Lfunction data - 8-2883e4-1.1-c0e4-0-5

Formats: - HTML - YAML - JSON - 2025-09-05T06:26:21.769262

• 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': '1289768381800453906017978423821,1709828528947374321777682890250,2192542048621351267357622390094,2428403765338741635398451422795', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 4, 'a5': 0, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.285554939393596, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [1, -2, 3, -2, 1]], [31, [1]]], 'bad_primes': [3, 31], 'central_character': '2883.1', 'coefficient_field': '1.1.1.1', 'conductor': 69084174032721, 'conductor_radical': 93, 'degree': 8, 'euler_factors': [[1, 0, -4, 0, 6, 0, -4, 0, 1], [1, -2, 3, -2, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, -1, 0, 1, -1, 1, 0, -1, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, 1, 0, -1, -1, -1, 0, 1, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, -1, 0, 1, -1, 1, 0, -1, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1], [1, 1, 0, -1, -1, -1, 0, 1, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, 1, 0, -1, -1, -1, 0, 1, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, -2, 3, -4, 5, -4, 3, -2, 1], [1, -1, 0, 1, -1, 1, 0, -1, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, 1, 0, -1, -1, -1, 0, 1, 1], [1, 1, 0, -1, -1, -1, 0, 1, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 2, 3, 4, 5, 4, 3, 2, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, -1, 0, 1, -1, 1, 0, -1, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, 2, 3, 4, 5, 4, 3, 2, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1]], 'euler_factors_factorization': [[[[1, -1], 4], [[1, 1], 4]], [[[1, -1, 1], 2]], [[[1, -1, 1], 2], [[1, 1, 1], 2]], [[[1, -1, 0, 1, -1, 1, 0, -1, 1], 1]], [[[1, -1, 1], 2], [[1, 1, 1], 2]], [[[1, 1, 0, -1, -1, -1, 0, 1, 1], 1]], [[[1, -1, 1], 2], [[1, 1, 1], 2]], [[[1, -1, 0, 1, -1, 1, 0, -1, 1], 1]], [[[1, -1], 4], [[1, 1], 4]], [[[1, -1], 4], [[1, 1], 4]], [1], [[[1, 1, 0, -1, -1, -1, 0, 1, 1], 1]], [[[1, -1, 1], 2], [[1, 1, 1], 2]], [[[1, 1, 0, -1, -1, -1, 0, 1, 1], 1]], [[[1, -1], 4], [[1, 1], 4]], [[[1, -1, 1], 2], [[1, 1, 1], 2]], [[[1, -1, 1], 2], [[1, 1, 1], 2]], [[[1, -1, 1, -1, 1], 2]], [[[1, -1, 0, 1, -1, 1, 0, -1, 1], 1]], [[[1, -1, 1], 2], [[1, 1, 1], 2]], [[[1, 1, 0, -1, -1, -1, 0, 1, 1], 1]], [[[1, 1, 0, -1, -1, -1, 0, 1, 1], 1]], [[[1, -1, 1], 2], [[1, 1, 1], 2]], [[[1, -1], 4], [[1, 1], 4]], [[[1, 1, 1, 1, 1], 2]], [[[1, -1], 4], [[1, 1], 4]], [[[1, -1, 0, 1, -1, 1, 0, -1, 1], 1]], [[[1, -1, 1], 2], [[1, 1, 1], 2]], [[[1, 1, 1, 1, 1], 2]], [[[1, -1, 1], 2], [[1, 1, 1], 2]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 5, 'label': '8-2883e4-1.1-c0e4-0-5', 'leading_term': '11.6494459783009470077430065293673002242196138703581381348017961200163195673295312420551675', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0, 0, 0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2883/1/h/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0146484375', 'prec': 40}, 'plot_values': [11.649445978300946, 11.679169164760642, 11.715517547090023, 11.768439894866045, 11.847782941167704, 11.957808786575917, 12.09607655202886, 12.259494340711305, 12.44544515583816, 12.653087160818526, 12.882328707705689, 13.133159246756533, 13.405023941147657, 13.696837805292464, 14.00719339431868, 14.334545726464418, 14.677315546145682, 15.033788785621113, 15.402061524742773, 15.780020847700152, 16.165346494514637, 16.55550222044854, 16.94772751846849, 17.33912438363427, 17.726599685890477, 18.10686224625867, 18.476517200620787, 18.83204948655182, 19.169785266172568, 19.4859863059472, 19.776944116729243, 20.038886489839154, 20.2680153735034, 20.460697994194778, 20.61341586289348, 20.72272301460086, 20.785396202738994, 20.7985484083874, 20.75951825428861, 20.66592121033987, 20.515864563839635, 20.307861335740977, 20.040801905460754, 19.714106540597985, 19.327791876581976, 18.882333952599062, 18.37873299404982, 17.818679654457565, 17.204403330539094, 16.53861761616238, 15.824665041037207, 15.066488239449699, 14.268452581405178, 13.435365360252472, 12.572589078754165, 11.685825314054977, 10.78102140133358, 9.864438345401881, 8.94257536367971, 8.021973804889193, 7.109186669076071, 6.210794985281109, 5.3332235571587265, 4.482637133745333, 3.6649436140510634, 2.885692035081571, 2.1499492305560444, 1.4622598368617503, 0.8266230292221505, 0.2463836107812748, -0.27580787325026485, -0.7379974659468952, -1.1389690218816766, -1.4782692853014971, -1.7561973205982155, -1.9737869736402136, -2.1327928347174345, -2.235650152190638, -2.285432761772856, -2.285793204522505, -2.240890043612576, -2.1553150492748743, -2.034020521613238, -1.8822199241092428, -1.7052938882376443, -1.508701503051845, -1.2978892583820731, -1.0781930650562088, -0.8547471026416394, -0.632399971293176, -0.41564643205391627, -0.20855632028081345, -0.01470326206896481, 0.16286929739022885, 0.3216749955418238, 0.45982318289599555, 0.5760307862961952, 0.6695944178084083, 0.7403812097330162, 0.788824455323375, 0.8158541454161802, 0.8228375630929691, 0.8115478646808384, 0.7840920396932443, 0.742811348417224, 0.6902167149075805, 0.6289356109421163, 0.5616050328053689, 0.490794134139207, 0.41895453927551723, 0.34835140607305304, 0.28099310267297867, 0.21859379658820804, 0.16254547880910356, 0.11388094547701191, 0.07326320283809597, 0.040990596575719164, 0.01700337116072248, 0.0009043732547242878, -0.00800580773151887, -0.010689042889989932, -0.008321473404603257, -0.0022376453079437954, 0.006126123299080464, 0.015291979634009974, 0.02380236082523323, 0.030276884905147076, 0.0334641541856711, 0.032292011163908944, 0.025907981271196482, 0.013708461777828938, -0.0046387859498969244, -0.029181815148872154, -0.05968545044209851, -0.09564417901425966, -0.13629947532259767, -0.1806685739945147, -0.22758790719017635, -0.27575765795426294, -0.32378658182062364, -0.37024841629380567, -0.41374098986248925, -0.45293512050507195, -0.48662173997811825, -0.513767370023795, -0.5335458359088163, -0.5453687463477818, -0.5489114307888365, -0.5441252548351819, -0.5312273666327781, -0.510699212059349, -0.483272468564059, -0.44988594786900227, -0.4116465297192268, -0.36979803611751233, -0.32566526944997787, -0.28059290860533515, -0.23589764256267926, -0.19282353753198375, -0.15248509168733684, -0.11582564327913003, -0.08358603747187972, -0.056279725899271084, -0.034176731846995025, -0.01730073890788835, -0.005436226228482081, 0.0018501741222995494, 0.005179969733391129, 0.0053255406955765505, 0.0031622829420112236, -0.00038437305384384223, -0.004393233317728132, -0.00800326980629158, -0.010467699452930055, -0.011202307204660634, -0.009827582071132311, -0.006199923741919743, -0.00043103599469030085, 0.007103804845701151, 0.015773718580536403, 0.02471412067868168, 0.032860081100898365, 0.03899744861795152, 0.041822872837376165, 0.040007505541620456, 0.03227419106158863, 0.017482583981460458, -0.005304351855661644, -0.03675051411887877, -0.07716681351659273, -0.12646731676122194, -0.18414170179899117, -0.24922366372923532, -0.32028343064775133, -0.3954688222031808, -0.47254338256336487, -0.5489334142171706, -0.6218236642311709, -0.6882663164962312, -0.7452818127258367, -0.7899808360524595, -0.81969690298664, -0.8321177065903275, -0.8254028400571002, -0.7982857838599876, -0.7501615968770728, -0.6811726601985707, -0.5922426816660287, -0.48507217925112234, -0.36212445176171715, -0.2265885364938218, -0.08226928379133898, 0.06653150309640922, 0.2151501653198621, 0.3587369422456237, 0.4924435034354029, 0.611610014525776, 0.7119710692854828, 0.7898443739713797, 0.8422877281084176, 0.8672643171153612, 0.8637576110223109, 0.8318360851675404, 0.7726872866963752, 0.6886272493827179, 0.5830002406943574, 0.46007060640798336, 0.3248874955672069, 0.1830631830966318, 0.040520521695161134, -0.09674860217070752, -0.22295414179304018, -0.3328065734460718, -0.4217734663956905, -0.4863216658871814, -0.524126655478837, -0.5342181008971515, -0.517075108365744, -0.47466768634338896, -0.4103889070946062, -0.3289246600193707, -0.23606437073623504, -0.1384180006556092, -0.04307003945219812, 0.04280542554027472, 0.11238039586254886, 0.15962333688704783, 0.17973614654177456, 0.16959244361722262, 0.12811373694891814, 0.05656972096871581, -0.041190112076220094, -0.15861332008918044, -0.2864696705018864, -0.4129892519543382, -0.5241309146891965, -0.6040118150467597, -0.6354490500419265, -0.6006488823117022, -0.4819872420678678, -0.2628266165894067, 0.07158775466949506, 0.5331521079498899, 1.1300881258973903, 1.8661554317166005, 2.739858297358737, 3.743942464743703, 4.865086625662262, 6.083663320488983, 7.373740250972709, 8.703704023890525, 10.036766565545088, 11.331686680805195, 12.543942542367459, 13.627495344954964, 14.536083337568126, 15.224799260601506, 15.651904996805907, 15.781266571816493, 15.583867937742603, 15.039197714826978, 14.136824596097046, 12.878579506711734, 11.279032097071946, 9.36559969433139, 7.1790068045639845, 4.773981946155641, 2.217681136149349, -0.41179699082552257, -3.0267604604711917, -5.531492098892278, -7.825396644918352, -9.80591365818688, -11.371614815520127, -12.425039702166092, -12.876256792666922, -12.646365986560868, -11.670676381233392, -9.901058471289781, -7.3085856233007505, -3.8858178928257163, 0.3520945794768301, 5.366748266785315, 11.096312586980345, 17.456290630456994, 24.340870163515127, 31.625013691976207, 39.167768601699244, 46.81519268188465, 54.40380663680791, 61.76605714945682, 68.73490796120726, 75.14700125982462, 80.84767881220185, 85.69806705975434, 89.57674278467813, 92.38234081463149, 94.0391012045618, 94.5000543198502, 93.74540960321742, 91.78389063807545, 88.65536798364765, 84.42804595229973, 79.19499875070142, 73.07370151759933, 66.2023224770723, 58.73476881191886, 50.836285485378816, 42.67990084721256, 34.43985150207859, 26.287197192203553, 18.385622618271395, 10.886325607613488, 3.923781914519998, -2.3870468934398907, -7.953500178675812, -12.707382104739354, -16.605695706155686, -19.631157068028774, -21.791460608021175, -23.117444819102076, -23.6610753639798, -23.49330061541705, -22.7000196707445, -21.378222283660214, -19.632541666358396, -17.571482267726225, -15.302976141859592, -12.930755702096448, -10.551187977345656, -8.250563363490683, -6.10252219813334, -4.166352544749266, -2.4860103568947096, -1.0899232529137568, 0.008888707738684613, 0.8119262853600261, 1.3337232895699822, 1.5999364707453285, 1.6451195579414046, 1.5102774715502032, 1.2403415829359512, 0.8815326686707227, 0.4788936897705696, 0.07421982448157004, -0.29584512797896473, -0.6014422922799186, -0.8203783722544585, -0.9386704974519734, -0.9507555511526429, -0.8590801441650169, -0.6732752191920527, -0.40909441858905654, -0.08692945484852918, 0.26974157742477844, 0.6359433149284942, 0.9870790141181687, 1.3005268493798743, 1.5568266977708065, 1.7409474061578714, 1.8434495183153747, 1.860606733416263, 1.7945255109607294, 1.6533013144904454, 1.450257916852694, 1.2028379109124387, 0.931715539822661, 0.6596050789452232, 0.40952749896482177, 0.20345539466729004, 0.06108396867285016, -0.001569742228473101, 0.02680681999017864, 0.15211878772161533, 0.37433082370642407, 0.6873977872479331, 1.07955513316186, 1.5337543656909234, 2.0286163744361367, 2.5396664786333587, 3.0405751846888487, 3.5045567129123825, 3.9060883357383376, 4.222358083130488, 4.434491806769954, 4.528822470939955, 4.497938850881146, 4.341183960193266, 4.064867167389431, 3.6822539028699883, 3.2131564232314997, 2.6829861271385003, 2.12166722009823, 1.5623048548573892, 1.039565962491223, 0.5879595877040463, 0.24019639423335679, 0.02549645573658716, -0.031974693274908775, 0.08567813547736083, 0.38901866721606776, 0.8805883386604597, 1.5547134817277055, 2.3974794932763115, 3.3871206257901694, 4.495138373650627, 5.687376933060174, 6.92515371824501, 8.167231605192207, 9.371627852934378, 10.49713495886237, 11.505026667244163, 12.361221071340251, 13.037027868642948, 13.510405504800376, 13.76730133713457, 13.80173187184282, 13.615372387633176, 13.218032682105767, 12.627233533427102, 11.866350179628387, 10.963566723791848, 9.951446954695282, 8.864748832345041, 7.738519053259996, 6.607027198976557, 5.502691670223233, 4.454247838337243, 3.4858041858527535, 2.616371055576052, 1.859334582464569, 1.2221645975421895, 0.7066284107331358, 0.30925060654023584, 0.021957039410706564, -0.1670984098653718, -0.27254897110439685, -0.3107220778177311, -0.2985798406612635, -0.25270242278974414, -0.18834717918609858, -0.11867838367888078, -0.05419508314592151, -0.002334843919070571, 0.03266739965649196, 0.04970250696561094, 0.050533860134510666, 0.03934624143684094, 0.022147480792575766, 0.006096725974690498, -0.0012219302004342187, 0.007471842028282905, 0.038483965670532264, 0.0965661065831747, 0.1844781367051996, 0.3026885724995986, 0.4492409165659759, 0.6198557360199274, 0.8081482096035377, 1.00595034200743, 1.203881460384381, 1.391959002099557, 1.5601646399192515, 1.6990878327576433, 1.8006749917534146, 1.8586043003248574, 1.8687041021419897, 1.8293841209708102, 1.7416855154313302, 1.6091201119097145, 1.437618773994523, 1.2352578913278736, 1.011605522622374, 0.7771963196855102, 0.5430638649226093, 0.3200003811632732, 0.1179062042887665, -0.05469960023298852, -0.1911308407988422, -0.2869142371466404, -0.33996711880651026, -0.3506448432279561, -0.3216507197791384, -0.2577855522573822, -0.16558284834403061, -0.05284469318761801, 0.07186677487654342, 0.19978058100036095, 0.32250756291893, 0.4325046608996563, 0.5234781287574709, 0.5907689789921037, 0.631572494094486, 0.6449259777848545, 0.631701572119986, 0.5945132383124574, 0.5373274392582217, 0.4650855946833619, 0.38337703298374576, 0.2979664980039967, 0.21430617338592436, 0.137188283404364, 0.0704533409467987, 0.01672495326907686, -0.02269002052470863, -0.047794614208428385, -0.05980088042186441, -0.06090103180961908, -0.05396857391124246, -0.04221649306728708, -0.028802546557041363, -0.01644908654326758, -0.007114202165654992, -0.0017188273800697739, 2.940868260448089e-05, -0.0003047954643313129, 5.5092807545615075e-05, 0.004912293708068157, 0.018800023990516584, 0.04658956932128731, 0.09302891783589129, 0.16225308789079462, 0.2573052628945826, 0.37969370874713065, 0.5290313789752343, 0.7027913143282165, 0.8962571234998413, 1.1025784187547123, 1.312964894134839, 1.5171080340554972, 1.7038458016554339, 1.861710241026822, 1.9796083678112952, 2.0477121267729883, 2.0582460237058533, 2.005979983724019, 1.8887961726384688, 1.708107355047166, 1.468997900600593, 1.1800398006361725, 0.8530062335846593, 0.5022231924245905, 0.14392051465518177, -0.20477457067322521, -0.5269740813016147, -0.8070822878983988, -1.0317347856061756, -1.1909309033167421, -1.2787838443847215, -1.2939628004560784, -1.2400023560007571, -1.1252766683488178, -0.9624520440323722, -0.7677566576567988, -0.5600108949769487, -0.3592160732540939, -0.18507851776244097, -0.05549747212710977, 0.015001871517924915, 0.016679991339806983, -0.05426274633890337, -0.1948260666877123, -0.39481654479095346, -0.6369051239516285, -0.8971918347424958, -1.1463167407604415, -1.351008617366048, -1.4760644655903845, -1.4867717709890467, -1.3513295008490889, -1.043408430980641, -0.5447871220416286, 0.15247694211353463, 1.0443011669074018, 2.1132179760238587, 3.3278162318706483, 4.642914391811738, 6.000343888077367, 7.331117580477978, 8.557909611371509, 9.59775193923302, 10.366093009938679, 10.781808282422906, 10.770360514369841, 10.267749838982933, 9.226066169618477, 7.616306896520441, 5.429980101972103, 2.6820060656060645, -0.5876167623666256, -4.315778511453104, -8.417627131083757, -12.787629401662883, -17.304216734478846, -21.83489909358283, -26.240758729150908, -30.381997147440327, -34.124129062036076, -37.34389111544941, -39.93491420690903, -41.811908192494265, -42.91406482271294, -43.20905057903335, -42.69445609878963, -41.39654881671591, -39.3695397148796, -36.69457110575471, -33.47440210274064, -29.828560402804694, -25.889287359050517, -21.79465244551888, -17.681940508210705, -13.68259914464903, -9.916971247583408, -6.48759057666417, -3.476414073714026, -0.9426175259236055, 1.0797542852117032, 2.5827950293097857, 3.582569241585383, 4.1170334734841365, 4.243045713346878, 4.0325993719698525, 3.5676430022868373, 2.9350012649655044, 2.2214133010291137, 1.5089600070487295, 0.8704944801319339, 0.36600736123657246, 0.04008565327900216, -0.07973321917188046, 0.01644278083650145, 0.3214231234092883, 0.8124446848587314, 1.4536635352424179, 2.199254746786793, 2.9968892045706275, 3.7917289127212044, 4.530371631813116, 5.164163991515728, 5.652405702652037, 5.96502500095636, 6.084154492034474, 6.004790125305346, 5.735068774369982, 5.295030638673117, 4.714990173322388, 4.033328581079503, 3.2936430132322765, 2.5414375002331524, 1.8212110194669497, 1.1735515049892553, 0.6323425127668739, 0.22271314020340954, -0.040357024777750085, -0.1527573815373497, -0.12119004673291535, 0.037610994748385154, 0.29843827095693176, 0.6296474320312093, 0.9954770643649823, 1.3587917437188777, 1.6840746107065478, 1.939670713399799, 2.099923609719304, 2.147235756342661, 2.0732911244934056, 1.8791380667559245, 1.5751376887911288, 1.1801549582132376, 0.7200148242082278, 0.22534215114001405, -0.270641060336431, -0.7346878498538874, -1.1361253572965813, -1.44917808970086, -1.6548485931029688, -1.7423601986703647, -1.7103324295216633, -1.5668007403918889, -1.3285067274249032, -1.0198233866369477, -0.6713762454403679, -0.3174686597438393, 0.00654717042163646, 0.2668012193557125, 0.4333559357128897, 0.4828416804744625, 0.4004620094171211, 0.18132482015092072, -0.16879705031545, -0.6332589021020062, -1.185302072873507, -1.7895829682354725, -2.4039558327753876, -2.9819606515939783, -3.4760278539149922, -3.840297345499317, -4.033419227452079, -4.021578913485807, -3.780921121192764, -3.2990756831109214, -2.576423262911741, -1.6264764529992364, -0.47532628603163196, 0.8393318284554202, 2.270279132651302, 3.763474899316661, 5.26035971984593, 6.700965064346273, 8.02825865171028, 9.190203547383824, 10.141890162659275, 10.849010577435802, 11.289743498309036, 11.454168685763726, 11.344846772620171, 10.977671874057584, 10.379436076128147, 9.585481644601046, 8.6385745346635, 7.586020267818709, 6.476372344588343, 5.3569889280528455, 4.27200248348017, 3.2595090875749353, 2.3501141036894238, 1.5660242895021363, 0.9203248203487564, 0.41703432289141507, 0.051883629968508954, -0.18660468251744977, -0.31559310531019463, -0.3561031032154422, -0.3311826441059412, -0.263989958768511, -0.17603470756416975, -0.08576658237458842, -0.007501830671842115, 0.049289312078781476, 0.08019354896727846, 0.08562457588679044, 0.07022846104487088, 0.04195822237924311, 0.010906833052591956, -0.011975570076899764, -0.016165283527084656, 0.007234551424999689, 0.06451451554375014, 0.15864599953291916, 0.2888576178909477, 0.4506285509543606, 0.6360612724723341, 0.8343918236716601, 1.0328768777732504, 1.218054194716639, 1.376693954660202, 1.496781243950792, 1.568839443108075, 1.5867342478086948, 1.5478700345054548, 1.453534504958559, 1.3092154985552866, 1.1237653105071688, 0.9086247605202105, 0.6772079354474404, 0.4438198123540115, 0.2222945530913569, 0.02503659651811321, -0.1378125677276584, -0.259251697418313, -0.3358643249411897, -0.36791376016627797, -0.3591987009883429, -0.31659992973935736, -0.2493083589732191, -0.16788669489924474, -0.0832192414376474, -0.005449534375515918, 0.05704374835304668, 0.09846911193994724, 0.1161851751969513, 0.11100782859202843, 0.08716368998656893, 0.051862673712776454, 0.014609043715114007, -0.013734016758159004, -0.022099138904979717, -0.0004164323034333619, 0.05921571763278253, 0.16150021059720235, 0.30715254993235186, 0.4924110243957564, 0.7090101426070976, 0.9445257196357619, 1.1830125450908835, 1.4061595558420596, 1.5948179386716803, 1.730398176509336, 1.7964030770599988, 1.7803140004975757, 1.6746977543201824, 1.4780612189963702, 1.1956095076252249, 0.8393488072666347, 0.4272179402383739, -0.017836184306115718, -0.46917236774241766, -0.8986532144654021, -1.2787737927415583, -1.584834133911952, -1.7971316799585901, -1.902756729996822, -1.8969320479977696, -1.7841061569978496, -1.5778235235649716, -1.2999301389509668, -0.9794094056144946, -0.6504130574217614, -0.3493264721477978, -0.11185567762754141, 0.029964075652932732, 0.05097390324023661, -0.06437802231675088, -0.32002351316420413, -0.7069532345321058, -1.2028204004996605, -1.7728165589965708, -2.37152260712319, -2.9459566133576685, -3.4394728717168115, -3.7962266507034346, -3.966231445257535, -3.9109032878365486, -3.6077248643344526, -3.053617082605904, -2.269131092832384, -1.300932272340735, -0.22000355497898033, 0.8792083944812981, 1.8798600021369198, 2.649092188545658, 3.0472627965554975, 2.931331769651851, 2.1624757911246717, 0.6207054593419202, -1.7896919423855437, -5.136121055630536, -9.446847509680413, -14.702915540278251, -20.842334710298196, -27.759198777019204, -35.29970747075315, -43.27122275696466, -51.4518447416479, -59.59326626831733, -67.42945512520369, -74.6942750429372, -81.13643619648185, -86.53839010294705, -90.7197919977399, -93.5412841709542, -94.88548805225119, -94.66240029632047, -92.84481871593003, -89.5070721756882, -84.91081296965281, -79.36042655444258], 'positive_zeros': ['1.01744785319254563633680935866004', '1.34881688111813669497844332957545', '1.72961070521057083969756575443661', '1.79132471176815784913935094853503', '1.91567279256723325850775734848290', '2.42699300375549371635289576143303', '2.48879222199384426746535480916973', '2.59370304921240172669784540959716', '2.73628733802795498688653071977852', '3.09894491594962057300634086381109', '3.35873048892368180947563464810831', '3.56664128045689956330690632640650', '3.67100109962997912643688113428004', '3.82051502018409079458829175889469', '4.21646364595958317774311483032273', '4.40805970154516567454665185291531', '4.88684229121382040607593207121963', '5.20005867571978764589651700068658', '5.33482320956236270498058127441871', '5.46752956099092504322238041428863', '5.72648802451290532709877088875097', '5.73446132254347911490935766187085', '6.11143029717960571168313149907338', '6.12984138892570850837899311394337', '6.65178131888186445211632935896412', '6.78301333430879920235250662537018', '6.87932764747160780006812648860549', '6.89073102628061941940093782513314', '7.27531223430914406521706644419229', '7.40377979514936588079982489723546', '7.66671107081127696613527175535059', '7.82123874280720697361108988426734', '7.82875547099513004962649312126501', '7.85112417643350528972404773426401', '8.238379663553752492327505514845522', '8.462215259844453526488994317676052', '8.486598404841199127328423712055703', '8.669000955731970123621907712791836', '8.918420523154487632564019935505153', '9.322770750282052068034587249665596'], 'prelabel': '8-2883e4-1.1-c0e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.199501742983705, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c0e4-0', 'trace_hash': 819291327773900820, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.01744785319254563633680935866', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.34881688111813669497844332958', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.72961070521057083969756575444', 'prec': 103}}
• 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': 4.285554939393596, 'bad_primes': [3, 31], 'central_character': '1.1', 'conductor': 69084174032721, 'conductor_radical': 93, 'degree': 8, 'dirichlet_coefficients': [1, 0, 2, 4, 0, 0, 1, 0, 1, 0, 0, 8, -1, 0, 0, 10, 0, 0, 1, 0, 2, 0, 0, 0, -2, 0, -2, 4, 0, 0, 0, 0, 0, 0, 0, 4, -1, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 20, 1, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 1, 20, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, -4, 4, 0, 0, -1, 0, -4, 0, 0, 8, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, -8], 'euler11': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler13': [1, 1, 0, -1, -1, -1, 0, 1, 1], 'euler17': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler19': [1, -1, 0, 1, -1, 1, 0, -1, 1], 'euler2': [1, 0, -4, 0, 6, 0, -4, 0, 1], 'euler23': [1, 0, -4, 0, 6, 0, -4, 0, 1], 'euler29': [1, 0, -4, 0, 6, 0, -4, 0, 1], 'euler3': [1, -2, 3, -2, 1, 0, 0, 0, 0], 'euler31': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler37': [1, 1, 0, -1, -1, -1, 0, 1, 1], 'euler41': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler43': [1, 1, 0, -1, -1, -1, 0, 1, 1], 'euler47': [1, 0, -4, 0, 6, 0, -4, 0, 1], 'euler5': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler53': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler59': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler61': [1, -2, 3, -4, 5, -4, 3, -2, 1], 'euler67': [1, -1, 0, 1, -1, 1, 0, -1, 1], 'euler7': [1, -1, 0, 1, -1, 1, 0, -1, 1], 'euler71': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler73': [1, 1, 0, -1, -1, -1, 0, 1, 1], 'euler79': [1, 1, 0, -1, -1, -1, 0, 1, 1], 'euler83': [1, 0, 2, 0, 3, 0, 2, 0, 1], 'euler89': [1, 0, -4, 0, 6, 0, -4, 0, 1], 'euler97': [1, 2, 3, 4, 5, 4, 3, 2, 1], 'euler_factors': [[1, 0, -4, 0, 6, 0, -4, 0, 1], [1, -2, 3, -2, 1, 0, 0, 0, 0], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, -1, 0, 1, -1, 1, 0, -1, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, 1, 0, -1, -1, -1, 0, 1, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, -1, 0, 1, -1, 1, 0, -1, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, -1, -1, -1, 0, 1, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, 1, 0, -1, -1, -1, 0, 1, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, -2, 3, -4, 5, -4, 3, -2, 1], [1, -1, 0, 1, -1, 1, 0, -1, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, 1, 0, -1, -1, -1, 0, 1, 1], [1, 1, 0, -1, -1, -1, 0, 1, 1], [1, 0, 2, 0, 3, 0, 2, 0, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 2, 3, 4, 5, 4, 3, 2, 1]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2883/1/h/b'], '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': '8-2883e4-1.1-c0e4-0-5', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0, 0, 0], 'order_of_vanishing': 0, 'prelabel': '8-2883e4-1.1-c0e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.199501742983705, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e4-0', 'trace_hash': 819291327773900820, 'z1': {'__RealLiteral__': 0, 'data': '1.01744785319254563633680935866', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '1289768381800453906017978423821,1709828528947374321777682890250,2192542048621351267357622390094,2428403765338741635398451422795', 'Lhash_array': ['1289768381800453906017978423821', '1709828528947374321777682890250', '2192542048621351267357622390094', '2428403765338741635398451422795'], 'factors': ['2-2883-93.56-c0-0-1', '2-2883-93.56-c0-0-4', '2-2883-93.5-c0-0-5', '2-2883-93.5-c0-0-6'], 'label': '8-2883e4-1.1-c0e4-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2883/1/h/b'}