# Stored data for newform 1024.4.a.d, downloaded from the LMFDB on 03 June 2024.
{"Nk2": 16384, "analytic_conductor": 60.41795584587839, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1]], "atkin_lehner_string": "-", "char_conductor": 1, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [1024, 1, [1023, 5], [1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 2, "field_disc": 8, "field_disc_factorization": [[2, 3]], "field_poly": [-2, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": true, "field_poly_root_of_unity": 8, "fricke_eigenval": -1, "has_non_self_twist": 1, "hecke_cutters": [[3, [-32, 0, 1]], [5, [-2, 0, 1]], [7, [-8, 1]]], "hecke_orbit": 4, "hecke_orbit_code": 13510798949221376, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 2, 1, 2, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "1024.4.a.d", "level": 1024, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": true, "level_is_prime_square": false, "level_is_square": true, "level_is_squarefree": false, "level_primes": [2], "level_radical": 2, "minimal_twist": "512.4.e.a", "nf_label": "2.2.8.1", "prim_orbit_index": 1, "qexp_display": "q+4\\beta q^{3}-\\beta q^{5}+8q^{7}+5q^{9}+4\\beta q^{11}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1024.4.a", "trace_display": [0, 0, 0, 16], "trace_hash": 1341968912951294151, "trace_moments": [{"__RealLiteral__": 0, "data": "0.010", "prec": 17}, {"__RealLiteral__": 0, "data": "1.971", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "15.662", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "155.548", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.507", "prec": 17}, "traces": [0, 2, 0, 0, 0, 0, 0, 16, 0, 10, 0, 0, 0, 0, 0, -16, 0, -48, 0, 0, 0, 0, 0, -368, 0, -246, 0, 0, 0, 0, 0, 352, 0, 64, 0, 0, 0, 0, 0, -48, 0, 400, 0, 0, 0, 0, 0, 416, 0, -558, 0, 0, 0, 0, 0, -16, 0, -1472, 0, 0, 0, 0, 0, 80, 0, 12, 0, 0, 0, 0, 0, -1872, 0, 812, 0, 0, 0, 0, 0, 1536, 0, -1678, 0, 0, 0, 0, 0, 1104, 0, -2612, 0, 0, 0, 0, 0, 368, 0, -944, 0, 0, 0, 0, 0, 1904, 0, -128, 0, 0, 0, 0, 0, -3440, 0, -2596, 0, 0, 0, 0, 0, -384, 0, -2598, 0, 0, 0, 0, 0, -3488, 0, -1600, 0, 0, 0, 0, 0, 352, 0, -2800, 0, 0, 0, 0, 0, -48, 0, -276, 0, 0, 0, 0, 0, -2608, 0, -240, 0, 0, 0, 0, 0, 4208, 0, -2944, 0, 0, 0, 0, 0, 7696, 0, -4358, 0, 0, 0, 0, 0, -1968, 0, -1728, 0, 0, 0, 0, 0, 5424, 0, 860, 0, 0, 0, 0, 0, -7392, 0, -5360, 0, 0, 0, 0, 0, -5360, 0, -7744, 0, 0, 0, 0, 0, -1840, 0, -1472, 0, 0, 0, 0, 0, 400, 0, 2816, 0, 0, 0, 0, 0, 5088, 0, -1230, 0, 0, 0, 0, 0, 512, 0, -7828, 0, 0, 0, 0, 0, 4544, 0, 4560, 0, 0, 0, 0, 0, 1104, 0, 5824, 0, 0, 0, 0, 0, 384, 0, -1404, 0, 0, 0, 0, 0, -15056, 0, -1052, 0, 0, 0, 0, 0, 16544, 0, -384, 0, 0, 0, 0, 0, 1760, 0, 3636, 0, 0, 0, 0, 0, 3200, 0, -8674, 0, 0, 0, 0, 0, 432, 0, -1408, 0, 0, 0, 0, 0, -14960, 0, -1356, 0, 0, 0, 0, 0, -15376, 0, 1360, 0, 0, 0, 0, 0, 1104, 0, 9280, 0, 0, 0, 0, 0, 4784, 0, 3328, 0, 0, 0, 0, 0, 1936, 0, 10596, 0, 0, 0, 0, 0, -9952, 0, 2944, 0, 0, 0, 0, 0, 1056, 0, 15292, 0, 0, 0, 0, 0, 4912, 0, 20138, 0, 0, 0, 0, 0, 3488, 0, 2000, 0, 0, 0, 0, 0, 3968, 0, -828, 0, 0, 0, 0, 0, 14592, 0, -128, 0, 0, 0, 0, 0, 8832, 0, 16576, 0, 0, 0, 0, 0, -11776, 0, -9456, 0, 0, 0, 0, 0, -3440, 0, -12848, 0, 0, 0, 0, 0, -1456, 0, 20160, 0, 0, 0, 0, 0, 2080, 0, 5904, 0, 0, 0, 0, 0, 19904, 0, 19856, 0, 0, 0, 0, 0, 14576, 0, -2790, 0, 0, 0, 0, 0, -25328, 0, 9616, 0, 0, 0, 0, 0, 96, 0, 29584, 0, 0, 0, 0, 0, -22400, 0, -2816, 0, 0, 0, 0, 0, 26160, 0, -1600, 0, 0, 0, 0, 0, -16480, 0, 2580, 0, 0, 0, 0, 0, -23088, 0, 24384, 0, 0, 0, 0, 0, -80, 0, -14976, 0, 0, 0, 0, 0, 16400, 0, 3740, 0, 0, 0, 0, 0, 6496, 0, 32384, 0, 0, 0, 0, 0, 34000, 0, -1200, 0, 0, 0, 0, 0, -8448, 0, 43378, 0, 0, 0, 0, 0, -2320, 0, 12736, 0, 0, 0, 0, 0, -24048, 0, -1196, 0, 0, 0, 0, 0, -25392, 0, 12288, 0, 0, 0, 0, 0, 1200, 0, -1536, 0, 0, 0, 0, 0, -13424, 0, -9648, 0, 0, 0, 0, 0, 45264, 0, -15876, 0, 0, 0, 0, 0, 4208, 0, 60, 0, 0, 0, 0, 0, 12016, 0, -30692, 0, 0, 0, 0, 0, 5488, 0, 12748, 0, 0, 0, 0, 0, -19968, 0, 8832, 0, 0, 0, 0, 0, -3200, 0, -20972, 0, 0, 0, 0, 0, -20896, 0, 29758, 0, 0, 0, 0, 0, -53360, 0, 39616, 0, 0, 0, 0, 0, -9360, 0, -5296, 0, 0, 0, 0, 0, 36528, 0, -1728, 0, 0, 0, 0, 0, -4144, 0, 4060, 0, 0, 0, 0, 0, 1152, 0, 2944, 0, 0, 0, 0, 0, 5424, 0, -28144, 0, 0, 0, 0, 0, -7552, 0, -42432, 0, 0, 0, 0, 0, 39152, 0, -3156, 0, 0, 0, 0, 0, -5040, 0, -9600, 0, 0, 0, 0, 0, 79120, 0, -3328, 0, 0, 0, 0, 0, 7680, 0, -64768, 0, 0, 0, 0, 0, 1728, 0, 15232, 0, 0, 0, 0, 0, -10832, 0, 29626, 0, 0, 0, 0, 0, 4464, 0, -7744, 0, 0, 0, 0, 0, -37680, 0, 6332, 0, 0, 0, 0, 0, 49280, 0, -35776, 0, 0, 0, 0, 0, -11776, 0, 9936, 0, 0, 0, 0, 0, 1296, 0, -69616, 0, 0, 0, 0, 0, -43296, 0, -27520, 0, 0, 0, 0, 0, -24288, 0, -6540, 0, 0, 0, 0, 0, -20768, 0, -4068, 0, 0, 0, 0, 0, -9984, 0, -13060, 0, 0, 0, 0, 0, -14928, 0, -48112, 0, 0, 0, 0, 0, -6096, 0, 36800, 0, 0, 0, 0, 0, 75056, 0, -7872, 0, 0, 0, 0, 0, -70032, 0, 13392, 0, 0, 0, 0, 0, 13200, 0, -29734, 0, 0, 0, 0, 0, -20784, 0, -11840, 0, 0, 0, 0, 0, 1840, 0, -30960, 0, 0, 0, 0, 0, -2784, 0, -8500, 0, 0, 0, 0, 0, 5808, 0, -4720, 0, 0, 0, 0, 0, 21232, 0, -99036, 0, 0, 0, 0, 0, 67440, 0, -27904, 0, 0, 0, 0, 0, -3184, 0, 8832, 0, 0, 0, 0, 0, -12800, 0, 6012, 0, 0, 0, 0, 0, 36256, 0, 5824, 0, 0, 0, 0, 0, 27280, 0, -41664, 0, 0, 0, 0, 0, 9520, 0, -99696, 0, 0, 0, 0, 0, 384, 0, -8980, 0, 0, 0, 0, 0, -73600, 0, 2816, 0, 0, 0, 0, 0, -99248, 0, -50544, 0, 0, 0, 0, 0, -22400, 0, 2370, 0, 0, 0, 0, 0, 40016, 0, 35328, 0, 0, 0, 0, 0, 5904, 0, -107824, 0, 0, 0, 0, 0, -55184, 0, -3004, 0, 0, 0, 0, 0, 6208, 0, 97600, 0, 0, 0, 0, 0, 75680, 0, -384, 0, 0, 0, 0, 0, -96784, 0, 47696, 0, 0, 0, 0, 0, -2208, 0, -12980, 0, 0, 0, 0, 0, 11264, 0, -49200, 0, 0, 0, 0, 0, -26704, 0, 73428, 0, 0, 0, 0, 0, -14944, 0, -13760, 0, 0, 0, 0, 0, 119632, 0, -119500, 0, 0, 0, 0, 0, -9904, 0, -20864, 0, 0, 0, 0, 0, 129872, 0, 14976, 0, 0, 0, 0, 0, -1920, 0, -59340, 0, 0, 0, 0, 0, -4368, 0, -76544, 0, 0, 0, 0, 0, -75328, 0, -12990, 0, 0, 0, 0, 0, -6496, 0, -62892, 0, 0, 0, 0, 0, 68064, 0, -288, 0, 0, 0, 0, 0, -14960, 0, 33664, 0, 0, 0, 0, 0, 127344, 0, 39744, 0, 0, 0, 0, 0, 102672, 0, 124624, 0, 0, 0, 0, 0, 10608, 0, -43968, 0, 0, 0, 0, 0, -17440, 0, -9788, 0, 0, 0, 0, 0, -13184, 0, 93948, 0, 0, 0, 0, 0, -124752, 0, 35200, 0, 0, 0, 0, 0, -12656, 0, 61568, 0, 0, 0, 0, 0, -51168, 0, 9280, 0, 0, 0, 0, 0, -34864, 0, -12288, 0, 0, 0, 0, 0, -163152, 0, -46188, 0, 0, 0, 0, 0, 4784, 0, 31196, 0, 0, 0, 0, 0, 44928, 0, -8448, 0, 0, 0, 0, 0, 3920, 0, -8316, 0, 0, 0, 0, 0, -108816, 0, 68634, 0, 0, 0, 0, 0, 81472, 0, -14000, 0, 0, 0, 0, 0, -13824, 0, -19488, 0, 0, 0, 0, 0, -27600, 0, 25540, 0, 0, 0, 0, 0, 8944, 0, 100032, 0, 0, 0, 0, 0, 28656, 0, 2944, 0, 0, 0, 0, 0, 70400, 0, 178112, 0, 0, 0, 0, 0, -90688, 0, 43392, 0, 0, 0, 0, 0, -240, 0, -34388, 0, 0, 0, 0, 0, 6880, 0, 48464, 0, 0, 0, 0, 0, -95120, 0, -1380, 0, 0, 0, 0, 0, 270848, 0, 11220, 0, 0, 0, 0, 0, 67536, 0, -140144, 0, 0, 0, 0, 0, 3648, 0, 196800, 0, 0, 0, 0, 0, 20896, 0, -59136, 0, 0, 0, 0, 0, -36864, 0, 3732, 0, 0, 0, 0, 0, -42880, 0, 12800, 0, 0, 0, 0, 0, -13040, 0, -101104, 0, 0, 0, 0, 0, 2992, 0, 83594, 0, 0, 0, 0, 0, 3968, 0, 40272, 0, 0, 0, 0, 0, -107600, 0, 17508, 0, 0, 0, 0, 0, -6960, 0, -42880, 0, 0, 0, 0, 0, -16240, 0, 185920, 0, 0, 0, 0, 0, -61952, 0, -106032, 0, 0, 0, 0, 0, 2960, 0, -3588, 0, 0, 0, 0, 0, 82112, 0, 181056, 0, 0, 0, 0, 0, -92576, 0, 164172, 0, 0, 0, 0, 0, -116800, 0, 16576, 0, 0, 0, 0, 0, 131760, 0, -14720, 0, 0, 0, 0, 0, 7552, 0, 73216, 0, 0, 0, 0, 0, -11776, 0, -5308, 0, 0, 0, 0, 0, 208320, 0, 143296, 0, 0, 0, 0, 0, -26496, 0, -26028, 0, 0, 0, 0, 0, -73152, 0, 91920, 0, 0, 0, 0, 0, -2208, 0, 162752, 0, 0, 0, 0, 0, 38480, 0, 3200, 0, 0, 0, 0, 0, 115152, 0, 62688, 0, 0, 0, 0, 0, -98208, 0, -21790, 0, 0, 0, 0, 0, -183248, 0, 20160, 0, 0, 0, 0, 0, 10416, 0, 72588, 0, 0, 0, 0, 0, 165424, 0, -15232, 0, 0, 0, 0, 0, 13312, 0, 73188, 0, 0, 0, 0, 0, 135984, 0, 40704, 0, 0, 0, 0, 0, -128096, 0, -199104, 0, 0, 0, 0, 0, -9840, 0, -133952, 0, 0, 0, 0, 0, 49920, 0, 24812, 0, 0, 0, 0, 0, 86000, 0, 38016, 0, 0, 0, 0, 0, -9600, 0, -100740, 0, 0, 0, 0, 0, 3760, 0, -7892, 0, 0, 0, 0, 0, -8832, 0, -17856, 0, 0, 0, 0, 0, 186672, 0, -2976, 0, 0, 0, 0, 0, -62624, 0, 344448, 0, 0, 0, 0, 0, -25328, 0, 103872, 0, 0, 0, 0, 0, -119328, 0, 22656, 0, 0, 0, 0, 0, -24400, 0, 192784, 0, 0, 0, 0, 0, -48256, 0, 4300, 0, 0, 0, 0, 0, 47056, 0, 36352, 0, 0, 0, 0, 0, -149408, 0, -57842, 0, 0, 0, 0, 0, 36480, 0, -142784, 0, 0, 0, 0, 0, 20768, 0, -167088, 0, 0, 0, 0, 0, -12432, 0, -2816, 0, 0, 0, 0, 0, -29808, 0, 104640, 0, 0, 0, 0, 0, -36960, 0, -150644, 0, 0, 0, 0, 0, 26160, 0, 8832, 0, 0, 0, 0, 0, 3440, 0, -26800, 0, 0, 0, 0, 0, 46592, 0, -29908, 0, 0, 0, 0, 0, -45696, 0, 102836, 0, 0, 0, 0, 0, -209920, 0, 144704, 0, 0, 0, 0, 0, -259072, 0, 93564, 0, 0, 0, 0, 0, 230256, 0, -153692, 0, 0, 0, 0, 0, 202960, 0, 3072, 0, 0, 0, 0, 0, -26800, 0, 24384, 0, 0, 0, 0, 0, -11232, 0, 15020, 0, 0, 0, 0, 0, -15120, 0, 170368, 0, 0, 0, 0, 0, 20784, 0, -282624, 0, 0, 0, 0, 0, -73248, 0, -99876, 0, 0, 0, 0, 0, -259792, 0, -9984, 0, 0, 0, 0, 0, 69616, 0, -120448, 0, 0, 0, 0, 0, 95888, 0, -119014, 0, 0, 0, 0, 0, -8416, 0, -17856, 0, 0, 0, 0, 0, 308752, 0, -31836, 0, 0, 0, 0, 0, -149216, 0, -269744, 0, 0, 0, 0, 0, -87216, 0, -7360, 0, 0, 0, 0, 0, 82560, 0, -105924, 0, 0, 0, 0, 0, 10992, 0, 132352, 0, 0, 0, 0, 0, 34000, 0, 27904, 0, 0, 0, 0, 0, 13392, 0, -139764, 0, 0, 0, 0, 0, 344080, 0, 62304, 0, 0, 0, 0, 0, 83200, 0, 268224, 0, 0, 0, 0, 0, 2000, 0, 18996, 0, 0, 0, 0, 0, -133584, 0, 3164, 0, 0, 0, 0, 0, 46240, 0, 14080, 0, 0, 0, 0, 0, 70576, 0, -226180, 0, 0, 0, 0, 0, 29088, 0, 12736, 0, 0, 0, 0, 0, -188928, 0, -355648, 0, 0, 0, 0, 0, -352240, 0, 40788, 0, 0, 0, 0, 0, -24048, 0, -129840, 0, 0, 0, 0, 0, -206048, 0, -203136, 0, 0, 0, 0, 0, 25440, 0, -111600, 0, 0, 0, 0, 0, 2112, 0, 247952, 0, 0, 0, 0, 0, -69392, 0, 206394, 0, 0, 0, 0, 0, 221328, 0, -213440, 0, 0, 0, 0, 0, -42768, 0, -19620, 0, 0, 0, 0, 0, 480608, 0, -326976, 0, 0, 0, 0, 0, 22400, 0, 62352, 0, 0, 0, 0, 0, 140256, 0, 3456, 0, 0, 0, 0, 0, -110032, 0, 15552, 0, 0, 0, 0, 0, -11264, 0, -342128, 0, 0, 0, 0, 0, -100656, 0, -62484, 0, 0, 0, 0, 0, -25008, 0, -39140, 0, 0, 0, 0, 0, -412880, 0, -7164, 0, 0, 0, 0, 0, 313536, 0, 256644, 0, 0, 0, 0, 0, -18288, 0, -119680, 0, 0, 0, 0, 0, 66192, 0, -22244, 0, 0, 0, 0, 0, -10848, 0, -143600, 0, 0, 0, 0, 0, -50752, 0, 384, 0, 0, 0, 0, 0, 22720, 0, 167568, 0, 0, 0, 0, 0, 83712, 0, -274160, 0, 0, 0, 0, 0, 12016, 0, 22800, 0, 0, 0, 0, 0, -135792, 0, -123008, 0, 0, 0, 0, 0, 92880, 0, -67712, 0, 0, 0, 0, 0, 10880, 0, 38400, 0, 0, 0, 0, 0, 241232, 0, -329472, 0, 0, 0, 0, 0, -145056, 0, -121118, 0, 0, 0, 0, 0, -49200, 0, -427200, 0, 0, 0, 0, 0, 5520, 0, 321276, 0, 0, 0, 0, 0, 173696, 0, 8832, 0, 0, 0, 0, 0, -13184, 0, -128128, 0, 0, 0, 0, 0, 74240, 0, -25500, 0, 0, 0, 0, 0, -3200, 0, -291540, 0, 0, 0, 0, 0, 142912, 0, 20864, 0, 0, 0, 0, 0, -132848, 0, 135868, 0, 0, 0, 0, 0, -105200, 0, -182764, 0, 0, 0, 0, 0, -144032, 0, 38272, 0, 0, 0, 0, 0, -8448, 0, 358608, 0, 0, 0, 0, 0, -116064, 0, 26900, 0, 0, 0, 0, 0, -281616, 0, -7020, 0, 0, 0, 0, 0, -27504, 0, 39616, 0, 0, 0, 0, 0, -9552, 0, 67200, 0, 0, 0, 0, 0, -46480, 0, -294400, 0, 0, 0, 0, 0, -59904, 0, 15488, 0, 0, 0, 0, 0, -424448, 0, 18036, 0, 0, 0, 0, 0, 84768, 0, -209472, 0, 0, 0, 0, 0, -75280, 0, -350336, 0, 0, 0, 0, 0, -91264, 0, -98992, 0, 0, 0, 0, 0, 257920, 0, -5260, 0, 0, 0, 0, 0, -23504, 0, 337076, 0, 0, 0, 0, 0, -41728, 0, 111778, 0, 0, 0, 0, 0, 100464, 0, 25984, 0, 0, 0, 0, 0, 23552, 0, -240944, 0, 0, 0, 0, 0, 3056, 0, 116112, 0, 0, 0, 0, 0, 1152, 0, 143680, 0, 0, 0, 0, 0, 82720, 0, -430932, 0, 0, 0, 0, 0, 70368, 0, 270336, 0, 0, 0, 0, 0, -35824, 0, 8448, 0, 0, 0, 0, 0, 173424, 0, 6624, 0, 0, 0, 0, 0, 122336, 0, -196716, 0, 0, 0, 0, 0, 416240, 0, 31168, 0, 0, 0, 0, 0, 407600, 0, -381248, 0, 0, 0, 0, 0, -40688, 0, -42432, 0, 0, 0, 0, 0, 68464, 0, -61568, 0, 0, 0, 0, 0, -295328, 0, 39296, 0, 0, 0, 0, 0, 39152, 0, 296848, 0, 0, 0, 0, 0, 161104, 0, 18180, 0, 0, 0, 0, 0, 34864, 0, 43200, 0, 0, 0, 0, 0, -235552, 0, 45812, 0, 0, 0, 0, 0, 116624, 0, 632960, 0, 0, 0, 0, 0, -375184, 0, -9012, 0, 0, 0, 0, 0, 62592, 0, 27904, 0, 0, 0, 0, 0, -234192, 0, 361536, 0, 0, 0, 0, 0, 16000, 0, -3328, 0, 0, 0, 0, 0, 28960, 0, -700, 0, 0, 0, 0, 0, 477664, 0, -43370, 0, 0, 0, 0, 0, 49152, 0, 444176, 0, 0, 0, 0, 0, 49776, 0, 66960, 0, 0, 0, 0, 0, -135600, 0, 31744, 0, 0, 0, 0, 0, 46000, 0, 159248, 0, 0, 0, 0, 0, -6624, 0, -463680, 0, 0, 0, 0, 0, -288432, 0, -52672, 0, 0, 0, 0, 0, 2160, 0, 117444, 0, 0, 0, 0, 0, -97936, 0, 2400, 0, 0, 0, 0, 0, -102560, 0, -15680, 0, 0, 0, 0, 0, -306176, 0, 116736, 0, 0, 0, 0, 0, -292032, 0, 30844, 0, 0, 0, 0, 0, 4464, 0, 194304, 0, 0, 0, 0, 0, -100992, 0, -46668, 0, 0, 0, 0, 0, -297936, 0, 4944, 0, 0, 0, 0, 0, 313536, 0, -192320, 0, 0, 0, 0, 0, 329120, 0, -316720, 0, 0, 0, 0, 0, -25968, 0, 70656, 0, 0, 0, 0, 0, -29712, 0, -6780, 0, 0, 0, 0, 0, 132608, 0, 291344, 0, 0, 0, 0, 0, -459712, 0, -35776, 0, 0, 0, 0, 0, 146880, 0, 44928, 0, 0, 0, 0, 0, 423120, 0, 272208, 0, 0, 0, 0, 0, 478032, 0, -11764, 0, 0, 0, 0, 0, 311536, 0, 410688, 0, 0, 0, 0, 0, -76880, 0, 38160, 0, 0, 0, 0, 0, -75648, 0, -21078, 0, 0, 0, 0, 0, 35696, 0, 6800, 0, 0, 0, 0, 0, -12112, 0, 319308, 0, 0, 0, 0, 0, 582544, 0, 366692, 0, 0, 0, 0, 0, -184704, 0, -213184, 0, 0, 0, 0, 0, -19488, 0, -27520, 0, 0, 0, 0, 0, -26160, 0, -4204, 0, 0, 0, 0, 0, -102784, 0, 59136, 0, 0, 0, 0, 0, 5520, 0, 104592, 0, 0, 0, 0, 0, 203584, 0, 193600, 0, 0, 0, 0, 0, -613392, 0, -204160, 0, 0, 0, 0, 0, 42880, 0, 272, 0, 0, 0, 0, 0, -200720, 0, -11648, 0, 0, 0, 0, 0, -374400, 0, 597952, 0, 0, 0, 0, 0, 161280, 0, 641792, 0, 0, 0, 0, 0, -67872, 0, -258060, 0, 0, 0, 0, 0, -36176, 0, -83584, 0, 0, 0, 0, 0, -105248, 0, 64768, 0, 0, 0, 0, 0, 31824, 0, 436048, 0, 0, 0, 0, 0, -14928, 0, 16640, 0, 0, 0, 0, 0, 294400, 0, 216140, 0, 0, 0, 0, 0, 47232, 0, -29364, 0, 0, 0, 0, 0, -601680, 0, 42880, 0, 0, 0, 0, 0, -365424, 0, 162400, 0, 0, 0, 0, 0, -212112, 0], "weight": 4, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0], [1, 0], [0, 0], [0, 4], [0, 0], [0, -1], [0, 0], [8, 0], [0, 0], [5, 0], [0, 0], [0, 4], [0, 0], [0, -3], [0, 0], [-8, 0], [0, 0], [-24, 0], [0, 0], [0, -92], [0, 0], [0, 32], [0, 0], [-184, 0], [0, 0], [-123, 0], [0, 0], [0, -88], [0, 0], [0, 69], [0, 0], [176, 0], [0, 0], [32, 0], [0, 0], [0, -8], [0, 0], [0, -215], [0, 0], [-24, 0], [0, 0], [200, 0], [0, 0], [0, -100], [0, 0], [0, -5], [0, 0], [208, 0], [0, 0], [-279, 0], [0, 0], [0, -96], [0, 0], [0, 263], [0, 0], [-8, 0], [0, 0], [-736, 0], [0, 0], [0, -108], [0, 0], [0, 339], [0, 0], [40, 0], [0, 0], [6, 0], [0, 0], [0, -484], [0, 0], [0, -736], [0, 0], [-936, 0], [0, 0], [406, 0], [0, 0], [0, -492], [0, 0], [0, 32], [0, 0], [768, 0], [0, 0], [-839, 0], [0, 0], [0, 364], [0, 0], [0, 24], [0, 0], [552, 0], [0, 0], [-1306, 0], [0, 0], [0, -24], [0, 0], [0, 704], [0, 0], [184, 0], [0, 0], [-472, 0], [0, 0], [0, 20], [0, 0]]}