Lfunction data - 1-3168-3168.493-r0-0-0

Formats: - HTML - YAML - JSON - 2025-09-29T17:29:42.323419

• lfunc_lfunctions •

  Column	Type
  A10	numeric
  A2	numeric
  A3	numeric
  A4	numeric
  A5	numeric
  A6	numeric
  A7	numeric
  A8	numeric
  A9	numeric
  Lhash	text
  a10	jsonb
  a2	jsonb
  a3	jsonb
  a4	jsonb
  a5	jsonb
  a6	jsonb
  a7	jsonb
  a8	jsonb
  a9	jsonb
  accuracy	smallint
  algebraic	boolean
  analytic_conductor	double precision
  analytic_normalization	numeric
  bad_lfactors	jsonb
  bad_primes	bigint[]
  central_character	text
  coeff_info	jsonb
  coefficient_field	text
  conductor	numeric
  conductor_radical	integer
  conjugate	text
  credit	text
  degree	smallint
  dirichlet_coefficients	jsonb
  euler_factors	jsonb
  euler_factors_factorization	jsonb
  gamma_factors	jsonb
  group	text
  index	smallint
  label	text
  leading_term	text
  load_key	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  origin	text
  plot_delta	numeric
  plot_values	jsonb
  positive_zeros	jsonb
  precision	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  root_number	text
  self_dual	boolean
  sign_arg	numeric
  spectral_label	text
  st_group	text
  symmetry_type	text
  trace_hash	bigint
  types	jsonb
  values	jsonb
  z1	numeric
  z2	numeric
  z3	numeric

  
  {'Lhash': 'dirichlet_L_3168.493', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.7771459614569709, -0.6293203910498375], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.7431448254773942, -0.6691306063588582], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 14.712130148910031, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [11, [1]]], 'bad_primes': [2, 3, 11], 'central_character': '3168.493', 'coeff_info': ['x^120 - 1', '0.998629534754574 + 0.0523359562429438*I', '\\\\zeta_{120}'], 'conductor': 3168, 'conductor_radical': 66, 'conjugate': 'dirichlet_L_3168.2821', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^193', 0, 'a^194', 0, 0, 0, 0, 0, 'a^127', 0, 0, 0, 'a^108', 0, 'a^111', 0, 0, 0, 'a^70', 0, 'a^146', 0, 0, 0, 'a^179', 0, 'a^112', 0, 0, 0, 'a^147', 0, 'a^129', 0, 0, 0, 'a^46', 0, 'a^125', 0, 0, 0, 'a^116', 0, 'a^148', 0, 0, 0, 'a^117', 0, 0, 0, 0, 0, 'a^169', 0, 'a^83', 0, 0, 0, 'a^80', 0, 'a^115', 0, 0, 0, 'a^138', 0, 'a^54', 0, 0, 0, 0, 0, 'a^92', 0, 0, 0, 'a^23', 0, 'a^61', 0, 0, 0, 'a^90', 0, 'a^201', 0, 0, 0, 'a^64', 0, 'a^32', 0, 0, 0], 'euler_factors': [[0], [0], [1, 'a^193'], [1, 'a^194'], [0], [1, 'a^127'], [1, 'a^108'], [1, 'a^111'], [1, 'a^70'], [1, 'a^179'], [1, 'a^112'], [1, 'a^129'], [1, 'a^46'], [1, 'a^125'], [1, 'a^116'], [1, 'a^117'], [1, 'a^169'], [1, 'a^83'], [1, 'a^115'], [1, 'a^138'], [1, 'a^54'], [1, 'a^92'], [1, 'a^23'], [1, 'a^90'], [1, 'a^32'], [1, 'a^137']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-3168-3168.493-r0-0-0', 'leading_term': '1.13465175483635818884529752312-0.745726198901940345186849429106*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/3168/493', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.3577710294751335, 0.8662974113882734, -0.031351266072662955, -0.7119215896235387, -0.01300825275795382, 2.152403506080591, 4.154707212003908, 3.9944393345442344, 1.4650985503886194, -1.3199977250638641, -2.006673098999397, -0.5777520807996712, 0.6737009307185094, 0.005078653193999853, -1.5073830813998956, -1.341434970777489, 0.9753122968325869, 2.859307712142933, 1.8515504555429332, -0.9845268490731768, -2.1693445174873385, -0.2906362622818882, 2.110915986882257, 2.005605409477722, 0.02452818553981594, -0.5728348094637845, 1.2701540497710093, 2.7853670138926483, 1.4931328206420478, -0.9494055138711447, -1.0750332038477652, 1.1276063913561543, 1.982435963160631, -0.40220433167455055, -3.0919485127399455, -2.52812932994682, 0.20162563839788403, 1.0784674175959714, -0.7114368903674545, -1.7156013908244774, 0.13606603885356958, 2.1775505488967766, 1.3874311672246615, -0.5482938093146603, 0.09081447718811259, 2.723448889883139, 2.8983225219680517, -0.7152795678561136, -3.8617566671954657, -2.9546888904706026, -0.23622537733233004, 0.25324894231060235, -0.9639476929667713, -0.5746185914398646, 1.0200117677112226, -0.011403168849057161, -3.966378803279207, -6.004396830141402, -3.416173059911732, -0.0595519896153414, -0.3679071633522244, -2.589186586699797, -2.253151907239989, 0.3064396664976583, 1.1198581237458163, -0.0926598757572237, 0.3712699509361921, 2.905651555521923, 3.0194217709393625, -0.9757146074871124, -4.218729482597002, -2.6233542939397823, 0.7477725132030593, 1.020913794563719, -0.7058119865687343, -0.3183931182581739, 1.5206983423464289, 0.9112115189103043, -1.4725756378583017, -0.9958457922444015, 2.476871939135725, 3.639868252597995, 0.6618590646037434, -1.6553046309185748, -0.23815632317531452, 1.167589845380315, -0.8693083444569436, -3.157105867943445, -1.7927829717718815, 0.6817483687362231, 0.04655716146661016, -1.820040795967088, -0.690214948416877, 1.695038755276733, 0.5049182251365654, -3.066757665726432, -3.4599260569324155, -0.5945235026848948, 0.058391871042721914, -2.5823615621549507, -3.4301011867139106, -0.6657417133060621, 1.219982306304553, 0.10657751112368216, -0.060044447753780636, 2.5155171568812977, 3.435770286089465, 0.5450921462751732, -1.1133505370192491, 1.9924219126005094, 5.176645207774992, 3.5103104862181955, 0.10708246728974878, -0.09465792375963543, 1.1345093283677243, 0.12405647679976411, -0.9258239018006207, 1.1803666950999243, 2.961758959843934, -0.08943728919812188, -4.412608677498364, -3.7043975473793016, 0.26641231837414725, 1.1421503933875587, -0.9348889204667462, -1.0427940904008595, 0.47884348622381456, -0.5520259087033241, -2.8559273010300132, -1.7558583979335332, 1.0850920145042355, 0.06224236925234733, -3.4786692850073533, -3.017929036191502, 1.2890240250268612, 2.9329037388574886, 0.7600204156517956, -0.12167329038203684, 1.087515167499558, 0.11312827476439358, -2.483191301144127, -1.4894720543214515, 2.37660906148424, 2.8711551692883477, -0.20609374051893797, -0.6854674649139652, 2.1745719243431063, 2.679467843751243, 0.18411528618861944, 0.23895489758959504, 3.2992495228960634, 3.620490900067371, 0.4634111332492683, -0.8276159995207066, 0.28060499292891294, -1.0619960664491672, -4.211430350236305, -3.298846358191558, 1.055483016669745, 2.0869242688155074, -0.6396007418799582, -0.938600451834156, 1.7082645280912725, 1.614604211990272, -1.417961969291572, -1.902314527207094, 0.22345106391883596, 0.21920444537082384, -0.7761028208814927, 2.1323899133727195, 6.326452679276432, 4.975148240752028, -0.17824308581669293, -1.6493650800787274, 0.4987511722431362, 0.4133810636882606, -1.5366893001998099, -0.74869867013405, 1.2153890194068855, 0.26272142445143604, -0.5565794886958495, 3.1220584302571943, 6.687031766023177, 3.9044246271737855, -1.2898450620887385, -1.8366957357744946, 0.2327427458728348, -0.30777315402999744, -1.3139941776304473, 0.6341131617747618, 1.7995350906109864, -0.8500191023943656, -2.265368713500885, 0.8590885103483289, 2.7766592541214443, -0.21514191116881018, -2.2434022611560263, 0.634834072800282, 2.9753892750272626, 1.1119699546142172, -0.3395040175619639, 0.8605207634368386, 0.12993728799259055, -2.918678892250558, -2.283246603508926, 2.0289297150673584, 3.001672693277209, 0.09782615769884395, -0.19554217796943887, 2.196188464247421, 1.3499349045477544, -1.6367898273147166, -0.5676215359467943, 2.963854778339686, 2.701214743418678, 0.13338346064055837, 0.320063180870012, 0.7986637642882848, -2.3675733924219164, -4.673278387276991, -1.6969143540837457, 1.149693104382872, -1.1491186021956148, -3.375805791439419, -0.7952016876428436, 1.7556112398165067, 0.5176022058774838, 0.04874798300142483, 2.442641773880471, 2.695251561431923, 0.22708630282130093, 0.7735423358514198, 3.5077568689467853, 1.4040878137363078, -4.20753817591262, -5.024930339426877, -1.1543019506481829, 0.2864970427054597, -0.7817823093673927, 0.301365925398597, 1.5387454945962455, -0.6075735672472765, -1.8022406623118739, 1.4280534352210208, 2.904833571406448, -1.5356723571812576, -5.004749855441939, -2.449697169416256, 0.43355622895881263, -0.4501443652015292, -0.6423636623324048, 1.283639682869926, 0.40758372372659135, -2.532966333003286, -1.4797010111412305, 1.735216168842514, 0.40021087559783175, -2.9716218382883013, -1.489866865587011, 1.9859436331539644, 1.0365681882167783, -1.2528473708152137, 0.28935484829513175, 1.9935142663684515, 0.3288638627104875, 0.055922390470023155, 3.145855679114458, 3.2708332081510187, -0.9238161368962516, -2.3008208622451254, 0.2239731849394055, 0.04957828633595311, -2.457409861972963, -0.8374718152578862, 3.060748087164999, 2.5459619435777467, -0.08067401507626493, 0.9205454563393719, 2.4978109308057754, 0.4556973354687717, -0.875604640600993, 1.1170226441998443, 0.4024849725019897, -4.521283926873378, -5.752559833284398, -1.4314470518886455, 0.5977949992788589, -1.4676419343429046, -1.384407556888334, 0.8908130822419918, 0.34736732193954833, -0.7389712584933867, 1.8902670662448993, 3.625004804542479, 0.42684814553825773, -1.327789621965105, 2.463759951700868, 4.620872579052429, 1.0760622812800946, -1.417709427756105, 0.3592026173420131, 0.9942737320855719, -0.4320250904322869, 0.3622101945729816, 0.8543474006785983, -3.474609664327921, -6.97450622092033, -3.270977178268262, 1.636078178622602, 0.8172619627578123, -1.0946629010330817, 0.468903042531547, 0.824965818298546, -1.8721685711278782, -2.0343381156823916, 0.21448048515868112, -1.083061572924755, -3.7649155319271608, -1.5617312591839856, 1.6539343225648273, -0.6484986255698646, -3.8242091270773884, -1.889588533838795, 0.4193747845716467, -1.0169651503032822, -1.0312645038577257, 2.1025944229824973, 2.216751220298236, -0.688484015829646, -0.119576990595161, 2.2724511719116682, 0.31981660457071165, -2.4301769187374314, -0.11088842475328359, 2.395713308792257, -0.04013761679815772, -1.7764284448060743, 0.8809567859352415, 1.6764246598627697, -1.490905935945361, -2.2420868031921786, -0.12221975213530707, -0.6086073265426745, -1.4822782091880784, 2.0416684353806507, 4.602848952731088, 0.8374813981055551, -2.4530216922316064, 0.4069864914126171, 3.047304994090191, 1.1284021270487936, -0.021731874760364037, 1.0399910965746162, -0.40476449507323475, -2.212468827841108, 0.7072270906951695, 3.3985450402045148, 0.09205848182612454, -2.981444876415868, -0.2603302250489048, 1.7392238716550317, -1.2180276691457248, -2.6746566558418463, -0.18182547602937005, 0.6088641341120841, -0.2905334461453131, 1.2220593676421805, 1.0949518657759822, -4.66345408165811, -8.360928454521703, -4.125492968835038, 0.5637372577477138, 0.08771604088572371, -0.10206665786257094, 1.900119092135565, 0.6222639843996909, -2.551672198983431, -1.594312404308224, 0.311483920789062, -1.9368051120147942, -3.1570226238816863, 0.47731199412449826, 1.9207880710576855, -1.7152829801956093, -2.814136935536749, 0.14768495100547585, 0.1211366864518727, -2.2913178742190548, -1.074981618014875, 0.7165551846233821, -1.7898397703298161, -3.39904728507666, -0.40952323526715606, 0.9435036060491798, -0.9786168573393934, 0.7073525589825841, 5.000606432976645, 3.972304132153317, -0.09636150360449797, 0.21325085790328732, 1.7067702564190153, -0.8618866721113729, -2.6058178301014574, -0.22746485330589813, 0.6078393309266448, -0.8352512734709386, 1.152497157430646, 3.5880161811573315, -0.36569201544305796, -5.274728326210113, -3.0735557477044377, 1.0973242370492549, 0.6266591650500735, -0.21261558721027674, 1.2521933335521278, 0.22374038669730328, -2.154109877139632, -0.24753004336349543, 1.8281633273047886, -1.8550690702735457, -4.919824078257251, -1.4505646049723047, 1.4423128807434094, -1.0311200470585822, -2.2623076302168013, -0.008607302597820143, -0.010523607182136815, -1.328494517940688, 0.610371035520225, 1.4514417459839517, -2.208599739896283, -2.824094437590244, 2.504018699932452, 4.602265902670084, 0.7638682224731035, -0.9103867864561296, 0.647117450208372, -0.05869480583564002, -0.41325412925333976, 3.3651116912464265, 5.127342026871825, 1.6451222445595302, 0.09756882705501546, 1.904215551115723, 0.04806229310037326, -3.701267470199647, -1.8925304895712147, 1.7775820316142485, 0.6350054803647498, -0.6031502575542985, 2.1989305820793708, 2.947272740582598, 0.029787293101987567, 0.049384075051010695, 1.9912913685403697, -0.12846232461719218, -2.2197053780083933, 0.9319369988926757, 2.8976927601731055, -0.3597151199060429, -1.342657216508746, 1.9318724723515974, 1.662528034929207, -1.9264178549053665, -1.7367822632478862, 0.14366996139012006, -1.0486514370184237, -1.0655522744060093, 1.5368513052073702, -0.3282197424718453, -5.511303412772229, -4.518995211409741, 0.6969304796912235, 0.8124117552167175, -1.8578433766037137, -0.7838399848942225, 0.5165530687934311, -0.7579077794385308, 0.3750116109006073, 2.802321711289535, 0.11775426316207208, -3.361109154122687, -0.3672693887923784, 3.0318519769986922, 0.18521155123123076, -2.2368038128767838, 0.3169915036946367, 1.405091373984356, -0.4758974104014014, -0.049320528299976095, 0.22614574724786501, -3.6583999935887705, -5.304281637235992, -1.3507236082473821, -0.1497828718989901, -3.6789957706361336, -3.2032843295855447, 1.2210925722934203, 1.6163983731032712, -0.21776760327479225, 0.9382416647009654, 0.7997315687143132, -2.554761026899394, -2.067398471721612, 1.9127269230874009, 1.2095551616358033, -2.1079890115698285, -1.05716899875709, 0.15989549740522302, -2.858877565835505, -3.1698651157180375, 1.5818055338715953, 2.966692631145638, 0.018306210497321646, -0.24147950930647477, 0.5177194910901728, -2.0046742730247815, -2.381390709570291, 1.6930237939940045, 2.2773783530745537, -1.2007431348415056, -0.5234712516046742, 2.2908911966033045, -0.20542056112889545, -3.4095335665239666, -1.1359127612438373, 0.8812987528704095, -0.9454209225222194, -0.967883197326219, 0.5525282710161648, -1.2138060205215013, -1.3648532167588596, 4.382711236964692, 7.132708774201311, 2.1124422180964064, -1.3193162529914892, 0.5870855800104041, 0.7301573481531213, -0.9771903106074213, 0.33744273175103856, 0.8676777490691717, -2.01503102091871, -1.666542917995136, 1.7781511665570071, -0.25493843351080525, -5.1267432742182155, -3.5222063280941422, 0.7298143991568351, 0.02008949185503826, -1.2462159142377, 0.5710756373339556, 0.09064184674511896, -2.105656518156119, -0.16060101013939637, 1.680744166376821, -1.8143058199355748, -3.4613997683734725, 0.6700930925911036, 2.011826467938232, -1.3332645932290228, -1.2353502510774501, 1.4386199607878802, 0.4025160129714255, -0.5143529763184976, 2.1935655097397224, 2.0596134853706527, -1.527475626770233, -0.7127509012411717, 2.494717553842809, 0.7174877841631252, -1.722860649644364, 0.19946165646948336, -0.09776759002193085, -4.454076624036596, -4.249372549691519, 0.27099872488581905, 0.8510177474337033, -0.6938413857742594, 0.4652850342014734, -0.22151222336549803, -3.486745053715051, -1.7234121939437865, 2.9499274629059555, 1.6948316066542077, -1.6231997642801466, 0.25843854287002, 1.6414926126003246, -1.8014503291409252, -2.890203418133537, -0.08491247335643716, -0.00046455750865390973, -1.1086585547766459, 0.4530094092461079, -0.9517783923593308, -6.149845586267252, -5.265990872296014, 1.3946797049941864, 2.7959950086854914, -0.38197100195185263, -0.059281240940276335, 1.1661275876985346, -0.4486405946386958, 0.10983353647800209, 2.479251093347257, 0.49402509001024775, -1.4633397338517213, 2.763404287269558, 5.4731940681976985, 1.0599550912030093, -1.8847713807947255, 0.14339545706226364, -0.09757620929219138, -2.056778810366591, -0.26976118744340805, 0.8174125424615262, -2.0667685719680144, -2.192227592791963, 0.44880012137861863, -1.8338247126025364, -5.330340136956397, -2.0900261146521437, 2.0403285326446574, 0.7304251907923638, 0.14534885376745643, 2.353383886706083, 0.8888050662412107, -1.866965139930028, 0.3439204988219016, 2.2717668889317317, -0.21732159980614563, -0.1268371667120961, 3.2419183940908916, 2.189964110349255, -0.4730211014375986, 2.07696861674423, 3.8680422468485522, 0.022582407506175198, -1.5701718666603623, 1.4979803256735205, 1.711099516652146, -0.13436801062727077], 'positive_zeros': ['0.61510877338437935930813586500', '1.25257433528913509307065683013', '2.64836905682801747403220249500', '3.54368158576388413619113839890', '4.06355576072159101143728706720', '4.88596518554338686603627093530', '5.82828948984059385604669538278', '6.59484283080516131162484219032', '7.504266739281222133442398337855', '7.94347013206272675256904525267', '8.9271046321501626273894108563', '9.54036544614509072556208733128', '10.274153663661037685835540194883', '11.22452124443628397309906363828', '11.771950173802349949418531878697', '12.48399362706470005122742351834', '13.32612725210768643729039619216', '13.73703955147101845898983169138', '14.63600749042338827178377842011', '15.66531610137558617745522908912', '16.00916420119625534755696518287', '16.66649036126918521265983644257', '17.18631395987554846679219967250', '18.448095436377249251443486411470', '18.68676791344359473000188176192', '19.64723107372022693318594731409', '20.28490762142685509662107743057', '20.55613810127615192241273630626', '21.49844449329668340261744903017', '22.4144758185058845740818534923', '22.98663976848900126356205559123', '23.4901816547485979448126090022', '24.177266835005772525191756234540', '24.78752556340362303443194426139', '25.68322476754341226075375927582', '26.2814309725629980194752305381', '26.78388306934020863574489169693', '27.69807965616777910230153856702', '28.13187523941231446762370486889', '28.82769236979961449944013165125', '29.4207497606135606399463973893', '30.396985582148704540470361795171', '30.636288422180395402247780776380', '31.63054115939484915691533379709', '32.21084142357358894860138185935', '32.51169546601643676604917417080', '33.48958112673392884466862883146', '33.90853560110160107015175575546', '35.01628493210294449956411348909', '35.333714668485757111577578740007', '35.958379695901014185280579629227', '36.43395315860685078029532273594', '37.18184336456837601587766942191', '38.1000966784134900434539661440', '38.612817305247575758110785114041', '39.25353860785284751787247253582', '39.61085369974651235150143896760', '40.48402638657604182069538733604', '40.94330919621032842809353864207', '41.782417430381469183877906147023', '42.62900819562755459662298737076', '42.8545171203745055126279605725', '43.45095688214784442327563883289', '44.18310198457469006637497646162', '44.9773048239396463138774622024', '45.401075216264479596116892295470', '46.2798217206836506752797601873', '46.52650418687278573296120651977', '47.55105177660175300547800028875', '48.03220483163554091545373420376', '48.30231030093466319998132370315', '49.29472572307872704092050722866', '49.92720071249672430638410057886', '50.43019287776562587474903841915', '51.105232477246417476423625981479', '51.83620923844055072686107538071', '52.23346987147490240328320773020', '52.64469178054116050745835420993', '53.73718751149270361407682897435', '54.30011704313732970142768523670', '54.75115235908173772062577062672', '55.410021559488603214284129777661', '55.97908488598601074552118859522', '56.33373593882452662345456746082', '57.40512185564757218116069634490', '58.07357316920200398633824687177', '58.37770861724450861650570763584', '58.98735470095939382651373702169', '59.60806760890586946726237278002', '60.244556619559325099147876594891', '60.92035818483592798469387046485', '61.51197699286695919243791289567', '62.3407396539875575785211796251', '62.622324081818286803668982891972', '63.13984953436125184964703546438', '63.917084453686161734580974133788', '64.69985915781519787367230422800', '65.029031804734566557556283705533', '65.7519292129312305694724600728', '66.29873987172292500535074698071', '67.21757364208434701131398084082', '67.41916756859074604149896512286', '67.92772751816291131067515213154', '68.880259452889313480046160229906', '69.27380388747860566189097476578', '70.06615816083319147397430777015', '70.72530894298961507602381718143', '70.92632540260097382135010633322', '71.92328562338746824205416287606', '72.06754190476597454542883786100', '72.89079819431823901278968376772', '73.88076473595213307844162140510', '74.151361461359023517919822089226', '74.64184585012846773372159602707', '75.24768096198212012565011395620', '75.82541870758296141230505735611', '76.477246993819277011572074123853', '77.40935390895301455029227351654', '77.72324172375231160685652922819', '78.2330057609627809814687328062', '78.79161193772133085353719806398', '79.50049907653553048304901795791', '80.03257325682917315668886368326', '80.73913682511712765538528602366', '81.35827163939922680557437658568', '81.84232162857730925329619977022', '82.55433821983406650123914725915', '82.80349907823360898532516164801', '83.68281489788372510852015795084', '84.344517462715466278120878152888', '84.6938757188754429535916822989', '85.37412992843273588378114129836', '86.23083728959376847416367267218', '86.42204896177269256523164837079', '87.23970079792529076963087314641', '87.65983162790293944664755691370', '88.15702356502757908079695188638', '89.18196491028448558881222214181', '89.49204491622026851837157117205', '90.17434123647306963750382525544', '90.681036844052970695334751661154', '91.07143118171424777343153953728', '91.9090210089298179863649615335', '92.33240476532182799161409992681', '93.205905021599273610338593932', '93.701113652170577485668685572022', '94.262995674709641963210651076194', '94.622184047992539244455131529099', '95.0956511256440180347538518230', '96.11196845319734365123452019718', '96.65322050392773577995009153932', '97.12015516406423631034215072171', '97.60884477687603128792306887953', '98.39147997346421647017997089320', '98.6233911928076955882711853579', '99.48958795521608027826612011496', '99.95179205043019797342146331632', '100.82060300401674572768283064811', '101.089855259136968380931081150884', '101.67478313219784198368119347721', '102.4134442271853015181500588770', '102.82600378163144160561028411633', '103.46354892951938248172549556785', '104.07127610194978855958652512550', '104.683962527854453780339493785992', '105.227423610148372851134562624711', '105.8021095149121225007007786921', '106.59423180241605423484581566784', '106.74899285436390381859072242515', '107.35808544967707764618457600865', '108.17505107023179508019881266740', '108.72072073824914052772348247308', '109.56544085462262766422878045873', '109.69759053177394604398023128728', '110.26588195166872333045048636836', '110.88693606056572933325867819229', '111.56832697324791559454939439781', '112.20812507542086467455156766865', '112.71015429613764277619095115560', '113.46085652585787770673906736578', '113.91136444916893411087405100481', '114.17992978334461030499503556979', '114.76990316825783207892323148575', '115.86994355160332892581510197530', '116.26788619372648719310165638048', '116.58147720263653008124651725830', '117.241953241440396953369753246421', '118.00825304630975394498130414576', '118.223875312134671068058818793090', '119.026995539555504117223768746439', '119.55800998187241780581190573538', '120.29457330607691184849902371300', '120.64059847158644532664788567375', '121.37236207846280815661899243930', '121.70511174191028853011629718578', '122.53876003364357656346162146842', '122.96699148369466351970876244452', '123.38181157198331530843673402355', '124.363230089488153629712644166773', '124.65761145545058989254260314753', '125.23627348727564798414538615813', '125.96499444828667957988093886793', '126.36810716284898062535206640271', '126.76767284166161043133837510966', '127.48192534958754010873431871086', '128.32404379017888329703159856569', '128.86433289447595579654898989645', '129.12371346201927380705493578735', '129.71177676347482491949444188245', '130.334196167126750801340661978654', '130.82295707270245369726223417984', '131.66032537898219318529553028069', '132.09151898907614948747592909302', '132.81389671922111243091931974339', '133.12305338339506467215969233656', '133.68156593897948349011405189724', '134.20949184735460656659341529934', '134.86763637079818568402988199635', '135.68959631180959448305554069646', '136.11514939917343084940157476399', '136.55184503479897674359193267975', '136.92886337555324723535232019359', '138.02793382386355589851392621690', '138.08728800900236788959739888579', '138.75352730331092515869943121011', '139.506585985327248139327381430435', '140.077211239839440895216183119455', '140.410932221270978804303540342', '141.2539465327656381855376893788', '141.55533919934098017098105815802', '142.17642487928436911515819689294', '142.744539430838409817640627241041', '143.407549549406742614430819557727', '143.88795351674204768567020704786', '144.51315766590883601403238076519', '145.25432116524133310747865614212', '145.428781369168761213037335080380', '146.06200738223052661836580816966', '146.54147214385549796250528438771', '147.44708155415099366972551143902', '147.8950540071140332126538116193', '148.54768202408323553739002058748', '148.89577597187306700975190765497', '149.33344907315147501274026595849', '150.00757914584129862484865709435', '150.6473285275083080793410251342', '151.26327095207646092453322740261', '151.84391217863439883466857446886', '152.41186494544393583469186846307', '152.8223876244688179557791456001', '153.15603670535972195582478886870', '154.19750549790528342423049103997', '154.35163501812148229441151074692', '155.21671639984033766481218666854', '155.86401699195188971325174192929', '156.07903611869761965413527046497', '156.645513821514300190867214136476', '157.34038457419200488424188567859', '157.91102465135491004279356963239', '158.57878625853477982759326498007', '158.78234628192426152181011286351', '159.58841669873995727540048330532', '160.31489165612377187637885470004', '160.6749798145458588430933149365', '161.03507525129202510311762111761', '161.752035872269501838196010594368', '162.3837416220651262175840254461', '162.859604914249721093315091839716', '163.4234003140741153362188604649', '164.16759343478210353407277510269', '164.55390888788463524716687814387', '165.15294924124943824287663688266', '165.47341829393560112558100801143', '166.034824071332611398903146801637', '166.99807135864112736917954684499', '167.42346027528961622972725746189', '167.92254355361289409149841244152', '168.38923491016249177539621767324', '168.85991797510230617541932859153', '169.51214773448992319175902734152', '169.98456206026432132463284424702', '170.858204730417110181870474680352', '171.25259363162331147196874655672', '171.78404725813897817527755909339', '172.19879285357783096610034208209', '172.82693803038365730279103021474', '173.31043601458022992712662345411', '174.01694220324552161204429138506', '174.56558474353038849476985172902', '175.125457047321021652075502878', '175.68031017645045827092406089573', '176.01970793412682949181677478956', '176.73300875010367641994926922039', '177.24650056051850401100379903985', '177.87270195099107316542115762772', '178.41161431112455602527881715005', '178.740679556135556136815003327060', '179.66417226693657247393085531009', '180.13198933438328826236259955168', '180.533400386529413787729957187371', '180.91321546887689765213923794102', '181.66439770621701014881243347874', '182.312044751115609033595882570449', '182.788341192052022529438369215576', '183.297511324066216857082307527116', '184.07473752605516925387536843544', '184.37491230986873599859647080195', '184.9182340460220463193910344714', '185.2338984612204834062804383347', '186.17901065489213373931940663780', '186.826778375016048213550679025644', '187.19647437345087262122371794437', '187.73406368377604115938970780792', '188.111404181341408997062520181629', '188.79195589139430094113486282744', '189.21376356521005720060633378693', '190.063376284406840336749478253', '190.60365379838557705447506390243', '190.92386425203109326990954021855', '191.59280156251866837903995418699', '191.98659450537292011009479076985', '192.73083343256094493886795093172', '192.977370590215365912719403758224', '193.86938186718362057393378504401', '194.493724252441589190654237820194', '194.656777120825646281095635378093', '195.38766061611054311003711374545', '195.908302024995581562440682975245', '196.53721233649853410123857126450', '196.88818385309299948213215707415', '197.704336183943140736441024342032', '197.94143631302527137181711716611', '198.75161793348764927853730875979', '199.23308563398373315365400128259', '199.947277337823103088878022036'], 'prelabel': '1-3168-3168.493-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 14.712130148910031, 'root_angle': -0.1850782411807179, 'root_number': '0.396696670967223314210480757969-0.917949754204184404212752258090*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(120)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.921496303357988036350853722657-0.224794341495079433917210222961*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.615108773384', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.25257433529', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.64836905683', 'prec': 44}}
• lfunc_search •

  Column	Type
  algebraic	boolean
  analytic_conductor	double precision
  bad_primes	bigint[]
  central_character	text
  conductor	numeric
  conductor_radical	bigint
  degree	smallint
  dirichlet_coefficients	numeric[]
  euler11	numeric[]
  euler13	numeric[]
  euler17	numeric[]
  euler19	numeric[]
  euler2	numeric[]
  euler23	numeric[]
  euler29	numeric[]
  euler3	numeric[]
  euler31	numeric[]
  euler37	numeric[]
  euler41	numeric[]
  euler43	numeric[]
  euler47	numeric[]
  euler5	numeric[]
  euler53	numeric[]
  euler59	numeric[]
  euler61	numeric[]
  euler67	numeric[]
  euler7	numeric[]
  euler71	numeric[]
  euler73	numeric[]
  euler79	numeric[]
  euler83	numeric[]
  euler89	numeric[]
  euler97	numeric[]
  euler_factors	numeric[]
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  is_instance_Artin	boolean
  is_instance_BMF	boolean
  is_instance_CMF	boolean
  is_instance_DIR	boolean
  is_instance_ECNF	boolean
  is_instance_ECQ	boolean
  is_instance_G2Q	boolean
  is_instance_HMF	boolean
  is_instance_MaassGL3	boolean
  is_instance_MaassGL4	boolean
  is_instance_MaassGSp4	boolean
  is_instance_NF	boolean
  label	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  self_dual	boolean
  spectral_label	text
  trace_hash	bigint
  z1	numeric

  
  {'algebraic': True, 'analytic_conductor': 14.712130148910031, 'bad_primes': [2, 3, 11], 'central_character': '3168.493', 'conductor': 3168, 'conductor_radical': 66, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3168/493'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-3168-3168.493-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-3168-3168.493-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 14.712130148910031, 'root_angle': -0.1850782411807179, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.615108773384', 'prec': 47}}
• lfunc_instances •

  Column	Type
  Lhash	text
  Lhash_array	text[]
  factors	text[]
  label	text
  type	text
  url	text

  
  {'Lhash': 'dirichlet_L_3168.493', 'Lhash_array': ['dirichlet_L_3168.493'], 'factors': ['1-3168-3168.493-r0-0-0'], 'label': '1-3168-3168.493-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3168/493'}