# Stored data for newform 1200.4.a.br, downloaded from the LMFDB on 04 November 2024. {"Nk2": 19200, "analytic_conductor": 70.80229200688873, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, 1], [3, -1], [5, -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": [1200, 1, [751, 901, 401, 577], [1, 1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 2, "field_disc": 109, "field_disc_factorization": [[109, 1]], "field_poly": [-27, -1, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": 1, "has_non_self_twist": 0, "hecke_cutters": [[7, [-435, 2, 1]], [11, [-3860, -16, 1]]], "hecke_orbit": 44, "hecke_orbit_code": 193654784044041392, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 4, "hecke_ring_index_factorization": [[2, 2]], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "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": "1200.4.a.br", "level": 1200, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 3, 5], "level_radical": 30, "minimal_twist": "600.4.a.s", "nf_label": "2.2.109.1", "prim_orbit_index": 1, "qexp_display": "q+3q^{3}+(-1-\\beta )q^{7}+9q^{9}+(8-3\\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": "1200.4.a", "trace_display": [0, 6, 0, -2], "trace_hash": 1542042017771888239, "trace_moments": [{"__RealLiteral__": 0, "data": "0.019", "prec": 17}, {"__RealLiteral__": 0, "data": "1.909", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.141", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "62.204", "prec": 20}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.002", "prec": 17}, "traces": [0, 2, 0, 6, 0, 0, 0, -2, 0, 18, 0, 16, 0, 82, 0, 0, 0, 8, 0, 210, 0, -6, 0, -40, 0, 0, 0, 54, 0, -240, 0, -218, 0, 48, 0, 0, 0, 364, 0, 246, 0, 84, 0, -274, 0, 0, 0, -524, 0, 188, 0, 24, 0, 444, 0, 0, 0, 630, 0, 1084, 0, 774, 0, -18, 0, 0, 0, -210, 0, -120, 0, -1108, 0, 492, 0, 0, 0, 2600, 0, 1328, 0, 162, 0, 28, 0, 0, 0, -720, 0, 1424, 0, -1826, 0, -654, 0, 0, 0, 2370, 0, 144, 0, 828, 0, -1936, 0, 0, 0, -1348, 0, 962, 0, 1092, 0, -1704, 0, 0, 0, 738, 0, 4352, 0, 5314, 0, 252, 0, 0, 0, 248, 0, -822, 0, 3268, 0, 662, 0, 0, 0, 884, 0, 656, 0, -1572, 0, -4576, 0, 0, 0, 564, 0, 972, 0, -1494, 0, 72, 0, 0, 0, -194, 0, 1332, 0, -832, 0, -4838, 0, 0, 0, -1244, 0, 2456, 0, 1890, 0, -7536, 0, 0, 0, 3252, 0, 3700, 0, 2770, 0, 2322, 0, 0, 0, 13144, 0, -54, 0, 1312, 0, 494, 0, 0, 0, -1276, 0, 826, 0, -630, 0, -632, 0, 0, 0, -360, 0, 4296, 0, 1618, 0, -3324, 0, 0, 0, -7630, 0, 1476, 0, -8392, 0, -5650, 0, 0, 0, 1772, 0, 8922, 0, 7800, 0, -1820, 0, 0, 0, 3984, 0, 1140, 0, 9810, 0, 486, 0, 0, 0, 6866, 0, 84, 0, 7648, 0, -2936, 0, 0, 0, -8128, 0, -9084, 0, -2160, 0, 6612, 0, 0, 0, 4272, 0, 8696, 0, -4776, 0, -5478, 0, 0, 0, 3018, 0, -1962, 0, -5872, 0, 1946, 0, 0, 0, -2700, 0, 12006, 0, 7110, 0, -9684, 0, 0, 0, 432, 0, 104, 0, 4634, 0, 2484, 0, 0, 0, 12234, 0, -5808, 0, -3612, 0, 9534, 0, 0, 0, -5432, 0, -4536, 0, -4044, 0, 5200, 0, 0, 0, 2886, 0, 10988, 0, -6128, 0, 3276, 0, 0, 0, -13494, 0, -5112, 0, -25288, 0, -1246, 0, 0, 0, -7148, 0, -10444, 0, 2214, 0, 1200, 0, 0, 0, 13056, 0, 15084, 0, 9204, 0, 15942, 0, 0, 0, 14202, 0, 756, 0, -3060, 0, 11654, 0, 0, 0, -8096, 0, -4346, 0, 744, 0, -3936, 0, 0, 0, -2466, 0, -3732, 0, -4520, 0, 9804, 0, 0, 0, 4974, 0, 1986, 0, 10964, 0, 6758, 0, 0, 0, -23248, 0, -4446, 0, 2652, 0, -8060, 0, 0, 0, 1968, 0, 1716, 0, -12124, 0, -4716, 0, 0, 0, -4262, 0, -13728, 0, -4920, 0, 20078, 0, 0, 0, -5072, 0, -15722, 0, 1692, 0, -22984, 0, 0, 0, 2916, 0, -17712, 0, -7176, 0, -4482, 0, 0, 0, 7692, 0, 216, 0, -16604, 0, 4408, 0, 0, 0, -23088, 0, -32054, 0, -582, 0, 10888, 0, 0, 0, 3996, 0, 8700, 0, 32364, 0, -2496, 0, 0, 0, -16478, 0, -14514, 0, -26208, 0, -5320, 0, 0, 0, -24180, 0, 1242, 0, -3732, 0, 17588, 0, 0, 0, 7368, 0, -7980, 0, -5724, 0, 5670, 0, 0, 0, 27200, 0, -22608, 0, 13072, 0, 1506, 0, 0, 0, -40112, 0, -22662, 0, 9756, 0, 8676, 0, 0, 0, 11100, 0, -3728, 0, -6038, 0, 8310, 0, 0, 0, -32600, 0, 6966, 0, -26072, 0, 23088, 0, 0, 0, -2524, 0, -19954, 0, 39432, 0, 1824, 0, 0, 0, -162, 0, 19424, 0, 14354, 0, 3936, 0, 0, 0, 15766, 0, 1482, 0, -27932, 0, -4296, 0, 0, 0, -47380, 0, -30738, 0, -3828, 0, 22092, 0, 0, 0, 2478, 0, -17008, 0, 12270, 0, -1890, 0, 0, 0, -5584, 0, -1896, 0, -42412, 0, -30764, 0, 0, 0, -33644, 0, 4298, 0, -1080, 0, 2064, 0, 0, 0, 12888, 0, -42144, 0, 30054, 0, 4854, 0, 0, 0, 11196, 0, -9972, 0, 9984, 0, 24176, 0, 0, 0, 10440, 0, -12256, 0, -22890, 0, -35916, 0, 0, 0, 4428, 0, -17204, 0, -48252, 0, -25176, 0, 0, 0, 5672, 0, -16950, 0, -4272, 0, -3692, 0, 0, 0, 9368, 0, -16322, 0, 5316, 0, -59024, 0, 0, 0, 26766, 0, 23436, 0, 1800, 0, 23400, 0, 0, 0, -12744, 0, -5460, 0, 8, 0, 29500, 0, 0, 0, -24372, 0, 18298, 0, 11952, 0, 12208, 0, 0, 0, 3420, 0, 33416, 0, -6784, 0, 29430, 0, 0, 0, -1554, 0, 1458, 0, 20704, 0, -21860, 0, 0, 0, -98472, 0, -7880, 0, 20598, 0, 14984, 0, 0, 0, 252, 0, 12684, 0, 50584, 0, 22944, 0, 0, 0, 30762, 0, -8808, 0, 25048, 0, 47870, 0, 0, 0, 58396, 0, -11282, 0, -24384, 0, 11100, 0, 0, 0, -27252, 0, 6204, 0, -84728, 0, -6480, 0, 0, 0, 12738, 0, 19836, 0, -19224, 0, 38710, 0, 0, 0, 8336, 0, 50224, 0, 12816, 0, -11760, 0, 0, 0, 26088, 0, 65340, 0, 37178, 0, -14328, 0, 0, 0, -24410, 0, -16434, 0, -43300, 0, 12086, 0, 0, 0, 45516, 0, -45628, 0, 9054, 0, -7968, 0, 0, 0, -5886, 0, -18304, 0, -19106, 0, -17616, 0, 0, 0, 36542, 0, 5838, 0, 1440, 0, -20450, 0, 0, 0, -25952, 0, 26904, 0, -8100, 0, 824, 0, 0, 0, 36018, 0, 83872, 0, 55918, 0, 21330, 0, 0, 0, 47294, 0, -29052, 0, -8264, 0, 14526, 0, 0, 0, 38732, 0, 71256, 0, 1296, 0, -44556, 0, 0, 0, 312, 0, 34008, 0, -11304, 0, 13902, 0, 0, 0, 6728, 0, 7452, 0, -64084, 0, -83488, 0, 0, 0, -25068, 0, -49534, 0, 36702, 0, 5148, 0, 0, 0, -17424, 0, 20296, 0, 17996, 0, -10836, 0, 0, 0, 22, 0, 28602, 0, -15828, 0, 936, 0, 0, 0, -472, 0, 30636, 0, -16296, 0, 44192, 0, 0, 0, -13608, 0, 4348, 0, 34812, 0, -12132, 0, 0, 0, 2112, 0, 15600, 0, 84940, 0, -96576, 0, 0, 0, 55420, 0, 21856, 0, 8658, 0, 35672, 0, 0, 0, 32964, 0, 1120, 0, 76134, 0, -18384, 0, 0, 0, 30228, 0, 9828, 0, 97880, 0, -30544, 0, 0, 0, 44004, 0, 63834, 0, -40482, 0, -7108, 0, 0, 0, -15336, 0, 2792, 0, -48106, 0, -75864, 0, 0, 0, 5616, 0, -3738, 0, -34796, 0, 27298, 0, 0, 0, -14344, 0, 4162, 0, -21444, 0, -96892, 0, 0, 0, -31332, 0, 16984, 0, -12710, 0, 6642, 0, 0, 0, 21550, 0, 3600, 0, -35024, 0, -16266, 0, 0, 0, -22896, 0, 18782, 0, 39168, 0, -34960, 0, 0, 0, 45252, 0, 56956, 0, 16, 0, 27612, 0, 0, 0, -1162, 0, 47826, 0, 34928, 0, 4626, 0, 0, 0, 69172, 0, 129250, 0, 42606, 0, 10244, 0, 0, 0, 2268, 0, -15268, 0, -64008, 0, -9180, 0, 0, 0, 15858, 0, 34962, 0, 106844, 0, 31946, 0, 0, 0, -2016, 0, -29822, 0, -24288, 0, -41648, 0, 0, 0, -13038, 0, -162160, 0, 7454, 0, 2232, 0, 0, 0, 38804, 0, -11808, 0, 17104, 0, 8490, 0, 0, 0, 51408, 0, 77782, 0, -7398, 0, -40884, 0, 0, 0, -11196, 0, -104268, 0, -24938, 0, -13560, 0, 0, 0, 23224, 0, 29412, 0, 25552, 0, -145464, 0, 0, 0, -28216, 0, -7464, 0, 14922, 0, 7036, 0, 0, 0, 5958, 0, 154192, 0, 97652, 0, 32892, 0, 0, 0, -130872, 0, 20274, 0, 8408, 0, 55628, 0, 0, 0, 35148, 0, -6264, 0, -69744, 0, -49280, 0, 0, 0, -13338, 0, -20188, 0, 42048, 0, 7956, 0, 0, 0, 23220, 0, -24180, 0, -24192, 0, -76416, 0, 0, 0, 28520, 0, -61524, 0, 5904, 0, 15484, 0, 0, 0, 5148, 0, 101544, 0, 125074, 0, -36372, 0, 0, 0, -49858, 0, -14148, 0, 14388, 0, -54314, 0, 0, 0, 53856, 0, 36010, 0, -12786, 0, -43024, 0, 0, 0, -41184, 0, 19344, 0, -84474, 0, -14760, 0, 0, 0, -47386, 0, 60234, 0, 108260, 0, -11098, 0, 0, 0, 50008, 0, 32200, 0, -15216, 0, 81036, 0, 0, 0, -47166, 0, -17980, 0, 2196, 0, 5076, 0, 0, 0, -53130, 0, -68952, 0, 146784, 0, -9374, 0, 0, 0, 146056, 0, -61936, 0, 8748, 0, 127392, 0, 0, 0, -53136, 0, -141628, 0, -162686, 0, -21528, 0, 0, 0, -14704, 0, -13446, 0, 3600, 0, 52416, 0, 0, 0, 6444, 0, 52142, 0, 23076, 0, -19448, 0, 0, 0, 648, 0, -119060, 0, -56918, 0, -49812, 0, 0, 0, 46428, 0, 13224, 0, -77940, 0, 62830, 0, 0, 0, 216496, 0, -53726, 0, -69264, 0, -11992, 0, 0, 0, -96162, 0, 113364, 0, -139408, 0, -1746, 0, 0, 0, -58222, 0, 32664, 0, -20816, 0, -172744, 0, 0, 0, -30604, 0, 6166, 0, 11988, 0, 9512, 0, 0, 0, 26100, 0, 78316, 0, -39256, 0, 97092, 0, 0, 0, 45738, 0, -7488, 0, -5432, 0, 114474, 0, 0, 0, -37060, 0, -38624, 0, -49434, 0, 277360, 0, 0, 0, -43542, 0, -28008, 0, -57718, 0, -78624, 0, 0, 0, -157706, 0, -15960, 0, -149796, 0, 88864, 0, 0, 0, -19872, 0, 55484, 0, -72540, 0, 117484, 0, 0, 0, 3726, 0, -51692, 0, 163856, 0, -11196, 0, 0, 0, 22768, 0, 52764, 0, -3476, 0, 23136, 0, 0, 0, 41448, 0, -4796, 0, 22104, 0, -28448, 0, 0, 0, -23940, 0, -282512, 0, 67390, 0, -17172, 0, 0, 0, -50664, 0, 17010, 0, 36464, 0, 86634, 0, 0, 0, 180176, 0, 14934, 0, 81600, 0, -121764, 0, 0, 0, -67824, 0, -193220, 0, 13498, 0, 39216, 0, 0, 0, -85022, 0, 4518, 0, 103816, 0, 134162, 0, 0, 0, -24964, 0, 60454, 0, -120336, 0, 97356, 0, 0, 0, -67986, 0, 98508, 0, -93468, 0, 29268, 0, 0, 0, -157716, 0, 26028, 0, -47720, 0, 71302, 0, 0, 0, -110352, 0, 45714, 0, 33300, 0, 93264, 0, 0, 0, -11184, 0, -180600, 0, -19214, 0, -18114, 0, 0, 0, 133216, 0, 24930, 0, 163140, 0, 47448, 0, 0, 0, -148252, 0, -279984, 0, -97800, 0, -24852, 0, 0, 0, 20898, 0, -60280, 0, -132840, 0, -78216, 0, 0, 0, -69572, 0, 69264, 0, 48216, 0, -113498, 0, 0, 0, -28664, 0, 71116, 0, -7572, 0, 32868, 0, 0, 0, -59862, 0, -4608, 0, -126466, 0, 118296, 0, 0, 0, -37714, 0, 5472, 0, 153008, 0, -105850, 0, 0, 0, 26372, 0, -68120, 0, -486, 0, 177588, 0, 0, 0, 58272, 0, -187460, 0, -123104, 0, 43062, 0, 0, 0, -114408, 0, 11808, 0, -182424, 0, -54920, 0, 0, 0, 385616, 0, -154234, 0, 47298, 0, -40484, 0, 0, 0, 4446, 0, -200008, 0, 22022, 0, -83796, 0, 0, 0, 2104, 0, -12888, 0, -51344, 0, 69844, 0, 0, 0, -89616, 0, -2082, 0, -142140, 0, -24588, 0, 0, 0, -92214, 0, -89392, 0, -56360, 0, -11484, 0, 0, 0, -56142, 0, 66276, 0, 25780, 0, -110434, 0, 0, 0, -75172, 0, 133174, 0, 7434, 0, -30856, 0, 0, 0, -51024, 0, 163344, 0, 19302, 0, 36810, 0, 0, 0, 218736, 0, -5670, 0, 62376, 0, 51656, 0, 0, 0, -50976, 0, 51288, 0, -16752, 0, 223764, 0, 0, 0, -5688, 0, -55372, 0, 224416, 0, -127236, 0, 0, 0, -326488, 0, -92292, 0, -82476, 0, 234898, 0, 0, 0, 24328, 0, -99676, 0, -100932, 0, 248008, 0, 0, 0, 12894, 0, -409376, 0, -11706, 0, -3240, 0, 0, 0, -66134, 0, 6192, 0, 10740, 0, -57886, 0, 0, 0, 104628, 0, -35256, 0, 38664, 0, -124672, 0, 0, 0, -126432, 0, -75788, 0, -52974, 0, 90162, 0, 0, 0, -21384, 0, 14562, 0, 44108, 0, -57672, 0, 0, 0, 1504, 0, 27344, 0, 33588, 0, -73392, 0, 0, 0, -29916, 0, 63396, 0, -111456, 0, 29952, 0, 0, 0, -53400, 0, 72528, 0, 173592, 0, 25878, 0, 0, 0, 231692, 0, -182650, 0, 31320, 0, 57464, 0, 0, 0, -36768, 0, 110580, 0, -32874, 0, -68670, 0, 0, 0, -212000, 0, -107748, 0, 106968, 0, -101366, 0, 0, 0, 55576, 0, 87152, 0, 13284, 0, -55980, 0, 0, 0, -51612, 0, 195560, 0, 68686, 0, -144756, 0, 0, 0, -152872, 0, -75528, 0, -119104, 0, -171620, 0, 0, 0, -143784, 0, -37610, 0, 17016, 0, 142492, 0, 0, 0, -50850, 0, 13128, 0, -126616, 0, -12816, 0, 0, 0, 132146, 0, -11076, 0, 124108, 0, 22874, 0, 0, 0, 4208, 0, -140910, 0, 28104, 0, -130204, 0, 0, 0, -48966, 0, -267756, 0, -266066, 0, 15948, 0, 0, 0, -31968, 0, -177072, 0, -35660, 0, 89116, 0, 0, 0, 230536, 0, 158248, 0, 80298, 0, -99256, 0, 0, 0, 70308, 0, -17536, 0, 149842, 0, 5400, 0, 0, 0, 313266, 0, 70200, 0, -100888, 0, -49874, 0, 0, 0, -2400, 0, 5434, 0, -38232, 0, -976, 0, 0, 0, -16380, 0, 109496, 0, 452600, 0, 24, 0, 0, 0, -34476, 0, 88500, 0, -85000, 0, -79342, 0, 0, 0, -53808, 0, -203590, 0, -73116, 0, -482624, 0, 0, 0, 54894, 0, 34632, 0, -179624, 0, 35856, 0, 0, 0, 11750, 0, 36624, 0, 21884, 0, 60702, 0, 0, 0, -199848, 0, -74146, 0, 10260, 0, 102316, 0, 0, 0, 100248, 0, 358512, 0, 10204, 0, -20352, 0, 0, 0, -371216, 0, 88290, 0, 160020, 0, 26496, 0, 0, 0, 47212, 0, 118218, 0, -4662, 0, 267048, 0, 0, 0, 4374, 0, 197576, 0, 156146, 0, 62112, 0, 0, 0, 206558, 0, -65580, 0, 348364, 0, 26850, 0, 0, 0, 150696, 0, 55210, 0, -295416, 0, 141972, 0, 0, 0, -23640, 0, -66072, 0, -133502, 0, 61794, 0, 0, 0, -95928, 0, 44952, 0, -33448, 0, -316360, 0, 0, 0, -16388, 0, 330822, 0, 756, 0, 26840, 0, 0, 0, 38052, 0, -310720, 0, 104506, 0, 151752, 0, 0, 0, 175748, 0, 68832, 0, 456088, 0, -6540, 0, 0, 0, -23064, 0, -43778, 0, 92286, 0, -67932, 0, 0, 0, -26424, 0, -73908, 0, -191078, 0, 75144, 0, 0, 0, 5424, 0, 143610, 0, -183776, 0, 184918, 0, 0, 0, 205100, 0, 599826, 0, 175188, 0, -70184, 0, 0, 0, -33846, 0, 186496, 0, -155774, 0, -73152, 0, 0, 0, 227616, 0, 33300, 0, -455320, 0, 6984, 0, 0, 0, 113332, 0, 29696, 0, -81756, 0, -40280, 0, 0, 0, 18612, 0, 137812, 0, 76938, 0, -254184, 0, 0, 0, 220250, 0, -19440, 0, -376740, 0, 207746, 0, 0, 0, 30464, 0, -58010, 0, 38214, 0, -476976, 0, 0, 0, 59508, 0, 47440, 0, 236522, 0, -57672, 0, 0, 0, 285860, 0, 116130, 0, 97248, 0, -82990, 0, 0, 0, -322640, 0, 65214, 0, 25008, 0, 161396, 0, 0, 0, 150672, 0, 150132, 0, -278622, 0, 38448, 0, 0, 0, 24544, 0, -35280, 0, 160304, 0, 97544, 0, 0, 0, 130400, 0, 66456, 0, 78264, 0, 163736, 0, 0, 0, 196020, 0, -230036, 0, 448216, 0, 111534, 0, 0, 0, -168786, 0, -42984, 0, -17276, 0, 160428, 0, 0, 0, 131680, 0, -364496, 0, -73230, 0, -21656, 0, 0, 0, -49302, 0, 101464, 0, 15624, 0, -129900, 0, 0, 0, -51728, 0, 36258, 0, -366568, 0, -182498, 0, 0, 0, -147328, 0, 284420, 0, 136548, 0, -240944, 0, 0, 0, -136884, 0, 321340, 0, -147720, 0, 27162, 0, 0, 0, 315016, 0, -23904, 0, 42972, 0, -203568, 0, 0, 0, -68072, 0, 344638, 0, -17658, 0, -85716, 0, 0, 0, -54912, 0, 312048, 0, 118742, 0, -57318, 0, 0, 0, 173916, 0, -52848, 0, -43256, 0, -475712, 0, 0, 0, -183388, 0, -113914, 0, 109626, 0, -83904, 0, 0, 0, 17514, 0, 59536, 0, 137360, 0, 4320, 0, 0, 0, 190162, 0, -61350, 0, 188356, 0, 469400, 0, 0, 0, 94304, 0, -9842, 0, -77856, 0, 248084, 0, 0, 0, 80712, 0, -73212, 0, -174368, 0, -24300, 0, 0, 0, -93446, 0, 2472, 0, 216580, 0, -449594, 0, 0, 0, 46968, 0, 55008, 0, 108054, 0, 98052, 0, 0, 0, 251616, 0, 161832, 0, 108682, 0, 167754, 0, 0, 0, 234490, 0, 63990, 0, 61780, 0, -123478, 0, 0, 0, 51224, 0, 111144, 0, 141882, 0, -279048, 0, 0, 0, -87156, 0, 181624, 0, -27040, 0, -24792, 0, 0, 0, 1456, 0, 43578, 0, -5232, 0, 268562, 0, 0, 0, -204028, 0, -235208, 0, 116196, 0, 116028, 0, 0, 0, 213768, 0, 644504, 0, 316470, 0, 3888, 0, 0, 0, 54620, 0, -133668, 0, -346608, 0, -234944, 0, 0, 0, -20832, 0, 157626, 0, 936, 0, 25460, 0, 0, 0, 102024, 0, 254948, 0, 141864, 0, -33912, 0, 0, 0, -124874, 0, 41706, 0, -255180, 0, 93018, 0, 0, 0, -387176, 0, 126918, 0, 20184, 0, -45972, 0, 0, 0, 22356, 0, 1116, 0, 310966, 0, -192252, 0, 0, 0, -86168, 0, -250464, 0, 5856, 0, 378514, 0, 0, 0, 87972, 0, -40052, 0, -75204, 0, 166036, 0, 0, 0, -148602, 0, -186608, 0, -184720, 0, 110106, 0, 0, 0, -42086, 0, 15444, 0, -6272, 0, -367720, 0, 0, 0, 118332, 0, 488578, 0, -52272, 0, -148136, 0, 0, 0, 60888, 0, 140004, 0, 191104, 0, 53988, 0, 0, 0, -100366, 0, -32508, 0, 94020, 0, 169386, 0, 0, 0, 235812, 0, -191338, 0, 66, 0, -270448, 0, 0, 0, 85806, 0, -421168, 0, -138430, 0, -47484, 0, 0, 0, 400624, 0, 2808, 0, 6140, 0, 243254, 0, 0, 0, 44168, 0, -532536, 0, -1416, 0, -313836, 0, 0, 0, 91908, 0, 429600, 0, -116174, 0, -48888, 0, 0, 0, -40286, 0, 132576, 0, -70856, 0, -140306, 0, 0, 0, -244644, 0, -136814, 0, -40824, 0, -705216, 0, 0, 0, 13044, 0, 288404, 0, -132550, 0, 104436, 0, 0, 0, 14050, 0, -36396, 0, 115848, 0, -174696, 0, 0, 0, -379108, 0, -247346, 0, 6336, 0, 305452, 0, 0, 0, 46800, 0, 223160, 0, 29328, 0, 254820, 0, 0, 0, -46202, 0, -289728, 0, -76464, 0, -2464, 0, 0, 0, 97404, 0, -75816, 0, 166260, 0, -124668, 0, 0, 0, 65568, 0, -297316, 0, -25784, 0, 25974, 0, 0, 0, 292908, 0, 107016, 0, -127908, 0, -236276, 0, 0, 0, -244332, 0, -278360, 0, 98892, 0, -327164, 0, 0, 0, 3360, 0, -201124, 0, 317030, 0, 228402, 0, 0, 0, 205354, 0, -55152, 0, -116688, 0, 108686, 0, 0, 0, 241040, 0, 79732, 0, 90684, 0, 36360, 0, 0, 0, 29484, 0, 204120, 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], [3, 0], [0, 0], [0, 0], [0, 0], [-1, -1], [0, 0], [9, 0], [0, 0], [8, -3], [0, 0], [41, 2], [0, 0], [0, 0], [0, 0], [4, -5], [0, 0], [105, -1], [0, 0], [-3, -3], [0, 0], [-20, 1], [0, 0], [0, 0], [0, 0], [27, 0], [0, 0], [-120, 1], [0, 0], [-109, 9], [0, 0], [24, -9], [0, 0], [0, 0], [0, 0], [182, 10], [0, 0], [123, 6], [0, 0], [42, 3], [0, 0], [-137, -5], [0, 0], [0, 0], [0, 0], [-262, -12], [0, 0], [94, 2], [0, 0], [12, -15], [0, 0], [222, 3], [0, 0], [0, 0], [0, 0], [315, -3], [0, 0], [542, 8], [0, 0], [387, 4], [0, 0], [-9, -9], [0, 0], [0, 0], [0, 0], [-105, 37], [0, 0], [-60, 3], [0, 0], [-554, 29], [0, 0], [246, 6], [0, 0], [0, 0], [0, 0], [1300, -5], [0, 0], [664, -28], [0, 0], [81, 0], [0, 0], [14, 32], [0, 0], [0, 0], [0, 0], [-360, 3], [0, 0], [712, -4], [0, 0], [-913, -43], [0, 0], [-327, 27], [0, 0], [0, 0], [0, 0], [1185, 16], [0, 0], [72, -27], [0, 0]]}