Lfunction data - 1-3864-3864.2315-r0-0-0

Formats: - HTML - YAML - JSON - 2025-11-05T19:00:28.319080

• 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_3864.2315', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.9283679330160726, -0.3716624556603275], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 17.944340560412993, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1]], [23, [1]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '3864.2315', 'coeff_info': ['x^66 - 1', '0.995471922573085 + 0.0950560433041827*I', '\\\\zeta_{66}'], 'conductor': 3864, 'conductor_radical': 966, 'conjugate': 'dirichlet_L_3864.227', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^62', 0, 0, 0, 0, 0, 'a^52', 0, 'a^54', 0, 0, 0, 'a^49', 0, 'a^50', 0, 0, 0, 0, 0, 'a^58', 0, 0, 0, 'a^60', 0, 'a^64', 0, 0, 0, 0, 0, 'a^92', 0, 0, 0, 'a^18', 0, 'a^57', 0, 0, 0, 'a^77', 0, 0, 0, 0, 0, 'a^67', 0, 'a^48', 0, 0, 0, 'a^10', 0, 'a^53', 0, 0, 0, 'a^50', 0, 'a^25', 0, 0, 0, 'a^36', 0, 'a^61', 0, 0, 0, 0, 0, 'a^98', 0, 0, 0, 'a^15', 0, 'a^45', 0, 0, 0, 'a^35', 0, 0, 0, 0, 0, 'a^46', 0, 'a^18', 0, 0, 0], 'euler_factors': [[0], [0], [1, 'a^62'], [0], [1, 'a^52'], [1, 'a^54'], [1, 'a^49'], [1, 'a^50'], [0], [1, 'a^60'], [1, 'a^64'], [1, 'a^92'], [1, 'a^18'], [1, 'a^57'], [1, 'a^77'], [1, 'a^67'], [1, 'a^10'], [1, 'a^53'], [1, 'a^25'], [1, 'a^36'], [1, 'a^61'], [1, 'a^98'], [1, 'a^15'], [1, 'a^35'], [1, 'a^18'], [1, 'a^37']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-3864-3864.2315-r0-0-0', 'leading_term': '1.56791015080987661139150042362-1.64052335770420159597096998932*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/3864/2315', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [2.269286039305252, 1.4043196051113596, 0.21404846809459693, -0.615774274466558, 0.03944844584575581, 1.9224278638645331, 3.2314734705952506, 2.5247638311441785, 0.6003870095837016, -0.14474719323358684, 1.4309927637115738, 3.5122890864884164, 3.262681737056392, 0.3889459067054749, -2.219371768090126, -1.9642014601302074, 0.19028720449814726, 1.0984972354041602, -0.23814748265089378, -1.3949753970709582, -0.25832971935289234, 1.5432104150703583, 0.7759108504562632, -2.4591628177754945, -4.3166839584352035, -2.415740087245613, 0.723220437496584, 1.2384885015779936, -0.6023929443448645, -1.175550514235969, 0.704091093873432, 1.9846247286392285, 0.43747041069580755, -1.4996600732320111, -0.49394479752267084, 2.1250732595015807, 2.168410909700839, -0.7100238427244595, -2.141307804006624, 0.2341735011856817, 3.0215624451150505, 2.371291512665809, -0.19898396599349988, -0.8178964673765747, 0.16796412587293974, -0.7683164225988399, -3.529631681279838, -3.7993026942869133, -0.24540263503707785, 2.6194048962585614, 1.3190523884725271, -1.117788688257156, -0.3152540910101919, 2.2799914222595263, 2.2437408891080244, -0.11927046702057087, -0.6219399842363056, 1.1304124610166175, 1.0705609345931242, -1.6560529109297937, -2.5560627601737727, 0.4266166853561607, 2.7931163205559737, 0.788375694822189, -2.2727570236247887, -1.7233306436113152, 0.6856574280876917, 0.46515552520625436, -1.4653229984610396, -0.904249462718554, 1.4750835606120623, 1.2927396509910882, -1.030149831725916, -0.46879605040076716, 3.367074274023164, 4.775951385028704, 1.5789557474899052, -1.1612780230171431, 0.04479081241266334, 1.6694934175386262, 0.4830147407097976, -0.495240894144593, 1.5630010723402237, 3.1548005429224015, 0.8268784466735927, -1.7963223564867024, -0.17809314104537707, 2.716832519006629, 1.6234160042788106, -1.49286600091004, -1.1717845911946259, 1.5689155047549723, 1.543777795367495, -0.7992954623244848, -0.7590811080798827, 1.2082373192615166, 0.6353849559557012, -1.4959972312895164, 0.030823437852868674, 4.282834085290076, 4.708520564069352, 0.560379940496856, -1.859748978921294, -0.38244372517377395, 0.3389417558533363, -1.2162967937909204, -0.767894164634169, 2.331019260752525, 2.9586460786316247, 0.22140819900546313, -0.2634533132157621, 2.936745279676384, 4.038893327860763, 1.0316566188517775, -0.39631606021271004, 2.313282551811004, 3.9093141401220732, 1.5883418319577844, -0.069564208683174, 1.3479560248425648, 1.6508470251105571, -0.5585741452018883, -0.3329488544681951, 3.3246705690703844, 4.055231817889019, -0.3137182754914142, -3.2602587829113236, -1.211695439248355, 0.8452990596420362, -0.16383900083526431, -0.17191528079377827, 2.362604951429995, 2.6041310535760513, -0.47166890459222166, -1.115292047498479, 1.9666749657019598, 2.722172826401168, -0.3494895760405604, -1.1614277958055246, 1.7978920450692308, 2.3578085789434433, -1.1606912087812487, -2.807522281267749, -0.6843344208598977, 0.38912271530309506, -0.29486250372240497, 1.6710555799918176, 4.881021810618232, 3.082458968178237, -2.3146969915291034, -3.6183211016295918, -0.5723968565926372, 0.2376218571662978, -1.4987689719368262, -0.492727682771549, 2.30207883675343, 1.7153414353423253, -0.47311137142868953, 0.8166746032074095, 3.034260151136068, 1.2175379758337022, -1.0722676272334786, 1.5579539562718188, 5.003449745021, 3.1590620614872806, -0.49997800369194134, -0.36199667348817766, 0.6110371157027874, -1.5903001533781767, -3.161982846522756, -1.0507186649262807, -0.007976655468963492, -2.3710300991687507, -2.3281035378420043, 2.062524759412676, 3.768338671351655, 0.1287790817299187, -2.083266014399605, 0.010596324048753762, 0.97631936547663, -0.5863096685736231, 0.2662694411230446, 3.009664992495657, 2.1560020326982308, -0.5489040980166943, 0.9593725885023615, 4.187251469458691, 2.7085920147171305, -0.5908971122752718, 0.7099842865393773, 3.596550048529071, 2.202050108238221, -0.3526330239448003, 0.6489606880092338, 1.7137852771067943, -0.13977851811276992, -0.0708732898695097, 3.706965729738448, 4.583529839791452, 0.7109178530818014, -0.7021212788239712, 2.178306894476661, 2.401200086318809, -1.2709965282669975, -2.343299473312104, -0.281688555105571, -0.38555276116431214, -1.4460078246079842, 0.9271647846355467, 2.9338840049389656, -0.4429997744432742, -4.00440327998958, -1.8596471014172549, 1.0443843504245154, -0.5502687491247822, -1.941230405968859, 0.4343650378634204, 1.2222629510036025, -1.822275056426927, -2.7849010095192326, -0.3666655369980947, -0.041535734054227225, -1.061634608841751, 2.1028723219486554, 6.154741798470248, 3.805200150854583, -1.4513357465855237, -1.7678005440000797, 0.49137416813711954, -0.354031977419945, -1.4619318168100153, 0.2178150375574486, -0.06958368170609677, -3.7926769772045525, -4.258845027714975, -0.4662315701420854, 0.20891144665847378, -2.6551621795237725, -1.9326140536233396, 1.5417509571450942, 0.8454108955540564, -2.1606003434916152, -1.2025574572724111, 1.0586729235383352, -0.17927762744474196, -1.0893030207020842, 1.29501191328292, 1.482651639603562, -1.9204577222624433, -1.5303261695507437, 3.4243664594502716, 4.427753831789502, 0.4020246080823131, -1.1426055795249648, 0.26311280961907, -0.5486043231942047, -1.3990536797851367, 1.6236572466990877, 3.527392365521973, 0.4794585963366791, -1.2146222609964907, 1.6634341055924509, 2.207369010323419, -1.5942880813436213, -2.459191588698072, 0.4220622169669191, 0.0675062263592585, -2.869319870050615, -2.124083692344735, 0.2448765482822224, -0.5700402400282917, -0.8081861478391684, 2.303749290269115, 2.2582136839735023, -2.9798529577410497, -4.909667284587513, -1.0353315843574264, 0.7602389587407323, -1.205864044093057, -0.8630333384587372, 0.901249185354016, -0.8308160129430632, -2.45428448380597, 0.3340008335734621, 2.056892737756073, -0.6420599615632687, -0.988860580473809, 3.064035560683891, 3.747472502425837, -0.0018594077012953837, -0.5915880921266172, 1.745855110524307, 0.5376645387000543, -2.1015597410082303, -0.9861458214798444, 0.1886080466026892, -1.5859094288700473, -0.4435209043241274, 4.662970218915178, 5.351804460300796, 0.7296476639577603, -0.7479089084381042, 1.141773812736874, -0.4092124384794143, -3.3492259683871253, -1.9348546348615816, 0.2002441583052242, -0.9069347962849392, -0.40559788845001066, 2.7923614165895225, 1.6009622138493023, -3.3442010398491515, -3.4044761776107486, 0.32428580735624746, -0.06969094570076358, -2.4556577151999988, -0.8235648000990612, 0.987545049959776, -0.9725864939202672, -1.3048151180549128, 1.8140677845654807, 1.9979815243667693, -0.353190143751832, 1.3325753131347209, 3.9602731712089434, 0.6448001186570517, -3.5400210370344047, -1.5217159561740206, 1.5503913420125714, 0.386378586655786, -0.278063540914389, 1.2414569233631263, -0.27924493847882237, -2.9308487612532605, -0.5755141376870042, 2.3921021747439952, -0.45400155678271276, -3.3688595478220145, -0.8137380912091032, 0.8825724111467951, -1.753897603401412, -2.0451805400139613, 1.0791839994336745, 1.1871843060174205, -0.3527039694567923, 1.6847079931529787, 3.0192003643387197, -0.44054000403710525, -2.197435179956676, 0.4264601622886623, -0.2992491007700947, -5.024947680206193, -5.001248892833686, -0.5885593337701256, 0.43894121940728853, -0.5889764034563617, 0.8928277595735004, 1.0075212899532808, -1.6616113014585012, -0.1475983490452251, 5.017883195814146, 4.779964374449973, 0.2502523386931983, -0.17998745534419353, 1.3022334479732744, -1.1126192089537497, -2.7408781058940503, 0.16066351240543092, 1.111667191189295, -1.7927248633984627, -1.899681835036627, 0.3269114640904578, -0.4127317338477269, 0.1099834135208982, 6.175654955728016, 9.52711691104645, 4.765847778071963, 0.1222491937878864, 0.18823271569553235, -0.6907176997450765, -2.544196498656331, -0.4208728396480965, 1.7438877877835166, -0.6560272800414623, -1.5148481342534743, 2.060431782176771, 2.3063772290338664, -1.6549681076341094, -1.3615729981549043, 2.2048635037697832, 1.3941530208892838, -0.8969468685334983, 0.9292682889716493, 2.0412245147215704, -0.6002006452667672, -0.940109915416254, 1.068093328518191, -0.8981394848898402, -3.350409007237308, 0.20078047360851722, 3.5636869011497514, 0.4583217570911052, -2.1472123398472145, 0.24399550724076788, 1.1414680644793918, -0.6803730475406993, 0.32148953481577264, 1.5674712875847139, -1.2690562297672465, -2.0486758026396505, 2.4292527259727072, 3.8607129041598265, 0.34925435180063336, 0.24914514568031848, 3.0320378353162694, 1.2714874758195, -1.8147345884018484, -0.23448132784098913, 1.1604434495533376, -0.8980334467176252, -0.6803613334261764, 1.3319197223392563, -1.174715012632491, -3.9604027665434494, -0.2598082965404156, 3.438171201656524, 1.024827247688012, -0.6203550728573297, 1.8792778233416962, 1.7463261077391694, -0.9192702416361964, 0.08877396368453051, 1.7561166131716355, -0.09880504853371132, 0.3348434943180069, 4.40911885702094, 3.5713536615328794, -1.6153549580781243, -1.74611127300465, 1.3393228345834438, 0.09537469919892154, -1.7716668238419886, 0.1907306262185364, 0.438773200962539, -2.030143691022048, -0.6017110572954874, 2.458483737209787, 0.7326111507192982, -0.7477275907596579, 2.7488638670215315, 3.65517227451084, -0.7846086924590423, -1.8014058075001058, 1.3827950900792445, 0.9563691095768013, -1.3819259883992139, -0.2645801746535502, 0.1976885840575322, -1.6646521768429796, 0.7158222526785565, 5.2542395893355485, 3.1559187491057537, -1.618499313788684, -0.4930126378138048, 1.8150709642154719, -0.1952437749964151, -0.7793527592334775, 1.5517244660648215, 0.295415102050163, -2.3624019531445253, -0.20356803759041964, 1.9836122147538309, 0.05884837413553414, 0.6113103818513766, 4.106971143821502, 2.002089226114895, -3.283456945566984, -2.4650125116735757, 0.988780108399964, 0.20363004764757103, -0.49787364522311245, 1.3312130325594411, 0.27561589808096426, -1.544396667273442, 1.7725274579104509, 4.195174876723798, 0.03517931836630836, -2.575534361003326, 0.5899646431598816, 1.4649537197611007, -0.9614983543862768, 0.2249015014376753, 2.2166694450473536, -0.23127564587697405, -1.538381434344898, 0.9248492158967844, 0.34920071159265303, -2.2443253280749085, 0.05745638965491584, 2.504846176952524, -0.9669200671560795, -2.814402431355009, 1.4186974051888117, 3.236089860446741, 0.4021576594591017, -0.2005393619490639, 0.24891106482875677, -1.8760393779612339, -0.9630017760295552, 3.7160303150751464, 3.0922848398640164, -1.7305188731047882, -1.1926422398998213, 1.9166523582386497, 0.47529247557069443, -0.4838538628032041, 2.4967628155877537, 2.3286013731996045, -1.1834436181282983, -0.797676890605597, 0.9501340910476656, -0.6194658802496256, 0.19440268212975723, 4.363734010186168, 2.904471588092016, -2.654274791095605, -2.313545625598622, 1.0882248388230233, 0.010152631546787652, -1.238163622332065, 0.4355761863409293, -0.878925451354023, -3.8170137079337914, -1.841515449516472, 0.47078418549814194, -1.6116942460829482, -0.7309018507856542, 4.667433415520543, 4.768676837329878, -0.06076465784365859, -0.7527247694984154, 0.5659691958729065, -1.1694721571387496, -0.7957361287546733, 2.7279684517250566, 2.19350580920298, -0.23246691094595298, 1.902747540039524, 2.957740739483627, -1.2951789038904997, -2.326479009454182, 1.6457281834806097, 1.413432913678859, -2.0779318831501654, -1.2725069887151312, 0.23114811817697917, -1.6855797694423202, -1.4960480903082471, 0.37518044284437857, -2.529144888040763, -5.192670432309574, -1.0620530550351397, 2.0562504636665073, -0.8306532611308521, -1.4107254051759917, 1.7411584894788146, 1.0602169773847077, -1.053804542178606, 0.8665264238520648, 1.6672019021651145, -0.333373871139124, 1.7531466802129483, 5.206679644728732, 2.428762989967137, -0.7517875190744303, 1.7744036122737696, 2.4975324054148045, -1.1640459484289942, -0.9748111854761984, 1.9665236143915559, 0.47773825817257193, -1.4269691941869986, 0.45212291905930296, 0.6882406247515509, 0.21278656919643213, 5.306783414925443, 9.392900043357747, 4.661335370645802, -0.5464554766608068, 0.4154957980512428, 0.7931352225603772, -0.6504593973256894, 1.7430313112935252, 3.7843009642862846, 0.9145892534129385, 0.015591417974414106, 2.565293047462238, 0.887581726512958, -2.3944638261011644, -0.38708500052626893, 0.6679838270125485, -3.6533618822054588, -4.387921095512745, 0.30300163346675835, 1.4202940221977904, -0.42034540747501525, 0.252943082698924, -0.5319530506054568, -3.2870337493892317, -0.6301625659894199, 3.892041828572986, 1.490869683690163, -1.8693142286153537, 0.8166056459103245, 2.204101676975098, -0.918134487711342, -1.1845025920114718, 0.25532025523986446, -2.1058938483375425, -2.8871362609637465, 0.6419207041986766, 0.7161356499288671, -2.0133187511984216, -0.2407286072150026, 1.1029355687959674, -3.309485237767036, -4.815421186190423, -0.21315980206062335, 1.1141976341483677, -1.2682271612238682, -0.5476278702595158, 0.06432390107585095, -2.0370099099005046, -0.4531306755890512, 2.9056859740566976, 0.1709294339116684, -2.9398501981169702, 0.662305970497024, 2.9645817615718513, -0.38786807782170996, -1.3192311826658392], 'positive_zeros': ['0.68102555715886304662833825889', '1.241543804363296256737619982041', '2.63635628727811640681646840016', '2.874629908402212260077181394183', '4.09900655730321613252811078768', '4.971345785614896746550196138593', '5.58373368088702511684317672836', '6.288676550297548221300805243204', '6.96164858666285888170414759158', '8.03893613912937771558194858550', '8.65443720853316161259199872982', '9.278661979509371601625016751991', '10.055118633040030845007861178339', '10.68346998751237486982885623934', '11.491479199405641782057620118804', '12.166298248680110524232419195625', '13.095984010499291128885214969230', '13.67954954631139471609704729624', '13.93019393159261768708532316445', '15.01838462275526580740928759507', '15.76798309606819225707078460729', '16.288058035329607248048798355311', '17.16981258082589674057835950802', '17.624072142572946243985628764862', '18.26209982993503982078470814747', '19.02697436193945320428919590018', '19.75520809073082985192689933659', '20.519588653271544426299482099329', '21.010550960810236669811780606637', '21.67735791013639241920196838363', '22.354789391598239406324530360349', '22.859207579441229157756512479940', '23.88233250959816176816355863745', '24.36904688160409714894126797747', '25.0820633039818194028068572967', '25.43251458403687317334632932310', '26.32288462746904924517887821613', '26.89141594211422910429226428219', '27.64859192572627197105100722939', '28.25509268359535566991307515587', '28.94839870754540686309057393768', '29.49090251876336684014787533302', '30.08277554559107799222538638209', '30.622484123553155970398091446157', '31.604094785876000699463097372624', '32.253144379910055712531953653776', '32.58683584690045494284547828698', '33.21145620068369566514469905736', '34.09050765402146553727697109002', '34.412347990696217091491239185153', '35.42582903088832896427067452456', '35.70161518333837718413026230065', '36.80047825546694869583045977174', '36.921937270029286719697199454922', '37.73314639874735964287346920618', '38.161505595014522618094668155107', '39.04305819145311439552049718365', '39.81659040895630782459708090875', '40.27730572617853862939308418605', '40.65362729319360048044716958015', '41.514526679611115111440781611223', '42.00536871120991157427712993458', '42.778024489277586953394666904546', '43.265156469351990190249112488235', '43.96953111035987445078248652828', '44.79029474253223756627908066993', '45.15154855622517668282118333837', '45.43148657210984572386915902117', '46.42414190786338625098569020787', '47.260031345769092959752770503937', '47.549404921367516241555103759391', '48.17656003935965311462935992427', '48.96292405334915283498307718335', '49.27514775273536655179871960040', '50.116403890081217515409383885008', '50.504100181857943456601762720083', '51.50056978006874629501650523380', '51.94166009425115714592542821140', '52.32039275510347545346265305453', '53.28789634018518943781780396140', '53.43525626311019883797157677548', '54.24061738156358740858630512449', '55.009510655289448092207661846199', '55.623705623817124330194925490', '56.130959558798292235778526417', '56.529984793757621063964360561939', '57.40799352102491247375871437553', '57.7189451045112405962756419760', '58.66581524758946765234066806669', '58.99126580354536979234673539025', '59.92365941606422702117461624845', '60.209382282237801655819963086477', '60.916146863704173188051007929107', '61.25847522363270053500050263583', '62.24952072866777466964452724441', '62.59795838510817890361807179221', '63.33284886148096016638688740534', '64.133244423015484886278266715742', '64.27593001512756743234336973594', '64.91534892905291769188854035941', '65.59739036526854681260134890900', '66.40221948642368448917890675565', '66.8127167640032952803560064091', '67.45291775650497125748201151785', '67.95803928426941385181305345399', '68.81231530512459348610170639263', '69.05266010654718941093518832906', '69.538755815310417171319592813085', '70.52133438509764442297827376757', '71.15493521208624476858482831930', '71.50609554774628385203876148514', '72.15122776165132940375713642047', '72.49179255225751391038935774008', '73.48510006318948795800849111982', '73.77817239451472895169112140377', '74.534787876707975627842552993315', '75.0784327178203692619286356381', '75.75480038700274040645854192086', '76.2248786977690937899014141426', '76.72806042126565478026965042168', '77.33005950997238554305244593182', '77.917704770008475944066681865466', '78.78408472019021770597072983212', '79.30173281578373888418143847359', '79.58887071699464438985036677665', '80.17924120426352331372796804928', '80.97820269434949015927884532496', '81.40935335234623751841415169443', '82.06452260098668767274837814830', '82.760447845076341732261670571950', '83.13253493517560601133559599111', '84.00443533951595604524267349755', '84.26639840985010200035906772384', '84.78682317153287058390294332233', '85.461152182127923067944087161067', '86.33786235297669518483102746514', '86.70043443433688522886417358064', '87.30668689360158625690237647454', '87.720929725456585367051752826025', '88.40930617172549785538849164433', '88.99865514514468038546959319680', '89.46560733254468575037951481011', '90.3123216847754916030566026538', '90.703153436033989023145677028361', '91.301723775757509812077208017749', '92.02879618086108359403146150257', '92.243671362327776996355101121274', '92.8443024966206115565060910664', '93.80925259201398065499322049802', '94.18357308378629945580468007356', '94.64980176978339978021590648703', '95.55110711509053272604587376644', '95.75258265697152986622287494963', '96.29299943790054334614999229448', '96.97539963122332470249209207113', '97.7760392433128606071524647396', '98.116975881933040910803794300429', '98.83743253750948415710682334779', '99.255418691920985063027503660485', '99.827363830261381933652416585278', '100.55312207948375407622157392598', '100.80241507511765745705230561546', '101.59860304377804872156200100709', '102.303688961913704746201684645170', '102.876131342107150339225910014272', '103.188290737561941076830197372050', '103.72330123438962668133260632727', '104.416495925373857934407324427349', '104.96908490318566014767474641092', '105.69911195047793613299441602029', '106.070976813351200592725570131510', '106.7628667385564336062138261884', '107.37242959308448024329878613711', '107.6179922060330070032111633088', '108.40461109113186466794434210414', '109.01145859448028710235933885677', '109.34983411818214946195679572655', '110.37144179411599476967711369189', '110.72433816423098476180202247854', '111.10892404551047862784514034941', '111.682071596253940138458282536325', '112.19717344632362669980565463405', '113.15010898115504269242293165707', '113.46538830901555155351977272492', '113.96085575369205556957319543345', '114.67242992743214812348207189588', '115.13232714527322895928988863035', '115.86851299151514050859135475950', '116.17030588175450756932024267507', '116.55285335268538488910884475029', '117.8363523670632879359907921537', '118.044427247521765586458955650485', '118.32379168919986293307947827216', '119.09965523426209252164260136978', '119.62430471259584182943931187336', '120.14800025592247432633645337750', '120.8037424505764293972407113200', '121.36076529396350459803144973017', '122.01782465200759705894130337951', '122.39656734321243241062966125659', '123.058783853333582750135091169089', '123.56387220957468772145310231641', '123.98403345067415537421757195001', '124.67579008432190701875582158502', '125.34393272007028797618672388858', '125.91190784183845095760360891696', '126.43240476955099001234243931178', '126.831659335265937473088882758867', '127.38823381451293759858141957644', '127.97344286066389686895722604988', '128.79011723609658043855051161398', '129.031186103533943901484603645503', '129.78603878196647016325583665629', '130.33818736529694590201442924012', '130.81632869889900970697210509652', '131.33457248797237390889763359314', '131.78595443876617036212721946557', '132.514437971236733808384303732254', '133.221908450141170337368727688470', '133.54012828983269909724388174906', '134.245559907769737166216095656026', '134.67697557540299625115874001936', '135.2977976865583975328720900452', '135.59010429477101871518646858113', '136.455072878354548485164959178942', '137.029420770011521020545046425650', '137.5098812040743663154373773485', '138.10004525296641231831852489888', '138.49545459104405742849983557875', '139.11176028408864789950938489692', '139.760986233879650097878811484453', '140.09880058527681527841398876512', '140.88339279743107919546661892202', '141.42345270959394055191974439118', '141.97806950448622560186568656341', '142.54437805231184942151099062283', '142.8494288378036015194545692054', '143.39096000718725384281478325513', '144.24054405180726507538732924844', '144.7318370007804762165264038641', '145.28961974099750405683628254738', '145.73058127976411316852283307323', '146.27681658553287433889562611674', '146.89218248739779928852308642800', '147.50942736628992148276875265347', '147.74299195018701251912945877231', '148.543375236923299542285332686358', '149.25449338659115798936919254117', '149.71950094540389316950031625572', '150.094391102579450962102856882499', '150.65517416183083920683772393454', '151.12939016445365172920481879993', '151.87707495637781158711174501232', '152.4499597008195468616462934263', '152.98764542732375199317801680201', '153.41387065381014851571746248733', '154.04098128913549463061708773579', '154.57426954319616701975233005783', '155.03542058746222101201482137838', '155.62068347204957097546644348771', '156.18549417295649497138608109489', '156.78576343106391695320228599886', '157.555491072933891826736765276592', '157.86938981483322341371161411327', '158.180859315199976021931477506911', '158.81762349578661070348506566946', '159.56153566340097636399830802340', '160.09792501985520502801585965574', '160.68176711511300901735774017188', '161.00677066942901726071062262795', '161.75666573671358209276034064002', '162.2859958185910683153310781689', '162.71607067898365787111521567460', '163.1077619662683324138281477666', '163.90154037032390634245017267940', '164.558031208032247153997995533531', '165.00123618009632375639706181042', '165.53817612502526243390619436345', '165.84594595590377231681718036018', '166.73644771051797858056109009686', '166.990437357642390317398135597175', '167.54769722417428226280517439419', '168.43243709448852408768493366157', '168.872369758549163394680345029275', '169.20723322102584865905531436653', '169.76092732177514844683273462957', '170.55392305047274441361707213584', '170.73076167677110478279381249121', '171.47716448412671434348390179722', '172.05889935497018621101925234744', '172.61466400263618405495520206686', '173.29831585594320488141916796906', '173.50648720099660773101891870532', '174.25722183117570659069935960356', '174.478693662210987286931126252448', '175.3735901150897508140928388755', '175.8652456610301160338214347052', '176.38750311327589581058027125241', '176.987498416509997288444079614729', '177.40223404107415078422306837250', '178.05089759750100387928616580964', '178.281701214920943545348110220312', '179.23551318345896375918233169010', '179.52476255895963372639285118624', '180.211088709026955859353517490591', '180.71502070272632730148976433304', '181.29700207488907235049628975716', '181.812321964433342506833753676304', '182.34467015068876635253543808178', '182.45639138799408247303342841661', '183.6847586943346744252840287136', '184.00167096572669002601003731114', '184.507799655327689130866536450654', '184.83858731036653754372496774930', '185.72946521015085212036423261103', '185.934930332475090050336216513692', '186.62740015543860614040879210344', '187.22434495133830631272507347244', '187.56839049290161490580784370881', '188.415432001201732638268386555863', '188.96231696378533490216061037537', '189.30844120668987013202114696079', '189.619866767684179733790533457697', '190.34752236150125224022471333077', '191.03211739066812054344204901531', '191.497286905204436037215279999256', '192.09834572761893739121648349848', '192.68524339326495233018061643565', '192.89024120434698827988155043960', '193.69142642536197471986393481735', '194.13498283319666766634314234759', '194.70994340723674573264902116345', '195.108285839832206239016005125573', '195.95282003581016320676049912717', '196.389265677980006941089056997381', '196.97234989556761680598547224229', '197.201124807298224955089111323843', '197.84633724821141806695032331998', '198.44815649051415109888353135851', '199.02140454528533511896770656878', '199.65441539026132739824224053663'], 'prelabel': '1-3864-3864.2315-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.944340560412993, 'root_angle': -0.2572027537666501, 'root_number': '-0.0452407898001002878797940753866-0.998976111295091551326967849492*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(66)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.28135363968258359730663936262-0.418794352331417103544067743986*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.681025557159', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.24154380436', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.63635628728', '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': 17.944340560412993, 'bad_primes': [2, 3, 7, 23], 'central_character': '3864.2315', 'conductor': 3864, 'conductor_radical': 966, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3864/2315'], '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': '1-3864-3864.2315-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': '1-3864-3864.2315-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 17.944340560412993, 'root_angle': -0.2572027537666501, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.681025557159', 'prec': 47}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_3864.2315', 'Lhash_array': ['dirichlet_L_3864.2315'], 'factors': ['1-3864-3864.2315-r0-0-0'], 'label': '1-3864-3864.2315-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3864/2315'}