/* 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([61, 61, 3*w - 10]) 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 - 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11],\ [9181, 9181, 35*w - 121],\ [9181, 9181, 51*w - 137],\ [9199, 9199, -89*w + 71],\ [9199, 9199, 18*w - 107],\ [9209, 9209, 49*w - 135],\ [9209, 9209, 37*w - 123],\ [9221, 9221, 59*w - 146],\ [9221, 9221, 28*w - 115],\ [9239, 9239, 88*w - 65],\ [9239, 9239, 23*w - 111],\ [9241, 9241, 45*w - 131],\ [9241, 9241, 41*w - 127],\ [9281, 9281, -99*w - 5],\ [9281, 9281, 99*w - 104],\ [9311, 9311, -97*w - 1],\ [9311, 9311, 97*w - 98],\ [9319, 9319, 25*w - 113],\ [9319, 9319, 88*w - 63],\ [9341, 9341, 17*w - 107],\ [9341, 9341, -90*w + 73],\ [9349, 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^2 + 2*x - 4 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, -3/2*e - 2, -1/2*e - 3, -1/2*e - 1, 2*e + 2, 1/2*e + 2, 3/2*e - 3, -5/2*e - 4, -e + 4, 5/2*e + 4, -e + 6, e + 6, -2*e - 10, -2*e - 2, 5*e + 4, -7/2*e, -1, 0, -3/2*e + 2, 2*e, -e - 8, 2*e + 8, -e + 2, -3/2*e - 11, 7/2*e + 7, e + 4, -2*e - 4, 3*e + 2, -3*e - 8, 2*e - 2, 7/2*e + 14, -8*e - 6, 4*e + 6, -3/2*e - 13, -6*e - 4, 7/2*e - 5, -11/2*e - 4, 5/2*e - 3, 1/2*e + 7, -9/2*e + 3, 5*e + 2, 9/2*e - 1, -e - 20, 14, -3*e - 2, -11/2*e + 7, -6*e - 6, 4*e + 24, -2*e - 8, 8*e + 14, 3*e + 8, 5*e, -7*e - 2, 10*e + 16, 4, 2*e + 12, 4*e + 2, -5/2*e - 10, 4*e + 4, -11/2*e + 15, 6*e + 4, 6*e + 12, 1/2*e - 16, -3*e - 14, 1/2*e + 4, -8*e, 9*e + 26, -3/2*e + 1, 6*e + 20, 5*e - 6, -10*e - 4, -6*e - 24, 5/2*e - 10, -5*e + 12, -13/2*e + 16, -7*e - 28, 5/2*e + 10, -e + 12, 4*e + 28, 4*e + 28, -13/2*e + 5, 10*e, -5/2*e + 26, -9/2*e + 5, 3/2*e - 17, -8*e - 16, 12*e + 18, 15/2*e - 6, -13/2*e - 17, 3/2*e + 36, 1/2*e + 28, 9/2*e - 23, -3*e - 20, 5*e + 2, 9*e - 10, -17/2*e, 2*e + 4, 9/2*e - 24, -9*e - 22, -7/2*e - 3, 3*e - 12, -11/2*e - 4, -9*e - 2, -15*e - 6, -6*e - 20, -4*e - 28, 4*e - 6, -7*e - 16, -17/2*e - 24, 29/2*e + 18, 23/2*e + 2, 4*e - 20, 9/2*e - 7, -2*e + 22, -19/2*e - 18, -7*e - 36, 3/2*e + 30, -7/2*e - 20, -12*e - 24, -20, -3/2*e + 3, -20*e - 14, e - 26, 23/2*e + 9, 3*e - 26, -9/2*e + 35, 2*e + 18, -21/2*e + 13, -4*e - 4, -2*e + 6, -29/2*e - 9, 14*e, 5*e + 14, 23/2*e + 7, 7*e + 14, -37/2*e - 21, -8*e + 4, 9*e - 10, 9*e - 10, e + 32, 13/2*e + 20, -2*e + 26, -7*e + 20, -11/2*e - 26, -5/2*e + 21, 10*e - 16, 25/2*e - 13, 8*e + 14, -4*e - 50, -37/2*e - 2, 23/2*e + 34, 6*e + 14, -9*e - 4, -7/2*e + 23, 17/2*e + 25, -5/2*e - 3, -4*e - 42, -3*e - 4, -43/2*e - 20, 9*e + 28, -8*e + 20, 11/2*e + 19, -3/2*e - 8, 3/2*e - 36, 4*e - 2, -14*e - 26, 11/2*e + 16, 11*e + 6, -10*e + 18, -17/2*e - 26, 6*e + 10, 51/2*e + 29, -13*e - 42, -11/2*e + 8, 12*e - 2, 60, 25*e + 28, e - 28, 21/2*e + 33, 4*e - 4, 15/2*e - 6, 35/2*e - 3, -22*e - 38, 6*e - 36, 16*e + 38, -35/2*e - 38, 7*e + 10, 6*e + 6, 8*e - 4, -12*e - 8, -6*e + 24, -13/2*e + 21, 35/2*e + 25, 13/2*e + 38, -4*e - 18, 15/2*e - 1, 1/2*e - 28, -13*e - 36, -21/2*e - 33, -23/2*e + 21, -6*e + 40, -3*e + 4, -5*e + 14, -21*e - 10, 29/2*e + 45, -19*e - 10, 21/2*e + 13, 9*e - 24, 5/2*e + 55, 4*e - 20, -e - 26, 17/2*e + 22, e + 44, -19/2*e - 10, 22*e + 34, -5/2*e - 5, -14*e + 6, -56, -9/2*e - 6, 31/2*e + 49, 7*e + 32, -22*e - 40, 41/2*e + 21, e - 52, 17*e + 12, -33/2*e - 22, 13/2*e + 28, 15/2*e + 23, 15/2*e - 27, -21/2*e - 61, 23/2*e + 54, 27/2*e + 44, -19*e - 14, -5/2*e - 19, -20*e - 30, -45/2*e - 2, -e - 24, -5*e - 66, 12, 12, -20*e, 9/2*e - 14, 5/2*e + 47, 13*e + 10, -31/2*e, 18*e + 34, -45/2*e - 17, 18*e + 44, -e - 4, -40, 8*e - 10, -4*e - 12, -13*e - 38, 18*e + 24, 12*e, 5/2*e - 30, 27/2*e - 13, 23*e + 48, -3/2*e + 64, 25*e + 40, 6*e - 34, 5/2*e - 32, -5*e + 20, 31*e + 26, -e + 10, e, -9*e - 62, 23*e + 26, 2*e + 58, 10*e + 18, -27/2*e - 17, 2*e + 14, 2*e - 18, -29/2*e - 44, 13*e + 32, 23/2*e - 7, -5/2*e - 20, -13/2*e - 62, -8*e + 12, -28, -6*e + 20, 21/2*e - 4, -11*e - 36, 45/2*e + 8, 41/2*e + 18, 15/2*e - 2, 7/2*e - 44, -5/2*e - 35, 4*e + 10, -2*e - 10, -27*e - 40, 11*e + 48, -41/2*e - 27, -4*e - 14, 25*e - 4, -2*e + 40, -29*e - 42, -11/2*e - 54, 1/2*e + 71, -1/2*e - 28, -5/2*e - 18, -21*e - 22, 55/2*e + 30, -7/2*e + 17, -35/2*e - 68, 16*e - 24, 35/2*e + 46, -14*e + 32, -4*e - 18, -29/2*e, -10*e + 24, 51/2*e + 56, 21/2*e - 24, 10*e + 66, 17*e + 62, 25/2*e - 12, -11*e - 34, -23/2*e - 29, 5*e + 28, 13/2*e + 69, 9/2*e + 48, 45/2*e + 30, 2*e + 24, -11*e - 46, -11/2*e + 35, -31/2*e - 21, -27*e - 10, -3/2*e - 30, -17/2*e - 14, 19/2*e - 11, 13/2*e + 22, -5*e + 2, 29/2*e + 25, -7*e - 38, 2*e - 34, 29*e + 48, -4*e - 54, -2*e - 2, 15*e - 28, -e - 72, 28*e + 2, 45/2*e + 14, -e + 82, -17/2*e - 51, 51/2*e + 29, 6*e + 80, -66, 49/2*e + 44, 18*e - 12, -30*e - 20, -e - 62, -1/2*e - 18, 10*e + 46, 6*e + 66, 9/2*e + 37, -49/2*e - 4, -5*e - 12, -7/2*e + 58, 28*e + 8, -20*e, -13*e + 14, -9*e - 68, 5*e - 14, -8*e + 20, 22*e + 4, -21*e - 60, -31/2*e + 29, -22*e - 16, -2*e - 44, -29*e - 2, 7/2*e + 39, -13*e - 18, 6*e + 8, 26*e + 32, -16*e + 6, 18*e - 40, -45/2*e + 10, -12*e - 58, -3/2*e + 72, -4*e - 24, 31*e + 56, -4*e + 14, -3*e - 10, -4*e + 26, 86, 14*e + 78, -2*e - 18, -7*e + 38, 33*e + 36, -30*e - 52, -47/2*e - 61, -15*e - 26, -14*e + 10, -14*e - 52, -49/2*e - 13, 43/2*e + 5, 10*e + 26, 5*e - 42, -15/2*e - 49, -7/2*e - 38, -9*e + 14, -63/2*e - 13, 17/2*e + 37, -53/2*e - 67, 3*e - 34, 18*e + 46, 21*e + 8, 33/2*e - 37, -35/2*e - 22, 16*e + 44, -45/2*e - 27, -10*e - 2, -3*e + 56, 11*e + 66, 13*e + 56, -17*e - 12, 6*e + 28, 10*e - 24, 23/2*e - 47, -2*e - 58, -9*e + 70, 1/2*e + 9, 13*e + 24, 35/2*e + 14, -12*e + 22, -25*e - 4, 20*e - 12, -4*e + 56, 35/2*e - 36, 30*e + 18, -25/2*e - 33, -63/2*e - 9, -47/2*e - 49, 12*e - 48, 10*e + 24, 35/2*e + 45, 22*e + 38, -16*e - 2, -61/2*e - 7, -25*e - 40, 28*e + 36, 71/2*e + 65, -33*e - 42, -39/2*e - 53, -13*e - 8, 4*e + 64, -1/2*e + 40, 6*e - 22, -27/2*e + 29, 36*e + 26, -15/2*e + 42, 23/2*e + 19, 45/2*e - 5, 47/2*e - 23, e + 74, 6*e + 30, 15/2*e + 69, -63/2*e - 38, -33/2*e - 51, -16*e - 16, -24*e - 38, -19/2*e + 68, 2*e + 26, 15*e + 4, 4*e + 28, 14*e + 68, 14, -2*e + 26, -20*e - 8, 31/2*e + 34, 13/2*e + 48, -6*e + 12, -63/2*e - 31, -59/2*e - 8, 9*e + 32, -19*e - 48, 7*e - 54, -31/2*e + 14, 3*e + 30, -22*e - 52, 49/2*e + 72, 19*e - 22, -13*e - 48, 4*e - 38, 10*e - 68, 15/2*e + 49, -11*e + 64, 50*e + 50, -26*e - 4, -31*e - 2, -7/2*e - 31, -11/2*e - 61, 3/2*e - 34, -36*e - 40, -23*e - 74, 5*e + 46, -3*e + 86, -28*e - 50, -13*e - 32, 27/2*e + 78, -35/2*e + 47, 45/2*e + 35, -65/2*e - 31, 63/2*e + 39, -23*e - 14, 8*e - 64, -24, -5*e - 82, -39/2*e - 56, 31*e + 36, -11/2*e - 45, -24*e - 64, 2, 3*e + 30, 11/2*e - 60, -21/2*e - 22, -17*e - 98, -57/2*e - 46, 45/2*e - 22, 4*e + 94, -6*e - 42, -25*e + 32, 5/2*e + 65, -23/2*e - 62, -5*e + 76, 31*e - 20, -3/2*e + 3, 37/2*e - 58, 85/2*e + 39, 9*e + 46, -28*e - 48, -11/2*e + 21, -39/2*e + 60, -7/2*e - 52, -e - 18, -21/2*e - 80, 6*e + 8, -9/2*e + 22, 31/2*e + 77, -37/2*e - 10, -20*e - 80, -32*e - 12, -9*e - 34, -2*e - 90, 21/2*e - 44, 5*e - 92, -e, 31/2*e - 40, -40, -19*e + 36, e - 2, 33/2*e - 15, 12*e + 54, -16*e + 10, -4*e + 74, 6*e + 52, -75/2*e - 56, -20*e - 64, -57/2*e - 37, -28*e + 4, -12*e + 48, -3*e + 46, 28*e - 16, -57/2*e + 11, -55/2*e - 56, -22*e + 6, -21/2*e - 36, -10*e - 98, 15*e + 56, -14*e + 56, 49/2*e + 34, 25/2*e + 21, 18*e - 22, 27/2*e + 27, -5*e - 20, 27*e + 16, 15/2*e + 67, -9/2*e - 51, -32*e - 22, -17/2*e + 72, 30*e + 50, 63/2*e + 29, -73/2*e - 65, 57/2*e + 23, 18*e - 2, -13*e + 16, -45/2*e - 45, 3*e + 62, 10*e + 58, -18*e - 40, -28*e - 52, -91/2*e - 24, 22*e + 26, 15*e + 80, -3/2*e - 39, -48*e - 60, -57/2*e + 13, -11*e - 110, -35*e + 10, 39/2*e + 50, 20*e + 32, -48*e - 50, 3*e + 36, -18*e + 68, 7*e - 26, 29/2*e + 86, -14*e - 66, -29/2*e + 13, 9*e + 4, -13*e - 64, 8*e - 46, -10*e - 80, 18*e - 4, 47/2*e + 15, 23/2*e + 56, 89/2*e + 77, -29*e - 68, -5*e + 60, 25*e + 64, 2*e - 38, 3*e + 6, 7*e - 14, -17/2*e - 97, 19/2*e - 32, -6*e + 32, 4*e + 44, 3*e - 78, 31/2*e + 61, 27*e, 10*e - 8, 12*e + 12, -6*e - 22, 49/2*e + 4, -6*e - 14, -28*e - 6, 9/2*e + 95, 12*e - 74, -21*e - 2, 11*e - 70, 23/2*e + 36, -27*e + 6, 25*e + 56, 35/2*e + 18, 35*e + 8, 14*e + 50, -16*e + 14, -12*e + 24, -17*e + 18, -2*e - 16, 20*e - 2, -17*e - 16, -28*e + 8, 14*e + 66, -7/2*e + 14, -87/2*e - 24, -19/2*e - 70, -39/2*e - 8, 27*e - 8, -9/2*e - 32, -8, 13*e - 24, -79/2*e + 6, -2*e - 12, -91/2*e - 58, 59/2*e + 11, 6*e + 82, 48*e + 60, -29/2*e + 16, 83/2*e + 56, 15/2*e - 53, -6*e - 14, 21/2*e + 43, -11*e - 8, 45*e + 22, -49/2*e - 41, 51/2*e - 12, 17/2*e + 33, 21*e + 48, -33/2*e + 52, -9/2*e + 54, 8*e + 102, 25/2*e + 33, -63/2*e - 101, 31/2*e + 98, -25/2*e - 82, 63/2*e + 8, -33/2*e - 54, 6*e + 4, 32*e + 8, 25*e + 74, -42*e - 36, 93/2*e + 64, -33/2*e - 95, 43/2*e - 37, -30*e + 18, 43/2*e + 24, -14*e - 44, 59/2*e + 2, 2*e - 60, 21/2*e + 37, 32*e + 66, -9*e + 54, 23/2*e + 80, -6*e - 74, -4*e + 40, 31*e + 50, 34*e + 4, 4*e - 14, 27/2*e + 109, 10*e - 86, -3/2*e + 111, -13*e + 72, 37/2*e - 39, 13/2*e, 51/2*e - 33, -15/2*e - 77, -33/2*e + 61, 73/2*e + 4, -2*e + 88, -27/2*e + 45, 24, 5*e + 52, 21/2*e - 22, 3/2*e - 21, 13*e - 32, 15/2*e + 13, -24*e + 62, -65/2*e + 6, -83/2*e - 73, 4*e + 94, 18*e - 38, -14*e + 72, 41/2*e + 70, -20*e - 12, 39/2*e - 70, 95/2*e + 24, 1/2*e - 82, 8*e - 40, 21/2*e - 6, -4*e + 30, 11*e + 48, 15*e + 98, 5*e - 100, -47/2*e - 87, 25/2*e - 19, -10*e - 26, -21*e + 60, 37*e + 92, 9/2*e - 102, -17/2*e - 89, -3*e - 8, -21*e - 74, -91/2*e - 91, -e + 20, 28*e + 30, 22*e + 28, -51/2*e - 29, -25/2*e - 51, -8*e - 120, 32*e + 62, -7*e - 22, -11*e - 44, -31/2*e - 6, -5*e + 68, 16*e - 68, -18*e + 50, 13*e - 12, -38, 17*e + 94, 54*e + 74, 37*e + 66, 48*e + 50, -89/2*e - 61, e + 16, -37/2*e + 36, 47/2*e + 45, -4*e + 74, 5*e - 6, 9*e - 88, 63/2*e + 12, -29/2*e - 37, -12*e - 4, -46*e - 20, -11*e - 84, 11/2*e - 58, -23/2*e + 15, -13*e - 24, 97/2*e + 66, -4*e - 28, -21/2*e - 40, -15/2*e - 86, 21*e + 14, -19*e + 28, -9/2*e - 71, -9*e - 2, 12*e + 120, -4*e - 48, -15*e - 4, 63/2*e + 27, 48*e + 70, 43/2*e + 32, 28*e + 58, 57/2*e + 40, 85/2*e + 104, -87/2*e - 55, -28*e - 78, 3/2*e - 55, 22*e + 22, 51/2*e + 82, 24*e + 76, 49/2*e + 27, -29/2*e + 64, -25/2*e + 23, 28*e + 86, -17/2*e + 5, -21*e, 3/2*e + 89, -12*e + 4, 16*e - 74, 1/2*e - 13, -1/2*e - 70, -11*e - 124, -3/2*e + 92, -11/2*e - 87, -6*e + 24, 9*e - 72, -10*e - 70, 5*e - 20, 2*e + 150, -65/2*e + 25, -10*e - 72, 26*e + 60, -36*e - 64, 2*e - 50, -15*e + 4, 13*e, -48*e - 98, -45*e - 10, 12*e - 16, 16*e + 56, -33/2*e - 76, -49*e - 76, 9/2*e + 13, 18*e + 14, 57/2*e - 54, -45/2*e + 2, 71/2*e + 53, 40*e + 110, 3/2*e - 147, 13*e + 38, -69/2*e + 12, 57/2*e + 56, 9*e + 76, 26*e + 104, 48, -14*e + 34, 11/2*e + 76, 48*e + 36, -2*e + 38, 14*e - 24, 11*e - 40, 15/2*e + 65, -30*e + 20, 27/2*e - 25, 3/2*e + 97, -5/2*e - 90, -35/2*e - 77, 6*e + 46, -14*e + 22, -81/2*e - 99, 9/2*e - 14, 5/2*e + 100, 33*e + 56, -17*e + 14, 71/2*e + 77, -2*e - 90, -63/2*e + 11, -9*e - 76, 19*e - 30, -33/2*e - 47, 19/2*e - 115, -41*e - 52, 8*e - 18, 10*e + 62, -45/2*e + 23, 19/2*e - 11, 20*e + 76, 47/2*e + 30, -93/2*e - 44, 20*e - 82, -19/2*e - 93, -15*e + 74, -35*e - 98, 18*e - 22, -13/2*e + 64, -37/2*e - 93, 7/2*e + 16, -23*e - 84, -59/2*e + 5, 31*e + 28, 31/2*e + 79, -5*e - 20, 65/2*e - 58, -20*e + 34, -40*e - 96, 1/2*e - 97, -5/2*e + 31, 23*e + 74, -39/2*e + 84, -37*e - 30, 51*e + 36, 23*e - 72, 109/2*e + 95, -18*e - 116, 29*e + 2, 18*e - 36, 38*e + 58, 33/2*e + 119, -13*e - 6, 6*e - 132, 91/2*e + 35, -17/2*e - 67, 54*e + 60, -33*e + 30, 57/2*e + 25, -63*e - 60, 11*e + 14, 15/2*e + 47, 19*e - 70, 69/2*e + 116, -63*e - 82, -56, -3*e - 62, 45/2*e + 12, 5*e + 40, -6*e + 2, -47/2*e - 17, -12*e - 90, 25*e + 84, -24*e + 50, 2*e + 148, -69/2*e - 26, -99/2*e - 66, -5/2*e + 9, 10*e + 32, -11/2*e - 30, -3*e - 160, -38*e - 78, 2*e + 102, 33*e - 22, -2*e - 54, -23*e - 42, -19/2*e - 33, -4*e - 14, 42*e + 78, -14*e - 14, -56*e - 44, 16*e + 30, -16*e - 48, 40*e + 44, 42*e - 26, 22*e - 50, 50*e + 24, 17*e + 34, 3/2*e - 57, 13/2*e - 20, -5*e - 134, 6*e + 28, 11*e + 52, 40*e + 62, 13*e + 114, 5/2*e - 4, -40*e - 66, -27*e - 38, -14*e + 64, 69*e + 52, -3/2*e + 89, 9/2*e + 59, -42*e - 88, 26*e + 6, 11/2*e + 42, 15*e - 52, -17*e + 64, 15*e + 90, -22*e + 26, 1/2*e + 22, -31*e - 106, -79/2*e - 17, 15*e - 14, 59/2*e - 40, -29*e - 66, -36*e, -10*e + 78, -52*e - 22, -23/2*e - 129, 72*e + 58, -26*e + 20, 3*e - 94, 19*e + 14, -71/2*e - 8, 8*e + 96, 71/2*e + 36, 28*e + 122, -2*e + 86, 5/2*e - 48, 31/2*e - 82, -89/2*e - 41, 20*e + 24, 57/2*e - 24, -14*e + 80, 33/2*e + 48, -2*e + 32, 48*e + 38, 31*e - 32, -23/2*e - 71, -93/2*e - 113, 53/2*e + 59, -2*e, -43/2*e - 23, -67/2*e + 37, -8*e + 28, -19*e - 10, -18*e - 38, -e - 92, 22*e + 22, 57/2*e - 57, 103/2*e + 63, -26*e - 92, -12*e - 90, -7*e - 22, -23*e - 64, -39*e - 46, 23/2*e + 37, 39/2*e + 59, -35/2*e + 34, -32*e - 2, -68*e - 48, 39/2*e - 5, -25*e - 88, -5*e + 122, 95/2*e + 48, -43*e - 104, -97/2*e - 21, -19/2*e - 123, -5/2*e - 14, e - 78, 85/2*e - 23, 95/2*e + 76, 83/2*e + 85, -32*e - 90, -12*e + 60, 4*e - 144, -47/2*e - 23, 7*e + 150, -51*e - 16, -e - 80, -65/2*e - 11, 33/2*e - 101, 25*e - 48, -39*e + 24, 26*e + 82, -67/2*e - 101, -e + 18, 47/2*e - 27, 7/2*e + 21, -12*e - 134, 47*e + 56, -37/2*e + 89, 43/2*e + 87, 40*e + 10, -22*e - 86, -18*e + 18, -38*e - 118, 126, 50*e + 8, -44*e - 18, -22*e - 56, 17*e + 90, 3*e - 68, 31*e + 40, -55/2*e - 12, -39*e + 30, 12*e + 2, -16*e + 18, -12*e + 18, -36*e - 48, -5*e + 94, -38*e - 82, -63/2*e - 90, 48*e + 86, 18, 71/2*e + 104, 13*e - 68, -6*e + 120, -35*e - 130, 3/2*e + 13, -7/2*e + 17, -9/2*e - 9, -28*e + 12, 8*e - 106, -69/2*e - 27, -46*e - 16, 10*e + 88, -46*e - 66, -22*e + 72, -26*e + 30, 45/2*e + 100, 33*e + 32, -37/2*e + 28, -4*e - 60, -30*e - 88, 23/2*e + 154, -61/2*e - 68, -29/2*e - 24, -27*e - 60, 49/2*e - 54, -47*e - 66, 65*e + 56, 149/2*e + 67, 11/2*e - 22, 63/2*e - 82, -27*e - 22, -3*e - 8, -31/2*e + 8, -5/2*e - 118, -13*e + 12, -24*e + 54, 37*e + 28, 28*e - 40, 42*e + 76, 65/2*e - 6, -18*e + 76, -35/2*e - 108, -37*e + 36, 41/2*e + 154, 38*e + 20, -4*e - 70, 97/2*e + 86, 18*e + 80, 44*e + 74, 7*e + 60, -113/2*e - 10, 95/2*e + 30, -26*e - 114, 59/2*e - 26, 3/2*e + 145, -8*e - 10, 19*e + 10, 35*e - 62, 16*e + 2, -8*e - 42, -21/2*e + 110, 17*e + 58, -20*e - 98, -32*e - 16, 91/2*e + 77, -30*e + 56, 3/2*e - 55, -57/2*e - 73, 30*e + 32, 8*e - 44, -105/2*e - 3, 20*e + 22, -81/2*e - 53, -21*e - 42, 14*e + 132, -139/2*e - 86, -5*e - 92, -43/2*e - 118, -39/2*e + 45, -50*e - 66, 2*e - 4, -42*e - 94, -71/2*e + 2, 19/2*e + 25, 3*e + 114, -23*e - 4, -57*e - 2, 17/2*e - 35, 14*e + 58, 109/2*e + 57, -20*e - 94, -89/2*e + 13, 18*e + 168, -27/2*e - 31, -42*e - 18, -9*e - 90, 75/2*e + 36, 45*e + 76, -62*e - 22, 25*e + 70, -2*e + 186, -24*e - 14, 25*e - 86, -25*e + 40, -59*e - 90, 91/2*e + 23, -6*e - 170, 7*e - 80, 29/2*e - 38, 50*e + 110, 21*e - 6, -9/2*e - 142, 13/2*e - 63, 14*e + 70, -34*e - 42, -15/2*e - 35, 15/2*e + 88, 17*e + 56, -5*e + 114, 2*e - 76, -44*e - 74, -32*e - 72, 23/2*e + 23, -35*e + 54, -45/2*e - 14, -20*e + 20, 27*e + 14, 15/2*e - 28, 26*e + 120, 55*e + 6, -105/2*e - 111, -4*e - 90, -105/2*e + 12, -87/2*e + 29, -21*e - 40, 35*e - 10, -52*e - 100, e + 100, 11/2*e + 72, -23*e + 44, -2*e - 22, 20*e - 70] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([61, 61, 3*w - 10])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]