/* 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, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([121, 11, 11]) primes_array = [ [2, 2, -w - 4],\ [2, 2, -w + 5],\ [5, 5, 4*w - 21],\ [5, 5, -4*w - 17],\ [9, 3, 3],\ [11, 11, 2*w - 11],\ [11, 11, -2*w - 9],\ [17, 17, -6*w - 25],\ [17, 17, -6*w + 31],\ [47, 47, 24*w + 101],\ [47, 47, 24*w - 125],\ [49, 7, -7],\ [53, 53, 2*w - 7],\ [53, 53, -2*w - 5],\ [67, 67, 4*w - 19],\ [67, 67, 4*w + 15],\ [71, 71, 16*w - 83],\ [71, 71, 16*w + 67],\ [73, 73, 2*w - 5],\ [73, 73, -2*w - 3],\ [79, 79, 10*w + 43],\ [79, 79, 10*w - 53],\ [89, 89, 2*w - 1],\ [97, 97, 8*w - 43],\ [97, 97, 8*w + 35],\ [107, 107, 2*w - 15],\ [107, 107, -2*w - 13],\ [109, 109, 10*w + 41],\ [109, 109, 10*w - 51],\ [131, 131, -4*w - 13],\ [131, 131, 4*w - 17],\ [139, 139, -30*w + 157],\ [139, 139, 52*w - 271],\ [157, 157, 26*w - 135],\ [157, 157, 26*w + 109],\ [167, 167, 2*w - 17],\ [167, 167, -2*w - 15],\ [169, 13, -13],\ [173, 173, 4*w - 25],\ [173, 173, -4*w - 21],\ [179, 179, 12*w + 49],\ [179, 179, 12*w - 61],\ [199, 199, 8*w - 39],\ [199, 199, 8*w + 31],\ [223, 223, -6*w - 29],\ [223, 223, -6*w + 35],\ [227, 227, 44*w + 185],\ [227, 227, 58*w + 245],\ [233, 233, 16*w + 69],\ [233, 233, 16*w - 85],\ [251, 251, 20*w + 83],\ [251, 251, 20*w - 103],\ [257, 257, -8*w - 37],\ [257, 257, -8*w + 45],\ [263, 263, 14*w - 75],\ [263, 263, 14*w + 61],\ [269, 269, -4*w - 23],\ [269, 269, 4*w - 27],\ [271, 271, -38*w + 199],\ [271, 271, 38*w + 161],\ [277, 277, 12*w - 65],\ [277, 277, -12*w - 53],\ [283, 283, 28*w - 145],\ [283, 283, 28*w + 117],\ [307, 307, -4*w - 5],\ [307, 307, 4*w - 9],\ [311, 311, 2*w - 21],\ [311, 311, -2*w - 19],\ [317, 317, -6*w - 19],\ [317, 317, 6*w - 25],\ [331, 331, 4*w - 7],\ [331, 331, -4*w - 3],\ [347, 347, -4*w - 1],\ [347, 347, 4*w - 5],\ [361, 19, -19],\ [367, 367, 16*w + 65],\ [367, 367, 16*w - 81],\ [373, 373, 4*w - 29],\ [373, 373, -4*w - 25],\ [401, 401, 6*w - 23],\ [401, 401, -6*w - 17],\ [409, 409, 24*w - 127],\ [409, 409, 24*w + 103],\ [443, 443, -46*w + 241],\ [443, 443, 46*w + 195],\ [449, 449, -56*w + 293],\ [449, 449, 90*w - 469],\ [461, 461, 10*w + 37],\ [461, 461, 10*w - 47],\ [463, 463, 8*w + 27],\ [463, 463, -8*w + 35],\ [467, 467, 22*w + 95],\ [467, 467, 22*w - 117],\ [479, 479, -10*w + 57],\ [479, 479, -10*w - 47],\ [487, 487, 2*w - 25],\ [487, 487, -2*w - 23],\ [509, 509, 20*w - 107],\ [509, 509, 20*w + 87],\ [523, 523, 34*w + 145],\ [523, 523, -34*w + 179],\ [529, 23, -23],\ [587, 587, 2*w - 27],\ [587, 587, -2*w - 25],\ [601, 601, 8*w - 49],\ [601, 601, -8*w - 41],\ [607, 607, -56*w + 291],\ [607, 607, 56*w + 235],\ [613, 613, 82*w + 345],\ [613, 613, 82*w - 427],\ [619, 619, 20*w + 81],\ [619, 619, 20*w - 101],\ [631, 631, 40*w - 207],\ [631, 631, 40*w + 167],\ [641, 641, 26*w + 107],\ [641, 641, 26*w - 133],\ [643, 643, -6*w - 35],\ [643, 643, 6*w - 41],\ [659, 659, 74*w + 313],\ [659, 659, -74*w + 387],\ [673, 673, 118*w - 615],\ [673, 673, -64*w + 335],\ [691, 691, -10*w - 49],\ [691, 691, -10*w + 59],\ [701, 701, -6*w - 7],\ [701, 701, 6*w - 13],\ [733, 733, -4*w - 31],\ [733, 733, 4*w - 35],\ [751, 751, 42*w + 179],\ [751, 751, -42*w + 221],\ [757, 757, 34*w + 141],\ [757, 757, 34*w - 175],\ [761, 761, 14*w - 67],\ [761, 761, 14*w + 53],\ [769, 769, 22*w + 89],\ [769, 769, 22*w - 111],\ [797, 797, 6*w - 5],\ [797, 797, 6*w - 1],\ [809, 809, 18*w - 89],\ [809, 809, 18*w + 71],\ [811, 811, 2*w - 31],\ [811, 811, -2*w - 29],\ [821, 821, -66*w + 343],\ [821, 821, 66*w + 277],\ [823, 823, -14*w - 65],\ [823, 823, -14*w + 79],\ [841, 29, -29],\ [881, 881, 40*w - 211],\ [881, 881, 40*w + 171],\ [907, 907, -62*w + 325],\ [907, 907, 62*w + 263],\ [911, 911, -10*w + 61],\ [911, 911, -10*w - 51],\ [929, 929, -10*w - 31],\ [929, 929, 10*w - 41],\ [937, 937, -72*w + 377],\ [937, 937, 72*w + 305],\ [947, 947, 36*w - 185],\ [947, 947, 36*w + 149],\ [961, 31, -31],\ [971, 971, 84*w + 353],\ [971, 971, 130*w + 549],\ [977, 977, -8*w - 45],\ [977, 977, 8*w - 53],\ [983, 983, -8*w - 17],\ [983, 983, 8*w - 25],\ [997, 997, 14*w - 65],\ [997, 997, 14*w + 51],\ [1013, 1013, -4*w - 35],\ [1013, 1013, 4*w - 39],\ [1019, 1019, 50*w + 213],\ [1019, 1019, -50*w + 263],\ [1021, 1021, -12*w - 59],\ [1021, 1021, -12*w + 71],\ [1051, 1051, 44*w + 183],\ [1051, 1051, 44*w - 227],\ [1063, 1063, 8*w - 23],\ [1063, 1063, -8*w - 15],\ [1069, 1069, 10*w - 39],\ [1069, 1069, -10*w - 29],\ [1093, 1093, 36*w + 155],\ [1093, 1093, 36*w - 191],\ [1117, 1117, 26*w + 105],\ [1117, 1117, 26*w - 131],\ [1123, 1123, 68*w + 285],\ [1123, 1123, 68*w - 353],\ [1153, 1153, 38*w - 195],\ [1153, 1153, 38*w + 157],\ [1193, 1193, -16*w + 91],\ [1193, 1193, -16*w - 75],\ [1201, 1201, -10*w - 27],\ [1201, 1201, 10*w - 37],\ [1229, 1229, 100*w + 423],\ [1229, 1229, -100*w + 523],\ [1237, 1237, 94*w + 395],\ [1237, 1237, 148*w + 625],\ [1291, 1291, 30*w - 161],\ [1291, 1291, 30*w + 131],\ [1301, 1301, -20*w - 91],\ [1301, 1301, -20*w + 111],\ [1303, 1303, 8*w - 15],\ [1303, 1303, -8*w - 7],\ [1319, 1319, 46*w + 197],\ [1319, 1319, 46*w - 243],\ [1327, 1327, 58*w + 247],\ [1327, 1327, -58*w + 305],\ [1367, 1367, 24*w - 119],\ [1367, 1367, 24*w + 95],\ [1369, 37, -37],\ [1399, 1399, -8*w - 1],\ [1399, 1399, 8*w - 9],\ [1423, 1423, 8*w - 5],\ [1423, 1423, 8*w - 3],\ [1429, 1429, 62*w + 259],\ [1429, 1429, 62*w - 321],\ [1433, 1433, 18*w + 67],\ [1433, 1433, 18*w - 85],\ [1471, 1471, 16*w - 73],\ [1471, 1471, 16*w + 57],\ [1481, 1481, 130*w + 547],\ [1481, 1481, 130*w - 677],\ [1493, 1493, 4*w - 45],\ [1493, 1493, -4*w - 41],\ [1511, 1511, 2*w - 41],\ [1511, 1511, -2*w - 39],\ [1523, 1523, 12*w - 47],\ [1523, 1523, -12*w - 35],\ [1531, 1531, -78*w + 409],\ [1531, 1531, 78*w + 331],\ [1549, 1549, -10*w - 21],\ [1549, 1549, 10*w - 31],\ [1553, 1553, 22*w + 85],\ [1553, 1553, 22*w - 107],\ [1597, 1597, -108*w + 565],\ [1597, 1597, 166*w - 865],\ [1601, 1601, 8*w - 59],\ [1601, 1601, -8*w - 51],\ [1607, 1607, 184*w - 959],\ [1607, 1607, -98*w + 513],\ [1613, 1613, 42*w + 173],\ [1613, 1613, 42*w - 215],\ [1619, 1619, 10*w - 67],\ [1619, 1619, -10*w - 57],\ [1627, 1627, -18*w + 103],\ [1627, 1627, -18*w - 85],\ [1657, 1657, -14*w - 45],\ [1657, 1657, 14*w - 59],\ [1669, 1669, -4*w - 43],\ [1669, 1669, 4*w - 47],\ [1681, 41, -41],\ [1693, 1693, 122*w - 635],\ [1693, 1693, -122*w - 513],\ [1699, 1699, -6*w - 47],\ [1699, 1699, 6*w - 53],\ [1709, 1709, -20*w - 93],\ [1709, 1709, -20*w + 113],\ [1723, 1723, -14*w + 85],\ [1723, 1723, -14*w - 71],\ [1733, 1733, 18*w + 65],\ [1733, 1733, 18*w - 83],\ [1741, 1741, -10*w - 17],\ [1741, 1741, 10*w - 27],\ [1759, 1759, 32*w + 129],\ [1759, 1759, 32*w - 161],\ [1789, 1789, 36*w + 157],\ [1789, 1789, 36*w - 193],\ [1801, 1801, 50*w - 257],\ [1801, 1801, 50*w + 207],\ [1847, 1847, 2*w - 45],\ [1847, 1847, -2*w - 43],\ [1849, 43, -43],\ [1861, 1861, -14*w - 43],\ [1861, 1861, 14*w - 57],\ [1867, 1867, 44*w + 181],\ [1867, 1867, 44*w - 225],\ [1871, 1871, -10*w - 59],\ [1871, 1871, 10*w - 69],\ [1873, 1873, -16*w - 79],\ [1873, 1873, -16*w + 95],\ [1877, 1877, 28*w - 153],\ [1877, 1877, -28*w - 125],\ [1879, 1879, 30*w - 163],\ [1879, 1879, -30*w - 133],\ [1889, 1889, 64*w + 273],\ [1889, 1889, -64*w + 337],\ [1901, 1901, 10*w - 23],\ [1901, 1901, -10*w - 13],\ [1913, 1913, 158*w - 823],\ [1913, 1913, 158*w + 665],\ [1933, 1933, 22*w - 105],\ [1933, 1933, 22*w + 83],\ [1949, 1949, 58*w + 241],\ [1949, 1949, 58*w - 299],\ [1979, 1979, -12*w - 29],\ [1979, 1979, 12*w - 41],\ [1997, 1997, -106*w + 551],\ [1997, 1997, 106*w + 445],\ [2003, 2003, -106*w + 555],\ [2003, 2003, 106*w + 449],\ [2011, 2011, 20*w - 93],\ [2011, 2011, 20*w + 73],\ [2027, 2027, 2*w - 47],\ [2027, 2027, -2*w - 45],\ [2029, 2029, 10*w - 19],\ [2029, 2029, -10*w - 9],\ [2039, 2039, 14*w - 87],\ [2039, 2039, -14*w - 73],\ [2063, 2063, 74*w + 315],\ [2063, 2063, -74*w + 389],\ [2069, 2069, 30*w - 149],\ [2069, 2069, 30*w + 119],\ [2081, 2081, -10*w - 7],\ [2081, 2081, 10*w - 17],\ [2083, 2083, 52*w + 215],\ [2083, 2083, 52*w - 267],\ [2087, 2087, 62*w - 327],\ [2087, 2087, 62*w + 265],\ [2089, 2089, 98*w + 411],\ [2089, 2089, 98*w - 509],\ [2111, 2111, 40*w - 203],\ [2111, 2111, 40*w + 163],\ [2131, 2131, 10*w - 71],\ [2131, 2131, -10*w - 61],\ [2137, 2137, 46*w - 235],\ [2137, 2137, 46*w + 189],\ [2141, 2141, 90*w - 467],\ [2141, 2141, 90*w + 377],\ [2153, 2153, 82*w + 343],\ [2153, 2153, 82*w - 425],\ [2161, 2161, 10*w - 13],\ [2161, 2161, -10*w - 3],\ [2203, 2203, 46*w + 199],\ [2203, 2203, 46*w - 245],\ [2207, 2207, 24*w - 115],\ [2207, 2207, 24*w + 91],\ [2221, 2221, 10*w - 3],\ [2221, 2221, 10*w - 7],\ [2243, 2243, -12*w - 25],\ [2243, 2243, 12*w - 37],\ [2267, 2267, 36*w + 145],\ [2267, 2267, 36*w - 181],\ [2269, 2269, 60*w + 257],\ [2269, 2269, 60*w - 317],\ [2293, 2293, 44*w - 235],\ [2293, 2293, 44*w + 191],\ [2297, 2297, 8*w - 65],\ [2297, 2297, -8*w - 57],\ [2309, 2309, -18*w + 79],\ [2309, 2309, 18*w + 61],\ [2339, 2339, 20*w - 91],\ [2339, 2339, 20*w + 71],\ [2371, 2371, -116*w + 603],\ [2371, 2371, 116*w + 487],\ [2381, 2381, 54*w - 277],\ [2381, 2381, 54*w + 223],\ [2383, 2383, -26*w + 145],\ [2383, 2383, -26*w - 119],\ [2393, 2393, -104*w + 545],\ [2393, 2393, 104*w + 441],\ [2399, 2399, -10*w - 63],\ [2399, 2399, 10*w - 73],\ [2411, 2411, 2*w - 51],\ [2411, 2411, -2*w - 49],\ [2423, 2423, 48*w - 245],\ [2423, 2423, 48*w + 197],\ [2437, 2437, -28*w - 127],\ [2437, 2437, -28*w + 155],\ [2447, 2447, -16*w - 49],\ [2447, 2447, 16*w - 65],\ [2467, 2467, 38*w + 167],\ [2467, 2467, 38*w - 205],\ [2503, 2503, -34*w - 151],\ [2503, 2503, 34*w - 185],\ [2531, 2531, 70*w + 299],\ [2531, 2531, 70*w - 369],\ [2539, 2539, 100*w - 519],\ [2539, 2539, 100*w + 419],\ [2549, 2549, -20*w - 97],\ [2549, 2549, -20*w + 117],\ [2579, 2579, 12*w - 31],\ [2579, 2579, -12*w - 19],\ [2591, 2591, 160*w - 833],\ [2591, 2591, 160*w + 673],\ [2617, 2617, 34*w - 169],\ [2617, 2617, 34*w + 135],\ [2621, 2621, 134*w + 563],\ [2621, 2621, -220*w - 929],\ [2659, 2659, 20*w + 69],\ [2659, 2659, 20*w - 89],\ [2671, 2671, 16*w - 63],\ [2671, 2671, -16*w - 47],\ [2687, 2687, -22*w - 105],\ [2687, 2687, -22*w + 127],\ [2719, 2719, 54*w + 233],\ [2719, 2719, 54*w - 287],\ [2741, 2741, 68*w + 291],\ [2741, 2741, 68*w - 359],\ [2749, 2749, 70*w - 361],\ [2749, 2749, 70*w + 291],\ [2767, 2767, -102*w + 535],\ [2767, 2767, 102*w + 433],\ [2777, 2777, -126*w + 655],\ [2777, 2777, 126*w + 529],\ [2791, 2791, -18*w + 109],\ [2791, 2791, -18*w - 91],\ [2801, 2801, -8*w - 61],\ [2801, 2801, 8*w - 69],\ [2803, 2803, 28*w + 107],\ [2803, 2803, 28*w - 135],\ [2837, 2837, 52*w + 225],\ [2837, 2837, 52*w - 277],\ [2843, 2843, -12*w - 13],\ [2843, 2843, 12*w - 25],\ [2857, 2857, 112*w + 475],\ [2857, 2857, -112*w + 587],\ [2887, 2887, -16*w - 45],\ [2887, 2887, 16*w - 61],\ [2897, 2897, 152*w + 643],\ [2897, 2897, -152*w + 795],\ [2903, 2903, 32*w - 157],\ [2903, 2903, 32*w + 125],\ [2917, 2917, -14*w - 31],\ [2917, 2917, 14*w - 45],\ [2927, 2927, 64*w - 329],\ [2927, 2927, 64*w + 265],\ [2939, 2939, 50*w - 267],\ [2939, 2939, 50*w + 217],\ [2953, 2953, -16*w - 85],\ [2953, 2953, -16*w + 101],\ [2957, 2957, 86*w + 359],\ [2957, 2957, 86*w - 445],\ [2969, 2969, 110*w + 461],\ [2969, 2969, 110*w - 571],\ [2971, 2971, 20*w + 67],\ [2971, 2971, -20*w + 87],\ [3001, 3001, 94*w - 487],\ [3001, 3001, 94*w + 393],\ [3037, 3037, 12*w - 85],\ [3037, 3037, -12*w - 73],\ [3079, 3079, -30*w - 137],\ [3079, 3079, -30*w + 167],\ [3083, 3083, -12*w - 5],\ [3083, 3083, 12*w - 17],\ [3119, 3119, 72*w - 371],\ [3119, 3119, 72*w + 299],\ [3137, 3137, -32*w - 145],\ [3137, 3137, -32*w + 177],\ [3187, 3187, 42*w - 227],\ [3187, 3187, -42*w - 185],\ [3203, 3203, 12*w - 7],\ [3203, 3203, 12*w - 5],\ [3209, 3209, -40*w - 177],\ [3209, 3209, 40*w - 217],\ [3221, 3221, 34*w + 133],\ [3221, 3221, 34*w - 167],\ [3229, 3229, 38*w - 189],\ [3229, 3229, 38*w + 151],\ [3251, 3251, -10*w - 69],\ [3251, 3251, 10*w - 79],\ [3253, 3253, 76*w - 401],\ [3253, 3253, 76*w + 325],\ [3257, 3257, -88*w + 463],\ [3257, 3257, 88*w + 375],\ [3259, 3259, -110*w + 577],\ [3259, 3259, 110*w + 467],\ [3271, 3271, 80*w + 333],\ [3271, 3271, 80*w - 413],\ [3301, 3301, 206*w - 1073],\ [3301, 3301, 206*w + 867],\ [3313, 3313, -24*w - 115],\ [3313, 3313, -24*w + 139],\ [3329, 3329, 16*w - 103],\ [3329, 3329, 16*w + 87],\ [3343, 3343, 128*w + 537],\ [3343, 3343, 128*w - 665],\ [3361, 3361, -120*w + 629],\ [3361, 3361, 120*w + 509],\ [3371, 3371, 60*w - 307],\ [3371, 3371, 60*w + 247],\ [3373, 3373, 22*w + 75],\ [3373, 3373, 22*w - 97],\ [3391, 3391, 170*w + 719],\ [3391, 3391, -170*w + 889],\ [3407, 3407, 24*w - 109],\ [3407, 3407, 24*w + 85],\ [3449, 3449, -160*w + 837],\ [3449, 3449, 242*w - 1261],\ [3461, 3461, 14*w - 37],\ [3461, 3461, -14*w - 23],\ [3463, 3463, 32*w - 155],\ [3463, 3463, 32*w + 123],\ [3467, 3467, 98*w + 417],\ [3467, 3467, -98*w + 515],\ [3469, 3469, -140*w + 733],\ [3469, 3469, 278*w - 1449],\ [3481, 59, -59],\ [3491, 3491, -180*w - 757],\ [3491, 3491, 180*w - 937],\ [3511, 3511, 2*w - 61],\ [3511, 3511, -2*w - 59],\ [3539, 3539, 86*w - 453],\ [3539, 3539, 86*w + 367],\ [3559, 3559, 40*w - 199],\ [3559, 3559, 40*w + 159],\ [3571, 3571, -20*w - 63],\ [3571, 3571, 20*w - 83],\ [3581, 3581, -28*w + 159],\ [3581, 3581, -28*w - 131],\ [3607, 3607, -18*w - 95],\ [3607, 3607, 18*w - 113],\ [3613, 3613, 4*w - 65],\ [3613, 3613, -4*w - 61],\ [3617, 3617, 8*w - 75],\ [3617, 3617, -8*w - 67],\ [3631, 3631, -22*w - 109],\ [3631, 3631, -22*w + 131],\ [3659, 3659, 68*w - 349],\ [3659, 3659, 68*w + 281],\ [3671, 3671, 16*w - 53],\ [3671, 3671, -16*w - 37],\ [3691, 3691, -30*w - 139],\ [3691, 3691, -30*w + 169],\ [3721, 61, -61],\ [3727, 3727, 56*w - 285],\ [3727, 3727, 56*w + 229],\ [3733, 3733, 62*w + 255],\ [3733, 3733, 62*w - 317],\ [3739, 3739, -14*w - 83],\ [3739, 3739, 14*w - 97],\ [3793, 3793, 96*w + 409],\ [3793, 3793, -96*w + 505],\ [3823, 3823, -6*w - 65],\ [3823, 3823, 6*w - 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61],\ [8269, 8269, -22*w - 39],\ [8273, 8273, 42*w - 197],\ [8273, 8273, 42*w + 155],\ [8287, 8287, 118*w + 505],\ [8287, 8287, 118*w - 623],\ [8293, 8293, -4*w - 91],\ [8293, 8293, 4*w - 95],\ [8297, 8297, -34*w + 149],\ [8297, 8297, 34*w + 115],\ [8311, 8311, 136*w - 703],\ [8311, 8311, 136*w + 567],\ [8317, 8317, 26*w - 95],\ [8317, 8317, -26*w - 69],\ [8377, 8377, -8*w - 95],\ [8377, 8377, 8*w - 103],\ [8387, 8387, 36*w + 125],\ [8387, 8387, 36*w - 161],\ [8419, 8419, -28*w - 81],\ [8419, 8419, 28*w - 109],\ [8423, 8423, 192*w - 997],\ [8423, 8423, 192*w + 805],\ [8447, 8447, 144*w - 745],\ [8447, 8447, 144*w + 601],\ [8527, 8527, 184*w - 955],\ [8527, 8527, 184*w + 771],\ [8539, 8539, -20*w - 9],\ [8539, 8539, 20*w - 29],\ [8543, 8543, 152*w - 787],\ [8543, 8543, 152*w + 635],\ [8597, 8597, -226*w + 1175],\ [8597, 8597, 226*w + 949],\ [8599, 8599, 160*w - 829],\ [8599, 8599, 160*w + 669],\ [8623, 8623, 32*w - 135],\ [8623, 8623, -32*w - 103],\ [8629, 8629, 116*w + 497],\ [8629, 8629, 116*w - 613],\ [8641, 8641, -26*w - 67],\ [8641, 8641, 26*w - 93],\ [8669, 8669, 4*w - 97],\ [8669, 8669, -4*w - 93],\ [8677, 8677, -12*w - 103],\ [8677, 8677, 12*w - 115],\ [8713, 8713, 322*w + 1355],\ [8713, 8713, 322*w - 1677],\ [8731, 8731, -20*w - 3],\ [8731, 8731, 20*w - 23],\ [8747, 8747, 2*w - 95],\ [8747, 8747, -2*w - 93],\ [8761, 8761, -48*w + 269],\ [8761, 8761, -48*w - 221],\ [8779, 8779, -20*w - 1],\ [8779, 8779, 20*w - 21],\ [8803, 8803, -6*w - 95],\ [8803, 8803, 6*w - 101],\ [8807, 8807, 96*w + 395],\ [8807, 8807, 96*w - 491],\ [8819, 8819, 20*w - 19],\ [8819, 8819, 20*w - 1],\ [8821, 8821, -34*w + 147],\ [8821, 8821, 34*w + 113],\ [8831, 8831, 22*w - 151],\ [8831, 8831, -22*w - 129],\ [8861, 8861, 100*w + 431],\ [8861, 8861, 100*w - 531],\ [8969, 8969, 50*w + 191],\ [8969, 8969, 50*w - 241],\ [8971, 8971, 162*w + 689],\ [8971, 8971, -162*w + 851],\ [8999, 8999, 194*w + 823],\ [8999, 8999, -194*w + 1017],\ [9007, 9007, 296*w - 1541],\ [9007, 9007, 296*w + 1245],\ [9011, 9011, 10*w - 111],\ [9011, 9011, -10*w - 101],\ [9029, 9029, 210*w + 881],\ [9029, 9029, 210*w - 1091],\ [9067, 9067, 244*w + 1025],\ [9067, 9067, -418*w - 1765],\ [9103, 9103, -54*w - 245],\ [9103, 9103, -54*w + 299],\ [9127, 9127, 2*w - 97],\ [9127, 9127, -2*w - 95],\ [9133, 9133, -204*w + 1069],\ [9133, 9133, 204*w + 865],\ [9151, 9151, -42*w + 241],\ [9151, 9151, -42*w - 199],\ [9157, 9157, 146*w - 755],\ [9157, 9157, 146*w + 609],\ [9187, 9187, 124*w - 639],\ [9187, 9187, 124*w + 515],\ [9199, 9199, 6*w - 103],\ [9199, 9199, -6*w - 97],\ [9203, 9203, 74*w - 399],\ [9203, 9203, 74*w + 325],\ [9209, 9209, 30*w - 119],\ [9209, 9209, -30*w - 89],\ [9239, 9239, 48*w + 181],\ [9239, 9239, 48*w - 229],\ [9257, 9257, -32*w + 195],\ [9257, 9257, -32*w - 163],\ [9277, 9277, 314*w + 1321],\ [9277, 9277, 314*w - 1635],\ [9281, 9281, 154*w - 797],\ [9281, 9281, 154*w + 643],\ [9311, 9311, 70*w - 379],\ [9311, 9311, -70*w - 309],\ [9323, 9323, 412*w - 2147],\ [9323, 9323, -254*w + 1329],\ [9337, 9337, 34*w - 145],\ [9337, 9337, -34*w - 111],\ [9341, 9341, -68*w - 301],\ [9341, 9341, 68*w - 369],\ [9343, 9343, 448*w - 2335],\ [9343, 9343, -234*w + 1225],\ [9349, 9349, 430*w - 2241],\ [9349, 9349, -244*w + 1277],\ [9377, 9377, 186*w - 965],\ [9377, 9377, 186*w + 779],\ [9413, 9413, 178*w + 745],\ [9413, 9413, 178*w - 923],\ [9433, 9433, -16*w - 115],\ [9433, 9433, 16*w - 131],\ [9439, 9439, -10*w - 103],\ [9439, 9439, 10*w - 113],\ [9473, 9473, 22*w - 47],\ [9473, 9473, -22*w - 25],\ [9479, 9479, -288*w - 1211],\ [9479, 9479, 288*w - 1499],\ [9491, 9491, 76*w - 383],\ [9491, 9491, 76*w + 307],\ [9521, 9521, 160*w + 681],\ [9521, 9521, -160*w + 841],\ [9533, 9533, 124*w - 655],\ [9533, 9533, 124*w + 531],\ [9539, 9539, 52*w + 199],\ [9539, 9539, 52*w - 251],\ [9587, 9587, 44*w - 205],\ [9587, 9587, 44*w + 161],\ [9601, 9601, -8*w - 101],\ [9601, 9601, 8*w - 109],\ [9613, 9613, -22*w - 23],\ [9613, 9613, 22*w - 45],\ [9623, 9623, -34*w + 205],\ [9623, 9623, -34*w - 171],\ [9629, 9629, 38*w + 131],\ [9629, 9629, 38*w - 169],\ [9661, 9661, -148*w + 779],\ [9661, 9661, 148*w + 631],\ [9679, 9679, 40*w - 181],\ [9679, 9679, 40*w + 141],\ [9697, 9697, 192*w + 815],\ [9697, 9697, -192*w + 1007],\ [9719, 9719, 72*w + 289],\ [9719, 9719, 72*w - 361],\ [9721, 9721, 350*w - 1823],\ [9721, 9721, 350*w + 1473],\ [9733, 9733, 82*w + 333],\ [9733, 9733, 82*w - 415],\ [9743, 9743, 112*w + 463],\ [9743, 9743, 112*w - 575],\ [9769, 9769, -40*w + 233],\ [9769, 9769, -40*w - 193],\ [9781, 9781, 28*w + 151],\ [9781, 9781, 28*w - 179],\ [9791, 9791, 24*w - 67],\ [9791, 9791, -24*w - 43],\ [9811, 9811, 220*w + 923],\ [9811, 9811, 220*w - 1143],\ [9829, 9829, 50*w + 189],\ [9829, 9829, 50*w - 239],\ [9839, 9839, 170*w + 723],\ [9839, 9839, -170*w + 893],\ [9857, 9857, 26*w - 85],\ [9857, 9857, -26*w - 59],\ [9859, 9859, 68*w - 339],\ [9859, 9859, 68*w + 271],\ [9871, 9871, 90*w + 391],\ [9871, 9871, 90*w - 481],\ [9883, 9883, 148*w - 765],\ [9883, 9883, 148*w + 617],\ [9887, 9887, 122*w - 645],\ [9887, 9887, 122*w + 523],\ [9901, 9901, 106*w + 437],\ [9901, 9901, 106*w - 543],\ [9923, 9923, 26*w - 171],\ [9923, 9923, -26*w - 145],\ [9929, 9929, -16*w - 117],\ [9929, 9929, 16*w - 133],\ [9967, 9967, 22*w - 155],\ [9967, 9967, -22*w - 133],\ [9973, 9973, -36*w - 179],\ [9973, 9973, -36*w + 215]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-2, -2, 1, 1, -5, 1, 1, -2, -2, 8, 8, -10, -6, -6, -7, -7, -3, -3, 4, 4, -10, -10, 15, -7, -7, 18, 18, 10, 10, -18, -18, 10, 10, -7, -7, -12, -12, -10, -6, -6, -15, -15, 0, 0, 19, 19, 18, 18, 24, 24, -23, -23, -2, -2, 14, 14, 10, 10, -28, -28, -2, -2, 4, 4, 8, 8, 12, 12, 13, 13, 7, 7, 28, 28, -38, -17, -17, -26, -26, 2, 2, -30, -30, -11, -11, 35, 35, 12, 12, -11, -11, -27, -27, 20, 20, 23, 23, 15, 15, -16, -16, -45, 28, 28, 2, 2, -22, -22, -16, -16, -25, -25, 7, 7, -33, -33, 29, 29, 10, 10, 14, 14, 17, 17, 2, 2, -36, -36, -23, -23, -22, -22, 12, 12, 20, 20, 53, 53, 0, 0, -38, -38, 22, 22, 39, 39, -58, -43, -43, -12, -12, 12, 12, -30, -30, 8, 8, -27, -27, -13, 47, 47, -27, -27, 39, 39, 38, 38, 39, 39, -10, -10, 22, 22, 2, 2, 44, 44, -20, -20, -51, -51, 48, 48, 24, 24, -31, -31, -21, -21, 2, 2, 60, 60, 18, 18, -8, -8, 27, 27, 39, 39, -30, -30, 68, 68, -72, -72, -65, 60, 60, 29, 29, -70, -70, 54, 54, 22, 22, 32, 32, -36, -36, 37, 37, -41, -41, 32, 32, -15, -15, -56, -56, -32, -32, 2, 2, 33, 33, -6, -6, -20, -20, 78, 78, -2, -2, 50, 50, -18, -6, -6, 40, 40, -45, -45, -46, -46, -6, -6, 17, 17, -40, -40, 10, 10, 52, 52, -52, -52, -50, 62, 62, 28, 28, -3, -3, -6, -6, 18, 18, -35, -35, 70, 70, 77, 77, -36, -36, 54, 54, -40, -40, 30, 30, -72, -72, 4, 4, -13, -13, 63, 63, 45, 45, 60, 60, 24, 24, 70, 70, -18, -18, 89, 89, 48, 48, -10, -10, -38, -38, -68, -68, 73, 73, -58, -58, -26, -26, -13, -13, -1, -1, 48, 48, 22, 22, -56, -56, 93, 93, 25, 25, 29, 29, -57, -57, 60, 60, 10, 10, -28, -28, -18, -18, -36, -36, 54, 54, -75, -75, 62, 62, -31, -31, -82, -82, 3, 3, 3, 3, 14, 14, 57, 57, 0, 0, -20, -20, 20, 20, -58, -58, 18, 18, 22, 22, 40, 40, 72, 72, 23, 23, -70, -70, -58, -58, 50, 50, 48, 48, -42, -42, 42, 42, 52, 52, 44, 44, -62, -62, 4, 4, -82, -82, -57, -57, 38, 38, 54, 54, 88, 88, -72, -72, -50, -50, -86, -86, 3, 3, 70, 70, -53, -53, 27, 27, 13, 13, -20, -20, 29, 29, -90, -90, 8, 8, -2, -2, -6, -6, -10, -10, -103, -103, 70, 70, -48, -48, 74, 74, 58, 58, -60, -60, -3, -3, -73, -73, 4, 4, -100, -100, 44, 44, -88, -88, -103, -103, 4, 4, 92, 92, 18, 18, 40, 40, -38, -38, -96, -96, 38, 38, -85, -85, -93, 17, 17, 12, 12, 20, 20, 0, 0, -28, -28, 32, 32, 58, 58, -26, -26, 63, 63, 32, 32, 30, 30, -78, -78, 92, 92, 22, 23, 23, 114, 114, -60, -60, 34, 34, 84, 84, -42, -42, 54, 54, 58, 58, -22, -22, 12, 12, -57, -57, -90, -90, 102, 102, -46, -46, -32, -32, 54, 54, 22, 22, 28, 28, 25, 25, -31, -31, 94, 94, 20, 20, 62, 62, 4, 4, 20, 20, -98, -98, 33, 33, 10, 10, -113, -113, -53, -53, -41, -41, 39, 39, -60, -60, -62, -62, -107, -107, 55, 55, -117, -117, -6, -6, 108, 108, 42, 42, 102, 102, -82, -82, 8, 8, 5, 5, -36, -36, -12, -12, -10, -10, 112, 112, -36, -36, 89, 89, 18, 18, 20, 20, -80, -80, 114, 114, 22, 22, 129, 129, -48, -48, 30, 30, 110, 110, 77, 77, -132, -132, -68, -68, -88, -88, 93, 93, -126, -126, 32, 32, -42, -42, -52, -52, -1, -1, 44, 44, -45, -45, 54, 54, 15, 15, -48, -48, 8, 8, 132, 132, -32, -32, 29, 29, -111, -111, 28, 28, 97, 97, -60, -60, -50, -50, -18, -18, -96, -96, 87, 87, -21, -21, -76, -76, 77, 77, -2, -2, -11, -11, 138, 138, 14, 14, -110, -110, 82, 82, -2, -2, -5, -5, -3, -3, -95, -95, 27, 27, 48, 48, 0, 0, 8, 8, -122, -122, 134, 134, 104, 104, -33, -33, 64, 64, 60, 60, 17, 17, 113, 113, -48, -48, -57, -57, 77, 77, -72, -72, -8, -8, 19, 19, -30, -30, 104, 104, 102, 102, -92, -92, -78, -78, -12, -12, 80, 80, -137, -137, 10, 10, -55, -55, 59, 59, 123, 123, 94, 94, -18, -18, 8, 8, -101, -101, -42, -42, -26, -26, -26, -26, -8, -8, -48, -48, 97, 97, 57, 57, 94, 94, 4, 4, 52, 52, 59, 59, -86, -86, -128, -128, -115, -115, -102, -102, -30, -30, -132, -132, -132, -132, -30, -30, -23, -23, 12, 12, -147, -147, 89, 89, 50, 50, 38, 38, -86, -86, 60, 60, -138, -138, -22, -22, -18, -18, -80, -80, 68, 68, 130, 130, -72, -72, -93, -93, 48, 48, 69, 69, -95, -95, 4, 4, 40, 40, -83, -83, 60, 60, -120, -120, 29, 29, 7, 7, -11, -11, 24, 24, -127, -127, 64, 64, 85, 85, 122, 122, -130, 38, 38, -72, -72, 30, 30, 8, 8, 142, 142, 23, 23, -126, -126, 23, 23, -60, -60, 24, 24, 15, 15, -3, -3, -145, -145, -105, -105, -142, -142, 153, 153, -6, -6, 78, 78, 162, 162, -66, -66, 25, 25, -110, -110, -21, -21, 59, 59, 138, 138, -7, -7, -25, -25, -48, -48, -80, -80, -148, -148, 135, 135, 138, 138, -43, -43, 78, 78, 24, 24, 145, 145, 123, 123, -45, -45, -138, -138, 109, 109, 64, 64, 38, 38, 159, 159, -130, -130, 50, 50, -51, -51, -151, -151, 33, 33, 92, 92, 19, 19, 55, 55, -21, -21, 14, 14, 17, 17, -96, -96, -122, -122, -165, -165, 127, 127, 20, 20, 18, 18, -136, -136, -26, -26, 85, 85, 137, 137, 130, 130, -18, -18, 135, 135, 77, 77, 168, 168, 123, 123, -28, -28, -130, -130, -35, -35, 169, 169, -17, -17, 99, 99, -100, -100, -26, -26, -72, -72, -6, -6, -117, -117, -38, -38, 18, 18, -92, -92, 168, 168, -60, -60, -156, -156, -152, -152, 148, 148, 145, 145, -126, -126, 78, 78, 80, 80, 74, 74, 145, 145, -108, -108, -130, -130, 98, 98, -61, -61, 82, 82, -32, -32, -13, -13, 55, 55, 124, 124, 48, 48, 50, 50, -78, -78, 157, 157, 12, 12, 15, 15, -128, -128, 25, 25, 153, 153, -38, -38, 115, 115, -147, -147, 14, 14, -12, -12, 79, 79, 102, 102, 63, 63, 58, 58, 80, 80, -166, -166, 120, 120, -60, -60, 88, 88, 43, 43, 132, 132, -13, -13, 134, 134, -67, -67, 42, 42, -151, -151, -100, -100, -142, -142, -166, -166, 94, 94, 65, 65, 114, 114, 60, 60, -108, -108, -78, -78, -36, -36, 0, 0, 18, 18, -173, -173, 64, 64, -61, -61, 25, 25, -13, -13, 30, 30, 178, 178, 110, 110, -178, -178, 49, 49, 164, 164, -5, -5, -18, -18, -108, -108, 62, 62, -80, -80, -45, -45, -117, -117, -85, -85, -128, -128, -81, -81, -117, -117, 102, 102, 49, 49, 0, 0, 43, 43, 4, 4] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([11, 11, 2*w - 11])] = -1 AL_eigenvalues[ZF.ideal([11, 11, -2*w - 9])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]