Lfunction data - 1-143-143.8-r0-0-0

Formats: - HTML - YAML - JSON - 2026-07-10T21:15:39.737971

• 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_143.8', 'a10': [1.0, 0.0], 'a2': [-0.9510565162951535, -0.30901699437494745], 'a3': [-0.8090169943749475, 0.5877852522924731], 'a4': [0.8090169943749475, 0.5877852522924731], 'a5': [-0.9510565162951535, 0.30901699437494745], 'a6': [0.9510565162951535, -0.30901699437494745], 'a7': [0.5877852522924731, -0.8090169943749475], 'a8': [-0.5877852522924731, -0.8090169943749475], 'a9': [0.30901699437494745, -0.9510565162951535], 'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [13, [1]]], 'bad_primes': [11, 13], 'central_character': '143.8', 'coeff_info': ['x^20 - 1', '0.951056516295154 + 0.309016994374947*I', '\\\\zeta_{20}'], 'conductor': 143, 'conductor_radical': 143, 'conjugate': 'dirichlet_L_143.18', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^11', 'a^8', 'a^2', 'a^9', 'a^19', 'a^17', 'a^13', 'a^16', 'a^0', 0, 'a^10', 0, 'a^8', 'a^17', 'a^4', 'a^4', 'a^7', 'a^3', 'a^11', 'a^5', 0, 'a^10', 'a^1', 'a^18', 0, 'a^4', 'a^19', 'a^2', 'a^8', 'a^1', 'a^15', 0, 'a^15', 'a^6', 'a^18', 'a^7', 'a^14', 0, 'a^2', 'a^3', 'a^16', 'a^0', 0, 'a^5', 'a^1', 'a^3', 'a^12', 'a^14', 'a^9', 'a^12', 0, 'a^16', 'a^15', 0, 'a^10', 'a^11', 'a^13', 'a^7', 'a^19', 'a^14', 'a^12', 'a^13', 'a^6', 0, 0, 'a^5', 'a^6', 'a^18', 'a^17', 'a^9', 'a^9', 'a^17', 'a^18', 'a^6', 'a^5', 0, 0, 'a^6', 'a^13', 'a^12', 'a^14', 'a^19', 'a^7', 'a^13', 'a^11', 'a^10', 0, 'a^15', 'a^16', 0, 'a^12', 'a^9', 'a^14', 'a^12', 'a^3', 'a^1', 'a^5', 0, 'a^0'], 'euler_factors': [[1, 'a^11'], [1, 'a^8'], [1, 'a^9'], [1, 'a^17'], [0], [0], [1, 'a^4'], [1, 'a^3'], [1, 'a^10'], [1, 'a^2'], [1, 'a^1'], [1, 'a^7'], [1, 'a^3'], [1, 'a^0'], [1, 'a^3'], [1, 'a^16'], [1, 'a^7'], [1, 'a^14'], [1, 'a^5'], [1, 'a^9'], [1, 'a^17'], [1, 'a^6'], [1, 'a^19'], [1, 'a^15'], [1, 'a^1'], [1, 'a^16']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-143-143.8-r0-0-0', 'leading_term': '0.440011466615231731655739772173+0.165121926905332435679262502241*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/143/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.46997376681876357, 0.5808206222193418, 0.6291869133245513, 0.39459417839865585, -0.24227599113015588, -1.2246708435272249, -2.3070469395026865, -3.1157083278793922, -3.287794186497345, -2.647856723883429, -1.3422272672137334, 0.15305120090525465, 1.1905514337354164, 1.234172875758293, 0.14362785387230437, -1.6925390694328704, -3.477266818316335, -4.357750604599925, -3.853576837819783, -2.133518687251327, 0.03270203740781827, 1.6555756549961114, 2.0525779653068748, 1.2260273278251264, -0.14111781683991012, -1.0907882264252338, -0.9680350681299104, 0.18108316367218147, 1.6504567115917126, 2.5395392792185825, 2.3461798318363134, 1.28910400246831, 0.1316676543026267, -0.3791683696681058, -0.0602123039772265, 0.586284711826407, 0.7958359361707782, 0.21896733630482168, -0.6668545003585097, -0.7822637056364924, 0.7741112296841005, 3.919583603774317, 7.378553172940854, 9.322782000605262, 8.505970062730915, 5.132163117807929, 0.8201945513066333, -2.368107221707116, -3.197724862158444, -1.9542463247634394, -0.08759446799096995, 0.9073555050794548, 0.5309074061303228, -0.5219040337197871, -1.0981295020663506, -0.6214093942723623, 0.4331963681294707, 1.002011008589616, 0.41885259530047175, -0.9392384020032372, -1.9285772675711736, -1.626001868030261, -0.1770735358797313, 1.2628169691182378, 1.4970653615102967, 0.3566414355165758, -1.0827154497663931, -1.389756668611294, -0.056361058100664135, 1.9518101436678486, 2.9221502871425917, 1.8507958178116806, -0.6097272685397952, -2.586449867412729, -2.520812449932432, -0.5345945668181431, 1.5686142951929973, 1.7400317333439859, -0.6041020625736048, -4.038462085541241, -6.229128209132812, -5.7653441930897245, -3.1935797108522106, -0.4291751397931621, 0.8730860472128517, 0.5451590373541672, -0.2784087588529011, -0.4456014038459776, 0.11257309782757013, 0.493765635953023, -0.049051855025182035, -1.169071603883928, -1.6836411373937894, -0.816438647227743, 0.8418849496775618, 1.7315735854988556, 0.839508837096825, -1.1008330057189377, -2.0106091348199495, -0.29502799260038687, 3.5064336957473587, 6.854434028554209, 7.184595001209872, 4.062780103989664, -0.3979478284186966, -3.266295696018791, -3.149945371374419, -1.112303804612576, 0.571112392649906, 0.5528872800301098, -0.5629023656209916, -1.1594629157082466, -0.43089883754517955, 0.785992206022198, 0.9703477691936284, -0.38155204380300295, -2.1103202250828046, -2.5025156496291787, -1.032707505879016, 1.0594246853642364, 1.9753607184881476, 1.1275634013892137, -0.34345381704327427, -0.8303580567615074, 0.04035355391392037, 1.0924645899441001, 1.0400894439901975, 0.1402863965068521, 0.17405450422219315, 2.5657000600442865, 6.495265294554888, 9.089467373477033, 7.807778208079274, 2.8733267634043314, -2.6382773069412084, -5.284804105481472, -4.072323760477296, -1.0174634781608909, 0.955234395152329, 0.6634613465778425, -0.6415632548642909, -0.975877662656645, 0.2226991939508515, 1.6949644366843626, 1.9286700195367739, 0.8323760128325466, -0.31487828086199443, -0.4553258537013804, 0.026005085835658012, -0.1077887862731538, -1.2312603399938862, -2.090622299806258, -1.0687263215647353, 1.7787202150222916, 4.254311792781602, 3.930927350862441, 0.647547022603322, -3.058144750323561, -4.23628614798348, -2.3380410712287176, 0.3070127605242856, 0.8790994680377604, -1.1074044073149971, -3.4349100389583658, -3.5953806399351667, -1.4100492548912826, 0.8840126297644519, 1.0890474232622687, -0.638416153225102, -2.069411346455753, -1.3877694590290508, 0.8680401196952936, 2.4741274115601, 1.967076705860393, 0.133733951637717, -1.0235803747774632, -0.559441205445201, 0.5093386038172042, 0.6060361573342293, -0.44525411893604044, -1.2553579105536454, -0.6837542549378418, 0.5975256816413453, 0.79629670436506, -0.7312343846266798, -2.357492970726282, -1.8122324507655534, 1.017511112205458, 3.333764458337638, 1.952871701218263, -3.2791015889767174, -8.820173187062895, -10.465042056312631, -7.157489342316289, -1.7881793715716157, 1.7072535622967262, 1.8721284267022136, 0.3916490001253661, -0.3441793693315931, 0.20505298328892219, 0.7647424283838085, 0.3665643283561979, -0.27437549796583854, 0.20173578195262692, 1.7715692848757663, 2.696627053995669, 1.480608967695289, -1.1877577872892695, -2.9585932852029573, -2.376268363293392, -0.5168765812811261, 0.29506422016023565, -0.7311018925062647, -1.8688072213361628, -0.9742534460834374, 1.715468479747542, 3.469281722497926, 2.008483070240721, -1.746917690158646, -4.371570452606541, -3.4866999712630684, -0.27874700102289474, 1.8482706755188025, 1.0036797568548006, -1.2333489752954248, -1.7576121573715826, 0.5027833857561494, 3.4400476059556384, 4.205262115270875, 2.323540586689146, -0.026617809387513482, -0.6572289161581093, 0.29922216753161723, 0.9844494656916588, 0.3125823390537579, -0.8187768014511869, -0.9669349097531044, -0.17906972191176257, 0.1210931351434049, -0.7416054211745668, -1.462558371950828, -0.3455594787589582, 2.0456786737792694, 2.6918168998569225, -0.7646912724906286, -6.880107527054466, -11.092537175014936, -9.983364450052989, -4.692161573715215, 0.2562671442875413, 1.4775895749401373, -0.27600895135115044, -1.6826472399073484, -0.8511568071513829, 0.8792247982989869, 1.0804124298017095, -0.6133180724854341, -2.184765182435401, -1.8832857211765295, -0.36157111836779554, 0.33972677670725854, -0.4785128781462313, -1.2997806516903831, -0.4949687355410129, 1.344575678741719, 1.9417966804384923, 0.18313410433950378, -2.308161896122835, -2.9725494978936853, -1.3487724651990538, 0.439800219164331, 0.39432111119288255, -0.8682959353607328, -1.0729910065331618, 0.43886414083860403, 1.3743062260818102, -0.8587715280224042, -5.502723167390189, -8.424034390466929, -6.255307608098359, -0.18894181832045231, 4.986436685212457, 5.668524542395776, 2.7720751076087287, 0.11547914022071894, 0.06838411210841301, 1.5092619030133192, 1.9829077286210146, 0.906975602617691, -0.12568570673697665, 0.1388296296565893, 0.8929583032722379, 0.5691326312637441, -0.8035875421746891, -1.5522583879741827, -0.76871088523465, 0.16644243107446996, -0.72770590350103, -3.1502592632094912, -4.393290533030324, -2.5982462065550975, 0.5302707633899385, 1.2674209768124758, -1.7490193062207688, -5.509281766962901, -5.702471620913299, -1.5242749093858565, 3.35988894881941, 4.826996132669144, 2.58698824022321, -0.1048864420350095, -0.5704336281674325, 0.5065599002725822, 0.7502444807005322, -0.37225151588076666, -0.8605013664679202, 0.9018172957579702, 3.616351459630182, 4.36668581830574, 2.153130061084037, -0.848438470459991, -1.884008127168604, -0.73696258328213, 0.4977460397659974, 0.39347991591750064, -0.16396686356328874, 0.2614591576427522, 1.165631019296421, 0.5924297912871663, -1.865229886475302, -3.7876293189048518, -2.659128208619114, 0.5428538027371577, 1.7754142471679208, -1.4818658677855259, -6.817284715111014, -9.079704778759313, -5.978516616803849, -0.6262684969710051, 1.9480262535223334, 0.18894368115823568, -2.874096267187766, -3.62981335119467, -1.8513197328407673, -0.10633905250490178, -0.07246346149397148, -0.7507062792255051, -0.4836022857037198, 0.48859375346442707, 0.5570019892917871, -0.6130922591725148, -1.3300965941058287, -0.29599371311975353, 1.1834131624800523, 0.5933541618182934, -2.3051510105197273, -4.615780941422555, -3.6392446247153374, -0.3453549011761735, 1.6243229327646822, 0.42079646030814954, -1.7051613726251609, -1.3058798489620067, 1.777803094064798, 4.130592702070093, 3.1306473420850374, 0.39200730744687573, -0.1952279974041093, 2.6057367719638918, 5.741766404606465, 5.593608998364085, 2.330049221597006, -0.5104919949222494, -0.4392446092513771, 1.2744436502149363, 1.7773059116691439, 0.4567472136785624, -0.6340538914874785, 0.05639627775291529, 1.3924759169119372, 1.2750833385402767, -0.3276140049360164, -1.3589769498880226, -0.622620252506459, 0.5733324447421182, 0.4681246082139127, -0.41213749856735793, -0.05415912322464501, 1.4798838054351287, 0.9137202206756752, -4.473326248464836, -12.453865682939863, -16.860773328572904, -13.728423369342078, -5.646913971496533, 0.9019046063600927, 2.1819623823060486, 0.1812416116901229, -0.9469978909320342, 0.03960664931104805, 1.0211016749914574, 0.3173259895910851, -0.9011170477341306, -0.6337780548577463, 0.8187419910008679, 1.2378861083122028, -0.22198029544776102, -1.6526065391766545, -1.0199221585803453, 0.8590308724098973, 1.2827766813575354, -0.6183611095068502, -2.5712704853262642, -2.1895357989246547, -0.21774136790201604, 0.5659316148477164, -0.6518880331373462, -1.4485571092174239, 0.3728722290865255, 3.2612032983528856, 3.462132510861377, -0.013320904961860024, -3.5989599166463115, -3.3164608765543373, 0.2478304889131259, 2.6100644158234414, 0.9873335241910858, -2.295914394904616, -2.885128711162075, 0.11130833943543805, 3.2113036407061664, 3.0822809654135908, 0.4432256535681718, -1.411801849473611, -0.9463003883567656, 0.27657396674710194, 0.4314830704838403, -0.06870549477477463, 0.16738633234891281, 0.8845912445434903, 0.4989889308193285, -1.0212358992849038, -1.3352424074132592, 1.144662443853055, 4.354790042702382, 4.524204400221318, 1.0674213903185406, -2.102926770001178, -1.1840674865896719, 2.591925146086335, 4.244444606389708, 1.2136478168150384, -3.3779163396099365, -4.543175151530655, -1.4189218245033794, 2.105537514768659, 2.5072502483640258, 0.6087292401250188, -0.39195948208479614, 0.4978797089328374, 1.2535693240130241, 0.400725256564091, -0.566667561543873, 0.5471203498681065, 3.1043905001856875, 4.122034400867933, 2.2692401099795174, -0.24949365737651408, -0.63149601523642, 0.8611620503886936, 1.5922997685109552, 0.44734984195007793, -0.7316054710438451, -0.15213210048925832, 1.0706016404532546, 0.647326052069974, -0.9793754582333107, -0.6231109930861474, 2.9934583362749705, 6.267163583780027, 4.325941080505462, -2.674547279111586, -8.764239771936927, -8.49654327388893, -2.8741068497543605, 2.2712880342421027, 3.0717763736256147, 1.091508548165348, -0.059483048045782555, 0.40710686309899935, 0.4679465233281406, -0.8692174665231236, -1.9514976184299915, -1.1936344350550032, 0.33873471573779573, 0.48473036073262127, -0.7299587690659304, -1.1559221996679396, 0.08742713983138069, 1.103300584141855, 0.16099771761999918, -1.1768729639604032, 0.18627129841288334, 4.146448853463732, 6.494598140995111, 3.893854623611877, -1.5236606482173265, -4.326470352603175, -2.267035690234842, 1.2814022685535755, 2.0005353353325357, 0.045188354290297904, -0.8971246178265453, 0.8415591313304677, 2.6337302927429205, 1.545013722441151, -1.2701115710485296, -2.028134214063117, 0.4684657123447354, 3.179639982690765, 2.929861143203058, 0.45240318072015756, -1.0553954289177754, -0.4262630314795667, 0.3637384132838838, -0.3904123170471734, -1.5650983118324429, -1.2138640819442161, 0.20946013561750293, 0.5225987578137593, -0.6267291514933042, -0.9985833946718696, 0.6270150028352799, 1.8752352554801457, -0.2214954601805469, -4.31008498376733, -5.253840995498052, -0.4887728119135255, 5.930283642346355, 7.497594584123014, 2.8538661427953174, -2.7654953478928026, -3.9609171946709414, -1.1480275964567885, 1.1302711036633786, 0.4432020435847552, -1.2038352727696149, -1.1602283683374912, 0.12940003656328555, 0.5116622552623512, -0.2752831504648221, -0.5483304668064702, 0.0608765066927545, -0.431383153977872, -3.1567605515846795, -5.823272296076808, -5.203187403595489, -1.5963100987330343, 1.216726088102663, 0.8293665632442456, -0.8491696336103427, -0.7110472514061108, 0.9656259843867532, 1.2400846423020828, -0.499684769902836, -0.8611950076955609, 2.8812234349015147, 8.16621082853433, 9.55050968143006, 5.4714136865675975, 0.310324470493692, -1.1514001178262887, 0.5264879662018652, 1.0307455644904613, -1.418845251817626, -3.875093600921257, -3.1793180601156608, -0.42279623801910904, 0.8119784685005726, -0.5311726080362238, -1.957066774275194, -1.3732184082774836, 0.12332201220116916, 0.450393831511284, -0.14821363121305903, 0.12281837099302433, 1.2971269277571218, 1.4344240575155183, 0.10672124809678377, -0.1646574948039526, 2.3780334334788122, 5.02343106322362, 3.207002721041396, -3.050743071626843, -7.801297999349341, -5.781138874158852, 1.0965494953983992, 5.912336374755048, 4.872462779794909, 0.985984407666773, -0.8242991703096574, 0.07911042067777391, 0.6163022290813984, -0.6615766353913384, -1.6582081337550678, -0.5350429356818459, 1.1045241253394742, 0.6037063170075518, -1.5719508440703158, -2.368062831752402, -0.642996471524127, 1.1641963171633707, 0.7034672098750295, -0.8615600333896696, -0.8448392787120658, 0.674004620551683, 0.9300948468323473, -1.1026732447957228, -2.7778692782093657, -1.5643556008354627, 1.0202168814006645, 1.4813265086417027, -0.39647410714387454, -1.1021917903270637, 1.1130876997971229, 2.8453247207765355, -0.12484123482004346, -6.32604928975384, -9.328520668841852, -5.47526483867776, 1.4742767383840831, 4.931169713399161, 3.111415264236152, -0.055151000051926795, -0.8825296964822162, -0.04383635595300564, -0.012709372244734122, -0.8570691482446046, -0.7571191629226481, 0.4273655471201077, 0.740708771402762], 'positive_zeros': ['1.152522027534157389097841668484', '3.4033308607555479655726216649', '4.40296764731940860137855291109', '6.24502861163529183365975003580', '7.46692728764230722524359307833', '8.39819994406826356075231798978', '10.04728582076037380668048045315', '10.65506922219411421206268173653', '11.63728857883778531337834566046', '12.3876373612967415672434941251', '14.44031487560478808564461976587', '15.642169792581980216701543307884', '16.410425477191490712892947057667', '17.37276274711905515193031681949', '18.23003058308851761424474151489', '19.407954487738171461153267631746', '20.38362060682394348695489067234', '21.259038202264872807817001289417', '22.4268225845765364155799893272', '23.506374821256843344932592122904', '24.31477898365766705241669708398', '26.00361124346935459489408090055', '26.757422718505122861169219260516', '27.44689355237233465092309609118', '28.109254368000968663576745246678', '29.21808902072884780911680655843', '30.1384992832617597806250364187', '30.96666947497524464662349948786', '32.47018347145138866654166282766', '33.61186331296932589974951775757', '34.2273732898640305654644371536', '35.104523695727025303482086876691', '35.87052443428755251152215724081', '37.022974045432028508911781151264', '38.0434498119724298124132440100', '38.739752782622522942526488600313', '39.75363715288017701098693769091', '39.93759474702144121659040634240', '41.71567760942842611142046845618', '42.93373083092150814188724733052', '43.59399794599613369914008490563', '44.33181025329995605391806794289', '45.51600766650360924319190852463', '46.22901160573490368960033961786', '46.50690995793177200005190955551', '47.63187496504256905062661306864', '48.79957299821506287324659176214', '49.954562269741618394968342244484', '50.485051685469345457193494383393', '51.73224664006463463914422008895', '52.4012310189810912494196590388', '53.32445167424815340659878937376', '54.398483821430255236283624787960', '55.1530012286834708552117767151', '55.82396325519280146966493256859', '56.72361139230447082393519652848', '57.37986318163113337591871633219', '58.33836865362381042165873973155', '59.19887038602673831560886596942', '60.75021251022462948770596155613', '61.662256934854907414430765960780', '62.10799277491418063873992322745', '62.96022685040887687461109205570', '63.37915826469347446985379918306', '64.55296190522075280024503725292', '65.73900920858358962714567944902', '66.07950566736790220252423858957', '66.9993709087173320205812120513', '67.98673937271396981411169486409', '69.089936302493406649470955187332', '69.82498851255851288022030250435', '70.57363428588031203213335594321', '71.87014418896239789404157732647', '72.420213157107685795599319260573', '73.20479115803472171027755990669', '74.1411311484133568044551977785', '74.4508273202547838697097353576', '75.361114693533072121348916667950', '76.20366284919854245557273305493', '77.78950449139048091072830856379', '78.39763409382464300438350582530', '79.20673729950348500238294205750', '79.90596556596243217567814003862', '81.02717395481513203009343750144', '81.427766021447559958261962883462', '82.2744839819990923030871732855', '83.1469262372974737993771186216', '84.27278311797898591093382209361', '84.791914870271624266312686852450', '85.548966462715091606358645122518', '86.17494737956077846301162883429', '87.5091088725697885767412352319', '88.77741612690926959924300559404', '89.0424583881880250529905388118', '90.24566201601032007067888356189', '90.565638122353565669954140371448', '91.3901389561791653647166631134', '92.40196103333211957483264907982', '92.65798510436169636155901941571', '94.00186526640782455496833752686', '94.543826209911848659828248500222', '95.71320947320390143839254669894', '96.85716673146578386536683019864', '97.362084501377149817088811360049', '98.03503024434053278828149343257', '98.6340461424444306611376911398', '99.899900103891788011176783776073', '100.778784197259172901430051753488', '101.43585728521893457350886759892', '101.7755867732990532880157951795', '102.59211151783855069740633425648', '103.695385740106803460784339967146', '104.275222539270471592935224382168', '105.669293773309538380806001666542', '106.26855312419921458482542305394', '107.54145379493819937503719325805', '107.77501180481066440795460889712', '108.58989212391199086076563937076', '109.23135103994735770218306836140', '110.05367224023702086927862953954', '110.70452287519313101757534976791', '111.90919648137113788313025410973', '112.55524646941425371084828666519', '113.27464427241124982833138300115', '114.43691872618944093178656447118', '114.72700794760862625548045695592', '116.16692222688491902579362605944', '116.649075614601230226833354576774', '117.59193393497924811347953894124', '118.11225150009195601464177965560', '119.003895526585588222097484601507', '119.82952493745471372454127370144', '120.46702367515279877469336037426', '120.95045931852215934641025982586', '121.643168974395447345445763295', '123.37627604841190189748511989288', '124.08975856167029433552165087044', '124.678958530991972892692497976141', '125.383403603034664195624792561936', '126.07912118047759665334022249782', '126.83854155787436214858197386474', '127.66704544241947442684196570342', '128.35761438138255486400326857360', '129.414817342945067565888583816183', '129.86820083882338720346654327762', '130.58413555142120428504138295252', '131.56154730286456415083916502186', '132.47971207531180486995441943532', '133.215533580819345778266935157782', '134.05336914621849998508917746992', '135.05160484226712114576469087346', '135.8509820455151463238483578370', '136.50384430074371673187135731341', '136.78849770396581032412842362723', '137.611106115218038261191183480465', '138.32727661841408467696517518594', '139.45684520756382019332862413785', '140.10595322497581207237342787610', '141.01538290297170403145434609704', '141.982891213289183672611680272368', '142.927624723474737020623892952373', '143.31005926938172649143871699271', '144.15563663222469696286507306197', '144.601152341797512344285774319085', '145.89621935846615254873872170838', '146.39992162544929859810098079037', '147.276235403771701507004426828181', '147.84743888386344531296256684731', '148.56005866391721283163845129643', '149.13691568667559008821134749686', '150.20514129647610063945769824092', '151.39913003952314707143878611605', '152.44195085269165625863576906043', '152.61128758102191746942804245906', '153.26240433181428561112634956451', '154.29289512338700016736660997715', '154.82680662874490925271541036969', '155.607793779179007974552800620169', '156.279546021041412009174907149167', '156.85568548137026044695084472315', '158.03517879158742085519504119341', '158.93564957364799441031787079017', '159.69432820653007237024187669948', '160.19930856803789978331186368839', '161.10601405686647277306996363796', '161.83043374288287454026669812682', '162.87250209312306080711296545217', '163.55666131044783039607807593846', '163.96347447052197903489839733308', '164.94917230024784591815020138355', '165.47428691162546477533211458867', '166.15460465485772602542509376956', '166.856355128999914029858873659778', '167.83495227970376236876000951421', '168.89222343835871138074604107622', '169.804342467951505733587350977497', '170.38836726182465273997010231118', '171.21586726974743183983310530105', '171.777670813479068112951682830942', '172.46391120683560243775683032131', '172.704101456467684594045786488495', '174.20262927388001145990124658982', '174.82986353177696186520014634532', '175.44976331270145856513738367868', '176.16857403839039673788189062557', '176.67297777549227261909422867732', '178.15217209414522987674392620742', '178.66503241445544422201673697571', '179.227290079499388017841436867875', '180.36880443508848949353412126433', '180.84922668512546627157452975158', '181.842821154595293375253098170', '182.413348722590911947355866772206', '182.76890366615213647257660369712', '183.775834494140401690960140267512', '184.10006255368166169256888784443', '185.17287500068188210743708270333', '186.202163536556527063155773833450', '187.291865890369239729747074329958', '187.79331228058870229720222945122', '188.309372582071824723814359713618', '189.14848032814254229777487711424', '189.78158919933743404143832745012', '190.712241571988159381009837268', '191.38239988200317168094001484832', '192.05348662733952528568018037017', '192.67020174594942128664279835711', '193.61711927334738038525525778518', '194.31467206743396201322971003895', '194.875566679714156099085260857737', '195.6177674133080091532990842408', '196.80406042875511613101131243017', '197.805016009883496964758321389110', '198.457173891919220737482432029788', '198.74393975490949226453517892165', '199.57825975261192334158770326443'], 'prelabel': '1-143-143.8-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': 0.11427484657981525, 'root_number': '0.753116390810882759089093987159+0.657887301816952313537833256077*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.11427484658', 'prec': 44}, 'spectral_label': 'r0-0', 'st_group': 'mu(20)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.517873127893077965964204072984+0.0662743111874795338399810216751*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.15252202753', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.40333086076', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.40296764732', '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': 0.6640892081105222, 'bad_primes': [11, 13], 'central_character': '143.8', 'conductor': 143, 'conductor_radical': 143, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/143/8'], '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': '1-143-143.8-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': '1-143-143.8-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': 0.11427484657981525, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.15252202753', 'prec': 44}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_143.8', 'Lhash_array': ['dirichlet_L_143.8'], 'factors': ['1-143-143.8-r0-0-0'], 'label': '1-143-143.8-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/143/8'}