/* 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([-18, -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],\ [3, 3, -4*w - 15],\ [3, 3, -4*w + 19],\ [19, 19, -6*w - 23],\ [19, 19, 6*w - 29],\ [23, 23, 14*w - 67],\ [23, 23, -14*w - 53],\ [25, 5, -5],\ [37, 37, 2*w - 7],\ [37, 37, -2*w - 5],\ [41, 41, 30*w - 143],\ [41, 41, 40*w - 191],\ [49, 7, -7],\ [61, 61, 10*w + 37],\ [61, 61, -10*w + 47],\ [67, 67, -4*w - 13],\ [67, 67, 4*w - 17],\ [71, 71, 2*w - 13],\ [71, 71, -2*w - 11],\ [73, 73, 2*w - 1],\ [79, 79, -8*w + 37],\ [79, 79, 8*w + 29],\ [89, 89, -16*w + 77],\ [89, 89, -16*w - 61],\ [97, 97, -24*w - 91],\ [97, 97, 24*w - 115],\ [109, 109, -84*w - 317],\ [109, 109, 84*w - 401],\ [121, 11, -11],\ [127, 127, -6*w + 31],\ [127, 127, 6*w + 25],\ [137, 137, 18*w + 67],\ [137, 137, 18*w - 85],\ [149, 149, 4*w + 19],\ [149, 149, 4*w - 23],\ [169, 13, -13],\ [173, 173, -6*w - 19],\ [173, 173, 6*w - 25],\ [181, 181, 12*w + 47],\ [181, 181, -12*w + 59],\ [211, 211, 4*w - 11],\ [211, 211, -4*w - 7],\ [223, 223, 102*w - 487],\ [223, 223, 64*w - 305],\ [227, 227, -12*w + 55],\ [227, 227, -12*w - 43],\ [251, 251, 2*w - 19],\ [251, 251, -2*w - 17],\ [257, 257, -6*w + 23],\ [257, 257, -6*w - 17],\ [269, 269, 20*w + 77],\ [269, 269, -20*w + 97],\ [283, 283, -4*w - 1],\ [283, 283, 4*w - 5],\ [289, 17, -17],\ [293, 293, -126*w - 475],\ [293, 293, -68*w - 257],\ [311, 311, 24*w - 113],\ [311, 311, 24*w + 89],\ [317, 317, 54*w - 257],\ [317, 317, 54*w + 203],\ [347, 347, -94*w - 355],\ [347, 347, 94*w - 449],\ [349, 349, 60*w - 287],\ [349, 349, 60*w + 227],\ [353, 353, -8*w + 43],\ [353, 353, 8*w + 35],\ [359, 359, -146*w - 551],\ [359, 359, 146*w - 697],\ [367, 367, 6*w + 29],\ [367, 367, 6*w - 35],\ [373, 373, -36*w + 173],\ [373, 373, -36*w - 137],\ [383, 383, -22*w + 107],\ [383, 383, 22*w + 85],\ [389, 389, -44*w - 167],\ [389, 389, 44*w - 211],\ [397, 397, -12*w + 61],\ [397, 397, 12*w + 49],\ [401, 401, -6*w - 13],\ [401, 401, 6*w - 19],\ [419, 419, -12*w - 41],\ [419, 419, 12*w - 53],\ [439, 439, -8*w + 31],\ [439, 439, -8*w - 23],\ [457, 457, 62*w - 295],\ [457, 457, 62*w + 233],\ [461, 461, 6*w - 17],\ [461, 461, -6*w - 11],\ [463, 463, 32*w + 119],\ [463, 463, 32*w - 151],\ [479, 479, 10*w + 43],\ [479, 479, -10*w + 53],\ [487, 487, 18*w + 71],\ [487, 487, -18*w + 89],\ [499, 499, 6*w - 37],\ [499, 499, -6*w - 31],\ [503, 503, 2*w - 25],\ [503, 503, -2*w - 23],\ [509, 509, 42*w + 157],\ [509, 509, 42*w - 199],\ [523, 523, -78*w - 295],\ [523, 523, 78*w - 373],\ [547, 547, 116*w - 553],\ [547, 547, 138*w - 659],\ [557, 557, -6*w - 7],\ [557, 557, 6*w - 13],\ [587, 587, -46*w + 221],\ [587, 587, -46*w - 175],\ [593, 593, 6*w - 11],\ [593, 593, -6*w - 5],\ [607, 607, -54*w - 205],\ [607, 607, 54*w - 259],\ [619, 619, 28*w + 103],\ [619, 619, -28*w + 131],\ [641, 641, -6*w - 1],\ [641, 641, 6*w - 7],\ [653, 653, 6*w - 5],\ [653, 653, 6*w - 1],\ [659, 659, 26*w + 101],\ [659, 659, -26*w + 127],\ [661, 661, -14*w - 47],\ [661, 661, 14*w - 61],\ [673, 673, -26*w + 121],\ [673, 673, 26*w + 95],\ [727, 727, -8*w - 17],\ [727, 727, 8*w - 25],\ [733, 733, -22*w + 101],\ [733, 733, -22*w - 79],\ [739, 739, -20*w + 91],\ [739, 739, -20*w - 71],\ [757, 757, 156*w - 745],\ [757, 757, -156*w - 589],\ [787, 787, -6*w - 35],\ [787, 787, 6*w - 41],\ [797, 797, -4*w - 31],\ [797, 797, 4*w - 35],\ [809, 809, 78*w - 371],\ [809, 809, 78*w + 293],\ [811, 811, -18*w + 91],\ [811, 811, 18*w + 73],\ [821, 821, -28*w + 137],\ [821, 821, 28*w + 109],\ [827, 827, 2*w - 31],\ [827, 827, -2*w - 29],\ [839, 839, 48*w + 179],\ [839, 839, 48*w - 227],\ [841, 29, -29],\ [853, 853, -12*w + 65],\ [853, 853, 12*w + 53],\ [857, 857, 8*w - 49],\ [857, 857, -8*w - 41],\ [877, 877, 58*w + 217],\ [877, 877, 58*w - 275],\ [911, 911, 96*w + 361],\ [911, 911, 96*w - 457],\ [937, 937, 24*w + 95],\ [937, 937, -24*w + 119],\ [941, 941, -148*w - 559],\ [941, 941, 148*w - 707],\ [947, 947, -12*w + 47],\ [947, 947, 12*w + 35],\ [953, 953, 16*w + 67],\ [953, 953, -16*w + 83],\ [961, 31, -31],\ [967, 967, 248*w + 935],\ [967, 967, -114*w - 431],\ [997, 997, -36*w + 175],\ [997, 997, 36*w + 139],\ [1013, 1013, 18*w - 79],\ [1013, 1013, -18*w - 61],\ [1019, 1019, 226*w - 1079],\ [1019, 1019, 132*w - 629],\ [1021, 1021, 86*w - 409],\ [1021, 1021, 86*w + 323],\ [1031, 1031, -50*w + 241],\ [1031, 1031, -50*w - 191],\ [1049, 1049, -30*w + 139],\ [1049, 1049, 30*w + 109],\ [1063, 1063, 56*w - 265],\ [1063, 1063, 56*w + 209],\ [1087, 1087, 8*w - 13],\ [1087, 1087, -8*w - 5],\ [1091, 1091, 10*w + 49],\ [1091, 1091, -10*w + 59],\ [1093, 1093, 12*w + 55],\ [1093, 1093, -12*w + 67],\ [1097, 1097, 66*w + 247],\ [1097, 1097, 66*w - 313],\ [1103, 1103, -24*w + 109],\ [1103, 1103, -24*w - 85],\ [1171, 1171, 90*w + 341],\ [1171, 1171, 90*w - 431],\ [1187, 1187, -74*w - 281],\ [1187, 1187, 74*w - 355],\ [1193, 1193, 32*w + 125],\ [1193, 1193, -32*w + 157],\ [1217, 1217, -42*w + 197],\ [1217, 1217, 42*w + 155],\ [1223, 1223, 2*w - 37],\ [1223, 1223, -2*w - 35],\ [1229, 1229, 4*w - 41],\ [1229, 1229, -4*w - 37],\ [1237, 1237, -132*w - 499],\ [1237, 1237, 274*w + 1033],\ [1249, 1249, 10*w - 29],\ [1249, 1249, -10*w - 19],\ [1259, 1259, 12*w - 43],\ [1259, 1259, -12*w - 31],\ [1277, 1277, -52*w + 251],\ [1277, 1277, 52*w + 199],\ [1279, 1279, -6*w - 41],\ [1279, 1279, 6*w - 47],\ [1289, 1289, 18*w - 77],\ [1289, 1289, -18*w - 59],\ [1291, 1291, -270*w - 1019],\ [1291, 1291, 270*w - 1289],\ [1381, 1381, -60*w - 229],\ [1381, 1381, -60*w + 289],\ [1399, 1399, 112*w + 421],\ [1399, 1399, 112*w - 533],\ [1423, 1423, -16*w - 49],\ [1423, 1423, 16*w - 65],\ [1433, 1433, -8*w - 47],\ [1433, 1433, 8*w - 55],\ [1451, 1451, 36*w + 131],\ [1451, 1451, -36*w + 167],\ [1459, 1459, 6*w - 49],\ [1459, 1459, -6*w - 43],\ [1483, 1483, 18*w + 77],\ [1483, 1483, -18*w + 95],\ [1487, 1487, -24*w - 83],\ [1487, 1487, 24*w - 107],\ [1531, 1531, 30*w + 119],\ [1531, 1531, -30*w + 149],\ [1549, 1549, -84*w - 319],\ [1549, 1549, 84*w - 403],\ [1571, 1571, 22*w + 91],\ [1571, 1571, -22*w + 113],\ [1579, 1579, 210*w - 1003],\ [1579, 1579, -210*w - 793],\ [1583, 1583, 72*w - 341],\ [1583, 1583, 72*w + 269],\ [1597, 1597, 12*w + 59],\ [1597, 1597, -12*w + 71],\ [1607, 1607, 14*w + 65],\ [1607, 1607, -14*w + 79],\ [1609, 1609, 82*w + 307],\ [1609, 1609, 82*w - 389],\ [1663, 1663, 42*w + 163],\ [1663, 1663, -42*w + 205],\ [1667, 1667, -12*w - 25],\ [1667, 1667, 12*w - 37],\ [1697, 1697, -282*w - 1063],\ [1697, 1697, -176*w - 665],\ [1733, 1733, -4*w - 43],\ [1733, 1733, 4*w - 47],\ [1753, 1753, 46*w + 169],\ [1753, 1753, -46*w + 215],\ [1777, 1777, 22*w - 95],\ [1777, 1777, -22*w - 73],\ [1787, 1787, 12*w - 35],\ [1787, 1787, -12*w - 23],\ [1789, 1789, -10*w - 1],\ [1789, 1789, 10*w - 11],\ [1801, 1801, 110*w - 523],\ [1801, 1801, 110*w + 413],\ [1823, 1823, -202*w - 763],\ [1823, 1823, 202*w - 965],\ [1831, 1831, 18*w + 79],\ [1831, 1831, -18*w + 97],\ [1849, 43, -43],\ [1861, 1861, 12*w - 73],\ [1861, 1861, -12*w - 61],\ [1871, 1871, 38*w + 149],\ [1871, 1871, -38*w + 187],\ [1873, 1873, -326*w - 1229],\ [1873, 1873, -168*w - 635],\ [1879, 1879, 80*w + 299],\ [1879, 1879, 80*w - 379],\ [1889, 1889, 16*w + 73],\ [1889, 1889, -16*w + 89],\ [1901, 1901, 90*w + 337],\ [1901, 1901, 90*w - 427],\ [1907, 1907, 358*w - 1709],\ [1907, 1907, -358*w - 1351],\ [1933, 1933, 26*w - 115],\ [1933, 1933, -26*w - 89],\ [1973, 1973, -332*w - 1253],\ [1973, 1973, 332*w - 1585],\ [1979, 1979, 228*w + 859],\ [1979, 1979, 228*w - 1087],\ [1987, 1987, -28*w - 97],\ [1987, 1987, 28*w - 125],\ [2003, 2003, 12*w - 31],\ [2003, 2003, -12*w - 19],\ [2017, 2017, 38*w + 137],\ [2017, 2017, -38*w + 175],\ [2053, 2053, -34*w - 121],\ [2053, 2053, -34*w + 155],\ [2063, 2063, -26*w + 133],\ [2063, 2063, 26*w + 107],\ [2069, 2069, -18*w + 71],\ [2069, 2069, 18*w + 53],\ [2081, 2081, -8*w - 53],\ [2081, 2081, 8*w - 61],\ [2099, 2099, -12*w - 17],\ [2099, 2099, 12*w - 29],\ [2111, 2111, 58*w + 223],\ [2111, 2111, -58*w + 281],\ [2113, 2113, -72*w + 347],\ [2113, 2113, 72*w + 275],\ [2129, 2129, -40*w + 197],\ [2129, 2129, 40*w + 157],\ [2141, 2141, 54*w + 199],\ [2141, 2141, -54*w + 253],\ [2153, 2153, 152*w - 727],\ [2153, 2153, 152*w + 575],\ [2209, 47, -47],\ [2213, 2213, -66*w + 311],\ [2213, 2213, 66*w + 245],\ [2239, 2239, -186*w - 703],\ [2239, 2239, -352*w - 1327],\ [2251, 2251, 402*w - 1919],\ [2251, 2251, -402*w - 1517],\ [2267, 2267, -12*w - 13],\ [2267, 2267, 12*w - 25],\ [2269, 2269, 36*w + 143],\ [2269, 2269, -36*w + 179],\ [2281, 2281, -14*w - 29],\ [2281, 2281, 14*w - 43],\ [2287, 2287, -246*w - 929],\ [2287, 2287, 246*w - 1175],\ [2309, 2309, 4*w - 53],\ [2309, 2309, -4*w - 49],\ [2311, 2311, 136*w - 647],\ [2311, 2311, 136*w + 511],\ [2333, 2333, 28*w + 115],\ [2333, 2333, -28*w + 143],\ [2339, 2339, 12*w - 23],\ [2339, 2339, -12*w - 11],\ [2371, 2371, 76*w - 359],\ [2371, 2371, 76*w + 283],\ [2377, 2377, -96*w + 461],\ [2377, 2377, -96*w - 365],\ [2393, 2393, 128*w + 485],\ [2393, 2393, 128*w - 613],\ [2411, 2411, 396*w + 1493],\ [2411, 2411, -178*w - 673],\ [2417, 2417, -104*w - 395],\ [2417, 2417, 104*w - 499],\ [2441, 2441, 126*w - 599],\ [2441, 2441, 126*w + 473],\ [2447, 2447, -48*w + 223],\ [2447, 2447, 48*w + 175],\ [2459, 2459, 12*w - 19],\ [2459, 2459, -12*w - 7],\ [2473, 2473, -48*w + 235],\ [2473, 2473, 48*w + 187],\ [2531, 2531, 10*w - 71],\ [2531, 2531, -10*w - 61],\ [2539, 2539, -20*w + 79],\ [2539, 2539, 20*w + 59],\ [2543, 2543, 96*w + 359],\ [2543, 2543, 96*w - 455],\ [2549, 2549, -18*w - 49],\ [2549, 2549, 18*w - 67],\ [2551, 2551, -18*w + 101],\ [2551, 2551, 18*w + 83],\ [2557, 2557, 106*w + 397],\ [2557, 2557, 106*w - 503],\ [2579, 2579, -12*w - 1],\ [2579, 2579, 12*w - 13],\ [2591, 2591, -24*w - 77],\ [2591, 2591, 24*w - 101],\ [2593, 2593, 74*w + 275],\ [2593, 2593, 74*w - 349],\ [2609, 2609, -42*w + 193],\ [2609, 2609, -42*w - 151],\ [2647, 2647, 16*w - 53],\ [2647, 2647, -16*w - 37],\ [2663, 2663, 144*w + 541],\ [2663, 2663, 144*w - 685],\ [2677, 2677, 14*w - 37],\ [2677, 2677, -14*w - 23],\ [2683, 2683, 162*w - 775],\ [2683, 2683, 162*w + 613],\ [2689, 2689, 264*w - 1261],\ [2689, 2689, -264*w - 997],\ [2693, 2693, 44*w + 173],\ [2693, 2693, -44*w + 217],\ [2699, 2699, -60*w + 281],\ [2699, 2699, 60*w + 221],\ [2707, 2707, 6*w - 61],\ [2707, 2707, -6*w - 55],\ [2713, 2713, -24*w + 127],\ [2713, 2713, 24*w + 103],\ [2719, 2719, -90*w + 433],\ [2719, 2719, -90*w - 343],\ [2749, 2749, -22*w - 67],\ [2749, 2749, 22*w - 89],\ [2777, 2777, -18*w - 47],\ [2777, 2777, 18*w - 65],\ [2797, 2797, 134*w - 637],\ [2797, 2797, 134*w + 503],\ [2801, 2801, 8*w - 67],\ [2801, 2801, -8*w - 59],\ [2809, 53, -53],\ [2843, 2843, 2*w - 55],\ [2843, 2843, -2*w - 53],\ [2851, 2851, 342*w - 1633],\ [2851, 2851, 244*w - 1163],\ [2879, 2879, -106*w + 509],\ [2879, 2879, -106*w - 403],\ [2897, 2897, 16*w + 79],\ [2897, 2897, -16*w + 95],\ [2917, 2917, -36*w + 181],\ [2917, 2917, 36*w + 145],\ [2939, 2939, -130*w - 493],\ [2939, 2939, 130*w - 623],\ [2957, 2957, -4*w - 55],\ [2957, 2957, 4*w - 59],\ [2969, 2969, -30*w - 101],\ [2969, 2969, 30*w - 131],\ [2999, 2999, -46*w + 227],\ [2999, 2999, 46*w + 181],\ [3001, 3001, -14*w - 17],\ [3001, 3001, 14*w - 31],\ [3011, 3011, 180*w - 857],\ [3011, 3011, 180*w + 677],\ [3041, 3041, 54*w + 197],\ [3041, 3041, -54*w + 251],\ [3067, 3067, -404*w - 1523],\ [3067, 3067, -222*w - 839],\ [3089, 3089, -64*w + 311],\ [3089, 3089, 64*w + 247],\ [3121, 3121, 26*w - 109],\ [3121, 3121, -26*w - 83],\ [3137, 3137, -464*w - 1751],\ [3137, 3137, 464*w - 2215],\ [3163, 3163, -68*w + 319],\ [3163, 3163, 68*w + 251],\ [3187, 3187, -6*w - 59],\ [3187, 3187, 6*w - 65],\ [3203, 3203, -36*w - 125],\ [3203, 3203, 36*w - 161],\ [3209, 3209, 18*w - 61],\ [3209, 3209, -18*w - 43],\ [3221, 3221, -308*w - 1163],\ [3221, 3221, 308*w - 1471],\ [3253, 3253, 14*w - 25],\ [3253, 3253, -14*w - 11],\ [3301, 3301, -12*w - 71],\ [3301, 3301, 12*w - 83],\ [3323, 3323, 252*w - 1201],\ [3323, 3323, 386*w - 1843],\ [3331, 3331, 20*w - 73],\ [3331, 3331, -20*w - 53],\ [3359, 3359, 10*w - 77],\ [3359, 3359, -10*w - 67],\ [3361, 3361, -72*w + 349],\ [3361, 3361, 72*w + 277],\ [3407, 3407, 86*w + 329],\ [3407, 3407, -86*w + 415],\ [3413, 3413, 18*w - 59],\ [3413, 3413, -18*w - 41],\ [3433, 3433, -14*w - 5],\ [3433, 3433, 14*w - 19],\ [3449, 3449, -78*w + 367],\ [3449, 3449, 78*w + 289],\ [3463, 3463, 64*w + 235],\ [3463, 3463, -64*w + 299],\ [3467, 3467, -206*w - 779],\ [3467, 3467, 206*w - 985],\ [3469, 3469, -60*w + 293],\ [3469, 3469, 60*w + 233],\ [3481, 59, -59],\ [3527, 3527, 2*w - 61],\ [3527, 3527, -2*w - 59],\ [3529, 3529, -240*w - 907],\ [3529, 3529, -430*w - 1621],\ [3539, 3539, -26*w + 139],\ [3539, 3539, 26*w + 113],\ [3541, 3541, 14*w - 13],\ [3541, 3541, 14*w - 1],\ [3559, 3559, -32*w - 107],\ [3559, 3559, 32*w - 139],\ [3571, 3571, 100*w + 373],\ [3571, 3571, 100*w - 473],\ [3581, 3581, 150*w - 713],\ [3581, 3581, 150*w + 563],\ [3583, 3583, 16*w - 41],\ [3583, 3583, -16*w - 25],\ [3593, 3593, 8*w - 73],\ [3593, 3593, -8*w - 65],\ [3613, 3613, 12*w - 85],\ [3613, 3613, -12*w - 73],\ [3623, 3623, -24*w + 95],\ [3623, 3623, 24*w + 71],\ [3631, 3631, 198*w - 947],\ [3631, 3631, 198*w + 749],\ [3659, 3659, 50*w + 197],\ [3659, 3659, -50*w + 247],\ [3673, 3673, 34*w - 149],\ [3673, 3673, -34*w - 115],\ [3677, 3677, 4*w - 65],\ [3677, 3677, -4*w - 61],\ [3691, 3691, 18*w + 89],\ [3691, 3691, -18*w + 107],\ [3719, 3719, 120*w - 569],\ [3719, 3719, 120*w + 449],\ [3727, 3727, -102*w - 389],\ [3727, 3727, -102*w + 491],\ [3739, 3739, -30*w + 157],\ [3739, 3739, 30*w + 127],\ [3761, 3761, -232*w - 877],\ [3761, 3761, -474*w - 1787],\ [3769, 3769, -456*w - 1721],\ [3769, 3769, 456*w - 2177],\ [3793, 3793, 58*w + 211],\ [3793, 3793, -58*w + 269],\ [3797, 3797, -18*w - 37],\ [3797, 3797, 18*w - 55],\ [3821, 3821, -68*w + 331],\ [3821, 3821, 68*w + 263],\ [3823, 3823, 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8243, -38*w + 205],\ [8273, 8273, 54*w - 239],\ [8273, 8273, -54*w - 185],\ [8287, 8287, -54*w + 275],\ [8287, 8287, 54*w + 221],\ [8297, 8297, 222*w - 1055],\ [8297, 8297, 222*w + 833],\ [8363, 8363, -84*w + 389],\ [8363, 8363, 84*w + 305],\ [8377, 8377, -638*w - 2405],\ [8377, 8377, 384*w + 1451],\ [8387, 8387, -106*w + 515],\ [8387, 8387, 106*w + 409],\ [8389, 8389, -36*w + 197],\ [8389, 8389, 36*w + 161],\ [8419, 8419, 140*w + 521],\ [8419, 8419, 140*w - 661],\ [8431, 8431, 582*w - 2779],\ [8431, 8431, 424*w - 2021],\ [8443, 8443, 258*w + 977],\ [8443, 8443, 258*w - 1235],\ [8467, 8467, 172*w - 815],\ [8467, 8467, 172*w + 643],\ [8537, 8537, 32*w + 149],\ [8537, 8537, -32*w + 181],\ [8539, 8539, 30*w + 143],\ [8539, 8539, 30*w - 173],\ [8543, 8543, 192*w + 719],\ [8543, 8543, 192*w - 911],\ [8573, 8573, -148*w - 565],\ [8573, 8573, -148*w + 713],\ [8623, 8623, -186*w + 893],\ [8623, 8623, -186*w - 707],\ [8641, 8641, 120*w + 461],\ [8641, 8641, -120*w + 581],\ [8663, 8663, -24*w - 31],\ [8663, 8663, 24*w - 55],\ [8669, 8669, 150*w - 709],\ [8669, 8669, -150*w - 559],\ [8681, 8681, -30*w - 73],\ [8681, 8681, 30*w - 103],\ [8689, 8689, -22*w - 1],\ [8689, 8689, 22*w - 23],\ [8693, 8693, 114*w + 421],\ [8693, 8693, -114*w + 535],\ [8699, 8699, -194*w - 737],\ [8699, 8699, 194*w - 931],\ [8719, 8719, -234*w - 887],\ [8719, 8719, 234*w - 1121],\ [8737, 8737, -26*w - 47],\ [8737, 8737, 26*w - 73],\ [8741, 8741, -66*w - 233],\ [8741, 8741, -66*w + 299],\ [8761, 8761, -50*w - 167],\ [8761, 8761, 50*w - 217],\ [8779, 8779, 210*w - 1007],\ [8779, 8779, -210*w - 797],\ [8783, 8783, -218*w - 827],\ [8783, 8783, 218*w - 1045],\ [8821, 8821, 12*w - 113],\ [8821, 8821, -12*w - 101],\ [8831, 8831, -24*w - 29],\ [8831, 8831, 24*w - 53],\ [8837, 8837, 126*w + 467],\ [8837, 8837, -126*w + 593],\ [8839, 8839, 114*w + 439],\ [8839, 8839, -114*w + 553],\ [8849, 8849, -496*w - 1873],\ [8849, 8849, 496*w - 2369],\ [8887, 8887, 32*w - 115],\ [8887, 8887, -32*w - 83],\ [8929, 8929, -38*w + 151],\ [8929, 8929, 38*w + 113],\ [8933, 8933, 292*w + 1105],\ [8933, 8933, 292*w - 1397],\ [8941, 8941, 230*w - 1093],\ [8941, 8941, 230*w + 863],\ [8963, 8963, 74*w + 293],\ [8963, 8963, -74*w + 367],\ [8971, 8971, -18*w - 113],\ [8971, 8971, 18*w - 131],\ [9011, 9011, -36*w - 103],\ [9011, 9011, -36*w + 139],\ [9029, 9029, -30*w - 71],\ [9029, 9029, 30*w - 101],\ [9043, 9043, -102*w + 497],\ [9043, 9043, 102*w + 395],\ [9049, 9049, 96*w + 373],\ [9049, 9049, -96*w + 469],\ [9109, 9109, 36*w + 163],\ [9109, 9109, -36*w + 199],\ [9127, 9127, 402*w + 1519],\ [9127, 9127, -664*w - 2503],\ [9133, 9133, 314*w - 1495],\ [9133, 9133, 314*w + 1181],\ [9137, 9137, -726*w - 2737],\ [9137, 9137, -368*w - 1391],\ [9157, 9157, 94*w + 343],\ [9157, 9157, -94*w + 437],\ [9161, 9161, 210*w + 787],\ [9161, 9161, 210*w - 997],\ [9173, 9173, -172*w - 655],\ [9173, 9173, -172*w + 827],\ [9199, 9199, 200*w - 949],\ [9199, 9199, 200*w + 749],\ [9221, 9221, 414*w - 1973],\ [9221, 9221, 652*w - 3113],\ [9239, 9239, 432*w - 2059],\ [9239, 9239, 626*w - 2989],\ [9277, 9277, 276*w + 1045],\ [9277, 9277, 276*w - 1321],\ [9283, 9283, 54*w + 223],\ [9283, 9283, -54*w + 277],\ [9319, 9319, -40*w - 121],\ [9319, 9319, -40*w + 161],\ [9341, 9341, -20*w - 119],\ [9341, 9341, 20*w - 139],\ [9343, 9343, 6*w - 103],\ [9343, 9343, -6*w - 97],\ [9371, 9371, -62*w + 313],\ [9371, 9371, 62*w + 251],\ [9413, 9413, 268*w - 1283],\ [9413, 9413, 268*w + 1015],\ [9419, 9419, -14*w - 107],\ [9419, 9419, 14*w - 121],\ [9421, 9421, -26*w - 41],\ [9421, 9421, 26*w - 67],\ [9433, 9433, -34*w - 91],\ [9433, 9433, 34*w - 125],\ [9463, 9463, -18*w - 115],\ [9463, 9463, 18*w - 133],\ [9467, 9467, 108*w + 397],\ [9467, 9467, -108*w + 505],\ [9491, 9491, -36*w - 101],\ [9491, 9491, -36*w + 137],\ [9539, 9539, -394*w - 1489],\ [9539, 9539, -708*w - 2669],\ [9547, 9547, 28*w - 83],\ [9547, 9547, -28*w - 55],\ [9551, 9551, 24*w - 43],\ [9551, 9551, -24*w - 19],\ [9587, 9587, 276*w - 1313],\ [9587, 9587, 276*w + 1037],\ [9601, 9601, -134*w + 631],\ [9601, 9601, 134*w + 497],\ [9613, 9613, 252*w - 1207],\ [9613, 9613, -252*w - 955],\ [9661, 9661, 86*w + 311],\ [9661, 9661, -86*w + 397],\ [9677, 9677, -244*w - 925],\ [9677, 9677, 244*w - 1169],\ [9697, 9697, -144*w + 695],\ [9697, 9697, 144*w + 551],\ [9721, 9721, 72*w + 287],\ [9721, 9721, -72*w + 359],\ [9733, 9733, 228*w - 1093],\ [9733, 9733, -228*w - 865],\ [9781, 9781, -540*w - 2039],\ [9781, 9781, 540*w - 2579],\ [9791, 9791, -120*w + 563],\ [9791, 9791, 120*w + 443],\ [9817, 9817, -82*w + 377],\ [9817, 9817, -82*w - 295],\ [9839, 9839, -10*w - 103],\ [9839, 9839, 10*w - 113],\ [9851, 9851, -156*w - 581],\ [9851, 9851, 156*w - 737],\ [9857, 9857, -8*w - 101],\ [9857, 9857, 8*w - 109],\ [9859, 9859, -68*w + 307],\ [9859, 9859, -68*w - 239],\ [9871, 9871, -80*w + 367],\ [9871, 9871, -80*w - 287],\ [9887, 9887, 24*w - 37],\ [9887, 9887, -24*w - 13],\ [9901, 9901, -70*w + 317],\ [9901, 9901, -70*w - 247],\ [9929, 9929, 64*w + 259],\ [9929, 9929, -64*w + 323],\ [9931, 9931, -76*w - 271],\ [9931, 9931, -76*w + 347]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-2, -2, -1, -1, 0, 0, -1, -1, -9, 3, 3, -8, -8, -10, 12, 12, -7, -7, -3, -3, 4, -10, -10, 15, 15, -7, -7, 10, 10, 1, 8, 8, -7, -7, -10, -10, -10, -6, -6, 7, 7, 12, 12, 19, 19, 18, 18, -23, -23, -2, -2, 10, 10, 4, 4, -30, 24, 24, 12, 12, 13, 13, 28, 28, 30, 30, -21, -21, -20, -20, -17, -17, -26, -26, -1, -1, -15, -15, -2, -2, 2, 2, 20, 20, 40, 40, -12, -12, 12, 12, -11, -11, 20, 20, 23, 23, 20, 20, -26, -26, 15, 15, -16, -16, 8, 8, -2, -2, 28, 28, 44, 44, -22, -22, -25, -25, -33, -33, -41, -41, 10, 10, 37, 37, 14, 14, 3, 3, -36, -36, 50, 50, -22, -22, -32, -32, 53, 53, 0, 0, -38, -38, 22, 22, -52, -52, -5, -5, -58, 14, 14, 8, 8, -12, -12, 12, 12, 8, 8, 42, 42, -27, -27, 34, 34, -13, -32, -32, 38, 38, 39, 39, -10, -10, 22, 22, 32, 32, -55, -55, 44, 44, 8, 8, -58, -58, -51, -51, -42, -42, -51, -51, -3, -3, -12, -12, -21, -21, -42, -42, 14, 14, 60, 60, 18, 18, 40, 40, -25, -25, -47, -47, -15, -15, 0, 0, -8, -8, -68, -68, 60, 60, 29, 29, 54, 54, 52, 52, -20, -20, 49, 49, 58, 58, 32, 32, -15, -15, -28, -28, -30, -30, 34, 34, -32, -32, 33, 33, -10, -10, 4, 4, 48, 48, -42, -42, -6, -6, 34, 34, 8, 8, -57, -57, 10, 10, 52, 52, -56, -56, -43, -43, -50, 62, 62, -3, -3, -6, -6, -35, -35, 70, 70, 77, 77, -52, -52, 54, 54, 79, 79, 30, 30, -22, -22, 4, 4, -17, -17, 84, 84, 24, 24, 70, 70, -18, -18, 35, 35, -38, -38, -86, -86, 20, 20, -58, -58, -26, -26, -30, 4, 4, -70, -70, -48, -48, 93, 93, 25, 25, 7, 7, 38, 38, 60, 60, -13, -13, 59, 59, 10, 10, -28, -28, 3, 3, 54, 54, 62, 62, -22, -22, 42, 42, 3, 3, -50, -50, -11, -11, 57, 57, 0, 0, 34, 34, -20, -20, -98, -98, 13, 13, 20, 20, -58, -58, 14, 14, -30, -30, 38, 38, 39, 39, -7, -7, -16, -16, 5, 5, -41, -41, -55, -55, -17, -17, -56, -56, -70, -70, 50, 50, -42, -42, -42, -42, 52, 52, -70, 4, 4, 2, 2, -40, -40, 38, 38, 88, 88, -50, -50, 3, 3, 70, 70, -80, -80, 27, 27, 62, 62, 42, 42, 13, 13, 25, 25, 22, 22, 8, 8, -26, -26, -2, -2, -6, -6, -10, -10, -103, -103, 74, 74, -73, -73, -76, -76, -43, -43, -45, -45, -88, -88, 18, 18, 9, 9, -66, -66, 40, 40, -96, -96, 38, 38, -85, -85, -93, 18, 18, -35, -35, 20, 20, 42, 42, 0, 0, -28, -28, 32, 32, -96, -96, -26, -26, -26, -26, 4, 4, 32, 32, 30, 30, -76, -76, -62, -62, 92, 92, -55, -55, 23, 23, -60, -60, -88, -88, 40, 40, 34, 34, -82, -82, -3, -3, 84, 84, 19, 19, -73, -73, 74, 74, 54, 54, 58, 58, 7, 7, -22, -22, -57, -57, 0, 0, 54, 54, -96, -96, -92, -92, -46, -46, -32, -32, 54, 54, 15, 15, 22, 22, 28, 28, -123, -123, -60, -60, 92, 92, 62, 62, -25, -25, -36, -36, -42, -42, 85, 85, 88, 88, -63, -63, -68, -68, 64, 64, -16, -16, 70, 70, -113, -113, -53, -53, 39, 39, -60, -60, 55, 55, -117, -117, 72, 72, 42, 42, 83, 83, 102, 102, 78, 78, -82, -82, 8, 8, -36, -36, -10, -10, 112, 112, -112, -112, -36, -36, -8, -8, -52, -52, 89, 89, 18, 18, -80, -80, 64, 64, 114, 114, 17, 17, 22, 22, 30, 30, 129, 129, -48, -48, -101, -101, -36, -36, 105, 105, -132, -132, 5, 5, -126, -126, 115, 115, -42, -42, -52, -52, -1, -1, 28, 28, 40, 40, -3, -3, 15, 15, 93, 93, 2, 2, -32, -32, 29, 29, 15, 15, 48, 48, 28, 28, 97, 97, -60, -60, -80, -80, -18, -18, -96, -96, 63, 63, -70, -70, 57, 57, -22, -22, -76, -76, -126, -126, 23, 23, -11, -11, -15, -15, -2, -2, 109, 109, -3, -3, 128, 128, -95, -95, 44, 44, 48, 48, 22, 22, -122, -122, 104, 104, 64, 64, 60, 60, 4, 4, -57, -57, -125, -125, -110, -110, -146, -146, -72, -72, 19, 19, -30, -30, 25, 25, 104, 104, 92, 92, -1, -1, -78, -78, 100, 100, -66, -66, 80, 80, 33, 33, -68, -68, -27, -27, 73, 73, -63, -63, -101, -101, -42, -42, -26, -26, 48, 48, -8, -8, -16, -16, 57, 57, 94, 94, 52, 52, -86, -86, 113, 113, 90, 90, 4, 4, -38, -38, -62, -62, -128, -128, -115, -115, -30, -30, -132, -132, -132, -132, -23, -23, -76, -76, -86, -86, 60, 60, -12, -12, -75, -75, -22, -22, -28, -28, -37, -37, 105, 105, 52, 52, -91, -91, -18, -18, 117, 117, -3, -3, -80, -80, 68, 68, -98, -98, 130, 130, -28, -28, 48, 48, -50, -50, -122, -122, -95, -95, -38, -38, 40, 40, 15, 15, -83, -83, -120, -120, 7, 7, 117, 117, 104, 104, -132, -132, 64, 64, 122, 122, -130, -90, -90, -88, -88, 38, 38, -72, -72, 30, 30, 8, 8, -128, -128, -101, -101, 23, 23, 164, 164, -62, -62, -60, -60, 120, 120, -72, -72, -145, -145, -73, -73, -142, -142, 162, 162, 25, 25, -110, -110, -21, -21, 138, 138, -25, -25, -150, -150, -80, -80, -88, -88, -43, -43, 78, 78, -87, -87, -42, -42, 24, 24, -92, -92, 109, 109, 64, 64, 40, 40, -33, -33, -130, -130, -70, -70, 84, 84, 107, 107, -51, -51, 92, 92, 28, 28, -21, -21, 58, 58, 14, 14, 60, 60, -36, -36, -147, -147, 20, 20, 74, 74, -30, -30, -48, -48, -136, -136, -26, -26, 137, 137, -75, -75, -46, -46, -42, -42, 77, 77, 112, 112, 123, 123, -130, -130, 107, 107, 169, 169, -17, -17, 99, 99, -26, -26, -72, -72, -117, -117, 84, 84, -92, -92, 168, 168, 110, 110, -60, -60, 107, 107, 54, 54, -122, -122, 13, 13, 145, 145, -126, -126, -146, -146, 74, 74, -108, -108, 124, 124, -130, -130, 132, 132, 90, 90, -86, -86, 135, 135, 40, 40, -2, -2, -108, -108, -13, -13, 55, 55, 69, 69, -78, -78, 157, 157, 3, 3, -70, -70, 90, 90, -62, -62, -40, -40, 109, 109, -133, -133, 129, 129, -128, -128, -38, -38, 115, 115, 144, 144, -130, -130, 85, 85, -12, -12, 79, 79, 78, 78, 63, 63, -138, -138, 24, 24, 80, 80, -103, -103, -60, -60, 43, 43, -166, -166, -20, -20, 42, 42, -151, -151, -78, -78, -166, -166, 0, 0, -78, -78, 94, 94, 184, 184, 8, 8, -108, -108, 0, 0, -2, -2, 27, 27, 18, 18, -173, -173, 64, 64, -13, -13, 138, 138, 178, 178, -178, -178, 49, 49, -18, -18, -108, -108, -102, -102, -45, -45, -48, -48, -117, -117, -85, -85, -128, -128, -117, -117, 102, 102, 0, 0, 57, 57] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([121, 11, -11])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]