Lfunction data - 16-882e8-1.1-c2e8-0-1

Formats: - HTML - YAML - JSON - 2024-05-18T06:28:26.796743

• 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': '39035428915284608713331621784,591894194516502492263249882627,791719921872418228273344623845,1139054596710150269767794916937,1417730594593814237606645724493,1518557780191188442703275621104,2066060610207416292739206641566,2366728225268479099209381084171', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -4, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 111283069656.67323, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 4, 0, 12, 0, 16, 0, 16]], [3, [1]], [7, [1]]], 'bad_primes': [2, 3, 7], 'central_character': '882.1', 'coefficient_field': '1.1.1.1', 'conductor': 366225584701948244050176, 'conductor_radical': 42, 'degree': 16, 'euler_factors': [[1, 0, 4, 0, 12, 0, 16, 0, 16], [1], [1, 0, -32, 0, -482, 0, -8192, 0, 1237411, 0, -5120000, 0, -188281250, 0, -7812500000, 0, 152587890625], [1], [1, 0, -160, 0, -10082, 0, -1024000, 0, 684036643, 0, -14992384000, 0, -2161166238242, 0, -502148540275360, 0, 45949729863572161], [1, 0, 760, 0, 330844, 0, 92555080, 0, 18570219526, 0, 2643465639880, 0, 269879614658524, 0, 17706544693085560, 0, 665416609183179841], [1, 0, 1024, 0, 619390, 0, 268435456, 0, 89646749059, 0, 22419997720576, 0, 4320714401380990, 0, 596605170923275264, 0, 48661191875666868481], [1, 0, 1180, 0, 783658, 0, 410758000, 0, 172124299123, 0, 53530393318000, 0, 13309305045583978, 0, 2611711604498069980, 0, 288441413567621167681], [1, 0, -1216, 0, 549310, 0, -449511424, 0, 371584428739, 0, -125791726403584, 0, 43017007324706110, 0, -26648183309336710336, 0, 6132610415680998648961], [1, 0, 2120, 0, 4514524, 0, 5093815160, 0, 5464486082566, 0, 3602758680179960, 0, 2258374437226345564, 0, 750087340395594366920, 0, 250246473680347348787521], [1, 0, 3844, 0, 9235210, 0, 14200058896, 0, 16204929711379, 0, 13114052591692816, 0, 7876627837885497610, 0, 3027775740883185281284, 0, 727423121747185263828481], [1, 64, -2916, -109696, 15781226, 354186432, -29010130064, -23081726528, 59363733657267, -31598883616832, -54369654370876304, 908745482291882688, 55431232082683887146, -527482471316748363904, -19195888049029542879396, 576771922943680531180096, 12337511914217166362274241], [1, 0, -512, 0, 11401348, 0, -4348757504, 0, 48465387028870, 0, -12288549353260544, 0, 91038911291188255108, 0, -11552507033787487273472, 0, 63759030914653054346432641], [1, -416, 90504, -13258336, 1447488476, -123953645088, 8575607156536, -487565190246368, 22989545777145222, -901508036765534432, 29318294322372433336, -783555991848143553312, 16918535207007448426076, -286532293967579836749664, 3616506425675452214596104, -30736308655161617566426784, 136614025729312093462315201], [1, 0, 6724, 0, 24149770, 0, 76001667856, 0, 199192663651219, 0, 370863894605233936, 0, 575037096285595944970, 0, 781271532424570240092484, 0, 566977372488557307219621121], [1, 0, -10660, 0, 69445738, 0, -302838874000, 0, 993844670444083, 0, -2389544381358394000, 0, 4323670148268488229418, 0, -5236819919376700808473060, 0, 3876269050118516845397872321], [1, 0, 11812, 0, 80407786, 0, 412012434832, 0, 1657164032871859, 0, 4992503409348318352, 0, 11806310405174595643306, 0, 21015879904245360451798372, 0, 21559177407076402401757871041], [1, 0, 13828, 0, 115718506, 0, 661025359888, 0, 2860286608124659, 0, 9152452029977025808, 0, 22184083849319739382186, 0, 36704337616587021397262788, 0, 36751693856637464631913392961], [1, -208, 9084, -382304, 194772842, -16132806768, 189386507248, -51112315259824, 8101250499518451, -229443183201349936, 3816350423321825008, -1459347600078373719792, 79090955602046583543722, -696878184031356608998496, 74331818529684874301192124, -7640302833882554310162340432, 164890958756244164895763202881], [1, 0, 8576, 0, 129227140, 0, 693213336704, 0, 5297380635806854, 0, 17615716177267639424, 0, 83448881987790331153540, 0, 140729439183735596287250816, 0, 416997623116370028124580469121], [1, 0, 17092, 0, 162305866, 0, 1248299110672, 0, 7753362375583699, 0, 35449498984949127952, 0, 130893203609308396979146, 0, 391441805210611501897316932, 0, 650377879817809571042122834561], [1, 416, 83196, 12805312, 1802200202, 215193060576, 21795043632112, 2037440724486752, 172976468754407571, 12715667561521819232, 848918714869296601072, 52310733541196258640096, 2734133803669583835325322, 121244229340174557985131712, 4916177351791162864722365436, 153416690065050210761486484896, 2301619141096101839813550846721], [1, 0, 50488, 0, 1145722588, 0, 15231716995336, 0, 129624788516164870, 0, 722871714545811390856, 0, 2580502085138638830358108, 0, 5396662710709522849220208568, 0, 5072820298953863752478356399681], [1, 0, 20992, 0, 205013566, 0, 2312605007872, 0, 23946317498418499, 0, 145098020741711921152, 0, 807054108932664759430846, 0, 5184822551641982849251512832, 0, 15496731425178936435099327730561], [1, 0, -41480, 0, 999338524, 0, -15477214339640, 0, 172830759683498566, 0, -1370186657371218998840, 0, 7832249320152686905345564, 0, -28780581134090768252238300680, 0, 61425365346268570446197767595521], [1, 0, 11104, 0, -115646690, 0, 342277513216, 0, 33435863545530019, 0, 35617535278539759616, 0, -1252287937501918346198690, 0, 12512265134585391778221975904, 0, 117257864492369852051862561201601], [1, 0, 25540, 0, 264116938, 0, 4164881866000, 0, 64595873156038483, 0, 468761123279223946000, 0, 3345754350461079554515018, 0, 36413933050051410266737859140, 0, 160470643909878751793805444097921], [1, 0, -15520, 0, -81506402, 0, -934577152000, 0, 55171744744717603, 0, -122504000187876352000, 0, -1400431734842247721024802, 0, -34954013460671978201395791520, 0, 295216374856540727739668685278401], [1, -248, -9084, 2079728, 1144285226, -108353497224, -12540681524336, -267051596177096, 331114835587218867, -3172840014180077576, -1770219541661946506096, -181719662204380385805384, 22800599927656184891319146, 492347252023211479085314928, -25550246877715813508346620604, -8287483027545917207461604739128, 397030588105939686862303733490241], [1, 0, None, None, None, None, None, None, None, None, None, None, None, None, None, 0, 706732552679793116819634555191041]], 'euler_factors_factorization': [[[[1, 0, 2, 0, 4], 2]], [1], [[[1, 0, -16, 0, -369, 0, -10000, 0, 390625], 2]], [1], [[[1, 0, -80, 0, -8241, 0, -1171280, 0, 214358881], 2]], [[[1, 0, 190, 0, 28561], 4]], [[[1, 0, 512, 0, 178623, 0, 42762752, 0, 6975757441], 2]], [[[1, 0, 590, 0, 217779, 0, 76889390, 0, 16983563041], 2]], [[[1, 0, -608, 0, 89823, 0, -170143328, 0, 78310985281], 2]], [[[1, 0, 530, 0, 707281], 4]], [[[1, -31, 961], 4], [[1, 31, 961], 4]], [[[1, 16, -1113, 21904, 1874161], 4]], [[[1, 0, -128, 0, 2825761], 4]], [[[1, -52, 1849], 8]], [[[1, 0, 3362, 0, 6423363, 0, 16405487522, 0, 23811286661761], 2]], [[[1, 0, -5330, 0, 20518419, 0, -42056263730, 0, 62259690411361], 2]], [[[1, 0, 5906, 0, 22763475, 0, 71565134066, 0, 146830437604321], 2]], [[[1, 0, 6914, 0, 33957555, 0, 95730144674, 0, 191707312997281], 2]], [[[1, -52, -1785, -233428, 20151121], 4]], [[[1, 0, 2144, 0, 25411681], 4]], [[[1, 0, 8546, 0, 44635875, 0, 242691367586, 0, 806460091894081], 2]], [[[1, 104, 4575, 649064, 38950081], 4]], [[[1, -34, 6889], 4], [[1, 34, 6889], 4]], [[[1, 0, 10496, 0, 47423775, 0, 658542561536, 0, 3936588805702081], 2]], [[[1, 0, -10370, 0, 88529281], 4]], [[[1, 0, 5552, 0, -73235697, 0, 577743346352, 0, 10828567056280801], 2]], [[[1, 0, 12770, 0, 50522019, 0, 1437274750370, 0, 12667700813876161], 2]], [[[1, 0, -7760, 0, -70862001, 0, -1017177703760, 0, 17181861798319201], 2]], [[[1, -62, -8037, -736622, 141158161], 4]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 1, 'label': '16-882e8-1.1-c2e8-0-1', 'leading_term': '0.15927988256176355146336642741099437484441426831006783926740769023889959618609289086798430', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, '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': [2, 2, 2, 2, 2, 2, 2, 2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/882/3/n/i', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0078125', 'prec': 30}, 'plot_values': [0.15927988256176356, 0.14980772232853984, 0.11932044815156753, 0.06817721340479407, -0.0031239727737677973, -0.09392154627026748, -0.20336752942300915, -0.3304071251740766, -0.4737665348139357, -0.6320645193468355, -0.8038659747083422, -0.9876221376461997, -1.181689879851183, -1.3843524408085943, -1.5938400383419484, -1.8083501011769552, -2.0260448744273245, -2.2449920183467325, -2.463222095118757, -2.678762361472361, -2.889653951735008, -3.0939688314583593, -3.289826774090496, -3.475413225027832, -3.649019086740935, -3.8090618008940353, -3.9540849656326533, -4.082768216061995, -4.193937792914829, -4.286576917910475, -4.359834685926404, -4.413030951614144, -4.445654702290917, -4.457374814328304, -4.44804268335112, -4.417695537388235, -4.366556737196536, -4.295033579868443, -4.203713488973269, -4.093360860314633, -3.964909618552758, -3.819451927011504, -3.658228359911833, -3.482615023819601, -3.294109853380752, -3.0943179896790776, -2.884936327302338, -2.6677375919266324, -2.444552304286262, -2.2172506735248336, -1.987724428566999, -1.7578679423569739, -1.5295594892780613, -1.304642778315472, -1.0849096523453994, -0.8720821255249206, -0.6677943718520424, -0.47357670676110075, -0.2908406445422847, -0.12086472856900482, 0.03521789021906418, 0.176430093431339, 0.30195966141802566, 0.41116730895456094, 0.5035922687732519, 0.5789558664433974, 0.6371635223485027, 0.6783040799379474, 0.7026470641743071, 0.7106380960331978, 0.7028923374585279, 0.6801857872101383, 0.6434447284747216, 0.5937337748422208, 0.5322430399372179, 0.4602720047687603, 0.3792126230374795, 0.2905316609397809, 0.1957516642214048, 0.09643151234223346, -0.005853338034506029, -0.10953038667208971, -0.21304884551574038, -0.3149004233102352, -0.4136390364519975, -0.5078993733268214, -0.5964139025757732, -0.678028587506347, -0.751717048814243, -0.8165926863145145, -0.8719184581212976, -0.9171167794682344, -0.9517772788509011, -0.9756598249299154, -0.9886954762149913, -0.990985256250278, -0.9827964510560125, -0.964556332948767, -0.9368434548626632, -0.9003788438291636, -0.8560130383836931, -0.8047094208480612, -0.7475270897918265, -0.6856022518892819, -0.6201283336656365, -0.5523350843751315, -0.4834674466389109, -0.41476478172646136, -0.3474370600487885, -0.2826425865569831, -0.22146697110515345, -0.16490320703650488, -0.11383320669998086, -0.06901115407241946, -0.031049276327057233, -0.00040506617544662125, 0.022628858878045863, 0.037931193513515996, 0.04555518380943582, 0.04572855079734708, 0.03885000065543354, 0.02548240025696907, 0.006342902264127355, -0.01771110923871447, -0.04569949597185164, -0.07653988251485086, -0.10907103938218767, -0.14207883041774738, -0.17432434730077756, -0.2045734345775089, -0.23162838625428953, -0.2543608948483618, -0.2717447555908781, -0.28288827619163043, -0.2870658129664946, -0.2837478391658834, -0.2726289394618492, -0.25365342567212795, -0.22703803296640632, -0.19329002222841982, -0.15322092176694807, -0.10795547547535994, -0.05893534034523179, -0.007917212806103632, 0.04303447253987689, 0.09156126199361563, 0.13503139037998613, 0.17056635489706287, 0.19507342916650733, 0.20528400960678422, 0.19779747877587753, 0.16913009364739529, 0.11576853492975533, 0.03422819709966362, -0.07888567813095032, -0.22681500141122432, -0.41258428421138577, -0.6389355381396022, -0.9082636528761423, -1.2225528187225054, -1.5833155893851159, -1.9915369510569332, -2.44762523220458, -2.951366291984475, -3.501884800068871, -4.097613786407862, -4.736272859303776, -5.414856028381328, -6.129630206003376, -6.876146737071336, -7.6492712697131084, -8.44321130513789, -9.251557260437798, -10.067336779167668, -10.883082595486684, -11.690909416790822, -12.48259700212139, -13.24968954459648, -13.983617368916947, -14.675791845036743, -15.317712646341231, -15.901086364350407, -16.417953677969184, -16.8608002690361, -17.222669769977895, -17.49728482667585, -17.67918300055681, -17.76379152807039, -17.74750832363713, -17.627792670748256, -17.403231314114297, -17.07357766518055, -16.639787495401638, -16.104049497536792, -15.469818880034767, -14.741771002209967, -13.925762178812743, -13.028790234490108, -12.058908517060203, -11.025134253692952, -9.937346000148546, -8.806174140495973, -7.642890187297729, -6.4592350427094685, -5.267262484332867, -4.0791717507579675, -2.9071313684271893, -1.7631096870895726, -0.6587058689742615, 0.39501369347403187, 1.3876722206493355, 2.3097521585773286, 3.152747855635682, 3.909296707971687, 4.573291115460426, 5.139972858515209, 5.6060079664079945, 5.969542263655593, 6.230240604669537, 6.3893031902876904, 6.449449311922312, 6.414866078664437, 6.291141147372738, 6.085173163580534, 5.805060673624076, 5.459974031827892, 5.060017732455543, 4.616062832624459, 4.139550584043836, 3.642296783837299, 3.136292791696005, 2.6335028680989954, 2.145661159482607, 1.6840733448204481, 1.2594285339492048, 0.8816042377085921, 0.5594890480400702, 0.30082927246012453, 0.1120952555978174, -0.0016304251333156448, -0.036740842390301724, 0.008832811473471104, 0.13558473932607282, 0.34242806876391857, 0.6267187312365389, 0.9843072372503896, 1.409617366099923, 1.8957504587181495, 2.4346136891589962, 3.017075136798043, 3.63314278625662, 4.272149533714318, 4.922951517979956, 5.57413557840863, 6.214231214514634, 6.831923172887704, 7.4162660053698435, 7.95690957772884, 8.444295059040016, 8.869815439429185, 9.22596682397215, 9.506481964512975, 9.706439716845733, 9.82234949569986, 9.852231309430318, 9.79565037269341, 9.653708046476723, 9.42898480350968, 9.125468571967664, 8.748462817293749, 8.304469849162635, 7.801060578624183, 7.246739588695645, 6.650742918849382, 6.022850302871852, 5.373166003200311, 4.711910394540852, 4.049217870564629, 3.3949401816528155, 2.758471185542267, 2.1485626482232014, 1.573147216746972, 1.0391985191439426, 0.5526054049926351, 0.1180799850272261, -0.2609050401741115, -0.5821499438466934, -0.8447341558572539, -1.0490013158365674, -1.1965097990579445, -1.2899580685921617, -1.3330790931837726, -1.3305130721008236, -1.2876629328189928, -1.2105383288950098, -1.1055862180759293, -0.9795104173659528, -0.8390922076973397, -0.6910142354431547, -0.5416854948418858, -0.39708032009994326, -0.26259434780975327, -0.1429196332005625, -0.04193629292938595, 0.037368525488722444, 0.09295443829527562, 0.12375459710632736, 0.12967365293763997, 0.11155706799202544, 0.07113352676878044, 0.010932102522796468, -0.0658243485722555, -0.15534613282522625, -0.25342053388871444, -0.35556983490320354, -0.4572158588646954, -0.5538481640185294, -0.6411931479040454, -0.7153750480806075, -0.7730658338733867, -0.8116201730502522, -0.8291926800181123, -0.8248354731167402, -0.7985612779530348, -0.7513843064467097, -0.6853292323375866, -0.6034048379490304, -0.5095503775722287, -0.4085526363582445, -0.30593609368234437, -0.2078279931306787, -0.12079564165883261, -0.05166931556013707, -0.00734587754930247, 0.0054124754665088, -0.019818691225789407, -0.08892530888152246, -0.2070612770950184, -0.37846609466754244, -0.6063006878570677, -0.892507061457079, -1.2377009414140967, -1.641094882407616, -2.1004554095199164, -2.612096139631565, -3.1709083481532363, -3.770429521541579, -4.4029419991094, -5.0596204421880815, -5.730707027721043, -6.405711450788527, -7.0736335406773465, -7.72320323588493, -8.343136835249831, -8.922408018603091, -9.450498573737779, -9.917649233748097, -10.315093322112222, -10.63526894871202, -10.872004407484567, -11.020671779154666, -11.078313375138832, -11.043749221060438, -10.91758947705768, -10.702214947739787, -10.401721931193807, -10.021824585045598, -9.569717109053792, -9.05389927967918, -8.483980752633055, -7.870467224467158, -7.224471204561471, -6.557430990935973, -5.880831989987952, -5.20592931148548, -4.543479182585224, -3.9034874304047604, -3.294985497634855, -2.7258339468429202, -2.2025414321974512, -1.730138069117881, -1.3120975679346585, -0.9503059983769339, -0.6450782107240669, -0.39522176981506996, -0.1981461310200857, -0.0500150051629512, 0.0540656305055034, 0.11982386187947323, 0.1535717325260192, 0.16193712065208868, 0.15158583394703354, 0.12894256946557017, 0.09991935937455022, 0.06966076143310285, 0.04231508173914829, 0.02083889956698562, 0.006841998504843871, 0.00047883237251051804, 0.00039138964209395, 0.003706900791156809, 0.00609226235433101, 0.0018652119160975087, -0.01584060764395782, -0.054859449178853166, -0.12373071640190335, -0.2313963639798785, -0.38686778654846504, -0.5988684302884922, -0.8754652136388955, -1.2237096905745348, -1.649280783341661, -2.15614660539268, -2.7462588472321836, -3.41929800143839, -4.17246765641724, -5.00033605386454, -5.894764901234495, -6.844964622234841, -7.8375434391648735, -8.856639336990725, -9.884147845861166, -10.900046305767145, -11.88273220874495, -12.809429649680839, -13.656698562919475, -14.401102723229144, -15.01966255969468, -15.49036936741579, -15.79277454683447, -15.908526255282073, -15.821834135039149, -15.519928267589824, -14.9935358646532, -14.237448640943391, -13.250607847208446, -12.03621943495791, -10.601852970434454, -8.959371079568658, -7.124794811320829, -5.118087575903613, -2.962917115471492, -0.6864614998491815, 1.6812887385831277, 4.10816604497817, 6.5604645951886065, 9.003599502791838, 11.402781859192512, 13.723702249751987, 15.933166738935679, 17.99965241415616, 19.894103820419975, 21.590602434564985, 23.066836534617025, 24.304501260552225, 25.289621341912778, 26.012777872760434, 26.469227881363302, 26.65892549552341, 26.586531411448917, 26.261231689026534, 25.696401974147264, 24.90922793223153, 23.92025253669816, 22.752860196639954, 21.432720726810473, 19.987221369445937, 18.44481889838555, 16.83436451273088, 15.184473770602404, 13.522932283649736, 11.876143111820074, 10.268627942496735, 8.722599001462678, 7.25759345584386, 5.890149825262977, 4.633619834213841, 3.4980660483150445, 2.4902448247812967, 1.6136718793879459, 0.8687651040158019, 0.2530493492020606, -0.23859359205741604, -0.6135711389990083, -0.8811988652065033, -1.0523013617515746, -1.1387999284086805, -1.1532993692591245, -1.1086861596044904, -1.0177578926025892, -0.8928668763488986, -0.7455911707913654, -0.5864729958657665, -0.42481289731011285, -0.2685203924480006, -0.12402198661790283, 0.0037749962234153588, 0.11146816699624154, 0.1970938024056323, 0.2600125505743508, 0.30075678818911106, 0.3208496606922357, 0.3226046383482302, 0.3089145854437419, 0.2830415663774798, 0.24840897655404234, 0.20840592517080928, 0.16621358722145757, 0.12466041016052094, 0.08610959272750578, 0.05238098565355938, 0.0247087239029678, 0.0037338710607126785, -0.01047039647329031, -0.01834197988576322, -0.020746667101429143, -0.018874043405247343, -0.01411913261327334, -0.007956439396167957, -0.0018131692768583582, 0.003051845127804647, 0.0056568712343371035, 0.005387959178069757, 0.0020670259111239724, -0.00400652296503151, -0.012042859394575898, -0.020778507552100253, -0.02852268722434696, -0.0332310097216913, -0.03260332183504757, -0.024201517757691606, -0.005581651186585251, 0.025565352649243193, 0.07127083722882077, 0.13315095206813726, 0.2122819864530919, 0.3090931885046001, 0.4232836873498358, 0.5537702625555312, 0.6986650570833246, 0.8552872122070708, 1.0202125154755544, 1.1893665443522459, 1.3581384118208235, 1.5215238930564159, 1.6742969323537737, 1.8112062318084068, 1.9271670362253106, 2.017458973328458, 2.0779379075003734, 2.105222600884834, 2.0968399573957144, 2.051354751672421, 1.9684693468466374, 1.8490897946557119, 1.6953245075859524, 1.5104526738433488, 1.298863642108518, 1.0659127246826139, 0.8177503330427487, 0.5611234467732854, 0.30315013827476306, 0.05107139624731389, -0.18801434300739664, -0.4074033853468562, -0.601039316597766, -0.7637506094952861, -0.8914494675066561, -0.9812928050469759, -1.0318011883070046, -1.042933537355363, -1.016092059127851, -0.9540737110299587, -0.8609645913910621, -0.7419814638209318, -0.603266128599127, -0.4516391748722521, -0.29432254286277354, -0.1386387372685924, 0.008308806997594132, 0.13994965736899512, 0.25054178824922646, 0.3354376379410768, 0.39131125501892805, 0.41633653237750634, 0.4103098443773138, 0.37471304746883455, 0.3126953821932456, 0.2289806685823112, 0.12970822472175783, 0.022209637274422937, -0.08527264065667634, -0.18391582944720278, -0.2646861373134395, -0.3187408386775878, -0.3378394124667782, -0.3147394240898829, -0.24356871352251477, -0.1201586423966267, 0.05767604486100832, 0.28992370796215794, 0.5742355469808141, 0.9058659806219784, 1.2777362829013916, 1.6805847330581278, 2.1032048547728044, 2.532771065998996, 2.9552434482488645, 3.3558411182007415, 3.719586083503718, 4.031867412572709, 4.279021448638074, 4.4489076626154525, 4.531453806544503, 4.519154017974286, 4.40750051922007, 4.195339720606993, 3.8851404781449634, 3.4830893192870396, 2.999081426415464, 2.446590606384731, 1.8424119265481214, 1.2062816364749371, 0.5603822207290714, -0.07127054724001651, -0.6635425491126412, -1.1909403988165905, -1.628406837288706, -1.9521278138842197, -2.140327818842619, -2.1740281014067104, -2.0377648568927844, -1.7202767919233597, -1.2149552327490192, -0.5201843753929491, 0.3604544904294563, 1.4181280395674958, 2.6388514061099846, 4.003741580255565, 5.489357170142078, 7.068265111969339, 8.709813056539073, 10.380961227217355, 12.047157646102203, 13.673263928645143, 15.22450880824601, 16.66742424407346, 17.970742792051084, 19.106318412062077, 20.049923046956042, 20.781952769678888, 21.287891518557384, 21.558645193040867, 21.590730411380076, 21.38630213700408, 20.953030860289793, 20.303804491351645, 19.45628903349773, 18.432385454759697, 17.257463115770875, 15.95954756332574, 14.5684683020049, 13.11497765851256, 11.629868704636152, 10.143115978469146, 8.683077147671375, 7.275778930346705, 5.9442566975632545, 4.708041378100966, 3.582776553849733, 2.5799948673974433, 1.7070482911749199, 0.9671629474857497, 0.35962613940994625, -0.11990737052437243, -0.4790044570110622, -0.7279537230510047, -0.8791994542129868, -0.9467170854404198, -0.945390720132128, -0.8904038040915353, -0.7966605770518713, -0.6782579150450605, -0.5480271363323577, -0.4171554328189944, -0.2949058242187632, -0.1884475999755476, -0.10278581075455501, -0.040788411216818386, -0.003304556891123452, 0.01063468256007143, 0.0035464170276675155, -0.020827897228872093, -0.05788355040785036, -0.10252173213945401, -0.14951340703865523, -0.19384215148949227, -0.23101180395864548, -0.25730731716975697, -0.26999477022640533, -0.26744639144660504, -0.2491848682925681, -0.21586334129136409, -0.16917970567714435, -0.11173201995672159, -0.046824828438651565, 0.02176316050458083, 0.09004082079004704, 0.15407429222623384, 0.21024040629161053, 0.25545542862984144, 0.2873674897074197, 0.30450207299028315, 0.3063538150770076, 0.2934290048696304, 0.26720895237079306, 0.23004029367124915, 0.1849790352661216, 0.1355889556608859, 0.08570532240048163, 0.03917739972255944, -0.0003934017435472225, -0.02990620848375466, -0.04700137175540737, -0.05024822328385254, -0.03927372178448307, -0.014824424335247357, 0.02124563120067159, 0.06606496850558732, 0.11591231219558581, 0.16646058217821558, 0.21308847711893, 0.2512435030451754, 0.27684025860237166, 0.2866749163080979, 0.27883490251191745, 0.2530828040450817, 0.21119442777706054, 0.15721749973555618, 0.09763535609081385, 0.041424596556891013, -6.92035298203537e-06, -0.0130096234633582, 0.01798831357174087, 0.11003198550783216, 0.2810662099551873, 0.5492727007578456, 0.9323304589473895, 1.4466219042436403, 2.1064157609370295, 2.9230576235380097, 3.9041957478803417, 5.053065004538766, 6.367931033539926, 7.8417522894249805, 9.461903408484014, 11.21008749248249, 13.062460615704529, 14.989959894506677, 16.958837866067775, 18.93140242168894, 20.866996871091143, 22.723306264620273, 24.45741943141526, 26.02703246016982, 27.391743461059928, 28.514361027194965, 29.36221054436077, 29.908224635746105, 30.132002530586895, 30.020883944133022, 29.570276553449553, 28.78389066201643, 27.673805106024624, 26.260346776773552, 24.571602400966967, 22.64259529180299, 20.51436731069761, 18.232917301783985, 15.847663469141237, 13.409936971769769, 10.971484846298917, 8.582966864476965, 6.292381164641165, 4.143659167623667, 2.175412193306011, 0.4198065266243489, -1.09825307510297, -2.3616659539386413, -3.361431467633452, -4.096669258336323, -4.574325526649107, -4.8086150100846785, -4.8202600369574675, -4.635576972232523, -4.285182342211098, -3.802673171190411, -3.2232891941918504, -2.5825114212314224, -1.9147291573051313, -1.2520144292767912, -0.623050933983579, -0.052247778648644605, 0.4410075541753329, 0.8428068909428312, 1.144920219667768, 1.3447297080805296, 1.4449200048004962, 1.4529503988987118, 1.3803396308327174, 1.2418003834133997, 1.0542594490756108, 0.835822360238852, 0.6047095361808612, 0.37824600177321593, 0.17194757224123944, -0.001258412023835418, -0.13164481676059303, -0.21310406271516433, -0.2433414980835372, -0.2238480990141798, -0.15964906668233142, -0.05885027266606624, 0.0679911812036007, 0.20863795987326464, 0.35004548853362855, 0.4792963171458493, 0.5845253941046793, 0.6557976700444368, 0.685879317472197, 0.6708586376813436, 0.6105794304342024, 0.508856054832103, 0.3734520646057612, 0.21581012930504134, 0.050511923762267104, -0.10548155848247304, -0.2337878012475303, -0.31572348775682185, -0.3335410018711083, -0.2717261842831041, -0.11829586288535536, 0.13398274114761685, 0.4865140417266969, 0.9339852309734977, 1.4637211576002105, 2.0553277417620524, 2.680658447801735, 3.3041277556173068, 3.8834342598739724, 4.37070442753928, 4.713812727178249, 4.858000151977749, 4.747739319062943, 4.328769266519473, 3.5502306889913573, 2.3668314392794136, 0.740998727737489, -1.355037227321641, -3.9377202122967483, -7.010861736745136, -10.564640587217784, -14.575011920248626, -19.00356728741419, -23.798013940909243, -28.89309694940904, -34.211782436212935, -39.66714613662103, -45.16451418992888, -50.603861566657244, -55.88243413985997, -60.897655866299885, -65.55045802230647, -69.74783806795534, -73.40566306643433, -76.4508830340738, -78.82347582182265, -80.47807471318336, -81.38518593389081, -81.53244827408616, -80.92485320390371, -79.58404003607905, -77.54791889834445, -74.86884938570347, -71.61173593116428, -67.85196127347986, -63.67322521011773, -59.16544976303575, -54.42158556485764, -49.534964668495896, -44.597107609576156, -39.69485792639086, -34.90815426446804, -30.308284760778882, -25.95667584327922, -21.903764340942487, -18.18816522148743, -14.8365704307934, -11.864096537762634, -9.274654948119029, -7.061865044847215, -5.210317619228939, -3.697038608413242, -2.4929948471096157, -1.5647554639369425, -0.8761780272445197, -0.39002185194814143, -0.06938079654385144, 0.12100821343558057, 0.21366672330863457, 0.23752379665775705, 0.21731723507545794, 0.17325800426786292, 0.12094926749228077, 0.07153812950377492, 0.03206839516461014, 0.005993312905943692, -0.0061931393663755985, -0.006251603762669118, 0.0025357490075337257, 0.01608005794073055, 0.03014134587127229, 0.040890447157606466, 0.04535075694836487, 0.0417021862691338, 0.029440128121620508, 0.009388960088105957, -0.016420605806946004, -0.0449919061054536, -0.072695700577508, -0.09566651432226456, -0.11022841188165233, -0.11331388191002283, -0.10285068971644046, -0.07808294493758224, -0.03980028947823359, 0.009543666849273675, 0.06583577990392234, 0.12343254821230999, 0.17541501716149396, 0.21394709721276992, 0.23071571605118094, 0.21744105268296238, 0.16642301638275664, 0.07109150256698461, -0.07348197231150637, -0.27017015891576107, -0.519443900829131, -0.8191445921831143, -1.164389945458248, -1.5476245439464962, -1.9588193023063953, -2.3858155634829243, -2.8148318586953747, -3.2311904241999647, -3.619943383982238, -3.966527580943982, -4.257470720064137, -4.481069229423541, -4.628000529976532, -4.691835764269905, -4.669473247964322, -4.5615048501588085, -4.3720821327759305, -4.108707999408668, -3.7819088814006308, -3.404748206065308, -2.9922018196237685, -2.5604245791880347, -2.125971399214252, -1.7049532894793777, -1.3121023766017426, -0.959987413726483, -0.6583532453248861, -0.4136008345252755, -0.22843829859649045, -0.10172611424360019, -0.028528917774987103, -0.0003811746591182799, -0.005772719679450831, -0.03082169040144847, -0.06009707570652936, -0.07755191019203467, -0.06752188625485361, -0.015739401829650054, 0.08968869643742661, 0.2573871928980824, 0.4919992671582776, 0.7936635483151214, 1.157713498037768, 1.5746275278340418, 2.0302475983001638, 2.5062820295765316, 2.9810507108221165, 3.430485626652674, 3.8292886648970397, 4.152207917448153, 4.3753869753520105, 4.477722103603581, 4.44217542861178, 4.256946609163514, 3.9164590971551654, 3.422142873831025, 2.782763451221096, 2.014468976021004, 1.1405184844284153, 0.19065073144976685, -0.7999204205239128, -1.7917199652496791, -2.7425111530594357, -3.60912154145112, -4.349320747826181, -4.923684760925198, -5.297424012411907, -5.442160325406453, -5.337376412643674, -4.97149968898538, -4.342836423005548, -3.4603585305056717, -2.3435335765690737, -1.021811239451748, 0.4662406594737247, 2.0742591600737708, 3.74979012510151, 5.436197143074918, 7.074677029176916, 8.606257579639742, 9.974414695424551, 11.127425818103008, 12.020589500603224, 12.618083078059176, 12.894311205854446, 12.834950770302418, 12.437533478537526, 11.711547801061734, 10.678264915694605, 9.369987052669982, 7.828804015379651, 6.104765720597341, 4.253860709663575, 2.335811776701914, 0.4117442805614034, -1.4581763827580392, -3.217055619329039, -4.813564027228738, -6.203927659387746, -7.353385756820138, -8.237310901520416, -8.841892880240378, -9.16436822470665, -9.21280425939136, -9.0054634333304, -8.569879148805585, -7.941128040060618, -7.1599655327789655, -6.270843336607478, -5.319828310869304, -4.352520151167306, -3.41206028063793, -2.5373473956125876, -1.7613679196748349, -1.109817580133873, -0.6002269667538385, -0.24149971785973806, -0.03386816109367259, 0.03074269584110728, -0.032027465001380935, -0.2000325035010862, -0.4459871894094872, -0.739072373037033, -1.046664886099394, -1.3361067585115878, -1.5764296554854753, -1.739957348183886, -1.8036884849643728, -1.750420835126805, -1.5696030555845528, -1.257814165937681, -0.8188804222723794, -0.2636337448981561, 0.3906691366659161, 1.1212486670890573, 1.9010070107030195, 2.6998392882593794, 3.4860798607105195, 4.228011687145114, 4.895353674026693, 5.460656663220685, 5.900545909396355, 6.19679072610184, 6.337099288030362, 6.315503682410257, 6.13250288600653, 5.794924975371551, 5.315507159470703, 4.712220909121159, 4.007366739665863, 3.226454962022275, 2.397041186042906, 1.5474594084217026, 0.7056010822734813, -0.10222365923765676, -0.8523059142374002, -1.5244011501343029, -2.102486045692841, -2.575210702474953, -2.9360361940646986, -3.1831845532406975, -3.3193741951440225, -3.351371583149256, -3.289386913483637, -3.1463764355790484, -2.9372965352790836, -2.6781668845768083, -2.385239351048284, -2.0742027912968757, -1.7595012317103094, -1.4537830152627735, -1.1674926658862044, -0.90862916757542, -0.6826229231406837, -0.49236525105594375, -0.3384038706921717, -0.2192409181393347, -0.13172393348853007, -0.07149299574232203, -0.03345037812171072, -0.012221242607683966, -0.002577638408823575, 0.00019617683422421285, 2.0390064410975363e-05, -0.00016887694035686872, 0.0014914178276877403, 0.005800177565495268, 0.012591031652837835, 0.020907463638896083, 0.029234877724469307, 0.03576737122458657, 0.038685581376504394, 0.03642028180740034, 0.027881237126429335, 0.012632894026582426, -0.00899869225572846, -0.03589641249535075, -0.06620110896520917, -0.0974361575171546, -0.1266994627792312, -0.15090474009232913, -0.16705452510143534, -0.17252909851168172, -0.16535974866128667, -0.1444598420142522, -0.10980331070659823, -0.06253089725959765, -0.004970295671654092, 0.05943835618114641, 0.12630582058857104, 0.19054490439536909, 0.24669692022771741, 0.28930627451188534, 0.3133234589553037, 0.3145123060393945, 0.2898343301018739, 0.2377716442960276, 0.15857858176319006, 0.054427049257216906, -0.0705727442475766, -0.21047095752083037, -0.357702580317566, -0.5034335505822277, -0.6380204581380635, -0.7515494294877613, -0.8344390915833831, -0.8780457799760467, -0.8752510488445434, -0.8209987008802819, -0.7127443573650736, -0.5507882863924064, -0.33846233262137615, -0.0821465029948049, 0.20890732350823785, 0.522939480431377, 0.8461876499474074, 1.1635306589861047, 1.4592424516630196, 1.7178263338414679, 1.9249073659895815, 2.068085902429346, 2.1377028426194613, 2.127485890803925, 2.0350407259063594, 1.8621529182203316, 1.6148763243013233, 1.3034044658068709, 0.9417413497598423, 0.5470645524630693, 0.13890294873243036, -0.26181128142105853, -0.6337976149756864, -0.9565376193847868, -1.2113839595672102, -1.382607485494862, -1.4583191861303995, -1.431212400681735, -1.299071386648868, -1.0650238382591244, -0.7375197264582593, -0.33003014175990525, 0.13952601366906628, 0.649636576867398, 1.1763479061407927, 1.6944441927584892, 2.178720784550915, 2.6052960969534578, 2.9528779597982804, 3.203916944668369, 3.345610099201273, 3.3707643205747573, 3.2782484412615247, 3.0729904328087976, 2.7657269745630138, 2.3724617899429985, 1.9136311827038737, 1.413019184335562, 0.8965395562653168, 0.3907769765597033, -0.07862073018257984, -0.4884568436093996, -0.8193398487349678, -1.0568370592358145, -1.192368816895446, -1.2237808452531218, -1.1555648991530751, -0.9987612080831921, -0.7704296066964715, -0.49270806037008813, -0.1915658110941889, 0.1046935559547214, 0.3671099937721007, 0.5678364203509839, 0.681910239791326, 0.6889448571521638, 0.5746320643392796, 0.331927327846985, -0.03811796201595964, -0.5259311695574052, -1.1134501541964288, -1.7746507336700033, -2.476467391094428, -3.1801514925468384, -3.8430490871349146, -4.420586862487715, -4.868427999273034, -5.144713604565156, -5.2123478874933005, -5.04106100605984, -4.609123564990542, -3.9048004155004024, -2.9273836366154566, -1.6875922429872123, -0.2075027781179546, 1.4800115678044528, 3.332359202078187, 5.298877256588509, 7.322799670731165, 9.343542499326396, 11.29932364366774, 13.129702575750839, 14.778058361600154, 16.194037234161968, 17.335657714116326, 18.170890001158508, 18.678860102574095, 18.85061974964266, 18.689512061109195, 18.21063020616453, 17.439911913357914, 16.412916649720202, 15.172838399190713, 13.768368606216772, 12.251441550269483, 10.674926582541374, 9.09037016885803, 7.545780694001608, 6.083792663232491, 4.740068267116324, 3.5420908092193355, 2.508519358996499, 1.6490167112365153, 0.9645244436164626, 0.44794863870664464, 0.08529780725711139, -0.14292371959827616, -0.2601273082013049, -0.29192399765621246, -0.26440574127835337, -0.20252474370229073, -0.12866141159477334, -0.06145145754084157, -0.014927921360195003, 0.001954867704070976, -0.01458581611783694, -0.06343729259748747, -0.13920208506405313, -0.2330912015432809, -0.3340354550740902, -0.42994490880015795, -0.5090032381772022, -0.5608985912960758, -0.5779148126548426, -0.5558087899008622, -0.49441172879943923, -0.3979104927437272, -0.27478757112508795, -0.1374113261264512, -0.0012658846978613287, 0.11608026152822712, 0.19620336076571174, 0.22118423038680063, 0.17501221266417208, 0.044941570553911465, -0.17728842283571278, -0.4944723796970691, -0.9033144799567874, -1.394158041976904, -1.9511050717045555, -2.552540889729733, -3.1720509694170964, -3.779694797270746, -4.343637980950515, -4.832133588238921, -5.215381515703574, -5.467402297594063, -5.567829439441761, -5.503485760552056, -5.269647264364283, -4.870924806844029, -4.321763525689868, -3.6464640878537447, -2.878293650831597, -2.0582250427459297, -1.2332864908967816, -0.45452626745201746, 0.22531757896909482, 0.7543426477043602, 1.084055851937653, 1.1718343148937855, 0.9833580060637377, 0.49460209977621433, -0.3066374469759073, -1.4197299961556604, -2.830775540618141, -4.512837838181365, -6.426798204800768, -8.522814532038346, -10.742185794940342, -13.019655755212936, -15.286037677165133, -17.47103040250123, -19.506294452280347, -21.328345280486083, -22.881042536194443, -24.11805221926402, -25.004377630328978, -25.517483868278063, -25.647935908860894, -25.399567077718455, -24.789289295882146, -23.845684658594088, -22.607415603090367, -21.121502909854758, -19.44072474724316, -17.621116844289958, -15.719566184259184, -13.791672973840539, -11.889524444479914, -10.059609978461863, -8.341390199416782, -6.766326118877736, -5.357120109889173, -4.127587855793224, -3.0830338408114732, -2.2210140600168056, -1.5322840686398311, -1.0020903473786362, -0.6116393405858914, -0.3396135346719623, -0.1636353142621166, -0.06163691816161058, -0.01303800043248941, 0.00033496314638208297, -0.0063962201506831285, -0.021515031043716028, -0.036771837798542664, -0.047181771408778043, -0.050600800719527356, -0.047136398158210475, -0.03845976385625367, -0.027090524283808738, -0.015717582782260604, -0.006617880390932074, -0.0012234369243660252, 0.00012788797113699044, -0.001760996343627409, -0.005102290729967348, -0.00746264515872469, -0.006251261234049386, 0.0006916663584376465, 0.014465268732060528, 0.03450243560019369, 0.058055819605769755, 0.07983667648636632, 0.09185893381333103, 0.08351907822146801, 0.04193750670190001, -0.04743583702138147, -0.1999700202077257, -0.4307962378913495, -0.7536184274668314, -1.179468691369697, -1.7154831329489835, -2.363767477986845, -3.1204539124801185, -3.975029509004928, -4.910007110859951, -5.901025441904218, -6.9175154176038935, -7.923729322407494, -8.880032574769743, -9.744584000000232, -10.475315255934841, -11.032096264982897, -11.378977669436667, -11.486452428387357, -11.33376893153363, -10.910421365116658, -10.217173196404648, -9.266744971655088, -8.083937286513848, -6.705145964129207, -5.177262333010237, -3.555992769006717, -1.9035466224230462, -0.28574527945935707, 1.2309632694370012, 2.582586357437064, 3.710652384683163, 4.5651060606069285, 5.106884665575754, 5.310151185505346, 5.164007354641484, 4.672968239079405, 3.8568423612482094, 2.749939075265752, 1.3995639947584684, -0.13613235342431704, -1.790860075447092, -3.49337624258071, -5.171043475168591, -6.753470481800208, -8.175868119244106, -9.382074617011131, -10.32712030322147, -10.97920661717221, -11.321089972106458, -11.350706491514448, -11.081059671082606, -10.538849619611574, -9.762523233105826, -8.799825757678754, -7.704914867132882, -6.535218024992874, -5.348204296749987, -4.1981672034997075, -3.1333774926584126, -2.193354905465192, -1.4069375314882484, -0.7911164855924754, -0.35062474529081206, -0.07829162311321454, 0.043872464931816874, 0.042924511383417255, -0.04729395142793861, -0.18884227751628246, -0.3426164298521841, -0.47130310535973563, -0.5421540056219529, -0.5293907257656562, -0.4160906971410411, -0.1954303907915111, 0.12880491073931125, 0.5424965101851673, 1.0222384493854564, 1.5370904918142216, 2.0509761230598746, 2.525486475455277, 2.9228700804872045, 3.2091190760490873, 3.3569306028781205, 3.34820628967498, 3.175967212990625, 2.845538428497404, 2.3748519315798204, 1.7937046962744885, 1.1421185803048144, 0.46781222907207076, -0.17716519333035083, -0.7405090881699798, -1.174125745282297, -1.4388086199060899, -1.5087721754350027, -1.3757354328807965, -1.052380721036105, -0.5749321576600813, -0.004651906574226931, 0.5721061600892074, 1.0452465383217404, 1.2837499790618025, 1.1398369062443656, 0.4543490747399299, -0.9367965213480491, -3.195320224419588, -6.472751169855393, -10.902439970275967, -16.592011792319216, -23.616574909031065, -32.01263298536798, -41.77326861438757, -52.844820980759295, -65.12539948309004, -78.46573074552812, -92.67174232214674, -107.5104684142854, -122.71537872151133, -137.99340198850734, -153.03348429926015, -167.51602375704195, -181.1233868696467, -193.55205311790436, -204.52382852386148, -213.79489338222547, -221.1612016595202, -226.464590095903, -229.59740565349827, -230.5053917020715, -229.18956554885563, -225.70870550975286, -220.17661402212062, -212.75344553664743, -203.63847508745198, -193.0627801004033, -181.28117411455003, -168.56371417146187, -155.1877789857732, -141.4323761370535, -127.56708170751533, -113.84259760847726, -100.484784026776, -87.6900431376698, -75.62206291194897, -64.40994171366178, -54.14798383184567, -44.89696321502385, -36.684401541604025, -29.507303233550715, -23.336085597101857, -18.11901786736941, -13.786937980073255, -10.25802385957385, -7.442407219610307, -5.246548100871247, -3.5769835253406805, -2.343649215154149, -1.4625739954846162, -0.8578673008267315, -0.4630139021189343, -0.22151573089785734, -0.08696637228453316, -0.02267047543557095, -0.0008276527570737637, -0.0014469231810403545, -0.011100199050938502, -0.02161507093170138, -0.028795884042509642, -0.031247902505356993, -0.029348137102543824, -0.024400728435458933, -0.01800043206870559, -0.0115983443685558, -0.00625120746344222, -0.0025249397938176587, -0.0005166728601242064, 4.325966749334156e-05, -0.0003535358582529503, -0.001146944321058263, -0.001842022914753611, -0.002104179691188461, -0.0018057159324905334, -0.001022403773104057, 1.3691584685763282e-05, 0.000993359155201522, 0.001624466735913672, 0.001722965411011389, 0.0012845322347117818, 0.0005236450484534179, -0.00012853769241041182, -7.02983737882257e-05, 0.0013833269577377815, 0.00488253426337217, 0.010910608594194762, 0.019657216241304617, 0.030915934505035023, 0.044024930334331566, 0.05786727923370761, 0.07094167545665289, 0.0815116655613159, 0.08782842348179191, 0.08841234984026165, 0.08237369127642022, 0.06973640296646323, 0.051740462278619996, 0.03108775311235446, 0.012095881747904727, 0.0007231823956072016, 0.0044410973251149495, 0.03193911872558519, 0.09266194967453206, 0.19619405469541, 0.351514001224702, 0.5661534994398091, 0.8453093979615733, 1.1909693228721325, 1.6011141447583446, 2.0690809492954414, 2.5832074988135814, 3.126683354269551, 3.677713638506746, 4.210050001091667, 4.693800039939839, 5.096563392780909, 5.384858244897522, 5.52583630366255, 5.489325110558643, 5.249585119541366, 4.787098330303488, 4.090139804921864, 3.156013046400805, 1.9919818073099957, 0.615758762425431, -0.944438216747727, -2.650229347427715, -4.454441834350858, -6.302979705028561, -8.136997498753713, -9.895365531814067, -11.517371851397169, -12.945526189075045, -14.128298370062257, -15.022651300591194, -15.59663472245086, -15.831204855051702, -15.721132063132947, -15.275432705427715, -14.51711387859321, -13.482217412403148, -12.218185795474513, -10.78166239107807, -9.235905274929006, -7.647393214334584, -6.082472785927279, -4.60409267895104, -3.2687148279530294, -2.123565022392382, -1.204355862928335, -0.5336152547570784, -0.11979435563121389, 0.042839275152811725, -0.026496328577589347, -0.2965152960042407, -0.7259186953981411, -1.2659714056611577, -1.863492599907126, -2.4642096578965025, -3.015989629810731, -3.471837143344815, -3.7925457834749037, -3.9488436414851398, -3.922918272716304, -3.7092480419700107, -3.314859804028639, -2.7587249288933218, -2.0700688454950376, -1.2862736808034332, -0.4503598213803143, 0.3918320669107148, 1.1945857548369725, 1.915170055924016, 2.5164653110773485, 2.969495132328511, 3.2552009795154286, 3.3654906906189095, 3.3035806569414814, 3.0836121246896497, 2.7295738695929854, 2.273614005877931, 1.753876464125846, 1.2119251319069801, 0.6898485129369852, 0.2274121045298462, -0.14059150229041795, -0.3866424699703291, -0.4922925794652736, -0.44935170104415045, -0.26042771075592175, 0.06126458198540543, 0.49286659013214157, 1.0034993021860634, 1.5564363945205686, 2.1116906100226935, 2.6288156323728162, 3.069760595510289, 3.4016535446098186, 3.599309327187169, 3.6472132731847204, 3.540893226578013, 3.2875887964690107, 2.906123009352471, 2.4259271211925864, 1.8855410079331325, 1.3304559245259662, 0.8104156142554443, 0.3763494581939242, 0.07715489972814801, -0.043493646433477424, 0.04989710444756524, 0.3822500941624588, 0.9660794742936974, 1.8002742266758538, 2.869715909060867, 4.145632670150979, 5.586718141433851, 7.141102778823673, 8.749330777881681, 10.347209427717328, 11.868968327812867, 13.250698268455695, 14.433922652553719, 15.368406869496159, 16.014657548383326, 16.346431710000687, 16.352023344408455, 16.03418469239537, 15.409755189797988, 14.508666469529139, 13.372390888818918, 12.051295641177605, 10.601916668044938, 9.084175042105908, 7.557769989406191, 6.079055780175441, 4.698337861568904, 3.457605961975256, 2.388792653396294, 1.5125594722415834, 0.8378650708272215, 0.36214226933351473, 0.07216230796793133, -0.054468873600480264, -0.04737055240651882, 0.05886576776317944, 0.22711146292930467, 0.4201690888115393, 0.6031337369846319, 0.745466760128209, 0.8226717215931115, 0.8175030916380902, 0.7206567751168166, 0.5309297653231849, 0.25485424260921324, -0.09416404708668971, -0.4971247555963803, -0.9310226199968514, -1.3705867790880444, -1.7900777295955734, -2.1650282105828347, -2.473836581151289, -2.6991704876293734, -2.829006648502425, -2.8571339171964967, -2.7832974528921515, -2.612979021876769, -2.356825836579447, -2.029782702773877, -1.6500098166163042, -1.2377082627507414, -0.813708491883554, -0.3981012446699838, -0.009098201426169366, 0.33790961966353045, 0.6310515702662254, 0.8624059478405791, 1.0281569430792783, 1.1285157533037702, 1.1673305202535298, 1.1514648702295096, 1.0900391359966628, 0.9935951787873539, 0.8732486867115469, 0.7398901623136646, 0.603506996198081, 0.4726075454300223, 0.3537927980407383, 0.25155853351678, 0.16828936078742485, 0.1044223417550428, 0.058749781904628755, 0.02882329778259673, 0.011412456519648301, 0.002969836555414908, 7.471381276069063e-05, -0.00019585661370117812, 1.4925409203928472e-06, -0.000574387417588927, -0.002224361603555432, -0.004401532370441163, -0.005903971317011332, -0.0051421697880327435, -0.0004450979200159633, 0.009631126736056352, 0.026027141461140046, 0.04896820156329323, 0.07784020102255573, 0.11116868162626964, 0.14670902952034148, 0.18164615191388056, 0.21286869066114888, 0.23729710655508854, 0.25223383839426844, 0.2556976216376422, 0.24670616393425648, 0.22547261026359697, 0.19348963760967816, 0.15348584270456045, 0.10923029653097757, 0.06521937336529735, 0.026264449697033163, -0.0029891700156640666, -0.018571162460801274, -0.017674911176392024, 0.0009263593317904706, 0.03658300488383304, 0.08663222475296593, 0.14644655160963324, 0.20967900273339365, 0.2687008166754001, 0.31521098611703996, 0.34097792239349883, 0.3386555818010613, 0.302591361260108, 0.22956806401229454, 0.11941137580482021, -0.02460837888662992, -0.19563834950125705, -0.3834089474468873, -0.5747164909787722, -0.7542452671507948, -0.9057425403063797, -1.0132560269080686, -1.0625065236291136, -1.0423074091261035, -0.9458800933623336, -0.7719467543960553, -0.525506638321306, -0.21820133074595902, 0.13185375310282627, 0.5009173581294337, 0.8609428329721047, 1.1813947969684666, 1.4314825640509672, 1.5826958554112445, 1.61150488813881, 1.5020966052559277, 1.2489999047133915, 0.8589801666470549, 0.3523431053879544, -0.23653700557581225, -0.859591039198138, -1.4563764192470203, -1.956376290840666, -2.2822762777866923, -2.354314662300711, -2.0951923015079967, -1.4352526337319989, -0.31770093767122737, 1.2964036464398865, 3.4237002893328032, 6.054939325766554, 9.15241492313606, 12.648569692979763, 16.44741075484388, 20.427540446819876, 24.44633102519912, 28.34569602673675, 31.959157995646304, 35.11991223965557, 37.66962191484951, 39.46743830547372, 40.39748905080918, 40.37817163051471, 39.36982983184703, 37.38039192658328, 34.46888774529206, 30.74646478344292, 26.375071408716735, 21.566555554530392, 16.57004874816056, 11.655487249901505, 7.10195490139409, 3.186468607993322, 0.17367388039234555], 'positive_zeros': ['0.03079352378980187538175791332858', '0.46692219008134979802435586625987', '0.62455689424978458740766306722718', '0.898555640256923677376455525854172', '0.955334106245506702167768762874885', '1.11839224021079960517888589039569', '1.19793086511203118455852807188266', '1.62983444320969843995399415032044', '1.86701937019741116816137993847412', '1.88196913434763835167470646821805', '2.22106233778886646765961350702348', '2.37103737867408959900075742429026', '2.42308916534264778618435192353683', '2.60386918675537119048704712433165', '2.61258257681649529932823204328208', '3.01899763950392449172835795301989', '3.11108427663612944949034455380475', '3.11549585126076218429334722239821', '3.14195992459433403532709786233797', '3.45541767891553326525560274121347', '3.76159348810727315268540997404794', '3.87475106111704264679430078516650', '4.00173630717864800740184014161369', '4.05728323014081302355498492662948', '4.08897508553099291669857340828758', '4.15012203729976056466890601659150', '4.39225137760570007200194025567411', '4.52297633917584844820548104081033', '4.61096906919207085672933278427101', '4.67740337678872984169244307757376', '4.87409940061590476988732130745287', '4.95793232015362432069053198499349', '5.26346927790917366389860362625700', '5.38389822688274306959447934693892', '5.39996612460034179219126034862218', '5.51316371530350122540520631959319', '5.63272540297457754930745775259619', '5.67536468999573868420855742201826', '5.78906124745967072415492299332851', '5.80172549617075988545761976265976', '6.14266249350804087733364253316273', '6.26639422719396098655097111532010', '6.37493587022995412822738759129568', '6.42565601917691281033340965081121', '6.52587528955171536987792436425928', '6.57436500274929503721198127621165', '6.69828577807953877736472825469273', '7.08828701353977840900505394242291', '7.15909437515633945378230796889707', '7.17793690628276218230562371582564', '7.23737980334886595524776654867722', '7.31109164118457615893950753098787', '7.37918501566396288244658205314788', '7.64097637874395832645773062749559', '7.64487862096188319489426183218080', '7.68899774124508865296003765282466', '7.86089397059710409043728047124846', '7.974197116581436654873198120817195', '8.134504949609339376478550985355658', '8.314847253665054380929533286996246', '8.325688336662269314031050672461548', '8.432964996008390930273506230545602', '8.600546067943758801556206448112541', '8.818810460672198868259011247123685', '8.828397534399514849049943929522781', '8.837706171519843750538477975288969', '8.918877700145175967419945002610747', '9.016252348040195577398505603466001', '9.105106169811218368092245168145767', '9.213226618877579294235541872945620', '9.346422073002434701038696222164070', '9.435264068290663197691964169258507', '9.576757471161298049146820222806963', '9.661238423997856247973914919495401', '9.718050732264773752628271381502624', '9.844760973919052173144349638511094', '10.08839408591359901585865172280029', '10.15367435949240676187410848381971', '10.15898976300905940811910662710134', '10.53641527736618549063991512283662'], 'prelabel': '16-882e8-1.1-c2e8-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.902321829151794, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c2e8-0', 'trace_hash': 1706841161536200640, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.03079352378980187538175791333', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.46692219008134979802435586626', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.62455689424978458740766306723', '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': 111283069656.67323, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 366225584701948244050176, 'conductor_radical': 42, 'degree': 16, 'dirichlet_coefficients': [1, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 416, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 208, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -416, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -128], 'euler11': [1, 0, -160, 0, -10082, 0, -1024000, 0, 684036643, 0, -14992384000, 0, -2161166238242, 0, -502148540275360, 0, 45949729863572161], 'euler13': [1, 0, 760, 0, 330844, 0, 92555080, 0, 18570219526, 0, 2643465639880, 0, 269879614658524, 0, 17706544693085560, 0, 665416609183179841], 'euler17': [1, 0, 1024, 0, 619390, 0, 268435456, 0, 89646749059, 0, 22419997720576, 0, 4320714401380990, 0, 596605170923275264, 0, 48661191875666868481], 'euler19': [1, 0, 1180, 0, 783658, 0, 410758000, 0, 172124299123, 0, 53530393318000, 0, 13309305045583978, 0, 2611711604498069980, 0, 288441413567621167681], 'euler2': [1, 0, 4, 0, 12, 0, 16, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, -1216, 0, 549310, 0, -449511424, 0, 371584428739, 0, -125791726403584, 0, 43017007324706110, 0, -26648183309336710336, 0, 6132610415680998648961], 'euler29': [1, 0, 2120, 0, 4514524, 0, 5093815160, 0, 5464486082566, 0, 3602758680179960, 0, 2258374437226345564, 0, 750087340395594366920, 0, 250246473680347348787521], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 0, 3844, 0, 9235210, 0, 14200058896, 0, 16204929711379, 0, 13114052591692816, 0, 7876627837885497610, 0, 3027775740883185281284, 0, 727423121747185263828481], 'euler37': [1, 64, -2916, -109696, 15781226, 354186432, -29010130064, -23081726528, 59363733657267, -31598883616832, -54369654370876304, 908745482291882688, 55431232082683887146, -527482471316748363904, -19195888049029542879396, 576771922943680531180096, 12337511914217166362274241], 'euler41': [1, 0, -512, 0, 11401348, 0, -4348757504, 0, 48465387028870, 0, -12288549353260544, 0, 91038911291188255108, 0, -11552507033787487273472, 0, 63759030914653054346432641], 'euler43': [1, -416, 90504, -13258336, 1447488476, -123953645088, 8575607156536, -487565190246368, 22989545777145222, -901508036765534432, 29318294322372433336, -783555991848143553312, 16918535207007448426076, -286532293967579836749664, 3616506425675452214596104, -30736308655161617566426784, 136614025729312093462315201], 'euler47': [1, 0, 6724, 0, 24149770, 0, 76001667856, 0, 199192663651219, 0, 370863894605233936, 0, 575037096285595944970, 0, 781271532424570240092484, 0, 566977372488557307219621121], 'euler5': [1, 0, -32, 0, -482, 0, -8192, 0, 1237411, 0, -5120000, 0, -188281250, 0, -7812500000, 0, 152587890625], 'euler53': [1, 0, -10660, 0, 69445738, 0, -302838874000, 0, 993844670444083, 0, -2389544381358394000, 0, 4323670148268488229418, 0, -5236819919376700808473060, 0, 3876269050118516845397872321], 'euler59': [1, 0, 11812, 0, 80407786, 0, 412012434832, 0, 1657164032871859, 0, 4992503409348318352, 0, 11806310405174595643306, 0, 21015879904245360451798372, 0, 21559177407076402401757871041], 'euler61': [1, 0, 13828, 0, 115718506, 0, 661025359888, 0, 2860286608124659, 0, 9152452029977025808, 0, 22184083849319739382186, 0, 36704337616587021397262788, 0, 36751693856637464631913392961], 'euler67': [1, -208, 9084, -382304, 194772842, -16132806768, 189386507248, -51112315259824, 8101250499518451, -229443183201349936, 3816350423321825008, -1459347600078373719792, 79090955602046583543722, -696878184031356608998496, 74331818529684874301192124, -7640302833882554310162340432, 164890958756244164895763202881], 'euler7': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler71': [1, 0, 8576, 0, 129227140, 0, 693213336704, 0, 5297380635806854, 0, 17615716177267639424, 0, 83448881987790331153540, 0, 140729439183735596287250816, 0, 416997623116370028124580469121], 'euler73': [1, 0, 17092, 0, 162305866, 0, 1248299110672, 0, 7753362375583699, 0, 35449498984949127952, 0, 130893203609308396979146, 0, 391441805210611501897316932, 0, 650377879817809571042122834561], 'euler79': [1, 416, 83196, 12805312, 1802200202, 215193060576, 21795043632112, 2037440724486752, 172976468754407571, 12715667561521819232, 848918714869296601072, 52310733541196258640096, 2734133803669583835325322, 121244229340174557985131712, 4916177351791162864722365436, 153416690065050210761486484896, 2301619141096101839813550846721], 'euler83': [1, 0, 50488, 0, 1145722588, 0, 15231716995336, 0, 129624788516164870, 0, 722871714545811390856, 0, 2580502085138638830358108, 0, 5396662710709522849220208568, 0, 5072820298953863752478356399681], 'euler89': [1, 0, 20992, 0, 205013566, 0, 2312605007872, 0, 23946317498418499, 0, 145098020741711921152, 0, 807054108932664759430846, 0, 5184822551641982849251512832, 0, 15496731425178936435099327730561], 'euler97': [1, 0, -41480, 0, 999338524, 0, -15477214339640, 0, 172830759683498566, 0, -1370186657371218998840, 0, 7832249320152686905345564, 0, -28780581134090768252238300680, 0, 61425365346268570446197767595521], 'euler_factors': [[1, 0, 4, 0, 12, 0, 16, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -32, 0, -482, 0, -8192, 0, 1237411, 0, -5120000, 0, -188281250, 0, -7812500000, 0, 152587890625], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -160, 0, -10082, 0, -1024000, 0, 684036643, 0, -14992384000, 0, -2161166238242, 0, -502148540275360, 0, 45949729863572161], [1, 0, 760, 0, 330844, 0, 92555080, 0, 18570219526, 0, 2643465639880, 0, 269879614658524, 0, 17706544693085560, 0, 665416609183179841], [1, 0, 1024, 0, 619390, 0, 268435456, 0, 89646749059, 0, 22419997720576, 0, 4320714401380990, 0, 596605170923275264, 0, 48661191875666868481], [1, 0, 1180, 0, 783658, 0, 410758000, 0, 172124299123, 0, 53530393318000, 0, 13309305045583978, 0, 2611711604498069980, 0, 288441413567621167681], [1, 0, -1216, 0, 549310, 0, -449511424, 0, 371584428739, 0, -125791726403584, 0, 43017007324706110, 0, -26648183309336710336, 0, 6132610415680998648961], [1, 0, 2120, 0, 4514524, 0, 5093815160, 0, 5464486082566, 0, 3602758680179960, 0, 2258374437226345564, 0, 750087340395594366920, 0, 250246473680347348787521], [1, 0, 3844, 0, 9235210, 0, 14200058896, 0, 16204929711379, 0, 13114052591692816, 0, 7876627837885497610, 0, 3027775740883185281284, 0, 727423121747185263828481], [1, 64, -2916, -109696, 15781226, 354186432, -29010130064, -23081726528, 59363733657267, -31598883616832, -54369654370876304, 908745482291882688, 55431232082683887146, -527482471316748363904, -19195888049029542879396, 576771922943680531180096, 12337511914217166362274241], [1, 0, -512, 0, 11401348, 0, -4348757504, 0, 48465387028870, 0, -12288549353260544, 0, 91038911291188255108, 0, -11552507033787487273472, 0, 63759030914653054346432641], [1, -416, 90504, -13258336, 1447488476, -123953645088, 8575607156536, -487565190246368, 22989545777145222, -901508036765534432, 29318294322372433336, -783555991848143553312, 16918535207007448426076, -286532293967579836749664, 3616506425675452214596104, -30736308655161617566426784, 136614025729312093462315201], [1, 0, 6724, 0, 24149770, 0, 76001667856, 0, 199192663651219, 0, 370863894605233936, 0, 575037096285595944970, 0, 781271532424570240092484, 0, 566977372488557307219621121], [1, 0, -10660, 0, 69445738, 0, -302838874000, 0, 993844670444083, 0, -2389544381358394000, 0, 4323670148268488229418, 0, -5236819919376700808473060, 0, 3876269050118516845397872321], [1, 0, 11812, 0, 80407786, 0, 412012434832, 0, 1657164032871859, 0, 4992503409348318352, 0, 11806310405174595643306, 0, 21015879904245360451798372, 0, 21559177407076402401757871041], [1, 0, 13828, 0, 115718506, 0, 661025359888, 0, 2860286608124659, 0, 9152452029977025808, 0, 22184083849319739382186, 0, 36704337616587021397262788, 0, 36751693856637464631913392961], [1, -208, 9084, -382304, 194772842, -16132806768, 189386507248, -51112315259824, 8101250499518451, -229443183201349936, 3816350423321825008, -1459347600078373719792, 79090955602046583543722, -696878184031356608998496, 74331818529684874301192124, -7640302833882554310162340432, 164890958756244164895763202881], [1, 0, 8576, 0, 129227140, 0, 693213336704, 0, 5297380635806854, 0, 17615716177267639424, 0, 83448881987790331153540, 0, 140729439183735596287250816, 0, 416997623116370028124580469121], [1, 0, 17092, 0, 162305866, 0, 1248299110672, 0, 7753362375583699, 0, 35449498984949127952, 0, 130893203609308396979146, 0, 391441805210611501897316932, 0, 650377879817809571042122834561], [1, 416, 83196, 12805312, 1802200202, 215193060576, 21795043632112, 2037440724486752, 172976468754407571, 12715667561521819232, 848918714869296601072, 52310733541196258640096, 2734133803669583835325322, 121244229340174557985131712, 4916177351791162864722365436, 153416690065050210761486484896, 2301619141096101839813550846721], [1, 0, 50488, 0, 1145722588, 0, 15231716995336, 0, 129624788516164870, 0, 722871714545811390856, 0, 2580502085138638830358108, 0, 5396662710709522849220208568, 0, 5072820298953863752478356399681], [1, 0, 20992, 0, 205013566, 0, 2312605007872, 0, 23946317498418499, 0, 145098020741711921152, 0, 807054108932664759430846, 0, 5184822551641982849251512832, 0, 15496731425178936435099327730561], [1, 0, -41480, 0, 999338524, 0, -15477214339640, 0, 172830759683498566, 0, -1370186657371218998840, 0, 7832249320152686905345564, 0, -28780581134090768252238300680, 0, 61425365346268570446197767595521]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/882/3/n/i'], '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': '16-882e8-1.1-c2e8-0-1', 'motivic_weight': 2, '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': [2, 2, 2, 2, 2, 2, 2, 2], 'order_of_vanishing': 0, 'prelabel': '16-882e8-1.1-c2e8-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.902321829151794, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2e8-0', 'trace_hash': 1706841161536200640, 'z1': {'__RealLiteral__': 0, 'data': '0.03079352378980187538175791333', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '39035428915284608713331621784,591894194516502492263249882627,791719921872418228273344623845,1139054596710150269767794916937,1417730594593814237606645724493,1518557780191188442703275621104,2066060610207416292739206641566,2366728225268479099209381084171', 'Lhash_array': ['39035428915284608713331621784', '591894194516502492263249882627', '791719921872418228273344623845', '1139054596710150269767794916937', '1417730594593814237606645724493', '1518557780191188442703275621104', '2066060610207416292739206641566', '2366728225268479099209381084171'], 'label': '16-882e8-1.1-c2e8-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/882/3/n/i'}