Lfunction data - 8-440e4-1.1-c0e4-0-2

Formats: - HTML - YAML - JSON - 2026-06-25T20:21:43.304380

• 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': '1194582629272334230695922055751,2383527843398215035860441605174,2413119756176256390256363413966,2420285155054132283172460806685', 'a10': 1, 'a2': -1, 'a3': 0, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 3, 'a8': 0, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.00232508697556599, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [1, 1, 1, 1, 1]], [5, [1, 1, 1, 1, 1]], [11, [1, 1, 1, 1, 1]]], 'bad_primes': [2, 5, 11], 'central_character': '440.1', 'coefficient_field': '1.1.1.1', 'conductor': 37480960000, 'conductor_radical': 110, 'degree': 8, 'euler_factors': [[1, 1, 1, 1, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 1, 1, 1, 1], [1, -3, 3, -1, 0, -1, 3, -3, 1], [1, 1, 1, 1, 1], [1, -3, 3, -1, 0, -1, 3, -3, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 2, 3, 4, 5, 4, 3, 2, 1], [1, 2, 3, 4, 5, 4, 3, 2, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 2, 3, 4, 5, 4, 3, 2, 1], [1, -3, 3, -1, 0, -1, 3, -3, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 2, 3, 4, 5, 4, 3, 2, 1], [1, 2, 3, 4, 5, 4, 3, 2, 1], [1, 2, 3, 4, 5, 4, 3, 2, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 2, 3, 4, 5, 4, 3, 2, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 2, 3, 4, 5, 4, 3, 2, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1]], 'euler_factors_factorization': [[[[1, 1, 1, 1, 1], 1]], [[[1, -1, 1, -1, 1], 1], [[1, 1, 1, 1, 1], 1]], [[[1, 1, 1, 1, 1], 1]], [[[1, -1], 4], [[1, 1, 1, 1, 1], 1]], [[[1, 1, 1, 1, 1], 1]], [[[1, -1], 4], [[1, 1, 1, 1, 1], 1]], [[[1, -1, 1, -1, 1], 1], [[1, 1, 1, 1, 1], 1]], [[[1, 1, 1, 1, 1], 2]], [[[1, 1, 1, 1, 1], 2]], [[[1, -1, 1, -1, 1], 1], [[1, 1, 1, 1, 1], 1]], [[[1, -1, 1, -1, 1], 1], [[1, 1, 1, 1, 1], 1]], [[[1, 1, 1, 1, 1], 2]], [[[1, -1], 4], [[1, 1, 1, 1, 1], 1]], [[[1, -1], 4], [[1, 1], 4]], [[[1, 1, 1, 1, 1], 2]], [[[1, 1, 1, 1, 1], 2]], [[[1, 1, 1, 1, 1], 2]], [[[1, -1, 1, -1, 1], 1], [[1, 1, 1, 1, 1], 1]], [[[1, -1], 4], [[1, 1], 4]], [[[1, -1, 1, -1, 1], 1], [[1, 1, 1, 1, 1], 1]], [[[1, -1, 1, -1, 1], 1], [[1, 1, 1, 1, 1], 1]], [[[1, -1, 1, -1, 1], 1], [[1, 1, 1, 1, 1], 1]], [[[1, -1, 1, -1, 1], 1], [[1, 1, 1, 1, 1], 1]], [[[1, 1, 1, 1, 1], 2]], [[[1, -1, 1, -1, 1], 1], [[1, 1, 1, 1, 1], 1]], [[[1, -1, 1, -1, 1], 1], [[1, 1, 1, 1, 1], 1]], [[[1, 1, 1, 1, 1], 2]], [[[1, -1, 1, -1, 1], 1], [[1, 1, 1, 1, 1], 1]], [[[1, -1], 4], [[1, 1], 4]], [[[1, -1, 1, -1, 1], 1], [[1, 1, 1, 1, 1], 1]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 2, 'label': '8-440e4-1.1-c0e4-0-2', 'leading_term': '0.26272526628340520319548873983703242164567654128259026619853189840216476112075277096525126', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, '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': [0, 0, 0, 0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/440/1/bh/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.017578125', 'prec': 37}, 'plot_values': [0.26272526628340515, 0.26403221165188306, 0.2656241431508281, 0.26784636246754456, 0.2710545160984392, 0.2755416582962442, 0.28129645066184444, 0.28823265956538374, 0.2962642150915042, 0.30532078097597704, 0.3154062215906963, 0.3265452681913074, 0.3387643824615023, 0.3520828530623604, 0.3664853729126017, 0.381941986555776, 0.3984140106927487, 0.4158538097893419, 0.4342084150066656, 0.4534136586971953, 0.47339093975297175, 0.49404542416850705, 0.5152640963019101, 0.5369147096812886, 0.5588445339324942, 0.5808802866254263, 0.602831000331888, 0.6244843515205556, 0.6456050265546499, 0.6659356143047169, 0.6852005221629414, 0.7031034803667545, 0.7193272099008482, 0.7335359340563331, 0.7453814324416818, 0.7545015277092986, 0.7605211909539354, 0.7630568843960354, 0.761724731643056, 0.7561403079508914, 0.7459213188529151, 0.7306938869197676, 0.7101031096710501, 0.6838135134573257, 0.6515128171907186, 0.6129198014805506, 0.5677969476458116, 0.5159503932956996, 0.4572337692353347, 0.391556699951357, 0.31889847763704254, 0.23930585555509334, 0.1528954465129076, 0.05986127277681338, -0.0395124648222828, -0.14485755308352058, -0.25572255292004115, -0.3715682191383371, -0.491758278218538, -0.6155709627459345, -0.7422045069767359, -0.870777541115807, -1.0003262186975779, -1.1298214653574008, -1.2581798610302328, -1.3842703192444474, -1.5069196633727595, -1.6249342184563946, -1.737115265994491, -1.8422718627179482, -1.9392352603376968, -2.026881354107112, -2.1041479688886295, -2.170051627663445, -2.2237086914544566, -2.2643532024458595, -2.2913513824323064, -2.304218020709019, -2.302639474271663, -2.28648036297346, -2.255789546417214, -2.2108103341117746, -2.1519984843340714, -2.0800118174206745, -1.9957023541703487, -1.900114627971305, -1.7944916421948776, -1.6802443011393087, -1.5589268838806878, -1.4322200150007285, -1.301920016951976, -1.1698900576103388, -1.0380206805563015, -0.9081985351575527, -0.782279797694301, -0.66203119322718, -0.5490830730384582, -0.44489098952212724, -0.35070085935190504, -0.26749376531020574, -0.19594438576120346, -0.13638814341808045, -0.08879236827121312, -0.05272173437622176, -0.027317503111389713, -0.011285865848800607, -0.0028925832131011567, 3.6017442084479244e-05, 9.955486291594969e-05, 0.0003005950033736876, 0.004012006726604988, 0.014933201441644757, 0.03703662741006342, 0.07450501801698745, 0.13165672309658777, 0.2128643906491865, 0.32246794380946125, 0.4646806181851449, 0.6434851376653944, 0.862533662359127, 1.1250473600049102, 1.433715221686596, 1.7905929363133342, 2.1970125001885803, 2.6534983989266934, 3.159694958793805, 3.7143141057685587, 4.315083108377393, 4.958708301510897, 5.640868899621501, 6.356262238774777, 7.098605388217519, 7.860665954363541, 8.63434888382994, 9.410873401772768, 10.180819742688033, 10.934223664209583, 11.66075816564778, 12.3500455450008, 12.991710827040464, 13.575508175562522, 14.09156762349559, 14.530805677493003, 14.884923251794564, 15.1465084760306, 15.309290265460788, 15.368574746755016, 15.321119884693651, 15.165151668938462, 14.900554015731887, 14.529240964633788, 14.05486104657012, 13.482680349010737, 12.819650807777068, 12.074640635768985, 11.25796828121332, 10.381146091299778, 9.456807162583685, 8.498759946270251, 7.521412463406563, 6.53942344931731, 5.567521315437002, 4.620411562325837, 3.7122054126310298, 2.8560721178034445, 2.0640328125816234, 1.3468086365696441, 0.7133902434068544, 0.1708039621780677, -0.27601370522056135, -0.6243093672883767, -0.8736911642493799, -1.0261591772063365, -1.0860631445626694, -1.0600366603606988, -0.9568847143766278, -0.7873852596996723, -0.5640520502931041, -0.3008743735088991, -0.01297324182575012, 0.2837657777371693, 0.5730692099449374, 0.8386742758649561, 1.0647572030320687, 1.236335563361132, 1.3396571329558058, 1.3626000929682596, 1.2950020069457249, 1.1289368008413032, 0.8589616590234643, 0.4823510491495599, -0.0008202905283647747, -0.5876472060358882, -1.272405807634767, -2.0466130630676997, -2.89923095243073, -3.816907304508873, -4.78426821147364, -5.784295652119632, -6.798724441222982, -7.808458918082278, -8.794052807308354, -9.736303560731306, -10.616640563252744, -11.417533758025675, -12.122982658157184, -12.719134258604978, -13.19443556896745, -13.539837510933534, -13.749104151266584, -13.819250389164825, -13.750310059845784, -13.54521667219224, -13.209820773752787, -12.753026771818282, -12.186184036749925, -11.522667370604193, -10.777625661036351, -9.967840657996764, -9.110915767202647, -8.224720698336142, -7.327025906461507, -6.435241629120319, -5.565677304001976, -4.733086265286096, -3.950400419778326, -3.228564053066446, -2.576112151992542, -1.9990101266779123, -1.5006543139842836, -1.0819559492749726, -0.7413426916710272, -0.4749471467915716, -0.27689802979520844, -0.13965893172209864, -0.05435985662454971, -0.01121330472150486, 4.272090181291666e-05, -0.010288878601474316, -0.03228136781562848, -0.056789109668409686, -0.07580646431700151, -0.08275252295740383, -0.07270698948491358, -0.04257390645790223, 0.008848317972303442, 0.08091861025379389, 0.17124022723791962, 0.27582896722826383, 0.38938215963394157, 0.5056749202453195, 0.61790278365657, 0.7190721892046262, 0.8024581777663912, 0.862143544384978, 0.8933739752699239, 0.8929118301486636, 0.8594003813731181, 0.7937292023047867, 0.6991233382955224, 0.5811969633620829, 0.44796703910529395, 0.3097945355136392, 0.1790671163610511, 0.06984697247962324, -0.0025356069958417248, -0.021978567099302255, 0.027768173036590252, 0.16247976310908782, 0.39681879965948097, 0.743679835399543, 1.2135593118944117, 1.8139809751671947, 2.548998115499133, 3.4188368853122295, 4.419583838859393, 5.5429844305043, 6.776441803118287, 8.1033601715739, 9.50327997157713, 10.952174699114954, 12.423075553660405, 13.887223287574086, 15.314461575646318, 16.673851328614692, 17.93472101590253, 19.068347213546925, 20.04815900891484, 20.850254201604923, 21.4544296029892, 21.8458406744642, 22.014550333667227, 21.955524588889887, 21.669190840513988, 21.162540345151857, 20.447826332438666, 19.54187098859703, 18.46595730976782, 17.24614465814251, 15.91136102877329, 14.49224247188421, 13.020549336925166, 11.528898500564493, 10.0488584595182, 8.609840369853082, 7.238514507751353, 5.958467218617708, 4.78896716174354, 3.7444404487970915, 2.8343630143724923, 2.063334212211049, 1.4308719584803966, 0.9316985737627324, 0.5562806121068898, 0.2914742300320489, 0.12118208378387459, 0.02721568329309452, -0.009778355812612858, -0.009395701242430672, 0.009440321382509373, 0.02934557296315784, 0.03524013178520401, 0.014988208797218612, -0.04011194329905663, -0.1350207491252912, -0.270839707999825, -0.4448988081178293, -0.651031438373103, -0.8800199589193312, -1.1202141097116143, -1.3583406677163663, -1.5803239893387493, -1.7721636188196799, -1.9208828972964458, -2.0155536480857794, -2.0480250395971074, -2.013587310216176, -1.9115823157447231, -1.7459307346004826, -1.5251424921507946, -1.2622178681541054, -0.9744253894738498, -0.6828936762025732, -0.411734059668039, -0.18711749545366405, -0.03626230355451269, 0.013721360752278493, -0.06285188271912037, -0.2890097863819377, -0.6839337684349337, -1.2618332130222862, -2.030995113482747, -2.99303066545291, -4.142341346269959, -5.465943042410576, -6.943504610090234, -8.547616404554233, -10.244419236822834, -11.994841950135124, -13.755599850095875, -15.480376668722668, -17.121422809062906, -18.631851229524656, -19.9668512530658, -21.085026706114938, -21.950124487231044, -22.533357655254353, -22.81380206580031, -22.77893055446504, -22.42548054505725, -21.760696671587947, -20.801262545143906, -19.572493832514525, -18.107836202670512, -16.448537534669416, -14.641333054081418, -12.73657972721318, -10.786720102066221, -8.844846327854988, -6.9621687563870305, -5.186075788401213, -3.5585711032813663, -2.114873452674613, -0.8819169034732253, 0.12256606554206433, 0.8905779538852638, 1.424124099241242, 1.7349852935348864, 1.8440923624152956, 1.780608334318102, 1.5807404137691852, 1.286085449898888, 0.9418625008645918, 0.5950473325801963, 0.29241953554991423, 0.07858300674393995, -0.00587309366792912, 0.07393682224293271, 0.3457669737378113, 0.8291210233211616, 1.5343952154312568, 2.462401471093968, 3.6045433118966383, 4.943051337912029, 6.45147344847577, 8.095707257538233, 9.835972284239999, 11.627892422539087, 13.42379922873886, 15.174672945102248, 16.833117852244232, 18.354143398766663, 19.696234630217944, 20.823126241663186, 21.706527206360473, 22.325596321557065, 22.6669327053912, 22.725337241409783, 22.505350295630574, 22.019232836488808, 21.285773604022054, 20.32992490536841, 19.183041099351726, 17.880100132041328, 16.457985603138297, 14.954593367415393, 13.40840520083507, 11.856104963854389, 10.331264889522007, 8.8637383894996, 7.479400896256726, 6.198992087137933, 5.037779599042338, 4.005695523685503, 3.1076827580916007, 2.3438103122070175, 1.7098114913475901, 1.1978124911419314, 0.797113373641998, 0.4949438188621314, 0.27727541575221787, 0.1295967304111344, 0.03761022889435394, -0.012150521932171393, -0.03183919697126952, -0.031949141618861115, -0.021092465474569676, -0.0059148635913063895, 0.008857268897686957, 0.020269964174026586, 0.02691379819279618, 0.02862049261074931, 0.026133072879094606, 0.02077067097097437, 0.014103311362874925, 0.007665030142958964, 0.002725172890530285, 0.00012035233845995767, 0.0001574884631087232, 0.002597738042544134, 0.00669844681849543, 0.011310429559442142, 0.015035361430515893, 0.016394185167840053, 0.01399670141808818, 0.00671534597375218, -0.006140672180336983, -0.024740691474394255, -0.0486859493245955, -0.07699479595710111, -0.10813212120137479, -0.1401459884728744, -0.1708198106178531, -0.19784039785955004, -0.2189964460400475, -0.23239580083736516, -0.2366397674883235, -0.2309659962990257, -0.21536963880699395, -0.19064124565915108, -0.15833330646707394, -0.12067368271759056, -0.08043135928753274, -0.04069448678772132, -0.00461737769142095, 0.024846151167719807, 0.04521379111739154, 0.05473361326263296, 0.0525953923693898, 0.039081656143137154, 0.01564201635208426, -0.015133443799791582, -0.04963091126267147, -0.08342602847111558, -0.11160258364909764, -0.1291324482461142, -0.13130427670744735, -0.11419342337715475, -0.07514677216355665, -0.013187028376434672, 0.07063171968655724, 0.17295265904907384, 0.28800600780662633, 0.4076397606155349, 0.5214704173935404, 0.6172234078224861, 0.6813639319404965, 0.6996748171092648, 0.6579391473018322, 0.542809245043813, 0.34291626323206925, 0.04952910694574288, -0.34276036538380306, -0.835287843145099, -1.4245689874133751, -2.1022850788897847, -2.8552948764226427, -3.66573924718178, -4.511443592953722, -5.366853582207153, -6.203956843115061, -6.993380745255018, -7.7059410961530235, -8.313963107552816, -8.792491793648791, -9.12065148494912, -9.283373705009774, -9.271944388713754, -9.084416389027226, -8.726108418505186, -8.21025317130279, -7.5569275062735235, -6.7920075170754535, -5.946234399983624, -5.054292437248596, -4.152430729876065, -3.2764273984793304, -2.45982741868389, -1.732285209938058, -1.1173268003359536, -0.6307501816577419, -0.27950744772916564, -0.06093528275294644, 0.03775382230074647, 0.039282203290618815, -0.02442592994726984, -0.11343874696161532, -0.18149655589104852, -0.1781343846811655, -0.05111327897751439, 0.25098326322233505, 0.7760243227420494, 1.565608207575403, 2.6525483111203303, 4.05893960499502, 5.794304910104559, 7.854144975647451, 10.219320485572485, 12.8569421660539, 15.720508252362306, 18.75066733341689, 21.877324110395055, 25.023950221948567, 28.1089902773007, 31.04801225067238, 33.7574941047389, 36.16100352264501, 38.18972238154189, 39.78395250746045, 40.89638289160838, 41.49745842180337, 41.57309618628191, 41.12387622686848, 40.16606200863808, 38.73422416472063, 36.87604824599517, 34.64923940445335, 32.120299353609845, 29.364481206948536, 26.45965168731854, 23.482646518991704, 20.507416113263588, 17.60407916767293, 14.83449966282574, 12.250198253302903, 9.891715768681545, 7.788653624751035, 5.958430627960591, 4.406634467080546, 3.128226780871444, 2.1090976283348355, 1.3273602470782149, 0.7552575451392363, 0.36125470502103213, 0.11208129807332787, -0.025442919739885796, -0.0827186356600846, -0.08794737484750227, -0.06504931112699686, -0.032996872601810515, -0.00551589880620143, 0.008863745810340079, 0.006416043542461443, -0.012473823475691405, -0.04417432779747485, -0.08280435943429354, -0.12131886012579218, -0.15250616679199724, -0.16987712903583363, -0.16842588737685169, -0.14519319372605985, -0.09951378629744512, -0.033077351966402754, 0.05022203366574844, 0.14472376010058963, 0.2435422629967917, 0.339156446405103, 0.424100593609483, 0.49180147941710906, 0.5370649907172091, 0.5564655452707605, 0.5487000054569274, 0.5148950333175407, 0.45833054277672997, 0.38410303779579735, 0.29875362207139344, 0.2098098351125506, 0.12496316768661075, 0.05137511780682096, -0.004920514597572063, -0.039567158343676016, -0.05037212323911548, -0.03753378266590851, -0.0036730662934796846, 0.04631057117207565, 0.10562575582744194, 0.16614839964231576, 0.21910132922452571, 0.25584583992975435, 0.2686851274426108, 0.2516022723004226, 0.20091013140082714, 0.1157861581118115, -0.001500198680423344, -0.1455817643126859, -0.30821771619130434, -0.4787865010942233, -0.645037646114723, -0.7939825079106936, -0.9129317544787579, -0.9906767927677006, -1.0184629934044256, -0.9908732049764614, -0.9066114483604728, -0.7690966469409162, -0.5864482876768481, -0.37126550755612886, -0.14013953611183957, 0.08724231995636797, 0.28939816975691623, 0.4444148348544287, 0.5314750837888089, 0.5326207945605578, 0.4341745740660024, 0.22795411047439837, -0.08765213467027692, -0.5068590694095527, -1.0165537037468926, -1.5966600931962023, -2.2208603835669565, -2.857952667176582, -3.4737200153508536, -4.032855949330019, -4.501154337118192, -4.848250822291087, -5.049642855507768, -5.088402088367165, -4.95683293528082, -4.658179904022082, -4.206549066027145, -3.6264283295113557, -2.951951163947697, -2.2257771289490287, -1.4963470067591542, -0.8151010153079538, -0.23363024031452553, 0.19943147277991083, 0.44177830208510577, 0.460274980965696, 0.23336820550582466, -0.2469135759266492, -0.973954563379378, -1.9263441723883004, -3.068506206418106, -4.352407517930584, -5.719906914938455, -7.105637277380113, -8.440700127141787, -9.657502966177672, -10.693056610158063, -11.492325129278942, -12.012017931633928, -12.224926688266345, -12.120230252923712, -11.703789510660382, -10.998629644292288, -10.04530006043505, -8.897445609531164, -7.618046956212957, -6.276098464690995, -4.943119054497514, -3.6865707877559366, -2.5649665854744526, -1.6240424871461172, -0.893415913067408, -0.38291986086903035, -0.08111305621778372, 0.04476221479243921, 0.047699429016186005, -0.0013786599059568167, -0.017473736279297686, 0.09362497635148678, 0.42962335942452146, 1.0854800832313354, 2.1470656699207953, 3.6850268131954453, 5.749155165356031, 8.363865000475329, 11.524849974425962, 15.197211541288226, 19.315716667246637, 23.786226497362264, 28.48857163072624, 33.28138775445278, 38.00976946270613, 42.511369559967875, 46.62326152051644, 50.19025004317589, 53.075219696400424, 55.16395019037743, 56.3699451441308, 56.63976640920335, 55.958799154146824, 54.34944332007735, 51.86935473152184, 48.60965632166009, 44.6924283786476, 40.26255223639876, 35.48040617917914, 30.51474994357152, 25.535005896738653, 20.70266149367349, 16.164207195566377, 12.044819701197927, 8.442502902097969, 5.425444632417778, 3.0305985727848803, 1.2631949873297517, 0.0976261636531694, -0.5179870120173787, -0.657255791871957, -0.41051351233630395, 0.12153715840101557, 0.8347803230152363, 1.6274370134128906, 2.4056347949670163, 3.0895195971805935, 3.6162499676290794, 3.941741301812967, 4.042082140912487, 3.9148021066349736, 3.575700781633334, 3.055606626506046, 2.397373029810438, 1.6527797165665805, 0.8766657733369415, 0.12239273101020802, -0.5617112642565849, -1.1354393417482245, -1.5699194426030467, -1.8490642229721341, -1.9698856814214962, -1.9420656956611557, -1.7864532491603677, -1.5326196094408517, -1.2159468966186253, -0.8744439166197976, -0.5452525468988756, -0.2614650073214892, -0.04940761561613182, 0.07352959673281251, 0.10017873578920156, 0.03398711448143866, -0.11143284115328352, -0.31360402156319495, -0.5433366327390515, -0.7673428245959236, -0.9512224533432511, -1.062679442340137, -1.0744041260619073, -0.9666231871576216, -0.7291971168896273, -0.3629097637528149, 0.12028191321941398, 0.6976149332541411, 1.3367504994463737, 1.9983311416750824, 2.6385493640662174, 3.2119233591370957, 3.6746604849596864, 3.9889127546102228, 4.124951969868355, 4.063080265616033, 3.7956027947334827, 3.3287892248359956, 2.68163337263466, 1.884497241848836, 0.9776593284487389, 0.009352424643607304, -0.9682628182011167, -1.902541556281512, -2.7435728220175606, -3.447655954636221, -3.980308774616796, -4.31822993612901, -4.450736866895611, -4.380954586369562, -4.124803950681045, -3.7093622862733686, -3.1709507162629347, -2.5529456924468654, -1.9017749089884048, -1.263347215851875, -0.679926560827035, -0.18730144364851067, 0.18818184007351593, 0.4313848687058219, 0.5391857530618221, 0.5204894198046607, 0.395352883190141, 0.19313040085860567, -0.05007643473495208, -0.294480319783275, -0.5000005435884858, -0.6296874852166492, -0.6529583746277052, -0.5483308922079396, -0.305432916273556, 0.07369908371602757, 0.5742591018007427, 1.1696899347577425, 1.8232076318893287, 2.489953962208893, 3.120094570690319, 3.6632286078128455, 4.0714654288777155, 4.302529489143058, 4.323219727198489, 4.113247164027317, 3.6659342042166347, 2.988669634189412, 2.1032172016574417, 1.0454826552406626, -0.13764052590782022, -1.3912160777798057, -2.655296733099555, -3.8686437041590818, -4.972964147874509, -5.916279728251248, -6.6560071385185156, -7.162216102103435, -7.418773953437132, -7.423626346565471, -7.188739613789259, -6.739833329584669, -6.113288762548706, -5.353084778054286, -4.507927627591336, -3.6284195016538674, -2.762834640328412, -1.953951673554727, -1.2367178404283865, -0.636493771276501, -0.1677135414220014, 0.16620908786781668, 0.37211567544257246, 0.4656962842027415, 0.4692478896088535, 0.40901203799831976, 0.3123759591155444, 0.20509373468537515, 0.10859469635163507, 0.037890081537729166, 0.00014547681765190765, -0.006017212510088904, 0.009615897639864725, 0.029831766663409236, 0.03170015421318775, -0.011137591979491253, -0.12576363680533695, -0.3370798884828718, -0.66496384876415, -1.1219554368785019, -1.7112918829142065, -2.4255062549867676, -3.2460000530451643, -4.144289975750721, -5.083074347595678, -6.017973439446316, -6.900481792047165, -7.682735496926143, -8.319952160777289, -8.773090229562808, -9.012234958073373, -9.020891303748215, -8.795909673034428, -8.347394880099998, -7.698846553774344, -6.887259474704562, -5.959000781277163, -4.966166471038964, -3.9633109648878593, -3.0041275810911605, -2.136313054558521, -1.3977303128879794, -0.813555082113507, -0.394151754114041, -0.13360826247945912, -0.009799269697146503, 0.014312888896786405, -0.011742004519278084, -0.029421493235099346, 0.024568639834965447, 0.21347512731149398, 0.595545044937624, 1.219290138147439, 2.1191062203574833, 3.311728264077496, 4.794545772043432, 6.544341071826641, 8.517009729971193, 10.649301442338281, 12.864123993194772, 15.073233352051995, 17.180844634408654, 19.089688746356043, 20.710905710502765, 21.966078836277145, 22.790179592648077, 23.136833943424215, 22.986387167722896, 22.342351393849384, 21.229550478938812, 19.69449647999672, 17.80728863004803, 15.652616640918081, 13.323790861441603, 10.919131407069028, 8.539240233000525, 6.2780415148487165, 4.217555987226717, 2.4249449777839183, 0.9503546285148302, -0.17638733073808183, -0.946153429362538, -1.3693942421950216, -1.4744015520262137, -1.3044409516719335, -0.9139036995843337, -0.364197865315338, 0.2803803900160068, 0.9571147172735736, 1.6086547170437173, 2.1861363679086243, 2.651734115529789, 2.979961655285085, 3.158003203394485, 3.1853733812972873, 3.072999622933284, 2.840788588708007, 2.5151019661280802, 2.1262513808387578, 1.7059649565762742, 1.284436658327813, 0.8881617248760563, 0.5383615188874183, 0.2498611272006545, 0.030546015115461407, -0.11840353093843647, -0.20179460951440098, -0.22934753594060645, -0.2141261467458303, -0.17088671855303456, -0.11449836768070384, -0.058502731911462734, -0.013847871432538536, 0.011931925614250912, 0.015120405632320446, -0.004201206276199982, -0.04255364740269557, -0.09377624807007809, -0.1499771163922063, -0.20268924152307974, -0.2439274161931159, -0.267114569274647, -0.26785685711477386, -0.2445312020261326, -0.1983628800775048, -0.1332286032537774, -0.055245309533574774, 0.027839446913152963, 0.10763344766511328, 0.17607514072352026, 0.22637300913148206, 0.2538575215036736, 0.2563413994148228, 0.2343193138001309, 0.19094015084934396, 0.13188714934463325, 0.0651954959512377, 0.00033187361138752334, -0.05331277394796858, -0.08855712465161707, -0.10038695598337044], 'positive_zeros': ['0.942359534289069936298232069660623', '1.88027193216260198049203875648479', '1.90361583526390890951689268276945', '1.90926833830897970862286288611694', '2.95940450687167707467735651701629', '3.14725705661514812305844321937458', '3.35739528430371123996751629381418', '4.16355447724190280730310117904993', '4.16650527135973297854551414471640', '4.30406733288640467429795235764458', '4.65731196269482711007823960314125', '4.68677146207509353573017999423727', '5.56492710492019753904178142926306', '5.59965569299876557005614545240558', '5.66630941715995649230358771886427', '6.07227384501106205875941073051570', '6.08895901824075764272385281884588', '6.74761370673886706917019624373817', '6.95696077081742688410481928523393', '6.96644416191614110142747530473228', '7.78146330002105350293180902704401', '7.86416696857003306102926389910540', '8.035039239007306342141434803689356', '8.048381792993070636340859293256944', '8.183983189476524650027166011425605', '8.510290383492235168048121009058097', '8.622618552708444610600095112258229', '8.774568398587416298084908474003104', '8.984916311161013413862630834387950', '9.535743269777322079230704123905347', '9.574637777965322706296818329343007', '9.654357997484594245754386976708259', '10.45462682551343250004835080605460', '10.55172311454319624934468491494421', '10.58974354698900865759302842387759', '10.76516345709444848377205198303535', '11.05480744611426148692345872033324', '11.12843514564958988751007606460395', '11.30253532847578394115441856339870', '11.55952278169472202022559021366829'], 'prelabel': '8-440e4-1.1-c0e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.46860282282389326, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c0e4-0', 'trace_hash': 540893063260450612, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.942359534289069936298232069661', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.88027193216260198049203875648', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.90361583526390890951689268277', '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': 0.00232508697556599, 'bad_primes': [2, 5, 11], 'central_character': '1.1', 'conductor': 37480960000, 'conductor_radical': 110, 'degree': 8, 'dirichlet_coefficients': [1, -1, 0, 0, -1, 0, 3, 0, -1, 1, -1, 0, 3, -3, 0, 0, 0, 1, -2, 0, 0, 1, -2, 0, 0, -3, 0, 0, 0, 0, 0, 1, 0, 0, -3, 0, -2, 2, 0, 0, 3, 0, 0, 0, 1, 2, -2, 0, 6, 0, 0, 0, -2, 0, 1, 0, 0, 0, -2, 0, 0, 0, -3, -1, -3, 0, 0, 0, 0, 3, 0, 0, 0, 2, 0, 0, -3, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -2, -1, 9, 0, 0, 2, 2, 0, 0, -6, 1, 0], 'euler11': [1, 1, 1, 1, 1, 0, 0, 0, 0], 'euler13': [1, -3, 3, -1, 0, -1, 3, -3, 1], 'euler17': [1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler19': [1, 2, 3, 4, 5, 4, 3, 2, 1], 'euler2': [1, 1, 1, 1, 1, 0, 0, 0, 0], 'euler23': [1, 2, 3, 4, 5, 4, 3, 2, 1], 'euler29': [1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler3': [1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler31': [1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler37': [1, 2, 3, 4, 5, 4, 3, 2, 1], 'euler41': [1, -3, 3, -1, 0, -1, 3, -3, 1], 'euler43': [1, 0, -4, 0, 6, 0, -4, 0, 1], 'euler47': [1, 2, 3, 4, 5, 4, 3, 2, 1], 'euler5': [1, 1, 1, 1, 1, 0, 0, 0, 0], 'euler53': [1, 2, 3, 4, 5, 4, 3, 2, 1], 'euler59': [1, 2, 3, 4, 5, 4, 3, 2, 1], 'euler61': [1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler67': [1, 0, -4, 0, 6, 0, -4, 0, 1], 'euler7': [1, -3, 3, -1, 0, -1, 3, -3, 1], 'euler71': [1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler73': [1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler79': [1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler83': [1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler89': [1, 2, 3, 4, 5, 4, 3, 2, 1], 'euler97': [1, 0, 1, 0, 1, 0, 1, 0, 1], 'euler_factors': [[1, 1, 1, 1, 1, 0, 0, 0, 0], [1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 1, 1, 1, 1, 0, 0, 0, 0], [1, -3, 3, -1, 0, -1, 3, -3, 1], [1, 1, 1, 1, 1, 0, 0, 0, 0], [1, -3, 3, -1, 0, -1, 3, -3, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 2, 3, 4, 5, 4, 3, 2, 1], [1, 2, 3, 4, 5, 4, 3, 2, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 2, 3, 4, 5, 4, 3, 2, 1], [1, -3, 3, -1, 0, -1, 3, -3, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 2, 3, 4, 5, 4, 3, 2, 1], [1, 2, 3, 4, 5, 4, 3, 2, 1], [1, 2, 3, 4, 5, 4, 3, 2, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, -4, 0, 6, 0, -4, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 2, 3, 4, 5, 4, 3, 2, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/440/1/bh/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': '8-440e4-1.1-c0e4-0-2', 'motivic_weight': 0, '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': [0, 0, 0, 0], 'order_of_vanishing': 0, 'prelabel': '8-440e4-1.1-c0e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.46860282282389326, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e4-0', 'trace_hash': 540893063260450612, 'z1': {'__RealLiteral__': 0, 'data': '0.942359534289069936298232069661', 'prec': 107}}
• lfunc_instances •

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

  
  {'Lhash': '1194582629272334230695922055751,2383527843398215035860441605174,2413119756176256390256363413966,2420285155054132283172460806685', 'Lhash_array': ['1194582629272334230695922055751', '2383527843398215035860441605174', '2413119756176256390256363413966', '2420285155054132283172460806685'], 'factors': ['2-440-440.59-c0-0-0', '2-440-440.339-c0-0-0', '2-440-440.379-c0-0-1', '2-440-440.179-c0-0-0'], 'label': '8-440e4-1.1-c0e4-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/440/1/bh/a'}