/* 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([49,49,-w + 8]) 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^4 - 12*x^2 + 25 K. = NumberField(heckePol) hecke_eigenvalues_array = [-e^2 + 6, e, -1, 2/5*e^3 - 14/5*e, 0, 1/5*e^3 - 2/5*e, 2/5*e^3 - 9/5*e, -e^2 + 8, -4/5*e^3 + 38/5*e, 2/5*e^3 - 24/5*e, -3/5*e^3 + 21/5*e, -2*e^2 + 7, 2*e^2 - 11, -2/5*e^3 + 24/5*e, -2*e^2 + 6, 2*e, 2*e^3 - 14*e, -2*e^2 + 4, 2*e^2 - 14, 6/5*e^3 - 62/5*e, 14, 6, -2/5*e^3 + 14/5*e, 2*e^2 - 20, -4*e^2 + 28, -1/5*e^3 + 32/5*e, -4/5*e^3 + 63/5*e, e^2 - 12, -4*e^2 + 32, 6/5*e^3 - 62/5*e, 1/5*e^3 - 2/5*e, 3/5*e^3 - 46/5*e, 6/5*e^3 - 52/5*e, -4/5*e^3 + 28/5*e, -2*e^3 + 16*e, -2*e^2 + 2, -1/5*e^3 + 27/5*e, 4*e^2 - 26, 2/5*e^3 - 34/5*e, 6/5*e^3 - 52/5*e, -3*e^2 + 10, -3*e^3 + 24*e, 3/5*e^3 - 41/5*e, 3/5*e^3 - 41/5*e, -10, -2*e^3 + 12*e, 6/5*e^3 - 62/5*e, 2*e^2 - 16, 4*e^2 - 14, 4/5*e^3 - 38/5*e, 4*e^2 - 29, 3*e^2 - 14, 2*e^2 - 28, -4*e^2 + 20, -e^2 - 2, 3*e, 2/5*e^3 - 39/5*e, -e^2, 3/5*e^3 - 21/5*e, -9/5*e^3 + 103/5*e, -4/5*e^3 + 43/5*e, 9/5*e^3 - 68/5*e, 6*e^2 - 30, 14/5*e^3 - 118/5*e, 1/5*e^3 + 33/5*e, -9/5*e^3 + 98/5*e, 3*e^2 - 4, -2, 6*e^2 - 36, -11/5*e^3 + 102/5*e, -3*e^2 + 24, 4, e^3 - 19*e, -3/5*e^3 + 41/5*e, 3/5*e^3 + 24/5*e, 9/5*e^3 - 108/5*e, -8/5*e^3 + 76/5*e, -2*e^2 + 8, -5*e^2 + 46, 4/5*e^3 - 13/5*e, -11/5*e^3 + 52/5*e, -4/5*e^3 + 73/5*e, 4/5*e^3 - 88/5*e, -14, -4*e^2 + 30, -4*e^2 + 16, -8/5*e^3 + 76/5*e, 4*e^2 - 12, -8*e^2 + 60, -4*e^2, 16, -26, 6*e^2 - 36, -2*e^2, 2*e^2 + 8, -6*e^2 + 44, -1/5*e^3 + 62/5*e, -7*e^2 + 48, 6*e^2 - 23, 19/5*e^3 - 158/5*e, 2*e^2 - 38, -4/5*e^3 + 58/5*e, -2*e^2 + 32, 2*e^2 - 14, -16, -4*e^2 + 44, 2/5*e^3 - 34/5*e, -6/5*e^3 + 72/5*e, -2*e^2 + 2, 0, 3*e^2 - 32, -6/5*e^3 + 67/5*e, -8*e^2 + 41, e^2 + 18, -6/5*e^3 - 18/5*e, 4/5*e^3 - 98/5*e, -2*e^3 + 16*e, 42, -4*e^2 + 8, 16/5*e^3 - 162/5*e, -7/5*e^3 + 29/5*e, -4*e^2 - 6, 24/5*e^3 - 153/5*e, -17/5*e^3 + 84/5*e, -14/5*e^3 + 108/5*e, 28/5*e^3 - 186/5*e, -6*e^2 + 26, 14/5*e^3 - 58/5*e, 2*e^2 + 21, -5*e^2 + 28, -3/5*e^3 + 86/5*e, 2/5*e^3 - 59/5*e, -12*e^2 + 60, -22/5*e^3 + 174/5*e, -4*e^2 + 38, 11/5*e^3 - 97/5*e, -2/5*e^3 + 94/5*e, -6*e^2 + 24, 18/5*e^3 - 116/5*e, -6*e^2 + 62, 2*e^2 - 27, -6*e^2 + 37, -9/5*e^3 + 38/5*e, -6*e^2 + 59, 8*e^2 - 54, 4*e^2 - 50, -2*e^2 - 9, 5*e^2 + 12, 14/5*e^3 - 178/5*e, 2*e^3 - 4*e, 8*e^2 - 40, 6*e^2 - 38, 20, -3/5*e^3 + 1/5*e, -33/5*e^3 + 271/5*e, -4*e^2 + 32, -4*e^3 + 35*e, -5*e^2 + 2, 27/5*e^3 - 184/5*e, 19/5*e^3 - 148/5*e, -6/5*e^3 + 47/5*e, e^3 - 6*e, 18/5*e^3 - 141/5*e, -4*e^3 + 34*e, -4/5*e^3 - 42/5*e, -2*e^2 + 39, -10*e^2 + 47, 8/5*e^3 - 96/5*e, 22/5*e^3 - 194/5*e, e^3 - 8*e, 4*e^2 - 39, -6/5*e^3 + 152/5*e, -14/5*e^3 + 48/5*e, 8*e^2 - 60, -4*e^3 + 28*e, 3/5*e^3 + 39/5*e, 8*e^2 - 22, -4/5*e^3 - 62/5*e, -22/5*e^3 + 194/5*e, -23/5*e^3 + 161/5*e, 4*e^2 - 12, -7/5*e^3 + 109/5*e, -21/5*e^3 + 207/5*e, 6*e^2 - 63, -14/5*e^3 + 103/5*e, 4*e^2 - 34, 54, 12/5*e^3 - 39/5*e, -e^2 + 26, 2*e^2 - 54, -8/5*e^3 + 16/5*e, 13*e^2 - 70, 27/5*e^3 - 204/5*e, -8*e^2 + 54, 7*e^3 - 53*e, -16*e^2 + 110, 4*e^2 - 36, 11/5*e^3 - 32/5*e, 4*e^2 - 53, 6/5*e^3 - 92/5*e, -16*e^2 + 106, 28, 24/5*e^3 - 178/5*e, 4*e^2 - 35, -9/5*e^3 + 108/5*e, -6*e^3 + 38*e, -22/5*e^3 + 154/5*e, 14*e^2 - 61, -6*e^2 + 29, -4*e^2 + 60, -17/5*e^3 + 199/5*e, -2*e^2 + 71, -26/5*e^3 + 227/5*e, 10*e^2 - 68, -6*e^2 + 32, -14/5*e^3 + 188/5*e, 4/5*e^3 + 72/5*e, -8*e^2 + 20, 2*e^3 - 30*e, -2*e^2 + 16, 0, -32/5*e^3 + 214/5*e, 4*e^2 + 34, 4*e^2 - 50, 12/5*e^3 - 144/5*e, 2*e^2 - 54, -24/5*e^3 + 108/5*e, 2*e^2 - 2, -10*e^2 + 54, -10*e^2 + 54, -2*e^2 + 78, 34/5*e^3 - 288/5*e, 4/5*e^3 - 108/5*e, 2*e^2 - 54, 27/5*e^3 - 209/5*e, -8*e^2 + 78, 8/5*e^3 - 66/5*e, -2*e^2 + 78, 18*e^2 - 116, 16/5*e^3 - 212/5*e, 2*e^2 + 58, 16/5*e^3 - 232/5*e, 2*e^2 - 4, -8*e^2 + 34, 14*e^2 - 85, 29/5*e^3 - 178/5*e, 16/5*e^3 - 122/5*e, 24/5*e^3 - 228/5*e, -23/5*e^3 + 261/5*e, 42, -9/5*e^3 + 28/5*e, -3*e^2 + 58, -8*e^2 + 40, -21/5*e^3 + 127/5*e, -17/5*e^3 + 119/5*e, 9/5*e^3 - 48/5*e, -24/5*e^3 + 223/5*e, -9*e^2 + 92, 42/5*e^3 - 359/5*e, 34/5*e^3 - 248/5*e, 2/5*e^3 - 104/5*e, -11/5*e^3 + 12/5*e, -20*e^2 + 129, -13*e^2 + 74, 7*e^2 - 58, 6/5*e^3 + 48/5*e, -6*e^2 + 26, 4*e^2 - 42, -16/5*e^3 + 122/5*e, -2*e^2, -4*e^2 + 86, -4/5*e^3 + 158/5*e, -10*e^2 + 52, 14*e^2 - 75, 4*e^2 + 10, 11/5*e^3 + 3/5*e, -6/5*e^3 - 28/5*e, -2*e^2 + 6, -7, -4/5*e^3 + 53/5*e, 4*e^2 - 27, 4*e^2 - 13, 10*e^2 - 90, -6/5*e^3 + 42/5*e, -1/5*e^3 + 112/5*e, 25*e, -6/5*e^3 - 63/5*e, 5*e^2 - 92, -18/5*e^3 + 151/5*e, 14*e^2 - 63, -18/5*e^3 + 156/5*e, 16*e^2 - 66, -13/5*e^3 + 131/5*e, e^3 + 17*e, 3*e^2 - 36, 10*e^2 - 85, -9*e^2 + 44, -7*e^3 + 70*e, -14/5*e^3 + 48/5*e, 32/5*e^3 - 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243, -28/5*e^3 + 36/5*e, 10*e^2 + 36, 18/5*e^3 - 311/5*e, 34*e^2 - 205, 58/5*e^3 - 361/5*e, 26*e^2 - 181, -14*e^3 + 130*e, 12/5*e^3 + 36/5*e, 4*e^2 + 58, 4*e^3 - 52*e, -68/5*e^3 + 606/5*e, -12*e^3 + 58*e, -44/5*e^3 + 388/5*e, 6*e^2 - 16, 34/5*e^3 - 268/5*e, -56/5*e^3 + 382/5*e, -12*e^2 + 166, -24/5*e^3 - 32/5*e, 14*e^2 - 155, 62/5*e^3 - 449/5*e, -22/5*e^3 + 214/5*e, -62/5*e^3 + 604/5*e, -12*e^2 + 120, -20*e^2 + 142, -34*e^2 + 230, -88/5*e^3 + 606/5*e, 11*e^2 - 12, -39/5*e^3 + 618/5*e, -82/5*e^3 + 709/5*e, -2/5*e^3 + 139/5*e, 14*e^2 - 105, 33/5*e^3 - 306/5*e, 31/5*e^3 - 102/5*e, 51/5*e^3 - 542/5*e, -31*e^2 + 114, -68/5*e^3 + 661/5*e, -16*e^3 + 112*e, -8/5*e^3 + 26/5*e, 52/5*e^3 - 404/5*e, -14*e^2 + 90, 136, -6*e^2 + 86, 116/5*e^3 - 812/5*e, 62/5*e^3 - 604/5*e, 4*e^2 - 180, 11*e^3 - 101*e, -24*e^2 + 106, -22*e^2 + 146, -38, 29/5*e^3 - 203/5*e, 21/5*e^3 + 53/5*e, 27/5*e^3 - 429/5*e, 16/5*e^3 - 87/5*e, -e^3 - 16*e, -28/5*e^3 + 46/5*e, 32/5*e^3 - 84/5*e, 38/5*e^3 - 276/5*e, -14*e^2 + 126, 20*e^2 - 137, 19*e^2 - 94, 2/5*e^3 - 219/5*e, -33*e^2 + 180, 8*e^2 + 61, -64/5*e^3 + 713/5*e, -20*e^2 + 122, -15*e^3 + 81*e, 16*e^2 - 160, -14*e^2 + 80, -33*e^2 + 178, -12*e^2 + 87, 47/5*e^3 - 229/5*e, -8*e^2 + 22, 66/5*e^3 - 362/5*e, 18*e^2 - 124, 8*e^3 - 50*e, 2*e^2 + 40, -9*e^2 + 36, -19*e^3 + 146*e, -81/5*e^3 + 642/5*e, -e^2 + 180, 26/5*e^3 - 322/5*e, 10*e^2 - 144, 8*e^2 + 32, -20*e^2 + 102, -14*e^2 + 100, -4*e^2 - 78, 18/5*e^3 - 91/5*e, -51/5*e^3 + 342/5*e, 24/5*e^3 - 208/5*e, -18*e^2 + 150, -18*e^2 + 97, -23*e^2 + 172, 26/5*e^3 - 327/5*e, -10*e^2 + 143, -68/5*e^3 + 556/5*e, -24*e^2 + 72, -56/5*e^3 + 262/5*e, -28/5*e^3 + 206/5*e, -14*e^2 + 188, 44/5*e^3 - 228/5*e, 59/5*e^3 - 433/5*e, -29/5*e^3 + 103/5*e, 16*e^2 - 13, 3*e^2 + 42, 26/5*e^3 - 72/5*e, -24*e^3 + 180*e, 14*e^2 - 9, 23*e^2 - 116, -6/5*e^3 + 177/5*e, 23/5*e^3 - 146/5*e, 2*e^2 - 114, 32/5*e^3 - 424/5*e, -23/5*e^3 + 266/5*e, 26*e^2 - 195, 34/5*e^3 - 98/5*e, -26/5*e^3 + 172/5*e, 15*e^2 + 8, 14*e^2 - 47, -e^2 + 54, 3*e^3 + 28*e, -12*e^2 + 142, 2*e^3 - 48*e, 4*e^2 - 30, 12*e^2 - 136, -13/5*e^3 + 366/5*e, 74/5*e^3 - 463/5*e, 15*e^2 - 180, -13*e^2 + 156, 24*e^2 - 218, 32*e^2 - 198, -47/5*e^3 + 349/5*e, -36*e^2 + 264, 8*e^2 - 134, -59/5*e^3 + 353/5*e, 9*e^2 + 24, -17*e^2 + 8, -106/5*e^3 + 687/5*e, 27*e^2 - 104, -86/5*e^3 + 672/5*e, 8*e^2 - 2, 6/5*e^3 - 162/5*e, 62, 42/5*e^3 - 214/5*e, -44/5*e^3 + 208/5*e, 8*e^2 - 102, -39/5*e^3 + 173/5*e, -2*e^3 + 20*e, -84/5*e^3 + 538/5*e, -9/5*e^3 + 83/5*e, 14*e^2 - 142, -34*e^2 + 200, 9/5*e^3 - 163/5*e, 52*e^2 - 304, -20*e^2 + 142, 44*e^2 - 300, -20*e^2 + 18, 40, 58/5*e^3 - 366/5*e, 4*e^2 - 46, -20*e^2 + 122, -2*e^3 + 12*e, 18/5*e^3 - 476/5*e, -12*e^3 + 66*e, 38/5*e^3 - 96/5*e, 16*e^2 - 10, -13/5*e^3 + 31/5*e, 33/5*e^3 - 211/5*e, 22*e^2 - 36, -32/5*e^3 + 214/5*e, -38/5*e^3 + 546/5*e, -24/5*e^3 + 378/5*e, -8*e^2 + 210, -56/5*e^3 + 502/5*e, 14*e^3 - 103*e, 94/5*e^3 - 763/5*e, 8*e^2 - 6, 8*e^2 + 78, -12*e^2 - 12, -5*e^3 - 13*e, -78/5*e^3 + 636/5*e, -22*e^2 + 140, -4*e^2 - 90, 58/5*e^3 - 386/5*e, 18*e^2 - 33, -37/5*e^3 + 154/5*e, -74/5*e^3 + 738/5*e, -76/5*e^3 + 502/5*e, -32*e^2 + 172, 12*e^3 - 54*e, -48/5*e^3 + 151/5*e, -7*e^2 + 118, 40*e^2 - 226, 26*e^2 - 114, -9*e^2 + 14, -40*e^2 + 269, -14*e^2 + 158, 74/5*e^3 - 668/5*e, 16*e^2 - 4, -4*e^2 - 68, 64/5*e^3 - 688/5*e, 28/5*e^3 - 106/5*e, 98/5*e^3 - 776/5*e, 20*e^2 - 226, -16*e^3 + 156*e, -16*e^2 + 212, 12*e^2 - 28, -16*e^2 + 70, -16/5*e^3 - 28/5*e, 22*e^2 - 16, 31/5*e^3 - 377/5*e, 79/5*e^3 - 453/5*e, -32*e^2 + 158, 2*e^3 - 2*e] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([7,7,-w + 1])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]