/* 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([676,338,-20*w + 42]) 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, -1, -2, -2, 0, -6, 4, -4, -2, 4, 4, 0, 0, -14, -6, -6, -12, 12, -4, 4, -12, 12, -6, 6, -6, -6, 8, 8, -14, -16, -16, -18, 18, 6, -6, 8, -8, -14, -14, 12, 12, 0, 0, 16, -16, -22, 22, 0, 0, -12, -12, -6, -6, 24, 24, 16, -16, 18, -18, 6, -6, -20, 20, 4, -4, -34, 34, -6, 6, -24, 24, -22, -22, 0, 0, 6, 6, -2, 2, 26, -26, 14, 14, 12, 12, 10, -10, -18, 18, -32, 32, 36, 36, 12, 12, -18, 18, -20, -20, 14, -18, 18, 36, 36, 6, 6, -38, 38, 12, -12, -18, 18, 24, 24, 10, -10, -8, 8, -24, -24, 12, 12, 10, -10, -30, -30, -8, -8, -14, 14, 44, -44, -22, -22, 30, -30, -10, 10, -54, 54, -18, -18, 34, 34, 50, 4, 4, 48, -48, -44, -44, 40, 40, 2, 2, 6, 6, -62, -8, 8, 12, 12, 18, -18, -12, 12, 2, -2, -10, 10, -32, -32, 56, 56, 2, 2, -32, 32, -42, 42, -48, 48, -42, -42, 28, -28, 52, 52, 18, -18, -24, -24, -58, 58, -38, -38, 12, -12, 18, 18, -16, 16, -60, -60, 4, 4, 54, 54, -12, 12, 16, 16, -18, -18, -2, -18, 18, -38, -38, 54, -54, 12, 12, -26, -26, -8, -8, 14, 14, -32, 32, -42, -42, -28, -28, -48, 48, -72, -72, -52, -52, 56, 56, 50, -50, -44, 44, -48, -48, -14, 14, 72, -72, 30, 30, 36, -36, -34, 34, 36, 36, -50, -4, -4, -78, 78, 18, -18, -54, -54, 28, -28, -70, 70, 32, 32, 22, 22, -40, 40, 60, -60, 46, -46, -10, 10, -12, -12, -48, -48, 10, -10, 0, 0, -40, 40, 66, 66, 18, -18, -80, -80, 6, 6, 28, -28, 10, 10, 30, -30, 84, 84, 72, -72, 38, 38, 44, 44, -72, 72, 2, 2, -36, 36, -42, -42, 78, 78, -80, 80, -50, -50, -12, 12, 62, -62, -80, -80, 10, -10, -6, -6, 40, 40, -18, 18, -20, 20, 76, -76, 18, -18, 70, 70, -18, -18, -96, 96, 24, -24, -48, -48, 52, 52, -94, -94, -56, 56, 60, 60, 90, 90, 40, 40, 38, -38, 6, 6, 70, 70, -18, 18, 16, -16, 22, 22, 48, 48, -36, 36, -68, -68, 24, -24, -16, 16, -18, -18, 42, -42, -54, -54, -32, 32, 42, -42, -46, 46, -6, 6, -20, 20, 42, 42, 12, 12, -98, -98, 72, 72, -66, -66, -60, -60, 18, -18, -28, 28, 58, -58, 60, -60, 30, 30, -70, 70, 56, -56, -22, 22, 0, 0, -30, -30, -76, -76, -46, -46, -20, 20, 54, -54, 14, -14, -6, -6, -46, 46, 36, 36, 108, 108, -68, 68, 74, -74, -88, -88, 12, -12, -20, -20, 12, -12, 64, -64, -6, 6, -14, -14, -6, -6, 60, 60, -50, 50, -8, -8, -62, 62, -72, -72, 90, -90, -100, -100, -16, 16, 98, 98, -30, -30, -24, -24, 58, 58, 60, -60, 24, -24, 46, -46, -100, -100, 58, -58, -72, -72, 50, 32, 32, -68, 68, -54, -54, -58, -58, -18, -18, 64, 64, -90, 90, 36, 36, 72, -72, 86, 86, 70, -70, -72, 72, -64, 64, 36, 36, -30, -30, -68, 68, -56, -56, -28, -28, -66, -66, -10, -10, 44, 44, -48, -48, -34, 34, 68, 68, 48, -48, -98, 98, -90, -90, -84, 84, -78, -78, -62, 62, -6, 6, 6, 6, 88, -88, -18, -18, 12, -12, 48, -48, -60, 60, 94, -94, 8, -8, 6, -6, 20, 20, 42, -42, -102, -102, -38, 38, 48, 48, -68, -68, 2, -2, -12, -12, -84, -84, -16, 16, 44, 44, 78, 78, -112, 112, -84, 84, 42, -42, 74, 74, -66, 66, 120, 120, 36, -36, 48, -48, -88, -88, 30, 30, -94, -94, 2, 2, 120, 120, -30, 30, -46, 46, -60, -60, 48, 48, -56, 56, -18, 18, -40, 40, -4, 4, 80, -80, -110, 84, -84, 6, -6, 0, 0, -60, -60, -62, 62, 38, 38, -80, -80, -60, -60, 30, -30, 80, -80, 138, -138, -28, -28, 54, -54, 18, 18, -96, -96, -72, -72, -76, 76, -146, 68, 68, 72, -72, 54, 54, -12, 12, 18, -18, -16, -16, -124, 124, -8, -8, 42, -42, 82, -82, 12, 12, 12, -12, 58, 58, 56, -56, -58, 58, -140, -140, 120, 120, 8, -8, -38, 38, 102, -102, -4, -4, -90, -90, -30, -30, -144, -144, 62, 62, 20, -20, 114, 114, -6, 6, 68, 68, 64, -64, -30, -30, 10, -10, 54, -54, -12, -12, 82, -82, 134, -134, -138, 138, -48, -48, 106, -106, 68, -68, 54, -54, 52, 52, 134, -134, 6, 6, -34, 34, -86, -86, -4, -4, -30, 30, 90, 90, -60, 60, -126, 126, -130, -88, 88, 114, 114, -114, -114, 80, -80, -58, 58, -12, 12, -24, 24, 132, -132, -62, 62, -8, -8, 24, -24, 112, 112, -122, -122, 28, 28, -52, 52, 44, 44, -154, 154, 54, 54, -14, 14, -122, -122, 28, -28, 70, 70, -12, 12, 20, -20, 58, 58, 90, 90, -146, -146, 88, 88, -102, 102, -48, 48, -110, -110, 84, -84, 94, -94, 72, -72, -78, 78, 6, -6, 44, -44, 48, -48, -42, -42, 74, -74, 70, -70, 36, 36, 24, -24, -112, -112, -150, 150, -60, -60, 16, -16, 110, -110, -138, -138, 120, 120, 104, 104, 156, -156, 30, 30, -88, 88, 66, 66, -92, 92, 86, 86, -142, -142, 132, 132, 82, -82, -58, -58, -20, -20, 138, 138, 52, 52, 114, -114, -70, -70, 60, -60, -36, -36, 66, -66, -84, 84, 14, 14, 146, -146, -118, 118, 96, 96, -88, -88, -28, 28, 120, -120, -150, 150, -58, -58, 68, 68, -24, 24, -38, 38, 0, 0, -22, 22, -90, -90, -6, 6, -114, -114, -76, 76, 62, -62, -40, -40, -126, -126, 12, 12, 66, -66, 138, 138, -100, -100, 24, -24, -28, -28, -66, 66, 10, -10, -96, -96, 102, -102, 156, 156, -58, -58, -20, 20, -14, 14, -60, -60, 114, -114, -132, -132, 104, -104, 64, -64, -150, -150, -56, -56, -82, -82, 10, 10, -132, -132, 122, -122, -122, -122, -76, 76, 120, 120, -16, 16, 144, 144, 148, 148, 42, 42, 66, -66, 50, -50, 144, -144, 22, 22, -16, -16, -84, 84, 30, -30, -50, 50, 34, 34, -64, -64, 10, 10, 12, -12, 6, 6, 24, -24, -156, 156, -70, 70, 0, 0, 8, 8, -18, -18, -126, 126, -40, 40, -14, -14, 76, -76, 106, -106, 42, -42, -82, -82, -120, 120, -60, 60, 10, -10, -108, 108, -150, 150, -44, 44, -180, 180, -140, -140, -176, -176, 136, 136, -94, 94, 150, -150, -78, -78, 190, 190, -32, 32, -60, -60, 120, 120, 150, 150, -30, -30, -4, -4, -50, -50, -162, 162, -26, 26, -180, 180, -122, 122, -172, -172, 94, 132, -132, 24, -24, 26, -26, -66, -66, 160, 160, -138, -138, -132, -132, -90, -90, -8, 8, 174, -174, 78, 78, -84, -84, 36, -36, -26, 26, -110, 110, 120, 120, 176, -176, 4, 4, 66, -66, 30, 30, 38, 38, -52, 52, -48, 48, 6, 6, 24, 24, 144, -144, 140, 140, -98, 98, 0, 0, -180, -180, -28, 28, -28, -28, 54, 54, -102, -102, -46, -46] 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 + 1])] = 1 AL_eigenvalues[ZF.ideal([2,2,w - 2])] = -1 AL_eigenvalues[ZF.ideal([13,13,2*w + 1])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]