/* 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([181, 181, -14*w - 1]) 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^4 - 12*x^2 + 8*x - 1 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, -e^3 - 1/2*e^2 + 11*e - 5/2, 1/2*e^2 - 5/2, 5/2*e^3 + e^2 - 61/2*e + 9, 3/2*e^3 - 37/2*e + 8, -2*e^3 - e^2 + 24*e - 7, 5/2*e^3 + e^2 - 57/2*e + 7, e^2 + 2*e - 5, -4*e^3 - 2*e^2 + 46*e - 14, -4*e^3 - 2*e^2 + 46*e - 12, -1/2*e^3 - e^2 + 11/2*e + 1, -2*e^3 + 24*e - 10, -2*e^3 - 1/2*e^2 + 26*e - 15/2, 3*e^3 + e^2 - 35*e + 7, 9/2*e^3 + e^2 - 111/2*e + 23, 1/2*e^3 + e^2 - 9/2*e - 5, -3*e^3 - 1/2*e^2 + 37*e - 17/2, e^3 - e^2 - 11*e + 17, e^3 - 11*e + 2, e^3 - 13*e + 12, 5/2*e^3 - 63/2*e + 16, 9/2*e^3 + e^2 - 103/2*e + 23, 1/2*e^2 - 2*e - 7/2, -e^3 + 9*e - 12, 2*e^3 + 3/2*e^2 - 20*e + 11/2, -8*e^3 - 5/2*e^2 + 94*e - 67/2, 3*e^3 - 1/2*e^2 - 37*e + 47/2, -6*e^3 - e^2 + 72*e - 21, 5/2*e^3 - e^2 - 73/2*e + 27, e^3 + 2*e^2 - 7*e - 8, 6*e^3 + 3*e^2 - 68*e + 19, -e^3 + 17*e - 2, 4*e^3 + 2*e^2 - 46*e + 12, 4*e^3 + 5/2*e^2 - 48*e + 19/2, 2*e^3 + e^2 - 24*e - 3, -3*e^3 + 35*e - 12, -2*e^3 - 5/2*e^2 + 24*e - 3/2, -7*e^3 - 2*e^2 + 83*e - 38, e^2 - 4*e - 7, -1, 4*e^3 + 5/2*e^2 - 42*e + 23/2, 7*e^3 + 4*e^2 - 87*e + 16, -2*e^3 - e^2 + 24*e - 17, -2*e^3 - e^2 + 24*e - 9, 1/2*e^3 - e^2 - 13/2*e + 13, -11/2*e^3 - 2*e^2 + 137/2*e - 30, 5*e^3 + 2*e^2 - 59*e + 14, 2*e^3 + 3/2*e^2 - 28*e - 17/2, 2*e^3 + 1/2*e^2 - 28*e + 33/2, 3/2*e^3 + e^2 - 33/2*e + 19, -8*e^3 - 4*e^2 + 92*e - 30, 3*e^3 + e^2 - 35*e + 17, 3*e^3 + e^2 - 37*e + 27, -2*e^3 + 28*e - 2, 5*e^3 + 3*e^2 - 59*e + 29, -4*e^2 - 4*e + 26, -13*e^3 - 4*e^2 + 155*e - 54, -e^3 - e^2 + 13*e - 7, 7/2*e^3 + e^2 - 87/2*e + 27, -e^3 + 9*e - 2, 8*e^3 + 2*e^2 - 88*e + 36, -3*e^3 - 2*e^2 + 33*e + 4, 23/2*e^3 + 3*e^2 - 283/2*e + 53, 6*e^3 + 2*e^2 - 66*e + 24, -19/2*e^3 - 3*e^2 + 219/2*e - 45, -3*e^3 + 35*e - 14, 10*e^3 + 2*e^2 - 126*e + 44, -4*e^3 + 1/2*e^2 + 46*e - 59/2, 3/2*e^3 - 45/2*e + 12, -15/2*e^3 - e^2 + 183/2*e - 45, -15/2*e^3 - 5*e^2 + 181/2*e - 11, 12*e^3 + 3*e^2 - 142*e + 61, -5*e^3 - e^2 + 67*e - 23, e^3 - 19*e - 4, -2*e^3 + 1/2*e^2 + 24*e - 53/2, -2*e^3 - 7/2*e^2 + 20*e + 5/2, 8*e^3 + 2*e^2 - 100*e + 42, 5/2*e^2 - 33/2, 1/2*e^3 + 3*e^2 - 21/2*e - 29, 5*e^3 + 3*e^2 - 57*e + 5, -8*e^3 - 9/2*e^2 + 92*e - 35/2, 2*e^3 - 2*e^2 - 34*e + 28, -2*e^3 + 30*e - 14, -9/2*e^3 + e^2 + 113/2*e - 41, 15*e^3 + 6*e^2 - 183*e + 58, 2*e^3 - 3*e^2 - 28*e + 41, -4*e^3 + 50*e - 28, -6*e^3 - 2*e^2 + 74*e - 30, 5*e^3 + 4*e^2 - 53*e + 2, -10*e^3 - 4*e^2 + 114*e - 32, 10*e^3 + 5*e^2 - 116*e + 49, e^3 + 2*e^2 - 11*e - 4, 9/2*e^3 - 4*e^2 - 115/2*e + 44, -3*e^3 + 35*e - 36, 23/2*e^3 + 3*e^2 - 283/2*e + 59, -15/2*e^3 - 6*e^2 + 169/2*e - 18, -3*e^3 - e^2 + 41*e - 23, -5*e^3 + 53*e - 40, 12*e^3 + e^2 - 140*e + 61, -14*e^3 - 11/2*e^2 + 164*e - 97/2, -11*e^3 - 4*e^2 + 119*e - 46, -8*e^3 - 13/2*e^2 + 86*e + 1/2, -8*e^3 - e^2 + 106*e - 55, 11*e^3 + 9/2*e^2 - 137*e + 81/2, -6*e^3 - 6*e^2 + 74*e + 8, -31/2*e^3 - 7*e^2 + 371/2*e - 63, -9*e^3 - 4*e^2 + 111*e - 32, -4*e^3 - 3*e^2 + 48*e + 25, -7*e^3 + e^2 + 83*e - 57, -13*e^3 - 5*e^2 + 155*e - 61, -23*e^3 - 19/2*e^2 + 269*e - 175/2, 31/2*e^3 + 3*e^2 - 363/2*e + 61, -21*e^3 - 4*e^2 + 249*e - 84, 5*e^3 + 3*e^2 - 57*e + 35, -3/2*e^3 + e^2 + 39/2*e - 31, 14*e^3 + 7*e^2 - 156*e + 43, -2*e^3 + 4*e^2 + 22*e - 46, 35/2*e^3 + 7*e^2 - 419/2*e + 73, -27/2*e^3 - 3*e^2 + 339/2*e - 63, -3*e^3 + 3/2*e^2 + 37*e - 9/2, -3*e^3 - 3*e^2 + 35*e + 27, -8*e + 4, -12*e^3 - 4*e^2 + 140*e - 46, 3*e^3 + 1/2*e^2 - 33*e + 49/2, -7*e^3 - 4*e^2 + 79*e + 8, 8*e^3 + 9/2*e^2 - 82*e + 15/2, -4*e^3 + 7/2*e^2 + 50*e - 75/2, e^2 - 33, 10*e^3 + 7*e^2 - 110*e + 27, -29/2*e^3 - 6*e^2 + 335/2*e - 46, 25/2*e^3 + 3*e^2 - 297/2*e + 27, -7/2*e^3 - 3*e^2 + 101/2*e + 11, 5*e^3 + 2*e^2 - 61*e + 18, 18*e^3 + 17/2*e^2 - 204*e + 95/2, 8*e^3 + 7/2*e^2 - 86*e + 27/2, 6*e^3 - 2*e^2 - 72*e + 66, 10*e^3 + 5*e^2 - 126*e + 25, 3*e^3 + e^2 - 33*e + 29, 2*e^3 - 3/2*e^2 - 28*e + 19/2, -7*e^3 + 2*e^2 + 81*e - 42, -e^3 - 2*e^2 + 13*e + 12, -10*e^3 - 11/2*e^2 + 122*e - 77/2, 11*e^3 + 3*e^2 - 129*e + 17, -18*e^3 - 5*e^2 + 222*e - 89, 24*e^3 + 10*e^2 - 284*e + 92, e^3 - 5*e^2 - 21*e + 35, -19*e^3 - 2*e^2 + 235*e - 94, -4*e^3 + 4*e^2 + 46*e - 62, -3*e^3 - 2*e^2 + 33*e + 28, 9*e^3 + 11/2*e^2 - 99*e + 47/2, -8*e^3 + 94*e - 44, 37/2*e^3 + 4*e^2 - 455/2*e + 92, -16*e^3 - 7*e^2 + 190*e - 47, -27/2*e^3 - 4*e^2 + 341/2*e - 56, 45/2*e^3 + 3*e^2 - 537/2*e + 103, -17*e^3 - 5*e^2 + 213*e - 69, 13*e^3 + 11/2*e^2 - 155*e + 67/2, 10*e^3 + 3*e^2 - 120*e + 35, 2*e^2 + 4*e - 38, 7*e^3 + 3*e^2 - 73*e + 23, 1/2*e^3 - 2*e^2 - 19/2*e + 6, -7/2*e^3 + 3*e^2 + 81/2*e - 31, 4*e^3 + 6*e^2 - 38*e - 14, 28*e^3 + 17/2*e^2 - 326*e + 221/2, 6*e^3 + e^2 - 68*e + 29, -2*e^3 - 4*e^2 + 18*e + 6, 4*e^3 - 2*e^2 - 42*e + 52, 3*e^3 + 3*e^2 - 29*e - 11, 3*e^2 + 8*e - 3, -13*e^3 - 3*e^2 + 159*e - 65, 23*e^3 + 12*e^2 - 261*e + 72, -7*e^3 - 5*e^2 + 85*e - 23, 9/2*e^3 - e^2 - 117/2*e + 67, -2*e^2 - 2*e + 18, -e^2 - 6*e + 13, -19*e^3 - 5*e^2 + 219*e - 91, -11*e^3 + 135*e - 68, -7*e^3 - 6*e^2 + 89*e + 4, -e^3 + 4*e^2 + 7*e - 40, -11*e^3 - 7*e^2 + 125*e - 7, 11/2*e^2 + 8*e - 35/2, -11*e^3 - 5*e^2 + 123*e - 25, -14*e^3 - 6*e^2 + 170*e - 42, 22*e^3 + 6*e^2 - 262*e + 66, -4*e^3 + 1/2*e^2 + 50*e - 35/2, 15*e^3 + 13/2*e^2 - 169*e + 57/2, -14*e^3 - 2*e^2 + 162*e - 64, -21/2*e^3 - 6*e^2 + 219/2*e - 26, -25/2*e^3 - 3*e^2 + 269/2*e - 67, 49/2*e^3 + 7*e^2 - 573/2*e + 95, 9*e^3 + 4*e^2 - 93*e + 48, 6*e^3 + 1/2*e^2 - 74*e + 123/2, -7*e^3 - 5*e^2 + 69*e + 17, e^3 + 1/2*e^2 - 23*e - 7/2, 17*e^3 + 5*e^2 - 191*e + 89, 3*e^3 + 3*e^2 - 31*e + 25, 4*e^3 + e^2 - 46*e + 25, -11/2*e^3 - e^2 + 135/2*e - 31, 33/2*e^3 + 7*e^2 - 421/2*e + 47, -10*e^3 - 2*e^2 + 124*e - 72, 8*e^3 - 100*e + 22, 3*e^3 - 2*e^2 - 39*e + 38, 2*e^3 - 22*e + 28, 17*e^3 + 4*e^2 - 201*e + 60, -39/2*e^3 - 5*e^2 + 479/2*e - 85, 14*e^3 + 15/2*e^2 - 164*e + 163/2, -e^3 + 4*e^2 + 11*e - 14, 47/2*e^3 + 11*e^2 - 541/2*e + 69, 7*e^3 + 11*e^2 - 79*e - 9, -15*e^3 - 4*e^2 + 163*e - 86, -4*e^3 - 2*e^2 + 42*e + 4, 21/2*e^3 + 3*e^2 - 227/2*e + 45, -53/2*e^3 - 12*e^2 + 587/2*e - 84, 18*e^3 + 6*e^2 - 230*e + 72, 16*e^3 + 6*e^2 - 176*e + 52, -6*e^3 + 68*e - 48, -6*e^3 + e^2 + 64*e - 53, -10*e^3 + 1/2*e^2 + 116*e - 131/2, 6*e^3 - 66*e + 52, 10*e^3 + 7*e^2 - 120*e + 11, -6*e^3 + 80*e - 70, -7*e^3 - 5*e^2 + 85*e - 27, 5*e^3 - 3*e^2 - 55*e + 43, -17*e^3 - 12*e^2 + 197*e - 62, 7*e^3 - 79*e + 40, -20*e^3 - 11/2*e^2 + 248*e - 169/2, 12*e^3 + 4*e^2 - 150*e + 44, -4*e^3 + 2*e^2 + 60*e - 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101, -31/2*e^3 + 2*e^2 + 433/2*e - 158, 53*e^3 + 25/2*e^2 - 639*e + 477/2, 22*e^3 + 15/2*e^2 - 262*e + 157/2, 8*e^3 - 5*e^2 - 116*e + 149, -48*e^3 - 31/2*e^2 + 542*e - 311/2, 18*e^3 + 20*e^2 - 192*e - 64, -2*e^3 + 7/2*e^2 + 8*e - 125/2, -2*e^3 + 13*e^2 + 26*e - 107, 25*e^3 + 14*e^2 - 279*e + 20, -40*e^3 - 17*e^2 + 446*e - 163, 30*e^3 + 17/2*e^2 - 350*e + 143/2, -26*e^3 + 11/2*e^2 + 348*e - 457/2, 10*e^3 + 17/2*e^2 - 84*e - 9/2, -13*e^3 - 11*e^2 + 121*e - 31, 56*e^3 + 14*e^2 - 660*e + 266, 52*e^3 + 2*e^2 - 640*e + 268, 57*e^3 + 28*e^2 - 665*e + 210, -43*e^3 - 19*e^2 + 475*e - 169, 48*e^3 + 21*e^2 - 578*e + 183, -8*e^3 - 31/2*e^2 + 118*e + 151/2, 31*e^3 + 13*e^2 - 359*e + 149, 27*e^3 + 16*e^2 - 289*e + 62, 6*e^3 + 14*e^2 - 54*e - 76, -10*e^3 + 2*e^2 + 134*e - 160, 14*e^3 + 37/2*e^2 - 154*e + 103/2, 3*e^3 + 3*e^2 - 49*e + 25, -55/2*e^3 + 6*e^2 + 717/2*e - 186, -50*e^3 - 13*e^2 + 610*e - 241, -11*e^3 - 22*e^2 + 87*e + 90, -10*e^3 - 11/2*e^2 + 150*e + 15/2, -19*e^3 - 15/2*e^2 + 217*e + 57/2, -42*e^3 - 3*e^2 + 514*e - 223, -67*e^3 - 26*e^2 + 779*e - 214, 30*e^3 + 33/2*e^2 - 350*e + 199/2, -36*e^3 - 7*e^2 + 454*e - 179, -46*e^3 - 21/2*e^2 + 522*e - 467/2, 32*e^3 + 16*e^2 - 352*e + 94, 45*e^3 + 10*e^2 - 515*e + 174, -4*e^3 - 17/2*e^2 + 14*e + 43/2, -9*e^3 - 6*e^2 + 81*e + 14, -3*e^3 - 8*e^2 + 63*e + 132, -21*e^3 - 2*e^2 + 253*e - 152, 34*e^3 + 18*e^2 - 406*e + 136, -76*e^3 - 24*e^2 + 936*e - 310, 4*e^3 + 7*e^2 - 20*e - 117, -24*e^3 + 11/2*e^2 + 286*e - 345/2, 26*e^3 + 25/2*e^2 - 296*e + 87/2, -20*e^3 - 4*e^2 + 270*e - 80, 5*e^3 - 63*e - 2, 4*e^3 - 12*e^2 - 36*e + 164, 35*e^3 + 26*e^2 - 397*e + 56, -17*e^3 - 2*e^2 + 241*e - 118, 59*e^3 + 16*e^2 - 733*e + 262, -79/2*e^3 - 18*e^2 + 1009/2*e - 106, 33/2*e^3 + 11*e^2 - 349/2*e + 23, -28*e^3 - 3*e^2 + 352*e - 135, 49/2*e^3 + e^2 - 553/2*e + 167, 21*e^3 - 3*e^2 - 241*e + 173, 56*e^3 + 12*e^2 - 696*e + 246, -16*e^3 + 11/2*e^2 + 198*e - 291/2, -74*e^3 - 53/2*e^2 + 852*e - 559/2, 9*e^3 + 16*e^2 - 101*e - 28, -37*e^3 - 4*e^2 + 427*e - 240, 36*e^3 + 14*e^2 - 428*e + 114, 40*e^3 + 16*e^2 - 456*e + 250, -21*e^3 - 4*e^2 + 237*e - 176, 49*e^3 + 16*e^2 - 589*e + 164, -9*e^3 + 107*e - 166, 6*e^3 + 23*e^2 - 68*e - 103, 49*e^3 + 26*e^2 - 549*e + 138, -4*e^3 - 3*e^2 + 18*e - 79, 47/2*e^3 + 4*e^2 - 501/2*e + 116, 17/2*e^3 - 11*e^2 - 233/2*e + 149, 59*e^3 + 27*e^2 - 671*e + 221, 71*e^3 + 28*e^2 - 835*e + 244, 9*e^2 + 8*e - 63, -80*e^3 - 32*e^2 + 956*e - 330, -5*e^3 - 19*e^2 + 59*e + 107, -85/2*e^3 - 15*e^2 + 969/2*e - 163, -2*e^3 - 2*e^2 + 26*e + 20, 12*e^3 + 11*e^2 - 132*e + 9, 19/2*e^3 + 9*e^2 - 247/2*e - 25, 30*e^3 + 13*e^2 - 360*e + 133, 27*e^3 + 27/2*e^2 - 285*e + 135/2, 10*e^3 + 11*e^2 - 102*e - 25, -67/2*e^3 - 13*e^2 + 871/2*e - 111, 61*e^3 + 14*e^2 - 715*e + 252, -38*e^3 - 27*e^2 + 426*e - 41, -12*e^3 + 2*e^2 + 158*e - 128, -6*e^3 - 3*e^2 + 52*e - 23, e^3 - 6*e^2 - 31*e + 138, -10*e^3 - 6*e^2 + 110*e + 120, -31/2*e^2 - 34*e + 201/2, -14*e^3 - 10*e^2 + 120*e - 38, 25*e^3 + 19/2*e^2 - 279*e + 287/2, -72*e^3 - 19*e^2 + 868*e - 277, 11*e^3 + 6*e^2 - 151*e + 6, -5*e^3 - 39/2*e^2 + 51*e + 193/2, 57*e^3 + 9*e^2 - 705*e + 237, -44*e^3 + 540*e - 234, 49/2*e^3 + 5*e^2 - 631/2*e + 179, -39*e^3 - 21*e^2 + 469*e - 131, -13*e^3 + 137*e - 62, 38*e^3 + 20*e^2 - 448*e + 214, 9*e^3 - 13/2*e^2 - 143*e + 311/2, 16*e^3 + 10*e^2 - 192*e - 48, -51*e^3 - 33/2*e^2 + 645*e - 401/2, 35/2*e^3 + 4*e^2 - 473/2*e + 64, 48*e^3 + 4*e^2 - 548*e + 266, -69*e^3 - 28*e^2 + 795*e - 264, 30*e^3 + 27/2*e^2 - 362*e + 233/2, 15/2*e^3 + 25*e^2 - 127/2*e - 107, -11*e^3 - 20*e^2 + 145*e + 104, 49*e^3 + 27/2*e^2 - 575*e + 399/2, 4*e^3 + 43/2*e^2 - 16*e - 347/2, -16*e^3 - 5/2*e^2 + 180*e - 71/2, -4*e^3 + 1/2*e^2 + 48*e - 81/2, 2*e^3 + 6*e^2 - 36*e + 50, 54*e^3 + 35/2*e^2 - 632*e + 311/2, 11*e^3 + 5*e^2 - 131*e - 1, -24*e^3 - 35/2*e^2 + 286*e + 61/2, -10*e^3 - 23/2*e^2 + 84*e + 125/2, -29*e^3 - 16*e^2 + 317*e + 20, -44*e^3 - 1/2*e^2 + 542*e - 493/2, 28*e^3 + 11/2*e^2 - 358*e + 217/2, -19*e^3 - 8*e^2 + 215*e + 8, -4*e^3 - 10*e^2 + 20*e + 68, 29*e^3 + 8*e^2 - 369*e + 188, 20*e^3 + 19*e^2 - 192*e - 29, -135/2*e^3 - 19*e^2 + 1615/2*e - 225, -39/2*e^3 - 19*e^2 + 401/2*e - 5, -34*e^3 - 10*e^2 + 414*e - 112, 55*e^3 + 16*e^2 - 647*e + 152, -40*e^3 - 12*e^2 + 502*e - 96, 32*e^3 + 5*e^2 - 400*e + 85, 6*e^3 - 3*e^2 - 98*e + 41, 47/2*e^3 - 577/2*e + 96, 43*e^3 + 16*e^2 - 513*e + 150, 109/2*e^3 + 29*e^2 - 1309/2*e + 187, -e^3 - 4*e^2 + 19*e + 34, 24*e^3 - 280*e + 124, 35*e^3 + 4*e^2 - 451*e + 242, -57*e^3 - 11*e^2 + 671*e - 227, -23*e^3 + 283*e - 74, 21/2*e^3 - 16*e^2 - 291/2*e + 192, -26*e^3 + 7/2*e^2 + 316*e - 247/2, 28*e^3 + 21/2*e^2 - 322*e + 109/2, 28*e^3 + 18*e^2 - 344*e + 80, 14*e^3 - 8*e^2 - 216*e + 202, -24*e^3 - 6*e^2 + 328*e - 116, -59*e^3 - 27/2*e^2 + 737*e - 475/2, -42*e^3 - 13/2*e^2 + 488*e - 377/2, -49*e^3 - 21*e^2 + 575*e - 205, 11*e^3 + 4*e^2 - 83*e + 66, 2*e^3 + 3*e^2 - 2*e + 83, 37*e^3 + 6*e^2 - 433*e + 172, 33*e^3 + 3*e^2 - 391*e + 173, -19/2*e^3 + 8*e^2 + 273/2*e - 96, -63/2*e^3 - 7*e^2 + 685/2*e - 185, -27/2*e^3 - 9*e^2 + 323/2*e - 87, 51*e^3 + 23*e^2 - 605*e + 161, -6*e^3 - 2*e^2 + 78*e - 52, 20*e^3 - 3/2*e^2 - 210*e + 255/2, 27/2*e^3 + 16*e^2 - 229/2*e - 56, 19*e^3 + 12*e^2 - 199*e + 52, -16*e^3 - 18*e^2 + 164*e + 104, 52*e^3 + 16*e^2 - 630*e + 184, 19*e^3 + 22*e^2 - 223*e - 48, 40*e^3 + 25*e^2 - 458*e + 65, -4*e^3 + 11*e^2 + 50*e - 75, -30*e^3 - 7*e^2 + 338*e - 181, -48*e^3 - 18*e^2 + 592*e - 190, 26*e^3 + 27*e^2 - 292*e + 43, 15/2*e^3 + 11*e^2 - 103/2*e - 53, -17*e^3 - 16*e^2 + 189*e - 66, 20*e^3 - 25/2*e^2 - 278*e + 427/2, 14*e^3 + 25/2*e^2 - 132*e - 55/2, 2*e^3 + e^2 - 32*e + 119, 30*e^3 + 5*e^2 - 344*e + 81, -20*e^3 - 25/2*e^2 + 208*e + 29/2, -32*e^3 - 7/2*e^2 + 364*e - 437/2, -64*e^3 - 37/2*e^2 + 742*e - 523/2, 24*e^3 + e^2 - 314*e + 83, e^3 + 13*e^2 - 11*e - 113, 11/2*e^3 - 6*e^2 - 125/2*e - 34, -5*e^3 + 35/2*e^2 + 115*e - 373/2, 59*e^3 + 20*e^2 - 719*e + 198, -9*e^3 + 99*e + 24, 44*e^3 + 7/2*e^2 - 512*e + 377/2, 77/2*e^3 + 27*e^2 - 853/2*e + 61, -51*e^3 - 23*e^2 + 643*e - 129, 22*e^3 - 5*e^2 - 238*e + 163, -69*e^3 - 29/2*e^2 + 807*e - 549/2, 24*e^3 + 25/2*e^2 - 312*e + 135/2, -19*e^3 - 19*e^2 + 219*e - 65, -115/2*e^3 - 9*e^2 + 1381/2*e - 287, 45/2*e^3 + 3*e^2 - 549/2*e + 153, -85/2*e^3 - 3*e^2 + 1105/2*e - 249, 20*e^3 + 9*e^2 - 192*e + 93, -10*e^3 - 19/2*e^2 + 102*e - 109/2, 31*e^3 + 20*e^2 - 329*e + 60, -18*e^3 - 33/2*e^2 + 216*e + 25/2, -21*e^3 + 247*e - 180, -30*e^3 - 15*e^2 + 310*e - 65, -25/2*e^3 - 19*e^2 + 329/2*e + 31, -3*e^3 + 18*e^2 + 63*e - 98, -44*e^3 - 21*e^2 + 538*e - 195, -38*e^3 - 22*e^2 + 452*e - 108, 59*e^3 + 24*e^2 - 703*e + 228, -19*e^3 - 12*e^2 + 237*e - 10, 10*e^3 - 4*e^2 - 132*e + 14, 17*e^3 + 4*e^2 - 175*e + 64, -25*e^3 - 10*e^2 + 305*e - 2, 36*e^3 + 12*e^2 - 436*e + 78, -45*e^3 - 34*e^2 + 513*e - 118, 47*e^3 + 22*e^2 - 593*e + 156, -30*e^3 - 2*e^2 + 348*e - 126, 19*e^2 - 113, -25*e^3 - 27*e^2 + 283*e + 35, -28*e^3 - 7*e^2 + 348*e - 51, 23*e^3 + 10*e^2 - 275*e + 98, 55/2*e^3 - e^2 - 733/2*e + 177, -81/2*e^3 - 7*e^2 + 1019/2*e - 265, 113/2*e^3 + 16*e^2 - 1419/2*e + 228, 23*e^3 + 14*e^2 - 271*e + 190, 40*e^3 + 3/2*e^2 - 498*e + 481/2, -2*e^3 + 2*e^2 + 56*e - 4, -19/2*e^3 - 15*e^2 + 259/2*e + 81, 49/2*e^3 + 24*e^2 - 583/2*e - 24, 19/2*e^3 + 13*e^2 - 211/2*e + 13, -52*e^3 - 28*e^2 + 584*e - 132, 26*e^3 + 1/2*e^2 - 306*e + 451/2, 41/2*e^3 + 6*e^2 - 511/2*e + 86, -38*e^3 - 19*e^2 + 400*e - 77, -60*e^3 - 14*e^2 + 700*e - 216, -4*e^3 + 31/2*e^2 + 82*e - 263/2, 1/2*e^3 - 3*e^2 - 65/2*e - 21, -69/2*e^3 - 11*e^2 + 751/2*e - 125, 35*e^3 + 23/2*e^2 - 385*e + 175/2, 51*e^3 + 21/2*e^2 - 617*e + 365/2, 31*e^3 + 13*e^2 - 361*e + 169, -16*e^3 - 43/2*e^2 + 166*e - 11/2, 93/2*e^3 + 37*e^2 - 1029/2*e + 55, -15*e^3 - 4*e^2 + 169*e - 110, 11*e^3 + 13*e^2 - 129*e + 81, -12*e^3 - 19/2*e^2 + 130*e - 103/2, -43*e^3 - 19*e^2 + 529*e - 179, -21*e^3 - e^2 + 213*e - 161, -37*e^3 - 7/2*e^2 + 427*e - 335/2, -20*e^3 - 2*e^2 + 246*e - 60, 39/2*e^3 + 12*e^2 - 529/2*e + 44, 19*e^3 - 8*e^2 - 269*e + 174, 2*e^3 - 9/2*e^2 - 68*e + 67/2, 16*e^3 + 12*e^2 - 172*e - 62, 11*e^3 + 3*e^2 - 151*e - 25, 11*e^3 - 2*e^2 - 123*e + 142, -59*e^3 - 20*e^2 + 691*e - 176, -6*e^3 + 12*e^2 + 94*e - 66, 57/2*e^3 + 16*e^2 - 663/2*e + 116, 3*e^2 + 22*e - 39, -48*e^3 - 15*e^2 + 580*e - 181, 45*e^3 + 9*e^2 - 553*e + 175, -6*e^3 - 8*e^2 + 50*e - 26, 20*e^3 - 2*e^2 - 222*e + 118, -6*e^3 + 13*e^2 + 120*e - 163, 17*e^3 + 15*e^2 - 183*e + 65, -13*e^3 + 5*e^2 + 147*e - 121, -119/2*e^3 - 38*e^2 + 1353/2*e - 158, -19/2*e^3 - 6*e^2 + 213/2*e + 18, 50*e^3 + 12*e^2 - 606*e + 152, -34*e^3 - 20*e^2 + 388*e - 58, 19/2*e^3 - 5*e^2 - 211/2*e + 55, 3*e^3 - 3*e^2 - 15*e + 31, -28*e^3 - 33/2*e^2 + 362*e - 15/2, -3*e^3 - 7*e^2 + 29*e - 39, -60*e^3 - 63/2*e^2 + 718*e - 411/2, -22*e^3 - 15*e^2 + 208*e + 5, 107/2*e^3 + 15*e^2 - 1313/2*e + 237, 19*e^3 + 17*e^2 - 197*e - 63, 9*e^3 - 4*e^2 - 97*e + 120, -e^3 - 27/2*e^2 - 33*e + 225/2, -45*e^3 - 16*e^2 + 499*e - 170] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([181, 181, -14*w - 1])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]