Lfunction data - 1-624-624.251-r0-0-0

Formats: - HTML - YAML - JSON - 2024-05-29T08:28:24.962613

• 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
  instance_types	text[]
  instance_urls	text[]
  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_624.251', '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': [-7.040766286173228e-31, 1.0], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.5, -0.8660254037844386], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 2.8978438172095515, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [13, [1]]], 'bad_primes': [2, 3, 13], 'central_character': '624.251', 'coeff_info': ['x^12 - 1', '0.866025403784439 + 0.500000000000000*I', '\\\\zeta_{12}'], 'conductor': 624, 'conductor_radical': 78, 'conjugate': 'dirichlet_L_624.179', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^3', 0, 'a^10', 0, 0, 0, 'a^17', 0, 0, 0, 0, 0, 'a^10', 0, 'a^13', 0, 0, 0, 'a^2', 0, 'a^6', 0, 0, 0, 'a^11', 0, 'a^0', 0, 0, 0, 'a^13', 0, 'a^5', 0, 0, 0, 'a^14', 0, 'a^13', 0, 0, 0, 'a^6', 0, 'a^8', 0, 0, 0, 'a^9', 0, 'a^8', 0, 0, 0, 'a^13', 0, 'a^13', 0, 0, 0, 0, 0, 'a^5', 0, 0, 0, 'a^4', 0, 'a^0', 0, 0, 0, 'a^15', 0, 'a^6', 0, 0, 0, 'a^3', 0, 'a^13', 0, 0, 0, 'a^14', 0, 0, 0, 0, 0, 'a^16', 0, 'a^10', 0, 0, 0], 'euler_factors': [[0], [0], [1, 'a^3'], [1, 'a^10'], [1, 'a^17'], [0], [1, 'a^10'], [1, 'a^13'], [1, 'a^2'], [1, 'a^11'], [1, 'a^0'], [1, 'a^5'], [1, 'a^14'], [1, 'a^13'], [1, 'a^6'], [1, 'a^9'], [1, 'a^13'], [1, 'a^13'], [1, 'a^5'], [1, 'a^4'], [1, 'a^0'], [1, 'a^6'], [1, 'a^3'], [1, 'a^14'], [1, 'a^10'], [1, 'a^5']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-624-624.251-r0-0-0', 'leading_term': '1.36190860968980290290056550657+0.472065611660627570246689268006*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/624/251', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.441402443060138, 1.6970992292947926, 1.7097595367617286, 0.9808008166069009, -0.4195153502956, -1.8329463759665954, -2.4226536974213477, -1.7736898563536596, -0.2890247916895565, 0.9791613153867316, 1.05296481090525, -0.18020450483450548, -1.7683387536424493, -2.367295496313694, -1.3455885308273474, 0.5859229968918815, 1.8494846516611094, 1.2996766229506147, -0.7332205165697727, -2.637322086976381, -2.8877398141656188, -1.4080370310631216, 0.3646891962905531, 0.8579337533717102, -0.07541869523515121, -0.9606107257887588, -0.16473374210413683, 2.3550189458368544, 4.802430154310755, 5.170540862570568, 3.2046620758341358, 0.6999184970560193, -0.25182890611783615, 0.6813054119563758, 1.8579655928196366, 1.5539813110516034, -0.05531464467106982, -1.01878340890961, 0.20354181040536684, 2.8553085799537707, 4.465032811474751, 3.3988367853749852, 0.634119779979396, -1.2562134035138088, -0.8571275654551236, 0.647337246356068, 0.9765896535903599, -0.5172925904417207, -2.0726989137277525, -1.6532903285341414, 0.48295129480061105, 1.8775696666341566, 0.6575614779691812, -2.201035078072575, -3.865634019455818, -2.8343988743367836, -0.5948284303235195, 0.22726248972294522, -0.9802199102429779, -2.1767143253870445, -1.329364325854455, 0.9090704304211066, 1.8794486087392532, 0.20125788314521578, -2.4020710050439793, -3.103702576615523, -1.4167167376006737, 0.20275765723897743, -0.5821938668566591, -3.041123206437576, -4.2541906678912405, -2.7428563133947907, -0.26960234550664475, 0.48116231487636146, -0.6470077540442074, -1.184663069811157, 0.5463107838437847, 2.970518115757721, 3.092470792820645, 0.38551807554232415, -2.3125805556521133, -2.186597987838447, 0.16043863004534895, 1.652962555622321, 0.7504166100230781, -0.756765029677799, -0.4713355941408258, 1.1194693734968388, 1.2028929746086907, -1.3988750055470958, -4.23796483636357, -4.109418975796293, -1.1456954436175588, 1.2952287227952592, 0.8738710841720382, -0.9408082426783076, -1.1645683293625475, 0.5590480823601075, 1.6576729360987759, 0.5127290333977854, -0.9842177474487719, 0.0635049158117722, 3.332847895645453, 5.269734030777105, 3.563003738756303, 0.14362931335024998, -1.3678602968092177, -0.2916042852853087, 0.6866894685751032, -0.3073054255320714, -1.572397647212025, -0.4282172723776536, 2.566507435917978, 3.9444021780502254, 1.9807244261642434, -0.8195177904878619, -1.0211844928894143, 1.14892184696515, 2.3087267179046282, 0.7736866338043236, -1.1281561508963698, -0.5237167976819986, 1.790116122693994, 2.4839830090665713, 0.5445304263019353, -1.2283198215167557, -0.3256852509491053, 1.6966645730890844, 1.3578133101918395, -1.6571034673236666, -3.8192866701151957, -2.594081376430916, 0.08443933383041813, 0.6635896495443074, -1.0206785734805859, -1.821129052469935, -0.1820517129435634, 1.4867043059944818, 0.5321190430394722, -1.69284216958182, -1.5516123404559734, 1.5076526600245843, 3.8460221583050083, 2.612578735122126, -0.3135746829203412, -1.1071532510594544, 0.6191215071652812, 1.6778101132126886, 0.376557007002606, -0.9808764292211472, 0.06469745119346218, 1.9042702183590499, 0.9442264977469961, -2.8600186302262687, -5.3613826452014255, -3.753232324611811, -0.34428938547345667, 0.8675034896607983, -0.33081387896181613, -0.8514032466636686, 0.3840305246973792, 0.6946467331832644, -1.8156769594781583, -4.58573354406417, -3.8370429819087493, -0.1472379687427628, 2.102735375477595, 0.8213874253191698, -1.1212702191662318, -0.49116198645437026, 1.5212453645731174, 1.510474431700069, -0.585232010326664, -1.33030990002021, 0.7032382117993713, 2.4501408516844245, 0.9721535401945072, -1.8523833475894103, -1.946495216537501, 0.865573359811715, 2.585490291479932, 1.0388399572421716, -1.0332419453643995, -0.43323470647044526, 1.528330828020964, 1.2844704964740012, -1.1768993151730502, -2.201199334484988, -0.30092770752028497, 1.3126356955729241, -0.3265185628478592, -3.1667615079582188, -3.1177036816405224, -0.29181843652905287, 1.175448521126214, -0.5428439539247246, -2.3259414490371886, -1.1512066921594775, 1.244744227136626, 1.3945599507777775, -0.20785001766766853, -0.021577748694987856, 2.427370745031242, 3.2053570790573196, -0.04407838287590627, -4.041310948037369, -4.295368423203627, -1.3748935866601342, 0.48799897335154785, -0.057524120003966325, -0.1631031928202503, 1.6453206236521025, 2.4995309635146667, -0.06897771121049318, -3.4055809631149674, -3.126844183982043, 0.27631163572670825, 2.0384843713439103, 0.1830416176252535, -1.8710384103489361, -0.9807068687206287, 1.0006447570326917, 0.809778346561202, -0.5768483163031349, 0.3100777303984257, 3.1771125708424006, 3.759245232252815, 0.46502537742376154, -2.7410933386546934, -2.1305823735960097, 0.31203244736297936, 0.3129385784557384, -1.9821372236389818, -2.708905633409999, -0.894132589097137, 0.05454775924933271, -1.6501045310474929, -2.8322228773971636, -0.49426784490293024, 2.887142270552146, 2.8252767965285894, -0.2778502134890919, -1.9003375149750612, -0.5870839773073493, 0.08575136354887664, -2.2034530744280643, -4.461775617506752, -3.237009726510453, -0.29440417893550824, 0.3056227653863686, -1.169264339338957, -0.8690253349992056, 1.772318659940159, 2.656548821888212, -0.2696922142698637, -3.213548659229001, -2.146793801409186, 1.079546635953131, 1.9169278226479696, 0.2224784131835199, -0.2681187191222145, 1.2687773724477158, 1.406018422403501, -1.1883168162490576, -2.752332577702852, -0.3554143830248125, 2.898492230313037, 2.338330949630556, -1.0651125077653922, -2.381148803823402, -0.4387118848517979, 0.976597224584352, -0.09240270215910555, -0.7335545110494703, 1.1722175983869123, 2.6665562247137875, 0.568866742170879, -2.6037283424157662, -2.064151115860093, 1.623059420719233, 3.2528488608459236, 1.013093929336565, -1.1720644980711414, -0.4133529099090433, 0.8530523699572271, -0.06385390393273992, -0.9369314128284466, 1.40845261201812, 4.802726122166966, 4.398671319364708, 0.43240476356347124, -1.8506783546329613, -0.25279479302347446, 1.4854091171125905, 0.4152416236484722, -0.8492571656530218, 0.803916797457847, 3.142954336927199, 2.221783019610315, -0.7554710236635378, -1.311620364647831, 0.7177110967477071, 0.9182902654380956, -2.028881841232385, -3.825568032125886, -1.6481477998209533, 1.1017542259399906, 0.44798796775723365, -1.70101048727711, -1.1290604872428893, 1.4470033062388223, 1.9261630849837297, 0.2165444087453316, 0.38289556222968496, 3.1850715598109884, 4.156358337140969, 1.000352842195087, -2.206636461385579, -1.4258467237512154, 0.9612005162906678, 0.4559344496265142, -2.0581421883854225, -2.2829089048521594, -0.08903967773484978, 0.6207603969690547, -0.7416217165046747, -0.20230721272379792, 3.389941100737004, 5.374078702002061, 2.5420701502548986, -1.3564601464362034, -1.3609619135462687, 1.181018005334347, 1.6469935497046126, -0.033774791417398045, -0.219040094813782, 1.1578299206739104, 0.3436820003106201, -2.8319906616096593, -3.4388976958748114, 0.6122317617045017, 4.520447939371325, 3.7571595104128352, 0.7029805462916452, -0.07107747108860218, 0.6614676370636849, -0.7523180988495226, -3.4555100661263416, -3.2947094727129187, -0.48502628450051, 0.23983442894128798, -2.2503768359173573, -3.3000929833840167, -0.3943524651834147, 2.397082743286058, 1.2200373673933178, -1.2392781336443877, -0.6952479914770063, 1.4125145252760176, 0.9620577003488177, -1.2125909967316726, -0.8761827867597085, 1.6846365855490766, 1.7625180821136917, -1.4924699717466725, -3.277338684388545, -1.2909688401355668, 0.34115207144678156, -1.6951727793618985, -4.149100293886123, -2.9411349477811077, -0.18033122795819845, -0.19261234935676505, -1.8719667403742783, -1.0064843855079053, 1.8188947816630177, 2.171196233976263, -0.0270652221772966, 0.020763749684940276, 3.4278175905778845, 5.094463385780047, 2.0725850151892784, -1.4922699325921458, -1.2819269217578106, 0.5740926210596976, 0.28667410139522553, -0.7148352887707377, 0.7046587126913679, 2.40561985643989, 0.04769431568196637, -4.6743963321747675, -5.686433125124605, -2.0887214548496105, 0.6157630220089657, -0.3740056728736462, -1.4519344432095738, -0.017125211582413105, 0.876175696456956, -1.2241232846193635, -3.022846486334297, -1.337785850811479, 0.6273365305004753, -1.4655247134549083, -5.158571571084762, -4.860530361650101, -1.0865177838706288, 0.6900793346970245, -0.7438902210375392, -1.276890753387171, 0.2974044517915392, 0.1741696019878743, -2.7607363060033028, -4.031982419616548, -1.378599537405262, 0.7720743189006741, -1.2628096375435944, -3.979497741422885, -2.7337565203268666, 0.3815924362089608, 0.623152523040727, -1.0470664378423282, -0.3593564143242843, 1.913194615949666, 1.2059701312223732, -2.2324344425900104, -3.3116379471051296, -0.9754497608479057, 0.12383932514764759, -1.711580370011868, -2.0219887133842858, 1.5357220719259286, 4.3819661476750404, 2.5848634492714444, -0.5668443220689362, -0.5228586173470864, 1.0241015767755428, 0.3506525366925356, -0.8343053944978304, 1.1646997572417963, 4.181001807340934, 3.1107275238002763, -0.9646779126408183, -2.057226575727916, 0.7636141897240363, 2.165365659880302, -0.022720165273315496, -1.6438046191421312, -0.33118591193803043, 0.48135140277326904, -1.2398763926031187, -1.7620830455097678, 1.2750456165223192, 3.4810686856434656, 0.832637626865902, -2.9931616705090605, -2.491817227048191, 0.6749904837143671, 1.2125414293196721, -0.6046952111074726, -0.5094431812109783, 1.2653198020468266, 0.8217058330835914, -1.1113066012568735, 0.2759777535557387, 4.709047362804112, 6.087100935250229, 2.4649363276882776, -0.7152481995427674, 0.1362773682806769, 1.5083102825331405, 0.24790365478548665, -0.6842750803517277, 1.3906800096690746, 2.964004016497257, 0.5624175900913919, -2.3700517755507993, -1.1903524397231993, 1.6988717081630076, 1.2389900981162865, -1.1760082401896184, -0.5124792038761352, 2.455378049610623, 2.496771564323148, -0.5281543331458332, -1.568443837997072, 0.32915270475571967, 0.729122554959379, -1.3399713270984928, -1.345935150298256, 1.9246182856003953, 3.385962704919307, 0.6488982154584285, -1.4083865883080753, 0.8181308277761582, 3.4070562039478136, 2.1913907363106553, 0.032607544672605196, 0.9960339642749695, 2.7920070843966243, 1.5981583290434944, -0.30084567543368823, 1.0871528912472375, 3.2686811889753007, 1.2670118637044756, -2.9734893521679107, -3.3320910557223877, 0.05115089910162922, 1.3464866751269629, -0.7334678751981087, -1.6308747582579937, 0.0022184267000060678, 0.42980569220484754, -0.8287216054776847, 0.7092022812536867, 5.4931629228425765, 7.405628027799749, 3.673459745183124, -0.23456697562620132, 0.2442689955509248, 1.854477650856424, 0.5879219625800233, -1.1665256900290712, -0.3269167609934746, 0.22833861622578958, -2.6257975659125083, -5.203765418015524, -2.9157398944295827, 1.1733809703283125, 1.294419120566348, -1.1847777135032225, -0.8669154577035771, 1.6586543006563357, 1.3983632151511602, -1.3808850336285328, -1.8007329562216312, 0.24590907328082323, 0.13186909817218512, -2.15652831493441, -1.56245904984261, 2.263709638809236, 3.520285971622463, 0.43871944892728654, -1.6270140837818214, 0.06495574777281223, 1.1769058653105449, -0.9488274788973516, -2.1691006779782858, 0.3794230907647031, 2.6515698852243434, 1.306448204792454, -0.08986763275063102, 1.7761202070545097, 3.234402655006211, 0.5527316400810606, -2.4467731858346053, -0.8808936593789495, 2.330905658386033, 1.737405588274355, -1.0241930031526332, -0.883885605651821, 1.2247204628060788, 0.9438350364027205, -0.6613638780653804, 0.4210628848370964, 2.244318844660156, -0.38407236765544767, -5.701651243644244, -6.722607692722528, -2.6846714240575533, 0.25822977651941476, -0.1607837644706091, 0.044138582514779985, 1.966521995795119, 1.653193591229139, -1.1660729450937524, -1.3542881512675597, 2.0207411927108616, 3.1550178476191126, -0.18251469462187536, -2.395583613259053, -0.01927399685541157, 2.3979662636758285, 0.9721851841307256, -0.940094314061973, -0.0771497824325796, 0.44907253394879326, -1.9083825690910763, -3.1261621100460317, -0.0814245808914021, 2.613011086786119, 0.2882404280314696, -3.314516012419886, -2.655258537161795, 0.11837840580518122, 0.10765447918951172, -1.0636274861286832, 0.7324472497062984, 3.316615393174562, 2.1614713883741765, -0.5626479689014252, 0.19462697155827136, 2.6554692405270583, 1.426125416774905, -2.203972684135552, -2.547712221595064, -0.1132683233662303, -0.3184516946472471, -2.9160393268921077, -2.451398810304484, 1.2343747449007505, 2.62799058812241, 0.7356386846097978, 0.07906527467758331, 1.0506532644936828, -0.9311000351483937, -5.459723774575402, -6.197834929759141, -1.9391070493338054, 0.8869671345149546, -0.7161842806401998, -2.045574368849427, -0.3977425100251697, 0.3101923886840817, -1.817656374692957, -2.551040434273742, -0.2406724405044299, 0.2418637814867443, -3.084560759766252, -4.626963716897654, -1.1350742097520923, 2.0636503320202193, 0.4256240351024867, -2.2140198081969977, -1.4444326028100603, 0.07071761160633713, -0.818628251229013, -1.0323252617052867, 1.928351378118548, 3.6129122299818053, 0.46590923075436985, -2.652230453933947], 'positive_zeros': ['1.1646214959645485596015303116', '2.558351703418256597485477489387', '3.402575754769575055345033920958', '4.59371713941824510335606351215', '5.524228023551525693788544695700', '6.79780782356987071776710658085', '7.48092947828693788809055832240', '8.15191744938308794887791103524', '9.82928704211076660780222477043', '10.14009386608915658424008885012', '11.23969524990097202714427885480', '11.84603908924156842079320536197', '13.2010335698998128953499079895', '13.92409877604965704572226064421', '14.60247106783712190596389138235', '15.55939942269725541000609319781', '16.3276129138138539816225083441', '17.62248621529293272307419379715', '17.91327103177840990823370454709', '18.936610316149074029068375101832', '19.71097232022956429129794559265', '20.866674397876199745306781584920', '21.139384361509941441004372385738', '22.54750604887214557617758267128', '22.9757031117652863818898992845', '23.68092261591930276795794697109', '24.723782362023327626790627699531', '25.604704034890572857176072803578', '26.3844887232940147824932456882', '26.97214039815189926723431074808', '27.67394176354812946350419884973', '28.86406215252539498335633540318', '29.520779149120950632393092490304', '30.22396100908272819593778614605', '31.02195563839442449068567814559', '31.55472635436671309199501899500', '32.82805031804384092937484190806', '33.49681663626396341225743446626', '34.00259974867937190586552542567', '34.737398628517427175331988144255', '35.827699563463108602543028023829', '36.41220092005745380856197432309', '37.29108051878026202272659861546', '37.888434229049484349406384678997', '38.81989077963534160730836103922', '39.422504620418225660498891859269', '40.15749407301471013246787503023', '41.23747248330628665561847862146', '41.70783040882201606874741774770', '42.525048003895700942844855505881', '43.19677073634359671145521675952', '43.926908975741899180951592936820', '44.96069315385659776580311081548', '45.53070649249930189371435645471', '46.31157769697898303679940210603', '46.86512028329572469861629757468', '47.590272892561622973743965752087', '48.79136893529396955741308640007', '49.3039964344086106854269225246', '49.91724356357546341229177217607', '50.43537767096662099913297997515', '51.57496994938464639592933918067', '52.29544088819878019150001179250', '52.887123538949102699583357975063', '53.66643188534648545735139552732', '54.2906787658951062795767220925', '55.10011104246650525612507209641', '55.85086082326050267251551992220', '56.69110649534869913769316899861', '57.2541221318601414706826001624', '57.984040920575873794966976260577', '58.78781648058218649921090162550', '59.33972632748250438011469722138', '60.34534758488882663590538682433', '60.8686489463423622481774037547', '61.70048354510686316138654216872', '62.45301454823855700912214520686', '62.81638282890656110392219142342', '63.7469618900021994738919258745', '64.8602246842450180778045081126', '65.293096358453318351853409335988', '65.66842374223514899063271329784', '66.556799823889116374568357162059', '67.4750391926395428336898125854', '68.14565743953651430947418896832', '68.887413862961041814700581014580', '69.53700643845004845300022021536', '69.95675422609110898204514357986', '70.9724462937027902703295234245', '71.82467365120036104813674029854', '72.23947894071336711565716430342', '73.30838234212972996383957414984', '73.463067791710098593851801405528', '74.41595127005898580142138445927', '75.28510541157676331242961757285', '76.06216921411696083867587595323', '76.27596836360354537415741822081', '77.54538626285707602311148834089', '77.8892509564750981923451019', '78.552999231168622742178017966205', '79.35328729452817007937150385385', '80.2006269914590041327811123814', '80.98187554818386769619537734670', '81.32331164354445191860535934998', '82.06376253972055094578232047408', '82.84163551131495183042701537540', '83.652187945047819847257764126800', '84.43411655130339592323190517721', '84.98144899130183730150873206960', '85.4713319123921216707973894723', '86.29926325536237771594013295834', '87.05556203255758262715490854688', '87.92052206427631790261887288333', '88.511862570977792782752436546441', '89.05017347432260819267231505541', '89.553170050863769794417886201662', '90.659605180126986864009122062607', '91.28132116182568075365282711263', '91.94239244668703107047200446172', '92.402345336593414983405918315286', '93.35041822743052219958217732905', '93.95717893974041151682448944070', '94.49520071040496884421807689389', '95.468484126225247122193429293606', '95.9974337688583821470056116576', '96.69888374859138248639352050820', '97.55608303762882776990425575315', '97.73249701247454787497298556684', '98.82559373241963678871141287088', '99.541861743060461334063433095514', '100.05938550311206736044511410186', '100.95126512259096202275223768353', '101.40398715740263037871750847317', '101.89927095718043889021340385078', '102.99351494889428160177192168979', '103.60359848562954350481556488286', '104.36783681785482803671768456986', '104.74203416291262113403240944740', '105.35185523886887429887507477190', '106.21256592432280133649642048870', '107.3161772436436162620387118096', '107.53138677135348607331122055408', '108.02672184882189076609497639834', '109.13048569167901479736754322898', '109.42175331416737395496209059068', '110.344583020444633152792248664146', '111.07112704467154270483637643241', '111.65758469262937307391670404414', '112.31870399366703644528185446893', '112.92323290772832909885333466890', '113.6210833030558527548791655293', '114.54663949768031171551448666548', '114.79839869883459275867178060415', '115.97296668982211411341508091950', '116.20766112213118383497667269302', '116.98586940505342243291215322112', '117.80802616699324540784752193077', '118.12204094497712394935620519343', '119.21599914219853890707214858438', '119.88241605634854050811964654922', '120.37720177127741296748338586179', '120.838869539108127017262552128296', '121.56581501808741943893362904723', '122.68896658275508877068673950588', '123.06180314627210730768809547361', '123.75275313930891582031248664910', '124.23327032357850679853625617532', '125.158799658453782057697129042177', '125.48483196902345558509989692193', '126.67329069224159965174931119661', '127.05988826203150586623776177457', '127.75423153245567923369296534266', '128.151166520143124733140497020239', '129.20127491673726159450637555316', '129.559312867969255131556709229997', '130.57567181330191223898709579562', '131.048955483265371783046652443429', '131.610588127065946258086980120496', '132.30345218270849974891212126878', '133.27840241753414355511929425916', '133.477724486973637846317607502460', '134.26290572282687937787886323763', '135.2363045393259961242901379761', '135.71804516939410770613319243978', '136.31297655628138801882223622263', '136.75533974181868425870484462876', '137.73403356664385780475847121285', '138.36355052550553435583825114679', '139.059956061448118729818166383001', '139.746359039581208318896258922297', '140.12169718747013314005989711308', '140.83050105968686760123202852786', '141.62048059261225779005234981327', '142.42520138962395230499591468954', '143.01703015444192612058954267435', '143.526743628305657619250920409135', '144.18130427373293210115546092136', '144.66311037009475740518923743527', '145.823829940880322568820317775001', '146.22891412189481748845169497446', '146.91615657849938564566597241652', '147.33391351604506706094249294331', '148.17184842582598355848275923964', '148.86467763832716329572549651632', '149.52180516110625419627578469906', '150.0563014070526027175721861296', '150.88277933774174868516626864265', '151.51211002054463838198912498804', '151.999293656206128157313598283295', '152.64531419129651838288164051396', '153.49732188453485083620500543564', '153.98665658774296947815195816780', '155.01391348836730356663190809210', '155.11644335648554197593266588845', '156.16062109261481282445361228313', '156.41449392619354805697893390333', '157.27663246524824244972794081302', '158.12010637144725197951616730421', '158.65608802491923697439200483669', '159.37458808033745676463238297256', '159.79428096557327378820999359750', '160.24685848907531856905168509885', '161.52755687734275683475555476764', '161.83608193968073855825086304860', '162.57841559341135028764292539713', '163.19325907856630469243146879836', '163.48595013351149616749999969415', '164.57940197061004408571980326064', '165.15614395074905887573226045741', '165.73087829874428242002914218448', '166.407633888199148963794093000753', '167.14500067205901023052146275195', '167.52089529983317531371202483804', '168.26110500369179960240377194799', '169.1011568317008182908446716274', '169.6790095142234094781895350476', '170.20263187527907610602339825726', '170.9029252751184208205979745091', '171.78513189845729900458756840055', '171.92356441823074726528855213537', '172.85564959911496167919420577292', '173.51265720655032016871279752999', '174.24514654598396516323003484575', '174.81177067878841848554362351078', '175.46872172764170459404993108806', '175.87947579103363571403039989146', '176.538131621258038904085841779287', '177.75125498841850299622048343121', '178.07033053487076949602408095843', '178.42809474556761979545504382545', '179.24599770464748575614801867102', '179.82804367920408485715808348305', '180.6107446202303391842768222289', '181.251705560597500619029862825147', '181.993899070908367539009537961555', '182.51564837938409580559331982872', '182.90186861755974899318621714185', '183.75621718622792961360956926320', '184.396279226570773103767700095180', '185.29309257954475259282560027571', '185.64746279629898946186805055697', '186.171945643600229378487779791595', '187.099472092619849191670334530333', '187.47569944025423493257794293741', '188.24338676806376785652094294146', '189.08303088586306719213985311185', '189.323246948012012893542236606512', '190.20974259582818465690018705016', '191.11316156148450531496481641910', '191.210018755693722290507215650359', '191.79470386543221130133421261884', '192.962661942409465276051172050898', '193.346918190574833632164606159891', '194.128827071464714356273940058278', '194.44372523524046167652833122415', '195.34586551714679850482738035667', '195.66064720445532955444020247095', '196.641237592194514564564146328921', '197.22759103981617223390408815142', '198.08298567429337511441017303597', '198.23172264762214130493803414496', '198.88664485354524808870077517409', '199.72025103809395347824621660604'], 'prelabel': '1-624-624.251-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8978438172095515, 'root_angle': 0.21241523611846672, 'root_number': '0.785481763783262023546351886565+0.618884802498765322601557253369*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.106207618059', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(12)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.11679831304332125691318971501+0.168923273690603811065808468939*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.16462149596', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.55835170342', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.40257575477', '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': 2.8978438172095515, 'bad_primes': [2, 3, 13], 'central_character': '624.251', 'conductor': 624, 'conductor_radical': 78, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/624/251'], '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': '1-624-624.251-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': '1-624-624.251-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8978438172095515, 'root_angle': 0.10620761805923336, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.16462149596', 'prec': 44}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_624.251', 'Lhash_array': ['dirichlet_L_624.251'], 'label': '1-624-624.251-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/624/251'}