Lfunction data - 12-29e6-1.1-c1e6-0-0

Formats: - HTML - YAML - JSON - 2024-04-28T05:23:48.252645

• 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': '3121709108871348086775702555917,3526534136693739926306137982643,4772212383493657620209068421081,5652960686393312569154862963081,5931318211444425057158254766132,6450645064099056945150443910685', 'a10': -2, 'a2': -2, 'a3': -5, 'a4': 2, 'a5': 1, 'a6': 10, 'a7': 1, 'a8': -7, 'a9': 17, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.00015418801928325165, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[29, [1, -6, -13, 316, -377, -5046, 24389]]], 'bad_primes': [29], 'central_character': '29.1', 'coefficient_field': '1.1.1.1', 'conductor': 594823321, 'conductor_radical': 29, 'degree': 12, 'euler_factors': [[1, 2, 2, 7, 10, 13, 27, 26, 40, 56, 32, 64, 64], [1, 5, 8, 4, 3, 3, -8, 9, 27, 108, 648, 1215, 729], [1, -1, 10, -12, 81, -91, 456, -455, 2025, -1500, 6250, -3125, 15625], [1, -1, 8, -22, 127, -169, 848, -1183, 6223, -7546, 19208, -16807, 117649], [1, 11, 68, 354, 1683, 6723, 23296, 73953, 203643, 471174, 995588, 1771561, 1771561], [1, 5, 12, -40, -111, 875, 6308, 11375, -18759, -87880, 342732, 1856465, 4826809], [1, -8, 110, -632, 4831, -20736, 110564, -352512, 1396159, -3105016, 9187310, -11358856, 24137569], [1, -1, -18, 156, 67, -1127, 9612, -21413, 24187, 1070004, -2345778, -2476099, 47045881], [1, 7, 26, 84, 431, -175, -12020, -4025, 227999, 1022028, 7275866, 45054401, 148035889], [1, -6, -13, 316, -377, -5046, 24389], [1, -5, -34, 388, -1649, -7283, 109220, -225773, -1584689, 11558908, -31399714, -143145755, 887503681], [1, -11, 42, -328, 4049, -22869, 100360, -846153, 5543081, -16614184, 78714762, -762783527, 2565726409], [1, -20, 394, -4596, 50223, -397592, 2931564, -16301272, 84424863, -316760916, 1113349834, -2317124020, 4750104241], [1, -13, 42, -50, 251, 17703, -219260, 761229, 464099, -3975350, 143589642, -1911109759, 6321363049], [1, -11, 18, 410, -2409, -12679, 224300, -595913, -5321481, 42567430, 87834258, -2522795077, 10779215329], [1, -3, -58, 648, -431, -23629, 179088, -1252337, -1210679, 96472296, -457647898, -1254586479, 22164361129], [1, 56, 1642, 32088, 460455, 5071808, 43842828, 299236672, 1602843855, 6590201352, 19896706762, 40035760744, 42180533641], [1, -3, -24, -74, 4633, -24883, -67236, -1517863, 17239393, -16796594, -332300184, -2533788903, 51520374361], [1, -19, 168, -904, 1419, 3983, 31592, 266861, 6369891, -271889752, 3385388328, -25652377033, 90458382169], [1, -21, 118, 546, -4409, -107373, 1690660, -7623483, -22225769, 195419406, 2998578358, -37888816371, 128100283921], [1, 25, 300, 3400, 39069, 348943, 2806700, 25472839, 208198701, 1322657800, 8519472300, 51826789825, 151334226289], [1, 9, 2, 210, -977, -72339, -812260, -5714781, -6097457, 103538190, 77900162, 27693507591, 243087455521], [1, -17, 136, -1776, 27843, -251219, 1969848, -20851177, 191810427, -1015493712, 6454331656, -66963690931, 326940373369], [1, -7, 30, 532, 7389, -23261, 663944, -2070229, 58528269, 375043508, 1882267230, -39088416143, 496981290961], [1, -1, 114, 382, 20669, 10611, 2196928, 1029267, 194474621, 348641086, 10092338034, -8587340257, 832972004929], [1, 29, 390, 3418, 16241, -40087, -1210448, -4048787, 165674441, 3521568818, 40583556390, 304792914529, 1061520150601], [1, -3, 74, 262, 12263, 50381, 152508, 5189243, 130098167, 286294474, 8328765194, -34778222229, 1194052296529], [1, 1, 104, 1782, 18059, 143225, 3120712, 15325075, 206757491, 2183026626, 13632278504, 14025517307, 1500730351849], [1, 9, -112, -2780, -10495, 175595, 3187836, 19139855, -124691095, -3600180620, -15809714032, 138476155941, 1677100110841], [1, 1, -70, 2666, -323, -65947, 4329648, -7452011, -4124387, 3846763402, -11413315270, 18424351793, 2081951752609]], 'euler_factors_factorization': [[[[1, 2, 2, 7, 10, 13, 27, 26, 40, 56, 32, 64, 64], 1]], [[[1, 5, 8, 4, 3, 3, -8, 9, 27, 108, 648, 1215, 729], 1]], [[[1, -1, 10, -12, 81, -91, 456, -455, 2025, -1500, 6250, -3125, 15625], 1]], [[[1, -1, 8, -22, 127, -169, 848, -1183, 6223, -7546, 19208, -16807, 117649], 1]], [[[1, 11, 68, 354, 1683, 6723, 23296, 73953, 203643, 471174, 995588, 1771561, 1771561], 1]], [[[1, 5, 12, -40, -111, 875, 6308, 11375, -18759, -87880, 342732, 1856465, 4826809], 1]], [[[1, -4, 47, -128, 799, -1156, 4913], 2]], [[[1, -1, -18, 156, 67, -1127, 9612, -21413, 24187, 1070004, -2345778, -2476099, 47045881], 1]], [[[1, 7, 26, 84, 431, -175, -12020, -4025, 227999, 1022028, 7275866, 45054401, 148035889], 1]], [[[1, -6, -13, 316, -377, -5046, 24389], 1]], [[[1, -5, -34, 388, -1649, -7283, 109220, -225773, -1584689, 11558908, -31399714, -143145755, 887503681], 1]], [[[1, -11, 42, -328, 4049, -22869, 100360, -846153, 5543081, -16614184, 78714762, -762783527, 2565726409], 1]], [[[1, -10, 147, -828, 6027, -16810, 68921], 2]], [[[1, -13, 42, -50, 251, 17703, -219260, 761229, 464099, -3975350, 143589642, -1911109759, 6321363049], 1]], [[[1, -11, 18, 410, -2409, -12679, 224300, -595913, -5321481, 42567430, 87834258, -2522795077, 10779215329], 1]], [[[1, -3, -58, 648, -431, -23629, 179088, -1252337, -1210679, 96472296, -457647898, -1254586479, 22164361129], 1]], [[[1, 28, 429, 4032, 25311, 97468, 205379], 2]], [[[1, -3, -24, -74, 4633, -24883, -67236, -1517863, 17239393, -16796594, -332300184, -2533788903, 51520374361], 1]], [[[1, -19, 168, -904, 1419, 3983, 31592, 266861, 6369891, -271889752, 3385388328, -25652377033, 90458382169], 1]], [[[1, -21, 118, 546, -4409, -107373, 1690660, -7623483, -22225769, 195419406, 2998578358, -37888816371, 128100283921], 1]], [[[1, 25, 300, 3400, 39069, 348943, 2806700, 25472839, 208198701, 1322657800, 8519472300, 51826789825, 151334226289], 1]], [[[1, 9, 2, 210, -977, -72339, -812260, -5714781, -6097457, 103538190, 77900162, 27693507591, 243087455521], 1]], [[[1, -17, 136, -1776, 27843, -251219, 1969848, -20851177, 191810427, -1015493712, 6454331656, -66963690931, 326940373369], 1]], [[[1, -7, 30, 532, 7389, -23261, 663944, -2070229, 58528269, 375043508, 1882267230, -39088416143, 496981290961], 1]], [[[1, -1, 114, 382, 20669, 10611, 2196928, 1029267, 194474621, 348641086, 10092338034, -8587340257, 832972004929], 1]], [[[1, 29, 390, 3418, 16241, -40087, -1210448, -4048787, 165674441, 3521568818, 40583556390, 304792914529, 1061520150601], 1]], [[[1, -3, 74, 262, 12263, 50381, 152508, 5189243, 130098167, 286294474, 8328765194, -34778222229, 1194052296529], 1]], [[[1, 1, 104, 1782, 18059, 143225, 3120712, 15325075, 206757491, 2183026626, 13632278504, 14025517307, 1500730351849], 1]], [[[1, 9, -112, -2780, -10495, 175595, 3187836, 19139855, -124691095, -3600180620, -15809714032, 138476155941, 1677100110841], 1]], [[[1, 1, -70, 2666, -323, -65947, 4329648, -7452011, -4124387, 3846763402, -11413315270, 18424351793, 2081951752609], 1]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 0, 'label': '12-29e6-1.1-c1e6-0-0', '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}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/29/2/d/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.029296875', 'prec': 37}, 'plot_values': [0.03191490629514787, 0.032265526567515614, 0.03265492229244334, 0.033126588011889266, 0.03372635391126483, 0.03450354785218641, 0.03551271378666806, 0.036805662318476616, 0.038400621270096275, 0.04030966473066459, 0.04254805307187493, 0.045133811469503106, 0.04808729396742081, 0.051434072483291446, 0.05521614135831767, 0.059484721329412515, 0.06429800223465468, 0.06972199156313663, 0.07583146566644774, 0.08270948807333867, 0.0904429975294801, 0.09912672828970878, 0.10886515708307525, 0.119773102708451, 0.1319763039809079, 0.1456124027655449, 0.16083307046698586, 0.17780374353580283, 0.19670381120168992, 0.21772709356927428, 0.2410822107627739, 0.26699203223266665, 0.2956908347624767, 0.3274253744604684, 0.3624547801356908, 0.401049458077797, 0.443489625254977, 0.4900622059949751, 0.5410539917796247, 0.5967507753354363, 0.6574344881648908, 0.7233786716132496, 0.7948432804820824, 0.872065909737607, 0.9552447380443396, 1.044536330201516, 1.1400492693411504, 1.241834628378422, 1.3498758105805233, 1.4640730448658468, 1.5842153118021958, 1.7099785936936773, 1.8409179851701736, 1.976455863721604, 2.1158706102862146, 2.2582797083114956, 2.402608597817773, 2.547598484668785, 2.691807353476119, 2.833608097843535, 2.9711902031880135, 3.1025595101870485, 3.2255298228382037, 3.337756331288536, 3.4367650530685934, 3.5199832970290332, 3.584777394478447, 3.6284967539024993, 3.6485254067550508, 3.6423519685025068, 3.607642486320328, 3.542319042513715, 3.444645278116279, 3.3133261119499466, 3.147631954856002, 2.947479012391211, 2.7135209018247464, 2.4472457729763737, 2.151069081641277, 1.8284367357050477, 1.4839496392775873, 1.1233612885306308, 0.7535920642024382, 0.38273882780312596, 0.02005824409381908, -0.324063524615291, -0.6381633144037829, -0.9099098994173077, -1.126295043796811, -1.2738428045009862, -1.3388579275003076, -1.3077195486250388, -1.167267397185258, -0.905214705640902, -0.5105409516291269, 0.02610184880315744, 0.711974019389671, 1.5517874264909652, 2.5471229530985915, 3.6961282789075747, 4.993239451465357, 6.428925145855684, 7.989500632888581, 9.656956388413052, 11.408752776100991, 13.218159052405792, 15.054598038438538, 16.88404678609253, 18.66955972642765, 20.371886920685707, 21.950241596765423, 23.363418466691545, 24.57085082481811, 25.533683365271163, 26.21587981022979, 26.58542448344051, 26.615795678597063, 26.286950737896458, 25.586185074861962, 24.508897477284247, 23.059176322545557, 21.250372756462692, 19.10587700803983, 16.65845855243467, 13.949582990004195, 11.028625613790828, 7.951817290978433, 4.781130592019793, 1.5832178823379968, -1.5731064397989512, -4.619045621850297, -7.487851401516496, -10.116848838520744, -12.44933943511729, -14.436447566603542, -16.03918871242145, -17.229868812945114, -17.993024248212155, -18.325955617488685, -18.23892708927902, -17.755202257082, -16.910036138597505, -15.749230207631463, -14.327365069401967, -12.705704296034058, -10.949961545234302, -9.12806455917419, -7.3070787978885505, -5.5504760701519755, -3.915709979218673, -2.4520745296931037, -1.1989572761776532, -0.18450030655306224, 0.5753827473495859, 1.077233264889377, 1.3296588183715, 1.3523955785692396, 1.1748957668000672, 0.8345129139826075, 0.3741504473453401, -0.16024190605017896, -0.7222161607478541, -1.2673178122802917, -1.75541324419803, -2.152792384978993, -2.4337511073821343, -2.5816166745179174, -2.589234063039346, -2.458894868984334, -2.2017473666742795, -1.8366871319930476, -1.388605988533871, -0.8864596561339895, -0.3612119508327776, 0.15625424464305007, 0.6371924565700562, 1.0570284333858402, 1.3967179869731456, 1.6436250614668138, 1.7919572320825439, 1.842715741253095, 1.8032819536890614, 1.6867340527400907, 1.5101330124366739, 1.2928297372836655, 1.0548203151870907, 0.8151658481835101, 0.5906351441904752, 0.39462087014097097, 0.23611535864344493, 0.11937822972362619, 0.044116710755932056, 0.006068316246363553, -0.0020856008836290384, 0.010418294003289431, 0.03370726443879079, 0.05857445082540929, 0.07760720359124777, 0.08601892239384734, 0.08210071571963408, 0.06724752441209544, 0.04550039949675705, 0.0226533732792469, 0.005025941518902877, -0.001970364660079633, 0.004682909634141286, 0.024231431252725113, 0.05107424284355485, 0.07417534461779836, 0.07706982052838456, 0.03853299249334731, -0.06608306537262404, -0.262909698777262, -0.5770993297050685, -1.0300690107989972, -1.6366817356832715, -2.4026207755546696, -3.322306174277665, -4.377837441136573, -5.538532410079197, -6.761510341273518, -7.993419645532617, -9.173224010865908, -10.236250786930585, -11.119802389384505, -11.767187423644266, -12.131973345230982, -12.182083076102408, -11.903105438475043, -11.300950814304173, -10.40381312217186, -9.259497579461852, -7.932269449301708, -6.498857200863165, -5.0433614072484, -3.651583752821049, -2.4049673950681525, -1.3734210912466087, -0.6100060965125421, -0.14713348043879068, 0.0057142663836404345, -0.1374849950363586, -0.5407383050503616, -1.1494631882103603, -1.8954420538344805, -2.702747576598477, -3.4941455341058103, -4.1977288308767555, -4.753798094702292, -5.119087984449343, -5.269356468100483, -5.200337174135235, -4.926861232204436, -4.4806386695862965, -3.9070813154775155, -3.2586883660141304, -2.5889410958809984, -1.9469134200924423, -1.372750648379115, -0.894544665432347, -0.5267336172837684, -0.2695651015525124, -0.11100000420802492, -0.030183021201408054, -0.0017878645218807727, -0.0006226343008764548, -0.0058446812627761646, -0.004211018091053935, 0.00823301768824978, 0.02645228349084178, 0.03880371383824718, 0.03132049586266923, -0.00654874058688365, -0.07540638103876159, -0.1594732833580394, -0.22122567117278463, -0.19804274229022034, -0.0016885875011514145, 0.4788555952930373, 1.3711679829307675, 2.8097676969606034, 4.923613798387348, 7.821614418531935, 11.577912776593244, 16.220389205616552, 21.71969470246284, 27.98147536998207, 34.84338667553993, 42.07740934872726, 49.400810953657874, 56.50136115310549, 63.05134313149147, 68.72568396923369, 73.2234943442394, 76.28928213136054, 77.73753843655048, 77.48434237259062, 75.5396398480279, 72.00162816406802, 67.05026383885982, 60.93529713850393, 53.96392197307708, 46.48964696895619, 38.87005790820338, 31.438772353756193, 24.485707437559284, 18.24184590117956, 12.870643474322973, 8.465011623374902, 5.041632372040502, 2.549023172560464, 0.8820460806922056, -0.10098585261092911, -0.5603767249517863, -0.6582570656474875, -0.5437653546660396, -0.3409370225974826, -0.14127180590854335, -0.001238312607121359, 0.05572389910828591, 0.0336095831846075, -0.04416994252846446, -0.14407292615855538, -0.23148266240816184, -0.2782785425490273, -0.2680456204092232, -0.19845914362409334, -0.0806503866100803, 0.06389164059975663, 0.2081582620465452, 0.325270656378675, 0.3939205618666711, 0.40262032230736156, 0.352037439907974, 0.2551541340290156, 0.13524397235411378, 0.021977827251940998, -0.0537467812179932, -0.06529034527053064, 0.0051329812392502455, 0.16312038690023153, 0.40051269412591456, 0.6958945420867403, 1.0174030805595564, 1.328175112178117, 1.5915222751014866, 1.7759293216544905, 1.8594497452981982, 1.8327545113197556, 1.7007596805862166, 1.482688515259223, 1.2075353015656862, 0.9090514937116366, 0.6206558386161699, 0.37062465850045895, 0.1783141390005461, 0.05177656351796704, -0.01300418660875444, -0.03009584644549057, -0.019817386544769465, -0.003981725616989744, -0.0009886833164019907, -0.021542119953300867, -0.06581891439969033, -0.12284240078527046, -0.17219304171483726, -0.1877929842613626, -0.14315074933445893, -0.017215176984150583, 0.20013082935272225, 0.504127100265169, 0.8735589173440781, 1.2720082718042764, 1.6520991340240758, 1.9625093363344681, 2.155651504761606, 2.195637796883924, 2.0652678743359987, 1.7707005697146532, 1.3429283689308136, 0.835273800326, 0.31628414592185905, -0.13952341266725554, -0.4623685781097171, -0.5981175946378499, -0.5177907971301006, -0.22355252486497437, 0.2502973286035948, 0.8406522709883669, 1.4630276725871252, 2.0223571684476407, 2.4265741254654962, 2.602506983755156, 2.505783716595513, 2.126961525444495, 1.4935250597638114, 0.6669829928914468, -0.2642339418919583, -1.19594047379558, -2.025053828911188, -2.6639123120904618, -3.0514246438801873, -3.1602617371658113, -2.999513542973743, -2.6129226914440578, -2.070151231469631, -1.4545881066208162, -0.8501867771766455, -0.3291753117136745, 0.05758391199085945, 0.2865182751977422, 0.36229629316583767, 0.31346717080833064, 0.1843698832901618, 0.025049271709487942, -0.11888962584402084, -0.21476389697920367, -0.24794694730562153, -0.22242544912578055, -0.15719004825049054, -0.07948838669603203, -0.01655637299409521, 0.012271029609253697, 0.0010554764341583823, -0.04135494114053378, -0.09441946029259599, -0.1329689980824759, -0.13683344107194234, -0.10081778958556048, -0.041800800886955286, -0.000709937551037546, -0.03783913993831882, -0.22102930734046844, -0.6076506375553496, -1.2230946814233645, -2.0404917098145177, -2.965891110673607, -3.8329101640316563, -4.410129064543531, -4.423743839186098, -3.5968218842308475, -1.6941982533681963, 1.4299590477769744, 5.788164164956614, 11.227113448499518, 17.414224219446766, 23.85442722116829, 29.935786851797015, 34.994304010267875, 38.39400205539876, 39.613389987123206, 38.331836663932386, 34.50953033642583, 28.406800673518735, 20.56808220914716, 11.770176016483399, 2.9348756857824365, -4.984409779517081, -11.133964749511572, -14.895083641957626, -15.98324767770808, -14.503415136937711, -10.953444670339701, -6.17265270977603, -1.2363376677977371, 2.7003823249529395, 4.5742786138585885, 3.580639301458779, -0.6870321898104937, -8.145398395157029, -18.198910370196078, -29.79652191700361, -41.55230115932086, -51.9178458223631, -59.38671033089299, -62.71107405032711, -61.10660340875704, -54.36135477915336, -42.878017649356956, -27.643418730417004, -10.122072523858355, 7.918210798410443, 24.647684959230688, 38.41883672811305, 47.96625501462964, 52.55428934540514, 52.05562793800653, 46.960875530621465, 38.32010927145576, 27.543160341822535, 16.17997674442961, 5.703430102582851, -2.6870761621257286, -8.215384351394151, -10.618545829627594, -10.16301835792784, -7.566176250651122, -3.853606022172396, -0.17839618411561767, 2.3706592836105687, 2.9447101622672887, 1.065887211762976, -3.3061521762228483, -9.7775460321057, -17.589391726015613, -25.74287844590315, -33.16822004268081, -38.885283012945095, -42.14227768410608, -42.51693496531356, -39.965975098285185, -34.820498342113645, -27.726971619299608, -19.527500645794902, -11.13172838643454, -3.3925971068739424, 3.0003001246942693, 7.599030426700332, 10.240566920570132, 11.025512243761188, 10.264868457462446, 8.407032795312773, 5.9553200878116215, 3.3892367204586584, 1.0977761912408606, -0.6651760148056789, -1.7900336102086145, -2.295485079214037, -2.295191803337522, -1.9560286683393202, -1.4558985297224847, -0.9449436808010506, -0.523260970198205, -0.23510452984862623, -0.0767000754904664, -0.01332080660659965, 9.848425088655422e-07, -0.00033268533821534575, 0.0011600167131057297, -0.004160930217331027, -0.04330108335873036, -0.14934293157197215, -0.3470006082240923, -0.640348604716868, -1.006133540924534, -1.3947094194310394, -1.7386748975341149, -1.9679617880764555, -2.0289886773819457, -1.8988292517565233, -1.5933071316755893, -1.1670103197832695, -0.704303342514648, -0.3027516003023069, -0.05185338506698233, -0.011524544328000505, -0.19609638291035678, -0.5670051283243623, -1.0361808089631173, -1.4806317942550444, -1.7664649331508238, -1.773906353483309, -1.4210075183682465, -0.6822812810587574, 0.40162191946844, 1.726741475325817, 3.1461868882430624, 4.494291953813661, 5.611164296538412, 6.366428807096902, 6.678260654613643, 6.527966593101999, 5.9695216523778765, 5.106590850917392, 4.069119310168269, 2.9915005757274487, 1.9926169136614544, 1.1614263800224462, 0.5483104556969013, 0.15861027950003706, -0.03919917338379472, -0.09892862823591604, -0.08087834650506569, -0.03802722739161835, -0.006483559549199254, -0.0011172046041616065, -0.017139514342428056, -0.036646492739187124, -0.03766001850075609, -0.0029544057315537575, 0.07356383204101154, 0.18428482293174603, 0.3096603309738266, 0.42356127123090004, 0.5005664182948839, 0.5230718177609703, 0.4860764925421062, 0.39845992838566685, 0.28077335433498307, 0.16002978648163355, 0.06277624779240368, 0.00818721744346354, 0.0032350103519370376, 0.041592641504326795, 0.10572540456639497, 0.17160114495433584, 0.21494624880385046, 0.2177331795467921, 0.17337154758192228, 0.08763241058049422, -0.023462259176859315, -0.13796019556007674, -0.23350727826699613, -0.2928100612465347, -0.3080180345140715, -0.2820527087710025, -0.22663447174457424, -0.15821703818401234, -0.09311706523514837, -0.043245045723832753, -0.013516825965516106, -0.0015482065391286938, -1.5359741132996773e-05, -0.0005588903711468389, 0.0022924666432320613, 0.008673769910990465, 0.013458310889583098, 0.009135049286753405, -0.00920184421562006, -0.0383491262263547, -0.06308166023211359, -0.05585246109952612, 0.018957127212276884, 0.1968428064439999, 0.5021233976329176, 0.9365129420374149, 1.4705736374789922, 2.042451633105472, 2.5692946726443866, 2.9613570351505905, 3.139948306072575, 3.0567951305426058, 2.709745541848304, 2.1517732255937756, 1.4883222415570063, 0.8477888149238693, 0.3479789337655323, 0.06263791111593595, -0.006699032369108059, 0.05363794551812315, 0.07302904116542157, -0.17349111373563147, -0.9136059836194401, -2.316213238530491, -4.432577059134805, -7.152943976164781, -10.191272677133751, -13.113970050142, -15.408156050093698, -16.579339669640376, -16.2622490938124, -14.325557879222396, -10.949643992366548, -6.635744492393558, -2.1512115941465937, 1.5868876077373757, 3.677251695738371, 3.423228477506927, 0.5114212784476198, -4.863119552743695, -11.955981231858209, -19.530425914234947, -26.01414658166123, -29.744344335913993, -29.269238810432114, -23.612509633724517, -12.484701893092405, 3.594135520580437, 23.29138385560613, 44.6024963384739, 65.17152842789959, 82.63563214155018, 94.95785596582196, 100.72330992025368, 99.34995137262716, 91.20597897606217, 77.62026039860078, 60.57164225351284, 42.344998729105136, 25.186314612141704, 10.982026665660454, 1.0103159037459966, -4.213305368180345, -4.965694951538933, -2.179419032932498, 2.790461608459311, 8.442832693286734, 13.403499520533055, 16.658550629113567, 17.689099570315356, 16.492103812699707, 13.503760474954419, 9.451267451562478, 5.170260591503104, 1.4228172725753236, -1.2557298823137883, -2.6326303010547765, -2.7778480195753805, -2.0006437618223702, -0.7438380783016421, 0.5374669929578039, 1.4841814645025957, 1.9019755340829805, 1.7813522148549676, 1.2706815279885635, 0.6132927275837042, 0.06720806367392172, -0.1671511629146642, 0.0048601827112418235, 0.5554749123102114, 1.3502609095857658, 2.191502471591589, 2.8811162964525363, 3.2706455176488207, 3.2916546568640968, 2.9640576372957095, 2.382113321029819, 1.6846827769635393, 1.0170870827533698, 0.4887705229889485, 0.1517092214579596, -0.0009638127752845186, -0.020133827771615046, 0.023973106318337847, 0.06812363239603536, 0.07602119006878578, 0.045020359157240994, -0.0012524998777820508, -0.03011592498233485, -0.019591834201950237, 0.027438785603255696, 0.08146834804093732, 0.09838391188414158, 0.0412634410504956, -0.09631981822552863, -0.2760469253353318, -0.41994453690391814, -0.43947696830595073, -0.284880109237282, -0.00459354802755511, 0.2014257431082921, -0.04645196413654208, -1.2936813779271017, -4.186806879327607, -9.36326294876315, -17.308383023659555, -28.20205820089049, -41.794125757574754, -57.376447704108415, -73.80595439220832, -89.60022012103346, -103.10671374100232, -112.72095759025531, -117.15185705980453, -115.73155876265609, -108.47190384811213, -96.04892301649961, -79.71487156388315, -61.127026457338765, -42.12805926961219, -24.49727871831475, -9.65629762981223, 1.5005970139025113, 8.667217269527674, 12.090355985689472, 12.45702955278903, 10.728163187861266, 7.922211100841944, 4.935544623420508, 2.4202001704324942, 0.7279582922612796, -0.07923328490301622, -0.16354289266793348, 0.19049312901613577, 0.6792832331789729, 1.0611826445817323, 1.2026276505218343, 1.0869149852445024, 0.7904605677757408, 0.4317917882841859, 0.1222095411364817, -0.06878387113736933, -0.1272912251253583, -0.08769431912347345, -0.009699380362689103, 0.05061871579148627, 0.06399745953126927, 0.03693255940693501, 0.004447867380780888, 0.0102545340220197, 0.08200522678349723, 0.2120231596777088, 0.3519247077268822, 0.4239133419880778, 0.34615581783889215, 0.0650900110394346, -0.4155950904319495, -1.022379707745997, -1.6203127366615762, -2.0419926396380212, -2.1310921707558563, -1.7896012918612794, -1.0142032542542714, 0.09275063760418192, 1.339113867730165, 2.483577241666008, 3.292543301446675, 3.6009957434390545, 3.3625930130999713, 2.6613594214529486, 1.6918028711547435, 0.7120318650940551, -0.020620821798737685, -0.3160810669804367, -0.10232280336673184, 0.5580495195035188, 1.4870747433062743, 2.4394062894071173, 3.166952264493146, 3.4858895462747053, 3.330578617074515, 2.760562351782397, 1.9339404574669483, 1.0572738142059936, 0.3248262063821018, -0.13571376423558046, -0.2967883124499457, -0.23124170477636705, -0.0751885458660518, 0.028761531984360912, -0.011746430840035285, -0.20143134795030546, -0.4546212908288867, -0.6322776898107153, -0.6076915268158185, -0.33849428429906026, 0.08234410070948368, 0.42212793035176266, 0.3686028880679093, -0.3487702721819037, -1.8028119491031454, -3.715472639044074, -5.353617209437142, -5.5195123061734135, -2.670783005334835, 4.847974492154703, 18.486049339478633, 39.12714219600987, 66.75778444131791, 100.26136917000878, 137.48749341513485, 175.433193555582, 210.56474338470005, 239.2676005564858, 258.35065253182887, 265.6072654798944, 260.420432329502, 243.63091846679524, 217.2994754597754, 184.37797446410008, 148.27195600843146, 112.40226169283399, 79.80230201278044, 52.56169981362515, 31.661302022017622, 17.059748350504115, 7.929712837973526, 2.980885648730407, 0.7936372408924721, 0.10298617800310225, -0.00014875905576006485, -0.001647963619043569, -0.02080339844038012, 0.0498045306960603, 0.37504840294745007, 1.0315632635456475, 1.9249438856893724, 2.787524939663491, 3.2501922763940234, 2.960669773271888, 1.7036234146986367, -0.5172791820313382, -3.4535459390488747, -6.6518748372445, -9.551834650052502, -11.621724767367322, -12.499325048592425, -12.059790757792547, -10.43232683540972, -7.964211293533514, -5.137614853777123, -2.4552047653860662, -0.312700837010289, 1.0728732550338806, 1.6783027977004898, 1.6455833332898495, 1.2199167588329785, 0.6731089853790312, 0.2270808032416838, -0.008411758014754097, -0.044332734647333574, 0.017629191041349513, 0.03683739569231971, -0.10965738273935086, -0.48017351402902403, -1.0449967621868677, -1.6955473153478913, -2.2797529737431614, -2.65024779859413, -2.7096216312969794, -2.439086800345065, -1.9032403612540396, -1.230196780831334, -0.5738866961003424, -0.07031233589737589, 0.19904088293455147, 0.2247749299309706, 0.06391359419653721, -0.1829265302365497, -0.4045546252080359, -0.5129418887423823, -0.4682020526941449, -0.28607296826794315, -0.024536031143148465, 0.23903640562675427, 0.4333325239537865, 0.5143024071933769, 0.4770646629552775, 0.35531763010713885, 0.2034788879362881, 0.0754447901126836, 0.007074601638302227, 0.006733159140492375, 0.055970189494136464, 0.11943392796375567, 0.16083488595054776, 0.1579215437617459, 0.11041796564405311, 0.038557606070992054, -0.026638409290531437, -0.057482295806626074, -0.04246336294248345, 0.008076808087467413, 0.06606573687547444, 0.09851581332814902, 0.08440962630416718, 0.028764547032063145, -0.03259461411166776, -0.04045087906966045, 0.06848589436048906, 0.33483148923731965, 0.7510904627234746, 1.2507247171829692, 1.7134635883334268, 1.9863197585330519, 1.918045716627578, 1.3998823450995639, 0.4052049234242101, -0.9840122589283296, -2.5942901236872618, -4.19489440214642, -5.542885441359187, -6.431734358656768, -6.734530552027935, -6.436433275082081, -5.6330885234755685, -4.499882803256003, -3.246960364367686, -2.071692155256508, -1.120135319940992, -0.4646827199008083, -0.10046167963014016, 0.036057297633230734, 0.0363153951415235, -0.012073119446389032, -0.0487113959831637, -0.04992551787103867, -0.02370198499038535, 0.005541896613126152, 0.015012945672596922, -0.002859964263639212, -0.03639446719311693, -0.061302628728031876, -0.05327972888026091, -0.0006582660592346488, 0.0881073323398137, 0.18566787287465092, 0.2563958664593542, 0.2735636648452463, 0.23158597048473553, 0.14896582241003853, 0.060797295803341395, 0.002416758523225228, -0.01052263442671649, 0.0020563027992483306, -0.017126873656296365, -0.14587817325537292, -0.4520905278717047, -0.958894283238648, -1.6173073464710914, -2.299395220933925, -2.820493981672781, -2.986560731960826, -2.6546685422101786, -1.7888392054203712, -0.49291704182381635, 0.9956607984644311, 2.3619131629769554, 3.297567581033472, 3.592698027167319, 3.2083298043069086, 2.305119772194769, 1.2099460901860815, 0.3167405896655177, -0.03998401642692307, 0.29340964289379484, 1.20898002246146, 2.3300960116796063, 3.101675878137454, 2.9478796929896967, 1.4517292692585329, -1.4876964419092686, -5.565992048227236, -10.086701337826513, -14.109359337320337, -16.691605026243106, -17.13341340762532, -15.170849851148935, -11.068907081997388, -5.589294479728108, 0.17329534193788257, 5.093274712007062, 8.30360013171435, 9.403152257454707, 8.53338752794122, 6.306905124056096, 3.6014855333585944, 1.2514483095707656, -0.21034445572654972, -0.6860748722748018, -0.4817703144912282, -0.11403456034077603, -0.006110218034974842, -0.17413535948560704, -0.041598042221762124, 1.5296397193567197, 5.964178984757708, 14.496850380882474, 27.612885339195955, 44.58703123205587, 63.28919692947966, 80.36589783935942, 91.82339789342232, 93.94780176801432, 84.37797612067533, 62.9232554658985, 31.996439440291724, -3.493097657134824, -36.85127310967832, -60.87213851485815, -69.51950677210156, -59.32691064422717, -30.328826082197846, 13.648225156353316, 65.45515524965474, 115.84243396087317, 155.39081232979402, 176.42525099333892, 174.49154820385874, 149.21012186843782, 104.33805161233121, 47.04567356751372, -13.543060615962196, -68.32729186618977, -109.91457001857142, -133.81449030544377, -138.98144771718387, -127.69139215186459, -104.80504103166125, -76.27736283876422, -47.794066205370754, -23.733170614886262, -6.569587136825379, 3.2217917004539434, 6.822848091406518, 6.3513480081999605, 4.062282437577309, 1.7224728582107962, 0.2779214835307014, -0.15703270528835755, -0.04778902866845143, -0.04186750047256729, -0.5831163562455582, -1.6779182932153778, -2.8762229106548767, -3.4554463212429143, -2.7238183165024616, -0.3201100087407363, 3.593868854745585, 8.313495973780505, 12.75469382450217, 15.765368031976013, 16.51024213292781, 14.715865100172477, 10.757527648998696, 5.571362956970186, 0.4084993301251943, -3.5026169308033146, -5.297042809179899, -4.701210871477119, -2.0777395555381077, 1.702391371593606, 5.517980818684165, 8.31803117685398, 9.423948009384764, 8.682805109987402, 6.465866120766, 3.531068811475197, 0.7897022435135691, -0.9577345173549602, -1.238251007140074, -0.002048493055567551, 2.401408456984905, 5.343420287348138, 8.09492154258938, 10.026722997901258, 10.7942488744303, 10.364688798989192, 8.964681622020162, 6.983071201458459, 4.852958584503032, 2.947709284735684, 1.5080944106311132, 0.6000890246420094, 0.14861775065025282, 0.0036015312186756182, 0.006690218349890232, 0.039303367311279806, 0.04277070660805933, 0.01222021557627944, -0.0273178475676216, -0.04867602097139372, -0.04159713741100577, -0.016816797145064056, 0.003459011428589968, 0.0008384656030027486, -0.026926915924854463, -0.06267289035348672, -0.07736473611090496, -0.045168389038319885, 0.04174891941179843, 0.16711068147826108, 0.29480675508652116, 0.3820696508600055, 0.3967614861318861, 0.33251394129157946, 0.21476944010207105, 0.08934582795955864, 0.0036240276854226532, -0.012506126541902552, 0.04068388984864924, 0.1315221112866269, 0.20901627267510134, 0.22505050348917627, 0.1558632694975013, 0.013467800627393183, -0.15774615415695759, -0.2981936260706881, -0.35804611863808705, -0.32081401911281177, -0.2122307178660815, -0.08915426569636788, -0.010984015634522828, -0.003622891129111278, -0.031050047343157167, 0.01196522595193932, 0.279146320630661, 0.9250280022244696, 2.041550171281678, 3.601218089881472, 5.441136154127201, 7.280633781996359, 8.772687537588778, 9.582990726181151, 9.47759356542599, 8.403504331605808, 6.537715089313319, 4.222159549987465, 1.8729799769522453, -0.11781653133051412, -1.4716974204801674, -2.0827620117586436, -2.0354729737723862, -1.5592202654554215, -0.9363880145010384, -0.40674871540288404, -0.09808549562793449, -0.0022630931459198225, -0.001553062316476969, 0.06319424730516122, 0.30752622516490125, 0.7358007833021747, 1.2169935970371373, 1.515094462409905, 1.3662429272629846, 0.5741577776842388, -0.9059455715331142, -2.923222767629648, -5.145056949553932, -7.133386280852335, -8.470594451302947, -8.865670066128608, -8.227134215614136, -6.6876889591615, -4.571480909733716, -2.310293462778008, -0.32109890139254094, 1.1006342407938532, 1.8322773017921088, 1.924963284528761, 1.5612922000116554, 0.9871391498004977, 0.43486290404786476, 0.05303947003978576, -0.11392860845781778, -0.10704318378188526, -0.011998453438605427, 0.08538380898425096, 0.13223365796081737, 0.12038525807980087, 0.0746782865777524, 0.02886191558016841, 0.003785599986200885, -0.0010481081401029165, 0.0004947097531306834, -0.00032635657927984943, 0.009572787063527596, 0.06708720123694173, 0.21336103585939986, 0.45716807770794043, 0.7397922044250443, 0.9177100720537303, 0.7762741686400114, 0.08051149361851073, -1.3443605429249614, -3.5210126466435017, -6.255311760163283, -9.158949501288296, -11.725654066721892, -13.447539734123191, -13.94673567671864, -13.091285643705769, -11.066743650437223, -8.323720260272346, -5.439617322550484, -2.949977122591427, -1.2006014995735907, -0.2680356152019893, 0.02645130968797774, 0.008734639212460022, -0.01819093839700987, 0.07189161575640216, 0.16329784184047305, -0.0337173650452327, -0.7847285673222386, -2.0582046824678604, -3.2729722827007257, -3.1793687304648404, 0.02915870614586757, 8.34241735154831, 23.418650812774008, 46.01593034411618, 75.48465266662404, 109.48217504177519, 144.03216778022912, 174.11998227182983, 195.03961751554178, 203.17618453040185, 196.65324346836647, 175.78121729289683, 143.12182425559965, 103.22271074335558, 61.9812993375315, 25.07560132851051, -3.1450078339819103, -20.30860985928063, -26.233396328206556, -22.713056261095222, -12.961785104854123, -0.7282774534336776, 10.589502675866969, 18.593117360649362, 22.194725405206643, 21.58347374157143, 17.911177036232175, 12.752247371035589, 7.596872967682173, 3.4959206640147884, 0.9083634789685974, -0.25189527203604467, -0.42509632595012614, -0.15415425930035145, 0.12695419262314475, 0.20303600546816986, 0.07617834840415993, -0.11959781492903386, -0.23765564738455774, -0.21249282057523786, -0.09040835699595988, 0.003991671722973477, -0.05739337791256467, -0.32686071275251505, -0.7367431586802514, -1.1135488425180649, -1.2412572996396523, -0.9476914331081884, -0.18106268032143555, 0.952515483787376, 2.211910045940085, 3.2998320220931996, 3.956882019277894, 4.040591503002596, 3.565005023739634, 2.691146979907818, 1.6715252647933787, 0.7567225975021045, 0.11889094795367629, -0.18736505549001442, -0.22019805551249877, -0.10861154161078657, 0.008087931412744985, 0.03518005196486765, -0.050176948199339384, -0.20503188942701014, -0.3526620802026432, -0.4245803437287159, -0.3938950775796793, -0.2823288186216274, -0.14358509849175732, -0.03381538250150962, 0.016273554667918827, 0.01418876629248002, -0.0030988934546103595, 0.006068124267124141, 0.06172816348553973, 0.14866992347478616, 0.22332984630728456, 0.2398915291558521, 0.18379072395636672, 0.08654658945471516, 0.011121647639598721, 0.009823794258802658, 0.06960586372732785, 0.07025565849812969, -0.2140587081770823, -1.0475034279192241, -2.610412985680502, -4.858517251408085, -7.416055846248789, -9.556138386917437, -10.29904871641029, -8.629983401049053, -3.792978312293728, 4.41285412793615, 15.423994403345251, 27.901196063281493, 40.03889961291139, 49.9095382345811, 55.85525340863498, 56.86386364465287, 52.82016149531196, 44.59819153709832, 33.94098903271943, 22.859344357237315, 13.121079029541306, 5.889755171571047, 1.5461171399885314, -0.2763465671655318, -0.4669690162766343, -0.0731634159510245, 0.07950634873868023, -0.36856300598967945, -1.2659059835294564, -2.0986797100154013, -2.2726173124542517, -1.411753190007037, 0.4410596208319208, 2.7901445325153666, 4.831249795862418, 5.726551119463424, 4.913576420268898, 2.3143378354713167, -1.614902571973461, -6.001352654555578, -9.805472548756143, -12.138515739906259, -12.563959254875416, -11.174782845835034, -8.507565395758817, -5.34530983729358, -2.469036229879718, -0.4380680233943482, 0.5432806341429072, 0.6353312618198622, 0.22524716360738403, -0.2632219481612223, -0.5332211702332522, -0.49847057139717965, -0.2672994406549423, -0.03988779154523817, 0.021061548226095635, -0.11581503892334023, -0.332598845240433, -0.42547661586794294, -0.21600675300208716, 0.34689479852007915, 1.1423582955810863, 1.9138059804559255, 2.3747244001883123, 2.343774568924553, 1.8474370722947238, 1.1038283732972023, 0.4197691262333487, 0.04373584372006871, 0.03780193041908193, 0.23801980284541088, 0.34968284306187236, 0.1708618566659528, -0.1465146245056824, 0.07951738740797329, 2.044371993430292, 7.186978049801999, 16.693665918679134, 30.932790319816245, 49.00574466848599, 68.59384924560429, 86.222381324916, 97.99340638497851, 100.73936023700361, 92.96488883185697, 75.46168349750309, 51.41106087494148, 25.85581538471034, 4.61066200245891, -7.205439407792482, -6.594843754165124, 6.492218274083984, 29.071208535068433, 55.80276235862842, 80.32571563731749, 97.01426450468578, 102.34941752801697, 95.6570915510181, 79.10438191374087, 56.962179403514476, 34.35928665579977, 15.84111895280759, 4.132603310607092, -0.3568144494357687, 0.685274126448143, 4.2664021857062755, 7.206095427337007, 7.247228544691659, 3.6930872485237507, -2.5548192389323736, -9.476267221488769, -14.746006716001402, -16.62638613827383, -14.673572242923827, -9.887908745646147, -4.343390545224105, -0.48313827670985154, -0.30890481928110763, -4.711555163816837, -13.153150414691176, -23.83261410324976, -34.24314248869599, -41.9100914318677, -45.08018808032822, -43.17684540247928, -36.91092483926435, -27.944083041796425, -18.33691120353516, -9.95614113378932, -4.005089002810691, -0.80257633607912, 0.1383081017512883, -0.2076929831337224, -0.7660637908838945, -0.7136348658251814, 0.2979650181226632, 2.1043699927240085, 4.201636300800273, 5.99696414869135, 7.020706254259875, 7.059741480088704, 6.19025665790327, 4.725325495965491, 3.0997309093875205, 1.6862977908156869, 0.6957555683711318, 0.16085010045055265, -0.01960484861474253, -0.006307779785597145, 0.05360744278319412, 0.0757605295057801, 0.04865010126878493, 0.009073231371160277, 0.0029331016690296386, 0.05287153294543757, 0.14660419537221672, 0.2462591286180799, 0.3092733133482824, 0.30949536420384677, 0.24876490743553537, 0.15445429954349457, 0.06497240621317256, 0.01069187480679338, 0.00037734083793904567, 0.019670370495839102, 0.042142167649410665, 0.04726025757174501, 0.03415577752181564, 0.014931576596603937, 0.0016446879282573169, -0.0011385055958107629], 'positive_zeros': ['2.46259427346092974642579421633890', '2.78194491136502306249726834987780', '3.76461178074972908672241363843588', '4.45939968424702078647269062605388', '4.67898505343392185417733475953490', '5.08866170452463378308470265617019', '5.63591874046606001267864523224786', '5.66325346560503472403248174040947', '5.96165855796953113502760425774505', '5.99289058272781368313125466694908', '6.16587374479562321953016828178224', '7.02558343554993958193798692433303', '7.03706179140409979728308016065741', '7.74090712307790665573723381080755', '7.75962509752452597228196744040326', '7.83506387503764677641644822333298', '7.965079999948813456966409270612085', '8.115387743568871256004602444771603', '9.136575573695839191221125418177129', '9.316771376289671385980121419354411', '9.389528532047503245348854437305573', '9.596757290493155621182311957348761', '9.850540473922797701672075212362720', '9.930267503431574766805015088399583', '10.45055346583592329462401095693170', '10.56142074247679254657255440393566', '10.57112998500381496376355919584992', '10.78410442425223783389636846113724', '11.18169602022353313051744050996644', '11.32356232577992504312304893362992', '11.62269724518465848846122598510576', '11.97719977952906570989708688883809', '12.13358214107421180852385838279880', '12.34594035035493455150221024239507', '12.39360401601599654544105072220366', '12.59967987249435458310029097237519', '12.60491504219486423836120456389178', '12.93725898884036577190654568953731', '13.36966913753902926624511352924788', '13.60184586560095550438219539100515', '13.70742248978829432316592761436331', '14.07884477605949240212508926179188', '14.40364204832305966722543618039015', '14.59145313481971096415539183856344', '14.68656156434386290435533914759974', '15.10250980532061201121595665961627', '15.36853698529461451713548474763852', '15.70315092209086603554001914015726', '15.71774688132796024959834704820566', '15.74392666089394564457930219586645', '15.78026043735343791501662921464364', '16.24860856719243446714544977751695', '16.25203566549428088037148208792232', '16.51348763886378539153465335734697', '16.98402567822991773204655584388131', '17.12766126523671246419827101119217', '17.13173060305881366439228969748818', '17.25737412043048777024071935887892', '17.62016045812302062496678613487031', '17.62954068797365083169444487301714'], 'prelabel': '12-29e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.4812132228666553, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e6-0', 'trace_hash': 684183239011479837, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.46259427346092974642579421634', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.78194491136502306249726834988', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.76461178074972908672241363844', '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': 0.00015418801928325165, 'bad_primes': [29], 'central_character': '1.1', 'conductor': 594823321, 'conductor_radical': 29, 'degree': 12, 'dirichlet_coefficients': [1, -2, -5, 2, 1, 10, 1, -7, 17, -2, -11, -10, -5, -2, -5, 14, 8, -34, 1, 2, -5, 22, -7, 35, -9, 10, -49, 2, 6, 10, 5, -21, 55, -16, 1, 34, 11, -2, 25, -7, 20, 10, 13, -22, 17, 14, 11, -70, -7, 18, -40, -10, 3, 98, -11, -7, -5, -12, -56, -10, 3, -10, 17, 42, -5, -110, 19, 16, 35, -2, 21, -119, -25, -22, 45, 2, -11, -50, -9, 14, 126, -40, 17, -10, 8, -26, -30, 77, 7, -34, -5, -14, -25, -22, 1, 105, 1, 14, -187, -18], 'euler11': [1, 11, 68, 354, 1683, 6723, 23296, 73953, 203643, 471174, 995588, 1771561, 1771561], 'euler13': [1, 5, 12, -40, -111, 875, 6308, 11375, -18759, -87880, 342732, 1856465, 4826809], 'euler17': [1, -8, 110, -632, 4831, -20736, 110564, -352512, 1396159, -3105016, 9187310, -11358856, 24137569], 'euler19': [1, -1, -18, 156, 67, -1127, 9612, -21413, 24187, 1070004, -2345778, -2476099, 47045881], 'euler2': [1, 2, 2, 7, 10, 13, 27, 26, 40, 56, 32, 64, 64], 'euler23': [1, 7, 26, 84, 431, -175, -12020, -4025, 227999, 1022028, 7275866, 45054401, 148035889], 'euler29': [1, -6, -13, 316, -377, -5046, 24389, 0, 0, 0, 0, 0, 0], 'euler3': [1, 5, 8, 4, 3, 3, -8, 9, 27, 108, 648, 1215, 729], 'euler31': [1, -5, -34, 388, -1649, -7283, 109220, -225773, -1584689, 11558908, -31399714, -143145755, 887503681], 'euler37': [1, -11, 42, -328, 4049, -22869, 100360, -846153, 5543081, -16614184, 78714762, -762783527, 2565726409], 'euler41': [1, -20, 394, -4596, 50223, -397592, 2931564, -16301272, 84424863, -316760916, 1113349834, -2317124020, 4750104241], 'euler43': [1, -13, 42, -50, 251, 17703, -219260, 761229, 464099, -3975350, 143589642, -1911109759, 6321363049], 'euler47': [1, -11, 18, 410, -2409, -12679, 224300, -595913, -5321481, 42567430, 87834258, -2522795077, 10779215329], 'euler5': [1, -1, 10, -12, 81, -91, 456, -455, 2025, -1500, 6250, -3125, 15625], 'euler53': [1, -3, -58, 648, -431, -23629, 179088, -1252337, -1210679, 96472296, -457647898, -1254586479, 22164361129], 'euler59': [1, 56, 1642, 32088, 460455, 5071808, 43842828, 299236672, 1602843855, 6590201352, 19896706762, 40035760744, 42180533641], 'euler61': [1, -3, -24, -74, 4633, -24883, -67236, -1517863, 17239393, -16796594, -332300184, -2533788903, 51520374361], 'euler67': [1, -19, 168, -904, 1419, 3983, 31592, 266861, 6369891, -271889752, 3385388328, -25652377033, 90458382169], 'euler7': [1, -1, 8, -22, 127, -169, 848, -1183, 6223, -7546, 19208, -16807, 117649], 'euler71': [1, -21, 118, 546, -4409, -107373, 1690660, -7623483, -22225769, 195419406, 2998578358, -37888816371, 128100283921], 'euler73': [1, 25, 300, 3400, 39069, 348943, 2806700, 25472839, 208198701, 1322657800, 8519472300, 51826789825, 151334226289], 'euler79': [1, 9, 2, 210, -977, -72339, -812260, -5714781, -6097457, 103538190, 77900162, 27693507591, 243087455521], 'euler83': [1, -17, 136, -1776, 27843, -251219, 1969848, -20851177, 191810427, -1015493712, 6454331656, -66963690931, 326940373369], 'euler89': [1, -7, 30, 532, 7389, -23261, 663944, -2070229, 58528269, 375043508, 1882267230, -39088416143, 496981290961], 'euler97': [1, -1, 114, 382, 20669, 10611, 2196928, 1029267, 194474621, 348641086, 10092338034, -8587340257, 832972004929], 'euler_factors': [[1, 2, 2, 7, 10, 13, 27, 26, 40, 56, 32, 64, 64], [1, 5, 8, 4, 3, 3, -8, 9, 27, 108, 648, 1215, 729], [1, -1, 10, -12, 81, -91, 456, -455, 2025, -1500, 6250, -3125, 15625], [1, -1, 8, -22, 127, -169, 848, -1183, 6223, -7546, 19208, -16807, 117649], [1, 11, 68, 354, 1683, 6723, 23296, 73953, 203643, 471174, 995588, 1771561, 1771561], [1, 5, 12, -40, -111, 875, 6308, 11375, -18759, -87880, 342732, 1856465, 4826809], [1, -8, 110, -632, 4831, -20736, 110564, -352512, 1396159, -3105016, 9187310, -11358856, 24137569], [1, -1, -18, 156, 67, -1127, 9612, -21413, 24187, 1070004, -2345778, -2476099, 47045881], [1, 7, 26, 84, 431, -175, -12020, -4025, 227999, 1022028, 7275866, 45054401, 148035889], [1, -6, -13, 316, -377, -5046, 24389, 0, 0, 0, 0, 0, 0], [1, -5, -34, 388, -1649, -7283, 109220, -225773, -1584689, 11558908, -31399714, -143145755, 887503681], [1, -11, 42, -328, 4049, -22869, 100360, -846153, 5543081, -16614184, 78714762, -762783527, 2565726409], [1, -20, 394, -4596, 50223, -397592, 2931564, -16301272, 84424863, -316760916, 1113349834, -2317124020, 4750104241], [1, -13, 42, -50, 251, 17703, -219260, 761229, 464099, -3975350, 143589642, -1911109759, 6321363049], [1, -11, 18, 410, -2409, -12679, 224300, -595913, -5321481, 42567430, 87834258, -2522795077, 10779215329], [1, -3, -58, 648, -431, -23629, 179088, -1252337, -1210679, 96472296, -457647898, -1254586479, 22164361129], [1, 56, 1642, 32088, 460455, 5071808, 43842828, 299236672, 1602843855, 6590201352, 19896706762, 40035760744, 42180533641], [1, -3, -24, -74, 4633, -24883, -67236, -1517863, 17239393, -16796594, -332300184, -2533788903, 51520374361], [1, -19, 168, -904, 1419, 3983, 31592, 266861, 6369891, -271889752, 3385388328, -25652377033, 90458382169], [1, -21, 118, 546, -4409, -107373, 1690660, -7623483, -22225769, 195419406, 2998578358, -37888816371, 128100283921], [1, 25, 300, 3400, 39069, 348943, 2806700, 25472839, 208198701, 1322657800, 8519472300, 51826789825, 151334226289], [1, 9, 2, 210, -977, -72339, -812260, -5714781, -6097457, 103538190, 77900162, 27693507591, 243087455521], [1, -17, 136, -1776, 27843, -251219, 1969848, -20851177, 191810427, -1015493712, 6454331656, -66963690931, 326940373369], [1, -7, 30, 532, 7389, -23261, 663944, -2070229, 58528269, 375043508, 1882267230, -39088416143, 496981290961], [1, -1, 114, 382, 20669, 10611, 2196928, 1029267, 194474621, 348641086, 10092338034, -8587340257, 832972004929]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/29/2/d/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': '12-29e6-1.1-c1e6-0-0', '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}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '12-29e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.4812132228666553, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e6-0', 'trace_hash': 684183239011479837, 'z1': {'__RealLiteral__': 0, 'data': '2.46259427346092974642579421634', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '3121709108871348086775702555917,3526534136693739926306137982643,4772212383493657620209068421081,5652960686393312569154862963081,5931318211444425057158254766132,6450645064099056945150443910685', 'Lhash_array': ['3121709108871348086775702555917', '3526534136693739926306137982643', '4772212383493657620209068421081', '5652960686393312569154862963081', '5931318211444425057158254766132', '6450645064099056945150443910685'], 'label': '12-29e6-1.1-c1e6-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/29/2/d/a'}