Lfunction data - 6-9300e3-1.1-c1e3-0-1

Formats: - HTML - YAML - JSON - 2026-03-18T09:58:45.500063

• 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': '1304897099301255358271735382380,1469546036440317660828639732417,1506682633555829558023476199130', 'a10': 0, 'a2': 0, 'a3': -3, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 409524.7621012392, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 3, 3, 1]], [5, [1]], [31, [1, -3, 3, -1]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '9300.1', 'coefficient_field': '1.1.1.1', 'conductor': 804357000000, 'conductor_radical': 930, 'degree': 6, 'euler_factors': [[1], [1, 3, 3, 1], [1], [1, 0, 13, -4, 91, 0, 343], [1, 5, 36, 103, 396, 605, 1331], [1, 2, 21, 70, 273, 338, 2197], [1, -5, 40, -173, 680, -1445, 4913], [1, 5, 44, 181, 836, 1805, 6859], [1, -1, 20, 101, 460, -529, 12167], [1, -3, 24, 69, 696, -2523, 24389], [1, -3, 3, -1], [1, 0, 73, 86, 2701, 0, 50653], [1, 18, 127, 662, 5207, 30258, 68921], [1, -16, 193, -1392, 8299, -29584, 79507], [1, -2, 121, -196, 5687, -4418, 103823], [1, 3, 124, 195, 6572, 8427, 148877], [1, -24, 325, -2998, 19175, -83544, 205379], [1, 12, 199, 1368, 12139, 44652, 226981], [1, -29, 412, -3897, 27604, -130181, 300763], [1, 6, 193, 764, 13703, 30246, 357911], [1, -8, 211, -1056, 15403, -42632, 389017], [1, 8, 31, -510, 2449, 49928, 493039], [1, 19, 344, 3213, 28552, 130891, 571787], [1, 17, 314, 3059, 27946, 134657, 704969], [1, 17, 226, 2181, 21922, 159953, 912673], [1, 16, 223, 2048, 22523, 163216, 1030301], [1, -3, 48, -1779, 4944, -31827, 1092727], [1, -2, 181, -26, 19367, -22898, 1225043], [1, 18, 427, 4096, 46543, 213858, 1295029], [1, -22, 399, -4900, 45087, -280918, 1442897]], 'euler_factors_factorization': [[1], [[[1, 1], 3]], [1], [[[1, 0, 13, -4, 91, 0, 343], 1]], [[[1, 5, 36, 103, 396, 605, 1331], 1]], [[[1, 2, 21, 70, 273, 338, 2197], 1]], [[[1, -5, 40, -173, 680, -1445, 4913], 1]], [[[1, 5, 44, 181, 836, 1805, 6859], 1]], [[[1, -1, 20, 101, 460, -529, 12167], 1]], [[[1, -3, 24, 69, 696, -2523, 24389], 1]], [[[1, -1], 3]], [[[1, 0, 73, 86, 2701, 0, 50653], 1]], [[[1, 18, 127, 662, 5207, 30258, 68921], 1]], [[[1, -16, 193, -1392, 8299, -29584, 79507], 1]], [[[1, -2, 121, -196, 5687, -4418, 103823], 1]], [[[1, 3, 124, 195, 6572, 8427, 148877], 1]], [[[1, -24, 325, -2998, 19175, -83544, 205379], 1]], [[[1, 12, 199, 1368, 12139, 44652, 226981], 1]], [[[1, -29, 412, -3897, 27604, -130181, 300763], 1]], [[[1, 6, 193, 764, 13703, 30246, 357911], 1]], [[[1, -8, 211, -1056, 15403, -42632, 389017], 1]], [[[1, 8, 31, -510, 2449, 49928, 493039], 1]], [[[1, 19, 344, 3213, 28552, 130891, 571787], 1]], [[[1, 17, 314, 3059, 27946, 134657, 704969], 1]], [[[1, 17, 226, 2181, 21922, 159953, 912673], 1]], [[[1, 16, 223, 2048, 22523, 163216, 1030301], 1]], [[[1, -3, 48, -1779, 4944, -31827, 1092727], 1]], [[[1, -2, 181, -26, 19367, -22898, 1225043], 1]], [[[1, 18, 427, 4096, 46543, 213858, 1295029], 1]], [[[1, -22, 399, -4900, 45087, -280918, 1442897], 1]]], 'gamma_factors': [[], [0, 0, 0]], 'group': 'GL2', 'index': 1, 'label': '6-9300e3-1.1-c1e3-0-1', '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}], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 3, 'origin': 'ModularForm/GL2/Q/holomorphic/9300/2/a/s', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.015625', 'prec': 27}, 'plot_values': [-2.6740845911455284e-181, 0.0001749711768348736, 0.0013974511110288696, 0.004703376103189217, 0.011105596355575403, 0.021582345584251122, 0.037065959121967, 0.058431811055292805, 0.08648693737247039, 0.12195975323672578, 0.1654900254464726, 0.2176177989969403, 0.27877520546606344, 0.3492782834539381, 0.42931669013984813, 0.5189489259297919, 0.61809706366322, 0.7265382976316612, 0.8439048563820349, 0.9696828701974604, 1.1032074791071032, 1.2436682767063336, 1.3901135261852107, 1.541451110092102, 1.6964595201078925, 1.8537983292933338, 2.0120174903175654, 2.169572714529091, 2.3248424664049354, 2.476147805835929, 2.621769622479502, 2.7599714482067434, 2.8890310851277867, 3.0072557932335955, 3.1130090149280885, 3.204753464959357, 3.281059284716994, 3.340631529035048, 3.382362413271642, 3.4053269447933157, 3.4088070029326367, 3.392348395854283, 3.355738830997046, 3.29902392933289, 3.222563104570326, 3.12698612255018, 3.0131967120229852, 2.8824205307780164, 2.7361390167868596, 2.5760775710314783, 2.404239421830997, 2.2228188062571776, 2.0341730124059323, 1.840837989767201, 1.64542670316895, 1.4505874083409829, 1.2590002695323006, 1.073270374058186, 0.8958780072151866, 0.7291598545427882, 0.5752088948239324, 0.4358254663155959, 0.3124910368986414, 0.20628825067714904, 0.11786346575069914, 0.047404528481374594, -0.005406948305705988, -0.04141085807223026, -0.06197396361394743, -0.06899698808355642, -0.06489926101722157, -0.05259582958697458, -0.03546140796938712, -0.01728060509718303, -0.0021901390191432038, 0.005395603095308908, 0.0008660292299803696, -0.020494044068512844, -0.06340361295421959, -0.1324823987241, -0.2321360786567134, -0.3664469032825378, -0.539065738195901, -0.7530945241115565, -1.0109884563551879, -1.3144642708027414, -1.6644079363118185, -2.060806510722281, -2.5026943445693566, -2.988117339354609, -3.514105627580344, -4.076675224749963, -4.670877580224128, -5.290813000549434, -5.929696465236646, -6.580012060427931, -7.2335533945103805, -7.881549955658081, -8.514931173199908, -9.12436675640003, -9.700436330465402, -10.233989628547983, -10.716150009707, -11.138498122425249, -11.49349661372706, -11.774417133162592, -11.975501548657643, -12.092405659073233, -12.122015839836463, -12.062551393631091, -11.913975820849286, -11.677684260088064, -11.35651908301132, -10.95510173674182, -10.479394490318423, -9.936617693445584, -9.335470320678315, -8.685595368712779, -7.997408572446202, -7.282199237639029, -6.551552548766745, -5.817121552015307, -5.090626938862479, -4.383305694273614, -3.705675529022909, -3.0674766709580945, -2.477219835393763, -1.9420000752354885, -1.4674388502941673, -1.0573926953690813, -0.713868380972617, -0.43702452191187485, -0.2250763570383119, -0.0743456781316724, 0.020634042964250743, 0.06701720968747436, 0.07345690417171169, 0.0498818962559428, 0.0072392277071394, -0.04280520385485313, -0.08818381744192562, -0.11677148664072097, -0.11673591782242967, -0.07688788801739072, 0.01297449687023122, 0.161742469353073, 0.376701211846726, 0.6632675877821389, 1.024772965459837, 1.46231821006325, 1.9746492685530825, 2.558106373454861, 3.2067088296850463, 3.9121810085138238, 4.664091915128272, 5.450210535474596, 6.256644175288155, 7.068146345461617, 7.868729620247688, 8.641833167510125, 9.370732150785262, 10.039338373135664, 10.632287124590436, 11.135349815701588, 11.5363076176541, 11.824848757221853, 11.99287764816257, 12.035326225236034, 11.949784447985678, 11.736618372479837, 11.399595568682196, 10.945228753725575, 10.382659597349223, 9.724018164623034, 8.983529680848637, 8.17718078551677, 7.32279923188601, 6.439039325449545, 5.544907960503621, 4.659623542759718, 3.8016386412394962, 2.9881479083966394, 2.2348447414915236, 1.5551465656726677, 0.9598218952106417, 0.4567918468796378, 0.05068932203560226, -0.25727879114745683, -0.46935117150170097, -0.5912568986414136, -0.6320570188216502, -0.6039056023754659, -0.5217244797180094, -0.40276358014820446, -0.26610796948807364, -0.1320923076815067, -0.021672731497547365, 0.044223540006608844, 0.04537779770242017, -0.037054172276792995, -0.21990539079020913, -0.5174016974411987, -0.9406286573542905, -1.497113843647899, -2.190452661858479, -3.02005309471576, -3.9811228366883102, -5.0645731764034085, -6.2571189086927115, -7.541784255078921, -8.898037872248697, -10.302232309401466, -11.728634228863735, -13.149648256505406, -14.536486942142787, -15.860613375739947, -17.09385289996595, -18.209117226346756, -19.182052835305043, -19.990837636564674, -20.61676231279469, -21.045832862297477, -21.26810892022672, -21.277979713170232, -21.075487814219816, -20.665174034026577, -20.055967122778977, -19.262074601984562, -18.301427786818387, -17.19521181186562, -15.968287127757947, -14.647441503918133, -13.260689751164756, -11.837312988376008, -10.406189090352015, -8.995059402312881, -7.630366513237871, -6.335929854532225, -5.132388746106184, -4.037055607627753, -3.0631280232947016, -2.2194686335061684, -1.5106586998369567, -0.9368113924938666, -0.49375253896977794, -0.17336905772036706, 0.03605433572296164, 0.14930567579948323, 0.18362874553413885, 0.15805853669239917, 0.09269636920042641, 0.007963978017596709, -0.07613441230813142, -0.14072385736699594, -0.16872409361468324, -0.14542328190923032, -0.058975930846406184, 0.09922492099447752, 0.33428919313041916, 0.6476777254928829, 1.0372707265481604, 1.4974469923827818, 2.019301495946876, 2.5911878077912895, 3.199027755585188, 3.8268084792406336, 4.4575050098176225, 5.073423277564047, 5.656802963130644, 6.190926408284502, 6.660276532486381, 7.051045070658036, 7.352192806781064, 7.5552574301859154, 7.65460481020684, 7.648235808360395, 7.537189386905129, 7.325464288641812, 7.020458602932088, 6.632043880079696, 6.172195828493782, 5.65507364145424, 5.09594820795155, 4.510676047512747, 3.915535723116029, 3.3262420128971035, 2.757445572008458, 2.2225071574079567, 1.7328041393336413, 1.297423855545027, 0.9230529391877771, 0.6136922283844901, 0.37064058189994875, 0.1926097673575571, 0.07583999605653702, 0.01436869274414192, 0.00037670128238402075, 0.02458172447875161, 0.07668931262148987, 0.14587213897130294, 0.22125125476303886, 0.29236831745026864, 0.3496341933687762, 0.38470958353326834, 0.3908379494414442, 0.36309618159027507, 0.29855349935395026, 0.19636208331962257, 0.05770163909842754, -0.11429819366742906, -0.31472002886582623, -0.5372291331094279, -0.7742972612210363, -1.0175354754063155, -1.2582859315212598, -1.4878370915920753, -1.6977863246713287, -1.880691910656142, -2.0301239350093616, -2.140912373633532, -2.2096899363359417, -2.2346849779982887, -2.215762605469556, -2.1547419689502942, -2.054937548599126, -1.92098689169335, -1.75891850563781, -1.575546604712627, -1.378165273231802, -1.174438472662188, -0.9718121240734556, -0.7772068006939411, -0.5968620038580499, -0.435925329258613, -0.29827366611934747, -0.18644635207080235, -0.10150587780917408, -0.043062152050739176, -0.009373517435465351, 0.0025270187700242273, -0.0033840406871608313, -0.022378765461892283, -0.049268041091957926, -0.07871609841750082, -0.10555933606745845, -0.12510689286036872, -0.13341833949131043, -0.12754295350294415, -0.10568914011995899, -0.06734432718848732, -0.013312694503248915, 0.054316640637085266, 0.1322614835896927, 0.21625705771499112, 0.30125839975061647, 0.3817055619797953, 0.45192663494665536, 0.5063927821137972, 0.540039392922244, 0.5487196715123084, 0.5293587912205205, 0.4801827187316775, 0.40104895320526796, 0.2933799031594633, 0.1601841261046037, 0.006131648384779917, -0.16276200159650758, -0.33935113091177405, -0.5155718722112737, -0.6829238926481823, -0.8328458691379954, -0.9571252236911754, -1.048376749758092, -1.1004215369818733, -1.1087134937854008, -1.070626641005032, -0.9856621734194637, -0.8556913524060539, -0.6849223874189183, -0.4798159132530883, -0.2490108592425668, -0.0029593133536695566, 0.2464576057878384, 0.4863216673356202, 0.7032572620816562, 0.8839984833830218, 1.0159514411328399, 1.0877854909811902, 1.0899805479787514, 1.0153091175556455, 0.8592336317290495, 0.6202226382847834, 0.29988971144935517, -0.09692033410492568, -0.562180036775301, -1.0850553944217258, -1.6521006919368086, -2.2476681649958534, -2.854806420332778, -3.4555587732308926, -4.031586478446902, -4.565419660079199, -5.040597613374624, -5.442266989217474, -5.758495225261497, -5.980012156178815, -6.1005465843968985, -6.117898298329064, -6.033166356965886, -5.850686450657477, -5.578657978874231, -5.227931568974191, -4.811568936281266, -4.344997580977965, -3.8446058692920984, -3.3271030060947235, -2.8093546644456575, -2.307125728155464, -1.83450509177836, -1.403686019581801, -1.0241623309696442, -0.702461610825895, -0.4421270482430104, -0.2435202621797612, -0.10398180226649827, -0.0181483664939247, 0.02169818978586025, 0.02510340592598876, 0.002840338844557325, -0.03373552997010152, -0.07336131593107878, -0.10552817898049466, -0.1210852091333246, -0.11277336477855192, -0.07565485322563152, -0.007391994665562686, 0.09159407385886156, 0.21815770532343334, 0.3665847448527116, 0.5288831110785617, 0.6953352499084113, 0.8549770306925295, 0.9962114035227235, 1.1077136505976224, 1.1789477867023992, 1.2008234476540183, 1.1666228495984432, 1.072223486867595, 0.9164827181255418, 0.7018231220875362, 0.43393876519870384, 0.12169771233315148, -0.22285075436641097, -0.5852865805882622, -0.9493988352772585, -1.2977512744156192, -1.6127667051174293, -1.8775629328718342, -2.076827821530869, -2.197779238873891, -2.2308870349157575, -2.1706349027900287, -2.0159654910364346, -1.7705285232563959, -1.442926432326282, -1.0464335244800542, -0.5985822693174391, -0.12069667251427454, 0.3630430662001607, 0.8265931489500916, 1.2431002570787433, 1.5861531394123096, 1.8310122496914383, 1.9558212642676809, 1.94270602703159, 1.77876642972985, 1.4568592780410423, 0.9761496732240228, 0.34245049900974406, -0.4319365226089922, -1.328351166971179, -2.322261123338888, -3.38458589982469, -4.482297899505757, -5.579577643405986, -6.640123515019987, -7.627731034748178, -8.507675825072367, -9.249474140903311, -9.826861227719041, -10.218847968882937, -10.412235243821936, -10.400576502686494, -10.184469751587429, -9.773233967044362, -9.182806351982862, -8.435137858485822, -7.558775685078188, -6.586071121631902, -5.551921733101871, -4.493435100011846, -3.447131740764604, -2.447562087710046, -1.5265732381997732, -0.7112447354288391, -0.022976608282479407, 0.5230052171130255, 0.9184820144804198, 1.1622740398092084, 1.260030240787762, 1.223778837807187, 1.0710407892548146, 0.8238281055282288, 0.507336590335511, 0.14850213332777895, -0.22545810325356888, -0.588479286028832, -0.9170361969140846, -1.1914567652572774, -1.3967466075319133, -1.5233189028109424, -1.567576821333232, -1.5317003933970144, -1.423401464143081, -1.2554979141831049, -1.0447247443550793, -0.8106358377604163, -0.5743661133641799, -0.356991027118962, -0.17810063357032033, -0.05437105827331224, 0.0017762705535571822, -0.016779487958249403, -0.11103219262019576, -0.2754406525979641, -0.49783411746913014, -0.7597939090724094, -1.0373871358616753, -1.3021804200797424, -1.522942164136757, -1.6671769969521795, -1.7028808260289323, -1.601073786099082, -1.337363208943964, -0.893669640510113, -0.26065359356568807, 0.5615729285737913, 1.562610862898745, 2.7204620167050217, 4.002263785202071, 5.364917234863837, 6.755521013795044, 8.113573214845514, 9.373064736373482, 10.464580807511425, 11.318369645892604, 11.867274531556225, 12.049652163478363, 11.812317787434248, 11.113271233361388, 9.924064096906967, 8.231666202312526, 6.039925838908814, 3.3699898919342193, 0.260614640937834, -3.2322788677249843, -7.038019010830788, -11.072161346410201, -15.238770732878077, -19.43568074668907, -23.55578867031978, -27.490392422571748, -31.136385586527826, -34.39654315734865, -37.18269802461108, -39.423347875946796, -41.061778577040315, -42.05789920374785, -42.39466440996437, -42.07355070546934, -41.11436668196634, -39.55938559702482, -37.4666118252105, -34.90765054244402, -31.969300198031476, -28.74586624897832, -25.33590667891345, -21.84191266977364, -18.363319015624985, -14.993347088682823, -11.817964866369538, -8.911048338393721, -6.332465652262768, -4.127554589843839, -2.3251801751806074, -0.9376856319139085, 0.038325956517691925, 0.6212387826933434, 0.8427176920755775, 0.7455648873195869, 0.3812900298970467, -0.19258972325024212, -0.9154277288976936, -1.7261520113476774, -2.56588822793736, -3.3805905186704654, -4.122784316199397, -4.7531812818599475, -5.242182481674722, -5.5700349196716035, -5.727006631088218, -5.713362136281513, -5.5380810318751355, -5.217787127982857, -4.775418943479238, -4.2382669379876745, -3.6363304838307564, -3.0003878312707637, -2.360318115243772, -1.7437028024853156, -1.1741382879082078, -0.6705736183349055, -0.24674766527895153, 0.08965098390158001, 0.3364306513815751, 0.496492798596871, 0.5776968482816789, 0.591452936644618, 0.5516879011078205, 0.47408293999436685, 0.3745114009828958, 0.2679710158944562, 0.167795909069851, 0.08461972995925596, 0.025821076675520138, -0.004760461647185029, -0.006985843167520028, 0.015779365695637978, 0.057077108360855534, 0.10796495172413002, 0.15779972633223852, 0.19511905100430185, 0.2085636643324386, 0.1877973824639461, 0.12434656942143593, 0.012300066591112099, -0.15112720156877804, -0.36532005353209346, -0.6261154224915935, -0.925875188945094, -1.2540415828952616, -1.597502856598419, -1.941236199620995, -2.2695649580670265, -2.5666689362056627, -2.8174328320620217, -3.0089528376936223, -3.1307054165846635, -3.17513781160734, -3.138875566645727, -3.0222164032975694, -2.8291448853706935, -2.5678671317764206, -2.2496363110595268, -1.8881825999478252, -1.4995511131101804, -1.1006138053584467, -0.7082154170869421, -0.33863302280254537, -0.006304642159404482, 0.2768585665954775, 0.5019125676964279, 0.6634926245275319, 0.7599708461181622, 0.7934177502877344, 0.7694181999506533, 0.6966099343764764, 0.5860905429089056, 0.45066603427592156, 0.3040015652293906, 0.15974065904386753, 0.03065443287877804, -0.07216627486278394, -0.14001225432922396, -0.1670459779192617, -0.15066555603670787, -0.0916090976546874, 0.006129417551631316, 0.13554581538763485, 0.2872597713276788, 0.45003404672951186, 0.611472962059529, 0.7591764531576188, 0.8812847098399995, 0.9672340045653527, 1.0089571615495547, 1.0010001286640606, 0.9409115681504054, 0.8300009224610416, 0.6727823940114565, 0.4767736476601488, 0.2525582211667366, 0.012666132318860688, -0.22912007975047857, -0.458286699368186, -0.6608501785853956, -0.8241689641666115, -0.9376334051163955, -0.993544561447303, -0.9875874927515198, -0.9191951470292243, -0.7916862650196634, -0.612105290271138, -0.3909567618167384, -0.14159805108366172, 0.12052382074642683, 0.3787050777571903, 0.6159821524219474, 0.8161471548811436, 0.9647366152163807, 1.0498866438865904, 1.0631039103855227, 0.9998536374044455, 0.8598454850005505, 0.6471739198792489, 0.37009291259147276, 0.04063946091079245, -0.3259267038585774, -0.7122059502327949, -1.0993989821634282, -1.4682772061948268, -1.80075949804976, -2.0804766373223127, -2.2936443682868735, -2.4305337355545102, -2.4853638283123454, -2.456614614301887, -2.347851039342839, -2.1667636454006627, -1.924746999985433, -1.6368698034637967, -1.3203128177856533, -0.9934250694004754, -0.675066009423533, -0.38301440543641346, -0.13299921077446472, 0.06204824460371868, 0.19299989865168457, 0.25500090776309403, 0.24774561611898574, 0.1755394662731535, 0.04699307738500336, -0.1254381084637687, -0.32624483915579766, -0.5378478035806873, -0.7416750557672437, -0.9192802450886446, -1.0534550706574617, -1.129318564141855, -1.135426626433868, -1.0646099831445508, -0.9139804958212421, -0.6845880585142442, -0.3820486145223313, -0.01995471269665979, 0.37999767678398805, 0.7944824923803638, 1.2210670871743876], 'positive_zeros': ['1.02938230697506083335543850569934', '1.15926741657025899105808825142713', '1.18856302618762972219282118363320', '2.08951152167661879438093231322672', '2.15856600204699639950180475872149', '2.24823154317755692587466973031804', '2.90851405399184208306949236780669', '3.06644889897971943243269149675147', '3.10429410426105606652106967065309', '3.84041751767292999672541330338434', '3.92329515302559605972157531243771', '4.00673111597917875836809944326229', '4.62070725668162641564162962936587', '4.62391282877875530425430365779723', '4.81806876255509662594645141164531', '5.29039373978434461983581070804865', '5.30779501046563223477825656852310', '5.47206633465311711979474823699219', '5.70371458248687966894143766641798', '5.95331007464350321655430170552404', '6.13705925059015201917987217145172', '6.64589951824960405501542024892290', '6.68888929489796509594068427206796', '6.79822957351552768413705694421902', '7.05253254049223060308533708880580', '7.30075958483676772354148313483464', '7.47599194734342963771651873913653'], 'prelabel': '6-9300e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.61747491320925, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1e3-0', 'trace_hash': 602856454915816913, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.02938230697506083335543850570', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.15926741657025899105808825143', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.18856302618762972219282118363', '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': 409524.7621012392, 'bad_primes': [2, 3, 5, 31], 'central_character': '1.1', 'conductor': 804357000000, 'conductor_radical': 930, 'degree': 6, 'dirichlet_coefficients': [1, 0, -3, 0, 0, 0, 0, 0, 6, 0, -5, 0, -2, 0, 0, 0, 5, 0, -5, 0, 0, 0, 1, 0, 0, 0, -10, 0, 3, 0, 3, 0, 15, 0, 0, 0, 0, 0, 6, 0, -18, 0, 16, 0, 0, 0, 2, 0, -13, 0, -15, 0, -3, 0, 0, 0, 15, 0, 24, 0, -12, 0, 0, 0, 0, 0, 29, 0, -3, 0, -6, 0, 8, 0, 0, 0, 0, 0, -8, 0, 15, 0, -19, 0, 0, 0, -9, 0, -17, 0, 0, 0, -9, 0, 0, 0, -17, 0, -30, 0], 'euler11': [1, 5, 36, 103, 396, 605, 1331], 'euler13': [1, 2, 21, 70, 273, 338, 2197], 'euler17': [1, -5, 40, -173, 680, -1445, 4913], 'euler19': [1, 5, 44, 181, 836, 1805, 6859], 'euler2': [1, 0, 0, 0, 0, 0, 0], 'euler23': [1, -1, 20, 101, 460, -529, 12167], 'euler29': [1, -3, 24, 69, 696, -2523, 24389], 'euler3': [1, 3, 3, 1, 0, 0, 0], 'euler31': [1, -3, 3, -1, 0, 0, 0], 'euler37': [1, 0, 73, 86, 2701, 0, 50653], 'euler41': [1, 18, 127, 662, 5207, 30258, 68921], 'euler43': [1, -16, 193, -1392, 8299, -29584, 79507], 'euler47': [1, -2, 121, -196, 5687, -4418, 103823], 'euler5': [1, 0, 0, 0, 0, 0, 0], 'euler53': [1, 3, 124, 195, 6572, 8427, 148877], 'euler59': [1, -24, 325, -2998, 19175, -83544, 205379], 'euler61': [1, 12, 199, 1368, 12139, 44652, 226981], 'euler67': [1, -29, 412, -3897, 27604, -130181, 300763], 'euler7': [1, 0, 13, -4, 91, 0, 343], 'euler71': [1, 6, 193, 764, 13703, 30246, 357911], 'euler73': [1, -8, 211, -1056, 15403, -42632, 389017], 'euler79': [1, 8, 31, -510, 2449, 49928, 493039], 'euler83': [1, 19, 344, 3213, 28552, 130891, 571787], 'euler89': [1, 17, 314, 3059, 27946, 134657, 704969], 'euler97': [1, 17, 226, 2181, 21922, 159953, 912673], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0], [1, 3, 3, 1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, 0, 13, -4, 91, 0, 343], [1, 5, 36, 103, 396, 605, 1331], [1, 2, 21, 70, 273, 338, 2197], [1, -5, 40, -173, 680, -1445, 4913], [1, 5, 44, 181, 836, 1805, 6859], [1, -1, 20, 101, 460, -529, 12167], [1, -3, 24, 69, 696, -2523, 24389], [1, -3, 3, -1, 0, 0, 0], [1, 0, 73, 86, 2701, 0, 50653], [1, 18, 127, 662, 5207, 30258, 68921], [1, -16, 193, -1392, 8299, -29584, 79507], [1, -2, 121, -196, 5687, -4418, 103823], [1, 3, 124, 195, 6572, 8427, 148877], [1, -24, 325, -2998, 19175, -83544, 205379], [1, 12, 199, 1368, 12139, 44652, 226981], [1, -29, 412, -3897, 27604, -130181, 300763], [1, 6, 193, 764, 13703, 30246, 357911], [1, -8, 211, -1056, 15403, -42632, 389017], [1, 8, 31, -510, 2449, 49928, 493039], [1, 19, 344, 3213, 28552, 130891, 571787], [1, 17, 314, 3059, 27946, 134657, 704969], [1, 17, 226, 2181, 21922, 159953, 912673]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9300/2/a/s'], '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': '6-9300e3-1.1-c1e3-0-1', '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}], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 3, 'prelabel': '6-9300e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.61747491320925, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 602856454915816913, 'z1': {'__RealLiteral__': 0, 'data': '1.02938230697506083335543850570', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '1304897099301255358271735382380,1469546036440317660828639732417,1506682633555829558023476199130', 'Lhash_array': ['1304897099301255358271735382380', '1469546036440317660828639732417', '1506682633555829558023476199130'], 'factors': ['2-9300-1.1-c1-0-50', '2-9300-1.1-c1-0-59', '2-9300-1.1-c1-0-62'], 'label': '6-9300e3-1.1-c1e3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9300/2/a/s'}