Lfunction data - 1-1368-1368.1307-r1-0-0

Formats: - HTML - YAML - JSON - 2025-12-28T15:25:50.033186

• 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_1368.1307', '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': [0.766044443118978, 0.6427876096865394], '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': 147.01201711904702, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [19, [1]]], 'bad_primes': [2, 3, 19], 'central_character': '1368.1307', 'coeff_info': ['x^18 - 1', '0.939692620785908 + 0.342020143325669*I', '\\\\zeta_{18}'], 'conductor': 1368, 'conductor_radical': 114, 'conjugate': 'dirichlet_L_1368.1211', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^20', 0, 'a^15', 0, 0, 0, 'a^9', 0, 'a^16', 0, 0, 0, 'a^11', 0, 0, 0, 0, 0, 'a^10', 0, 'a^4', 0, 0, 0, 'a^19', 0, 'a^0', 0, 0, 0, 'a^17', 0, 'a^0', 0, 0, 0, 'a^14', 0, 'a^8', 0, 0, 0, 'a^10', 0, 'a^12', 0, 0, 0, 'a^13', 0, 'a^11', 0, 0, 0, 'a^8', 0, 'a^25', 0, 0, 0, 'a^0', 0, 'a^13', 0, 0, 0, 'a^23', 0, 'a^8', 0, 0, 0, 'a^24', 0, 'a^20', 0, 0, 0, 'a^15', 0, 'a^13', 0, 0, 0, 'a^10', 0, 'a^13', 0, 0, 0, 0, 0, 'a^5', 0, 0, 0], 'euler_factors': [[0], [0], [1, 'a^20'], [1, 'a^15'], [1, 'a^9'], [1, 'a^16'], [1, 'a^11'], [0], [1, 'a^10'], [1, 'a^19'], [1, 'a^0'], [1, 'a^0'], [1, 'a^14'], [1, 'a^8'], [1, 'a^10'], [1, 'a^13'], [1, 'a^8'], [1, 'a^25'], [1, 'a^13'], [1, 'a^23'], [1, 'a^8'], [1, 'a^20'], [1, 'a^15'], [1, 'a^10'], [1, 'a^5'], [1, 'a^22']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-1368-1368.1307-r1-0-0', 'leading_term': '0.450953323569823452502107244867-1.14185381461554768529191286389*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/1368/1307', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.227676274101095, -0.5157871342895004, -1.7930615811323791, -1.8730398023470984, -0.6649084911921742, 1.0177136169720784, 1.8943843330152896, 1.2466726041256517, -0.3210077006927772, -1.254494241343453, -0.44839538209297725, 1.5678375367682738, 2.943662260772009, 2.2478148974604255, -0.0018496131203047668, -1.6952109443415861, -1.218669917523116, 0.8227884029713721, 2.1864313076560005, 1.4108077090587854, -0.5389897219908271, -1.3419502069799627, -0.019213503540798715, 1.850019267529041, 1.9572963973921889, 0.10810090630821693, -1.3622143476148703, -0.30501552902473805, 2.5363325767290954, 4.196657633909212, 2.9055604385993496, 0.1511199369499294, -1.1941577781808526, -0.3857319742390571, 0.4936855580295519, -0.43662366683768083, -2.074930429621924, -1.6183523279486864, 1.58058310353387, 4.680703206278643, 4.570789472173194, 1.6600936219390836, -0.7074377280294334, -0.5088860940646676, 0.6356155344676183, 0.11010975550220765, -1.809768557795005, -2.298735269661019, -0.14592822614829074, 2.1581437393157605, 1.6041576091075012, -1.1127209603006387, -2.30110757935202, -0.174389099336872, 2.7492269853685647, 3.0982074009967313, 1.1220496923571035, -0.0769912500998494, 0.700375352614749, 1.0303273515788849, -1.2355450339251126, -4.230360503037293, -4.26383051374115, -1.0530611560030252, 1.622318257706215, 1.0153164415599276, -0.9902689018777322, -0.9542299569471724, 0.9609248923380385, 1.3973062818949664, -0.9086745213966825, -3.0134866094153314, -2.1263236096437286, 0.14063091056987484, 0.19666076478588213, -1.9995975142855777, -2.7842519132056687, -0.416041656358149, 2.0473848147184994, 1.165839061899062, -1.7520673125879598, -2.6024929372575594, -0.5557707057984197, 1.0159445214198561, 0.016816803377668884, -1.1794173251034896, 0.14878595452809143, 2.264123853112852, 1.3781339234091674, -2.2335496543962483, -4.105779646642112, -2.0254797485923404, 0.7564912771163173, 0.5057425948570458, -1.5610683836893695, -1.7101515926150297, 0.1925037580631008, 0.7786807929659427, -0.8410378282256721, -1.2341283181597593, 1.7073879604439217, 4.716250720217558, 3.6626257184023894, -0.11966289555138612, -1.6990961579157753, 0.2083909283639876, 1.9047423441462839, 1.0076637775482362, -0.06028236563697115, 1.1364438316889833, 2.355548721934209, 0.29496694718118693, -3.3264174071814603, -3.666556266383491, -0.15265681641523637, 2.4751186507703427, 1.3432256208799336, -0.5618106063696124, 0.25193875196940113, 2.158927003276824, 1.7064155564119923, -0.09718718778613725, 0.5967180903583381, 3.581516476936867, 4.311535503519339, 1.1830838880042471, -1.6271281125874064, -0.7067500834287566, 1.346900263947885, 0.594394645294232, -1.5822152638206823, -0.9948066598567231, 2.0431667108075184, 3.086546316183828, 0.9477039964321111, -0.5460122907714136, 0.6086599837036474, 1.0472202047281998, -1.9045328314880496, -4.950479037087723, -3.7372761848187626, 0.0066743105828459635, 1.1794779145568897, -0.5911471537752127, -0.9793248491394742, 1.2872131483854807, 2.4208560386752906, 0.5370028163551958, -0.8653235614408477, 0.8444831983272117, 2.4849020683087444, 0.4652776539959805, -2.6043461112400896, -1.8363424734535643, 1.7807281020615255, 2.862610135293534, 0.28811692740723294, -1.5570169035323862, -0.538213840902583, 0.2541225186024018, -0.9116911391405823, -0.6885946977549103, 3.0291755601753394, 6.030231997949084, 3.809671820055792, -0.9546827169755367, -2.3669433157701922, -0.2627233283725367, 0.7113585393987836, -0.48021880967942143, -0.2923837459582491, 1.8916443934917497, 2.0166576497246096, -1.1040018673219796, -2.7643062412593022, -0.04555259560815105, 2.9824740555844103, 1.9609675522222227, -0.5819870847097791, 0.03614427024186839, 2.5252686870491887, 2.3394482674449377, -0.03259760449774214, -0.20782513833583094, 1.8638038909727845, 1.8307040097771712, -0.7231164652266804, -0.948220724338423, 2.6385741729814254, 4.95007440598752, 2.674208694121469, -0.366002833097862, -0.1688666728870386, 0.758073966478636, -1.2464957449083882, -3.7625864033023326, -2.5472150718208626, 0.5689596051455019, 0.7692990154986237, -1.2234822708294835, -0.8452030903557113, 1.4759131814469582, 0.7764608774490196, -3.1544777909542296, -4.605006401819354, -1.4602341219266093, 1.4013539743891066, 0.6810768852903425, -0.3494882048640794, 1.1028649769212149, 1.986899640369257, -0.2351003962262742, -1.8669759459314446, 0.6194800752215078, 3.4961867652040977, 1.6301318646921386, -2.5761293964741596, -3.141938772225068, -0.35795634025985734, 0.7833604301022896, -0.15222973674845602, 0.7047690975667982, 3.0802858505767228, 2.651326897034152, -0.19214528091150454, 0.049564703910805336, 4.195316439074597, 6.200575710636073, 3.1990863697224206, 0.04990807248375679, 0.5390588282149253, 1.451151329145866, -0.2971783267753272, -1.6412121715464163, 0.21150244315590902, 1.7226307594793824, -0.4697522476903789, -2.595925748457958, -0.12440271148931824, 3.732208392357199, 3.257404377812949, -0.02548005545255033, -0.6519236753104497, 1.0047819722103155, 0.5317954470847377, -1.3632842284828133, -0.21595937156924588, 3.025956607697797, 3.0531142346656486, 0.024922483880704602, -0.4763547788216851, 2.294806411138609, 2.924813411484928, 0.0039880114394865215, -1.3108270672011488, 0.9256796886579058, 1.8687038482625276, -0.8295269401527716, -2.5884445046115734, -0.5966545662654587, 1.1373110499559238, -0.11492748738788683, -0.509861875810623, 2.3708874254385006, 3.8053050769556553, 0.2701071923460454, -3.4570512635375237, -2.1840955167693163, 1.0137814286805658, 0.9765085947224231, -0.6135007321297055, 0.05311750554780986, 0.8266386876983246, -1.6661305236040773, -4.09187768476435, -1.7672074729425413, 2.2210457277902407, 1.9996447729689564, -0.6450994781001956, 0.15655578361235328, 3.4713681315509373, 3.638753699867365, 0.7930363826407704, -0.18193977698918845, 0.6964024564935587, -0.46863855364004425, -2.2712557937717643, 0.17998774798058959, 5.01767594931827, 5.252067759842295, 0.634080881248362, -1.9658138582225249, -0.353348057635675, 0.699913238005853, -0.40871496493569837, 0.14243240909119947, 2.4220189674615855, 1.5104291244268224, -2.5632320959460593, -3.5766078798261636, -0.16657401920098489, 1.6462641585268254, -0.44143997724475825, -1.2905575666357585, 1.2799507729869384, 2.33023263686256, -0.32789776778545154, -1.824257928878958, 0.1931566845540847, 1.1822413126105114, -0.8837346702893194, -1.2237783646690064, 2.109374361728824, 3.7582522776090093, 1.1213457254525234, -0.46969911007550397, 2.1658695860682013, 4.047458774205671, 1.6100784797009724, -0.8154416234450015, 0.16689410859651255, 0.701496249653594, -1.8721719146168552, -3.173091489870352, -0.5140483611248478, 1.3422068755399825, -0.5747752803973831, -1.3027228338451753, 2.4411472848839266, 5.341518070387056, 3.0076433798733597, -0.17221735336708782, 0.4279982213691573, 1.7528367372988936, 0.5016660759428616, -0.12833663038372603, 1.90444912271749, 1.7958768812634145, -2.91173099135032, -6.03517910268835, -2.9881268425858636, 1.1249613558129206, 0.8773818681233763, -0.571058731333516, 0.8169686534387631, 2.0357510769028293, 0.24375086743197072, -0.7438343664307218, 1.4393114334105979, 1.7900328467321964, -2.5324026809847644, -5.54761974867586, -2.7055741361581815, 1.0130851033482229, 0.5066575491988267, -0.9119927087690672, 0.4053335688415818, 1.0133079692691584, -1.666903241257889, -3.1136030048382546, -0.6226417551415548, 0.7083253720260689, -2.1902905733850364, -3.985510062188517, -1.153527003437403, 1.1507024149987997, -0.8352380499539777, -2.40240785881162, -0.007969957240277329, 1.9469308047606098, 0.4125171091516509, -0.29188831467928533, 2.099172221413423, 2.6310941682711637, -0.7166503505487295, -2.1902793007229353, 0.7973675372684236, 2.5684345649311457, 0.3123798870051338, -0.6853657333258455, 1.9707718693598073, 2.8143179517832633, -0.5130352073369704, -2.518863427045567, -0.6105271600550909, 0.6286518381130072, -0.26768862350471934, 1.2761982653129016, 5.109313268099195, 4.72172312512528, -0.35836637926062265, -2.6049655269745045, 0.22537308508976622, 1.9088828358319572, 0.05452558622831904, -0.6543853057622192, 0.816691555876738, 0.2769747050424129, -1.424435287053495, 0.9394024861730974, 5.484214211401632, 4.969597361040873, 0.04810632949301291, -1.7879065514862509, 0.21109565243614287, 0.16523881538107354, -2.1084751895657328, -1.6448802866120065, 0.5994705267843936, -0.25072597604194563, -2.3965626683113554, -0.9934936388148037, 1.0756001411496876, -1.7104904183296845, -5.849450670974902, -4.475528675255569, 0.033027953148771175, 0.9881794124616069, -0.49459220469133397, 0.1901034970476676, 0.995551020832812, -1.3358777070548642, -2.6226854618633157, 1.069909639784674, 4.585949163057756, 2.7439315902780197, -0.04659233457920203, 1.1918295847125941, 2.6231433741500183, 0.4444700246287178, -0.8459290967002299, 2.1319001526261614, 4.2405786210470895, 1.9041079614488783, -0.08028119317354701, 1.2269270419595024, 1.246360698322812, -1.5271063768506572, -1.4161731119660228, 2.6287320487812145, 3.7056785110240127, -0.03625261751303824, -1.9251023034534867, 0.22143023921773042, 0.7797458237391957, -1.5167791805182733, -1.476363599280408, 1.0477682945070825, 0.923142053994678, -0.8250939562101473, 1.2034080611056288, 4.692180097467762, 2.9371315893806718, -1.8935578010327303, -2.369712288705217, 0.5342881289075542, 0.5993589233360579, -1.175045497752786, -0.10897961397432128, 1.6186166135970776, 0.2232542791332047, -0.5500938495622656, 2.8722284696768368, 5.010204558876826, 1.1798502780187166, -2.7954748161545147, -1.0734241387578614, 1.911398230816457, 1.04815998672636, -0.3467235649402016, 0.6099593829228575, 0.023267050955757342, -3.02819379480676, -2.7078979661292664, 1.6539514607958166, 2.78065030459067, -0.8672696208648852, -2.187794074210995, 0.6301224360983286, 1.3659694497413777, -1.1502403386841848, -1.517344617488328, 0.13518289280353352, -1.2365735637361899, -3.852450579494314, -2.032560959306615, 1.7109750803849506, 1.206563092362279, -1.0339341460913254, 0.6385804642946921, 3.0533183896391636, 0.8474264680051025, -2.1802469451494053, -0.7189108937769898, 1.4240086628261317, -0.36381844202948666, -2.162055704640124, -0.5150312778616868, 0.11585879684455881, -2.416610891890283, -2.3593395257587346, 1.9360422343161103, 3.494382589042725, 0.13686625868914362, -1.3747122818000146, 1.0582370005825945, 1.5145691576349307, -0.9702243173028609, -0.7630600217873361, 1.9390968458419615, 1.5890042311800538, -0.7088603982703006, -0.00402465254656301, 0.8239435885618696, -3.4423334899908493, -8.118426545366924, -6.010493691131626, -0.754786338979921, 0.40649521530297, -0.694209400092939, 0.361606910895644, 1.0163578644701936, -0.5882137900397143, 0.5696688549898996, 5.569670430562398, 6.842679292291386, 1.9394183081738228, -1.3914472228146224, 0.30358429672355786, 1.026749669450714, -1.3117041488532297, -1.4825231650537787, 0.7871338197502298, 0.27088582063289557, -1.7664196800984788, 0.07090662472304007, 3.1026060740513923, 1.4131737085333695, -1.5380204211682575, 0.4976206090795059, 3.819128887707277, 2.30981363816675, -0.5243222435737428, 0.3658064747382563, 1.3258834711750387, -1.0714910369653008, -2.2505178931300875, -0.09475374731623222, -0.3649177065725391, -4.307495265911404, -4.888886741615281, -0.7162238919992909, 1.1893573819215142, -0.4153502309911881, 0.39183302729537567, 3.0734920338000693, 1.5518227428127123, -2.4048050346185463, -2.215829274383729, 0.4701096934575296, 0.31216721084763743, -0.1730255286000866, 2.7281315577401983, 4.19763193717053, 0.5467545384486968, -1.8212268012190431, 1.5651302160742055, 4.327237820203058, 1.8591600213609092, -0.5710080430065023, 0.27205216806916416, 0.0930485159589044, -1.547647547329734, 0.3507731632238572, 4.006213351234929, 2.7677631244093277, -1.0266787561658783, 0.028193738238844364, 3.5836980812198753, 2.39426553063112, -1.276609413107623, -1.1250525794524475, 0.6922154185907841, 0.04785103124409866, 0.23323305353843743, 3.175145088712295, 3.040422431954463, -1.672083696534051, -3.224518834637301, 0.7130922124201076, 2.528183189616848, -0.18428352759736877, -0.9932009489328036, 1.2336977803903197, 0.9809225357364022, -1.0906973135939746, -0.04249102749736459, 1.5139476754397825, -1.1174229276168015, -3.3490769342833526, 0.036381165705144394, 3.477734725926389, 1.1776437401096207, -1.850318791007279, -0.7682754825698165, -0.020431167046045345, -2.105016896805273, -1.7509202204891987, 1.7653444029225103, 1.9464529089028517, -1.297888662518183, -1.3719354227711549, 0.9602077224973167, -0.3430600039890652, -2.928537187978884, -0.8457081224554454, 2.23444491849519, 0.23242833301154, -2.7335529851816323, -1.109930913335266, 0.9648144246770912, -0.6114360773642494, -1.473878748625748, 0.37418361692839947, -0.3321150324123139, -3.4678717980458904, -1.9335140474312436, 3.4222472672901354, 4.1497626815886, 0.3475352995647249, -0.5609375432998293, 1.0648787658123098, -0.1384020709885262, -1.874324871602097, 0.15789008064730742, 1.9614093646730335, 0.1473613968013129, 0.16537232486012374, 4.32939749877053, 5.3187961488381, 0.696386064799073], 'positive_zeros': ['0.218653910338166797125506432849', '1.37104970240759811609361730191', '2.43663112924168335226517464071', '3.20279336758973997447192373286', '4.374755555656500706409082642451', '5.19460791975796115901825007467', '6.1608266309944334947078913049', '6.87796201929661662901402460539', '7.82825373662223337523592973292', '8.47614235247348664815841402064', '9.707212067910739838190989287494', '10.40724591108114713910707046339', '10.8505991750535443899105889490', '11.74136058201760667126024027820', '12.99514477562428098099977596152', '13.55994739450182336397901524453', '14.08345038041889873898634416028', '15.015908116967024527337499464943', '15.81386445362534224452016508241', '16.57938325691106180158890529333', '17.74054160484285345739280018492', '17.9028518469353820071457982728', '18.61993572592999785387762964681', '19.78068320666714859407048418584', '20.45956845571375157950880800700', '21.099869199571553643422671599819', '21.7755789395010456885894884103', '22.78680916327237434191443313508', '23.162094212416889455394022235486', '24.10326829499940714367109307345', '24.813278970641341972421773392901', '25.69817024722603457378665491018', '26.252998474440057764155206404449', '26.85531428481709967622897272901', '27.62903557838947152676225701624', '28.639035759718877069223993048682', '29.14119732138808097635964098774', '29.96800004153321639418238505887', '30.483925819579838965772946006176', '31.1025812040337918066963565983', '32.1766872146350648776208290012', '32.7871694294449497556226334134', '33.68249028631610378868215650289', '33.81326054005952792142347545079', '34.712458212070294045309405910303', '35.63702169830063916291049509343', '36.43453765036370619720268227130', '36.83450071648034161311410067277', '37.786558012840051947911025457774', '38.02866429140639258748748332615', '39.16123206987173757450119292534', '39.77817995321064162402267897731', '40.39137686575780167636967691967', '41.04719572904504186338030166298', '42.00569388697797270256543335448', '42.38293030754098208073857135190', '42.96070644101865728504950885467', '44.06183326447551516720768869295', '44.59454882236669884928759836442', '45.15624612988223740098758557823', '46.00900715614285787102973226934', '46.454793776951070406896284233140', '47.228396458886117324835871373446', '47.97256587770515261049020614538', '48.780159861748661274392821550098', '49.49361898469512511031579497870', '49.79042333611782856575921870460', '50.39284087408679225541327143548', '51.49160322663840314941575709184', '52.22555099272953780436573522666', '52.699137026609918770587385861959', '53.17520220976478592052010771306', '53.96460511315424533581203546616', '54.69110402060408194172329252309', '55.53011913303111040740586382693', '55.93264848922826849073170477677', '56.86963443806393787188180706752', '57.22583878448622655531349315520', '58.036244235268341742281121445196', '58.5428278172291298142168538727', '59.62863220027852311055593627391', '60.03601756848853605862207307601', '60.48651028870436346746217702005', '61.49283768062782327397385637136', '61.995045620731856785240940556723', '62.610480118869601289835822197189', '63.19637261820939297868133882062', '64.182542580008027744879148364811', '64.81886082043835085890142778647', '65.12597851231760573976556409694', '65.91237288961712146638249726635', '66.510767357985897103561712174786', '67.30211222419883356653267278348', '68.16992645755637249609933654590', '68.68906183135398027786906656904', '68.93687599742836358371770117302', '69.9739858849023360167226489660', '70.30696179466455683077094155316', '71.57506285295213828611979836761', '71.75208047715923752678038282117', '72.461491730422652516924951683968', '73.10005667390229912536028039519', '73.70465148394300020091014819954', '74.38394774752035797512616672085', '75.30945227746711874879017814247', '75.74936381141557668592753385682', '76.32912470996732239708083611554', '76.89671386380811875761920816274', '77.81548882564906299018000852938', '78.19356447326110674641693407866', '79.06290356132930194999537930520', '79.58100541410701818739598636938', '80.23419635014562654008898128966', '81.00605862233776987533734380310', '81.54227077159233987273552263885', '81.954802678176998895729123578', '82.829636947649614786444009402159', '83.63087432502270672972420152662', '84.22753723919092549900193428010', '84.67681386265001814806463311577', '85.15025026522163953918660324893', '86.05979223568526770617520944859', '86.78068010445242448192637590443', '87.17056069117189382354579025410', '88.25024355530754369809905298918', '88.507813763467463958622026298963', '88.99585016388790729275020037245', '89.675514036743432069244891843883', '90.66855701211219510648411031540', '91.302204900752057962179042330981', '91.76761881225685975240857613377', '92.1650564527971202381952481809', '92.93397120330369233227467468003', '93.7641480413557151864649653437', '94.32195564924005965000147445432', '94.86651047588252957887585496064', '95.59250689211119112038347339594', '96.225886798504747393969680799443', '96.760069684310548270870617244', '97.324249257818618649428510158715', '98.24843035846035349650530736533', '98.533470385741242690546824540075', '99.532568612515196719929579903681', '99.97018393061651118801910283657', '100.427070158161614514421950926012', '101.29946244049515699643526035096', '101.80532638170163477094286816986', '102.3288007868616954338055138325', '103.40503500342042622634354629883', '103.67455343134114268925356653946', '104.47427922022941905140756032777', '104.72093699546449566997408417448', '105.454696017695036775298564669170', '106.44777664128224287830795295894', '107.01491951202920640293371643163', '107.378343222012443941583023687690', '108.15848545170654843882734161577', '108.57487951687169425061621198664', '109.21812668864927163328490568802', '110.19451361230845194850773328859', '110.70212349006956482034795705222', '111.18477408221054052066722348935', '111.71011729346938369142551552937', '112.567969958650446729148762923619', '112.92574814155161788847528220975', '113.851247306771371520290675762464', '114.28572953539901081256420821397', '115.00076433693377885881295763349', '115.690987347655965365180095030066', '115.99581618881302014963072324831', '116.81523923193375262898205610518', '117.43220491354439210925443309179', '118.162103020329341235842616457281', '118.545683454327392261777737407787', '119.33365893675681992498102719344', '120.08381486962870204076806107099', '120.523242605341576290236593174992', '120.78619342923145328146220339713', '121.85288878569798912996677460362', '122.47971510150813992793946230798', '123.1330587163774946966121430267', '123.5822172532267146635587884489', '124.10402668362579445877297884243', '124.61877193620710593235552810443', '125.62839483224370751302587121434', '126.21637391306341075325467572402', '126.58783755674414975054457858709', '127.39362433422859376946944281972', '127.77975452221575833040765782160', '128.54298649177284368399824924939', '128.937501012065094988595460971590', '129.99699038347977631009825233995', '130.50162875631126716711736527262', '130.90059529703456100435381614384', '131.42144767152189562179280027821', '132.12013101590447181616182221909', '133.11037375103963365460328498333', '133.24981708327845183412583912805', '134.11222613866649241881548468141', '134.50267477170567054528684958577', '135.567752798813540671824226642916', '135.69115397382580809746786564290', '136.39815294360164389773640801042', '136.99670610716583377394346835779', '137.809700850390977558404916846227', '138.409205025342796198260065050247', '138.868188081528042145058817552505', '139.55215534302589385361511934898', '140.13476929761586980727512392050', '140.51774810827612199545058241909', '141.42880346341140807904809409626', '142.12145062746230891263104946352', '142.592758610478834919414844618700', '143.13932340847973817350216608259', '143.78218337406094344324016693387', '144.14275219856576562065445815187', '145.06805139932910597543035377534', '145.71382707315623259094367927193', '146.41918215747025710147603588855', '146.72208504544054198605499491393', '147.19043344059795978161454113517', '148.00995143613366242692333839097', '148.6818228540321713956319388376', '149.31061995398928171634196567829', '149.86475228766390360138387277012', '150.58091758506017586712443918965', '150.770831454717991845900251895996', '151.712031452839808120454816005185', '152.32330004314824486363464324026', '152.749139604705571922982507838241', '153.50410021379706770345475894458', '154.13580878758874668246234077918', '154.64849248761615327633399818015', '155.39521104579355444190504876257', '155.64783671076377298779215066863', '156.432092530813573835307615796599', '157.199257760100543633121221938001', '157.69341530500870557996049966085', '158.31472191002934840150106366622', '158.83856733738025919154444307845', '159.567655406490654970849631468938', '160.00063322423630892431607429681', '160.41432275011313481039574024326', '161.6370088582502031589462499650', '161.97362322346910908224927902539', '162.43376199383778717810399217426', '163.0136556019759405228373226816', '163.38571600255958036373433326589', '164.49644377745052536135846155751', '164.961495048378848009504762856878', '165.463627671700465468178286903447', '166.13149981715711720258238317636', '166.59787700796616772998777533650', '167.18146781280266317632742390188', '167.92896679648963561143399923196', '168.39838918434880752475543968254', '169.28334435504778850021911307987', '169.63065708430878506691229500754', '170.19979968758912033835543241099', '170.95252665909768754473329180654', '171.20507419125142880664357350529', '172.24502224273463396855586612068', '172.731024752962702209372580707751', '173.07651978215306682304407725773', '173.86293149219636666544448185096', '174.61615819466260458841964279908', '175.07121152953374149061613068954', '175.34790971204245565636083576406', '176.28851148363941331252605986211', '176.76766237653516505072813770246', '177.68335305571717907935928061981', '178.05849543807724306883896782338', '178.45467029763636169246932311099', '179.03396224275582470783361261926', '179.893170746365738368127812737014', '180.31010892969383145439030259731', '181.12255276049271334864600169728', '181.72265745532312648935640445667', '182.20038807323641255816430927850', '182.4593783351600273236899013275', '183.33304847306676456107233132044', '184.01250919846182260590810595582', '184.66793669338326470583815345534', '185.14570927282698467440785948536', '185.75408295827316177575601989788', '186.25539368525444773905088349873', '186.78253175461102302529735176468', '187.49773612453876211373404136470', '188.21528580977984357306872159998', '188.89562575514221390633207944239', '189.05659082584942701786351692971', '189.84433609692823015390160492325', '190.49687354615298376995477217459', '191.10085151981264639454800696313', '191.527863522111739589182610081096', '192.25230117234691000399869227985', '192.83091310802593724256402782326', '193.55287300567291437554147319672', '193.98029930348374176643495884261', '194.62144447891967758388596664600', '194.961637515419933836309104332572', '195.7376357268290474134862852295', '196.59776924690624452374710017201', '196.97639239624776129002026744055', '197.48292822489125383364013136263', '198.109122492688933624683408988672', '198.77234908300933673127821301451', '199.04233454377548217984940199504'], 'prelabel': '1-1368-1368.1307-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 147.01201711904702, 'root_angle': -0.38027447942595666, 'root_number': '-0.730148116191882669896063340246-0.683288905530775469598864125031*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.380274479426', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(18)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.08734278731384561471058221551-0.149047598795022835142248122760*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.218653910338', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.37104970241', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.43663112924', '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': 147.01201711904702, 'bad_primes': [2, 3, 19], 'central_character': '1368.1307', 'conductor': 1368, 'conductor_radical': 114, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1368/1307'], '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': '1-1368-1368.1307-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': '1-1368-1368.1307-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 147.01201711904702, 'root_angle': -0.38027447942595666, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.218653910338', 'prec': 47}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_1368.1307', 'Lhash_array': ['dirichlet_L_1368.1307'], 'factors': ['1-1368-1368.1307-r1-0-0'], 'label': '1-1368-1368.1307-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1368/1307'}