Formats: - HTML - YAML - JSON - 2026-10-12T13:31:56.731587
  • lfunc_lfunctions • Show schema
    {'Lhash': '673954995931993147638310061603', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 73.95999728570581], 'a6': [0, 0], 'a7': [112.7040599250805, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 46.19054010613843, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '288.145', 'coefficient_field': 'CDF', 'conductor': 288, 'conductor_radical': 6, 'conjugate': '2027988589754906635961640709826', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -73.95999728570581], [-3125.0, 0]], [[1.0, 0], [-112.7040599250805, 0], [16807.0, 0]], [[1.0, 0], [0, -575.407393864419], [-161051.0, 0]], [[1.0, 0], [0, 117.73545156126158], [-371293.0, 0]], [[1.0, 0], [-223.408119850161, 0], [1419857.0, 0]], [[1.0, 0], [0, -1752.258316667221], [-2476099.0, 0]], [[1.0, 0], [-2361.1527790260466, 0], [6436343.0, 0]], [[1.0, 0], [0, 3865.5162110807846], [-20511149.0, 0]], [[1.0, 0], [-1591.551280899034, 0], [28629151.0, 0]], [[1.0, 0], [0, 4736.44254676451], [-69343957.0, 0]], [[1.0, 0], [8153.876074905474, 0], [115856201.0, 0]], [[1.0, 0], [0, -4920.231477981232], [-147008443.0, 0]], [[1.0, 0], [21062.019235954347, 0], [229345007.0, 0]], [[1.0, 0], [0, 12708.95131300728], [-418195493.0, 0]], [[1.0, 0], [0, -14111.075246388664], [-714924299.0, 0]], [[1.0, 0], [0, -42030.612178069794], [-844596301.0, 0]], [[1.0, 0], [0, -54153.42940458937], [-1350125107.0, 0]], [[1.0, 0], [-43879.868584270414, 0], [1804229351.0, 0]], [[1.0, 0], [31290.626097374312, 0], [2073071593.0, 0]], [[1.0, 0], [-50211.45084644308, 0], [3077056399.0, 0]], [[1.0, 0], [0, -43706.98421351021], [-3939040643.0, 0]], [[1.0, 0], [64418.741513100395, 0], [5584059449.0, 0]], [[1.0, 0], [62350.91241947206, 0], [8587340257.0, 0]], [[1.0, 0], [0, -49960.45350473477], [-10510100501.0, 0]], [[1.0, 0], [159259.8900374422, 0], [11592740743.0, 0]], [[1.0, 0], [0, 135565.2759113777], [-14025517307.0, 0]], [[1.0, 0], [0, -115137.38477453438], [-15386239549.0, 0]], [[1.0, 0], [-19192.025707856028, 0], [18424351793.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-288-8.5-c5-0-6', 'leading_term': '1.906825876541445479900344921238362455602232382149340989', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/288/6/d/b/145/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 10}, 'plot_values': [1.9068258765414454, 1.6884179213001727, 1.4613067432491205, 1.2287400473325594, 0.9940426337225834, 0.760578498852695, 0.5317119472204729, 0.31076783902278926, 0.10099113217908047, -0.09449407832920799, -0.2727257669882079, -0.43094511175010164, -0.566637170036739, -0.6775706413134145, -0.7618361907752085, -0.8178827416831439, -0.8445510831010333, -0.8411040884639859, -0.8072528017598067, -0.743177625190929, -0.6495438378400482, -0.5275106915916732, -0.37873337044615774, -0.20535716397091974, -0.01000329593553234, 0.2042540345326199, 0.43391970010597153, 0.6751189154379055, 0.9236476767396354, 1.1750321095064997, 1.4245962400333074, 1.6675374723594918, 1.899008812784795, 2.114206645172102, 2.3084626285682353, 2.4773380713369426, 2.6167189404064284, 2.722909497876635, 2.792722427481457, 2.823563227281809, 2.8135066089080487, 2.761362663262005, 2.6667306323232842, 2.5300382697391033, 2.352564980808916, 2.136447205143637, 1.8846648406029152, 1.6010079009736096, 1.2900230460275302, 0.956940112760662, 0.6075793004026421, 0.24824020692174445, -0.11442553273076204, -0.4735557118709562, -0.8222303059683403, -1.153632221706482, -1.4612123278528848, -1.738854710186276, -1.981037839724579, -2.1829871961938276, -2.340814859265223, -2.4516416780502164, -2.513697860935704, -2.526398195617228, -2.490388611618069, -2.407561428773836, -2.2810373847045686, -2.115113387243418, -1.915175874798483, -1.6875806652468897, -1.4395012051130271, -1.1787481653652834, -0.9135643358382274, -0.6523997133878311, -0.40367252546507476, -0.17552264773318987, 0.024435569440429253, 0.18935368318946844, 0.3133752111053351, 0.3918398915124655, 0.42145900359907174, 0.4004551614177212, 0.32866079878329424, 0.207570594236039, 0.040344325519924576, -0.16824193795271936, -0.41189683577275554, -0.6829657841827834, -0.972631280950491, -1.2711569230263324, -1.5681689849627076, -1.852967904892419, -2.114860708422909, -2.343504324312947, -2.529248959162939, -2.6634702440250115, -2.738878776834581, -2.7497959826678753, -2.6923859081314103, -2.564833651996174, -2.367462592382832, -2.1027843677056235, -1.775477656359538, -1.392294117772672, -0.9618923322775594, -0.4946031270359425, -0.002132210718477854, 0.5027915324985897, 1.0068115128078128, 1.4963701582383717, 1.9581528254633578, 2.379533727845151, 2.749008120064441, 3.0565949460360136, 3.294194707553623, 3.4558884495667566, 3.5381654661236976, 3.5400695679396046, 3.4632564550074934, 3.31195782139474, 3.0928511813629367, 2.814837927655382, 2.488735684049291, 2.12689445793559, 1.742749295829144, 1.3503249600869351, 0.9637104528175463, 0.5965229019768941, 0.26138130402568954, -0.030589178930628146, -0.27020227950909004, -0.4505863844603262, -0.5674745569011118, -0.6193953396287272, -0.6077544515465866, -0.5368015992434187, -0.41348110269971416, -0.24716970743353284, -0.04930963968091203, 0.16705053681420745, 0.38779057735351036, 0.5983084751396934, 0.7841425543989095, 0.9316006859436249, 1.0283705954516662, 1.0640853177788632, 1.0308190272215194, 0.9234907308500219, 0.7401565900375896, 0.4821758281504809, 0.15424014070801803, -0.23573793976071286, -0.6768763782390255, -1.155707316986852, -1.656679880609578, -2.1627634228688715, -2.6561277214219152, -3.1188727009427133, -3.5337774238935973, -3.885036490381446, -4.158951742976168, -4.3445483313894915, -4.434086746746253, -4.423446314164846, -4.312360701901333, -4.104492073713044, -3.807337335237342, -3.431967219783169, -2.9926064081554835, -2.506070148011065, -1.9910795954378229, -1.4674840226525874, -0.9554228270324947, -0.47446368727430094, -0.04275504763047185, 0.3237687566291384, 0.6120930422992689, 0.8127056495210372, 0.9200287679965582, 0.9326777402429867, 0.8535324260288488, 0.6896151165328149, 0.4517778599807085, 0.15421099602482313, -0.1862067271706862, -0.5506882772168771, -0.9194138906207457, -1.2724621165641805, -1.5907530810936716, -1.8569593668614803, -2.056340679307504, -2.1774613699275704, -2.212754821778475, -2.158905480747521, -2.0170276522229234, -1.792629706500912, -1.4953626092132006, -1.1385622284026784, -0.7386051549915925, -0.3141072946232782, 0.11499724288813926, 0.5284528544069974, 0.9067061353577035, 1.2319057475859059, 1.4888279664933504, 1.6656802547098017, 1.7547405039016863, 1.752797119815831, 1.6613645684076033, 1.4866599178191817, 1.2393377811147914, 0.9339933055557161, 0.5884548499614558, 0.22289912389128955, -0.14116875830969594, -0.48202015807408444, -0.7788373012389278, -1.0128192187978693, -1.16820169187015, -1.2331370413942353, -1.200385860896588, -1.0677816548752872, -0.8384404105254515, -0.5206998667240085, -0.12778702143422005, 0.3227734622621029, 0.8099835638141976, 1.31038993246883, 1.799245841763141, 2.251758895362204, 2.644360832054277, 2.955933557445174, 3.1689267488569794, 3.2703070418658964, 3.252286731547372, 3.1127907498694105, 2.85563389021166, 2.490395178847952, 2.0319921728405395, 1.499973958019898, 0.9175668697143112, 0.3105206253338202, -0.2941861267969023, -0.8697135301440239, -1.3907294072141483, -1.8347062462883894, -2.1830762211652095, -2.422181037722952, -2.543963813771467, -2.546363652381021, -2.4333893742958703, -2.2148661991747627, -1.9058670749024982, -1.5258578652716324, -1.0976017385664834, -0.6458819310328346, -0.19611277931581197], 'positive_zeros': ['0.53165674816913544331693987421417', '1.50303773501428859636856697213569', '3.23027113170659459449867045506112', '4.74178007411790854998854416100219', '5.26305641055301408736743077913045', '6.62526604134952859068826132781602', '8.055421777994481797335486752037369', '8.639575829049295757144312262544832', '9.400835539203121263593938980059477', '10.88171391089330536346112034657568'], 'prelabel': '2-288-8.5-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.7963622700779, 'root_angle': -0.36616866899453704, 'root_number': '-0.66680202570134231371757190891238485123352585739021613435 - 0.7452349015717033797180882103617493210755690897544934387*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.36616866899453704', 'prec': 57}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.53165674816913544331693987421', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '1.50303773501428859636856697214', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.23027113170659459449867045506', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 46.19054010613843, 'bad_primes': [2, 3], 'central_character': '8.5', 'conductor': 288, 'conductor_radical': 6, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/288/6/d/b/145/4'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-288-8.5-c5-0-6', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-288-8.5-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.7963622700779, 'root_angle': -0.36616866899453704, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.53165674816913544331693987421', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '673954995931993147638310061603', 'Lhash_array': ['673954995931993147638310061603'], 'factors': ['2-288-8.5-c5-0-6'], 'label': '2-288-8.5-c5-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/288/6/d/b/145/4'}