/* 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([-7, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([53, 53, 3*w - 5]) primes_array = [ [4, 2, 2],\ [5, 5, w + 1],\ [5, 5, w - 2],\ [7, 7, w],\ [7, 7, -w + 1],\ [9, 3, 3],\ [13, 13, w + 4],\ [13, 13, w - 5],\ [23, 23, -w - 5],\ [23, 23, w - 6],\ [29, 29, 2*w - 1],\ [53, 53, 3*w - 5],\ [53, 53, -3*w - 2],\ [59, 59, -3*w - 1],\ [59, 59, 3*w - 4],\ [67, 67, 3*w - 13],\ [67, 67, -3*w - 10],\ [71, 71, 2*w - 11],\ [71, 71, -2*w - 9],\ [83, 83, -w - 9],\ [83, 83, w - 10],\ [103, 103, -w - 10],\ [103, 103, w - 11],\ [107, 107, -4*w - 1],\ [107, 107, 4*w - 5],\ [109, 109, 4*w - 17],\ [109, 109, -4*w - 13],\ [121, 11, -11],\ [139, 139, 5*w - 9],\ [139, 139, -5*w - 4],\ [149, 149, -w - 12],\ [149, 149, w - 13],\ [151, 151, -5*w - 3],\ [151, 151, 5*w - 8],\ [167, 167, 2*w - 15],\ [167, 167, -2*w - 13],\ [173, 173, 7*w - 17],\ [173, 173, 4*w - 19],\ [179, 179, 5*w - 4],\ [179, 179, 5*w - 1],\ [181, 181, 5*w - 2],\ [181, 181, 5*w - 3],\ [197, 197, 6*w - 11],\ [197, 197, -6*w - 5],\ [199, 199, -5*w - 17],\ [199, 199, 5*w - 22],\ [223, 223, 6*w - 25],\ [223, 223, -6*w - 19],\ [227, 227, 2*w - 17],\ [227, 227, -2*w - 15],\ [233, 233, -w - 15],\ [233, 233, w - 16],\ [239, 239, 5*w - 23],\ [239, 239, 8*w - 19],\ [241, 241, 3*w - 19],\ [241, 241, -3*w - 16],\ [257, 257, 6*w - 5],\ [257, 257, 6*w - 1],\ [277, 277, -3*w - 17],\ [277, 277, 3*w - 20],\ [281, 281, 9*w - 22],\ [281, 281, -9*w - 13],\ [283, 283, -7*w - 5],\ [283, 283, 7*w - 12],\ [289, 17, -17],\ [313, 313, 7*w - 10],\ [313, 313, -7*w - 3],\ [347, 347, -7*w - 23],\ [347, 347, 7*w - 30],\ [349, 349, 7*w - 6],\ [349, 349, 7*w - 1],\ [353, 353, 7*w - 2],\ [353, 353, 7*w - 5],\ [361, 19, -19],\ [373, 373, -w - 19],\ [373, 373, w - 20],\ [383, 383, 8*w - 13],\ [383, 383, -8*w - 5],\ [397, 397, -3*w - 20],\ [397, 397, 3*w - 23],\ [401, 401, -7*w - 24],\ [401, 401, 7*w - 31],\ [419, 419, -5*w - 22],\ [419, 419, 5*w - 27],\ [431, 431, 9*w - 17],\ [431, 431, -9*w - 8],\ [439, 439, -8*w - 1],\ [439, 439, 8*w - 9],\ [457, 457, 7*w - 32],\ [457, 457, 11*w - 26],\ [463, 463, 8*w - 5],\ [463, 463, 8*w - 3],\ [487, 487, 3*w - 25],\ [487, 487, -3*w - 22],\ [499, 499, -w - 22],\ [499, 499, w - 23],\ [509, 509, -4*w - 23],\ [509, 509, 4*w - 27],\ [521, 521, -5*w - 24],\ [521, 521, 5*w - 29],\ [523, 523, 13*w + 20],\ [523, 523, 13*w - 33],\ [547, 547, 2*w - 25],\ [547, 547, -2*w - 23],\ [557, 557, -9*w - 1],\ [557, 557, 9*w - 10],\ [571, 571, 10*w - 41],\ [571, 571, -10*w - 31],\ [587, 587, 9*w - 4],\ [587, 587, 9*w - 5],\ [593, 593, -w - 24],\ [593, 593, w - 25],\ [613, 613, 4*w - 29],\ [613, 613, -4*w - 25],\ [631, 631, 5*w - 31],\ [631, 631, -5*w - 26],\ [643, 643, -w - 25],\ [643, 643, w - 26],\ [647, 647, 2*w - 27],\ [647, 647, -2*w - 25],\ [661, 661, 10*w - 13],\ [661, 661, -10*w - 3],\ [673, 673, -9*w - 31],\ [673, 673, 9*w - 40],\ [683, 683, 11*w - 45],\ [683, 683, -11*w - 34],\ [691, 691, -3*w - 26],\ [691, 691, 3*w - 29],\ [701, 701, 15*w + 23],\ [701, 701, 15*w - 38],\ [709, 709, 10*w - 9],\ [709, 709, 10*w - 1],\ [719, 719, -10*w - 33],\ [719, 719, 10*w - 43],\ [761, 761, 15*w - 37],\ [761, 761, -15*w - 22],\ [787, 787, -11*w - 4],\ [787, 787, 11*w - 15],\ [811, 811, -5*w - 29],\ [811, 811, 5*w - 34],\ [821, 821, 11*w - 13],\ [821, 821, -11*w - 2],\ [857, 857, 11*w - 10],\ [857, 857, 11*w - 1],\ [863, 863, -w - 29],\ [863, 863, w - 30],\ [877, 877, 11*w - 5],\ [877, 877, 11*w - 6],\ [883, 883, 13*w - 25],\ [883, 883, -13*w - 12],\ [919, 919, -13*w - 11],\ [919, 919, 13*w - 24],\ [929, 929, 11*w - 48],\ [929, 929, -11*w - 37],\ [937, 937, 13*w - 53],\ [937, 937, -13*w - 40],\ [941, 941, 5*w - 36],\ [941, 941, -5*w - 31],\ [953, 953, -13*w - 10],\ [953, 953, 13*w - 23],\ [961, 31, -31],\ [977, 977, 7*w - 40],\ [977, 977, -7*w - 33],\ [991, 991, 3*w - 34],\ [991, 991, -3*w - 31],\ [1009, 1009, -5*w - 32],\ [1009, 1009, 5*w - 37],\ [1019, 1019, 12*w - 11],\ [1019, 1019, 12*w - 1],\ [1021, 1021, 14*w - 27],\ [1021, 1021, -14*w - 13],\ [1031, 1031, -13*w - 41],\ [1031, 1031, 13*w - 54],\ [1039, 1039, 10*w - 47],\ [1039, 1039, 17*w - 41],\ [1049, 1049, -w - 32],\ [1049, 1049, w - 33],\ [1051, 1051, -7*w - 34],\ [1051, 1051, 7*w - 41],\ [1069, 1069, 13*w - 19],\ [1069, 1069, -13*w - 6],\ [1093, 1093, 13*w - 18],\ [1093, 1093, -13*w - 5],\ [1097, 1097, 14*w - 25],\ [1097, 1097, -14*w - 11],\ [1103, 1103, 11*w - 50],\ [1103, 1103, 17*w - 40],\ [1109, 1109, 4*w - 37],\ [1109, 1109, -4*w - 33],\ [1151, 1151, -5*w - 34],\ [1151, 1151, 5*w - 39],\ [1153, 1153, 13*w - 15],\ [1153, 1153, -13*w - 2],\ [1193, 1193, 18*w - 43],\ [1193, 1193, 11*w - 51],\ [1213, 1213, 13*w - 3],\ [1213, 1213, 13*w - 10],\ [1217, 1217, -8*w - 37],\ [1217, 1217, 8*w - 45],\ [1223, 1223, 13*w - 5],\ [1223, 1223, 13*w - 8],\ [1231, 1231, 15*w - 61],\ [1231, 1231, -15*w - 46],\ [1277, 1277, -14*w - 5],\ [1277, 1277, 14*w - 19],\ [1283, 1283, 14*w - 59],\ [1283, 1283, -14*w - 45],\ [1289, 1289, 15*w - 26],\ [1289, 1289, -15*w - 11],\ [1301, 1301, 5*w - 41],\ [1301, 1301, -5*w - 36],\ [1321, 1321, -14*w - 3],\ [1321, 1321, 14*w - 17],\ [1327, 1327, 16*w - 31],\ [1327, 1327, -16*w - 15],\ [1367, 1367, -7*w - 38],\ [1367, 1367, 7*w - 45],\ [1369, 37, -37],\ [1399, 1399, -w - 37],\ [1399, 1399, w - 38],\ [1427, 1427, -13*w - 45],\ [1427, 1427, 13*w - 58],\ [1451, 1451, 7*w - 46],\ [1451, 1451, -7*w - 39],\ [1459, 1459, 5*w - 43],\ [1459, 1459, -5*w - 38],\ [1483, 1483, 9*w - 50],\ [1483, 1483, -9*w - 41],\ [1499, 1499, -15*w - 4],\ [1499, 1499, 15*w - 19],\ [1531, 1531, 13*w - 59],\ [1531, 1531, 20*w - 47],\ [1543, 1543, -17*w - 15],\ [1543, 1543, 17*w - 32],\ [1553, 1553, -w - 39],\ [1553, 1553, w - 40],\ [1559, 1559, -15*w - 1],\ [1559, 1559, 15*w - 16],\ [1567, 1567, 16*w - 25],\ [1567, 1567, -16*w - 9],\ [1571, 1571, 2*w - 41],\ [1571, 1571, -2*w - 39],\ [1579, 1579, -10*w - 43],\ [1579, 1579, 10*w - 53],\ [1601, 1601, 15*w - 2],\ [1601, 1601, 15*w - 13],\ [1619, 1619, 15*w - 11],\ [1619, 1619, 15*w - 4],\ [1637, 1637, 13*w - 60],\ [1637, 1637, 21*w - 50],\ [1657, 1657, 3*w - 43],\ [1657, 1657, -3*w - 40],\ [1669, 1669, 9*w - 52],\ [1669, 1669, -9*w - 43],\ [1681, 41, -41],\ [1733, 1733, 4*w - 45],\ [1733, 1733, -4*w - 41],\ [1741, 1741, -3*w - 41],\ [1741, 1741, 3*w - 44],\ [1747, 1747, 18*w - 73],\ [1747, 1747, -18*w - 55],\ [1753, 1753, 17*w - 27],\ [1753, 1753, -17*w - 10],\ [1789, 1789, -17*w - 9],\ [1789, 1789, 17*w - 26],\ [1811, 1811, 17*w - 71],\ [1811, 1811, -17*w - 54],\ [1823, 1823, 17*w - 25],\ [1823, 1823, -17*w - 8],\ [1831, 1831, 16*w - 3],\ [1831, 1831, 16*w - 13],\ [1847, 1847, 16*w - 5],\ [1847, 1847, 16*w - 11],\ [1849, 43, -43],\ [1861, 1861, 19*w - 37],\ [1861, 1861, -19*w - 18],\ [1879, 1879, 11*w - 58],\ [1879, 1879, -11*w - 47],\ [1889, 1889, 5*w - 48],\ [1889, 1889, -5*w - 43],\ [1901, 1901, -7*w - 44],\ [1901, 1901, 7*w - 51],\ [1907, 1907, 2*w - 45],\ [1907, 1907, -2*w - 43],\ [1913, 1913, -17*w - 5],\ [1913, 1913, 17*w - 22],\ [1949, 1949, -18*w - 11],\ [1949, 1949, 18*w - 29],\ [1973, 1973, -w - 44],\ [1973, 1973, w - 45],\ [1979, 1979, 10*w - 57],\ [1979, 1979, -10*w - 47],\ [1997, 1997, -7*w - 45],\ [1997, 1997, 7*w - 52],\ [2017, 2017, 19*w - 34],\ [2017, 2017, -19*w - 15],\ [2029, 2029, 15*w - 68],\ [2029, 2029, 23*w - 54],\ [2039, 2039, 17*w - 16],\ [2039, 2039, 17*w - 1],\ [2053, 2053, 17*w - 2],\ [2053, 2053, 17*w - 15],\ [2063, 2063, -w - 45],\ [2063, 2063, w - 46],\ [2081, 2081, 25*w - 62],\ [2081, 2081, -25*w - 37],\ [2083, 2083, 17*w - 12],\ [2083, 2083, 17*w - 5],\ [2087, 2087, 2*w - 47],\ [2087, 2087, -2*w - 45],\ [2089, 2089, 17*w - 11],\ [2089, 2089, 17*w - 6],\ [2111, 2111, -19*w - 13],\ [2111, 2111, 19*w - 32],\ [2113, 2113, 16*w - 71],\ [2113, 2113, -16*w - 55],\ [2137, 2137, -8*w - 47],\ [2137, 2137, 8*w - 55],\ [2141, 2141, 20*w - 81],\ [2141, 2141, -20*w - 61],\ [2153, 2153, 18*w - 23],\ [2153, 2153, -18*w - 5],\ [2179, 2179, 25*w - 61],\ [2179, 2179, -25*w - 36],\ [2203, 2203, 11*w - 61],\ [2203, 2203, -11*w - 50],\ [2209, 47, -47],\ [2213, 2213, -19*w - 60],\ [2213, 2213, 19*w - 79],\ [2237, 2237, -19*w - 10],\ [2237, 2237, 19*w - 29],\ [2239, 2239, -6*w - 47],\ [2239, 2239, 6*w - 53],\ [2267, 2267, 21*w - 41],\ [2267, 2267, -21*w - 20],\ [2269, 2269, -5*w - 47],\ [2269, 2269, 5*w - 52],\ [2287, 2287, -3*w - 47],\ [2287, 2287, 3*w - 50],\ [2297, 2297, -7*w - 48],\ [2297, 2297, 7*w - 55],\ [2311, 2311, 19*w - 27],\ [2311, 2311, -19*w - 8],\ [2333, 2333, 18*w - 5],\ [2333, 2333, 18*w - 13],\ [2371, 2371, 20*w - 33],\ [2371, 2371, -20*w - 13],\ [2377, 2377, 19*w - 25],\ [2377, 2377, -19*w - 6],\ [2383, 2383, 9*w - 59],\ [2383, 2383, -9*w - 50],\ [2411, 2411, 10*w - 61],\ [2411, 2411, -10*w - 51],\ [2423, 2423, 27*w - 67],\ [2423, 2423, -27*w - 40],\ [2437, 2437, 12*w - 65],\ [2437, 2437, -12*w - 53],\ [2441, 2441, -21*w - 17],\ [2441, 2441, 21*w - 38],\ [2459, 2459, 20*w - 31],\ [2459, 2459, -20*w - 11],\ [2503, 2503, -21*w - 65],\ [2503, 2503, 21*w - 86],\ [2539, 2539, -20*w - 9],\ [2539, 2539, 20*w - 29],\ [2543, 2543, -w - 50],\ [2543, 2543, w - 51],\ [2551, 2551, -18*w - 61],\ [2551, 2551, 18*w - 79],\ [2557, 2557, 29*w - 74],\ [2557, 2557, 29*w + 45],\ [2609, 2609, -22*w - 19],\ [2609, 2609, 22*w - 41],\ [2617, 2617, 19*w - 9],\ [2617, 2617, 19*w - 10],\ [2633, 2633, 16*w - 75],\ [2633, 2633, 27*w - 65],\ [2659, 2659, -28*w - 41],\ [2659, 2659, 28*w - 69],\ [2663, 2663, -11*w - 54],\ [2663, 2663, 11*w - 65],\ [2677, 2677, -12*w - 55],\ [2677, 2677, 12*w - 67],\ [2693, 2693, -4*w - 51],\ [2693, 2693, 4*w - 55],\ [2713, 2713, 23*w - 45],\ [2713, 2713, -23*w - 22],\ [2719, 2719, -9*w - 53],\ [2719, 2719, 9*w - 62],\ [2731, 2731, -20*w - 3],\ [2731, 2731, 20*w - 23],\ [2749, 2749, -w - 52],\ [2749, 2749, w - 53],\ [2777, 2777, 21*w - 31],\ [2777, 2777, -21*w - 10],\ [2789, 2789, -5*w - 52],\ [2789, 2789, 5*w - 57],\ [2791, 2791, 29*w - 72],\ [2791, 2791, -29*w - 43],\ [2797, 2797, 3*w - 55],\ [2797, 2797, -3*w - 52],\ [2819, 2819, 20*w - 19],\ [2819, 2819, 20*w - 1],\ [2833, 2833, -22*w - 15],\ [2833, 2833, 22*w - 37],\ [2837, 2837, 7*w - 60],\ [2837, 2837, -7*w - 53],\ [2843, 2843, 23*w - 43],\ [2843, 2843, -23*w - 20],\ [2851, 2851, 20*w - 17],\ [2851, 2851, 20*w - 3],\ [2887, 2887, 2*w - 55],\ [2887, 2887, -2*w - 53],\ [2909, 2909, 4*w - 57],\ [2909, 2909, -4*w - 53],\ [2953, 2953, 9*w - 64],\ [2953, 2953, -9*w - 55],\ [2957, 2957, 21*w - 26],\ [2957, 2957, -21*w - 5],\ [2963, 2963, -w - 54],\ [2963, 2963, w - 55],\ [2971, 2971, -23*w - 71],\ [2971, 2971, 23*w - 94],\ [3011, 3011, -5*w - 54],\ [3011, 3011, 5*w - 59],\ [3023, 3023, 23*w - 40],\ [3023, 3023, -23*w - 17],\ [3041, 3041, 21*w - 23],\ [3041, 3041, -21*w - 2],\ [3049, 3049, -25*w - 26],\ [3049, 3049, 25*w - 51],\ [3061, 3061, 31*w + 47],\ [3061, 3061, 31*w - 78],\ [3067, 3067, -7*w - 55],\ [3067, 3067, 7*w - 62],\ [3079, 3079, 23*w - 39],\ [3079, 3079, -23*w - 16],\ [3083, 3083, -19*w - 66],\ [3083, 3083, 19*w - 85],\ [3109, 3109, -22*w - 9],\ [3109, 3109, 22*w - 31],\ [3119, 3119, 10*w - 67],\ [3119, 3119, -10*w - 57],\ [3137, 3137, 23*w - 95],\ [3137, 3137, -23*w - 72],\ [3167, 3167, 21*w - 5],\ [3167, 3167, 21*w - 16],\ [3181, 3181, -12*w - 59],\ [3181, 3181, 12*w - 71],\ [3191, 3191, 21*w - 13],\ [3191, 3191, 21*w - 8],\ [3203, 3203, 14*w - 75],\ [3203, 3203, -14*w - 61],\ [3253, 3253, -22*w - 5],\ [3253, 3253, 22*w - 27],\ [3257, 3257, 8*w - 65],\ [3257, 3257, -8*w - 57],\ [3271, 3271, -25*w - 23],\ [3271, 3271, 25*w - 48],\ [3299, 3299, -w - 57],\ [3299, 3299, w - 58],\ [3301, 3301, 25*w - 101],\ [3301, 3301, -25*w - 76],\ [3307, 3307, 31*w - 76],\ [3307, 3307, -31*w - 45],\ [3313, 3313, 22*w - 25],\ [3313, 3313, -22*w - 3],\ [3319, 3319, -9*w - 58],\ [3319, 3319, 9*w - 67],\ [3329, 3329, 23*w - 34],\ [3329, 3329, -23*w - 11],\ [3331, 3331, 13*w - 74],\ [3331, 3331, -13*w - 61],\ [3359, 3359, -5*w - 57],\ [3359, 3359, 5*w - 62],\ [3371, 3371, -10*w - 59],\ [3371, 3371, 10*w - 69],\ [3373, 3373, -23*w - 10],\ [3373, 3373, 23*w - 33],\ [3389, 3389, 19*w - 87],\ [3389, 3389, 30*w - 71],\ [3413, 3413, -11*w - 60],\ [3413, 3413, 11*w - 71],\ [3457, 3457, 26*w - 51],\ [3457, 3457, -26*w - 25],\ [3467, 3467, 13*w - 75],\ [3467, 3467, -13*w - 62],\ [3529, 3529, -23*w - 6],\ [3529, 3529, 23*w - 29],\ [3533, 3533, -w - 59],\ [3533, 3533, w - 60],\ [3539, 3539, -25*w - 19],\ [3539, 3539, 25*w - 44],\ [3547, 3547, -22*w - 73],\ [3547, 3547, 22*w - 95],\ [3571, 3571, 2*w - 61],\ [3571, 3571, -2*w - 59],\ [3583, 3583, -6*w - 59],\ [3583, 3583, 6*w - 65],\ [3631, 3631, 10*w - 71],\ [3631, 3631, -10*w - 61],\ [3659, 3659, -25*w - 78],\ [3659, 3659, 25*w - 103],\ [3677, 3677, 7*w - 67],\ [3677, 3677, -7*w - 60],\ [3719, 3719, -25*w - 16],\ [3719, 3719, 25*w - 41],\ [3721, 61, -61],\ [3761, 3761, -8*w - 61],\ [3761, 3761, 8*w - 69],\ [3769, 3769, 35*w - 89],\ [3769, 3769, 35*w + 54],\ [3779, 3779, 23*w - 19],\ [3779, 3779, 23*w - 4],\ [3793, 3793, 23*w - 5],\ [3793, 3793, 23*w - 18],\ [3803, 3803, -27*w - 25],\ [3803, 3803, 27*w - 52],\ [3821, 3821, 23*w - 99],\ [3821, 3821, -23*w - 76],\ [3823, 3823, 23*w - 15],\ [3823, 3823, 23*w - 8],\ [3833, 3833, 23*w - 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111],\ [8783, 8783, 31*w - 141],\ [8783, 8783, 48*w - 113],\ [8803, 8803, -37*w - 15],\ [8803, 8803, 37*w - 52],\ [8807, 8807, 2*w - 95],\ [8807, 8807, -2*w - 93],\ [8821, 8821, -23*w - 101],\ [8821, 8821, 23*w - 124],\ [8839, 8839, 35*w - 24],\ [8839, 8839, 35*w - 11],\ [8849, 8849, -40*w - 123],\ [8849, 8849, 40*w - 163],\ [8861, 8861, 35*w - 13],\ [8861, 8861, 35*w - 22],\ [8867, 8867, 36*w - 41],\ [8867, 8867, -36*w - 5],\ [8887, 8887, -18*w - 97],\ [8887, 8887, 18*w - 115],\ [8923, 8923, -w - 94],\ [8923, 8923, w - 95],\ [8933, 8933, 37*w - 50],\ [8933, 8933, -37*w - 13],\ [8941, 8941, 35*w - 151],\ [8941, 8941, -35*w - 116],\ [8999, 8999, 40*w - 71],\ [8999, 8999, -40*w - 31],\ [9013, 9013, 21*w - 121],\ [9013, 9013, -21*w - 100],\ [9041, 9041, 54*w - 137],\ [9041, 9041, 54*w + 83],\ [9043, 9043, -34*w - 115],\ [9043, 9043, 34*w - 149],\ [9049, 9049, 24*w - 127],\ [9049, 9049, -24*w - 103],\ [9151, 9151, -7*w - 94],\ [9151, 9151, 7*w - 101],\ [9157, 9157, -12*w - 95],\ [9157, 9157, 12*w - 107],\ [9173, 9173, -38*w - 17],\ [9173, 9173, 38*w - 55],\ [9187, 9187, 2*w - 97],\ [9187, 9187, -2*w - 95],\ [9199, 9199, 40*w - 69],\ [9199, 9199, -40*w - 29],\ [9209, 9209, 35*w - 152],\ [9209, 9209, -35*w - 117],\ [9221, 9221, -39*w - 23],\ [9221, 9221, 39*w - 62],\ [9227, 9227, 36*w - 5],\ [9227, 9227, 36*w - 31],\ [9257, 9257, -37*w - 120],\ [9257, 9257, 37*w - 157],\ [9281, 9281, -13*w - 96],\ [9281, 9281, 13*w - 109],\ [9293, 9293, -4*w - 95],\ [9293, 9293, 4*w - 99],\ [9337, 9337, -8*w - 95],\ [9337, 9337, 8*w - 103],\ [9343, 9343, -6*w - 95],\ [9343, 9343, 6*w - 101],\ [9371, 9371, 36*w - 13],\ [9371, 9371, 36*w - 23],\ [9391, 9391, -40*w - 27],\ [9391, 9391, 40*w - 67],\ [9397, 9397, -49*w + 114],\ [9397, 9397, 33*w - 148],\ [9403, 9403, 52*w - 127],\ [9403, 9403, -52*w - 75],\ [9409, 97, -97],\ [9419, 9419, 37*w - 41],\ [9419, 9419, -37*w - 4],\ [9421, 9421, 20*w - 121],\ [9421, 9421, -20*w - 101],\ [9431, 9431, -41*w - 32],\ [9431, 9431, 41*w - 73],\ [9461, 9461, -17*w - 99],\ [9461, 9461, 17*w - 116],\ [9463, 9463, 37*w - 40],\ [9463, 9463, -37*w - 3],\ [9467, 9467, -39*w - 20],\ [9467, 9467, 39*w - 59],\ [9479, 9479, -35*w - 118],\ [9479, 9479, 35*w - 153],\ [9511, 9511, -25*w - 106],\ [9511, 9511, 25*w - 131],\ [9521, 9521, 5*w - 101],\ [9521, 9521, -5*w - 96],\ [9547, 9547, -44*w - 45],\ [9547, 9547, 44*w - 89],\ [9619, 9619, 37*w - 36],\ [9619, 9619, 37*w - 1],\ [9623, 9623, -43*w - 40],\ [9623, 9623, 43*w - 83],\ [9629, 9629, 11*w - 108],\ [9629, 9629, -11*w - 97],\ [9661, 9661, 33*w - 149],\ [9661, 9661, 50*w - 117],\ [9677, 9677, 17*w - 117],\ [9677, 9677, -17*w - 100],\ [9679, 9679, 10*w - 107],\ [9679, 9679, -10*w - 97],\ [9719, 9719, -5*w - 97],\ [9719, 9719, 5*w - 102],\ [9721, 9721, 55*w + 83],\ [9721, 9721, 55*w - 138],\ [9739, 9739, 6*w - 103],\ [9739, 9739, -6*w - 97],\ [9743, 9743, 37*w - 32],\ [9743, 9743, 37*w - 5],\ [9749, 9749, -25*w - 107],\ [9749, 9749, 25*w - 132],\ [9767, 9767, 39*w - 55],\ [9767, 9767, -39*w - 16],\ [9769, 9769, 37*w - 6],\ [9769, 9769, 37*w - 31],\ [9803, 9803, 31*w - 145],\ [9803, 9803, 52*w - 125],\ [9811, 9811, 44*w - 87],\ [9811, 9811, -44*w - 43],\ [9851, 9851, 45*w - 92],\ [9851, 9851, -45*w - 47],\ [9859, 9859, 53*w - 129],\ [9859, 9859, -53*w - 76],\ [9883, 9883, 37*w - 12],\ [9883, 9883, 37*w - 25],\ [9923, 9923, 37*w - 17],\ [9923, 9923, 37*w - 20],\ [9931, 9931, 41*w - 68],\ [9931, 9931, -41*w - 27],\ [9941, 9941, 55*w - 137],\ [9941, 9941, -55*w - 82],\ [9967, 9967, 56*w - 141],\ [9967, 9967, 56*w + 85]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^5 - 5*x^4 + x^3 + 26*x^2 - 37*x + 13 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, e^4 - 3*e^3 - 5*e^2 + 17*e - 6, -e^4 + 3*e^3 + 4*e^2 - 16*e + 11, -2*e^4 + 3*e^3 + 12*e^2 - 13*e, 5*e^4 - 11*e^3 - 26*e^2 + 58*e - 23, 4*e^4 - 9*e^3 - 21*e^2 + 48*e - 18, -4*e^4 + 12*e^3 + 17*e^2 - 66*e + 37, -4*e^4 + 10*e^3 + 19*e^2 - 54*e + 24, -7*e^4 + 16*e^3 + 36*e^2 - 85*e + 34, 3*e^4 - 8*e^3 - 13*e^2 + 44*e - 26, -8*e^4 + 20*e^3 + 40*e^2 - 108*e + 45, -1, 3*e^4 - 9*e^3 - 12*e^2 + 49*e - 29, -3*e^4 + 7*e^3 + 14*e^2 - 37*e + 22, 6*e^4 - 16*e^3 - 28*e^2 + 89*e - 40, 7*e^4 - 17*e^3 - 34*e^2 + 89*e - 40, -6*e^4 + 7*e^3 + 39*e^2 - 30*e - 6, -9*e^4 + 21*e^3 + 45*e^2 - 111*e + 45, 13*e^4 - 28*e^3 - 69*e^2 + 148*e - 58, 8*e^4 - 14*e^3 - 46*e^2 + 69*e - 12, -11*e^4 + 20*e^3 + 61*e^2 - 97*e + 26, -5*e^4 + 11*e^3 + 21*e^2 - 54*e + 42, e^4 - 2*e^3 - 3*e^2 + 7*e - 15, 3*e^4 - 2*e^3 - 21*e^2 + 2*e + 6, 12*e^4 - 30*e^3 - 58*e^2 + 160*e - 76, -3*e^4 + 10*e^3 + 7*e^2 - 54*e + 47, -20*e^4 + 45*e^3 + 100*e^2 - 235*e + 116, 6*e^4 - 11*e^3 - 31*e^2 + 58*e - 31, 9*e^4 - 17*e^3 - 50*e^2 + 82*e - 18, 12*e^4 - 28*e^3 - 64*e^2 + 148*e - 48, 9*e^4 - 13*e^3 - 53*e^2 + 59*e - 12, 4*e^4 - 14*e^3 - 15*e^2 + 86*e - 43, 14*e^4 - 34*e^3 - 67*e^2 + 180*e - 90, 2*e^4 - 4*e^3 - 12*e^2 + 23*e - 8, 6*e^4 - 10*e^3 - 33*e^2 + 48*e - 19, 12*e^4 - 28*e^3 - 60*e^2 + 144*e - 55, -5*e^4 + 18*e^3 + 18*e^2 - 104*e + 66, 7*e^4 - 19*e^3 - 34*e^2 + 106*e - 39, -16*e^4 + 37*e^3 + 82*e^2 - 194*e + 74, 2*e^4 + 2*e^3 - 19*e^2 - 18*e + 28, -14*e^4 + 19*e^3 + 88*e^2 - 91*e - 3, 10*e^4 - 27*e^3 - 43*e^2 + 141*e - 82, 21*e^4 - 44*e^3 - 113*e^2 + 229*e - 68, 12*e^4 - 23*e^3 - 67*e^2 + 119*e - 35, -13*e^4 + 24*e^3 + 75*e^2 - 120*e + 27, -17*e^4 + 34*e^3 + 91*e^2 - 180*e + 79, 12*e^4 - 33*e^3 - 53*e^2 + 183*e - 95, 26*e^4 - 59*e^3 - 134*e^2 + 310*e - 119, 17*e^4 - 39*e^3 - 82*e^2 + 201*e - 103, -21*e^4 + 56*e^3 + 98*e^2 - 302*e + 148, 28*e^4 - 61*e^3 - 147*e^2 + 320*e - 123, -14*e^4 + 32*e^3 + 66*e^2 - 161*e + 89, 8*e^4 - 26*e^3 - 29*e^2 + 146*e - 93, -22*e^4 + 49*e^3 + 110*e^2 - 261*e + 129, 9*e^4 - 26*e^3 - 39*e^2 + 137*e - 70, 32*e^4 - 78*e^3 - 156*e^2 + 412*e - 185, -11*e^4 + 23*e^3 + 57*e^2 - 125*e + 56, -10*e^4 + 13*e^3 + 63*e^2 - 55*e - 8, 16*e^4 - 28*e^3 - 91*e^2 + 138*e - 47, -13*e^4 + 35*e^3 + 62*e^2 - 190*e + 98, -10*e^4 + 27*e^3 + 49*e^2 - 153*e + 60, 2*e^4 - 11*e^3 - 3*e^2 + 64*e - 45, -13*e^4 + 35*e^3 + 59*e^2 - 183*e + 99, 21*e^4 - 48*e^3 - 109*e^2 + 254*e - 103, -31*e^4 + 78*e^3 + 148*e^2 - 420*e + 206, 17*e^4 - 50*e^3 - 75*e^2 + 270*e - 134, -5*e^4 + 16*e^3 + 15*e^2 - 96*e + 77, 4*e^4 - 16*e^3 - 11*e^2 + 90*e - 57, 19*e^4 - 55*e^3 - 84*e^2 + 302*e - 156, -5*e^4 + 7*e^3 + 25*e^2 - 30*e + 19, 25*e^4 - 65*e^3 - 115*e^2 + 341*e - 175, -21*e^4 + 41*e^3 + 115*e^2 - 202*e + 63, 29*e^4 - 54*e^3 - 164*e^2 + 275*e - 70, 4*e^4 - 9*e^3 - 18*e^2 + 41*e - 21, -19*e^4 + 37*e^3 + 104*e^2 - 179*e + 51, -5*e^4 + 24*e^3 + 10*e^2 - 136*e + 101, -5*e^4 + 11*e^3 + 30*e^2 - 48*e - 14, 13*e^4 - 30*e^3 - 67*e^2 + 156*e - 54, -14*e^4 + 39*e^3 + 67*e^2 - 219*e + 102, -21*e^4 + 43*e^3 + 114*e^2 - 226*e + 92, -11*e^4 + 15*e^3 + 69*e^2 - 64*e - 8, 13*e^4 - 24*e^3 - 75*e^2 + 127*e - 27, -23*e^4 + 63*e^3 + 106*e^2 - 335*e + 158, e^4 + e^3 - 5*e^2 - 5*e, -15*e^4 + 50*e^3 + 55*e^2 - 269*e + 161, -29*e^4 + 71*e^3 + 137*e^2 - 375*e + 185, 19*e^4 - 53*e^3 - 81*e^2 + 285*e - 142, 8*e^4 - 19*e^3 - 40*e^2 + 107*e - 55, -40*e^4 + 97*e^3 + 199*e^2 - 520*e + 212, -33*e^4 + 83*e^3 + 161*e^2 - 443*e + 186, -23*e^4 + 48*e^3 + 125*e^2 - 248*e + 60, 25*e^4 - 71*e^3 - 108*e^2 + 395*e - 215, 6*e^4 - 11*e^3 - 35*e^2 + 57*e - 10, -6*e^4 + 9*e^3 + 35*e^2 - 40*e - 1, 10*e^4 - 14*e^3 - 59*e^2 + 60*e - 8, -17*e^4 + 42*e^3 + 86*e^2 - 225*e + 98, -12*e^4 + 35*e^3 + 48*e^2 - 185*e + 111, e^4 - 3*e^3 - 6*e^2 + 10*e + 9, 2*e^4 - 8*e^3 - 5*e^2 + 36*e - 17, -37*e^4 + 67*e^3 + 214*e^2 - 346*e + 87, 2*e^4 + 3*e^3 - 25*e^2 - 27*e + 46, 16*e^4 - 47*e^3 - 66*e^2 + 255*e - 157, -10*e^4 + 28*e^3 + 45*e^2 - 155*e + 104, 20*e^4 - 30*e^3 - 116*e^2 + 137*e - 20, -25*e^4 + 66*e^3 + 109*e^2 - 351*e + 195, 27*e^4 - 72*e^3 - 124*e^2 + 393*e - 206, 42*e^4 - 94*e^3 - 218*e^2 + 497*e - 190, -6*e^4 + 20*e^3 + 22*e^2 - 103*e + 59, -30*e^4 + 69*e^3 + 163*e^2 - 371*e + 105, -e^4 - 17*e^3 + 33*e^2 + 107*e - 101, 4*e^4 - 15*e^3 - 8*e^2 + 76*e - 58, -19*e^4 + 37*e^3 + 101*e^2 - 188*e + 67, -22*e^4 + 51*e^3 + 112*e^2 - 272*e + 132, -2*e^4 + 11*e^3 - 6*e^2 - 63*e + 81, -26*e^4 + 59*e^3 + 127*e^2 - 315*e + 167, 28*e^4 - 61*e^3 - 149*e^2 + 323*e - 122, -7*e^4 + 32*e^3 + 14*e^2 - 186*e + 123, -30*e^4 + 75*e^3 + 143*e^2 - 392*e + 178, -29*e^4 + 69*e^3 + 147*e^2 - 360*e + 128, 36*e^4 - 88*e^3 - 176*e^2 + 463*e - 199, -14*e^4 + 42*e^3 + 55*e^2 - 234*e + 132, -44*e^4 + 105*e^3 + 213*e^2 - 551*e + 272, 22*e^4 - 37*e^3 - 126*e^2 + 177*e - 39, 20*e^4 - 33*e^3 - 118*e^2 + 158*e - 42, 13*e^4 - 16*e^3 - 86*e^2 + 78*e + 18, 18*e^4 - 34*e^3 - 94*e^2 + 167*e - 58, 14*e^4 - 39*e^3 - 66*e^2 + 212*e - 100, 31*e^4 - 70*e^3 - 160*e^2 + 375*e - 140, 30*e^4 - 62*e^3 - 157*e^2 + 314*e - 122, -22*e^4 + 28*e^3 + 139*e^2 - 125*e - 25, -13*e^4 + 27*e^3 + 72*e^2 - 131*e + 4, -7*e^4 + 15*e^3 + 43*e^2 - 89*e - 12, 22*e^4 - 55*e^3 - 107*e^2 + 281*e - 124, -36*e^4 + 81*e^3 + 190*e^2 - 428*e + 153, -19*e^4 + 59*e^3 + 80*e^2 - 326*e + 185, -23*e^4 + 50*e^3 + 123*e^2 - 268*e + 69, 67*e^4 - 160*e^3 - 328*e^2 + 847*e - 400, 5*e^4 + 3*e^3 - 43*e^2 - 22*e + 48, 10*e^4 - 19*e^3 - 63*e^2 + 93*e + 9, -28*e^4 + 69*e^3 + 140*e^2 - 367*e + 129, -2*e^4 - 5*e^3 + 22*e^2 + 31*e - 42, -27*e^4 + 60*e^3 + 145*e^2 - 311*e + 90, 16*e^4 - 47*e^3 - 69*e^2 + 257*e - 136, -37*e^4 + 91*e^3 + 175*e^2 - 473*e + 230, 52*e^4 - 131*e^3 - 253*e^2 + 717*e - 326, -57*e^4 + 132*e^3 + 292*e^2 - 697*e + 271, 39*e^4 - 85*e^3 - 200*e^2 + 433*e - 173, 20*e^4 - 42*e^3 - 105*e^2 + 211*e - 95, -42*e^4 + 75*e^3 + 238*e^2 - 381*e + 124, 5*e^4 - 11*e^3 - 19*e^2 + 52*e - 66, 57*e^4 - 135*e^3 - 284*e^2 + 706*e - 283, -38*e^4 + 80*e^3 + 201*e^2 - 406*e + 119, -21*e^4 + 36*e^3 + 125*e^2 - 187*e + 39, -2*e^4 + 7*e^3 - e^2 - 30*e + 67, 27*e^4 - 60*e^3 - 134*e^2 + 312*e - 140, -21*e^4 + 21*e^3 + 142*e^2 - 85*e - 48, -10*e^4 + 8*e^3 + 68*e^2 - 40*e - 24, e^4 - e^3 + e - 22, -23*e^4 + 51*e^3 + 120*e^2 - 273*e + 119, 11*e^4 - 24*e^3 - 63*e^2 + 129*e - 2, 51*e^4 - 125*e^3 - 248*e^2 + 661*e - 288, -34*e^4 + 66*e^3 + 189*e^2 - 330*e + 94, 9*e^4 - 6*e^3 - 66*e^2 + 12*e + 42, 38*e^4 - 82*e^3 - 193*e^2 + 420*e - 189, 49*e^4 - 140*e^3 - 211*e^2 + 754*e - 404, 18*e^4 - 27*e^3 - 108*e^2 + 121*e + 9, 36*e^4 - 66*e^3 - 198*e^2 + 328*e - 102, -23*e^4 + 60*e^3 + 100*e^2 - 329*e + 200, -34*e^4 + 55*e^3 + 202*e^2 - 272*e + 41, -23*e^4 + 44*e^3 + 122*e^2 - 210*e + 94, 5*e^4 - 24*e^3 - 3*e^2 + 146*e - 127, 13*e^4 - 37*e^3 - 51*e^2 + 196*e - 121, -2*e^4 + 30*e^3 - 25*e^2 - 167*e + 163, 26*e^4 - 41*e^3 - 154*e^2 + 200*e - 17, -55*e^4 + 132*e^3 + 270*e^2 - 708*e + 333, 57*e^4 - 121*e^3 - 305*e^2 + 623*e - 198, 29*e^4 - 60*e^3 - 150*e^2 + 298*e - 124, e^4 + 13*e^3 - 27*e^2 - 83*e + 90, 36*e^4 - 80*e^3 - 191*e^2 + 426*e - 163, -36*e^4 + 88*e^3 + 174*e^2 - 484*e + 236, 23*e^4 - 56*e^3 - 109*e^2 + 304*e - 159, -5*e^4 + 20*e^3 + 12*e^2 - 104*e + 85, 55*e^4 - 119*e^3 - 291*e^2 + 623*e - 206, 52*e^4 - 119*e^3 - 276*e^2 + 634*e - 215, -13*e^4 + 9*e^3 + 92*e^2 - 13*e - 68, 60*e^4 - 145*e^3 - 292*e^2 + 784*e - 392, -9*e^4 + 23*e^3 + 42*e^2 - 127*e + 73, e^4 - 13*e^3 + 10*e^2 + 80*e - 70, 4*e^4 - 18*e^3 - 9*e^2 + 87*e - 70, -38*e^4 + 113*e^3 + 161*e^2 - 602*e + 321, -31*e^4 + 91*e^3 + 130*e^2 - 507*e + 265, 59*e^4 - 119*e^3 - 323*e^2 + 621*e - 198, 10*e^4 - 11*e^3 - 67*e^2 + 59*e - 10, 24*e^4 - 62*e^3 - 106*e^2 + 325*e - 198, -8*e^4 + 39*e^3 + 21*e^2 - 230*e + 162, -57*e^4 + 152*e^3 + 261*e^2 - 822*e + 421, 26*e^4 - 47*e^3 - 143*e^2 + 227*e - 79, -61*e^4 + 139*e^3 + 322*e^2 - 745*e + 273, -31*e^4 + 70*e^3 + 156*e^2 - 360*e + 149, -38*e^4 + 87*e^3 + 188*e^2 - 461*e + 238, 33*e^4 - 56*e^3 - 190*e^2 + 269*e - 68, -12*e^4 + 39*e^3 + 42*e^2 - 222*e + 173, -43*e^4 + 101*e^3 + 217*e^2 - 530*e + 215, 10*e^4 - 3*e^3 - 78*e^2 + 5*e + 46, -42*e^4 + 84*e^3 + 232*e^2 - 439*e + 166, -14*e^3 + 23*e^2 + 100*e - 93, 29*e^4 - 75*e^3 - 130*e^2 + 406*e - 234, -14*e^4 + 49*e^3 + 64*e^2 - 279*e + 119, -e^4 + 12*e^3 - 10*e^2 - 75*e + 95, 70*e^4 - 152*e^3 - 375*e^2 + 800*e - 262, -30*e^4 + 69*e^3 + 158*e^2 - 352*e + 102, 58*e^4 - 146*e^3 - 282*e^2 + 796*e - 369, -25*e^4 + 51*e^3 + 130*e^2 - 267*e + 116, -14*e^4 + 40*e^3 + 65*e^2 - 231*e + 72, -25*e^4 + 34*e^3 + 156*e^2 - 145*e - 21, -4*e^4 - 16*e^3 + 50*e^2 + 91*e - 112, -30*e^4 + 58*e^3 + 172*e^2 - 304*e + 98, -32*e^4 + 87*e^3 + 150*e^2 - 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1525*e + 776, 62*e^4 - 133*e^3 - 360*e^2 + 717*e - 160, -112*e^4 + 280*e^3 + 559*e^2 - 1491*e + 579, -44*e^4 + 105*e^3 + 232*e^2 - 572*e + 251, -19*e^4 + 78*e^3 + 26*e^2 - 414*e + 362, -27*e^4 + 37*e^3 + 198*e^2 - 185*e - 118, 2*e^4 - 34*e^3 + 6*e^2 + 210*e - 63, 128*e^4 - 342*e^3 - 581*e^2 + 1837*e - 957, -38*e^4 + 84*e^3 + 195*e^2 - 450*e + 169, -36*e^4 + 105*e^3 + 152*e^2 - 551*e + 334, 39*e^4 - 152*e^3 - 125*e^2 + 882*e - 544, 8*e^4 + 10*e^3 - 107*e^2 - 43*e + 219, -18*e^4 + 34*e^3 + 75*e^2 - 160*e + 153, 77*e^4 - 196*e^3 - 354*e^2 + 1064*e - 572, -68*e^4 + 143*e^3 + 373*e^2 - 779*e + 207, 112*e^4 - 275*e^3 - 544*e^2 + 1447*e - 652, -193*e^4 + 496*e^3 + 915*e^2 - 2684*e + 1314, 81*e^4 - 202*e^3 - 367*e^2 + 1059*e - 568, 75*e^4 - 212*e^3 - 314*e^2 + 1141*e - 651, -41*e^4 + 90*e^3 + 209*e^2 - 450*e + 228, -10*e^4 + 68*e^3 + e^2 - 373*e + 271, -79*e^4 + 139*e^3 + 470*e^2 - 711*e + 66, -84*e^4 + 191*e^3 + 449*e^2 - 1035*e + 384, -21*e^4 + 10*e^3 + 167*e^2 - 42*e - 181, -70*e^4 + 146*e^3 + 382*e^2 - 733*e + 193, -134*e^4 + 294*e^3 + 678*e^2 - 1549*e + 766, 159*e^4 - 337*e^3 - 845*e^2 + 1734*e - 554, -92*e^4 + 230*e^3 + 432*e^2 - 1261*e + 680, -101*e^4 + 270*e^3 + 463*e^2 - 1453*e + 698, 76*e^4 - 157*e^3 - 415*e^2 + 827*e - 197, 43*e^4 - 114*e^3 - 196*e^2 + 607*e - 194, -93*e^4 + 246*e^3 + 436*e^2 - 1323*e + 689, -e^4 - 32*e^3 + 33*e^2 + 244*e - 174, -109*e^4 + 248*e^3 + 571*e^2 - 1322*e + 482, -49*e^4 + 143*e^3 + 205*e^2 - 777*e + 454, -54*e^4 + 89*e^3 + 310*e^2 - 431*e + 88, 44*e^4 - 94*e^3 - 217*e^2 + 491*e - 324, 136*e^4 - 358*e^3 - 624*e^2 + 1918*e - 976, -36*e^4 + 75*e^3 + 202*e^2 - 428*e + 113, 55*e^4 - 82*e^3 - 354*e^2 + 411*e + 54, 65*e^4 - 104*e^3 - 396*e^2 + 490*e + 21, 141*e^4 - 334*e^3 - 685*e^2 + 1753*e - 845, 17*e^4 - 6*e^3 - 141*e^2 - 17*e + 145, 64*e^4 - 91*e^3 - 393*e^2 + 433*e - 65, 96*e^4 - 175*e^3 - 537*e^2 + 886*e - 322, 38*e^4 - 84*e^3 - 212*e^2 + 484*e - 129, -48*e^4 + 81*e^3 + 276*e^2 - 397*e + 194, -53*e^4 + 140*e^3 + 269*e^2 - 736*e + 208, 2*e^4 - 20*e^3 + 34*e^2 + 116*e - 226, 42*e^4 - 110*e^3 - 231*e^2 + 622*e - 161, 18*e^4 - 40*e^3 - 105*e^2 + 167*e + 1, -4*e^4 + 41*e^3 - 13*e^2 - 195*e + 130, -164*e^4 + 356*e^3 + 867*e^2 - 1881*e + 718, 21*e^4 - 48*e^3 - 103*e^2 + 249*e - 182, -170*e^4 + 440*e^3 + 786*e^2 - 2354*e + 1154, 50*e^4 - 127*e^3 - 216*e^2 + 675*e - 414, 127*e^4 - 289*e^3 - 646*e^2 + 1529*e - 680, -41*e^4 + 140*e^3 + 146*e^2 - 818*e + 546, 66*e^4 - 168*e^3 - 295*e^2 + 876*e - 507, -3*e^4 + 50*e^3 - 27*e^2 - 269*e + 146, 39*e^4 - 126*e^3 - 152*e^2 + 711*e - 404, 129*e^4 - 282*e^3 - 654*e^2 + 1424*e - 638, -20*e^4 - 5*e^3 + 152*e^2 + 67*e - 184, -195*e^4 + 469*e^3 + 954*e^2 - 2511*e + 1219, 12*e^4 - 48*e^3 - 38*e^2 + 229*e - 117, 83*e^4 - 260*e^3 - 340*e^2 + 1434*e - 789, 7*e^4 - 75*e^3 + 48*e^2 + 448*e - 348, 14*e^4 - 101*e^3 + 30*e^2 + 586*e - 462, -32*e^4 + 36*e^3 + 217*e^2 - 140*e - 134, -23*e^4 + 2*e^3 + 210*e^2 + 8*e - 238, 40*e^4 - 92*e^3 - 218*e^2 + 531*e - 113, -14*e^4 - 8*e^3 + 103*e^2 + 100*e - 184, 16*e^4 - 97*e^3 - 7*e^2 + 574*e - 466, -31*e^4 + 75*e^3 + 175*e^2 - 407*e + 60, -52*e^4 + 80*e^3 + 311*e^2 - 373*e + 59, -55*e^4 + 174*e^3 + 213*e^2 - 984*e + 612, -82*e^4 + 231*e^3 + 338*e^2 - 1243*e + 705, 113*e^4 - 229*e^3 - 638*e^2 + 1184*e - 258, 33*e^4 - 58*e^3 - 218*e^2 + 279*e + 60, 95*e^4 - 185*e^3 - 506*e^2 + 949*e - 380, -8*e^4 - 36*e^3 + 103*e^2 + 245*e - 277, 8*e^4 - 20*e^3 - 65*e^2 + 97*e + 106, 96*e^4 - 205*e^3 - 513*e^2 + 1046*e - 374, -55*e^4 + 172*e^3 + 216*e^2 - 921*e + 560, -22*e^4 - 15*e^3 + 201*e^2 + 92*e - 277, 162*e^4 - 376*e^3 - 823*e^2 + 2011*e - 903, 202*e^4 - 481*e^3 - 1025*e^2 + 2571*e - 1029, 13*e^4 + 17*e^3 - 130*e^2 - 99*e + 182, 25*e^4 - 36*e^3 - 174*e^2 + 154*e + 98, 43*e^4 - 104*e^3 - 212*e^2 + 550*e - 289, 35*e^4 - 84*e^3 - 187*e^2 + 426*e - 125, 13*e^4 - 4*e^3 - 100*e^2 - 16*e + 15, -34*e^4 + 72*e^3 + 197*e^2 - 385*e + 78, -151*e^4 + 392*e^3 + 708*e^2 - 2132*e + 1083, 86*e^4 - 227*e^3 - 400*e^2 + 1230*e - 576, 10*e^4 - 35*e^3 - 11*e^2 + 202*e - 273, -114*e^4 + 268*e^3 + 602*e^2 - 1414*e + 448, 5*e^4 - 51*e^3 + 36*e^2 + 311*e - 276, -60*e^4 + 144*e^3 + 301*e^2 - 720*e + 310, -35*e^4 + 98*e^3 + 135*e^2 - 533*e + 328, -83*e^4 + 154*e^3 + 478*e^2 - 784*e + 138, -104*e^4 + 284*e^3 + 474*e^2 - 1554*e + 828, 45*e^4 - 159*e^3 - 162*e^2 + 907*e - 546, 12*e^4 - 72*e^3 - 10*e^2 + 414*e - 240, 118*e^4 - 238*e^3 - 626*e^2 + 1195*e - 491, 44*e^4 - 118*e^3 - 219*e^2 + 662*e - 259, -22*e^4 + 49*e^3 + 111*e^2 - 229*e + 52, -144*e^4 + 357*e^3 + 692*e^2 - 1912*e + 903, 44*e^4 - 82*e^3 - 253*e^2 + 438*e - 165, 152*e^4 - 405*e^3 - 680*e^2 + 2186*e - 1145, 65*e^4 - 131*e^3 - 346*e^2 + 652*e - 228, -19*e^4 - 18*e^3 + 186*e^2 + 179*e - 292, 18*e^4 - 31*e^3 - 134*e^2 + 179*e + 110, 90*e^4 - 226*e^3 - 432*e^2 + 1224*e - 551, 8*e^4 - 14*e^3 - 23*e^2 + 75*e - 105, -137*e^4 + 313*e^3 + 700*e^2 - 1645*e + 561, 173*e^4 - 452*e^3 - 791*e^2 + 2423*e - 1233, 39*e^4 - 90*e^3 - 219*e^2 + 444*e - 42, -118*e^4 + 289*e^3 + 575*e^2 - 1566*e + 738, -21*e^4 + 38*e^3 + 109*e^2 - 163*e + 153, 24*e^4 - 69*e^3 - 114*e^2 + 327*e - 115, -98*e^4 + 212*e^3 + 513*e^2 - 1080*e + 411, 42*e^4 - 43*e^3 - 278*e^2 + 181*e + 4, 140*e^4 - 324*e^3 - 706*e^2 + 1748*e - 792, -170*e^4 + 347*e^3 + 929*e^2 - 1791*e + 515, -27*e^4 + 2*e^3 + 212*e^2 + 10*e - 194, 42*e^4 - 90*e^3 - 215*e^2 + 429*e - 160, 2*e^4 + 5*e^3 - e^2 - 50*e - 115, 54*e^4 - 144*e^3 - 254*e^2 + 773*e - 429, -112*e^4 + 262*e^3 + 550*e^2 - 1359*e + 696, -91*e^4 + 236*e^3 + 401*e^2 - 1237*e + 681, -21*e^4 + 89*e^3 + 47*e^2 - 506*e + 337, 49*e^4 - 77*e^3 - 294*e^2 + 321*e + 2, 62*e^4 - 177*e^3 - 258*e^2 + 986*e - 559, -9*e^4 + 34*e^3 - 177*e + 147, 52*e^4 - 113*e^3 - 281*e^2 + 551*e - 117, -164*e^4 + 387*e^3 + 800*e^2 - 2017*e + 977, -65*e^4 + 108*e^3 + 359*e^2 - 522*e + 144, 8*e^4 - 30*e^3 - 50*e^2 + 194*e - 28, 47*e^4 - 119*e^3 - 209*e^2 + 633*e - 383, e^4 - 11*e^3 + 3*e^2 + 38*e + 2, -163*e^4 + 386*e^3 + 823*e^2 - 2079*e + 914, -28*e^4 + 33*e^3 + 183*e^2 - 188*e + 7, -82*e^4 + 205*e^3 + 397*e^2 - 1122*e + 534, 35*e^4 - 50*e^3 - 203*e^2 + 278*e - 109, 86*e^4 - 234*e^3 - 390*e^2 + 1302*e - 681, -18*e^4 + 84*e^3 + 40*e^2 - 465*e + 389, -40*e^4 + 72*e^3 + 247*e^2 - 361*e + 89, 53*e^4 - 98*e^3 - 295*e^2 + 514*e - 216, -55*e^4 + 66*e^3 + 361*e^2 - 308*e - 84, 5*e^4 - 28*e^3 - 23*e^2 + 185*e - 56, -178*e^4 + 456*e^3 + 823*e^2 - 2424*e + 1209, 18*e^4 + 8*e^3 - 160*e^2 - 86*e + 258, 59*e^4 - 114*e^3 - 329*e^2 + 569*e - 158, 102*e^4 - 213*e^3 - 522*e^2 + 1090*e - 539, 2*e^4 - 28*e^2 + 22*e + 57, 170*e^4 - 348*e^3 - 914*e^2 + 1805*e - 677, 169*e^4 - 314*e^3 - 954*e^2 + 1605*e - 475, -84*e^4 + 187*e^3 + 433*e^2 - 948*e + 302, -66*e^4 + 189*e^3 + 279*e^2 - 1058*e + 546, 74*e^4 - 136*e^3 - 440*e^2 + 675*e - 62, 145*e^4 - 371*e^3 - 695*e^2 + 2001*e - 935, 151*e^4 - 359*e^3 - 734*e^2 + 1910*e - 960, 164*e^4 - 375*e^3 - 846*e^2 + 1957*e - 686, 129*e^4 - 359*e^3 - 579*e^2 + 1992*e - 1082, 56*e^4 - 171*e^3 - 236*e^2 + 956*e - 532, -120*e^4 + 226*e^3 + 688*e^2 - 1137*e + 251, e^4 + 71*e^3 - 113*e^2 - 478*e + 466, -51*e^4 + 140*e^3 + 265*e^2 - 773*e + 259, -82*e^4 + 136*e^3 + 475*e^2 - 659*e + 184, -105*e^4 + 254*e^3 + 508*e^2 - 1335*e + 547, 97*e^4 - 223*e^3 - 467*e^2 + 1160*e - 565, 197*e^4 - 460*e^3 - 981*e^2 + 2429*e - 1066, -14*e^4 + 49*e^3 + 60*e^2 - 294*e + 189, -70*e^4 + 121*e^3 + 391*e^2 - 602*e + 173, -89*e^4 + 251*e^3 + 403*e^2 - 1331*e + 619, -14*e^4 + 17*e^3 + 77*e^2 - 120*e + 131, -11*e^4 - 23*e^3 + 126*e^2 + 150*e - 165, 47*e^4 - 62*e^3 - 291*e^2 + 296*e + 13, -47*e^4 + 122*e^3 + 203*e^2 - 685*e + 427, -58*e^4 + 123*e^3 + 282*e^2 - 655*e + 366, -102*e^4 + 234*e^3 + 533*e^2 - 1288*e + 450, 56*e^4 - 161*e^3 - 253*e^2 + 869*e - 353, 19*e^4 - 95*e^3 - 5*e^2 + 583*e - 499, -132*e^4 + 293*e^3 + 660*e^2 - 1508*e + 737, -90*e^4 + 224*e^3 + 427*e^2 - 1233*e + 657, 94*e^4 - 185*e^3 - 529*e^2 + 952*e - 256, 118*e^4 - 230*e^3 - 646*e^2 + 1212*e - 491, -21*e^4 + 24*e^3 + 127*e^2 - 105*e + 46, 80*e^4 - 134*e^3 - 490*e^2 + 660*e - 22, 121*e^4 - 315*e^3 - 567*e^2 + 1679*e - 849, -83*e^4 + 221*e^3 + 387*e^2 - 1236*e + 633, 177*e^4 - 459*e^3 - 828*e^2 + 2452*e - 1197, 138*e^4 - 317*e^3 - 711*e^2 + 1672*e - 617, -71*e^4 + 168*e^3 + 377*e^2 - 926*e + 243, -75*e^4 + 201*e^3 + 358*e^2 - 1073*e + 405, -40*e^4 + 55*e^3 + 229*e^2 - 256*e + 33, -129*e^4 + 332*e^3 + 616*e^2 - 1813*e + 830, -16*e^4 + e^3 + 118*e^2 + 31*e - 53, -12*e^4 - 4*e^3 + 100*e^2 + 46*e - 112, 100*e^4 - 295*e^3 - 422*e^2 + 1586*e - 847, 145*e^4 - 310*e^3 - 760*e^2 + 1605*e - 586, -40*e^4 + 66*e^3 + 243*e^2 - 296*e + 26, -37*e^4 + 108*e^3 + 173*e^2 - 630*e + 292, 71*e^4 - 116*e^3 - 389*e^2 + 550*e - 224, 122*e^4 - 281*e^3 - 619*e^2 + 1495*e - 635, 118*e^4 - 234*e^3 - 618*e^2 + 1156*e - 468, -116*e^4 + 285*e^3 + 561*e^2 - 1528*e + 784, 61*e^4 - 120*e^3 - 304*e^2 + 607*e - 350, 139*e^4 - 315*e^3 - 706*e^2 + 1641*e - 679, -24*e^4 + 46*e^3 + 108*e^2 - 209*e + 151, -105*e^4 + 239*e^3 + 527*e^2 - 1254*e + 630, 143*e^4 - 348*e^3 - 722*e^2 + 1876*e - 764, 29*e^4 - 55*e^3 - 163*e^2 + 290*e - 121, -69*e^4 + 205*e^3 + 277*e^2 - 1113*e + 650, 142*e^4 - 347*e^3 - 686*e^2 + 1855*e - 916, -52*e^4 + 166*e^3 + 201*e^2 - 927*e + 586, -37*e^4 + 74*e^3 + 174*e^2 - 341*e + 208, -40*e^4 + 146*e^3 + 122*e^2 - 790*e + 489, 162*e^4 - 366*e^3 - 841*e^2 + 1913*e - 642, -27*e^4 - 10*e^3 + 234*e^2 + 92*e - 308, -8*e^4 + 6*e^3 + 55*e^2 - 24*e + 21, -74*e^4 + 160*e^3 + 403*e^2 - 840*e + 175, 52*e^4 - 121*e^3 - 294*e^2 + 673*e - 175, -19*e^4 + 54*e^3 + 60*e^2 - 306*e + 217, 198*e^4 - 500*e^3 - 935*e^2 + 2683*e - 1335, 27*e^4 - 69*e^3 - 117*e^2 + 330*e - 148, -58*e^4 + 149*e^3 + 296*e^2 - 771*e + 229, 117*e^4 - 223*e^3 - 658*e^2 + 1102*e - 236, -99*e^4 + 220*e^3 + 530*e^2 - 1176*e + 403, 84*e^4 - 225*e^3 - 391*e^2 + 1191*e - 501, -3*e^4 + 52*e^3 - 21*e^2 - 286*e + 140, 8*e^4 - 15*e^3 - 54*e^2 + 92*e - 1, 66*e^4 - 137*e^3 - 367*e^2 + 723*e - 226, -7*e^4 - 5*e^3 + 42*e^2 + 81*e - 4, 38*e^4 - 101*e^3 - 170*e^2 + 532*e - 271, 18*e^4 - 70*e^3 - 51*e^2 + 394*e - 285, 129*e^4 - 329*e^3 - 598*e^2 + 1769*e - 902, -61*e^4 + 135*e^3 + 365*e^2 - 730*e + 91, 81*e^4 - 147*e^3 - 472*e^2 + 749*e - 115, 73*e^4 - 169*e^3 - 364*e^2 + 892*e - 379, 13*e^4 + 17*e^3 - 125*e^2 - 117*e + 159, 79*e^4 - 204*e^3 - 376*e^2 + 1118*e - 622, -76*e^4 + 137*e^3 + 439*e^2 - 655*e + 87, 49*e^4 - 127*e^3 - 227*e^2 + 705*e - 376, -44*e^4 + 96*e^3 + 225*e^2 - 491*e + 204, -128*e^4 + 236*e^3 + 708*e^2 - 1211*e + 458, 159*e^4 - 292*e^3 - 897*e^2 + 1445*e - 321, -21*e^4 + 21*e^3 + 127*e^2 - 88*e + 3, 54*e^4 - 136*e^3 - 238*e^2 + 737*e - 389, 17*e^4 + 10*e^3 - 141*e^2 - 93*e + 190, 97*e^4 - 253*e^3 - 452*e^2 + 1328*e - 691, -60*e^4 + 91*e^3 + 380*e^2 - 476*e + 39, 60*e^4 - 153*e^3 - 296*e^2 + 877*e - 334, 40*e^4 - 87*e^3 - 216*e^2 + 418*e - 118, -61*e^4 + 177*e^3 + 266*e^2 - 982*e + 532, -9*e^4 - 8*e^3 + 77*e^2 + 29*e - 38, 107*e^4 - 237*e^3 - 556*e^2 + 1223*e - 363, -e^4 - 54*e^3 + 65*e^2 + 383*e - 273] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([53, 53, 3*w - 5])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]