Lfunction data - 8-672e4-1.1-c1e4-0-2

Formats: - HTML - YAML - JSON - 2025-09-10T19:24:17.826969

• 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': '331157525671562974245162345647,1482149817426001695250438216931,2055553976345775189774130225975,2345168202204431904747017227988', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 829.0591566244398, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, -6, 0, 9]], [7, [1, 0, 2, 0, 49]]], 'bad_primes': [2, 3, 7], 'central_character': '672.1', 'coefficient_field': '1.1.1.1', 'conductor': 203928109056, 'conductor_radical': 42, 'degree': 8, 'euler_factors': [[1], [1, 0, -6, 0, 9], [1, 2, -7, 2, 76, 10, -175, 250, 625], [1, 0, 2, 0, 49], [1, 0, -3, 0, -112, 0, -363, 0, 14641], [1, 0, -28, 0, 534, 0, -4732, 0, 28561], [1, 2, -31, 2, 868, 34, -8959, 9826, 83521], [1, 0, 37, 0, 1008, 0, 13357, 0, 130321], [1, 0, 21, 0, -88, 0, 11109, 0, 279841], [1, 0, -92, 0, 3798, 0, -77372, 0, 707281], [1, 0, -19, 0, -600, 0, -18259, 0, 923521], [1, 6, -47, 54, 4188, 1998, -64343, 303918, 1874161], [1, 32, 548, 5984, 45670, 245344, 921188, 2205472, 2825761], [1, 0, 172, 0, 11094, 0, 318028, 0, 3418801], [1, 0, -91, 0, 6072, 0, -201019, 0, 4879681], [1, 42, 841, 10626, 92364, 563178, 2362369, 6252834, 7890481], [1, 0, -43, 0, -1632, 0, -149683, 0, 12117361], [1, 42, 857, 11298, 104508, 689178, 3188897, 9533202, 13845841], [1, 0, 13, 0, -4320, 0, 58357, 0, 20151121], [1, 0, -276, 0, 29126, 0, -1391316, 0, 25411681], [1, -30, 521, -6630, 65412, -483990, 2776409, -11670510, 28398241], [1, 0, -155, 0, 17784, 0, -967355, 0, 38950081], [1, 0, -52, 0, 14454, 0, -358228, 0, 47458321], [1, -26, 329, -4394, 52324, -391066, 2606009, -18329194, 62742241], [1, 0, -364, 0, 51942, 0, -3424876, 0, 88529281], [1, -14, -55, -686, 33004, -69286, -561055, -14424214, 104060401], [1, 0, 125, 0, 5016, 0, 1326125, 0, 112550881], [1, 0, 45, 0, -9424, 0, 515205, 0, 131079601], [1, 10, -143, 250, 36268, 27250, -1698983, 12950290, 141158161], [1, 0, 148, 0, 31014, 0, 1889812, 0, 163047361]], 'euler_factors_factorization': [[1], [[[1, 0, -3], 2]], [[[1, 1, -4, 5, 25], 2]], [[[1, 0, 2, 0, 49], 1]], [[[1, 0, -3, 0, -112, 0, -363, 0, 14641], 1]], [[[1, 0, -14, 0, 169], 2]], [[[1, 1, -16, 17, 289], 2]], [[[1, 0, 11, 0, 361], 1], [[1, 0, 26, 0, 361], 1]], [[[1, 0, 21, 0, -88, 0, 11109, 0, 279841], 1]], [[[1, 0, -46, 0, 841], 2]], [[[1, 0, -19, 0, -600, 0, -18259, 0, 923521], 1]], [[[1, 3, -28, 111, 1369], 2]], [[[1, 8, 41], 4]], [[[1, 0, 43], 4]], [[[1, 0, -91, 0, 6072, 0, -201019, 0, 4879681], 1]], [[[1, 21, 200, 1113, 2809], 2]], [[[1, 0, -43, 0, -1632, 0, -149683, 0, 12117361], 1]], [[[1, 21, 208, 1281, 3721], 2]], [[[1, 0, -109, 0, 4489], 1], [[1, 0, 122, 0, 4489], 1]], [[[1, 0, -138, 0, 5041], 2]], [[[1, -15, 148, -1095, 5329], 2]], [[[1, 0, -155, 0, 17784, 0, -967355, 0, 38950081], 1]], [[[1, 0, -26, 0, 6889], 2]], [[[1, -13, 80, -1157, 7921], 2]], [[[1, 0, -182, 0, 9409], 2]], [[[1, -7, -52, -707, 10201], 2]], [[[1, 0, 125, 0, 5016, 0, 1326125, 0, 112550881], 1]], [[[1, 0, 45, 0, -9424, 0, 515205, 0, 131079601], 1]], [[[1, 5, -84, 545, 11881], 2]], [[[1, 0, 74, 0, 12769], 2]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 2, 'label': '8-672e4-1.1-c1e4-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/672/2/bc/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.03125', 'prec': 24}, 'plot_values': [0.8413663275430915, 0.8286500779783266, 0.7922684488002318, 0.731927948416939, 0.6473913934563129, 0.5385773211230597, 0.4057279584842623, 0.24929921365130936, 0.06993408394762939, -0.13149659426975432, -0.3537433737325668, -0.5951198010526763, -0.8534800111657738, -1.1261354615825248, -1.4096416997602657, -1.6999199537910457, -1.9923264395938305, -2.2816223422887285, -2.561820461558975, -2.8264607089640146, -3.068802590706299, -3.281938308052078, -3.4588758045782924, -3.592918526479941, -3.677954179126836, -3.7087147037869137, -3.681095153449599, -3.5924504550903196, -3.441822748709578, -3.2301890351337015, -2.9608002885140747, -2.6390973620400047, -2.2726183636185033, -1.870956147362059, -1.4457575908915614, -1.0100754442593487, -0.577820991876184, -0.1632915858298841, 0.21932754578981203, 0.5569363289795536, 0.8382512093844087, 1.054413441278734, 1.199606688898403, 1.271618786677079, 1.272076321866568, 1.2065052064078412, 1.0842873043762968, 0.9180845679443167, 0.7230361255698295, 0.5158263030868254, 0.31359842220511136, 0.13241864021511346, -0.01416032705315707, -0.11643783287350404, -0.1698447908498565, -0.176012546946081, -0.14338147835827753, -0.08740540545490194, -0.030294193069880803, -3.928869976260464e-05, -0.02894936356938904, -0.1517261156868708, -0.4029732795884005, -0.814442894726087, -1.4122674896965, -2.214205204178353, -3.227005020331014, -4.444550909326262, -5.846624924587666, -7.398499574078766, -9.051923118199104, -10.746679524421422, -12.412923581306577, -13.974877135674873, -15.35676008306156, -16.486365193883966, -17.29898351856677, -17.742547540961006, -17.784595752673, -17.412553561566856, -16.63422366185709, -15.479147672073815, -14.000644519560442, -12.269306674304541, -10.367772665421057, -8.386679581234512, -6.420886713241477, -4.560116974253313, -2.8825806645299332, -1.450655906535683, -0.30763424104938614, 0.5260452643702338, 1.0532527561540321, 1.298476804110623, 1.3045741793782286, 1.1281884478936977, 0.8339295522614915, 0.4879662837318291, 0.15133863682209006, -0.12546585870045548, -0.3066786077304397, -0.3741588526378296, -0.32866080062229636, -0.18781232040811985, 0.01710555713397189, 0.24551438525678798, 0.4534712703066611, 0.6000694485711384, 0.6526956789122934, 0.5915883977851503, 0.41390423439636304, 0.13393236002091966, -0.21867512787339588, -0.6018937890970517, -0.9655404248540729, -1.2587294706378107, -1.4367767092021417, -1.467176636418825, -1.3345667965755268, -1.0444573867555433, -0.6240032631260465, -0.12011521928750706, 0.40514407149861775, 0.8809241250159595, 1.2353000157073095, 1.4038189627159299, 1.3383511304496398, 1.0129088589616497, 0.42760247126477324, -0.3896483488474815, -1.384775742684823, -2.4831575305744975, -3.596569521282725, -4.632123448740222, -5.504073822280812, -6.141744574766136, -6.495760985706122, -6.543771348800943, -6.295649811695343, -5.788136048946833, -5.078756214192948, -4.2398769139342125, -3.352193799093256, -2.491747305173749, -1.72126566717552, -1.0849840658678753, -0.6058005648385154, -0.2835015453036052, -0.09811190077021369, -0.016060316139214086, 0.0023687584014463994, -0.004820296095655276, -0.008618171584625554, 0.005881026438706531, 0.03734684514446039, 0.06948984548858828, 0.07571407056024039, 0.026440768297382893, -0.10258923531894992, -0.32192507540961535, -0.621298315248165, -0.9659182597159682, -1.2994419870217346, -1.5490288852754528, -1.6340987098700068, -1.4802399210547137, -1.038951563618274, -0.29912320810937487, 0.7031773200436235, 1.8767981214584146, 3.073173760691138, 4.099071693365022, 4.732884200414405, 4.745744981592951, 3.9309814014322244, 2.1320966298373114, -0.7339533412721987, -4.65737397709279, -9.521961516434311, -15.109290839001085, -21.11135704316021, -27.153642696456654, -32.834093664133285, -37.757096413932246, -41.56685937688601, -43.98566155167244, -44.859365538284976, -44.15550183977903, -41.95865077559251, -38.4676333428165, -33.99091057762426, -28.89070429405476, -23.541816810043983, -18.301947785184915, -13.48638523141023, -9.327792679024453, -5.962294692342691, -3.4312088325847374, -1.6912004502702864, -0.6300587356515294, -0.09305126304185626, 0.08906928999574618, 0.0747743868338111, -0.00874499301893776, -0.07770310140624044, -0.09473028540630173, -0.063413235746141, -0.01604239975069556, 0.0024153492907991324, -0.04906180271672511, -0.193803613845887, -0.42936436555887464, -0.7255962031772778, -1.0295847547895218, -1.2783919028900053, -1.4125339795106076, -1.3891474842599147, -1.1941788834450524, -0.8515831671202916, -0.4198893707879204, 0.016330571099431406, 0.35902657649567726, 0.5134959780377815, 0.4081248017309968, 0.00918565076545081, -0.670128522546142, -1.5683547302392615, -2.5828463251884153, -3.58368460266653, -4.433483784924652, -5.012816051805328, -5.237660334605823, -5.072030182734108, -4.5359277320378695, -3.7066712660415644, -2.701906361754308, -1.6600462480411067, -0.7193340727441108, 0.004328414554711177, 0.4374252964054721, 0.558839854370499, 0.4012617612896768, 0.04352735703115949, -0.40673581526907815, -0.8337268313010769, -1.135106712646156, -1.24283473930958, -1.133728560043825, -0.8312042356810693, -0.3995768679058361, 0.0697092224368825, 0.4803947794077244, 0.7517138403985757, 0.835255812186078, 0.7270379609322762, 0.4672790614067884, 0.1302771572012853, -0.1923867544882433, -0.41376837797858196, -0.47599625007521906, -0.3679612284326173, -0.1340837166564566, 0.1272756635415794, 0.27869535160631353, 0.16882193018660324, -0.33688567853455087, -1.326676068891679, -2.8171763894694526, -4.73744994676169, -6.92877574578961, -9.16961100606194, -11.201487158684872, -12.761942494737474, -13.628085168079787, -13.670795421754528, -12.865999077738456, -11.296972273864515, -9.15061740189548, -6.702163067174821, -4.2601026968745614, -2.1183687493158025, -0.5156943925266719, 0.3994923477560587, 0.5917627990936245, 0.13842455027615996, -0.7885212192743978, -1.9571800343973882, -3.1188019075339133, -4.048810320448703, -4.584193249582421, -4.653987790563297, -4.277543244537975, -3.5501969642939915, -2.620953002784895, -1.661567062826571, -0.8229990449213638, -0.20745478972676584, 0.14582082826620518, 0.2621685844463461, 0.21668714804749653, 0.10583345153789143, 0.014753025118938824, -0.013654696596803493, -0.0006564873167405502, -0.03749525284876088, -0.2740902575189705, -0.8911580551142926, -2.0608410759614855, -3.9037835059517403, -6.451162529231166, -9.623729072965903, -13.226301904238378, -16.960138791103713, -20.4598421600077, -23.362414523820977, -25.34916712104938, -26.185383145070553, -25.763842592844306, -24.148209832517907, -21.535046309552648, -18.215167620089986, -14.539033372689833, -10.879116817016545, -7.553364407317574, -4.784776895084761, -2.6873182635055533, -1.2681827275828261, -0.43917672974116584, -0.051819779463919594, 0.061070972843464015, 0.04801028518080294, 0.012188282784631426, -0.0010491503492953264, -2.9223628727470617e-05, -0.02830280282893788, -0.13845292216878263, -0.36481613816166536, -0.702159691309115, -1.0998688036338211, -1.4685210247180192, -1.697190180246718, -1.6817245101681604, -1.3615916939817454, -0.7375750723497022, 0.12129891995922307, 1.0821165607224654, 1.9695202534722624, 2.6068859302016105, 2.8556518981718946, 2.6503837310022806, 2.026057869584034, 1.117955924530611, 0.14141234382249546, -0.6447126636207765, -0.9893248525467441, -0.7030935490812689, 0.29912134080030306, 1.9720250208664913, 4.139437991825933, 6.523299485777336, 8.787340102830738, 10.595648098378605, 11.687061078453397, 11.914166565600084, 11.262135405360366, 9.853965724440393, 7.938440365087787, 5.821863205080386, 3.805612660127083, 2.134562714335175, 0.9557014588804152, 0.28852026573309236, 0.03246719798830562, -0.00032745076376042086, -0.03615507681211761, -0.2837652235847278, -0.8833461773703468, -1.871780672505662, -3.1753821768615316, -4.625684911550105, -5.993228549125521, -7.038089522319576, -7.574185872340315, -7.501471363873684, -6.822386132693023, -5.645399216158992, -4.1705449993204695, -2.6342321139817764, -1.2605131967398155, -0.22141635465704637, 0.3937446523203339, 0.591209969573267, 0.45926615439133966, 0.13888560232652244, -0.21525754612945586, -0.4750729111844731, -0.5676302336852752, -0.4879887773219118, -0.29436488249393816, -0.08360574483311672, 0.04141334647281423, 0.004652091300929805, -0.21846505236263652, -0.5920186523315406, -1.0272829714014764, -1.406562274757056, -1.6219291498868293, -1.6054265988473035, -1.3495989558269799, -0.9171925510428769, -0.4340648307182113, -0.050724105100144336, 0.09797997854503995, -0.0702555612290772, -0.554233446238089, -1.257858061989792, -2.007048550444447, -2.5865641076108297, -2.7887516103833256, -2.4687478384502155, -1.5890323096303693, -0.24074141923864095, 1.3703124459170035, 2.957548269843058, 4.207071197301444, 4.847335291751065, 4.723928767119272, 3.8273325598676693, 2.2991331622785594, 0.41378353417181984, -1.4759950382516114, -3.0194444856724423, -3.936040506284406, -4.073388178911026, -3.450190152681917, -2.238316978174319, -0.7178159786277437, 0.7837402371748778, 1.9653474390150647, 2.6254761790600756, 2.700403043719724, 2.271445020435343, 1.5413556510892488, 0.7697435755435663, 0.2008735642039066, -0.001330213028056083, 0.2001943531409206, 0.7029488687523568, 1.291877495459807, 1.6971847759561547, 1.6725961820899806, 1.0683275688970018, -0.11668945243926941, -1.7149755161086557, -3.4194217311122106, -4.85002757553548, -5.637312619022501, -5.515769592288232, -4.414708225294048, -2.4839327294930715, -0.07849315698702555, 2.2940537721172443, 4.070085101715601, 4.751134063288206, 4.006326374259808, 1.7485400431192533, -1.8320669312071267, -6.302850333443954, -11.060158558820833, -15.435381309844907, -18.838659173711473, -20.846509671575756, -21.25477402056096, -20.11016578927851, -17.71441100176341, -14.513851479602224, -11.000915024895534, -7.634650210846788, -4.77433015568383, -2.6162290544943323, -1.1920062193552916, -0.4025274613085959, -0.06986471712026794, 0.003208208721577827, -0.018788327835510422, -0.03567642374135768, -0.018720040504961077, 0.005953244126532642, -0.012064260100170936, -0.11402172784183459, -0.3070429685884832, -0.5557091507639595, -0.7901012702104946, -0.9282874852682316, -0.9091976121754127, -0.7144014005307656, -0.37757776434358464, 0.0194214057263068, 0.36711914743722807, 0.5639760245156386, 0.5468955725154492, 0.31221251562601315, -0.07741273444997543, -0.5115967731687903, -0.8649588677634534, -1.0348745984167391, -0.9766425501085014, -0.7225989098360358, -0.3769561886418956, -0.08837800840108812, -0.005484096588172322, -0.22709483097049668, -0.7619485304756145, -1.5095950176624926, -2.276509307852107, -2.8166113290419026, -2.887857898281991, -2.320069025050071, -1.0801523661173316, 0.7131089009374932, 2.801844578922242, 4.830287298286003, 6.424632294699672, 7.280223067722786, 7.226010825244778, 6.267392098518634, 4.601265696083287, 2.5608985242070683, 0.5387752998801111, -1.0982421307949617, -2.093771385305092, -2.3552622195278583, -1.9626393492699135, -1.1397173627889714, -0.19185326356140878, 0.585473989622534, 0.9818710649331822, 0.9213829870905872, 0.4754295418516488, -0.1697810058699039, -0.7747479083738558, -1.1214723008724514, -1.0876303415735216, -0.6798316862810004, -0.027628835073031984, 0.6558917606079129, 1.1442576998319511, 1.2818821211964075, 1.0422318508497361, 0.5505310661513089, 0.06281419039215365, -0.10872303871930387, 0.3047629434533346, 1.4286528365705908, 3.1723136721514775, 5.206574861716517, 7.000974297101817, 7.923046881089731, 7.394657003163996, 5.027160792770335, 0.7332652482001967, -5.203532812460219, -12.14737664540983, -19.222323096322654, -25.453530408388417, -29.94280745970514, -32.08490339104114, -31.65436223964761, -28.822309900337537, -24.125545543243366, -18.383158633936986, -12.495347219630624, -7.270165683576271, -3.2893968742046837, -0.8236489943611921, 0.1722628193789522, 0.003556634893005395, -0.8635892930869732, -1.9382314303295125, -2.818141905860098, -3.2515238712084673, -3.16536995488096, -2.6607763084888494, -1.929579747240066, -1.176934784248821, -0.5658299220829582, -0.18156685182983193, -0.01581986488161526, 0.005185490636029347, -0.02424952809412787, -0.03183689195021681, 0.003463339874034299, 0.04581730532076757, 0.02253847736325691, -0.1398213311962821, -0.4774949189808181, -0.9614068487305527, -1.49153139179468, -1.9246291699349816, -2.1131765681155117, -1.9487473154058002, -1.4045157637445362, -0.5631452837460348, 0.4076820340742557, 1.2972255715827539, 1.9025925527164669, 2.0852287736476454, 1.816999220727453, 1.187137287550814, 0.37593262578043807, -0.3977209583010391, -0.9396040267696542, -1.1377190902391496, -0.9961390620293429, -0.6322756446837934, -0.23436013250169638, 0.0014714710382232382, -0.05838226660782282, -0.4338342540805984, -1.0177676146593342, -1.5969413199543894, -1.9128995138089744, -1.7675388707186215, -1.0926176130459495, 0.010716839874275337, 1.2609470860464882, 2.2320821135507405, 2.470960156176708, 1.614595593836134, -0.5093500737701864, -3.8143177650625875, -7.942318392634384, -12.31614536847542, -16.253124800576177, -19.14009594250757, -20.536192803691854, -20.246029517741427, -18.37162427509393, -15.325157300253755, -11.669646655392514, -7.985319249576447, -4.768684494708109, -2.3527147438399125, -0.8347557444237671, -0.10267518853805638, 0.08895870139725078, 0.025854199742965597, -0.053426613085668956, -0.019805142122231868, 0.1289429501832338, 0.2985378036704998, 0.35846745329851637, 0.20933712788883835, -0.16260243939345448, -0.6661696243344747, -1.1306744846779817, -1.3583469640488486, -1.1930375560485675, -0.5889925063319673, 0.36736452897165983, 1.4740054679154166, 2.463568764241054, 3.0859158741397037, 3.1895010539630673, 2.7686775057851887, 1.972245695542557, 1.0664617479763423, 0.34115486052644145, 0.0093198447114316, 0.12405436659640696, 0.5355189633310284, 0.9099088576461218, 0.8078523198198546, -0.19491176987043596, -2.373024226492843, -5.753047540453625, -10.064312138454053, -14.76183556152003, -19.155840424222678, -22.54622469206336, -24.354678553399324, -24.261837020963434, -22.33386839342713, -18.94820919629674, -14.687580405433401, -10.22760223316158, -6.212152512386733, -3.0878329428723967, -1.0394816861971325, -0.0009691368404263214, 0.28131359495551916, 0.1470655730855144, -0.08797892353534176, -0.21624215048940884, -0.1771191909719292, -0.03829354269877072, 0.06273616387698483, -0.00593743467191837, -0.3036698411266148, -0.7859658551052169, -1.314869665953582, -1.7073637121174654, -1.8138386205562713, -1.578502413884459, -1.0689845328324534, -0.47027710736156947, -0.03582415048945591, 0.00244609622474519, -0.48429295399269434, -1.466864771325425, -2.7501909265180426, -4.019546010953444, -4.924317607205764, -5.18295755160594, -4.689138851105619, -3.5436099891479262, -2.0330256577149, -0.5628567222150856, 0.45170871206450164, 0.7167879866507797, 0.14765659644702614, -1.0993826102899422, -2.6689903821444054, -4.1049440697008555, -4.972210253268758, -4.98308309916435, -4.100562502907183, -2.531468433740289, -0.6642579418476879, 1.0329029065583135, 2.149154169754064, 2.4555127060954054, 1.9587582176674299, 0.8931246458732836, -0.34762529959214744, -1.3471526022964697, -1.7976382949915921, -1.593783929905737, -0.8670524336238965, 0.053517802892888724, 0.7429521660235897, 0.8157963550151273, 0.05818355059858771, -1.5013907463579346, -3.5836749018546556, -5.719006199412864, -7.3867838675346755, -8.154308210874149, -7.784174462727996, -6.303927303176808, -4.018073205624415, -1.407037058481082, 0.9983991150431443, 2.745536721374825, 3.5745828091934304, 3.462268579290715, 2.602297750262572, 1.3372951733257046, 0.04938416816719831, -0.9486427315694266, -1.4783493405363384, -1.523010431445546, -1.2135538850527114, -0.7482210773005007, -0.3172213604234817, -0.047781685160086164, 0.025748455526741994, -0.04325961008427235, -0.1557027702592264, -0.21822251673536588, -0.18687448418343183, -0.08428718156703909, 0.015152608148301064, 0.023279137686206874, -0.1166082034212744, -0.3950978000241593, -0.7279773131653707, -0.9804727363436964, -1.0227575086702738, -0.7803356740348957, -0.26923564724710153, 0.39195285358008836, 1.0081805425877735, 1.383639454200488, 1.3920342121828961, 1.0267132002580526, 0.41877770785581553, -0.19760464931350866, -0.5695357434833245, -0.5279518239842321, -0.07705111323490088, 0.5639237799373205, 0.9853754932604374, 0.6843392817399072, -0.7874096683594349, -3.677445300546112, -7.911517558096924, -13.04448391737861, -18.35811708465121, -22.993628604701442, -26.11152867155766, -27.098738066352727, -25.808009406820428, -22.522496963875515, -17.86083093194623, -12.656760761287687, -7.796008633077501, -3.9505786603933166, -1.4436388620777256, -0.22540738882158812, 0.061560343815190016, -0.06180361058838693, -0.09169149296440311, 0.30008160424148905, 1.178133877432516, 2.3551638131502317, 3.4788250627851474, 4.172182776799752, 4.202255297845489, 3.557349491153759, 2.446319960107726, 1.2365211789231092, 0.33114819481167646, -0.007503426314761525, 0.2340552152282163, 0.795833398765688, 1.2014626938785895, 0.902876597436194, -0.5307124858676723, -3.245095519392961, -7.027361379933643, -11.318365086797147, -15.315250987571345, -18.17004007665511, -19.271056032616418, -18.371069071733594, -15.639917440987329, -11.651982259314956, -7.280131366888762, -3.4236935201393024, -0.7900561828199849, 0.2556104815443246, -0.23816996221749062, -1.852392038218422, -3.938314993846902, -5.804698200722208, -6.917542409014358, -7.016814944236462, -6.145694405734335, -4.605792905339419, -2.8478774500014827, -1.3125977238391602, -0.3096527727775943, 0.050358162566284996, -0.14228160360404105, -0.6611176471792983, -1.2316516863724756, -1.6215676033351185, -1.7159331656410919, -1.523093083161668, -1.1408822908483116, -0.7072015455784288, -0.3459912919252362, -0.11881079794912243, -0.01946286725945344, 0.001683930216613815, -0.00014686641400753314, 0.0005122905311188206, -0.01639584997939473, -0.104839930724827, -0.3199098872037158, -0.6791633322978788, -1.134873337458295, -1.5739057253680624, -1.8585177599411409, -1.874855207057499, -1.579385328200516, -1.0332242794073232, -0.40279773133018604, 0.10971461820229819, 0.3484373899321307, 0.2803427263975357, 0.04928579878414976, -0.027550017641358237, 0.4648090339225321, 1.9158368503034917, 4.553199879210272, 8.329260343398387, 12.866269552497833, 17.497572064481854, 21.441380604686078, 23.95888561117441, 24.514460219272923, 22.93310313586037, 19.51235497864734, 14.890947471532591, 9.886958785051103, 5.323694608229383, 1.841360572013573, -0.25453950368710665, -1.0158461260691727, -0.7860611013991112, -0.06642883267693833, 0.6632774042139812, 1.0768966147421606, 1.068237153018159, 0.7432154988494918, 0.32503363393589335, 0.03398254013173888, -0.01435391595176959, 0.13769536905500163, 0.3112132946641068, 0.27537778826272075, -0.14007050329517579, -0.9488608804828744, -1.9743035853804207, -2.886645784306097, -3.309066777314976, -2.9782821787631084, -1.8593277231167629, -0.1950956070180287, 1.5212437609304303, 2.6712610336143703, 2.707749187427521, 1.3315036201192818, -1.3872199482026295, -4.988632904999385, -8.73456582163029, -11.788462803747578, -13.442119394620837, -13.355872179537727, -11.612157175759123, -8.669412561724595, -5.245845012607951, -2.1281688908115166, 0.09569895704073944, 1.1766818190105683, 1.2303731700606366, 0.663488523130559, -0.006882768403126225, -0.3659770532926132, -0.2659416094956576, 0.10229918975413214, 0.2589713430634748, -0.4015328150191619, -2.3877604986103997, -5.921243490143815, -10.817775369583222, -16.463667521745812, -21.92987698639012, -26.270368964010583, -28.715448965235463, -28.81745029737905, -26.572035573140717, -22.48696515893303, -17.354096298197632, -12.03265306434927, -7.275536021002746, -3.5930579237759273, -1.1672406226728476, 0.11194933577087335, 0.5465062898366885, 0.5053503806964798, 0.29831426077792544, 0.1152672973131108, 0.022442937036477355, 0.00018365526206405076, 0.00116640454641123, 4.845443100232044e-06, 0.011626371890674789, 0.07561523697225916, 0.2198674082805091, 0.4252268076835548, 0.6117861259825575, 0.6644874577896515, 0.4813375944265642, 0.025724014951301458, -0.6348018783720178, -1.3276608505666732, -1.8314852655692653, -1.9563515753828986, -1.628643896435103, -0.9549234991016627, -0.2092368682052597, 0.23982659248482183, 0.04497237557505411, -0.9881628152820373, -2.8042562492599683, -5.074614598825463, -7.263439765096996, -8.79872298395385, -9.234973768021343, -8.387163486194659, -6.418936751350986, -3.8399596980911284, -1.3185499882391292, 0.5222876748759938, 1.2947538841960116, 0.9975373778302071, 0.03991529928835185, -0.876022631859686, -0.9608817466299965, 0.41698377931276537, 3.5135493267074493, 8.096827031715884, 13.47410415956042, 18.693092484238562, 22.768666115458103, 24.907999788929455, 24.721165480407414, 22.375468854721454, 18.450688013432053, 13.750391702744258, 9.106380852845755, 5.185890067593059, 2.3560268285217734, 0.6681612304896202, -0.07781843980291422, -0.22557274847836017, -0.12838766316564096, -0.025714429653728485, 0.0026064796678970793, -0.006659539735602035, 0.012282105886717524], 'positive_zeros': ['0.26123722547201962325188344289546', '1.16921004664783307488677939991809', '1.62154617051077850456520448400886', '1.84395372839307911294820081728226', '1.85001151088652100575298502002937', '2.82274679960634504429462826563566', '3.07842873938826525849999839884641', '3.24760287114128486590638123730359', '3.48121328455370505507698299020390', '3.78835519489972937040244494181317', '4.01733358191744714963154794214146', '4.67484123865719220902953255914870', '4.70267326941240199478200948030279', '4.77290618329426056117389352783028', '4.91471594233920015700779617362592', '5.22888760136331035188951355901553', '5.49302041441799309490506587364173', '6.26058112726745435626685297025469', '6.34062073996813680506728900140679', '6.48493682941461070962935446646576', '6.50465166870952610464025306998058', '6.87374961567870506529979097335047', '7.00052384979541171784723511517435', '7.43726242189230491381760796311434', '7.56567377567572924432667711568382', '7.80776603522049181975625657124822', '8.011960259321632685666459425490068', '8.171767128272051233188596746841043', '8.263853658239158054141587216048623', '8.795762288897383122501619289229440', '8.880635316733805105435871622907479', '9.265460809364602051655111886692025', '9.415061680508884957187870578904463', '9.472053111216584380090179804947097', '9.475442942118388321758708709554522', '10.25865810487045676601876546193841', '10.36630428050503016539948449466765', '10.39210540796154114160246236509370', '10.40602900554137594703296855616116', '10.74592394244891863408669442661612'], 'prelabel': '8-672e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.3164513843010055, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e4-0', 'trace_hash': 1288753385891945047, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.26123722547201962325188344290', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.16921004664783307488677939992', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.62154617051077850456520448401', 'prec': 103}}
• 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': 829.0591566244398, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 203928109056, 'conductor_radical': 42, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 0, -2, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, -32, 0, 0, 0, -12, 0, 0, 0, -2, 0, 0, 0, -42, 0, 0, 0, 0, 0, 0, 0, -42, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 0, 0, 27, 0, 0, 0, 4, 0, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -3, 0, -112, 0, -363, 0, 14641], 'euler13': [1, 0, -28, 0, 534, 0, -4732, 0, 28561], 'euler17': [1, 2, -31, 2, 868, 34, -8959, 9826, 83521], 'euler19': [1, 0, 37, 0, 1008, 0, 13357, 0, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, 21, 0, -88, 0, 11109, 0, 279841], 'euler29': [1, 0, -92, 0, 3798, 0, -77372, 0, 707281], 'euler3': [1, 0, -6, 0, 9, 0, 0, 0, 0], 'euler31': [1, 0, -19, 0, -600, 0, -18259, 0, 923521], 'euler37': [1, 6, -47, 54, 4188, 1998, -64343, 303918, 1874161], 'euler41': [1, 32, 548, 5984, 45670, 245344, 921188, 2205472, 2825761], 'euler43': [1, 0, 172, 0, 11094, 0, 318028, 0, 3418801], 'euler47': [1, 0, -91, 0, 6072, 0, -201019, 0, 4879681], 'euler5': [1, 2, -7, 2, 76, 10, -175, 250, 625], 'euler53': [1, 42, 841, 10626, 92364, 563178, 2362369, 6252834, 7890481], 'euler59': [1, 0, -43, 0, -1632, 0, -149683, 0, 12117361], 'euler61': [1, 42, 857, 11298, 104508, 689178, 3188897, 9533202, 13845841], 'euler67': [1, 0, 13, 0, -4320, 0, 58357, 0, 20151121], 'euler7': [1, 0, 2, 0, 49, 0, 0, 0, 0], 'euler71': [1, 0, -276, 0, 29126, 0, -1391316, 0, 25411681], 'euler73': [1, -30, 521, -6630, 65412, -483990, 2776409, -11670510, 28398241], 'euler79': [1, 0, -155, 0, 17784, 0, -967355, 0, 38950081], 'euler83': [1, 0, -52, 0, 14454, 0, -358228, 0, 47458321], 'euler89': [1, -26, 329, -4394, 52324, -391066, 2606009, -18329194, 62742241], 'euler97': [1, 0, -364, 0, 51942, 0, -3424876, 0, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -6, 0, 9, 0, 0, 0, 0], [1, 2, -7, 2, 76, 10, -175, 250, 625], [1, 0, 2, 0, 49, 0, 0, 0, 0], [1, 0, -3, 0, -112, 0, -363, 0, 14641], [1, 0, -28, 0, 534, 0, -4732, 0, 28561], [1, 2, -31, 2, 868, 34, -8959, 9826, 83521], [1, 0, 37, 0, 1008, 0, 13357, 0, 130321], [1, 0, 21, 0, -88, 0, 11109, 0, 279841], [1, 0, -92, 0, 3798, 0, -77372, 0, 707281], [1, 0, -19, 0, -600, 0, -18259, 0, 923521], [1, 6, -47, 54, 4188, 1998, -64343, 303918, 1874161], [1, 32, 548, 5984, 45670, 245344, 921188, 2205472, 2825761], [1, 0, 172, 0, 11094, 0, 318028, 0, 3418801], [1, 0, -91, 0, 6072, 0, -201019, 0, 4879681], [1, 42, 841, 10626, 92364, 563178, 2362369, 6252834, 7890481], [1, 0, -43, 0, -1632, 0, -149683, 0, 12117361], [1, 42, 857, 11298, 104508, 689178, 3188897, 9533202, 13845841], [1, 0, 13, 0, -4320, 0, 58357, 0, 20151121], [1, 0, -276, 0, 29126, 0, -1391316, 0, 25411681], [1, -30, 521, -6630, 65412, -483990, 2776409, -11670510, 28398241], [1, 0, -155, 0, 17784, 0, -967355, 0, 38950081], [1, 0, -52, 0, 14454, 0, -358228, 0, 47458321], [1, -26, 329, -4394, 52324, -391066, 2606009, -18329194, 62742241], [1, 0, -364, 0, 51942, 0, -3424876, 0, 88529281]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/672/2/bc/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, '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': '8-672e4-1.1-c1e4-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-672e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.3164513843010055, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1288753385891945047, 'z1': {'__RealLiteral__': 0, 'data': '0.26123722547201962325188344290', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '331157525671562974245162345647,1482149817426001695250438216931,2055553976345775189774130225975,2345168202204431904747017227988', 'Lhash_array': ['331157525671562974245162345647', '1482149817426001695250438216931', '2055553976345775189774130225975', '2345168202204431904747017227988'], 'factors': ['2-672-21.5-c1-0-2', '2-672-21.17-c1-0-11', '2-672-21.5-c1-0-20', '2-672-21.17-c1-0-24'], 'label': '8-672e4-1.1-c1e4-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/672/2/bc/a'}