-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_143.21', 'a10': [1.0, 0.0], 'a2': [2.9010907910729803e-30, -1.0], 'a3': [1.0, 0.0], 'a4': [-1.0, -1.4081532572346456e-30], 'a5': [-7.040766286173228e-31, 1.0], 'a6': [2.9010907910729803e-30, -1.0], 'a7': [-7.040766286173228e-31, 1.0], 'a8': [-7.040766286173228e-31, 1.0], 'a9': [1.0, 0.0], 'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [13, [1]]], 'bad_primes': [11, 13], 'central_character': '143.21', 'coeff_info': ['x^4 - 1', '6.12323399573677e-17 + 1.00000000000000*I', '\\\\zeta_{4}'], 'conductor': 143, 'conductor_radical': 143, 'conjugate': 'dirichlet_L_143.109', 'degree': 1, 'dirichlet_coefficients': [1, '-I', 1, -1, 'I', '-I', 'I', 'I', 1, 1, 0, -1, 0, 1, 'I', 1, 1, '-I', '-I', '-I', 'I', 0, -1, 'I', -1, 0, 1, '-I', -1, 1, 'I', '-I', 0, '-I', -1, -1, '-I', -1, 0, -1, '-I', 1, 1, 0, 'I', 'I', '-I', 1, -1, 'I', 1, 0, 1, '-I', 0, -1, '-I', 'I', '-I', '-I', -1, 1, 'I', -1, 0, 0, 'I', -1, -1, 'I', 'I', 'I', 'I', -1, -1, 'I', 0, 0, -1, 'I', 1, -1, '-I', '-I', 'I', '-I', -1, 0, '-I', 1, 0, 1, 'I', -1, 1, '-I', 'I', 'I', 0, 1], 'euler_factors': [[1, 0], [1, 1], [1, '-I'], [1, 1], [0], [0], [1, '-I'], [1, 'I'], [1, 'I'], [1, 1], [1, 1], [1, 0], [1, -1], [1, 0], [1, 1], [1, 'I'], [1, 1], [1, 1], [1, '-I'], [1, '-I'], [1, '-I'], [1, 'I'], [1, 0], [1, -1], [1, 'I'], [1, -1]], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-143-143.21-r0-0-0', 'leading_term': '1.34680592565278997011617017674-0.199419855240011059689927309269*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/143/21', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.3614898016648582, 1.5809876296822925, 1.8886618123910033, 1.943654954489641, 1.6111283128959433, 0.9644674134732791, 0.23446570102467748, -0.28902700625964145, -0.395509640347394, -0.08023670999565291, 0.4122758778340799, 0.6754647782284728, 0.3446218095635808, -0.669872209320147, -2.049423474672847, -3.138757828993553, -3.231277320394013, -1.9520433594122024, 0.46260415661102056, 3.171322482783318, 5.068922866716089, 5.321903079493817, 3.820079092762416, 1.2759617844310278, -1.1202608143176078, -2.325737883868134, -2.0009469688616304, -0.6628444231294741, 0.6699952560409168, 1.1302601557918346, 0.5415497540300646, -0.5083870045071364, -1.1141913585302659, -0.7185968141460491, 0.4678541950408844, 1.6022995207898194, 1.821528855438048, 0.8974177921573189, -0.5536904577915084, -1.4908096260213908, -1.2140977924664016, 0.09038704518418447, 1.4618268483722043, 1.8860110595311073, 1.097747637516452, -0.17126776137917696, -0.7455419789165475, 0.015254771760469441, 1.5668349551585432, 2.4280409026906384, 1.2336419821379805, -2.1498583991882785, -6.309610053231468, -9.090337034055654, -8.99852741707706, -6.202187487276748, -2.3863778596851986, 0.431161105757776, 1.2384050138181315, 0.5337062074608655, -0.3221413554637327, -0.3153268196092367, 0.4563729003587735, 1.0524332887999037, 0.6830289793776876, -0.4959744394963137, -1.5102150801173628, -1.4955076594020849, -0.5598910281154479, 0.25962373328966437, -0.028312714539003612, -1.326120865230636, -2.344087333684529, -1.6576030884384751, 0.9231484324612506, 3.905460045807523, 5.114031677845384, 3.4138294736295407, -0.27416202339112333, -3.5825218259873797, -4.4995312824332245, -2.8919335722616055, -0.4802213852276689, 0.6911170604170245, -0.04422223841081316, -1.5616457841560376, -2.125957111478594, -1.0503378804290062, 0.6827660679624865, 1.3792888642018382, 0.25055285270974126, -1.8269107363988029, -3.1084482245558926, -2.570300097348748, -0.7921610705369531, 0.6736074899170162, 0.7981423632583942, -0.028211186710259656, -0.5506916538554909, -0.050947369065593384, 0.8696266949675798, 0.9734160882615852, -0.1283684001179596, -1.2611463721902874, -0.6430165639215802, 2.2621909325700758, 5.808652664638641, 7.256222496587097, 5.096881385299388, 0.5421111393764937, -3.28594529847342, -3.8635393713489963, -1.2901258611036186, 1.9529266307500515, 3.235622004864381, 1.9440829516140337, -0.3236660866306799, -1.5152834399825768, -1.0194463861120415, 0.08248595806123211, 0.438755369014775, -0.10748560198641473, -0.549577824097557, -0.10183744052671279, 0.6837772659766662, 0.3943139067178494, -1.6104785474319887, -4.191806783386549, -5.282987436432431, -3.8783375396536, -1.132335615480725, 0.6698811900150878, 0.33964938310197185, -1.0414909371815153, -1.2718876686348146, 0.5970447138921925, 3.1017306607648747, 3.706869900160175, 1.3830976196306533, -2.1849839295727396, -4.064945862980526, -2.8327753592053804, 0.10497511861149955, 1.9353234731538855, 1.1697962645029427, -1.041593189769289, -2.2485984577876543, -1.2213548225007822, 0.9411180048965135, 2.1360705803046667, 1.4804376300423792, 0.060308827906990804, -0.4633347875572399, 0.2720290569914605, 1.068584352249378, 0.7156208954507304, -0.5173932992631044, -1.2128785683033374, -0.583862967842154, 0.44041797640044245, 0.26218385314242465, -1.244151588247153, -2.0149884692300364, 0.32361750400157946, 5.688528915973082, 10.864591758745664, 11.98862044506669, 7.997767408198161, 1.6778271857068825, -2.7748444918035076, -3.315839700745504, -1.3302153799396332, 0.3614340868519995, 0.44668975688909884, -0.03313749527783727, 0.5055231072855793, 2.046615606194966, 2.9773807485577586, 2.103560344207621, 0.2120435235096239, -0.7072887203326208, 0.29595273110872033, 2.0390864108503637, 2.564546622587738, 1.3985753924285473, 0.07564683749213942, 0.28304557479329795, 1.778717125689861, 2.574098724136524, 1.2714913883258756, -1.1380154460825853, -2.221444280098572, -0.8677343476688995, 1.2828528470372214, 1.5446817870027016, -0.7192522571333724, -3.1055166596983406, -2.5940741299792935, 1.101779972930471, 4.92886251785625, 5.42758230636563, 2.169265363141557, -1.9043961963575853, -3.5062700606495385, -2.10933702518391, 0.04190429267843196, 0.6797228541612869, -0.2111797976431498, -0.9516573798440087, -0.5076190748165538, 0.3486668553821976, 0.31391188017295046, -0.5652867633872447, -0.9214675311816665, -0.008618097502020394, 0.997666950595935, 0.24665817989713149, -2.2878375661153227, -4.1865888237615785, -2.99847599787847, 0.8224386886326254, 3.9415685211598683, 3.4655485400250914, 0.06633424036268502, -2.6145012583194616, -1.777917162397714, 1.6152843553851945, 3.9856905599551147, 3.005354981828158, -0.09469852712983926, -2.176428224796985, -1.7039133710480447, -0.0864035448747772, 0.425002002242693, -0.4778760781899704, -1.0473852026239145, 0.01486965368657806, 1.6811406576756127, 1.7365560755318634, -0.45561461714477797, -2.9908748713033697, -3.500941070863381, -1.7917753754808645, 0.11293406261530337, 0.48309493284633, -0.2070193771413384, -0.29168271388914585, 0.5813397025041287, 0.844729578062342, -0.7073056277258417, -2.627306913492454, -1.7895848254552806, 2.9672165309862173, 8.71241229140871, 10.72600852008898, 7.159350051281296, 1.0348752260003804, -2.710313920316054, -1.997008409050933, 0.8800514852317404, 2.3062278406705627, 1.2430827419161758, -0.31203250496268886, -0.28128011541940867, 1.007825718248905, 1.6522099172268414, 0.851746313358436, -0.15783677868901874, 0.015098229427415233, 0.9000164628109693, 0.794626975428762, -0.7675764877199811, -2.0918483295520023, -1.4078341437586979, 0.595013872349763, 1.232427991195643, -0.9186718890396879, -3.914596128211184, -4.366150949267304, -1.401462139982903, 2.0501390792317573, 2.400313240928269, -0.5710446448844305, -3.5253171881381005, -3.43458361408333, -0.91746893066556, 0.8500327347594181, 0.16908268485848835, -1.1797105906747671, -0.34162336742349053, 2.8641038925093967, 5.503435814241522, 4.908893235243726, 1.731442102687822, -0.9593073726698701, -1.2359943028208071, -0.13776908502101912, 0.20235282176242791, -0.5976346695681917, -1.0322798147255465, -0.16932322884215606, 0.8440106788309267, 0.363186437913091, -1.265695212978868, -1.880099110111342, -0.3679111413192594, 1.5839887854098895, 1.5345460090017788, -0.17998815409531144, -0.1379634558820226, 4.221955835744573, 10.86866510510906, 14.448491831189934, 11.64052992114737, 4.68723177354789, -0.918694918516965, -1.944971746639625, 0.013377803133269677, 1.3166906524225157, 0.5787385434356771, -0.566759418844648, -0.4213402752847137, 0.4234427698932444, 0.2891232335079019, -0.883651680055597, -1.2888585835990394, 0.13212720718138407, 1.8920617823382355, 1.6622891173318475, -0.6033174116407661, -2.332828528064807, -1.4647656439467158, 0.9181889146688517, 1.9382648209438762, 0.5896473050714517, -1.0637994727104392, -0.7930793385255961, 0.6108522287811059, 0.2455944081395323, -2.8389526240251515, -5.7294630727677465, -4.7507268708801265, -0.031712711320091985, 4.192519120439126, 4.19904276963941, 0.8727405273518187, -1.593356726186648, -0.6822221137566772, 1.8566180746229066, 2.6759303625094972, 1.071191667690496, -0.5103771718663933, 0.0680380288115394, 1.9384373709841731, 2.63965137713136, 1.415120353634647, -0.06895878263235342, -0.2544345815753275, 0.2863241606318384, 0.11816287145346185, -0.5655768427112062, -0.12433975328801646, 1.6665132179290623, 2.2882786943670093, -0.7132159567718496, -5.9320751420243285, -8.576016891492262, -5.4995455809781255, 0.9563979517889296, 5.192414286425795, 4.318671656231016, 0.9083946680757343, -0.5374207267424665, 1.1180980973719794, 2.9603345759782287, 2.2568530345361077, -0.11203236513429035, -1.2145428392828057, -0.1011004369849566, 1.1783311831344276, 0.672130287217706, -0.7307375111100103, -0.6727354085716318, 1.2126297384088005, 2.635349128239064, 1.7409250520884516, -0.30762018584600737, -0.8528351480255093, 0.688330012719589, 2.1125746236246887, 1.548877393594068, 0.05836725296409942, 0.04546116642854133, 1.672143339368551, 2.417265089165524, 0.6689170646353577, -1.5647081168341281, -0.9571792044607156, 2.439759776066395, 4.444787940754418, 1.563733127694721, -4.361085062003506, -7.690503909131863, -5.193863999236707, 0.46154565548830784, 3.976545140562849, 3.2288287450804614, 0.7186519665116908, -0.336144224854696, 0.27418474544590626, 0.6224721603805942, -0.007001525118492686, -0.30374574090125683, 0.5670819492134315, 1.277469422469101, 0.20843866109944117, -1.8497045616011527, -2.3919012435269447, -0.6754140797783733, 0.9355624819019916, 0.02532923520769824, -2.3982420592784006, -3.0252415106866746, -0.8635538375051481, 0.8646170826735877, -1.4271729398747335, -6.759712166461543, -10.123510933846966, -8.190102196611665, -3.1504537245427224, 0.08121746007579272, -0.3785273262508941, -1.9003028212827027, -1.5165372045180827, 0.17104193603537235, 0.4194124499152757, -1.3165525577668735, -2.369308884080346, -0.5519439597652605, 2.6493222740441063, 3.8447934346549046, 2.0584773297752124, -0.2385368047812159, -0.573754827430148, 0.48832700179580435, 0.7197814605398494, -0.3269998722311535, -0.875331937249496, 0.08039068396682479, 1.04814944129604, 0.3871116736455153, -0.7367965945656877, 0.3656324724796181, 3.561728797994025, 4.730655306543032, 0.40446877619228494, -7.2056119158599685, -11.653055154781786, -9.148788996940198, -2.7052512032769025, 1.5147148750456072, 1.048499614402173, -1.0961948943848923, -1.1953992218080887, 0.5938442889024955, 1.4135189576604517, 0.1685244501816095, -1.151276998151328, -0.6576975051275477, 0.7473990093772529, 0.9844953156161205, -0.01267799646433818, -0.42985758078715447, 0.25413093648609475, 0.07467416408747937, -2.4561151272719552, -5.44914181839653, -5.450506752411584, -2.0031327433313773, 1.3400445388101074, 1.3408448279036924, -0.8958869683153854, -1.6855744734857612, 0.06393078306795853, 1.442842400902001, -0.09172329964020592, -2.6872682638873275, -2.2631529606344567, 1.8159806868567892, 5.335531734529776, 4.300574673444806, -0.0742228788011006, -2.9894506583358744, -2.0468330857483363, 0.26404458133546527, 0.4356624995009977, -1.457688046267311, -2.483469507175065, -1.2682251956594892, 0.3235081463984898, 0.24374160413681067, -0.7852136478650421, -0.6845329924499842, 0.6286623742747669, 1.1491303904432542, 0.021351960756174154, -1.0208897377282375, -0.4590562672423442, 0.20856638169423225, -1.5845456352749858, -5.056130332112066, -5.890048838016668, -1.6499286383164582, 4.089814024084255, 5.06825813985991, -0.32470197462444567, -6.887577304397084, -8.530639065340782, -4.92481693814195, -0.8611934123988655, 0.07930846219369564, -0.9193845829702352, -0.9453106376398062, 0.24224299223283852, 0.6275208025896936, -0.2728302886000877, -0.4343402273086544, 1.3442840592816485, 3.0589013799826628, 2.0080675605115053, -1.2407739828996045, -3.2844015739120986, -2.317581534795702, -0.33239083963468163, -0.04134169534031198, -1.1147941571682072, -1.2104815089860708, -0.06116716154915174, -0.2173948400428611, -3.0030134571917584, -5.6965872749423845, -4.688535197856478, -0.6785876343570832, 1.6128848793857882, -0.5258256448972742, -4.044623681954925, -4.027761124863068, -0.2358475157851812, 2.505274964386997, 0.6296555436705575, -3.5930981650936187, -5.1606344719917905, -2.6582358245316544, 0.5670440873842783, 1.2626608628937634, 0.07300413516448628, -0.42956813146961703, 0.25847443043013424, 0.4846920518064014, -0.32152278135362417, -0.6093177545204063, 0.5186639147966886, 1.4283865653554475, 0.41748338017377584, -1.0974705651778993, -0.0795337712984045, 3.4203024593398883, 5.3336589098643525, 2.6765106948203257, -1.950662077785601, -3.11255338342736, 0.560919435552148, 4.511995537071381, 4.10127087306576, 0.4008506595549174, -1.6934764355504077, -0.12162267494733, 2.0759092757893955, 1.534512851440155, -0.7510847999365566, -1.291391576488913, 0.6624398853164482, 2.2215189001720055, 1.2884696067764163, -0.45521787147559634, -0.3066325606588199, 1.3085117871007839, 1.557091921548166, -0.3970701280429718, -2.0131964635139536, -1.1079396143405706, 0.9181146168869999, 1.1865965439583712, -0.44810194747463883, -1.4291520014181953, -0.5643414485471161, 0.31363975064458716, -0.21105566279911114, -0.12216957340841128, 3.173341994718099, 7.681488608132715, 7.513258573661936, 0.015554903244823493, -9.741826006008473, -13.773470587720595, -9.844699095945598, -3.2666475549312177, -0.02956800117417248, -0.4669823802472935, -0.9351208914019591, 0.23584702473074415, 1.1196337334941804, 0.13052994077627061, -1.2418196050227843, -0.9164050201930324, 0.42685519301147645, 0.5295080029611858, -0.7244439711254644, -1.0987200238875852, 0.256323006610019, 1.125031379430303, -0.37798176358973284, -2.4154028619011956, -1.6690466679733806, 1.5970599579448412, 3.298117418760249, 1.1022165527744918, -2.0047209226349336, -1.6513281517312357, 1.7246819156302353, 3.2691161390390184, 0.3766811399190577, -3.6778140890137547, -4.226165360171094, -1.4082479737988314, 0.5705856293704622, -0.31054036026183623, -1.3015899268729227, 0.5394459628286087, 3.6089648330209125, 3.870032665817103], 'positive_zeros': ['1.99186038023159428592907653850', '2.86498193845507398310267851533', '3.87902836160945670415023845392', '5.57161013016443388615336441778', '7.34156714308083819189119634563', '8.57796918751578707860580631286', '9.53618723002762083502467689273', '10.51378756011140101897220819914', '11.75508572499933904760137322450', '12.794039622823664800730306192', '14.01622387828450638726706495356', '14.68395598549785445365728462994', '15.75899307621424045180797662702', '17.7475026724002339978638826385', '18.60771241545713260730512505506', '19.209487375541422627719730679583', '20.192459502316748997494280397885', '21.42777122515488642078797568691', '21.86527030567575588465633192701', '23.03001967850807613420195593503', '24.353270375809263249492422174126', '25.70539392596836969162759472809', '26.24020138640260851527912062714', '27.37102970789468360418788068494', '28.16549400790406089641513945318', '29.51637344008484848054353697432', '30.30260959012796097557153409075', '30.95475874483002861993282824768', '31.84665480277071448751082383358', '32.59101817222727591318665499793', '34.09852607701260661519269826392', '35.1159427575957659062633033744', '36.20144763701340151084647133623', '37.159556913721220960745154749923', '37.76475979724138363294081252849', '38.47502010730274103366856951033', '39.14819612038033253524254567562', '40.77939829710976396399983004722', '41.32994285841321862526039696802', '42.11256266067767034789109193533', '43.24487744323178309561330956617', '44.36349093812192779390007920656', '45.16854727446660686240250560637', '46.11392168988892343230649819144', '47.203752598673907678565885322312', '47.727958183325358601841828876341', '48.62453396955529099294114490321', '49.53443432763356563301101221387', '50.069110310467175383502235138861', '50.912378637556745456661804095530', '52.592894269488809624954584608295', '53.6532872063484372904901294603', '54.32979189597614922731507075518', '54.489732207389892636549989007', '55.977648561380267221015056999718', '56.505738036036262714923746050834', '57.85107843065811997021634003237', '58.01575083219583787842661850451', '59.225718109639455862591882890852', '60.11713997131545095781593883107', '60.85836111498644523035969081849', '61.79630089076164375477515843068', '62.968056850276862324785423484954', '64.05452090404738674200008867829', '64.629080673083891902496510873837', '65.480851913684384847932088579553', '66.06258984504084022869007777855', '66.87707782853024964056963767693', '67.53855849388528431849321257273', '68.68844989604538726374290824605', '69.69307811989573093968183402002', '70.48588999618630640634997822576', '71.552966596700435160979451148018', '72.52081598752205841741102828057', '72.98924368721052570835038423090', '73.747298677740734496708280382532', '74.63630516554377678529981571685', '75.911063282999977071380707763192', '76.47181277978546111552788237656', '76.99937207527682012971776692030', '77.70561500545871782989388830438', '78.5813942695492937246798781328', '80.06020995483146577909826082493', '80.84082279318633665456934252643', '81.79167239307826975827818326089', '82.268029286848979163247045289054', '83.364987203445826913711820021905', '83.74390787492144764500989103614', '84.55509541101703215989406889463', '85.53029482956615649925469216854', '86.15221091344811354434257805815', '87.299409365924459628204394116401', '88.075984607961174265112480860', '89.18008350740350445111211654886', '89.72100812477935030330061709585', '90.35527644489318529922715616754', '91.73455120011565670931830135195', '92.54684205799562198818744718298', '92.920171485280347833515670630997', '93.79148951285068829865738274493', '94.451776723839798165233875331780', '95.36399030929889462446795661640', '96.21488708580271188194353586605', '96.58172163507063252930173549453', '98.365916526912937679557480801937', '99.06056607809836565063373245889', '99.8212780188006432082047667370', '100.459230922432990694909929504934', '101.02679413901370002482881404518', '101.85440326078084443559368320760', '102.738713667734894341351234305675', '103.62865540494575674914270289212', '104.46702439802590382675591046182', '105.16784416100174197215185586861', '105.66170893615305378421603222677', '106.8768595545151056619095403405', '107.8916302739767223984310397294', '108.5226215570768497085958409866', '109.547956303844160248690845885080', '109.98656914899936933362528070320', '111.22814050803327228342593519241', '111.70412248790422940322567617325', '112.240221747967932683177005295812', '112.84018290385558571785624779420', '113.70076004136402740038356029432', '114.95339014366977855698228751364', '116.049030498569224863930853128833', '116.40167097132715682989443956406', '117.48417712788855735351358632204', '118.14389111552534466072890444160', '118.891276976038316866717961431480', '119.50776681347858248239483068003', '120.571683382379824353140697785410', '121.13795849150452305338025460272', '122.20548481069841830926379856472', '122.48624929089052623538807067051', '123.51685992073072053850221041853', '124.16520455035348514432151608989', '125.087147284237960045941542796231', '126.22358978314911420301289230244', '127.31962121253530473535011763465', '127.70857425190320321478254820706', '128.43458390145919690883461313402', '128.89826119896125383886891770297', '129.720183404480130416502975506280', '130.72347594215605151559369418946', '131.25364895482690551782674077604', '132.29311924755553429251435956161', '132.69189721528194648709770884892', '134.35657658654523129662619258085', '134.60648027271569927129735957754', '135.58843827832202977115636573264', '136.03664584342226682851965522164', '136.929261604084289447757882807632', '138.0803383216290838007395119358', '138.613038824741065539727989085228', '139.28973226036856506669687379582', '139.98143000986969443517269557648', '140.71179654586820785750852177837', '141.201796062507680355077903415121', '142.20561305462533957590671233761', '143.59492006479570473271561400902', '144.204647715047209987290092217795', '144.902314693500453356482595022017', '145.65512423359524707615430586591', '146.39030439648962069529767762492', '147.1836083584565438481465993752', '147.710830674671601961076695916194', '148.14136840735210485667902444273', '149.534883007649768442276667884006', '150.19101560924065685663596580392', '150.92852474125032746267672429968', '151.55196627415593434476807919709', '152.37881942322486585032681231678', '153.43229301312724241964363844116', '154.328898491456646258940166023806', '154.77605621637292101690047654172', '155.85035252980561244519984130122', '156.324956848145205793603799874591', '157.04682683754285991055749079870', '157.81695664486039421717359638545', '158.57403917462831749309018264991', '158.8405368556648722279241220461', '160.083093799677640444129531078909', '160.92335809247537085113003906232', '162.33410969275409018656662774921', '162.5369524921543360961667173984', '163.374306244811643363088627579700', '163.979017272004435460394107159485', '164.48324290822579055473233153332', '165.51100898790572895197129643619', '166.66000967574184586850212748082', '166.85639405515985832292401525337', '167.83276940235254130320042911975', '168.07416951015890717919580495722', '169.43075944299311013524094993171', '169.954380987727697275669247568146', '170.95511144398073805265908650045', '171.61096315234263151229370408789', '172.74233637353977611692860481808', '173.45703757804584879397462405627', '173.962916890122410605101620451695', '174.57957786003795869648690671836', '175.19802154298336975615253221597', '176.00880794309549371339406179166', '176.57159005070821716624560028180', '177.672475006202592013346144375228', '178.401137189818388934272774437404', '179.41009760312181533077750211723', '180.01428466149437093757359358499', '180.83049465017122237313063700317', '181.475176540623911316363572221862', '182.39814207087821884873316524366', '182.87887780668178476848918457482', '183.69754015340592885151791984884', '184.53592160817359167382115971832', '185.23611815591884803194647849715', '186.084434681564586521454579191723', '186.48245508816300655877635037510', '186.89805947868974931298388883719', '188.12548492137519511405210360523', '189.69822819160328791708287169451', '189.845803665614171514704699618332', '190.57596515300017583983939582689', '191.274806892184705247845096728730', '192.079326700386543006025660525089', '192.64506792162362460150117306572', '193.388991692883269388207829740904', '194.01118889837334412979082309334', '194.85582378126861935730990449686', '195.721187938994046286928436862666', '196.41270468856736562821602026655', '197.21400595823875524869328517213', '198.29151958202492180544527103061', '198.68931706857773871843341748324', '199.31806862080247285104761716783'], 'prelabel': '1-143-143.21-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': -0.09358352090549943, 'root_number': '0.957092026489052849592220722565-0.289784148688430089716825558519*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0467917604527', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(4)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.25864182481704648894563025212-0.257862269403826467323771957738*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.99186038023', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.86498193846', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.87902836161', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'bad_primes': [11, 13], 'central_character': '143.21', 'conductor': 143, 'conductor_radical': 143, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/143/21'], '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': '1-143-143.21-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': '1-143-143.21-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': -0.046791760452749714, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.99186038023', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_143.21', 'Lhash_array': ['dirichlet_L_143.21'], 'label': '1-143-143.21-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/143/21'}