Lfunction data - 16-3332e8-1.1-c1e8-0-2

Formats: - HTML - YAML - JSON - 2023-12-11T00:30:40.801048

• 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': '551120404380225331934709011364,590594129564085046271560248306,783818118043282909114322478016,1007476706680164797094651306938,1122200035824808891464044335792,1483661925948075857497746215488,1744040623870169449497928737539,1759720331322618215537337006470', 'a10': 0, 'a2': 0, 'a3': 4, 'a4': 0, 'a5': 4, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 251105831164.6035, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1]], [17, [1, 8, 28, 56, 70, 56, 28, 8, 1]]], 'bad_primes': [2, 7, 17], 'central_character': '3332.1', 'coefficient_field': '1.1.1.1', 'conductor': 15192874202374507341482622976, 'conductor_radical': 238, 'degree': 16, 'euler_factors': [[1], [1, -4, 16, -48, 125, -292, 616, -1180, 2165, -3540, 5544, -7884, 10125, -11664, 11664, -8748, 6561], [1, -4, 24, -84, 305, -860, 2480, -5972, 14293, -29860, 62000, -107500, 190625, -262500, 375000, -312500, 390625], [1], [1, 4, 36, 156, 772, 2860, 11940, 39604, 142038, 435644, 1444740, 3806660, 11302852, 25123956, 63776196, 77948684, 214358881], [1, -20, 242, -2108, 14688, -85220, 425054, -1848812, 7093070, -24034556, 71834126, -187228340, 419503968, -782685644, 1168087778, -1254970340, 815730721], [1, 8, 28, 56, 70, 56, 28, 8, 1], [1, -8, 130, -768, 7300, -34608, 246198, -970520, 5606838, -18439880, 88877478, -237376272, 951343300, -1901644032, 6115964530, -7150973912, 16983563041], [1, -4, 90, -540, 4440, -29276, 164982, -942116, 4535198, -21668668, 87275478, -356201092, 1242494040, -3475625220, 13323230010, -13619301788, 78310985281], [1, 16, 232, 2288, 20820, 156880, 1107792, 6773040, 39031606, 196418160, 931653072, 3826146320, 14725590420, 46929508912, 137999010472, 275998020944, 500246412961], [1, 8, 132, 1148, 10509, 76248, 557672, 3391732, 20312877, 105143692, 535922792, 2271504168, 9705282189, 32866265348, 117150485892, 220100912888, 852891037441], [1, -8, 262, -1752, 30896, -174584, 2158362, -10209672, 97900174, -377757864, 2954797578, -8843203352, 57904078256, -121490612664, 672220319158, -759455017064, 3512479453921], [1, -12, 252, -2556, 31145, -259212, 2352656, -16138476, 117350157, -661677516, 3954814736, -17865150252, 88008326345, -296128449756, 1197026268732, -2337051286572, 7984925229121], [1, 4, 134, -32, 6463, -33524, 283988, -1881912, 14761517, -80922216, 525093812, -2665392668, 22095710863, -4704270176, 847062648566, 1087274444428, 11688200277601], [1, -4, 212, -620, 19692, -29500, 1107892, -256724, 51399558, -12066028, 2447333428, -3062778500, 96090678252, -142193904340, 2285193649748, -2026492481852, 23811286661761], [1, 0, 182, 396, 18127, 76688, 1202396, 7128472, 67495349, 377809016, 3377530364, 11417079376, 143030749087, 165605415228, 4033913725478, 0, 62259690411361], [1, 16, 308, 3024, 35584, 259920, 2411692, 14703504, 135177774, 867506736, 8395099852, 53382109680, 431184173824, 2161931080176, 12991604361428, 39818423757104, 146830437604321], [1, -32, 780, -13760, 202241, -2496952, 26836056, -251837332, 2095384045, -15362077252, 99856964376, -566760661912, 2800196729681, -11621645101760, 40185892001580, -100567770752672, 191707312997281], [1, 0, 182, -380, 20055, -58520, 1944308, -4410912, 151707053, -295531104, 8727998612, -17600650760, 404130731655, -513047540660, 16463425554758, 0, 406067677556641], [1, 0, 282, -120, 39300, 5592, 3710766, 2456208, 279763670, 174390768, 18705971406, 2001438312, 998679063300, -216507522120, 36124280065722, 0, 645753531245761], [1, -24, 532, -7840, 111593, -1287208, 14379232, -136783428, 1257242741, -9985190244, 76626927328, -500745794536, 3169044907913, -16252881289120, 80509808385748, -265137564458328, 806460091894081], [1, -4, 412, -980, 78884, -128196, 9972860, -14036628, 919676534, -1108893612, 62240619260, -63205627644, 3072538189604, -3015515271020, 100152031674652, -76815635944636, 1517108809906561], [1, -28, 590, -8124, 100500, -988060, 9343514, -75809692, 692605078, -6292204436, 64367467946, -564959863220, 4769561260500, -32000766183732, 192894820287710, -759809427709556, 2252292232139041], [1, -20, 628, -9348, 170452, -2031132, 27607732, -271275276, 2973835350, -24143499564, 218680845172, -1431885094908, 10694540462932, -52199787729252, 312104250723508, -884626697910580, 3936588805702081], [1, -56, 2040, -52648, 1089417, -18429928, 264789328, -3243680020, 34414745117, -314636961940, 2491402787152, -16820497677544, 96445303719177, -452106289850536, 1699262890055160, -4524703930774328, 7837433594376961], [1, -8, 558, -4216, 152768, -1047592, 26447602, -159673720, 3170999438, -16127045720, 269791988002, -1079335085192, 15897099339968, -44310583712216, 592328244035358, -857708281685608, 10828567056280801], [1, -12, 562, -5596, 147200, -1256188, 24414942, -181435020, 2908578670, -18687807060, 259018119678, -1372670544676, 16567489683200, -64872977197828, 671057390649298, -1475848638509844, 12667700813876161], [1, 0, 354, -1432, 82164, -289560, 14129974, -50533696, 1664527542, -5407105472, 161774072326, -354723451080, 10770024336564, -20084540783624, 531258544554546, 0, 17181861798319201], [1, -4, 408, -1052, 84320, -148004, 12019736, -13667836, 1382882574, -1489794124, 142806483416, -191669472116, 11902456135520, -16186324005548, 684256845223128, -731215648326676, 19925626416901921], [1, 24, 688, 11264, 205164, 2705376, 38896440, 433426536, 5203559302, 48977198568, 496668642360, 3903578914272, 33451448772204, 207531898596352, 1432382805794992, 5646253153075608, 26584441929064321]], 'euler_factors_factorization': [[1], [[[1, -4, 16, -48, 125, -292, 616, -1180, 2165, -3540, 5544, -7884, 10125, -11664, 11664, -8748, 6561], 1]], [[[1, -4, 24, -84, 305, -860, 2480, -5972, 14293, -29860, 62000, -107500, 190625, -262500, 375000, -312500, 390625], 1]], [1], [[[1, 4, 36, 156, 772, 2860, 11940, 39604, 142038, 435644, 1444740, 3806660, 11302852, 25123956, 63776196, 77948684, 214358881], 1]], [[[1, -20, 242, -2108, 14688, -85220, 425054, -1848812, 7093070, -24034556, 71834126, -187228340, 419503968, -782685644, 1168087778, -1254970340, 815730721], 1]], [[[1, 1], 8]], [[[1, -8, 130, -768, 7300, -34608, 246198, -970520, 5606838, -18439880, 88877478, -237376272, 951343300, -1901644032, 6115964530, -7150973912, 16983563041], 1]], [[[1, -4, 90, -540, 4440, -29276, 164982, -942116, 4535198, -21668668, 87275478, -356201092, 1242494040, -3475625220, 13323230010, -13619301788, 78310985281], 1]], [[[1, 16, 232, 2288, 20820, 156880, 1107792, 6773040, 39031606, 196418160, 931653072, 3826146320, 14725590420, 46929508912, 137999010472, 275998020944, 500246412961], 1]], [[[1, 8, 132, 1148, 10509, 76248, 557672, 3391732, 20312877, 105143692, 535922792, 2271504168, 9705282189, 32866265348, 117150485892, 220100912888, 852891037441], 1]], [[[1, -8, 262, -1752, 30896, -174584, 2158362, -10209672, 97900174, -377757864, 2954797578, -8843203352, 57904078256, -121490612664, 672220319158, -759455017064, 3512479453921], 1]], [[[1, -12, 252, -2556, 31145, -259212, 2352656, -16138476, 117350157, -661677516, 3954814736, -17865150252, 88008326345, -296128449756, 1197026268732, -2337051286572, 7984925229121], 1]], [[[1, 4, 134, -32, 6463, -33524, 283988, -1881912, 14761517, -80922216, 525093812, -2665392668, 22095710863, -4704270176, 847062648566, 1087274444428, 11688200277601], 1]], [[[1, -4, 212, -620, 19692, -29500, 1107892, -256724, 51399558, -12066028, 2447333428, -3062778500, 96090678252, -142193904340, 2285193649748, -2026492481852, 23811286661761], 1]], [[[1, 0, 182, 396, 18127, 76688, 1202396, 7128472, 67495349, 377809016, 3377530364, 11417079376, 143030749087, 165605415228, 4033913725478, 0, 62259690411361], 1]], [[[1, 16, 308, 3024, 35584, 259920, 2411692, 14703504, 135177774, 867506736, 8395099852, 53382109680, 431184173824, 2161931080176, 12991604361428, 39818423757104, 146830437604321], 1]], [[[1, -32, 780, -13760, 202241, -2496952, 26836056, -251837332, 2095384045, -15362077252, 99856964376, -566760661912, 2800196729681, -11621645101760, 40185892001580, -100567770752672, 191707312997281], 1]], [[[1, 0, 182, -380, 20055, -58520, 1944308, -4410912, 151707053, -295531104, 8727998612, -17600650760, 404130731655, -513047540660, 16463425554758, 0, 406067677556641], 1]], [[[1, 0, 282, -120, 39300, 5592, 3710766, 2456208, 279763670, 174390768, 18705971406, 2001438312, 998679063300, -216507522120, 36124280065722, 0, 645753531245761], 1]], [[[1, -24, 532, -7840, 111593, -1287208, 14379232, -136783428, 1257242741, -9985190244, 76626927328, -500745794536, 3169044907913, -16252881289120, 80509808385748, -265137564458328, 806460091894081], 1]], [[[1, -4, 412, -980, 78884, -128196, 9972860, -14036628, 919676534, -1108893612, 62240619260, -63205627644, 3072538189604, -3015515271020, 100152031674652, -76815635944636, 1517108809906561], 1]], [[[1, -28, 590, -8124, 100500, -988060, 9343514, -75809692, 692605078, -6292204436, 64367467946, -564959863220, 4769561260500, -32000766183732, 192894820287710, -759809427709556, 2252292232139041], 1]], [[[1, -20, 628, -9348, 170452, -2031132, 27607732, -271275276, 2973835350, -24143499564, 218680845172, -1431885094908, 10694540462932, -52199787729252, 312104250723508, -884626697910580, 3936588805702081], 1]], [[[1, -56, 2040, -52648, 1089417, -18429928, 264789328, -3243680020, 34414745117, -314636961940, 2491402787152, -16820497677544, 96445303719177, -452106289850536, 1699262890055160, -4524703930774328, 7837433594376961], 1]], [[[1, -8, 558, -4216, 152768, -1047592, 26447602, -159673720, 3170999438, -16127045720, 269791988002, -1079335085192, 15897099339968, -44310583712216, 592328244035358, -857708281685608, 10828567056280801], 1]], [[[1, -12, 562, -5596, 147200, -1256188, 24414942, -181435020, 2908578670, -18687807060, 259018119678, -1372670544676, 16567489683200, -64872977197828, 671057390649298, -1475848638509844, 12667700813876161], 1]], [[[1, 0, 354, -1432, 82164, -289560, 14129974, -50533696, 1664527542, -5407105472, 161774072326, -354723451080, 10770024336564, -20084540783624, 531258544554546, 0, 17181861798319201], 1]], [[[1, -4, 408, -1052, 84320, -148004, 12019736, -13667836, 1382882574, -1489794124, 142806483416, -191669472116, 11902456135520, -16186324005548, 684256845223128, -731215648326676, 19925626416901921], 1]], [[[1, 24, 688, 11264, 205164, 2705376, 38896440, 433426536, 5203559302, 48977198568, 496668642360, 3903578914272, 33451448772204, 207531898596352, 1432382805794992, 5646253153075608, 26584441929064321], 1]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 2, 'label': '16-3332e8-1.1-c1e8-0-2', 'leading_term': '96.894929591619633405367129726500819175474418706095051598677705779150102305210459349497195', '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}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3332/2/a/u', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.00634765625', 'prec': 44}, 'plot_values': [96.89492959161964, 96.59278436708213, 96.27090175763226, 95.90902395358262, 95.48716457597358, 94.98569188624447, 94.38544439413616, 93.66787766020506, 92.81524062436262, 91.81492123749153, 90.67177252649981, 89.3952075189351, 87.99490936622944, 86.48075182543147, 84.8627231852482, 83.1508540907488, 81.35514964801742, 79.48451983704022, 77.54385606884823, 75.53728459960597, 73.46919889708721, 71.34424791615236, 69.16732272059758, 66.94354145590266, 64.67823268791027, 62.377133063202045, 60.046965185442524, 57.694677822241495, 55.327189140764595, 52.951358279342614, 50.57395732697444, 48.2016438412972, 45.8409340336063, 43.49813252618795, 41.179189347161206, 38.889834243991196, 36.635601183998304, 34.42180574410536, 32.2535234196298, 30.135568971829578, 28.072476931227314, 26.06849525203302, 24.127598896965395, 22.253429997796086, 20.44927157784062, 18.718036296367703, 17.062257078036282, 15.484079693891989, 13.98525735120302, 12.567150383395907, 11.230732319642655, 9.976578658584073, 8.80486680546665, 7.7153816943040825, 6.7075235655751175, 5.780317872303342, 4.932427274697874, 4.162168791929991, 3.4675363153561425, 2.846204726163181, 2.295546976325973, 1.8126567565151503, 1.3943727208244838, 1.0373041245235948, 0.7378577201499112, 0.4922667917329731, 0.296621345002664, 0.14689202847735416, 0.038960143980385456, -0.03135051322662106, -0.0682417861283157, -0.07590948068145592, -0.05851210623090158, -0.020140475868861613, 0.035210784305215126, 0.10367206462213584, 0.18152727888425427, 0.2652406788493522, 0.35148177462326763, 0.43714816765873243, 0.5193861166875249, 0.5956082775505441, 0.6635084603720415, 0.7210765597244946, 0.7666094345672528, 0.7987182122924609, 0.816332419527134, 0.8187009094232631, 0.8053895812922025, 0.7762760758007049, 0.7315422716242576, 0.6716631026462743, 0.597391610135332, 0.5097410388929585, 0.4099641620741947, 0.29953004508018904, 0.1800984837602566, 0.05349302386338246, -0.07832637351193424, -0.21329622957646305, -0.3492828433816123, -0.4841158279670444, -0.6156220967106658, -0.7416599188657889, -0.8601526596389929, -0.9691213078650696, -1.0667154012757543, -1.1512461284903799, -1.2212159631554855, -1.275345372216321, -1.3125968653028286, -1.3321960642871256, -1.333649501605358, -1.3167590189440406, -1.281633339922988, -1.2286953201263324, -1.1586841743311218, -1.0726533216280083, -0.9719638478385194, -0.8582735934690198, -0.7335219271177307, -0.5999109342612702, -0.45988393402045563, -0.3160962189950086, -0.17138285708448858, -0.028723737412944785, 0.10879430522324417, 0.23801785939378284, 0.3557693332020938, 0.45889051140630266, 0.5442870719580936, 0.6089765821843721, 0.6501349033090795, 0.6651412849625428, 0.6516220396574748, 0.6074921905858893, 0.5309944993850844, 0.4207358412066231, 0.2757220069089003, 0.0953858625685938, -0.12038981920404494, -0.37125457669355566, -0.6563781729282983, -0.9744445094220464, -1.3236517721231529, -1.7017176435097245, -2.1058876908322373, -2.5329579569170226, -2.9793026427986073, -3.4409069927222027, -3.9134062392459694, -4.392130244466118, -4.872153389768412, -5.348348003524814, -5.815439818857715, -6.268074552342582, -6.700884819187956, -7.108557748092799, -7.485903649698348, -7.827924845434338, -8.129883740721509, -8.387369100047213, -8.596360320332684, -8.753289646401372, -8.855098585997219, -8.899288633626938, -8.883965795736948, -8.80787817015247, -8.670445910178861, -8.471783938669102, -8.212718376166135, -7.894788478509881, -7.520240205286115, -7.092011053450578, -6.613705340465247, -6.089560063076152, -5.524401590923465, -4.9235945357184985, -4.292983924742737, -3.638823671999404, -2.9677004751488276, -2.286452808647724, -1.6020849894644027, -0.9216774000033363, -0.2522940306872121, 0.39911158571898914, 1.0257915847840164, 1.621297304855238, 2.1795695304153755, 2.6950248982909772, 3.162637210906204, 3.578012423112234, 3.9374561313706775, 4.238033636292994, 4.477622637786222, 4.6549480999234225, 4.769608085956506, 4.822089024376777, 4.8137688280447515, 4.746907602618632, 4.624625849683617, 4.450871070368341, 4.230372730836987, 3.9685797029213012, 3.671590083708266, 3.346072074453917, 2.9991757651123203, 2.638436912587986, 2.27167393317714, 1.9068790012562062, 1.5521036294784816, 1.2153447784143192, 0.9044311485720848, 0.6269102514633428, 0.3899380561660389, 0.20017278216035575, 0.0636743760679278, -0.014189021632757292, -0.028824055590228242, 0.0235189264026181, 0.14568563136368856, 0.3395689140790818, 0.6060725959778088, 0.9450886277257021, 1.3554880363149568, 1.8351302814862585, 2.3809018165621607, 2.988748091323899, 3.653719035362255, 4.370029806734704, 5.131133118571148, 5.929802195790995, 6.758223262394055, 7.608109690891341, 8.470858124512894, 9.337635434439477, 10.199482647098275, 11.047431480683498, 11.872620635792693, 12.666410245080025, 13.420492913022201, 14.127023105628092, 14.778792466704763, 15.369259648986315, 15.892606159677163, 16.343803215258806, 16.718667190497897, 17.01390301595345, 17.227135051584693, 17.356954023673815, 17.403008226096176, 17.365905217258764, 17.24715643472008, 17.049138752394427, 16.775045064041183, 16.428824810430402, 16.015115496241584, 15.539193450534372, 15.00696519113486, 14.424783829130918, 13.799324714715752, 13.137488258308274, 12.446302794313953, 11.7328289184455, 11.004066670212396, 10.26688616395759, 9.527992380931806, 8.79377321016276, 8.070208753176066, 7.362811499167839, 6.676576204536836, 6.015939864134895, 5.384751986799437, 4.786265273661659, 4.223148479747077, 3.6974441505995492, 3.2105699612902945, 2.763341487909296, 2.356003310036736, 1.9882674751849772, 1.6593582727079335, 1.3680656325626888, 1.112805107636891, 0.8916584440547657, 0.7024307600069829, 0.5427126593641773, 0.4099414105271212, 0.3014600897455685, 0.21457368811875296, 0.14660183422230857, 0.09492669293094001, 0.05703223423724168, 0.030541297436175723, 0.01324705214744542, 0.003137736414296182, -0.001585342960420302, -0.0024964139622530583, -0.0009401927004065797, 0.001967180439393702, 0.005332022115692508, 0.008472187493418114, 0.010901818027418193, 0.012312531055468886, 0.012551871693055393, 0.011599860268418132, 0.009544494892995402, 0.00655707516806246, 0.0028677537842840893, -0.0012578053353155532, -0.0055399768164449996, -0.00970441484549397, -0.013498555665987956, -0.016705065973783663, -0.019152021824487928, -0.02071976523508117, -0.021344595186562926, -0.02101917650535077, -0.019789971238963915, -0.017752056116554133, -0.015041738410812095, -0.011827442052120938, -0.008299387697711113, -0.00465861282413685, -0.0011057713785123289, 0.002169674402037542, 0.004999359847192628, 0.007244580963600134, 0.008803133459558509, 0.009614126678670926, 0.009660564249020327, 0.008969591409548866, 0.0076103755217432, 0.005689703547211411, 0.0033455098160615755, 0.0007386328712113112, -0.0019568129765827388, -0.004563990373167228, -0.006914294977892645, -0.00885815474113891, -0.01027508344874652, -0.011082391421661704, -0.011241984875187742, -0.010764725603442252, -0.009711885428459082, -0.008193313366460786, -0.006362032971456648, -0.0044051063478110905, -0.0025307622841473634, -0.0009518772286367116, 0.00013394213576147643, 0.0005672743900459045, 0.0002522546794806842, -0.0008162770625173861, -0.0025246635102165894, -0.004612274553663513, -0.0066441717450007425, -0.007985656964698582, -0.0077797969839666446, -0.0049289984375457145, 0.0019183116413789105, 0.0143749006218528, 0.034315139154592916, 0.06386874374287993, 0.1054059684050321, 0.1615140933622136, 0.23496519820213474, 0.3286751077758137, 0.44565371475989174, 0.5889471246191761, 0.7615746881684113, 0.9664680529796499, 1.206395064677102, 1.483880607745706, 1.8011268565043033, 2.1599330215042527, 2.5616163913471373, 3.0069365691818155, 3.4960347979211583, 4.02840994364813, 4.602853023066031, 5.217399750158533, 5.86930276918615, 6.555017204152344, 7.270200689406101, 8.009728807733918, 8.76775159865137, 9.537831031113704, 10.312955621951373, 11.085598275664948, 11.847809137311831, 12.591320931074495, 13.30766537195207, 13.98829895358865, 14.624779844726943, 15.209049589055162, 15.733460728984706, 16.190868483543703, 16.574758592263283, 16.879368575284435, 17.09979997996264, 17.23211927488729, 17.273501073941972, 17.222467935365845, 17.07877134996588, 16.84335787273747, 16.518370481584764, 16.107129713009513, 15.614094577541225, 15.044803629098652, 14.405849571697678, 13.704926563942815, 12.950529285813797, 12.151760117686926, 11.318181763642242, 10.459662302599185, 9.586215470217919, 8.707839073485934, 7.83438941716689, 6.9755075026150815, 6.140325801251344, 5.337289056603625, 4.57403041770718, 3.857264699734818, 3.1927005630292, 2.5849730214351396, 2.0376111113792756, 1.5530375642488352, 1.132498339583071, 0.776072949967859, 0.48272540672278924, 0.2503755716861661, 0.07598891818647374, -0.04431763053479664, -0.115155710326166, -0.14174031636990347, -0.12976205977177985, -0.08523920370742549, -0.014366530263398535, 0.07663270688589194, 0.18164853063717804, 0.29481671398392806, 0.41063718237332425, 0.5240746439246433, 0.6306578235935452, 0.7265565468007498, 0.8086365014806706, 0.8744932719137137, 0.9224656815978308, 0.9516289902584423, 0.9617686663295901, 0.953337611506315, 0.9274001734061317, 0.8855585135562778, 0.8298666684163095, 0.7627359783016481, 0.6868349182618739, 0.6049864062201373, 0.5200662522750809, 0.4349062392719272, 0.3521989732425389, 0.2744122334117135, 0.20371502452295878, 0.14191659964237405, 0.09041984957711766, 0.05018998434687779, 0.02173907770922839, 0.005126021201670824, -2.9392172538536256e-05, 0.005483191422964937, 0.02050769464434938, 0.04357590189848814, 0.07297093321910054, 0.10679755640764767, 0.14305670825153036, 0.17972156705869147, 0.2148137599636276, 0.2464760459594846, 0.2730390441149282, 0.29307994785760105, 0.3054713516030615, 0.30941867080121316, 0.3044850936635095, 0.2906035633076495, 0.26807499619941855, 0.23755307484493957, 0.2000163946047792, 0.1567290262550284, 0.10919096387046133, 0.05908026248846272, 0.008188975410678952, -0.041644802174490875, -0.08860659876949369, -0.13097420456632639, -0.16718290249200496, -0.1958850087793148, -0.21600159413298406, -0.22676451657885627, -0.22774710673153553, -0.21888198564916486, -0.20046627461089936, -0.17315359849972434, -0.13793288226800485, -0.09609460859598677, -0.049185586035354514, 0.0010463158324991685, 0.052716110949251764, 0.10387253933508657, 0.15256933108635343, 0.19693832123361227, 0.23526161179630706, 0.26603978693043184, 0.28805372866484835, 0.30041774639715996, 0.3026219838090447, 0.29456126437888563, 0.27654923236981177, 0.24931975295862294, 0.2140140255945612, 0.17215323032763072, 0.12559726455439313, 0.07649059181613249, 0.027195608857749198, -0.019785684826951894, -0.061889690590761444, -0.09657434513074102, -0.12140481650304838, -0.13413815096617865, -0.13280416011895452, -0.11577989271226971, -0.0818546293939583, -0.03027834843753809, 0.03920456956291585, 0.1263326983492219, 0.23031981336587914, 0.34986283445023825, 0.48316549654700236, 0.6279773115147058, 0.7816537426782393, 0.9412500129619783, 1.1035898798793893, 1.2653452680753576, 1.4231260506894465, 1.573572299479424, 1.7134463109928242, 1.839721700265617, 1.949680528755477, 2.041032786767761, 2.1119432073091304, 2.1610644764588742, 2.1875686416165836, 2.1911633965409183, 2.172092871074328, 2.131123013062052, 2.06952641555786, 1.989077805756262, 1.8919457067924044, 1.7806061555162676, 1.6577643744735295, 1.5262719414063275, 1.3890421157120012, 1.2489660009493595, 1.1088406604685197, 0.9713130789725436, 0.8387764165957391, 0.713305273115256, 0.5966142843951184, 0.4900307057867575, 0.39448140672370513, 0.31049419963604913, 0.23821530143869288, 0.17744028592364902, 0.12764089996921604, 0.08801389935940496, 0.05754036274026158, 0.03504923351293768, 0.01928230171202116, 0.008957845180548896, 0.0028303581074292754, -0.00025648357911799396, -0.001325788176746258, -0.0012325891940375452, -0.0006412070492428044, -1.589195453892157e-05, 0.0003751150700935476, 0.00044256888045665404, 0.00024731584128911336, -3.8910924762561204e-05, -0.00018112592476614333, 6.548277293333906e-05, 0.000899414665569196, 0.002417215453701241, 0.004561597915230743, 0.007076504664456469, 0.009472013186656858, 0.011001724742065002, 0.010655587533176124, 0.007169262460588803, -0.000949215994976454, -0.015375430564579616, -0.03790804965295637, -0.07039342987666816, -0.11463737837178506, -0.17230581154234034, -0.24482152659556344, -0.3332604807557541, -0.4382520183829862, -0.559888309149196, -0.6976480091894274, -0.8503389111509607, -1.0160630352050926, -1.1922067054760328, -1.375465853202909, -1.5619022431423875, -1.7470312518501379, -1.925941077029504, -2.0934411208779515, -2.244235887408987, -2.373119939068244, -2.475189227007299, -2.5460566880673143, -2.5820657828838165, -2.5804934067575918, -2.539732435085205, -2.459444490993973, -2.340673883039571, -2.185916091349016, -1.9991346397083514, -1.7857066908901618, -1.552308557023208, -1.3067376229070582, -1.0576696914093624, -0.8143551311783909, -0.5862598986476562, -0.3826604329570428, -0.21220305501990652, -0.0824414292495505, 0.0006274326640073128, 0.0330131075017507, 0.01314909343957166, -0.057742378615798035, -0.17535819479788556, -0.3321154742600098, -0.5170678815727625, -0.7159455423811152, -0.9113325971790441, -1.082994134534857, -1.2083585366014082, -1.263157217749239, -1.2222188957841085, -1.0604113089574045, -0.7537079492094424, -0.2803441452736181, 0.3779356792930434, 1.234572759573021, 2.2968662648612885, 3.564660077333976, 5.029084209102072, 6.671423382478706, 8.462240362293237, 10.360559199663555, 12.313268456059008, 14.254801288336656, 16.107107345416846, 17.779945257766137, 19.171518726842887, 20.169584970756247, 20.65323136683926, 20.494382719329, 19.55974449605284, 17.71314885758015, 14.818180848913784, 10.741046171274753, 5.353633625455594, -1.4631130040078035, -9.815441151702288, -19.794149626275484, -31.471722352207998, -44.89945091048131, -60.104786748429746, -77.08899265850656, -95.82516050650138, -116.25662776125638, -138.29610823880594, -161.82585904837728, -186.69803326523825, -212.73552127766146, -239.7333793049448, -267.4608413936078, -295.66389924203503, -324.0688123520033, -352.38739519784, -380.32080710506744, -407.5637530495244, -433.809197116171, -458.7532334668562, -482.10002567011907, -503.56672202908555, -522.8891661445906, -539.8296427141199, -554.1790472012901, -565.7597055000366, -574.4284646598992, -580.0791947792874, -582.6446514222596, -582.0976602889397, -578.452788773892, -571.7697454724521, -562.1488047191859, -549.7276328496577, -534.6786188068468, -517.2056129707244, -497.5401446205473, -475.9371982518669, -452.6716691651809, -428.03633105360154, -402.33312603922406, -375.8668164568208, -348.93983329770674, -321.84733139615145, -294.87254663561873, -268.28254155319905, -242.3250150983862, -217.22645487651982, -193.1869913814705, -170.3776869928406, -148.93920638385487, -128.98117201774895, -110.58218845886067, -93.79050439181603, -78.62548045945545, -65.07978131371462, -53.120646746553106, -42.692414646400195, -33.71963711575014, -26.110416896226557, -19.759869381259605, -14.553617099560537, -10.371261009517134, -7.089711095993764, -4.586090930777077, -2.7405672385890174, -1.4388824970120295, -0.5744918516159442, -0.050274986654063325, 0.2201924284057269, 0.31180967005978805, 0.28755553732448325, 0.19849338246494605, 0.0841432586148293, -0.026810883369541724, -0.11553125416871876, -0.1718128705901301, -0.19270959482905306, -0.18106391946437905, -0.14400399149904886, -0.0914647871475439, -0.03479104126332317, 0.014527910991775129, 0.045950347249228495, 0.050769592456383204, 0.02277495369120138, -0.04132503408730943, -0.14171815326753656, -0.27553396411745473, -0.4370989214134107, -0.6183735544606667, -0.8095370811475231, -0.9996792193808411, -1.1775551638339883, -1.3323590122946476, -1.454470682473765, -1.5361211663701695, -1.5719464158510716, -1.5593948867676335, -1.49895979524327, -1.394216298732576, -1.2516526956279934, -1.0802938549711818, -0.8911233027792531, -0.6963268768732157, -0.5083861152242747, -0.33905279459988236, -0.19824530688861258, -0.09291316599433813, -0.025919774250247874, 0.005004475373370371, 0.00818495987996733, -0.0012449433882435774, -0.0007979180982777362, 0.03966529454290539, 0.15795350825292656, 0.3992588978754493, 0.8155530757710429, 1.4646745586355503, 2.4091738027903262, 3.7148615391866238, 5.449101656398064, 7.678900337115853, 10.46883311645647, 13.878863876996673, 17.962115922867273, 22.76278864068409, 28.314612882925125, 34.6388982999154, 41.74282873275149, 49.61811251043238, 58.239950490447875, 67.56636475145407, 77.537922673728, 88.07831651775892, 99.09659761816933, 110.4875182179867, 122.1326384559568, 133.90214099884645, 145.65696855374497, 157.25124142551977, 168.53490451982606, 179.35738011422833, 189.57329980426394, 199.04341487632087, 207.63656774968956, 215.2322729968323, 221.72309946494167, 227.0167993631181, 231.03813600255864, 233.73142528259564, 235.06483539782107, 235.02782083861143, 233.6300661543808, 230.90105661216532, 226.8892568937693, 221.66092296397574, 215.29858004836808, 207.90013697936766, 199.5793421868836, 190.46017115230907, 180.6732707613073, 170.353357374293, 159.63664027959348, 148.65832630173097, 137.5502571667353, 126.43929398097893, 115.44670858870064, 104.68417200766449, 94.25171876944425, 84.2367033584783, 74.7130967085167, 65.74111718655332, 57.36718262129548, 49.624390585913986, 42.53350097132534, 36.10268162747038, 30.328323146985174, 25.19631320881964, 20.683433194890156, 16.75883082688026, 13.385524325555478, 10.52194809169108, 8.123473303438942, 6.143516205296221, 4.534796796737166, 3.2505273292915904, 2.245436780505968, 1.4766206802761954, 0.9042120748396805, 0.4918792161834935, 0.20714916282091056, 0.02155157450004703, -0.08934812489971168, -0.1460398158281034, -0.1652702433543659, -0.16033189305117077, -0.14141582246092613, -0.11600610145162216, -0.08929469326950189, -0.0645947651453474, -0.04373972372818887, -0.027454245218184424, -0.015686031473580598, -0.007890711509333763, -0.003265619967956947, -0.0009312825156464491, -6.216037331890385e-05, 2.9400331255697297e-05, -0.00014983636251473577, -0.00028298886074700055, -0.00022591591493709658, 2.788530334364227e-05, 0.0003923996720599263, 0.000736971091840434, 0.0009307203060691047, 0.0008786173824890217, 0.0005458422684964412, -3.134843034373754e-05, -0.0007484644534540183, -0.0014480981771758594, -0.001945222994126058, -0.002058998604713825, -0.0016469147224030542, -0.000636785667443938, 0.000947684402984633, 0.0029717493041497177, 0.00518814654442529, 0.007251567212140653, 0.008750130110387694, 0.009253552705972471, 0.00837614021002558, 0.0058516339461210124, 0.0016159766089165254, -0.004107217647575094, -0.010724428401953328, -0.017199624183659206, -0.021997793330408407, -0.02305078559457954, -0.01774945872071232, -0.0029651508182754254, 0.024894850147562278, 0.06979675771677395, 0.13595511217012327, 0.22767515431361762, 0.3491668082997448, 0.5043425533414237, 0.6966269024992022, 0.9287388018569457, 1.2024780191096696, 1.5185298424862304, 1.8762943680663589, 2.273750051029138, 2.707360499485731, 3.1720633339543878, 3.6614092008083516, 4.1676015039371075, 4.68161375106576, 5.193386219851369, 5.692074485258121, 6.166343783113665, 6.604701052742742, 6.995920714721493, 7.329641042931259, 7.596569743323856, 7.788758368377204, 7.899904829135732, 7.925612679131795, 7.8635962308582545, 7.713822082232777, 7.478655604612573, 7.163065830147658, 6.77426465983215, 6.321429100123408, 5.815432827820345, 5.268516826860514, 4.693909506010957, 4.105408682828526, 3.516984002340384, 2.9424168862275484, 2.3946478312962673, 1.8853057281708874, 1.424341098449496, 1.0197214625960367, 0.6771997206187547, 0.40016384141213207, 0.18958003920827363, 0.0440156030622498, -0.04029412206990891, -0.06923083243372323, -0.05048811690232281, 0.006797144606295744, 0.09246171060553286, 0.19576442553013274, 0.30584628119387813, 0.4121873335114562, 0.5050634831187717, 0.5759539869343433, 0.6178838078897988, 0.6256902693283128, 0.596204280643016, 0.5283400601218499, 0.42309640488402744, 0.28348176265140596, 0.11432046274598358, -0.07802229232599119, -0.2859783119775784, -0.5011640436174039, -0.7147993100322837, -0.9181374011841918, -1.1028827203420781, -1.2615776093360198, -1.3879712550355912, -1.477312268424735, -1.5265585167540108, -1.53449958261797, -1.5017868109576806, -1.430870389622284, -1.3258489005705747, -1.1922429212444812, -1.0366902794522987, -0.8665859911610629, -0.6896884971711171, -0.513712223949029, -0.345928099144525, -0.1927933747112587, -0.05963146710046591, 0.049621492130016875, 0.13259408678234375, 0.18856087558652798, 0.21842456063266602, 0.2246000721293478, 0.21080593198821868, 0.18177361729144503, 0.142890817430096, 0.09979858806055712, 0.05796459129640495, 0.022260816361356083, -0.0034269524143895605, -0.016530894069335833, -0.016048500888972687, -0.0026829034298942434, 0.021142130986216857, 0.05140568290054173, 0.08275664862115892, 0.10892157319427104, 0.12324433582954954, 0.11934039179993275, 0.09184050717175782, 0.03719177796752366, -0.04552301983048035, -0.15379433808874968, -0.280964747451697, -0.415621493366213, -0.5411497081238976, -0.6354889609884535, -0.6711308911529181, -0.6153886880538033, -0.43095983629304757, -0.07677503452198205, 0.4908831472225152, 1.316979930528616, 2.4460786949741005, 3.9204837018154604, 5.778226955806831, 8.050962135212453, 10.76190349487761, 13.924080779631664, 17.538491774821054, 21.592482055086066, 26.058472575235733, 30.893069678772356, 36.03662425351605, 41.413296607993516, 46.93195132176906, 52.488433230795714, 57.96692717308766, 63.24206024916972, 68.18171407832314, 72.65027210709933, 76.51223103120071, 79.6360891084885, 81.89895695803652, 83.19245352684011, 83.42522649757404, 82.5260147558143, 80.44684771035537, 77.16576454847308, 72.68894807740969, 67.05217976998173, 60.32209547516212, 52.59750280194361, 44.006168424260395, 34.70206250358822, 24.862401289610556, 14.683943984171536, 4.37862156350117, -5.8314035068362555, -15.718939266611097, -25.057368854649344, -33.627902047819795, -41.225695571536725, -47.665408615818755, -52.786338490336746, -56.45698813188116, -58.57893059218488, -59.090073017360986, -57.96769004803132, -55.22916678494338, -50.93157241256812, -45.17029739756871, -38.07664884733929, -29.814469799279227, -20.57587548002017, -10.576493716699114, -0.0504724499592092, 10.756829544067815, 21.595789743616315, 32.21921878948219, 42.38890496366253, 51.88182052485109, 60.49581638563487, 68.05461990158041, 74.4122141343809, 79.45662473266572, 83.11221701420976, 85.34079341400634, 86.14157516416245, 85.55009570246608, 83.63606579905193, 80.50042554945388, 76.27187649141152, 71.10193850231728, 65.15957073880749, 58.62555750150166, 51.686744298662404, 44.53031192832178, 37.33826943808566, 30.282404371727104, 23.51984065543283, 17.188775279293953, 11.405232094771533, 6.2607757933485715, 1.821141909686156, -1.8742089424400437, -4.811636401598246, -7.002027356698599, -8.478778378781758, -9.295068871804745, -9.520557131369245, -9.237682061667988, -8.537723222539368, -7.5167749771140935, -6.27178779568289, -4.896828530982259, -3.4796854067323424, -2.0988805862171955, -0.8212701074727187, 0.2997237412512182, 1.2252171604769744, 1.9312934058263163, 2.4087689621663437, 2.662339691533508, 2.7091685598060087, 2.576976851241792, 2.3017744883231623, 1.92533699112111, 1.4925449062734504, 1.0487074099914193, 0.6369892147614302, 0.29605096001665104, 0.05800804555690816, -0.05318896864882534, -0.02291745728641995, 0.15345337532268913, 0.4704199651327785, 0.9127205575965617, 1.456205213615875, 2.0691652294872718, 2.7140758984535682, 3.3495627454866863, 3.932566301902199, 4.420614649637917, 4.774093111106676, 4.958408987085834, 4.94595348927457, 4.717770638751215, 4.264813887982838, 3.588732840336236, 2.7022442695967435, 1.6290333309047547, 0.40317504090119316, -0.9319069123402665, -2.3249085155205065, -3.71853435437436, -5.051795190945232, -6.262212284036544, -7.288166685698633, -8.071306223024214, -8.558880252741332, -8.70591362151134, -8.47713651495169, -7.848589887308081, -6.808693149332979, -5.3587458098963365, -3.513121486781079, -1.2990366087387395, 1.2441221210429452, 4.06588857258877, 7.106189251047868, 10.297352776154996, 13.567010694017695, 16.840084946696223, 20.040932004185017, 23.095630262875936, 25.934183803139803, 28.492571968013213, 30.71458055430453, 32.553728829306365, 33.97566844173981, 34.95795131697386, 35.48997821619883, 35.57291528738959, 35.219247942440454, 34.451999659717444, 33.30365321717041, 31.815142492346773, 30.03515268187856, 28.01719583475056, 25.817426363793373, 23.492830159197084, 21.099496249599294, 18.69102391643097, 16.317110709467624, 14.022504610542969, 11.846342446185172, 9.820784381519125, 7.970479989792685, 6.312507264140037, 4.856578389351261, 3.6054839758473536, 2.5557407161850954, 1.6984275578831527, 1.0201355589644798, 0.5038325074228406, 0.1299251141649609, -0.12265916543071874, -0.2754557186945327, -0.3495474040080341, -0.3647786937391302, -0.33912244549789355, -0.28821587759268547, -0.22504363419880946, -0.15978532205801627, -0.09982707119034727, -0.0499178859923974, -0.012447232996843752, 0.012183434121431504, 0.025124388172307926, 0.02860786768901657, 0.025475171135641766, 0.01872209549601606, 0.011091170631661125, 0.004732178621667755, 0.0009463047657039817, 2.353554218296597e-05, 0.0011770463095240292, 0.0025726099702042147, 0.0014462237633840933, -0.005701699297180929, -0.022851570151088133, -0.05416807899224364, -0.10368233643899506, -0.1749736911570691, -0.27087184191602004, -0.3931987629619209, -0.5425644154363279, -0.7182294345209315, -0.9180434823494793, -1.138463199842253, -1.3746493246994482, -1.6206381514141546, -1.8695813165116302, -2.1140451177521467, -2.3463294817990796, -2.558810272497362, -2.744286433830237, -2.8963115793784415, -3.0094930339942247, -3.0797430643756587, -3.104472122139345, -3.082712259730514, -3.0151446227778695, -2.9040617261383885, -2.753259635721434, -2.5678621294460853, -2.3540858786061865, -2.1189585690509802, -1.8700011053750067, -1.6148838607689961, -1.3611025762968383, -1.1156726101731649, -0.8848521643339794, -0.6739091838622184, -0.4869424059572819, -0.326764287232185, -0.1948475528855017, -0.09133904058217546, -0.015160491242243094, 0.03584632876480719, 0.06473127449714929, 0.07521089696306724, 0.0714192749800455, 0.05764800667963696, 0.0380883053485305, 0.01658897980187483, -0.003544654299271504, -0.01970909072695374, -0.030113724388287216, -0.033839333074582846, -0.030841810228320662, -0.021901778542904947, -0.008518232695360669, 0.007262863078837731, 0.02303138140296408, 0.036213501301340885, 0.04428401791219638, 0.04497579208614517, 0.0364746747463555, 0.017588969887933778, -0.012104549048046984, -0.05213559996139546, -0.10114283150672847, -0.15691091693262, -0.2164476993252621, -0.2761090893291622, -0.33176583868156395, -0.37900425304966745, -0.413347110799508, -0.4304912576063208, -0.42657930937037997, -0.39843166929921203, -0.34374413215436456, -0.26124790507428325, -0.15082380838190335, -0.013564553428994798, 0.14821488109466924, 0.331015738480623, 0.5302778911248286, 0.7405536040695534, 0.9557215994210206, 1.1692343503303786, 1.3743871811898893, 1.564596845553055, 1.7336785045412253, 1.8761188038362044, 1.9873182832427319, 2.063783851388172, 2.1032702811953135, 2.1048652446739857, 2.069014718831522, 1.997488409161277, 1.8932943535765319, 1.7605554349273838, 1.60429702290689, 1.4302067319850853, 1.244376401933498, 1.0530329960660167, 0.8622714182898766, 0.6778018581910279, 0.5047262173249729, 0.3473526350761724, 0.20903383859148644, 0.0920686630869002, -0.0023372255227320166, -0.07405504301166581, -0.12396361054338877, -0.1538322760719604, -0.1661638087386075, -0.16400752275655625, -0.15074988321540403, -0.12989522573549184, -0.10485014904324913, -0.07872317409871557, -0.05415024816446561, -0.033155098655640376, -0.01705145818770942, -0.006391673609903223, -0.0009636441271979332, 0.00016385113749003825, -0.001448970937168479, -0.0037420489596934306, -0.0043158712532785064, -0.0006136454537663162, 0.009885534556819824, 0.029474584093302978, 0.06003785275484344, 0.1028921207003196, 0.15865861400664363, 0.22717365967381792, 0.30744359345575023, 0.3976471943850063, 0.49518848149906514, 0.5968011311615244, 0.6986813552649437, 0.7966561164212639, 0.886378642286562, 0.9635398040905192, 1.024084657655609, 1.0644230087139286, 1.0816244056217779, 1.0735826360593583, 1.0391282307449483, 0.9781074881597838, 0.8914177371575452, 0.7809938881891567, 0.6497462342560073, 0.5014518188177246, 0.34059680426999933, 0.17216157077769706, 0.001420225658603862, -0.1662732034246246, -0.3257067778784756, -0.4720258506417809, -0.600931650420462, -0.7088541772836816, -0.7931026536983178, -0.8519929403701496, -0.8848539046449699, -0.8920127461490344, -0.874748876476588, -0.8352074775210692, -0.7762774257428484, -0.7014398150419339, -0.614596304385933, -0.5198757840594442, -0.42141991174893534, -0.3231991906338435, -0.2288506688204951, -0.14153926168447065, -0.06384816844123038, 0.00229765720944667, 0.05567876253944726, 0.09580540713287305, 0.12286596157941594, 0.13765000000466518, 0.14145187608856458, 0.13595585700276472, 0.12310978126311212, 0.10499445221768812, 0.08369871722108213, 0.06120432863718563, 0.03926592155095355, 0.019327436454468105, 0.002468807562471816, -0.01062002679840611, -0.019638141626853248, -0.02464751887734509, -0.02602572096774913, -0.024402885326576813, -0.02058040863163142, -0.015442163749553166, -0.009866872413249761, -0.004647319028780114, -0.0004217057740659539, 0.002378562575216618, 0.0035615318894997336, 0.0031866977378436213, 0.0015556687170125074, -0.0008198290596937172, -0.0032682649796463934, -0.005022391641145869, -0.00529198143982978, -0.0033395533580272414, 0.0014464882507589515, 0.009485801847544594, 0.020954260981642173, 0.035750938103968524, 0.05348637988810311, 0.07349361184523862, 0.09486162622378191, 0.11648948292053236, 0.13715730595645814, 0.15560944839230542, 0.17064712486911907, 0.18122067903965164, 0.18651486703769607, 0.1860208992954344, 0.17958932719310086, 0.16745898456494307, 0.15025887808718633, 0.12898163720766131, 0.10492718660975589, 0.0796207211320041, 0.05470932820365409, 0.031843258427330226, 0.012549452815502364, -0.0018940809441968605, -0.010574081165468546, -0.01303902600469045, -0.009368102378609225, -0.00020650424106837773, 0.013237799295346544, 0.02923856835784742, 0.045637121354331366, 0.05996676236291893, 0.06961048043811284, 0.07198310464866849, 0.06472431265333718, 0.045893244610149916, 0.01415177998132326, -0.031077084299664753, -0.08948858628877666, -0.159824806095094, -0.23986564799236865, -0.32649854900149206, -0.4158381339009158, -0.5034087280344401, -0.5843868382195524, -0.6538914903134052, -0.7073087580169626, -0.7406334387516533, -0.7508182367600547, -0.73611752694562, -0.6963163316260039, -0.6329067039231996, -0.5491878690806092, -0.4502657998835377, -0.3429419543197158, -0.2354861245233957, -0.1372981001675422, -0.05845849903881238, -0.009160317897555607, 0.0008970938390972122, -0.03685780464027408, -0.12923112143457735, -0.2806568496563804, -0.4926571936516096, -0.7634088690145869, -1.0874709436984347, -1.4556937537680135, -1.8553142345564329, -2.270253245622978, -2.6816179786331618, -3.068403003973607, -3.408373358509147, -3.679138667717018, -3.859451689986943, -3.9303751664276456, -3.8764579539978925, -3.6868731684551266, -3.356431704007294, -2.886412043800085, -2.2851510369873194, -1.5683912951581251, -0.759351005984116, 0.11189863934739462, 1.0093184999245515, 1.892091501188755, 2.716139638781912, 3.435923948227959, 4.006468090750311, 4.385557546776, 4.536138689174, 4.428586222023723, 4.042727043300558, 3.3695962623593405, 2.4128256242016795, 1.1895784160363712, -0.2690411271126923, -1.9180932864970237, -3.699411865278436, -5.543301249633197, -7.370745358712155, -9.096108744141265, -10.630312641795646, -11.884381222028681, -12.773232666818819, -13.219579558651867, -13.157878672469401, -12.538089569657126, -11.328909617802047, -9.520420407882925, -7.126020856603017, -4.183530154026978, -0.7553717843764228, 3.072184196816089, 7.190735215756748, 11.472711704019972, 15.775211920727342, 19.94461571054957, 23.821865945168057, 27.24823963613804, 30.071404501268503, 32.15160176872207, 33.36785769823936, 33.62343964558576, 32.85065480254182, 31.01480623211736, 28.117074487260297, 24.19617387075076, 19.32867483582696, 13.627999676087237, 7.242082138061331, 0.3491760624849375, -6.8473874947696665, -14.12545269526848, -21.251179871271223, -27.986834187866386, -34.098950271249045, -39.36664747146248, -43.58991110540596, -46.596927775713624, -48.250596576481705, -48.45399997696029, -47.15456318483897, -44.34672469843745, -40.07299267067821, -34.42334681122999, -27.532845450870735, -19.577292821566566, -10.76769844730499, -1.3435268178177453, 8.435097273433147, 18.29595823743649, 27.963793062384166, 37.1696904425862, 45.66081234986231, 53.20834019689974, 59.61473029755452, 64.72003162047778, 68.40687532819256, 70.60396074789578, 71.28791577360859, 70.48366506221748, 68.26327323597863, 64.74174524607906, 60.07204244662027, 54.43911358613158, 48.05292067639263, 41.140717755676384, 33.9388651227076, 26.684399082581848, 19.606398823983653, 12.918254182556923, 6.810947460562638, 1.4473020564064094, -3.042607458379066, -6.564751016939324, -9.06305973791154, -10.520045373624518, -10.956038285820945, -10.426117427750084, -9.016308634152937, -6.838993900396364, -4.0275789505109385, -0.7306398274050899, 2.894219737675201, 6.686748390653489, 10.49091382832693, 14.160407944087835, 17.563336658169327, 20.58619247510972, 23.136905468769903, 25.14690868545927, 26.572193419829354, 27.393719838564476, 27.617557253149883, 27.271899655560635, 26.403957786662993, 25.076647662539024, 23.364901867275663, 21.35177594142036, 19.124519331725512, 16.770975183267904, 14.376459050380173, 12.01966600816711, 9.769824824139215, 7.684736478483752, 5.8094768594229915, 4.175764904621481, 2.8019690440604546, 1.693730169224929, 0.8450727630542813, 0.23974512049346033, -0.1468770330594218, -0.34563761767404577, -0.39137609727999584, -0.3207450910818547, -0.17017101273176002, 0.025952736098231538, 0.23677542540249558, 0.4361880619426193, 0.6036309115224973, 0.7245008801177709, 0.7901807399577832, 0.7977267756394238, 0.7492662355672371, 0.6511702183806715, 0.5130723610591237, 0.3467737700063594, 0.16513767135479865, -0.018957119265564273, -0.19354793735003134, -0.3483581348117501, -0.4753716913567538, -0.5691963010374473, -0.627216897170742, -0.6495249511360764, -0.6386566666069133, -0.599178452409868, -0.5371599758047911, -0.4595809116949277, -0.3737188434446156, -0.2865655789731563, -0.20431217748441802, -0.13192507916212845, -0.07285720220629652, -0.028904497952902095, -0.00020934199388021572, 0.014596507327285572, 0.018126566871499526, 0.013877497566919798, 0.005802216101138382, -0.0021449448349771653, -0.0064531749963144805, -0.004453854036072231, 0.0053596009353265445, 0.02311725194647089, 0.04748225158442606, 0.07569462046493568, 0.103749610386297, 0.1266943302446561, 0.1390248066466882, 0.13515677642526888, 0.1099363598643249, 0.059153016328550787, -0.019984455576585146, -0.12845084097910453, -0.2651347458995007, -0.42669519843213904, -0.6075691993878498, -0.8001445885550481, -0.9950958416743957, -1.1818712831241363, -1.3493097208661962, -1.4863713995116055, -1.5829630197388236, -1.6306670149298368, -1.623449250411622, -1.5582945746554362, -1.4357113164925064, -1.2600655376178473, -1.0397132566379501, -0.7869201011377946, -0.5175549931784916, -0.25047648848871407, -0.006763504687430198, 0.1912092702250223, 0.3208278770563355, 0.3603801642900193, 0.2902275721490373, 0.09393456734714399, -0.24075905156517424, -0.7210866487509634, -1.3486097185425274, -2.118817976798362, -3.0209922638029356, -4.038345130110176, -5.148441410458284, -6.323979487804504, -7.534104365684714, -8.745458145719772, -9.923399910483068, -11.033362923858018, -12.042222482761286, -12.919613682390947, -13.639140480557025, -14.17959477611039, -14.526345461904697, -14.671417761042438, -14.613531018710553, -14.358008002640423, -13.916407535802039, -13.305903429931481, -12.548443867122431, -11.669875683259903, -10.699152075227126, -9.6665455947786, -8.602229375860647, -7.5350893785499915, -6.4916647940843815, -5.49526063955596, -4.565266034708161, -3.716748508039452, -2.960316981501881, -2.3018961380664416, -1.7429401661642716, -1.2809104055193448, -0.9099085479629475, -0.6214175941753034, -0.4050996829773417, -0.2496042138205269, -0.1433303782614115, -0.07508188471520445, -0.03463815722053775, -0.013182405517840882, -0.0035648096327000113, -0.0004004964915436287, -1.39268429425282e-05, -0.0002519236899503062, -0.00019624649282994812, 0.0001874584498128953, 0.0004248097328237981, -0.00010872706534029051, -0.0018835308679769713, -0.0049967045177759005, -0.009059537485145996, -0.013201336453980854, -0.016186641385398024, -0.0166300938039495, -0.013279668779084779, -0.005328112460577263, 0.007295932056539841, 0.023710640263468617, 0.041991983975165716, 0.059263795223196226, 0.07200922594166494, 0.07663291922848445, 0.07028777609997998, 0.0519599946027174, 0.023783938304730395, -0.0074647251580866976, -0.028772030108747775, -0.019279952197319036, 0.05122563426019166, 0.22362290732009013, 0.5504227228672116, 1.0962727121607778, 1.9378786949448508, 3.163239737387546, 4.870116097394972, 7.163760186928905, 10.154185522798524, 13.952447754254793, 18.666231753301783, 24.39491766031069, 31.224233193342425, 39.220679711222445, 48.425952675303144, 58.852211395830864, 70.47986388800909, 83.25327042979123, 97.07767389871621, 111.81772128537408, 127.29731501444672, 143.30092744678205, 159.57646442658228, 175.8415544164406, 191.79623023027068, 207.12668132848287, 221.5119129581522, 234.63272476018668, 246.18118838787657, 255.87031736160165, 263.4435969621622, 268.6870190492998, 271.4465570947697, 271.62610341071644, 269.18872028870067, 264.1589621539081, 256.6232881238919, 246.72850037960245, 234.67821166767857, 220.73015847632854, 205.19608811775018, 188.4223531289048, 170.77617250952434, 152.63429184370747, 134.3714659631384, 116.34917059965622, 98.90494195956425, 82.3440149845076, 66.93346309709459, 52.88936997511745, 40.371006966892296, 29.47893558912145, 20.25537000070187, 12.686713000492173, 6.708095604651321, 2.2098532159542033, -0.9547158392208194, -2.9616074133108907, -4.006201930299085, -4.292890884201934, -4.0250626489514625, -3.3958852946560922, -2.580272689001148, -1.7283807364847452, -0.9608571389202247, -0.3657410917590033, 0.0025432655211929897, 0.12213735454075829, 0.0008428276632228781, -0.3283763791255729, -0.8131453222219386, -1.3882752904891005, -1.982774228001393, -2.5269404529641415, -2.958974300331802, -3.230661320675371, -3.3117708232849954, -3.192887861321104, -2.8864952930364356, -2.426242438542542, -1.8644542241061675, -1.2679204183931718, -0.7123010058773714, -0.2755375476403269, -0.030719306992406964, -0.038916300948699134, -0.34252018667524853, -0.9596297153039473, -1.8799800431297542, -3.0629053037111054, -4.437689262864881, -5.906530847247159, -7.3502246523164505, -8.636503719435003, -9.630832977573577, -10.209309170497178, -10.273175791251068, -9.764070062660565, -8.679433333647815, -7.08725011845586, -5.139220769194231, -3.0814936350043434, -1.2621223442544507, -0.13449484091684483, -0.2561304365978596, -2.2825414609708963, -6.9559352981436575, -15.088655479710974, -27.541535414967353, -45.19757386952801, -68.93157020375115, -99.57713402900727, -137.89406139034452, -184.5332348447814, -240.0018659042152, -304.63086142422566, -378.54534318156095, -461.63960928564586, -553.5577417946795, -653.6846864532969, -761.1564907821432, -874.8597552368141, -993.4413002884854, -1115.3286318835837, -1238.7581145255626, -1361.8103089603899, -1482.4516723971742, -1598.5911287142287, -1708.1639845206855, -1809.1629402744538, -1899.6809763464248, -1977.9611862241736, -2042.4436648701876, -2091.8080115145713, -2125.010115577125, -2141.3253865360457, -2140.4104393919656, -2122.2734640910153, -2087.260146856057, -2036.0438309208894, -1969.6070894436768, -1889.2152920655012, -1796.3829793530015, -1692.8452534524874, -1580.5414742317746, -1461.523391074413, -1337.8906372215222, -1211.7390304700411, -1085.1108246978065, -959.9482673521082, -838.0516792431771, -721.0485813929322, -610.3750446020204, -507.22825899371173, -412.5465711739589, -327.0044327699932, -251.01510404122035, -184.740577697201, -128.1079927823354, -80.83300122735578, -42.448311609457534, -12.327081535692853, 10.28445259504217, 26.231570433497154, 36.41611879293355, 41.76313267656799, 43.19000454920645, 41.578823903593516, 37.752530169549146, 32.45659011562131, 26.344592021671843, 19.968658207032142, 13.77479603397757, 8.102848816094749, 3.1905647984164087, -0.8189488208172709, -3.86716830993119, -5.967072471361034, -7.188955752646677, -7.645766168076785, -7.478548179886112, -6.842634414070257, -5.89513309412345, -4.784189191587519, -3.6403006464280088, -2.569589867288703, -1.649630228039921, -0.9276216865386055, -0.4206918965325777, -0.11807497049152184, 0.015148461713599138, 0.03311411458100482, 0.0034310310782751058, 0.001026003261079089, 0.10197267812289953, 0.3776740907006958, 0.8897051174926928, 1.685560434862611, 2.7954866360917734, 4.23053690088266, 5.981983911999802, 8.021815814753591, 10.304299951198445, 12.768495946586855, 15.34151589601223, 17.94231877771071, 20.48581209853414, 22.887047717212813, 25.065339248828103, 26.94796937055826, 28.47336636171291, 29.593628455250375, 30.276292231968302, 30.50529405265922, 30.281117477458782, 29.620401745084727, 28.555044708830597, 27.129036361154725, 25.395761792429578, 23.415382885244448, 21.25212491479215, 18.97159233529529, 16.638226828531963, 14.313071425618999, 12.052349917530117, 9.906036812594927, 7.91614764600942, 6.115469711430134, 4.526838413038737, 3.1629745206126723, 2.0268611582988516, 1.111836587598304, 0.4010749697327549, -0.12735615614827683, -0.49759070500285585, -0.7343543011875258, -0.8617722006341286, -0.9025449603679322], 'positive_zeros': ['0.43475734108515463502525547192741', '0.46589661966613965993927666612054', '0.61832347012825404223812651152317', '0.794758986820798593238873719151142', '0.885259736099810619523120277285958', '1.17040288994534890482874969268799', '1.37580546528844004142723143907088', '1.38817457350297941992360574867011', '1.86967287483556514081064458890401', '1.88753429925440673377817815429554', '1.95318806206666422542220214242719', '2.05236014544039079387587479111089', '2.12185972904597207072534096091324', '2.21431248410130303331426350607178', '2.22998758619064200829577280762036', '2.27741904580852919683964362799641', '2.73951632506840970770739499870153', '2.77501668657397723823843904394951', '2.96364176519670467990755345573332', '2.96466516312116932419056124280663', '3.10503167744979575370749266538718', '3.19908917824545086579352607242550', '3.31074229452828336802700565226084', '3.36722640436760921509794672440341', '3.66815107272191255448819501806996', '3.69452538797608346830589027071483', '3.71879737786751345914468132891060', '3.73154457695291260741851811483904', '3.78898819833989986959674772892285', '4.03704114848301523145750600403396', '4.05140204787000637561262632148072', '4.13525792869028015852812726466343', '4.27072067636669136190551254018934', '4.71717866697391026894789536631785', '4.75277361801580370315635727664477', '4.80311535919754489650313184130262', '4.82691922256461606151447953314793', '4.98123645088500077148172891073363', '4.99476484466996759052207179899872', '5.00227307683143456615607132168459', '5.50440371670438408391081985404690', '5.59991865772049512847707621172240', '5.60634669039491350946232102271819', '5.62982434307992907307550230988480', '5.66815811017413852373645383493144', '5.70935633126933544826944550826715', '5.76561691624716390849781732566897', '5.80897560335628165379811136194178', '6.10921585531970728125078072489739', '6.13123663781154831089336001237366', '6.21820582768612079921801213871978', '6.35728419678754612185715551093977', '6.42912693009325012409174231198793', '6.45007690567173264611580967832933', '6.50311814105352575721622381441019', '6.56451082728508960424300905688392', '6.80104675350490893402772286688176', '6.91897584985450433192522103167697', '7.09964646898825519975260089061802', '7.19009279548023835481797664768332', '7.27681623740452755856804976266415', '7.28834453139550542794320287628112', '7.40332831515169569416557151091836', '7.49991785942011047067275519888355', '7.74706079664815259884451543263123', '7.81677435096291897239955346133590', '7.86989897993242159194584187615498', '7.87040066890400722857062112065945', '7.892165173707304293127830946335254', '8.145645810533883411236497306271059', '8.193631503982321038110989994387599', '8.236388753181734590328500668889473', '8.281371182598922559619715773547762', '8.379476062494237666420072985022811', '8.562810630973310878637636408319939', '8.654732824494826196271615136423521', '8.659477724848826089415854707324687', '8.684150560448497575617921535116391', '8.855030857430132089092454736846742', '8.988038778088120228695426020351905'], 'prelabel': '16-3332e8-1.1-c1e8-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.158115348990427, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e8-0', 'trace_hash': 48908255186972185, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.43475734108515463502525547193', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.46589661966613965993927666612', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.61832347012825404223812651152', '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': 251105831164.6035, 'bad_primes': [2, 7, 17], 'central_character': '1.1', 'conductor': 15192874202374507341482622976, 'conductor_radical': 238, 'degree': 16, 'dirichlet_coefficients': [1, 0, 4, 0, 4, 0, 0, 0, 0, 0, -4, 0, 20, 0, 16, 0, -8, 0, 8, 0, 0, 0, 4, 0, -8, 0, -16, 0, -16, 0, -8, 0, -16, 0, 0, 0, 8, 0, 80, 0, 12, 0, -4, 0, 0, 0, 4, 0, 0, 0, -32, 0, 0, 0, -16, 0, 32, 0, -16, 0, 32, 0, 0, 0, 80, 0, 0, 0, 16, 0, 0, 0, 24, 0, -32, 0, 0, 0, 4, 0, 3, 0, 28, 0, -32, 0, -64, 0, 20, 0, 0, 0, -32, 0, 32, 0, 56, 0, 0, 0], 'euler11': [1, 4, 36, 156, 772, 2860, 11940, 39604, 142038, 435644, 1444740, 3806660, 11302852, 25123956, 63776196, 77948684, 214358881], 'euler13': [1, -20, 242, -2108, 14688, -85220, 425054, -1848812, 7093070, -24034556, 71834126, -187228340, 419503968, -782685644, 1168087778, -1254970340, 815730721], 'euler17': [1, 8, 28, 56, 70, 56, 28, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler19': [1, -8, 130, -768, 7300, -34608, 246198, -970520, 5606838, -18439880, 88877478, -237376272, 951343300, -1901644032, 6115964530, -7150973912, 16983563041], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, -4, 90, -540, 4440, -29276, 164982, -942116, 4535198, -21668668, 87275478, -356201092, 1242494040, -3475625220, 13323230010, -13619301788, 78310985281], 'euler29': [1, 16, 232, 2288, 20820, 156880, 1107792, 6773040, 39031606, 196418160, 931653072, 3826146320, 14725590420, 46929508912, 137999010472, 275998020944, 500246412961], 'euler3': [1, -4, 16, -48, 125, -292, 616, -1180, 2165, -3540, 5544, -7884, 10125, -11664, 11664, -8748, 6561], 'euler31': [1, 8, 132, 1148, 10509, 76248, 557672, 3391732, 20312877, 105143692, 535922792, 2271504168, 9705282189, 32866265348, 117150485892, 220100912888, 852891037441], 'euler37': [1, -8, 262, -1752, 30896, -174584, 2158362, -10209672, 97900174, -377757864, 2954797578, -8843203352, 57904078256, -121490612664, 672220319158, -759455017064, 3512479453921], 'euler41': [1, -12, 252, -2556, 31145, -259212, 2352656, -16138476, 117350157, -661677516, 3954814736, -17865150252, 88008326345, -296128449756, 1197026268732, -2337051286572, 7984925229121], 'euler43': [1, 4, 134, -32, 6463, -33524, 283988, -1881912, 14761517, -80922216, 525093812, -2665392668, 22095710863, -4704270176, 847062648566, 1087274444428, 11688200277601], 'euler47': [1, -4, 212, -620, 19692, -29500, 1107892, -256724, 51399558, -12066028, 2447333428, -3062778500, 96090678252, -142193904340, 2285193649748, -2026492481852, 23811286661761], 'euler5': [1, -4, 24, -84, 305, -860, 2480, -5972, 14293, -29860, 62000, -107500, 190625, -262500, 375000, -312500, 390625], 'euler53': [1, 0, 182, 396, 18127, 76688, 1202396, 7128472, 67495349, 377809016, 3377530364, 11417079376, 143030749087, 165605415228, 4033913725478, 0, 62259690411361], 'euler59': [1, 16, 308, 3024, 35584, 259920, 2411692, 14703504, 135177774, 867506736, 8395099852, 53382109680, 431184173824, 2161931080176, 12991604361428, 39818423757104, 146830437604321], 'euler61': [1, -32, 780, -13760, 202241, -2496952, 26836056, -251837332, 2095384045, -15362077252, 99856964376, -566760661912, 2800196729681, -11621645101760, 40185892001580, -100567770752672, 191707312997281], 'euler67': [1, 0, 182, -380, 20055, -58520, 1944308, -4410912, 151707053, -295531104, 8727998612, -17600650760, 404130731655, -513047540660, 16463425554758, 0, 406067677556641], 'euler7': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler71': [1, 0, 282, -120, 39300, 5592, 3710766, 2456208, 279763670, 174390768, 18705971406, 2001438312, 998679063300, -216507522120, 36124280065722, 0, 645753531245761], 'euler73': [1, -24, 532, -7840, 111593, -1287208, 14379232, -136783428, 1257242741, -9985190244, 76626927328, -500745794536, 3169044907913, -16252881289120, 80509808385748, -265137564458328, 806460091894081], 'euler79': [1, -4, 412, -980, 78884, -128196, 9972860, -14036628, 919676534, -1108893612, 62240619260, -63205627644, 3072538189604, -3015515271020, 100152031674652, -76815635944636, 1517108809906561], 'euler83': [1, -28, 590, -8124, 100500, -988060, 9343514, -75809692, 692605078, -6292204436, 64367467946, -564959863220, 4769561260500, -32000766183732, 192894820287710, -759809427709556, 2252292232139041], 'euler89': [1, -20, 628, -9348, 170452, -2031132, 27607732, -271275276, 2973835350, -24143499564, 218680845172, -1431885094908, 10694540462932, -52199787729252, 312104250723508, -884626697910580, 3936588805702081], 'euler97': [1, -56, 2040, -52648, 1089417, -18429928, 264789328, -3243680020, 34414745117, -314636961940, 2491402787152, -16820497677544, 96445303719177, -452106289850536, 1699262890055160, -4524703930774328, 7837433594376961], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -4, 16, -48, 125, -292, 616, -1180, 2165, -3540, 5544, -7884, 10125, -11664, 11664, -8748, 6561], [1, -4, 24, -84, 305, -860, 2480, -5972, 14293, -29860, 62000, -107500, 190625, -262500, 375000, -312500, 390625], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 4, 36, 156, 772, 2860, 11940, 39604, 142038, 435644, 1444740, 3806660, 11302852, 25123956, 63776196, 77948684, 214358881], [1, -20, 242, -2108, 14688, -85220, 425054, -1848812, 7093070, -24034556, 71834126, -187228340, 419503968, -782685644, 1168087778, -1254970340, 815730721], [1, 8, 28, 56, 70, 56, 28, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -8, 130, -768, 7300, -34608, 246198, -970520, 5606838, -18439880, 88877478, -237376272, 951343300, -1901644032, 6115964530, -7150973912, 16983563041], [1, -4, 90, -540, 4440, -29276, 164982, -942116, 4535198, -21668668, 87275478, -356201092, 1242494040, -3475625220, 13323230010, -13619301788, 78310985281], [1, 16, 232, 2288, 20820, 156880, 1107792, 6773040, 39031606, 196418160, 931653072, 3826146320, 14725590420, 46929508912, 137999010472, 275998020944, 500246412961], [1, 8, 132, 1148, 10509, 76248, 557672, 3391732, 20312877, 105143692, 535922792, 2271504168, 9705282189, 32866265348, 117150485892, 220100912888, 852891037441], [1, -8, 262, -1752, 30896, -174584, 2158362, -10209672, 97900174, -377757864, 2954797578, -8843203352, 57904078256, -121490612664, 672220319158, -759455017064, 3512479453921], [1, -12, 252, -2556, 31145, -259212, 2352656, -16138476, 117350157, -661677516, 3954814736, -17865150252, 88008326345, -296128449756, 1197026268732, -2337051286572, 7984925229121], [1, 4, 134, -32, 6463, -33524, 283988, -1881912, 14761517, -80922216, 525093812, -2665392668, 22095710863, -4704270176, 847062648566, 1087274444428, 11688200277601], [1, -4, 212, -620, 19692, -29500, 1107892, -256724, 51399558, -12066028, 2447333428, -3062778500, 96090678252, -142193904340, 2285193649748, -2026492481852, 23811286661761], [1, 0, 182, 396, 18127, 76688, 1202396, 7128472, 67495349, 377809016, 3377530364, 11417079376, 143030749087, 165605415228, 4033913725478, 0, 62259690411361], [1, 16, 308, 3024, 35584, 259920, 2411692, 14703504, 135177774, 867506736, 8395099852, 53382109680, 431184173824, 2161931080176, 12991604361428, 39818423757104, 146830437604321], [1, -32, 780, -13760, 202241, -2496952, 26836056, -251837332, 2095384045, -15362077252, 99856964376, -566760661912, 2800196729681, -11621645101760, 40185892001580, -100567770752672, 191707312997281], [1, 0, 182, -380, 20055, -58520, 1944308, -4410912, 151707053, -295531104, 8727998612, -17600650760, 404130731655, -513047540660, 16463425554758, 0, 406067677556641], [1, 0, 282, -120, 39300, 5592, 3710766, 2456208, 279763670, 174390768, 18705971406, 2001438312, 998679063300, -216507522120, 36124280065722, 0, 645753531245761], [1, -24, 532, -7840, 111593, -1287208, 14379232, -136783428, 1257242741, -9985190244, 76626927328, -500745794536, 3169044907913, -16252881289120, 80509808385748, -265137564458328, 806460091894081], [1, -4, 412, -980, 78884, -128196, 9972860, -14036628, 919676534, -1108893612, 62240619260, -63205627644, 3072538189604, -3015515271020, 100152031674652, -76815635944636, 1517108809906561], [1, -28, 590, -8124, 100500, -988060, 9343514, -75809692, 692605078, -6292204436, 64367467946, -564959863220, 4769561260500, -32000766183732, 192894820287710, -759809427709556, 2252292232139041], [1, -20, 628, -9348, 170452, -2031132, 27607732, -271275276, 2973835350, -24143499564, 218680845172, -1431885094908, 10694540462932, -52199787729252, 312104250723508, -884626697910580, 3936588805702081], [1, -56, 2040, -52648, 1089417, -18429928, 264789328, -3243680020, 34414745117, -314636961940, 2491402787152, -16820497677544, 96445303719177, -452106289850536, 1699262890055160, -4524703930774328, 7837433594376961]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3332/2/a/u'], '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': '16-3332e8-1.1-c1e8-0-2', '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}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '16-3332e8-1.1-c1e8-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.158115348990427, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e8-0', 'trace_hash': 48908255186972185, 'z1': {'__RealLiteral__': 0, 'data': '0.43475734108515463502525547193', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '551120404380225331934709011364,590594129564085046271560248306,783818118043282909114322478016,1007476706680164797094651306938,1122200035824808891464044335792,1483661925948075857497746215488,1744040623870169449497928737539,1759720331322618215537337006470', 'Lhash_array': ['551120404380225331934709011364', '590594129564085046271560248306', '783818118043282909114322478016', '1007476706680164797094651306938', '1122200035824808891464044335792', '1483661925948075857497746215488', '1744040623870169449497928737539', '1759720331322618215537337006470'], 'label': '16-3332e8-1.1-c1e8-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3332/2/a/u'}