# Stored data for newform 1344.4.a.br, downloaded from the LMFDB on 23 April 2024.
{"label": "1344.4.a.br", "space_label": "1344.4.a", "level": 1344, "weight": 4, "hecke_orbit": 44, "hecke_orbit_code": 193654784044041536, "dim": 2, "is_polredabs": true, "nf_label": "2.2.17.1", "trace_hash": 2240458044169254136, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[5, [8, -10, 1]], [11, [-1936, 22, 1]]], "qexp_display": "q+3q^{3}+(5-\\beta )q^{5}-7q^{7}+9q^{9}+(-11+\\cdots)q^{11}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 21504, "fricke_eigenval": -1, "atkin_lehner_string": "+-+", "analytic_conductor": 79.29856704771538, "hecke_ring_index": 2, "level_radical": 42, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [1344, 1, [127, 1093, 449, 577], [1, 1, 1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 1, "level_primes": [2, 3, 7], "conrey_indexes": [1], "field_disc": 17, "field_disc_factorization": [[17, 1]], "field_poly": [-4, -1, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.911", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.232", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "62.903", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [3, -1], [7, 1]], "trace_display": [0, 6, 10, -14], "traces": [0, 2, 0, 6, 0, 10, 0, -14, 0, 18, 0, -22, 0, 24, 0, 30, 0, -150, 0, 8, 0, -42, 0, 82, 0, -166, 0, 54, 0, 36, 0, -88, 0, -66, 0, -70, 0, -288, 0, 72, 0, -386, 0, -344, 0, 90, 0, 276, 0, 98, 0, -450, 0, -160, 0, 264, 0, 24, 0, -1076, 0, -156, 0, -126, 0, 188, 0, -1372, 0, 246, 0, 1102, 0, -240, 0, -498, 0, 154, 0, 412, 0, 162, 0, -464, 0, -1124, 0, 108, 0, -1746, 0, -168, 0, -264, 0, -1048, 0, 856, 0, -198, 0, -730, 0, 2096, 0, -210, 0, -1734, 0, -3164, 0, -864, 0, -2140, 0, -712, 0, 216, 0, 1050, 0, 1694, 0, -1158, 0, -1740, 0, 2796, 0, -1032, 0, -200, 0, -56, 0, 270, 0, 432, 0, 1960, 0, 828, 0, 484, 0, -908, 0, 294, 0, -288, 0, 288, 0, -1350, 0, -1120, 0, -3396, 0, -480, 0, -574, 0, -2020, 0, 792, 0, 3628, 0, -3970, 0, 72, 0, -2722, 0, 1162, 0, -3228, 0, 4630, 0, 608, 0, -468, 0, -1916, 0, -2464, 0, -378, 0, 3686, 0, 4072, 0, 564, 0, 2696, 0, -1864, 0, -4116, 0, -252, 0, -4004, 0, 738, 0, -12056, 0, 1200, 0, 3306, 0, 864, 0, 616, 0, -720, 0, -2548, 0, -8120, 0, -1494, 0, 5460, 0, -8992, 0, 462, 0, -248, 0, 5120, 0, 1236, 0, -3326, 0, -2936, 0, 486, 0, 490, 0, -2080, 0, -1392, 0, 12244, 0, -13244, 0, -3372, 0, -3682, 0, 2016, 0, 324, 0, 2258, 0, -188, 0, -5238, 0, 3178, 0, -4176, 0, -504, 0, 5566, 0, -12808, 0, -792, 0, -2672, 0, -3032, 0, -3144, 0, 2702, 0, 5538, 0, 2568, 0, 5334, 0, -3816, 0, -594, 0, -1260, 0, 2408, 0, -2190, 0, 4252, 0, 4496, 0, 6288, 0, -8620, 0, 10084, 0, -630, 0, -1440, 0, -12364, 0, -5202, 0, 11368, 0, -1312, 0, -9492, 0, -1932, 0, 4080, 0, -2592, 0, -6656, 0, -2580, 0, -6420, 0, -6512, 0, -686, 0, -2136, 0, 1846, 0, -7516, 0, 648, 0, -6518, 0, 3640, 0, 3150, 0, 6814, 0, 21130, 0, 5082, 0, 4852, 0, -13184, 0, -3474, 0, 1120, 0, 3204, 0, -5220, 0, -1744, 0, -20496, 0, 8388, 0, 10480, 0, -1848, 0, -3096, 0, 468, 0, 6192, 0, -600, 0, 5664, 0, -19060, 0, -168, 0, -8504, 0, -2416, 0, 810, 0, -2068, 0, 200, 0, 1296, 0, 7532, 0, -7896, 0, 5880, 0, 6652, 0, 8968, 0, 2484, 0, 8710, 0, 1092, 0, 1452, 0, 15158, 0, 1564, 0, -2724, 0, 36232, 0, 5296, 0, 882, 0, -6346, 0, -6996, 0, -864, 0, -18964, 0, -18568, 0, 864, 0, -1316, 0, 28068, 0, -4050, 0, 7782, 0, -3468, 0, -3360, 0, 23244, 0, 9604, 0, -10188, 0, 32208, 0, -11544, 0, -1440, 0, 7148, 0, -4408, 0, -1722, 0, 2580, 0, -5608, 0, -6060, 0, 9046, 0, 9268, 0, 2376, 0, -7714, 0, -3376, 0, 10884, 0, 32680, 0, 9508, 0, -11910, 0, -13206, 0, 1680, 0, 216, 0, 4224, 0, 38104, 0, -8166, 0, -1294, 0, -4312, 0, 3486, 0, 14080, 0, 16054, 0, -9684, 0, -8780, 0, -14824, 0, 13890, 0, -1078, 0, 2392, 0, 1824, 0, -18812, 0, -28716, 0, -1404, 0, 34960, 0, -2884, 0, -5748, 0, -22680, 0, 1040, 0, -7392, 0, -14524, 0, -14508, 0, -1134, 0, 31928, 0, -13604, 0, 11058, 0, -18026, 0, -15924, 0, 12216, 0, 3248, 0, 8492, 0, 1692, 0, -2340, 0, 21408, 0, 8088, 0, 15018, 0, 7868, 0, -5592, 0, 14454, 0, -25188, 0, -12348, 0, 242, 0, 35440, 0, -756, 0, 10792, 0, -16892, 0, -12012, 0, 504, 0, 8752, 0, 2214, 0, 12222, 0, 6678, 0, -36168, 0, 26836, 0, 156, 0, 3600, 0, 14320, 0, 1176, 0, 9918, 0, 50912, 0, -27896, 0, 2592, 0, 25604, 0, 29040, 0, 1848, 0, 3940, 0, 12872, 0, -2160, 0, -12846, 0, 50636, 0, -7644, 0, 7336, 0, 37380, 0, -24360, 0, 57068, 0, -8448, 0, -4482, 0, -3506, 0, -5992, 0, 16380, 0, -7122, 0, 12020, 0, -26976, 0, -696, 0, -20496, 0, 1386, 0, 23128, 0, 51764, 0, -744, 0, -3076, 0, 14080, 0, 15360, 0, 5110, 0, 21540, 0, 3708, 0, 18832, 0, 6160, 0, -9978, 0, -10840, 0, -14672, 0, -8808, 0, -13868, 0, 28688, 0, 1458, 0, -2624, 0, -18760, 0, 1470, 0, 17336, 0, -7924, 0, -6240, 0, -13730, 0, -10076, 0, -4176, 0, 12138, 0, 10512, 0, 36732, 0, 13952, 0, 78356, 0, -39732, 0, 12110, 0, 22148, 0, -10116, 0, -9784, 0, -27796, 0, -11046, 0, 46430, 0, 504, 0, 6048, 0, 64824, 0, -32692, 0, 972, 0, -33844, 0, -2096, 0, 6774, 0, 14980, 0, 8192, 0, -564, 0, 10798, 0, -61840, 0, -15714, 0, 69212, 0, 4984, 0, 9534, 0, 42844, 0, 22272, 0, -12528, 0, 3568, 0, -84064, 0, -1512, 0, 13240, 0, -59084, 0, 16698, 0, -34134, 0, -14160, 0, -38424, 0, -7350, 0, 13856, 0, -2376, 0, -10508, 0, -13314, 0, -8016, 0, -18218, 0, -11858, 0, -9096, 0, 3900, 0, 59476, 0, -9432, 0, 11150, 0, -22560, 0, 8106, 0, 15882, 0, -4124, 0, 16614, 0, 35112, 0, -16056, 0, 7704, 0, 12180, 0, 18468, 0, 16002, 0, -49438, 0, -93104, 0, -11448, 0, -20996, 0, -19572, 0, -1782, 0, -118576, 0, 27400, 0, -3780, 0, 20176, 0, 5268, 0, 7224, 0, 18476, 0, 9896, 0, -6570, 0, -71930, 0, -56232, 0, 12756, 0, 1400, 0, -84264, 0, 13488, 0, 9484, 0, 19144, 0, 18864, 0, 35158, 0, 392, 0, -25860, 0, -36256, 0, -34740, 0, 30252, 0, 16906, 0, 52616, 0, -1890, 0, 7530, 0, 9224, 0, -4320, 0, 18020, 0, 2552, 0, -37092, 0, -3024, 0, -42110, 0, -15606, 0, 17028, 0, -75684, 0, 34104, 0, 47336, 0, -13720, 0, -3936, 0, -36656, 0, 38280, 0, -28476, 0, -10504, 0, 3620, 0, -5796, 0, -99376, 0, -25320, 0, 12240, 0, -8096, 0, 25900, 0, -7776, 0, -3388, 0, 63496, 0, -19968, 0, -20224, 0, -20272, 0, -7740, 0, 12934, 0, 6356, 0, -19260, 0, -56270, 0, -8228, 0, -19536, 0, 11298, 0, 12152, 0, -2058, 0, 48886, 0, 39104, 0, -6408, 0, -43652, 0, -87864, 0, 5538, 0, 2016, 0, -46816, 0, -22548, 0, -78710, 0, -66108, 0, 1944, 0, -20112, 0, -2016, 0, -19554, 0, -27284, 0, 2712, 0, 10920, 0, -28116, 0, 7148, 0, 9450, 0, 10048, 0, 54392, 0, 20442, 0, -16720, 0, -112104, 0, 63390, 0, 7840, 0, -20652, 0, 15246, 0, 103392, 0, -32616, 0, 14556, 0, 62034, 0, 23772, 0, -39552, 0, 48650, 0, -22328, 0, -10422, 0, -48322, 0, 152768, 0, 3360, 0, -29040, 0, -9124, 0, 9612, 0, -54352, 0, -776, 0, -15660, 0, 4018, 0, 47008, 0, -5232, 0, -91872, 0, 21112, 0, -61488, 0, 100656, 0, 14140, 0, 25164, 0, -53460, 0, 22192, 0, 31440, 0, -20480, 0, 24152, 0, -5544, 0, -17484, 0, -161648, 0, -9288, 0, -67270, 0, -39116, 0, 1404, 0, -25396, 0, -360, 0, 18576, 0, 14492, 0, -48620, 0, -1800, 0, -46410, 0, 27790, 0, 16992, 0, -50446, 0, 59420, 0, -57180, 0, 1786, 0, -6600, 0, -504, 0, 1892, 0, -69408, 0, -25512, 0, -35148, 0, -62080, 0, -7248, 0, 19054, 0, 24920, 0, 2430, 0, 80502, 0, -26756, 0, -6204, 0, 99228, 0, -8134, 0, 600, 0, -17352, 0, 108920, 0, 3888, 0, -23184, 0, -17416, 0, 22596, 0, -48572, 0, -18348, 0, -23688, 0, -88880, 0, 8456, 0, 17640, 0, -32410, 0, 52040, 0, 19956, 0, 70112, 0, 6872, 0, 26904, 0, -38544, 0, -4256, 0, 7452, 0, 58464, 0, -12016, 0, 26130, 0, 18654, 0, 101176, 0, 3276, 0, -35926, 0, -39524, 0, 4356, 0, 51732, 0, 33648, 0, 45474, 0, 13412, 0, -125548, 0, 4692, 0, 6434, 0, 51448, 0, -8172, 0, -43896, 0, 17248, 0, 108696, 0, 17556, 0, 31656, 0, 15888, 0, 5300, 0, 63420, 0, 2646, 0, 19400, 0, 39496, 0, -19038, 0, -79860, 0, -36544, 0, -20988, 0, -25802, 0, 12640, 0, -2592, 0, -70544, 0, 19188, 0, -56892, 0, 64248, 0, -28504, 0, -55704, 0, -60048, 0, -95728, 0, 2592, 0, 914, 0, -114712, 0, -3948, 0, 71554, 0, -53170, 0, 84204, 0, 55924, 0, -39952, 0, -12150, 0, -18872, 0, -22332, 0, 23346, 0, -45612, 0, -194624, 0, -10404, 0, -33116, 0, 13048, 0, -10080, 0, -27016, 0, 96592, 0, 69732, 0, -172452, 0, 32948, 0, 28812, 0, -146620, 0, 96136, 0, -30564, 0, -1016, 0, -43952, 0, 96624, 0, 1764, 0, 42944, 0, -34632, 0, 41736, 0, -85904, 0, -4320, 0, 22030, 0, 28028, 0, 21444, 0, -24958, 0, 154792, 0, -13224, 0, 83790, 0, 158880, 0, -5166, 0, -80754, 0, -15436, 0, 7740, 0, -86944, 0, -85424, 0, -16824, 0, 84392, 0, 13444, 0, -18180, 0, -33296, 0, -13112, 0, 27138, 0, 104948, 0, -8400, 0, 27804, 0, -154852, 0, -34992, 0, 7128, 0, -122368, 0, 21864, 0, -23142, 0, 46752, 0, -16976, 0, -10128, 0, -138642, 0, -113680, 0, 32652, 0, -6048, 0, 103708, 0, 98040, 0, 78936, 0, 111876, 0, 28524, 0, 84620, 0, -4312, 0, -35730, 0, -45122, 0, 63268, 0, -39618, 0, 125048, 0, -138464, 0, 5040, 0, 38664, 0, -22464, 0, 648, 0, -62984, 0, 6248, 0, 12672, 0, 17836, 0, -9384, 0, 114312, 0, -26778, 0, -67376, 0, -24498, 0, -100532, 0, 56840, 0, -3882, 0, 85780, 0, -8104, 0, -12936, 0, -167484, 0, 3872, 0, 10458, 0, 176576, 0, 154828, 0, 42240, 0, -46182, 0, 31220, 0, 48162, 0, -38220, 0, 13360, 0, -29052, 0, -43120, 0, -2820, 0, -26340, 0, 54378, 0, 62944, 0, -44472, 0, -37498, 0, 114528, 0, 41670, 0, 72110, 0, 136944, 0, -3234, 0, 125170, 0, -19384, 0, 7176, 0, -31624, 0, 106128, 0, 5472, 0, 1736, 0, 106892, 0, -56436, 0, -23746, 0, -91828, 0, -86148, 0, -5200, 0, -35840, 0, -4212, 0, -45500, 0, 34232, 0, 104880, 0, -28832, 0, 39852, 0, -8652, 0, 134464, 0, -19476, 0, -17244, 0, -96658, 0, -179440, 0, -68040, 0, 23282, 0, 115916, 0, 3120, 0, -209556, 0, 63170, 0, -22176, 0, -70156, 0, 20552, 0, -43572, 0, -62472, 0, -27020, 0, -43524, 0, 70706, 0, 32656, 0, -3402, 0, 25344, 0, -41536, 0, 95784, 0, -80512, 0, -69416, 0, -40812, 0, -3430, 0, -89988, 0, 33174, 0, 23426, 0, -66876, 0, -54078, 0, -148148, 0, 14560, 0, -47772, 0, 208140, 0, 10488, 0, 36648, 0, -92104, 0, 38708, 0, 9744, 0, -61108, 0, 48424, 0, 25476, 0, -88384, 0, 102608, 0, 5076, 0, -85708, 0, 32856, 0, -7020, 0, -91232, 0, -56084, 0, 64224, 0, -163832, 0, 92708, 0, 24264, 0, -110166, 0, 113872, 0, 45054, 0, 24904, 0, 153296, 0, 23604, 0, -223774, 0, 138472, 0, -16776, 0, 172568, 0, 41992, 0, 43362, 0, 25774, 0, 536, 0, -75564, 0, 96946, 0, 50176, 0, -37044, 0, 163332, 0, -14112, 0, 726, 0, -102040, 0, 197744, 0, 106320, 0, -107256, 0, 80440, 0, -2268, 0, 16064, 0, -95988, 0, 32376, 0, -53680, 0, -87032, 0, -50676, 0, -15806, 0, 57824, 0, -36036, 0, 182888, 0, 96538, 0, 1512, 0, 270212, 0, 1316, 0, 26256, 0, 61622, 0, -111876, 0, 6642, 0, 98980, 0, -69992, 0, 36666, 0, -94938, 0, 35636, 0, 20034, 0, 33584, 0, -200480, 0, -108504, 0, -22246, 0, -20552, 0, 80508, 0, 182334, 0, -93776, 0, 468, 0, -95136, 0, 29232, 0, 10800, 0, 43784, 0, 134288, 0, 42960, 0, 55240, 0, 164984, 0, 3528, 0, -45480, 0, 99728, 0, 29754, 0, -423976, 0, 202388, 0, 152736, 0, -38962, 0, -281408, 0, -83688, 0, 74212, 0, 220228, 0, 7776, 0, -20728, 0, 89656, 0, 76812, 0, -31224, 0, 6148, 0, 87120, 0, 162350, 0, 259288, 0, 5544, 0, 99776, 0, 208576, 0, 11820, 0, 14472, 0, 28480, 0, 38616, 0, 18704, 0, -4180, 0, -6480, 0, -93886, 0, 1844, 0, -38538, 0, 122548, 0, 21224, 0, 151908, 0, -108084, 0, -88280, 0, -22932, 0, 163108, 0, -61180, 0, 22008, 0, 134180, 0, -125804, 0, 112140, 0, 86290, 0, 24324, 0, -73080, 0, -18914, 0, 150396, 0, 171204, 0, -23232, 0, 156828, 0, -25344, 0, 236768, 0, -38766, 0, -13446, 0, -266562, 0, -169056, 0, -10518, 0, 189992, 0, -58960, 0, -17976, 0, -193410, 0, -74480, 0, 49140, 0, -1244, 0, -128808, 0, -21366, 0, -37338, 0, 74984, 0, 36060, 0, -36542, 0, 79676, 0, -80928, 0, -18456, 0, 26712, 0, -2088, 0, -62956, 0, 83088, 0, -61488, 0, -17248, 0, 56288, 0, 4158, 0, 317440, 0, 29232, 0, 69384, 0, -98462, 0, 62576, 0, 155292, 0, 8820, 0, -7608, 0, -2232, 0, 137040, 0, -215204, 0, -9228, 0, -23500, 0, -16856, 0, 42240, 0, 41714, 0, 210848, 0, 46080, 0, -197984, 0, 3096, 0, 15330, 0, -81444, 0, 189592, 0, 64620, 0, -232368, 0, -64088, 0, 11124, 0, -29764, 0, -139552, 0, 56496, 0, -236282, 0, 84904, 0, 18480, 0, 113296, 0, -31472, 0, -29934, 0, -86572, 0, 61000, 0, -32520, 0, -213440, 0, -218960, 0, -44016, 0, 75140, 0, -138116, 0, -26424, 0, 34968, 0, -6452, 0, -41604, 0, 60340, 0, 293732, 0, 86064, 0, 133048, 0, 132064, 0, 4374, 0, 33968, 0, -70588, 0, -7872, 0, 60752, 0, -97104, 0, -56280, 0, -11088, 0, -39112, 0, 4410, 0, 173294, 0, 241842, 0, 52008, 0, -169156, 0, 18216, 0, -23772, 0, 10080, 0, -31924, 0, -18720, 0, 162258, 0, -137592, 0, -41190, 0, 91196, 0, 86548, 0, -30228, 0, 96276, 0, 178960, 0, -12528, 0, -152980, 0, -158604, 0, 36414, 0, -13692, 0, -83132, 0, 31536, 0, -142208, 0, -47984, 0, 110196, 0, -79576, 0, -110480, 0, 41856, 0, -10244, 0, 76436, 0, 235068, 0, 66398, 0, 9184, 0, -119196, 0, 74032, 0, -44648, 0, 36330, 0, 136804, 0, 233264, 0, 66444, 0, -107912, 0, 196676, 0, -30348, 0, -60768, 0, 270072, 0, -29352, 0, 13524, 0, 65124, 0, -83388, 0, 3922, 0, 122296, 0, -33138, 0, -62560, 0, -28560, 0, 139290, 0, -300432, 0, -464144, 0, 1512, 0, 64060, 0, -140860, 0, 18144, 0, 367396, 0, 63928, 0, 194472, 0, 153442, 0, -172728, 0, -98076, 0, 46592, 0, 80360, 0, 2916, 0, 14312, 0, 38168, 0, -101532, 0, -122618, 0, 18060, 0, -6288, 0, -293608, 0, 68288, 0, 20322, 0, 292384, 0, -81504, 0, 44940, 0, 164944, 0, -229632, 0, 24576, 0, -224760, 0, 130200, 0, -1692, 0, 45584, 0, -188428, 0, 32394, 0, -234438, 0, 5344, 0, -185520, 0, -46200, 0, 4802, 0, -47142, 0, -37544, 0, 170080, 0, 207636, 0, -38680, 0, 304, 0, 14952, 0, -115788, 0, 112264, 0, 28602, 0, 48278, 0, -88048, 0, 128532, 0, -12922, 0, -77440, 0, 66816, 0, -77408, 0, 11172, 0, -37584, 0, 12230, 0, 52612, 0, 10704, 0, 172534, 0, -90208, 0, -252192, 0, 216480, 0, -17976, 0, -4536, 0, -51950, 0, 131988, 0, 39720, 0, 121208, 0, -203936, 0, -177252, 0, 45626, 0, -267168, 0, 50094, 0, -376846, 0, 194712, 0, -102402, 0, 12476, 0, -25480, 0, -42480, 0, -444704, 0, 45240, 0, -115272, 0, -27760, 0, -128128, 0, -22050, 0, -276844, 0, -360628, 0, 41568, 0, -30988, 0, 42200, 0, -7128, 0, -47698, 0, 192640, 0, -31524, 0, 5412, 0, -186824, 0, -39942, 0, 192170, 0, -147910, 0, -24048, 0, -39074, 0, 116596, 0, -54654, 0, 303936, 0, -268080, 0, -35574, 0, 187326, 0, -115500, 0, -27288, 0, -307264, 0, 361344, 0, 11700, 0, -33964, 0, -128920, 0, 178428, 0, 12632, 0, -413908, 0, -28296, 0, -159232, 0, 92288, 0, 33450, 0, 131936, 0, -236528, 0, -67680, 0, 133288, 0, -86916, 0, 24318, 0, 200992, 0, -19920, 0, 47646, 0, -92046, 0, 250796, 0, -12372, 0, -7840, 0, 37924, 0, 49842, 0, -313792, 0, 86860, 0, 105336, 0, -28166, 0, -22428, 0, -48168, 0, 1288, 0, -86992, 0, 23112, 0, -338810, 0, 409264, 0, 36540, 0, -132508, 0, 146916, 0, 55404, 0, -297572, 0, 137856, 0, 48006, 0, 12208, 0, -418656, 0, -148314, 0, -11734, 0, -91720, 0, -279312, 0, -192852, 0, 143472, 0, -34344, 0, 165116, 0, -4472, 0, -62988, 0, 158704, 0, -81912, 0, -58716, 0, 440204, 0, 162752, 0, -5346, 0, 82382, 0, 55240, 0, -355728, 0, -73360, 0, -96540, 0, 82200, 0, -83204, 0, 293936, 0, -11340, 0, -310630, 0, 12936, 0, 60528, 0, -359398, 0, -50168, 0, 15804, 0, 4548, 0, -308032, 0, 21672, 0, 132174, 0, -365652, 0, 55428, 0, -117744, 0, -307800, 0, 29688, 0, -3276, 0, 232692, 0, -19710, 0, 30106, 0, -58076, 0, -215790, 0, -192336, 0, -43344, 0, -168696, 0, -124740, 0, -37824, 0, 38268, 0, 252352, 0, 19396, 0, 4200, 0, 146836, 0, 150864, 0, -252792, 0, 42144, 0, -235664, 0, 40464, 0, -39648, 0, -176932, 0, 28452, 0, 1152, 0, 23552, 0, 57432, 0, -245074, 0, 133420, 0, 56592, 0, 340978, 0, -53356, 0, 105474, 0, 172714, 0, 37792, 0, 1176, 0, 24512, 0, 186440, 0, -77580, 0, -145164, 0, -177000, 0, -108768, 0, 59528, 0, -273938, 0, -104220, 0, 69808, 0, -65752, 0, 90756, 0, 45932, 0, 16912, 0, 50718, 0, 139540, 0, -191752, 0, 157848, 0, 275200, 0, -236092, 0, -5670, 0, -60124, 0, -224976, 0, 22590, 0, 4974, 0, 223764, 0, 27672, 0, 14476, 0, -248088, 0, -12960, 0, -27152, 0, -291744, 0, 54060, 0, -239070, 0, -1400, 0, 7656, 0, 531992, 0, -399232, 0, -111276, 0, 279798, 0, 105936, 0, -9072, 0, -279254, 0, 251488, 0, -126330, 0, -69420, 0, -179400, 0, -46818, 0, -52724, 0, 199188, 0, 51084, 0, -59390, 0, -74320, 0, -227052, 0, 93748, 0, 55272, 0, 102312, 0, -266140, 0, -98616, 0, 142008, 0, 5808, 0, -87684, 0, -41160, 0, 103416, 0, -109784, 0, -11808, 0, 135878, 0, -434196, 0, -109968, 0, -46564, 0, -20472, 0, 114840, 0, 217672, 0, 99804, 0, -85428, 0, 152192, 0, -62776, 0, -31512, 0, 53144, 0, 134132, 0, 10860, 0, 393326, 0, 1320, 0, -17388, 0, 247406, 0, 230028, 0, -298128, 0, -211168, 0, 87464, 0, -75960, 0, -60970, 0, -124904, 0, 36720, 0, -384912, 0, 526064, 0, -24288, 0, 237920, 0, -7644, 0, 77700, 0, -322852, 0, 25112, 0, -23328, 0, 202860, 0], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "672.4.a.e", "char_is_minimal": false, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [0, 0], [3, 0], [0, 0], [5, -1], [0, 0], [-7, 0], [0, 0], [9, 0], [0, 0], [-11, -11], [0, 0], [12, -2], [0, 0], [15, -3], [0, 0], [-75, 11], [0, 0], [4, 32], [0, 0], [-21, 0], [0, 0], [41, 33], [0, 0], [-83, -10], [0, 0], [27, 0], [0, 0], [18, 32], [0, 0], [-44, 20], [0, 0], [-33, -33], [0, 0], [-35, 7], [0, 0], [-144, 14], [0, 0], [36, -6], [0, 0], [-193, 61], [0, 0], [-172, -76], [0, 0], [45, -9], [0, 0], [138, -110], [0, 0], [49, 0], [0, 0], [-225, 33], [0, 0], [-80, -18], [0, 0], [132, -44], [0, 0], [12, 96], [0, 0], [-538, -46], [0, 0], [-78, -148], [0, 0], [-63, 0], [0, 0], [94, -22], [0, 0], [-686, -6], [0, 0], [123, 99], [0, 0], [551, 55], [0, 0], [-120, -178], [0, 0], [-249, -30], [0, 0], [77, 77], [0, 0], [206, -106], [0, 0], [81, 0], [0, 0], [-232, 164], [0, 0], [-562, 130], [0, 0], [54, 96], [0, 0], [-873, -51], [0, 0], [-84, 14], [0, 0], [-132, 60], [0, 0], [-524, 156], [0, 0], [428, 50], [0, 0], [-99, -99], [0, 0]]}