/* 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([-6, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([578, 34, 17*w - 34]) primes_array = [ [2, 2, -w + 2],\ [3, 3, w - 3],\ [5, 5, w + 1],\ [5, 5, w - 1],\ [19, 19, w + 5],\ [19, 19, -w + 5],\ [23, 23, -2*w + 1],\ [23, 23, -2*w - 1],\ [29, 29, -3*w + 5],\ [29, 29, -3*w - 5],\ [43, 43, -w - 7],\ [43, 43, w - 7],\ [47, 47, 4*w - 7],\ [47, 47, 6*w - 13],\ [49, 7, -7],\ [53, 53, -3*w - 1],\ [53, 53, 3*w - 1],\ [67, 67, -7*w + 19],\ [67, 67, -3*w + 11],\ [71, 71, -4*w - 5],\ [71, 71, 4*w - 5],\ [73, 73, -4*w + 13],\ [73, 73, -6*w + 17],\ [97, 97, 2*w - 11],\ [97, 97, -2*w - 11],\ [101, 101, 5*w - 7],\ [101, 101, -5*w - 7],\ [121, 11, -11],\ [139, 139, -9*w + 25],\ [139, 139, -5*w + 17],\ [149, 149, -5*w - 1],\ [149, 149, 5*w - 1],\ [163, 163, -w - 13],\ [163, 163, w - 13],\ [167, 167, -6*w - 7],\ [167, 167, 6*w - 7],\ [169, 13, -13],\ [173, 173, 13*w - 29],\ [173, 173, 7*w - 11],\ [191, 191, 6*w - 5],\ [191, 191, -6*w - 5],\ [193, 193, -4*w + 17],\ [193, 193, 14*w - 37],\ [197, 197, 9*w - 17],\ [197, 197, -11*w + 23],\ [211, 211, -5*w - 19],\ [211, 211, 5*w - 19],\ [239, 239, 10*w - 19],\ [239, 239, -12*w + 25],\ [241, 241, -8*w + 25],\ [241, 241, -10*w + 29],\ [263, 263, -8*w - 11],\ [263, 263, 8*w - 11],\ [269, 269, -7*w - 5],\ [269, 269, 7*w - 5],\ [283, 283, -w - 17],\ [283, 283, w - 17],\ [289, 17, -17],\ [293, 293, -7*w - 1],\ [293, 293, 7*w - 1],\ [307, 307, 3*w - 19],\ [307, 307, -3*w - 19],\ [311, 311, -16*w + 35],\ [311, 311, 10*w - 17],\ [313, 313, -6*w - 23],\ [313, 313, 6*w - 23],\ [317, 317, 9*w - 13],\ [317, 317, 19*w - 43],\ [331, 331, -7*w + 25],\ [331, 331, -15*w + 41],\ [337, 337, 2*w - 19],\ [337, 337, -2*w - 19],\ [359, 359, 8*w - 5],\ [359, 359, -8*w - 5],\ [379, 379, 5*w - 23],\ [379, 379, -5*w - 23],\ [383, 383, -8*w - 1],\ [383, 383, 8*w - 1],\ [389, 389, 13*w - 25],\ [389, 389, -15*w + 31],\ [409, 409, -6*w + 25],\ [409, 409, 20*w - 53],\ [431, 431, 10*w - 13],\ [431, 431, -10*w - 13],\ [433, 433, -4*w - 23],\ [433, 433, 4*w - 23],\ [457, 457, -18*w + 49],\ [457, 457, -8*w + 29],\ [461, 461, -9*w - 5],\ [461, 461, 9*w - 5],\ [479, 479, -10*w - 11],\ [479, 479, 10*w - 11],\ [499, 499, -15*w + 43],\ [499, 499, -11*w + 35],\ [503, 503, 12*w - 19],\ [503, 503, 22*w - 49],\ [509, 509, 15*w - 29],\ [509, 509, -17*w + 35],\ [523, 523, -w - 23],\ [523, 523, w - 23],\ [547, 547, -7*w + 29],\ [547, 547, 23*w - 61],\ [557, 557, 11*w - 13],\ [557, 557, -11*w - 13],\ [571, 571, 3*w - 25],\ [571, 571, -3*w - 25],\ [577, 577, -8*w - 31],\ [577, 577, 8*w - 31],\ [599, 599, -10*w - 1],\ [599, 599, 10*w - 1],\ [601, 601, 2*w - 25],\ [601, 601, -2*w - 25],\ [619, 619, -w - 25],\ [619, 619, w - 25],\ [643, 643, -11*w + 37],\ [643, 643, -19*w + 53],\ [647, 647, 14*w - 23],\ [647, 647, -24*w + 53],\ [653, 653, 13*w - 19],\ [653, 653, 27*w - 61],\ [673, 673, -14*w + 43],\ [673, 673, -16*w + 47],\ [677, 677, 11*w - 7],\ [677, 677, -11*w - 7],\ [691, 691, -5*w - 29],\ [691, 691, 5*w - 29],\ [701, 701, 11*w - 5],\ [701, 701, -11*w - 5],\ [719, 719, 18*w - 35],\ [719, 719, -20*w + 41],\ [739, 739, -9*w - 35],\ [739, 739, 9*w - 35],\ [743, 743, 12*w - 11],\ [743, 743, -12*w - 11],\ [769, 769, -10*w + 37],\ [769, 769, -24*w + 65],\ [773, 773, 17*w - 31],\ [773, 773, -23*w + 49],\ [787, 787, -3*w - 29],\ [787, 787, 3*w - 29],\ [797, 797, 19*w - 37],\ [797, 797, -21*w + 43],\ [811, 811, 5*w - 31],\ [811, 811, -5*w - 31],\ [821, 821, 29*w - 65],\ [821, 821, 15*w - 23],\ [839, 839, -12*w - 5],\ [839, 839, 12*w - 5],\ [859, 859, -19*w + 55],\ [859, 859, -15*w + 47],\ [863, 863, -12*w - 1],\ [863, 863, 12*w - 1],\ [883, 883, -9*w + 37],\ [883, 883, 29*w - 77],\ [887, 887, -14*w - 17],\ [887, 887, 14*w - 17],\ [907, 907, 3*w - 31],\ [907, 907, -3*w - 31],\ [911, 911, 16*w - 25],\ [911, 911, 30*w - 67],\ [937, 937, 2*w - 31],\ [937, 937, -2*w - 31],\ [941, 941, -25*w + 53],\ [941, 941, 19*w - 35],\ [961, 31, -31],\ [983, 983, -28*w + 61],\ [983, 983, 18*w - 31],\ [1009, 1009, -6*w - 35],\ [1009, 1009, 6*w - 35],\ [1013, 1013, -13*w - 1],\ [1013, 1013, 13*w - 1],\ [1031, 1031, 20*w - 37],\ [1031, 1031, -26*w + 55],\ [1033, 1033, -14*w + 47],\ [1033, 1033, -24*w + 67],\ [1051, 1051, -15*w + 49],\ [1051, 1051, -23*w + 65],\ [1061, 1061, 15*w - 17],\ [1061, 1061, -15*w - 17],\ [1103, 1103, 32*w - 71],\ [1103, 1103, 18*w - 29],\ [1109, 1109, 17*w - 25],\ [1109, 1109, 35*w - 79],\ [1123, 1123, -11*w - 43],\ [1123, 1123, 11*w - 43],\ [1129, 1129, -4*w - 35],\ [1129, 1129, 4*w - 35],\ [1151, 1151, -14*w - 5],\ [1151, 1151, 14*w - 5],\ [1153, 1153, 6*w - 37],\ [1153, 1153, -6*w - 37],\ [1171, 1171, -3*w - 35],\ [1171, 1171, 3*w - 35],\ [1181, 1181, -15*w - 13],\ [1181, 1181, 15*w - 13],\ [1201, 1201, 2*w - 35],\ [1201, 1201, -2*w - 35],\ [1223, 1223, -28*w + 59],\ [1223, 1223, 22*w - 41],\ [1229, 1229, 15*w - 11],\ [1229, 1229, -15*w - 11],\ [1249, 1249, -10*w - 43],\ [1249, 1249, 10*w - 43],\ [1277, 1277, -31*w + 67],\ [1277, 1277, 21*w - 37],\ [1291, 1291, -25*w + 71],\ [1291, 1291, -17*w + 55],\ [1297, 1297, 8*w - 41],\ [1297, 1297, -8*w - 41],\ [1301, 1301, 15*w - 7],\ [1301, 1301, -15*w - 7],\ [1319, 1319, 18*w - 25],\ [1319, 1319, -18*w - 25],\ [1321, 1321, -20*w + 61],\ [1321, 1321, -22*w + 65],\ [1367, 1367, -16*w - 13],\ [1367, 1367, 16*w - 13],\ [1369, 37, -37],\ [1373, 1373, 17*w - 19],\ [1373, 1373, -17*w - 19],\ [1439, 1439, 20*w - 31],\ [1439, 1439, 38*w - 85],\ [1459, 1459, -15*w + 53],\ [1459, 1459, -31*w + 85],\ [1483, 1483, -11*w + 47],\ [1483, 1483, 39*w - 103],\ [1487, 1487, -16*w - 7],\ [1487, 1487, 16*w - 7],\ [1489, 1489, -16*w + 55],\ [1489, 1489, -30*w + 83],\ [1493, 1493, -33*w + 71],\ [1493, 1493, 23*w - 41],\ [1511, 1511, 16*w - 5],\ [1511, 1511, -16*w - 5],\ [1531, 1531, 5*w - 41],\ [1531, 1531, -5*w - 41],\ [1559, 1559, 42*w - 95],\ [1559, 1559, 20*w - 29],\ [1579, 1579, -25*w + 73],\ [1579, 1579, -21*w + 65],\ [1583, 1583, -18*w - 19],\ [1583, 1583, 18*w - 19],\ [1607, 1607, 24*w - 43],\ [1607, 1607, -34*w + 73],\ [1609, 1609, 10*w - 47],\ [1609, 1609, -10*w - 47],\ [1613, 1613, 17*w - 11],\ [1613, 1613, -17*w - 11],\ [1627, 1627, -3*w - 41],\ [1627, 1627, 3*w - 41],\ [1637, 1637, -19*w - 23],\ [1637, 1637, 19*w - 23],\ [1657, 1657, 2*w - 41],\ [1657, 1657, -2*w - 41],\ [1681, 41, -41],\ [1699, 1699, 5*w - 43],\ [1699, 1699, -5*w - 43],\ [1709, 1709, -17*w - 5],\ [1709, 1709, 17*w - 5],\ [1723, 1723, -9*w - 47],\ [1723, 1723, 9*w - 47],\ [1733, 1733, -17*w - 1],\ [1733, 1733, 17*w - 1],\ [1747, 1747, -33*w + 91],\ [1747, 1747, -17*w + 59],\ [1753, 1753, -4*w - 43],\ [1753, 1753, 4*w - 43],\ [1777, 1777, -32*w + 89],\ [1777, 1777, -18*w + 61],\ [1801, 1801, -10*w - 49],\ [1801, 1801, 10*w - 49],\ [1823, 1823, -18*w - 11],\ [1823, 1823, 18*w - 11],\ [1847, 1847, -36*w + 77],\ [1847, 1847, 26*w - 47],\ [1867, 1867, -27*w + 79],\ [1867, 1867, -23*w + 71],\ [1871, 1871, -20*w - 23],\ [1871, 1871, 20*w - 23],\ [1873, 1873, -24*w + 73],\ [1873, 1873, -26*w + 77],\ [1877, 1877, -19*w - 17],\ [1877, 1877, 19*w - 17],\ [1901, 1901, -39*w + 85],\ [1901, 1901, 25*w - 43],\ [1949, 1949, 45*w - 101],\ [1949, 1949, 23*w - 35],\ [1973, 1973, 27*w - 49],\ [1973, 1973, -37*w + 79],\ [1987, 1987, -37*w + 101],\ [1987, 1987, -17*w + 61],\ [1993, 1993, -6*w - 47],\ [1993, 1993, 6*w - 47],\ [1997, 1997, -19*w - 13],\ [1997, 1997, 19*w - 13],\ [2011, 2011, 45*w - 119],\ [2011, 2011, -13*w + 55],\ [2017, 2017, 8*w - 49],\ [2017, 2017, -8*w - 49],\ [2039, 2039, 20*w - 19],\ [2039, 2039, -20*w - 19],\ [2063, 2063, 22*w - 29],\ [2063, 2063, -22*w - 29],\ [2069, 2069, -43*w + 95],\ [2069, 2069, 25*w - 41],\ [2083, 2083, 11*w - 53],\ [2083, 2083, -11*w - 53],\ [2087, 2087, 24*w - 37],\ [2087, 2087, 46*w - 103],\ [2089, 2089, -20*w + 67],\ [2089, 2089, -34*w + 95],\ [2111, 2111, 20*w - 17],\ [2111, 2111, -20*w - 17],\ [2113, 2113, -4*w - 47],\ [2113, 2113, 4*w - 47],\ [2131, 2131, -15*w - 59],\ [2131, 2131, 15*w - 59],\ [2137, 2137, -22*w + 71],\ [2137, 2137, -32*w + 91],\ [2141, 2141, -19*w - 5],\ [2141, 2141, 19*w - 5],\ [2161, 2161, -12*w - 55],\ [2161, 2161, 12*w - 55],\ [2179, 2179, -29*w + 85],\ [2179, 2179, -25*w + 77],\ [2203, 2203, -w - 47],\ [2203, 2203, w - 47],\ [2207, 2207, 26*w - 43],\ [2207, 2207, -44*w + 97],\ [2213, 2213, -23*w - 31],\ [2213, 2213, 23*w - 31],\ [2237, 2237, 29*w - 53],\ [2237, 2237, -39*w + 83],\ [2251, 2251, -5*w - 49],\ [2251, 2251, 5*w - 49],\ [2281, 2281, -18*w + 65],\ [2281, 2281, -40*w + 109],\ [2309, 2309, 33*w - 65],\ [2309, 2309, -35*w + 71],\ [2333, 2333, -23*w - 29],\ [2333, 2333, 23*w - 29],\ [2347, 2347, 3*w - 49],\ [2347, 2347, -3*w - 49],\ [2351, 2351, -20*w - 7],\ [2351, 2351, 20*w - 7],\ [2357, 2357, -21*w - 17],\ [2357, 2357, 21*w - 17],\ [2371, 2371, -15*w + 61],\ [2371, 2371, 47*w - 125],\ [2377, 2377, 2*w - 49],\ [2377, 2377, -2*w - 49],\ [2381, 2381, 25*w - 37],\ [2381, 2381, 51*w - 115],\ [2399, 2399, -20*w - 1],\ [2399, 2399, 20*w - 1],\ [2423, 2423, 32*w - 61],\ [2423, 2423, -38*w + 79],\ [2447, 2447, 34*w - 67],\ [2447, 2447, -36*w + 73],\ [2467, 2467, 13*w - 59],\ [2467, 2467, -13*w - 59],\ [2473, 2473, -24*w + 77],\ [2473, 2473, -34*w + 97],\ [2477, 2477, 21*w - 13],\ [2477, 2477, -21*w - 13],\ [2521, 2521, -28*w + 85],\ [2521, 2521, -30*w + 89],\ [2539, 2539, 9*w - 55],\ [2539, 2539, -9*w - 55],\ [2543, 2543, -22*w - 19],\ [2543, 2543, 22*w - 19],\ [2549, 2549, 23*w - 25],\ [2549, 2549, -23*w - 25],\ [2591, 2591, 30*w - 53],\ [2591, 2591, -44*w + 95],\ [2593, 2593, -6*w - 53],\ [2593, 2593, 6*w - 53],\ [2617, 2617, -12*w - 59],\ [2617, 2617, 12*w - 59],\ [2621, 2621, 21*w - 5],\ [2621, 2621, -21*w - 5],\ [2659, 2659, 5*w - 53],\ [2659, 2659, -5*w - 53],\ [2663, 2663, 32*w - 59],\ [2663, 2663, -42*w + 89],\ [2683, 2683, -41*w + 113],\ [2683, 2683, -21*w + 73],\ [2687, 2687, 26*w - 37],\ [2687, 2687, 56*w - 127],\ [2689, 2689, -16*w + 65],\ [2689, 2689, 50*w - 133],\ [2693, 2693, 53*w - 119],\ [2693, 2693, 27*w - 41],\ [2707, 2707, 13*w - 61],\ [2707, 2707, -13*w - 61],\ [2711, 2711, -40*w + 83],\ [2711, 2711, 34*w - 65],\ [2713, 2713, 4*w - 53],\ [2713, 2713, -4*w - 53],\ [2731, 2731, -7*w - 55],\ [2731, 2731, 7*w - 55],\ [2741, 2741, 31*w - 55],\ [2741, 2741, -45*w + 97],\ [2789, 2789, 25*w - 31],\ [2789, 2789, -25*w - 31],\ [2803, 2803, -w - 53],\ [2803, 2803, w - 53],\ [2833, 2833, -36*w + 103],\ [2833, 2833, -26*w + 83],\ [2837, 2837, 29*w - 47],\ [2837, 2837, -51*w + 113],\ [2851, 2851, -27*w + 85],\ [2851, 2851, -35*w + 101],\ [2857, 2857, 12*w - 61],\ [2857, 2857, -12*w - 61],\ [2861, 2861, 35*w - 67],\ [2861, 2861, -41*w + 85],\ [2879, 2879, -22*w - 5],\ [2879, 2879, 22*w - 5],\ [2903, 2903, -22*w - 1],\ [2903, 2903, 22*w - 1],\ [2909, 2909, 25*w - 29],\ [2909, 2909, -25*w - 29],\ [2927, 2927, 24*w - 23],\ [2927, 2927, -24*w - 23],\ [2953, 2953, 54*w - 143],\ [2953, 2953, -16*w + 67],\ [2957, 2957, 31*w - 53],\ [2957, 2957, -49*w + 107],\ [2971, 2971, 3*w - 55],\ [2971, 2971, -3*w - 55],\ [2999, 2999, 30*w - 49],\ [2999, 2999, -52*w + 115],\ [3001, 3001, 2*w - 55],\ [3001, 3001, -2*w - 55],\ [3019, 3019, -w - 55],\ [3019, 3019, w - 55],\ [3023, 3023, 58*w - 131],\ [3023, 3023, 28*w - 41],\ [3049, 3049, -14*w - 65],\ [3049, 3049, 14*w - 65],\ [3067, 3067, -23*w + 79],\ [3067, 3067, -43*w + 119],\ [3119, 3119, -50*w + 109],\ [3119, 3119, 32*w - 55],\ [3121, 3121, 10*w - 61],\ [3121, 3121, -10*w - 61],\ [3163, 3163, 19*w - 73],\ [3163, 3163, -19*w - 73],\ [3167, 3167, 24*w - 17],\ [3167, 3167, -24*w - 17],\ [3169, 3169, -40*w + 113],\ [3169, 3169, -26*w + 85],\ [3187, 3187, -7*w - 59],\ [3187, 3187, 7*w - 59],\ [3191, 3191, 30*w - 47],\ [3191, 3191, 56*w - 125],\ [3217, 3217, -38*w + 109],\ [3217, 3217, -28*w + 89],\ [3221, 3221, -25*w - 23],\ [3221, 3221, 25*w - 23],\ [3259, 3259, -35*w + 103],\ [3259, 3259, -31*w + 95],\ [3307, 3307, -17*w + 71],\ [3307, 3307, 57*w - 151],\ [3313, 3313, -14*w - 67],\ [3313, 3313, 14*w - 67],\ [3331, 3331, -5*w - 59],\ [3331, 3331, 5*w - 59],\ [3359, 3359, 40*w - 79],\ [3359, 3359, -42*w + 85],\ [3361, 3361, 12*w - 65],\ [3361, 3361, -12*w - 65],\ [3389, 3389, -25*w - 19],\ [3389, 3389, 25*w - 19],\ [3407, 3407, -24*w - 7],\ [3407, 3407, 24*w - 7],\ [3413, 3413, -27*w - 31],\ [3413, 3413, 27*w - 31],\ [3433, 3433, -24*w + 83],\ [3433, 3433, -46*w + 127],\ [3457, 3457, 2*w - 59],\ [3457, 3457, -2*w - 59],\ [3461, 3461, -25*w - 17],\ [3461, 3461, 25*w - 17],\ [3481, 59, -59],\ [3499, 3499, -11*w - 65],\ [3499, 3499, 11*w - 65],\ [3527, 3527, 26*w - 23],\ [3527, 3527, -26*w - 23],\ [3529, 3529, -20*w - 77],\ [3529, 3529, 20*w - 77],\ [3533, 3533, 27*w - 29],\ [3533, 3533, -27*w - 29],\ [3547, 3547, -43*w + 121],\ [3547, 3547, -27*w + 89],\ [3557, 3557, 61*w - 137],\ [3557, 3557, 31*w - 47],\ [3571, 3571, 5*w - 61],\ [3571, 3571, -5*w - 61],\ [3581, 3581, -25*w - 13],\ [3581, 3581, 25*w - 13],\ [3623, 3623, -48*w + 101],\ [3623, 3623, 38*w - 71],\ [3643, 3643, -31*w + 97],\ [3643, 3643, -39*w + 113],\ [3671, 3671, -46*w + 95],\ [3671, 3671, 40*w - 77],\ [3673, 3673, -34*w + 103],\ [3673, 3673, -36*w + 107],\ [3677, 3677, -29*w - 37],\ [3677, 3677, 29*w - 37],\ [3691, 3691, -15*w - 71],\ [3691, 3691, 15*w - 71],\ [3697, 3697, 2*w - 61],\ [3697, 3697, -2*w - 61],\ [3701, 3701, 25*w - 7],\ [3701, 3701, -25*w - 7],\ [3719, 3719, -30*w - 41],\ [3719, 3719, 30*w - 41],\ [3721, 61, -61],\ [3739, 3739, -9*w - 65],\ [3739, 3739, 9*w - 65],\ [3767, 3767, 26*w - 17],\ [3767, 3767, -26*w - 17],\ [3769, 3769, -50*w + 137],\ [3769, 3769, -24*w + 85],\ [3793, 3793, -16*w - 73],\ [3793, 3793, 16*w - 73],\ [3797, 3797, 39*w - 73],\ [3797, 3797, -49*w + 103],\ [3821, 3821, -29*w - 35],\ [3821, 3821, 29*w - 35],\ [3863, 3863, -28*w - 29],\ [3863, 3863, 28*w - 29],\ [3889, 3889, 10*w - 67],\ [3889, 3889, -10*w - 67],\ [3907, 3907, -47*w + 131],\ [3907, 3907, -27*w + 91],\ [3911, 3911, -60*w + 133],\ [3911, 3911, 34*w - 55],\ [3917, 3917, -31*w - 43],\ [3917, 3917, 31*w - 43],\ [3931, 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-40*w - 19],\ [9239, 9239, 40*w - 19],\ [9241, 9241, 30*w - 121],\ [9241, 9241, -30*w - 121],\ [9283, 9283, 19*w - 107],\ [9283, 9283, -19*w - 107],\ [9293, 9293, 57*w - 101],\ [9293, 9293, -83*w + 179],\ [9311, 9311, 40*w - 17],\ [9311, 9311, -40*w - 17],\ [9337, 9337, 12*w - 101],\ [9337, 9337, -12*w - 101],\ [9341, 9341, -45*w - 53],\ [9341, 9341, 45*w - 53],\ [9403, 9403, -w - 97],\ [9403, 9403, w - 97],\ [9413, 9413, -43*w - 41],\ [9413, 9413, 43*w - 41],\ [9431, 9431, 40*w - 13],\ [9431, 9431, -40*w - 13],\ [9433, 9433, 14*w - 103],\ [9433, 9433, -14*w - 103],\ [9437, 9437, -81*w + 173],\ [9437, 9437, 59*w - 107],\ [9461, 9461, 41*w - 25],\ [9461, 9461, -41*w - 25],\ [9479, 9479, -40*w - 11],\ [9479, 9479, 40*w - 11],\ [9533, 9533, 47*w - 61],\ [9533, 9533, -47*w - 61],\ [9547, 9547, -67*w + 191],\ [9547, 9547, -47*w + 151],\ [9551, 9551, 40*w - 7],\ [9551, 9551, -40*w - 7],\ [9601, 9601, 10*w - 101],\ [9601, 9601, -10*w - 101],\ [9619, 9619, -65*w + 187],\ [9619, 9619, -49*w + 155],\ [9623, 9623, -42*w - 31],\ [9623, 9623, 42*w - 31],\ [9629, 9629, 95*w - 211],\ [9629, 9629, 53*w - 85],\ [9643, 9643, -39*w + 137],\ [9643, 9643, -79*w + 217],\ [9649, 9649, -64*w + 185],\ [9649, 9649, -50*w + 157],\ [9677, 9677, 101*w - 227],\ [9677, 9677, 51*w - 77],\ [9697, 9697, -52*w + 161],\ [9697, 9697, -62*w + 181],\ [9719, 9719, 60*w - 109],\ [9719, 9719, -82*w + 175],\ [9721, 9721, -40*w + 139],\ [9721, 9721, -78*w + 215],\ [9739, 9739, -59*w + 175],\ [9739, 9739, -55*w + 167],\ [9743, 9743, 42*w - 29],\ [9743, 9743, -42*w - 29],\ [9749, 9749, 45*w - 49],\ [9749, 9749, -45*w - 49],\ [9767, 9767, 44*w - 43],\ [9767, 9767, -44*w - 43],\ [9769, 9769, -24*w - 115],\ [9769, 9769, 24*w - 115],\ [9787, 9787, 27*w - 119],\ [9787, 9787, -27*w - 119],\ [9791, 9791, -90*w + 197],\ [9791, 9791, 56*w - 95],\ [9811, 9811, -87*w + 235],\ [9811, 9811, -35*w + 131],\ [9817, 9817, -8*w - 101],\ [9817, 9817, 8*w - 101],\ [9839, 9839, 62*w - 115],\ [9839, 9839, -80*w + 169],\ [9859, 9859, 31*w - 125],\ [9859, 9859, -31*w - 125],\ [9883, 9883, 11*w - 103],\ [9883, 9883, -11*w - 103],\ [9887, 9887, 46*w - 53],\ [9887, 9887, -46*w - 53],\ [9907, 9907, -7*w - 101],\ [9907, 9907, 7*w - 101],\ [9931, 9931, -75*w + 209],\ [9931, 9931, -43*w + 145],\ [9941, 9941, 45*w - 47],\ [9941, 9941, -45*w - 47]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-1, 1, 3, 0, -1, -1, -6, 0, -6, -6, -1, 8, -3, 0, -10, -12, 9, 2, 2, -15, 6, 11, -7, 11, 2, 0, -3, 5, -1, -1, -18, 6, -16, 2, 0, 9, 20, 15, -6, -18, -24, 2, 20, -12, 6, -16, -7, -27, 6, -10, -10, 27, -18, -24, -6, -4, 32, 1, -18, 6, 20, -16, 15, -24, -4, -22, 3, -12, 14, 14, 5, 23, 3, 0, 8, 8, 3, 24, -3, 24, 20, -34, 36, 12, -16, 2, -10, 26, -3, -12, 15, 30, 5, -13, 9, 42, -6, -21, 20, 29, -4, -22, 30, -18, 47, -7, -10, 8, 18, -9, -37, 26, -28, -1, 14, 14, -12, -21, -30, -27, -22, -31, 3, 42, -10, -10, -42, 42, -36, 24, 38, -34, 48, 36, -49, -22, -12, -9, -52, 38, -18, 15, 38, -34, 36, -39, 9, 42, 35, -55, 21, -24, -7, 11, -3, 36, 38, -16, 15, -12, -46, 17, -9, -42, 8, 18, 24, 35, -1, -27, 12, -6, -15, 47, 11, -1, -28, -12, -57, -39, 30, -42, 6, 26, -46, 44, -10, -54, 48, -64, 44, 14, -4, -39, -18, -43, -25, 0, -33, -30, 3, 14, -40, -39, -18, 17, -37, 32, -4, 30, 27, 12, 0, -34, 47, -45, -42, -28, -15, 24, 24, 39, 38, 2, -49, 41, -24, 33, 50, -49, 75, 6, 39, -18, -40, -40, -51, -12, -4, 14, 24, 45, -12, -27, -40, -40, 63, 24, -1, 53, 12, -42, 2, 2, 35, 44, 26, 3, 24, -4, -58, -6, -45, -58, 50, -46, -19, 50, -58, -34, 2, 36, -39, -12, -3, 50, -4, -72, -3, -16, 56, -3, 48, 18, 54, 21, 36, -6, 66, -4, 41, 50, -58, 18, 72, -70, -52, 2, -52, -84, 3, -3, 48, -75, -66, 23, -4, 27, -60, -70, 65, -57, -42, 62, 17, 77, 41, 86, -4, 30, -30, -34, 56, -52, 2, 44, 8, -66, -75, 42, -30, 15, -36, -52, 29, 59, 41, -42, 45, -39, 66, -10, -46, 9, 90, 21, 84, 32, -49, -22, -67, -6, -15, -45, 36, -15, 54, 3, 54, -52, 2, 80, -64, -27, -78, 26, 53, 62, 8, -21, -84, -39, -54, 3, 18, -49, 59, 2, 47, 15, 0, 38, 20, -69, -18, 92, 83, -48, -21, -100, -10, -39, 30, -19, 17, 12, 0, -79, -79, -76, 14, 0, -75, 42, 81, 32, 68, -55, -1, 66, -51, 2, -70, -28, -46, 12, 18, 30, -105, 30, 24, -54, 75, -6, 57, -34, 2, -42, 39, 65, -97, -102, -72, -82, -19, 92, -70, -72, -3, -91, -37, 80, -82, -102, -99, -4, 50, -76, -94, -108, 0, 26, 62, 38, 56, 87, -42, -1, 62, -99, 90, -52, 20, -97, -7, -100, 44, 20, 2, 48, -69, 32, -4, -78, 6, -51, 60, 81, 6, 95, 5, 29, -43, 6, 30, -1, -76, 5, -96, -33, -85, 5, 69, 48, 92, 47, 27, 24, -28, 71, -48, -6, 0, -12, -100, -1, 42, -60, -43, 29, 24, 39, -4, 104, -94, -58, 87, 90, 42, -24, 80, 44, 116, 78, 12, -103, 122, 35, -46, -12, -69, 30, 105, 12, 69, -106, -106, 68, -13, 0, 84, 6, -66, 8, -10, 105, 90, 26, 44, -108, -48, 6, 33, 23, 95, 56, 74, -82, -19, -21, 36, 80, 80, 51, 12, 35, -55, -63, -30, -49, 50, -75, -12, -25, 2, 14, -40, -124, -115, 111, 90, 95, -49, -69, 66, 27, -90, 11, -43, -127, 17, 38, 2, 126, -39, -4, -103, -30, -6, -108, 57, -18, -18, 6, -18, -10, -73, 72, 93, -103, 95, -6, -78, -100, -109, -40, -4, 123, -66, 74, 2, 9, 18, 86, 86, -30, 78, 8, -28, -22, -76, -81, 0, 42, 96, 47, 29, -130, 14, -114, -90, 48, 18, -60, -45, -58, -22, -78, 57, 6, 72, 90, 51, 48, 6, 75, -138, -40, 86, -30, 36, 38, 56, 116, 116, -16, 38, -54, -135, -96, -108, -88, 20, -15, 18, 44, 17, -106, -34, -1, 44, -6, -54, -82, 80, 95, -49, 84, 15, 110, 92, -54, 33, 33, -60, -48, -57, -112, 32, -9, 36, 72, 30, -94, 140, 90, 126, 29, -7, 120, 36, 87, -18, 72, -90, 2, -106, 146, 128, 23, -31, -42, -21, -3, -114, -66, -15, -84, 111, -55, -82, -49, 41, 71, -46, 48, 123, -141, 12, -132, 57, 38, 56, -82, -100, 72, -15, -43, 101, -85, -22, -126, 66, 90, -75, 30, -33, 50, 50, -147, -72, -121, 68, 108, -66, -48, -72, 27, 102, -73, 17, -100, -118, -118, -28, 84, 18, 102, 36, 95, -130, -42, -15, -76, -76, -117, -72, 122, -76, -45, 0, -57, 36, 80, -73, -108, 27, 15, -120, 98, -118, 68, -94, -10, -64, -24, 141, 83, 110, 24, -111, 98, -64, 72, 33, 18, -27, 128, 74, 98, 8, -60, 21, 32, 117, 72, -24, -93, -69, -18, 6, 36, 12, 18, -46, 152, -60, 51, 62, -10, -55, 17, -6, -108, 38, -16, -28, 44, 149, -31, 20, -52, -46, -136, 105, -144, -103, 113, -46, 8, -88, -88, -24, -42, 48, 66, -145, 17, -42, 117, 104, -94, 44, -37, 33, -144, 90, 84, -91, -109, 75, -6, -52, -34, 110, 65, -15, 24, 54, 102, 32, 104, 113, -148, 104, 117, -30, 69, 108, 12, -96, 14, -31, -150, 135, 156, -57, -112, 14, 83, -79, 39, -12, 0, 84, 66, 36, -138, -57, 74, -70, 108, -9, -127, 17, -40, -94, -66, 15, 32, -4, -120, 144, 114, -30, 146, 47, -22, -22, -114, 48, 62, 98, 74, 20, 29, -52, -52, -70, -40, 86, -66, -57, 20, 110, -142, 74, -18, -18, -76, 86, -135, -30, -30, -33, 77, 59, -21, 30, 117, 108, -16, 56, 15, 126, 2, -34, 158, -22, 96, 111, -43, -79, -156, 72, -58, -85, -6, 66, 141, 162, -75, -24, -48, -129, 128, -88, -154, 98, 0, -27, -114, 30, 18, -57, -61, -90, 78, -154, 44, -16, -16, -7, 11, 53, -91, 45, 108, -22, -40, -36, -102, 84, -24, 74, 11, 141, -24, -72, -42, 138, 102, 50, 140, -16, -124, 62, 62, 15, 168, 101, 83, 30, 18, 8, 170, 101, -70, 152, 62, 32, -130, 0, -84, 165, 48, 68, -22, 123, 6, 65, -79, -45, 60, 47, 2, -34, -34, -36, 129, -154, -82, 138, -78, -18, 75, 17, 17, 39, -18, 162, 18, -7, -25, -114, 171, 140, -40, 2, -52, 74, 128, -142, 2, -114, 33, 32, 140, -76, -130, 51, -24, -124, 29, 60, 135, 33, -72, -6, -51, 126, -24, -148, 50, -106, 146, 138, -30, -168, -144, -178, 128, 42, 39, -163, -55, -159, 42, -73, -55, 164, -34, 77, -4, 47, 20, 111, 96, 8, -28, 75, -24, 3, 54, -49, 122, 110, -178, -6, 24, 27, -96, -40, -40, 63, 132, 116, -154, -117, 84, 81, 30, -61, 29, 150, -90, -138, -48, -90, 57, -30, 123, 182, -160, -72, -75, 77, 5, -67, -4, -168, -30, 48, 45, 74, -124, -70, 74, -153, -108, -58, 104, -174, 0, -34, -16, 101, -52, 126, -45, 15, -60, 168, -21, -4, -130, -166, 68, 96, -168, -106, -16, -28, -118, 39, -144, 20, -151, 92, 146, 24, 60, -124, 164, -13, 113, -6, 159] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([2, 2, -w + 2])] = 1 AL_eigenvalues[ZF.ideal([289, 17, -17])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]