Lfunction data - 1-3864-3864.443-r0-0-0

Formats: - HTML - YAML - JSON - 2025-11-07T05:41:23.665766

• 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_3864.443', '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': [-0.9954719225730846, 0.09505604330418266], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 17.944340560412993, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1]], [23, [1]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '3864.443', 'coeff_info': ['x^66 - 1', '0.995471922573085 + 0.0950560433041827*I', '\\\\zeta_{66}'], 'conductor': 3864, 'conductor_radical': 966, 'conjugate': 'dirichlet_L_3864.3707', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^98', 0, 0, 0, 0, 0, 'a^13', 0, 'a^63', 0, 0, 0, 'a^37', 0, 'a^62', 0, 0, 0, 0, 0, 'a^64', 0, 0, 0, 'a^48', 0, 'a^49', 0, 0, 0, 0, 0, 'a^89', 0, 0, 0, 'a^21', 0, 'a^6', 0, 0, 0, 'a^44', 0, 0, 0, 0, 0, 'a^58', 0, 'a^45', 0, 0, 0, 'a^19', 0, 'a^71', 0, 0, 0, 'a^29', 0, 'a^64', 0, 0, 0, 'a^42', 0, 'a^40', 0, 0, 0, 0, 0, 'a^41', 0, 0, 0, 'a^45', 0, 'a^69', 0, 0, 0, 'a^17', 0, 0, 0, 0, 0, 'a^94', 0, 'a^54', 0, 0, 0], 'euler_factors': [[0], [0], [1, 'a^98'], [0], [1, 'a^13'], [1, 'a^63'], [1, 'a^37'], [1, 'a^62'], [0], [1, 'a^48'], [1, 'a^49'], [1, 'a^89'], [1, 'a^21'], [1, 'a^6'], [1, 'a^44'], [1, 'a^58'], [1, 'a^19'], [1, 'a^71'], [1, 'a^64'], [1, 'a^42'], [1, 'a^40'], [1, 'a^41'], [1, 'a^45'], [1, 'a^17'], [1, 'a^54'], [1, 'a^34']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-3864-3864.443-r0-0-0', 'leading_term': '1.19404542842797765858248433678-0.449962605997673700002444581557*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/3864/443', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.2760136488086526, 0.6656801359026285, -0.6146421221146479, -1.9078398588044467, -1.7570198014873335, 0.23283715556707754, 2.459031064334081, 2.7100885949548976, 0.6402554777326009, -1.5800671106446162, -1.601362968782456, 0.3157300155197667, 1.6136819845075823, 0.7545612452050415, -0.6716499520443097, -0.08836100983572949, 2.287429692494368, 3.309304570604963, 1.0556429776140126, -2.2536931846226453, -2.9209475028342697, -0.6675356110201357, 1.0897598858139659, 0.12658910585324917, -1.5383986249530377, -0.9386290326845659, 1.132343626220714, 1.2758836114663359, -1.0737640298825037, -2.404558894524462, -0.4144366377635761, 2.154731339676002, 1.3918518174748877, -1.8279356102143844, -3.05504229510231, -0.9321278670655513, 1.0534511901214711, 0.39405570269803636, -0.5243156320537573, 1.2110683628350125, 3.723647463057439, 3.2100906264696105, 0.495536865196932, 0.15500393334614396, 3.111045550005426, 4.823240058774762, 2.398266333113012, -0.8626271089983788, -0.9156889315074441, 0.7443570969282473, 0.3798405910950306, -1.1615070902582714, -0.1495833176860151, 2.772907803925505, 2.8782191710758367, -0.6749957664405093, -2.9390128211325344, -1.144111364315591, 0.8716663481982663, -0.5822824359545463, -2.7815847550857296, -1.611584925130407, 1.1424272327197318, 1.1201854857590625, -0.8638536288103251, -0.739690439764247, 0.8242903573447233, -0.671955227490257, -4.8697678937895335, -5.978549390642159, -2.2054937778841612, 1.170186597664908, 0.5961926614723692, -0.5605407800843545, 0.855931663980209, 1.9203873912780745, -0.2808000950176782, -2.469443565081333, -1.0090808379432392, 0.9694406034017683, -1.037521448171814, -4.433086286158966, -3.8058438597194426, -0.5351362215185032, -0.18119325945051806, -2.484865598801101, -2.3456692057263453, 0.4409407450444041, 1.078298394226236, -0.8965129127026441, -0.986077914903762, 1.0136855571033636, 0.1467338313215248, -3.8206423109574477, -4.717925188636572, -0.6600592352197662, 2.4022195373427424, 0.986117832833701, -0.7370726234586855, 0.22800041917520755, 0.4178394488371392, -2.037226498123306, -2.66869949529598, 0.7441895804025633, 3.049057855165203, 0.8777992985783248, -1.0889150315100709, 0.9173334558731837, 2.558076226181612, -0.1634566592548259, -3.072840586120942, -1.6325327803877867, 0.8714741185054123, 0.2968014635334865, -0.5882737551072723, 1.1487600347987537, 1.5898936713170368, -2.303274934731762, -5.314926930420544, -2.6327631044500337, 1.2926425157639998, 0.8596472468531485, -0.9968148105202794, 0.3270812006330052, 2.0002021660243057, 0.22810613210774172, -1.5854958307852527, 0.12873593437600722, 1.4071699636215185, -1.306531176448678, -3.336489377368513, -0.5155245930482031, 2.3604220397114366, 0.47594825698646154, -1.957743890150218, -0.1959122127334003, 2.0990026623808675, 0.839011708660849, -0.4398951041945899, 1.3686657771296364, 2.112409642525231, -0.6279822521868635, -1.5083712004876517, 2.151681871842359, 4.182952747772634, 0.9380749380473382, -1.8407794368512054, -0.1899396132851801, 1.170677179467527, -0.7752590103041438, -1.6005063976672333, 0.42339735388275535, 0.3583435575949237, -2.5451299175151747, -2.3625391124343507, 1.363739382986527, 1.8241518157805579, -1.8383361570220387, -2.7534738066036324, 0.2630480267934777, 1.060873166762252, -1.0813958028658388, -0.7152313266703916, 1.8279495475842062, 1.351972915398707, -0.7097148057730803, 0.8036204656777786, 3.2420926458836012, 0.9618528510378508, -2.5823364030434623, -0.9079142423232709, 2.8290850713314537, 2.163567429009678, -0.43389344697920684, 0.12352319378044462, 1.0495107331090998, -1.118727708384419, -2.216410726830687, 0.37826719805299525, 0.9704155095980388, -3.022789300373038, -4.857193134293594, -1.3765955058124069, 0.9603689016214767, -0.8063648828013026, -1.0333541699207092, 1.8512121417237357, 2.197715665688645, -0.40652215625362065, -0.32810778658338996, 1.6965848784321569, 0.20891897243815777, -2.53503414624501, -0.7547429796814852, 2.081687372200573, -0.4711896762628715, -4.6021762735376335, -3.4865686711338753, -0.11630634047317562, 0.06400162389259903, -0.26614211330733467, 1.5078533279835362, 0.730968348372301, -3.8099436121878822, -5.068781832489935, -1.2463978486115619, 0.2852667161512795, -2.332344901953032, -2.508984055566439, 0.33651420318516845, -0.1475467755398036, -3.265179987389621, -2.741320913481152, -0.042277668355062026, -0.6306382556014206, -2.051866698977511, -0.3591001724270921, -0.20503005154489604, -4.983308909763681, -7.701740193499746, -3.704965558768325, 0.29606378068609285, -0.4101781343671712, -0.7752199906693117, 1.3911279496288937, 1.0656942120109876, -1.5342480678519763, -0.713196824530392, 1.6729892339336843, -0.40103193544546856, -3.5843185995415734, -1.4541148108355955, 1.8841576173860133, 0.1480429599276642, -2.43630637435571, -0.8339288122944266, 0.3460110920298714, -2.1736742354628578, -2.97992176854562, -0.25444068343627835, 0.29071769198983216, -1.3301416571616604, 0.7391703604866049, 4.032206252691842, 1.3994275288403224, -3.7314543226137533, -3.363184564442972, -0.14711859870358066, -0.3497894617879487, -1.1748657729412695, 0.728017775945415, 0.7187647931050622, -2.5886951655136823, -2.6027883196008887, 1.181597208401925, 1.4063155899904711, -1.4978563592455472, -0.25822630636192345, 3.358923596471949, 2.296034662581127, -0.744638869405363, 0.39501236569374704, 2.3246890629250188, 0.7006834013295894, -0.16017037567865547, 1.6696459925946614, 0.29153379490898745, -4.12365412046807, -3.6425559632465374, 1.1376184168261512, 2.00842925851181, -0.11987241553450075, 1.4623899901444388, 4.148433906977919, 2.303789681720961, -0.2427500644155366, 0.6292298357304517, 0.4489158861629529, -1.9961093185570449, -0.26563335035130403, 4.8695650899906, 4.85494227636302, 0.4563455046049494, -0.15062528374759554, 1.821455544333479, 0.19148860059345033, -1.9684014720584186, -0.11203329129143323, 0.961019006713257, -1.750406998697251, -2.397651556613205, 0.01909732231873274, -1.1000321029193882, -4.482919644424684, -2.654788918178256, 1.5813626826748701, 0.4701555478479042, -2.649598624288633, -1.2502901709955978, 0.9686033476290912, 0.06649631927423133, 0.5868674691111058, 3.2778207517999096, 1.9601960668957301, -1.7110559599240958, -0.16267114530379226, 3.6621414430266115, 2.043212343109512, -1.3385761612189877, 0.0038450084456459472, 1.729548322181282, -0.34412689852418066, -0.9726292998618802, 1.3846562345442128, 0.5402426662207019, -2.700630865986062, -1.765305339322199, 0.6090836907466401, -1.3978995529173457, -2.6920017185492005, 1.814069717220362, 5.046067289523747, 2.0234418361312243, -0.5585758585686613, 0.605522005351004, 0.3554982903096341, -0.8068723881016879, 1.7697146598591986, 3.760659402356125, 0.15738184748542178, -2.4169430857839367, 1.0172473323747173, 3.117394421493112, -0.0031178207295739216, -1.4720224738951022, 0.13634614037304377, -1.2993973298691712, -3.9390450579354397, -1.770937849997394, 1.3427915699709938, 0.43780176270194915, 0.37907303367400647, 3.107329975224907, 1.5799822227504392, -3.7785243264668615, -3.7982802426311864, 0.6853659651374612, 1.1249864753652121, -0.9934670208652709, 0.19166615821346036, 1.4089455182667971, -0.061253459430403306, 1.2613938004661762, 5.130182705337058, 3.788165512932075, -0.909619997749875, -0.5862020281159251, 1.906286508683455, -0.32131678707349565, -2.774045229575, -0.5725262943459531, 0.4545726467481523, -2.219745523397949, -2.164915750917757, 0.6173329327346602, 0.18564311857273713, -0.5358817895918293, 3.101895579729644, 4.580325056595544, -0.45078820003779274, -3.6187031436983856, -0.8612768271222424, 0.41083897101225497, -1.3017445533365397, 0.08357872867075275, 2.5461493068459022, 0.8819111907060654, -0.5173447786195519, 1.4567357804222847, 0.22414890474238064, -4.720947540759747, -4.465581891655861, 0.43798217766745556, 1.1783108950195238, -0.6524520853221584, 1.2747234796801128, 2.8912949492491737, 0.12579528778064342, -1.1991781925425404, 0.5333637055166016, -0.895233666505344, -3.680348238670572, -1.3551680381738194, 1.3361717209110486, -1.708746312333698, -3.7922327789036987, 0.009320580457223953, 2.280149680116919, 0.020505038869068182, -0.2633579453697139, 1.160595154840671, -0.7729710306208475, -2.005221224864439, 1.275026377203316, 2.2037135458968944, -1.4354691168039577, -1.2884102249680331, 2.8104144640230313, 2.159914703074747, -1.5401902070944453, -0.7698524439163683, 1.2385435223740437, -0.15854360658627276, -0.08460790481406213, 2.4122701107024382, 0.7248415135119199, -2.932803156510752, -1.074926389250992, 2.061439114983338, 0.11215471753527051, -0.9214487134670847, 2.911832438780382, 3.903349924940882, 0.17403366572956253, -0.5914457897085338, 1.3160779824356659, 0.28599692219045453, -0.47797982318371446, 1.4493162845557457, -0.8139120467906344, -7.11020037875283, -7.283559240261695, -1.7658676675628127, -0.06929560845472303, -0.9853622020844671, 1.2187318437223347, 2.191944816752919, -0.7844914440957347, -0.9285415027000959, 2.0836191179153967, 1.1636594423154074, -1.2791043290726274, 0.4563482987534265, 0.7611926217847902, -4.092715929597571, -5.533305364827059, -1.0057768145486454, 0.5640220230492332, -1.6705903510204885, -0.9340418213410524, 0.4882717696894747, -1.4616308103737563, -1.5098934513256563, 1.3156752759512789, -0.44102063829610105, -4.623791713329777, -2.458386074683775, 1.9758257756935917, 0.6226876935891399, -1.5834596896272723, 0.274549786630729, 0.4892469920010268, -1.7119737846952807, -0.07595738743641953, 2.4003828663579845, -0.21379578570926025, -2.4116642424350774, -0.27112892703980046, -0.8154435738360943, -4.372931387559499, -2.323475678903969, 2.8782520317724867, 2.2689100043789985, -0.6883442804708417, 0.2708210430845892, 0.8806474888678468, -0.4696253022886892, 1.583099152921359, 3.8202451267946667, -0.1381439711259766, -3.6474945395234055, -0.20325255676618562, 2.6088938784635896, 0.5344809605052441, 0.7639429982629999, 3.418163929235767, 1.6693973469023329, -1.1598770518035866, 0.3176751986598294, 0.7159992262182616, -2.147152742141448, -1.5811721554336309, 0.6242292101959857, -2.763159061174036, -6.288124490435903, -2.7443331346344535, 0.881499711890281, -0.6797760826689295, -0.7588791883332937, 1.751621617247113, 0.7138032553218013, -1.0157484539187978, 1.0902300746631748, 1.0714375721258356, -2.6811626663328347, -1.710834282769087, 2.8426295593700015, 1.7799884387934821, -1.6168118443367079, 0.2387603968080977, 2.344520168432218, 0.4376254036804505, 0.5122793163498536, 2.591821997379225, 0.5343125059957158, -1.7593541910745238, 0.6773267522554516, 0.9498533981033275, -3.3987037933047173, -3.4290842433271536, 0.7325261375507715, 0.1305601651380228, -2.711418397046188, -1.125249518140984, 0.012154269789964877, -2.473298803392052, -2.1386923408191336, 0.5683614232688061, -0.2914327725995444, -0.11090532766932333, 5.266431721155243, 6.947462103519538, 1.6497809639337044, -0.7543991908035312, 1.3401260144047251, 0.5030275857203268, -0.9939789003142447, 1.4283515299697875, 2.0796368774866276, -0.5873129019261277, 0.46171189543059143, 2.8952695891718045, -0.28801493006805035, -3.2716065248275834, -0.36348715037875357, 0.7480475855068507, -2.6193766959628, -2.1669230107146764, 1.2988597983387178, 0.3609647651648594, -1.478443175546116, 0.16347196101600908, -0.11881397042367946, -2.0782692278495185, 1.06571278558128, 4.479807317045032, 0.7251409386223769, -2.7741390425832013, 0.14071196629459698, 1.6527076979689688, -0.9538246592849831, -0.9188351418251988, 0.1601240427705425, -2.132647986939495, -1.9837796304345199, 2.220858674708178, 1.9384043204486017, -1.8643559364559397, -0.8643090240959624, 1.0642996964684155, -1.736562356251531, -2.047387299816946, 2.8529851209251356, 3.8577471674189727, 0.41611698640892675, -0.09872586504592862, 0.215392690456711, -1.4006846754191762, 0.9835755867509484, 5.549375998189813, 3.0297163120346253, -2.2286696157581076, -0.7290697109652495, 2.1672360934724377, 0.295061187735999, -0.3918472899948532, 1.113013971921124, -1.382822100050436, -4.059817927624108, -1.3496702739794062, 0.44855490319742247, -1.1159284498962054, 1.1803384189968826, 4.835933050481724, 1.8926096070527811, -1.6848734830723502, 0.9533331440854302, 2.4756197967745255, -0.5900713671639211, -1.0932487848294261, 0.22289102018689835, -1.7565128262491623, -1.957189090813176, 1.7650756150577953, 1.445170301010556, -1.531210308768333, 1.54927619417815, 5.64837982612878, 2.719619959325681, -0.5895837905596175, 0.7240496599293643, 0.5287532425035754, -0.6799462229626092, 2.3644361698394927, 4.079158779328587, 0.5026520036328628, -0.5515442398519601, 1.662619134598099, -0.5227686254576434, -2.994116671731174, 1.2104055897416384, 4.451767072326668, 1.3093229281013303, -0.42588588291517915, 0.7981349287923832, -0.9286252587447777, -2.112625263963262, 0.6652226324218092, 0.380313160130576, -2.7741537250548096, -0.12354929533917143, 4.274368179795784, 1.8240216646284484, -1.3391711462442344, 0.29942794485410085, -0.23081966883490432, -3.4675757121438258, -2.1970874207022764, 0.4357791858574756, -0.32527966134703873, 1.1134279982769786], 'positive_zeros': ['0.49301666153626838754575692307', '1.53329703243339350372992358493', '2.5761676904459978292424204280', '3.39092867573510049023863429320', '4.20371168156407639940742711613', '4.70204555104107171067391863237', '5.717468477000566833194381638382', '6.644650372385986160573403930664', '7.20776935023743712456370803236', '7.95113528852594439377252474903', '8.62362167719511591204567796819', '9.41663420077917918030011663401', '10.13978614824496022730744635163', '11.04681290524308399112086892393', '11.64613764295892797703275390134', '12.030607029349444299655276127017', '13.211427153787574169463324532237', '13.40610224813951572030532083386', '14.58153697474718138216545325174', '15.159409609037389312155878767', '15.694466502896195448751099368470', '16.26734987641305833978775051140', '17.13450030314880632491909257434', '17.94301983456282778415163532202', '18.36699326750509975502394872471', '19.23013926636922665454820005574', '19.856659636306170940573727045395', '20.44238385590205875288757973633', '20.87213737438593889492907787817', '22.038296783769487081949648483203', '22.606427374899971154434257188388', '22.99011377499947034155584991447', '23.72194937617388486986359383469', '24.49143906446638737854202533601', '24.904261426694739670244674820663', '26.02248643054103600985848070250', '26.21291767960998425834928744946', '27.13523401871339078810778757796', '27.67741783931395059458991997035', '28.27516763248258711474411602042', '28.764152517141709457996457125', '29.731763346475005775445764631686', '30.43942835772204775297258206764', '30.888662479584443421729609227506', '31.32170549436815862269569772263', '32.13062400110442043268178628223', '32.901265832715261649683502171121', '33.33942803907388318536364956397', '34.04972435280262629530175407218', '34.85800388275853224388208824881', '35.36968059709662726520068734482', '35.77121621112859833999081024278', '36.40797644216415897822835341092', '37.36839433398931342112902783737', '37.92579984234820835258033326251', '38.39573199176929198357900270087', '39.08778676989065906807193405630', '39.67206323912565306633862689855', '40.1979052981292656582302761258', '40.976258282280733901741136055276', '41.60579550976778018083307980018', '42.20679333924511909922966632497', '42.93748045627097527958215868604', '43.24645456027071530613059372463', '44.00004927506894922271903825976', '44.530735300594707181438900012003', '45.38223704692975351162445186309', '45.96019637428541248247672484637', '46.46394955746823246036200315266', '47.12431741385460768117849290845', '47.54576149699669923476895223004', '48.32313994323955414599224220948', '48.91531131273986795254384846613', '49.66012653767176850935546454947', '50.15865402883005246221241787299', '50.71066200283947492589206379989', '51.421872775317329459122616972296', '51.78839900868261228150222439919', '52.568283353204310411435162466', '53.19163667359017880153260291796', '53.986189638130508682221133266579', '54.35287688666855330077153126281', '54.873215619354331160043641260953', '55.58506229118184307816794556475', '56.03658084435169508278318462345', '56.9890311532216120838977035846', '57.38978008435867620477300627993', '57.93587190724896126973451612138', '58.69469530139065065021110691103', '59.10954113194916552287471712181', '59.706931572985931938147876807368', '60.374492554551593265206885030982', '60.90635675290926816787928389118', '61.893848045622259901483848939968', '62.20662316960735040540259662333', '62.56439366171951698298412988625', '63.184875850233212195275848057141', '64.18353720837265859363304221327', '64.42719240674252289065163423438', '65.267304710827253178849435893615', '65.60833984756638327065974214549', '66.57181025827895482830957585925', '66.76207222687772030326010085663', '67.5558233189659746811426877709', '67.78616678993636112718106390610', '69.0137309046104536945089545833', '69.29926010550204876198465270372', '69.81018255032103541471850233770', '70.43264656411675661726117013245', '71.01261942183770597369042359687', '71.53096593947842112634547753785', '72.29300556210578100331544788900', '72.82537281251284013858548759361', '73.54746271418032229846683367447', '73.82061149651655771637130675132', '74.72063532001268446310363323095', '75.0535828396782174413820930372', '75.56481504282535890099959005274', '76.32605051422039957120119236742', '77.21457210342956684027881635223', '77.425047877497117491389163216096', '78.0233751849518438177556023677', '78.51603402913742023979098858836', '79.27374379949700157302145869759', '79.82907109295896555122355174364', '80.333386191786570770316410382952', '81.14217016695914757897756312432', '81.51674960821674175813372733285', '82.29684189651152074363196361063', '82.53855796241442931963186372724', '83.146928746042365802868268061550', '83.98193988141813869859204611747', '84.65450110532832052916386009415', '84.82577720824765641606502789849', '85.87274488780164564098794915385', '86.11577980116292957355111960710', '86.62217032325731152920919744814', '87.20466964624522733088525099976', '88.17140947495674030251297074461', '88.46062379757928646982796646599', '89.08129944256285386068120726169', '89.700396659852804650322309052006', '90.136571101637413296245622625', '90.933763134315198495538531524630', '91.124535536050768447954557357618', '92.04590497422424613145701767877', '92.53907643539188057860760284223', '93.25490160186875023745935949459', '93.76844947110986775197290243398', '93.96514848731802769776613068674', '94.83311880837674550574732186535', '95.32424030888142445861693606934', '96.09154435268265129707498181808', '96.56209014358370366703217100855', '97.14639016929340899114404025638', '97.63379474790538404338048908568', '98.174382948898044448213738642863', '98.93290425603367709398850778191', '99.23113328040249938840463922306', '99.900176305325624827617118020693', '100.80314248168125795036344276272', '101.12759334747185911773633218000', '101.62540376307490222381332885346', '102.02717731007225870224465884226', '102.82271497241552409358098724475', '103.36767716923276126955466529393', '104.062229029383308454973551981923', '104.64830625501649910225428058431', '104.839308448737813140884479532525', '105.7641583893350320069106916346', '106.34844627921703122480610045112', '106.48711621796062520469462345751', '107.27938502946435635474909068302', '108.06936807415940113264475139066', '108.57841069662269601120916153212', '109.036833487527421650853013050375', '109.671241624645225947367670904494', '109.85444488911727546254580173660', '110.8609489476752799421396178644', '111.307951734894994603991681797458', '111.84895569918835806863508930841', '112.56490798736446254623284168800', '112.88342200430443550606153809159', '113.66439375947150315562647064209', '114.09269852481771371644948800313', '114.44923395316049051487968075402', '115.289032127087865292941483205890', '116.02946765606231783129329158473', '116.332417182035010155799352734666', '116.86670711614380875328560224954', '117.60550826687832338732872137443', '117.920008823820853208269517084952', '118.45339623814268129081791420737', '119.34173350069895056552715029694', '119.84866266016705228391893484948', '120.17719924436833349368419563719', '120.949549258424480523080278723193', '121.45586549368629195332898832807', '121.783002042955592844306058290704', '122.603319234184412609541277218405', '123.00009667222528567311420743130', '123.749371840213999579791449904706', '124.37781973570314631053297366004', '124.73430645600084013790222241113', '125.23023735813979911728598814412', '125.83497935186531122389880753247', '126.44369487388785719778289754550', '126.97350882682111274221720549930', '127.66272788171811032254785025971', '128.209512915522072052206952159539', '128.72340282511429446243705513137', '129.074189570971553941772312458137', '129.73956810131240817260416086623', '130.39110583902954005738291285433', '130.94871497147242916059293857883', '131.34919628502850554309139908420', '132.204236454095142823196674529633', '132.58978151979450541748433823292', '133.16948875423068798483035905596', '133.526701150794852769482799161683', '134.01400025843108443952734110571', '135.19985946425258405367179240888', '135.28539673694049092264548717333', '135.807724500901910955646834214119', '136.48420183477977931682656300646', '136.97002075653712158423316351244', '137.612499129089169378509411665668', '138.07245328092448973105707285235', '138.50367898327117336334006576040', '139.456215930188937476362110600575', '139.77502306973083483460443681108', '140.44255301058841564441895413104', '140.74513732738014337704032983098', '141.405470363038691879122033535955', '141.8440053398212612423546746092', '142.64366375598484137201190454582', '143.18153977199625667826709503911', '143.713369443030722961364198195635', '144.129517943426587392582328638359', '144.694174015534002343925715405647', '145.29583107804993220530901705499', '145.98355287315987650980119371912', '146.1498018945880496579737014709', '146.99959720667088552690166632328', '147.70423597210552519772915181911', '148.0820828423620434588033494392', '148.611845371744390182632966118198', '148.903683720181000994851609977448', '149.679996419663445810094010807893', '150.32530184620459758756869288470', '151.065004556623361115128643230850', '151.09709923362482617113543959924', '152.01476563546405016617373266001', '152.4581990703503073902899133963', '152.89978523773171565129606138162', '153.60333478040085619739661691823', '153.87249079704361288760363138943', '154.86678041900794248566361003499', '155.22153552768192028976828857712', '155.71588081413360906440433789284', '156.33104429874055666573561910957', '156.74866497989966714112766965868', '157.28172568608136982976842747234', '157.920888035210191481833048637672', '158.5687943311502260738104774821', '159.04160082751078846295506219220', '159.77596445158581819321087095939', '159.90214081821151695166008947090', '160.66997602332883699164698292223', '161.18331447497255329792203146245', '161.642241462795284132773101073171', '162.43201584985996629189975919444', '162.82458218462597292962689823570', '163.59395506161579597075150545433', '163.75289949724933258775860037589', '164.59589484358473029040195455011', '164.953677774027705938692573503248', '165.3225609905710402417358016845', '166.3614989795344915810147466958', '166.68784040198211965357963547805', '167.249307294693782346388539519387', '167.66585730994282833708125416063', '168.356729034868240538716987382045', '168.70379558408339625728002390123', '169.35689170906337875680950914342', '170.0316192958795676574110753175', '170.39585663117338588315422709346', '171.11169930156719576916620291600', '171.601746178156312323441719634710', '172.1602303347575219511994800181', '172.48353427058158062346098867988', '173.059096197635852140330708748913', '173.78986660232012663903308009145', '174.36384511744047373929400163175', '174.888781371180060060965533794068', '175.47642166889023917908794349624', '175.67084505072619399950369772223', '176.39892227246747014091555934233', '177.019265004519959421231659339223', '177.58486112678200004346234503067', '177.97077344454231482333942037154', '178.57918730836099379859161577765', '179.4318722160375514351718179255', '179.715958278777374535552347554266', '180.048484119551346189965360130666', '180.5595915275913882547788945486', '181.40178062688593488235981887525', '181.92955678099862925288312262502', '182.537626080297101255250190213138', '182.88343032558372499246155543073', '183.32632065951334242248970560325', '184.19405799593137943839000116652', '184.47556794789125561170861626793', '184.913285481493704427842965951053', '185.74016959783520806780540852351', '186.174356377558280712426624391', '186.81660626699191385137942004218', '187.3806483844915606384022318692', '187.58111129269328737488389528656', '188.291383037204128206043484620058', '188.87244727568925821026224305541', '189.283160776864034756092889979032', '190.20092605927640411061084609115', '190.505413753872609797427057664465', '191.02005566322393456523447473239', '191.36601478736701013991516721712', '192.23228075711365819111674778538', '192.57552947338713649557649657711', '193.08538354701215411478619424900', '193.68502654529326272830120146250', '194.50122686076341668446417843878', '194.79297946319109305354299306448', '195.20641914763152197776600996614', '195.86651356035414960206809754003', '196.28538365575297178937397841105', '196.88192655678788900209911812517', '197.62609680785250397898181067389', '198.080664946147473636439200438', '198.41304610301693924979827796950', '199.28030757406940160499390551908', '199.59795990751827368673982946541', '199.88344756690220575931406690500'], 'prelabel': '1-3864-3864.443-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.944340560412993, 'root_angle': -0.11471307824892125, 'root_number': '0.751302051523341962132890047277-0.659958504284032709120018670649*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(66)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.931621122501748699622021548376-0.0349353160575745473469753730543*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.493016661536', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.53329703243', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.57616769045', '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': 17.944340560412993, 'bad_primes': [2, 3, 7, 23], 'central_character': '3864.443', 'conductor': 3864, 'conductor_radical': 966, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3864/443'], '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': '1-3864-3864.443-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': '1-3864-3864.443-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.944340560412993, 'root_angle': -0.11471307824892125, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.493016661536', 'prec': 47}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_3864.443', 'Lhash_array': ['dirichlet_L_3864.443'], 'factors': ['1-3864-3864.443-r0-0-0'], 'label': '1-3864-3864.443-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3864/443'}