# Stored data for newform 162.7.d.f, downloaded from the LMFDB on 30 March 2023.
{"level_primes": [2, 3], "is_polredabs": true, "sato_tate_group": "6.2.3.c6", "rm_discs": [], "conrey_indexes": [53, 107], "cm_discs": [], "trace_hash": 1782010804593341056, "level_radical": 6, "hecke_ring_index_proved": true, "self_twist_type": 0, "related_objects": [], "prim_orbit_index": 4, "is_cm": false, "hecke_orbit": 6, "analytic_conductor": 37.26876154641586, "inner_twist_count": 4, "field_disc_factorization": [[2, 16], [3, 4]], "is_rm": false, "char_order": 6, "level_is_square": false, "weight_parity": -1, "label": "162.7.d.f", "field_poly_is_real_cyclotomic": false, "is_self_twist": false, "is_twist_minimal": true, "minimal_twist": "162.7.b.a", "field_poly_is_cyclotomic": true, "dim": 8, "trace_zratio": {"__RealLiteral__": 0, "data": "0.509", "prec": 17}, "traces": [0, 8, 0, 0, 128, 0, 0, 4, 0, 0, 5280, 0, 0, -3836, 0, 0, -4096, 0, 0, 20488, 0, 0, 27072, 0, 0, 25700, 0, 0, 256, 0, 0, 40096, 0, 0, -60528, 0, 0, -40400, 0, 0, 84480, 0, 0, -184940, 0, 0, 325440, 0, 0, 470484, 0, 0, 122752, 0, 0, 1899720, 0, 0, -24624, 0, 0, -609056, 0, 0, -262144, 0, 0, 2008972, 0, 0, -8160, 0, 0, 1051648, 0, 0, 327808, 0, 0, 848716, 0, 0, 1411584, 0, 0, 987840, 0, 0, -866304, 0, 0, 70520, 0, 0, 1965408, 0, 0, -3621728, 0, 0, 1644800, 0, 0, -5273216, 0, 0, -71808, 0, 0, -2485640, 0, 0, 4096, 0, 0, 6866100, 0, 0, -4118976, 0, 0, 3180884, 0, 0, -1283072, 0, 0, 4084072, 0, 0, -6441360, 0, 0, 69320, 0, 0, -3873792, 0, 0, -5652680, 0, 0, 8811744, 0, 0, -27489240, 0, 0, -646400, 0, 0, -1441088, 0, 0, -196416, 0, 0, -17582264, 0, 0, -2703360, 0, 0, -13699232, 0, 0, -10312896, 0, 0, 1475760, 0, 0, -11836160, 0, 0, 419800, 0, 0, 2547024, 0, 0, 21806992, 0, 0, 5207040, 0, 0, -9779292, 0, 0, 1706880, 0, 0, -11321036, 0, 0, -15055488, 0, 0, -17190752, 0, 0, 6110688, 0, 0, 45804060, 0, 0, 7856128, 0, 0, 21073876, 0, 0, 3069984, 0, 0, -530224, 0, 0, 30395520, 0, 0, -19653812, 0, 0, 56631648, 0, 0, 36183196, 0, 0, 787968, 0, 0, 74317680, 0, 0, 143904, 0, 0, -65193440, 0, 0, -38979584, 0, 0, 11561516, 0, 0, 20262000, 0, 0, 150262560, 0, 0, -4194304, 0, 0, 228524, 0, 0, 20973120, 0, 0, 51260940, 0, 0, -64287104, 0, 0, -169554296, 0, 0, -46846512, 0, 0, 5508208, 0, 0, -522240, 0, 0, 93016360, 0, 0, 71313408, 0, 0, 131833304, 0, 0, 16826368, 0, 0, -65235240, 0, 0, -52905888, 0, 0, 1783232, 0, 0, -10489856, 0, 0, 149868016, 0, 0, 56984160, 0, 0, 120930772, 0, 0, 54317824, 0, 0, -158754276, 0, 0, -960480, 0, 0, -371834600, 0, 0, 22585344, 0, 0, 57551092, 0, 0, 67605312, 0, 0, -89220488, 0, 0, -31610880, 0, 0, 1881728, 0, 0, -54160752, 0, 0, -78625184, 0, 0, -55443456, 0, 0, -93895020, 0, 0, -65472, 0, 0, -259268136, 0, 0, 1128320, 0, 0, 95868640, 0, 0, -76408800, 0, 0, -196499504, 0, 0, -62893056, 0, 0, 129647584, 0, 0, -176007264, 0, 0, -3918240, 0, 0, -231790592, 0, 0, 49849020, 0, 0, 63186864, 0, 0, -29473328, 0, 0, 26316800, 0, 0, 148937360, 0, 0, 8422272, 0, 0, -268160, 0, 0, 168742912, 0, 0, -784982160, 0, 0, 803232, 0, 0, -284182916, 0, 0, -4595712, 0, 0, 4109228, 0, 0, 37768800, 0, 0, 279123496, 0, 0, -39770240, 0, 0, 73853920, 0, 0, 55728480, 0, 0, 279201780, 0, 0, -131072, 0, 0, 1023482736, 0, 0, 35684736, 0, 0, 103649248, 0, 0, 439430400, 0, 0, -31519280, 0, 0, -161692080, 0, 0, 5164256, 0, 0, -65903616, 0, 0, -177870800, 0, 0, -23479296, 0, 0, 109409888, 0, 0, -101788288, 0, 0, 227121520, 0, 0, 310541040, 0, 0, -90543636, 0, 0, -82116608, 0, 0, 245537020, 0, 0, -235061088, 0, 0, -43054920, 0, 0, 65345152, 0, 0, -3635956, 0, 0, -343472928, 0, 0, 376502472, 0, 0, 206123520, 0, 0, 100870936, 0, 0, 416309664, 0, 0, -20245756, 0, 0, 4436480, 0, 0, -241974720, 0, 0, -156972912, 0, 0, 391962088, 0, 0, -61980672, 0, 0, -227219264, 0, 0, 1381435200, 0, 0, 13366568, 0, 0, 180885760, 0, 0, -802448488, 0, 0, 261686448, 0, 0, 579579120, 0, 0, 563951616, 0, 0, 842590264, 0, 0, -9293280, 0, 0, 937677112, 0, 0, -439827840, 0, 0, -592634232, 0, 0, -1890749664, 0, 0, -64262920, 0, 0, 20684800, 0, 0, -4799160, 0, 0, -562646880, 0, 0, -143158940, 0, 0, -92229632, 0, 0, -548874716, 0, 0, -51959760, 0, 0, 666305728, 0, 0, -3142656, 0, 0, 335965096, 0, 0, -41581632, 0, 0, -624685000, 0, 0, 562632448, 0, 0, 117521344, 0, 0, -598724304, 0, 0, 451272348, 0, 0, -173015040, 0, 0, 522999280, 0, 0, -200618880, 0, 0, -1399155984, 0, 0, -219187712, 0, 0, -931803300, 0, 0, 6092544, 0, 0, -1913966648, 0, 0, 330012672, 0, 0, -2815850520, 0, 0, 1268605920, 0, 0, 873571228, 0, 0, 94448640, 0, 0, -6505432, 0, 0, -625411008, 0, 0, -2329094520, 0, 0, -189378560, 0, 0, 916294348, 0, 0, -1023379584, 0, 0, 92523780, 0, 0, -13433600, 0, 0, 168639656, 0, 0, -734276448, 0, 0, -322363748, 0, 0, 163009536, 0, 0, -2673167940, 0, 0, 475469568, 0, 0, 15072896, 0, 0, 348911872, 0, 0, 1530823348, 0, 0, 1526443680, 0, 0, 1269264232, 0, 0, -166625280, 0, 0, 697228000, 0, 0, -15857760, 0, 0, -1855225620, 0, 0, -625874688, 0, 0, -86958356, 0, 0, -1556959536, 0, 0, 2945727520, 0, 0, 27310080, 0, 0, 20270780, 0, 0, 1275433728, 0, 0, 982724380, 0, 0, 362273152, 0, 0, 3033199600, 0, 0, 567543936, 0, 0, 844656336, 0, 0, -963551232, 0, 0, 719158276, 0, 0, 1981680960, 0, 0, -1365955120, 0, 0, -275052032, 0, 0, -955468152, 0, 0, -3917253216, 0, 0, 30029400, 0, 0, -195542016, 0, 0, 465904960, 0, 0, -425233440, 0, 0, -1347897064, 0, 0, 2931459840, 0, 0, 2716200088, 0, 0, 5223168, 0, 0, -907880288, 0, 0, 125698048, 0, 0, -231987420, 0, 0, 3275465664, 0, 0, 2816897108, 0, 0, -674364032, 0, 0, -99625112, 0, 0, 44966400, 0, 0, -1251722888, 0, 0, 196478976, 0, 0, -1416128432, 0, 0, -222754944, 0, 0, -951828120, 0, 0, -8483584, 0, 0, 1719121676, 0, 0, -395328960, 0, 0, 2196715504, 0, 0, -972656640, 0, 0, 6426162832, 0, 0, 1749600672, 0, 0, 47009024, 0, 0, -1257843968, 0, 0, 1709499960, 0, 0, 1528822656, 0, 0, 700689240, 0, 0, 906106368, 0, 0, -2408232800, 0, 0, 59438400, 0, 0, -4266713664, 0, 0, -1157862272, 0, 0, 604542616, 0, 0, -1708924032, 0, 0, -1155771500, 0, 0, 50429952, 0, 0, 1204791372, 0, 0, 563334528, 0, 0, 6857437384, 0, 0, 1189082880, 0, 0, 4146936480, 0, 0, 1204689600, 0, 0, -2010829576, 0, 0, -4604928, 0, 0, -10179431640, 0, 0, 512021760, 0, 0, 2285574612, 0, 0, -4172380160, 0, 0, -758586284, 0, 0, -3403056480, 0, 0, -99203104, 0, 0, -623673344, 0, 0, -3309420564, 0, 0, 7775064000, 0, 0, -126689220, 0, 0, -369968512, 0, 0, 5260479640, 0, 0, -36922848, 0, 0, 2578515832, 0, 0, 1296768000], "hecke_ring_index_factorization": [[3, 6]], "nf_label": "8.0.5308416.1", "field_poly": [1, 0, 0, 0, -1, 0, 0, 0, 1], "has_non_self_twist": 1, "char_values": [162, 6, [83], [5]], "Nk2": 7938, "field_poly_root_of_unity": 24, "analytic_rank": 0, "char_orbit_label": "d", "weight": 7, "trace_display": [0, 0, 0, 4], "analytic_rank_proved": true, "char_parity": -1, "level_is_squarefree": false, "hecke_ring_index": 729, "level_is_prime": false, "char_is_minimal": false, "qexp_display": "q+4\\zeta_{24}^{3}q^{2}+(2^{5}-2^{5}\\zeta_{24})q^{4}+(95\\zeta_{24}^{5}+\\cdots)q^{5}+\\cdots", "self_twist_discs": [], "char_is_real": false, "field_disc": 5308416, "level_is_prime_power": false, "relative_dim": 4, "hecke_cutters": [[5, [717201875390625, 0, -1181025562500, 0, 1918029375, 0, -44100, 0, 1]]], "space_label": "162.7.d", "level": 162, "is_self_dual": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 9, 3, 1, 3, 0], [1, 1, 3, 2, -1, 2, 0], [1, 1, 9, 4, -1, 6, 0]], "char_degree": 2, "char_conductor": 9, "char_orbit_index": 4, "hecke_ring_generator_nbound": 7, "hecke_orbit_code": 22518204412723362, "trace_moments": [{"__RealLiteral__": 0, "data": "0.114", "prec": 17}, {"__RealLiteral__": 0, "data": "7.218", "prec": 17}, {"__RealLiteral__": 0, "data": "6.589", "prec": 17}, {"__RealLiteral__": 0, "data": "378.634", "prec": 24}, {"__RealLiteral__": 0, "data": "868.998", "prec": 24}, {"__RealLiteral__": 0, "data": "34192.984", "prec": 30}], "id": null, "projective_field": null, "embedded_related_objects": null, "projective_image_type": null, "artin_image": null, "atkin_lehner_string": null, "atkin_lehner_eigenvals": null, "artin_field": null, "projective_image": null, "artin_field_label": null, "projective_field_label": null, "fricke_eigenval": null, "artin_degree": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [32, -32, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 95, -25, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 128, 0, -128, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [660, 0, 0, 0, -100, 0, 0, 0], [0, 0, 0, 991, 0, 0, -290, 290], [0, 0, 0, 0, 0, 0, 0, 0], [-959, 959, -362, 0, 362, 0, 0, 0], [0, 0, 0, 0, 0, 0, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1024, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1795, 0, -1795, 0, -193], [0, 0, 0, 0, 0, 0, 0, 0], [2561, 0, 0, 0, 547, 0, 0, 0], [0, 0, 0, 3040, 0, 0, -800, 800], [0, 0, 0, 0, 0, 0, 0, 0], [6768, -6768, 1160, 0, -1160, 0, 0, 0], [0, 0, 0, 0, 0, 6385, -2600, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 6425, -4125, 0, 0, 0, 0, 0], [0, 0, 0, -5284, 0, 5284, 0, -2896], [0, 0, 0, 0, 0, 0, 0, 0], [32, 0, 0, 0, 32, 0, 0, 0], [0, 0, 0, -5672, 0, 0, 9805, -9805], [0, 0, 0, 0, 0, 0, 0, 0], [10024, -10024, 2826, 0, -2826, 0, 0, 0], [0, 0, 0, 0, 0, -4096, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -15132, -772, 0, 0, 0, 0, 0], [0, 0, 0, 325, 0, -325, 0, 140], [0, 0, 0, 0, 0, 0, 0, 0], [-5050, 0, 0, 0, 2303, 0, 0, 0], [0, 0, 0, 8056, 0, 0, 4376, -4376], [0, 0, 0, 0, 0, 0, 0, 0], [21120, -21120, 3200, 0, -3200, 0, 0, 0], [0, 0, 0, 0, 0, 33629, -23146, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -46235, -14799, 0, 0, 0, 0, 0], [0, 0, 0, 31712, 0, -31712, 0, 9280], [0, 0, 0, 0, 0, 0, 0, 0], [40680, 0, 0, 0, -10400, 0, 0, 0], [0, 0, 0, 60168, 0, 0, 2502, -2502], [0, 0, 0, 0, 0, 0, 0, 0], [117621, -117621, 2, 0, -2, 0, 0, 0], [0, 0, 0, 0, 0, 42200, -33000, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 30688, -11584, 0, 0, 0, 0, 0], [0, 0, 0, 20681, 0, -20681, 0, 36874], [0, 0, 0, 0, 0, 0, 0, 0], [237465, 0, 0, 0, -45075, 0, 0, 0], [0, 0, 0, 0, 0, 0, 256, -256], [0, 0, 0, 0, 0, 0, 0, 0], [-6156, 6156, -39220, 0, 39220, 0, 0, 0], [0, 0, 0, 0, 0, -72788, 16858, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -152264, -32409, 0, 0, 0, 0, 0], [0, 0, 0, 51400, 0, -51400, 0, 22608], [0, 0, 0, 0, 0, 0, 0, 0], [-32768, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -243145, 0, 0, 83705, -83705], [0, 0, 0, 0, 0, 0, 0, 0], [502243, -502243, -5307, 0, 5307, 0, 0, 0], [0, 0, 0, 0, 0, -57440, -6176, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2040, 560, 0, 0, 0, 0, 0], [0, 0, 0, -242831, 0, 242831, 0, 65072], [0, 0, 0, 0, 0, 0, 0, 0], [131456, 0, 0, 0, -38535, 0, 0, 0], [0, 0, 0, -29412, 0, 0, 18424, -18424], [0, 0, 0, 0, 0, 0, 0, 0], [81952, -81952, -17504, 0, 17504, 0, 0, 0], [0, 0, 0, 0, 0, -3770, 1402, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 212179, -131623, 0, 0, 0, 0, 0], [0, 0, 0, 97280, 0, -97280, 0, 25600], [0, 0, 0, 0, 0, 0, 0, 0], [176448, 0, 0, 0, -92584, 0, 0, 0], [0, 0, 0, -388866, 0, 0, 133176, -133176], [0, 0, 0, 0, 0, 0, 0, 0], [246960, -246960, 31365, 0, -31365, 0, 0, 0], [0, 0, 0, 0, 0, -125744, -118392, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -216576, 37120, 0, 0, 0, 0, 0], [0, 0, 0, 43270, 0, -43270, 0, 245729], [0, 0, 0, 0, 0, 0, 0, 0], [8815, 0, 0, 0, -597, 0, 0, 0], [0, 0, 0, 204320, 0, 0, -83200, 83200], [0, 0, 0, 0, 0, 0, 0, 0], [491352, -491352, -10008, 0, 10008, 0, 0, 0], [0, 0, 0, 0, 0, 13555, 26230, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -905432, 93770, 0, 0, 0, 0, 0], [0, 0, 0, 470492, 0, -470492, 0, 16], [0, 0, 0, 0, 0, 0, 0, 0], [205600, 0, 0, 0, -132000, 0, 0, 0]]}