + 33],\ [3463, 3463, -38*w - 105],\ [3463, 3463, 38*w - 143],\ [3467, 3467, 36*w + 67],\ [3467, 3467, 36*w - 103],\ [3469, 3469, 36*w - 137],\ [3469, 3469, -36*w - 101],\ [3481, 59, -59],\ [3499, 3499, -54*w + 193],\ [3499, 3499, -86*w + 297],\ [3527, 3527, 24*w - 47],\ [3527, 3527, -24*w - 23],\ [3529, 3529, 24*w - 103],\ [3529, 3529, -24*w - 79],\ [3533, 3533, 46*w - 141],\ [3533, 3533, 46*w + 95],\ [3539, 3539, 100*w - 331],\ [3539, 3539, 52*w - 163],\ [3547, 3547, -6*w - 59],\ [3547, 3547, 6*w - 65],\ [3581, 3581, -30*w + 77],\ [3581, 3581, 30*w + 47],\ [3593, 3593, -22*w - 9],\ [3593, 3593, 22*w - 31],\ [3613, 3613, -92*w + 317],\ [3613, 3613, -52*w + 187],\ [3631, 3631, -78*w + 271],\ [3631, 3631, -62*w + 219],\ [3659, 3659, 28*w - 67],\ [3659, 3659, 28*w + 39],\ [3671, 3671, 96*w - 317],\ [3671, 3671, 56*w - 177],\ [3697, 3697, -8*w - 61],\ [3697, 3697, 8*w - 69],\ [3721, 61, -61],\ [3727, 3727, 18*w + 71],\ [3727, 3727, -18*w + 89],\ [3733, 3733, -28*w - 87],\ [3733, 3733, -28*w + 115],\ [3761, 3761, 34*w + 59],\ [3761, 3761, 34*w - 93],\ [3779, 3779, 60*w + 131],\ [3779, 3779, 60*w - 191],\ [3793, 3793, -104*w + 357],\ [3793, 3793, -48*w + 175],\ [3797, 3797, 22*w - 25],\ [3797, 3797, -22*w - 3],\ [3803, 3803, 36*w + 65],\ [3803, 3803, 36*w - 101],\ [3853, 3853, 12*w - 77],\ [3853, 3853, -12*w - 65],\ [3863, 3863, 64*w + 141],\ [3863, 3863, 64*w - 205],\ [3877, 3877, -76*w + 265],\ [3877, 3877, -68*w + 239],\ [3911, 3911, 24*w - 41],\ [3911, 3911, -24*w - 17],\ 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36*w - 157],\ [8647, 8647, -154*w + 529],\ [8647, 8647, -74*w + 269],\ [8663, 8663, 88*w - 279],\ [8663, 8663, -144*w + 475],\ [8677, 8677, -44*w + 179],\ [8677, 8677, -44*w - 135],\ [8681, 8681, 54*w - 151],\ [8681, 8681, 54*w + 97],\ [8713, 8713, -32*w - 115],\ [8713, 8713, 32*w - 147],\ [8737, 8737, -112*w + 391],\ [8737, 8737, -104*w + 365],\ [8741, 8741, 70*w - 213],\ [8741, 8741, 70*w + 143],\ [8747, 8747, 44*w + 63],\ [8747, 8747, 44*w - 107],\ [8753, 8753, 34*w - 45],\ [8753, 8753, -34*w - 11],\ [8761, 8761, -72*w + 263],\ [8761, 8761, -160*w + 549],\ [8779, 8779, -10*w - 93],\ [8779, 8779, 10*w - 103],\ [8803, 8803, 2*w - 95],\ [8803, 8803, -2*w - 93],\ [8807, 8807, 48*w + 77],\ [8807, 8807, -48*w + 125],\ [8819, 8819, 92*w - 293],\ [8819, 8819, 92*w + 201],\ [8861, 8861, 34*w - 43],\ [8861, 8861, -34*w - 9],\ [8893, 8893, 4*w - 97],\ [8893, 8893, -4*w - 93],\ [8941, 8941, -68*w - 183],\ [8941, 8941, 68*w - 251],\ [8951, 8951, 96*w - 307],\ [8951, 8951, 96*w + 211],\ [9001, 9001, -40*w + 169],\ [9001, 9001, -40*w - 129],\ [9007, 9007, -66*w - 179],\ [9007, 9007, 66*w - 245],\ [9011, 9011, -36*w - 23],\ [9011, 9011, 36*w - 59],\ [9013, 9013, -12*w - 95],\ [9013, 9013, 12*w - 107],\ [9041, 9041, 66*w - 197],\ [9041, 9041, 66*w + 131],\ [9043, 9043, -146*w + 503],\ [9043, 9043, -82*w + 295],\ [9059, 9059, 100*w - 321],\ [9059, 9059, 100*w + 221],\ [9067, 9067, 54*w - 209],\ [9067, 9067, -54*w - 155],\ [9091, 9091, -62*w - 171],\ [9091, 9091, 62*w - 233],\ [9109, 9109, 60*w - 227],\ [9109, 9109, -60*w - 167],\ [9133, 9133, -132*w + 457],\ [9133, 9133, -92*w + 327],\ [9137, 9137, 34*w - 37],\ [9137, 9137, -34*w - 3],\ [9157, 9157, 28*w + 111],\ [9157, 9157, -28*w + 139],\ [9173, 9173, 54*w - 149],\ [9173, 9173, 54*w + 95],\ [9199, 9199, -14*w - 97],\ [9199, 9199, 14*w - 111],\ [9203, 9203, 108*w + 241],\ [9203, 9203, 108*w - 349],\ [9209, 9209, -38*w - 33],\ [9209, 9209, 38*w - 71],\ [9239, 9239, 112*w - 363],\ [9239, 9239, 120*w - 391],\ [9241, 9241, 32*w + 117],\ [9241, 9241, 32*w - 149],\ [9257, 9257, 58*w - 165],\ [9257, 9257, 58*w + 107],\ [9277, 9277, -4*w - 95],\ [9277, 9277, 4*w - 99],\ [9281, 9281, 34*w - 33],\ [9281, 9281, 34*w - 1],\ [9323, 9323, 36*w - 55],\ [9323, 9323, -36*w - 19],\ [9337, 9337, -16*w - 99],\ [9337, 9337, 16*w - 115],\ [9341, 9341, 34*w - 3],\ [9341, 9341, 34*w - 31],\ [9343, 9343, -158*w + 543],\ [9343, 9343, -78*w + 283],\ [9371, 9371, 164*w - 543],\ [9371, 9371, 84*w - 263],\ [9397, 9397, -116*w + 405],\ [9397, 9397, -108*w + 379],\ [9403, 9403, 38*w - 165],\ [9403, 9403, -38*w - 127],\ [9413, 9413, 38*w - 69],\ [9413, 9413, -38*w - 31],\ [9421, 9421, 12*w - 109],\ [9421, 9421, -12*w - 97],\ [9437, 9437, 34*w - 27],\ [9437, 9437, 34*w - 7],\ [9439, 9439, -46*w - 141],\ [9439, 9439, -46*w + 187],\ [9463, 9463, -22*w - 105],\ [9463, 9463, 22*w - 127],\ [9467, 9467, -36*w - 17],\ [9467, 9467, 36*w - 53],\ [9473, 9473, 34*w - 9],\ [9473, 9473, 34*w - 25],\ [9479, 9479, -40*w - 41],\ [9479, 9479, 40*w - 81],\ [9521, 9521, 34*w - 13],\ [9521, 9521, 34*w - 21],\ [9533, 9533, 34*w - 15],\ [9533, 9533, 34*w - 19],\ [9539, 9539, 52*w + 87],\ [9539, 9539, 52*w - 139],\ [9587, 9587, 68*w - 203],\ [9587, 9587, 68*w + 135],\ [9601, 9601, 40*w - 171],\ [9601, 9601, -40*w - 131],\ [9619, 9619, 14*w - 113],\ [9619, 9619, -14*w - 99],\ [9661, 9661, -28*w + 141],\ [9661, 9661, -28*w - 113],\ [9677, 9677, 82*w - 255],\ [9677, 9677, 82*w + 173],\ [9719, 9719, 40*w - 79],\ [9719, 9719, -40*w - 39],\ [9733, 9733, 52*w - 205],\ [9733, 9733, -52*w - 153],\ [9739, 9739, -86*w + 309],\ [9739, 9739, -150*w + 517],\ [9743, 9743, 56*w - 155],\ [9743, 9743, 56*w + 99],\ [9767, 9767, 64*w - 187],\ [9767, 9767, 64*w + 123],\ [9769, 9769, -16*w - 101],\ [9769, 9769, 16*w - 117],\ [9803, 9803, 156*w - 515],\ [9803, 9803, 92*w - 291],\ [9817, 9817, -96*w + 341],\ [9817, 9817, -136*w + 471],\ [9833, 9833, 74*w + 151],\ [9833, 9833, 74*w - 225],\ [9851, 9851, 36*w - 47],\ [9851, 9851, -36*w - 11],\ [9859, 9859, 66*w - 247],\ [9859, 9859, -66*w - 181],\ [9871, 9871, 18*w - 121],\ [9871, 9871, -18*w - 103],\ [9883, 9883, -58*w - 165],\ [9883, 9883, 58*w - 223],\ [9901, 9901, -60*w - 169],\ [9901, 9901, 60*w - 229],\ [9929, 9929, -42*w - 47],\ [9929, 9929, 42*w - 89],\ [9931, 9931, 22*w - 129],\ [9931, 9931, -22*w - 107],\ [9941, 9941, 86*w - 269],\ [9941, 9941, 170*w - 563],\ [9949, 9949, -44*w + 183],\ [9949, 9949, -44*w - 139],\ [9967, 9967, 2*w - 101],\ [9967, 9967, -2*w - 99]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-1, -1, -1, -1, 2, 2, -6, 6, 6, -8, -8, 6, 6, 2, 2, 2, -4, -4, -12, -12, 2, 2, -2, -2, 8, 8, 12, 12, 12, 12, 22, 22, 14, 14, 4, 4, 0, 0, -22, 6, 6, 22, 22, 14, 14, 0, 0, 16, 16, -12, -12, 6, 6, -30, -30, -24, -24, 16, 16, 18, 18, 6, 6, -22, -22, -20, -20, -4, -4, 8, 8, -38, -32, -32, 28, 28, -2, -2, -26, -26, 24, 24, 34, 34, 30, 30, 16, 16, -8, -8, -16, -16, -4, -4, -4, -4, 32, 32, 18, 14, 14, 44, 44, 42, 42, -30, -30, -38, -38, 44, 44, 16, 16, 20, 20, -4, -4, -26, -26, -18, -18, -28, -28, -50, -50, 38, 38, 0, 0, -40, -40, -8, -8, -10, -10, -6, -6, -54, -54, 14, 14, 24, 24, -20, -20, -2, -2, 10, 10, -36, -36, -20, -20, -8, -8, 12, 12, 54, 54, -22, -22, 40, 40, 4, 4, 46, 46, 40, 40, -16, -16, 8, 8, 28, 28, 6, 6, -54, -54, -12, -12, 40, 40, -46, -46, 44, 44, 12, 12, 60, 60, -2, -2, -30, -30, -56, -56, -18, -18, -42, -42, 0, 0, -36, -36, -6, -6, 4, 4, 48, 48, -24, -24, 26, 26, -6, -6, -16, -16, -36, -36, -4, -4, -50, -50, 58, 58, 4, 4, -16, -16, -30, -30, 6, 6, 0, 0, -66, -66, -22, -22, 24, 24, -40, -40, -16, -16, 10, 10, -70, -70, -18, -18, -28, -28, -74, -74, 60, 60, 28, 28, -18, -18, 62, 62, 36, 36, 10, 10, 80, 80, -36, -36, 56, 56, 32, 32, 40, 40, -86, 18, 18, -66, -66, 16, 16, 26, 26, -30, -30, -60, -60, 46, 46, -8, -8, -36, -36, -18, -18, -28, -28, 82, 82, -18, -18, 72, 72, -54, -54, -4, -4, 0, 0, -16, -16, -14, -14, 34, 34, 58, 58, -2, -2, 56, 56, 2, 2, -46, -46, -36, -36, 20, 20, -72, -72, -30, 14, 14, -28, -28, -50, -50, 26, 26, -86, -86, 38, 38, 54, 54, -40, -40, -76, -76, -26, -26, -52, -52, 0, 0, 42, 42, -6, -6, 76, 76, -14, -14, 18, 18, -52, -52, 12, 12, 10, 10, 78, 78, -84, -84, -64, -64, 14, 14, -2, -2, 40, 40, -30, -30, 34, 34, 24, 24, 86, 86, 2, 2, 28, 28, 76, 76, -50, -50, -10, -10, -18, -18, 26, 26, -52, -52, -70, -58, -58, 40, 40, -24, -24, 0, 0, 44, 44, 10, 10, -46, -46, 28, 28, 32, 32, 42, 42, -92, -92, -44, -44, -50, -50, -26, -26, 76, 76, -48, -48, 58, 58, -72, -72, -78, -78, 36, 36, 58, 58, 2, 2, -12, -12, 36, 36, 72, 72, -4, -4, -58, -58, 10, 10, 20, 20, -16, -16, 96, 96, 90, 90, -70, -70, 18, 18, 86, 86, 24, 24, 52, 52, 14, 14, -102, 76, 76, -72, -72, 58, 58, 6, 6, 4, 4, -28, -28, 46, 46, -22, -22, 46, 46, -16, -16, -36, -36, 48, 48, 2, 2, -86, 32, 32, -42, -42, 10, 10, -60, -60, -62, -62, -98, -98, 4, 4, -82, -82, 96, 96, -122, -122, -48, -48, 24, 24, -12, -12, 66, 66, -28, -28, -72, -72, 6, 6, -54, -54, 52, 52, -60, -60, 10, 10, 100, 100, -2, -2, -48, -48, 50, 50, 38, 38, 78, 78, -8, -8, -110, -110, 94, 94, -52, -52, -26, -26, 34, 34, 18, 18, -80, -80, 100, 100, 102, 102, 30, 30, -96, -96, -114, -114, -66, -66, -104, -104, 80, 80, -12, -12, 114, 114, -120, -120, 98, 98, 46, 46, -40, -40, 84, 84, 24, 24, 40, 40, -4, -4, 14, 14, 6, 6, -46, -46, 116, 116, -14, -14, 24, 24, 50, 50, 84, 84, -48, -48, -32, -32, -92, -92, -58, -58, 66, 66, -94, -94, -6, -6, 46, 46, -96, -96, 70, 70, 48, 48, 40, 40, -68, -68, -104, -104, -142, -12, -12, 42, 42, 100, 100, -140, -140, 122, 122, 24, 24, -12, -12, 132, 132, 86, 86, 14, 14, 0, 0, -56, -56, 66, 66, 58, 58, 86, 86, 50, -124, -124, -42, -42, 68, 68, -58, -58, -98, -98, -78, -78, -116, -116, -134, -134, -26, -26, 16, 16, 16, 16, -12, -12, 96, 96, 128, 128, 2, 2, 46, 46, -50, -50, 0, 0, -22, -22, 32, 32, 108, 108, 100, 100, -10, -10, -58, -58, 0, 0, 54, 54, -130, -130, -8, -8, -44, -44, 16, 16, 32, 32, -112, -112, 112, 112, -84, -84, 106, 106, -62, -62, 48, 48, 44, 44, 44, 44, -90, -90, 56, 56, -42, -42, 4, 4, 48, 48, 10, 10, 82, 82, -42, -42, -62, -62, -38, -38, -4, -4, -10, -10, 44, 44, -58, -58, -58, -58, -142, -18, -18, -8, -8, -48, -48, -108, -108, -2, -2, -24, -24, 2, 2, 122, 122, 138, 138, -96, -96, 118, 118, 92, 92, -68, -68, 134, 134, -16, -16, -100, -100, -70, -70, 140, 140, 32, 32, 94, 94, 100, 100, -18, -18, 80, 80, 110, 110, -86, -86, -52, -52, -2, -2, -56, -56, 36, 36, -130, -130, 90, 90, -16, -16, -108, -108, -84, -84, 24, 24, 50, 50, -112, -112, -28, -28, 86, 86, 150, 150, 92, 92, -120, -120, -120, -120, 120, 120, 74, 74, -48, -48, 122, 122, -30, -30, -12, -12, 28, 28, 134, 134, -60, -60, -30, -30, 110, 110, 72, 72, -78, -78, 58, 58, 114, 114, -86, -86, -12, -12, -168, -168, -158, -158, 60, 60, 36, 36, 84, 84, 62, 62, -162, -162, 72, 72, 138, 138, 118, 118, -106, -106, 24, 24, 16, 16, 70, 70, 88, 88, 18, 18, -46, -46, 64, 64, 156, 156, -124, -124, -86, -86, -34, -34, -128, -128, 78, 78, 2, 2, 64, 64, 30, 30, 30, 30, -144, -144, 108, 108, 16, 16, -142, 90, 90, -114, -114, 0, 0, 20, 20, 130, 130, -10, -10, -74, -74, 42, 42, -96, -96, 138, 138, 110, 110, -106, -106, -42, -42, -164, -164, -168, -168, -62, -62, -84, -84, -18, -18, 106, 106, -24, -24, 156, 156, -18, -18, -94, -94, -132, -132, -96, -96, -112, -112, 128, 128, 66, 66, 52, 52, -24, -24, 44, 44, 6, 6, -138, -138, 146, 146, -26, -26, -88, -88, -16, -16, 134, 134, -30, -30, -166, -166, -158, -158, 126, 126, 68, 68, -54, -54, -22, -22, -44, -44, 124, 124, -96, -96, 52, 52, 126, 126, -34, -34, 110, 110, -160, -160, -38, -38, -48, -48, -76, -76, -106, -106, 18, 18, 84, 84, -76, -76, -108, -108, -140, -140, -122, -122, -146, -146, 186, 186, 6, 6, -18, -18, -16, -16, -188, -188, -102, -102, -96, -96, 26, 26, -118, -118, 94, 94, -30, -30, 4, 4, -166, -166, -66, -66, -40, -40, 108, 108, -10, -10, -4, -4, 22, 22, 174, 174, 142, 142, -40, -40, -80, -80, 100, 100, 66, 66, -120, -120, -174, -174, -186, -186, 84, 84, -36, -36, -110, -110, -164, -164, 62, 62, -90, -90, 136, 136, -74, -74, 20, 20, -8, -8, 72, 72, 58, 58, 12, 12, -54, -54, -158, -158, 60, 60, 68, 68, 40, 40, 36, 36, -18, -18, -150, -150, -60, -60, 174, 174, -82, -82, -80, -80] 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, 2*w - 7])] = 1 AL_eigenvalues[ZF.ideal([11, 11, 4*w - 13])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]