# Stored data for newform 350.8.c.i, downloaded from the LMFDB on 11 June 2024.
{"Nk2": 22400, "analytic_conductor": 109.33475891944262, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 5, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 3, "char_orbit_label": "c", "char_order": 2, "char_parity": 1, "char_values": [350, 2, [127, 101], [1, 2]], "cm_discs": [], "conrey_index": 99, "dim": 4, "field_disc": 1228081936, "field_disc_factorization": [[2, 4], [8761, 2]], "field_poly": [4796100, 0, 4381, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[3, [4769856, 0, 4393, 0, 1]]], "hecke_orbit": 9, "hecke_orbit_code": 36028934592135518, "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, 5, 2, 1, 2, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": false, "label": "350.8.c.i", "level": 350, "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, 5, 7], "level_radical": 70, "minimal_twist": "70.8.a.g", "nf_label": "4.0.1228081936.2", "prim_orbit_index": 2, "qexp_display": "q-8\\beta _{2}q^{2}+(\\beta _{1}-2\\beta _{2})q^{3}-2^{6}q^{4}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "7.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "350.8.c", "trace_display": [0, 0, 0, 0], "trace_hash": 576450595471366715, "trace_moments": [{"__RealLiteral__": 0, "data": "0.061", "prec": 17}, {"__RealLiteral__": 0, "data": "3.889", "prec": 17}, {"__RealLiteral__": 0, "data": "0.709", "prec": 17}, {"__RealLiteral__": 0, "data": "76.592", "prec": 20}, {"__RealLiteral__": 0, "data": "20.980", "prec": 20}, {"__RealLiteral__": 0, "data": "2059.278", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.508", "prec": 17}, "traces": [0, 4, 0, 0, -256, 0, -80, 0, 0, -38, 0, 9030, 0, 0, -10976, 0, 16384, 0, 0, -87404, 0, -3430, 0, 0, 5120, 0, 143152, 0, 0, -18522, 0, 414056, 0, 0, -600528, 0, 2432, 0, 0, 491546, 0, 529596, 0, 0, -577920, 0, 650208, 0, 0, -470596, 0, 469410, 0, 0, 176240, 0, 702464, 0, 0, -3810816, 0, -238636, 0, 0, -1048576, 0, 8860752, 0, 0, 13712652, 0, -1225344, 0, 0, 2289152, 0, 5593856, 0, 0, 25241518, 0, -18995596, 0, 0, 219520, 0, -8402336, 0, 0, 22356660, 0, 6137642, 0, 0, 8121744, 0, -327680, 0, 0, 5565060, 0, 26712624, 0, 0, -9161728, 0, 10819104, 0, 0, 31243978, 0, 70628140, 0, 0, 486496, 0, 1185408, 0, 0, -25747638, 0, 88228342, 0, 0, -26499584, 0, 104272, 0, 0, -2993692, 0, 104279964, 0, 0, 69158912, 0, 38433792, 0, 0, -161136644, 0, -2744838, 0, 0, -155648, 0, -50194112, 0, 0, -173686176, 0, 75058370, 0, 0, -24778320, 0, -31458944, 0, 0, -10654152, 0, 27877668, 0, 0, -33894144, 0, -33585600, 0, 0, 148157898, 0, 41848, 0, 0, 111179568, 0, 36986880, 0, 0, 92655936, 0, 202407068, 0, 0, -41613312, 0, -81452992, 0, 0, 7556290, 0, 426196542, 0, 0, -182256784, 0, 30118144, 0, 0, -237657152, 0, 401138680, 0, 0, -30042240, 0, -37508432, 0, 0, -217657572, 0, -252035302, 0, 0, -223640928, 0, -11279360, 0, 0, -314681068, 0, 302296926, 0, 0, -44957696, 0, -121981440, 0, 0, -174227228, 0, 379904742, 0, 0, -19232384, 0, 243892224, 0, 0, 779275446, 0, -545619856, 0, 0, 15272704, 0, -388646592, 0, 0, 288815304, 0, 1330693884, 0, 0, -968129920, 0, 67108864, 0, 0, 98147392, 0, 69431664, 0, 0, -567088128, 0, 239836576, 0, 0, 521126808, 0, 1124726768, 0, 0, 454535328, 0, -877609728, 0, 0, -49665952, 0, 505245738, 0, 0, 78422016, 0, -137943312, 0, 0, 183347978, 0, 720311914, 0, 0, 9411920, 0, -146505728, 0, 0, -1052570748, 0, -360250156, 0, 0, -358006784, 0, -20577984, 0, 0, 3301750142, 0, -961892292, 0, 0, 343085696, 0, -1615457152, 0, 0, 1744983774, 0, -1707055860, 0, 0, 1215718144, 0, -1772754272, 0, 0, 348219774, 0, 2201888144, 0, 0, -743864880, 0, -14049280, 0, 0, 943498284, 0, -245165016, 0, 0, 537749504, 0, -1704423984, 0, 0, 1752821896, 0, 868794610, 0, 0, 62759424, 0, -1430826240, 0, 0, -2955843072, 0, -1662783588, 0, 0, -392809088, 0, -3684519424, 0, 0, -241315332, 0, 463869084, 0, 0, -2033793360, 0, -519791616, 0, 0, -21328016, 0, 609374368, 0, 0, 20971520, 0, -2622695072, 0, 0, 1087159842, 0, 512056404, 0, 0, 3877779744, 0, -356163840, 0, 0, 20858516, 0, 2776702950, 0, 0, -1709607936, 0, 50824368, 0, 0, -281864960, 0, 2198476776, 0, 0, -546555456, 0, 586350592, 0, 0, -2757794136, 0, 3352645334, 0, 0, -692422656, 0, -8076544512, 0, 0, -4090242474, 0, -4861579338, 0, 0, -1136169664, 0, -1999614592, 0, 0, 5487294532, 0, 4470662, 0, 0, -4520200960, 0, -26843984, 0, 0, -5065412370, 0, -4900568616, 0, 0, 447119760, 0, -31135744, 0, 0, 1835993370, 0, -3534627660, 0, 0, -75866112, 0, -239493600, 0, 0, 2965188352, 0, -717335996, 0, 0, 1447891408, 0, 1647848832, 0, 0, -1213382844, 0, -4845616964, 0, 0, -5646613888, 0, 1525102720, 0, 0, 7997819132, 0, 8090132610, 0, 0, -3063673568, 0, 1695973376, 0, 0, 2677670194, 0, -13639652622, 0, 0, -6673408, 0, -12473920224, 0, 0, 8013614424, 0, -2152072552, 0, 0, -4160371584, 0, 191596288, 0, 0, -11631023490, 0, -2280451488, 0, 0, -6673917696, 0, 10415158560, 0, 0, -8863735660, 0, 27792192, 0, 0, 2906577600, 0, -4426170368, 0, 0, -1062370470, 0, 19888002170, 0, 0, -2459762688, 0, -1348802224, 0, 0, -2303540548, 0, 155403684, 0, 0, 10100918720, 0, 10312745216, 0, 0, 4717247324, 0, 22057102926, 0, 0, 175669632, 0, -15190350704, 0, 0, -11625600024, 0, 8486781536, 0, 0, -1453211424, 0, 9961472, 0, 0, 16132259432, 0, -1439982600, 0, 0, 3212423168, 0, 14146755216, 0, 0, -8882900944, 0, 2697163632, 0, 0, 19972388880, 0, 11115915264, 0, 0, 13363545258, 0, 5020073600, 0, 0, -4803735680, 0, 17818430496, 0, 0, 4766823978, 0, -4272150690, 0, 0, 3008725232, 0, 1585812480, 0, 0, 18593512084, 0, 28800357660, 0, 0, 2013372416, 0, -322178192, 0, 0, 126462876, 0, 27681228278, 0, 0, -18781343808, 0, 681865728, 0, 0, -5051516352, 0, 5244637704, 0, 0, -1784170752, 0, 13216756128, 0, 0, -8819909568, 0, -3492297032, 0, 0, 10295601808, 0, 2169225216, 0, 0, 13233594018, 0, -13985271676, 0, 0, 2149478400, 0, -2818258144, 0, 0, -36890665570, 0, -60028556592, 0, 0, 43557624320, 0, -9482105472, 0, 0, -7814259614, 0, 21327791658, 0, 0, -2678272, 0, 1291315424, 0, 0, -5334116496, 0, 37504976936, 0, 0, 2552388384, 0, -7115492352, 0, 0, 3386576784, 0, -10494204606, 0, 0, -2367160320, 0, 21774835728, 0, 0, 4292381734, 0, 980656684, 0, 0, -1288061040, 0, -5929979904, 0, 0, 23835447780, 0, -1608174022, 0, 0, -12954052352, 0, 39057137440, 0, 0, -40706311268, 0, -19682707668, 0, 0, 19833283472, 0, 2663251968, 0, 0, 11092328650, 0, -10015203148, 0, 0, 5212991488, 0, -11694980960, 0, 0, -9588604788, 0, -24952013038, 0, 0, -6314130864, 0, -483602560, 0, 0, 3635606484, 0, 23521679856, 0, 0, -27276578688, 0, 22538881728, 0, 0, -32867946224, 0, 21818095284, 0, 0, 94540672, 0, 11664434176, 0, 0, -10721579184, 0, -133395667776, 0, 0, -1927561216, 0, 30600780576, 0, 0, 630589764, 0, -5229954240, 0, 0, 27588526640, 0, 15210057728, 0, 0, 19448304822, 0, 1883680980, 0, 0, -25672875520, 0, 18550001600, 0, 0, -39200560038, 0, 9412743692, 0, 0, -66982228320, 0, 1922703360, 0, 0, -824588464, 0, -55307166498, 0, 0, 2400539648, 0, 10456879104, 0, 0, -7219906268, 0, 19609064308, 0, 0, 19744016416, 0, 13930084608, 0, 0, -61166403972, 0, -47015085194, 0, 0, 16130259328, 0, 134158752, 0, 0, -44529590470, 0, -113619666696, 0, 0, 654817184, 0, 14313019392, 0, 0, -33829225112, 0, -16663222632, 0, 0, 721879040, 0, 56805421120, 0, 0, 88470365394, 0, -58028651624, 0, 0, -12262332480, 0, 20139588352, 0, 0, 73273779030, 0, 9347957892, 0, 0, -19347003264, 0, -18370995360, 0, 0, -41508570320, 0, -30631526010, 0, 0, 36728236704, 0, 2877292544, 0, 0, -16377877512, 0, 26432223552, 0, 0, 7806812160, 0, -70242146128, 0, 0, 11216656932, 0, -37752768624, 0, 0, 50684781920, 0, 11150542592, 0, 0, -557220218, 0, -68430466490, 0, 0, -24313903488, 0, -43014237056, 0, 0, -20026740636, 0, 10282993196, 0, 0, 114507809328, 0, 1230872576, 0, 0, 51545125202, 0, -166353215388, 0, 0, -15609102336, 0, -18588536736, 0, 0, 43316685812, 0, 37378980900, 0, 0, 458623392, 0, -49873628544, 0, 0, 19488202188, 0, -57640934364, 0, 0, 34919670784, 0, -37627517088, 0, 0, -13186949052, 0, 157488233232, 0, 0, 58536472928, 0, -977453056, 0, 0, 104548746600, 0, 6528483064, 0, 0, 24873381888, 0, -5529939696, 0, 0, 21908280552, 0, 37630341344, 0, 0, 3362343936, 0, -18484179456, 0, 0, 149785230620, 0], "weight": 8, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, 0, -8, 0], [0, 1, -2, 0], [-64, 0, 0, 0], [0, 0, 0, 0], [-24, 0, 0, 8], [0, 0, -343, 0], [0, 0, 512, 0], [-12, 0, 0, 5], [0, 0, 0, 0], [2193, 0, 0, 129], [0, -64, 128, 0], [0, -51, 4448, 0], [-2744, 0, 0, 0], [0, 0, 0, 0], [4096, 0, 0, 0], [0, -75, -18804, 0], [0, -40, 56, 0], [-21842, 0, 0, -18], [0, 0, 0, 0], [-1029, 0, 0, 343], [0, -1032, -18576, 0], [0, -1542, 19548, 0], [1536, 0, 0, -512], [0, 0, 0, 0], [35992, 0, 0, -408], [0, 2165, 6590, 0], [0, 0, 21952, 0], [-5421, 0, 0, 1581], [0, 0, 0, 0], [104036, 0, 0, -1044], [0, 0, -32768, 0], [0, 1935, 277866, 0], [-149832, 0, 0, -600], [0, 0, 0, 0], [768, 0, 0, -320], [0, -7980, 67546, 0], [0, 144, 174880, 0], [125187, 0, 0, -4601], [0, 0, 0, 0], [135096, 0, 0, -5394], [0, -2744, 5488, 0], [0, 42, -262552, 0], [-140352, 0, 0, -8256], [0, 0, 0, 0], [168720, 0, 0, -12336], [0, 603, 254106, 0], [0, 4096, -8192, 0], [-117649, 0, 0, 0], [0, 0, 0, 0], [108063, 0, 0, 18579], [0, 3264, -284672, 0], [0, 1602, 338898, 0], [35400, 0, 0, 17320], [0, 0, 0, 0], [175616, 0, 0, 0], [0, -21806, 4300, 0], [0, -12648, 30720, 0], [-952608, 0, 0, -192], [0, 0, 0, 0], [-33340, 0, 0, -52638], [0, 8352, -823936, 0], [0, -1715, 2401, 0], [-262144, 0, 0, 0], [0, 0, 0, 0], [2207448, 0, 0, 15480], [0, -43320, 2139556, 0], [0, 4800, 1203456, 0], [3440250, 0, 0, -24174], [0, 0, 0, 0], [-248544, 0, 0, -115584], [0, 2560, -3584, 0], [0, 34128, -1551502, 0], [604208, 0, 0, -63840], [0, 0, 0, 0], [1397888, 0, 0, 1152], [0, -44247, -796446, 0], [0, 36808, -964688, 0], [6296449, 0, 0, 27861], [0, 0, 0, 0], [-4754319, 0, 0, 10840], [0, 43152, -1037616, 0], [0, -34164, -1066632, 0], [65856, 0, 0, -21952], [0, 0, 0, 0], [-2100752, 0, 0, 336], [0, -8583, 3470070, 0], [0, 66048, 1188864, 0], [5565240, 0, 0, 47850], [0, 0, 0, 0], [1543157, 0, 0, -17493], [0, 98688, -1251072, 0], [0, 106124, -2492344, 0], [2028024, 0, 0, 4824], [0, 0, 0, 0], [-98304, 0, 0, 32768], [0, -88719, -5739884, 0], [0, 0, 941192, 0], [1386234, 0, 0, 10062], [0, 0, 0, 0]]}