/* 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([676, 26, 26]) 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 - 13],\ [3833, 3833, 23*w - 10],\ [3851, 3851, 5*w - 66],\ [3851, 3851, -5*w - 61],\ [3853, 3853, 4*w - 65],\ [3853, 3853, -4*w - 61],\ [3863, 3863, 33*w - 80],\ [3863, 3863, 19*w - 90],\ [3877, 3877, -26*w - 19],\ [3877, 3877, 26*w - 45],\ [3881, 3881, -25*w - 13],\ [3881, 3881, 25*w - 38],\ [3911, 3911, 35*w + 53],\ [3911, 3911, 35*w - 88],\ [3919, 3919, -15*w - 67],\ [3919, 3919, 15*w - 82],\ [3931, 3931, 25*w - 37],\ [3931, 3931, -25*w - 12],\ [3943, 3943, 21*w - 95],\ [3943, 3943, 32*w - 75],\ [3967, 3967, -3*w - 62],\ [3967, 3967, 3*w - 65],\ [3989, 3989, 33*w - 79],\ [3989, 3989, 20*w - 93],\ [4001, 4001, 26*w - 43],\ [4001, 4001, -26*w - 17],\ [4003, 4003, 28*w - 55],\ [4003, 4003, -28*w - 27],\ [4007, 4007, -24*w - 1],\ [4007, 4007, 24*w - 25],\ [4027, 4027, -27*w - 83],\ [4027, 4027, 27*w - 110],\ 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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 K = QQ e = 1 hecke_eigenvalues_array = [1, -1, -1, 1, 1, 3, -1, -1, -4, -4, 2, 12, 12, -10, -10, -2, -2, -5, -5, 0, 0, -8, -8, -4, -4, 19, 19, -18, 7, 7, -18, -18, -9, -9, 0, 0, 20, 20, -9, -9, 0, 0, 9, 9, -10, -10, -21, -21, -24, -24, -11, -11, 9, 9, 18, 18, -15, -15, 12, 12, -26, -26, 4, 4, -25, -1, -1, -9, -9, 7, 7, 4, 4, -2, -4, -4, 27, 27, -22, -22, 24, 24, 21, 21, 33, 33, -22, -22, 10, 10, 16, 16, -16, -16, -32, -32, 34, 34, 39, 39, -36, -36, 37, 37, 33, 33, 33, 33, -28, -28, -22, -22, 26, 26, -5, -5, 14, 14, -38, -38, -10, -10, 37, 37, -44, -44, -8, -8, -12, -12, 38, 38, -22, -22, 6, 6, 32, 32, -28, -28, -25, -25, 46, 46, -11, -11, -39, -39, -47, -47, 24, 24, -36, -36, -42, -42, 25, 25, 23, 23, -46, -30, -30, -30, -30, 2, 2, 54, 54, 21, 21, -32, -32, 18, 18, 7, 7, 44, 44, 20, 20, -26, -26, -22, -22, -44, -44, 46, 46, -24, -24, 13, 13, 18, 18, -32, -32, -28, -28, 34, 34, -28, -28, 18, 18, -60, -60, -54, -54, 42, 42, -8, -8, -44, -44, 52, 52, -65, -49, -49, 21, 21, -18, -18, 4, 4, -7, -7, 72, 72, -29, -29, -24, -24, 14, 14, 48, 48, 35, 35, 4, 4, 26, 26, -22, -22, 10, 10, 0, 0, 34, 34, 53, 53, -82, 12, 12, -8, -8, -2, -2, 18, 18, -30, -30, 69, 69, 32, 32, 75, 75, -70, -70, -61, 14, 14, -31, -31, -70, -70, 12, 12, 11, 11, 24, 24, 60, 60, -28, -28, 13, 13, 59, 59, -40, -40, -84, -84, 52, 52, -60, -60, 48, 48, -81, -81, -44, -44, 23, 23, 53, 53, -16, -16, 56, 56, -32, -32, 0, 0, -16, -16, -74, -74, 48, 48, 75, 44, 44, -16, -16, -28, -28, 56, 56, 2, 2, 62, 62, 51, 51, 58, 58, -67, -67, -50, -50, -2, -2, 32, 32, -66, -66, -33, -33, -26, -26, 6, 6, -4, -4, 40, 40, 13, 13, 17, 17, -24, -24, -18, -18, -22, -22, 70, 70, 86, 86, -56, -56, -3, -3, 32, 32, 13, 13, -23, -23, -45, -45, -12, -12, -29, -29, -8, -8, -3, -3, -22, -22, -23, -23, 48, 48, -71, -71, -18, -18, -103, -103, -53, -53, 88, 88, 68, 68, -28, -28, 46, 46, -25, -25, 88, 88, -54, -54, 84, 84, -10, -10, -100, -100, 59, 59, 72, 72, 56, 56, -38, -38, 23, 23, 12, 12, -33, -33, -24, -24, 74, 74, -35, -35, 68, 68, 6, 6, 80, 80, 45, 45, 52, 52, -2, -2, -10, -10, -60, -60, -82, -82, -114, -114, -28, -28, -21, -21, -44, -44, 70, 70, -40, -40, 75, 75, -49, -49, -53, -53, -40, -40, -106, -106, -51, -51, -92, -92, 107, 107, 21, 21, -8, -8, -50, -50, 3, 3, 10, 10, -58, 87, 87, -10, -10, 91, 91, -14, -14, 24, 24, 56, 56, -82, -82, -100, -100, 37, 37, -66, -66, 63, 63, 0, 0, -66, -66, 83, 83, 56, 56, 96, 96, -60, -60, -71, -71, -70, -70, 75, 75, 77, 77, 18, 18, 45, 45, -106, -106, -14, -14, 55, 55, 122, 122, 5, 5, -18, -18, -71, -71, 86, 86, -51, -51, 72, 72, -77, -77, 2, 2, 60, 60, -126, -126, 56, 56, -5, -5, 68, 68, -102, -102, -17, -17, 80, 80, 27, 27, -56, -56, 26, 26, -94, -94, -64, -64, -11, -11, -23, -23, 100, 100, -9, -9, -56, -56, -29, -29, -35, -35, -92, -92, 114, 114, -54, -54, 68, 68, 30, 30, 42, 42, 130, 130, -92, -92, -54, -54, 48, 48, 86, 86, -7, -7, -100, -100, 56, 56, -43, -43, 25, 25, -81, -81, -110, -110, 74, 74, 45, 45, 0, 0, -88, -88, 131, 131, -21, -21, -128, -128, 76, 76, 0, 0, -87, -87, -10, -10, -40, -40, 107, 107, 132, 132, -24, -24, -1, -1, 96, 96, 66, 66, -12, -12, -86, -86, 60, 60, -46, 90, 90, 12, 12, 144, 144, 24, 24, -10, -10, 35, 35, 58, 58, 61, 61, 60, 60, 63, 63, 58, 58, 81, 81, -92, -92, -16, -16, -54, -54, -32, -32, 132, 132, -30, -30, 52, 52, -17, -17, -126, -126, 132, 132, 38, 38, 118, 118, 47, 47, 30, 30, 116, 116, -144, -144, -137, -137, -57, -57, 110, 110, -150, -150, 26, 26, -112, -112, 62, 62, 135, 135, -110, -110, -88, -88, 30, 30, 18, 18, -136, -136, -144, -144, 114, 114, 67, 67, 83, 83, -42, -42, -40, -40, -25, -25, 5, 5, -91, -91, 66, 66, -93, -93, 52, 52, -147, -147, -142, -63, -63, -36, -36, -72, -72, 133, 133, 41, 41, -96, -96, 98, 98, -108, -108, 24, 24, 30, 30, -16, -16, -94, -94, 24, 24, 6, 6, -23, -23, 97, 97, 87, 87, -2, -2, 97, 97, -18, -18, 86, 86, -30, -30, -37, -37, -1, -1, -140, -140, 96, 96, -5, -5, -79, -79, 114, 114, 103, 103, -21, -21, 140, 140, 102, 102, 7, 7, -19, -19, 46, 46, -1, -1, -68, -68, 74, 74, -86, -86, -39, -39, -141, -141, 3, 3, -66, -66, -96, -96, -80, -80, -32, -32, -16, -16, 91, 91, -85, -85, -42, -42, -75, -75, -126, -126, 117, 117, -46, -46, -12, -12, 32, 32, -8, -8, 48, 48, -135, -135, 112, 112, -50, -50, 165, 165, -7, -7, 58, 58, -98, -98, 129, 129, -2, -2, 97, 97, -72, -72, -21, -21, 108, 108, -16, -16, 163, 163, -8, -8, 54, 54, 35, 35, 32, 32, -126, -126, 66, 66, -166, -166, -122, -122, -77, -77, -166, -166, 88, 88, -152, -152, 27, 27, 34, 34, -84, -84, 6, 6, -72, -72, -60, -60, 132, 132, -53, -53, -84, -84, 88, 88, 69, 69, 54, 54, -24, -24, 28, 28, 12, 12, 86, 86, -106, -106, -142, 94, 94, -56, -56, 56, 56, -19, -19, -31, -31, -67, -67, -115, -115, 123, 123, 90, 90, 38, 38, -148, -148, -102, -102, -10, -10, -40, -40, 161, 161, 125, 125, 12, 12, 24, 24, -84, -84, -36, -36, 44, 44, 49, 49, -32, -32, -50, -50, -26, -26, 76, 76, 10, 10, 16, 16, -99, -99, -23, -23, 46, 46, 100, 100, 66, 66, -166, -166, 98, 98, 58, 58, -91, -91, 146, 146, -45, -45, 143, 143, -86, -86, 70, 70, -134, -134, -7, -7, 6, 6, 102, 102, 111, 111, 54, 54, 9, 9, 107, 107, -8, -8, 79, 79, -161, -161, -57, -57, 47, 47, 118, 118, 142, 142, -32, -32, 180, 180, -58, -58, 12, 12, -98, -98, -162, -162, 136, 136, -5, -5, 39, 39, 81, 81, -173, -173, -16, -16, -102, -102, 93, 93, 186, 186, -105, -105, 75, 75, -77, -77, -106, -106, -78, -78, 33, 33, -94, -94, -109, -109, 2, 12, 12, 14, 14, -32, -32, 12, 12, -84, -84, -108, -108, 128, 128, 104, 104, 30, 30, 56, 56, -5, -5, -36, -36, 40, 40, -145, -145, 130, 130, 111, 111, 116, 116, 139, 139, 178, 178, 7, 7, 34, 34, 94, 94, 26, 26, 11, 11, -163, -163, -123, -123, -10, -10, 35, 35, 12, 12, 97, 97, -180, -180, 70, 70] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([4, 2, 2])] = -1 AL_eigenvalues[ZF.ideal([13, 13, w + 4])] = 1 AL_eigenvalues[ZF.ideal([13, 13, w - 5])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]