/* 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([-4, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([128, 64, -6*w - 2]) primes_array = [ [2, 2, -w + 2],\ [2, 2, -w - 1],\ [9, 3, 3],\ [13, 13, -2*w + 3],\ [13, 13, 2*w + 1],\ [17, 17, -2*w + 1],\ [19, 19, -2*w + 7],\ [19, 19, 2*w + 5],\ [25, 5, -5],\ [43, 43, 4*w - 7],\ [43, 43, 4*w + 3],\ [47, 47, -2*w + 9],\ [47, 47, 2*w + 7],\ [49, 7, -7],\ [53, 53, 4*w - 13],\ [53, 53, 6*w - 13],\ [59, 59, -4*w - 1],\ [59, 59, 4*w - 5],\ [67, 67, 4*w - 3],\ [67, 67, 4*w - 1],\ [83, 83, 2*w - 11],\ [83, 83, -2*w - 9],\ [89, 89, 6*w - 11],\ [89, 89, 6*w + 5],\ [101, 101, 10*w - 23],\ [101, 101, 4*w - 15],\ [103, 103, 8*w + 9],\ [103, 103, 8*w - 17],\ [121, 11, -11],\ [127, 127, 2*w - 13],\ [127, 127, -2*w - 11],\ [137, 137, -6*w - 1],\ [137, 137, 6*w - 7],\ [149, 149, 6*w - 5],\ [149, 149, 6*w - 1],\ [151, 151, 8*w - 15],\ [151, 151, 8*w + 7],\ [157, 157, 14*w + 19],\ [157, 157, 4*w + 13],\ [179, 179, 2*w - 15],\ [179, 179, -2*w - 13],\ [191, 191, 8*w - 13],\ [191, 191, 8*w + 5],\ [223, 223, -8*w - 3],\ [223, 223, 8*w - 11],\ [229, 229, 10*w - 19],\ [229, 229, 10*w + 9],\ [239, 239, 2*w - 17],\ [239, 239, -2*w - 15],\ [251, 251, 12*w + 13],\ [251, 251, 12*w - 25],\ [257, 257, 8*w - 27],\ [257, 257, 14*w - 31],\ [263, 263, 8*w - 7],\ [263, 263, 8*w - 1],\ [271, 271, 8*w - 5],\ [271, 271, 8*w - 3],\ [281, 281, 10*w + 7],\ [281, 281, 10*w - 17],\ [293, 293, 4*w - 21],\ [293, 293, -4*w - 17],\ [307, 307, 2*w - 19],\ [307, 307, -2*w - 17],\ [331, 331, 6*w - 25],\ [331, 331, -6*w - 19],\ [349, 349, 14*w + 15],\ [349, 349, 14*w - 29],\ [353, 353, 18*w - 41],\ [353, 353, 8*w - 29],\ [359, 359, 16*w - 35],\ [359, 359, 10*w - 33],\ [373, 373, -4*w - 19],\ [373, 373, 4*w - 23],\ [383, 383, 2*w - 21],\ [383, 383, -2*w - 19],\ [389, 389, -10*w - 1],\ [389, 389, 10*w - 11],\ [409, 409, 10*w - 9],\ [409, 409, 10*w - 1],\ [421, 421, 10*w - 3],\ [421, 421, 10*w - 7],\ [433, 433, 14*w - 27],\ [433, 433, -14*w - 13],\ [443, 443, 12*w - 19],\ [443, 443, -12*w - 7],\ [457, 457, 22*w - 51],\ [457, 457, 8*w - 31],\ [461, 461, 4*w - 25],\ [461, 461, -4*w - 21],\ [463, 463, 16*w + 17],\ [463, 463, 16*w - 33],\ [467, 467, 2*w - 23],\ [467, 467, -2*w - 21],\ [491, 491, -12*w - 5],\ [491, 491, 12*w - 17],\ [509, 509, 14*w - 25],\ [509, 509, 14*w + 11],\ [523, 523, -6*w - 23],\ [523, 523, 6*w - 29],\ [529, 23, -23],\ [557, 557, -4*w - 23],\ [557, 557, 4*w - 27],\ [563, 563, -12*w - 1],\ [563, 563, 12*w - 13],\ [569, 569, 26*w + 35],\ [569, 569, 26*w - 61],\ [577, 577, 14*w - 23],\ [577, 577, -14*w - 9],\ [587, 587, 12*w - 11],\ [587, 587, 12*w - 1],\ [593, 593, 18*w + 19],\ [593, 593, 18*w - 37],\ [599, 599, 10*w - 37],\ [599, 599, 24*w - 55],\ [613, 613, 12*w - 41],\ [613, 613, 22*w - 49],\ [631, 631, 6*w - 31],\ [631, 631, -6*w - 25],\ [647, 647, 16*w + 13],\ [647, 647, 16*w - 29],\ [659, 659, 2*w - 27],\ [659, 659, -2*w - 25],\ [661, 661, 4*w - 29],\ [661, 661, -4*w - 25],\ [701, 701, 18*w - 35],\ [701, 701, -18*w - 17],\ [727, 727, 16*w + 11],\ [727, 727, 16*w - 27],\ [733, 733, -14*w - 3],\ [733, 733, 14*w - 17],\ [739, 739, 20*w + 21],\ [739, 739, 20*w - 41],\ [757, 757, 26*w - 59],\ [757, 757, 12*w - 43],\ [761, 761, 22*w - 47],\ [761, 761, 22*w + 25],\ [769, 769, -14*w - 1],\ [769, 769, 14*w - 15],\ [773, 773, -4*w - 27],\ [773, 773, 4*w - 31],\ [797, 797, 14*w - 13],\ [797, 797, 14*w - 1],\ [829, 829, 14*w - 9],\ [829, 829, 14*w - 5],\ [841, 29, -29],\ [859, 859, 20*w - 39],\ [859, 859, -20*w - 19],\ [863, 863, -16*w - 7],\ [863, 863, 16*w - 23],\ [883, 883, 2*w - 31],\ [883, 883, -2*w - 29],\ [919, 919, 16*w - 21],\ [919, 919, -16*w - 5],\ [937, 937, 26*w - 57],\ [937, 937, 16*w - 53],\ [953, 953, -8*w - 31],\ [953, 953, 8*w - 39],\ [961, 31, -31],\ [967, 967, 16*w - 19],\ [967, 967, -16*w - 3],\ [971, 971, 20*w - 37],\ [971, 971, 20*w + 17],\ [977, 977, -18*w - 11],\ [977, 977, 18*w - 29],\ [1019, 1019, -10*w - 33],\ [1019, 1019, 10*w - 43],\ [1021, 1021, -4*w - 31],\ [1021, 1021, 4*w - 35],\ [1033, 1033, 22*w - 43],\ [1033, 1033, -22*w - 21],\ [1039, 1039, 16*w - 15],\ [1039, 1039, 16*w - 1],\ [1063, 1063, 16*w - 3],\ [1063, 1063, 16*w - 13],\ [1069, 1069, 34*w - 79],\ [1069, 1069, 12*w - 47],\ [1087, 1087, 16*w - 9],\ [1087, 1087, 16*w - 7],\ [1097, 1097, 8*w - 41],\ [1097, 1097, -8*w - 33],\ [1103, 1103, 32*w - 73],\ [1103, 1103, 14*w - 51],\ [1109, 1109, 26*w + 29],\ [1109, 1109, 26*w - 55],\ [1123, 1123, 28*w - 61],\ [1123, 1123, 18*w - 59],\ [1171, 1171, 20*w - 33],\ [1171, 1171, -20*w - 13],\ [1181, 1181, 18*w - 23],\ [1181, 1181, -18*w - 5],\ [1223, 1223, 24*w - 47],\ [1223, 1223, -24*w - 23],\ [1237, 1237, 38*w + 51],\ [1237, 1237, 38*w - 89],\ [1249, 1249, 8*w - 43],\ [1249, 1249, -8*w - 35],\ [1259, 1259, 20*w - 31],\ [1259, 1259, -20*w - 11],\ [1277, 1277, -18*w - 1],\ [1277, 1277, 18*w - 19],\ [1279, 1279, 2*w - 37],\ [1279, 1279, -2*w - 35],\ [1283, 1283, 36*w - 83],\ [1283, 1283, 14*w - 53],\ [1291, 1291, -6*w - 35],\ [1291, 1291, 6*w - 41],\ [1301, 1301, -4*w - 35],\ [1301, 1301, 4*w - 39],\ [1307, 1307, 28*w - 59],\ [1307, 1307, 28*w + 31],\ [1327, 1327, 32*w - 71],\ [1327, 1327, 18*w - 61],\ [1361, 1361, 18*w - 5],\ [1361, 1361, 18*w - 13],\ [1369, 37, -37],\ [1373, 1373, 18*w - 7],\ [1373, 1373, 18*w - 11],\ [1381, 1381, -22*w - 15],\ [1381, 1381, 22*w - 37],\ [1409, 1409, -8*w - 37],\ [1409, 1409, 8*w - 45],\ [1427, 1427, 2*w - 39],\ [1427, 1427, -2*w - 37],\ [1429, 1429, 26*w - 51],\ [1429, 1429, -26*w - 25],\ [1447, 1447, 6*w - 43],\ [1447, 1447, -6*w - 37],\ [1453, 1453, 4*w - 41],\ [1453, 1453, -4*w - 37],\ [1471, 1471, 40*w - 93],\ [1471, 1471, 14*w - 55],\ [1481, 1481, 22*w - 35],\ [1481, 1481, -22*w - 13],\ [1483, 1483, 28*w + 29],\ [1483, 1483, 28*w - 57],\ [1487, 1487, 24*w - 43],\ [1487, 1487, 24*w + 19],\ [1511, 1511, -10*w - 39],\ [1511, 1511, 10*w - 49],\ [1531, 1531, -20*w - 3],\ [1531, 1531, 20*w - 23],\ [1543, 1543, 22*w - 71],\ [1543, 1543, 32*w - 69],\ [1549, 1549, 20*w - 67],\ [1549, 1549, 34*w - 75],\ [1579, 1579, -20*w - 1],\ [1579, 1579, 20*w - 21],\ [1583, 1583, 2*w - 41],\ [1583, 1583, -2*w - 39],\ [1597, 1597, 12*w - 53],\ [1597, 1597, -12*w - 41],\ [1607, 1607, 24*w - 41],\ [1607, 1607, 24*w + 17],\ [1613, 1613, -4*w - 39],\ [1613, 1613, 4*w - 43],\ [1619, 1619, 20*w - 19],\ [1619, 1619, 20*w - 1],\ [1657, 1657, -22*w - 9],\ [1657, 1657, 22*w - 31],\ [1667, 1667, 44*w + 59],\ [1667, 1667, 44*w - 103],\ [1681, 41, -41],\ [1699, 1699, 20*w - 11],\ [1699, 1699, 20*w - 9],\ [1709, 1709, 30*w + 31],\ [1709, 1709, 30*w - 61],\ [1721, 1721, 16*w - 61],\ [1721, 1721, 42*w - 97],\ [1733, 1733, 22*w - 29],\ [1733, 1733, -22*w - 7],\ [1747, 1747, 2*w - 43],\ [1747, 1747, -2*w - 41],\ [1753, 1753, 8*w - 49],\ [1753, 1753, -8*w - 41],\ [1759, 1759, 18*w - 65],\ [1759, 1759, 40*w - 91],\ [1777, 1777, 24*w - 77],\ [1777, 1777, 34*w - 73],\ [1783, 1783, -6*w - 41],\ [1783, 1783, 6*w - 47],\ [1787, 1787, 36*w - 79],\ [1787, 1787, 22*w - 73],\ [1789, 1789, -12*w - 43],\ [1789, 1789, 12*w - 55],\ [1801, 1801, -22*w - 5],\ [1801, 1801, 22*w - 27],\ [1811, 1811, 28*w + 25],\ [1811, 1811, 28*w - 53],\ [1823, 1823, 24*w - 37],\ [1823, 1823, -24*w - 13],\ [1861, 1861, 22*w - 25],\ [1861, 1861, -22*w - 3],\ [1871, 1871, 14*w - 59],\ [1871, 1871, -14*w - 45],\ [1879, 1879, -10*w - 43],\ [1879, 1879, 10*w - 53],\ [1889, 1889, 30*w - 59],\ [1889, 1889, -30*w - 29],\ [1913, 1913, -22*w - 1],\ [1913, 1913, 22*w - 23],\ [1951, 1951, 32*w + 33],\ [1951, 1951, 32*w - 65],\ [1973, 1973, 26*w - 43],\ [1973, 1973, -26*w - 17],\ [1987, 1987, 18*w - 67],\ [1987, 1987, 44*w - 101],\ [1993, 1993, 22*w - 3],\ [1993, 1993, 22*w - 19],\ [1997, 1997, 34*w - 71],\ [1997, 1997, 34*w + 37],\ [2027, 2027, 36*w - 77],\ [2027, 2027, 26*w - 83],\ [2039, 2039, 22*w - 75],\ [2039, 2039, 40*w - 89],\ [2053, 2053, 22*w - 13],\ [2053, 2053, 22*w - 9],\ [2083, 2083, 14*w - 61],\ [2083, 2083, -14*w - 47],\ [2087, 2087, -24*w - 7],\ [2087, 2087, 24*w - 31],\ [2089, 2089, -26*w - 15],\ [2089, 2089, 26*w - 41],\ [2099, 2099, 2*w - 47],\ [2099, 2099, -2*w - 45],\ [2129, 2129, -8*w - 45],\ [2129, 2129, 8*w - 53],\ [2141, 2141, 4*w - 49],\ [2141, 2141, -4*w - 45],\ [2143, 2143, 32*w - 63],\ [2143, 2143, -32*w - 31],\ [2161, 2161, 50*w + 67],\ [2161, 2161, 50*w - 117],\ [2243, 2243, 28*w + 19],\ [2243, 2243, 28*w - 47],\ [2269, 2269, 46*w - 105],\ [2269, 2269, 20*w - 73],\ [2287, 2287, 2*w - 49],\ [2287, 2287, -2*w - 47],\ [2293, 2293, 38*w - 81],\ [2293, 2293, 38*w + 43],\ [2297, 2297, 26*w - 37],\ [2297, 2297, -26*w - 11],\ [2311, 2311, 40*w - 87],\ [2311, 2311, 26*w - 85],\ [2333, 2333, -4*w - 47],\ [2333, 2333, 4*w - 51],\ [2347, 2347, -6*w - 47],\ [2347, 2347, 6*w - 53],\ [2371, 2371, -28*w - 17],\ [2371, 2371, 28*w - 45],\ [2381, 2381, 30*w - 53],\ [2381, 2381, 30*w + 23],\ [2389, 2389, -26*w - 9],\ [2389, 2389, 26*w - 35],\ [2393, 2393, -16*w - 51],\ [2393, 2393, 16*w - 67],\ [2399, 2399, 24*w - 19],\ [2399, 2399, 24*w - 5],\ [2423, 2423, 24*w - 17],\ [2423, 2423, 24*w - 7],\ [2447, 2447, 24*w - 13],\ [2447, 2447, 24*w - 11],\ [2467, 2467, 52*w - 121],\ [2467, 2467, 18*w - 71],\ [2473, 2473, 26*w - 33],\ [2473, 2473, -26*w - 7],\ [2503, 2503, 32*w - 59],\ [2503, 2503, 32*w + 27],\ [2531, 2531, -14*w - 51],\ [2531, 2531, 14*w - 65],\ [2549, 2549, 26*w - 31],\ [2549, 2549, -26*w - 5],\ [2551, 2551, 6*w - 55],\ [2551, 2551, -6*w - 49],\ [2593, 2593, 24*w - 83],\ [2593, 2593, 46*w - 103],\ [2609, 2609, -34*w - 31],\ [2609, 2609, 34*w - 65],\ [2617, 2617, -26*w - 3],\ [2617, 2617, 26*w - 29],\ [2633, 2633, -16*w - 53],\ [2633, 2633, 16*w - 69],\ [2671, 2671, 32*w + 25],\ [2671, 2671, 32*w - 57],\ [2677, 2677, -26*w - 1],\ [2677, 2677, 26*w - 27],\ [2687, 2687, 2*w - 53],\ [2687, 2687, -2*w - 51],\ [2699, 2699, 36*w - 71],\ [2699, 2699, -36*w - 35],\ [2707, 2707, 28*w - 39],\ [2707, 2707, -28*w - 11],\ [2711, 2711, 10*w - 61],\ [2711, 2711, -10*w - 51],\ [2719, 2719, 56*w + 75],\ [2719, 2719, 56*w - 131],\ [2729, 2729, 26*w - 25],\ [2729, 2729, 26*w - 1],\ [2741, 2741, -4*w - 51],\ [2741, 2741, 4*w - 55],\ [2753, 2753, 8*w - 59],\ [2753, 2753, -8*w - 51],\ [2767, 2767, -14*w - 53],\ [2767, 2767, 14*w - 67],\ [2789, 2789, 54*w - 125],\ [2789, 2789, 20*w - 77],\ [2797, 2797, 34*w - 63],\ [2797, 2797, 34*w + 29],\ [2801, 2801, 30*w - 47],\ [2801, 2801, -30*w - 17],\ [2803, 2803, 28*w - 37],\ [2803, 2803, -28*w - 9],\ [2837, 2837, 26*w - 7],\ [2837, 2837, 26*w - 19],\ [2843, 2843, 22*w - 81],\ [2843, 2843, 52*w - 119],\ [2857, 2857, 26*w - 17],\ [2857, 2857, 26*w - 9],\ [2903, 2903, 48*w - 107],\ [2903, 2903, 26*w - 89],\ [2909, 2909, 46*w - 101],\ [2909, 2909, 28*w - 93],\ [2939, 2939, -10*w - 53],\ [2939, 2939, 10*w - 63],\ [2957, 2957, 4*w - 57],\ [2957, 2957, -4*w - 53],\ [2971, 2971, 28*w - 33],\ [2971, 2971, -28*w - 5],\ [3001, 3001, 38*w - 75],\ [3001, 3001, -38*w - 37],\ [3011, 3011, -14*w - 55],\ [3011, 3011, 14*w - 69],\ [3041, 3041, -30*w - 13],\ [3041, 3041, 30*w - 43],\ [3061, 3061, 58*w - 135],\ [3061, 3061, 20*w - 79],\ [3079, 3079, 40*w + 41],\ [3079, 3079, 40*w - 81],\ [3109, 3109, -12*w - 55],\ [3109, 3109, 12*w - 67],\ [3119, 3119, 2*w - 57],\ [3119, 3119, -2*w - 55],\ [3137, 3137, -16*w - 57],\ [3137, 3137, 16*w - 73],\ [3163, 3163, 28*w - 27],\ [3163, 3163, 28*w - 1],\ [3181, 3181, -4*w - 55],\ [3181, 3181, 4*w - 59],\ [3187, 3187, 44*w + 49],\ [3187, 3187, 44*w - 93],\ [3209, 3209, -8*w - 55],\ [3209, 3209, 8*w - 63],\ [3217, 3217, 46*w - 99],\ [3217, 3217, 32*w - 103],\ [3221, 3221, 38*w - 73],\ [3221, 3221, -38*w - 35],\ [3229, 3229, 50*w - 111],\ [3229, 3229, 28*w - 95],\ [3251, 3251, 28*w - 5],\ [3251, 3251, 28*w - 23],\ [3299, 3299, 36*w + 29],\ [3299, 3299, 36*w - 65],\ [3307, 3307, 28*w - 9],\ [3307, 3307, 28*w - 19],\ [3313, 3313, 34*w + 23],\ [3313, 3313, 34*w - 57],\ [3319, 3319, 40*w - 79],\ [3319, 3319, -40*w - 39],\ [3323, 3323, 28*w - 11],\ [3323, 3323, 28*w - 17],\ [3331, 3331, 28*w - 15],\ [3331, 3331, 28*w - 13],\ [3347, 3347, 2*w - 59],\ [3347, 3347, -2*w - 57],\ [3391, 3391, -32*w - 15],\ [3391, 3391, 32*w - 47],\ [3413, 3413, 4*w - 61],\ [3413, 3413, -4*w - 57],\ [3433, 3433, 38*w + 33],\ [3433, 3433, 38*w - 71],\ [3449, 3449, 8*w - 65],\ [3449, 3449, -8*w - 57],\ [3467, 3467, 44*w + 47],\ [3467, 3467, 44*w - 91],\ [3469, 3469, -34*w - 21],\ [3469, 3469, 34*w - 55],\ [3511, 3511, -32*w - 13],\ [3511, 3511, 32*w - 45],\ [3517, 3517, 46*w - 97],\ [3517, 3517, 46*w + 51],\ [3527, 3527, 26*w - 93],\ [3527, 3527, 56*w - 127],\ [3557, 3557, 28*w - 97],\ [3557, 3557, 54*w - 121],\ [3571, 3571, 30*w - 101],\ [3571, 3571, 52*w - 115],\ [3583, 3583, 2*w - 61],\ [3583, 3583, -2*w - 59],\ [3613, 3613, -12*w - 59],\ [3613, 3613, 12*w - 71],\ [3617, 3617, -34*w - 19],\ [3617, 3617, 34*w - 53],\ [3623, 3623, -32*w - 11],\ [3623, 3623, 32*w - 43],\ [3637, 3637, 38*w - 69],\ [3637, 3637, 38*w + 31],\ [3659, 3659, 36*w + 25],\ [3659, 3659, 36*w - 61],\ [3671, 3671, -10*w - 59],\ [3671, 3671, 10*w - 69],\ [3673, 3673, 16*w - 77],\ [3673, 3673, -16*w - 61],\ [3691, 3691, -6*w - 59],\ [3691, 3691, 6*w - 65],\ [3697, 3697, 8*w - 67],\ [3697, 3697, -8*w - 59],\ [3719, 3719, 64*w - 149],\ [3719, 3719, 22*w - 87],\ [3721, 61, -61],\ [3727, 3727, 32*w - 41],\ [3727, 3727, -32*w - 9],\ [3739, 3739, 44*w + 45],\ [3739, 3739, 44*w - 89],\ [3761, 3761, 30*w - 23],\ [3761, 3761, 30*w - 7],\ [3793, 3793, 62*w - 143],\ [3793, 3793, 24*w - 91],\ [3821, 3821, 30*w - 17],\ [3821, 3821, 30*w - 13],\ [3823, 3823, 32*w - 39],\ [3823, 3823, -32*w - 7],\ [3833, 3833, 38*w - 67],\ [3833, 3833, 38*w + 29],\ [3851, 3851, 60*w - 137],\ [3851, 3851, 26*w - 95],\ [3863, 3863, 48*w - 101],\ [3863, 3863, 48*w + 53],\ [3877, 3877, 12*w - 73],\ [3877, 3877, -12*w - 61],\ [3889, 3889, 34*w - 49],\ [3889, 3889, -34*w - 15],\ [3911, 3911, -32*w - 5],\ [3911, 3911, 32*w - 37],\ [3919, 3919, 30*w - 103],\ [3919, 3919, 56*w - 125],\ [3923, 3923, 52*w - 113],\ [3923, 3923, 34*w - 111],\ [3929, 3929, 32*w - 107],\ 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109],\ [9059, 9059, 60*w + 49],\ [9091, 9091, 52*w - 75],\ [9091, 9091, -52*w - 23],\ [9103, 9103, 56*w - 93],\ [9103, 9103, -56*w - 37],\ [9127, 9127, 64*w - 123],\ [9127, 9127, -64*w - 59],\ [9133, 9133, 36*w - 139],\ [9133, 9133, 98*w - 227],\ [9137, 9137, -8*w - 93],\ [9137, 9137, 8*w - 101],\ [9161, 9161, 70*w - 143],\ [9161, 9161, 70*w + 73],\ [9181, 9181, 50*w - 63],\ [9181, 9181, -50*w - 13],\ [9199, 9199, 2*w - 97],\ [9199, 9199, -2*w - 95],\ [9227, 9227, 26*w - 123],\ [9227, 9227, -26*w - 97],\ [9239, 9239, 96*w - 221],\ [9239, 9239, 38*w - 143],\ [9257, 9257, 54*w - 83],\ [9257, 9257, -54*w - 29],\ [9281, 9281, 62*w - 115],\ [9281, 9281, 62*w + 53],\ [9283, 9283, -52*w - 21],\ [9283, 9283, 52*w - 73],\ [9337, 9337, 32*w - 133],\ [9337, 9337, -32*w - 101],\ [9341, 9341, -4*w - 95],\ [9341, 9341, 4*w - 99],\ [9349, 9349, 74*w - 155],\ [9349, 9349, 74*w + 81],\ [9371, 9371, 60*w + 47],\ [9371, 9371, 60*w - 107],\ [9397, 9397, 58*w + 41],\ [9397, 9397, 58*w - 99],\ [9403, 9403, 92*w - 209],\ [9403, 9403, 42*w - 151],\ [9409, 97, -97],\ [9419, 9419, 76*w + 85],\ [9419, 9419, 76*w - 161],\ [9431, 9431, 48*w - 5],\ [9431, 9431, 48*w - 43],\ [9433, 9433, 24*w - 121],\ [9433, 9433, -24*w - 97],\ [9437, 9437, -28*w - 99],\ [9437, 9437, 28*w - 127],\ [9439, 9439, -18*w - 95],\ [9439, 9439, 18*w - 113],\ [9461, 9461, 90*w - 203],\ [9461, 9461, 44*w - 155],\ [9467, 9467, -52*w - 19],\ [9467, 9467, 52*w - 71],\ [9473, 9473, 78*w - 167],\ [9473, 9473, 56*w - 179],\ [9511, 9511, 54*w - 175],\ [9511, 9511, 80*w - 173],\ [9521, 9521, -16*w - 95],\ [9521, 9521, 16*w - 111],\ [9533, 9533, 52*w - 171],\ [9533, 9533, 82*w - 179],\ [9539, 9539, 50*w - 167],\ [9539, 9539, 84*w - 185],\ [9587, 9587, 2*w - 99],\ [9587, 9587, -2*w - 97],\ [9601, 9601, 50*w - 57],\ [9601, 9601, -50*w - 7],\ [9613, 9613, 62*w - 113],\ [9613, 9613, 62*w + 51],\ [9623, 9623, 48*w - 11],\ [9623, 9623, 48*w - 37],\ [9631, 9631, 30*w - 131],\ [9631, 9631, -30*w - 101],\ [9643, 9643, 52*w - 69],\ [9643, 9643, -52*w - 17],\ [9677, 9677, -66*w - 61],\ [9677, 9677, 66*w - 127],\ [9689, 9689, -54*w - 25],\ [9689, 9689, 54*w - 79],\ [9733, 9733, 4*w - 101],\ [9733, 9733, -4*w - 97],\ [9739, 9739, 100*w - 231],\ [9739, 9739, 38*w - 145],\ [9743, 9743, 48*w - 31],\ [9743, 9743, 48*w - 17],\ [9749, 9749, -20*w - 97],\ [9749, 9749, 20*w - 117],\ [9767, 9767, 48*w - 19],\ [9767, 9767, 48*w - 29],\ [9791, 9791, 48*w - 25],\ [9791, 9791, 48*w - 23],\ [9811, 9811, -52*w - 15],\ [9811, 9811, 52*w - 67],\ [9817, 9817, 74*w + 79],\ [9817, 9817, 74*w - 153],\ [9839, 9839, 64*w + 55],\ [9839, 9839, 64*w - 119],\ [9851, 9851, 68*w - 133],\ [9851, 9851, -68*w - 65],\ [9859, 9859, -18*w - 97],\ [9859, 9859, 18*w - 115],\ [9907, 9907, 76*w + 83],\ [9907, 9907, 76*w - 159],\ [9929, 9929, 8*w - 105],\ [9929, 9929, -8*w - 97],\ [9941, 9941, -58*w - 37],\ [9941, 9941, 58*w - 95],\ [9949, 9949, -50*w - 1],\ [9949, 9949, 50*w - 51]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [1, 0, 2, 2, 6, 2, -8, -4, -6, 4, 8, -8, -8, 2, -2, 10, -12, 8, 0, 4, 4, 16, -6, 10, -10, -14, 8, -16, -14, -8, 8, -6, -6, -6, 14, -16, 24, -14, -10, 0, 20, 0, 0, -8, -24, -22, -2, 24, -8, 8, 20, -22, 10, -16, 8, -16, 0, 18, 18, -10, -14, 4, -16, -8, 20, -2, 10, -6, -6, 0, -24, 6, 2, 0, 32, 6, 2, 26, -6, 34, -26, 18, 2, -24, 20, 10, -22, -22, 30, 8, 8, -24, 12, -16, 28, 22, -14, 16, -4, 34, -6, -18, -4, 24, 42, 10, 26, -6, 0, 12, -30, -30, 0, 8, 26, -18, 0, -40, -8, -16, 36, -16, 38, 2, 26, 14, 8, 16, 50, 22, -8, 44, 2, 38, -38, -6, 34, 2, -2, 42, 2, -26, 14, -6, 10, 44, 16, 24, 8, -48, -28, 0, 24, 18, -46, 10, 42, -62, 8, 32, 32, 12, 2, 18, 40, -12, 10, -34, 10, -6, -24, 8, -48, -8, -42, 18, 16, -48, 26, -54, 0, 16, 18, 22, -64, 36, 4, -16, 38, -30, -56, -16, -38, -50, -22, 10, -68, 16, 54, 18, -8, -24, -64, 68, 52, -40, 6, 2, 56, 36, -16, -64, -46, 66, 58, 6, 66, -58, 2, 2, -30, -48, -28, -54, -34, 40, 48, -22, -66, -16, -16, 26, 10, 40, 4, 0, 48, -8, 16, -56, -44, -32, -24, -50, 58, 12, 0, 48, -32, 38, 2, 56, 32, -14, -42, -24, 12, 58, 26, -48, -44, 2, 80, 20, -66, 10, 66, -30, -54, 30, 44, -24, 42, 26, -32, 0, 58, -70, 16, -56, 60, 32, -10, 50, 10, 58, -60, 48, -8, 72, -34, -22, 56, 24, 8, 0, -30, -30, 66, -30, 8, -72, -54, 30, -44, 80, -38, 58, -42, -78, -32, 12, -56, -32, 82, 54, -20, -40, 72, -16, -46, -14, 56, -4, -54, 10, 50, 54, 40, -8, 50, 34, -8, 44, -82, -6, -16, -64, -42, -46, -54, -22, 80, 8, 34, -58, -64, 12, -84, 88, 74, 30, -82, -6, -14, 82, 64, 64, 88, 48, 48, 0, 60, 8, -30, 34, 32, -24, 20, 48, 14, -38, -24, 80, 42, 74, -78, 18, -22, 10, -6, 26, -80, -96, 38, -62, 40, 24, 68, 72, 28, -72, 0, 40, -40, -24, 42, 42, 38, -94, 2, 34, 8, -88, -54, 62, 46, -38, -14, -78, 16, 4, -10, -78, 24, 36, 2, 34, 40, -80, 26, -18, -68, 0, 10, 30, -100, -32, 90, -70, 32, -60, 66, -78, -34, 42, -64, -72, -22, -66, -40, -72, -78, -78, -72, -60, -102, 78, 36, 80, -22, 10, -46, 18, -18, -6, 70, 34, 24, 60, -40, 12, -92, 40, 74, -22, -80, -40, -56, -108, 28, -88, 100, 48, -64, 32, -18, -6, -6, -38, -6, 106, -12, 24, 58, 14, -96, -8, -2, 74, -32, -72, 66, 70, -68, -8, 88, -56, -2, -86, 114, -62, -96, 40, -86, 62, 20, 24, -96, 8, 18, -14, -12, 56, 18, 82, 0, -88, 74, 40, 8, 48, 44, -86, -22, -94, 2, -18, 90, 72, -24, -6, -54, -92, -88, -88, 48, -86, 62, 50, -110, 32, -24, -56, -56, -84, 104, 10, 74, -48, -20, 16, 8, -124, -96, -42, -78, 118, 18, 24, -60, -48, 96, -50, 26, 100, -96, -72, 72, -14, -62, -122, 66, 12, 0, -94, 6, 82, 82, 58, 42, 2, -90, -8, 16, -30, 50, -120, -4, 0, 48, -68, 0, -14, 82, 80, -40, 18, 18, 4, -112, -106, 114, 22, -78, -70, 90, -128, 16, -16, -84, 50, -14, -68, -80, -100, 8, -96, 16, 68, -8, -14, -42, 56, -24, 76, 120, 90, 58, -22, -22, 18, 98, 0, 88, 8, 44, 64, 48, -120, -64, -38, 58, 18, -74, 10, 94, -32, 56, 82, 118, -18, -102, 96, 4, 48, -64, 16, 24, 90, -18, 56, 112, -72, 92, -72, -88, 2, 4, -8, 10, -134, 16, 16, -124, 40, -10, 50, 10, 58, 24, -88, 108, -48, -30, 82, -16, 32, -22, 30, -44, 88, -110, 22, 10, 30, -96, 0, -96, 56, -32, -116, 34, -12, 48, 24, 48, -54, 126, -20, 0, 18, -110, -40, -88, 104, 68, -88, 128, 18, 18, 58, -6, 16, 124, -72, 76, 98, -126, 40, -48, -2, 10, -76, 8, -16, 104, -64, -8, -86, 62, 106, 10, -80, -20, 6, -30, -82, -102, 48, 0, 114, 18, -108, -64, 90, 90, 42, 30, -92, 0, -120, 104, -54, -22, -78, -110, -82, -38, 60, 16, -50, -70, 58, -86, 90, 122, 144, 64, 114, -42, -16, 140, -50, 90, 32, 52, -86, -54, 110, 90, 34, -126, -62, -26, -136, 28, 138, -130, -82, -70, -96, 92, -30, 6, 2, -32, 88, -46, 2, 70, 2, -56, 152, 98, 102, 56, 100, -96, -120, -84, 8, 18, 34, 24, 64, -120, 96, -40, -24, -74, 146, -104, 84, 68, -8, -92, -16, -78, 118, -86, -118, 50, -142, -86, 138, 8, 140, -6, 10, -24, 60, -20, 128, -78, -110, 78, -70, -46, -62, -64, 104, 74, -54, -56, -136, 42, -98, -156, -136, 90, 46, -128, 152, -126, -110, 90, -114, 44, -8, 40, -104, -18, -102, -134, 78, -142, -142, -116, 80, -144, 24, 160, 48, 30, 74, 40, 100, 24, 40, 2, -46, -102, 122, -112, 136, 48, -8, 40, -20, 10, -86, 40, 128, -54, -162, 100, 40, 18, -14, -50, 90, 148, 144, -6, 90, 26, 154, -48, 68, 138, -22, 8, -164, 18, 18, 106, -54, 120, 52, 100, 0, -46, -78, 24, -28, 98, 70, -134, 90, -62, -26, -64, -96, 120, 128, -72, 92, -72, -32, -158, 34, -22, 94, 28, 56, 72, 0, -90, 98, -168, -72, -70, -22, -54, 126, 58, 90, 10, -66, 20, 72, -46, -30, -16, 120, -50, -6, -100, -24, -78, -62, -134, -38, 8, -28, -32, 104, -144, 12, -134, -50, -82, -70, 120, -168, 174, -38, 12, 104, -70, 90, -176, 4, -110, -46, 140, -80, -66, 138, -24, 140, 80, 40, 112, -16, -102, -70, 160, 24, 86, -110, 10, -86, 104, -124, -22, 74, -126, 6, 8, -100, 24, 176, -80, -128, 136, -168, -32, -108, 6, -126, 66, -78, 74, -150, 8, -104, -50, -38, -96, 112, -156, 48, 74, 62, 50, 162, -78, 114, 104, -88, -142, -78, -112, -100, 114, -14, 64, -168, -8, -100, 30, -86, -32, -128, -160, 88, 34, -14, -18, -6, 112, 88, 34, -90, 4, -8, 2, 130, 74, -34, 58, -50, 0, -8, -156, 64, 106, -70, 164, -112, 78, 26, 32, -140, 72, -100, -8, -52, 48, -128, 144, 56, -26, 34, -134, 154, 42, -86, 142, -70, 8, 40, 52, 120, 40, 112, -182, 42, -30, 98, -64, 4, 114, 50, -102, 142, 114, 86, 36, -168, 158, -86, -28, 184, 2, -104, 180, 120, 64, 58, 90, -50, -134, 64, -96, -78, -74, 192, -164, -6, 90, 88, -80, 162, 162, 134, 162, 8, 60, -36, 120, 90, 122, 94, 106, -48, -24, 120, 168, -120, 4, 2, 102, 170, -54, -42, -142, -116, 32, -128, 80, 90, 142, 8, 0, 24, -152, 132, -144, -86, -118, 72, 40, -56, -76, -80, -44, 56, -4, 170, 10, 138, 94, -26, 130] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([2, 2, -w + 2])] = -1 AL_eigenvalues[ZF.ideal([2, 2, -w - 1])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]