# Stored data for newform 350.6.c.h, downloaded from the LMFDB on 07 December 2024.
{"Nk2": 12600, "analytic_conductor": 56.13433693454322, "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": 2, "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 4, "has_non_self_twist": 1, "hecke_cutters": [[3, [529, 0, 1]], [11, [-555, 1]]], "hecke_orbit": 8, "hecke_orbit_code": 31525334931210590, "hecke_ring_generator_nbound": 3, "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": "350.6.c.h", "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": "70.6.a.a", "nf_label": "2.0.4.1", "prim_orbit_index": 2, "qexp_display": "q-4 i q^{2}+23 i q^{3}-16 q^{4}+92 q^{6}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "5.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "350.6.c", "trace_display": [0, 0, 0, 0], "trace_hash": 1018013294508804776, "trace_moments": [{"__RealLiteral__": 0, "data": "0.013", "prec": 17}, {"__RealLiteral__": 0, "data": "1.981", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "15.800", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "156.418", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.508", "prec": 17}, "traces": [0, 2, 0, 0, -32, 0, 184, 0, 0, -572, 0, 1110, 0, 0, 392, 0, 512, 0, 0, 4076, 0, -2254, 0, 0, -2944, 0, 1928, 0, 0, 10002, 0, 11392, 0, 0, -11928, 0, 9152, 0, 0, -11086, 0, -4848, 0, 0, -17760, 0, 9840, 0, 0, -4802, 0, 68586, 0, 0, -7912, 0, -6272, 0, 0, -11448, 0, -72224, 0, 0, -8192, 0, 102120, 0, 0, -56580, 0, 32160, 0, 0, -44816, 0, -65216, 0, 0, 128294, 0, -93502, 0, 0, 36064, 0, -4816, 0, 0, 143352, 0, -23618, 0, 0, -185304, 0, 47104, 0, 0, -317460, 0, -114300, 0, 0, -30848, 0, 202368, 0, 0, -176794, 0, 257692, 0, 0, 374992, 0, -160032, 0, 0, 146118, 0, 293948, 0, 0, -182272, 0, -112112, 0, 0, 27692, 0, -104244, 0, 0, 528832, 0, 190848, 0, 0, 698972, 0, 1065498, 0, 0, -146432, 0, 643856, 0, 0, -352164, 0, 766666, 0, 0, 217560, 0, 177376, 0, 0, -1163616, 0, -120540, 0, 0, 77568, 0, 850272, 0, 0, 626424, 0, -1165736, 0, 0, 920184, 0, 284160, 0, 0, -332376, 0, -394640, 0, 0, -157440, 0, 1048064, 0, 0, 96922, 0, -674442, 0, 0, 1208200, 0, 76832, 0, 0, -601960, 0, -3040784, 0, 0, -1097376, 0, -927112, 0, 0, 2262180, 0, -2452358, 0, 0, -1102896, 0, 126592, 0, 0, -3702172, 0, 718662, 0, 0, 100352, 0, -1644432, 0, 0, 248528, 0, -1250970, 0, 0, -551408, 0, 183168, 0, 0, 1091262, 0, 1622620, 0, 0, 1155584, 0, -446016, 0, 0, -4889064, 0, -1795476, 0, 0, 2007328, 0, 131072, 0, 0, 548996, 0, -2860572, 0, 0, -1633920, 0, 798896, 0, 0, 2487804, 0, 1475248, 0, 0, -1083744, 0, 905280, 0, 0, -3258112, 0, 347958, 0, 0, -514560, 0, 1070040, 0, 0, -1606448, 0, -6947150, 0, 0, -441784, 0, 717056, 0, 0, -592860, 0, 58996, 0, 0, 1043456, 0, 3411408, 0, 0, 5330894, 0, 1412532, 0, 0, 2767312, 0, -2052704, 0, 0, 5551110, 0, 6341652, 0, 0, 1496032, 0, -732688, 0, 0, 2269974, 0, -4286744, 0, 0, 304776, 0, -577024, 0, 0, 9455484, 0, 6322560, 0, 0, 77056, 0, 4331544, 0, 0, -6034204, 0, 476698, 0, 0, -1053216, 0, -2293632, 0, 0, 3679008, 0, 3354690, 0, 0, 377888, 0, -6644608, 0, 0, 1386528, 0, -2479008, 0, 0, -6620040, 0, 2964864, 0, 0, 9534152, 0, -11542136, 0, 0, -753664, 0, -2084128, 0, 0, -7977906, 0, 3667860, 0, 0, -3273696, 0, 5079360, 0, 0, -4593652, 0, 8615874, 0, 0, 1828800, 0, 1960392, 0, 0, 478412, 0, 6231528, 0, 0, -2814240, 0, 493568, 0, 0, -9269232, 0, -4202150, 0, 0, -3237888, 0, 2958720, 0, 0, -6152730, 0, 3309678, 0, 0, 2232832, 0, 2828704, 0, 0, -11673676, 0, 1373372, 0, 0, -4123072, 0, -4970056, 0, 0, 6851394, 0, -2690640, 0, 0, 10381416, 0, -5999872, 0, 0, -2949198, 0, 17754624, 0, 0, 2560512, 0, -8699328, 0, 0, -6478192, 0, -15912044, 0, 0, 11803048, 0, -2337888, 0, 0, -3769788, 0, 2700164, 0, 0, -4703168, 0, -10524800, 0, 0, 4212956, 0, 19080306, 0, 0, 3929264, 0, 2916352, 0, 0, -9564862, 0, -1752462, 0, 0, 1793792, 0, 5461200, 0, 0, 15283548, 0, -7887236, 0, 0, -4757424, 0, -443072, 0, 0, -24906378, 0, 12880212, 0, 0, 1667904, 0, -8226960, 0, 0, 9846886, 0, 3274128, 0, 0, 13188384, 0, -8461312, 0, 0, -2665110, 0, -4113554, 0, 0, -3053568, 0, -2172856, 0, 0, 20656064, 0, 20384076, 0, 0, -17605040, 0, -11183552, 0, 0, 290164, 0, 38065230, 0, 0, -17047968, 0, 4408424, 0, 0, 15000588, 0, -4457576, 0, 0, -950208, 0, 2342912, 0, 0, 11983736, 0, -10415832, 0, 0, -10301696, 0, 13400952, 0, 0, 23216896, 0, 18823752, 0, 0, -4391160, 0, 5634624, 0, 0, 25722978, 0, 3163252, 0, 0, -12266656, 0, -10515600, 0, 0, -11272254, 0, 11164566, 0, 0, 18644824, 0, -3480960, 0, 0, -26353852, 0, 2432940, 0, 0, -2838016, 0, 1468520, 0, 0, -16705164, 0, 2525278, 0, 0, 21653232, 0, 18617856, 0, 0, -9197760, 0, -31771836, 0, 0, 1928640, 0, -24309264, 0, 0, -6353640, 0, -12838784, 0, 0, -16265048, 0, -1241088, 0, 0, 2659218, 0, -14743760, 0, 0, -13604352, 0, 12817376, 0, 0, 28577822, 0, -40084320, 0, 0, 5242768, 0, -10022784, 0, 0, -14800450, 0, -59693142, 0, 0, 18651776, 0, -941192, 0, 0, -12192672, 0, -1109912, 0, 0, -33781968, 0, -14722944, 0, 0, 50021136, 0, -15494394, 0, 0, -4546560, 0, -18020616, 0, 0, 37811042, 0, -36692084, 0, 0, 13442856, 0, 5318016, 0, 0, 36785556, 0, 11357122, 0, 0, 6314240, 0, 27043216, 0, 0, 37796614, 0, -1795164, 0, 0, -13506584, 0, 2519040, 0, 0, -52864678, 0, -22593268, 0, 0, -16769024, 0, -14496928, 0, 0, 13510476, 0, -7907750, 0, 0, 9641928, 0, -1550752, 0, 0, -31401900, 0, 22865724, 0, 0, 10791072, 0, 559968, 0, 0, -47415268, 0, 27355188, 0, 0, 1377376, 0, -19331200, 0, 0, -9880224, 0, 17848800, 0, 0, -1229312, 0, -9590448, 0, 0, 47305020, 0, 20144292, 0, 0, -24472280, 0, 9631360, 0, 0, -69072066, 0, -40998672, 0, 0, 48652544, 0, 10981888, 0, 0, -1079442, 0, 27954364, 0, 0, -24872880, 0, 17558016, 0, 0, 6754748, 0, -35627358, 0, 0, 14833792, 0, -2243808, 0, 0, -17136832, 0, 101228980, 0, 0, 64305424, 0, -36194880, 0, 0, -71350164, 0, 8997704, 0, 0, 39237728, 0, 52996944, 0, 0, -25348438, 0, 13780920, 0, 0, -14155904, 0, 17646336, 0, 0, -52794808, 0, 5463696, 0, 0, -2025472, 0, 14722448, 0, 0, 71203170, 0, -31862128, 0, 0, 20053920, 0, 59234752, 0, 0, -77055474, 0, 39485472, 0, 0, -11498592, 0, -9576336, 0, 0, -24589768, 0, -51893610, 0, 0, -32399088, 0, -1605632, 0, 0, 56971392, 0, 75432672, 0, 0, 26310912, 0, 70533272, 0, 0, 32689800, 0, 22538496, 0, 0, 42379360, 0, -3976448, 0, 0, -63675682, 0, -107207738, 0, 0, 20015520, 0, 17398016, 0, 0, -37711632, 0, -9786476, 0, 0, -3031752, 0, 8822528, 0, 0, -8443990, 0, -58388208, 0, 0, -2930688, 0, -2672880, 0, 0, -38792324, 0, -124506084, 0, 0, -57877248, 0, -17460192, 0, 0, 13275864, 0, 7630530, 0, 0, -25961920, 0, -11089680, 0, 0, 139778268, 0, -36292872, 0, 0, 29415088, 0, -18489344, 0, 0, 79560360, 0, 50563084, 0, 0, 7136256, 0, -59651928, 0, 0, 1480920, 0, 80311168, 0, 0, 6303360, 0, 78225024, 0, 0, -11080756, 0], "weight": 6, "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], [1, 0], [0, -4], [0, 23], [-16, 0], [0, 0], [92, 0], [0, 49], [0, 64], [-286, 0], [0, 0], [555, 0], [0, -368], [0, 241], [196, 0], [0, 0], [256, 0], [0, -1491], [0, 1144], [2038, 0], [0, 0], [-1127, 0], [0, -2220], [0, 1230], [-1472, 0], [0, 0], [964, 0], [0, -989], [0, -784], [5001, 0], [0, 0], [5696, 0], [0, -1024], [0, 12765], [-5964, 0], [0, 0], [4576, 0], [0, -5602], [0, -8152], [-5543, 0], [0, 0], [-2424, 0], [0, 4508], [0, -602], [-8880, 0], [0, 0], [4920, 0], [0, -23163], [0, 5888], [-2401, 0], [0, 0], [34293, 0], [0, -3856], [0, 25296], [-3956, 0], [0, 0], [-3136, 0], [0, 46874], [0, -20004], [-5724, 0], [0, 0], [-36112, 0], [0, -22784], [0, -14014], [-4096, 0], [0, 0], [51060, 0], [0, 66104], [0, 23856], [-28290, 0], [0, 0], [16080, 0], [0, -18304], [0, 80482], [-22408, 0], [0, 0], [-32608, 0], [0, 27195], [0, 22172], [64147, 0], [0, 0], [-46751, 0], [0, 9696], [0, 106284], [18032, 0], [0, 0], [-2408, 0], [0, 115023], [0, 35520], [71676, 0], [0, 0], [-11809, 0], [0, -19680], [0, 131008], [-92652, 0], [0, 0], [23552, 0], [0, 151025], [0, 9604], [-158730, 0], [0, 0]]}