Lfunction data - 8-21e8-1.1-c5e4-0-2

Formats: - HTML - YAML - JSON - 2025-11-06T07:01:47.695333

• 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': '187973109690549621004312872626,956676558153066826660011448166,1584308992904874007963532030303,1638676329408336956694010609093', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 112, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25026295.531106696, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '441.1', 'coefficient_field': '1.1.1.1', 'conductor': 37822859361, 'conductor_radical': 21, 'degree': 8, 'euler_factors': [[1, 0, -112, 0, 5184, 0, -114688, 0, 1048576], [1], [1, 0, 7208, 0, 32520066, 0, 70390625000, 0, 95367431640625], [1], [1, 0, 24920, 0, 52030100802, 0, 646360621056920, 0, 672749994932560009201], [1, 0, 1168178, 0, 616876943619, 0, 161043257291181122, 0, 19004963774880799438801], [1, 0, 5394836, 0, 11308051667622, 0, 10875956469922681364, 0, 4064231406647572522401601], [1, 0, -3892390, 0, 16049807493627, 0, -23864500991202034390, 0, 37589973457545958193355601], [1, 0, 16765028, 0, 153119563387494, 0, 694516620439139467172, 0, 1716155831334586342923895201], [1, 0, -39690532, 0, 1235249049211158, 0, -16698093905933093396932, 0, 176994576151109753197786640401], [1, 0, -104235718, 0, 4355527800705483, 0, -85434542986553844450118, 0, 671790528819082282036142601601], [1, -812, 277623082, -168955340960, 28885799074176931, -11716031898450578720, 1334974013527679031190618, -270758369576874029355856316, 23122483666661158726686253786801], [1, 0, 463410104, 0, 80532549742627506, 0, 6220195946874292403259704, 0, 180167782956420929503029846064801], [1, -18788, 720404626, -8700481148744, 169074883586298619, -1279044187027706845592, 15569011833207154232535874, -59690798032611990976045999916, 467056167777397914441056671494001], [1, 0, -233454160, 0, 118823475676986498, 0, -12279486232844625992053840, 0, 2766668711962335809450748011342401], [1, 0, -1562699908, 0, 960282691346828214, 0, -273296633850539968045099492, 0, 30585627290848204916791848989276401], [1, 0, 2810246396, 0, 2996604708159030006, 0, 1436364013898348601648640796, 0, 261240335504588722483367157995242801], [1, 0, -2770439068, 0, 3345518980700942358, 0, -1976273071351722803307855868, 0, 508858109619679129936596364708525201], [1, -120788, 10871653282, -599378336094440, 26541994979701677931, -809235740152987767105080, 19817260600408831895901925618, -297266404869391346110887249993884, 3322737661703085672358476688602579601], [1, 0, -7185535000, 0, 19418465411076012402, 0, -23390666469305786715627535000, 0, 10596610576391421032662867140133202401], [1, 0, -2603033278, 0, 10289197221000971619, 0, -11186863051110721435338443422, 0, 18469587772135192290560825407466407201], [1, 157540, 21615294946, 1698651012861880, 116492564980183775131, 5226844968794479157170120, 204659580156136768707689546146, 4589836449218732706888946840410460, 89648251976843595444986830377401534401], [1, 0, 7675955360, 0, 45762155046589889298, 0, 119100439516913534205226036640, 0, 240747534123068430155382383568465195601], [1, 0, 125527988, 0, 62367379178875199238, 0, 3914178565188155935472124788, 0, 972299657790850297934682879408841327201], [1, 0, -34340864428, 0, 442308567794554593894, 0, -2532378196763499999427295884972, 0, 5437943429267472574499737549036572950401], [1, 0, 40025795816, 0, 621440507758271678466, 0, 4421337964554481675627858811816, 0, 12201900399479668244827490915525641902001], [1, 0, 10719199178, 0, 297508583623233353019, 0, 1440570734876624786924818935722, 0, 18061112346694138117573133075817258818401], [1, 0, -18514165852, 0, 479123855756753785974, 0, -3642016648484592156956772561148, 0, 38696844624861790832365403138487376998001], [1, 826420, 317658714346, 73422743323834240, 11123736081737571593731, 1129699917125254097808357760, 75201370126035426650172622610746, 3010220354334960330428853682853256580, 56044107677782919374398655242916531006801], [1, 0, -63755323072, 0, 1695098782988218508994, 0, -21642174063416713378445697896128, 0, 115230877647233745723406127208308085892801]], 'euler_factors_factorization': [[[[1, 0, -56, 0, 1024], 2]], [1], [[[1, 0, 3604, 0, 9765625], 2]], [1], [[[1, 0, 12460, 0, 25937424601], 2]], [[[1, 0, 584089, 0, 137858491849], 2]], [[[1, 0, 2697418, 0, 2015993900449], 2]], [[[1, 0, -1946195, 0, 6131066257801], 2]], [[[1, 0, 8382514, 0, 41426511213649], 2]], [[[1, 0, -19845266, 0, 420707233300201], 2]], [[[1, 0, -52117859, 0, 819628286980801], 2]], [[[1, -203, 69343957], 4]], [[[1, 0, 231705052, 0, 13422659310152401], 2]], [[[1, -4697, 147008443], 4]], [[[1, 0, -116727080, 0, 52599132235830049], 2]], [[[1, 0, -781349954, 0, 174887470365513049], 2]], [[[1, 0, 1405123198, 0, 511116753300641401], 2]], [[[1, 0, -1385219534, 0, 713342911662882601], 2]], [[[1, -30197, 1350125107], 4]], [[[1, 0, -3592767500, 0, 3255243551009881201], 2]], [[[1, 0, -1301516639, 0, 4297625829703557649], 2]], [[[1, 39385, 3077056399], 4]], [[[1, 0, 3837977680, 0, 15516041187205853449], 2]], [[[1, 0, 62763994, 0, 31181719929966183601], 2]], [[[1, 0, -17170432214, 0, 73742412689492826049], 2]], [[[1, 0, 20012897908, 0, 110462212541120451001], 2]], [[[1, 0, 5359599589, 0, 134391637934412192049], 2]], [[[1, 0, -9257082926, 0, 196715135728956532249], 2]], [[[1, 206605, 15386239549], 4]], [[[1, 0, -31877661536, 0, 339456738992222314849], 2]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 2, 'label': '8-21e8-1.1-c5e4-0-2', 'leading_term': '4.3870391128632941340719209044948064363714974481713961676896883922173354381667889570550295', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, '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': [5, 5, 5, 5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/441/6/c/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.015625', 'prec': 27}, 'plot_values': [4.3870391128632935, 4.323651684136884, 4.163407190928876, 3.9034781921559625, 3.5424190904391306, 3.081853647092042, 2.528576402023048, 1.8911521622341152, 1.1789759071735537, 0.40162576406404893, -0.4312489851113929, -1.3093101438385961, -2.221544133395431, -3.1562766473525743, -4.101534074492153, -5.045301361214307, -5.975680957545943, -6.881088724688513, -7.750317100986343, -8.572661023680258, -9.338059622833793, -10.037243464284375, -10.661902160159851, -11.204741721614068, -11.659575261596958, -12.02140103881137, -12.286469320503281, -12.45228575555004, -12.517644325769881, -12.482624592459047, -12.348606953722397, -12.118201394292306, -11.795205432682868, -11.384521373817647, -10.892104359103762, -10.324842577430534, -9.690449247255996, -8.99733052017461, -8.254483236190794, -7.471349860443565, -6.6576717012259055, -5.823341929278059, -4.978275728790021, -4.132271549941825, -3.2948684239144486, -2.475216335647092, -1.6819483684311114, -0.9230791763455113, -0.20590732557144492, 0.4630728082403363, 1.07827019588109, 1.6350345174404837, 2.129684514991498, 2.5595406307675748, 2.922977339677018, 3.219382156749058, 3.4491133450708067, 3.6134755202754856, 3.7147182761213777, 3.7559240086594596, 3.740912061060296, 3.6741692762629325, 3.5608005259494595, 3.4063740550830808, 3.2167998944249545, 2.998237967325269, 2.7570189048957547, 2.499487455939244, 2.231886238847383, 1.9602680902416287, 1.6904159093365878, 1.4277214425035634, 1.1771021566365487, 0.9429421907020165, 0.7290408848627922, 0.5385505097647104, 0.37394408399493634, 0.23700142976220367, 0.1288055644370811, 0.04974483703811984, -0.00046494891188495494, -0.0227453766211111, -0.01860942460599196, 0.009893104203752398, 0.060240542849010086, 0.12951248940527954, 0.21447050556629302, 0.31164012574195, 0.41739585510599053, 0.5280483982567397, 0.6399351226285893, 0.7494989149324316, 0.8533651826065346, 0.9484150619546433, 1.0318588980477663, 1.1012847736396, 1.1547023449151625, 1.1905801879557512, 1.2078816277504738, 1.2060668231970726, 1.1850901723280556, 1.1453931603726795, 1.0878941891592702, 1.0139437286625188, 0.9252794889258591, 0.8239809391874734, 0.7124196560744994, 0.593183385583666, 0.4690087530503604, 0.34271568411775855, 0.21713734728890824, 0.09504117087400304, -0.02093443137021422, -0.12834136818719474, -0.224986589960526, -0.30898413115059814, -0.3787914651511996, -0.43324422174875565, -0.47159108492198276, -0.49349996261520696, -0.4990553983751398, -0.488754374553944, -0.463496893569688, -0.42454696201188, -0.3734932235110972, -0.3122077848013663, -0.24279519469664332, -0.16752753841169582, -0.0887838735905942, -0.008987428064168182, 0.06946565346398936, 0.14426893278311448, 0.2132634289243421, 0.2744978307040964, 0.3262890536289621, 0.36725656992010064, 0.39635400890301464, 0.41290166605922635, 0.41661069074333607, 0.4075743696000502, 0.38626016351791786, 0.3534990534985577, 0.3104648746481777, 0.2586244378427809, 0.1996917732727682, 0.135578242408188, 0.06833798917702691, 9.573103326680126e-05, -0.0670193949214245, -0.1309389865565052, -0.18971882745947227, -0.24160424952281961, -0.28508830450386463, -0.3189591644860028, -0.34234315766948537, -0.3547354822203132, -0.35602116726738775, -0.3464793937394707, -0.3267837931596414, -0.2979835098523161, -0.261471615324145, -0.21894059904825736, -0.17233497058311487, -0.12378766818686056, -0.07554558286365322, -0.029892513396347267, 0.010928957853763558, 0.04479990294015758, 0.06980924866830279, 0.08433085837826632, 0.08709846829442754, 0.07726770820339471, 0.054468215340386095, 0.018844037021392226, -0.028912149168943236, -0.08755424433953318, -0.1552931443576444, -0.22981876446257848, -0.30833100333982727, -0.38760674582117993, -0.4640778877328823, -0.5339169087847698, -0.5931296396248776, -0.6376755254162416, -0.6635889242533144, -0.6670996348302471, -0.6447503713443297, -0.593524786995845, -0.5109654089002376, -0.39527776690181426, -0.24541197199887818, -0.06114614043284755, 0.15685081796457556, 0.4069874534569148, 0.6867621654680768, 0.9927598437276816, 1.320679088599279, 1.6654080911250875, 2.0211576153057527, 2.3815378875259174, 2.739675991159335, 3.088390306895317, 3.4204239775979635, 3.7285609532716926, 4.005792562340099, 4.2455315365032, 4.441883261058588, 4.589730403538674, 4.684875337337049, 4.7242070520805015, 4.705925071698673, 4.629520765585853, 4.4958158581094745, 4.307008561861658, 4.06677340710211, 3.780099113715344, 3.453175807020154, 3.09329595216466, 2.7087949450264825, 2.3087604817256286, 1.9027899335186846, 1.5007815058978675, 1.1127452245544165, 0.7484605748329684, 0.41719593108735714, 0.12747509194066683, -0.11315071718347922, -0.2983761808281316, -0.42333695380181957, -0.4847610541618649, -0.4811165315244941, -0.4126970874891426, -0.2816349491891096, -0.09188305353359015, 0.15081652252286742, 0.439088652477992, 0.7641197791202462, 1.1158700922898015, 1.4833124105401674, 1.8547773357170723, 2.2182942925986535, 2.56193798351662, 2.8742003751326295, 3.144378311359522, 3.362928398200523, 3.5218139697211677, 3.6148470761764644, 3.6379410350698156, 3.589318755770918, 3.469697112106771, 3.282419636696942, 3.0334392011076803, 2.7312565920711016, 2.3868192481983415, 2.0133444481886227, 1.6259959241845627, 1.2415278055295238, 0.877888569849338, 0.553771249575749, 0.28807082539125883, 0.09933701983670548, 0.005223465623161733, 0.02192671418258467, 0.16361677243358677, 0.4419177640787717, 0.8654389714339029, 1.4393309691156033, 2.164924420804347, 3.039507022167981, 4.056142500957833, 5.203562755404151, 6.466209052255075, 7.824494487318767, 9.254975511826459, 10.73070574491721, 12.22176893239107, 13.695977836517589, 15.119314224281359, 16.45670742306785, 17.67299393658072, 18.733718732215014, 19.605665372361425, 20.25786188454892, 20.662713244278205, 20.79643015485382, 20.63943789671595, 20.177340064707813, 19.401795373793576, 18.310233721430528, 16.905951408999513, 15.198806147722069, 13.205362943539289, 10.947916817565215, 8.454165046005075, 5.757480001747701, 2.8961280721606504, -0.08809975147893798, -3.150561624890412, -6.243969864681899, -9.319841960570681, -12.329844476684695, -15.226546820171476, -17.96402508549956, -20.499366569061362, -22.79361581858244, -24.8122733426502, -26.52605044188551, -27.911778090909873, -28.95272834516674, -29.63863553456449, -29.966199270865452, -29.939103703960342, -29.5676635259683, -28.868333169305927, -27.863644761369695, -26.581472092867283, -25.054165741865983, -23.317694599279204, -21.411007019956866, -19.374965023852795, -17.251310623676748, -15.081707560878067, -12.90683302061561, -10.765475660665924, -8.693722677798307, -6.724213448203326, -4.885403174275791, -3.2011834998877458, -1.6905655689635322, -0.3673975580202305, 0.7598807455849599, 1.6879893027235662, 2.418569209530146, 2.9579344189020698, 3.3167733046925774, 3.509437633087568, 3.553312400319573, 3.46820369930807, 3.27570093221054, 2.9983457224749137, 2.6589199829432384, 2.279788142688052, 1.8822585599032966, 1.485986651917096, 1.1084976203461656, 0.7647876126754086, 0.46698781704273146, 0.22421065208165747, 0.04248227562179749, -0.07525115221748224, -0.12902640378818434, -0.12159288205772668, -0.05811382552112982, 0.05418062123255777, 0.20643581463073807, 0.3886453905119475, 0.5900957846507219, 0.7998334790014772, 1.0072106324219805, 1.202259342596924, 1.3760164598383111, 1.520860975796006, 1.63089979455266, 1.7020257293315968, 1.7319542467464482, 1.7202818384122094, 1.6685639837405233, 1.5800330000986786, 1.4593531026454367, 1.3124191608465237, 1.1461645253833501, 0.9681035034786122, 0.7859660801045278, 0.6073990737462522, 0.43969037304032593, 0.28938113389148334, 0.16199504335904605, 0.06184553262113495, -0.008110139591952474, -0.046405644798076025, -0.053097967171007995, -0.029729054202686053, 0.02076896875024409, 0.0942168261370629, 0.18538911092434213, 0.28825865734769485, 0.396282555808356, 0.5026867224979283, 0.6007571021528555, 0.684136619027349, 0.7471336478101203, 0.7849403036969922, 0.7938233385021127, 0.7712931991525644, 0.716254655650191, 0.6290070749187154, 0.5112161168359473, 0.3658598435541412, 0.19713971211730513, 0.010258351621614875, -0.18880247529999905, -0.393515052484711, -0.5970691540816456, -0.7926724555810926, -0.9738196933077807, -1.1345545318320749, -1.269736566282807, -1.3752196910240997, -1.448001300829346, -1.4863496608864888, -1.4899028559273544, -1.459604531236719, -1.3976500294453102, -1.3074047688241943, -1.1932707875182897, -1.060423440901882, -0.9146003550438698, -0.7618702704470299, -0.6083568332011139, -0.4599513174634808, -0.32208662538073507, -0.1995101214210323, -0.09605664493541677, -0.014518057271197723, 0.043447764458875486, 0.0773892190706261, 0.08807655867523514, 0.07740955147421437, 0.0483111511638839, 0.004589077007802081, -0.04926389662298698, -0.10830829869167974, -0.16739244910239612, -0.22142035052529138, -0.26560602050444027, -0.29569403869416616, -0.3081686416628718, -0.3004731521341642, -0.27111603165299736, -0.21972524904555624, -0.1470989843613135, -0.05521621875003913, 0.052898482864268445, 0.17332591414415507, 0.3013856952897621, 0.43184935375430766, 0.5592423799608812, 0.6780976332792186, 0.7831713396976621, 0.8697249725919872, 0.9338070482274105, 0.9724270389833718, 0.9836848672879898, 0.966909805004445, 0.92274264647404, 0.8530937903071975, 0.7610636455738558, 0.6508309371415644, 0.52748021189823, 0.3967533377735024, 0.26478504203326203, 0.1378173708015794, 0.02188697688062165, -0.0774706850281571, -0.155496134029523, -0.20846068959382483, -0.2338975450189419, -0.2307340090903841, -0.19937337492523122, -0.1417267424724627, -0.06117704592457884, 0.03756585987336772, 0.1486516429799875, 0.26532690423118843, 0.38025278995272527, 0.4858419578043963, 0.5745955386333329, 0.6394666347593794, 0.6742710573464649, 0.6739715366567768, 0.6349279937921183, 0.5551382250680912, 0.43445709331817933, 0.2745971288370141, 0.0790967013948111, -0.14675164558422665, -0.39605634589846606, -0.660645940467747, -0.9313920577296843, -1.1985830908020907, -1.4523766366477429, -1.6832354720831066, -1.8823359728650373, -2.042013116976837, -2.156198566265037, -2.2206561334063566, -2.2331799095449276, -2.193792706378777, -2.1048409930142973, -1.9708128697283722, -1.7981466544707834, -1.5950041085405582, -1.3709297908602516, -1.1363048813905225, -0.9018507980341952, -0.6781111070492503, -0.4749086926674466, -0.3007650345008282, -0.1624309063957894, -0.06447252352548771, -0.008951464423262874, 0.00478014837437263, -0.01985918674665851, -0.07675385539603458, -0.15732514767118333, -0.2509054392665935, -0.3452340445813197, -0.42708455962604813, -0.48302277830964224, -0.500169251150623, -0.46699752567382297, -0.37416264435224256, -0.2153237595237408, 0.012225393555178592, 0.3070029855811261, 0.6628991228409242, 1.0689537105603897, 1.5093866257623416, 1.963764362199992, 2.40740654148007, 2.8122161467067803, 3.1474953428545556, 3.3808703572729275, 3.4795262955074913, 3.411958742179016, 3.149092890781527, 2.66546270775225, 1.9406891627713077, 0.9613799875607048, -0.27831331255957314, -1.7760687661632482, -3.5205553338607487, -5.490421979249725, -7.655000785360593, -9.974871502900791, -12.402336997077098, -14.881926481486829, -17.35239837153672, -19.748518893986287, -22.00284283110376, -24.047423686710037, -25.816392458592933, -27.248228658280606, -28.288000133355325, -28.889124463655268, -29.015369619468267, -28.64248404924932, -27.759564798065888, -26.369550035357207, -24.489673745329934, -22.151532944510127, -19.40055186396893, -16.294526674878924, -12.902347820138282, -9.302345533378926, -5.579891397845552, -1.8243307356402159, 1.8732056144359737, 5.422365591596108, 8.736653947542635, 11.73690435806573, 14.352932828071504, 16.525559094904533, 18.208769452376742, 19.372099571201414, 20.00048275395905, 20.094451984623145, 19.670366352880897, 18.76070035538421, 17.411726218907386, 15.681685031736466, 13.6391559173127, 11.36131042580876, 8.930266745664126, 6.430309473517824, 3.945451887924075, 1.5567562617873152, -0.6609453449504343, -2.641113383186638, -4.32733007970117, -5.675403853434585, -6.654631547945886, -7.247980313109547, -7.452299019870142, -7.278766732179758, -6.751582550305025, -5.906246040564701, -4.788111545811035, -3.451129208345497, -1.9548956423039723, -0.36204157414952576, 1.26394767156658, 2.860679942479828, 4.369665257615531, 5.7384279427074105, 6.922127566239879, 7.884714785964849, 8.600172681506569, 9.053135915639114, 9.239059773949297, 9.163636595963624, 8.842208352948344, 8.29883022846272, 7.564983616378656, 6.677510991595101, 5.677056169535302, 4.606412373060875, 3.5086369049394923, 2.4247342825981852, 1.3924162975705499, 0.4448912420950092, -0.3904415654907369, -1.0932865054954544, -1.6504699916960284, -2.0559739480261685, -2.3109382343165707, -2.423467711569582, -2.407419964239328, -2.2813552503208916, -2.0674580535018583, -1.7903742175208774, -1.4755722834928569, -1.1480066700071594, -0.8308995347171436, -0.5446450647795068, -0.3057642287695428, -0.12621203351631866, -0.01293533159706281, 0.03232251898228088, 0.012929476430644477, -0.06299806290344859, -0.18317702107406614, -0.3319691539160387, -0.49135556517266693, -0.6419763522847992, -0.7642313536332882, -0.8394645827439727, -0.8509966651930668, -0.7850132651169517, -0.6313563083152252, -0.3841862351059682, -0.042299942313623475, 0.39075213560600564, 0.9067423976032389, 1.4931609511162802, 2.1337472069489443, 2.8091301375343884, 3.4977011592824354, 4.17689046381977, 4.823959418372954, 5.4168297566542405, 5.935156080874952, 6.361736847058368, 6.682749605716679, 6.888100445903348, 6.97203347372559, 6.9338946382060245, 6.777417299374807, 6.510303653870893, 6.144099146439069, 5.694061161672602, 5.177790559485439, 4.6143249793436425, 4.023547681555666, 3.425576729081091, 2.839467810939959, 2.282434372835002, 1.7693653757955543, 1.312414077034928, 0.9204011798067272, 0.5986462611134787, 0.34902632207460016, 0.17014885678663738, 0.05758037920601005, 0.004305472660007958, 0.0012884836600095212, 0.03807475914378222, 0.10343795446732931, 0.1860432554236351, 0.2750651243570785, 0.36072794870353053, 0.4347765460135153, 0.49082826236991095, 0.5245902642736913, 0.5339428764862699, 0.5188950842096276, 0.48141685081585295, 0.4251625244560466, 0.35509649723422765, 0.27706428198756805, 0.19733808264255606, 0.1221502398865568, 0.05722771929329967, 0.0074132150950080985, -0.0236425325161603, -0.0337224856067831, -0.022185893718112786, 0.010046047122650482, 0.06057085635229396, 0.1256690673276819, 0.2006054404237575, 0.27998676929822525, 0.35809581269979657, 0.42927937822956397, 0.48843181399947716, 0.5313125268182902, 0.5547785160156066, 0.5570280862626508, 0.5378534797838156, 0.4985727775760123, 0.44191256487171593, 0.37188350578408136, 0.2936042272117088, 0.21286845090729017, 0.1357532635441264, 0.06824610268970219, 0.01584574200980058, -0.016874624660955195, -0.02659567798151294, -0.011509830562290053, 0.028480522101066823, 0.09169070083126442, 0.17469696149867564, 0.27248300233750933, 0.37867333134878495, 0.4858819274977317, 0.5861241836165513, 0.6713001041398219, 0.7336705363833044, 0.7663179807846598, 0.7635938590159796, 0.7215336548179836, 0.6381435012422105, 0.5135529557587964, 0.35009949432535875, 0.1522964391707785, -0.07335909836863884, -0.31871000540944755, -0.5743323805747166, -0.8299904988136917, -1.0751999244837673, -1.2997819996942168, -1.4944223121627298, -1.6511232117277275, -1.76371178813089, -1.8281590316697414, -1.8427911951693468, -1.8083104310299545, -1.7278532685178247, -1.606778886946599, -1.4522959664556132, -1.27300595727864, -1.0785021598474487, -0.8787757486495138, -0.6835604060050282, -0.5017794305078113, -0.34109525270681484, -0.20744097633949946, -0.10466722446007325, -0.03438097339009287, 0.004075074611089601, 0.013528862015308708, -0.0012812225118757985, -0.034103107687963596, -0.07768173956689058, -0.12433455335038969, -0.16655736289927775, -0.19763471880063704, -0.21225292493767425, -0.20696135801224555, -0.1805054515925967, -0.13404715498583616, -0.07124542397425716, 0.0019609773818232636, 0.07771427779047688, 0.14673222867347116, 0.1989920976516209, 0.22456923235325257, 0.21449291696736864, 0.1616292655696937, 0.061590103655355194, -0.08651728231674986, -0.27948475969287495, -0.5095575288945292, -0.7642673687446813, -1.0265556535047766, -1.2751254481296534, -1.4850928410461357, -1.6290859829431568, -1.6783844292462553, -1.6042276305256216, -1.37935511348109, -0.979837459528751, -0.38648107338755644, 0.413805396936229, 1.4267121018440867, 2.6493112088764867, 4.069546278673626, 5.666055762088998, 7.408311523583353, 9.25721793736948, 11.16613682674833, 13.082470769119315, 14.949407706918956, 16.708417853475407, 18.30130358828124, 19.672660943273627, 20.77209578404335, 21.55733369077997, 21.99581417020513, 22.06606958650896, 21.758775014963774, 21.078630383121954, 20.044005859882326, 18.68571735003812, 17.04599753948307, 15.178124950201562, 13.143776546606386, 11.009553969837802, 8.84444750475037, 6.717849732289496, 4.695970869409737, 2.8383014567609766, 1.1953543537064497, -0.19306408964553404, -1.2999758688727907, -2.112490281348165, -2.631979400940178, -2.8738042465783535, -2.8663823815057654, -2.6494083836731974, -2.2715567716748444, -1.7879859932350364, -1.257023863467165, -0.7367512817240052, -0.28175557809956253, 0.05990226920034392, 0.24980700959498864, 0.26162517570588417, 0.08283928517466937, -0.28412563080820286, -0.8214790284355241, -1.496608415575491, -2.263437528976309, -3.064362556883515, -3.8330201122229384, -4.497720059722426, -4.985236556641282, -5.224396416721637, -5.150188989466783, -4.707887443382933, -3.8565803153939093, -2.5711893603898943, -0.8451817588839904, 1.3073964224630905, 3.8515024791790955, 6.733389252979808, 9.880771563203998, 13.204177456360382, 16.60042706856908, 19.959428744004867, 23.166220192769465, 26.10440692101054, 28.661526603792485, 30.737680320906676, 32.24663231276312, 33.118209632993114, 33.302225920174536, 32.77508444461522, 31.537389087127536, 29.61271531273276, 27.047853989871594, 23.91486670485335, 20.304937398619533, 16.323601759090746, 12.08765270093253, 7.723060852733758, 3.357564170996681, -0.8848424695752157, -4.887792863014032, -8.545929675360165, -11.769817615134645, -14.488834528437994, -16.65296870685324, -18.234381176642266, -19.22743142873806, -19.647511081323284, -19.52957569940557, -18.926643949033625, -17.90570714498667, -16.543823551121726, -14.92465084573483, -13.135205717994637, -11.260942755204196, -9.382025867336601, -7.570471785294547, -5.887831229863837, -4.382694195599137, -3.0895180002284075, -2.0283204707035387, -1.2050510334546134, -0.6124909439646574, -0.23191584315536734, -0.03523266262887928, 0.012498185843924944, -0.04965327103502263, -0.1812224286963888, -0.34301254141352616, -0.49955055326374564, -0.6210859094182497, -0.6851443174218126, -0.6775982901790525, -0.59314326055647, -0.43511545772094734, -0.21485873387113621, 0.049400916160969116, 0.3341693306132117, 0.6125044032961521, 0.8559677517914983, 1.0366796925739616, 1.1294597016384984, 1.113460120522544, 0.9735784724804937, 0.7015719451306497, 0.2969020733556595, -0.23327700807081075, -0.8744589441572055, -1.605447261309499, -2.3994257450480223, -3.2255387839525547, -4.050535370814631, -4.840467352625686, -5.562717749308011, -6.187709113371747, -6.690251941371205, -7.0507753733259735, -7.256712914373935, -7.302818259712428, -7.190984519325616, -6.930050144721565, -6.53565319327098, -6.028837744053338, -5.434544717455433, -4.78031714205609, -4.095140351540577, -3.4074901691156443, -2.7437064543111833, -2.126784570655268, -1.5753617314854456, -1.1028445514446803], 'positive_zeros': ['0.14828463746769552031443452354776', '0.75468473566835023871698259068438', '1.24979942629272847968503275083226', '1.29268769258130562025058400408601', '1.74710176235442751716154765179680', '2.01739255479933881249554429200884', '2.29689719757942935435621367996640', '2.58933106513905038230819515287159', '2.70975650112290544812193074253370', '2.98900578736296688526922740684741', '3.52347665508884056450203721397052', '3.64692671653357850429727224917588', '4.08066114608593548930152815035617', '4.08689958905320875226658929099363', '4.62454574620141833145212226422176', '5.14542435634167089942258351532986', '5.44223390206349742057369840140378', '5.50884554000070117412252600126122', '5.90400914627467593282873625068101', '5.96321008597775115178918433746685', '6.23520017098937006706551661418367', '6.61274152126536380856745338596621', '6.70455833360453284440412933821045', '6.89886540446257584069131528741500', '7.22195220674832965177337714421312', '7.35370854806969782177881819208645', '7.56819243626806368420680608802053', '7.973838961579830323940563402575341', '7.990052859688551753641227149943355', '8.171141311296215299376077957906761', '8.418638775209536471515999042296821', '8.851403928481144919053121468959198', '9.167059962803639957576501104306728', '9.378485146560667299912727334311002', '9.695531987180635100770294703494370', '9.955890600249935911133489986055844', '9.987990835757001583106179462163319', '10.17355542855233035545154420231476', '10.69062441260384355201759306148324', '10.98733463072745213960102476490891'], 'prelabel': '8-21e8-1.1-c5e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.410069235001842, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5e4-0', 'trace_hash': 2276146892445137256, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.14828463746769552031443452355', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.75468473566835023871698259068', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.24979942629272847968503275083', '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': 25026295.531106696, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 37822859361, 'conductor_radical': 21, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7360, 0, 0, 0, 0, 0, 0, 0, 0, -7208, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 812, 0, 0, 0, 0, 0, 18788, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 358400, 0, 0, 120788, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -157540, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -807296], 'euler11': [1, 0, 24920, 0, 52030100802, 0, 646360621056920, 0, 672749994932560009201], 'euler13': [1, 0, 1168178, 0, 616876943619, 0, 161043257291181122, 0, 19004963774880799438801], 'euler17': [1, 0, 5394836, 0, 11308051667622, 0, 10875956469922681364, 0, 4064231406647572522401601], 'euler19': [1, 0, -3892390, 0, 16049807493627, 0, -23864500991202034390, 0, 37589973457545958193355601], 'euler2': [1, 0, -112, 0, 5184, 0, -114688, 0, 1048576], 'euler23': [1, 0, 16765028, 0, 153119563387494, 0, 694516620439139467172, 0, 1716155831334586342923895201], 'euler29': [1, 0, -39690532, 0, 1235249049211158, 0, -16698093905933093396932, 0, 176994576151109753197786640401], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 0, -104235718, 0, 4355527800705483, 0, -85434542986553844450118, 0, 671790528819082282036142601601], 'euler37': [1, -812, 277623082, -168955340960, 28885799074176931, -11716031898450578720, 1334974013527679031190618, -270758369576874029355856316, 23122483666661158726686253786801], 'euler41': [1, 0, 463410104, 0, 80532549742627506, 0, 6220195946874292403259704, 0, 180167782956420929503029846064801], 'euler43': [1, -18788, 720404626, -8700481148744, 169074883586298619, -1279044187027706845592, 15569011833207154232535874, -59690798032611990976045999916, 467056167777397914441056671494001], 'euler47': [1, 0, -233454160, 0, 118823475676986498, 0, -12279486232844625992053840, 0, 2766668711962335809450748011342401], 'euler5': [1, 0, 7208, 0, 32520066, 0, 70390625000, 0, 95367431640625], 'euler53': [1, 0, -1562699908, 0, 960282691346828214, 0, -273296633850539968045099492, 0, 30585627290848204916791848989276401], 'euler59': [1, 0, 2810246396, 0, 2996604708159030006, 0, 1436364013898348601648640796, 0, 261240335504588722483367157995242801], 'euler61': [1, 0, -2770439068, 0, 3345518980700942358, 0, -1976273071351722803307855868, 0, 508858109619679129936596364708525201], 'euler67': [1, -120788, 10871653282, -599378336094440, 26541994979701677931, -809235740152987767105080, 19817260600408831895901925618, -297266404869391346110887249993884, 3322737661703085672358476688602579601], 'euler7': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler71': [1, 0, -7185535000, 0, 19418465411076012402, 0, -23390666469305786715627535000, 0, 10596610576391421032662867140133202401], 'euler73': [1, 0, -2603033278, 0, 10289197221000971619, 0, -11186863051110721435338443422, 0, 18469587772135192290560825407466407201], 'euler79': [1, 157540, 21615294946, 1698651012861880, 116492564980183775131, 5226844968794479157170120, 204659580156136768707689546146, 4589836449218732706888946840410460, 89648251976843595444986830377401534401], 'euler83': [1, 0, 7675955360, 0, 45762155046589889298, 0, 119100439516913534205226036640, 0, 240747534123068430155382383568465195601], 'euler89': [1, 0, 125527988, 0, 62367379178875199238, 0, 3914178565188155935472124788, 0, 972299657790850297934682879408841327201], 'euler97': [1, 0, -34340864428, 0, 442308567794554593894, 0, -2532378196763499999427295884972, 0, 5437943429267472574499737549036572950401], 'euler_factors': [[1, 0, -112, 0, 5184, 0, -114688, 0, 1048576], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 7208, 0, 32520066, 0, 70390625000, 0, 95367431640625], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 24920, 0, 52030100802, 0, 646360621056920, 0, 672749994932560009201], [1, 0, 1168178, 0, 616876943619, 0, 161043257291181122, 0, 19004963774880799438801], [1, 0, 5394836, 0, 11308051667622, 0, 10875956469922681364, 0, 4064231406647572522401601], [1, 0, -3892390, 0, 16049807493627, 0, -23864500991202034390, 0, 37589973457545958193355601], [1, 0, 16765028, 0, 153119563387494, 0, 694516620439139467172, 0, 1716155831334586342923895201], [1, 0, -39690532, 0, 1235249049211158, 0, -16698093905933093396932, 0, 176994576151109753197786640401], [1, 0, -104235718, 0, 4355527800705483, 0, -85434542986553844450118, 0, 671790528819082282036142601601], [1, -812, 277623082, -168955340960, 28885799074176931, -11716031898450578720, 1334974013527679031190618, -270758369576874029355856316, 23122483666661158726686253786801], [1, 0, 463410104, 0, 80532549742627506, 0, 6220195946874292403259704, 0, 180167782956420929503029846064801], [1, -18788, 720404626, -8700481148744, 169074883586298619, -1279044187027706845592, 15569011833207154232535874, -59690798032611990976045999916, 467056167777397914441056671494001], [1, 0, -233454160, 0, 118823475676986498, 0, -12279486232844625992053840, 0, 2766668711962335809450748011342401], [1, 0, -1562699908, 0, 960282691346828214, 0, -273296633850539968045099492, 0, 30585627290848204916791848989276401], [1, 0, 2810246396, 0, 2996604708159030006, 0, 1436364013898348601648640796, 0, 261240335504588722483367157995242801], [1, 0, -2770439068, 0, 3345518980700942358, 0, -1976273071351722803307855868, 0, 508858109619679129936596364708525201], [1, -120788, 10871653282, -599378336094440, 26541994979701677931, -809235740152987767105080, 19817260600408831895901925618, -297266404869391346110887249993884, 3322737661703085672358476688602579601], [1, 0, -7185535000, 0, 19418465411076012402, 0, -23390666469305786715627535000, 0, 10596610576391421032662867140133202401], [1, 0, -2603033278, 0, 10289197221000971619, 0, -11186863051110721435338443422, 0, 18469587772135192290560825407466407201], [1, 157540, 21615294946, 1698651012861880, 116492564980183775131, 5226844968794479157170120, 204659580156136768707689546146, 4589836449218732706888946840410460, 89648251976843595444986830377401534401], [1, 0, 7675955360, 0, 45762155046589889298, 0, 119100439516913534205226036640, 0, 240747534123068430155382383568465195601], [1, 0, 125527988, 0, 62367379178875199238, 0, 3914178565188155935472124788, 0, 972299657790850297934682879408841327201], [1, 0, -34340864428, 0, 442308567794554593894, 0, -2532378196763499999427295884972, 0, 5437943429267472574499737549036572950401]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/6/c/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': '8-21e8-1.1-c5e4-0-2', 'motivic_weight': 5, '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': [5, 5, 5, 5], 'order_of_vanishing': 0, 'prelabel': '8-21e8-1.1-c5e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.410069235001842, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5e4-0', 'trace_hash': 2276146892445137256, 'z1': {'__RealLiteral__': 0, 'data': '0.14828463746769552031443452355', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '187973109690549621004312872626,956676558153066826660011448166,1584308992904874007963532030303,1638676329408336956694010609093', 'Lhash_array': ['187973109690549621004312872626', '956676558153066826660011448166', '1584308992904874007963532030303', '1638676329408336956694010609093'], 'factors': ['2-21e2-21.20-c5-0-6', '2-21e2-21.20-c5-0-35', '2-21e2-21.20-c5-0-49', '2-21e2-21.20-c5-0-50'], 'label': '8-21e8-1.1-c5e4-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/6/c/a'}