Lfunction data - 1-3e4-81.23-r1-0-0

Formats: - HTML - YAML - JSON - 2026-05-13T16:53:45.712437

• 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_81.23', 'a10': [0.766044443118978, -0.6427876096865394], 'a2': [0.28680323271109026, 0.9579895123154889], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.8354878114129364, 0.549508978070806], 'a5': [-0.39607976603915684, -0.918216106880274], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.05814482891047583, 0.9983081582712682], 'a8': [-0.766044443118978, -0.6427876096865394], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 8.704658908364626, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]]], 'bad_primes': [3], 'central_character': '81.23', 'coeff_info': ['x^54 - 1', '0.993238357741943 + 0.116092914125230*I', '\\\\zeta_{54}'], 'conductor': 81, 'conductor_radical': 3, 'conjugate': 'dirichlet_L_81.74', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^11', 0, 'a^22', 'a^37', 0, 'a^14', 'a^33', 0, 'a^48', 'a^35', 0, 'a^34', 'a^25', 0, 'a^44', 'a^39', 0, 'a^42', 'a^5', 0, 'a^46', 'a^13', 0, 'a^20', 'a^45', 0, 'a^36', 'a^29', 0, 'a^4', 'a^1', 0, 'a^50', 'a^51', 0, 'a^30', 'a^53', 0, 'a^16', 'a^43', 0, 'a^26', 'a^3', 0, 'a^24', 'a^23', 0, 'a^28', 'a^31', 0, 'a^2', 'a^9', 0, 'a^18', 'a^47', 0, 'a^40', 'a^19', 0, 'a^32', 'a^15', 0, 'a^12', 'a^17', 0, 'a^52', 'a^7', 0, 'a^8', 'a^21', 0, 'a^6', 'a^41', 0, 'a^10', 'a^49', 0, 'a^38', 'a^27', 0, 'a^0', 'a^11', 0, 'a^22', 'a^37', 0, 'a^14', 'a^33', 0, 'a^48', 'a^35', 0, 'a^34', 'a^25', 0, 'a^44', 'a^39', 0, 'a^42'], 'euler_factors': [[1, 'a^11'], [0], [1, 'a^37'], [1, 'a^14'], [1, 'a^35'], [1, 'a^34'], [1, 'a^39'], [1, 'a^42'], [1, 'a^13'], [1, 'a^29'], [1, 'a^4'], [1, 'a^30'], [1, 'a^43'], [1, 'a^26'], [1, 'a^23'], [1, 'a^9'], [1, 'a^19'], [1, 'a^32'], [1, 'a^52'], [1, 'a^21'], [1, 'a^6'], [1, 'a^38'], [1, 'a^11'], [1, 'a^33'], [1, 'a^44'], [1, 'a^5']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-3e4-81.23-r1-0-0', 'leading_term': '0.363356729056739016287823282456-0.336210340829568556119255740641*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/81/23', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.4950409132905552, -0.27317433222357823, -1.1965954129193646, -2.211962614041872, -3.180059822605683, -3.8960883730602553, -4.143866655795211, -3.774344014864588, -2.7795471280382475, -1.3304270925705801, 0.24566067362646826, 1.5528531978565712, 2.258002312445063, 2.218768946603081, 1.5531310650611199, 0.6099300229407795, -0.16204817727341395, -0.40177928011717845, -0.0010953206781421589, 0.8340056145474155, 1.6680611837615875, 2.0416847350261755, 1.7071308873556823, 0.7746496637614485, -0.3187644731908724, -1.02303820016592, -0.976769401615591, -0.24069902436652083, 0.6774932633276445, 1.0501292300355387, 0.31532868340476733, -1.573820183731128, -4.03765980554867, -6.0883825426389615, -6.795876149729067, -5.769804535246263, -3.3942101420926205, -0.6665836153502049, 1.2949750247149272, 1.8204146537161026, 1.0184597090807015, -0.3218821619666471, -1.207840018924942, -1.0223747923224191, 0.13573342318971285, 1.5540136313117583, 2.3833922840855295, 2.1868361391252495, 1.206798664172486, 0.17691698473001854, -0.1973494931959005, 0.26228534764344413, 1.077088650730736, 1.4563468175287166, 0.8928323491838813, -0.4086787693870191, -1.5977093440614984, -1.737081352687126, -0.496898278894792, 1.5049053090754105, 2.9979460707788554, 2.848645309522656, 0.8409427381190724, -2.090178253419057, -4.373038123576902, -4.761354923117674, -3.1214019270979345, -0.5136740127479724, 1.498385921886306, 1.8549931110404805, 0.6444373158905294, -1.0429772335575862, -1.9278294012864887, -1.4324085765638728, -0.01813950796618368, 1.2469447576679407, 1.5373259755331494, 0.8803157225757632, 0.06711314065086449, -0.04801455874639234, 0.709405577075877, 1.6579157326787881, 1.8128038072922905, 0.7374112614462014, -1.005221042239761, -2.2105248887775746, -1.9692083694939508, -0.4561397306602376, 1.0932656327058692, 1.2770009388466366, -0.3504569845619111, -2.8028508192659487, -4.264581782920337, -3.384315096094365, -0.3123176397471336, 3.316008245222088, 5.4733996433870935, 5.117686150748358, 2.8374302904412034, 0.3083414840576042, -0.9881266697127606, -0.7829756870182749, -0.016110298021530897, 0.11229151894659499, -0.792021507804887, -2.019741275902781, -2.4424279568062954, -1.5552404474463617, 0.04242647105073934, 1.1528877949965712, 1.0304920297416074, 0.043988196043988945, -0.6581022361600486, -0.21240356370621202, 1.104282525040267, 2.033965402727603, 1.4482745930570151, -0.5192875747053847, -2.3497995499963187, -2.2476437973136036, 0.35857540961352585, 4.172226442477812, 6.852610700359722, 6.7225566799301255, 4.017216069912162, 0.6687696456447282, -1.1986229626565217, -0.8427505703766616, 0.708226157983615, 1.6991393457633623, 1.1777947646563305, -0.2950804151316461, -1.3006677464795495, -0.9226449750788575, 0.4322421423272244, 1.4660006727318549, 1.2296225751307701, -0.00016356573396485733, -1.020523626526192, -0.880020327709051, 0.19851927740340508, 1.053611932010945, 0.7845598416293675, -0.23203498561064095, -0.547240070330417, 1.0134502701192083, 4.061268232100263, 6.671036325256713, 6.853505183424236, 4.267808714743609, 0.6529253135887989, -1.4903662610357784, -0.9054001405074703, 1.431566140943911, 3.19353628517245, 2.6906661566156216, 0.2445836532274326, -2.2061256957637267, -2.8509907601019098, -1.5191697165259086, 0.3468454015449174, 1.1213813913489528, 0.4391100739899401, -0.666372721105742, -0.9549257775072594, -0.2653261205211938, 0.37948102391854904, -0.08297398230867895, -1.5476901581568343, -2.7332558025057647, -2.434803786958695, -0.8055135556711466, 0.6652711264614493, 0.5599179679094646, -0.9995423268485062, -2.31405282010748, -1.673836313262578, 0.8824314011437902, 3.3320673810456505, 3.324741371648019, 0.31110540842845136, -3.8074537798686086, -6.1734683932910155, -5.328206673129744, -2.3427550919637996, 0.24566774862303267, 0.6681338672376039, -0.710680027393155, -2.044246766192488, -1.904408071456129, -0.5564517335059528, 0.5393345591101689, 0.35934307453636416, -0.6335113322126313, -1.0649610552930269, -0.19312795321596643, 1.2277536684609727, 1.6929106348580445, 0.541670012967909, -1.277237546182409, -2.1236426090992473, -1.3664660990682411, -0.08537191357532412, 0.05208761822634048, -1.322992080660549, -2.5916157875302113, -1.532369523268614, 2.4170200245444877, 7.227845670594088, 9.737271218552817, 8.284252254159227, 4.121575125418305, 0.2904069128782169, -0.9933442259596978, -0.027582244074803468, 1.0795904115320543, 0.6616779531264995, -0.9599655457465487, -2.0567615352628295, -1.4453590489491674, 0.2583056894762166, 1.3275029640013678, 0.7477817368036167, -0.7742085225127631, -1.6437398202727926, -1.1049975451507794, 0.019308963264078147, 0.3650512420493328, -0.3198053567898008, -0.7758171707406858, 0.3746667630787709, 2.895533991381805, 4.823731100795064, 4.311298959041914, 1.6389031539246701, -0.749192283852551, -0.4410221581348395, 2.5674269092826068, 5.694877100741054, 6.086721596099019, 3.2427495840676657, -0.5668578331309866, -2.472467893232392, -1.6184841729696196, 0.29261596116023725, 0.9165393216704687, -0.3956574477789055, -2.1685573563389524, -2.5467320910826277, -1.2577990646713852, 0.24982303038697912, 0.497603765495892, -0.4410400684352142, -1.1858484988482025, -0.7635453010500362, 0.20174040793610984, 0.20846136354304037, -1.2810041252064064, -2.998292541589957, -3.1091515095009257, -1.2866345930869203, 0.6933236922365299, 0.6696422521215102, -1.5599824448147113, -3.7974079406726453, -3.560733827585837, -0.7024310202271662, 2.202872763984423, 2.2464691301382933, -0.9592971039370848, -4.81841799399017, -6.164073089841484, -4.1500491208209365, -0.8013340853785463, 1.160893334301528, 0.8781142646871238, -0.25309018684785917, -0.4910363892168266, 0.29400720458262647, 0.7207577235026166, -0.24069347914805103, -1.8874010549445448, -2.4931068037556603, -1.2834591171782483, 0.6166453609465483, 1.3956027458147926, 0.5774823305574261, -0.4735214178471188, -0.20516331611387517, 1.1744867675609507, 1.7706266578753904, 0.19993645406259236, -2.4777827476834013, -3.4169124377998434, -0.8268014989920407, 3.9049667077089034, 7.178975593865337, 6.467310020007446, 2.6683593887602677, -0.8397785703149576, -1.46011095214737, 0.35839568301665625, 2.020027106067643, 1.6751064011797543, -0.024975870980875378, -1.0124997150569714, -0.28834640531005046, 1.0284764809733247, 1.1444633627151766, -0.2620884392707104, -1.689578883903213, -1.602251921040748, -0.22090959743453803, 0.7862484105392639, 0.3256047624712889, -0.8086903478743164, -0.9390906890844269, 0.322662140959427, 1.3749136958459043, 0.4291304343387129, -2.120788856408052, -3.598222881344025, -1.669162994678147, 2.975426986927618, 6.87866586135622, 6.996949792605301, 3.605961128333666, -0.0842197878203354, -1.1940780072989061, 0.1026046843250748, 1.164370236365853, -0.03807616889534081, -2.752078553889379, -4.423665634112993, -3.5508077903783923, -1.190407356192734, 0.4095807060934157, 0.30679164238139617, -0.38286775676157314, -0.1626651719080644, 0.9046034296307369, 1.3540933537679025, 0.3184201925197645, -1.1591085901464746, -1.2238918458610148, 0.5015479821509837, 2.2344116626412807, 1.9667443249909649, -0.11139617643582672, -1.6119806234899243, -0.6110741761879184, 1.9513648843306732, 2.999477297601922, 0.6262386573167427, -3.582436062775373, -5.88225098765093, -4.1042867681581985, 0.14196968359176876, 3.1269864973674593, 2.7119742727635336, 0.1814156211265086, -1.552018242615603, -1.1529774869668894, 0.06615952713039909, 0.11394615397235827, -1.2179781355532582, -2.273563878618993, -1.718509639604145, -0.20630052911216443, 0.5009565309436466, -0.19354352508600478, -0.9184402042525259, -0.052850981470700185, 2.121446116808411, 3.545313237766721, 2.7677340843615443, 0.7411520126383032, -0.26834497270042557, 0.4865113207866391, 1.0667013597579627, -1.0020445936720772, -5.521055158483057, -9.124334869568086, -8.415606460932674, -3.5284288979392704, 1.7783768031946088, 3.702075800747576, 1.8884311663218056, -0.7615688605812458, -1.480147200094835, -0.35047214470596394, 0.45619659803533286, -0.35693871516151726, -1.6802532613162016, -1.5601693928463203, 0.24656581811126743, 1.8976107123215369, 1.6682504690453197, -0.019088057866800207, -1.2087348013300492, -0.8413915868063597, 0.05670317646459516, -0.10488221864757147, -1.220710698674191, -1.470824317912964, 0.2499902212497237, 2.4570739679482805, 2.354430109511245, -0.8927534164053887, -4.715027432545694, -5.532594074174353, -2.580571533610993, 1.1142047193007034, 1.8537643709017355, -0.863154909113777, -3.962374387683792, -4.240798050626754, -1.73270506512022, 0.6660128694000158, 0.6316708539582881, -1.1459315446061522, -2.1526383119569608, -1.1715281749908597, 0.4497686551067593, 0.7022509841289892, -0.5583177763156041, -1.5847047781369388, -1.0824814118490271, 0.1511339724050003, 0.37608453803522046, -0.6885876803062065, -1.391038226292109, -0.33589215855065446, 1.5273940722776225, 1.7603456222886698, -0.5462465029782573, -3.2789385907020656, -3.447322424991329, -0.696031437437638, 2.001423572110779, 1.5551077562530347, -1.658901790003128, -4.024186566911107, -2.616205596947908, 1.5503727011631756, 4.6156166492398825, 4.0250810859376465, 1.0504505068996668, -0.9764258417570421, -0.4168914816290168, 1.2784443989281322, 1.7999171655985806, 0.8039202057784836, -0.07843836395429901, 0.27622276800834417, 0.9039143352067336, 0.12081545672823643, -2.021538653488289, -3.4930976414443164, -2.7023074715911353, -0.5295046203915613, 0.691859766548515, 0.05035194752785554, -0.8786928184354594, -0.26161892846109464, 1.2329352547686299, 0.8339526812393575, -2.8791830174168105, -7.576059232648574, -9.063060886387072, -5.7011376171923684, -0.37938076624593453, 2.35711063151044, 0.9235845792078039, -2.0310894567041893, -2.9061870577621045, -1.045194106295309, 1.1064624901957467, 1.3253277576901794, 0.17656241356301583, -0.11676376817246624, 1.26020626223355, 2.697908221903127, 2.353314899596607, 0.5859960016392585, -0.5189441393117767, 0.14353547142909293, 1.3263315927265777, 1.1763944133648252, -0.22232342376144643, -0.919120278456317, 0.2226924768119224, 1.7790519978315655, 1.4771310481196982, -0.5968218460996599, -1.5073469344818264, 1.2083340110185024, 6.172738208612672, 9.015499435877029, 6.877387193923574, 1.546979732814708, -2.4133010985403116, -2.446658584306487, -0.2741903015255421, 0.6964914550640802, -0.5154251004140661, -1.6946367514358025, -0.5839046357461535, 2.1648268475910677, 3.8205635853056794, 2.9133257387713374, 0.8232708738663308, -0.19136523466845295, 0.21590178097870766, 0.44785657925246475, -0.5109839507551766, -1.5629308017837706, -1.074207274600106, 0.5998850008088349, 1.2176842478817838, -0.4726683275220106, -2.7897289145424, -2.9097046946744607, -0.4260731892364393, 1.847355981759669, 1.16584215511054, -1.6175743128568718, -2.7601308296871827, -0.026965131959278882, 4.400140622142344, 6.11551763147822, 3.356635011679494, -1.1019042449144294, -3.14663965260502, -1.7497629748501047, 0.4663634692000662, 0.774755794039242, -0.5645868655678175, -1.234590277060377, -0.1618201996974069, 1.2115165049216166, 1.1126482375515159, -0.07063904018465211, -0.3712254533842041, 0.965110904212565, 2.3324268416945473, 1.894230542369856, 0.15449397238162013, -0.5824380687606024, 0.6922572612307676, 2.147212643820559, 1.3824493564243059, -1.265590271875911, -2.8223187027194636, -1.4248890276108193, 0.9015281580692458, 0.2464197393955239, -4.441160806013406, -9.566296967197875, -10.476300141257834, -6.4248485312172035, -1.2076355939347752, 1.1094340624714665, 0.25393781805111215, -0.9109284730782579, -0.38057616966623503, 0.8205140685774993, 0.6530493309500423, -0.8340820212847233, -1.5129084228046763, -0.12625634610996386, 1.906415731470981, 2.2753467628588373, 0.7505683014580907, -0.633328742947134, -0.3706162629603439, 0.5684553581401868, 0.2968446355322005, -1.0924055358158857, -1.4315808847032117, 0.39401320585851013, 2.2662787006071565, 0.9539131854881658, -3.6676993019003747, -7.6599749002958735, -7.037298388452619, -2.2613251575764175, 2.1932444850361175, 2.8096481254430157, 0.6866904808670086, -0.3151299537214539, 1.5717317416140937, 4.125790425687235, 4.221498562745337, 1.7372692109113261, -0.5600473673167442, -0.6477519660553911, 0.45223330508893717, 0.4701068803358411, -0.9177610850095084, -1.8069933097875133, -0.8673607047560572, 0.7594189729943406, 1.0763698383710425, 0.05129518031644303, -0.3697247218479912, 0.8255303448980162, 1.9521011237963257, 0.7321750249672004, -2.3233693641055484, -3.9592662862918133, -2.0902234623960676, 1.255685791750604, 2.0178553613800823, -1.0011787099667164, -4.458879167327398, -4.3033312810155895, -0.5722639001144503, 2.6820264465473183, 2.217217214619349, -0.7385605447439301, -2.30211767735864, -0.7032452576698719, 1.9282958039619043, 2.605218110316505, 1.1320187156522896, -0.18645945242955514, 0.10472320111300999, 0.90969385129961, 0.6064225008975695, -0.3412945859628393, 0.012862093205618165, 2.119009084573175, 3.868115743192547, 3.1713494705724683, 0.7946387443328383, -0.51495734482645, 0.38649355068727487, 1.584893774273565, 0.9360385164333159, -0.5390718944668128], 'positive_zeros': ['0.20894345207890676410712156456', '3.07473948499261211020509268739', '4.91813922531657441151025791821', '5.62550559540942635239908718588', '7.40408799169888742101201837272', '8.51591018667244545920768409184', '9.44138874578974627967751968747', '11.649834833079240368025539153970', '12.73601158967182409515282805973', '13.72020782899272261220099578299', '15.39229807930233114643092781769', '15.81458540547049414045884208205', '17.097486041989516456339537228311', '18.20699500632264013620279377098', '19.46785013976502761027485779497', '21.00213821187028607593779073953', '21.99085356037206344837254490961', '23.12871578365785566535057565866', '24.41553581495347872145209722164', '24.72288504158318736821455545447', '26.07276812625422679067416840945', '27.267575932418893064730758575676', '28.075956980612592163331993380', '29.40119005333053009929463990005', '30.98643488120245369056025227063', '31.88341485840188860527194686552', '32.25261587483398102976926428065', '33.74149276078441211975906791590', '34.700657155318393204137348463812', '35.37176575680009646899515511803', '36.48947018463050433933684791276', '37.46791802711739585681149608293', '39.14086321329416415347657858276', '39.86374585908134989603899733720', '40.87680867802827808379520410040', '41.78226953301758976483614226726', '42.812462104863817936060358119860', '43.69828369102983568142182808405', '44.615530079029345087771083849869', '45.16053130057008035472421335182', '46.941519487267060019872942329575', '47.63301791429732822280076199875', '48.77705914094812479106539399182', '49.93379798292690317667903466583', '50.74104448754813338292851999115', '51.658609314361397440960778474895', '52.1630510857958056929628578952', '53.58146278651093215947798395564', '54.19541601882422154828020493887', '55.21789196551971261045153002002', '56.27380182877798847071853262956', '57.76973789653647488296903540166', '58.30266094645174680188051940999', '59.50071938403761055913144903622', '60.12124273265373949899211382254', '60.97992812502558503839300374061', '61.96702172244794992305527145157', '63.15563925572727798905622184243', '63.45806905058464156644377998073', '64.51927605423759221812555103332', '66.28521450895607729164047146606', '66.88101966587575868477272056170', '67.638758141699355996589871986393', '68.70311844428663492805192857076', '69.53225389500480546207036040083', '70.618473635536785063304393830963', '71.13327475134687138714167409966', '71.81316614632543364513449363834', '73.31022533157400083227600077598', '73.81262497616262280750167595591', '75.26036257508784536781637137222', '76.19591201341900600767121271315', '76.807419153886139351506186210944', '78.05810031026318105814880467550', '78.62514655749081737665484665449', '79.61143267993680034418695992357', '80.06627078488366312258049866188', '81.43065027603356598302998166805', '81.9942050188250168055044244334', '83.18893799019103691348432499369', '83.98765320029628463134779411003', '85.40330837992749613061503239006', '86.1708276762058038049851891532', '86.774249731743333766477123382482', '87.44971696835255926226265983664', '88.64114636709321325346702101230', '89.52034312876217086683440978294', '90.055578344356008710091328625289', '90.961806089573093584340042903591', '91.934135378649415590400985538035', '93.34153919875493545216929571656', '94.0119686188594198086422567257', '94.99536163602553792929234958242', '95.689517142937547014525045737311', '96.51544203303598832343446856020', '97.54729922694198796247605835490', '98.21290129229120212642394489518', '98.99675776960606973892968209581', '99.747907985928236158650185868531', '100.7486470720162783363729434046', '102.177804418816537413624933075633', '102.79352352234288308589515934884', '103.4323384988016739349674606812', '104.8809386192045097256126355433', '105.43726964271117080174167478171', '105.993784164090795873580060975788', '106.93671091618234030957504212059', '107.738340391336122370467740784323', '108.73469659690879547396958480949', '109.454625917422525601891913222528', '110.361548151859854521170739484058', '111.5520532248888567190876767355', '112.52230528642511243495813746991', '113.415016441145342065875461926571', '113.78923662717066865327345131102', '115.04972575830928655764214889053', '115.56622360269639090607352466461', '116.25921470711746288690744748549', '117.65537053693826476468924002170', '117.98394954368074350539898654894', '118.65148491947305666462751640296', '120.19343434684803900762586171493', '121.14568558428252372389869295503', '121.9612732456840397942318572881', '122.41487071422625504214889876162', '123.40126622879683961211469365867', '124.37164059711023206652389611589', '125.28307956970801046338915768822', '125.58253541535971345520474843614', '126.52970765329347802451512194948', '127.43155469237410871831123197689', '128.64015286944259398725111110303', '129.29769061615873169065508688852', '130.51031287165129592161963947837', '131.06190047635489672323302957098', '132.08676946649177224806332754531', '132.69531169130088147013330255967', '133.70474326734322097227808038682', '134.19935581389259018409150451186', '135.05524178014960714253680939958', '135.88067928454511682493596457277', '136.94000772746942264986020775168', '137.66614470484564182938110890465', '138.640434910534284161148766624144', '139.80749047473582564148580564298', '140.39010478856910254005042706674', '141.50367570208730365306915260610', '141.74772253081534190472840487506', '142.521718548400858902476716798006', '143.83823217392158600216228106700', '144.388218505597526371745613212425', '145.05416955368386774412502765057', '145.72231214866793766461403660001', '147.21359312776855541002232317711', '147.90710282613280392602311026252', '148.88133359751880190020402234764', '149.7447487009155924413267600163', '150.04688901962636705078190317169', '151.36377042128880548930476032263', '151.83890388597353723708829293662', '152.76491014422164155900323523681', '153.39726356126314717722842502052', '154.290533889196183372453919214037', '154.90552359932874512192293093267', '156.34507738123013057282902674661', '157.23184644861425958459861493656', '157.71548994884685496671953512941', '158.51045573127664194506856612274', '159.87594275725445610164190123016', '160.206042952410219979649739526795', '160.808994263406122241610512678588', '161.764567456274605253213873466163', '162.43863234978257750728167299213', '163.482367180036703229459141772849', '164.20040148023470994335017259155', '165.00196328281800941407287616161', '166.166224673113739639021820888058', '167.10568994014031564220716488439', '167.6934023354299233935744862084', '168.468817227329262389207837943917', '169.35481366316815599822896857669', '169.80904076138549932871947488463', '170.968361092280393606754252940106', '171.43645261176450816542630573511', '172.35883194431591525261484929672', '173.29655809500602615202142192125', '173.77485931613194137541128597213', '175.41710837951561345403780874808', '175.988448295106096243643037656696', '176.65265410640108759949323927321', '177.336205597383102254212965426254', '178.14333076096750716424955337315', '179.1972273151971307438861576275', '179.79952038677483938572991051816', '180.387838580694542840519912199', '181.19884757053734517817887857053', '181.953694301124908833115720690504', '183.26042829817249208300978128177', '184.17849495502672053850024123573', '184.47243546212901631572293114063', '185.83371553976368696979058218004', '186.42964425947502851646663242041', '187.000936277615545514034014557053', '187.96811032618765356130955132671', '188.765051413434604355257959204765', '189.19999396226291063154460875589', '190.08214527538946803387671778059', '191.1238466445115497839185031566', '191.79537242254717085550451263770', '192.85468465418612995153006155634', '193.67392401716309676248033675693', '194.45356765444789012806704627625', '195.54826374879333818219502416473', '195.89888310670824372131794657023', '196.74703299187421455833492972812', '197.184613472207767194462316250280', '198.563717037767131329776899360310', '198.979512407235632402154805469406', '199.86350667364608115435755293988'], 'prelabel': '1-3e4-81.23-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.704658908364626, 'root_angle': -0.23765432098765432, 'root_number': '0.0774924206719309462623706995201-0.996992941167792064800001681034*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.237654320988', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(54)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.750375694319999514903821435048+0.188737164127246620562654433871*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.208943452079', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '3.07473948499', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.91813922532', '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': 8.704658908364626, 'bad_primes': [3], 'central_character': '81.23', 'conductor': 81, 'conductor_radical': 3, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/81/23'], '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': '1-3e4-81.23-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-3e4-81.23-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.704658908364626, 'root_angle': -0.23765432098765432, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.208943452079', 'prec': 47}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_81.23', 'Lhash_array': ['dirichlet_L_81.23'], 'factors': ['1-3e4-81.23-r1-0-0'], 'label': '1-3e4-81.23-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/81/23'}