Lfunction data - 12-432e6-1.1-c3e6-0-0

Formats: - HTML - YAML - JSON - 2024-06-18T02:04:28.330140

• 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': '622869328768522533404620716338,757744997873450516919874190117,985151601666282664445166406422,1150339430551579807038578445634,2037174240808280347976227097924,2389799681979887785214603703730', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -6, 'a6': 0, 'a7': 6, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 274219860.65276814, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '432.1', 'coefficient_field': '1.1.1.1', 'conductor': 6499837226778624, 'conductor_radical': 6, 'degree': 12, 'euler_factors': [[1], [1], [1, 6, -168, -48, 12300, -82506, -1453754, -10313250, 192187500, -93750000, -41015625000, 183105468750, 3814697265625], [1, -6, -384, 14908, -19944, -2637054, 91900446, -904509522, -2346391656, 601591573156, -5315054285184, -28485369059658, 1628413597910449], [1, -51, -195, -3534, 550059, 94832265, -5462621714, 126221744715, 974463072099, -8332987139994, -611993533460595, -213039656640198201, 5559917313492231481], [1, -12, -1176, -39316, -1016784, 27173412, 16823666094, 59699986164, -4907822162256, -416926497348868, -27398548104037656, -614230716169089084, 112455406951957393129], [1, -222, 28551, -2827950, 259523835, -22538855508, 1742432021242, -110733397110804, 6264274474457115, -335360585339691150, 16634447495146906311, -635457917435179106046, 14063084452067724991009], [1, 30, 26355, 1236226, 362584035, 15130227420, 3186329911602, 103778229873780, 17058085363109835, 398914921874542054, 58331914691988673155, 455433810896243948970, 104127350297911241532841], [1, -210, -2760, 384324, 552096960, -31196345610, -3505833433730, -379565937036870, 81730164287797440, 692226195464106012, -60484363432376085960, -55993399447522161577470, 3244150909895248285300369], [1, 456, 70032, 12639372, 4198346304, 668355791208, 72647268176734, 16300529391771912, 2497274291253355584, 183361214647311314268, 24778356897445407879312, 3934910068904772105072744, 210457284365172120330305161], [1, 48, -52116, 3001864, 1349663076, -123641386272, -37354727750178, -3683400538429152, 1197830948059782756, 79368149937720490744, -41049833639924059344276, 1126332575608544924637648, 699053619999045038539170241], [1, 96, 265206, 20979968, 30997452663, 1984533630624, 2039724947269428, 100522581991997472, 79530982909186477167, 2726593142125042017536, 1745838369660812396732886, 32010841723374269480495328, 16890053810563300749953435929], [1, 897, 374295, 115110024, 34022054553, 9337061108679, 2414891032993726, 643519588671265359, 161608305619738659273, 37684942325255276165064, 8445401601975561619187895, 1394923188547409506067075097, 107178930967531784356353269521], [1, 129, -34971, -31517366, -3902024493, 741901043133, 1052539440287118, 58986326236375431, -24666113446343159157, -15840395299309449715538, -1397428248611069559319371, 409842077187936280386945603, 252599333573498060811820806649], [1, -522, 122448, 9346068, -15946914792, 4059391014414, -1114759766751410, 421458153289504722, -171895228376183246568, 10459469502490631370156, 14227414723724535508453968, -6297067839128232220609409046, 1252453015827223091648143056289], [1, -2208, 2747478, -2368790976, 1563772023447, -820812743476896, 350567222051984884, -122200138810609845792, 34660007851106363391663, -7816450219194240227951808, 1349723031749461461900745398, -161486831370975192351669850656, 10888439761782913818722623349689], [1, -453, -119643, 31203366, -1587796437, 12368009864103, -5050047108050786, 2540129497879610037, -66974101025938437117, 270314629185959689324674, -212868516710432412845793483, -165530633311959496406717213247, 75047496554032956760519149093721], [1, 402, -527280, -85634608, 245321825076, 19877822718498, -59790452550726954, 4511888078467394538, 12639072266839277276436, -1001423616554583273551728, -1399585127167631229559496880, 242199687383086242328347278202, 136753052840548005895349735207881], [1, -213, -776787, 87320974, 400716501795, -21812260017825, -135770111734985634, -6560320759741100475, 36248166460796884493355, 2375701082648976763318378, -6356229669773043202752105507, -524205585299701598847724809159, 740195513856780056217081017732809], [1, -120, 1304922, 62445336, 880685715903, 48116431626576, 400606331819372908, 17221400159899442736, 112816090252343444895663, 2863025032459791139669416, 21413356021282488546916034202, -704784715126259202464079666120, 2102085018129621311776010144838961], [1, -750, 1712631, -856289182, 1329382873611, -552522395417796, 658769703611156538, -214940604698244746532, 201181128619768160559579, -50411102825464803859617166, 39222757447908658267370921751, -6681964518676125729884823642750, 3465863721549107204083472585375569], [1, 552, -1152564, -248520632, 1114530677604, 108173831172696, -604232203209226626, 53333917547554863144, 270928426518852340851684, -29785594379808965652657608, -68106748320710488917927164724, 16082199568165167285785823637848, 14364405059580771582276370834385761], [1, 612, -1223124, -415004184, 1212827483508, 194529560235444, -723127027932774218, 111229473658343818428, 396522270290290209898452, -77580988094057306634046152, -130739733825342149133053762964, 37404409915177886945984989356684, 34946659039493167390823397237402409], [1, -924, 2894898, -2881858956, 4446969403551, -3535399630903992, 4122185243102599804, -2492347142398756336248, 2210060595040844157602511, -1009677739816367853794181804, 715012025300270239440382335858, -160887413897363340067772795764476, 122749609618842355502421774953773681], [1, -93, -1689729, 354366248, 1310601420297, -224207143910091, -1053719651856288018, -204627806653854483243, 1091694292727587084643913, 269400227868486204019595816, -1172405558802460456800539333889, -58892360589721412902024663777149, 577951262543040979328274795306257089], [1, 822, -700008, -1935780432, -785220658644, 651750065264550, 1871252128852916038, 671498743992131129550, -833527551818795292445044, -2117134549628969944581689232, -788786535692619860220605989608, 954316481314138795907237874333822, 1196147475686664860781049986817531801], [1, -618, -2681664, 747541444, 5221886911416, -645431049900018, -6358850748853729122, -705279934864096969086, 6235206058791001587275064, 975372029932190945004997852, -3823411642863471615565439087424, -962823863459272510762832664587526, 1702433061239903677780481956434843889], [1, None, None, None, None, None, None, None, None, None, None, None, 3379932275732534791891466777752413049], [1, 2040, 8156982, 11762489624, 26471262415239, 28846821790094544, 45697896231022513140, 37357470776004347221776, 44394957130698524267505999, 25546872163875496694710279736, 22942855997036998227976688025942, 7430664217762540928432106571743960, 4717120417286669419611030657597553321], [1, -612, -3705720, 879617916, 9727871342784, -956970311363604, -15943255343356931498, -1380809591355610120788, 20252958791264015005323456, 2642409109066323299081179068, -16062528942842337379878575059320, -3827613471150737942421383608645284, 9024267965168278308669913635234402529]], 'euler_factors_factorization': [[1], [1], [[[1, 6, -168, -48, 12300, -82506, -1453754, -10313250, 192187500, -93750000, -41015625000, 183105468750, 3814697265625], 1]], [[[1, -6, -384, 14908, -19944, -2637054, 91900446, -904509522, -2346391656, 601591573156, -5315054285184, -28485369059658, 1628413597910449], 1]], [[[1, -51, -195, -3534, 550059, 94832265, -5462621714, 126221744715, 974463072099, -8332987139994, -611993533460595, -213039656640198201, 5559917313492231481], 1]], [[[1, -12, -1176, -39316, -1016784, 27173412, 16823666094, 59699986164, -4907822162256, -416926497348868, -27398548104037656, -614230716169089084, 112455406951957393129], 1]], [[[1, -111, 8115, -513210, 39868995, -2679270159, 118587876497], 2]], [[[1, 15, 13065, 422138, 89612835, 705688215, 322687697779], 2]], [[[1, -210, -2760, 384324, 552096960, -31196345610, -3505833433730, -379565937036870, 81730164287797440, 692226195464106012, -60484363432376085960, -55993399447522161577470, 3244150909895248285300369], 1]], [[[1, 456, 70032, 12639372, 4198346304, 668355791208, 72647268176734, 16300529391771912, 2497274291253355584, 183361214647311314268, 24778356897445407879312, 3934910068904772105072744, 210457284365172120330305161], 1]], [[[1, 48, -52116, 3001864, 1349663076, -123641386272, -37354727750178, -3683400538429152, 1197830948059782756, 79368149937720490744, -41049833639924059344276, 1126332575608544924637648, 699053619999045038539170241], 1]], [[[1, 48, 131451, 4180336, 6658387503, 123154867632, 129961739795077], 2]], [[[1, 897, 374295, 115110024, 34022054553, 9337061108679, 2414891032993726, 643519588671265359, 161608305619738659273, 37684942325255276165064, 8445401601975561619187895, 1394923188547409506067075097, 107178930967531784356353269521], 1]], [[[1, 129, -34971, -31517366, -3902024493, 741901043133, 1052539440287118, 58986326236375431, -24666113446343159157, -15840395299309449715538, -1397428248611069559319371, 409842077187936280386945603, 252599333573498060811820806649], 1]], [[[1, -522, 122448, 9346068, -15946914792, 4059391014414, -1114759766751410, 421458153289504722, -171895228376183246568, 10459469502490631370156, 14227414723724535508453968, -6297067839128232220609409046, 1252453015827223091648143056289], 1]], [[[1, -1104, 764331, -340574064, 113791306287, -24469454686416, 3299763591802133], 2]], [[[1, -453, -119643, 31203366, -1587796437, 12368009864103, -5050047108050786, 2540129497879610037, -66974101025938437117, 270314629185959689324674, -212868516710432412845793483, -165530633311959496406717213247, 75047496554032956760519149093721], 1]], [[[1, 402, -527280, -85634608, 245321825076, 19877822718498, -59790452550726954, 4511888078467394538, 12639072266839277276436, -1001423616554583273551728, -1399585127167631229559496880, 242199687383086242328347278202, 136753052840548005895349735207881], 1]], [[[1, -213, -776787, 87320974, 400716501795, -21812260017825, -135770111734985634, -6560320759741100475, 36248166460796884493355, 2375701082648976763318378, -6356229669773043202752105507, -524205585299701598847724809159, 740195513856780056217081017732809], 1]], [[[1, -60, 650661, 70262328, 232878729171, -7686017035260, 45848500718449031], 2]], [[[1, -375, 786003, -133393466, 305768529051, -56750334858375, 58871586708267913], 2]], [[[1, 552, -1152564, -248520632, 1114530677604, 108173831172696, -604232203209226626, 53333917547554863144, 270928426518852340851684, -29785594379808965652657608, -68106748320710488917927164724, 16082199568165167285785823637848, 14364405059580771582276370834385761], 1]], [[[1, 612, -1223124, -415004184, 1212827483508, 194529560235444, -723127027932774218, 111229473658343818428, 396522270290290209898452, -77580988094057306634046152, -130739733825342149133053762964, 37404409915177886945984989356684, 34946659039493167390823397237402409], 1]], [[[1, -462, 1340727, -821513604, 945170972463, -229605356423982, 350356403707485209], 2]], [[[1, -93, -1689729, 354366248, 1310601420297, -224207143910091, -1053719651856288018, -204627806653854483243, 1091694292727587084643913, 269400227868486204019595816, -1172405558802460456800539333889, -58892360589721412902024663777149, 577951262543040979328274795306257089], 1]], [[[1, 822, -700008, -1935780432, -785220658644, 651750065264550, 1871252128852916038, 671498743992131129550, -833527551818795292445044, -2117134549628969944581689232, -788786535692619860220605989608, 954316481314138795907237874333822, 1196147475686664860781049986817531801], 1]], [[[1, -618, -2681664, 747541444, 5221886911416, -645431049900018, -6358850748853729122, -705279934864096969086, 6235206058791001587275064, 975372029932190945004997852, -3823411642863471615565439087424, -962823863459272510762832664587526, 1702433061239903677780481956434843889], 1]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 0, 'label': '12-432e6-1.1-c3e6-0-0', 'leading_term': '19.0141466467646408717703079700533250178834750674607543453081787157682799870628536418559394', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, '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': [3, 3, 3, 3, 3, 3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/432/4/i/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.01171875', 'prec': 34}, 'plot_values': [19.014146646764644, 18.952412467347568, 18.85062967603969, 18.702723273831825, 18.503013711005025, 18.246349216355924, 17.928629953594957, 17.550978442816408, 17.118109162624403, 16.635153112451945, 16.10746580305583, 15.540540165559909, 14.939291260195743, 14.307734430043983, 13.649943534669818, 12.970153960401559, 12.272739055205482, 11.562241274285569, 10.84351383141673, 10.121423084155996, 9.400732196417163, 8.686048472534189, 7.981776946809437, 7.2920536296431715, 6.6207331206685485, 5.971381908978884, 5.347249951215443, 4.751246697546818, 4.1859289424307375, 3.6534837528309483, 3.1556992623887195, 2.6939560870943033, 2.269224874383064, 1.882068438703529, 1.5326494259503496, 1.2207381203957968, 0.9457274290859181, 0.7066529024545047, 0.5022166883750315, 0.33081536562709646, 0.19056893108011813, 0.07935375631904204, -0.005160858844704886, -0.06547422743678655, -0.1042146494848988, -0.12409895536092655, -0.12789081945255665, -0.11835917199465505, -0.09823736646769668, -0.07018372489452418, -0.036743878787551074, -0.0003144056399795581, 0.03689034356231294, 0.07286800127881538, 0.10585430828419465, 0.1343455984132367, 0.15711706287986196, 0.1732359197646443, 0.1820697477728281, 0.18328992516316, 0.17687066939995716, 0.16308301182192494, 0.14248258662752758, 0.11589311884152716, 0.08438552834151869, 0.04925310763685896, 0.011983114897207374, -0.025776772027802597, -0.06225428638340242, -0.09559047536945542, -0.12387932362313532, -0.14520878382881244, -0.15770294962652082, -0.15956356223109164, -0.1491104187247812, -0.12482010435832047, -0.08536331333203827, -0.029639557775331535, 0.04319335255559997, 0.1336934318409782, 0.24211324385258592, 0.3683832154267781, 0.512099492640727, 0.672520322251355, 0.8485675550532914, 1.0388338101998766, 1.2415961050950857, 1.4548352415565238, 1.676261999885986, 1.903348063044719, 2.1333615065008575, 2.363407114951998, 2.5904744136346847, 2.8114879617167197, 3.0233546205242723, 3.2230145068546183, 3.4074929190747727, 3.5739556450364987, 3.719772168434422, 3.842556848441689, 3.940211082417936, 4.0109646387620375, 4.053413687954702, 4.066567764548794, 4.049873413299261, 4.003219840967153, 3.9269476836176187, 3.821851344248358, 3.689185553443913, 3.5306588126419456, 3.348394888966409, 3.1448976099400765, 2.9230118189183916, 2.6858839556470313, 2.436925766181367, 2.179738177921074, 1.9180445025124835, 1.6556228805817252, 1.3962396292595702, 1.1435932549969738, 0.9012359224958024, 0.6724960197986826, 0.4604149028497063, 0.2676871752306537, 0.09661258909678648, -0.050951407495842455, -0.17363795368852675, -0.27059942919317137, -0.3415255215470932, -0.3866495331175716, -0.4067440004756353, -0.4031096785884099, -0.3775479415940166, -0.3323208414860591, -0.2701005774876138, -0.19390893703193543, -0.1070472084664561, -0.013016299806635065, 0.08456979059630983, 0.18207549853606614, 0.2759388607472368, 0.3627691224080353, 0.4394440432203951, 0.5032037844475015, 0.551739857231121, 0.5832780930659367, 0.5966555863116194, 0.5913820225243174, 0.5676883668562538, 0.5265618787737993, 0.46976591556098113, 0.39984665919130186, 0.3201172072279413, 0.23462082612867244, 0.148078894571102, 0.06582144486589064, -0.006297587044185344, -0.06200357104923605, -0.09472293726752222, -0.09771424840824658, -0.06420930066211838, 0.01243767583685846, 0.13859421941450314, 0.3201911353727968, 0.5625674813763482, 0.8703188948004461, 1.2471530122617749, 1.6957553797373397, 2.217671237013415, 2.8132061341966725, 3.4813499890753845, 4.2197145958577345, 5.024501385844171, 5.890500835385115, 6.811109202834642, 7.7783791434443605, 8.783109215036514, 9.814943168599202, 10.86252533786354, 11.913643079710614, 12.955395841578529, 13.974397916270595, 14.957021161293525, 15.889653165037597, 16.758918457068628, 17.551882179384172, 18.256282309998657, 18.860770550377882, 19.35522426399903, 19.73095712992957, 19.980815869448858, 20.09932806635714, 20.082830816918875, 19.929614900464884, 19.640124863885852, 19.216850084609444, 18.664266110607173, 17.988784963209092, 17.198679206588558, 16.30406674309999, 15.316737401720571, 14.249844073355748, 13.117668252948619, 11.935379209061136, 10.718822938583203, 9.484264618636594, 8.248032159370167, 7.026184942907962, 5.8342226547960765, 4.6868262917102355, 3.597625309864856, 2.5789065019450548, 1.6413924951532404, 0.7940501705843601, 0.043951438118991486, -0.6038225438340263, -1.1462573517436565, -1.5824274025679914, -1.9134703938045166, -2.142510305938545, -2.2745444947317446, -2.316293402562643, -2.275995337830388, -2.1631791904402573, -1.9884170886388097, -1.7630444024432304, -1.4988758309120724, -1.207892483605024, -0.9019402126013185, -0.5924411258847267, -0.29011830288500584, -0.0047330245339970226, 0.25515239505465054, 0.4823716078459417, 0.6713098464857422, 0.8180199382542632, 0.920305390718995, 0.9777499867424659, 0.9916856881284917, 0.9651203045531112, 0.9026225626889525, 0.8101716637992893, 0.6949771860980875, 0.5652346467924628, 0.42986626226420815, 0.29824830965927307, 0.1799271577152714, 0.0843324560245348, 0.020485001721854905, -0.0032877708173801225, 0.02039006964787999, 0.09771114227995681, 0.23348425073599763, 0.43097135183374297, 0.6917614446232376, 1.0156955602967168, 1.4008391895570333, 1.8435046125026406, 2.3383355884554304, 2.878419695062848, 3.455432884273241, 4.059838674937523, 4.681120693426669, 5.308080374057474, 5.929117514463271, 6.532493752471606, 7.1066139811710185, 7.640317049068771, 8.123201863280894, 8.545925514046234, 8.900369385953837, 9.17982379790238, 9.379141795342207, 9.494881374598744, 9.525464455268052, 9.471112783581761, 9.333788304189707, 9.117119692835445, 8.826298964370125, 8.468007275095319, 8.050174899418584, 7.581692334287738, 7.0721666232334215, 6.5316693638113215, 5.97052603790674, 5.399053787486292, 4.827225913125405, 4.2644317649532875, 3.719268097948556, 3.1993729962810273, 2.7113058832911356, 2.260379241248691, 1.8505800872882108, 1.484549649629118, 1.163605104894899, 0.8878088747051989, 0.6560477575380232, 0.4661496395929969, 0.31504358948381217, 0.19894085664278738, 0.11352995277536873, 0.05417514486235081, 0.016114750211745018, -0.005344406428126881, -0.014647341840346379, -0.01583312379456562, -0.012404171930396423, -0.007225993355991488, -0.0024617334451196454, 0.00045658883971165087, 0.0008198428825723933, -0.00140247445232854, -0.005640111257411202, -0.010829579961011701, -0.015546241868137821, -0.018154830026113216, -0.01697215974163605, -0.010434036913514957, 0.002742924010554805, 0.023410397022157272, 0.05185602625783726, 0.08769654343326302, 0.12980369653493215, 0.17626673626301437, 0.22439284663875803, 0.2707482960030145, 0.3112417614239104, 0.34125286956003964, 0.3557921492722838, 0.349686857045569, 0.3177939290413396, 0.25523080679898724, 0.15762262533722413, 0.02134297792967875, -0.15627267648417267, -0.3767251618205818, -0.6401777198813201, -0.9453195479406252, -1.2892843832361731, -1.6676314796810547, -2.0743727206176747, -2.502055327227964, -2.9419045323949984, -3.384054090768898, -3.8178269968409526, -4.232023478385924, -4.615254928084503, -4.956308006600154, -5.244566308332416, -5.470439467314123, -5.625709032872557, -5.703852764097825, -5.700341881245825, -5.612918830644795, -5.441862628330668, -5.190034265308889, -4.862902688452054, -4.468469768114429, -4.017127237846816, -3.5214862206937325, -2.9960120916564277, -2.4565821987684107, -1.920040295447486, -1.403671025056486, -0.9246605364095396, -0.49950395459574654, -0.14338816576428073, 0.13036139956202222, 0.3107933284597765, 0.3898023985994375, 0.3625457475771036, 0.2277444741663909, -0.012130388378936947, -0.35078120430239185, -0.7781227112142921, -1.280432114659802, -1.840651717210221, -2.438811291686367, -3.052543237032534, -3.657691513983324, -4.2290233613631125, -4.741004553930419, -5.168570393542217, -5.487913184539918, -5.67725788181206, -5.717627222116987, -5.593605872781081, -5.2938625116097136, -4.8115988606405375, -4.144901491542992, -3.2969661236240118, -2.2762253582811467, -1.0962169266043882, 0.2247302750588739, 1.6638913653343566, 3.1946677172929903, 4.787249342499651, 6.409434040964675, 8.02751065302089, 9.607146856344091, 11.114296851066559, 12.516157108169782, 13.782220575083752, 14.885045988804698, 15.801013550693142, 16.510915079415895, 17.00045995524451, 17.260864797061167, 17.288992238737748, 17.08725516098593, 16.663542990152045, 16.030877410442592, 15.20711774831728, 14.214456893434113, 13.078495418176484, 11.827467851743226, 10.491450112695981, 9.101482259763086, 7.688783930535865, 6.283704315701707, 4.914874587830513, 3.6084973172331254, 2.3877334704969724, 1.2721940865677235, 0.2774833752576053, -0.5850762333483235, -1.308523543632674, -1.890202744355508, -2.331598456865724, -2.638043024648805, -2.8182749660835302, -2.883908023901443, -2.848838438282865, -2.728623134788237, -2.539854465667188, -2.2994667417946415, -2.024102278532096, -1.729544949316089, -1.4302267168273441, -1.1388186867990993, -0.8659123493313376, -0.61980630289917, -0.4064150270787428, -0.2292855037325263, -0.08970207274794488, 0.01311521410446281, 0.0817147327879748, 0.12007258850755763, 0.13321364815932138, 0.12681807517303992, 0.10683114488739598, 0.07907141940731573, 0.04889258152293871, 0.020902226298352783, -0.001252776805820215, -0.015027114166082248, -0.01904313786537988, -0.013073344667889978, 0.002052259216187241, 0.024604021884032965, 0.05216480816758277, 0.0818840896589194, 0.11075323577601508, 0.13588275649501227, 0.1547640829549256, 0.16550162809735777, 0.1670017845548281, 0.1590879760785376, 0.142543373271877, 0.11907666767523917, 0.09120824634013769, 0.0620816062678347, 0.035193588749851304, 0.014065996889017883, 0.0018795256836819953, 0.0010845058045398889, 0.013008424802228625, 0.037482439569822515, 0.07251729978177902, 0.11404934343457232, 0.15577499656829127, 0.18909150920957407, 0.20316118959110743, 0.18510763681418055, 0.12034122263719564, -0.0069876801008072345, -0.21341563986907502, -0.515486889256693, -0.9290013732802808, -1.4682127796032676, -2.1449997268752554, -2.9680449395572013, -3.9420818422109196, -5.0672532717101735, -6.3385662012450625, -7.745478874207235, -9.271660328017385, -10.89499175878988, -12.587923522829097, -14.317841530145559, -16.047715271155372, -17.736894119036982, -19.34212706071362, -20.8190624812374, -22.123528454483164, -23.21274613252251, -24.04681250356084, -24.590015937631758, -24.812423522504794, -24.69127559871077, -24.21159069831367, -23.366949263409925, -22.16013239750885, -20.60343533069028, -18.718949434281537, -16.53778737982871, -14.09931934343694, -11.450291496735428, -8.643719448968856, -5.737544268038729, -2.7928044492646116, 0.12821268635746763, 2.963703153781818, 5.654085219946339, 8.143838244669169, 10.3833046580316, 12.330028937124137, 13.949879428671347, 15.217919888558104, 16.119123654846362, 16.64907593868468, 16.813585273259154, 16.62812864867117, 16.117117155502232, 15.312928641313585, 14.254998615604954, 12.988231774170549, 11.561093293366467, 10.02391148692682, 8.427199433925855, 6.8201235669258855, 5.248939397060573, 3.7554054086526705, 2.3755836137022053, 1.138934752479332, 0.06768958228907396, -0.8235382695285841, -1.5278215836828934, -2.0456479012817628, -2.384373840526314, -2.5574486284460263, -2.5835120940514202, -2.4852095047329406, -2.2878797026156468, -2.0182643924312655, -1.7032326179862556, -1.3686037269002846, -1.038033281137728, -0.7320043638635302, -0.4670909525626266, -0.2554477928558335, -0.10454490177347123, -0.017125486500515052, 0.008614058234327267, -0.02139877179943204, -0.09772462295826975, -0.2081779249420595, -0.33869996263973273, -0.4742984370140301, -0.5999988115584332, -0.7017589162996756, -0.7673091801632083, -0.7868901742602347, -0.7538125130200787, -0.6648208640674776, -0.5202777465159545, -0.3241532475639197, -0.08382093296770457, 0.19035621904201147, 0.48560874878282745, 0.7874421150999079, 1.0804013004241024, 1.3488893536479583, 1.5780660620241944, 1.7546705841336538, 1.867685321384149, 1.908913649634455, 1.8734230488743213, 1.7598955232758349, 1.5707811236621791, 1.3121210640488055, 0.9932348699060674, 0.6262733802131827, 0.2256691461939607, -0.19248627104426913, -0.6113171121882499, -1.0140150786868063, -1.3846471949259176, -1.7088975634685306, -1.9747004308960767, -2.172832592051297, -2.2973509555231995, -2.345844729792424, -2.319462660439837, -2.2227666521114573, -2.063436115426584, -1.851818169877895, -1.6003388888736836, -1.322822250471288, -1.0337045622823564, -0.7472441626494495, -0.47677085110373135, -0.23398985555419619, -0.028379707498545185, 0.13329009108158807, 0.24729738477121455, 0.31310475327192694, 0.3333221725676126, 0.3135059915379767, 0.26179798819336825, 0.1884173515186568, 0.10501516712794437, 0.023966943043498952, -0.042369777946060186, -0.08240042272021957, -0.08600625586720481, -0.04518574776057682, 0.04545438354227381, 0.18834225918386685, 0.3827375306346444, 0.6247010272120553, 0.9072834522814565, 1.2208716269868736, 1.5536600766572668, 1.892249380149746, 2.2223351523336476, 2.529534129137694, 2.800235546267545, 3.0222467757775666, 3.1854333122864027, 3.2822622175730065, 3.308259017477897, 3.262400976581855, 3.1470382885176558, 2.9677146619349126, 2.732847893265042, 2.4532744037107395, 2.1417504069717888, 1.8121571735602635, 1.4786407652388107, 1.1548317557234347, 0.8530904846706545, 0.58385834778573, 0.3550811352108052, 0.17176240364419465, 0.03576741512559963, -0.054166895360915776, -0.10221714490591877, -0.11506433378750969, -0.10127384858646643, -0.07050941410417395, -0.03263467974879508, 0.0032511844269617622, 0.029790549047922003, 0.04231499542462387, 0.03968272003270458, 0.024948072217551295, 0.0058222362449054125, -0.005113629484795511, 0.009522617680028619, 0.07154405261371717, 0.20653179094734897, 0.44289244884466117, 0.8106655858543204, 1.3401378884820043, 2.060312612941853, 2.9972972323664386, 4.1726802791707795, 5.6019777485848055, 7.293339189131451, 9.246491678998852, 11.451845742895994, 13.889959802291639, 16.531384301130508, 19.337162879691927, 22.259852854494664, 25.244541501757734, 28.230192493366967, 31.15134029618436, 33.940305472576085, 36.530197977896115, 38.85668374267957, 40.86022186967037, 42.487967272046674, 43.69567079886654, 44.45037874082449, 44.731309344429704, 44.529981081697926, 43.85082607707944, 42.710836587471555, 41.13964635370972, 39.17878827829205, 36.87905159940221, 34.298675334302764, 31.501556699115987, 28.555096261964394, 25.52843534736639, 22.489205684988242, 19.501157215392595, 16.622328097939477, 13.903581160232417, 11.387500974304741, 9.107080168318303, 7.0849821182836665, 5.333570101078494, 3.8553445656031555, 2.6437912788337314, 1.6843787557653207, 0.9557959872582676, 0.4315490289969243, 0.08165813143607692, -0.1256395497372809, -0.2222661328643606, -0.23879529584901757, -0.20313351247201752, -0.13946373620573713, -0.06748568690847373, -0.00197116813755849, 0.047372775908374666, 0.07573501133847463, 0.08275230572172708, 0.07183372611242059, 0.04930967115234007, 0.023466698724275682, 0.003538537256694296, -0.001285968180820082, 0.017223676836142295, 0.06555680508975935, 0.1478646569813601, 0.2655723859436963, 0.41720901198334254, 0.5984561186990728, 0.8024072950757359, 1.0200668103412953, 1.2409638760353365, 1.4538318730163788, 1.6473723497558463, 1.8109961586261492, 1.9355857564056915, 2.0141494480657265, 2.042187283057214, 2.01797010860917, 1.942660505552365, 1.820232991097003, 1.6572714139091442, 1.4624151165106198, 1.2457549375558328, 1.0181828498158045, 0.7907063008709473, 0.5737631063619986, 0.37651900156584456, 0.20629441616121913, 0.06817254409886819, -0.03522937016926613, -0.10381976749474663, -0.13991811913544544, -0.14793694671258234, -0.1339054118506708, -0.10488144553764767, -0.06829873985573519, -0.031294512548196436, -4.486578950080155e-05, 0.020796048326093733, 0.028510842340425935, 0.022552166592582315, 0.004564415899546407, -0.021824106991579804, -0.05144727214714219, -0.07826369910597988, -0.09620204852196716, -0.10014659768803406, -0.08700096090123173, -0.05675432708142516, -0.01347086417761074, 0.03386952958709439, 0.07075314742980053, 0.07681824081409554, 0.02588398368975232, -0.11364604470027811, -0.37797369311583395, -0.8067024394980271, -1.4412510252343862, -2.322993655056415, -3.491174997326905, -4.980641305447956, -6.819530573398813, -9.02710452136178, -11.611880299289448, -14.56993241814978, -17.883604269383174, -21.52070843559293, -25.434429380006687, -29.56439094599842, -33.83755798275072, -38.169774460703515, -42.46799573502967, -46.63318639319618, -50.564568345763895, -54.16296138016957, -57.33358597839047, -59.989438465747575, -62.0545989313607, -63.468446408376074, -64.18866593801773, -64.19150531956151, -63.472672548548445, -62.04767612099111, -59.951983828906286, -57.24138243203545, -53.98822058790984, -50.27824939302509, -46.2075592134354, -41.87925356156468, -37.40062566527867, -32.878844449976334, -28.416359355247927, -24.107500058941554, -20.035578118660656, -16.270627291612975, -12.867519571937798, -9.86460116034828, -7.283271828223188, -5.128411033133676, -3.3894559556475006, -2.0419969986369835, -1.0500945935627228, -0.3689183518806892, 0.05243363961339758, 0.2680202873201028, 0.3322455030230076, 0.29708110057252196, 0.20967875341938746, 0.11049342292875584, 0.031897289084181914, -0.0026689257281410435, 0.02101614036926355, 0.10824874069865353, 0.2561918846019188, 0.45507213960801063, 0.6897115847811119, 0.9413611811408891, 1.1895491089203358, 1.4138693395517588, 1.5956406944110295, 1.7193609506340766, 1.7740126526605822, 1.753781643420666, 1.658262082297293, 1.492363400703221, 1.2658555452873745, 0.992708420895847, 0.6900445309071453, 0.37665849727217765, 0.07164687706570619, -0.20692575637445004, -0.4432316361058413, -0.6246991296902225, -0.7429520932608751, -0.7943101351317645, -0.7799139235479925, -0.7055104591723736, -0.580913467396727, -0.41921100825960733, -0.23571875089230004, -0.04677409532459946, 0.13152303581856817, 0.2845489042842477, 0.40027579423869836, 0.4701624754088714, 0.48978712894433013, 0.4591677266934718, 0.38275017231879405, 0.269054307208908, 0.12994403306589836, -0.020358715155669428, -0.16643935279569588, -0.2929852814806888, -0.38614490392858014, -0.4348234965677819, -0.4317881514313806, -0.3745255768813371, -0.26576162672758796, -0.11365186374098883, 0.06843688749732119, 0.2626073813749527, 0.44745781210996993, 0.5994340025909751, 0.6944105340679111, 0.7094097699365304, 0.6243960876483401, 0.42397391321589956, 0.09889357098482902, -0.35275065849876197, -0.9248041074828888, -1.6027697218171277, -2.3639804199650474, -3.178306916336479, -4.009382847725956, -4.816491591622614, -5.5568015968703115, -6.187537936683689, -6.668415644765538, -6.964100368038902, -7.046669634230134, -6.898054217674374, -6.511282519603132, -5.8914021246849595, -5.05593727645021, -4.034734801837896, -2.8692767455908457, -1.6109367920854203, -0.31861086550496376, 0.9438863922686049, 2.110750626580483, 3.1174329194538246, 3.904065550687287, 4.418550910105487, 4.619276063164592, 4.477384219906331, 3.9785846331917942, 3.12445746768423, 1.9324731235499175, 0.43539033585175246, -1.3200506063064574, -3.2750595786950742, -5.36135778106497, -7.504407165205671, -9.626801637634953, -11.651776270915436, -13.506584534641215, -15.125962493836953, -16.455263656209247, -17.452369127771856, -18.08924074177971, -18.352904090564095, -18.24575585014343, -17.785554000744984, -17.003459879088616, -15.941884440405527, -14.652090145426662, -13.19152626050376, -11.621299883641274, -10.002786743164146, -8.394392844270417, -6.849008844236397, -5.411869889285433, -4.11899950821286, -2.9961303079058337, -2.0580354395476856, -1.308731027048123, -0.7422562267072413, -0.3439309899316355, -0.09199614506113224, 0.04039756654219699, 0.08305622304875887, 0.06660872189384211, 0.02048625146260972, -0.02888092052581261, -0.059551753443520546, -0.05514041964890235, -0.0054223380438076585, 0.09350761772914801, 0.23951658030670248, 0.425139760331442, 0.6386286786740889, 0.8652122957099404, 1.0884793145162788, 1.291818811125754, 1.459868289788201, 1.579694272936812, 1.6417780022130222, 1.6406287452115016, 1.5751012634544848, 1.4484777913490918, 1.2680837428475522, 1.0446039808039935, 0.7912484194791998, 0.5226947742510363, 0.25402542245056686, -0.00035981722837865877, -0.227769270726445, -0.41802009838374504, -0.5640389754385178, -0.6621964366851089, -0.7123770064121396, -0.7177336053303217, -0.6841968724995072, -0.6198094421243626, -0.5339445394525795, -0.436429964727232, -0.33665287046756515, -0.24276558571212078, -0.16107271878307847, -0.09562987639824093, -0.04808550727909642, -0.017764123491170732, -0.002022027615731703, 0.003154416178968823, 0.0023713077167837942, -6.488696678944208e-05, -0.0010794423273939203, 0.00027979371924441687, 0.002080729768661882, -0.001048073867197734, -0.018201954933442573, -0.06216547101830299, -0.14903744898473317, -0.2975171035537359, -0.5278738522494667, -0.8606483348383732, -1.3151822256549686, -1.9080928663721803, -2.651715507008751, -3.552654122086874, -4.61053789517096, -5.817147974044471, -7.156193393125154, -8.603239858067393, -10.126148290751035, -11.685943584858313, -13.238179431977747, -14.735288634063993, -16.128662619426336, -17.37058788980363, -18.416637606817584, -19.227721113811874, -19.77259330764415, -20.029933104900024, -19.988744839914165, -19.64898621715836, -19.02186346006823, -18.12937538297627, -17.003908535080114, -15.685844741436362, -14.22134012012197, -12.66016325445566, -11.053494958750091, -9.451683981862827, -7.901522951363642, -6.443888243964094, -5.112154550829773, -3.9311071258287607, -2.9164475463114456, -2.074566416236632, -1.4028674220568866, -0.8908237343324649, -0.5214492501597784, -0.27306507494556126, -0.12122766411466637, -0.04068560703772812, -0.0072857193885014, 0.00035359943398856526, -0.0004818324275547502, 0.00250419170287034, 0.016212347425720103, 0.04224986442387343, 0.07751599820146782, 0.11521343505774, 0.1462061763613182, 0.16060559080672163, 0.14943833568603132, 0.10625421874135083, 0.02854228543133705, -0.08116828582059281, -0.2146551527143469, -0.3578555809579832, -0.4912126944499757, -0.5905979505977773, -0.6287277265075859, -0.5770429099718026, -0.40781041443580596, -0.09632162762985344, 0.37686964515368226, 1.0238392085253303, 1.847564759595247, 2.8408218494853146, 3.985603123924056, 5.2531356639533735, 6.604543060323057, 7.992362309285914, 9.3632007720773, 10.660188785421147, 11.825788170085922, 12.804885255013257, 13.547980649355432, 14.015097717030851, 14.178222973551701, 14.022656275072368, 13.548181390437529, 12.76949891506478, 11.716474463784301, 10.433088971071971, 8.974259426868482, 7.4028956765121, 5.786573857338779, 4.194087356896955, 2.69203836970039, 1.3403645173209437, 0.1888689492530368, -0.7254420977741106, -1.3802630063430146, -1.768967345420072, -1.9009895594061288, -1.8010718338960605, -1.507414331353729, -1.0690227126235157, -0.5423919632427425, 0.012206623513798472, 0.534648142195459, 0.9689227171189523, 1.2668206593736238, 1.3911089833571655, 1.3179171185378067, 1.0382026487888503, 0.5583484151096746, -0.10023499984740354, -0.9024930070499618, -1.8023174071465198, -2.745681899399098, -3.674033828510654, -4.528113890072315, -5.251830084625269, -5.796352987313513, -6.123649104902316, -6.208453842550855, -6.039900319426856, -5.622338855933002, -4.975288492344822, -4.13256417380774, -3.139493867147336, -2.049913899609614, -0.9228413741250201, 0.1811767325343275, 1.2040012946162932, 2.093853853409727, 2.808485117139886, 3.3176110542801216, 3.6045983768824477, 3.667615915838475, 3.5197286187667753, 3.1873038527725526, 2.7078911187358727, 2.127478655690857, 1.4973726208590579, 0.8708535321622639, 0.2989867226123075, -0.17296621951848268, -0.5085323744845986, -0.682362355284685, -0.6818388835005751, -0.5079624180074321, -0.17507594794828177, 0.2904270618061143, 0.8522145543491431, 1.4667049147931186, 2.0862583185201116, 2.6628805479190456, 3.151858054234834, 3.515130722161214, 3.7241593180200043, 3.762076658046829, 3.62517286600109, 3.323367528855214, 2.8797093155787508, 2.3289221277866785, 1.7150549456545459, 1.088520615906563, 0.5026481172975338, 0.009918884748452959, -0.3417243401345382, -0.5123354759334605, -0.4728312565675393, -0.20721677828566734, 0.2859728859447259, 0.9931893830090956, 1.8864913487022827, 2.9255137416417556, 4.059683981947331, 5.231086300332252, 6.377927954871047, 7.438458619527911, 8.355551033821289, 9.080080759954138, 9.57336029566998, 9.809402312058038, 9.77648602325891, 9.478528078623325, 8.934831644437244, 8.17771686739065, 7.250280460436098, 6.203638490822575, 5.093902324445227, 3.9789960802101403, 2.9142488937071205, 1.9489363094812897, 1.123517577493829, 0.4674982174796534, -0.002009313591605447, -0.28108691472374986, -0.3787143982931704, -0.3155174939382547, -0.12180577919843978, 0.16488653695782712, 0.5026984514501924, 0.8487285325585692, 1.1622097495031614, 1.4074096324680916, 1.556074597532199, 1.589255747304493, 1.4985056772869174, 1.2862588736685585, 0.9653838984849924, 0.5579990339478254, 0.09352340127933201, -0.3936770238198569, -0.8668649120981824, -1.2896923777856084, -1.628896272118559, -1.8569088979613573, -1.9539679082448211, -1.9092644341436504, -1.7216547488741913, -1.399729107949211, -0.9612499292500643, -0.4319659316185316, 0.15649428647262464, 0.7688616547852255, 1.3685894822028024, 1.9202665468723696, 2.3920951937300297, 2.758036360383631, 2.9992926362251726, 3.105280387244242, 3.074031137944833, 2.912226268687253, 2.6346071889845875, 2.2623581507963375, 1.8213647680280374, 1.3402674173321334, 0.8484933074932529, 0.3744226390401431, -0.05674878923129279, -0.4246009333612951, -0.7145725548078568, -0.9185585745257794, -1.0349503209621573, -1.0683200899482985, -1.0286691498089018, -0.9302439562989905, -0.7901013935599415, -0.6265435329332653, -0.4575479201048253, -0.2993059775789269, -0.1651059898485273, -0.0644859428566846, -0.0027299354421947046, 0.01924569133881514, 0.004596830172834877, -0.040141385716924174, -0.10597805121980804, -0.18251466967699717, -0.25907927862074315, -0.3258250126722633, -0.37471004610329284, -0.4003224662104398, -0.4002268404180688, -0.3750483744117806, -0.3282606394637395, -0.26564906402939026, -0.19457524984810246, -0.12307513538772961, -0.05878680277786832, -0.007985789518154813, 0.025240094820141362, 0.03958160337889892, 0.03682080950733067, 0.021841043120479707, 0.0022552249464326034, -0.01228914132984575, -0.011054997059014108, 0.016665226700562467, 0.08034983215097763, 0.1870684145331623, 0.3404822450917659, 0.540090966918101, 0.7808200030464816, 1.0530020454200473, 1.3428115711710258, 1.6332311263574089, 1.9052207734720745, 2.139154672393254, 2.316435627073535, 2.4211619552712205, 2.4419165911395986, 2.3729546151574628, 2.214853052262045, 1.974826605092298, 1.6665086208816005, 1.3092843707686534, 0.9269266596129593, 0.5455046031828786, 0.19116566027483192, -0.11218363723654848, -0.3451637414496762, -0.49504885524635167, -0.5575044419386209, -0.5376080693635563, -0.4500710900972088, -0.31863760221276766, -0.17466242875348545, -0.05476501338742229, 0.00225565054101192, -0.04099221419991881, -0.21662965904689735, -0.5476142371743995, -1.044090957737658, -1.700389694370298, -2.492910438648517, -3.3792834593189305, -4.298761410812973, -5.174012794413689, -5.914267166449738, -6.419693082220556, -6.587053629393479, -6.316872701696781, -5.520278575792338, -4.125612669284453, -2.084654809211306, 0.6218888854163883, 3.97971143028656, 7.936952621419543, 12.404908590489281, 17.26012873948045, 22.348084250893912, 27.488781068764236, 32.48388294695754, 37.12517708271124, 41.20594652332875, 44.53198817082712, 46.932211199431705, 48.268737034818194, 48.44696359956172, 47.41948009929409, 45.189129898238214, 41.810522852356385, 37.38892331142592, 32.07958022606922, 26.087670471906968, 19.659422315545843, 13.070532999971656, 6.611579322896112, 0.5609279004403018, -4.867773300237543, -9.509230863019651, -13.233467646640348, -15.938514704111629], 'positive_zeros': ['0.49135726252674069610118451685559', '0.59775540494914384027184748724913', '0.77714758427039338474854648909499', '0.907457804496342490142682764620698', '1.46057386210535738927917856939661', '1.60704711569694752369754695300515', '1.82700293904237494811054717978566', '1.88521954042354041232958766442337', '2.50855212387265743601596999697437', '2.70723383414267774836789762095797', '2.91386058460510839239441432550468', '2.92258370283736793171487750835690', '3.54702745411424664082801721627658', '3.61841275277353791608314136765253', '3.63871941325803115186987531066625', '3.72457717035284500132820565104019', '3.90391361374538676016876685428778', '4.29472883958698800722248547965727', '4.35888272961016239601942745538897', '4.60355272866450698454612507944431', '4.97232425510854870651248075460153', '5.21309041669300756428632695391312', '5.31952230396786253254015676130635', '5.36590699786218827201142200309372', '5.55997900315628847411395823757965', '5.56272297047842735543954622615702', '5.68308956393512371229913626627684', '6.10494894329335736355939460757899', '6.38753063443207193491379755348430', '6.59050428146243355153276393982832', '6.60353944791242709294304998921743', '6.76543356199108393010424069277863', '6.95557525873795872850284980942614', '7.18543081733009177634657152752821', '7.29290503708181730524802468319858', '7.34259974804988356250551071267054', '7.67978664136904650093866855614460', '7.75664788777459684889428784316968', '7.82074058873975976961512964787901', '7.83561052768409857556289583536718', '8.441318957885998607343805793167232', '8.519927193899569603015086230562265', '8.605216276222903088937081103753824', '8.615261309539596262799341875380578', '8.936942791596996798686845524861202', '9.035177563126775349624004968861579', '9.084284733118586703694844138611143', '9.179089866010545083259512908396359', '9.225654588517308564091878127860935', '9.806709419216872215282923563498809', '9.888223004249781631397133525360902', '9.895743152782518353590147244877203', '10.11616536141683539518595881109409', '10.24515533876450891943331456777933', '10.35779456018455401185458771613370', '10.46059654366238936345170826877961', '10.56146063106554445987496295208883', '10.79587681856731326501514790541684', '10.92493364198701590962332837701505', '11.28047410035701244660470409145989'], 'prelabel': '12-432e6-1.1-c3e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.048645870179444, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e6-0', 'trace_hash': 2195563696884184821, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.49135726252674069610118451686', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.59775540494914384027184748725', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.77714758427039338474854648909', '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': 274219860.65276814, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 6499837226778624, 'conductor_radical': 6, 'degree': 12, 'dirichlet_coefficients': [1, 0, 0, 0, -6, 0, 6, 0, 0, 0, 51, 0, 12, 0, 0, 0, 222, 0, -30, 0, 0, 0, 210, 0, 204, 0, 0, 0, -456, 0, -48, 0, 0, 0, -36, 0, -96, 0, 0, 0, -897, 0, -129, 0, 0, 0, 522, 0, 420, 0, 0, 0, 2208, 0, -306, 0, 0, 0, 453, 0, -402, 0, 0, 0, -72, 0, 213, 0, 0, 0, 120, 0, 750, 0, 0, 0, 306, 0, -552, 0, 0, 0, -612, 0, -1332, 0, 0, 0, 924, 0, 72, 0, 0, 0, 180, 0, 93, 0, 0, 0], 'euler11': [1, -51, -195, -3534, 550059, 94832265, -5462621714, 126221744715, 974463072099, -8332987139994, -611993533460595, -213039656640198201, 5559917313492231481], 'euler13': [1, -12, -1176, -39316, -1016784, 27173412, 16823666094, 59699986164, -4907822162256, -416926497348868, -27398548104037656, -614230716169089084, 112455406951957393129], 'euler17': [1, -222, 28551, -2827950, 259523835, -22538855508, 1742432021242, -110733397110804, 6264274474457115, -335360585339691150, 16634447495146906311, -635457917435179106046, 14063084452067724991009], 'euler19': [1, 30, 26355, 1236226, 362584035, 15130227420, 3186329911602, 103778229873780, 17058085363109835, 398914921874542054, 58331914691988673155, 455433810896243948970, 104127350297911241532841], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, -210, -2760, 384324, 552096960, -31196345610, -3505833433730, -379565937036870, 81730164287797440, 692226195464106012, -60484363432376085960, -55993399447522161577470, 3244150909895248285300369], 'euler29': [1, 456, 70032, 12639372, 4198346304, 668355791208, 72647268176734, 16300529391771912, 2497274291253355584, 183361214647311314268, 24778356897445407879312, 3934910068904772105072744, 210457284365172120330305161], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 48, -52116, 3001864, 1349663076, -123641386272, -37354727750178, -3683400538429152, 1197830948059782756, 79368149937720490744, -41049833639924059344276, 1126332575608544924637648, 699053619999045038539170241], 'euler37': [1, 96, 265206, 20979968, 30997452663, 1984533630624, 2039724947269428, 100522581991997472, 79530982909186477167, 2726593142125042017536, 1745838369660812396732886, 32010841723374269480495328, 16890053810563300749953435929], 'euler41': [1, 897, 374295, 115110024, 34022054553, 9337061108679, 2414891032993726, 643519588671265359, 161608305619738659273, 37684942325255276165064, 8445401601975561619187895, 1394923188547409506067075097, 107178930967531784356353269521], 'euler43': [1, 129, -34971, -31517366, -3902024493, 741901043133, 1052539440287118, 58986326236375431, -24666113446343159157, -15840395299309449715538, -1397428248611069559319371, 409842077187936280386945603, 252599333573498060811820806649], 'euler47': [1, -522, 122448, 9346068, -15946914792, 4059391014414, -1114759766751410, 421458153289504722, -171895228376183246568, 10459469502490631370156, 14227414723724535508453968, -6297067839128232220609409046, 1252453015827223091648143056289], 'euler5': [1, 6, -168, -48, 12300, -82506, -1453754, -10313250, 192187500, -93750000, -41015625000, 183105468750, 3814697265625], 'euler53': [1, -2208, 2747478, -2368790976, 1563772023447, -820812743476896, 350567222051984884, -122200138810609845792, 34660007851106363391663, -7816450219194240227951808, 1349723031749461461900745398, -161486831370975192351669850656, 10888439761782913818722623349689], 'euler59': [1, -453, -119643, 31203366, -1587796437, 12368009864103, -5050047108050786, 2540129497879610037, -66974101025938437117, 270314629185959689324674, -212868516710432412845793483, -165530633311959496406717213247, 75047496554032956760519149093721], 'euler61': [1, 402, -527280, -85634608, 245321825076, 19877822718498, -59790452550726954, 4511888078467394538, 12639072266839277276436, -1001423616554583273551728, -1399585127167631229559496880, 242199687383086242328347278202, 136753052840548005895349735207881], 'euler67': [1, -213, -776787, 87320974, 400716501795, -21812260017825, -135770111734985634, -6560320759741100475, 36248166460796884493355, 2375701082648976763318378, -6356229669773043202752105507, -524205585299701598847724809159, 740195513856780056217081017732809], 'euler7': [1, -6, -384, 14908, -19944, -2637054, 91900446, -904509522, -2346391656, 601591573156, -5315054285184, -28485369059658, 1628413597910449], 'euler71': [1, -120, 1304922, 62445336, 880685715903, 48116431626576, 400606331819372908, 17221400159899442736, 112816090252343444895663, 2863025032459791139669416, 21413356021282488546916034202, -704784715126259202464079666120, 2102085018129621311776010144838961], 'euler73': [1, -750, 1712631, -856289182, 1329382873611, -552522395417796, 658769703611156538, -214940604698244746532, 201181128619768160559579, -50411102825464803859617166, 39222757447908658267370921751, -6681964518676125729884823642750, 3465863721549107204083472585375569], 'euler79': [1, 552, -1152564, -248520632, 1114530677604, 108173831172696, -604232203209226626, 53333917547554863144, 270928426518852340851684, -29785594379808965652657608, -68106748320710488917927164724, 16082199568165167285785823637848, 14364405059580771582276370834385761], 'euler83': [1, 612, -1223124, -415004184, 1212827483508, 194529560235444, -723127027932774218, 111229473658343818428, 396522270290290209898452, -77580988094057306634046152, -130739733825342149133053762964, 37404409915177886945984989356684, 34946659039493167390823397237402409], 'euler89': [1, -924, 2894898, -2881858956, 4446969403551, -3535399630903992, 4122185243102599804, -2492347142398756336248, 2210060595040844157602511, -1009677739816367853794181804, 715012025300270239440382335858, -160887413897363340067772795764476, 122749609618842355502421774953773681], 'euler97': [1, -93, -1689729, 354366248, 1310601420297, -224207143910091, -1053719651856288018, -204627806653854483243, 1091694292727587084643913, 269400227868486204019595816, -1172405558802460456800539333889, -58892360589721412902024663777149, 577951262543040979328274795306257089], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 6, -168, -48, 12300, -82506, -1453754, -10313250, 192187500, -93750000, -41015625000, 183105468750, 3814697265625], [1, -6, -384, 14908, -19944, -2637054, 91900446, -904509522, -2346391656, 601591573156, -5315054285184, -28485369059658, 1628413597910449], [1, -51, -195, -3534, 550059, 94832265, -5462621714, 126221744715, 974463072099, -8332987139994, -611993533460595, -213039656640198201, 5559917313492231481], [1, -12, -1176, -39316, -1016784, 27173412, 16823666094, 59699986164, -4907822162256, -416926497348868, -27398548104037656, -614230716169089084, 112455406951957393129], [1, -222, 28551, -2827950, 259523835, -22538855508, 1742432021242, -110733397110804, 6264274474457115, -335360585339691150, 16634447495146906311, -635457917435179106046, 14063084452067724991009], [1, 30, 26355, 1236226, 362584035, 15130227420, 3186329911602, 103778229873780, 17058085363109835, 398914921874542054, 58331914691988673155, 455433810896243948970, 104127350297911241532841], [1, -210, -2760, 384324, 552096960, -31196345610, -3505833433730, -379565937036870, 81730164287797440, 692226195464106012, -60484363432376085960, -55993399447522161577470, 3244150909895248285300369], [1, 456, 70032, 12639372, 4198346304, 668355791208, 72647268176734, 16300529391771912, 2497274291253355584, 183361214647311314268, 24778356897445407879312, 3934910068904772105072744, 210457284365172120330305161], [1, 48, -52116, 3001864, 1349663076, -123641386272, -37354727750178, -3683400538429152, 1197830948059782756, 79368149937720490744, -41049833639924059344276, 1126332575608544924637648, 699053619999045038539170241], [1, 96, 265206, 20979968, 30997452663, 1984533630624, 2039724947269428, 100522581991997472, 79530982909186477167, 2726593142125042017536, 1745838369660812396732886, 32010841723374269480495328, 16890053810563300749953435929], [1, 897, 374295, 115110024, 34022054553, 9337061108679, 2414891032993726, 643519588671265359, 161608305619738659273, 37684942325255276165064, 8445401601975561619187895, 1394923188547409506067075097, 107178930967531784356353269521], [1, 129, -34971, -31517366, -3902024493, 741901043133, 1052539440287118, 58986326236375431, -24666113446343159157, -15840395299309449715538, -1397428248611069559319371, 409842077187936280386945603, 252599333573498060811820806649], [1, -522, 122448, 9346068, -15946914792, 4059391014414, -1114759766751410, 421458153289504722, -171895228376183246568, 10459469502490631370156, 14227414723724535508453968, -6297067839128232220609409046, 1252453015827223091648143056289], [1, -2208, 2747478, -2368790976, 1563772023447, -820812743476896, 350567222051984884, -122200138810609845792, 34660007851106363391663, -7816450219194240227951808, 1349723031749461461900745398, -161486831370975192351669850656, 10888439761782913818722623349689], [1, -453, -119643, 31203366, -1587796437, 12368009864103, -5050047108050786, 2540129497879610037, -66974101025938437117, 270314629185959689324674, -212868516710432412845793483, -165530633311959496406717213247, 75047496554032956760519149093721], [1, 402, -527280, -85634608, 245321825076, 19877822718498, -59790452550726954, 4511888078467394538, 12639072266839277276436, -1001423616554583273551728, -1399585127167631229559496880, 242199687383086242328347278202, 136753052840548005895349735207881], [1, -213, -776787, 87320974, 400716501795, -21812260017825, -135770111734985634, -6560320759741100475, 36248166460796884493355, 2375701082648976763318378, -6356229669773043202752105507, -524205585299701598847724809159, 740195513856780056217081017732809], [1, -120, 1304922, 62445336, 880685715903, 48116431626576, 400606331819372908, 17221400159899442736, 112816090252343444895663, 2863025032459791139669416, 21413356021282488546916034202, -704784715126259202464079666120, 2102085018129621311776010144838961], [1, -750, 1712631, -856289182, 1329382873611, -552522395417796, 658769703611156538, -214940604698244746532, 201181128619768160559579, -50411102825464803859617166, 39222757447908658267370921751, -6681964518676125729884823642750, 3465863721549107204083472585375569], [1, 552, -1152564, -248520632, 1114530677604, 108173831172696, -604232203209226626, 53333917547554863144, 270928426518852340851684, -29785594379808965652657608, -68106748320710488917927164724, 16082199568165167285785823637848, 14364405059580771582276370834385761], [1, 612, -1223124, -415004184, 1212827483508, 194529560235444, -723127027932774218, 111229473658343818428, 396522270290290209898452, -77580988094057306634046152, -130739733825342149133053762964, 37404409915177886945984989356684, 34946659039493167390823397237402409], [1, -924, 2894898, -2881858956, 4446969403551, -3535399630903992, 4122185243102599804, -2492347142398756336248, 2210060595040844157602511, -1009677739816367853794181804, 715012025300270239440382335858, -160887413897363340067772795764476, 122749609618842355502421774953773681], [1, -93, -1689729, 354366248, 1310601420297, -224207143910091, -1053719651856288018, -204627806653854483243, 1091694292727587084643913, 269400227868486204019595816, -1172405558802460456800539333889, -58892360589721412902024663777149, 577951262543040979328274795306257089]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/432/4/i/d'], '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': '12-432e6-1.1-c3e6-0-0', 'motivic_weight': 3, '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': [3, 3, 3, 3, 3, 3], 'order_of_vanishing': 0, 'prelabel': '12-432e6-1.1-c3e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.048645870179444, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e6-0', 'trace_hash': 2195563696884184821, 'z1': {'__RealLiteral__': 0, 'data': '0.49135726252674069610118451686', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '622869328768522533404620716338,757744997873450516919874190117,985151601666282664445166406422,1150339430551579807038578445634,2037174240808280347976227097924,2389799681979887785214603703730', 'Lhash_array': ['622869328768522533404620716338', '757744997873450516919874190117', '985151601666282664445166406422', '1150339430551579807038578445634', '2037174240808280347976227097924', '2389799681979887785214603703730'], 'label': '12-432e6-1.1-c3e6-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/432/4/i/d'}