Lfunction data - 8-1805e4-1.1-c1e4-0-0

Formats: - HTML - YAML - JSON - 2024-07-27T10:14:18.262484

• 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
  instance_types	text[]
  instance_urls	text[]
  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': '388302634208324266037133861112,1208425522907897720608694121952,1632568443955140736537711557827,2276643760315575513194553271676', 'a10': 4, 'a2': 1, 'a3': 3, 'a4': -1, 'a5': 4, 'a6': 3, 'a7': -4, 'a8': 2, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 43153.62199339725, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1, -4, 6, -4, 1]], [19, [1]]], 'bad_primes': [5, 19], 'central_character': '1805.1', 'coefficient_field': '1.1.1.1', 'conductor': 10614726900625, 'conductor_radical': 95, 'degree': 8, 'euler_factors': [[1, -1, 2, -5, 6, -10, 8, -8, 16], [1, -3, 10, -22, 44, -66, 90, -81, 81], [1, -4, 6, -4, 1], [1, 4, 27, 69, 272, 483, 1323, 1372, 2401], [1, 2, 19, 47, 179, 517, 2299, 2662, 14641], [1, -7, 59, -250, 1180, -3250, 9971, -15379, 28561], [1, 1, 38, 68, 822, 1156, 10982, 4913, 83521], [1], [1, -2, 75, -145, 2398, -3335, 39675, -24334, 279841], [1, 1, 53, 281, 1251, 8149, 44573, 24389, 707281], [1, 0, 57, -5, 2675, -155, 54777, 0, 923521], [1, 2, 117, 99, 5802, 3663, 160173, 101306, 1874161], [1, 8, 77, 13, 714, 533, 129437, 551368, 2825761], [1, -1, 74, 68, 3460, 2924, 136826, -79507, 3418801], [1, 12, 133, 763, 5768, 35861, 293797, 1245876, 4879681], [1, 5, 126, 568, 7684, 30104, 353934, 744385, 7890481], [1, 5, 111, 385, 8011, 22715, 386391, 1026895, 12117361], [1, 0, 114, 88, 9515, 5368, 424194, 0, 13845841], [1, -4, 232, -828, 22174, -55476, 1041448, -1203052, 20151121], [1, -20, 375, -4165, 42925, -295715, 1890375, -7158220, 25411681], [1, 20, 387, 4161, 44118, 303753, 2062323, 7780340, 28398241], [1, -17, 388, -4009, 48638, -316711, 2421508, -8381663, 38950081], [1, -1, 270, -194, 31408, -16102, 1860030, -571787, 47458321], [1, -11, 266, -1549, 27690, -137861, 2106986, -7754659, 62742241], [1, -1, 122, -1096, 12292, -106312, 1147898, -912673, 88529281], [1, 12, 385, 3289, 57059, 332189, 3927385, 12363612, 104060401], [1, -10, 387, -3015, 58536, -310545, 4105683, -10927270, 112550881], [1, -20, 401, -5329, 64014, -570203, 4591049, -24500860, 131079601], [1, -34, 829, -13023, 160291, -1419507, 9849349, -44030986, 141158161], [1, 13, 412, 4438, 67568, 501494, 5260828, 18757661, 163047361]], 'euler_factors_factorization': [[[[1, -1, 2, -5, 6, -10, 8, -8, 16], 1]], [[[1, -3, 10, -22, 44, -66, 90, -81, 81], 1]], [[[1, -1], 4]], [[[1, 4, 27, 69, 272, 483, 1323, 1372, 2401], 1]], [[[1, 2, 19, 47, 179, 517, 2299, 2662, 14641], 1]], [[[1, -7, 59, -250, 1180, -3250, 9971, -15379, 28561], 1]], [[[1, 1, 38, 68, 822, 1156, 10982, 4913, 83521], 1]], [1], [[[1, -2, 75, -145, 2398, -3335, 39675, -24334, 279841], 1]], [[[1, 1, 53, 281, 1251, 8149, 44573, 24389, 707281], 1]], [[[1, 0, 57, -5, 2675, -155, 54777, 0, 923521], 1]], [[[1, 2, 117, 99, 5802, 3663, 160173, 101306, 1874161], 1]], [[[1, 8, 77, 13, 714, 533, 129437, 551368, 2825761], 1]], [[[1, -1, 74, 68, 3460, 2924, 136826, -79507, 3418801], 1]], [[[1, 12, 133, 763, 5768, 35861, 293797, 1245876, 4879681], 1]], [[[1, 5, 126, 568, 7684, 30104, 353934, 744385, 7890481], 1]], [[[1, 5, 111, 385, 8011, 22715, 386391, 1026895, 12117361], 1]], [[[1, 0, 114, 88, 9515, 5368, 424194, 0, 13845841], 1]], [[[1, -4, 232, -828, 22174, -55476, 1041448, -1203052, 20151121], 1]], [[[1, -20, 375, -4165, 42925, -295715, 1890375, -7158220, 25411681], 1]], [[[1, 20, 387, 4161, 44118, 303753, 2062323, 7780340, 28398241], 1]], [[[1, -17, 388, -4009, 48638, -316711, 2421508, -8381663, 38950081], 1]], [[[1, -1, 270, -194, 31408, -16102, 1860030, -571787, 47458321], 1]], [[[1, -11, 266, -1549, 27690, -137861, 2106986, -7754659, 62742241], 1]], [[[1, -1, 122, -1096, 12292, -106312, 1147898, -912673, 88529281], 1]], [[[1, 12, 385, 3289, 57059, 332189, 3927385, 12363612, 104060401], 1]], [[[1, -10, 387, -3015, 58536, -310545, 4105683, -10927270, 112550881], 1]], [[[1, -20, 401, -5329, 64014, -570203, 4591049, -24500860, 131079601], 1]], [[[1, -34, 829, -13023, 160291, -1419507, 9849349, -44030986, 141158161], 1]], [[[1, 13, 412, 4438, 67568, 501494, 5260828, 18757661, 163047361], 1]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 0, 'label': '8-1805e4-1.1-c1e4-0-0', 'leading_term': '6.1112271811309396643989036300923744306424094877803018006895149622518162463789820148792024', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1805/2/a/o', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0146484375', 'prec': 40}, 'plot_values': [6.111227181130941, 6.073460957013499, 6.025814762012322, 5.958432739483909, 5.861586570185724, 5.727818537472274, 5.558124396098429, 5.355666613466819, 5.123669764787468, 4.8648454625478506, 4.579778539277127, 4.268637169045157, 3.9317373092233217, 3.5696841883123906, 3.1837630226302926, 2.7755164334560782, 2.346606329297755, 1.89877961056166, 1.4337769258004875, 0.9534390212334886, 0.459738673115987, -0.04520656410556593, -0.5590939632362922, -1.0794903587614941, -1.6038544872480778, -2.129535491867699, -2.6537558923272466, -3.1736517888226436, -3.686294002703825, -4.188687721167744, -4.677751588768929, -5.150381488946504, -5.603482255337059, -6.03397389209575, -6.438781331097087, -6.81490356063773, -7.159449097673233, -7.469648780698638, -7.742859000916539, -7.976628175876015, -8.16873102656566, -8.317186252066133, -8.420274024063389, -8.476587631218734, -8.485059238463293, -8.444977959204094, -8.356017537761636, -8.218262090668526, -8.032215782687354, -7.798814872313167, -7.5194576463225316, -7.195995753003004, -6.830721475321597, -6.426366909953343, -5.986126213655218, -5.513609114178418, -5.012802780368205, -4.488053083063205, -3.9440701268213374, -3.3858475386205553, -2.818601109759511, -2.24773118579491, -1.6788066213982782, -1.117461266330782, -0.5693177320556043, -0.039935712975807273, 0.4652237332062491, 0.9409062752481999, 1.3821414008091133, 1.7842973882714448, 2.143127105528712, 2.4548587981162053, 2.7162567661525987, 2.9246646245329053, 3.0780453714377054, 3.175034378421916, 3.2149672443540567, 3.1978957930592986, 3.124604355833751, 2.9966117460638904, 2.8161557482645434, 2.586170633779461, 2.310265020061301, 1.9926720137374223, 1.6381900890540726, 1.2521198973102574, 0.8401982239174292, 0.40851034709159273, -0.036600463694381274, -0.48862736028167286, -0.941002432507596, -1.3871949234490955, -1.8208098285724574, -2.2356930563987887, -2.626050153619535, -2.986521015898999, -3.3122576799209376, -3.5990134912504477, -3.843249636660131, -4.042155180537922, -4.1936779681560035, -4.296572697519676, -4.350467258615286, -4.355810422677487, -4.313841680528031, -4.226583580116534, -4.0968501663307775, -3.928125944738854, -3.7244789078415885, -3.490499561521662, -3.2312517420672826, -2.952109410104801, -2.6586365696751915, -2.356493856755153, -2.0513520571598116, -1.7487299668329985, -1.4538784512529617, -1.1716885728387094, -0.9066028003889558, -0.6625006728121822, -0.4426259651907327, -0.24953225309731045, -0.08502955180304106, 0.04984820808917113, 0.15484636325062465, 0.2304822334637473, 0.27803720862243425, 0.2994996564395091, 0.2974955640104231, 0.2752176286670681, 0.2363538164690514, 0.1849640694962143, 0.1253625291756214, 0.062006573906800325, -0.0006134649568634065, -0.05811577320053404, -0.10634915877333918, -0.1415020448564476, -0.1602076336023741, -0.15964798712709627, -0.13763237437528464, -0.09265944915276801, -0.023970969434914263, 0.06842290410566865, 0.1837417694535247, 0.32044862018069536, 0.47627628411844175, 0.6482903966393264, 0.8329666662009633, 1.0262795573457875, 1.223805504096625, 1.4208460788501585, 1.6125535196971488, 1.7940615585011879, 1.9606282270408033, 2.1077637617489313, 2.2313511590252184, 2.327765815980959, 2.3940004321080885, 2.4277379068023164, 2.427413291666472, 2.392270567404241, 2.3224160717756313, 2.218799145148352, 2.0831854875797133, 1.9181244649725362, 1.7269062583667436, 1.5134539131652338, 1.2822168490275956, 1.0380610304933353, 0.7861474365331701, 0.531780626102734, 0.2802680356116964, 0.03678100885383951, -0.1937907724196898, -0.40696682419880126, -0.5987877789442759, -0.7659204034210451, -0.9057592281891395, -1.0164718654462146, -1.0970310653146982, -1.147236982449809, -1.1677256420701059, -1.1599117815345137, -1.1259272457674796, -1.0685503692655414, -0.9911159314696789, -0.8973851574309734, -0.791422242315356, -0.6774659408804293, -0.5597842251315949, -0.44253811179680247, -0.32965925055060963, -0.2247278964353458, -0.13084408593644536, -0.050556054935981976, 0.014198555012971176, 0.06214732858369716, 0.09273108789441242, 0.10607326596787615, 0.10294613380601376, 0.08473260042747133, 0.05337082702790479, 0.011238749325719137, -0.03895056981804536, -0.0942549273673539, -0.1516292994535914, -0.20806071570331805, -0.260681412028661, -0.3068794624885212, -0.3444252276706345, -0.3715463448324979, -0.3869800868719082, -0.39002242806896115, -0.38058523243941117, -0.35916294652274317, -0.32678830318595015, -0.28498997806646686, -0.23575413677839968, -0.18139558947200363, -0.12443844592952664, -0.06750976719786722, -0.013240707037510546, 0.03588721760092452, 0.07766580011995255, 0.11025825511710058, 0.13228008210032854, 0.14288748878245142, 0.14182494858561143, 0.12944018444433317, 0.10667421025969785, 0.07502869733616238, 0.03649729565079518, -0.006530380402557365, -0.05138441255572952, -0.09525151843192414, -0.1353288097987961, -0.16898480944614086, -0.19391492557426346, -0.20829726961762446, -0.21093944132939735, -0.201401449781871, -0.1800711688896774, -0.14823406934809435, -0.10811151793379159, -0.0628425376395271, -0.016374034461946088, 0.026610419430740613, 0.0608055306892842, 0.08047853127948522, 0.07978036166529844, 0.05291451046094834, -0.005647691519395222, -0.10086791709919621, -0.2367349682814727, -0.41613087958529377, -0.640650462719445, -0.9103518431757255, -1.2234492854465817, -1.576364916352356, -1.963728370219614, -2.378335390840755, -2.8111219777261445, -3.2514711695513867, -3.6874545660119544, -4.106063608230368, -4.493526957218824, -4.835791521320508, -5.118924813656842, -5.329532091253784, -5.455300911583138, -5.485437029949208, -5.411022676517753, -5.22540638148794, -4.924720023433676, -4.508012881195293, -3.9773369718069667, -3.3378765874825027, -2.5981722080909453, -1.7698036027441837, -0.8670828988083844, 0.09319291094424782, 1.091935429979368, 2.1084666267550625, 3.121137129140306, 4.1078642055962655, 5.046636887848024, 5.916322806747225, 6.697330940730661, 7.372172427977479, 7.925978984515747, 8.347047816101192, 8.627222181737173, 8.76215949656785, 8.751528779231322, 8.599032996305194, 8.312298820320992, 7.902666885138938, 7.3848940076572855, 6.776652254692951, 6.097966326816328, 5.370592469791984, 4.617332277875428, 3.8612850764272264, 3.1251158356014446, 2.4303256853440773, 1.7965302199319773, 1.240875719769733, 0.7775188513696165, 0.41717199560517687, 0.16676016639811325, 0.0293125472149674, 0.003918775628221084, 0.08579706218143972, 0.26656912017112694, 0.5346502536717027, 0.8756715736990306, 1.2730348586420879, 1.7087227718517155, 2.163895997459121, 2.619493354155102, 3.05696682803576, 3.4592594677407216, 3.8111677536735384, 4.099721191726024, 4.314698116882248, 4.4493286360147835, 4.500096582429559, 4.4666323853890395, 4.351757895718623, 4.1616575470872235, 3.9051188869112115, 3.5929747803728898, 3.2377280844083214, 2.853269804593104, 2.453897426217212, 2.0536300619562526, 1.6657325567652659, 1.3023335636500644, 0.973703107015301, 0.687851786574344, 0.4503330080281883, 0.26414717196541987, 0.1296061556750036, 0.04444997518897, 0.004108952142168627, 0.002045911427980242, 0.030174121965386304, 0.0793875555475751, 0.14013442130814968, 0.20300112137809698, 0.25930937843581686, 0.3016766834033392, 0.32450918650359273, 0.3244110516512718, 0.3004895385955941, 0.2545307517625608, 0.19103896327353062, 0.11713311793560328, 0.04230439589224842, -0.021958181918462463, -0.06266608724982022, -0.0659349446121673, -0.01764294126112724, 0.09585207657968373, 0.2869720171770049, 0.5662308917861041, 0.9415833828236618, 1.417816536696996, 1.9960761734643273, 2.6736882982921317, 3.443919142449742, 4.295863663532334, 5.214634329971823, 6.182085655613011, 7.177054980604304, 8.175789723886133, 9.152804227675984, 10.0824219547892, 10.939135445484823, 11.698211494678041, 12.336802099135586, 12.835752903505584, 13.179504323886883, 13.356336855344221, 13.35915530272921, 13.186864821223377, 12.843417718525599, 12.337353388937158, 11.681885992362437, 10.8954280604222, 9.999885079373685, 9.019598451130081, 7.980825842428613, 6.911521167556443, 5.8394758491015235, 4.7911883168456155, 3.7912253595456056, 2.861796166201023, 2.0214926404181686, 1.2846925797685564, 0.6613515266528984, 0.15695009989891937, -0.22773247036280242, -0.49639774547881327, -0.6567814915568108, -0.7201193557764, -0.7005042375776142, -0.6140858855869606, -0.4782303294760009, -0.3106873488477424, -0.128725796245486, 0.0516493339481535, 0.21637576284325963, 0.3539089270320677, 0.4556229183938596, 0.5160383077250427, 0.5329000973971332, 0.5071108700552897, 0.4424109032477574, 0.3449541336448215, 0.2227957361434898, 0.08528285434014682, -0.05765921086261858, -0.1961982230793344, -0.3212390598362885, -0.4250537854701197, -0.5017551650997497, -0.547626523457938, -0.5613424705467989, -0.5440826383456742, -0.4993345509382536, -0.43257904875133424, -0.3508843278839688, -0.2623990335164803, -0.1756190101901683, -0.09867441743646992, -0.03863948947461214, -0.0008612800919010418, 0.011689960713292594, -0.0010983511203660609, -0.036156062043511975, -0.08707935755113642, -0.1441844512274632, -0.19477573657718472, -0.223619063805213, -0.21365005402117512, -0.14681891728566016, -0.00505058637931878, 0.2286817552516485, 0.5691702130775582, 1.0279292370922295, 1.612219480594908, 2.3241567052485426, 3.1599831286777382, 4.10969957197116, 5.156907341954587, 6.278929420954206, 7.447373418577216, 8.628898228024118, 9.786202080019958, 10.879363277007144, 11.867725914846284, 12.7113824171778, 13.372766012298793, 13.818506116855108, 14.021671160971913, 13.962842766124464, 13.63116886962304, 13.025492371311477, 12.155534726848066, 11.041496306868257, 9.713604700334507, 8.2115869193648, 6.583908106889728, 4.885731271805919, 3.176934103462646, 1.5200468545449113, -0.022071253701027197, -1.3889079966609077, -2.5247429563386956, -3.3810080179060535, -3.918610163181828, -4.1096458092223935, -3.9387786485288623, -3.4042910336463246, -2.518609933068438, -1.3079700627921127, 0.18821500314199183, 1.918501889842779, 3.8215049054195593, 5.828008162940005, 7.8632258966908815, 9.849650659343663, 11.710957247903442, 13.374294642402823, 14.772642573321047, 15.847718128224864, 16.553720741343053, 16.857892355459967, 16.74126896159892, 16.199927678382814, 15.24667845849045, 13.908978811954588, 12.22738596070776, 10.254507242174999, 8.054061505938272, 5.696936652395158, 3.2581774863826785, 0.8145204685109094, -1.5580850505971484, -3.7882276896590543, -5.81167362087742, -7.573458811308658, -9.029940678267646, -10.150371175516742, -10.917559783233253, -11.328136431626527, -11.392704680217935, -11.13461352846928, -10.588352452292822, -9.797852398187256, -8.814744869682825, -7.695440610436388, -6.498439533643743, -5.281900614670189, -4.101387153854052, -3.007279092022962, -2.042792767694573, -1.242491351149802, -0.6311989028016641, -0.22329121721490855, -0.022580565220845242, -0.022683299498706358, -0.20785423892224406, -0.5542360653090869, -1.0313874733523456, -1.6040742545037714, -2.234358286274498, -2.88352956438885, -3.513961808096286, -4.09095411785399, -4.584573815009715, -4.970694794436486, -5.231810332479686, -5.357675969266552, -5.345730398153208, -5.200533392301476, -4.933099341543145, -4.560104314293297, -4.1028681072499245, -3.585769097892349, -3.0348041988893595, -2.4761974865348986, -1.9349834357154023, -1.433671494718485, -0.9912137359617386, -0.6221762455337234, -0.33612571152120974, -0.1374535498184848, -0.025447425430934794, 0.005413356096057585, -0.0351598846065028, -0.13412751781739904, -0.27602366312333915, -0.4439738184744584, -0.6209563403457834, -0.7907653201963092, -0.9388343599217676, -1.0530503760601717, -1.124646710618718, -1.1483643780276782, -1.1224689055813892, -1.048730268832345, -0.9323865964065007, -0.7813798939365382, -0.605608481159569, -0.4162359930824553, -0.2250307282371145, -0.043357484247115594, 0.11862966982262142, 0.2526124285768812, 0.35258393276085365, 0.415272152272581, 0.4403074855270462, 0.4301710484745034, 0.3899482151687647, 0.3269244775155065, 0.2500351302735209, 0.16919683459104434, 0.0945609073682182, 0.03578796802535551, 0.0013491603049243083, -0.002112932214187414, 0.029723716366754704, 0.09854682541123977, 0.2032204850309285, 0.33979210463204096, 0.5018277109233837, 0.6807610503994027, 0.8663411485668382, 1.0472984123086382, 1.2123535054488626, 1.350762638989224, 1.4528902321794088, 1.510937068597622, 1.5198705418478726, 1.4774348960892114, 1.3841965807250702, 1.243691611874106, 1.0626107333407766, 0.8500002849177914, 0.6166274226188424, 0.37446912397567017, 0.13618172169160966, -0.08601475891154006, -0.2811278635124026, -0.43999218106344656, -0.5558261276010198, -0.624816250487077, -0.6463354219123958, -0.6229523479193029, -0.5603284089342667, -0.46684300171540205, -0.35299934875359235, -0.23072483338056377, -0.11260314108451361, -0.010954060472837078, 0.06305501461298404, 0.1002169332767881, 0.09399781479960481, 0.041099005515536864, -0.058193618039836005, -0.19988381041984468, -0.3763801511574936, -0.5768566152991351, -0.7878189991222776, -0.9938823603125974, -1.1787585655999098, -1.326218227886408, -1.4211056452700364, -1.450398372393556, -1.4042348501329707, -1.2765471184652903, -1.0656065926020204, -0.7744114550151985, -0.410729171508342, 0.013254404715306459, 0.4813757902002197, 0.9742003377807681, 1.4702509187864448, 1.9470359346462993, 2.382066493203251, 2.754118564644706, 3.0449597721999466, 3.2399812369609533, 3.328777638954459, 3.305912477047144, 3.1719451193085266, 2.93278683603468, 2.599154683487804, 2.186225740907203, 1.7133947661037685, 1.2025386607930442, 0.6766673420563999, 0.15887843073666066, -0.3285896394904534, -0.7659976277460496, -1.1371531440965563, -1.4300801326925352, -1.6375150915445897, -1.7572741540499766, -1.7921120393891792, -1.7492984281680968, -1.6400402154160132, -1.4784846671571805, -1.2805825044592483, -1.0629440084811694, -0.8417326628693351, -0.6314202696835968, -0.4438057746075511, -0.28731076281007456, -0.16654301609332411, -0.08210540283129014, -0.030807970162127704, -0.006216468613101124, 0.0005099076050733795, -0.00046941016524970175, 0.001054446766259553, 0.013983553009279167, 0.04456999067963574, 0.09519223684899471, 0.16333511402312, 0.24087121096258166, 0.313787972637671, 0.362285731540249, 0.3612968348843578, 0.2815135746577245, 0.09101829198108287, -0.2430167871956136, -0.7523347285651275, -1.4652840671817229, -2.4043239640707497, -3.584102319953066, -5.0095809363121715, -6.674372191188028, -8.559781006578973, -10.634549947564969, -12.854907142268962, -15.165372748668965, -17.501149776502256, -19.790058254011598, -21.95476230302655, -23.91601731419979, -25.59784442771227, -26.92995836221021, -27.850339547197255, -28.308743796413733, -28.27178505851559, -27.723125374561224, -26.663832685891634, -25.113454767898922, -23.111936511886846, -20.716210668381425, -17.997310204661716, -15.038080526949674, -11.931153137225278, -8.773490102934783, -5.661905864063219, -2.6892041324260494, 0.05957625921512986, 2.511071377497608, 4.606454580268506, 6.303763202541532, 7.580010314922703, 8.430721808801175, 8.869061064072783, 8.924828951180702, 8.643290601359906, 8.080696964878609, 7.300525281030689, 6.370283752753885, 5.358526357110463, 4.329752999333371, 3.340976930716421, 2.439420927745241, 1.6608838331270124, 1.0276849024015913, 0.548386064652525, 0.21862543024108808, 0.022655446289622013, -0.06480526118848333, -0.07575749696558952, -0.0456882687398731, -0.010247553039980704, -0.002077283812510102, -0.04782501825299932, -0.16566677182617265, -0.36361917010464956, -0.6386307357441532, -0.9765091386095731, -1.3528357935663677, -1.735051081823143, -2.084949372364417, -2.3617676372646037, -2.525905908283972, -2.54321905308857, -2.3883753382385873, -2.048022734359885, -1.5236715254455984, -0.8338915484712656, -0.01458802561370742, 0.8814581998106339, 1.7860474015103711, 2.61861845371799, 3.2905078769586407, 3.7097060465015086, 3.7864681949138013, 3.4402020235461244, 2.6052903682304644, 1.2365591267867109, -0.6853896864751239, -3.1491087371056055, -6.110198320004107, -9.490308990433341, -13.17740438244993, -17.02795009266313, -20.871474478903533, -24.51628330538674, -27.756798794843622, -30.383171386651476, -32.19002076203961, -32.98567475203832, -32.602218334113715, -30.906149121591042, -27.804846885980275, -23.25274875740429, -17.256676665651636, -9.878715934660445, -1.2352651796116334, 8.50462506301604, 19.123492335586224, 30.365051950491267, 41.94162812287094, 53.54244180098579, 64.84568025847086, 75.53727560683006, 85.31772207823998, 93.91029631016997, 101.07367035889321, 106.62072660172258, 110.41662482030969, 112.3797884911932, 112.48761909390663, 110.78683016143067, 107.37997696821554, 102.41714845135928, 96.09266783832817, 88.64489893629616, 80.33631826825116, 71.44060321925129, 62.23476758595281, 52.99355895868505, 43.97256497199465, 35.39854906692357, 27.464196392846784, 20.324714488699403, 14.091164699915362, 8.829187458466198, 4.5606303557883825, 1.2664507822870654, -1.1095462550372417, -2.6546254502601943, -3.4801272031606274, -3.7142253677179777, -3.493858680667619, -2.957036176404956, -2.23589763433612, -1.4506323126329481, -0.704245050951278, -0.07889947099215541, 0.36632087199736696, 0.5962661583418257, 0.5990366604550196, 0.3841113239171999, -0.020540316880048412, -0.5723491318967253, -1.2185065614152897, -1.9004372536018634, -2.5583862085409117, -3.1360315384232065, -3.5839823001360935, -3.862690320834564, -3.9447947866963706, -3.816614932810918, -3.4781298773131293, -2.9424664987476343, -2.2347072451477064, -1.3895769104642701, -0.4489076650231336, 0.5408838115808086, 1.5317287216523556, 2.4776500253786224, 3.336777722956961, 4.073099536694336, 4.658396733248527, 5.074532761921275, 5.312902609199137, 5.373909099830677, 5.2666893466101, 5.008975998401692, 4.624501329869889, 4.1409821557113125, 3.5885869895606546, 2.998599735433103, 2.400922971459005, 1.8224649379156113, 1.2861078344690855, 0.8099704288934584, 0.4066280226683951, 0.0830215901696978, -0.1592393854318748, -0.32336072068347943, -0.41656765806259466, -0.44910837799159603, -0.4332073969883722, -0.3820348009162779, -0.30865520339560404, -0.2251538738232917, -0.14194995728187243, -0.06729838991606658, -0.0070193827289000985, 0.03554940243557277, 0.059418582646654665, 0.06564695659761852, 0.05689464452326278, 0.03693082296166436, 0.01011374613833948, -0.019140051729308393, -0.04678761041030702, -0.06949571297917051, -0.08489298739440944, -0.09172068646318468, -0.0897927638112384, -0.07988685608487446, -0.06357310572991921, -0.042964524334831417, -0.020416191754044584, 0.001735618259461232, 0.021413002499621674, 0.03702545459930402, 0.04758001791437837, 0.05271454510374542, 0.05268461770351869, 0.04830799011082166, 0.04078344182651181, 0.03150481225988348, 0.021885750336309615, 0.0131937084339611, 0.0063779718467493335, 0.001971924436642466, 5.9304459816632354e-05, 0.0002963212952326287, 0.001993667924221332, 0.004257720703535574, 0.006166720027975573, 0.006965169870942559, 0.006256280517912555, 0.004165988748687463, 0.0014603545068064747, -0.00039911917179574606, 0.0007218713489749657, 0.007528742732548906, 0.023120719570937365, 0.05075051056653193, 0.09353420776551417, 0.15413017609387633, 0.2344228913895117, 0.3352768827219267, 0.45629747884658345, 0.5956528978326211, 0.7500324159428301, 0.9148494828733984, 1.0843290282590918, 1.2517003484215978, 1.4096000567099913, 1.5507863760139127, 1.6683717159386766, 1.7561482111212197, 1.8091052734150883, 1.8241707201122428, 1.8000923558602264, 1.737427797979335, 1.6386852578926876, 1.5085528203337935, 1.3532112302513712, 1.1798564067582225, 0.9963852318282241, 0.811120734074351, 0.6319628464193363, 0.4658668754898976, 0.31852852325511405, 0.1941495292282168, 0.0950825995172058, 0.02179661761001439, -0.026978242466282523, -0.054014960037233696, -0.06327192665760717, -0.059435172412116336, -0.047422716204102724, -0.03190158336068061, -0.016826319103481594, -0.0050597258266997696, 0.0018847047545820098, 0.003961231480278211, 0.0025583307441705513, 0.0003103402084860503, 0.0007695572364039502, 0.00796833196211376, 0.025911664942071616, 0.05803890847611107, 0.10671026113402868, 0.17281069639441685, 0.2554428561972338, 0.3517525227808812, 0.45697466996252234, 0.564825387018262, 0.6678483230737636, 0.7579106181071725, 0.8269484887416741, 0.8680309147522267, 0.8758606653385386, 0.8473039648814799, 0.7820110313202899, 0.6830585231488249, 0.556576466575036, 0.41135507452992137, 0.2583990361376565, 0.11024751564300775, -0.020521111201679917, -0.12262428855077008, -0.18737553801127535, -0.21010035478979489, -0.19153984646354646, -0.1387963322416978, -0.0659628228398697, 0.005590403252368648, 0.047605051032378484, 0.025821760467581792, -0.09866308838174043, -0.3672544199041365, -0.8212206979050627, -1.4989322998131, -2.4332595467264446, -3.6500829005562863, -5.166172438700465, -6.987301239959768, -9.104107210336153, -11.47929195578396, -14.049225495666168, -16.726331551970926, -19.418740776909054, -22.098748416313565, -24.774831860127783], 'positive_zeros': ['0.30631676752128210527202595982324', '0.953279651893298734050298226696318', '1.28786942053371100008424776250320', '1.79595525762831313268118671784471', '1.96274365843339118862116095576891', '2.08425907450006956228066763648371', '2.53645489756928128075821024328528', '2.86754082881879396300246703029737', '2.97709438206567097364884155445052', '3.25572831647002704529776690324828', '3.41092448632297249398630390655589', '3.60886012544964603176212143468195', '3.69029952371709733739284118189060', '4.11481977160444074387543562783061', '4.56584503445334664662144746159009', '4.56684970062580303927838719419156', '5.05780752010583385045590106770866', '5.06582444282989457149768264811631', '5.26796861619405731763144706432794', '5.32040464985557127612995396669667', '5.89412080158017210107251601799114', '6.03087779086326366838430068011712', '6.19038164273225385999761287710821', '6.41652300670887493039467820259617', '6.44464758554663210699469466173291', '6.56289709165895704729721456629358', '7.00173243198180024961901028183030', '7.14672383282260545714046161218593', '7.46101228642419869243027143209970', '7.79830742212353896298134328371824', '7.80217009315196699771784659323771', '8.210641440477554150810095754989055', '8.222270959542748869425981394801216', '8.485165806935015430826822184027035', '8.672928982456712744637489878632693', '8.688452569833422037957568778834751', '9.002945506606027377132293083016586', '9.186398665007881909931929701587549', '9.250056929534238012382171164264388', '9.477105475227032730908261940951794'], 'prelabel': '8-1805e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.7964453854679796, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e4-0', 'trace_hash': 653070537207434048, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.30631676752128210527202595982', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.953279651893298734050298226696', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.28786942053371100008424776250', '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': 43153.62199339725, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 10614726900625, 'conductor_radical': 95, 'degree': 8, 'dirichlet_coefficients': [1, 1, 3, -1, 4, 3, -4, 2, -1, 4, -2, -3, 7, -4, 12, 3, -1, -1, 0, -4, -12, -2, 2, 6, 10, 7, -11, 4, -1, 12, 0, -2, -6, -1, -16, 1, -2, 0, 21, 8, -8, -12, 1, 2, -4, 2, -12, 9, -11, 10, -3, -7, -5, -11, -8, -8, 0, -1, -5, -12, 0, 0, 4, 10, 28, -6, 4, 1, 6, -16, 20, -2, -20, -2, 30, 0, 8, 21, 17, 12, -1, -8, 1, 12, -4, 1, -3, -4, 11, -4, -28, -2, 0, -12, 0, -6, 1, -11, 2, -10], 'euler11': [1, 2, 19, 47, 179, 517, 2299, 2662, 14641], 'euler13': [1, -7, 59, -250, 1180, -3250, 9971, -15379, 28561], 'euler17': [1, 1, 38, 68, 822, 1156, 10982, 4913, 83521], 'euler19': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler2': [1, -1, 2, -5, 6, -10, 8, -8, 16], 'euler23': [1, -2, 75, -145, 2398, -3335, 39675, -24334, 279841], 'euler29': [1, 1, 53, 281, 1251, 8149, 44573, 24389, 707281], 'euler3': [1, -3, 10, -22, 44, -66, 90, -81, 81], 'euler31': [1, 0, 57, -5, 2675, -155, 54777, 0, 923521], 'euler37': [1, 2, 117, 99, 5802, 3663, 160173, 101306, 1874161], 'euler41': [1, 8, 77, 13, 714, 533, 129437, 551368, 2825761], 'euler43': [1, -1, 74, 68, 3460, 2924, 136826, -79507, 3418801], 'euler47': [1, 12, 133, 763, 5768, 35861, 293797, 1245876, 4879681], 'euler5': [1, -4, 6, -4, 1, 0, 0, 0, 0], 'euler53': [1, 5, 126, 568, 7684, 30104, 353934, 744385, 7890481], 'euler59': [1, 5, 111, 385, 8011, 22715, 386391, 1026895, 12117361], 'euler61': [1, 0, 114, 88, 9515, 5368, 424194, 0, 13845841], 'euler67': [1, -4, 232, -828, 22174, -55476, 1041448, -1203052, 20151121], 'euler7': [1, 4, 27, 69, 272, 483, 1323, 1372, 2401], 'euler71': [1, -20, 375, -4165, 42925, -295715, 1890375, -7158220, 25411681], 'euler73': [1, 20, 387, 4161, 44118, 303753, 2062323, 7780340, 28398241], 'euler79': [1, -17, 388, -4009, 48638, -316711, 2421508, -8381663, 38950081], 'euler83': [1, -1, 270, -194, 31408, -16102, 1860030, -571787, 47458321], 'euler89': [1, -11, 266, -1549, 27690, -137861, 2106986, -7754659, 62742241], 'euler97': [1, -1, 122, -1096, 12292, -106312, 1147898, -912673, 88529281], 'euler_factors': [[1, -1, 2, -5, 6, -10, 8, -8, 16], [1, -3, 10, -22, 44, -66, 90, -81, 81], [1, -4, 6, -4, 1, 0, 0, 0, 0], [1, 4, 27, 69, 272, 483, 1323, 1372, 2401], [1, 2, 19, 47, 179, 517, 2299, 2662, 14641], [1, -7, 59, -250, 1180, -3250, 9971, -15379, 28561], [1, 1, 38, 68, 822, 1156, 10982, 4913, 83521], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -2, 75, -145, 2398, -3335, 39675, -24334, 279841], [1, 1, 53, 281, 1251, 8149, 44573, 24389, 707281], [1, 0, 57, -5, 2675, -155, 54777, 0, 923521], [1, 2, 117, 99, 5802, 3663, 160173, 101306, 1874161], [1, 8, 77, 13, 714, 533, 129437, 551368, 2825761], [1, -1, 74, 68, 3460, 2924, 136826, -79507, 3418801], [1, 12, 133, 763, 5768, 35861, 293797, 1245876, 4879681], [1, 5, 126, 568, 7684, 30104, 353934, 744385, 7890481], [1, 5, 111, 385, 8011, 22715, 386391, 1026895, 12117361], [1, 0, 114, 88, 9515, 5368, 424194, 0, 13845841], [1, -4, 232, -828, 22174, -55476, 1041448, -1203052, 20151121], [1, -20, 375, -4165, 42925, -295715, 1890375, -7158220, 25411681], [1, 20, 387, 4161, 44118, 303753, 2062323, 7780340, 28398241], [1, -17, 388, -4009, 48638, -316711, 2421508, -8381663, 38950081], [1, -1, 270, -194, 31408, -16102, 1860030, -571787, 47458321], [1, -11, 266, -1549, 27690, -137861, 2106986, -7754659, 62742241], [1, -1, 122, -1096, 12292, -106312, 1147898, -912673, 88529281]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1805/2/a/o'], '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': '8-1805e4-1.1-c1e4-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-1805e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.7964453854679796, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 653070537207434048, 'z1': {'__RealLiteral__': 0, 'data': '0.30631676752128210527202595982', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '388302634208324266037133861112,1208425522907897720608694121952,1632568443955140736537711557827,2276643760315575513194553271676', 'Lhash_array': ['388302634208324266037133861112', '1208425522907897720608694121952', '1632568443955140736537711557827', '2276643760315575513194553271676'], 'label': '8-1805e4-1.1-c1e4-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1805/2/a/o'}