/* 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([-22, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([72, 12, -18*w + 84]) primes_array = [ [2, 2, -3*w + 14],\ [3, 3, -w + 5],\ [3, 3, w + 5],\ [7, 7, 2*w + 9],\ [7, 7, 2*w - 9],\ [11, 11, -7*w + 33],\ [13, 13, -w - 3],\ [13, 13, -w + 3],\ [25, 5, -5],\ [29, 29, 3*w + 13],\ [29, 29, -3*w + 13],\ [59, 59, -w - 9],\ [59, 59, w - 9],\ [61, 61, 11*w - 51],\ [61, 61, 25*w - 117],\ [67, 67, 9*w - 43],\ [67, 67, -9*w - 43],\ [79, 79, 2*w - 3],\ [79, 79, -2*w - 3],\ [89, 89, 4*w - 21],\ [89, 89, -4*w - 21],\ [97, 97, -18*w + 85],\ [97, 97, 24*w - 113],\ [101, 101, -9*w - 41],\ [101, 101, -9*w + 41],\ [109, 109, 5*w + 21],\ [109, 109, -5*w + 21],\ [113, 113, -8*w - 39],\ [113, 113, 8*w - 39],\ [127, 127, 4*w - 15],\ [127, 127, -4*w - 15],\ [137, 137, 2*w - 15],\ [137, 137, -2*w - 15],\ [149, 149, -3*w - 7],\ [149, 149, 3*w - 7],\ [151, 151, 20*w - 93],\ [151, 151, 34*w - 159],\ [163, 163, 3*w - 19],\ [163, 163, -3*w - 19],\ [167, 167, 6*w + 25],\ [167, 167, 6*w - 25],\ [173, 173, 3*w - 5],\ [173, 173, -3*w - 5],\ [179, 179, -5*w - 27],\ [179, 179, 5*w - 27],\ [197, 197, -3*w - 1],\ [197, 197, 3*w - 1],\ [239, 239, 60*w - 281],\ [239, 239, 18*w - 83],\ [251, 251, 13*w - 63],\ [251, 251, -85*w + 399],\ [257, 257, -26*w + 123],\ [257, 257, 44*w - 207],\ [263, 263, 6*w - 23],\ [263, 263, -6*w - 23],\ [271, 271, -4*w - 9],\ [271, 271, 4*w - 9],\ [277, 277, 29*w - 135],\ [277, 277, 43*w - 201],\ [289, 17, -17],\ [293, 293, 21*w - 97],\ [293, 293, 63*w - 295],\ [313, 313, -12*w - 59],\ [313, 313, 12*w - 59],\ [331, 331, -3*w - 23],\ [331, 331, 3*w - 23],\ [349, 349, 7*w - 27],\ [349, 349, 7*w + 27],\ [353, 353, 2*w - 21],\ [353, 353, -2*w - 21],\ [359, 359, -12*w - 53],\ [359, 359, 12*w - 53],\ [361, 19, -19],\ [373, 373, 89*w - 417],\ [373, 373, 19*w - 87],\ [379, 379, 15*w - 73],\ [379, 379, -15*w - 73],\ [401, 401, 10*w - 51],\ [401, 401, -10*w - 51],\ [419, 419, -w - 21],\ [419, 419, w - 21],\ [431, 431, -6*w - 19],\ [431, 431, 6*w - 19],\ [433, 433, -6*w - 35],\ [433, 433, 6*w - 35],\ [439, 439, 38*w - 177],\ [439, 439, 52*w - 243],\ [443, 443, 7*w - 39],\ [443, 443, -7*w - 39],\ [449, 449, -14*w - 69],\ [449, 449, 14*w - 69],\ [461, 461, 15*w - 67],\ [461, 461, -15*w - 67],\ [467, 467, 67*w - 315],\ [467, 467, -31*w + 147],\ [479, 479, 30*w - 139],\ [479, 479, 72*w - 337],\ [499, 499, 21*w - 101],\ [499, 499, -105*w + 493],\ [503, 503, 6*w - 17],\ [503, 503, -6*w - 17],\ [521, 521, 58*w - 273],\ [521, 521, -40*w + 189],\ [529, 23, -23],\ [541, 541, -5*w - 3],\ [541, 541, 5*w - 3],\ [557, 557, 9*w - 35],\ [557, 557, 9*w + 35],\ [577, 577, 6*w - 37],\ [577, 577, -6*w - 37],\ [587, 587, -11*w - 57],\ [587, 587, 11*w - 57],\ [607, 607, 28*w + 129],\ [607, 607, -28*w + 129],\ [613, 613, 23*w - 105],\ [613, 613, 121*w - 567],\ [617, 617, -8*w - 45],\ [617, 617, 8*w - 45],\ [619, 619, -9*w - 49],\ [619, 619, 9*w - 49],\ [641, 641, 2*w - 27],\ [641, 641, -2*w - 27],\ [643, 643, -3*w - 29],\ [643, 643, 3*w - 29],\ [677, 677, -21*w - 95],\ [677, 677, 21*w - 95],\ [683, 683, -23*w - 111],\ [683, 683, -23*w + 111],\ [691, 691, -33*w + 157],\ [691, 691, 93*w - 437],\ [701, 701, 39*w - 181],\ [701, 701, 81*w - 379],\ [733, 733, -17*w - 75],\ [733, 733, 17*w - 75],\ [743, 743, -6*w - 7],\ [743, 743, 6*w - 7],\ [821, 821, 9*w - 31],\ [821, 821, -9*w - 31],\ [853, 853, -7*w - 15],\ [853, 853, 7*w - 15],\ [859, 859, 75*w - 353],\ [859, 859, -51*w + 241],\ [877, 877, 37*w - 171],\ [877, 877, 107*w - 501],\ [881, 881, 32*w - 153],\ [881, 881, -32*w - 153],\ [883, 883, 69*w - 325],\ [883, 883, -57*w + 269],\ [887, 887, -18*w + 79],\ [887, 887, 18*w + 79],\ [907, 907, 21*w - 103],\ [907, 907, -21*w - 103],\ [919, 919, -32*w + 147],\ [919, 919, 32*w + 147],\ [929, 929, 16*w - 81],\ [929, 929, -16*w - 81],\ [941, 941, 9*w - 29],\ [941, 941, -9*w - 29],\ [947, 947, -7*w - 45],\ [947, 947, 7*w - 45],\ [961, 31, -31],\ [967, 967, 8*w - 21],\ [967, 967, -8*w - 21],\ [971, 971, -5*w - 39],\ [971, 971, 5*w - 39],\ [977, 977, -28*w + 135],\ [977, 977, -28*w - 135],\ [997, 997, 7*w - 9],\ [997, 997, -7*w - 9],\ [1031, 1031, -30*w + 137],\ [1031, 1031, -30*w - 137],\ [1049, 1049, 10*w - 57],\ [1049, 1049, -10*w - 57],\ [1063, 1063, 14*w + 57],\ [1063, 1063, 14*w - 57],\ [1069, 1069, 7*w - 3],\ [1069, 1069, -7*w - 3],\ [1117, 1117, 13*w - 51],\ [1117, 1117, 13*w + 51],\ [1123, 1123, -27*w - 131],\ [1123, 1123, 27*w - 131],\ [1151, 1151, 96*w - 449],\ [1151, 1151, 54*w - 251],\ [1153, 1153, 18*w - 91],\ [1153, 1153, -18*w - 91],\ [1171, 1171, 3*w - 37],\ [1171, 1171, -3*w - 37],\ [1193, 1193, 8*w - 51],\ [1193, 1193, -8*w - 51],\ [1223, 1223, -24*w - 107],\ [1223, 1223, 24*w - 107],\ [1229, 1229, 15*w + 61],\ [1229, 1229, 15*w - 61],\ [1231, 1231, 20*w + 87],\ [1231, 1231, -20*w + 87],\ [1259, 1259, -59*w + 279],\ [1259, 1259, 95*w - 447],\ [1291, 1291, 15*w - 79],\ [1291, 1291, -15*w - 79],\ [1307, 1307, -11*w - 63],\ [1307, 1307, 11*w - 63],\ [1319, 1319, 12*w - 43],\ [1319, 1319, -12*w - 43],\ [1321, 1321, -12*w - 67],\ [1321, 1321, 12*w - 67],\ [1327, 1327, -8*w - 9],\ [1327, 1327, 8*w - 9],\ [1369, 37, -37],\ [1381, 1381, 19*w + 81],\ [1381, 1381, -19*w + 81],\ [1399, 1399, -8*w - 3],\ [1399, 1399, 8*w - 3],\ [1409, 1409, 136*w - 639],\ [1409, 1409, -46*w + 219],\ [1429, 1429, 25*w - 111],\ [1429, 1429, -25*w - 111],\ [1433, 1433, 2*w - 39],\ [1433, 1433, -2*w - 39],\ [1447, 1447, 74*w - 345],\ [1447, 1447, 88*w - 411],\ [1471, 1471, -10*w - 27],\ [1471, 1471, 10*w - 27],\ [1483, 1483, -3*w - 41],\ [1483, 1483, 3*w - 41],\ [1487, 1487, -12*w - 41],\ [1487, 1487, 12*w - 41],\ [1489, 1489, -24*w - 119],\ [1489, 1489, 24*w - 119],\ [1493, 1493, 9*w - 17],\ [1493, 1493, -9*w - 17],\ [1499, 1499, -w - 39],\ [1499, 1499, w - 39],\ [1523, 1523, -7*w - 51],\ [1523, 1523, 7*w - 51],\ [1559, 1559, -42*w + 193],\ [1559, 1559, 42*w + 193],\ [1571, 1571, 127*w - 597],\ [1571, 1571, -55*w + 261],\ [1583, 1583, 66*w - 307],\ [1583, 1583, 108*w - 505],\ [1597, 1597, 17*w + 69],\ [1597, 1597, 17*w - 69],\ [1609, 1609, 6*w - 49],\ [1609, 1609, -6*w - 49],\ [1613, 1613, 9*w - 13],\ [1613, 1613, -9*w - 13],\ [1663, 1663, 16*w - 63],\ [1663, 1663, 16*w + 63],\ [1669, 1669, 35*w - 159],\ [1669, 1669, -35*w - 159],\ [1681, 41, -41],\ [1693, 1693, 13*w - 45],\ [1693, 1693, -13*w - 45],\ [1697, 1697, -64*w + 303],\ [1697, 1697, 118*w - 555],\ [1699, 1699, 9*w - 59],\ [1699, 1699, -9*w - 59],\ [1721, 1721, -38*w - 183],\ [1721, 1721, -38*w + 183],\ [1733, 1733, -9*w - 7],\ [1733, 1733, 9*w - 7],\ [1747, 1747, -21*w - 107],\ [1747, 1747, 21*w - 107],\ [1753, 1753, -48*w + 229],\ [1753, 1753, 162*w - 761],\ [1759, 1759, -10*w - 21],\ [1759, 1759, 10*w - 21],\ [1787, 1787, 109*w - 513],\ [1787, 1787, -73*w + 345],\ [1789, 1789, 83*w - 387],\ [1789, 1789, 97*w - 453],\ [1823, 1823, 114*w - 533],\ [1823, 1823, 72*w - 335],\ [1847, 1847, 48*w + 221],\ [1847, 1847, -48*w + 221],\ [1849, 43, -43],\ [1861, 1861, -29*w - 129],\ [1861, 1861, 29*w - 129],\ [1873, 1873, -12*w - 71],\ [1873, 1873, 12*w - 71],\ [1877, 1877, -27*w - 119],\ [1877, 1877, 27*w - 119],\ [1907, 1907, 13*w - 75],\ [1907, 1907, -13*w - 75],\ [1933, 1933, 11*w - 27],\ [1933, 1933, -11*w - 27],\ [1949, 1949, 75*w - 349],\ [1949, 1949, 117*w - 547],\ [1997, 1997, 51*w - 235],\ [1997, 1997, 177*w - 829],\ [1999, 1999, 22*w + 93],\ [1999, 1999, -22*w + 93],\ [2003, 2003, -w - 45],\ [2003, 2003, w - 45],\ [2011, 2011, -3*w - 47],\ [2011, 2011, 3*w - 47],\ [2017, 2017, -6*w - 53],\ [2017, 2017, 6*w - 53],\ [2027, 2027, -47*w + 225],\ [2027, 2027, 47*w + 225],\ [2053, 2053, 157*w - 735],\ [2053, 2053, 59*w - 273],\ [2063, 2063, 24*w + 103],\ [2063, 2063, -24*w + 103],\ [2083, 2083, 147*w - 691],\ [2083, 2083, -63*w + 299],\ [2087, 2087, 18*w - 71],\ [2087, 2087, 18*w + 71],\ [2099, 2099, 11*w - 69],\ [2099, 2099, -11*w - 69],\ [2111, 2111, -30*w - 133],\ [2111, 2111, 30*w - 133],\ [2113, 2113, 36*w - 175],\ [2113, 2113, -36*w - 175],\ [2137, 2137, -66*w + 313],\ [2137, 2137, 144*w - 677],\ [2141, 2141, -15*w - 53],\ [2141, 2141, 15*w - 53],\ [2161, 2161, 12*w - 73],\ [2161, 2161, -12*w - 73],\ [2179, 2179, -21*w - 109],\ [2179, 2179, 21*w - 109],\ [2203, 2203, 3*w - 49],\ [2203, 2203, -3*w - 49],\ [2207, 2207, 12*w - 31],\ [2207, 2207, -12*w - 31],\ [2209, 47, -47],\ [2213, 2213, 123*w - 575],\ [2213, 2213, 81*w - 377],\ [2221, 2221, 11*w - 21],\ [2221, 2221, -11*w - 21],\ [2239, 2239, 20*w + 81],\ [2239, 2239, 20*w - 81],\ [2267, 2267, 31*w - 153],\ [2267, 2267, -31*w - 153],\ [2281, 2281, -18*w - 97],\ [2281, 2281, 18*w - 97],\ [2287, 2287, -14*w - 45],\ [2287, 2287, 14*w - 45],\ [2297, 2297, 182*w - 855],\ [2297, 2297, -56*w + 267],\ [2309, 2309, 57*w - 263],\ [2309, 2309, 183*w - 857],\ [2347, 2347, -81*w + 383],\ [2347, 2347, 129*w - 607],\ [2351, 2351, 84*w - 391],\ [2351, 2351, 126*w - 589],\ [2377, 2377, 126*w - 593],\ [2377, 2377, -84*w + 397],\ [2383, 2383, 16*w - 57],\ [2383, 2383, -16*w - 57],\ [2389, 2389, 17*w - 63],\ [2389, 2389, -17*w - 63],\ [2437, 2437, -11*w - 15],\ [2437, 2437, 11*w - 15],\ [2467, 2467, 111*w - 523],\ [2467, 2467, -99*w + 467],\ [2473, 2473, -102*w + 481],\ [2473, 2473, 108*w - 509],\ [2477, 2477, 21*w + 85],\ [2477, 2477, 21*w - 85],\ [2503, 2503, 166*w - 777],\ [2503, 2503, 68*w - 315],\ [2531, 2531, -65*w + 309],\ [2531, 2531, 173*w - 813],\ [2539, 2539, -45*w - 217],\ [2539, 2539, -45*w + 217],\ [2543, 2543, -12*w - 25],\ [2543, 2543, 12*w - 25],\ [2549, 2549, -15*w - 49],\ [2549, 2549, 15*w - 49],\ [2551, 2551, -26*w + 111],\ [2551, 2551, 26*w + 111],\ [2579, 2579, -w - 51],\ [2579, 2579, w - 51],\ [2591, 2591, -36*w - 161],\ [2591, 2591, 36*w - 161],\ [2633, 2633, 28*w - 141],\ [2633, 2633, -28*w - 141],\ [2647, 2647, -32*w - 141],\ [2647, 2647, 32*w - 141],\ [2689, 2689, -6*w - 59],\ [2689, 2689, 6*w - 59],\ [2699, 2699, -5*w - 57],\ [2699, 2699, 5*w - 57],\ [2707, 2707, -9*w - 67],\ [2707, 2707, 9*w - 67],\ [2719, 2719, 212*w - 993],\ [2719, 2719, 58*w - 267],\ [2729, 2729, -74*w + 351],\ [2729, 2729, 164*w - 771],\ [2731, 2731, -27*w - 137],\ [2731, 2731, 27*w - 137],\ [2741, 2741, 15*w - 47],\ [2741, 2741, -15*w - 47],\ [2749, 2749, -235*w + 1101],\ [2749, 2749, -53*w + 243],\ [2753, 2753, -32*w - 159],\ [2753, 2753, 32*w - 159],\ [2767, 2767, 82*w - 381],\ [2767, 2767, 152*w - 711],\ [2777, 2777, -44*w - 213],\ [2777, 2777, 44*w - 213],\ [2789, 2789, 93*w - 433],\ [2789, 2789, 135*w - 631],\ [2791, 2791, 14*w - 39],\ [2791, 2791, -14*w - 39],\ [2803, 2803, 51*w - 245],\ [2803, 2803, -243*w + 1141],\ [2809, 53, -53],\ [2819, 2819, -61*w + 291],\ [2819, 2819, 205*w - 963],\ [2837, 2837, 39*w - 175],\ [2837, 2837, -39*w - 175],\ [2843, 2843, -13*w - 81],\ [2843, 2843, 13*w - 81],\ [2879, 2879, -12*w - 17],\ [2879, 2879, 12*w - 17],\ [2897, 2897, 4*w - 57],\ [2897, 2897, -4*w - 57],\ [2903, 2903, 18*w + 65],\ [2903, 2903, 18*w - 65],\ [2917, 2917, -31*w + 135],\ [2917, 2917, 31*w + 135],\ [2953, 2953, 24*w - 125],\ [2953, 2953, -24*w - 125],\ [2963, 2963, 11*w - 75],\ [2963, 2963, -11*w - 75],\ [2971, 2971, -15*w - 89],\ [2971, 2971, 15*w - 89],\ [2999, 2999, -12*w - 13],\ [2999, 2999, 12*w - 13],\ [3001, 3001, 30*w - 151],\ [3001, 3001, -30*w - 151],\ [3019, 3019, -39*w - 191],\ [3019, 3019, 39*w - 191],\ [3041, 3041, -22*w - 117],\ [3041, 3041, 22*w - 117],\ [3067, 3067, 21*w - 113],\ [3067, 3067, -21*w - 113],\ [3079, 3079, 22*w - 87],\ [3079, 3079, 22*w + 87],\ [3083, 3083, -19*w + 105],\ [3083, 3083, -19*w - 105],\ [3089, 3089, 196*w - 921],\ [3089, 3089, -70*w + 333],\ [3109, 3109, -17*w - 57],\ [3109, 3109, 17*w - 57],\ [3119, 3119, 12*w - 7],\ [3119, 3119, -12*w - 7],\ [3167, 3167, -12*w - 1],\ [3167, 3167, 12*w - 1],\ [3169, 3169, -60*w + 287],\ [3169, 3169, 60*w + 287],\ [3181, 3181, 19*w + 69],\ [3181, 3181, 19*w - 69],\ [3217, 3217, -42*w - 205],\ [3217, 3217, 42*w - 205],\ [3229, 3229, 47*w - 213],\ [3229, 3229, -47*w - 213],\ [3253, 3253, 91*w - 423],\ [3253, 3253, 161*w - 753],\ [3257, 3257, 14*w - 87],\ [3257, 3257, -14*w - 87],\ [3259, 3259, -9*w - 71],\ [3259, 3259, 9*w - 71],\ [3319, 3319, -52*w - 237],\ [3319, 3319, -52*w + 237],\ [3323, 3323, 187*w - 879],\ [3323, 3323, -79*w + 375],\ [3331, 3331, 15*w - 91],\ [3331, 3331, -15*w - 91],\ [3343, 3343, -62*w + 285],\ [3343, 3343, 62*w + 285],\ [3347, 3347, 49*w - 237],\ [3347, 3347, -49*w - 237],\ [3371, 3371, 37*w - 183],\ [3371, 3371, -37*w - 183],\ [3373, 3373, -29*w + 123],\ [3373, 3373, 29*w + 123],\ [3407, 3407, 18*w - 61],\ [3407, 3407, -18*w - 61],\ [3433, 3433, -6*w - 65],\ [3433, 3433, 6*w - 65],\ [3457, 3457, 24*w - 127],\ [3457, 3457, -24*w - 127],\ [3461, 3461, -21*w - 79],\ [3461, 3461, 21*w - 79],\ [3491, 3491, 23*w - 123],\ [3491, 3491, -23*w - 123],\ [3499, 3499, 225*w - 1057],\ [3499, 3499, -69*w + 329],\ [3511, 3511, 86*w - 399],\ [3511, 3511, 184*w - 861],\ [3517, 3517, 119*w - 555],\ [3517, 3517, 133*w - 621],\ [3527, 3527, 78*w - 361],\ [3527, 3527, 204*w - 955],\ [3529, 3529, -36*w - 179],\ [3529, 3529, 36*w - 179],\ [3533, 3533, 39*w - 173],\ [3533, 3533, -39*w - 173],\ [3541, 3541, -35*w + 153],\ [3541, 3541, 35*w + 153],\ [3547, 3547, 9*w - 73],\ [3547, 3547, -9*w - 73],\ [3559, 3559, -28*w + 117],\ [3559, 3559, 28*w + 117],\ [3581, 3581, 15*w - 37],\ [3581, 3581, -15*w - 37],\ [3583, 3583, 14*w - 27],\ [3583, 3583, -14*w - 27],\ [3607, 3607, -16*w - 45],\ [3607, 3607, 16*w - 45],\ [3617, 3617, -4*w - 63],\ [3617, 3617, 4*w - 63],\ [3637, 3637, -13*w - 9],\ [3637, 3637, 13*w - 9],\ [3671, 3671, 30*w + 127],\ [3671, 3671, -30*w + 127],\ [3697, 3697, 6*w - 67],\ [3697, 3697, -6*w - 67],\ [3709, 3709, 13*w - 3],\ [3709, 3709, -13*w - 3],\ [3793, 3793, 216*w - 1015],\ [3793, 3793, -78*w + 371],\ [3797, 3797, 63*w - 289],\ [3797, 3797, 273*w - 1279],\ [3823, 3823, -34*w + 147],\ [3823, 3823, 34*w + 147],\ [3833, 3833, 58*w - 279],\ [3833, 3833, -292*w + 1371],\ [3847, 3847, 26*w + 105],\ [3847, 3847, 26*w - 105],\ [3851, 3851, 13*w - 87],\ [3851, 3851, -13*w - 87],\ [3863, 3863, -36*w + 157],\ [3863, 3863, 36*w + 157],\ [3881, 3881, 2*w - 63],\ [3881, 3881, -2*w - 63],\ [3911, 3911, 84*w - 389],\ [3911, 3911, 210*w - 983],\ [3931, 3931, -33*w - 167],\ [3931, 3931, 33*w - 167],\ [3947, 3947, -w - 63],\ [3947, 3947, w - 63],\ [3967, 3967, -56*w + 255],\ [3967, 3967, -56*w - 255],\ [3989, 3989, -15*w - 31],\ [3989, 3989, 15*w - 31],\ [4019, 4019, -71*w + 339],\ [4019, 4019, 251*w - 1179],\ [4021, 4021, -61*w - 279],\ [4021, 4021, -61*w + 279],\ [4027, 4027, -3*w - 65],\ [4027, 4027, 3*w - 65],\ [4049, 4049, 50*w - 243],\ [4049, 4049, -50*w - 243],\ [4051, 4051, 207*w - 973],\ [4051, 4051, -87*w + 413],\ [4057, 4057, 12*w - 85],\ [4057, 4057, -12*w - 85],\ [4073, 4073, 46*w - 225],\ [4073, 4073, -46*w - 225],\ [4111, 4111, -16*w - 39],\ [4111, 4111, 16*w - 39],\ [4127, 4127, 54*w - 245],\ [4127, 4127, -54*w - 245],\ [4129, 4129, -90*w + 427],\ [4129, 4129, 204*w - 959],\ [4133, 4133, 159*w - 743],\ [4133, 4133, 117*w - 545],\ [4139, 4139, 31*w - 159],\ [4139, 4139, -31*w - 159],\ [4157, 4157, 27*w + 109],\ [4157, 4157, 27*w - 109],\ [4211, 4211, -5*w - 69],\ [4211, 4211, 5*w - 69],\ [4217, 4217, 8*w - 75],\ [4217, 4217, -8*w - 75],\ [4231, 4231, 14*w - 9],\ [4231, 4231, -14*w - 9],\ [4253, 4253, 69*w + 317],\ [4253, 4253, -69*w + 317],\ [4273, 4273, -96*w + 455],\ [4273, 4273, 198*w - 931],\ [4283, 4283, 67*w + 321],\ [4283, 4283, -67*w + 321],\ [4337, 4337, -14*w - 93],\ [4337, 4337, 14*w - 93],\ [4339, 4339, -99*w + 469],\ [4339, 4339, 195*w - 917],\ [4373, 4373, 21*w - 73],\ [4373, 4373, -21*w - 73],\ [4391, 4391, 24*w - 91],\ [4391, 4391, -24*w - 91],\ [4397, 4397, 57*w - 259],\ [4397, 4397, -57*w - 259],\ [4409, 4409, 4*w - 69],\ [4409, 4409, -4*w - 69],\ [4421, 4421, -15*w - 23],\ [4421, 4421, 15*w - 23],\ [4463, 4463, -48*w - 215],\ [4463, 4463, 48*w - 215],\ [4481, 4481, -22*w - 123],\ [4481, 4481, 22*w - 123],\ [4513, 4513, 186*w - 875],\ [4513, 4513, -108*w + 511],\ [4517, 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[8263, 8263, -86*w - 393],\ [8269, 8269, -65*w - 291],\ [8269, 8269, 65*w - 291],\ [8273, 8273, -92*w + 441],\ [8273, 8273, 92*w + 441],\ [8293, 8293, 91*w - 417],\ [8293, 8293, 413*w - 1935],\ [8297, 8297, 4*w - 93],\ [8297, 8297, -4*w - 93],\ [8311, 8311, -26*w - 81],\ [8311, 8311, 26*w - 81],\ [8353, 8353, 24*w - 145],\ [8353, 8353, -24*w - 145],\ [8363, 8363, 11*w - 105],\ [8363, 8363, -11*w - 105],\ [8369, 8369, 266*w - 1251],\ [8369, 8369, -140*w + 663],\ [8387, 8387, -41*w - 213],\ [8387, 8387, 41*w - 213],\ [8389, 8389, 23*w - 57],\ [8389, 8389, -23*w - 57],\ [8419, 8419, -9*w - 101],\ [8419, 8419, 9*w - 101],\ [8423, 8423, 72*w - 325],\ [8423, 8423, -72*w - 325],\ [8447, 8447, 24*w - 65],\ [8447, 8447, -24*w - 65],\ [8461, 8461, -59*w - 261],\ [8461, 8461, 59*w - 261],\ [8527, 8527, 46*w + 195],\ [8527, 8527, -46*w + 195],\ [8537, 8537, -26*w - 153],\ [8537, 8537, 26*w - 153],\ [8539, 8539, -81*w - 391],\ [8539, 8539, -81*w + 391],\ [8543, 8543, -84*w + 383],\ [8543, 8543, -84*w - 383],\ [8563, 8563, 39*w - 205],\ [8563, 8563, -39*w - 205],\ [8597, 8597, 99*w + 455],\ [8597, 8597, -99*w + 455],\ [8599, 8599, 28*w - 93],\ [8599, 8599, -28*w - 93],\ [8623, 8623, -22*w - 45],\ [8623, 8623, 22*w - 45],\ [8627, 8627, -w - 93],\ [8627, 8627, w - 93],\ [8663, 8663, -48*w + 205],\ [8663, 8663, 48*w + 205],\ [8699, 8699, -19*w - 129],\ [8699, 8699, 19*w - 129],\ [8713, 8713, 12*w - 109],\ [8713, 8713, -12*w - 109],\ [8719, 8719, -20*w - 9],\ [8719, 8719, 20*w - 9],\ [8737, 8737, -36*w - 193],\ [8737, 8737, 36*w - 193],\ [8741, 8741, 21*w - 31],\ [8741, 8741, -21*w - 31],\ [8761, 8761, -30*w - 169],\ [8761, 8761, 30*w - 169],\ [8779, 8779, 351*w - 1649],\ [8779, 8779, -111*w + 529],\ [8803, 8803, -33*w - 181],\ [8803, 8803, 33*w - 181],\ [8807, 8807, 66*w - 295],\ [8807, 8807, -66*w - 295],\ [8821, 8821, 31*w - 111],\ [8821, 8821, -31*w - 111],\ [8839, 8839, 32*w - 117],\ [8839, 8839, 32*w + 117],\ [8849, 8849, -56*w - 279],\ [8849, 8849, 56*w - 279],\ [8861, 8861, -21*w - 29],\ [8861, 8861, 21*w - 29],\ [8863, 8863, -52*w + 225],\ [8863, 8863, 52*w + 225],\ [8867, 8867, -101*w - 483],\ [8867, 8867, 101*w - 483],\ [8887, 8887, 64*w - 285],\ [8887, 8887, -64*w - 285],\ [8951, 8951, 24*w - 61],\ [8951, 8951, -24*w - 61],\ [8963, 8963, 239*w - 1125],\ [8963, 8963, -167*w + 789],\ [8969, 8969, -80*w - 387],\ [8969, 8969, 80*w - 387],\ [9001, 9001, 18*w - 127],\ [9001, 9001, -18*w - 127],\ [9043, 9043, -87*w + 419],\ [9043, 9043, -87*w - 419],\ [9067, 9067, 21*w - 137],\ [9067, 9067, -21*w - 137],\ [9091, 9091, 345*w - 1621],\ [9091, 9091, -117*w + 557],\ [9103, 9103, 44*w + 183],\ [9103, 9103, -44*w + 183],\ [9127, 9127, 22*w - 39],\ [9127, 9127, -22*w - 39],\ [9151, 9151, 376*w - 1761],\ [9151, 9151, 110*w - 507],\ [9161, 9161, 68*w - 333],\ [9161, 9161, -68*w - 333],\ [9173, 9173, 21*w - 23],\ [9173, 9173, -21*w - 23],\ [9181, 9181, -85*w - 387],\ [9181, 9181, 85*w - 387],\ [9227, 9227, 97*w + 465],\ [9227, 9227, -97*w + 465],\ [9239, 9239, 78*w - 353],\ [9239, 9239, -78*w - 353],\ [9241, 9241, 342*w - 1607],\ [9241, 9241, -120*w + 571],\ [9319, 9319, 100*w + 459],\ [9319, 9319, -100*w + 459],\ [9337, 9337, -48*w - 245],\ [9337, 9337, 48*w - 245],\ [9341, 9341, -21*w - 19],\ [9341, 9341, 21*w - 19],\ [9349, 9349, -43*w + 177],\ [9349, 9349, 43*w + 177],\ [9377, 9377, 14*w - 117],\ [9377, 9377, -14*w - 117],\ [9391, 9391, 316*w - 1479],\ [9391, 9391, 134*w - 621],\ [9403, 9403, -63*w - 311],\ [9403, 9403, 63*w - 311],\ [9413, 9413, -21*w - 17],\ [9413, 9413, 21*w - 17],\ [9419, 9419, 289*w - 1359],\ [9419, 9419, -145*w + 687],\ [9437, 9437, 39*w - 155],\ [9437, 9437, 39*w + 155],\ [9479, 9479, -48*w + 203],\ [9479, 9479, 48*w + 203],\ [9491, 9491, -53*w - 267],\ [9491, 9491, 53*w - 267],\ [9497, 9497, 16*w - 123],\ [9497, 9497, -16*w - 123],\ [9511, 9511, 200*w - 933],\ [9511, 9511, 214*w - 999],\ [9533, 9533, 21*w - 13],\ [9533, 9533, -21*w - 13],\ [9601, 9601, 12*w - 113],\ [9601, 9601, -12*w - 113],\ [9613, 9613, 23*w - 45],\ [9613, 9613, -23*w - 45],\ [9619, 9619, -21*w - 139],\ [9619, 9619, 21*w - 139],\ [9631, 9631, -50*w + 213],\ [9631, 9631, 50*w + 213],\ [9677, 9677, 21*w - 5],\ [9677, 9677, -21*w - 5],\ [9679, 9679, 28*w - 87],\ [9679, 9679, -28*w - 87],\ [9689, 9689, -154*w + 729],\ [9689, 9689, 280*w - 1317],\ [9719, 9719, -72*w - 323],\ [9719, 9719, 72*w - 323],\ [9739, 9739, 45*w - 233],\ [9739, 9739, -45*w - 233],\ [9743, 9743, -36*w - 137],\ [9743, 9743, 36*w - 137],\ [9767, 9767, 282*w - 1319],\ [9767, 9767, 156*w - 725],\ [9769, 9769, 96*w - 461],\ [9769, 9769, -450*w + 2113],\ [9781, 9781, -25*w - 63],\ [9781, 9781, 25*w - 63],\ [9817, 9817, 6*w - 103],\ [9817, 9817, -6*w - 103],\ [9829, 9829, 167*w - 777],\ [9829, 9829, 265*w - 1239],\ [9857, 9857, -106*w + 507],\ [9857, 9857, 106*w + 507],\ [9859, 9859, 51*w - 259],\ [9859, 9859, -51*w - 259],\ [9883, 9883, -27*w - 161],\ [9883, 9883, 27*w - 161],\ [9923, 9923, 271*w - 1275],\ [9923, 9923, -163*w + 771],\ [9931, 9931, 327*w - 1537],\ [9931, 9931, -135*w + 641],\ [9941, 9941, -111*w + 511],\ [9941, 9941, 111*w + 511],\ [9973, 9973, 49*w + 207],\ [9973, 9973, -49*w + 207]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [0, -1, -1, 0, 0, 4, -2, -2, -6, 6, 6, 4, 4, -2, -2, -4, -4, -8, -8, -6, -6, 2, 2, -18, -18, -2, -2, 18, 18, -8, -8, -6, -6, 14, 14, -16, -16, 12, 12, 24, 24, 6, 6, 12, 12, -18, -18, -16, -16, 20, 20, 2, 2, -8, -8, 8, 8, -26, -26, -30, -18, -18, -6, -6, 20, 20, 30, 30, 2, 2, -24, -24, -22, -10, -10, 20, 20, -30, -30, 12, 12, 32, 32, -14, -14, 0, 0, 20, 20, -14, -14, -26, -26, -36, -36, -16, -16, 12, 12, 24, 24, 26, 26, 18, -18, -18, -26, -26, 2, 2, -44, -44, -40, -40, 38, 38, 42, 42, -44, -44, -14, -14, 12, 12, -2, -2, 4, 4, -4, -4, 6, 6, 14, 14, -8, -8, 30, 30, -10, -10, -12, -12, -18, -18, 50, 50, -4, -4, 8, 8, 4, 4, 16, 16, 50, 50, 6, 6, 12, 12, 2, -16, -16, 36, 36, -30, -30, -26, -26, -40, -40, 26, 26, 16, 16, 14, 14, -50, -50, -36, -36, 0, 0, -62, -62, -20, -20, -22, -22, 24, 24, 38, 38, 8, 8, -60, -60, 4, 4, -28, -28, 8, 8, -22, -22, -40, -40, -38, -10, -10, 0, 0, 18, 18, -10, -10, -6, -6, 48, 48, -40, -40, -60, -60, -64, -64, 50, 50, -50, -50, 20, 20, -36, -36, -40, -40, 60, 60, -16, -16, 78, 78, 10, 10, 54, 54, -8, -8, 22, 22, -46, -66, -66, -14, -14, -4, -4, 26, 26, 62, 62, -52, -52, -38, -38, 40, 40, -12, -12, 62, 62, -80, -80, -8, -8, -70, -58, -58, 50, 50, -18, -18, 12, 12, -18, -18, -74, -74, -58, -58, -40, -40, -20, -20, 84, 84, 2, 2, 36, 36, -58, -58, 48, 48, -20, -20, -8, -8, -84, -84, 48, 48, 2, 2, -38, -38, -58, -58, 18, 18, 12, 12, 84, 84, -32, -32, -94, 30, 30, -2, -2, 24, 24, 84, 84, -22, -22, 72, 72, -54, -54, 78, 78, 52, 52, 0, 0, -22, -22, -24, -24, -10, -10, 38, 38, -68, -68, 42, 42, -42, -42, -32, -32, -52, -52, 36, 36, 80, 80, -2, -2, 16, 16, 60, 60, -96, -96, -70, -70, 48, 48, -62, -62, -12, -12, 60, 60, 24, 24, -6, -6, -28, -28, 46, 46, 62, 62, 18, 18, 40, 40, -22, -22, 46, 46, 64, 64, -100, -100, -102, 12, 12, 46, 46, -76, -76, 0, 0, -30, -30, -40, -40, -58, -58, 10, 10, 28, 28, -12, -12, 88, 88, -38, -38, -28, -28, -14, -14, 20, 20, -80, -80, 36, 36, 50, 50, 70, 70, 0, 0, 16, 16, 34, 34, -66, -66, 82, 82, 14, 14, 38, 38, 90, 90, 20, 20, 64, 64, 4, 4, -4, -4, 104, 104, -20, -20, -12, -12, -66, -66, -64, -64, -54, -54, 34, 34, 14, 14, -20, -20, 52, 52, 0, 0, -98, -98, -88, -88, 74, 74, 118, 118, -74, -74, 36, 36, 0, 0, -26, -26, -56, -56, -64, -64, 114, 114, 38, 38, -72, -72, -14, -14, -2, -2, -14, -14, 94, 94, 56, 56, -70, -70, -16, -16, 36, 36, 24, 24, -6, -6, 120, 120, -60, -60, 52, 52, 88, 88, 30, 30, 44, 44, -26, -26, 52, 52, -46, -46, -100, -100, 90, 90, 26, 26, -8, -8, 0, 0, 34, 34, -66, -66, 116, 116, 54, 54, 28, 28, -6, -6, 112, 112, -10, -10, -14, -14, 36, 36, -30, -30, 12, 12, 62, 62, 24, 24, -90, -90, 90, 90, 94, 94, -96, -96, 66, 66, -30, -30, 30, 30, 92, 92, 70, 70, -112, -112, 88, 88, 118, 118, -60, -60, 38, 38, -56, -56, 44, 44, -28, -28, 50, 50, -64, -64, -78, -78, 12, 12, -64, -64, 44, 44, 64, 64, 128, 128, 66, 66, -50, -50, -72, -72, 78, 78, 74, 74, 96, 96, -56, -56, -100, -100, 10, 10, -82, -82, 72, 72, 84, 84, -124, -124, 66, 66, -24, -24, -78, -74, -74, -34, -34, 76, 76, -6, -6, 114, 114, 104, 104, 12, 12, 100, 100, -82, -82, 32, 32, 10, 10, 16, 16, 98, 98, -90, -90, -46, -52, -52, -34, -34, 114, 114, 8, 8, -102, -102, 0, 0, -20, -20, 74, 74, 126, 126, -76, -76, 16, 16, 148, 148, 38, 38, -62, -62, -114, -114, 112, 112, -72, -72, -22, -22, -10, -10, -54, -54, -28, -28, -10, -10, 32, 32, -82, -82, -10, -10, -90, -90, -100, -100, 24, 24, -102, -102, 32, 32, 14, 14, 66, 66, 68, 68, 126, 126, 90, 90, -96, -96, 12, 12, -10, -10, -84, -84, 52, 52, -44, -44, -112, -112, -6, -6, 104, 104, -18, -18, 106, 106, 12, 12, -74, -74, -32, -32, -52, -52, -10, -10, 128, 128, 38, 38, -80, -80, 130, 130, -138, -138, 70, 70, 112, 112, 104, 104, 92, 92, 42, 42, -62, -62, -96, -96, 26, 26, 30, 30, 70, 70, -124, -124, -78, -78, 28, 28, -70, -70, -60, -60, -70, -70, -56, -56, -108, -108, 88, 88, -40, -40, -36, -36, 86, 86, 80, 80, -30, -30, 124, 124, 38, 38, 86, 86, 2, 2, -140, -140, 36, 36, -132, -132, -22, -22, 96, 96, 64, 64, -150, 54, 54, -144, -144, -110, -110, 50, 50, -88, -88, -86, -86, 126, 126, 36, 36, -4, -4, -136, -136, 12, 12, 46, 46, -40, -40, 16, 16, 82, 82, -8, -8, -38, -38, 10, 10, 124, 124, 32, 32, -50, -50, -100, -100, -106, -106, -138, -138, -12, -12, 108, 108, -158, -158, -140, -140, -36, -36, -74, -74, -94, -94, 122, 122, 52, 52, 28, 28, 70, 70, 122, 122, 16, 16, 2, 2, 28, 28, 10, 10, 46, 46, 68, 68, -104, -104, -22, -22, -102, -102, 30, 30, -56, -56, 100, 100, 18, 18, 70, 70, 2, 2, -74, -74, -76, -76, -82, -82, 10, 10, -90, -90, -46, -46, -144, -144, 14, 14, 66, 66, 6, 6, 76, 76, 96, 96, -64, -64, 62, 62, 150, 150, 90, 90, 132, 132, 18, 18, 30, 30, 88, 88, -166, -166, -90, -90, -114, -114, 36, 36, 132, 132, 168, 168, -46, -46, -86, -86, -52, -52, 16, 16, -18, -18, -14, -14, -58, -58, 122, 122, -96, -96, 130, 130, -60, -60, -110, -110, 140, 140, 70, 70, 28, 28, -24, -24, 48, 48, -50, -50, -56, -56, 26, 26, -140, -140, 144, 144, -4, -4, 62, 62, -160, -160, -184, -184, -68, -68, -72, -72, -60, -60, 74, 74, -152, -152, 98, 98, -18, -18, -134, -134, -60, -60, 124, 124, 136, 136, 54, 54, 32, 32, 130, 130, -122, -122, 40, 40, -132, -132, 0, 0, -168, -168, 12, 12, 170, 170, 170, 170, 28, 28, 148, 148, -52, -52, 88, 88, 0, 0, 8, 8, -134, -134, 126, 126, 94, 94, 20, 20, 24, 24, -102, -102, 96, 96, -134, -134, -106, -106, -154, -154, -62, -62, -184, -184, -28, -28, 126, 126, -44, -44, 150, 150, 56, 56, -20, -20, 42, 42, -32, -32, -138, -138, -126, -126, 62, 62, -116, -116, -152, -152, 54, 54, 120, 120, -54, -54, -120, -120, 4, 4, 112, 112, -88, -88, 106, 106, -10, -10, -6, -6, 22, 22, 18, 18, 44, 44, 148, 148, 156, 156, 148, 148, -82, -82, 6, 6] 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, -3*w + 14])] = -1 AL_eigenvalues[ZF.ideal([3, 3, -w + 5])] = 1 AL_eigenvalues[ZF.ideal([3, 3, w + 5])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]