-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_837.412', 'a10': [-0.10452846326765347, 0.9945218953682733], 'a2': [-0.9975640502598242, 0.0697564737441253], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9902680687415704, -0.13917310096006544], 'a5': [0.17364817766693036, -0.984807753012208], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.848048096156426, 0.5299192642332049], 'a8': [-0.9781476007338057, 0.20791169081775934], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [31, [1]]], 'bad_primes': [3, 31], 'central_character': '837.412', 'coeff_info': ['x^45 - 1', '0.990268068741570 + 0.139173100960065*I', '\\\\zeta_{45}'], 'conductor': 837, 'conductor_radical': 93, 'conjugate': 'dirichlet_L_837.193', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^22', 0, 'a^44', 'a^35', 0, 'a^4', 'a^21', 0, 'a^12', 'a^4', 0, 'a^38', 'a^26', 0, 'a^43', 'a^36', 0, 'a^42', 'a^34', 0, 'a^26', 'a^26', 0, 'a^25', 'a^15', 0, 'a^3', 'a^22', 0, 0, 'a^20', 0, 'a^13', 'a^39', 0, 'a^0', 'a^19', 0, 'a^11', 'a^2', 0, 'a^37', 'a^3', 0, 'a^3', 'a^28', 0, 'a^8', 'a^2', 0, 'a^37', 'a^6', 0, 'a^39', 'a^25', 0, 'a^44', 'a^23', 0, 'a^10', 0, 0, 'a^42', 'a^28', 0, 'a^20', 'a^35', 0, 'a^16', 'a^21', 0, 'a^9', 'a^22', 0, 'a^41', 'a^8', 0, 'a^16', 'a^33', 0, 'a^24', 'a^37', 0, 'a^26', 'a^14', 0, 'a^25', 'a^39', 0, 'a^42', 'a^25', 0, 'a^5', 'a^32', 0, 'a^34', 'a^30', 0, 'a^24'], 'euler_factors': [[1, 'a^22'], [0], [1, 'a^35'], [1, 'a^4'], [1, 'a^4'], [1, 'a^38'], [1, 'a^36'], [1, 'a^42'], [1, 'a^26'], [1, 'a^22'], [0], [1, 'a^0'], [1, 'a^2'], [1, 'a^37'], [1, 'a^28'], [1, 'a^6'], [1, 'a^23'], [1, 'a^10'], [1, 'a^20'], [1, 'a^21'], [1, 'a^9'], [1, 'a^16'], [1, 'a^37'], [1, 'a^39'], [1, 'a^34'], [1, 'a^1']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-837-837.412-r0-0-0', 'leading_term': '1.05497762042920866073319400496-0.508413811034954393784018962118*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/837/412', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.171094523451272, 0.9619074065138498, 0.5104913902588492, -0.1945722563287038, -0.6406932832493258, -0.3047176100373762, 0.752918765327322, 1.692672026804598, 1.3873376128741541, -0.6297736987173853, -3.5007176292694835, -5.374371701887246, -4.712661630861929, -1.624787339434814, 1.9713485785377554, 3.7182754710775643, 2.715032540244655, 0.2935211082465065, -1.1296641048507035, -0.1994927104251472, 2.1820194508345647, 3.7647821537732775, 3.1203218506139523, 0.9589993373337208, -0.698527363029143, -0.606609430016248, 0.5569672336495597, 1.1566770197445084, 0.5372725474720225, -0.2928222980871862, -0.02286543760439345, 1.177636996463, 1.6701383872533624, 0.29783312866361333, -2.00134800573551, -3.019527245938329, -1.8143663792583773, 0.017524853228162697, 0.09110473192007047, -1.8002389964278245, -3.0662532557900253, -1.1512870374347695, 3.210708475804919, 6.232082511422298, 4.929502015981397, 0.43755322950516917, -3.0530481035217587, -2.681921839117998, 0.26103595747191644, 2.1712298656274114, 1.3019369596320076, -0.6304167575039414, -1.0138771777727955, 0.38043959600582744, 1.4612384842253479, 0.8125671116128846, -0.4950474374977126, -0.6104344359360913, 0.3557803172097821, 0.42252561170599995, -1.3902122970790034, -3.401537850024959, -3.2979250448423323, -1.2360577635315877, 0.29502854170746684, -0.1363341110941677, -0.891106079515321, 0.3415136487600692, 2.7963796687866016, 2.9391500360101275, -0.9094125004130117, -5.520585925773007, -5.813497806570258, -0.808383210645937, 4.891398641151433, 6.182421638357264, 2.9840207339694786, -0.42181322006420535, -0.9329010809337149, 0.20754523499207964, 0.2007841080394573, -1.0329681991450208, -1.06803554726899, 1.049211314141637, 3.0539349852286795, 2.4968544021217847, 0.12726719865421673, -1.2409796079468103, -0.6288829930753682, 0.14613638332357717, -0.33653034508840274, -0.7853531154257853, 0.574414306473354, 2.644436126784082, 2.4889039700390696, -0.22012020255643475, -2.003216772899034, -0.15528408198095414, 2.986127684137646, 2.598147485239586, -2.0654975271711464, -6.089727180574854, -4.943897631392076, -0.26928254490997133, 2.39548494638239, 0.8073173641806407, -1.6202885044331699, -1.090526058408002, 1.4130327138624061, 2.103532308365786, 0.06761854777311752, -1.7115090075697812, -1.0016208481230782, 0.613501953360025, 0.588986066769386, -0.6100002033345909, -0.5676452044643557, 0.9807216526313721, 1.7112188522533465, 0.6196385461053917, -0.1772265690660673, 1.0590466924617021, 2.419673839434095, 1.0046678316086068, -2.1341357186705148, -2.7348022699730667, 0.5386230402407738, 3.6253832044606202, 2.5876016925087075, -0.5845741827455989, -0.7053235697496347, 2.876714383496486, 4.861296310982853, 1.33830379175966, -4.506880938141113, -6.514958318902463, -3.561526043139268, -0.24900671646733255, -0.07498213212272341, -1.3838511166275886, -1.1964657370167922, 0.013048486746050404, -0.0943758870727964, -1.234357860792594, -0.9003815645390514, 1.1239859358201882, 1.938118283866523, 0.09055865936541274, -1.8791414147201049, -1.3050228718239631, 0.458777756969836, 0.4230901140680308, -0.9921358020397629, -0.7783746064194615, 1.0327131508540357, 0.5272554224853313, -3.7178083481161512, -6.899853565595913, -3.9436425624448526, 2.7670550065467756, 5.726697990314916, 2.1604263975016114, -2.5731228431961637, -2.7295971380638275, 0.4196644819257066, 1.78398860477222, 0.31681834705353107, -0.47644831611702854, 1.0101351444506927, 2.0094892107527538, 0.3824261921593061, -1.7149849946221567, -1.4983737435165887, -0.10375762870578437, -0.36894017295157583, -1.8252467238985914, -1.5240274465690193, 0.7503087697070344, 1.9032192879511798, 0.6794501535561022, -0.364044077261397, 0.34450271876530675, 0.22065936066935202, -2.7924105301799447, -5.188585634843319, -2.0607468105382796, 4.738918581280965, 7.6179615709652975, 3.355545981330274, -2.3821527753789167, -3.0638492843646974, 0.07681020876034209, 1.3160397934019235, -0.38471566207799146, -0.6955034139261287, 2.1921725566982957, 4.4127520771254085, 2.7564441020492447, -0.29768998850811357, -0.8048346538993167, 0.6426618027518531, 0.8014964962368121, -0.48196609012713715, -0.6038738306501019, 0.6781767766175766, 0.8487478837541849, -0.4300022199895605, -0.34436306669093525, 1.7682180504990757, 2.30686574224523, -0.8385628306807055, -4.030910920229185, -3.0735860812068774, 0.12054479264943145, 0.7889793897458561, -0.3674857182149294, 2.055687984519494, 8.666581020895778, 12.522862163910407, 8.672387365987758, 1.6277829020420498, -0.9666357574781802, 1.2590291520848687, 2.5397847111879335, 0.6050934316841894, -0.8174770984987367, 0.7140916721710868, 2.3529866868383476, 1.3049090348606578, -0.5475071887678766, -0.4854274733704291, 0.2572446486830818, -0.6726129199852, -1.8950716397452747, -0.6334588679917372, 1.8706934541293652, 2.001061641868075, 0.03795674464684021, -0.17902046964302123, 1.9563629422918902, 2.6008526253887507, 0.43530336613873255, -0.5315358421647675, 1.8526508935635646, 2.9185521482156584, -1.6935195757511066, -7.608478199706855, -6.772667084700618, 0.6151687862484956, 5.927480789540329, 4.248702242535268, 0.20655818941661241, -0.40622060785419833, 1.2064704643098334, 0.9554313346723659, -0.7066529743062457, -0.7532457854242505, 0.07295593826236212, -1.363202045390533, -4.26947264791051, -4.582937225146771, -1.757192475237486, 0.3462614116424192, -0.07195519114434829, -0.4750753637296969, 0.5328223983198669, 0.6053289588704073, -1.1741854178970517, -1.5571219917821395, 0.9303964143950718, 1.9499732550994135, -1.9042375011638806, -6.116169742514673, -4.160906038405159, 1.9454490250667238, 4.056917024597182, 0.28065972535981015, -2.501776794293146, 0.09651235559479984, 3.4636960176188567, 2.273064384826092, -1.006850492510635, -1.115016995668241, 1.133819403085593, 1.1648389830844033, -1.0677656928537287, -1.579867401486489, 0.1833859031828221, 0.6929825122798945, -0.9683309652723269, -1.6981870073979204, -0.4214838394932433, 0.09042419841111608, -1.1061953566217164, -1.1226444697772644, 0.9139834558166487, 1.433138315016946, -1.06157586301319, -2.3391807633925277, 0.4571108669279551, 2.9882125035762264, 0.6001839980628706, -3.0708268963029863, -1.3548201660666623, 4.213540381995459, 5.8605500151471075, 2.037477171757338, -0.4255220233335647, 2.0521019191117285, 4.15704727924361, 1.1114221715733061, -3.331531350412576, -3.388061468188608, -0.2784967792758589, 1.0330210042978654, 0.08032365772895667, -0.22076051586874798, -2.4832048444495393e-05, -1.4326012562009105, -3.148558416425913, -1.9218283197896113, 0.9939209879540318, 1.3137381028446644, -0.9074827441042814, -1.5059767513939564, 0.14593159951149173, 0.2800488446363428, -1.6751857142429056, -1.6842443965870284, 0.7275591946601688, 0.28734154000077683, -4.394249415810584, -6.235431024070405, -0.34879109346418236, 6.848503859456949, 6.35097689338173, -0.1359395030621181, -3.6228240141591534, -1.5872956181190747, 0.3540446132583194, -0.6704667951088963, -1.1341209560225107, 0.7768526587142182, 1.6075233333779373, -0.3820676272314568, -1.6886716274671936, -0.1086883588651696, 1.3072506680116627, 0.2086930918665522, -0.8079164404257713, 0.36911574027375227, 1.0579010032713572, -0.8871789567545225, -2.502354067074981, -1.1533602269613035, 0.3169634191055978, -0.8835825428183273, -1.7186697164452407, 0.5785868592837905, 1.2646302425226974, -5.0228044641511715, -13.382199718383848, -13.826738302126408, -6.053034818538579, 0.2833335419749416, 0.2521742837590072, -0.8811275837209095, 1.2704292283594478, 3.130172281617455, 1.1862648556113928, -1.130502653865279, -0.05901243576876004, 1.5772478972795267, -0.05325500157497298, -2.6502880889250315, -2.1984905641083277, -0.06753342986913875, 0.23039114510417197, -0.5073472349851367, 0.15434488049842615, 0.8024012619052658, -0.5587702354490343, -1.218838567412567, 1.7420376319055553, 4.880189423584525, 3.424747507752561, 0.0068385724570424675, 0.4322792562711181, 3.0732663603984043, 1.5062854182504597, -3.448947552940939, -4.3173969180931975, -0.18236950975756927, 1.007103127279248, -4.044450058797521, -8.036260032319207, -5.078554240333534, 0.19606048530152292, 1.223623799338261, -0.4202803286628815, -0.0851933201333588, 1.2055519670691797, 0.16224935875100782, -1.6171787182761526, -0.9174395537646433, 0.6400635931411995, -0.030910079708527237, -1.279144803913158, -0.23114103223200405, 1.078528435353788, -0.40068591284727356, -2.243991778040511, -0.8195754136283695, 1.3967332940879649, 0.1903601960759324, -2.0187013564414302, -0.40386735106210997, 2.6449283524836735, 1.4893347441267863, -1.2946189347120813, 1.9894926765619374, 10.024021778263696, 12.563936875346657, 6.27639470789473, -0.2057769094449316, -0.2008026336609591, 2.1313482471284586, 1.2365242792001734, -0.7953132852787531, -0.3283512197575369, 0.592393304287378, -0.6921047530013176, -1.7110259248095734, -0.14927179829938778, 0.9629380281843071, -0.9655569615648364, -2.6582701394828763, -0.9100254712264381, 1.436666093448776, 0.9725023571388379, -0.25638062741614265, 0.278424731847478, 0.43392951128172075, -0.8466616985325158, 0.9841553254779465, 7.737696929711096, 11.997883506757923, 7.436202920616711, -0.05762908984428224, -1.0194951858356514, 2.746071666204361, 2.491734809003428, -2.1243558733867354, -3.5815853943813085, -0.4453579673011168, 0.9174030411033034, -1.540391272239484, -2.7105542812743835, -0.7021785172984919, 0.0736763137185707, -2.0057853456753145, -2.8349176237528133, -0.8381506492204885, 0.2896820003755254, -0.8570482375756578, -1.0797238442751231, 0.3877552384875139, 0.3845479380499113, -1.1017720777397075, -0.39218453804769327, 2.004136839066168, 1.4450125956796704, -1.5845100656522957, -1.4875278438748314, 1.5184156887131919, 0.6671088206816422, -4.542226377542892, -5.675113134439023, 0.36102557239815064, 5.233336256126549, 2.9179190243956525, -0.929036624261075, -0.09469652178553155, 1.5557391122943478, -1.3519352931264759, -5.111784912412036, -3.8168003752137594, 0.10541791536646865, 0.924222269550169, -0.6003248076961589, -0.5302367932666162, 0.37557646972478137, -0.3513484913963346, -0.9766710459941751, 0.3586848697867789, 0.6649098085448809, -2.1928616140410084, -4.185513429654531, -1.9960441155226525, 0.5943468048689011, -0.27047801414657896, -1.512198807580987, -0.045201661709318955, 0.3855574865950646, -2.8549723367198307, -4.015554587495214, 1.134550149280963, 5.362274462766961, 0.5932500854541536, -7.7689231508617915, -8.68798113070376, -2.642559098653733, 0.9667448428639785, -0.3588916387076234, -1.092954102455191, 0.2407057621256927, -0.2770493311694541, -2.5230081523971895, -2.3208773348065943, -0.1029365489324683, -0.026225695050021022, -1.5249414362133682, -0.6726689648757582, 1.5890486739981307, 1.2665254517517845, -0.6244395572819852, -0.31977348309962705, 0.905245808974704, -0.2342380256362957, -1.4160653247718915, 0.9129010478770999, 3.3425506557740334, 1.373725071072, -0.7903654019753483, 2.7737136720583697, 7.168557459609202, 3.492254121772285, -5.034175392912974, -6.998182768028036, -1.0092456359264268, 3.314310030833851, 1.775428285660861, -0.1454409537631817, 0.3485835920712941, -0.44298089835478993, -2.9216371823284386, -2.36227934837493, 1.37263743394115, 2.7460327644855416, 0.525530304527646, -0.7331569880143896, 0.22940736694052505, 0.09344204078080884, -1.2632758357658762, -0.8064632634832585, 0.5077214380429618, -0.4009964686690062, -1.3427035016774802, 1.344535373905921, 4.131131285169251, 1.6377816492804451, -2.365740084006914, -0.5731976796116748, 4.308259349459071, 3.96484647016315, -0.30354607606001405, -0.1351823891745055, 4.060287495328156, 3.9022983239513014, -1.0467564576908803, -2.314014363640842, 2.0127265857917926, 4.355860341327886, 1.5230545927247865, -1.0031667875097443, -0.23077883855656228, 0.403552034384664, -0.3156503344833588, 0.5843657001305502, 2.597391852388612, 1.8994237298116305, -0.6290735642267369, -0.7172646790364698, 0.9282572282161726, 0.6296466136538814, -0.07111281481014972, 2.2897013229507266, 4.651998189013595, 2.3061116128342007, -1.4668564432851918, -1.1072759844905766, 0.3944256859159223, -2.1901271579393837, -4.3035528092651685, 1.1409522405526966, 9.101307881444018, 8.998669161525438, 2.3713667284122124, -0.2387565892275989, 2.7993219897313026, 3.614357545700305, 0.17717167487039392, -1.5960380999480888, -0.06740090967127975, 0.4078508080080049, -0.815787748775328, -0.4633108413797607, 0.5446859035090492, -1.0499627143367185, -3.1035979551323924, -1.6846966164593027, 0.7479811282591718, -0.20028082844785042, -2.3702521416123896, -1.6710778840918619, -0.019511353390753446, -0.30236310414693846, 0.14473482244167582, 2.6658939451712125, 1.8558336212613256, -3.929029037089236, -5.729546506139822, 2.043877314730884, 10.163548658582359, 8.37268011964101, 1.4097626720625906, -0.6062078201974711, 1.2208156479870682, 0.1202620343792913, -2.445702250768993, -1.2352191662482455, 1.3768799741975886, 0.35514781220999325, -1.8479914386718497, -0.5881818932605086, 1.7492472624222095, 1.0668560117442243, -0.43153106363701366, 0.35179687213188593, 0.9657945402905562, -0.6399187286465524], 'positive_zeros': ['0.8519289551696091888735999531', '1.66829670726934624294574818300', '2.735904181031489448128075328740', '4.19609181699789043059578881193', '5.35368334923902502255233286159', '5.96781316307366195380601080277', '7.3343994825111602050409838188', '7.98262566968367940202869802278', '8.923515355911918359679814236648', '9.38258939192394575730419741654', '10.3541381375495019846531813681', '11.55817153901651358092799292956', '11.8980682656637268826283693738', '12.90341210151146935196061965572', '14.09173129359306568821353446085', '14.97324019595240499908865597873', '15.82441387114124005227782706238', '16.49103801344732961825932762701', '17.3675557145093454941133024748', '18.01374294059996088942207213156', '18.540602958836483385682931989987', '19.89738895998413912416543379066', '20.27122869102281911481810782072', '20.88856851322073116701377775973', '21.81824127693770454477545481652', '22.85178211315689001752970763135', '24.007604969339277343915770280093', '24.624534765316157553259558643508', '25.05970543747999580352490353443', '25.80785472407828209090703861745', '26.892536382309056575261206634004', '27.704084817966276975794256962793', '27.99008775268297988917190267887', '28.66083166388153493647567567455', '29.66462579972890631744758801288', '30.32703771497926668775062978929', '31.12981079363897069548213501137', '32.20633395915681825061471559205', '32.89920630267310970055677608965', '33.57557876761962240592075957320', '34.38335854937004871581265112439', '35.176018096831482886554216902084', '35.7766104257998607621277212405', '36.37964208866842803361102460891', '37.34592393398074454299782122274', '37.59584829439901114252438039427', '38.537420295196829592937069215764', '39.334133405633813863549342534907', '40.24488019436785764443569438188', '40.70464299262526123157418801459', '41.63231341371921580180721629833', '42.86120242867549717702262616153', '43.10407080104479792225181928706', '44.05765704086179382985513977444', '44.34285647888377937625319124671', '45.14922737156147141013966637291', '45.94859539083006732894841117702', '46.778618038569353039682309238173', '47.28317133275741121934319934720', '47.94758943430638305395264518798', '48.49130910389073952546136084294', '49.55764542837037544009406707481', '50.43607786157362230648773649577', '51.20777278280505016086942031672', '51.93409922319084770170293603228', '52.32643529994096916753816716366', '53.17248341778707369369513862179', '54.1074677478533456226300576868', '54.25520818969445189640244980620', '55.21529506080460661076072609459', '56.07783727193283335313009703300', '56.455058422684836603890998004150', '56.91223793545674644654498348464', '57.9105635373099039973918288228', '58.91348089231858415003935185293', '59.67956912101792616941941910305', '60.25030124108667342360019668733', '60.727007519614434158848570595209', '61.83532791759175754365462700134', '62.36436700354503650266690266583', '63.00844622389662720889775575742', '63.5924436202994202250075499013', '64.27111643916346513694801984484', '64.75195059316568032222072290660', '65.56066830825835879100561594319', '66.547723716056779256091542424019', '67.055726057888512111873022185947', '67.32344218624415045089087355474', '68.85802186341876874878206388146', '69.23440815237345208107583460206', '70.08063448989052676668195316357', '70.5248512656082853534608045009', '71.44613703132224221830667082908', '72.03124531520083987663273047768', '72.3492517299845286886937573350', '73.1999567335572416377606680829', '74.06965268809426915361883598661', '74.41134893134557542546128177208', '75.37315381751675140987037252244', '75.72911853906648924379725568622', '76.47965728213960747086612970376', '77.476002727511792558157146590451', '78.462136597682613700711970559507', '78.8328496362045430289363289396', '79.54527870852316618759121875759', '80.243149077127591037656046547701', '80.388780131353972499115937558504', '81.78069653070898363450514000009', '82.16434718509414431815589055648', '82.67024135259932487126764235659', '83.24898810393067355737929133773', '83.96213097301365974076875765085', '84.569963765610540211345016977839', '85.52264645636970761935646867974', '86.268928879993596639481871828220', '86.86789447727243398091779339460', '87.701123127176200522969089517479', '88.27827458287599194442110302891', '88.917465687280516360986288914946', '89.655731296549879286158166114985', '90.1521112374308131641073238098', '91.04868807712158411243129989837', '91.288289289913887715938883099091', '92.05807466365981934601316076474', '92.69955363526693600128675926916', '93.400113234710520649427677662739', '94.10509073509746860527144884317', '94.76759198022554489530692544665', '95.8050623224059113611163170128', '96.04566959342239281478296240138', '96.94354174085416003991222265549', '97.84459077011144554199471219634', '98.463570518498386274582800226662', '98.9156271992715433686322928468', '99.06248126340793673978770812111', '100.19534979353772664629710594413', '100.81556794984839970901690608349', '101.53397431649477171619835448329', '101.9298464628565110537694623651', '102.71524710226144595250527849123', '103.15154367291048457931825240080', '104.07544127685227309505166705668', '104.9933321318260428809116968044', '105.82118521586761890321612692592', '106.11158940665568428663930013810', '106.76596301747198993573049157121', '107.45160700197647280113293841358', '108.14020880740094386526368584299', '108.78802809512620597019683499076', '109.30495143220448178804312336612', '109.88953696501951766627602226004', '110.81075200597343094498797139113', '111.09007870898719456904385529541', '111.8126124421440134073379297240', '112.28887103087510919621222582132', '113.72294465914782484472712366630', '114.10365773203545437521663665442', '114.549167466435043063786150573762', '115.43495759566323854129392101131', '115.94559349196132183418023725552', '116.556876655049207920210776808951', '117.51420609807731048093767610660', '117.89611210889291965836163127655', '118.396866032007415362248577442678', '118.96631440104333086196632683961', '119.54416817323347102091365644802', '120.62603201135259435457180491100', '120.87882661391982923515156957347', '121.65973157270450653822824679309', '122.51409346439486063869882793659', '122.903745842906872142116072601371', '124.04639419039546094537912013047', '124.59536257648003387787349108002', '125.01744904190107646364026138871', '125.64871904317778195062757194661', '126.40336149341795581561642676501', '126.86903177753647721676832853148', '127.537607610107637577952143730336', '128.07353786117336805394320797618', '128.84151707029731474506106947441', '129.396685461691376544629888455125', '130.035894021198826632606490472255', '130.75897501364514773354966411229', '131.14500818198116275081843882874', '132.48221222245768795331613077736', '132.83686953837483425854654968029', '133.59853036206605321627501908079', '134.13407038999456679782359434070', '134.56766131624855956263517092583', '135.3345531059827926132112387408', '135.82172106913703231120097872328', '136.660094273919437420595647096680', '137.393419861540623157397847188463', '137.72092327258705359614912531413', '138.23484422307503039380674625544', '138.67447162964209519451398343306', '139.99652897153366449082215560466', '140.40408879692818478393657239940', '141.11115121730287308198579197221', '141.91876430054204311948937968307', '142.333879541619540694343382073404', '143.24654845474177802371777737878', '143.45770967933653643562666890040', '144.51438319016320484311789332804', '144.80437653225028262642915556506', '145.54091984563685977585711662505', '146.019059618684535952743601391816', '146.61355596634619065263165957853', '147.33340143860568803494961586822', '147.96394771294686582040090637012', '148.4851581593449551510493696416', '149.35956842745685876191097639919', '150.20466179595133025605436701285', '150.63648931816361063226460009845', '151.15234855442777373699001306248', '152.17655539790117980841418654959', '152.68474901880638278886378603498', '153.27044231279045085024781028538', '153.66020980824987615337655051267', '154.30753945740790103064247766368', '154.78862013857157186192067352720', '155.82595421803473318490936531769', '156.20634584984964253467993187300', '156.88233375695615702939467140997', '157.244550431831456179910793226955', '158.071627537308882091339365567147', '158.77121906566776946637143898034', '159.851098272607179307812016779005', '160.257650023710972955975717551909', '160.875308341638152377383302406585', '161.20274664795415201347018777666', '162.208010070059022200152996098817', '162.493967228637989423860291117196', '163.21088936438874922058246992451', '163.941559832637755616075525393186', '164.439111021532979488454713789536', '164.96347117821481022828837098147', '165.54032819765245917783070883849', '166.38124566131604600518590851335', '166.69361428372197482401791704372', '167.625114703695236262115325137878', '168.48501989488669952318573917849', '169.3138205637105049011098444687', '169.54268742419603962063377837741', '169.92890519348490283917353900814', '170.82531490394769412528022551228', '171.63307681226321503248774196521', '172.12044900664284940960088750457', '172.52278509630648551020629002019', '173.28223820794553359513131226353', '173.67639404331225742938465049796', '174.26177710866325461481575844523', '175.10573110316260244304993845239', '175.66085899722110812515761973827', '176.53440018901002094623724986742', '176.88712210683012503881465068097', '177.74554896168691640860802090517', '178.31103207872240412198445274616', '179.20068831550272763393794468555', '179.740816334509232770790840386954', '180.17093823345711746569065460727', '180.52057127637827745011824231420', '181.4725804078593689421044661661', '182.00327058599768572435311976198', '182.665369885023747523260876424399', '182.839315685384004754263800980846', '183.91617041247371206146815464136', '184.536554273386563077443436007999', '184.791305554350102969354562631101', '185.58261960079126112557746683459', '186.73214085505059440961213583295', '186.92045916532033407003608914747', '187.82801596011369871656403510956', '188.450047644093371109966567449960', '188.8595332528998295105132930433', '189.47789707306718102729836916551', '189.860764491482174015751291518499', '190.808614682950992540855847357209', '191.22390787775661005334002747893', '192.1966435102412749082527724208', '192.35980305632744418169792364499', '192.78743503906487989587974929060', '193.552372736145124702462906365993', '194.31253931629496698607032418357', '195.41201522601516520772791257860', '195.733945507538431686628964505945', '196.262848332855632586853201744329', '196.99819865316454574167027897474', '197.54079544105825369148873550511', '198.1898489949249156046846316284', '198.92887256458160302999952206168', '199.29632809902103014722835130182', '199.89741895007314443378180527757'], 'prelabel': '1-837-837.412-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': -0.28589225366707693, 'root_number': '0.623052580250125351901734175722-0.782179955153327301300096138168*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.142946126834', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(45)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.865891886452648012786987289146-0.167051569470461202822504464558*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.85192895517', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.66829670727', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.73590418103', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.8870116586608887, 'bad_primes': [3, 31], 'central_character': '837.412', 'conductor': 837, 'conductor_radical': 93, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/837/412'], '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': '1-837-837.412-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': '1-837-837.412-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8870116586608887, 'root_angle': -0.14294612683353847, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.85192895517', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_837.412', 'Lhash_array': ['dirichlet_L_837.412'], 'label': '1-837-837.412-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/837/412'}
Lfunction data - 1-837-837.412-r0-0-0