# Stored data for newform 312.4.a.d, downloaded from the LMFDB on 26 September 2025.
{"Nk2": 4992, "analytic_conductor": 18.408595921791072, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1], [3, -1], [13, -1]], "atkin_lehner_string": "---", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [312, 1, [79, 157, 209, 145], [1, 1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 2, "field_disc": 17, "field_disc_factorization": [[17, 1]], "field_poly": [-4, -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": [[5, [64, 18, 1]]], "hecke_orbit": 4, "hecke_orbit_code": 13510798949220664, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 2, "hecke_ring_index_factorization": [[2, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": true, "is_maximal": true, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": true, "label": "312.4.a.d", "level": 312, "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, 13], "level_radical": 78, "minimal_twist": "312.4.a.d", "nf_label": "2.2.17.1", "prim_orbit_index": 1, "qexp_display": "q+3q^{3}+(-9-\\beta )q^{5}+(-5+5\\beta )q^{7}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "312.4.a", "trace_display": [0, 6, -18, -10], "trace_hash": 1341884598391770136, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.913", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.553", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "67.687", "prec": 20}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "traces": [0, 2, 0, 6, 0, -18, 0, -10, 0, 18, 0, 4, 0, 26, 0, -54, 0, -52, 0, -142, 0, -30, 0, -280, 0, -54, 0, 54, 0, -424, 0, -178, 0, 12, 0, -80, 0, 136, 0, 78, 0, -226, 0, -72, 0, -162, 0, 176, 0, 214, 0, -156, 0, -788, 0, 440, 0, -426, 0, 728, 0, -736, 0, -90, 0, -234, 0, 1054, 0, -840, 0, -660, 0, 24, 0, -162, 0, -2400, 0, 40, 0, 162, 0, 1344, 0, 60, 0, -1272, 0, 314, 0, -130, 0, -534, 0, 904, 0, -264, 0, 36, 0, -1224, 0, 1320, 0, -240, 0, 512, 0, -180, 0, 408, 0, -1000, 0, 2928, 0, 234, 0, 2300, 0, 4010, 0, -678, 0, 2124, 0, -220, 0, -216, 0, 272, 0, 2580, 0, -486, 0, -1858, 0, 1716, 0, 528, 0, 52, 0, 4020, 0, 642, 0, -1478, 0, 6098, 0, -468, 0, 480, 0, 384, 0, -2364, 0, -640, 0, 5638, 0, 1320, 0, -720, 0, 338, 0, -1278, 0, -24, 0, 3330, 0, 2184, 0, 3360, 0, -5000, 0, -2208, 0, 612, 0, -5816, 0, -270, 0, -7104, 0, 4836, 0, -702, 0, -3850, 0, -28, 0, 3162, 0, 1100, 0, 1388, 0, -2520, 0, -5520, 0, -3152, 0, -1980, 0, 3640, 0, 6500, 0, 72, 0, -676, 0, -6538, 0, -486, 0, -4300, 0, 3812, 0, -7200, 0, -4016, 0, -5664, 0, 120, 0, 1436, 0, -4440, 0, 486, 0, -226, 0, -1846, 0, 4032, 0, 6040, 0, 5152, 0, 180, 0, 5160, 0, -9860, 0, -3816, 0, 720, 0, 6820, 0, 942, 0, -3840, 0, -1242, 0, -390, 0, -8676, 0, -836, 0, -1602, 0, 4910, 0, -9308, 0, 2712, 0, 4360, 0, -3578, 0, -792, 0, -13774, 0, -6824, 0, 108, 0, -3640, 0, -14600, 0, -3672, 0, 5332, 0, -7470, 0, 3960, 0, 9456, 0, -2364, 0, -720, 0, -1826, 0, 2008, 0, 1536, 0, 8180, 0, -702, 0, -540, 0, 19520, 0, -1530, 0, 1224, 0, -5848, 0, 3220, 0, -3000, 0, -16064, 0, -6140, 0, 8784, 0, -5904, 0, 3688, 0, 702, 0, -8322, 0, 8592, 0, 6900, 0, 10512, 0, 478, 0, 12030, 0, -7764, 0, -20260, 0, -2034, 0, 5300, 0, 9492, 0, 6372, 0, -5512, 0, -3614, 0, -660, 0, 7976, 0, 18880, 0, -648, 0, 1588, 0, 2384, 0, 816, 0, 9024, 0, -13576, 0, 7740, 0, 2618, 0, -2314, 0, -1458, 0, 25976, 0, 15280, 0, -5574, 0, -2280, 0, -9784, 0, 5148, 0, -10328, 0, -21484, 0, 1584, 0, 8748, 0, 10140, 0, 156, 0, -4392, 0, 960, 0, 12060, 0, 15392, 0, 832, 0, 1926, 0, -7824, 0, 4620, 0, -4434, 0, 10546, 0, -9496, 0, 18294, 0, -1040, 0, -13104, 0, -1404, 0, -15802, 0, -18666, 0, 1440, 0, 13416, 0, -23460, 0, 1152, 0, 41744, 0, 10566, 0, -7092, 0, 15244, 0, 1768, 0, -1920, 0, 2716, 0, 28694, 0, 16914, 0, -19224, 0, 8576, 0, 3960, 0, -9960, 0, -1962, 0, -2160, 0, 16864, 0, 16388, 0, 1014, 0, -3306, 0, 37620, 0, -3834, 0, -13648, 0, -56768, 0, -72, 0, 3848, 0, 19700, 0, 9990, 0, 18092, 0, 19762, 0, 6552, 0, -2938, 0, -15624, 0, 10080, 0, 24228, 0, -6812, 0, -15000, 0, -2188, 0, -10212, 0, -6624, 0, 27860, 0, -47120, 0, 1836, 0, 23082, 0, -936, 0, -17448, 0, 29024, 0, -4804, 0, -810, 0, -14264, 0, -13316, 0, -21312, 0, 216, 0, 13924, 0, 14508, 0, -18280, 0, -5384, 0, -2106, 0, -22592, 0, 24980, 0, -11550, 0, 7970, 0, -14240, 0, -84, 0, 15832, 0, -40300, 0, 9486, 0, -34186, 0, -6396, 0, 3300, 0, 2288, 0, -44016, 0, 4164, 0, -28922, 0, 51650, 0, -7560, 0, -38800, 0, -12026, 0, -16560, 0, -25568, 0, -7886, 0, -9456, 0, -5024, 0, 2782, 0, -5940, 0, -26796, 0, 2150, 0, 10920, 0, -29104, 0, -2352, 0, 19500, 0, 10128, 0, -18904, 0, 216, 0, -56880, 0, 20920, 0, -2028, 0, -9280, 0, 61808, 0, -19614, 0, -19560, 0, -30696, 0, -1458, 0, -4772, 0, -380, 0, -12900, 0, -21924, 0, 11180, 0, 11436, 0, -10244, 0, 49366, 0, -21600, 0, -11976, 0, 13628, 0, -12048, 0, 25924, 0, -29852, 0, -16992, 0, -20740, 0, -7572, 0, 360, 0, 11456, 0, 5720, 0, 4308, 0, 38256, 0, 2240, 0, -13320, 0, 7776, 0, -64452, 0, 1458, 0, -34032, 0, 30580, 0, -678, 0, 53040, 0, 17090, 0, -5538, 0, -33236, 0, 35300, 0, 12096, 0, 52520, 0, -25552, 0, 18120, 0, -56752, 0, 57016, 0, 15456, 0, 10062, 0, 19940, 0, 540, 0, 9464, 0, 9612, 0, 15480, 0, 1610, 0, 25002, 0, -29580, 0, 23152, 0, 35808, 0, -11448, 0, -10732, 0, -13190, 0, 2160, 0, 74020, 0, -9568, 0, 20460, 0, -3300, 0, 44384, 0, 2826, 0, -105624, 0, 27520, 0, -11520, 0, 37392, 0, 22786, 0, -3726, 0, -44248, 0, -27800, 0, -1170, 0, -34846, 0, 13168, 0, -26028, 0, -15164, 0, 14368, 0, -2508, 0, -25964, 0, 1040, 0, -4806, 0, 9172, 0, 42334, 0, 14730, 0, -3042, 0, -29570, 0, -27924, 0, 2992, 0, 43840, 0, 8136, 0, 8528, 0, 19736, 0, 13080, 0, 13152, 0, -19436, 0, -10734, 0, 131456, 0, 13702, 0, -2376, 0, -12320, 0, 23040, 0, -41322, 0, -41432, 0, -38516, 0, -20472, 0, -33232, 0, 36120, 0, 324, 0, 32384, 0, -14328, 0, -10920, 0, 31004, 0, 23752, 0, -43800, 0, 50372, 0, 49788, 0, -11016, 0, -34368, 0, 35056, 0, 15996, 0, 80920, 0, 15608, 0, -22410, 0, -8580, 0, -36720, 0, 11880, 0, -4594, 0, -33894, 0, 28368, 0, 39152, 0, -15480, 0, -7092, 0, -9110, 0, 23888, 0, -2160, 0, -34960, 0, 312, 0, -5478, 0, -16696, 0, 73728, 0, 6024, 0, 37000, 0, -6714, 0, 4608, 0, -28836, 0, -3770, 0, 24540, 0, -7992, 0, -25920, 0, -2106, 0, 8506, 0, 104872, 0, -1620, 0, -12404, 0, 43524, 0, 58560, 0, 45984, 0, -23372, 0, -4590, 0, 5488, 0, -38068, 0, 3672, 0, -31200, 0, -15664, 0, -17544, 0, 58940, 0, 67912, 0, 9660, 0, 7320, 0, 25120, 0, -9000, 0, -72316, 0, -58864, 0, -48192, 0, 17730, 0, 520, 0, -18420, 0, 13904, 0, -33288, 0, 26352, 0, 34640, 0, -74792, 0, -17712, 0, -102600, 0, 15136, 0, 11064, 0, 44852, 0, 28234, 0, 2106, 0, 17352, 0, -21140, 0, -24966, 0, 58418, 0, 28968, 0, 25776, 0, 4232, 0, 94820, 0, 20700, 0, -17816, 0, -51912, 0, 31536, 0, 17472, 0, -73600, 0, 1434, 0, -37760, 0, 4566, 0, 36090, 0, -25912, 0, 14008, 0, -23292, 0, -20574, 0, 34460, 0, -60780, 0, -86464, 0, 780, 0, -6102, 0, -34612, 0, 72760, 0, 15900, 0, 40992, 0, -65800, 0, 28476, 0, -48696, 0, -109134, 0, 19116, 0, -9560, 0, -127240, 0, -16536, 0, -22112, 0, 16872, 0, -10842, 0, -71060, 0, -60660, 0, -1980, 0, -42332, 0, -72692, 0, 23928, 0, 111632, 0, 71904, 0, 56640, 0, 4082, 0, 66468, 0, -1944, 0, -52040, 0, 51308, 0, 4764, 0, 30800, 0, -53060, 0, 7152, 0, 68688, 0, -153200, 0, 2448, 0, -79774, 0, -1690, 0, 27072, 0, -119896, 0, 44036, 0, -40728, 0, -24672, 0, -30944, 0, 23220, 0, -53672, 0, -85564, 0, 7854, 0, 61244, 0, -14664, 0, -6942, 0, 98380, 0, -6964, 0, -4374, 0, -105270, 0, 107056, 0, 77928, 0, -8752, 0, -36378, 0, 45840, 0, 9278, 0, -114716, 0, -16722, 0, 11752, 0, -21780, 0, -6840, 0, 89952, 0, -195256, 0, -29352, 0, 33216, 0, -48192, 0, 15444, 0, -96360, 0, -68776, 0, -30984, 0, 66864, 0, -3432, 0, -64452, 0, -112192, 0, -1860, 0, 4752, 0, 41432, 0, -114852, 0, 26244, 0, 141628, 0, -2450, 0, 30420, 0, -55880, 0, -74660, 0, 468, 0, -84766, 0, 97644, 0, -13176, 0, 68000, 0, 18080, 0, 2880, 0, 28476, 0, 17776, 0, 36180, 0, 86412, 0, 95040, 0, 46176, 0, -15912, 0, 23440, 0, 2496, 0, 101776, 0, -71588, 0, 5778, 0, 26172, 0, -5048, 0, -23472, 0, 29352, 0, -92328, 0, 13860, 0, -13440, 0, 17160, 0, -13302, 0, -113648, 0, 90388, 0, 31638, 0, 17688, 0, -97620, 0, -28488, 0, 32768, 0, -105184, 0, 54882, 0, -3212, 0, -61792, 0, -3120, 0, 140284, 0, 7086, 0, -39312, 0, 28354, 0, 9008, 0, -4212, 0, -25120, 0, 169116, 0, -47406, 0, 5892, 0, 81324, 0, -55998, 0, 6656, 0, -26040, 0, 4320, 0, -98496, 0, -19658, 0, 40248, 0, 87536, 0, -28788, 0, -70380, 0, -48974, 0, -62688, 0, 3456, 0, 113624, 0, -2340, 0, 125232, 0, -35168, 0, -18386, 0, 31698, 0, 47304, 0, -12572, 0, -21276, 0, -27980, 0, -16800, 0, 45732, 0, -45280, 0, -229840, 0, 5304, 0, 53418, 0, 8644, 0, -5760, 0, -17320, 0, 156216, 0, 8148, 0, 118976, 0, -5220, 0, 86082, 0, 200320, 0, 111556, 0, 50742, 0, -13000, 0, 81482, 0, -57672, 0, -14760, 0, 70840, 0, 25728, 0, -23052, 0, 35060, 0, 11880, 0, 63068, 0, 70848, 0, -29880, 0, 53170, 0, 38064, 0, -5886, 0, 94624, 0, -106064, 0, -6480, 0, 122560, 0, -81304, 0, 50592, 0, 25256, 0, -97516, 0, 49164, 0, -50252, 0, -75146, 0, 3042, 0, 31920, 0, 43128, 0, -9918, 0, 51984, 0, 87260, 0, 112860, 0, 61960, 0, 165424, 0, -11502, 0, -103904, 0, -79584, 0, -40944, 0, 29900, 0, 142568, 0, -170304, 0, -160566, 0, -74768, 0, -216, 0, 149648, 0, 121940, 0, 11544, 0, 40588, 0, -107762, 0, 59100, 0, -23304, 0, 52130, 0, 29970, 0, -120856, 0, -52782, 0, 54276, 0, -15448, 0, 11572, 0, 59286, 0, 130640, 0, 156672, 0, 19656, 0, -118576, 0, 660, 0, -8814, 0, -40626, 0, 21060, 0, -46872, 0, -62724, 0, -106588, 0, 30240, 0, -22968, 0, -34928, 0, 72684, 0, 33164, 0, 1196, 0, -20436, 0, 27612, 0, 18114, 0, -45000, 0, -55740, 0, 124224, 0, -6564, 0, -34612, 0, 305016, 0, -30636, 0, 79108, 0, -170240, 0, -19872, 0, 2784, 0, -2860, 0, 83580, 0, 16184, 0, 94236, 0, -141360, 0, -13984, 0, -200908, 0, 5508, 0, 18872, 0, 44652, 0, 69246, 0, 82920, 0, -93942, 0, -2808, 0, -93936, 0, -100030, 0, -52344, 0, -110852, 0, -84220, 0, 87072, 0, -104200, 0, 37884, 0, -14412, 0, -80766, 0, 211752, 0, -2430, 0, 3536, 0, 99968, 0, -42792, 0, -238946, 0, -155968, 0, -39948, 0, 86880, 0, -32640, 0, -63936, 0, -15010, 0, -19094, 0, 648, 0, -101096, 0, 33540, 0, 41772, 0, -154160, 0, -14184, 0, 43524, 0, -208352, 0, -168192, 0, -54840, 0, 1556, 0, -101330, 0, -16152, 0, -13104, 0, -21072, 0, -6318, 0, 41880, 0, -98232, 0, -67776, 0, -48712, 0, 114780, 0, 74940, 0, 148280, 0, 303360, 0, -34650, 0, -29916, 0, 53548, 0, 23910, 0, -24154, 0, -20478, 0, -42720, 0, 120332, 0, 28048, 0, -252, 0, 102192, 0, -140848, 0, 47496, 0, 115300, 0, 87796, 0, -120900, 0, 48806, 0, 22308, 0, 28458, 0, -192288, 0, 106352, 0, -102558, 0, 107008, 0, 118880, 0, -19188, 0, -79096, 0, 135216, 0, 9900, 0, -55816, 0, -11674, 0, 6864, 0, 210560, 0, -77600, 0, -132048, 0, -153200, 0, 15004, 0, 12492, 0, -4400, 0, 106874, 0, -86766, 0, 50376, 0, 20640, 0, 154950, 0, 676, 0, 70968, 0, -22680, 0, -64892, 0, -110174, 0, -116400, 0, 25504, 0, 99568, 0, -36078, 0, 14026, 0, -45590, 0, -49680, 0, -259940, 0, 52260, 0, -76704, 0, -74504, 0, 108140, 0, -23658, 0, 81112, 0, -101740, 0, -28368, 0, 85940, 0, -275176, 0, -15072, 0, -241040, 0, -160416, 0, 8346, 0, 176394, 0, -40640, 0, -17820, 0, 27812, 0, 191648, 0, -80388, 0, 113760, 0, 57632, 0, 6450, 0, -6200, 0, 105536, 0, 32760, 0, -19214, 0, 12340, 0, -87312, 0, -201620, 0, -36732, 0, -7056, 0, -10236, 0, 136988, 0, 58500, 0, 25056, 0, -74272, 0, 30384, 0, -68272, 0, 79274, 0, -56712, 0, -101560, 0, 229488, 0, 648, 0, -65052, 0, -169992, 0, -170640, 0, -26408, 0, -102720, 0, 62760, 0, 156660, 0, -62958, 0, -6084, 0, 65208, 0, 111124, 0, -27840, 0, -125290, 0, -11528, 0, 185424, 0, -103280, 0, -66436, 0, -58842, 0, -56482, 0, 115588, 0, -58680, 0, 6240, 0, -180256, 0, -92088, 0, -365376, 0, -88190, 0, -4374, 0, 72720, 0, 5388, 0, -14316, 0, 84824, 0, -197744, 0, -1140, 0, -216852, 0, 4992, 0, -38700, 0, -151732, 0, 45392, 0, -65772, 0, 130920, 0, 37020, 0, 33540, 0, -127108, 0, 155832, 0, 34308, 0, -65368, 0, -40000, 0, -30732, 0, -18154, 0, 54668, 0, 148098, 0, -77904, 0, -213860, 0, -64800, 0, 205536, 0, 147040, 0, -35928, 0, 114088, 0, 26748, 0, 40884, 0, -8320, 0, 149800, 0, -36144, 0, -153292, 0, 122880, 0, 77772, 0, 236196, 0, 141896, 0, -89556, 0, 37864, 0, -47640, 0, -50976, 0, -50376, 0, 73294, 0, -62220, 0, 215304, 0, -59304, 0, -22716, 0, 108108, 0, -96824, 0, 1080, 0, -22240, 0, -116596, 0, 34368, 0, 45844, 0, -326, 0, 17160, 0, 222844, 0, 63700, 0, 12924, 0, -281262, 0, -34592, 0, 114768, 0, 89768, 0, 57648, 0, 6720, 0, 22844, 0, 116536, 0, -39960, 0, -9360, 0, 94212, 0, 23328, 0, -98960, 0, -31186, 0, -193356, 0, 34816, 0, -115136, 0, 4374, 0, 73248, 0, -84740, 0, -102096, 0, -113840, 0, 4394, 0, 91740, 0, -28776, 0, 190230, 0, -2034, 0, 256888, 0, 297442, 0, 159120, 0, -97080, 0, -4520, 0, 51270, 0, 33440, 0, -51236, 0, -16614, 0, -142506, 0, 190400, 0, -99708, 0, 41040, 0, 492480, 0, 105900, 0, 103040, 0, 254408, 0, 36288, 0, 73244, 0, -17700, 0, 157560, 0, -312, 0, -26366, 0, -76656, 0, 30384, 0, -119816, 0, 54360, 0, -234360, 0, 246948, 0, -170256, 0, 23704, 0, -173680, 0, 171048, 0, 163222, 0, 43290, 0, 46368, 0, 4432, 0, 208880, 0, 30186, 0, 99372, 0, 93856, 0, 59820, 0, 47824, 0, 280176, 0, 1620, 0, 121840, 0, -305654, 0, 28392, 0, -185168, 0, 98324, 0, 28836, 0, -192110, 0, -14376, 0, 46440, 0, 128384, 0, -4420, 0, 4830, 0, -160528, 0, 235824, 0, 75006, 0, 43680, 0, 114812, 0, -88740, 0, 215918, 0, -104696, 0, 69456, 0, 70648, 0, -110212, 0, 107424, 0, 103360, 0, 210830, 0, -34344, 0, -240336, 0, -65000, 0, -32196, 0, -69516, 0, 393260, 0, -39570, 0, -86232, 0, -386848, 0, 6480, 0, -206016, 0, -152210, 0, 222060, 0, -154544, 0, -263280, 0, -28704, 0, 148194, 0, 41444, 0, 61380, 0, 303360, 0, 91232, 0, -9900, 0, 12112, 0, -170176, 0, 133152, 0, 110864, 0, -200802, 0, 8478, 0, 7956, 0, -271056, 0, -316872, 0, 327212, 0, 92664, 0, 82560, 0, 215064, 0, -77096, 0, -34560, 0, 245768, 0, 1008, 0, 112176, 0, 366120, 0, -75608, 0, 68358, 0, -204560, 0, -204800, 0, -11178, 0, 169060, 0, -192180, 0, -132744, 0, 260088, 0, -313232, 0, -83400, 0, -262976, 0, 210552, 0, -3510, 0, -244564, 0, -203872, 0, -104538, 0, 4008, 0, 23504, 0, 39504, 0, -157800, 0, 234000, 0, -78084, 0, 139862, 0, 268124, 0, -45492, 0, -92352, 0, 132480, 0, 43104, 0, 161704, 0, -36704, 0, -7524, 0, 16264, 0, -314192, 0, -77892, 0, 107716, 0, -46374, 0, 3120, 0, -20496, 0, 62868, 0, -14418, 0, 178640, 0, -162384, 0, 27516, 0, -104712, 0, 4088, 0, 127002, 0, -63648, 0, -267930, 0, 44190, 0, -102048, 0, -225548, 0, -9126, 0, -50144, 0, 172168, 0, -88710, 0, 125432, 0, 103092, 0, -83772, 0, -24676, 0, -159952, 0, 8976, 0, -302880, 0, -108948, 0, 131520, 0, -50050, 0, 204264, 0, 24408, 0, -136108, 0, -39800, 0, 25584, 0, -195912, 0, -3816, 0, 59208, 0, -352232, 0, -21892, 0, 39240, 0, 544640, 0, -364, 0, 39456, 0, 54672, 0, 252580, 0, -58308, 0, -97916, 0, -25648, 0, -32202, 0, 192880, 0, -28308, 0, 394368, 0, -159652, 0, -150140, 0, 41106, 0, -254344, 0, -286768, 0, -7128, 0, 194346, 0, -87200, 0, -36960, 0, 98328, 0, -249408, 0, 69120, 0, 398950, 0, -97344, 0, -123966, 0, 14300, 0, -159984, 0, -124296, 0, -292098, 0, -29050, 0, -115548, 0, 289096, 0, -224860, 0, -61416, 0, -231438, 0, -268962, 0, -99696, 0, -168596, 0, 18044, 0, 108360, 0, 77328, 0, 35538, 0, 972, 0, 184464, 0, -92848, 0, 97152, 0, -195600, 0, -14246, 0, -42984, 0, -180312, 0, -301992, 0, -32760, 0, 282794, 0, -163720, 0, 93012, 0, 67940, 0, -405960, 0, 71256, 0, 97620, 0, 179496, 0, -131400, 0, 56096, 0, -65648, 0, 151116, 0, -71760, 0, 28242, 0, 149364, 0, 104260, 0, 73404, 0, -33048, 0, 95260, 0, 54352, 0, -103104, 0, 8744, 0, -244480, 0, 105168, 0, 182006, 0, -40976, 0, 47988, 0, -188224, 0, -88968, 0, 242760, 0, 192604, 0, -185936, 0, 46824, 0, -273664, 0, -189744, 0, -67230, 0, 373760, 0, -149530, 0, -25740, 0, -224516, 0, 96704, 0, -110160, 0, -198374, 0, -104500, 0, 35640, 0, -538552, 0, -314668, 0, -13782, 0, 1014, 0, 322368, 0, -101682, 0, 47320, 0, 92636, 0, 85104, 0, -132054, 0, -193942, 0, 117456, 0, 201280, 0, 14894, 0, -46440, 0, 58008, 0, -264888, 0, -21276, 0, 112316, 0, 84500, 0, -27330, 0, 275472, 0, -384760, 0, 71664, 0, -137040, 0, -242156, 0, -6480, 0, 247372, 0, 84000, 0, -104880, 0, 146640, 0, 22092, 0, 936, 0, -310080, 0, 413696, 0, -16434, 0, 125080, 0, -93428, 0, -50088, 0, -19364, 0, -5340, 0, 221184, 0, 90272, 0, -412388, 0, 18072, 0, -8788, 0, -293280, 0, 111000, 0, -404116, 0, 282200, 0, -20142, 0, -239012, 0, 19888, 0, 13824, 0, 64296, 0, 420320, 0, -86508, 0, 70530, 0, -84994, 0, -11310, 0, -258360, 0, 38720, 0, 73620, 0, -201008, 0, 24192, 0, -23976, 0, -139632, 0, -106752, 0, -77760, 0, -53248, 0, 509456, 0, -6318, 0, 214836, 0, 291720, 0, 25518, 0, -232600, 0, 93304, 0, 314616, 0, -299504, 0, 236448, 0, -4860, 0, -111872, 0, -106780, 0, -37212, 0, -55900, 0, -322068, 0, 130572, 0, 107954, 0, 773912, 0, 175680, 0, 56296, 0, -143300, 0, 137952, 0, -27382, 0, -184282, 0, -70116, 0, -178380, 0, 49556, 0, -13770, 0, 299776, 0, 52772, 0, 16464, 0, -290448, 0, -143352, 0, -114204, 0, 140700, 0, -124944, 0, 11016, 0, -236000, 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], [-9, -1], [0, 0], [-5, 5], [0, 0], [9, 0], [0, 0], [2, -14], [0, 0], [13, 0], [0, 0], [-27, -3], [0, 0], [-26, 12], [0, 0], [-71, 11], [0, 0], [-15, 15], [0, 0], [-140, -12], [0, 0], [-27, 18], [0, 0], [27, 0], [0, 0], [-212, -6], [0, 0], [-89, 33], [0, 0], [6, -42], [0, 0], [-40, -40], [0, 0], [68, -54], [0, 0], [39, 0], [0, 0], [-113, 19], [0, 0], [-36, -88], [0, 0], [-81, -9], [0, 0], [88, 120], [0, 0], [107, -50], [0, 0], [-78, 36], [0, 0], [-394, 8], [0, 0], [220, 124], [0, 0], [-213, 33], [0, 0], [364, 8], [0, 0], [-368, 38], [0, 0], [-45, 45], [0, 0], [-117, -13], [0, 0], [527, -107], [0, 0], [-420, -36], [0, 0], [-330, -78], [0, 0], [12, 222], [0, 0], [-81, 54], [0, 0], [-1200, 80], [0, 0], [20, -276], [0, 0], [81, 0], [0, 0], [672, -68], [0, 0], [30, -82], [0, 0], [-636, -18], [0, 0], [157, -219], [0, 0], [-65, 65], [0, 0], [-267, 99], [0, 0], [452, -28], [0, 0], [-132, -10], [0, 0], [18, -126], [0, 0]]}