/* 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([144,48,-3*w + 15]) 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 - 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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^3 - 7*x - 2 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, 0, -1, e^2 - 2*e - 5, -e^2 + 3, 2*e, -e^2 + 5, e^2 - 2*e - 3, -e^2 - 2*e + 5, -e^2 - 2*e + 7, -e^2 + 2*e + 3, -2*e + 2, -2*e^2 + 10, -2*e^2 + 2*e + 6, 6, 2*e^2 - 2*e - 10, 4, 4, 2*e^2 + 2*e - 8, 4, 2*e^2 - 6, -2*e^2 + 14, -4*e^2 + 18, 4*e^2 - 4*e - 18, 2*e^2 - 16, -2*e^2 + 4*e + 8, -e^2 + 9, e^2 + 2*e + 5, 3*e^2 - 6*e - 15, -3*e^2 - 2*e + 21, 3*e^2 - 4*e - 15, 2*e^2 + 4*e - 16, -2*e^2 - 4*e + 12, -2*e - 8, -2*e^2 + 8*e + 16, 2*e^2 - 2*e, 4*e - 4, -3*e^2 + 6*e + 19, -3*e^2 - 6*e + 15, 2*e^2 - 4*e - 26, 2*e + 10, -2*e^2 - 6*e + 24, 4*e^2 - 4*e - 24, -3*e^2 - 2*e + 5, -3*e^2 + 6*e + 21, 8*e + 2, -2*e^2 - 2*e + 6, 2*e^2 + 2*e - 4, 4*e^2 - 28, -2*e^2 - 2, -6*e + 10, 4*e^2 - 22, -18, -2*e^2 + 12*e + 14, 2*e^2 + 6, 3*e^2 + 2*e - 5, -e^2 - 2*e + 11, 2*e^2 - 6*e - 18, 2*e^2 - 2*e - 22, -4*e^2 + 26, -2*e^2 + 2*e - 10, -4*e^2 + 4*e + 20, -4*e^2 + 4*e + 20, 5*e^2 + 2*e - 35, 5*e^2 - 2*e - 15, e^2 - 6*e + 11, e^2 - 2*e - 9, 4*e^2 - 6*e - 28, 8*e^2 - 2*e - 36, -2*e^2 - 4*e + 22, 8*e^2 - 10*e - 38, 2*e^2 - 2*e - 30, 4*e + 6, 4*e^2 + 4*e - 8, 4*e - 4, 2, 8*e - 14, -5*e^2 + 2*e + 21, 3*e^2 - 6*e - 11, -3*e^2 + 6*e + 31, -e^2 + 4*e + 23, 5*e^2 - 39, e^2 - 4*e - 15, 6*e^2 - 10, -2*e - 10, -e^2 + 12*e - 5, -5*e^2 - 8*e + 35, -6*e + 4, 6*e^2 - 8*e - 16, -2*e^2 + 6*e + 4, -8*e^2 + 8*e + 40, 4*e - 16, -2*e^2 - 10*e + 8, -2*e^2 - 4*e + 2, 4*e^2 + 6*e - 22, 2*e^2 - 4, -4*e^2 + 2*e, -6*e^2 + 2*e + 24, -4*e^2 + 12*e + 20, e^2 - 4*e + 17, -2*e^2 + 4*e - 16, 2*e^2 + 8*e, 2*e^2 + 8*e - 30, 2*e^2 - 8*e + 2, -2*e^2 + 8*e + 4, -2*e^2 + 4*e + 8, 3*e^2 + 10*e - 7, 3*e^2 + 2*e - 31, -4*e^2 - 8*e + 24, -6*e^2 - 2*e + 28, 4*e^2 + 4*e - 22, -8*e^2 - 4*e + 30, -4*e^2 - 12*e + 24, -8*e^2 - 4*e + 36, 5*e^2 - 6*e - 49, -7*e^2 + 10*e + 43, -3*e^2 - 6*e + 9, e^2 - 2*e + 9, -4*e^2 + 8*e - 4, -2*e^2 + 14*e + 12, -4*e - 16, 4*e^2 + 4*e + 4, e^2 + 2*e + 27, -3*e^2 + 2*e + 31, 6*e^2 - 4*e - 48, 2*e^2 - 8, 4*e^2 - 4*e - 48, 8*e, -4*e^2 + 12*e + 22, 8*e + 22, 7*e^2 + 8*e - 27, -7*e^2 + 14*e + 53, e^2 + 2*e - 1, -e^2 - 4*e - 17, -8*e^2 + 14, -8*e^2 - 8*e + 38, -e^2 + 6*e + 17, -13*e^2 + 2*e + 49, 2*e^2 - 4*e - 28, -2*e^2 - 4*e + 16, 6*e - 8, 2*e^2 - 8*e + 4, 8*e^2 - 42, -8*e - 10, 4*e^2 - 10, 4*e^2 + 4*e - 28, -8*e - 12, -6*e^2 + 12*e + 26, 2*e^2 + 14, e^2 - 8*e - 37, 3*e^2 + 6*e - 29, 3*e^2 - 2*e - 57, -e^2 - 6*e - 25, -4*e^2 - 18, -4*e^2 - 8*e + 22, 6*e^2 - 4*e - 36, 2*e^2 + 8*e + 4, 6*e^2 + 2*e - 18, -e^2 - 6*e - 9, -5*e^2 - 2*e + 15, 10*e^2 - 8*e - 46, -2*e^2 - 4*e - 6, -2*e^2 + 8*e - 4, -6*e^2 + 12*e + 28, -8*e^2 + 4*e + 24, 4, -e^2 + 6*e + 5, e^2 + 4*e - 19, -e^2 + 23, 7*e^2 - 17, -9*e^2 + 8*e + 33, 9*e^2 - 6*e - 19, 7*e^2 - 10*e - 61, -e^2 + 14*e - 5, -7*e^2 - 16*e + 41, -5*e^2 + 14*e + 49, -7*e^2 - 6*e + 13, 3*e^2 + 12*e - 15, -8*e^2 - 4*e + 22, 4*e + 6, 4*e^2 + 16*e - 20, 8*e^2 - 4*e - 52, 4*e^2 - 10, 4*e - 18, 5*e^2 - 10*e - 31, -3*e^2 + 2*e + 45, -3*e^2 + 10*e + 37, -e^2 + 16*e + 5, -4*e^2 - 4*e + 34, -4*e^2 + 8*e + 30, -6*e^2 - 8*e + 22, 2*e^2 + 8*e - 34, -5*e^2 - 14*e + 33, -5*e^2 + 14*e + 5, -7*e^2 + 2*e + 43, -7*e^2 + 2*e + 43, -10*e^2 + 20*e + 58, -14*e^2 + 12*e + 54, -6, 4*e^2 - 16*e - 18, -8*e^2 + 64, -2*e^2 - 2*e - 4, 6*e^2 + 8*e - 10, 8*e^2 - 6*e - 22, 8*e^2 - 8*e - 36, -24*e + 4, -4*e^2 + 20*e + 34, 4*e^2 - 8*e - 2, -4*e^2 + 8*e + 40, -10*e^2 + 6*e + 56, -9*e^2 + 20*e + 53, e^2 - 18*e + 1, 10*e^2 - 72, 2*e^2 + 12*e + 20, -8*e^2 + 4*e + 14, -2*e^2 + 4*e + 40, 2*e^2 - 4*e - 28, 7*e^2 + 14*e - 23, -5*e^2 + 14*e + 5, -6*e^2 + 6*e + 34, -6*e^2 + 14*e + 26, 4*e^2 + 12*e - 44, -10*e^2 + 10*e + 28, -16*e + 10, 2*e^2 + 2*e - 50, 9*e^2 + 8*e - 57, -9*e^2 + 14*e + 35, 3*e^2 - 6*e + 9, 11*e^2 + 6*e - 43, 8*e^2 + 16*e - 48, -8*e + 8, 4*e^2 - 70, 8*e^2 - 12*e - 30, 2*e^2 + 14*e - 12, 4*e^2 + 8*e - 64, 2*e^2 - 12*e - 30, -6*e - 10, 2*e^2 - 20*e - 14, 8*e^2 - 2*e + 2, 4*e^2 + 12*e - 52, -4*e^2 - 20*e + 20, 11*e^2 - 14*e - 29, -5*e^2 - 14*e + 11, 5*e^2 + 4*e - 71, -e^2 + 2*e + 41, 7*e^2 + 10*e - 45, -9*e^2 - 2*e + 31, -16*e^2 + 2*e + 78, -6*e^2 - 8*e + 54, 3*e^2 - 2*e - 11, -9*e^2 - 10*e + 57, 12*e^2 - 12*e - 72, -8*e^2 - 20*e + 68, -14*e^2 + 4*e + 28, 2*e^2 - 8*e - 32, 6*e^2 - 8*e + 22, -2*e + 30, -8*e^2 - 4*e + 34, -4*e^2 - 8*e + 50, -6*e^2 - 4*e + 22, 10*e^2 - 28*e - 66, -5*e^2 + 6*e + 9, -7*e^2 - 20*e + 47, 19*e^2 - 6*e - 81, -6*e^2 + 12*e + 72, 12*e^2 - 14*e - 48, -8*e^2 - 18*e + 68, -8*e^2 + 2*e + 48, 2*e^2 - 14*e - 46, 8*e^2 - 8*e - 42, 5*e^2 - 2*e - 7, 21*e^2 - 6*e - 67, 3*e^2 - 2*e + 17, 11*e^2 - 18*e - 39, -4*e^2 - 4*e + 32, -4*e^2 + 12*e - 8, -12*e^2 + 4*e + 26, 12*e^2 - 4*e - 54, -3*e^2 - 10*e - 11, e^2 - 6*e - 11, -2*e^2 - 12*e - 14, 2*e^2 + 4*e + 46, -3*e^2 + 8*e + 29, -e^2 - 18*e + 29, e^2 - 27, 9*e^2 - 16*e - 19, 6*e^2 + 4*e - 14, -10*e^2 + 16*e + 38, 14*e^2 + 2*e - 80, -8*e^2 + 20*e + 28, -4*e^2 + 74, 8*e^2 - 12*e - 38, 4*e + 12, 12*e^2 - 4*e - 56, 7*e^2 - 12*e - 51, -3*e^2 + 2*e + 9, -14*e^2 + 4*e + 64, -2*e^2 + 24, 10*e^2 + 4*e - 56, 6*e^2 - 20*e - 60, -2*e^2 + 14*e + 44, 4*e^2 - 4*e - 24, 2*e^2 + 4*e - 12, -2*e^2 + 12*e + 8, -8*e^2 + 76, 4*e^2 - 12*e - 52, 5*e^2 + 12*e - 27, -15*e^2 + 53, 10*e^2 - 4*e - 44, 6*e^2 - 12*e - 8, 4*e^2 - 12*e - 52, 4*e^2 - 4*e + 20, -10*e^2 + 24*e + 74, 6*e^2 - 12*e - 2, -8*e^2 + 12*e + 82, 4*e^2 + 8*e + 26, -15*e^2 + 22*e + 69, -e^2 - 11, -10*e^2 + 20*e + 30, -6*e^2 + 24*e + 38, -9*e^2 + 10*e + 33, -9*e^2 + 10*e + 1, 8*e^2 - 20*e - 64, -6*e^2 + 6*e - 20, 10*e^2 - 22*e - 34, -2*e^2 + 14*e + 6, 18*e^2 - 10*e - 90, 4*e^2 - 4*e + 46, 9*e^2 - 16*e - 25, -5*e^2 - 6*e - 5, -5*e^2 - 2*e - 15, 11*e^2 - 2*e - 63, 20*e^2 - 16*e - 88, 8*e^2 - 4*e - 8, 17*e^2 - 6*e - 37, -7*e^2 + 22*e + 71, 7*e^2 - 6*e - 65, 7*e^2 + 10*e - 57, 9*e^2 - 22*e - 21, 13*e^2 - 6*e - 73, 10*e^2 + 4*e - 36, -18*e^2 + 8*e + 52, 5*e^2 - 8*e - 53, 15*e^2 + 2*e - 41, 16*e^2 - 16*e - 46, 4*e^2 + 4*e - 78, 21*e^2 - 12*e - 93, 7*e^2 - 6*e - 77, 11*e^2 - 6*e - 41, 3*e^2 - 26*e - 13, -8*e^2 + 6*e, -14*e^2 - 24*e + 84, -3*e^2 + 13, 7*e^2 - 18*e - 3, 8*e^2 - 8*e - 10, -4*e^2 - 8*e + 2, 6*e^2 + 24*e - 54, -8*e^2 + 2*e + 6, -6*e^2 - 16*e + 46, 18*e^2 - 16*e - 74, 6*e - 6, 6*e^2 + 4*e - 66, 7*e^2 - 18*e - 89, -7*e^2 + 12*e + 63, 5*e^2 - 2*e - 33, 21*e^2 - 10*e - 73, -4*e^2 + 4*e + 24, -8*e - 56, 2*e^2 - 8*e - 30, 14*e^2 - 28*e - 86, -12*e^2 + 16*e + 30, -16*e^2 + 32*e + 90, -12*e^2 - 12*e + 64, 4*e^2 - 4*e - 32, 3*e^2 + 14*e - 59, -5*e^2 - 2*e + 93, -10*e^2 + 6*e + 70, 2*e^2 + 6*e - 70, -9*e^2 - 18*e + 45, 7*e^2 + 6*e + 5, -8*e^2 - 2*e + 4, 12*e^2 + 6*e - 88, -15*e^2 + 20*e + 91, -5*e^2 - 10*e + 31, -14*e^2 + 2*e + 78, 4*e^2 + 4*e + 2, 6*e^2 + 16*e - 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4*e + 38, -13*e^2 + 22*e + 63, -5*e^2 + 38*e + 95, -7*e^2 - 38*e + 115, -11*e^2 + 42*e + 7, 11*e^2 - 24*e - 61, -9*e^2 + 20*e + 59, -4*e^2 + 44*e - 12, -6*e^2 + 38*e + 36, 27*e^2 - 18*e - 87, 3*e^2 - 10*e - 167, 3*e^2 + 34*e - 19, -31*e^2 + 36*e + 133, -19*e^2 - 22*e + 53, -15*e^2 - 22*e + 81, 10*e^2 - 58*e - 40, 4*e^2 + 12, 31*e^2 - 16*e - 143, 17*e^2 - 30*e - 35, -10*e^2 + 12*e + 62, -18*e^2 + 12*e + 54, -11*e^2 + 20*e + 43, 3*e^2 - 2*e - 37, 22*e^2 - 60*e - 120, -22*e^2 + 4*e - 4, -24*e^2 + 12*e + 14, -4*e^2 + 48*e - 10, 37*e^2 - 22*e - 157, -11*e^2 + 18*e + 11, 4*e^2 + 20*e - 88, -4*e^2 - 4*e - 40, 6*e^2 + 2*e + 26, 8*e^2 - 12*e - 98, 16*e^2 - 20*e - 132, 10*e^2 + 14*e - 80, -34*e^2 + 18*e + 124, 12*e^2 + 20*e - 76, 2*e^2 + 2*e - 22, 8*e^2 + 8*e - 2, -e^2 + 46*e - 3, 7*e^2 - 10*e - 115, -16*e^2 + 4*e + 146, 24*e^2 - 4*e - 46, 4*e^2 + 36*e - 88, 24*e^2 - 144, -12*e^2 - 32*e + 42, 16*e^2 - 12*e - 150, 16*e^2 + 44*e - 112, -14*e^2 - 34*e + 116, 6*e^2 + 12*e - 148, 6*e^2 - 12*e + 84, 22*e^2 - 16*e - 142, -2*e^2 + 48*e - 6, 20*e^2 + 8*e - 8, 26*e^2 - 22*e - 104, -2*e^2 + 42*e + 10, -12*e^2 + 24*e + 46, -6*e^2 + 32*e + 86, -14*e^2 + 20*e + 170, 7*e^2 - 14*e - 17, -15*e^2 + 20*e + 163, 10*e^2 + 12, -6*e^2 - 28*e + 104, -18*e^2 + 20*e + 24, -18*e^2 + 28*e + 120, -28*e^2 - 4*e + 80, -18*e^2 - 42*e + 92, -15*e^2 + 10*e - 21, 21*e^2 + 2*e - 113, -16*e^2 + 48*e + 44, -18*e^2 - 2*e + 40, 23*e^2 + 42*e - 155, -13*e^2 - 18*e - 11, -8*e^2 - 38*e + 68, 14*e^2 + 12*e - 148, 9*e^2 + 6*e - 137, 9*e^2 - 30*e - 53, 4*e^2 - 18*e - 90, 14*e^2 + 32*e - 110, -10*e^2 - 38*e + 60, -8*e^2 - 4*e - 32, 11*e^2 - 36*e - 33, 11*e^2 - 4*e - 33, -6*e^2 - 14*e + 32, -4*e^2 - 56*e + 64, 38*e^2 - 28*e - 164, 16*e^2 + 22*e - 48, 33*e^2 - 20*e - 137, 7*e^2 - 10*e - 17, -12*e^2 + 24*e + 144, -12*e^2 - 24*e + 32, -21*e^2 + 153, -11*e^2 - 34*e + 105, 32*e^2 - 16*e - 88, 12*e^2 - 36*e - 24, 3*e^2 - 58*e - 41, -17*e^2 + 18*e + 39, -17*e^2 + 16*e + 131, -3*e^2 + 18*e + 27, 2*e^2 - 6*e - 106, -22*e^2 + 14*e + 122, -18*e^2 - 12*e + 52, -14*e^2 + 52*e + 64, -3*e^2 + 4*e - 15, -29*e^2 + 38*e + 97, 13*e^2 + 30*e - 139, -15*e^2 - 38*e + 109, 10*e^2 - 52*e - 50, -22*e^2 + 24*e + 146, -20*e^2 + 10*e + 114, 6*e^2 - 16*e - 22, 6*e^2 + 48*e - 56, 14*e^2 - 36*e - 60, 2*e^2 - 16*e - 28, -6*e^2 - 20*e + 144, 25*e^2 + 16*e - 85, 19*e^2 + 6*e - 61, -7*e^2 + 6*e - 45, 17*e^2 - 2*e - 93, -14*e^2 - 4*e + 68, -2*e^2 + 28*e - 32, 3*e^2 + 14*e + 81, 29*e^2 - 12*e - 167, -6*e^2 - 18*e - 52, 4*e - 8, 13*e^2 - 16*e + 13, 15*e^2 - 34*e - 123, -12*e^2 + 44*e + 60, -26*e^2 + 38*e + 200, -16*e^2 + 32*e + 82, 24*e^2 - 140, -2*e^2 - 38*e + 44, 2*e^2 - 14*e - 60, -40*e^2 + 4*e + 148, -17*e^2 + 54*e + 141, 23*e^2 - 26*e - 171, 8*e^2 - 126, 4*e^2 + 30, 3*e^2 - 14*e + 67, -25*e^2 + 30*e + 75, 24*e^2 - 32*e - 46, 24*e^2 - 48*e - 86, 6*e^2 + 12*e - 14, 10*e^2 + 40*e - 46, 30*e^2 - 36*e - 188, -22*e^2 + 12*e + 40, -3*e^2 - 18*e + 101, -15*e^2 + 10*e + 189, -10*e^2 - 20*e + 100, -14*e^2 + 24*e + 28, 2*e^2 - 28*e - 92, -42*e^2 + 20*e + 152, -4*e^2 + 4*e - 12, 6*e^2 + 30*e - 88, -24*e^2 + 36*e + 96, 8*e^2 - 20*e + 56, -35*e^2 + 18*e + 123, 5*e^2 + 2*e - 93, 24*e^2 - 24*e - 114, -24*e + 86, 16*e^2 - 12*e + 28, -30*e^2 - 2*e + 120, 21*e^2 + 8*e - 109, -9*e^2 + 34*e + 71, -28*e^2 - 20*e + 140, 8*e^2 + 36, 8*e^2 + 24*e - 62, -8*e^2 + 4*e - 18, -10*e^2 + 28*e + 68, 14*e^2 + 44*e - 116, 9*e^2 - 54*e - 5, 5*e^2 + 2*e + 135, 8*e^2 + 40*e - 4, -36*e^2 + 4*e + 140, 6*e^2 + 4*e + 54, 14*e^2 - 24*e - 6, -14*e^2 - 22*e + 106, 16*e^2 - 12*e + 66, -28*e^2 + 8*e + 116, 18*e^2 + 22*e - 144, -30*e^2 - 16*e + 174, 2*e^2 - 24*e + 54, -27*e^2 - 6*e + 125, 27*e^2 - 44*e - 123, 7*e^2 + 14*e - 83, 23*e^2 - 18*e - 131, 6*e^2 + 20*e + 54, 6*e^2 - 20*e - 34, -16*e^2 + 84, -8*e^2 + 20*e + 40, -17*e^2 + 18*e - 21, -25*e^2 + 46*e + 87, 36*e^2 - 4*e - 156, 4*e^2 - 20*e + 68, 4*e^2 + 32*e - 26, -20*e^2 + 12*e + 18, 26*e^2 - 44*e - 148, -6*e^2 - 48*e + 72, 17*e^2 - 79, -e^2 - 30*e + 89] 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([9,3,3])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]