# Stored data for newform 1620.4.i.j, downloaded from the LMFDB on 21 May 2024.
{"Nk2": 25920, "analytic_conductor": 95.5830942092998, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 9, "char_degree": 2, "char_is_minimal": false, "char_is_real": false, "char_orbit_index": 9, "char_orbit_label": "i", "char_order": 3, "char_parity": 1, "char_values": [1620, 3, [811, 1541, 1297], [3, 2, 3]], "cm_discs": [], "conrey_index": 541, "dim": 2, "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 6, "has_non_self_twist": 1, "hecke_cutters": [[7, [256, -16, 1]], [11, [3600, 60, 1]]], "hecke_orbit": 10, "hecke_orbit_code": 40532946469258836, "hecke_ring_generator_nbound": 7, "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, 9, 3, 1, 3, 0]], "is_cm": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": false, "label": "1620.4.i.j", "level": 1620, "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": "20.4.a.a", "nf_label": "2.0.3.1", "prim_orbit_index": 3, "qexp_display": "q+5\\zeta_{6}q^{5}+(2^{4}-2^{4}\\zeta_{6})q^{7}+(-60+\\cdots)q^{11}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "3.2.3.c3", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1620.4.i", "trace_display": [0, 0, 5, 16], "trace_hash": 2251728238888802442, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.958", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11.446", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "103.952", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.002", "prec": 17}, "traces": [0, 2, 0, 0, 0, 5, 0, 16, 0, 0, 0, -60, 0, -86, 0, 0, 0, -36, 0, 88, 0, 0, 0, 48, 0, -25, 0, 0, 0, -186, 0, -176, 0, 0, 0, 160, 0, 508, 0, 0, 0, 186, 0, 100, 0, 0, 0, 168, 0, 87, 0, 0, 0, 996, 0, -600, 0, 0, 0, -252, 0, 58, 0, 0, 0, 430, 0, 1036, 0, 0, 0, -336, 0, 1012, 0, 0, 0, 960, 0, -272, 0, 0, 0, 948, 0, -90, 0, 0, 0, 2028, 0, -2752, 0, 0, 0, 220, 0, 766, 0, 0, 0, -1314, 0, 448, 0, 0, 0, -3096, 0, 556, 0, 0, 0, -558, 0, -240, 0, 0, 0, -288, 0, -2269, 0, 0, 0, -250, 0, 688, 0, 0, 0, 780, 0, 704, 0, 0, 0, 666, 0, -884, 0, 0, 0, 10320, 0, -1860, 0, 0, 0, -114, 0, 40, 0, 0, 0, 880, 0, 154, 0, 0, 0, 1536, 0, 4360, 0, 0, 0, 3696, 0, -5199, 0, 0, 0, 1302, 0, 400, 0, 0, 0, 8616, 0, 3100, 0, 0, 0, 1270, 0, 1080, 0, 0, 0, 48, 0, -1058, 0, 0, 0, 7428, 0, -3536, 0, 0, 0, 2976, 0, -930, 0, 0, 0, -2640, 0, 4036, 0, 0, 0, 1000, 0, -5632, 0, 0, 0, 1548, 0, -680, 0, 0, 0, 2388, 0, 3874, 0, 0, 0, -6324, 0, 1680, 0, 0, 0, 5424, 0, 3886, 0, 0, 0, -435, 0, -3784, 0, 0, 0, 10200, 0, -5760, 0, 0, 0, 2178, 0, 4064, 0, 0, 0, -6144, 0, 2490, 0, 0, 0, -1644, 0, 16960, 0, 0, 0, -1500, 0, 1138, 0, 0, 0, 5706, 0, 3028, 0, 0, 0, 5952, 0, -9178, 0, 0, 0, 3390, 0, 1260, 0, 0, 0, 4128, 0, -1600, 0, 0, 0, 580, 0, -8312, 0, 0, 0, 6552, 0, 1366, 0, 0, 0, 2598, 0, -11160, 0, 0, 0, -1584, 0, 4300, 0, 0, 0, -2688, 0, 3292, 0, 0, 0, -5180, 0, -6194, 0, 0, 0, 21120, 0, 13760, 0, 0, 0, -10020, 0, 3130, 0, 0, 0, 4194, 0, -840, 0, 0, 0, 8208, 0, -9846, 0, 0, 0, 2530, 0, -7496, 0, 0, 0, 7968, 0, 5842, 0, 0, 0, 31992, 0, -824, 0, 0, 0, 2568, 0, -4800, 0, 0, 0, 13086, 0, -864, 0, 0, 0, -2720, 0, 20908, 0, 0, 0, -10830, 0, -15136, 0, 0, 0, -15240, 0, 8566, 0, 0, 0, -8064, 0, 9480, 0, 0, 0, 13884, 0, -4286, 0, 0, 0, 450, 0, -928, 0, 0, 0, -12672, 0, -17948, 0, 0, 0, 2112, 0, 2968, 0, 0, 0, -12372, 0, 5070, 0, 0, 0, -22788, 0, -22320, 0, 0, 0, -6880, 0, 358, 0, 0, 0, -7530, 0, 13768, 0, 0, 0, -26760, 0, 33152, 0, 0, 0, 6000, 0, -1100, 0, 0, 0, -6336, 0, -21844, 0, 0, 0, 7660, 0, -10016, 0, 0, 0, 12900, 0, 3348, 0, 0, 0, -2688, 0, 8116, 0, 0, 0, 9888, 0, -13140, 0, 0, 0, -5466, 0, 8096, 0, 0, 0, -2240, 0, 10080, 0, 0, 0, -20148, 0, -27656, 0, 0, 0, 3168, 0, 9863, 0, 0, 0, 15996, 0, -7740, 0, 0, 0, -10440, 0, -30452, 0, 0, 0, 1390, 0, 13228, 0, 0, 0, -8184, 0, 4352, 0, 0, 0, 16980, 0, -17200, 0, 0, 0, -10284, 0, 2790, 0, 0, 0, 1770, 0, -6068, 0, 0, 0, -2400, 0, 43012, 0, 0, 0, -15168, 0, -29880, 0, 0, 0, 12108, 0, -7744, 0, 0, 0, -30948, 0, -2880, 0, 0, 0, -2520, 0, 12790, 0, 0, 0, 11345, 0, -11576, 0, 0, 0, -28896, 0, 40252, 0, 0, 0, -27942, 0, 22540, 0, 0, 0, 16224, 0, -625, 0, 0, 0, -9144, 0, -10256, 0, 0, 0, 1720, 0, 7482, 0, 0, 0, -12798, 0, 21148, 0, 0, 0, -32928, 0, 30240, 0, 0, 0, -24234, 0, -3900, 0, 0, 0, -22836, 0, -26318, 0, 0, 0, 7040, 0, -17856, 0, 0, 0, 3480, 0, -28802, 0, 0, 0, 2526, 0, -12256, 0, 0, 0, 46152, 0, 6660, 0, 0, 0, -42828, 0, -7868, 0, 0, 0, 4420, 0, -3348, 0, 0, 0, -43020, 0, 22352, 0, 0, 0, 21024, 0, -30014, 0, 0, 0, 8448, 0, 25800, 0, 0, 0, 1632, 0, 14336, 0, 0, 0, -4650, 0, 9952, 0, 0, 0, -1800, 0, 33946, 0, 0, 0, -124320, 0, 46840, 0, 0, 0, -14592, 0, 570, 0, 0, 0, -24768, 0, -9056, 0, 0, 0, 400, 0, -35108, 0, 0, 0, -36438, 0, 4448, 0, 0, 0, -21672, 0, 9022, 0, 0, 0, -2940, 0, 8800, 0, 0, 0, 8184, 0, 10080, 0, 0, 0, -770, 0, -5252, 0, 0, 0, -17856, 0, -9976, 0, 0, 0, 12294, 0, -3024, 0, 0, 0, -30360, 0, 3840, 0, 0, 0, -31092, 0, 38728, 0, 0, 0, 10900, 0, 4400, 0, 0, 0, -7314, 0, -11984, 0, 0, 0, -27000, 0, -89204, 0, 0, 0, -1566, 0, -18480, 0, 0, 0, 35448, 0, -10207, 0, 0, 0, -51990, 0, -72608, 0, 0, 0, 12192, 0, -12590, 0, 0, 0, 24906, 0, -23204, 0, 0, 0, -39696, 0, 13020, 0, 0, 0, -16320, 0, 89096, 0, 0, 0, -2000, 0, -27542, 0, 0, 0, 41436, 0, 50344, 0, 0, 0, -12864, 0, 5504, 0, 0, 0, 7392, 0, 21540, 0, 0, 0, 65472, 0, -17928, 0, 0, 0, 7750, 0, 23092, 0, 0, 0, -14208, 0, 56880, 0, 0, 0, 24960, 0, -53168, 0, 0, 0, 14448, 0, -6350, 0, 0, 0, 162, 0, 3828, 0, 0, 0, 10800, 0, -59468, 0, 0, 0, 17142, 0, -8928, 0, 0, 0, 26436, 0, -43516, 0, 0, 0, -55764, 0, 480, 0, 0, 0, -10656, 0, -1185, 0, 0, 0, 5290, 0, -12656, 0, 0, 0, -5832, 0, -28288, 0, 0, 0, -6894, 0, -60840, 0, 0, 0, -45264, 0, 18570, 0, 0, 0, 9600, 0, 104032, 0, 0, 0, -8840, 0, 13858, 0, 0, 0, 82560, 0, 4536, 0, 0, 0, 43824, 0, 8740, 0, 0, 0, -36786, 0, -14880, 0, 0, 0, -57756, 0, -6374, 0, 0, 0, -9300, 0, 46784, 0, 0, 0, -22008, 0, -40826, 0, 0, 0, -1044, 0, 37264, 0, 0, 0, -3648, 0, -26400, 0, 0, 0, 26058, 0, -12308, 0, 0, 0, -20180, 0, -640, 0, 0, 0, 54852, 0, -8000, 0, 0, 0, 45960, 0, 41194, 0, 0, 0, -47244, 0, 2500, 0, 0, 0, -163056, 0, 16128, 0, 0, 0, -14080, 0, -69176, 0, 0, 0, -24372, 0, 34306, 0, 0, 0, 85260, 0, 4928, 0, 0, 0, 50904, 0, -7740, 0, 0, 0, 67950, 0, -78840, 0, 0, 0, -6800, 0, 94156, 0, 0, 0, -11088, 0, -32132, 0, 0, 0, -4176, 0, 11782, 0, 0, 0, -53760, 0, 23880, 0, 0, 0, -18648, 0, 34880, 0, 0, 0, -19370, 0, -44704, 0, 0, 0, 40416, 0, 142468, 0, 0, 0, -87204, 0, 2552, 0, 0, 0, 22812, 0, -15810, 0, 0, 0, 118272, 0, -140360, 0, 0, 0, 4200, 0, 92880, 0, 0, 0, 12390, 0, 83184, 0, 0, 0, 119064, 0, -69192, 0, 0, 0, 39642, 0, -27120, 0, 0, 0, -16680, 0, -47954, 0, 0, 0, 38860, 0, 6048, 0, 0, 0, -20832, 0, -51878, 0, 0, 0, -3390, 0, 23904, 0, 0, 0, -50880, 0, -4350, 0, 0, 0, 55254, 0, 59488, 0, 0, 0, 18920, 0, -6446, 0, 0, 0, -18216, 0, 66960, 0, 0, 0, 18600, 0, -3746, 0, 0, 0, 68928, 0, 25500, 0, 0, 0, 92760, 0, -131752, 0, 0, 0, -14400, 0, 24800, 0, 0, 0, 32736, 0, 45584, 0, 0, 0, -81036, 0, 19456, 0, 0, 0, 43620, 0, -10890, 0, 0, 0, 60186, 0, -76196, 0, 0, 0, 40640, 0, 47524, 0, 0, 0, 82062, 0, 60688, 0, 0, 0, -51972, 0, -17280, 0, 0, 0, 226008, 0, -61440, 0, 0, 0, 67608, 0, 51910, 0, 0, 0, -12450, 0, -14120, 0, 0, 0, 112560, 0, -35200, 0, 0, 0, -768, 0, 38528, 0, 0, 0, 4896, 0, -4110, 0, 0, 0, -14784, 0, -33856, 0, 0, 0, 42400, 0, 12096, 0, 0, 0, 2418, 0, 31248, 0, 0, 0, 187008, 0, 27726, 0, 0, 0, -68346, 0, 7500, 0, 0, 0, 59424, 0, -77246, 0, 0, 0, 11380, 0, 44528, 0, 0, 0, 133128, 0, -28288, 0, 0, 0, -20640, 0, 78712, 0, 0, 0, 5568, 0, 57060, 0, 0, 0, 20802, 0, -17064, 0, 0, 0, -15140, 0, -23908, 0, 0, 0, -32364, 0, -144464, 0, 0, 0, 27972, 0, 27058, 0, 0, 0, 16170, 0, 14880, 0, 0, 0, -129600, 0, -93600, 0, 0, 0, -22945, 0, -19856, 0, 0, 0, -79164, 0, 66058, 0, 0, 0, -59136, 0, 113944, 0, 0, 0, 42240, 0, -16950, 0, 0, 0, -47988, 0, 2512, 0, 0, 0, 12600, 0, 129152, 0, 0, 0, -74406, 0, -85916, 0, 0, 0, -94200, 0, -14258, 0, 0, 0, 154788, 0, 41280, 0, 0, 0, 46020, 0, -11968, 0, 0, 0, 8000, 0, 39960, 0, 0, 0, 41520, 0, -36504, 0, 0, 0, 47244, 0, 15312, 0, 0, 0, 65172, 0, 1450, 0, 0, 0, 106080, 0, -54488, 0, 0, 0, -20780, 0, -92628, 0, 0, 0, -49728, 0, 55840, 0, 0, 0, 49536, 0, 31660, 0, 0, 0, 86130, 0, -32760, 0, 0, 0, -57144, 0, 10880, 0, 0, 0, 13660, 0, -223760, 0, 0, 0, -33972, 0, -195134, 0, 0, 0, 41712, 0, -105044, 0, 0, 0, 19152, 0, 25980, 0, 0, 0, -38208, 0, 25400, 0, 0, 0, 55800, 0, 18970, 0, 0, 0, -117636, 0, 123968, 0, 0, 0, 35088, 0, -23066, 0, 0, 0, 27702, 0, -3960, 0, 0, 0, 74664, 0, 242524, 0, 0, 0, 10750, 0, 105892, 0, 0, 0, -50592, 0, -8064, 0, 0, 0, -1788, 0, 13680, 0, 0, 0, -87648, 0, 13440, 0, 0, 0, -13788, 0, -29584, 0, 0, 0, 32920, 0, -7340, 0, 0, 0, 2400, 0, -30824, 0, 0, 0, 104244, 0, -96446, 0, 0, 0, 173568, 0, -51800, 0, 0, 0, 24288, 0, 34325, 0, 0, 0, 30970, 0, -62176, 0, 0, 0, 89232, 0, -84020, 0, 0, 0, -73086, 0, 78244, 0, 0, 0, 67080, 0, 52800, 0, 0, 0, 111252, 0, 93744, 0, 0, 0, 34400, 0, 23652, 0, 0, 0, 89322, 0, 14164, 0, 0, 0, -18480, 0, -121088, 0, 0, 0, -74274, 0, 50100, 0, 0, 0, 42672, 0, 102058, 0, 0, 0, 31300, 0, -8312, 0, 0, 0, -8064, 0, 62422, 0, 0, 0, 81600, 0, -15776, 0, 0, 0, 37200, 0, 41940, 0, 0, 0, 10788, 0, -46080, 0, 0, 0, 4200, 0, -123026, 0, 0, 0, -114552, 0, -63008, 0, 0, 0, 68316, 0, 51610, 0, 0, 0, -130800, 0, 20520, 0, 0, 0, 69696, 0, -47564, 0, 0, 0, -24615, 0, -76024, 0, 0, 0, 60732, 0, 22098, 0, 0, 0, -26112, 0, 55728, 0, 0, 0, 99144, 0, -12650, 0, 0, 0, -44352, 0, -91496, 0, 0, 0, -74960, 0, -443520, 0, 0, 0, 98304, 0, 33704, 0, 0, 0, -14976, 0, 69507, 0, 0, 0, -10008, 0, 79680, 0, 0, 0, -311940, 0, 109378, 0, 0, 0, -29210, 0, 30772, 0, 0, 0, -167808, 0, 23716, 0, 0, 0, 131310, 0, 81880, 0, 0, 0, -13152, 0, 79980, 0, 0, 0, -209604, 0, -20416, 0, 0, 0, -2060, 0, 135680, 0, 0, 0, -79722, 0, 78120, 0, 0, 0, -151368, 0, 91008, 0, 0, 0, 29514, 0, -12840, 0, 0, 0, -57816, 0, 10044, 0, 0, 0, -48000, 0, 62496, 0, 0, 0, -63612, 0, -104438, 0, 0, 0, -9804, 0, -18208, 0, 0, 0, -385392, 0, 130860, 0, 0, 0, 68262, 0, 60112, 0, 0, 0, 4320, 0, 19712, 0, 0, 0, 252984, 0, -6880, 0, 0, 0, -91296, 0, -258480, 0, 0, 0, -1554, 0, -6800, 0, 0, 0, 164280, 0, 96896, 0, 0, 0, 52270, 0, -33428, 0, 0, 0, -93000, 0, -139610, 0, 0, 0, -329964, 0, 66976, 0], "weight": 4, "weight_parity": 1, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [0, 0], [0, 0], [0, 0], [0, 5], [0, 0], [16, -16], [0, 0], [0, 0], [0, 0], [-60, 60], [0, 0], [0, -86], [0, 0], [0, 0], [0, 0], [-18, 0], [0, 0], [44, 0], [0, 0], [0, 0], [0, 0], [0, 48], [0, 0], [-25, 25], [0, 0], [0, 0], [0, 0], [-186, 186], [0, 0], [0, -176], [0, 0], [0, 0], [0, 0], [80, 0], [0, 0], [254, 0], [0, 0], [0, 0], [0, 0], [0, 186], [0, 0], [100, -100], [0, 0], [0, 0], [0, 0], [168, -168], [0, 0], [0, 87], [0, 0], [0, 0], [0, 0], [498, 0], [0, 0], [-300, 0], [0, 0], [0, 0], [0, 0], [0, -252], [0, 0], [58, -58], [0, 0], [0, 0], [0, 0], [430, -430], [0, 0], [0, 1036], [0, 0], [0, 0], [0, 0], [-168, 0], [0, 0], [506, 0], [0, 0], [0, 0], [0, 0], [0, 960], [0, 0], [-272, 272], [0, 0], [0, 0], [0, 0], [948, -948], [0, 0], [0, -90], [0, 0], [0, 0], [0, 0], [1014, 0], [0, 0], [-1376, 0], [0, 0], [0, 0], [0, 0], [0, 220], [0, 0], [766, -766], [0, 0], [0, 0], [0, 0]]}