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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': -2, 'Lhash': '2156491365468153089', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [-0.6666666666666666, 0], 'algebraic': True, 'analytic_conductor': 1069.6121051554555, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, -1]], [13, [1, 1]], [23, [1, 1]]], 'bad_primes': [2, 7, 13, 23], 'central_character': '133952.1', 'coefficient_field': '1.1.1.1', 'conductor': 133952, 'conductor_radical': 4186, 'degree': 2, 'euler_factors': [[1], [1, 1, 3], [1, -1, 5], [1, -1], [1, 5, 11], [1, 1], [1, 0, 17], [1, 3, 19], [1, 1], [1, 10, 29], [1, -4, 31], [1, -6, 37], [1, 0, 41], [1, 2, 43], [1, 6, 47], [1, -12, 53], [1, 6, 59], [1, 0, 61], [1, -7, 67], [1, -8, 71], [1, 8, 73], [1, -8, 79], [1, -1, 83], [1, 2, 89], [1, -1, 97]], 'gamma_factors': [[], [0]], 'index': 33, 'label': '2-133952-1.1-c1-0-33', 'leading_term': '4.23417259444', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/Q/133952/bb', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.8639886805702949, 0.6786752983464175, -0.9186877736812549, -2.96308759128861, -3.595528121854806, -1.903475123200841, 0.6748108432533865, 1.610199263679451, 0.3786897814443903, -0.5633257175654904, 1.019039364999022, 3.567856944742623, 3.273490928706386, -0.4602533450098306, -3.364865160256135, -1.793401140938114, 2.056304511285001, 3.208199150054193, 1.016795361734666, -0.5584718953378409, 0.3411348667442257, 1.053227620489106, -0.004634830113206034, -0.2402898645530998, 1.689766068247054, 2.197942326598645, -1.07827810473178, -3.890865923056009, -1.839059057091374, 1.835320583001925, 1.749371358323244, -0.1256886260339812, 1.308799065763427, 3.952564985344251, 2.133359950554394, -2.009426527167615, -1.563133924216947, 2.518385997742782, 3.192484783610318, 0.2755349477750329, -0.223126473361802, 1.829183492099198, 1.452303221291824, -0.601098658210334, 0.01927976967987087, 1.329865537542042, -0.648533808792434, -2.351369722487023, 0.4774924757390184, 3.14206857446782, 0.9235979275126615, -1.405572789564932, 0.05640753479631984, 0.1715514735639389, -3.224593628741245, -3.453373018009046, 0.7140943747493906, 1.414806868832142, -2.1299271408496, -2.183731020786096, 0.7002318384802999, -0.7695492281224279, -4.054304118181414, -1.842874798407383, 2.157987319453054, 1.174614407178077, -0.9955158092448307, 0.1152239395752264, 0.2750930418508172, -1.968852644087652, -1.610548700829483, 0.3800342935211313, -0.4955431404291805, -0.5800410108969072, 2.867379986076023, 2.419139846928146, -3.595664200139078, -4.823176752789965, 0.01542803799342746, 0.2543833023737606, -3.903352348565568, -3.058871578922993, 0.3964939357465647, -0.6507954761414746, -1.843921067431483, 0.5107912780067083, 0.4015707425532839, -2.104711371463382, -0.09530466826531121, 3.210110793986305, 1.334232038605384, -0.8365284483278086, 0.5264146718808397, -0.004814514983170953, -1.824600713578219, 0.5410164978062098, 2.280049277558917, -0.7081548842849166, -0.3008295917636785, 4.871377135509934, 4.565955806469087, -0.1023190371300442, 0.08507348122356324, 1.439843789883564, -1.048331264020123, -0.562444622055614, 2.66902921957076, -0.7264652694165022, -6.31013375014624, -4.1309239555966, -0.06421781704764971, -0.661935764945155, -0.08434551939492278, 2.255934375479985, 0.7571969462378553, -0.9257520733571961, 0.3327519895994094, -0.4239229787078796, -0.7040972281631266, 4.293371234259725], 'positive_zeros': ['0.6296099474105745', '1.677962964673616', '2.310410977678216', '2.638571389024318', '3.473092269400504', '4.113716430204857', '4.861940874993625', '5.189211039599451', '5.749066988360018', '6.045427897217565', '6.684678810318189', '7.360616542793982', '7.966584610279597', '8.109104180747597', '8.867599597790845', '9.347833176622969', '10.02927083286091', '10.28211510620032', '10.90899582776399', '11.24746461291917', '11.69528003089523', '12.22082663035225', '12.81629010184421', '13.24296678152557', '13.51767895947789', '14.20594217113104', '14.60564779276663', '15.17191943128578', '15.44551713700771', '16.09551556153815', '16.60066206876862', '16.98293201946662', '17.28648293283142', '17.92708727819492', '18.17613749316662', '18.55349065140266', '19.10780215872765', '19.74906047763877'], 'prelabel': '2-133952-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 32.704924784433544, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2156491365468153089, 'z1': {'__RealLiteral__': 0, 'data': '0.6296099474105745', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.677962964673616', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.310410977678216', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1069.6121051554555, 'bad_primes': [2, 7, 13, 23], 'central_character': '1.1', 'conductor': 133952, 'conductor_radical': 4186, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 1, 0, 1, 0, -2, 0, -5, 0, -1, 0, -1, 0, 0, 0, -3, 0, -1, 0, -1, 0, -4, 0, 5, 0, -10, 0, 4, 0, 5, 0, 1, 0, 6, 0, 1, 0, 0, 0, -2, 0, -2, 0, -6, 0, 1, 0, 0, 0, 12, 0, -5, 0, 3, 0, -6, 0, 0, 0, -2, 0, -1, 0, 7, 0, 1, 0, 8, 0, -8, 0, 4, 0, -5, 0, 8, 0, 1, 0, 1, 0, 0, 0, 10, 0, -2, 0, -1, 0, -4, 0, -3, 0, 1, 0, 10, 0], 'euler11': [1, 5, 11], 'euler13': [1, 1, 0], 'euler17': [1, 0, 17], 'euler19': [1, 3, 19], 'euler2': [1, 0, 0], 'euler23': [1, 1, 0], 'euler29': [1, 10, 29], 'euler3': [1, 1, 3], 'euler31': [1, -4, 31], 'euler37': [1, -6, 37], 'euler41': [1, 0, 41], 'euler43': [1, 2, 43], 'euler47': [1, 6, 47], 'euler5': [1, -1, 5], 'euler53': [1, -12, 53], 'euler59': [1, 6, 59], 'euler61': [1, 0, 61], 'euler67': [1, -7, 67], 'euler7': [1, -1, 0], 'euler71': [1, -8, 71], 'euler73': [1, 8, 73], 'euler79': [1, -8, 79], 'euler83': [1, -1, 83], 'euler89': [1, 2, 89], 'euler97': [1, -1, 97], 'euler_factors': [[1, 0, 0], [1, 1, 3], [1, -1, 5], [1, -1, 0], [1, 5, 11], [1, 1, 0], [1, 0, 17], [1, 3, 19], [1, 1, 0], [1, 10, 29], [1, -4, 31], [1, -6, 37], [1, 0, 41], [1, 2, 43], [1, 6, 47], [1, -12, 53], [1, 6, 59], [1, 0, 61], [1, -7, 67], [1, -8, 71], [1, 8, 73], [1, -8, 79], [1, -1, 83], [1, 2, 89], [1, -1, 97]], 'index': 33, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/133952/bb'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-133952-1.1-c1-0-33', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-133952-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 32.704924784433544, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2156491365468153089, 'z1': {'__RealLiteral__': 0, 'data': '0.6296099474105745', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2156491365468153089', 'Lhash_array': ['2156491365468153089'], 'label': '2-133952-1.1-c1-0-33', 'type': 'ECQ', 'url': 'EllipticCurve/Q/133952/bb'}