/* 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, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([121, 11, -11]) primes_array = [ [2, 2, w - 3],\ [3, 3, w - 2],\ [3, 3, w + 2],\ [7, 7, w],\ [19, 19, 2*w - 3],\ [19, 19, 2*w + 3],\ [25, 5, 5],\ [29, 29, -w - 6],\ [29, 29, w - 6],\ [31, 31, 4*w + 9],\ [31, 31, -4*w + 9],\ [37, 37, -3*w + 10],\ [37, 37, -6*w + 17],\ [47, 47, -3*w - 4],\ [47, 47, 3*w - 4],\ [53, 53, 2*w - 9],\ [53, 53, 2*w + 9],\ [59, 59, 3*w - 2],\ [59, 59, -3*w - 2],\ [83, 83, -6*w - 13],\ [83, 83, -6*w + 13],\ [103, 103, 4*w - 3],\ [103, 103, -4*w - 3],\ [109, 109, -6*w + 19],\ [109, 109, -6*w - 19],\ [113, 113, -13*w + 36],\ [113, 113, -4*w + 15],\ [121, 11, -11],\ [131, 131, -6*w + 11],\ [131, 131, -6*w - 11],\ [137, 137, -w - 12],\ [137, 137, w - 12],\ [139, 139, -5*w - 6],\ [139, 139, 5*w - 6],\ [149, 149, -5*w + 18],\ [149, 149, -14*w + 39],\ [167, 167, -9*w + 20],\ [167, 167, -9*w - 20],\ [169, 13, -13],\ [193, 193, 3*w - 16],\ [193, 193, -3*w - 16],\ [197, 197, 2*w - 15],\ [197, 197, -2*w - 15],\ [199, 199, -7*w - 12],\ [199, 199, -7*w + 12],\ [223, 223, -8*w + 15],\ [223, 223, -8*w - 15],\ [227, 227, 6*w - 5],\ [227, 227, -6*w - 5],\ [233, 233, -16*w + 45],\ [233, 233, -7*w + 24],\ [251, 251, -6*w - 1],\ [251, 251, 6*w - 1],\ [271, 271, -11*w + 24],\ [271, 271, -11*w - 24],\ [277, 277, -21*w + 58],\ [277, 277, -6*w + 23],\ [281, 281, -8*w + 27],\ [281, 281, -17*w + 48],\ [283, 283, 13*w - 30],\ [283, 283, -14*w + 33],\ [289, 17, -17],\ [307, 307, 7*w - 6],\ [307, 307, -7*w - 6],\ [311, 311, -9*w - 16],\ [311, 311, -9*w + 16],\ [317, 317, -w - 18],\ [317, 317, w - 18],\ [337, 337, -3*w - 20],\ [337, 337, 3*w - 20],\ [367, 367, -8*w - 9],\ [367, 367, 8*w - 9],\ [373, 373, -6*w + 25],\ [373, 373, -27*w + 74],\ [383, 383, -12*w - 25],\ [383, 383, -12*w + 25],\ [389, 389, -19*w + 54],\ [389, 389, -10*w + 33],\ [401, 401, -5*w - 24],\ [401, 401, 5*w - 24],\ [419, 419, -15*w - 34],\ [419, 419, -15*w + 34],\ [421, 421, 3*w - 22],\ [421, 421, -3*w - 22],\ [439, 439, -8*w - 3],\ [439, 439, 8*w - 3],\ [449, 449, -11*w + 36],\ [449, 449, -11*w - 36],\ [457, 457, -9*w + 32],\ [457, 457, -24*w + 67],\ [467, 467, -9*w - 10],\ [467, 467, 9*w - 10],\ [479, 479, -12*w + 23],\ [479, 479, -12*w - 23],\ [503, 503, 9*w - 8],\ [503, 503, -9*w - 8],\ [523, 523, -11*w + 18],\ [523, 523, -11*w - 18],\ [529, 23, -23],\ [541, 541, -15*w + 46],\ [541, 541, -15*w - 46],\ [557, 557, 7*w + 30],\ [557, 557, 7*w - 30],\ [563, 563, 9*w - 2],\ [563, 563, -9*w - 2],\ [569, 569, -w - 24],\ [569, 569, w - 24],\ [587, 587, -18*w + 41],\ [587, 587, -18*w - 41],\ [607, 607, -13*w - 24],\ [607, 607, -13*w + 24],\ [613, 613, -3*w - 26],\ [613, 613, 3*w - 26],\ [617, 617, -4*w - 27],\ [617, 617, 4*w - 27],\ [619, 619, 10*w - 9],\ [619, 619, -10*w - 9],\ [641, 641, -8*w + 33],\ [641, 641, -35*w + 96],\ [643, 643, -14*w + 27],\ [643, 643, -14*w - 27],\ [647, 647, -12*w + 19],\ [647, 647, -12*w - 19],\ [653, 653, -14*w + 45],\ [653, 653, -14*w - 45],\ [673, 673, -12*w + 41],\ [673, 673, -27*w + 76],\ [691, 691, 10*w - 3],\ [691, 691, -10*w - 3],\ [701, 701, 2*w - 27],\ [701, 701, -2*w - 27],\ [709, 709, 6*w - 31],\ [709, 709, -6*w - 31],\ [719, 719, -12*w - 17],\ [719, 719, 12*w - 17],\ [727, 727, -17*w + 36],\ [727, 727, -17*w - 36],\ [757, 757, -18*w + 55],\ [757, 757, -18*w - 55],\ [787, 787, -22*w + 51],\ [787, 787, -22*w - 51],\ [809, 809, -16*w - 51],\ [809, 809, -16*w + 51],\ [811, 811, -11*w - 6],\ [811, 811, 11*w - 6],\ [821, 821, -37*w + 102],\ [821, 821, -10*w + 39],\ [839, 839, -12*w - 13],\ [839, 839, 12*w - 13],\ [859, 859, 13*w - 18],\ [859, 859, -13*w - 18],\ [877, 877, 9*w + 38],\ [877, 877, 9*w - 38],\ [887, 887, 12*w - 11],\ [887, 887, -12*w - 11],\ [953, 953, 7*w - 36],\ [953, 953, -7*w - 36],\ [971, 971, -21*w + 46],\ [971, 971, -21*w - 46],\ [977, 977, 4*w - 33],\ [977, 977, -4*w - 33],\ [983, 983, -12*w - 5],\ [983, 983, 12*w - 5],\ [1009, 1009, -21*w + 64],\ [1009, 1009, -21*w - 64],\ [1033, 1033, 9*w + 40],\ [1033, 1033, 9*w - 40],\ [1039, 1039, 13*w - 12],\ [1039, 1039, -13*w - 12],\ [1061, 1061, 2*w - 33],\ [1061, 1061, -2*w - 33],\ [1063, 1063, -16*w - 27],\ [1063, 1063, -16*w + 27],\ [1091, 1091, 15*w - 22],\ [1091, 1091, -15*w - 22],\ [1093, 1093, 3*w - 34],\ [1093, 1093, -3*w - 34],\ [1117, 1117, 6*w - 37],\ [1117, 1117, -6*w - 37],\ [1123, 1123, -17*w - 30],\ [1123, 1123, -17*w + 30],\ [1129, 1129, -15*w - 52],\ [1129, 1129, 15*w - 52],\ [1151, 1151, -21*w + 44],\ [1151, 1151, -21*w - 44],\ [1201, 1201, -45*w + 124],\ [1201, 1201, -12*w + 47],\ [1213, 1213, -18*w - 59],\ [1213, 1213, -18*w + 59],\ [1223, 1223, -24*w - 53],\ [1223, 1223, -24*w + 53],\ [1229, 1229, -41*w + 114],\ [1229, 1229, -14*w + 51],\ [1231, 1231, -19*w - 36],\ [1231, 1231, -19*w + 36],\ [1259, 1259, -27*w + 62],\ [1259, 1259, -27*w - 62],\ [1279, 1279, -20*w + 39],\ [1279, 1279, -20*w - 39],\ [1289, 1289, -w - 36],\ [1289, 1289, w - 36],\ [1291, 1291, 14*w - 9],\ [1291, 1291, -14*w - 9],\ [1297, 1297, -24*w + 73],\ [1297, 1297, -24*w - 73],\ [1307, 1307, -18*w - 31],\ [1307, 1307, -18*w + 31],\ [1319, 1319, -15*w - 16],\ [1319, 1319, 15*w - 16],\ [1373, 1373, -22*w - 69],\ [1373, 1373, -22*w + 69],\ [1381, 1381, -3*w - 38],\ [1381, 1381, 3*w - 38],\ [1399, 1399, -23*w + 48],\ [1399, 1399, -23*w - 48],\ [1409, 1409, -4*w - 39],\ [1409, 1409, 4*w - 39],\ [1427, 1427, -18*w - 29],\ [1427, 1427, -18*w + 29],\ [1429, 1429, -6*w - 41],\ [1429, 1429, 6*w - 41],\ [1447, 1447, -17*w - 24],\ [1447, 1447, 17*w - 24],\ [1453, 1453, -39*w + 110],\ [1453, 1453, -18*w + 61],\ [1459, 1459, -25*w + 54],\ [1459, 1459, -25*w - 54],\ [1481, 1481, -23*w + 72],\ [1481, 1481, -23*w - 72],\ [1483, 1483, -26*w + 57],\ [1483, 1483, -26*w - 57],\ [1487, 1487, -21*w - 40],\ [1487, 1487, -21*w + 40],\ [1493, 1493, 2*w - 39],\ [1493, 1493, -2*w - 39],\ [1511, 1511, -15*w - 8],\ [1511, 1511, 15*w - 8],\ [1531, 1531, -29*w - 66],\ [1531, 1531, -29*w + 66],\ [1543, 1543, -31*w + 72],\ [1543, 1543, -31*w - 72],\ [1549, 1549, 9*w - 46],\ [1549, 1549, -9*w - 46],\ [1559, 1559, -15*w - 4],\ [1559, 1559, 15*w - 4],\ [1567, 1567, 16*w - 15],\ [1567, 1567, -16*w - 15],\ [1571, 1571, 15*w - 2],\ [1571, 1571, -15*w - 2],\ [1597, 1597, 6*w - 43],\ [1597, 1597, -6*w - 43],\ [1621, 1621, -27*w + 82],\ [1621, 1621, -27*w - 82],\ [1627, 1627, -19*w - 30],\ [1627, 1627, -19*w + 30],\ [1681, 41, -41],\ [1699, 1699, -17*w - 18],\ [1699, 1699, 17*w - 18],\ [1709, 1709, -25*w - 78],\ [1709, 1709, -25*w + 78],\ [1733, 1733, -58*w + 159],\ [1733, 1733, -13*w + 54],\ [1783, 1783, 16*w - 3],\ [1783, 1783, -16*w - 3],\ [1789, 1789, -15*w + 58],\ [1789, 1789, -54*w + 149],\ [1801, 1801, 12*w - 53],\ [1801, 1801, 12*w + 53],\ [1811, 1811, -30*w - 67],\ [1811, 1811, -30*w + 67],\ [1823, 1823, -24*w + 47],\ [1823, 1823, -24*w - 47],\ [1847, 1847, -33*w - 76],\ [1847, 1847, -33*w + 76],\ [1849, 43, -43],\ [1867, 1867, -22*w + 39],\ [1867, 1867, -22*w - 39],\ [1873, 1873, -3*w - 44],\ [1873, 1873, 3*w - 44],\ [1877, 1877, -14*w + 57],\ [1877, 1877, -59*w + 162],\ [1879, 1879, 17*w - 12],\ [1879, 1879, -17*w - 12],\ [1901, 1901, 10*w - 51],\ [1901, 1901, -10*w - 51],\ [1907, 1907, -18*w - 19],\ [1907, 1907, 18*w - 19],\ [1913, 1913, 4*w - 45],\ [1913, 1913, -4*w - 45],\ [1931, 1931, -21*w + 34],\ [1931, 1931, -21*w - 34],\ [1933, 1933, 9*w - 50],\ [1933, 1933, -9*w - 50],\ [1951, 1951, -19*w - 24],\ [1951, 1951, 19*w - 24],\ [1979, 1979, 18*w - 17],\ [1979, 1979, -18*w - 17],\ [1987, 1987, -17*w - 6],\ [1987, 1987, 17*w - 6],\ [1997, 1997, 2*w - 45],\ [1997, 1997, -2*w - 45],\ [2017, 2017, 12*w + 55],\ [2017, 2017, 12*w - 55],\ [2053, 2053, 3*w - 46],\ [2053, 2053, -3*w - 46],\ [2063, 2063, -21*w - 32],\ [2063, 2063, -21*w + 32],\ [2069, 2069, -11*w - 54],\ [2069, 2069, 11*w - 54],\ [2081, 2081, -28*w - 87],\ [2081, 2081, -28*w + 87],\ [2099, 2099, -18*w - 13],\ [2099, 2099, 18*w - 13],\ [2129, 2129, 5*w - 48],\ [2129, 2129, -5*w - 48],\ [2131, 2131, -26*w + 51],\ [2131, 2131, -26*w - 51],\ [2137, 2137, 9*w - 52],\ [2137, 2137, -9*w - 52],\ [2153, 2153, 8*w - 51],\ [2153, 2153, -8*w - 51],\ [2203, 2203, 19*w - 18],\ [2203, 2203, -19*w - 18],\ [2213, 2213, -29*w + 90],\ [2213, 2213, -29*w - 90],\ [2221, 2221, -18*w + 67],\ [2221, 2221, -57*w + 158],\ [2237, 2237, -22*w + 75],\ [2237, 2237, -49*w + 138],\ [2239, 2239, -28*w - 57],\ [2239, 2239, -28*w + 57],\ [2243, 2243, 18*w - 5],\ [2243, 2243, -18*w - 5],\ [2267, 2267, -18*w - 1],\ [2267, 2267, 18*w - 1],\ [2269, 2269, -66*w + 181],\ [2269, 2269, -15*w + 62],\ [2287, 2287, -29*w + 60],\ [2287, 2287, -29*w - 60],\ [2293, 2293, -27*w + 86],\ [2293, 2293, -27*w - 86],\ [2297, 2297, -w - 48],\ [2297, 2297, w - 48],\ [2333, 2333, -17*w + 66],\ [2333, 2333, -62*w + 171],\ [2351, 2351, -24*w + 41],\ [2351, 2351, -24*w - 41],\ [2371, 2371, -31*w - 66],\ [2371, 2371, -31*w + 66],\ [2377, 2377, -33*w + 100],\ [2377, 2377, -33*w - 100],\ [2381, 2381, -50*w + 141],\ [2381, 2381, -23*w + 78],\ [2383, 2383, -19*w - 12],\ [2383, 2383, 19*w - 12],\ [2389, 2389, -21*w + 74],\ [2389, 2389, -54*w + 151],\ [2399, 2399, -27*w - 52],\ [2399, 2399, -27*w + 52],\ [2411, 2411, 21*w - 26],\ [2411, 2411, -21*w - 26],\ [2417, 2417, 13*w - 60],\ [2417, 2417, -13*w - 60],\ [2437, 2437, -3*w - 50],\ [2437, 2437, 3*w - 50],\ [2467, 2467, -34*w - 75],\ [2467, 2467, -34*w + 75],\ [2473, 2473, -12*w - 59],\ [2473, 2473, 12*w - 59],\ [2521, 2521, 15*w - 64],\ [2521, 2521, 15*w + 64],\ [2539, 2539, -38*w - 87],\ [2539, 2539, -38*w + 87],\ [2549, 2549, 10*w - 57],\ [2549, 2549, -10*w - 57],\ [2551, 2551, 40*w - 93],\ [2551, 2551, -41*w + 96],\ [2557, 2557, -6*w - 53],\ [2557, 2557, 6*w - 53],\ [2579, 2579, -30*w - 61],\ [2579, 2579, -30*w + 61],\ [2633, 2633, -32*w + 99],\ [2633, 2633, -32*w - 99],\ [2657, 2657, -64*w + 177],\ [2657, 2657, -19*w + 72],\ [2659, 2659, -22*w - 27],\ [2659, 2659, 22*w - 27],\ [2663, 2663, -24*w + 37],\ [2663, 2663, -24*w - 37],\ [2687, 2687, 21*w - 20],\ [2687, 2687, -21*w - 20],\ [2689, 2689, -60*w + 167],\ [2689, 2689, -21*w + 76],\ [2707, 2707, -26*w - 45],\ [2707, 2707, -26*w + 45],\ [2713, 2713, 12*w - 61],\ [2713, 2713, -12*w - 61],\ [2719, 2719, -20*w - 9],\ [2719, 2719, 20*w - 9],\ [2741, 2741, -5*w - 54],\ [2741, 2741, 5*w - 54],\ [2753, 2753, -11*w - 60],\ [2753, 2753, 11*w - 60],\ [2791, 2791, -20*w - 3],\ [2791, 2791, 20*w - 3],\ [2797, 2797, -9*w - 58],\ [2797, 2797, 9*w - 58],\ [2801, 2801, 8*w - 57],\ [2801, 2801, -8*w - 57],\ [2803, 2803, -23*w - 30],\ [2803, 2803, 23*w - 30],\ [2819, 2819, -30*w + 59],\ [2819, 2819, -30*w - 59],\ [2837, 2837, -26*w + 87],\ [2837, 2837, -53*w + 150],\ [2857, 2857, 24*w - 83],\ [2857, 2857, -24*w - 83],\ [2887, 2887, -28*w - 51],\ [2887, 2887, -28*w + 51],\ [2903, 2903, -39*w - 88],\ [2903, 2903, -39*w + 88],\ [2909, 2909, -w - 54],\ [2909, 2909, w - 54],\ [2939, 2939, -42*w - 97],\ [2939, 2939, -42*w + 97],\ [2969, 2969, 16*w + 69],\ [2969, 2969, 16*w - 69],\ [2971, 2971, -29*w - 54],\ [2971, 2971, -29*w + 54],\ [2999, 2999, -33*w + 68],\ [2999, 2999, -33*w - 68],\ [3023, 3023, -21*w - 8],\ [3023, 3023, 21*w - 8],\ [3049, 3049, 15*w - 68],\ [3049, 3049, 15*w + 68],\ [3061, 3061, -18*w + 73],\ [3061, 3061, -75*w + 206],\ [3079, 3079, 25*w - 36],\ [3079, 3079, -25*w - 36],\ [3083, 3083, 21*w - 2],\ [3083, 3083, -21*w - 2],\ [3089, 3089, -35*w + 108],\ [3089, 3089, -35*w - 108],\ [3109, 3109, -30*w + 97],\ [3109, 3109, -30*w - 97],\ [3137, 3137, 4*w - 57],\ [3137, 3137, -4*w - 57],\ [3163, 3163, -22*w - 15],\ [3163, 3163, 22*w - 15],\ [3167, 3167, -27*w - 44],\ [3167, 3167, -27*w + 44],\ [3191, 3191, -24*w - 29],\ [3191, 3191, 24*w - 29],\ [3217, 3217, 12*w - 65],\ [3217, 3217, -12*w - 65],\ [3221, 3221, 2*w - 57],\ [3221, 3221, -2*w - 57],\ [3229, 3229, -6*w - 59],\ [3229, 3229, 6*w - 59],\ [3251, 3251, -39*w - 86],\ [3251, 3251, -39*w + 86],\ [3257, 3257, 7*w - 60],\ [3257, 3257, -7*w - 60],\ [3301, 3301, 3*w - 58],\ [3301, 3301, -3*w - 58],\ [3307, 3307, -22*w - 9],\ [3307, 3307, 22*w - 9],\ [3313, 3313, -21*w + 80],\ [3313, 3313, -72*w + 199],\ [3323, 3323, -42*w + 95],\ [3323, 3323, -42*w - 95],\ [3329, 3329, -29*w + 96],\ [3329, 3329, -56*w + 159],\ [3331, 3331, -34*w - 69],\ [3331, 3331, -34*w + 69],\ [3359, 3359, -45*w + 104],\ [3359, 3359, -45*w - 104],\ [3361, 3361, -27*w + 92],\ [3361, 3361, -60*w + 169],\ [3389, 3389, -14*w - 69],\ [3389, 3389, 14*w - 69],\ [3391, 3391, -35*w + 72],\ [3391, 3391, -35*w - 72],\ [3407, 3407, -24*w - 25],\ [3407, 3407, 24*w - 25],\ [3413, 3413, -37*w - 114],\ [3413, 3413, -37*w + 114],\ [3463, 3463, -28*w - 45],\ [3463, 3463, -28*w + 45],\ [3469, 3469, 6*w - 61],\ [3469, 3469, -6*w - 61],\ [3491, 3491, -30*w + 53],\ [3491, 3491, -30*w - 53],\ [3499, 3499, -37*w + 78],\ [3499, 3499, -37*w - 78],\ [3527, 3527, -33*w - 64],\ [3527, 3527, -33*w + 64],\ [3529, 3529, 9*w - 64],\ [3529, 3529, -9*w - 64],\ [3547, 3547, -38*w + 81],\ [3547, 3547, -38*w - 81],\ [3557, 3557, -82*w + 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144],\ [8849, 8849, -35*w + 132],\ [8849, 8849, -116*w + 321],\ [8867, 8867, -42*w - 59],\ [8867, 8867, 42*w - 59],\ [8923, 8923, -67*w - 150],\ [8923, 8923, -67*w + 150],\ [8929, 8929, -45*w + 152],\ [8929, 8929, -96*w + 271],\ [8933, 8933, 22*w - 111],\ [8933, 8933, -22*w - 111],\ [8941, 8941, -57*w - 178],\ [8941, 8941, -57*w + 178],\ [8951, 8951, 36*w - 11],\ [8951, 8951, -36*w - 11],\ [8963, 8963, -54*w + 107],\ [8963, 8963, -54*w - 107],\ [8969, 8969, -41*w + 144],\ [8969, 8969, -104*w + 291],\ [9007, 9007, -37*w - 24],\ [9007, 9007, 37*w - 24],\ [9013, 9013, -21*w - 110],\ [9013, 9013, 21*w - 110],\ [9041, 9041, 5*w - 96],\ [9041, 9041, -5*w - 96],\ [9043, 9043, -71*w - 162],\ [9043, 9043, -71*w + 162],\ [9091, 9091, -74*w - 171],\ [9091, 9091, -74*w + 171],\ [9103, 9103, -76*w + 177],\ [9103, 9103, -76*w - 177],\ [9109, 9109, -66*w + 199],\ [9109, 9109, -66*w - 199],\ [9127, 9127, -52*w + 99],\ [9127, 9127, -52*w - 99],\ [9137, 9137, 19*w - 108],\ [9137, 9137, -19*w - 108],\ [9157, 9157, 6*w - 97],\ [9157, 9157, -6*w - 97],\ [9181, 9181, -18*w - 107],\ [9181, 9181, 18*w - 107],\ [9187, 9187, -46*w + 75],\ [9187, 9187, -46*w - 75],\ [9203, 9203, 39*w - 38],\ [9203, 9203, -39*w - 38],\ [9209, 9209, -w - 96],\ [9209, 9209, w - 96],\ [9221, 9221, 13*w - 102],\ [9221, 9221, -13*w - 102],\ [9239, 9239, -48*w - 83],\ [9239, 9239, -48*w + 83],\ [9241, 9241, -15*w - 104],\ [9241, 9241, 15*w - 104],\ [9277, 9277, -33*w + 130],\ [9277, 9277, -126*w + 347],\ [9293, 9293, -23*w - 114],\ [9293, 9293, 23*w - 114],\ [9323, 9323, -42*w - 55],\ [9323, 9323, 42*w - 55],\ [9343, 9343, 43*w - 60],\ [9343, 9343, -43*w - 60],\ [9349, 9349, -51*w + 166],\ [9349, 9349, -51*w - 166],\ [9371, 9371, -51*w - 94],\ [9371, 9371, -51*w + 94],\ [9377, 9377, -56*w + 177],\ [9377, 9377, -56*w - 177],\ [9409, 97, -97],\ [9433, 9433, 9*w - 100],\ [9433, 9433, -9*w - 100],\ [9437, 9437, -94*w + 267],\ [9437, 9437, -49*w + 162],\ [9439, 9439, 37*w - 12],\ [9439, 9439, -37*w - 12],\ [9461, 9461, -37*w + 138],\ [9461, 9461, -118*w + 327],\ [9463, 9463, -41*w - 48],\ [9463, 9463, 41*w - 48],\ [9467, 9467, -66*w + 145],\ [9467, 9467, -66*w - 145],\ [9473, 9473, -32*w + 129],\ [9473, 9473, -131*w + 360],\ [9491, 9491, 39*w - 34],\ [9491, 9491, -39*w - 34],\ [9511, 9511, -55*w - 108],\ [9511, 9511, -55*w + 108],\ [9521, 9521, -20*w - 111],\ [9521, 9521, 20*w - 111],\ [9539, 9539, 42*w - 53],\ [9539, 9539, -42*w - 53],\ [9547, 9547, 37*w - 6],\ [9547, 9547, -37*w - 6],\ [9551, 9551, -45*w - 68],\ [9551, 9551, 45*w - 68],\ [9601, 9601, -12*w - 103],\ [9601, 9601, 12*w - 103],\ [9613, 9613, 18*w - 109],\ [9613, 9613, -18*w - 109],\ [9623, 9623, -39*w - 32],\ [9623, 9623, 39*w - 32],\ [9629, 9629, -65*w + 198],\ [9629, 9629, -65*w - 198],\ [9631, 9631, -56*w + 111],\ [9631, 9631, -56*w - 111],\ [9661, 9661, 15*w - 106],\ [9661, 9661, -15*w - 106],\ [9679, 9679, 40*w - 39],\ [9679, 9679, -40*w - 39],\ [9689, 9689, -4*w - 99],\ [9689, 9689, 4*w - 99],\ [9697, 9697, -36*w + 137],\ [9697, 9697, -123*w + 340],\ [9719, 9719, -72*w - 163],\ [9719, 9719, -72*w + 163],\ [9743, 9743, -51*w - 92],\ [9743, 9743, -51*w + 92],\ [9769, 9769, -60*w - 187],\ [9769, 9769, -60*w + 187],\ [9781, 9781, 27*w - 122],\ [9781, 9781, 27*w + 122],\ [9791, 9791, -75*w + 172],\ [9791, 9791, -75*w - 172],\ [9803, 9803, -54*w + 103],\ [9803, 9803, -54*w - 103],\ [9829, 9829, -30*w + 127],\ [9829, 9829, -141*w + 386],\ [9857, 9857, 44*w - 153],\ [9857, 9857, -44*w - 153],\ [9859, 9859, -58*w - 117],\ [9859, 9859, -58*w + 117],\ [9883, 9883, 38*w - 15],\ [9883, 9883, -38*w - 15],\ [9887, 9887, -48*w + 79],\ [9887, 9887, -48*w - 79],\ [9931, 9931, -50*w - 87],\ [9931, 9931, -50*w + 87],\ [9941, 9941, -58*w + 183],\ [9941, 9941, -58*w - 183],\ [9949, 9949, -6*w - 101],\ [9949, 9949, 6*w - 101],\ [9967, 9967, -59*w + 120],\ [9967, 9967, -59*w - 120]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-2, -1, -1, -2, 0, 0, -9, 0, 0, 7, 7, 3, 3, 8, 8, -6, -6, 5, 5, -6, -6, -16, -16, 10, 10, 9, 9, 1, -18, -18, -7, -7, 10, 10, -10, -10, -12, -12, -10, 4, 4, -2, -2, 0, 0, 19, 19, 18, 18, 24, 24, -23, -23, -28, -28, -2, -2, -18, -18, 4, 4, -30, 8, 8, 12, 12, 13, 13, -22, -22, -17, -17, -26, -26, -1, -1, -15, -15, 2, 2, 20, 20, 22, 22, 40, 40, 35, 35, -12, -12, -27, -27, 20, 20, -26, -26, -16, -16, -45, -8, -8, -2, -2, 4, 4, 0, 0, 28, 28, -22, -22, -16, -16, 18, 18, -25, -25, -33, -33, 29, 29, -7, -7, -41, -41, 14, 14, 17, 17, 2, 2, -25, -25, 15, 15, 3, 3, -22, -22, -32, -32, 0, 0, -38, -38, 22, 22, -5, -5, -15, -15, -12, -12, -22, -22, 34, 34, 47, 47, -27, -27, 39, 39, -10, -10, -16, -16, 5, 5, -13, -13, 44, 44, -58, -58, -51, -51, 48, 48, 24, 24, 50, 50, 2, 2, 2, 2, -41, -41, 14, 14, 60, 60, -18, -18, -25, -25, -15, -15, 0, 0, -8, -8, 48, 48, 28, 28, -30, -30, 39, 39, -68, -68, 60, 60, -15, -15, -12, -12, -70, -70, 28, 28, -71, -71, -20, -20, 32, 32, 49, 49, 58, 58, -36, -36, 37, 37, 32, 32, -36, -36, -15, -15, -60, -60, -52, -52, -28, -28, -32, -32, 22, 22, 78, 78, -18, 40, 40, -45, -45, -6, -6, 59, 59, 10, 10, 52, 52, 12, 12, -56, -56, -52, -52, -50, 28, 28, -6, -6, 18, 18, -35, -35, 77, 77, -52, -52, -36, -36, -18, -18, 54, 54, -23, -23, 30, 30, -22, -22, -72, -72, -17, -17, 84, 84, 24, 24, 70, 70, -18, -18, 35, 35, 20, 20, -68, -68, 73, 73, -26, -26, -1, -1, 4, 4, 22, 22, 78, 78, -70, -70, -56, -56, 93, 93, 25, 25, 38, 38, 29, 29, -57, -57, 59, 59, -48, -48, -28, -28, 3, 3, -18, -18, -36, -36, -50, -50, -75, -75, 62, 62, -22, -22, -82, -82, 3, 3, -11, -11, 72, 72, 0, 0, -20, -20, -98, -98, 13, 13, 20, 20, 39, 39, 38, 38, 40, 40, 39, 39, 23, 23, 5, 5, -17, -17, -56, -56, -70, -70, -58, -58, 49, 49, 42, 42, -42, -42, 52, 52, 44, 44, -25, -25, -62, -62, -82, -82, -57, -57, 54, 54, -25, -25, -50, -50, 70, 70, -53, -53, -80, -80, 39, 39, -40, -40, 37, 37, -20, -20, 29, 29, 25, 25, 80, 80, 8, 8, -26, -26, 18, 18, -8, -8, 23, 23, -103, -103, 70, 70, -48, -48, 58, 58, -73, -73, 98, 98, 4, 4, -76, -76, -100, -100, -43, -43, -45, -45, -88, -88, 15, 15, 92, 92, 18, 18, 9, 9, -96, -96, -85, -85, 17, 17, 100, 100, 18, 18, -35, -35, 53, 53, -27, -27, 0, 0, 32, 32, -96, -96, -26, -26, -26, -26, 32, 32, -72, -72, 34, 34, 30, 30, -78, -78, -62, -62, 23, 23, 22, 23, 23, 114, 114, -88, -88, -30, -30, 19, 19, 54, 54, -70, -70, 12, 12, -57, -57, 0, 0, 54, 54, -60, -60, -107, -107, -92, -92, 102, 102, -46, -46, -32, -32, 54, 54, -123, -123, 103, 103, -60, -60, 92, 92, -36, -36, -98, -98, 10, 10, -55, -55, -68, -68, -16, -16, 70, 70, 39, 39, -2, -2, 55, 55, -30, -30, 108, 108, 72, 72, 49, 49, 102, 102, 82, 82, -106, -106, -85, -82, -82, 8, 8, 112, 112, -112, -112, -36, -36, -8, -8, 122, 122, 20, 20, -80, -80, -73, -73, 73, 73, 114, 114, 25, 25, -36, -36, -96, -96, 30, 30, 129, 129, -48, -48, 30, 30, 8, 8, 110, 110, -76, -76, -132, -132, 72, 72, -126, -126, 115, 115, 30, 30, 32, 32, -42, -42, 98, 98, 28, 28, 44, 44, 119, 119, -45, -45, -38, -38, -3, -3, 15, 15, -133, 10, 10, 8, 8, 93, 93, -10, -10, -111, -111, 97, 97, -60, -60, -80, -80, -50, -50, 48, 48, -96, -96, 63, 63, 87, 87, -21, -21, -76, -76, -130, 23, 23, 77, 77, 138, 138, 14, 14, 82, 82, -108, -108, -95, -95, 48, 48, 0, 0, 134, 134, -25, -25, 104, 104, 7, 7, -33, -33, 113, 113, 4, 4, -57, -57, -125, -125, 114, 114, -146, -146, -138, -138, 118, 118, -8, -8, 19, 19, -30, -30, -78, -78, -12, -12, -66, -66, 80, 80, 2, 2, -38, -38, -55, -55, -68, -68, 123, 123, 40, 40, -63, -63, 105, 105, -42, -42, 48, 48, -26, -26, 100, 100, -48, -48, -16, -16, 57, 57, 94, 94, 52, 52, 59, 59, 113, 113, -62, -62, -58, -102, -102, 19, 19, -30, -30, -53, -53, -30, -30, -23, -23, 50, 50, 38, 38, -86, -86, 60, 60, -28, -28, 105, 105, -55, -55, -3, -3, -98, -98, 74, 74, -28, -28, -72, -72, -93, -93, -50, -50, 48, 48, -122, -122, -38, -38, 4, 4, 15, 15, -83, -83, 102, 102, -120, -120, 60, 60, -11, -11, -56, -56, 65, 65, 24, 24, -108, -108, -127, -127, 64, 64, 85, 85, 108, 108, 38, 38, -72, -72, -128, -128, 142, 142, 23, 23, -98, -98, 120, 120, 23, 23, -62, -62, 24, 24, 15, 15, -3, -3, -105, -105, -142, -142, 153, 153, -6, -6, -21, -21, 59, 59, -141, -141, -7, -7, -25, -25, -36, -36, 69, 69, -88, -88, 103, 103, -148, -148, -142, -142, 138, 138, -87, -87, 24, 24, 145, 145, 142, 142, -30, -30, -138, -138, 40, 40, -33, -33, 38, 38, 159, 159, -70, -70, 84, 84, 107, 107, 42, 42, 50, 50, -51, -51, 33, 33, 19, 19, 28, 28, 55, 55, -21, -21, 17, 17, 88, 88, -122, -122, 47, -132, -132, 74, 74, -30, -30, -48, -48, 85, 85, 137, 137, -62, -62, -75, -75, 135, 135, -86, -86, 77, 77, 112, 112, 168, 168, 84, 84, -112, -112, 123, 123, -130, -130, 107, 107, 169, 169, -46, -46, -100, -100, -72, -72, -108, -108, -117, -117, 18, 18, 59, 59, 84, 84, 130, 130, -60, -60, -15, -15, 107, 107, -152, -152, -36, -36, 72, 72, 13, 13, 145, 145, -126, -126, 78, 78, 80, 80, 74, 74, -137, -137, 98, 98, 132, 132, 90, 90, 135, 135, 88, 88, -2, -2, -13, -13, 69, 69, 50, 50, -78, -78, -70, -70, 90, 90, -57, -57, -36, -36, -40, -40, 109, 109, -133, -133, 52, 52, 129, 129, 15, 15, 153, 153, 119, 119, 42, 42, 144, 144, 67, 67, 14, 14, 85, 85, -12, -12, 78, 78, 63, 63, 82, 82, 58, 58, -166, -166, 120, 120, -103, -103, -60, -60, -133, -133, 43, 43, -66, -66, 134, 134, -151, -151, -100, -100, -78, -78, -142, -142, -145, 94, 94, 38, 38, 65, 65, 62, 62, 184, 184, 8, 8, 114, 114, -108, -108, -38, -38, -78, -78, 0, 0, -2, -2, 27, 27, -173, -173, 64, 64, -61, -61, 25, 25, -118, -118, -13, -13, 30, 30, -175, -175, 178, 178, 110, 110, 164, 164, -5, -5, -18, -18, -108, -108, 144, 144, -80, -80, -117, -117, -85, -85, -81, -81, -117, -117, 57, 57, 42, 42, -10, -10, 43, 43] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([121, 11, -11])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]