Lfunction data - 1-143-143.42-r0-0-0

Formats: - HTML - YAML - JSON - 2024-04-25T13:56:18.105949

• 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_143.42', 'a10': [-0.5, 0.8660254037844386], 'a2': [0.9135454576426009, -0.4067366430758002], 'a3': [0.6691306063588582, 0.7431448254773942], 'a4': [0.6691306063588582, -0.7431448254773942], 'a5': [-0.8090169943749475, 0.5877852522924731], 'a6': [0.9135454576426009, 0.4067366430758002], 'a7': [0.6691306063588582, -0.7431448254773942], 'a8': [0.30901699437494745, -0.9510565162951535], 'a9': [-0.10452846326765347, 0.9945218953682733], 'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [13, [1]]], 'bad_primes': [11, 13], 'central_character': '143.42', 'coeff_info': ['x^15 - 1', '0.913545457642601 + 0.406736643075800*I', '\\\\zeta_{15}'], 'conductor': 143, 'conductor_radical': 143, 'conjugate': 'dirichlet_L_143.126', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^14', 'a^2', 'a^13', 'a^6', 'a^1', 'a^13', 'a^12', 'a^4', 'a^5', 0, 'a^0', 0, 'a^12', 'a^8', 'a^11', 'a^1', 'a^3', 'a^7', 'a^4', 'a^0', 0, 'a^5', 'a^14', 'a^12', 0, 'a^6', 'a^11', 'a^8', 'a^7', 'a^9', 'a^10', 0, 'a^0', 'a^4', 'a^2', 'a^8', 'a^6', 0, 'a^3', 'a^2', 'a^14', 'a^10', 0, 'a^10', 'a^4', 'a^12', 'a^13', 'a^11', 'a^11', 'a^3', 0, 'a^9', 'a^5', 0, 'a^10', 'a^9', 'a^7', 'a^13', 'a^6', 'a^1', 'a^8', 'a^2', 'a^9', 0, 0, 'a^5', 'a^14', 'a^7', 'a^3', 'a^1', 'a^1', 'a^3', 'a^7', 'a^14', 'a^5', 0, 0, 'a^9', 'a^2', 'a^8', 'a^1', 'a^6', 'a^13', 'a^7', 'a^9', 'a^10', 0, 'a^5', 'a^9', 0, 'a^3', 'a^11', 'a^11', 'a^13', 'a^12', 'a^4', 'a^10', 0, 'a^10'], 'euler_factors': [[1, 'a^14'], [1, 'a^2'], [1, 'a^6'], [1, 'a^13'], [0], [0], [1, 'a^1'], [1, 'a^7'], [1, 'a^5'], [1, 'a^8'], [1, 'a^9'], [1, 'a^8'], [1, 'a^2'], [1, 'a^10'], [1, 'a^12'], [1, 'a^9'], [1, 'a^13'], [1, 'a^1'], [1, 'a^5'], [1, 'a^1'], [1, 'a^3'], [1, 'a^9'], [1, 'a^6'], [1, 'a^5'], [1, 'a^4'], [1, 'a^14']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-143-143.42-r0-0-0', 'leading_term': '2.04971479114843437893258242134+0.000193101907093619487301735674857*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/143/42', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [2.049714800244418, 2.3431514198250722, 2.8180596893596177, 2.978154187980225, 2.594352574168134, 1.6942284028990533, 0.5173662203621306, -0.5724767650972977, -1.2305316172135754, -1.2866494702389015, -0.8396768918278329, -0.22753806507436636, 0.1359767749724652, -0.008416005985490393, -0.5890144261350716, -1.196300300864254, -1.2835136111472965, -0.49269815428844727, 1.071073008788837, 2.7989172202652353, 3.842435868865664, 3.576589242673855, 2.00959434576131, -0.12296208492699716, -1.6874721377341566, -1.7628367246449281, -0.19274247546462875, 2.266422162641822, 4.332045200567302, 4.920068344843157, 3.7787636628875108, 1.6284686251968186, -0.30051923767610156, -1.0500242075406971, -0.5285770495438363, 0.4814649136869835, 0.9142192996979907, 0.2017144035315974, -1.3065089149165454, -2.59340796249014, -2.721648143399515, -1.5329667955422095, 0.22519189276603632, 1.4515941546095346, 1.5093903100047585, 0.6780943489408474, -0.1247218656177064, -0.14255342153486536, 0.5469673578771457, 1.0675481428512614, 0.5177958593314036, -1.1141670275498088, -2.6791559261157762, -2.572224465523289, 0.02921721454453169, 4.333962543581033, 8.230695072589395, 9.602599036287026, 7.750624788247745, 3.8709326325279423, 0.21045160932995957, -1.4777237946694106, -1.0245216077713521, 0.30447386458153347, 0.9961593512311369, 0.5056889921479368, -0.4755602571505843, -0.8378350742433023, -0.16554956856005174, 0.8691882558181108, 1.171362808393238, 0.3104285568163411, -1.0061722347977664, -1.558008501669444, -0.7935642605773454, 0.5392742775904568, 0.9753029822580762, -0.3161896562418256, -2.6227943689992057, -4.12800267254087, -3.4242154243764604, -0.809570932212634, 1.8244831623727489, 2.5112407498235543, 0.8606289120345677, -1.6114412685297803, -2.808930395987505, -1.8992932632416726, -0.04316960662230195, 0.6569704290815861, -0.9329770784215903, -3.915265301986022, -6.098447016192535, -5.872324227103227, -3.539543501157963, -0.943146949600374, 0.2018874354214862, -0.2920048707005695, -1.195528264248879, -1.2520356450366918, -0.4180851812129717, 0.24931787808593373, -0.13796747938074144, -1.2467132750387497, -1.826068721896281, -1.0826034132913782, 0.3329938210307636, 0.8741876388681858, -0.23315987900645702, -1.879968538530916, -1.816223367266908, 1.233765343010394, 6.035459502007363, 9.488692128514884, 9.083076676770595, 5.034808201739148, 0.1548583351318847, -2.4703154516892787, -1.91086183337365, 0.19545091621646052, 1.4592901225572779, 0.9378280649868171, -0.3402976999202034, -0.8111215940766998, -0.12458218878226492, 0.6185718538304582, 0.2779048849143688, -0.8928685218898755, -1.4086075658100792, -0.18269553235480163, 2.1330354188419167, 3.611022200893749, 2.9282097108675362, 0.7253546615679279, -1.0158097466306872, -0.9719230894192867, 0.24170552968593506, 0.8910484896797687, 0.18882305642417205, -0.6530343398661793, 0.34901752484888476, 3.614262249403242, 7.052693128145728, 7.724182594817422, 4.633470572740386, -0.11750662398761808, -3.0865025601231832, -2.5419687687020427, 0.12858588549152333, 1.9674864885908077, 1.3358552199695464, -0.7278700666671245, -1.8820727189311943, -0.9866040169399969, 0.8859288271438883, 1.8177883760301359, 1.1305397823796257, -0.09631016144452612, -0.4776671751870222, 0.062265269786520125, 0.3991385876402153, -0.16613084664125372, -0.8113035677947241, -0.09752573162825616, 2.0481790310186905, 3.664305004039703, 2.5148035114830907, -1.3687090180396593, -5.172487596584519, -5.699528625946093, -2.454551074519971, 1.7454510662085827, 3.384954468964771, 1.5218264064737934, -1.5522697221077753, -2.826793297895856, -1.5610958373071737, 0.31838490406973285, 0.6091783089989533, -0.7446516267313262, -1.8152509650737596, -1.0817345800680425, 0.7598038942159098, 1.6085700649786139, 0.3981760276959824, -1.6653293187652074, -2.4688713665379276, -1.3570286213738973, 0.2303386398958746, 0.5365483122829328, -0.44604931392550407, -1.0642961928467651, -0.12148585863235267, 1.541484076396109, 1.9725867591724406, 0.5138709185804903, -1.2292600579255817, -1.205957901380604, 0.45359037892432646, 1.1832599296993411, -1.2515360337253603, -5.859705764979701, -8.774179697948577, -6.846096358053548, -0.8745067825540395, 4.941120154615791, 6.827473950720011, 4.644565947172992, 1.3681092439564502, -0.23138997492237828, -0.00987695766405981, 0.3321299797185007, -0.20886576793732078, -0.8256342197623481, -0.3272440065142427, 0.9806041041112051, 1.4959489169889009, 0.3942202611388429, -1.1054319784835602, -1.0545150240452748, 0.7918602378486156, 2.4554658861892054, 1.987714853749993, -0.07313364181254638, -1.097754110767297, 0.5891885613925363, 3.4870299046329882, 4.2876317819815535, 1.519994783636987, -2.6173597456789626, -4.437544035219213, -2.6370100894206523, 0.43547370048970135, 1.4875690343080552, -0.14403608200828438, -2.0647129122632846, -1.8473139695121867, 0.12830636281934504, 1.2914252554970806, 0.07046608048997811, -2.2053106395240034, -2.8996860160174553, -1.1628226341590444, 1.1709658914495689, 1.8299034643090661, 0.6779751330012865, -0.43588108217741167, -0.14758253087602213, 0.8372761400754359, 0.9551348809249922, 0.03755025525135547, -0.4927941136177837, 0.16035728267926236, 0.533576842439077, -1.599377665898006, -6.028558159903762, -9.232543409885624, -7.533301210474926, -1.1708647414962838, 5.357655679482381, 7.447269598303736, 4.724191913323503, 0.9604975797551498, -0.1547768806810408, 1.3900614891408005, 2.7236327361626067, 1.858925188056619, -0.15879165267281342, -0.9605096318710049, 0.0909182731307807, 1.3459676640674394, 1.226705245874503, 0.22758744988934382, -0.03199176248209525, 0.6994339028971633, 0.7382530703445727, -1.255798423399734, -4.102019527450194, -5.067359522271804, -3.0608706718670433, -0.11263483305657823, 0.8802074341593391, -0.4841991813155621, -1.7897103750247583, -0.9782406236689904, 0.9346746978327016, 1.1146259405831875, -1.3008718219720932, -3.6510388122830015, -2.6446064450630997, 1.5951571928382873, 5.272778250747077, 4.991824957015532, 1.4915419038130704, -1.2882101999759639, -0.6477689064328195, 2.126942560727397, 3.6914795278661323, 2.6083602816130154, 0.5806901974490611, -0.12118044869058872, 0.5494175880784806, 0.8520129374327815, -0.055582365566829474, -0.9761386822579896, -0.5366488233115022, 0.671146932113835, 0.7824947376493353, -0.6547550926524508, -1.7732767538868608, -0.822874602427959, 1.1142986981601355, 1.0229159871408688, -2.1282670125639918, -5.296242129876035, -4.229985691894907, 1.5936562182927485, 7.7795354838812845, 9.292137093320582, 5.520976079088797, 0.491088923776753, -1.7348701063783587, -0.9738734052610618, 0.04783635834107497, -0.3580415214179448, -1.0912368085439152, -0.5187855481146416, 0.7651380875213247, 0.5667448253311655, -1.7728926310735267, -4.083011808146674, -3.8341277077536358, -1.2587648089045822, 0.938936703606004, 0.9163045665216429, -0.25504297905910245, -0.3856909239200136, 0.745555077072051, 1.2395655321142829, 0.030135113469265576, -1.229431957892083, -0.2079378876737094, 2.6706402217283705, 4.193621570848732, 2.290961686042302, -0.9269100258231168, -1.2449651589498791, 2.5747229782550765, 6.8986934727434575, 7.107754979328104, 2.8084666700624656, -1.7949129332067317, -2.704059484796079, -0.3036125826866516, 1.8074340739516495, 1.369084179328671, -0.3502464778038395, -0.9324554465988321, -0.0884665793658096, 0.4455022960465479, -0.271399215579507, -1.076956889693152, -0.6553329672626308, 0.3035342339460717, 0.0824610061782619, -1.2206846222454917, -1.2536342353594645, 1.4650834661741863, 4.8836528675626765, 5.231108172021647, 1.583250335814543, -2.5698350615897634, -3.1326501521838246, -0.1477578081792026, 2.410398898214134, 1.586616515832064, -1.0388187508285567, -1.6089732320983374, 0.983345117394704, 3.733511032691103, 3.4219483314222945, 0.6258019622097369, -1.2383021137335517, -0.35093354063333515, 1.4549183149527527, 1.4727015834349482, -0.2340538902375432, -1.18169518506867, -0.08819856492546813, 1.3187476392420538, 0.7334441559425886, -1.4983280026787498, -2.8101757978785185, -1.8476288125982046, -0.13368133974889368, 0.24136565850709057, -0.4877652773685366, -0.4443450222945778, 0.6851879053340885, 0.8192666658350559, -1.2831857323462426, -3.112160334403383, -0.5485856532424623, 6.779751157330497, 13.706184958388658, 14.331975949530555, 8.267623056786011, 0.977887654660106, -2.1580267759591636, -1.024094369607847, 0.5145468695683744, -0.07682748570063093, -1.5265518137971632, -1.5134118483203984, -0.15493642087171147, 0.5209115299712385, -0.18613685807557512, -0.6598583521186406, 0.403505640135438, 1.7729735815895853, 1.3116230558817996, -0.7776429767447268, -1.8904212581098658, -0.5424372392861263, 1.384758125779738, 1.0485302055492423, -1.3960642662730023, -2.835106970205876, -1.4709059391270534, 0.4329833581244129, -0.6389240431056183, -4.563619608573627, -7.210788191879998, -5.4164248442122975, -0.9570412307782711, 1.6834999939429025, 0.857486803631009, -0.6073717818466392, 0.35686948993095763, 2.7577818149925877, 2.9162634843143715, -0.44156077394807547, -4.2415723469433235, -4.79178971328033, -2.1734457177756923, 0.3210022206551488, 0.5217505585122558, -0.434432886381877, -0.5010260042438842, 0.26423426975186526, 0.35783742830029613, -0.30455534787300415, -0.021289545908216686, 1.8300484026569612, 3.1749266802204774, 1.8636130326493925, -0.8628022045177873, -1.3995490292297217, 1.3379948485949673, 3.706892839184305, 1.4744129933085668, -4.505463274789673, -8.560041250383161, -6.5991636904748, -0.8544015136288794, 2.89787372260815, 2.008329668023274, -0.7461914378638661, -1.4756744343696828, 0.06064955620918794, 1.1786070838554774, 0.5691248218878966, -0.16791232340348264, 0.520799843862188, 1.5296268515451472, 0.81273823519456, -1.225223293132534, -1.917525233717112, -0.09934061762831314, 1.9733040395823158, 1.5447048663283731, -0.83044769140603, -1.9978143586899502, -0.5242681665093479, 1.4502226488761925, 1.4329659400583772, 0.18136838724107418, 0.37683648887044363, 2.22337282726887, 2.579976610291382, -0.5555162881553937, -4.307073477478468, -3.7012158473513805, 1.9935684751528469, 7.654829074048148, 7.953151038509626, 3.347139653760175, -0.9719843167914661, -1.4593940424285654, 0.3296492390750169, 0.9722486748295349, -0.05101923866590691, -0.4478681585428473, 0.8954638878606361, 2.1974017690982426, 1.5897085774277186, -0.06196678308827077, -0.5546194970485371, 0.33033157302014216, 0.7163767100397679, -0.17129556413707617, -0.638407782596381, 0.5593585462384398, 1.3862946602567603, -1.2686199695861824, -6.673823502116501, -9.735196228185055, -6.680658592530484, -0.029678901234248836, 3.9195569280901155, 2.2995717499176935, -1.4651097448678367, -2.525070173240551, -0.5428611309186134, 0.8758752232680731, -0.2770887287038458, -1.856739318688858, -1.152591055138867, 0.9911805851003228, 1.4924640837460343, -0.3535041634718941, -1.7939056685705197, -0.6073786328234768, 1.6830814483238576, 1.9947099872055671, 0.023311089910779695, -1.509886575009902, -0.8607829908364093, 0.4539590365303452, 0.29527807461472544, -0.7348427833705302, -0.37905403386217795, 1.4556112923465994, 2.2222573418484504, 0.7173918367342615, -0.4558373404561378, 1.7330533774585068, 5.836558698205393, 6.872504281216152, 2.7471736923796413, -2.3204129945979206, -2.5247532746847154, 2.3579552569433306, 6.647835628850299, 5.705021812059012, 1.1580050088640177, -1.8986755043724448, -1.3444805929897903, 0.36261293394354094, 0.4986842038547981, -0.45715812323475713, -0.6047743026374985, 0.017599261701702222, -0.12711898431577678, -0.9790231561949584, -0.5612833758400829, 1.6715644817041546, 3.130869821730577, 1.3267140485226705, -2.277695654150002, -3.709361417147308, -1.7029127295890645, 0.6476610489852339, 0.38516388820310216, -0.9945783611779775, 0.21717360893942506, 4.1326424128704575, 6.32732011430774, 3.571138446471939, -1.545329516475973, -3.6574657519241165, -1.3527842499062062, 1.4975977806039027, 1.3193354940940343, -0.6214978589868363, -0.7678046546925477, 1.2400597709833103, 2.1388683882176402, 0.014503174826270407, -2.763320479539465, -2.837482109934413, -0.45677150876638983, 1.190929832169, 0.5821045273535547, -0.4419534883376942, 0.025964866998512273, 1.052990172686794, 0.7168815737717708, -0.5410449866647753, -0.6091954843827833, 0.6124758157169438, 0.741210862006104, -0.9236084548216621, -0.972589543460973, 3.984041235490026, 11.528143798606413, 14.612424981168585, 9.512360525969308, 0.649308734344239, -4.247509589851122, -2.6817647557845703, 0.9821985947815116, 1.990054535017062, 0.6111142447364337, -0.023524691838790912, 0.767651626284001, 0.6987667678947344, -1.2560120991251271, -2.9153926620651527, -2.177726759832615, -0.23921356700290622, 0.3059029118629343, -0.5325396343667961, -0.33102645742812614, 1.6416136766513623, 2.9165448431146768, 1.546431705228776, -0.5479892458563581, -0.04615859293575984, 2.7953535656027246, 4.146960488480713, 1.9643572265310205, -1.0359152163709922, -1.3037371412759478, 0.3819860993847068, 0.23679274431917935, -2.5090513346535586, -3.9018721245281753, -0.8496842415767345, 3.8406959038005617, 4.53823588183204], 'positive_zeros': ['2.01373714220077335367070326843', '3.58734302442645209608662928856', '4.055942106798863021606040758419', '5.4242558675520829492662520060', '7.16883558825074512302467811363', '8.15183663890480901823303853870', '9.939644378778813773283027348472', '10.78568864693392321319572040740', '11.61074140914501886616888793103', '13.083545719142929488229986965459', '14.30670510552270939960162626592', '14.771743781478938315454162413651', '15.74083851382916959879909773144', '16.87254483930570450862497816913', '18.77373218997839024399015641190', '19.61348765960596026242242350472', '20.46950095925797515900605070653', '21.29861956664167934322839431612', '22.26021167749742968851856058806', '23.30562413584905107360896876060', '24.01187345639553101597384804992', '25.39725880342944619668475243866', '26.35625082263200551823470828646', '27.508473119731723583152559918114', '27.99416127342209017329455477429', '29.88470036565832790363539804016', '30.206434981581944750078609480382', '31.40049422785624123013219087551', '31.82398604139368012187736963829', '33.04691326905235322243771290095', '33.706182420886642468141842088100', '34.5914536418744807519390482754', '36.26180879691978977190757208113', '37.15788191531873383960312492055', '38.03564082838360747734795647472', '38.790398106868631525439781419497', '39.45766387861784059769941388987', '40.339861354422170756221540952767', '41.665872497508836426541658477156', '42.44014005300028543158038421490', '43.17756112444876137492714581851', '43.69732261348216285076558627749', '45.30417440495810884069098683280', '46.23538124293468081014378713095', '47.07937627876146412591442552220', '47.975910572526314998093197753620', '49.032533077443989090355421383359', '49.658121005345075326325355168444', '50.25013072145310140245303794247', '50.9559179363434701208975082294', '52.09040354302385681414484018703', '53.29754616008948347751814691356', '54.21126779485203041300819327373', '55.246191579766160535773020057389', '55.790031596533397576942148821202', '56.74668496964127466426571189312', '57.56003301724761743827741404496', '58.69303111235006879818121066399', '59.253615438484169716866482643966', '60.02316028960064341198871430984', '61.01705496716293345555044348872', '61.796402146501446847647798306885', '62.388679816996694650647842069834', '63.79090807541613477183218213097', '65.22104499690467964203433560016', '65.63024065587764032368617585825', '66.16741601951553764972493042242', '66.958607151785218404113399869712', '67.88566428927898666981040670398', '68.63542386284688114813681118701', '69.67629172437773327344971685760', '70.24221104811150081692444996182', '71.361522540969864194936557221330', '72.44872573086636105054232966774', '73.10541190163484220688703562316', '74.04299360383494735322941824096', '74.697494073566855438325111773795', '75.76858650527743124361472267507', '76.71568535893152133181170714346', '77.23549561831180068336531222894', '78.1368273952187679379066065991', '78.69604888286656144734223234443', '79.19638078711409901052026177197', '80.67459859989529888030576129733', '82.02318951118790778261570595822', '82.2463681750234530015461314559', '83.409929968371865560906403699451', '84.04377329082869088961258857625', '85.10327701780354207226392886087', '85.33540364121564892604683437347', '86.09186144980191881503269044942', '87.515475323812118804949577491383', '88.041710928475303478409152948715', '88.903496141931868905561751973215', '89.54726209181315935669290356803', '90.51982824103496153229790424404', '91.69391024366518247651101453996', '92.26872250408702873016558903166', '93.5916574209103671480461188386', '93.84258903502797277257212796941', '94.673306276387403752047388903313', '95.44763274917456222812088063346', '96.129301408383568801568097563988', '97.00057778651573392892767083156', '97.629348848643115651913797998060', '98.677736333594100468460613319491', '100.04007402923421428100690353295', '100.902991782386673811344272894291', '101.09947681440018519107078647954', '101.99394426891714390828259135885', '102.59918912031279109656219010734', '103.89753314734374287744702723507', '104.6122901774455754891679650742', '105.1253775130006254312609343858', '105.943053281273389815328144484964', '106.589268957176395299430093054337', '107.71013272892844249832938085877', '108.258489014201653112713164431386', '109.545806350815315269189204848557', '110.34561811118968450936058060944', '111.18077439888590192412384738741', '111.902889189952518066731352807583', '112.41791643543157324319735914007', '113.31974366684443552118316762951', '113.77400061419619122046715410405', '114.552464167338085066270834817925', '115.72977064345340780957635362847', '116.57558010434840493937657519875', '117.37156157242571822609643805025', '118.031303333961963194429753057590', '119.133337164810446055121310570791', '119.743776631834918862715901958116', '120.58479004053572259196669903047', '121.26593348562425692850509900730', '121.98790016998776562526089772705', '123.16106587671072600589800566113', '123.55493064297826148823524177616', '124.19772563834060398279966246628', '124.84128908803929455727978148221', '125.65529946064781359640282607449', '127.24514334081333027147325088921', '127.97993582857197184625746621385', '128.42088841731354720129388516766', '129.41243134334738791750061152046', '129.93972069119645985364212946141', '130.54274423115735328595187602283', '131.45234478446525314546721344166', '132.26353383068241274853941864933', '132.95962575282543820569855470448', '133.959924134457669323280789846397', '134.2955968608355931319376414810', '135.70110821376884449185344328690', '136.396476557199271723451963201436', '136.82085828538317833720865799719', '137.78039738424316536192796387558', '139.00243692591328776283541213145', '139.54142919229387669565179609625', '140.20343805618077206662083084754', '140.79416033476104497951178487623', '141.2554456089807095669293306696', '142.39356330777684082418415527147', '143.00007593030640736374917307783', '143.83654636137935263308297170787', '145.04900982674625166160983718340', '145.84375946454530794346196726479', '146.55201539525448545466668210642', '147.372461957889596035736787662936', '147.65494252491978910485191319706', '148.5659668774861766197345789886', '149.387273112726457383509609081612', '150.207327661273744323766890534531', '151.00853629409933172943703406953', '151.966245792315817927577806435072', '152.049134994966964898264258811724', '153.08401343945368029836522736472', '153.96966802147980286161670627087', '155.21763985941151564738834828680', '155.87923125747719037603918582207', '156.5486248356328897437708981731', '157.01643374938112075680350067320', '158.11106495662774026258389501145', '158.65008013096222432374924789698', '159.32603923352571055805460090062', '159.88888988667371646665652992903', '160.52768008454508715377470428753', '161.87647503762314697318355692913', '162.681982143617273828071099599156', '163.51359364993858602238234210697', '164.01722069039876066882391598794', '164.85261932797571009071237477002', '165.5759801659400297498945114354', '166.32899890740146588833373032518', '167.190701664656407993436040009333', '167.99441832976144655559919674032', '168.52379119496816055257390241241', '169.13768541176383301011039565214', '170.121558700698374681836185477873', '170.44262760414559761008647611856', '171.713326386223606608718140301527', '172.369815474543215061963663654899', '173.52199643345444281331307430451', '174.292421243205234693968692405595', '174.850497234619969137271175403021', '175.61333810750423796658201755073', '175.875545480189000664249961090090', '176.658346653504294779757362985694', '177.615173635712117657059282536221', '178.63439302814844435541722148843', '179.13907669402611098980861866096', '179.66419374423574969622067432934', '180.83741821942561171661258974132', '181.68699626232960209206457218344', '182.39279309480438081865608005551', '182.94944431440534303542407906285', '183.75145122401261569363146116951', '184.74565660162553866200308570897', '185.45520932549475514793743353750', '185.93021044445169496771558726117', '186.73414365767497995290646140580', '187.35129924868865573106169130106', '187.96855997671388450431610533987', '188.53456516316800002479570325828', '190.026131527059568676067580564494', '190.84185131923854724999298880692', '191.751874973390998107529025048715', '191.89494630607143924006215178679', '192.63719137888745532251630554918', '193.80331973436280098848945690621', '194.193022922501333235658939613771', '194.75624783305253994100580492221', '195.832031294628211502741130094371', '196.256651238407688691503066604337', '197.37242636860734783313484694775', '198.048729836523457079620685901260', '198.47487896801371736080258494168', '199.42857637505111925305544531360'], 'prelabel': '1-143-143.42-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': 5.9975413313536066e-05, 'root_number': '0.999999982249268799576506154184+0.000188418316746962076086039824716*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0000299877066568', 'prec': 64}, 'spectral_label': 'r0-0', 'st_group': 'mu(15)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.86422160640913299322052447590-0.0326810325166387341098622915271*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.0137371422', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '3.58734302443', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.0559421068', 'prec': 40}}
• 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': 0.6640892081105222, 'bad_primes': [11, 13], 'central_character': '143.42', 'conductor': 143, 'conductor_radical': 143, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/143/42'], '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': '1-143-143.42-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': '1-143-143.42-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': 2.9987706656768033e-05, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.0137371422', 'prec': 40}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_143.42', 'Lhash_array': ['dirichlet_L_143.42'], 'label': '1-143-143.42-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/143/42'}