/* 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([41, 41, -6*w + 5]) 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 = [-2, -1, -4, -2, 5, -1, 6, 9, 2, -10, 4, -1, 0, -6, -3, 4, 6, -8, 9, -12, -11, -4, -8, -1, 11, 4, -2, 12, 20, -1, 0, -7, 10, 3, -16, -2, 16, 12, -16, 0, 7, -4, 3, 18, -17, 2, -19, -1, 6, 16, 2, 25, 11, 0, 14, -10, -3, -15, -15, 9, 30, -4, -31, -24, -4, 10, -14, 28, -11, -25, 2, 2, -30, 26, 10, 10, -17, -31, -28, 0, 9, -40, -2, -16, -15, 34, -40, 30, 28, -28, -24, -24, 16, -26, -4, 3, -43, 6, 18, -3, 19, 17, -11, -11, 10, 5, 26, 12, -16, 7, 28, 18, 46, 16, 2, 12, 33, 16, -12, 11, -45, 13, 20, 30, -19, -32, 38, 48, 34, 40, -16, -32, 38, 13, -1, 0, -28, 26, -2, 28, -28, -46, -18, 18, 46, 0, 35, -15, 20, 21, -42, 9, -19, -46, -25, -22, -29, 11, 46, -15, -8, -16, -2, -54, 44, 47, 12, 14, 35, 45, -46, 53, -10, 21, -42, -5, -40, 40, -16, -50, 6, 28, -28, -45, -3, -46, -39, 18, 25, -60, 66, 62, 48, -2, -30, 12, 12, 0, -28, 4, 25, 70, -21, -22, 20, -40, -54, -17, 4, 42, 0, -38, 4, 20, -64, -24, 60, 61, -32, 38, 0, -49, -60, -18, -5, -40, 5, -51, -18, 38, 18, -31, 30, 2, -2, -65, 62, 20, 58, -26, -42, 0, -57, -22, -67, 10, -15, -57, -3, 60, -23, -44, 48, 34, 21, 63, -39, 31, -65, -2, -10, 46, 6, 34, 2, 30, 28, 42, 20, 6, -18, -4, -51, 12, 10, -32, 27, 20, -72, -65, 86, -42, 56, -32, -18, 18, -3, 84, 77, -51, -30, -21, 0, 60, 18, 13, -64, 48, -29, 40, -65, -39, 45, 70, 14, 3, -60, 5, -16, 24, 24, -10, -17, 21, -49, -72, 33, -12, 30, -38, 88, 77, -21, -1, 34, -74, 73, 40, -32, -25, 0, 14, 5, -23, -33, 16, 63, 0, 0, -7, 72, 72, -26, -54, -24, -38, 21, 0, 27, -50, 30, 2, 80, -81, -8, -64, -52, -66, -15, 48, -11, 87, -75, 23, -44, 5, 34, 83, 2, -33, 46, -10, -10, -24, -40, 2, -92, 90, -66, 18, -35, -98, -44, 12, 79, 16, 12, 61, -60, -39, -45, -94, -49, 21, -12, 37, 26, 89, -71, 34, 18, -38, 48, -15, -40, 93, -74, 90, 20, -60, -60, -36, 90, 59, -39, 54, -9, 56, 84, -68, 79, 53, 18, 81, 18, -50, -50, 9, -33, 31, 80, 4, -10, -44, -37, 10, -39, -56, 0, 108, 94, -19, -68, 75, -30, -70, -28, -1, -92, -38, 46, 35, 42, 81, -94, -96, -82, 17, 10, 81, 46, -16, -44, -46, -60, 94, 108, -30, -2, -40, 58, 33, -9, -49, -84, 42, -105, 58, -40, -107, -9, -54, 30, 25, 46, -36, 34, 102, -31, 82, 26, 48, -36, -77, -84, -30, 103, -110, -47, 40, 33, -70, 77, -45, -59, -5, -103, -79, 110, -15, 27, 90, 76, 46, -52, 66, -32, -92, 69, 0, 77, 3, 66, 16, 16, 73, 80, -31, 60, -91, 112, 63, -21, 100, -40, 60, 53, -107, -58, 6, -36, -70, -56, -4, 87, 96, -44, 0, -98, -100, 33, -68, -82, 46, -45, -66, 60, 20, 41, -106, -92, -108, -45, 82, 26, -32, 80, -14, 70, -46, -102, -82, 44, -75, 128, -58, 5, -15, -29, -110, 30, 88, 32, -14, -84, -17, 67, -113, 48, 72, -117, -57, 41, 70, 112, -18, 101, -32, 52, -42, 105, 54, -121, 109, -10, -21, -84, 72, 121, -88, -30, 12, -14, 56, 54, -86, -63, 7, 72, -47, 55, 34, 93, -19, 60, 60, -87, 81, -117, 72, -45, 46, -86, -30, 111, -120, 98, -21, -54, -61, 5, 75, 112, -14, -19, -68, 60, 116, -14, 56, -10, -66, 94, 17, -71, 97, 4, -45, 59, -32, -70, 35, 100, 79, 54, 131, 140, 28, 10, 122, -105, -56, -30, -30, 90, -22, 42, 28, 81, -108, -85, 34, 108, 24, -106, 6, 56, 112, -67, 17, -110, -96, -74, 24, -23, 12, -19, 16, 123, 39, -24, 18, -109, -45, 39, 90, -1, 24, -130, 107, 86, 84, 35, 31, 108, -45, 74, -9, -72, -120, 62, -126, -42, -45, -136, 34, -106, -138, -138, -30, 33, -4, 108, -8, -120, -72, -93, 63, 42, -60, -116, -24, -52, 14, -14, -50, 20, -31, -17, -98, -112, 58, -138, -53, 66, -86, -86, -67, -25, 6, 69, 82, -16, 79, 114, -58, 61, -112, -84, -81, 101, 11, -80, 147, -63, -110, 2, 67, -24, -10, -108, 20, 20, 101, -39, -101, 4, -140, 0, 114, -82, -142, -30, -10, 74, 42, -91, -127, 76, 26, -16, -18, 94, 27, 20, -42, -42, 110, -9, 140, -28, -105, -14, 72, 23, 54, -65, -138, 107, -31, -24, -127, 76, 80, -4, -8, 90, 94, 38, 38, -46, 19, -30, 79, 65, -70, -35, 129, 150, -107, 82, 125, -22, -77, 0, -66, 109, 20, -64, -131, -82, 6, 90, 5, -100, 108, 108, 124, 33, -19, -131, -79, -30, -140, 56, -32, -60, -80, 53, -56, -98, -77, 147, -24, -24, 118, 55, 100, 93, 110, -114, 94, -32, 38, 66, 82, -44, 79, -135, 138, 66, 150, 83, 83, -61, 114, -31, 53, -49, -28, 139, 20, 30, -12, -36, 104, -86, 40, -35, -14, 52, -95, 54, 12, -18, -53, 60, 130, 33, 138, -106, -106, -54, 114, -53, -46, 90, -36, 100, 142, 14, 56, 10, 108, 98, 112, 58, -47, 76, 90, 146, 132, -80, -17, 12, -44, -22, -92, -154, -84, 94, 24, -86, 110, -74, 24, -87, -45, 56, 98, -5, -124, 58, 51, 46, -136, -127, -134, 80, 31, -162, -1, -58, -58, -18, -88, -78, -113, -7, 49, 140, 56, 39, 116, 62, -50, 81, 123, -103, 30, -72, -86, 62, -113, 122, 143, 96, -16, -35, -70, 107, -138, 102, 74, -80, 137, 45, -123, -120, 76, 102, -24, -142, -107, 31, -32, -99, 90, -84, -14, 45, 38, 18, -38, -131, -103, 34, -43, 44, 9, -45, 53, 105, 112, 10, 122, 60, 144, 38, 157, 14, -175, 19, 75, 32, -52, 104, 160, -68, 30, -52, -31, 69, -64, -38, 102, 38, -74, -28, -140, 105, -154, 165, 32, -154, -42, 160, -85, -52, -10, 46, -24, -82, 37, -95, -88, -1, -148, 152, -72, 171, -60, -43, 111, 19, 68, -5, -145, 49, -21, -96, -75, -72, 33, 146, -1, -33, -68, -168, -154, 124, 180, 24, 115, -176, 48, 150, -130, 117, -128, 117, -135, 42, 105, -11, 87, 14, 56, 117, -114, -22, -22, -159, 79, 146, 41, -11, 66, 80, 10, -15, 90, -156, 5, 2, 100, -30, 110, 150, 122, -56, -126, -103, 37, 126, -42, -145, -5, -46, 31, 39, -80, -58, 89, 48, 62, 68, -135, -152, 166, 159, 7, -175, 87, -165, -45, 88, 96, -44, -33, 9, -42, 126, 20, -64, -33, 114, -43, -36, -66, -150, 89, 54, 44, 100, 54, -135, -98, 28, 151, 18, -26, -19, 160, -169, -54, 30, 116, -10, -50, 76, -4, 31, 174, -120, 54, -9, -53, -109, -15, -127, -51, 124, -110, -131, -170, 68, 171, 10, 158, 39, -68, -40, 102, 102, -3, 60, 41, -1, -54, -26, -116, -25] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([41, 41, -6*w + 5])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]