/* 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([-1, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([124, 62, -10*w + 4]) primes_array = [ [4, 2, 2],\ [5, 5, -2*w + 1],\ [9, 3, 3],\ [11, 11, -3*w + 2],\ [11, 11, -3*w + 1],\ [19, 19, -4*w + 3],\ [19, 19, -4*w + 1],\ [29, 29, w + 5],\ [29, 29, -w + 6],\ [31, 31, -5*w + 2],\ [31, 31, -5*w + 3],\ [41, 41, -6*w + 5],\ [41, 41, w - 7],\ [49, 7, -7],\ [59, 59, 2*w - 9],\ [59, 59, 7*w - 5],\ [61, 61, 3*w - 10],\ [61, 61, -3*w - 7],\ [71, 71, -8*w + 7],\ [71, 71, w - 9],\ [79, 79, 8*w - 5],\ [79, 79, 3*w - 11],\ [89, 89, -10*w - 1],\ [89, 89, 10*w - 11],\ [101, 101, 4*w - 13],\ [101, 101, 5*w - 14],\ [109, 109, -11*w - 1],\ [109, 109, 11*w - 12],\ [131, 131, -12*w - 1],\ [131, 131, 12*w - 13],\ [139, 139, 2*w - 13],\ [139, 139, -11*w + 9],\ [149, 149, 7*w - 18],\ [149, 149, 4*w - 15],\ [151, 151, 5*w - 16],\ [151, 151, 6*w - 17],\ [169, 13, -13],\ [179, 179, 7*w - 19],\ [179, 179, 5*w - 17],\ [181, 181, -14*w - 1],\ [181, 181, 14*w - 15],\ [191, 191, 2*w - 15],\ [191, 191, -13*w + 11],\ [199, 199, 3*w - 16],\ [199, 199, -13*w + 10],\ [211, 211, 6*w - 19],\ [211, 211, 7*w - 20],\ [229, 229, -14*w + 11],\ [229, 229, 3*w - 17],\ [239, 239, -16*w - 1],\ [239, 239, 16*w - 17],\ [241, 241, 9*w - 23],\ [241, 241, 5*w - 19],\ [251, 251, 2*w - 17],\ [251, 251, -15*w + 13],\ [269, 269, 15*w - 11],\ [269, 269, 4*w - 19],\ [271, 271, -17*w - 1],\ [271, 271, 17*w - 18],\ [281, 281, 7*w - 22],\ [281, 281, 8*w - 23],\ [289, 17, -17],\ [311, 311, 5*w - 21],\ [311, 311, 16*w - 11],\ [331, 331, -17*w + 14],\ [331, 331, 3*w - 20],\ [349, 349, 17*w - 12],\ [349, 349, 5*w - 22],\ [359, 359, 10*w - 27],\ [359, 359, 7*w - 24],\ [379, 379, -20*w - 1],\ [379, 379, 20*w - 21],\ [389, 389, 5*w - 23],\ [389, 389, 18*w - 13],\ [401, 401, 7*w - 25],\ [401, 401, 11*w - 29],\ [409, 409, 3*w - 22],\ [409, 409, -19*w + 16],\ [419, 419, -21*w - 1],\ [419, 419, 21*w - 22],\ [421, 421, -19*w + 15],\ [421, 421, 4*w - 23],\ [431, 431, 19*w - 14],\ [431, 431, 5*w - 24],\ [439, 439, 6*w - 25],\ [439, 439, 19*w - 13],\ [449, 449, 8*w - 27],\ [449, 449, 11*w - 30],\ [461, 461, -22*w - 1],\ [461, 461, 22*w - 23],\ [479, 479, 23*w - 25],\ [479, 479, -23*w - 2],\ [491, 491, 13*w - 33],\ [491, 491, 7*w - 27],\ [499, 499, 11*w - 31],\ [499, 499, 9*w - 29],\ [509, 509, 4*w - 25],\ [509, 509, -21*w + 17],\ [521, 521, 5*w - 26],\ [521, 521, 21*w - 16],\ [529, 23, -23],\ [541, 541, 25*w - 28],\ [541, 541, -25*w - 3],\ [569, 569, -22*w + 17],\ [569, 569, 5*w - 27],\ [571, 571, 25*w - 27],\ [571, 571, -25*w - 2],\ [599, 599, -25*w - 1],\ [599, 599, 25*w - 26],\ [601, 601, 13*w - 35],\ [601, 601, 9*w - 31],\ [619, 619, 5*w - 28],\ [619, 619, -23*w + 18],\ [631, 631, 23*w - 17],\ [631, 631, 6*w - 29],\ [641, 641, 23*w - 16],\ [641, 641, 7*w - 30],\ [659, 659, 13*w - 36],\ [659, 659, 10*w - 33],\ [661, 661, 11*w - 34],\ [661, 661, 12*w - 35],\ [691, 691, 28*w - 31],\ [691, 691, -28*w - 3],\ [701, 701, -27*w - 1],\ [701, 701, 27*w - 28],\ [709, 709, 4*w - 29],\ [709, 709, -25*w + 21],\ [719, 719, 13*w - 37],\ [719, 719, 11*w - 35],\ [739, 739, 6*w - 31],\ [739, 739, 25*w - 19],\ [751, 751, 7*w - 32],\ [751, 751, 25*w - 18],\ [761, 761, 8*w - 33],\ [761, 761, 25*w - 17],\ [769, 769, 9*w - 34],\ [769, 769, 16*w - 41],\ [809, 809, 7*w - 33],\ [809, 809, 26*w - 19],\ [811, 811, -29*w - 1],\ [811, 811, 29*w - 30],\ [821, 821, -27*w + 23],\ [821, 821, 4*w - 31],\ [829, 829, 17*w - 43],\ [829, 829, 9*w - 35],\ [839, 839, -27*w + 22],\ [839, 839, 5*w - 32],\ [859, 859, 31*w - 34],\ [859, 859, -31*w - 3],\ [881, 881, 8*w - 35],\ [881, 881, 27*w - 19],\ [911, 911, 13*w - 40],\ [911, 911, 14*w - 41],\ [919, 919, -32*w - 3],\ [919, 919, 32*w - 35],\ [929, 929, -31*w - 1],\ [929, 929, 31*w - 32],\ [941, 941, 33*w - 37],\ [941, 941, -33*w - 4],\ [971, 971, 11*w - 39],\ [971, 971, 17*w - 45],\ [991, 991, -32*w - 1],\ [991, 991, 32*w - 33],\ [1009, 1009, 29*w - 21],\ [1009, 1009, 8*w - 37],\ [1019, 1019, 33*w - 35],\ [1019, 1019, -33*w - 2],\ [1021, 1021, 29*w - 20],\ [1021, 1021, 9*w - 38],\ [1031, 1031, 19*w - 48],\ [1031, 1031, 10*w - 39],\ [1039, 1039, 18*w - 47],\ [1039, 1039, 11*w - 40],\ [1049, 1049, 16*w - 45],\ [1049, 1049, 13*w - 42],\ [1051, 1051, 14*w - 43],\ [1051, 1051, 15*w - 44],\ [1061, 1061, -30*w + 23],\ [1061, 1061, 7*w - 37],\ [1069, 1069, -35*w - 4],\ [1069, 1069, 35*w - 39],\ [1091, 1091, 36*w - 41],\ [1091, 1091, -36*w - 5],\ [1109, 1109, 19*w - 49],\ [1109, 1109, 11*w - 41],\ [1129, 1129, -31*w + 24],\ [1129, 1129, 7*w - 38],\ [1151, 1151, 35*w - 37],\ [1151, 1151, -35*w - 2],\ [1171, 1171, 10*w - 41],\ [1171, 1171, 21*w - 52],\ [1181, 1181, 11*w - 42],\ [1181, 1181, 20*w - 51],\ [1201, 1201, 15*w - 46],\ [1201, 1201, 16*w - 47],\ [1229, 1229, 38*w - 43],\ [1229, 1229, -38*w - 5],\ [1231, 1231, 9*w - 41],\ [1231, 1231, 32*w - 23],\ [1249, 1249, 37*w - 40],\ [1249, 1249, -37*w - 3],\ [1259, 1259, -36*w - 1],\ [1259, 1259, 36*w - 37],\ [1279, 1279, 17*w - 49],\ [1279, 1279, 15*w - 47],\ [1289, 1289, 8*w - 41],\ [1289, 1289, 33*w - 25],\ [1291, 1291, 37*w - 39],\ [1291, 1291, -37*w - 2],\ [1301, 1301, -39*w - 5],\ [1301, 1301, 39*w - 44],\ [1319, 1319, 33*w - 23],\ [1319, 1319, 10*w - 43],\ [1321, 1321, -38*w - 3],\ [1321, 1321, 38*w - 41],\ [1361, 1361, 16*w - 49],\ [1361, 1361, 17*w - 50],\ [1369, 37, -37],\ [1381, 1381, 9*w - 43],\ [1381, 1381, 34*w - 25],\ [1399, 1399, -35*w + 29],\ [1399, 1399, 6*w - 41],\ [1409, 1409, 11*w - 45],\ [1409, 1409, 23*w - 57],\ [1429, 1429, 13*w - 47],\ [1429, 1429, 21*w - 55],\ [1439, 1439, 39*w - 41],\ [1439, 1439, -39*w - 2],\ [1451, 1451, 41*w - 46],\ [1451, 1451, -41*w - 5],\ [1459, 1459, 35*w - 26],\ [1459, 1459, 9*w - 44],\ [1471, 1471, 40*w - 43],\ [1471, 1471, -40*w - 3],\ [1481, 1481, -39*w - 1],\ [1481, 1481, 39*w - 40],\ [1489, 1489, 35*w - 24],\ [1489, 1489, 11*w - 46],\ [1499, 1499, 7*w - 43],\ [1499, 1499, -36*w + 29],\ [1511, 1511, 13*w - 48],\ [1511, 1511, 22*w - 57],\ [1531, 1531, 17*w - 52],\ [1531, 1531, 18*w - 53],\ [1549, 1549, -41*w - 3],\ [1549, 1549, 41*w - 44],\ [1559, 1559, -40*w - 1],\ [1559, 1559, 40*w - 41],\ [1571, 1571, 11*w - 47],\ [1571, 1571, 36*w - 25],\ [1579, 1579, -37*w + 30],\ [1579, 1579, 7*w - 44],\ [1601, 1601, -37*w + 29],\ [1601, 1601, 8*w - 45],\ [1609, 1609, 43*w - 48],\ [1609, 1609, -43*w - 5],\ [1619, 1619, 19*w - 55],\ [1619, 1619, 17*w - 53],\ [1621, 1621, 9*w - 46],\ [1621, 1621, 37*w - 28],\ [1669, 1669, 12*w - 49],\ [1669, 1669, 37*w - 25],\ [1699, 1699, 22*w - 59],\ [1699, 1699, 15*w - 52],\ [1709, 1709, 17*w - 54],\ [1709, 1709, 20*w - 57],\ [1721, 1721, -42*w - 1],\ [1721, 1721, 42*w - 43],\ [1741, 1741, 38*w - 27],\ [1741, 1741, 11*w - 49],\ [1759, 1759, 43*w - 45],\ [1759, 1759, -43*w - 2],\ [1789, 1789, 15*w - 53],\ [1789, 1789, 23*w - 61],\ [1801, 1801, 21*w - 59],\ [1801, 1801, 17*w - 55],\ [1811, 1811, 39*w - 29],\ [1811, 1811, 10*w - 49],\ [1831, 1831, 7*w - 47],\ [1831, 1831, -40*w + 33],\ [1849, 43, -43],\ [1861, 1861, 46*w - 51],\ [1861, 1861, -46*w - 5],\ [1871, 1871, 25*w - 64],\ [1871, 1871, 14*w - 53],\ [1879, 1879, -40*w + 31],\ [1879, 1879, 9*w - 49],\ [1889, 1889, 16*w - 55],\ [1889, 1889, 23*w - 62],\ [1901, 1901, 19*w - 58],\ [1901, 1901, 20*w - 59],\ [1931, 1931, 45*w - 47],\ [1931, 1931, -45*w - 2],\ [1949, 1949, -47*w - 5],\ [1949, 1949, 47*w - 52],\ [1951, 1951, 13*w - 53],\ [1951, 1951, 27*w - 67],\ [1979, 1979, -45*w - 1],\ [1979, 1979, 45*w - 46],\ [1999, 1999, 21*w - 61],\ [1999, 1999, 19*w - 59],\ [2011, 2011, 41*w - 30],\ [2011, 2011, 11*w - 52],\ [2029, 2029, 12*w - 53],\ [2029, 2029, 41*w - 29],\ [2039, 2039, 48*w - 53],\ [2039, 2039, -48*w - 5],\ [2069, 2069, -46*w - 1],\ [2069, 2069, 46*w - 47],\ [2081, 2081, 25*w - 66],\ [2081, 2081, 16*w - 57],\ [2089, 2089, 17*w - 58],\ [2089, 2089, 24*w - 65],\ [2099, 2099, 22*w - 63],\ [2099, 2099, 19*w - 60],\ [2111, 2111, 47*w - 49],\ [2111, 2111, -47*w - 2],\ [2129, 2129, 8*w - 51],\ [2129, 2129, -43*w + 35],\ [2131, 2131, -49*w - 5],\ [2131, 2131, 49*w - 54],\ [2141, 2141, 42*w - 29],\ [2141, 2141, 13*w - 55],\ [2161, 2161, -47*w - 1],\ [2161, 2161, 47*w - 48],\ [2179, 2179, -43*w + 33],\ [2179, 2179, 10*w - 53],\ [2209, 47, -47],\ [2221, 2221, 43*w - 31],\ [2221, 2221, 12*w - 55],\ [2239, 2239, 43*w - 30],\ [2239, 2239, 13*w - 56],\ [2251, 2251, -44*w + 35],\ [2251, 2251, 9*w - 53],\ [2269, 2269, 15*w - 58],\ [2269, 2269, 28*w - 71],\ [2281, 2281, 16*w - 59],\ [2281, 2281, 27*w - 70],\ [2309, 2309, 20*w - 63],\ [2309, 2309, 23*w - 66],\ [2311, 2311, 21*w - 64],\ [2311, 2311, 22*w - 65],\ [2339, 2339, 44*w - 31],\ [2339, 2339, 13*w - 57],\ [2341, 2341, -50*w - 3],\ [2341, 2341, 50*w - 53],\ [2351, 2351, -49*w - 1],\ [2351, 2351, 49*w - 50],\ [2371, 2371, 29*w - 73],\ [2371, 2371, 15*w - 59],\ [2381, 2381, -51*w - 4],\ [2381, 2381, 51*w - 55],\ [2389, 2389, 7*w - 53],\ [2389, 2389, -46*w + 39],\ [2399, 2399, 11*w - 56],\ [2399, 2399, 45*w - 34],\ [2411, 2411, 25*w - 69],\ [2411, 2411, 19*w - 63],\ [2441, 2441, 45*w - 32],\ [2441, 2441, 13*w - 58],\ [2459, 2459, 14*w - 59],\ [2459, 2459, 45*w - 31],\ [2521, 2521, -47*w + 39],\ [2521, 2521, 8*w - 55],\ [2531, 2531, 22*w - 67],\ [2531, 2531, 23*w - 68],\ [2539, 2539, 52*w - 55],\ [2539, 2539, -52*w - 3],\ [2549, 2549, -51*w - 1],\ [2549, 2549, 51*w - 52],\ [2551, 2551, -47*w + 38],\ [2551, 2551, 9*w - 56],\ [2579, 2579, 10*w - 57],\ [2579, 2579, -47*w + 37],\ [2591, 2591, -55*w - 7],\ [2591, 2591, 55*w - 62],\ [2609, 2609, 29*w - 75],\ [2609, 2609, 17*w - 63],\ [2621, 2621, -54*w - 5],\ [2621, 2621, 54*w - 59],\ [2659, 2659, 55*w - 61],\ [2659, 2659, -55*w - 6],\ [2671, 2671, 14*w - 61],\ [2671, 2671, 47*w - 33],\ [2689, 2689, 47*w - 32],\ [2689, 2689, 15*w - 62],\ [2699, 2699, 53*w - 55],\ [2699, 2699, -53*w - 2],\ [2711, 2711, 11*w - 59],\ [2711, 2711, -48*w + 37],\ [2719, 2719, 17*w - 64],\ [2719, 2719, 30*w - 77],\ [2729, 2729, 57*w - 65],\ [2729, 2729, -57*w - 8],\ [2731, 2731, 18*w - 65],\ [2731, 2731, 29*w - 76],\ [2741, 2741, 28*w - 75],\ [2741, 2741, 19*w - 66],\ [2749, 2749, 20*w - 67],\ [2749, 2749, 27*w - 74],\ [2789, 2789, -55*w - 4],\ [2789, 2789, 55*w - 59],\ [2791, 2791, -49*w + 39],\ [2791, 2791, 10*w - 59],\ [2801, 2801, 57*w - 64],\ [2801, 2801, -57*w - 7],\ [2809, 53, -53],\ [2819, 2819, -49*w + 38],\ [2819, 2819, 11*w - 60],\ [2851, 2851, 55*w - 58],\ [2851, 2851, -55*w - 3],\ [2861, 2861, -54*w - 1],\ [2861, 2861, 54*w - 55],\ [2879, 2879, 25*w - 73],\ [2879, 2879, 23*w - 71],\ [2909, 2909, -58*w - 7],\ [2909, 2909, 58*w - 65],\ [2939, 2939, -57*w - 5],\ [2939, 2939, 57*w - 62],\ [2969, 2969, -55*w - 1],\ [2969, 2969, 55*w - 56],\ [2971, 2971, 19*w - 68],\ [2971, 2971, 30*w - 79],\ [2999, 2999, 23*w - 72],\ [2999, 2999, 26*w - 75],\ [3001, 3001, 24*w - 73],\ [3001, 3001, 25*w - 74],\ [3011, 3011, 10*w - 61],\ [3011, 3011, -51*w + 41],\ [3019, 3019, -59*w - 7],\ [3019, 3019, 59*w - 66],\ [3041, 3041, -51*w + 40],\ [3041, 3041, 11*w - 62],\ [3049, 3049, 58*w - 63],\ [3049, 3049, -58*w - 5],\ [3061, 3061, 33*w - 83],\ [3061, 3061, 17*w - 67],\ [3079, 3079, -56*w - 1],\ [3079, 3079, 56*w - 57],\ [3089, 3089, 19*w - 69],\ [3089, 3089, 31*w - 81],\ [3109, 3109, 21*w - 71],\ [3109, 3109, 29*w - 79],\ [3119, 3119, 51*w - 37],\ [3119, 3119, 14*w - 65],\ [3121, 3121, 23*w - 73],\ [3121, 3121, 27*w - 77],\ [3169, 3169, -61*w - 8],\ [3169, 3169, 61*w - 69],\ [3181, 3181, 58*w - 61],\ [3181, 3181, -58*w - 3],\ [3191, 3191, -57*w - 1],\ [3191, 3191, 57*w - 58],\ [3209, 3209, 19*w - 70],\ [3209, 3209, 32*w - 83],\ [3221, 3221, 31*w - 82],\ [3221, 3221, 20*w - 71],\ [3229, 3229, -59*w - 4],\ [3229, 3229, 59*w - 63],\ [3251, 3251, 25*w - 76],\ [3251, 3251, 26*w - 77],\ [3259, 3259, 52*w - 37],\ [3259, 3259, 15*w - 67],\ [3271, 3271, 11*w - 64],\ [3271, 3271, -53*w + 42],\ [3299, 3299, 17*w - 69],\ [3299, 3299, 35*w - 87],\ [3301, 3301, 12*w - 65],\ [3301, 3301, -53*w + 41],\ [3319, 3319, 61*w - 67],\ [3319, 3319, -61*w - 6],\ [3329, 3329, 13*w - 66],\ [3329, 3329, 53*w - 40],\ [3331, 3331, 33*w - 85],\ [3331, 3331, 19*w - 71],\ [3359, 3359, 59*w - 61],\ [3359, 3359, -59*w - 2],\ [3361, 3361, -62*w - 7],\ [3361, 3361, 62*w - 69],\ [3371, 3371, 23*w - 75],\ [3371, 3371, 29*w - 81],\ [3389, 3389, -54*w + 43],\ [3389, 3389, 11*w - 65],\ [3391, 3391, 61*w - 66],\ [3391, 3391, -61*w - 5],\ [3449, 3449, 54*w - 41],\ [3449, 3449, 13*w - 67],\ [3461, 3461, 61*w - 65],\ [3461, 3461, -61*w - 4],\ [3469, 3469, 33*w - 86],\ [3469, 3469, 20*w - 73],\ [3491, 3491, 22*w - 75],\ [3491, 3491, 31*w - 84],\ [3499, 3499, 23*w - 76],\ [3499, 3499, 30*w - 83],\ [3511, 3511, 26*w - 79],\ [3511, 3511, 27*w - 80],\ [3529, 3529, 61*w - 64],\ [3529, 3529, -61*w - 3],\ [3539, 3539, -60*w - 1],\ [3539, 3539, 60*w - 61],\ [3541, 3541, -55*w + 43],\ [3541, 3541, 12*w - 67],\ [3559, 3559, -56*w + 47],\ [3559, 3559, 9*w - 65],\ [3571, 3571, 55*w - 42],\ [3571, 3571, 13*w - 68],\ [3581, 3581, 19*w - 73],\ [3581, 3581, 35*w - 89],\ [3631, 3631, 11*w - 67],\ [3631, 3631, -56*w + 45],\ [3659, 3659, -61*w - 1],\ [3659, 3659, 61*w - 62],\ [3671, 3671, 55*w - 38],\ [3671, 3671, 17*w - 72],\ [3691, 3691, 18*w - 73],\ [3691, 3691, 37*w - 92],\ [3701, 3701, -63*w - 4],\ [3701, 3701, 63*w - 67],\ [3709, 3709, 19*w - 74],\ [3709, 3709, 36*w - 91],\ [3719, 3719, 10*w - 67],\ [3719, 3719, -57*w + 47],\ [3739, 3739, 34*w - 89],\ [3739, 3739, 21*w - 76],\ [3761, 3761, 32*w - 87],\ [3761, 3761, 23*w - 78],\ [3769, 3769, 24*w - 79],\ [3769, 3769, 31*w - 86],\ [3779, 3779, 26*w - 81],\ [3779, 3779, 29*w - 84],\ [3821, 3821, -57*w + 44],\ [3821, 3821, 13*w - 70],\ [3851, 3851, 14*w - 71],\ [3851, 3851, 57*w - 43],\ [3881, 3881, 11*w - 69],\ [3881, 3881, -58*w + 47],\ [3889, 3889, 67*w - 75],\ [3889, 3889, -67*w - 8],\ [3911, 3911, 31*w - 87],\ [3911, 3911, 25*w - 81],\ [3919, 3919, 29*w - 85],\ [3919, 3919, 27*w - 83],\ [3929, 3929, 17*w - 74],\ [3929, 3929, 57*w - 40],\ [3931, 3931, 68*w - 77],\ [3931, 3931, -68*w - 9],\ [3989, 3989, 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9349, -89*w + 68],\ [9349, 9349, 21*w - 110],\ [9371, 9371, 34*w - 121],\ [9371, 9371, 53*w - 140],\ [9391, 9391, 27*w - 115],\ [9391, 9391, 88*w - 61],\ [9409, 97, -97],\ [9419, 9419, 50*w - 137],\ [9419, 9419, 37*w - 124],\ [9421, 9421, 106*w - 121],\ [9421, 9421, -106*w - 15],\ [9431, 9431, 38*w - 125],\ [9431, 9431, 49*w - 136],\ [9439, 9439, 89*w - 66],\ [9439, 9439, 23*w - 112],\ [9461, 9461, 43*w - 130],\ [9461, 9461, 44*w - 131],\ [9479, 9479, -103*w - 10],\ [9479, 9479, 103*w - 113],\ [9491, 9491, 105*w - 118],\ [9491, 9491, -105*w - 13],\ [9511, 9511, 31*w - 119],\ [9511, 9511, 57*w - 145],\ [9521, 9521, 25*w - 114],\ [9521, 9521, 89*w - 64],\ [9539, 9539, 17*w - 108],\ [9539, 9539, -91*w + 74],\ [9551, 9551, -104*w - 11],\ [9551, 9551, 104*w - 115],\ [9601, 9601, -103*w - 9],\ [9601, 9601, 103*w - 112],\ [9619, 9619, -107*w - 15],\ [9619, 9619, 107*w - 122],\ [9629, 9629, 61*w - 150],\ [9629, 9629, 28*w - 117],\ [9631, 9631, 37*w - 125],\ [9631, 9631, 51*w - 139],\ [9649, 9649, -91*w + 72],\ [9649, 9649, 19*w - 110],\ [9661, 9661, 60*w - 149],\ [9661, 9661, 29*w - 118],\ [9679, 9679, 45*w - 133],\ [9679, 9679, 43*w - 131],\ [9689, 9689, -106*w - 13],\ [9689, 9689, 106*w - 119],\ [9719, 9719, 58*w - 147],\ [9719, 9719, 31*w - 120],\ [9721, 9721, -103*w - 8],\ [9721, 9721, 103*w - 111],\ [9739, 9739, 17*w - 109],\ [9739, 9739, -92*w + 75],\ [9749, 9749, 105*w - 116],\ [9749, 9749, -105*w - 11],\ [9769, 9769, 56*w - 145],\ [9769, 9769, 33*w - 122],\ [9781, 9781, 101*w - 105],\ [9781, 9781, -101*w - 4],\ [9791, 9791, 34*w - 123],\ [9791, 9791, 55*w - 144],\ [9811, 9811, 54*w - 143],\ [9811, 9811, 35*w - 124],\ [9829, 9829, 36*w - 125],\ [9829, 9829, 53*w - 142],\ [9839, 9839, 103*w - 110],\ [9839, 9839, -103*w - 7],\ [9851, 9851, 19*w - 111],\ [9851, 9851, -92*w + 73],\ [9859, 9859, 38*w - 127],\ [9859, 9859, 51*w - 140],\ [9871, 9871, 50*w - 139],\ [9871, 9871, 39*w - 128],\ [9901, 9901, 44*w - 133],\ [9901, 9901, 45*w - 134],\ [9929, 9929, 31*w - 121],\ [9929, 9929, 59*w - 149],\ [9931, 9931, 25*w - 116],\ [9931, 9931, 91*w - 66],\ [9941, 9941, -93*w + 76],\ [9941, 9941, 17*w - 110],\ [9949, 9949, -106*w - 11],\ [9949, 9949, 106*w - 117]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [1, 0, -2, -6, 0, 2, 2, 0, 6, 1, -4, 6, -6, 14, -12, 0, 8, -10, -12, 0, 8, 8, 6, -6, 12, 12, -16, 20, -18, 6, 14, -4, 18, 6, 8, 8, -10, 0, -6, 2, -16, -24, 0, -16, -16, -22, 14, -22, -4, -24, 24, -10, 26, -12, 6, 0, 6, -16, 20, 6, -18, 2, -24, 0, -10, 8, -10, 26, 36, -12, -16, 20, -24, -30, 18, 30, -22, -22, 12, 0, 26, -10, -36, 12, 8, 8, 18, 18, 30, 12, -24, 24, 30, 24, 32, 14, -24, -30, -18, 30, -10, -16, 20, -6, -18, -40, -22, -12, 12, -10, -10, 26, 8, 20, -16, -30, 42, -42, 30, 32, -4, 44, -28, 18, -6, 8, 26, -48, 24, 20, 38, -4, -4, -42, 30, -22, 14, 6, -30, 56, 20, 18, 24, 20, 2, 24, 0, -4, -22, 30, 30, 24, -24, -16, 20, -30, 18, 54, 0, 48, -24, -16, -52, -34, -34, 54, -12, -22, -40, -48, 24, -4, -4, -6, -30, -28, -28, 6, 6, -10, 8, -6, -12, 60, -42, -22, 50, -24, 24, 2, -16, -6, 24, -22, 14, 18, 54, 8, 8, -46, 26, 30, -54, 56, -16, 18, -6, 14, 50, -18, -24, 0, 24, 26, -46, 6, -42, -34, -40, -58, -40, 32, 6, -18, 44, -10, 72, 24, 24, 48, 56, 56, -40, 32, -18, 6, 50, -22, 30, -12, -24, -12, 56, 2, -34, 20, 60, 24, -6, 24, -58, 32, -6, 66, -10, 26, 12, 36, -16, -52, 14, -40, 62, -46, -6, -66, -30, 18, -40, -40, -40, -4, -46, 8, 2, -34, 42, 60, 32, -40, -58, -28, -64, -12, 0, 80, -64, -18, 18, -42, -18, -72, 72, -36, -42, 8, 8, 60, 54, -52, 56, -76, 50, -76, -40, -24, -24, 66, 24, 30, 30, 74, 74, 6, -12, -24, -60, 6, -6, -10, -28, -42, -30, 74, 2, 56, 92, 14, 8, -28, -64, 44, -70, 38, -16, 2, -58, -58, 36, -6, -64, -64, -54, -78, 20, 56, 24, 60, -4, 50, 60, -72, -40, -76, 48, -60, -12, 6, -6, -42, 36, -24, -70, -70, -18, 30, -70, 2, 66, 6, -40, 32, -6, -24, -60, -24, -90, 6, 30, -84, 86, 32, 8, -28, 62, 62, -18, -90, -24, -48, -16, -52, 102, 30, 32, -22, -66, 48, 86, -40, -60, 78, -88, -88, -90, 30, 38, 84, 102, -10, 8, 18, -30, 48, -12, -12, 78, 30, -42, 102, -90, 2, 92, -24, -96, -22, -58, -6, 90, -58, -4, 42, -66, 26, 26, 74, 20, -16, 56, 30, 54, -40, 32, -72, -48, -46, -46, 74, -34, -58, 50, 0, -24, -66, 42, -6, -90, -82, 26, -36, 6, 2, 110, -40, 32, 84, 6, -100, -46, -64, 8, 30, -18, -16, 56, 36, -24, -22, 86, -48, -30, 12, 96, 80, -100, -66, -18, -30, 66, -40, -40, 90, -6, 62, 80, -16, -16, -34, 2, 24, -84, 86, -58, -40, -112, 26, 80, 36, -72, -76, 68, 6, -102, -84, 0, -52, 56, 108, 54, 20, -16, 48, -96, -40, 32, 30, 102, -46, 98, -66, -30, -6, -18, -30, -66, 6, -6, 2, -34, 48, 24, -40, -40, 30, -90, -10, -10, -48, 42, -78, -18, -60, -84, 80, -10, 54, 102, 2, 92, -84, -48, 42, -84, -112, 68, -64, 116, 98, 98, -78, -102, 56, -16, 98, -118, 42, -108, -10, 8, -6, -96, 56, 20, 18, 90, -72, -126, 50, 14, 0, -48, -30, 30, -106, 56, 30, -18, 24, 0, -90, -114, -36, 108, 14, 14, -84, -60, -102, -66, 134, 56, 56, -112, 50, -10, -10, -52, -16, -22, -22, -40, -40, -42, 54, -46, -82, -72, 0, 48, 36, 102, 78, 86, 86, 96, 120, 80, 80, -16, 74, 72, -72, -130, 50, -28, 80, -34, 2, 48, 48, -102, -30, -40, -94, 48, -120, 54, 90, -52, -88, 2, 74, -4, -76, -54, 90, -82, 62, 102, -84, 108, -24, -12, 90, -34, 20, -102, 90, 90, -60, 26, 116, 8, -136, 48, 48, -4, -4, 90, 132, 26, 26, -24, 48, -30, 12, 12, 96, 26, 62, -72, 108, -70, 48, 120, 78, -18, -60, 120, 2, -106, 140, 104, -18, -78, 14, 50, 84, 24, -100, 80, -42, -102, 84, -24, 122, -130, 144, -90, 62, 134, 74, 74, -48, 24, 96, 72, -10, 98, -18, 42, 80, -10, 90, 144, 110, -106, 14, -58, 60, 144, 30, 0, -118, -10, -34, 128, 104, 32, 18, -78, -10, 44, -64, -100, 6, -54, 92, 2, 24, 108, 38, 38, -72, -96, 14, -22, -144, -84, 66, 72, -30, -66, -24, -138, 32, 104, 102, 78, 98, 44, -132, -36, 38, 38, -54, -36, -112, -76, -136, 8, 38, 20, -90, 156, 74, -88, 60, 72, -100, -100, 72, -6, 20, 20, 24, -12, 126, 30, -96, 144, -10, 98, 134, 8, -78, -36, 50, 50, -78, 126, -82, 44, -10, 80, -70, 146, -78, 24, -102, 30, 50, 50, 72, -120, -54, -6, -34, 128, 18, -6, 36, 24, -58, -22, -156, 24, 2, 92, 56, -16, -30, 30, -22, 140, -144, 0, -130, -40, 72, -24, 126, -54, -90, 84, 50, -112, 48, 72, -82, 98, 74, 74, -54, -78, 104, -112, 14, 66, -24, 60, -96, -34, -34, 24, 108, -22, -58, -48, 42, -64, 152, -30, 90, -30, -36, 56, 20, -40, 68, 60, -24, -60, -60, -162, -150, 146, -34, -48, 12, -76, -112, 24, 48, 20, -34, -126, 36, -52, -70, 50, -58, -12, -30, 114, -30, -136, 116, 134, 62, 14, -94, 126, 24, -46, 98, 102, -18, 110, -70, 150, 66, 6, 42, -42, -66, 116, 44, -12, 0, 38, -106, -72, -108, -76, 32, 170, -28, -100, 80, -138, -114, 2, 164, 86, -94, -12, -126, 140, 86, 74, 56, -52, 92, -130, -94, 114, -120, -18, -102, 68, 68, 18, 144, 48, -144, -162, -96, -40, 68, 30, -150, 56, 38, -12, -12, -112, 86, 84, 96, -30, 126, 26, -154, -16, -16, 0, 48, -118, -46, 120, -132, -46, -64, -88, 56, 74, 2, 60, -72, -40, 14, -24, -144, -46, 80, 6, 66, -112, 104, -130, 122, 54, 162, 74, 38, 14, -166, -24, 156, -136, -100, -16, 38, -72, -120, 170, 98, -100, 80, -40, 140, 104, 140, 126, -162, -64, 26, 110, 110, -12, -84, -138, 78, -130, -22, 54, -66, 80, 8, -52, -16, -90, 132, -166, 86, -130, -184, -150, -48, -88, -106, -108, 96, 128, -88, 30, -30, 132, 66, -142, -142, -58, 104, -180, -168, -54, 54, -154, 116, -48, 72, -70, 38, 90, -60, 108, -120, -138, -78, -22, 122, 84, 84, 128, 56, 146, -88, 152, 80, 90, 162, -142, 110, 56, -52, 66, -42, 24, -36, 84, 0, -118, 62, 102, -30, -36, 72, 32, -40, 66, 30, 80, -100, 12, -36, -112, 104, -130, -54, -108, -82, 26, -180, -60, -64, 152, 60, -186, -24, 132, -66, -42, -64, 44, -78, -102, 168, -18, 168, 48, -154, -82, 8, -64, -18, 30, -88, -160, -178, 74, 158, 50, -76, 140, -18, -30, 192, -120, 38, 38, -142, -178, -150, 84, -166, 122, 98, -46, 0, -84, -124, -70, 92, -52, -48, -96, 90, 24, 140, 140, -64, 152, -34, 128, -90, 66, 14, 104, 132, 138, 14, 104] 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([31, 31, -5*w + 2])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]