Lfunction data - 1-3751-3751.1028-r0-0-0

Formats: - HTML - YAML - JSON - 2025-10-08T22:44:27.177978

• 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_3751.1028', 'a10': [0.5800569095711982, 0.8145759520503357], 'a2': [-0.9983691039261356, 0.057088810862767986], 'a3': [0.6691306063588582, -0.7431448254773942], 'a4': [0.9934817353485502, -0.11399140989054063], 'a5': [-0.5326077245747999, -0.8463622225284244], 'a6': [-0.6256140694947214, 0.7801327041281206], 'a7': [0.7976796275621554, 0.6030814304654896], 'a8': [-0.985353835847693, 0.17052219263262378], 'a9': [-0.10452846326765347, -0.9945218953682733], 'algebraic': True, 'analytic_conductor': 17.41957076659139, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [31, [1]]], 'bad_primes': [11, 31], 'central_character': '3751.1028', 'coeff_info': ['x^165 - 1', '0.999275047800474 + 0.0380707084693900*I', '\\\\zeta_{165}'], 'conductor': 3751, 'conductor_radical': 341, 'conjugate': 'dirichlet_L_3751.2660', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^81', 'a^143', 'a^162', 'a^109', 'a^59', 'a^17', 'a^78', 'a^121', 'a^25', 0, 'a^140', 'a^151', 'a^98', 'a^87', 'a^159', 'a^119', 'a^37', 'a^68', 'a^106', 'a^160', 0, 'a^60', 'a^56', 'a^53', 'a^67', 'a^99', 'a^14', 'a^57', 'a^3', 0, 'a^75', 0, 'a^35', 'a^126', 'a^118', 'a^47', 'a^149', 'a^129', 'a^22', 'a^103', 'a^76', 'a^155', 0, 'a^65', 'a^141', 'a^18', 'a^137', 'a^34', 'a^134', 'a^97', 'a^148', 'a^61', 'a^15', 0, 'a^95', 'a^46', 'a^138', 'a^62', 'a^84', 'a^84', 0, 'a^138', 'a^156', 'a^95', 0, 'a^70', 'a^116', 'a^38', 'a^42', 'a^79', 'a^34', 'a^82', 'a^128', 'a^31', 'a^65', 0, 'a^45', 'a^131', 'a^103', 'a^77', 'a^19', 'a^94', 'a^157', 'a^63', 'a^71', 'a^35', 0, 'a^75', 'a^146', 'a^3', 'a^57', 0, 'a^99', 'a^12', 'a^53', 'a^111', 'a^115', 0, 'a^50'], 'euler_factors': [[1, 'a^81'], [1, 'a^143'], [1, 'a^109'], [1, 'a^17'], [0], [1, 'a^151'], [1, 'a^119'], [1, 'a^68'], [1, 'a^60'], [1, 'a^57'], [0], [1, 'a^47'], [1, 'a^103'], [1, 'a^155'], [1, 'a^18'], [1, 'a^61'], [1, 'a^62'], [1, 'a^84'], [1, 'a^70'], [1, 'a^79'], [1, 'a^82'], [1, 'a^131'], [1, 'a^94'], [1, 'a^75'], [1, 'a^111'], [1, 'a^51']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-3751-3751.1028-r0-0-0', 'leading_term': '0.0700500163719533870596163340576+0.0935348888499724691728113575866*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/3751/1028', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.11685794892041983, 0.9195586607575961, 1.323718457383198, 0.8942909481319173, 0.0805343929757377, -0.00044934424535817964, 0.9583016954166761, 1.6972322068967562, 0.735074412655474, -1.420821376984418, -2.151823459443347, 0.3414488613001925, 4.167065611242187, 4.968225577748839, 0.7668328224699779, -5.112874621652924, -7.1979875052369335, -3.97838134660857, 0.3808380955946368, 1.0622039398726049, -1.8226846146849085, -4.040162798240748, -2.9735865358987605, -0.4991711825612362, 0.3643316192598923, -0.3797188242217065, -0.6204597840716851, 0.08557381845277481, 0.20883242172220784, -0.4040651488873886, 0.3139350133606685, 2.93275684919757, 4.400941664930752, 2.0254431559259403, -1.947330638223577, -2.8281029031272977, -0.11389927893146679, 1.8745513228986348, 0.7137089279343594, -0.5020406735003926, 1.3757830796840755, 3.7358145072694824, 1.9818413008090372, -2.5917017681595174, -3.800123741497318, 0.24238972397127, 4.007820102593642, 2.733395789286275, -0.7935725121145671, -1.3044075346567368, 0.612421398856818, 0.31602806317121696, -2.602698698676746, -3.6360658627402564, -1.0552655827064488, 1.2831543243441526, 0.4542742776628288, -1.1520719544605353, -0.6340002948304636, 0.5431134282222407, -0.0068591703660342606, -0.8757648996129755, 0.22144649706555303, 1.7250039452649413, 1.055443316549815, -0.3209037965498901, 0.09731922329743334, 0.0025667368024087462, -3.9379203557565408, -7.620743471903606, -2.9645362988537745, 8.878894511495037, 16.01032532815756, 11.167368944880566, 1.4152435904994565, -2.609291233845968, -0.6665341412934928, 0.48329890750392046, -0.9017739991320631, -1.1510639972908523, 0.2928604222413779, 0.4081044372018343, -0.5113238579780782, 0.7653074847703216, 3.4219776007186082, 3.2170600656833295, 0.2098884312146171, -1.1554301572056744, -0.039314733671673686, -0.10571905697090533, -1.783962344737474, -1.2308939830054255, 1.6798326694957906, 2.2223940594446594, -0.32669626235535204, -0.7880482075888845, 2.31589031317459, 3.6654173721197365, 1.1034750061286847, -0.07829506860003253, 2.6984752612185123, 3.904658197049095, 0.49863014401100286, -1.147814398051661, 3.6330820739438727, 8.209538619813488, 5.082921518754833, -1.3411368120112706, -2.201655607954888, 1.5592912323590102, 2.5837244939537594, 0.046815356528200125, -0.9897641800421115, 0.27644723151381206, 0.48166287020813353, -0.32274001360258114, 0.27953790010337803, 1.0896737178826004, -0.08019600518922287, -1.1129201853725825, 0.1595993119500079, 0.8932738569215486, -0.6936584111058461, -0.10761308143815664, 4.853199648411542, 7.31535564347784, 2.162261086503544, -3.7500773483984347, -2.522257107764002, 1.1844151816372892, -0.8437301968820281, -5.007361817537941, -2.6603018611839726, 3.7786833745693964, 5.117724982360352, 1.165867388121529, -0.8814196049655522, 0.11835530615110301, -0.2355322856208863, -1.624513536384288, -0.6832811779465559, 0.8369613155478892, -0.12872437386087793, -0.5426508133212794, 2.7946750898969532, 5.431387892920343, 2.6610442990635015, -1.4678039720161091, -1.357453272963883, 0.7336517709593812, 0.6130954151157336, -0.10322810909771277, 0.5422731915419314, 0.14685738026696968, -1.1325319641178127, 1.0419317509989656, 4.747192216560046, 1.9149497054016635, -6.101540990400289, -7.317601815867423, 0.8473670008516442, 5.863920065989719, 0.9581029375240242, -4.426252713684203, -2.3638061822913428, 1.296861519039912, 0.2875615462859441, -1.3865880571823548, 0.2483267170156432, 1.4819655545278276, -0.12882875544570285, -1.0363843651814761, 0.0013082305597189212, -0.14203159955039119, -1.2153837516697727, -0.23931818438386906, 1.1697739154371654, 0.20627316128787684, -0.18583971376854685, 2.3048767588228167, 2.612562671119586, -1.975594582714874, -4.3934486568796975, -0.43172095771924973, 2.4087789334187186, -0.7757572247915491, -2.2342834213209093, 3.324606717473954, 7.7757714456414915, 4.555299446075033, 0.018827919897836908, 0.037708191681718996, 0.2654638122208307, -1.8863586342440801, -1.1346921493702968, 2.954511671388131, 2.8570976284695444, -2.1995262169099816, -3.9435467600902587, -0.44373158543539404, 1.4560615477616308, -0.08176748092968211, -0.3353122180972592, 0.9262587713231262, 0.26999700695980683, -0.8547562304695473, 0.04027255456854181, -0.00022250094759383677, -2.5358432490206817, -3.050448942545739, -0.39757085088604416, 0.28999144031851615, -1.1637735403040672, 0.3191965819672246, 2.336802192807388, -1.1017078625989558, -3.6146249899983136, 5.455456353889746, 18.76896556045645, 18.9532300828351, 6.619055835799914, -1.7837740059818268, -0.8233471314576638, 0.7689087357027737, -0.47712519793792435, -0.29619197238348005, 0.9826437048949491, 0.17702679255566972, -0.5425407620792527, 0.90537363507732, 1.283541382283344, -0.06633738500780295, 0.7982466291486066, 2.5824638430040636, 0.12522374724143748, -3.8534295624151538, -2.828686788451022, 0.5331046542517823, 0.15188241510886755, -1.022546128172858, 1.4207578613058012, 3.000244250973728, 0.46641448204047214, -0.5320010270248341, 1.4459176609078936, -0.9774674039899414, -7.27037490330013, -6.790799884278323, 0.739721976752054, 3.5224684305822906, -0.3128687983981785, -0.8822603273805943, 2.911923115808245, 2.9526065009960774, -0.2690057440826467, 0.006940412586380028, 1.7062012418672043, -0.6933862506708601, -3.5485665716686046, -1.8569595281281386, 0.5399291738441597, -0.24223904678363328, -1.0353061338858576, -0.10337691573097778, -0.005092785667674059, -0.11668366590963511, 1.274612910245717, 1.1531864114072323, -0.5961212844800433, 2.3085537864707173, 8.288192808518392, 6.116029572905871, -3.5722770639306094, -5.7348632265552695, 2.472309420029564, 6.47444358776979, 1.2331809094299095, -2.1537277518861497, 0.14888762590237462, 0.23428903745234164, -2.4849781765968615, -1.3432435040443662, 1.7346511851474515, 0.6421234712918741, -1.7889265792390256, -0.935807330486019, 0.22875819405661824, -0.05818361346853186, 1.9012766625193804, 4.704201075798471, 2.8099107589708634, -1.073999268067759, -0.6407904288545825, 1.396928647496111, 0.38067987015098687, 0.015742409649517102, 2.7648282480999935, 3.2551056914818344, 0.4095847757036196, 0.015480223347840874, 1.368065554097816, -0.4013194447327059, -1.0825359137875665, 3.903852643181071, 6.291586599771299, 0.4027369145310964, -2.8263039823606135, 3.545792069515407, 7.360123090004134, 0.4418863194302486, -5.785375915403636, -2.504703903818858, 2.1486877081740414, 1.3897267764571848, -0.12418942829203812, 0.2940741725402902, -0.23791979836429844, -0.8598242530697603, 0.2519642080210911, 0.09037516757778652, -1.6542889410567128, -0.6389643144160759, 1.633390879213247, 0.1335701803669505, -1.9642493476911942, 0.08332437957978343, 1.6858788989167695, -0.17825656623433597, 0.798730592551453, 4.420185708008326, 0.6437886006395901, -8.582341034324399, -9.037895299437821, -0.9516860057973193, 1.339451063643271, -3.3677295586041183, -3.9437092158416895, -0.1774211625840634, 0.3363712540746017, -0.795062320281274, 0.39823312392890553, 0.15991502303950997, -2.036923355262905, -0.03886705702131429, 4.287554306472053, 2.7912216360363007, -2.135129042734424, -2.3800145661507557, 0.08724553289005924, -0.142593489641474, -0.5160529857729061, 1.0208836792871927, 0.6620915428892784, -1.2121814050212336, -0.6059680529901983, 0.17940889799871987, -1.3869218689433838, -0.9942269078997266, 0.7599150221123826, -3.3660462447918285, -8.671777895170257, -2.5578860655413185, 9.091065862327856, 8.880484806369068, -0.303606621448389, -1.8096711269969976, 3.6003057801205696, 3.6791571772695697, -0.038453769784238805, 0.34567989038601615, 1.6955317884481205, -0.17777130236286698, -0.7789224977279687, 1.2790064172385878, 1.188543395947509, -0.4539414886011107, 0.016109540267960534, 0.4548769534403967, -0.5605698298803546, 0.02396466576345955, 0.17450241779968745, -3.9817806371260893, -6.164129140188071, -0.5031966473816273, 4.414945400228731, 1.1629220570245011, -2.4287548031169086, -0.6028897240355277, 0.23593586988175902, -1.2113717177456729, 1.1589757680842947, 3.560216873764732, -0.9404276874746919, -4.722887159913084, 0.15048103088701242, 4.6145767269474955, 1.20294129385392, -1.2919985208264164, 2.1058876762695067, 3.092187494880724, -0.2682978113909913, -0.48025891146594296, 1.7476473447500573, 0.5331836942124881, -1.270819445227245, 0.023038968181284435, 0.17951127237032588, -2.003398598686275, -1.7283020483170415, 0.19301700418985318, -0.10998210710636974, -0.31546665511034394, 0.7443981563202959, -0.8199583720210303, -2.7304688646739375, -0.13351248122991224, 0.7761969784614602, -4.581679848256194, -4.405268922678136, 6.981068608373922, 12.73500012229415, 3.3098341061324597, -5.1076026428670325, -1.4061152482031933, 3.010332983317026, 0.4719984583858037, -1.4578904744913848, 0.11694328240793958, 0.28889751083472515, -0.21176303234161303, 0.5528690153517357, -0.819961565066015, -3.1704370111693914, -1.2726984599114122, 1.4489090817479484, -0.2812875760472934, -1.2330303643377176, 2.461437037014762, 4.032823898372744, 1.045122850752255, -0.15104712380053553, 0.70688049762749, -0.35208784111941793, -0.16128755136703168, 2.0630425418253164, -1.0764268759823823, -7.757160981180775, -6.801066372729728, -0.6314628019817202, -0.50943619075987, -2.9437094382542317, 0.08299187886803343, 1.4596120431244446, -3.9326219802870606, -5.039839160436796, 1.9815027765304105, 4.528684150407616, -0.4899322967948175, -2.029757453527404, 1.3572247162586322, 1.823330185469554, 0.09633108881927162, 0.47413717363269514, 0.6011392015349992, -0.4526956312080598, 0.06475281061708846, 0.2738926429050638, -1.3435527724041236, -0.6732744165318154, 1.2918468595827175, -0.9561826730552977, -3.1992024774562027, 0.18925675842234638, 1.2333554667910183, -4.8014121248141075, -5.948208391002559, 1.9673532243940255, 4.893102418485928, -0.525155623012122, -1.0499723401668004, 4.152257413931681, 3.7490856761381957, -0.4188319070349344, -0.07521404332970462, 0.710551697525748, -2.2117459734178855, -2.5518940431503503, 0.6941551209301297, 0.8850939178321837, -0.6116715070725354, 0.7414693909968838, 0.9914231794918634, -1.4577809049131503, -0.6761413249553927, 1.9741581604416965, -0.21719697713947297, -3.5432918773527375, -1.8480199825112515, 0.3574733652740717, -0.521480656013747, -0.33453189785164167, 0.4057462962963144, -1.5907392510030252, -2.0040897684118764, 0.43691637591402627, -0.36280603284871, 1.1065297838024557, 15.974413125722165, 31.633891279981526, 26.025991138104192, 6.952075056139518, -1.9047543478399787, -0.0878975832233273, -0.3175169991690717, -1.6070508199648246, 0.18248393380332464, 0.21529647231911722, -1.9198115574625925, -1.0070243268794572, 0.7783879690244708, -0.038157217285282305, 0.2163762177417568, 2.001437181624973, 1.1003909362751596, -0.20501969144643137, 1.0656707992731262, 0.691332696571987, -0.7926568974117769, 2.7585755934363503, 6.629132704779678, 3.048376740439015, -0.6250469195334233, 2.3923011089537205, 2.685262964530827, -3.310265417629496, -3.9540478745894316, 1.4643063678519392, 1.166568062672879, -2.7758096625687854, -0.735928881940788, 2.353810058502207, 0.03705323034639949, -1.3236950262298017, 0.21189795348895663, -2.005721903828756, -4.660358884633154, -0.8355226330464648, 2.5503349541389517, -1.0315329297853653, -3.895844036292785, -1.451428617180293, 0.14737795274875012, -0.4573945515364342, 0.2324782702245006, 0.4339877152981481, -0.3327420278490531, 1.1500567351796933, 1.7960597842582688, -1.2290535380432894, -1.2645170412908435, 2.8115220298075423, 2.273390154931949, -0.32718570217490894, 4.245747757361251, 7.475076056268604, -1.218885615944969, -8.776598677092748, -3.380931496592918, 1.4491438768844749, -3.9734750004568786, -7.158314969194194, -2.0958228466597566, 0.9524471874530529, -0.5089349484685903, -0.232351239128199, 0.7234105328361013, -0.038790621771279135, 0.1308792854345271, -0.07398418688747549, -2.4201156071021326, -1.6743453094391825, 2.1280893389134503, 1.042860514763518, -2.94098055949142, -1.6303528983562905, 0.9648284255443302, -1.0910514847884953, -1.85944755960939, 0.9598935590634292, 0.5580412516217326, -1.4494986179488412, 0.22357157781408507, -0.46065125026043713, -5.393595812156899, -3.6598811819446646, 3.7732975963062385, 3.2780284975101637, -2.033391322128882, 0.4193144532553657, 4.7027194167577795, 1.1869712139999014, -1.8457870923471922, 1.5773806535146877, 2.5979141736254743, -0.8515163285817052, -1.2186189832497207, 0.3410611506436694, -0.5066488422020933, -0.19107520930743493, 1.7041717490379051, 0.32285623268002456, -1.86551156021104, -0.7335139719669442, 0.17336770433377263, -0.2704475388979381, 0.9048453973810177, 0.8644029548850681, -0.3485303745207542, 4.641550818569007, 10.136163358594857, 1.9408870708319097, -10.601430536895396, -7.126933163984059, 4.50277687704622, 4.40230866465334, -2.207874834520572, -2.0748661681334024, 0.2409367100446545, -0.3133967570058159, 1.1383598490245714, 2.8447082375952135, 0.15746310275590797, -1.2739524604576493, 1.2909886351608355, 1.1214785446965276, -1.119819063858552, 0.47259634811484647, 1.8733193763196438, -0.6525196001734289, -1.3026894498251362, 0.38337582644847445], 'positive_zeros': ['1.29515580079869830553343397669', '1.56276680993127280520969686007', '2.61053383999298467370705995664', '3.408895467371142367005120203122', '4.4143965443808680314230943979', '5.588457695999409526411432403494', '6.07700596409734247111778566615', '7.28040164888186674851085600794', '7.67885967272923146552873493002', '8.39997431279280964270382962611', '8.857142929419312450325465522412', '9.316848751347365225969600547023', '10.46282192561884669720192521074', '11.26126339993254992869769301645', '11.99324186326071425090398142008', '12.332610408662601448814885370756', '13.26061632571008929091452542498', '14.047780465067060010088352021063', '14.91753346829695250461370316167', '15.52015360967844670389771377687', '15.97967434023487871205250095605', '16.97958102360456576710759810287', '17.571784965960613853428924872713', '18.26198453344090089772114256216', '18.74826913214932376269770599719', '19.33724607853153611490594952384', '20.20734418289939545991309298228', '20.59356815784623997759538998393', '20.93792081739807843017685751914', '21.961673398322749963552398580206', '23.1853576575430078361642150823', '23.84200174938523750460585245263', '24.19924223730636836824734363600', '24.93294537827265376893893220740', '25.430000694215859828422249189672', '25.83089715743811234303035764777', '26.89842682625151547468312557675', '27.51119647683957002248746635997', '27.78637535839315024249851561125', '28.57399434973893275523141139909', '29.33526951290373570288383518625', '29.7878428138318778395600035296', '30.77345847878007127338039533171', '30.95603449149714631282652402768', '31.91522698000462964040120791431', '32.30315832779889194871918980387', '33.35901410009345697809438594893', '33.93729158839365869114546472181', '34.69329781951152235660636542376', '35.24749319406891459164266806053', '35.78796261243371688691190028057', '36.17555041985221833311148676668', '36.860737705833014985379294775209', '37.471750191193663561309391799378', '38.00460166492852210110602769809', '38.44763870896934744811109504639', '39.46643149608185387979551314190', '40.17979869081665820469361426922', '40.56562696001096466833424996117', '41.375783509923837115733600972244', '42.292083918951314840562072315104', '42.775970382013371981794508643507', '43.071291537472825725893123055680', '43.85574320873190633675967705571', '44.35052425049777703148585956736', '44.767689193958350401180192405081', '45.80162065852842677391423119684', '46.43313492881006366296404841876', '47.07246433319870230416205613167', '47.28050635405070812483383506817', '47.84276584001558595198790695657', '48.35091708229567575601776341592', '49.14026320753294924094642604770', '49.971254999860067362235091123438', '50.66545324332026084743149740675', '51.415379142607465499030142682305', '51.90995494490633746739489575085', '52.4676090400650478663794170367', '53.10506447961441414112133386735', '53.74955836812845563586604755455', '54.02040310516176793608605008985', '54.72622835548936126573034814542', '55.355987908450120162059847903106', '55.66254526017380776640222956462', '56.44589815770023170546993523992', '57.214029718851513730812146725689', '57.75597141739383232429537639869', '58.28435967042959461732949761308', '59.37761602058011702301984344431', '59.67830170065733787941626576911', '60.0499393453216408409504290113', '60.716331381836810598030102693505', '61.433426161350085398675699953528', '62.22482512397462898113072634376', '62.797084102337205175163985789113', '63.20496067263211592135542476106', '63.802328362873532817952851877546', '64.3646605009226600592915575269', '64.68745831742245462252655772559', '65.68007785999620922356314567267', '66.0009817609911831894918722741', '66.528899757876085597022473694578', '67.120806843865726192601389348417', '67.67574756088649205799993505793', '68.94973071771163974391619090527', '69.46989168268980823461654597112', '69.895073217079510411360602336199', '70.37353741588616407680606454133', '70.97474680146221513175169577631', '71.398444962788661725982074612246', '72.16395753869320919420073599862', '72.357354987826141077319784234391', '73.133622919399688888311026263396', '73.99335033127863332377263622803', '74.398631951178479180223861755056', '74.86093250209054261835148581654', '75.67802736858617592081711162993', '76.02820278276405821035660795641', '76.50470170589475551673715084376', '77.46824925212716484697224003638', '78.09992323948134374055524657239', '78.51897477826535732816556443191', '79.34001688472009946642278202401', '79.68652076913693084969110882545', '80.255926556757852786186552700440', '81.13685278074898339563039345373', '81.51442748712606573615256441953', '82.22834703432314957934751293405', '82.4969444245812884712936297707', '82.85324033508462280037940559920', '83.611743999112610638292648136081', '83.90547966512499809441559762541', '84.88373998198405555201591214334', '85.54106347230257853371175061219', '86.31430577616915706881296819226', '86.856874566384390311216666431567', '87.21626847666490620231016771952', '87.92860147545952348110100501234', '88.50334768995339701154236853595', '89.24523917885403794963792493479', '89.56899290530251926568973040934', '89.726364190965924682809755756725', '90.82787981601789584756128468802', '91.327848333495223902129146997878', '91.94937669465722921828081921192', '92.184424082562884569111681009123', '93.18639288045954871625796689022', '93.43420376055400510485740357450', '94.016418010791284540622702055643', '94.47139544134739826385032496473', '95.33036469282308714578485520395', '95.79850009808057621525998771098', '96.57733771307980900045744332145', '97.320501302527769641734049388119', '98.0543335216850449880366239486', '98.27422333920457501624586337076', '98.682886064061852841201148317320', '99.31220802390531314443713406933', '99.70487925761672222095559030776', '100.3841290187085489556851699824', '100.95111104480780503957491818110', '101.554161135142301052688297130510', '102.15664383518643735457559841606', '102.41885610413071548745299172556', '103.14773452604503354222773702944', '104.107003666682727823306333030902', '104.47961448870374702523762737567', '105.3325822286100005654877942878', '105.69279334468380130135491248265', '106.169563576690999637124803649668', '106.585708768249303149543227407598', '107.19014249856499617423563584358', '107.976740199790666065116647197397', '108.7318866660462269312187638454', '109.02461175493758852602471974593', '109.4938382464184542341175544608', '110.09879982870093038794244378333', '110.75385433754013411577458988855', '110.996244541766240028917546958362', '111.68998392012039313138333185617', '111.99837726050144034856743792959', '112.87644258560396250007445904233', '113.73745490894707138571653340051', '114.17194415144235323277316210441', '114.99469566696640284964064940917', '115.25979702462704209145911109416', '115.913463675747746173873215843707', '116.3776512831448696917554460917', '117.07438706283432260044769942933', '117.495705548008325707049870897476', '117.95458425219581962658641009247', '118.43205814302219765591937367497', '118.77407411253685738797335959715', '119.70841321621340127025788793850', '120.38057613610251760600522659924', '121.01780995054557350176275771713', '121.299662149030395703644868342704', '121.78107733528645951607901495210', '122.4544160126754137377704362731', '123.11839104133646843831588115592', '123.82966158812376427233541471503', '124.214142627698356697539245793748', '124.972024297171274465426171772255', '125.374371107703614390584383342181', '125.99978620885924504172038969943', '126.55824834965880994634679630692', '126.90628437171988198710948007866', '127.76353206809807263006302488744', '128.0910208812321554194469537097', '128.52421612517602647258927722072', '128.96702760237346252183497118377', '129.69929845829826051229167602710', '130.06475032461067501291952445468', '130.766074773605635784069600160220', '131.64797803614043827791091519044', '132.25343677684084008015028214707', '132.85236506507898219804564810241', '133.414222416134141028323986321109', '133.84888102483212782738877636235', '134.1616861758188473547550529731', '134.584134514401951836411580310803', '135.42037062433463986477741325185', '135.9066981786657910367506598833', '136.38160725483880702344624113597', '137.329141852262033475370657720346', '137.55436454831376139747330585592', '138.05154422512905402367680177205', '138.460452202225871951593867081241', '139.00840627532452332422662247649', '140.05662607423945763373543941654', '140.25525903308039477977371133005', '140.93149350888288567726208566855', '141.35945711268419113237768318218', '142.106084633610863513463683448943', '142.78319641094660877003448809485', '143.31525020853217083039714355386', '144.1151487793736455561743966545', '144.1843205272277947566049552983', '144.848735128760025433869588446', '145.29391200897215574215123603223', '145.68935981595066816001854703412', '146.333293921545634085650190655467', '146.79440630084378083109031648019', '147.486425075083352973727232803', '147.897604330072759099709814335018', '148.67811103172964977075790120717', '149.34429116908496245112765102541', '149.75596888514998462731576408607', '150.57916009238966790755948192126', '150.94875467820680322389867117796', '151.350204597000298103868168987841', '152.11411425768618833649636002929', '152.64080580904522048348396232199', '153.00686980724179082462053777835', '153.566937387932126408244122866957', '154.12843173051163582846948552276', '154.67162065101441339907346064479', '155.51998285709304699878384849484', '155.80764812850938912133010269600', '156.3274344665898955845916647051', '156.66316554510591231201518222474', '157.43038357862574255661203806988', '157.7592527264843726115792845953', '158.069641444959361430387649129950', '159.54999368774847768082999331143', '160.01363830771536820377911684436', '160.260518475971815361505643763475', '160.909111048932586401761420625183', '161.28245278661214866679956077437', '162.00692715046944365548843058604', '162.48935275627458873778269373678', '162.76900500723683154234776365942', '163.625065284515124508696731587578', '163.84186005646235242937923160159', '164.47428342184812053911615317836', '164.81771170075788578339532197194', '165.81669673450615315629721482832', '166.057667563566676425535978267656', '166.71189550167328316691383817446', '167.407761913554355644793017685451', '167.893052178386602514986353883131', '168.48819079559418440172153012866', '169.065991201837891401798669303109', '169.61667127781732360281837943743', '169.800734785501932128211210762026', '170.67170866310191385844077348326', '171.18685380553264887231746621658', '172.07813945963067904655117296568', '172.281677567082772984254226662948', '172.746538939260903780167866351251', '173.259018960049209089575960668809', '173.56863280736279513109323236212', '174.260443104176045926056956769765', '174.788786189962619187496138232547', '175.51903933858883081732219481726', '175.69190160437792090740118025527', '176.530194962669318736401104262637', '177.32689829373618048531292157030', '177.63174351628450411274377345800', '178.57157973850435822995528087534', '178.96469784397602911853638517889', '179.423895299855446189779824143238', '179.983415868374202818646311013878', '180.25485739434739370280094582252', '180.61040737894654830672681498034', '181.38033403192052097561829804582', '181.94794011099199302401951730800', '182.6422293988126501682790241829', '183.01003525052725308684697227108', '183.64074742183404300096709285140', '184.12712782086232784767431175094', '184.655847696455753522047081626863', '184.96040352843142704200703490436', '185.77114805431406082970768582430', '186.417616334664115470080185423702', '186.852508642503985620813368977658', '187.56908306642235393379319202315', '188.00983168422926278227062981784', '188.66961665111293909540165276726', '189.26411012931922757946308389814', '189.563983955706818669258085562994', '190.02987156875322644006585922515', '190.659116141026714409889209458562', '191.398435280863652604333454592902', '191.662516562497271345817714782023', '191.99520177951155676096145813243', '192.642263076927010356465061878091', '192.87300839808272052114597337466', '193.791256085693330080038485304968', '194.55016097190133963434756263959', '195.18962650843015939722940466877', '195.863894937413340489342431043423', '196.11873824015815832435786132807', '196.4104246486543625788748362926', '197.201665920635330744296586761808', '197.668601705235621975644916430660', '198.253685047773607543009210447216', '198.69842462002035980827927845472', '199.3053079509640330121156594650', '199.89853451713863506916416112380'], 'prelabel': '1-3751-3751.1028-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.41957076659139, 'root_angle': 0.2953876542445678, 'root_number': '-0.281329266795229708591129478574+0.959611298205923825464658289196*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(165)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.671290525943286400177911824425-0.222696283438664729659382732545*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.2951558008', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '1.56276680993', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.61053383999', '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': 17.41957076659139, 'bad_primes': [11, 31], 'central_character': '3751.1028', 'conductor': 3751, 'conductor_radical': 341, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3751/1028'], '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': '1-3751-3751.1028-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': '1-3751-3751.1028-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.41957076659139, 'root_angle': 0.2953876542445678, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.2951558008', 'prec': 40}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_3751.1028', 'Lhash_array': ['dirichlet_L_3751.1028'], 'factors': ['1-3751-3751.1028-r0-0-0'], 'label': '1-3751-3751.1028-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3751/1028'}