/* 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([-5, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([28, 14, -2*w - 6]) primes_array = [ [3, 3, w + 1],\ [4, 2, 2],\ [5, 5, w],\ [5, 5, w - 1],\ [7, 7, -w - 3],\ [17, 17, -2*w + 3],\ [17, 17, -2*w - 1],\ [37, 37, w + 6],\ [37, 37, -w + 7],\ [41, 41, 3*w + 1],\ [41, 41, -3*w + 4],\ [43, 43, 3*w + 8],\ [43, 43, 3*w - 11],\ [47, 47, 3*w - 2],\ [47, 47, 3*w - 1],\ [59, 59, -5*w - 6],\ [59, 59, -4*w - 3],\ [67, 67, -w - 8],\ [67, 67, w - 9],\ [79, 79, 2*w - 11],\ [79, 79, -2*w - 9],\ [83, 83, 4*w - 3],\ [83, 83, 4*w - 1],\ [89, 89, -6*w - 7],\ [89, 89, -5*w - 4],\ [101, 101, -5*w - 3],\ [101, 101, 5*w - 8],\ [109, 109, 5*w - 18],\ [109, 109, 5*w + 13],\ [121, 11, -11],\ [127, 127, -w - 11],\ [127, 127, w - 12],\ [131, 131, 5*w - 2],\ [131, 131, 5*w - 3],\ [151, 151, -w - 12],\ [151, 151, w - 13],\ [163, 163, 3*w - 16],\ [163, 163, -3*w - 13],\ [167, 167, -8*w - 9],\ [167, 167, -7*w - 6],\ [169, 13, -13],\ [173, 173, -6*w - 1],\ [173, 173, 6*w - 7],\ [193, 193, -3*w - 14],\ [193, 193, 3*w - 17],\ [211, 211, 6*w + 17],\ [211, 211, 6*w - 23],\ [227, 227, 7*w - 9],\ [227, 227, -7*w - 2],\ [251, 251, 7*w - 6],\ [251, 251, 7*w - 1],\ [257, 257, 7*w - 3],\ [257, 257, 7*w - 4],\ [269, 269, -10*w - 11],\ [269, 269, -9*w - 8],\ [277, 277, 4*w - 21],\ [277, 277, -4*w - 17],\ [293, 293, -9*w - 7],\ [293, 293, 9*w - 16],\ [311, 311, -8*w - 1],\ [311, 311, 8*w - 9],\ [331, 331, -5*w - 19],\ [331, 331, 5*w - 24],\ [337, 337, -w - 18],\ [337, 337, w - 19],\ [353, 353, 9*w - 13],\ [353, 353, -9*w - 4],\ [361, 19, -19],\ [373, 373, 3*w - 22],\ [373, 373, -3*w - 19],\ [379, 379, 2*w - 21],\ [379, 379, -2*w - 19],\ [383, 383, 9*w - 11],\ [383, 383, -9*w - 2],\ [419, 419, 9*w - 2],\ [419, 419, 9*w - 7],\ [421, 421, 5*w - 26],\ [421, 421, -5*w - 21],\ [457, 457, -w - 21],\ [457, 457, w - 22],\ [461, 461, 10*w - 13],\ [461, 461, -10*w - 3],\ [463, 463, 2*w - 23],\ [463, 463, -2*w - 21],\ [467, 467, -13*w - 14],\ [467, 467, -12*w - 11],\ [479, 479, 11*w - 18],\ [479, 479, -11*w - 7],\ [487, 487, -6*w - 23],\ [487, 487, 6*w - 29],\ [499, 499, 10*w - 37],\ [499, 499, 10*w + 27],\ [503, 503, -11*w - 6],\ [503, 503, 11*w - 17],\ [509, 509, 10*w - 9],\ [509, 509, 10*w - 1],\ [521, 521, 10*w - 3],\ [521, 521, 10*w - 7],\ [529, 23, -23],\ [541, 541, -4*w - 23],\ [541, 541, 4*w - 27],\ [547, 547, -w - 23],\ [547, 547, w - 24],\ [563, 563, -11*w - 3],\ [563, 563, 11*w - 14],\ [571, 571, -5*w - 24],\ [571, 571, 5*w - 29],\ [587, 587, 12*w - 19],\ [587, 587, -12*w - 7],\ [593, 593, -11*w - 1],\ [593, 593, 11*w - 12],\ [613, 613, 7*w - 33],\ [613, 613, -7*w - 26],\ [631, 631, 9*w - 37],\ [631, 631, 10*w - 39],\ [647, 647, -13*w - 9],\ [647, 647, 13*w - 22],\ [673, 673, -7*w - 27],\ [673, 673, 7*w - 34],\ [677, 677, -13*w - 8],\ [677, 677, 13*w - 21],\ [709, 709, -3*w - 26],\ [709, 709, 3*w - 29],\ [719, 719, -16*w - 17],\ [719, 719, -15*w - 14],\ [739, 739, -5*w - 27],\ [739, 739, 5*w - 32],\ [751, 751, -w - 27],\ [751, 751, w - 28],\ [757, 757, -4*w - 27],\ [757, 757, 4*w - 31],\ [761, 761, -15*w - 13],\ [761, 761, -17*w - 19],\ [773, 773, 14*w - 23],\ [773, 773, -14*w - 9],\ [797, 797, 13*w - 16],\ [797, 797, -13*w - 3],\ [823, 823, 3*w - 31],\ [823, 823, -3*w - 28],\ [839, 839, 15*w - 26],\ [839, 839, -15*w - 11],\ [841, 29, -29],\ [857, 857, 13*w - 12],\ [857, 857, 13*w - 1],\ [877, 877, 4*w - 33],\ [877, 877, -4*w - 29],\ [881, 881, 13*w - 4],\ [881, 881, 13*w - 9],\ [883, 883, -3*w - 29],\ [883, 883, 3*w - 32],\ [887, 887, 13*w - 6],\ [887, 887, 13*w - 7],\ [907, 907, 9*w - 41],\ [907, 907, -9*w - 32],\ [919, 919, 13*w - 49],\ [919, 919, 13*w + 36],\ [929, 929, -14*w - 3],\ [929, 929, 14*w - 17],\ [941, 941, -15*w - 8],\ [941, 941, 15*w - 23],\ [961, 31, -31],\ [967, 967, 6*w - 37],\ [967, 967, -6*w - 31],\ [971, 971, 15*w - 22],\ [971, 971, -15*w - 7],\ [983, 983, -16*w - 11],\ [983, 983, 16*w - 27],\ [991, 991, 5*w - 36],\ [991, 991, -5*w - 31],\ [1009, 1009, 3*w - 34],\ [1009, 1009, -3*w - 31],\ [1013, 1013, 14*w - 11],\ [1013, 1013, 14*w - 3],\ [1033, 1033, 8*w - 41],\ [1033, 1033, -8*w - 33],\ [1049, 1049, -15*w - 4],\ [1049, 1049, 15*w - 19],\ [1051, 1051, -w - 32],\ [1051, 1051, w - 33],\ [1087, 1087, 14*w + 39],\ [1087, 1087, 14*w - 53],\ [1091, 1091, 15*w - 17],\ [1091, 1091, -15*w - 2],\ [1093, 1093, 12*w - 49],\ [1093, 1093, 13*w - 51],\ [1097, 1097, 17*w - 29],\ [1097, 1097, -17*w - 12],\ [1109, 1109, -15*w - 1],\ [1109, 1109, 15*w - 16],\ [1117, 1117, -w - 33],\ [1117, 1117, w - 34],\ [1129, 1129, 5*w - 38],\ [1129, 1129, -5*w - 33],\ [1151, 1151, 15*w - 2],\ [1151, 1151, 15*w - 13],\ [1171, 1171, 15*w + 41],\ [1171, 1171, 15*w - 56],\ [1181, 1181, 15*w - 7],\ [1181, 1181, 15*w - 8],\ [1193, 1193, -19*w - 17],\ [1193, 1193, -21*w - 23],\ [1201, 1201, -5*w - 34],\ [1201, 1201, 5*w - 39],\ [1213, 1213, 3*w - 37],\ [1213, 1213, -3*w - 34],\ [1217, 1217, -18*w - 13],\ [1217, 1217, 18*w - 31],\ [1223, 1223, 16*w - 19],\ [1223, 1223, -16*w - 3],\ [1259, 1259, -21*w - 22],\ [1259, 1259, -20*w - 19],\ [1277, 1277, -17*w - 7],\ [1277, 1277, 17*w - 24],\ [1297, 1297, 9*w - 46],\ [1297, 1297, -9*w - 37],\ [1301, 1301, -18*w - 11],\ [1301, 1301, 18*w - 29],\ [1303, 1303, 7*w - 43],\ [1303, 1303, -7*w - 36],\ [1307, 1307, -17*w - 6],\ [1307, 1307, 17*w - 23],\ [1319, 1319, 16*w - 3],\ [1319, 1319, 16*w - 13],\ [1327, 1327, -w - 36],\ [1327, 1327, w - 37],\ [1361, 1361, 17*w - 21],\ [1361, 1361, -17*w - 4],\ [1381, 1381, -9*w - 38],\ [1381, 1381, 9*w - 47],\ [1423, 1423, 2*w - 39],\ [1423, 1423, -2*w - 37],\ [1427, 1427, -17*w - 1],\ [1427, 1427, 17*w - 18],\ [1429, 1429, -5*w - 37],\ [1429, 1429, 5*w - 42],\ [1433, 1433, -19*w - 12],\ [1433, 1433, 19*w - 31],\ [1453, 1453, 17*w + 46],\ [1453, 1453, 17*w - 63],\ [1471, 1471, 14*w - 57],\ [1471, 1471, 15*w - 59],\ [1487, 1487, 17*w - 14],\ [1487, 1487, 17*w - 3],\ [1511, 1511, 17*w - 11],\ [1511, 1511, 17*w - 6],\ [1549, 1549, 7*w - 46],\ [1549, 1549, -7*w - 39],\ [1553, 1553, 19*w - 28],\ [1553, 1553, -19*w - 9],\ [1559, 1559, -21*w - 17],\ [1559, 1559, -25*w - 29],\ [1571, 1571, 20*w - 33],\ [1571, 1571, -20*w - 13],\ [1579, 1579, 2*w - 41],\ [1579, 1579, -2*w - 39],\ [1597, 1597, -4*w - 39],\ [1597, 1597, 4*w - 43],\ [1601, 1601, -18*w - 1],\ [1601, 1601, 18*w - 19],\ [1613, 1613, -21*w - 16],\ [1613, 1613, 21*w - 37],\ [1621, 1621, 11*w - 53],\ [1621, 1621, -11*w - 42],\ [1637, 1637, 18*w - 17],\ [1637, 1637, 18*w - 1],\ [1663, 1663, 18*w - 67],\ [1663, 1663, 18*w + 49],\ [1697, 1697, 18*w - 7],\ [1697, 1697, 18*w - 11],\ [1721, 1721, -23*w - 21],\ [1721, 1721, -25*w - 27],\ [1723, 1723, -7*w - 41],\ [1723, 1723, 7*w - 48],\ [1747, 1747, -6*w - 41],\ [1747, 1747, 6*w - 47],\ [1759, 1759, -3*w - 41],\ [1759, 1759, 3*w - 44],\ [1789, 1789, 17*w - 66],\ [1789, 1789, 15*w - 62],\ [1801, 1801, -w - 42],\ [1801, 1801, w - 43],\ [1811, 1811, -20*w - 7],\ [1811, 1811, 20*w - 27],\ [1823, 1823, 19*w - 18],\ [1823, 1823, 19*w - 1],\ [1831, 1831, 9*w - 52],\ [1831, 1831, -9*w - 43],\ [1847, 1847, -27*w - 31],\ [1847, 1847, -23*w - 19],\ [1873, 1873, 8*w - 51],\ [1873, 1873, -8*w - 43],\ [1889, 1889, 19*w - 7],\ [1889, 1889, 19*w - 12],\ [1907, 1907, -23*w - 18],\ [1907, 1907, 23*w - 41],\ [1931, 1931, -20*w - 3],\ [1931, 1931, 20*w - 23],\ [1933, 1933, 3*w - 46],\ [1933, 1933, -3*w - 43],\ [1949, 1949, -26*w - 27],\ [1949, 1949, -25*w - 24],\ [1973, 1973, -21*w - 8],\ [1973, 1973, 21*w - 29],\ [1979, 1979, -20*w - 1],\ [1979, 1979, 20*w - 21],\ [1999, 1999, -7*w - 44],\ [1999, 1999, 7*w - 51],\ [2011, 2011, 19*w + 53],\ [2011, 2011, 19*w - 72],\ [2017, 2017, -11*w - 46],\ [2017, 2017, 11*w - 57],\ [2053, 2053, -12*w - 47],\ [2053, 2053, 12*w - 59],\ [2063, 2063, 24*w - 43],\ [2063, 2063, -24*w - 19],\ [2083, 2083, 13*w - 61],\ [2083, 2083, -13*w - 48],\ [2099, 2099, 20*w - 11],\ [2099, 2099, 20*w - 9],\ [2137, 2137, 19*w - 73],\ [2137, 2137, 19*w + 54],\ [2141, 2141, -22*w - 9],\ [2141, 2141, 22*w - 31],\ [2143, 2143, 17*w - 69],\ [2143, 2143, 18*w - 71],\ [2179, 2179, 10*w - 57],\ [2179, 2179, -10*w - 47],\ [2221, 2221, 5*w - 51],\ [2221, 2221, -5*w - 46],\ [2243, 2243, 21*w - 2],\ [2243, 2243, 21*w - 19],\ [2251, 2251, -w - 47],\ [2251, 2251, w - 48],\ [2267, 2267, -28*w - 29],\ [2267, 2267, -27*w - 26],\ [2269, 2269, 12*w - 61],\ [2269, 2269, -12*w - 49],\ [2273, 2273, 21*w - 4],\ [2273, 2273, 21*w - 17],\ [2293, 2293, 7*w - 54],\ [2293, 2293, -7*w - 47],\ [2309, 2309, 21*w - 13],\ [2309, 2309, 21*w - 8],\ [2311, 2311, -6*w - 47],\ [2311, 2311, 6*w - 53],\ [2347, 2347, -w - 48],\ [2347, 2347, w - 49],\ [2351, 2351, -25*w - 18],\ [2351, 2351, 25*w - 43],\ [2357, 2357, 23*w - 32],\ [2357, 2357, -23*w - 9],\ [2377, 2377, 21*w - 79],\ [2377, 2377, 21*w + 58],\ [2389, 2389, 17*w - 71],\ [2389, 2389, 20*w - 77],\ [2393, 2393, -26*w - 21],\ [2393, 2393, -31*w - 36],\ [2399, 2399, 24*w - 37],\ [2399, 2399, -24*w - 13],\ [2411, 2411, -25*w - 17],\ [2411, 2411, 25*w - 42],\ [2437, 2437, -9*w - 49],\ [2437, 2437, 9*w - 58],\ [2441, 2441, 22*w - 21],\ [2441, 2441, 22*w - 1],\ [2473, 2473, 8*w - 57],\ [2473, 2473, -8*w - 49],\ [2477, 2477, 22*w - 3],\ [2477, 2477, 22*w - 19],\ [2503, 2503, 3*w - 52],\ [2503, 2503, -3*w - 49],\ [2521, 2521, -5*w - 49],\ [2521, 2521, 5*w - 54],\ [2557, 2557, -11*w - 51],\ [2557, 2557, 11*w - 62],\ [2579, 2579, -25*w - 14],\ [2579, 2579, 25*w - 39],\ [2609, 2609, -30*w - 31],\ [2609, 2609, -29*w - 28],\ [2621, 2621, -23*w - 1],\ [2621, 2621, 23*w - 24],\ [2647, 2647, -w - 51],\ [2647, 2647, w - 52],\ [2663, 2663, -24*w - 7],\ [2663, 2663, 24*w - 31],\ [2671, 2671, -11*w - 52],\ [2671, 2671, 11*w - 63],\ [2683, 2683, 2*w - 53],\ [2683, 2683, -2*w - 51],\ [2687, 2687, 23*w - 2],\ [2687, 2687, 23*w - 21],\ [2689, 2689, 8*w - 59],\ [2689, 2689, -8*w - 51],\ [2693, 2693, -29*w - 27],\ [2693, 2693, -31*w - 33],\ [2713, 2713, -7*w - 51],\ [2713, 2713, 7*w - 58],\ [2729, 2729, 25*w - 36],\ [2729, 2729, -25*w - 11],\ [2731, 2731, 5*w - 56],\ [2731, 2731, -5*w - 51],\ [2767, 2767, 9*w - 61],\ [2767, 2767, -9*w - 52],\ [2777, 2777, 23*w - 11],\ [2777, 2777, 23*w - 12],\ [2789, 2789, -31*w - 32],\ [2789, 2789, -30*w - 29],\ [2797, 2797, 21*w - 82],\ [2797, 2797, 19*w - 78],\ [2809, 53, -53],\ [2819, 2819, 25*w - 34],\ [2819, 2819, -25*w - 9],\ [2851, 2851, -15*w - 56],\ [2851, 2851, 15*w - 71],\ [2857, 2857, -w - 53],\ [2857, 2857, w - 54],\ [2861, 2861, 25*w - 33],\ [2861, 2861, -25*w - 8],\ [2897, 2897, -27*w - 17],\ [2897, 2897, 27*w - 44],\ [2903, 2903, 24*w - 23],\ [2903, 2903, 24*w - 1],\ [2939, 2939, 25*w - 31],\ [2939, 2939, -25*w - 6],\ [2957, 2957, 27*w - 43],\ [2957, 2957, -27*w - 16],\ [2999, 2999, 24*w - 17],\ [2999, 2999, 24*w - 7],\ [3019, 3019, -13*w - 56],\ [3019, 3019, 13*w - 69],\ [3023, 3023, 24*w - 13],\ [3023, 3023, 24*w - 11],\ [3041, 3041, 25*w - 28],\ [3041, 3041, -25*w - 3],\ [3049, 3049, 7*w - 61],\ [3049, 3049, -7*w - 54],\ [3061, 3061, -5*w - 54],\ [3061, 3061, 5*w - 59],\ [3067, 3067, 14*w - 71],\ [3067, 3067, -14*w - 57],\ [3083, 3083, -29*w - 22],\ [3083, 3083, 29*w - 51],\ [3109, 3109, 15*w - 73],\ [3109, 3109, -15*w - 58],\ [3167, 3167, -33*w - 34],\ [3167, 3167, -32*w - 31],\ [3187, 3187, -w - 56],\ [3187, 3187, w - 57],\ [3191, 3191, 25*w - 3],\ [3191, 3191, 25*w - 22],\ [3209, 3209, 25*w - 4],\ [3209, 3209, 25*w - 21],\ [3217, 3217, 24*w + 67],\ [3217, 3217, 24*w - 91],\ [3229, 3229, 20*w - 83],\ [3229, 3229, 23*w - 89],\ [3251, 3251, 25*w - 7],\ [3251, 3251, 25*w - 18],\ [3259, 3259, -3*w - 56],\ [3259, 3259, 3*w - 59],\ [3271, 3271, -11*w - 57],\ [3271, 3271, 11*w - 68],\ [3301, 3301, -w - 57],\ [3301, 3301, w - 58],\ [3313, 3313, -17*w - 61],\ [3313, 3313, 17*w - 78],\ [3319, 3319, 10*w - 67],\ [3319, 3319, -10*w - 57],\ [3323, 3323, -31*w - 26],\ [3323, 3323, -36*w - 41],\ [3343, 3343, 2*w - 59],\ [3343, 3343, -2*w - 57],\ [3359, 3359, 29*w - 47],\ [3359, 3359, -29*w - 18],\ [3361, 3361, 25*w - 94],\ [3361, 3361, 25*w + 69],\ [3407, 3407, -27*w - 7],\ [3407, 3407, 27*w - 34],\ [3449, 3449, 26*w - 23],\ [3449, 3449, 26*w - 3],\ [3461, 3461, -33*w - 31],\ [3461, 3461, -35*w - 37],\ [3469, 3469, -12*w - 59],\ [3469, 3469, 12*w - 71],\ [3491, 3491, 28*w - 39],\ [3491, 3491, -28*w - 11],\ [3511, 3511, 15*w - 76],\ [3511, 3511, -15*w - 61],\ [3527, 3527, -37*w - 42],\ [3527, 3527, -32*w - 27],\ [3529, 3529, 5*w - 63],\ [3529, 3529, -5*w - 58],\ [3533, 3533, 26*w - 17],\ [3533, 3533, 26*w - 9],\ [3571, 3571, -10*w - 59],\ [3571, 3571, 10*w - 69],\ [3607, 3607, 9*w - 68],\ [3607, 3607, -9*w - 59],\ [3613, 3613, -3*w - 59],\ [3613, 3613, 3*w - 62],\ [3617, 3617, -27*w - 1],\ [3617, 3617, 27*w - 28],\ [3637, 3637, -4*w - 59],\ [3637, 3637, 4*w - 63],\ [3659, 3659, -29*w - 13],\ [3659, 3659, 29*w - 42],\ [3671, 3671, 27*w - 26],\ [3671, 3671, 27*w - 1],\ [3691, 3691, 25*w - 96],\ [3691, 3691, 25*w + 71],\ [3697, 3697, -16*w - 63],\ [3697, 3697, 16*w - 79],\ [3701, 3701, 30*w - 47],\ [3701, 3701, -30*w - 17],\ [3721, 61, -61],\ [3733, 3733, 12*w - 73],\ [3733, 3733, -12*w - 61],\ [3739, 3739, 17*w - 81],\ [3739, 3739, -17*w - 64],\ [3779, 3779, -36*w - 37],\ [3779, 3779, -35*w - 34],\ [3797, 3797, 27*w - 8],\ [3797, 3797, 27*w - 19],\ [3821, 3821, 27*w - 16],\ [3821, 3821, 27*w - 11],\ [3823, 3823, 2*w - 63],\ [3823, 3823, -2*w - 61],\ [3847, 3847, 26*w - 99],\ [3847, 3847, 26*w + 73],\ [3863, 3863, -29*w - 9],\ [3863, 3863, 29*w - 38],\ [3881, 3881, -35*w - 33],\ [3881, 3881, -37*w - 39],\ [3889, 3889, -8*w - 61],\ [3889, 3889, 8*w - 69],\ [3907, 3907, 6*w - 67],\ [3907, 3907, -6*w - 61],\ [3911, 3911, -33*w - 26],\ [3911, 3911, 33*w - 59],\ [3923, 3923, 31*w - 49],\ [3923, 3923, -31*w - 18],\ [3931, 3931, 15*w - 79],\ [3931, 3931, -15*w - 64],\ [3943, 3943, 13*w - 76],\ [3943, 3943, -13*w - 63],\ [3947, 3947, 28*w - 27],\ [3947, 3947, 28*w - 1],\ [3989, 3989, -31*w - 17],\ [3989, 3989, 31*w - 48],\ [4007, 4007, 32*w - 53],\ [4007, 4007, -32*w - 21],\ [4027, 4027, -w - 63],\ [4027, 4027, w - 64],\ [4049, 4049, -30*w - 11],\ [4049, 4049, 30*w - 41],\ [4057, 4057, -11*w - 63],\ [4057, 4057, 11*w - 74],\ [4073, 4073, 29*w - 33],\ [4073, 4073, -29*w - 4],\ [4079, 4079, -39*w - 43],\ [4079, 4079, -35*w - 31],\ [4091, 4091, 28*w - 9],\ [4091, 4091, 28*w - 19],\ [4099, 4099, -10*w - 63],\ [4099, 4099, 10*w - 73],\ [4111, 4111, 19*w - 87],\ [4111, 4111, -19*w - 68],\ [4133, 4133, 34*w - 61],\ [4133, 4133, -34*w - 27],\ [4153, 4153, -8*w - 63],\ [4153, 4153, 8*w - 71],\ [4157, 4157, 33*w - 56],\ [4157, 4157, -33*w - 23],\ [4159, 4159, 5*w - 68],\ [4159, 4159, -5*w - 63],\ [4201, 4201, 24*w - 97],\ [4201, 4201, 25*w - 99],\ [4217, 4217, -38*w - 39],\ [4217, 4217, -37*w - 36],\ [4241, 4241, -30*w - 7],\ [4241, 4241, 30*w - 37],\ [4243, 4243, 3*w - 67],\ [4243, 4243, -3*w - 64],\ [4259, 4259, 29*w - 2],\ [4259, 4259, 29*w - 27],\ [4283, 4283, 29*w - 26],\ [4283, 4283, 29*w - 3],\ [4289, 4289, -31*w - 12],\ [4289, 4289, 31*w - 43],\ [4327, 4327, 29*w + 79],\ [4327, 4327, 29*w - 108],\ [4363, 4363, 23*w - 96],\ [4363, 4363, 27*w - 104],\ [4373, 4373, 29*w - 21],\ [4373, 4373, 29*w - 8],\ [4409, 4409, 29*w - 12],\ [4409, 4409, 29*w - 17],\ [4447, 4447, -14*w - 67],\ [4447, 4447, 14*w - 81],\ [4451, 4451, -35*w - 27],\ [4451, 4451, 35*w - 62],\ [4457, 4457, -33*w - 19],\ [4457, 4457, 33*w - 52],\ [4493, 4493, -31*w - 8],\ [4493, 4493, 31*w - 39],\ [4519, 4519, 15*w - 83],\ [4519, 4519, -15*w - 68],\ [4561, 4561, 5*w - 71],\ [4561, 4561, -5*w - 66],\ [4583, 4583, 31*w - 37],\ [4583, 4583, -31*w - 6],\ [4603, 4603, 2*w - 69],\ [4603, 4603, -2*w - 67],\ [4621, 4621, 11*w - 78],\ [4621, 4621, -11*w - 67],\ [4637, 4637, -42*w - 47],\ [4637, 4637, -37*w - 32],\ [4657, 4657, 31*w - 114],\ [4657, 4657, 31*w + 83],\ [4663, 4663, -13*w - 68],\ [4663, 4663, 13*w - 81],\ [4679, 4679, -40*w - 41],\ [4679, 4679, -39*w - 38],\ [4703, 4703, 31*w - 34],\ [4703, 4703, -31*w - 3],\ [4721, 4721, 30*w - 17],\ [4721, 4721, 30*w - 13],\ [4729, 4729, 27*w - 106],\ [4729, 4729, 25*w - 102],\ [4751, 4751, 32*w - 41],\ [4751, 4751, -32*w - 9],\ [4783, 4783, -3*w - 68],\ [4783, 4783, 3*w - 71],\ [4787, 4787, 33*w - 47],\ [4787, 4787, -33*w - 14],\ [4789, 4789, -20*w - 73],\ [4789, 4789, 20*w - 93],\ [4793, 4793, -39*w - 37],\ [4793, 4793, -41*w - 43],\ [4813, 4813, -13*w - 69],\ [4813, 4813, 13*w - 82],\ [4831, 4831, 9*w - 77],\ [4831, 4831, -9*w - 68],\ [4871, 4871, -35*w - 22],\ [4871, 4871, 35*w - 57],\ [4877, 4877, -38*w - 33],\ [4877, 4877, -43*w - 48],\ [4889, 4889, 31*w - 3],\ [4889, 4889, 31*w - 28],\ [4909, 4909, 28*w - 109],\ [4909, 4909, 25*w - 103],\ [4919, 4919, -41*w - 42],\ [4919, 4919, -40*w - 39],\ [4931, 4931, 37*w - 66],\ [4931, 4931, -37*w - 29],\ [4951, 4951, -10*w - 69],\ [4951, 4951, 10*w - 79],\ [4957, 4957, 4*w - 73],\ [4957, 4957, -4*w - 69],\ [4973, 4973, 31*w - 24],\ [4973, 4973, 31*w - 7],\ [4993, 4993, -8*w - 69],\ [4993, 4993, 8*w - 77],\ [4999, 4999, -7*w - 69],\ [4999, 4999, 7*w - 76],\ [5003, 5003, 31*w - 22],\ [5003, 5003, 31*w - 9],\ [5023, 5023, 18*w - 91],\ [5023, 5023, -18*w - 73],\ [5039, 5039, 31*w - 18],\ [5039, 5039, 31*w - 13],\ [5041, 71, -71],\ [5077, 5077, 19*w - 93],\ [5077, 5077, -19*w - 74],\ [5081, 5081, 38*w - 69],\ [5081, 5081, -38*w - 31],\ [5087, 5087, -32*w - 1],\ [5087, 5087, 32*w - 33],\ [5099, 5099, 35*w - 54],\ [5099, 5099, -35*w - 19],\ [5107, 5107, -w - 71],\ [5107, 5107, w - 72],\ [5119, 5119, -13*w - 71],\ [5119, 5119, 13*w - 84],\ [5167, 5167, -21*w - 76],\ [5167, 5167, 21*w - 97],\ [5171, 5171, -35*w - 18],\ [5171, 5171, 35*w - 53],\ [5209, 5209, -3*w - 71],\ [5209, 5209, 3*w - 74],\ [5233, 5233, 32*w - 119],\ [5233, 5233, 32*w + 87],\ [5297, 5297, 33*w - 37],\ [5297, 5297, -33*w - 4],\ [5309, 5309, -35*w - 16],\ [5309, 5309, 35*w - 51],\ [5329, 73, -73],\ [5333, 5333, -39*w - 32],\ [5333, 5333, 39*w - 71],\ [5351, 5351, 32*w - 21],\ [5351, 5351, 32*w - 11],\ [5381, 5381, -37*w - 24],\ [5381, 5381, 37*w - 61],\ [5393, 5393, 34*w - 43],\ [5393, 5393, -34*w - 9],\ [5413, 5413, 33*w + 89],\ [5413, 5413, 33*w - 122],\ [5417, 5417, -43*w - 44],\ [5417, 5417, -42*w - 41],\ [5419, 5419, -5*w - 72],\ [5419, 5419, 5*w - 77],\ [5443, 5443, -7*w - 72],\ [5443, 5443, 7*w - 79],\ [5477, 5477, 33*w - 32],\ [5477, 5477, 33*w - 1],\ [5501, 5501, 35*w - 48],\ [5501, 5501, -35*w - 13],\ [5503, 5503, 3*w - 76],\ [5503, 5503, -3*w - 73],\ [5507, 5507, 33*w - 2],\ [5507, 5507, 33*w - 31],\ [5519, 5519, -41*w - 37],\ [5519, 5519, -45*w - 49],\ [5527, 5527, -11*w - 73],\ [5527, 5527, 11*w - 84],\ [5569, 5569, 5*w - 78],\ [5569, 5569, -5*w - 73],\ [5581, 5581, 9*w - 82],\ [5581, 5581, -9*w - 73],\ [5591, 5591, -40*w - 33],\ [5591, 5591, -47*w - 54],\ [5623, 5623, -17*w - 76],\ [5623, 5623, 17*w - 93],\ [5653, 5653, -3*w - 74],\ [5653, 5653, 3*w - 77],\ [5669, 5669, 34*w - 37],\ [5669, 5669, -34*w - 3],\ [5711, 5711, 33*w - 14],\ [5711, 5711, 33*w - 19],\ [5717, 5717, 33*w - 16],\ [5717, 5717, 33*w - 17],\ [5737, 5737, -9*w - 74],\ [5737, 5737, 9*w - 83],\ [5749, 5749, 7*w - 81],\ [5749, 5749, -7*w - 74],\ [5779, 5779, 23*w - 104],\ [5779, 5779, -23*w - 81],\ [5791, 5791, 15*w - 91],\ [5791, 5791, -15*w - 76],\ [5801, 5801, -43*w - 41],\ [5801, 5801, -45*w - 47],\ [5813, 5813, 34*w - 33],\ [5813, 5813, 34*w - 1],\ [5821, 5821, -20*w - 79],\ [5821, 5821, 20*w - 99],\ [5839, 5839, 33*w - 124],\ [5839, 5839, 33*w + 91],\ [5843, 5843, 36*w - 49],\ [5843, 5843, -36*w - 13],\ [5879, 5879, -35*w - 6],\ [5879, 5879, 35*w - 41],\ [5881, 5881, 16*w - 93],\ [5881, 5881, -16*w - 77],\ [5897, 5897, -47*w - 52],\ [5897, 5897, -42*w - 37],\ [5923, 5923, 22*w - 103],\ [5923, 5923, -22*w - 81],\ [5927, 5927, 37*w - 54],\ [5927, 5927, -37*w - 17],\ [5939, 5939, -45*w - 46],\ [5939, 5939, -44*w - 43],\ [5981, 5981, 38*w - 59],\ [5981, 5981, -38*w - 21],\ [6007, 6007, -11*w - 76],\ [6007, 6007, 11*w - 87],\ [6011, 6011, -35*w - 3],\ [6011, 6011, 35*w - 38],\ [6043, 6043, -18*w - 79],\ [6043, 6043, 18*w - 97],\ [6047, 6047, -47*w - 51],\ [6047, 6047, -43*w - 39],\ [6053, 6053, 34*w - 13],\ [6053, 6053, 34*w - 21],\ [6073, 6073, 32*w + 91],\ [6073, 6073, 32*w - 123],\ [6089, 6089, -35*w - 1],\ [6089, 6089, 35*w - 36],\ [6091, 6091, 29*w - 117],\ [6091, 6091, 30*w - 119],\ [6131, 6131, -37*w - 14],\ [6131, 6131, 37*w - 51],\ [6133, 6133, 12*w - 89],\ [6133, 6133, -12*w - 77],\ [6173, 6173, -41*w - 31],\ [6173, 6173, 41*w - 72],\ [6199, 6199, 10*w - 87],\ [6199, 6199, -10*w - 77],\ [6211, 6211, -6*w - 77],\ [6211, 6211, 6*w - 83],\ [6217, 6217, 9*w - 86],\ [6217, 6217, -9*w - 77],\ [6221, 6221, 35*w - 32],\ [6221, 6221, 35*w - 3],\ [6257, 6257, 37*w - 49],\ [6257, 6257, -37*w - 12],\ [6263, 6263, -39*w - 22],\ [6263, 6263, 39*w - 61],\ [6299, 6299, 35*w - 29],\ [6299, 6299, 35*w - 6],\ [6301, 6301, 15*w - 94],\ [6301, 6301, -15*w - 79],\ [6317, 6317, 37*w - 48],\ [6317, 6317, -37*w - 11],\ [6337, 6337, 11*w - 89],\ [6337, 6337, -11*w - 78],\ [6343, 6343, -23*w - 84],\ [6343, 6343, 23*w - 107],\ [6359, 6359, 35*w - 26],\ [6359, 6359, 35*w - 9],\ [6367, 6367, -14*w - 79],\ [6367, 6367, 14*w - 93],\ [6379, 6379, 2*w - 81],\ [6379, 6379, -2*w - 79],\ [6389, 6389, 35*w - 24],\ [6389, 6389, 35*w - 11],\ [6421, 6421, 36*w - 133],\ [6421, 6421, 36*w + 97],\ [6427, 6427, -21*w - 83],\ [6427, 6427, 21*w - 104],\ [6451, 6451, 35*w + 96],\ [6451, 6451, 35*w - 131],\ [6469, 6469, -12*w - 79],\ [6469, 6469, 12*w - 91],\ [6473, 6473, 41*w - 69],\ [6473, 6473, -41*w - 28],\ [6547, 6547, 9*w - 88],\ [6547, 6547, -9*w - 79],\ [6551, 6551, -40*w - 23],\ [6551, 6551, 40*w - 63],\ [6553, 6553, -8*w - 79],\ [6553, 6553, 8*w - 87],\ [6569, 6569, 41*w - 68],\ [6569, 6569, -41*w - 27],\ [6577, 6577, 16*w - 97],\ [6577, 6577, -16*w - 81],\ [6599, 6599, -45*w - 41],\ [6599, 6599, -49*w - 53],\ [6619, 6619, 37*w - 136],\ [6619, 6619, 37*w + 99],\ [6637, 6637, -w - 81],\ [6637, 6637, w - 82],\ [6653, 6653, 39*w - 56],\ [6653, 6653, -39*w - 17],\ [6661, 6661, -19*w - 83],\ [6661, 6661, 19*w - 102],\ [6673, 6673, -17*w - 82],\ [6673, 6673, 17*w - 99],\ [6679, 6679, 35*w - 132],\ [6679, 6679, 35*w + 97],\ [6703, 6703, 2*w - 83],\ [6703, 6703, -2*w - 81],\ [6719, 6719, 40*w - 61],\ [6719, 6719, -40*w - 21],\ [6737, 6737, 43*w - 76],\ [6737, 6737, -43*w - 33],\ [6761, 6761, 42*w - 71],\ [6761, 6761, -42*w - 29],\ [6763, 6763, 18*w - 101],\ [6763, 6763, -18*w - 83],\ [6779, 6779, 36*w - 13],\ [6779, 6779, 36*w - 23],\ [6803, 6803, 36*w - 19],\ [6803, 6803, 36*w - 17],\ [6829, 6829, -15*w - 82],\ [6829, 6829, 15*w - 97],\ [6841, 6841, 5*w - 86],\ [6841, 6841, -5*w - 81],\ [6863, 6863, -39*w - 14],\ [6863, 6863, 39*w - 53],\ [6871, 6871, 10*w - 91],\ [6871, 6871, -10*w - 81],\ [6883, 6883, 7*w - 88],\ [6883, 6883, -7*w - 81],\ [6947, 6947, 37*w - 3],\ [6947, 6947, 37*w - 34],\ [6967, 6967, -w - 83],\ [6967, 6967, w - 84],\ [6971, 6971, -52*w - 59],\ [6971, 6971, -45*w - 38],\ [6977, 6977, 37*w - 4],\ [6977, 6977, 37*w - 33],\ [6997, 6997, -21*w - 86],\ [6997, 6997, 21*w - 107],\ [7013, 7013, -46*w - 41],\ [7013, 7013, -51*w - 56],\ [7019, 7019, 41*w - 63],\ [7019, 7019, -41*w - 22],\ [7039, 7039, -17*w - 84],\ [7039, 7039, 17*w - 101],\ [7057, 7057, 9*w - 91],\ [7057, 7057, -9*w - 82],\ [7103, 7103, -41*w - 21],\ [7103, 7103, 41*w - 62],\ [7177, 7177, -24*w - 89],\ [7177, 7177, 24*w - 113],\ [7187, 7187, 37*w - 18],\ [7187, 7187, 37*w - 19],\ [7207, 7207, -6*w - 83],\ [7207, 7207, 6*w - 89],\ [7219, 7219, -10*w - 83],\ [7219, 7219, 10*w - 93],\ [7229, 7229, -39*w - 8],\ [7229, 7229, 39*w - 47],\ [7283, 7283, 39*w - 46],\ [7283, 7283, -39*w - 7],\ [7307, 7307, -52*w - 57],\ [7307, 7307, -47*w - 42],\ [7309, 7309, 20*w - 107],\ [7309, 7309, -20*w - 87],\ [7333, 7333, 37*w - 139],\ [7333, 7333, 37*w + 102],\ [7349, 7349, -50*w - 51],\ [7349, 7349, -49*w - 48],\ [7351, 7351, -5*w - 84],\ [7351, 7351, 5*w - 89],\ [7393, 7393, 32*w - 129],\ [7393, 7393, 33*w - 131],\ [7417, 7417, 19*w - 106],\ [7417, 7417, -19*w - 87],\ [7433, 7433, -39*w - 4],\ [7433, 7433, 39*w - 43],\ [7451, 7451, -43*w - 26],\ [7451, 7451, 43*w - 69],\ [7459, 7459, 22*w - 111],\ [7459, 7459, -22*w - 89],\ [7477, 7477, -w - 86],\ [7477, 7477, w - 87],\ [7481, 7481, 38*w - 29],\ [7481, 7481, 38*w - 9],\ [7517, 7517, 38*w - 27],\ [7517, 7517, 38*w - 11],\ [7523, 7523, 39*w - 41],\ [7523, 7523, -39*w - 2],\ [7559, 7559, -40*w - 9],\ [7559, 7559, 40*w - 49],\ [7561, 7561, -15*w - 86],\ [7561, 7561, 15*w - 101],\ [7577, 7577, 38*w - 21],\ [7577, 7577, 38*w - 17],\ [7603, 7603, -17*w - 87],\ [7603, 7603, 17*w - 104],\ [7607, 7607, -48*w - 43],\ [7607, 7607, -53*w - 58],\ [7639, 7639, 25*w - 117],\ [7639, 7639, -25*w - 92],\ [7643, 7643, 39*w - 38],\ [7643, 7643, 39*w - 1],\ [7649, 7649, -51*w - 52],\ [7649, 7649, -50*w - 49],\ [7669, 7669, 13*w - 99],\ [7669, 7669, -13*w - 86],\ [7681, 7681, 16*w - 103],\ [7681, 7681, -16*w - 87],\ [7687, 7687, 26*w - 119],\ [7687, 7687, -26*w - 93],\ [7691, 7691, -55*w - 63],\ [7691, 7691, -47*w - 39],\ [7703, 7703, -41*w - 13],\ [7703, 7703, 41*w - 54],\ [7723, 7723, 2*w - 89],\ [7723, 7723, -2*w - 87],\ [7727, 7727, -43*w - 23],\ [7727, 7727, 43*w - 66],\ [7753, 7753, -7*w - 86],\ [7753, 7753, 7*w - 93],\ [7817, 7817, -42*w - 17],\ [7817, 7817, 42*w - 59],\ [7829, 7829, 39*w - 7],\ [7829, 7829, 39*w - 32],\ [7853, 7853, 39*w - 31],\ [7853, 7853, 39*w - 8],\ [7879, 7879, -5*w - 87],\ [7879, 7879, 5*w - 92],\ [7901, 7901, 43*w - 64],\ [7901, 7901, -43*w - 21],\ [7933, 7933, -7*w - 87],\ [7933, 7933, 7*w - 94],\ [7937, 7937, -47*w - 37],\ [7937, 7937, 47*w - 84],\ [7963, 7963, 3*w - 91],\ [7963, 7963, -3*w - 88],\ [8017, 8017, 39*w + 107],\ [8017, 8017, 39*w - 146],\ [8039, 8039, 40*w - 39],\ [8039, 8039, 40*w - 1],\ [8059, 8059, 5*w - 93],\ [8059, 8059, -5*w - 88],\ [8069, 8069, -41*w - 7],\ [8069, 8069, 41*w - 48],\ [8081, 8081, 45*w - 73],\ [8081, 8081, -45*w - 28],\ [8089, 8089, 35*w - 138],\ [8089, 8089, 33*w - 134],\ [8101, 8101, -20*w - 91],\ [8101, 8101, 20*w - 111],\ [8111, 8111, 40*w - 3],\ [8111, 8111, 40*w - 37],\ [8123, 8123, -41*w - 6],\ [8123, 8123, 41*w - 47],\ [8147, 8147, -43*w - 18],\ [8147, 8147, 43*w - 61],\ [8191, 8191, 21*w - 113],\ [8191, 8191, -21*w - 92],\ [8231, 8231, 40*w - 7],\ [8231, 8231, 40*w - 33],\ [8233, 8233, 13*w - 102],\ [8233, 8233, -13*w - 89],\ [8237, 8237, 42*w - 53],\ [8237, 8237, -42*w - 11],\ [8269, 8269, 12*w - 101],\ [8269, 8269, -12*w - 89],\ [8273, 8273, -41*w - 3],\ [8273, 8273, 41*w - 44],\ [8291, 8291, -47*w - 34],\ [8291, 8291, 47*w - 81],\ [8311, 8311, -10*w - 89],\ [8311, 8311, 10*w - 99],\ [8317, 8317, -9*w - 89],\ [8317, 8317, 9*w - 98],\ [8353, 8353, -23*w - 94],\ [8353, 8353, 23*w - 117],\ [8363, 8363, -41*w - 1],\ [8363, 8363, 41*w - 42],\ [8443, 8443, 2*w - 93],\ [8443, 8443, -2*w - 91],\ [8447, 8447, 43*w - 57],\ [8447, 8447, -43*w - 14],\ [8467, 8467, 41*w - 152],\ [8467, 8467, 41*w + 111],\ [8501, 8501, -50*w - 43],\ [8501, 8501, -57*w - 64],\ [8521, 8521, 15*w - 106],\ [8521, 8521, -15*w - 91],\ [8527, 8527, 39*w + 109],\ [8527, 8527, 39*w - 148],\ [8543, 8543, -51*w - 46],\ [8543, 8543, -56*w - 61],\ [8563, 8563, 37*w - 144],\ [8563, 8563, 33*w - 136],\ [8573, 8573, 49*w - 88],\ [8573, 8573, -49*w - 39],\ [8609, 8609, 46*w - 73],\ [8609, 8609, -46*w - 27],\ [8627, 8627, 47*w - 78],\ [8627, 8627, -47*w - 31],\ [8647, 8647, 6*w - 97],\ [8647, 8647, -6*w - 91],\ [8669, 8669, 41*w - 8],\ [8669, 8669, 41*w - 33],\ [8677, 8677, 11*w - 102],\ [8677, 8677, -11*w - 91],\ [8689, 8689, 8*w - 99],\ [8689, 8689, -8*w - 91],\ [8693, 8693, 41*w - 9],\ [8693, 8693, 41*w - 32],\ [8699, 8699, 49*w - 87],\ [8699, 8699, -49*w - 38],\ [8719, 8719, -15*w - 92],\ [8719, 8719, 15*w - 107],\ [8731, 8731, 41*w + 112],\ [8731, 8731, 41*w - 153],\ [8737, 8737, -w - 93],\ [8737, 8737, w - 94],\ [8741, 8741, -53*w - 51],\ [8741, 8741, -55*w - 57],\ [8753, 8753, 41*w - 12],\ [8753, 8753, 41*w - 29],\ [8761, 8761, 40*w + 111],\ [8761, 8761, 40*w - 151],\ [8779, 8779, 23*w - 119],\ [8779, 8779, -23*w - 96],\ [8783, 8783, 41*w - 27],\ [8783, 8783, 41*w - 14],\ [8803, 8803, 38*w - 147],\ [8803, 8803, 33*w - 137],\ [8819, 8819, 41*w - 23],\ [8819, 8819, 41*w - 18],\ [8821, 8821, 35*w - 141],\ [8821, 8821, 36*w - 143],\ [8837, 8837, 43*w - 51],\ [8837, 8837, -43*w - 8],\ [8861, 8861, 42*w - 41],\ [8861, 8861, 42*w - 1],\ [8863, 8863, 7*w - 99],\ [8863, 8863, -7*w - 92],\ [8867, 8867, -57*w - 62],\ [8867, 8867, -52*w - 47],\ [8887, 8887, -9*w - 92],\ [8887, 8887, 9*w - 101],\ [8929, 8929, 25*w - 123],\ [8929, 8929, -25*w - 98],\ [8941, 8941, 4*w - 97],\ [8941, 8941, -4*w - 93],\ [8951, 8951, 43*w - 49],\ [8951, 8951, -43*w - 6],\ [8963, 8963, -51*w - 43],\ [8963, 8963, -59*w - 67],\ [8971, 8971, -14*w - 93],\ [8971, 8971, 14*w - 107],\ [9013, 9013, -13*w - 93],\ [9013, 9013, 13*w - 106],\ [9029, 9029, -50*w - 39],\ [9029, 9029, 50*w - 89],\ [9067, 9067, -11*w - 93],\ [9067, 9067, 11*w - 104],\ [9109, 9109, 28*w - 129],\ [9109, 9109, -28*w - 101],\ [9151, 9151, -25*w - 99],\ [9151, 9151, 25*w - 124],\ [9157, 9157, 29*w - 131],\ [9157, 9157, -29*w - 102],\ [9161, 9161, 42*w - 11],\ [9161, 9161, 42*w - 31],\ [9173, 9173, -46*w - 21],\ [9173, 9173, 46*w - 67],\ [9181, 9181, -5*w - 94],\ [9181, 9181, 5*w - 99],\ [9199, 9199, 43*w + 116],\ [9199, 9199, 43*w - 159],\ [9203, 9203, -44*w - 9],\ [9203, 9203, 44*w - 53],\ [9239, 9239, -56*w - 57],\ [9239, 9239, -55*w - 54],\ [9241, 9241, -21*w - 97],\ [9241, 9241, 21*w - 118],\ [9257, 9257, 42*w - 19],\ [9257, 9257, 42*w - 23],\ [9277, 9277, -9*w - 94],\ [9277, 9277, 9*w - 103],\ [9281, 9281, -50*w - 37],\ [9281, 9281, 50*w - 87],\ [9283, 9283, -27*w - 101],\ [9283, 9283, 27*w - 128],\ [9319, 9319, 35*w - 143],\ [9319, 9319, 38*w - 149],\ [9323, 9323, -44*w - 7],\ [9323, 9323, 44*w - 51],\ [9341, 9341, -47*w - 24],\ [9341, 9341, 47*w - 71],\ [9349, 9349, -20*w - 97],\ [9349, 9349, 20*w - 117],\ [9371, 9371, -45*w - 13],\ [9371, 9371, 45*w - 58],\ [9391, 9391, -29*w - 103],\ [9391, 9391, 29*w - 132],\ [9403, 9403, -17*w - 96],\ [9403, 9403, 17*w - 113],\ [9409, 97, -97],\ [9413, 9413, -49*w - 32],\ [9413, 9413, 49*w - 81],\ [9433, 9433, 23*w - 122],\ [9433, 9433, -23*w - 99],\ [9467, 9467, 43*w - 6],\ [9467, 9467, 43*w - 37],\ [9491, 9491, -53*w - 46],\ [9491, 9491, -60*w - 67],\ [9497, 9497, 43*w - 7],\ [9497, 9497, 43*w - 36],\ [9533, 9533, -59*w - 64],\ [9533, 9533, -54*w - 49],\ [9539, 9539, -44*w - 3],\ [9539, 9539, 44*w - 47],\ [9551, 9551, 43*w - 9],\ [9551, 9551, 43*w - 34],\ [9601, 9601, 25*w - 126],\ [9601, 9601, -25*w - 101],\ [9613, 9613, -17*w - 97],\ [9613, 9613, 17*w - 114],\ [9619, 9619, -13*w - 96],\ [9619, 9619, 13*w - 109],\ [9623, 9623, 51*w - 89],\ [9623, 9623, -51*w - 38],\ [9643, 9643, 7*w - 103],\ [9643, 9643, -7*w - 96],\ [9661, 9661, -19*w - 98],\ [9661, 9661, 19*w - 117],\ [9677, 9677, 43*w - 16],\ [9677, 9677, 43*w - 27],\ [9697, 9697, -w - 98],\ [9697, 9697, w - 99],\ [9719, 9719, -59*w - 63],\ [9719, 9719, -55*w - 51],\ [9739, 9739, -15*w - 97],\ [9739, 9739, 15*w - 112],\ [9743, 9743, -49*w - 29],\ [9743, 9743, 49*w - 78],\ [9749, 9749, 51*w - 88],\ [9749, 9749, -51*w - 37],\ [9769, 9769, -5*w - 97],\ [9769, 9769, 5*w - 102],\ [9781, 9781, -20*w - 99],\ [9781, 9781, 20*w - 119],\ [9787, 9787, -14*w - 97],\ [9787, 9787, 14*w - 111],\ [9791, 9791, -47*w - 19],\ [9791, 9791, 47*w - 66],\ [9803, 9803, 44*w - 41],\ [9803, 9803, 44*w - 3],\ [9811, 9811, 6*w - 103],\ [9811, 9811, -6*w - 97],\ [9829, 9829, -25*w - 102],\ [9829, 9829, 25*w - 127],\ [9833, 9833, -54*w - 47],\ [9833, 9833, -61*w - 68],\ [9871, 9871, 11*w - 108],\ [9871, 9871, -11*w - 97],\ [9887, 9887, -48*w - 23],\ [9887, 9887, 48*w - 71],\ [9907, 9907, -26*w - 103],\ [9907, 9907, 26*w - 129],\ [9929, 9929, 45*w - 49],\ [9929, 9929, -45*w - 4],\ [9949, 9949, 15*w - 113],\ [9949, 9949, -15*w - 98]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-2, 1, 0, 0, 1, 6, 6, 2, 2, 6, 6, 8, 8, -12, -12, -6, -6, -4, -4, 8, 8, -6, -6, -6, -6, 0, 0, 2, 2, -22, -16, -16, 18, 18, 8, 8, -16, -16, -12, -12, -10, -12, -12, 14, 14, -4, -4, 18, 18, -18, -18, 18, 18, -12, -12, -10, -10, 24, 24, -24, -24, 8, 8, 14, 14, 18, 18, -34, 14, 14, -16, -16, 36, 36, 6, 6, -10, -10, -10, -10, 12, 12, 32, 32, -6, -6, -36, -36, -16, -16, -4, -4, 0, 0, 36, 36, 6, 6, -46, 38, 38, 8, 8, 30, 30, 32, 32, -42, -42, -6, -6, 2, 2, -16, -16, -12, -12, 26, 26, -12, -12, -46, -46, 12, 12, -16, -16, -40, -40, 2, 2, -18, -18, 24, 24, -12, -12, -40, -40, 12, 12, -22, -18, -18, -22, -22, -54, -54, 20, 20, -36, -36, 44, 44, 56, 56, 6, 6, -24, -24, -46, 32, 32, -6, -6, -36, -36, -16, -16, -34, -34, -36, -36, 26, 26, -30, -30, 44, 44, 8, 8, 30, 30, -22, -22, -6, -6, 36, 36, -34, -34, 50, 50, -12, -12, 20, 20, 60, 60, 66, 66, 14, 14, 26, 26, -6, -6, -24, -24, 18, 18, 24, 24, -34, -34, -48, -48, 8, 8, 42, 42, -24, -24, 32, 32, -18, -18, -22, -22, 56, 56, -30, -30, 26, 26, 42, 42, 50, 50, 32, 32, 0, 0, 0, 0, -34, -34, 42, 42, -12, -12, 66, 66, -40, -40, -58, -58, 66, 66, -72, -72, 74, 74, 0, 0, 8, 8, -42, -42, -6, -6, -4, -4, 56, 56, 32, 32, -10, -10, -34, -34, 42, 42, -24, -24, -40, -40, 12, 12, 2, 2, 18, 18, 42, 42, -30, -30, 62, 62, 84, 84, -60, -60, 30, 30, -16, -16, -40, -40, -70, -70, 38, 38, 24, 24, 32, 32, 30, 30, 50, 50, -72, -72, 56, 56, -88, -88, -10, -10, 54, 54, 92, 92, 18, 18, 2, 2, 18, 18, -82, -82, -12, -12, -64, -64, 80, 80, -24, -24, -24, -24, -70, -70, 14, 14, 18, 18, -36, -36, 42, 42, 62, 62, -30, -30, -10, -10, 84, 84, -16, -16, 38, 38, 38, 38, -78, -78, -42, -42, 36, 36, 56, 56, 24, 24, 8, 8, 20, 20, -12, -12, 62, 62, -48, -48, -94, -94, -42, -42, -4, -4, 32, 32, -18, -18, 60, 60, 62, 62, -70, -66, -66, 44, 44, -22, -22, 12, 12, 54, 54, 0, 0, 6, 6, -96, -96, 36, 36, -40, -40, 0, 0, 78, 78, -10, -10, -70, -70, -64, -64, 30, 30, -22, -22, 60, 60, -16, -16, 24, 24, 30, 30, 86, 86, -46, -46, -90, -90, 56, 56, -40, -40, -82, -82, 2, 2, 80, 80, -66, -66, -40, -40, -96, -96, -58, -58, 72, 72, -102, -102, 48, 48, 50, 50, 102, 102, -16, -16, 72, 72, 74, 74, 108, 108, -64, -64, 8, 8, -58, -58, -42, -42, 2, 2, 90, 90, -120, -120, -52, -52, -46, -46, -12, -12, -58, -46, -46, -40, -40, 54, 54, -12, -12, 96, 96, -64, -64, -40, -40, -24, -24, -18, -18, 110, 110, 20, 20, 72, 72, -66, -66, 8, 8, 56, 56, 6, 6, 12, 12, 72, 72, -112, -112, -30, -30, -10, -10, 6, 6, 24, 24, -42, -42, -4, -4, -64, -64, 108, 108, 86, 86, 72, 72, 56, 56, -10, -10, -6, -6, 30, 30, 32, 32, -18, -18, 18, 18, 90, 90, -64, -64, 44, 44, -24, -24, -54, -54, -16, -16, 114, 114, -102, -102, 48, 48, -16, -16, -118, -118, -12, -12, -4, -4, -22, -22, -108, -108, 50, 50, -16, -16, 96, 96, -84, -84, 66, 66, 50, 50, -60, -60, 104, 104, -54, -54, -34, -34, -90, -90, 26, 26, 80, 80, -60, -60, 12, 12, 126, 126, 86, 86, 36, 36, -66, -66, 56, 56, -10, -10, -96, -96, -46, -46, -40, -40, -42, -42, -16, -16, 0, 0, -142, -70, -70, 114, 114, -12, -12, -78, -78, 68, 68, -64, -64, -16, -16, -54, -54, -10, -10, -58, -58, 18, 18, 24, 24, -142, -120, -120, 84, 84, -24, -24, -54, -54, 86, 86, 54, 54, -88, -88, -100, -100, 12, 12, -132, -132, -40, -40, -6, -6, 0, 0, 56, 56, -10, -10, 110, 110, -84, -84, 8, 8, 74, 74, 72, 72, 132, 132, -120, -120, -22, -22, -46, -46, 128, 128, 32, 32, -90, -90, 24, 24, 62, 62, 8, 8, 6, 6, 84, 84, -58, -58, -18, -18, -124, -124, 0, 0, 6, 6, -24, -24, 32, 32, -6, -6, 104, 104, 108, 108, -108, -108, -10, -10, -30, -30, 116, 116, 66, 66, -130, -130, -108, -108, -64, -64, 20, 20, 26, 26, 96, 96, -42, -42, 156, 156, 126, 126, 2, 2, -12, -12, 110, 110, 8, 8, -24, -24, 32, 32, 116, 116, -24, -24, -130, -130, 20, 20, -100, -100, 134, 134, 78, 78, 140, 140, -72, -72, -106, -106, 42, 42, 62, 62, 24, 24, -40, -40, 50, 50, -72, -72, 2, 2, 14, 14, 56, 56, 8, 8, 96, 96, -42, -42, 138, 138, -112, -112, -54, -54, 90, 90, -10, -10, -34, -34, 12, 12, -40, -40, 80, 80, -30, -30, 56, 56, 42, 42, 78, 78, 50, 50, 84, 84, -114, -114, -160, -160, 2, 2, 96, 96, -58, -58, -18, -18, 152, 152, 128, 128, 168, 168, -54, -54, 54, 54, -106, -106, 134, 134, -120, -120, -64, -64, 50, 50, 38, 38, 54, 54, -102, -102, 80, 80, 26, 26, -30, -30, -60, -60, -78, -78, -144, -144, 146, 146, -30, -30, 44, 44, 60, 60, -64, -64, -114, -114, 30, 30, -70, -70, -130, -130, 128, 128, -162, -162, -84, -84, -124, -124, -120, -120, -58, -58, 18, 18, 60, 60, -120, -120, 104, 104, 156, 156, -166, -166, 126, 126, -100, -100, -46, -46, -108, -108, -4, -4, -108, -108, 42, 42, -46, -46, -70, -70, -84, -84, -6, -6, -6, -6, -160, -160, 60, 60, 26, 26, -84, -84, -46, -46, -6, -6, -126, -126, 176, 176, -106, -106, 146, 146, 114, 114, 164, 164, -36, -36, -172, -172, 12, 12, -10, -10, 104, 104, -108, -108, -76, -76, -72, -72, -102, -102, 30, 30, 8, 8, -108, -108, -142, -142, 122, 122, -144, -144, -18, -18, -64, -64, 20, 20, -82, -82, -120, -120, -42, -42, -22, -22, -4, -4, 84, 84, -124, -124, 54, 54, 74, 74, -12, -12, 132, 132, -136, -136, 42, 42, 32, 32, -34, -34, 122, 122, -108, -108, 42, 42, -28, -28, -166, -166, 120, 120, -40, -40, -70, -70, -136, -136, 122, 122, -42, -42, 108, 108, -34, -34, 128, 128, 90, 90, -48, -48, 170, 170, -186, -186, 62, 62, 138, 138, 32, 32, -112, -112, 18, 18, -48, -48, -46, -46, -30, -30, 104, 104, -136, -136, -94, -132, -132, 74, 74, 78, 78, 78, 78, 150, 150, 48, 48, -78, -78, 180, 180, 62, 62, 38, 38, 116, 116, 24, 24, 32, 32, 86, 86, 108, 108, -58, -58, 24, 24, 20, 20, -84, -84, 60, 60, -58, -58, -46, -46, -148, -148, 12, 12, 126, 126, -16, -16, 110, 110, 126, 126, -136, -136, -96, -96, -28, -28, 54, 54, -22, -22] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([4, 2, 2])] = -1 AL_eigenvalues[ZF.ideal([7, 7, -w - 3])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]