-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '599223332052803864393108129402', 'a10': [3.4469681065046496, 0.0], 'a2': [-2.1235830039787724, 0.0], 'a3': [-3.2405198830173334, 0.0], 'a4': [2.5096047747875065, 0.0], 'a5': [-1.6231850132753776, 0.0], 'a6': [6.881512947630888, 0.0], 'a7': [1.557377033571504, 0.0], 'a8': [-1.0821880384851783, 0.0], 'a9': [7.500969112230672, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.06397754167328, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[71, [[1.0, 0], [-1.0, 0]]], [113, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [71, 113], 'central_character': '8023.1', 'coefficient_field': 'CDF', 'conductor': 8023, 'conductor_radical': 8023, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.1235830039787724, 0], [2.0, 0]], [[1.0, 0], [3.2405198830173334, 0], [3.0, 0]], [[1.0, 0], [1.6231850132753776, 0], [5.0, 0]], [[1.0, 0], [-1.557377033571504, 0], [7.0, 0]], [[1.0, 0], [-2.8668279262025917, 0], [11.0, 0]], [[1.0, 0], [2.308574275958311, 0], [13.0, 0]], [[1.0, 0], [-5.434266383124102, 0], [17.0, 0]], [[1.0, 0], [-1.2066345092430362, 0], [19.0, 0]], [[1.0, 0], [5.071950210909791, 0], [23.0, 0]], [[1.0, 0], [7.510055745664547, 0], [29.0, 0]], [[1.0, 0], [-0.6924659442420705, 0], [31.0, 0]], [[1.0, 0], [-6.78376738069251, 0], [37.0, 0]], [[1.0, 0], [1.5026685346789033, 0], [41.0, 0]], [[1.0, 0], [1.7871734656215972, 0], [43.0, 0]], [[1.0, 0], [-0.4906765697013631, 0], [47.0, 0]], [[1.0, 0], [-12.526141858337404, 0], [53.0, 0]], [[1.0, 0], [-7.128140421875758, 0], [59.0, 0]], [[1.0, 0], [1.3894193817360943, 0], [61.0, 0]], [[1.0, 0], [-7.746744716421153, 0], [67.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-12.611427929948563, 0], [73.0, 0]], [[1.0, 0], [-2.526337655685388, 0], [79.0, 0]], [[1.0, 0], [12.48548391479266, 0], [83.0, 0]], [[1.0, 0], [13.924608963151993, 0], [89.0, 0]], [[1.0, 0], [-14.238311151149958, 0], [97.0, 0]], [[1.0, 0], [7.202375960191301, 0], [101.0, 0]], [[1.0, 0], [-9.69318106688391, 0], [103.0, 0]], [[1.0, 0], [3.2219080035008423, 0], [107.0, 0]], [[1.0, 0], [10.780807630053431, 0], [109.0, 0]], [[1.0, 0], [1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 121, 'label': '2-8023-1.1-c1-0-121', 'leading_term': '0.33710810472475034588824817965012', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/8023/2/a/d/1/22', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [0.33710810472475033, 0.3333859737135907, 0.32226118097343426, 0.30386103697914213, 0.2784058408902959, 0.24622019930086186, 0.2077472413059436, 0.1635642653144977, 0.11439814548315586, 0.06113873595153672, 0.004848532359657887, -0.05323303232108996, -0.11169208522788145, -0.16895077717114979, -0.2232865872673502, -0.2728610152954648, -0.3157578592831005, -0.3500309128416634, -0.3737605455954314, -0.38511825605992384, -0.38243791551050743, -0.36429206093564187, -0.3295712537571914, -0.27756420875112586, -0.20803612586489284, -0.12130243856087716, -0.018295038354239273, 0.09938204153564228, 0.229410488906476, 0.36873201771263786, 0.5135417971415902, 0.659303362146703, 0.8007869284760006, 0.9321324930756949, 1.046938457836273, 1.1383757822352825, 1.199326864118326, 1.2225474874808715, 1.2008492854294222, 1.127299272721354, 0.9954321354100387, 0.7994701571232411, 0.5345449453320971, 0.1969145294555709, -0.21583103271192658, -0.7045826540738143, -1.2685509769051655, -1.9051378556404643, -2.6098470953658595, -3.3762402952774897, -4.195942716837259, -5.058702930740211, -5.952508615481703, -6.863759312956845, -7.777495231807964, -8.67767937414133, -9.547528400013983, -10.369885796859746, -11.127629152016718, -11.804101702056375, -12.383556918823704, -12.851603752462433, -13.195639344523778, -13.40525560013019, -13.472606007529064, -13.392719544291904, -13.163749425664502, -12.787145830119924, -12.267743561151967, -11.613757836651061, -10.836683984628758, -9.951099697184725, -8.974371569348495, -7.926270829220786, -6.828506344505679, -5.704186055663001, -4.577220822755552, -3.4716871686931516, -2.4111674492911703, -1.4180874843259876, -0.5130725624759241, 0.28565707554256925, 0.9628307070978074, 1.506592260236493, 1.9088688254879074, 2.165627960686937, 2.2770125210710526, 2.2473455918310665, 2.085002352382419, 1.8021502205675577, 1.4143632539547686, 0.9401213563261663, 0.4002091771928976, -0.1829664709376691, -0.786118482121487, -1.385855761553259, -1.9594672975787804, -2.485686456915286, -2.9454080868348314, -3.3223321691670384, -3.6035099539337057, -3.7797716530350725, -3.8460188039679943, -3.801369189028185, -3.6491475512893126, -3.396721090269362, -3.0551846308508614, -2.6389062079555283, -2.1649493609550032, -1.6523934547596653, -1.1215776223844507, -0.5932972640417001, -0.08798428097589461, 0.3750967502545831, 0.7786045168130831, 1.107798641504665, 1.351111544212271, 1.500590968036258, 1.552194703015222, 1.5059249466893152, 1.3657962640765593, 1.139637985598313, 0.8387388238990489, 0.477348203093314, 0.0720549831605141, -0.358930349856672, -0.7965596198760395, -1.2217635373261921, -1.6162657705451735, -1.9633592229226542, -2.248610633246836, -2.4604625380633585, -2.5907059668902925, -2.634802813816518, -2.592043412386442, -2.465532153869257, -2.2620017118478013, -1.9914642228370483, -1.6667152674941568, -1.3027133501758938, -0.9158634589853243, -0.5232379153233786, -0.14177085555063712, 0.21253584278625573, 0.5253576671234792, 0.7847081483613523, 0.9814834185157549, 1.1098642732788433, 1.1675560068863429, 1.155853954062401, 1.0795310147002994, 0.9465520597630825, 0.7676286088005393, 0.5556351159552115, 0.3249152063703764, 0.09051191084344587, -0.13263994753691152, -0.3305187832624009, -0.4907779560000541, -0.6034251280233225, -0.6613839212030517, -0.660908017364192, -0.6018249126708021, -0.4875948493251354, -0.325179610520883, -0.12472543122021675, 0.10092622704696624, 0.3368773450468599, 0.5669308352659211, 0.774429730591899, 0.9431362397760744, 1.0581061832080934, 1.1065138959687233, 1.0783845454876664, 0.9671949017857956, 0.7703097469292148, 0.4892290354945318, 0.1296302411868292, -0.29879941135512295, -0.7827354408199411, -1.305777371477988, -1.8491729062210611, -2.3926704489563524, -2.9154583772348595, -3.397144487526882, -3.8187264078216567, -4.163503668185751, -4.417884582514502, -4.572046032092918, -4.620411429366364, -4.561921231024788, -4.400080908759504, -4.142782734907863, -3.8019095024531144, -3.392739752030961, -2.9331846070586285, -2.442895346400355, -1.9422878687816363, -1.4515348218871131, -0.9895781036402957, -0.5732135573897835, -0.21629599232866864, 0.07089366511219429, 0.28208592737639937, 0.41524236193758846, 0.4725464454075842, 0.4601673310038018, 0.38781068871883145, 0.26808255317650737, 0.11570251645712201, -0.05338896537478537, -0.2229784178285261, -0.37752847488391705, -0.50307431678602, -0.588016423685978, -0.6237645638786428, -0.6051964806519184, -0.530905455708521, -0.40322321484247353, -0.2280178078267688, -0.014279382035968693, 0.22648059839956886, 0.48097991027244197, 0.7350199901566287, 0.9743918189742578, 1.1857774788230477, 1.3575915214007914, 1.4807096066922238, 1.54903843159411, 1.5598904294433358, 1.514138560832927, 1.4161400576271408, 1.2734324324711404, 1.0962195594123312, 0.8966792789490925, 0.688135924412263, 0.4841506300029646, 0.29758861929298325, 0.13972541547607367, 0.01945279699682526, -0.05735969104381536, -0.08830056605922695, -0.07461444007631629, -0.0211416951594088, 0.06400439481510892, 0.17001010900782915, 0.2841533436307191, 0.39276967680346625, 0.48233345783330683, 0.5405848162156476, 0.5576273389926751, 0.5269195355505041, 0.44608637578836435, 0.3174851481604927, 0.14847234385903635, -0.04866534665009652, -0.257133377377768], 'positive_zeros': ['0.47270386015272579471446645489349', '1.22641630038309791778688002863998', '2.03906527797524504524695526053146', '3.77931907986419932170470423864550', '4.34492729890603398172261953875736', '5.25853334764402512845104398841628', '5.82047779500617414934382346473167', '6.67446934880850889058952309456922', '7.28418522953307271112537432193131', '7.76073826757487956433970776107390'], 'prelabel': '2-8023-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.003997597555442, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.47270386015272579471446645489', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.22641630038309791778688002864', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.03906527797524504524695526053', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 64.06397754167328, 'bad_primes': [71, 113], 'central_character': '1.1', 'conductor': 8023, 'conductor_radical': 8023, 'degree': 2, 'index': 121, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8023/2/a/d/1/22'], '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': '2-8023-1.1-c1-0-121', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-8023-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.003997597555442, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.47270386015272579471446645489', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '599223332052803864393108129402', 'Lhash_array': ['599223332052803864393108129402'], 'label': '2-8023-1.1-c1-0-121', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8023/2/a/d/1/22'}