-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2349.239', 'a10': [-0.024930691738072875, -0.9996891820008162], 'a2': [0.9767436117621412, -0.21441062679318745], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.908056166236305, -0.41884842002832484], 'a5': [0.18999309021918998, -0.9817854275089658], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.0912947110386483, -0.9958239180379078], 'a8': [0.7971325072229225, -0.6038044103254774], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 252.43510834257418, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [29, [1]]], 'bad_primes': [3, 29], 'central_character': '2349.239', 'coeff_info': ['x^378 - 1', '0.999861854691106 + 0.0166214179197262*I', '\\\\zeta_{378}'], 'conductor': 2349, 'conductor_radical': 87, 'conjugate': 'dirichlet_L_2349.344', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^365', 0, 'a^352', 'a^295', 0, 'a^278', 'a^339', 0, 'a^282', 'a^263', 0, 'a^4', 'a^265', 0, 'a^326', 'a^273', 0, 'a^240', 'a^269', 0, 'a^250', 'a^181', 0, 'a^212', 'a^369', 0, 'a^252', 0, 0, 'a^64', 'a^313', 0, 'a^260', 'a^195', 0, 'a^318', 'a^227', 0, 'a^256', 'a^175', 0, 'a^146', 'a^237', 0, 'a^168', 'a^179', 0, 'a^178', 'a^199', 0, 'a^356', 'a^225', 0, 'a^180', 'a^239', 0, 0, 'a^7', 0, 'a^26', 'a^51', 0, 'a^300', 'a^299', 0, 'a^346', 'a^247', 0, 'a^182', 'a^39', 0, 'a^258', 'a^305', 0, 'a^214', 'a^163', 0, 'a^122', 'a^243', 0, 'a^162', 'a^149', 0, 'a^190', 'a^133', 0, 'a^224', 'a^15', 0, 'a^282', 'a^155', 0, 'a^166', 'a^157', 0, 'a^2', 'a^165', 0, 'a^186'], 'euler_factors': [[1, 'a^365'], [0], [1, 'a^295'], [1, 'a^278'], [1, 'a^263'], [1, 'a^4'], [1, 'a^273'], [1, 'a^240'], [1, 'a^181'], [0], [1, 'a^64'], [1, 'a^318'], [1, 'a^175'], [1, 'a^146'], [1, 'a^179'], [1, 'a^225'], [1, 'a^7'], [1, 'a^26'], [1, 'a^346'], [1, 'a^39'], [1, 'a^258'], [1, 'a^122'], [1, 'a^149'], [1, 'a^15'], [1, 'a^2'], [1, 'a^377']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-2349-2349.239-r1-0-0', 'leading_term': '-0.926970915599339342099287266808-3.51000503691459306149458062912*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/2349/239', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-3.6303457738255305, -0.5406972797814431, 1.0022383312644256, 0.5882204263382524, -0.9143837406125082, -1.817621968972885, -0.9803619279117193, 1.0530412422419717, 2.463820642769557, 1.9671514361699731, 0.19520045291136717, -0.9636154366207474, -0.471394112567717, 0.7159656559608438, 0.9137641226717542, -0.09701172515530321, -0.7595674288936456, 0.128475068527522, 1.5821383724322362, 1.5605862824548515, -0.12422362457653043, -1.0862882163389789, 0.6697964123816516, 3.6842585352377255, 4.302294368387263, 1.3112420828295437, -1.9527524372106373, -1.3520846262373798, 2.7466707950815743, 5.555211705721222, 3.675678264430204, -0.665930244083192, -2.5150653002610204, -0.428314111781749, 2.153900652675459, 1.9292372983225332, 0.015190836051811978, -0.23796467799254137, 1.694885688726893, 2.9885381938151494, 1.8611696619124978, 0.047586255823808904, -0.1828839771673894, 0.5291439634894172, 0.20493906309860888, -0.6596188798494498, 0.3858081233314113, 3.360250815361405, 4.85110355482678, 2.7546286561145736, -0.3482762982510746, -0.896591352979738, 0.2378811211323913, -0.6484579030041174, -3.5340815093606985, -3.747994666412434, 0.8423850189862868, 5.265132277014316, 3.457359625765749, -3.1012290030752157, -6.922842760484, -4.398013355891331, 0.09415609961248467, 1.1763433437275073, -0.45038110738226045, -0.7914412835510714, 0.6322218614522342, 0.9867612170295718, -0.18802905225897715, -0.1287002179591085, 1.914735695814962, 2.8557487817484457, 0.8477558292446833, -1.4365604587706682, -1.1131244287562336, 0.3567519755196788, 0.17507594211057945, -0.6916047490584099, 0.42671525190946746, 2.3143270104897113, 1.3583250913639737, -1.5864844409001482, -1.3617081272184226, 2.9421098516945223, 5.095651057350864, 0.8516627333819065, -4.696134596241041, -4.006478576202621, 1.7895750732046822, 4.851776830330852, 2.359901116430808, -0.44207053443241623, 0.4644892350776975, 2.1976730884758293, 1.2208632784788884, -0.5107857989118076, 0.15692311493902192, 1.5140733108093372, 0.2301030942717883, -2.3384901625354497, -2.3751128679163935, -0.22095128845381723, 0.5807644669667167, -0.3078868574317507, -0.07663440068293927, 1.2720977338700545, 0.8615459341592454, -0.8548307461765424, -0.06334054385684784, 2.8686344953609746, 2.40554956726267, -2.7724097899994167, -5.939242951836363, -2.3780651147459553, 2.6717692120403713, 2.1732124269530178, -1.5581428888392779, -1.385675992650459, 2.405777599884689, 3.0882058427160253, -0.5930396722901591, -2.4560207739839317, 0.3170084042790805, 2.8139390046721373, 1.282803413776093, -1.0703779896607855, -0.6541982666339956, 0.6441014637154111, 0.23763586346031576, -0.25005967961971337, 0.7280673873408936, 0.649644475886961, -2.0537376784663057, -3.79734175663473, -1.6850999155013697, 1.0432042005274986, 0.7280283231534088, -0.23892534725588008, 1.2899766001553687, 2.239299822651645, -0.9996726338117103, -4.157351324861564, -1.1193599183119431, 4.723667124060147, 4.930069094069323, 0.14802146804769845, -0.6995516881493284, 4.552575505046053, 7.8636581800229, 4.592631967335625, 0.2767716039966397, 0.19091392855744538, 1.4642002055201033, 0.3377893539926104, -0.9390192853282227, 0.20041346923263142, 1.1470406803062172, -0.337607943595171, -1.3989908479443378, 0.04715121490862383, 0.8482603719490208, -1.0994459491995623, -2.300585894697249, -0.35259234606302786, 1.1681869811325853, -0.38660726442864923, -1.599207898748547, -0.08726408849313096, 0.5231338691268216, -1.2750228648109125, 0.1995718638583184, 7.220183030392687, 11.048871368816075, 4.314023081610819, -5.971898117332357, -8.148304240517108, -2.848974136457523, 0.640445649424777, -0.05242633645806665, -0.08084802277850146, 1.0120263375994725, -0.7406924758052856, -4.068780385107813, -3.7115685973480863, -0.24469625598469763, 1.0367054879618047, -0.23593416560260888, -0.06660869554814697, 1.3796679387837458, 0.7035355994120125, -1.1679113760874504, -0.8938866784060526, 0.21479392634289204, -0.6361098480380084, -0.8490802924227179, 2.5512685828279125, 5.2117161348648295, 2.3087461848790274, -1.5596696188787236, 0.13235929743993324, 3.4261064841496944, 0.7711765333103932, -4.400494363809356, -3.1084639313512863, 2.917775798601772, 4.175680185559715, -0.03175415187136436, -1.7479910435747856, 0.6048329107988524, 0.8796261472272645, -1.9666724396801858, -2.523316623205834, -0.07947063081311082, 0.5730912361531386, -0.9681922925228486, -0.663788504636225, 1.1995927378613822, 1.0035478831131797, -0.37786750211987397, 0.10529846536983273, 0.6593697346892508, -1.2445809756602981, -2.195896099672256, 0.839587409086885, 3.1893196930205434, 0.5919703005531856, -2.146173710021311, -0.10714112293955082, 2.102253160165092, -0.14067904792891844, -1.3577252576711503, 3.2758712294535193, 6.497286532406742, 0.8846055808381733, -6.748170933376751, -6.045533608280363, 0.030778503096896767, 2.014276594072722, -0.13973951729661932, -0.5122652606543733, 0.5818574345173019, -0.4078202973483956, -1.6645341280370762, -0.5081070034226198, 0.1792829882789602, -1.7163991197561745, -2.304990880101236, 0.42184898971058754, 1.9733000144812753, 0.19658167816353364, -0.6756061274649034, 0.88136752819635, 0.8902789270910454, -0.8733231667385204, -0.2560077312494703, 1.14353986281488, -1.8598261608830822, -5.391858720381982, -0.7990245046408146, 8.377097414442314, 9.80305375884744, 2.848551259628924, -1.0820909456291083, 1.2533627590857652, 1.684248502868137, -2.1079483594452655, -3.185685485260854, 0.015735266106337555, 1.3883678147895218, -0.24959622632903627, -0.30516854614649014, 0.9688887942067481, -0.22059761386979526, -1.9415455638926404, -0.19995378328199814, 2.2891783116520203, 1.3355290311257628, -0.4828197764126776, 0.22480667461441994, 0.933596350634415, -0.05748061407070843, 0.5330564727689122, 2.3761775555673283, 0.1253477955964399, -4.730156808598108, -4.0790111398631, 1.1252484362576072, 0.9179075089353508, -4.947678658456009, -5.5559325646890345, 1.064900078265338, 4.485728021569265, 1.1418731917382732, -1.1057457715071937, 0.3227231926206332, -0.6544509443095637, -4.147297652038154, -3.3416370413260363, 1.3662261407661913, 2.7660777892939263, 0.28669876453822624, -0.6761542959535174, 0.21221289007715857, -0.004230843324504012, 0.1512071455663325, 2.166671890207435, 2.4100162938421676, -0.2512195359901454, -0.8165892927473566, 1.6264622106819415, 1.3491012235299311, -2.0597280749776825, -2.3859448865641983, 0.2880544380836808, 0.23486267596294264, -0.3037595548763471, 5.1094733036479205, 11.45416192814248, 8.667342066335568, 0.7782682608771193, -0.3128536019772395, 4.023722504059201, 3.3729440203518997, -1.6348835551785377, -2.3051572435863483, 0.8281981386197336, 1.0212262592992727, -0.8020957422298014, -0.05662898874300609, 1.1946721600942256, -0.032526149349551225, -0.5509736827953594, 1.3772373361093553, 1.6937212159116584, -0.31568906404585606, -0.21603194272767334, 1.4801719853710402, 0.13365944859280432, -2.3639739256359853, -1.013385638633531, 1.5004310573945876, 0.5858846002632327, -0.34786068040281987, 1.5079579371624543, 0.2611518972725749, -5.543660909496065, -5.487314414052641, 4.156844599065094, 10.454852974666045, 5.016408737769252, -2.1445414858560308, -1.4887526477372799, 1.3974865050053575, 0.1509431051530205, -1.3063252433644286, -0.12918757640352974, -0.1657631633949754, -1.369549672828985, 0.7672254839611273, 4.111707436998357, 2.859424290840773, -0.7927834863698716, -1.1926296938978005, 0.14912570154200794, -0.16078392302301056, 0.0014757291573860034, 1.4462933695236977, 0.3975555110951286, -2.0892747114173194, -0.6039948718647785, 2.523037599866015, 0.9650561118899588, -1.345219212616655, 2.774993430139018, 7.392014032842801, 3.268945246198449, -3.456201281641464, -2.0986104167142035, 2.859658850264803, 2.071328075778168, -0.5406344801580352, 2.0385542510892236, 4.876792412438932, 2.0847640925693214, -1.1836975444454416, -0.21455918369701638, 0.4607604524554161, -1.6673126875323971, -2.0825643090411208, -0.10957460694171833, -0.054744863856191386, -1.0661689495876963, 0.40464837074239135, 1.7848943039274787, 0.1697658853953484, -0.7639429371689417, 0.6359660134562881, -0.08425980503412347, -2.2073375315277657, 0.579558894776992, 5.683852642874253, 4.302954039376687, -1.0882644363660816, -1.2718758974489208, 1.2474608346181555, -1.14240411723841, -3.3619186368184995, 2.2395517614089844, 8.00640664813495, 3.9800292604764738, -3.263918898877878, -3.3878158269919916, -0.021254913454528165, -0.14920187385473963, -0.9675468841756971, 0.6792729759700333, 1.1205295724261748, -0.5069419105476847, -0.3434587112342322, 0.5125763411768749, -1.3562417278852723, -2.655974418182003, -0.14488873599634708, 1.3431563049289155, -1.2140840406422702, -2.5458310819933927, -0.5550648754569825, 0.025560536777306207, -0.6408899240147063, 1.3860458339196613, 2.0663847544489817, -2.8806575037447626, -4.684129004362523, 4.132936779103285, 12.614790296996098, 8.845412277308844, 0.6157299994891707, -0.5398397648938132, 0.8971647128116543, -2.1193833924918493, -4.468276810957221, -1.8202357069703987, 0.13978253516160224, -1.1300578374883863, -0.6408955652816222, 1.5756834442835594, 0.798283412933233, -0.9791758217331598, 0.4677164750960502, 1.942198658137398, 0.4463504408447428, 0.11343797337558861, 2.3483624651028876, 2.359190193743509, 0.19598729310608018, 0.2130910516514696, 0.3030907771058983, -2.593347117579919, -3.052101752240012, 1.1003205064774826, 0.4358252677233012, -7.717620858698551, -10.505756915087007, -2.665792689047011, 3.1847058142014113, 0.3228513641378694, -1.9046104077163417, 0.8181548173652501, 1.1896650465172707, -1.6053688861340103, -0.8280306570954791, 1.7315498050986313, -0.26382798178396977, -3.380340949064237, -1.8492628688669754, 0.5806369996641467, -0.24638188861931803, -0.8531254857769726, 0.3474936970636578, 0.012825951590226911, -0.9785193901688711, 0.011893137875421763, -0.6093403143798768, -4.553261650244227, -5.190124925231764, -0.6838470646560341, 1.1527642904216855, -0.99491769040568, 0.18511155374736327, 3.476495877375392, 1.7992248193926639, -0.12545548481035604, 5.477102593110666, 10.433314518607398, 4.447500984498566, -4.03291089406931, -3.276374882870643, 1.1687381603731766, 0.6004798535034679, -0.7487497474337429, 1.3575228442181886, 1.8565900265693163, -0.6289356569299136, -0.6451975961484702, 1.4232724400321937, 0.9599555479013935, -0.29256374508328153, 0.1776064017714756, -1.1332752397849717, -4.3305392903343325, -3.6081417728193714, 0.2532345619655686, 0.9804618881416884, -0.08336727681598542, 1.2044489679305195, 0.9180986753055912, -2.997080930856658, -3.1553536611000745, 1.6672971619807906, 2.271105878199353, -0.7557145697588232, 3.306771872322231, 11.131214202399557, 8.510887440958856, -2.1495858525473435, -5.7505958874396885, -1.5296307453035458, 0.09975206356391807, -1.2065635824070253, -0.15664841226642381, 0.9367497356092369, -0.05095350501994806, 0.9372342612345064, 3.1490338104697453, 1.0167583955972954, -2.926360854189603, -2.379704960505432, 0.02236346366901952, -0.3829991988146791, -0.7682352713908243, 0.5556448980249469, 0.1937409377185469, -0.3466058859563077, 2.5252598200257044, 3.729010755080543, -0.5805070153671221, -2.1988115886369544, 2.6395527424620138, 3.148265800210973, -4.104009807486539, -6.245687843978631, 0.6799130147118837, 4.221579674998906, 0.6443844866801596, -0.5036785917216964, 1.5282578761397252, -0.625720069560857, -4.023285561347676, -1.8728965000421334, 1.3076300664596792, -0.05019700808622568, -1.4388711465821, 0.07810356558223003, 0.24977618348345915, -0.8366128287654873, 0.7131567332862468, 2.2370138931637706, 0.4754977144385929, -0.5069791935006348, 0.953932461285673, 0.4516622417071423, -0.6803858291861895, 2.2384547880061287, 4.378371829015361, 0.5517107349063087, -1.7706366511255345, 2.3275414421118166, 3.4570566352116634, -2.051644058229359, -3.1392577205107743, 2.6439415822917054, 3.767535024614956, -0.7757939593264825, -0.5005495844121272, 3.0670073517200414, 0.37697112696644447, -4.883149382265261, -3.793946384096886, 0.035429914035623546, 0.253433869585717, -0.23612178896872624, 0.69904955532835, -0.006833431780301446, -0.8745180155626958, 1.107590974393384, 1.8634173518445478, -0.7871945664842568, -0.9947575410742139, 2.1435770872313005, 2.176536970119545, -0.1849613728650311, 0.6301567805163983, 1.7477281978217152, -0.3097180831656888, -0.10361343897718521, 2.591362521434873, -1.1696902819257473, -8.295538649808115, -4.944270252628569, 5.545471726634341, 6.399084358644643, -1.6643772818153848, -4.218169655102722, -0.743578449317467, -0.04391500077890725, -0.6597547036509492, 1.2699867964786742, 1.22409487005329, -1.7997879898954012, -1.6815625426003313, 0.8481419223589042, 0.13585472936435775, -1.5275701748114, -0.320024842722582, 0.1148961939268606, -1.3995720828786369, -0.11355543090885503, 2.5446217149108037, 1.3715605069342909, -0.531371008024717, 0.5879120344838202, 0.2522481149246185, -1.8021872167539241, 0.8994385557656135, 3.982674566571373, -2.562045040865465, -11.0587117970737, -7.246512231969615, 2.176211096299511, 2.669458063023675, -1.5062479618187148], 'positive_zeros': ['0.386668803626972099554900278284', '1.06851075591772862598437677601', '2.03297888817237327677223048574', '3.16007478407284638909692708891', '3.86910887181102298572278198820', '4.66166234043054094021286232889', '5.28543444577204060463664125626', '6.229040575080048503050301651987', '6.79820716974435973371697833847', '7.91709643886821746300664962582', '8.55610590549226838006256270560', '9.63573660285042400625257974503', '10.35519424355440900617864590502', '11.25310100891016172822445254044', '11.617788322306972981282425848813', '12.82526487456453586053145599048', '13.20514224451750013489161343996', '13.81260298324276301645382379219', '14.31924184848939889506940319637', '15.579018114106499459124592682503', '16.167813983067616269528862729138', '16.4587473864298026298352820725', '17.45425591542812228092370597210', '18.29643231851536081533226939400', '19.36614994659911999604338651049', '19.91707826809801579875603225283', '20.495232781714174967029974196397', '21.19884625053197559155868703628', '21.590505759559745644255558580510', '22.5938984619023930322634152493', '23.342116472779282019655072320623', '23.80000568501552099972079319462', '24.30766650431482380670061913898', '25.13949030531928503974554004198', '25.74167145692587282890292847244', '26.60359565443543596651717653767', '27.40751445258797960265354174335', '28.35160883668813687926764597580', '28.67898232503701954794494868140', '29.56158096442670910572052269712', '29.97032008155721372198783091892', '30.65198274615442694187092952864', '31.59947140527248714123966311686', '32.08342471848045906650935759634', '32.519177088874743971640914053055', '33.26949391595817262057129477416', '33.75763767047841903842707306349', '34.537212921012902769970188904132', '35.43848497516956097698313991260', '36.1100201181630646532125794185', '36.68343013677044407139484499776', '37.45436655096735050911310637446', '38.098681958848997954576067760745', '38.891060417291442444190114786328', '39.50402634506334589262876501440', '40.07909397159301525682198129435', '40.42728702668326016351005436555', '41.03577266699779098375230962711', '42.037462575338118600654303426086', '42.6619450570701629930294370312', '42.91386540700938491286245929210', '43.67967366221597123782359850392', '44.4317078762129478389707786700', '45.32365531834560337293496994142', '45.68517935798433044255747125221', '46.917598143957057726683204146', '47.1461581489499114383393625211', '47.86715481439030239460662790802', '48.401987489384263521333837758522', '49.010183288477628268013715145407', '49.67972414012674222688218720418', '50.16986768964620474498817932516', '50.980620419945194455221227246618', '51.50869624209122514834327447728', '52.20210203527134479477287279866', '52.606233467022238038638978070250', '53.11179454761107329294036427183', '54.18316498809870789967513480333', '55.200398563275095343333951007154', '55.61079129388793901429476097003', '55.95872978227637648509550323030', '56.48829768285726413030012411554', '57.525634936200092413868084975', '58.06610581170268362047080563866', '58.45222855966670479377467413908', '59.16837219156623818544741734435', '59.89500321747195496874647521256', '60.159080740803348241314497919566', '60.735175803146848327167860241238', '61.71367092154119410950104335298', '62.17720263997285981519269345079', '62.85456053271212097560898632841', '63.59690273252955433134066983914', '64.37264800346066483744898334217', '64.92636568350197714472345240775', '65.42131653965779830700255110434', '66.26113680767157577462675736357', '66.686361562454605996882223332017', '67.2944103585429997947347606769', '68.01287619133796462814739868989', '68.41030876541019521313931179098', '68.89631971303924726711862459852', '69.62099431269396856227380228191', '70.358673713546609964844728079108', '70.94711610183893497955210570148', '71.54902017414404492297921795061', '72.003592719801675725465304186229', '72.84351608013758717607509626347', '73.748130284984528710656180689846', '74.353666376036538327990348176358', '74.81105318003513543159612268704', '75.240813045613017583398204201429', '76.04179001726778256666831119061', '76.30146859903152722059485181856', '77.14587834912668745726310634615', '77.84159397958004667378444756220', '78.279573730997430011393271992752', '78.89903716343884346185286936653', '79.413702143842899299343438640222', '79.86643162532219008537106503217', '80.652489564229107561059194592488', '81.71216886520178632938515629298', '82.06057831244160563318643702081', '82.65219109119781367925430857310', '83.43600788276007346159713629080', '84.015000847176425977980350142285', '84.44082722377477978204718578940', '84.97000789570179930016806743735', '85.64491827260548788010442553284', '86.43921740738850240167042342748', '86.825554144505415098856037333372', '87.47932115351877165651891042552', '87.706847093811081562485370021446', '88.44560807341758113625862144361', '89.29915546330794802685413198666', '89.74455666159095060200517837967', '90.57825480957437744812452940064', '91.342441483934729892573248358429', '91.80781531742803983884962957205', '92.11333931168962759740844092424', '93.03154737876807554961227940059', '93.78879734969462478786290295663', '94.288533074860591974179525237172', '94.68538739342100826120371771552', '94.95908419847382540819992410447', '95.90771283820517199543828706046', '96.36604609010658843599977536347', '97.00272822610252498032383702785', '97.77116406922026596504556537022', '98.16960692758331407768647816142', '98.47632489184259180452084561082', '99.734343100920907558898662326225', '100.02719379534531119919841976844', '100.82863096942363811665948291870', '101.4730260432508340025238929951', '102.029062061282596157057010166409', '102.5094793618426789413875098443', '103.11901641506614644788039920317', '103.5484522381503220084631617717', '104.32048860967283903655042468241', '104.72484033433865303119149330831', '105.3265078476496295472682514020', '106.03836457125101500352653425297', '106.659898318585217272871831931490', '106.958385604497354262782170783952', '107.51738937269255761586018252700', '108.31965571887955692631574728803', '109.249425429958928843137419486349', '109.81464837838357291526691806809', '110.33165352026298039547193846271', '110.97201536963330308093682693887', '111.20757409388952905657689973994', '111.80899534334904444001463334948', '112.7301961777439880233608825574', '113.38098274418207835384777098434', '113.68109419647526086934739305693', '114.06212999627727988761111273549', '114.731684217523920713162991798828', '115.36331747174562919387979331172', '116.02151301907420958649546935334', '116.41132597793152762618342477616', '117.316414710651182567646515631724', '117.929184980093342964790999000839', '118.63303731016032011072410135909', '118.89079581547840881592874535406', '119.84271188109590322921501528480', '120.34806404990520728069853475056', '120.71502663772142713146967220863', '121.58597747491001221271328161003', '121.86082055414325501078483024964', '122.44486336340122274144646428199', '123.15000103864560867388688095287', '123.6159077210325475224031024676', '124.051476056279583655246010612229', '124.653346607858619477392032836743', '125.5487481905528205152927967944', '126.06430384489279783790905983529', '126.474043490110230901194219493165', '127.09801151914174451239358537903', '127.9639691240423886612433032183', '128.75336016222875097227193284671', '129.03112940314735339912620820721', '129.5805837525008940549345808560', '130.209981820406772440111055242461', '130.70384256248115202026530958313', '131.074776932634524432271361910515', '131.88933095090401331295331987924', '132.38049437589744011006219274763', '133.23331891261571521008366404983', '133.44678369037223724479478294790', '133.8978577584143342059674815314', '134.533393751484861729049137078331', '135.19774641288488423661281793641', '136.28996474601885870983327686530', '136.63896649733411781236291754520', '137.018156297581649348646993276879', '138.03366346696428394521190576737', '138.19677885160711888695236620475', '138.83333577933459259353103819922', '139.48058794806539138531248204577', '139.93995427920643356465267309179', '140.71611796388731779575757849028', '140.91125167310978967420904453275', '141.9253632293784319452089355290', '142.1157850178311948596843776319', '142.549308243091069841332765215526', '143.355388817205599350595948185469', '143.77284794430773908725534147757', '144.78223691131890373338677142815', '145.33509899815251350365823791660', '145.856132220793695396071016648547', '146.380340818185612277792533029561', '146.95683814818898707397141813433', '147.4788893313767670238341925876', '148.31948280795530485114428557909', '148.70157781573261686157498113373', '149.28093423413769238707231422318', '149.690456384747797152430732087447', '150.30927689419575642746599561599', '150.53924520489260050776471321469', '151.613167609353456315077403207432', '152.04619464561091668845820941674', '152.48352934570813377632108747693', '153.300335343929476030499244033386', '153.45758987644156187852646620251', '154.51374819724283549404076944517', '155.20448975003659333503871639492', '155.70365156707827805416692247453', '156.08463114373669754103488295277', '156.79286913343712354910428762306', '157.28000971479026600623720109460', '158.00006436988719331000545890276', '158.34090096497124235789826048962', '158.58722379820987087761095435336', '159.662347902499501808777678888712', '160.23872593727849759063241080497', '160.37841275164297222888617127777', '161.023049201840092084353256028480', '161.76745432735661040386480587848', '162.388714040669912600803016411457', '162.65125393979290463815082904880', '163.68248197895852572842745241026', '164.53595494774063044148806770154', '164.71690038741576839535277078868', '165.3373942788079919747393744889', '165.91703795985204731861277657181', '166.09271131863439614168069722347', '166.94539110927606152777107087748', '167.80655203537279970059329677837', '168.0220751848374323500099737979', '168.61802312090701134105239069029', '169.10658342942773076189224549681', '169.440765629429273102202790204360', '170.27613743309565783131808204923', '170.78685281962545545079372949189', '171.40051182011340113025475449616', '172.159775561173583440882465531006', '172.87007225558309382986023041666', '173.200469534855346052314186965393', '173.7029841345950718622453479424', '174.51730227379303291019314852017', '174.99393036556208728613685774475', '175.60999519219719844828168696668', '175.99594673345578786516215120581', '176.47066938160297489763427224333', '177.25601342029923421886635971185', '177.6238926295837853535251138220', '178.199059756582553167454738188646', '178.5600223086690826177438680315', '179.410422047454970522147021115866', '179.853508618269267028577697624256', '180.517953149520614671379460311847', '181.11568908101126004922676141539', '181.81499300451662498073962822770', '182.22739830023577327013280034024', '182.83224418196990370298306972853', '183.74522730935765575051198854738', '184.135942595377735167418606334185', '184.46490997847006784160913522478', '184.99867036152449267894288739849', '185.48677672486047828863587831950', '186.16361449813100184269724482804', '186.66870197169767645792893026852', '187.46039254143509155992428861786', '187.71053694398348193255471575588', '188.39460303182597472413709872609', '188.76181415430173453100950219729', '189.32460335238577779698188147438', '190.14152646080329886387234285444', '190.87121614418785793660762930001', '191.66779874943941404350274464173', '191.862197996897545605112214383208', '192.32356636704997184979544037643', '192.94210662282694492539163687677', '193.62529721402106104377907545974', '194.081047733532577173464158902617', '194.751172772800947082313019888685', '195.02834236763931286354907072263', '195.63656117395546217175463369686', '196.41853498225142774749540179719', '196.758032194377222397790163520826', '197.22151258778486900755397347701', '197.75348876612825665134543200122', '198.35689063125538788558214647387', '199.28580678257721903120763797835', '199.86362221173112262499288080171'], 'prelabel': '1-2349-2349.239-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 252.43510834257418, 'root_angle': 0.41781273901342225, 'root_number': '-0.869603411709525789592251969083+0.493750854523972428995783392189*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.417812739013', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(378)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.44205446297204606954683338812-1.22741559401193945391948693586*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.386668803627', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.06851075592', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.03297888817', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 252.43510834257418, 'bad_primes': [3, 29], 'central_character': '2349.239', 'conductor': 2349, 'conductor_radical': 87, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2349/239'], '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': '1-2349-2349.239-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': '1-2349-2349.239-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 252.43510834257418, 'root_angle': 0.41781273901342225, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.386668803627', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2349.239', 'Lhash_array': ['dirichlet_L_2349.239'], 'factors': ['1-2349-2349.239-r1-0-0'], 'label': '1-2349-2349.239-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2349/239'}
Lfunction data - 1-2349-2349.239-r1-0-0