Lfunction data - 32-840e16-1.1-c1e16-0-0

Formats: - HTML - YAML - JSON - 2025-09-26T17:06:44.629187

• 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
  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': '87717104635722446327634384947,491795308374294949828230219296,586814472040161990286951018984,739241882170417767736408228542,911436060783358951294433041251,921055622832912684281894117204,983140610181135308943532121551,1189264726523047498974737578243,1452522076853806133284546891711,1583966325543472539599151724287,1853579778324305314990553073068,1950055695554077421810848597881,2281282012634645338768954217501,2294703414763981657709945441992,2411403695209604549801728054917,2571953100752400533705368020987', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -16, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16784263508638.938, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, 1, 2, 2, -2, -9, 20, -70, 60, -81, -54, 162, 486, 729, 0, 6561]], [5, [1, 16, 120, 560, 1820, 4368, 8008, 11440, 12870, 11440, 8008, 4368, 1820, 560, 120, 16, 1]], [7, [1, -2, 4, -34, 20, 54, -196, 1590, -4714, 11130, -9604, 18522, 48020, -571438, 470596, -1647086, 5764801]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '840.1', 'coefficient_field': '1.1.1.1', 'conductor': 61442457392708813112505175900160000000000000000, 'conductor_radical': 210, 'degree': 32, 'euler_factors': [[1], [1, 0, 1, 2, 2, -2, -9, 20, -70, 60, -81, -54, 162, 486, 729, 0, 6561], [1, 16, 120, 560, 1820, 4368, 8008, 11440, 12870, 11440, 8008, 4368, 1820, 560, 120, 16, 1], [1, -2, 4, -34, 20, 54, -196, 1590, -4714, 11130, -9604, 18522, 48020, -571438, 470596, -1647086, 5764801], [1, 0, -98, 0, 4677, 0, -145778, 0, 3365990, 0, -61993422, 0, 956138939, 0, -12739504414, 0, 149122019666, 0, -1541480034094, 0, 13998830205899, 0, -109825128671742, 0, 721529849857190, 0, -3781105883484578, 0, 14678429517924117, 0, -37215483691157618, 0, 45949729863572161], [1, 0, -62, 0, 2189, 0, -56298, 0, 1188526, 0, -21616414, 0, 350156979, 0, -5148156634, 0, 69670246018, 0, -870038471146, 0, 10000833477219, 0, -104338301642926, 0, 969517170907246, 0, -7761157374115002, 0, 50999508333110909, 0, -244117335913355918, 0, 665416609183179841], [1, 0, 114, -196, 6541, -19736, 279342, -973588, 9906158, -34190532, 288802250, -983850976, 7042955907, -23427311044, 148964955926, -463899371944, 2734099308930, -7886289323048, 43050872262614, -115098379159172, 588234720308547, -1396927695230432, 6970984236730250, -14029697530044036, 69102955380221678, -115455733502961236, 563151768139224558, -676390145527444888, 3810932053719866701, -1941297294449563652, 19195072227771705906, 0, 48661191875666868481], [1, 0, -192, 0, 18200, 0, -1136320, 0, 52494236, 0, -1907281216, 0, 56456539944, 0, -1389647467328, 0, 28750954230662, 0, -501662735705408, 0, 7357472742042024, 0, -89729725121471296, 0, 891539166395131676, 0, -6966853210064432320, 0, 40282331527004130200, 0, -153409283670313751232, 0, 288441413567621167681], [1, 0, -176, 0, 16600, 0, -1097616, 0, 56000348, 0, -2314599984, 0, 79690491368, 0, -2321865829264, 0, 57730745485894, 0, -1228267023680656, 0, 22300666794912488, 0, -342643866310825776, 0, 4385442427958877788, 0, -45470401532280560784, 0, 363782765571537328600, 0, -2040339193118819966384, 0, 6132610415680998648961], [1, 0, -222, 0, 26333, 0, -2171770, 0, 137753198, 0, -7082097518, 0, 304034253475, 0, -11089366548570, 0, 346812558599170, 0, -9326157267347370, 0, 215037650832051475, 0, -4212596765302617278, 0, 68910543173406399278, 0, -913679348064377525770, 0, 9317004686149616256653, 0, -66057927654027480892782, 0, 250246473680347348787521], [1, 0, -236, 0, 29072, 0, -2456356, 0, 159264268, 0, -8416386060, 0, 375234642352, 0, -14382750977508, 0, 478150921280358, 0, -13821823689385188, 0, 346537072139561392, 0, -7469573608967086860, 0, 135835066761801458188, 0, -2013298860495012421156, 0, 22898932450300718651792, 0, -178638768712107931595756, 0, 727423121747185263828481], [1, -12, 204, -2548, 30544, -315516, 3204644, -29388068, 260621516, -2160117596, 17303305260, -130636973540, 956432790256, -6653840316492, 44780826644644, -287677700045588, 1792998139554726, -10644074901686756, 61304951676517636, -337036973551269276, 1792509034618975216, -9058884675767897780, 44395547268570611340, -205064018216303332268, 915427720199743164236, -3819324446496028941236, 15409801057562625290756, -56135856353368231668108, 201069686066378037622864, -620614383302575166151556, 1838460504382981693136556, -4001355215421783685061916, 12337511914217166362274241], [1, 32, 872, 16384, 274232, 3817280, 48731960, 551477536, 5831203740, 56373518304, 515488156008, 4384273868096, 35539636596616, 270512950758784, 1970604382806776, 13541976868055776, 89216269810380230, 555221051590286816, 3312585967498190456, 18644023079246152064, 100426519048890224776, 507945314501177663296, 2448622476038870429928, 10978983623412782617824, 46561725859670732112540, 180543782510495265560096, 654112496595974399435960, 2100760006189800848860480, 6187631072050019941364792, 15156889228329183302795264, 33074286113966367275484392, 49763146079729213148435232, 63759030914653054346432641], [1, -32, 952, -19424, 357592, -5515360, 77660136, -975180704, 11318069276, -120359053216, 1193913076408, -11001602170720, 95153617423464, -770195411016672, 5873756113211176, -42078669686599968, 284532009262738694, -1809382796523798624, 10860575053327464424, -61235926543702540704, 325311282400956146664, -1617328405622967388960, 7547158004923444847992, -32715830679326621670112, 132287860453650549086876, -490118617133769360277472, 1678350655611249383997864, -5125389518930002869279520, 14289244296054719220386392, -33375562350059216212560032, 70338860191619855584707448, -101666251705534581181257824, 136614025729312093462315201], [1, 4, 358, 1016, 66037, 135600, 8474646, 13153612, 846912054, 1034902316, 69207254810, 68533780576, 4751856535867, 3963078874536, 278875561511018, 206074401591908, 14105075484489906, 9685496874819676, 616036115377838762, 411458737990951128, 23187544052796018427, 15717880385939184032, 745999901925960982490, 524305440706305692308, 20166065695094811767094, 14720608020570233244404, 445759025605848181437654, 335224789565392068286800, 7672936970065637261300917, 5548375701418512508164232, 91886781055184932541704102, 48253393403281472954861372, 566977372488557307219621121], [1, 0, -336, 0, 57368, 0, -6570480, 0, 562971676, 0, -38226667216, 0, 2167136874280, 0, -110899294229232, 0, 5697668480853766, 0, -311516117489912688, 0, 17099752330905728680, 0, -847269656933529046864, 0, 35050442258125031611036, 0, -1149094626287196178193520, 0, 28182540819399866039444888, 0, -463661944051200306177887184, 0, 3876269050118516845397872321], [1, -24, 800, -14744, 293880, -4447736, 67718496, -875251000, 11106099164, -125700063288, 1385158876704, -13954407369016, 136513206958408, -1236675854856728, 10872242802330464, -89065877344947160, 708055161210923142, -5254886763351882440, 37846277194912345184, -253987250394619939912, 1654179809982741721288, -9976344906254198119784, 58426740596942843199264, -312823649143523471224872, 1630713400327103620887644, -7582295753273554014689000, 34612057813922471511052896, -134125430647644513356770024, 522870537272233874836988280, -1547716717336896552283914376, 4954708970313450709970208800, -8769834877454807756647269576, 21559177407076402401757871041], [1, 0, -532, 0, 140064, 0, -24493116, 0, 3211893356, 0, -337476552116, 0, 29598825516320, 0, -2223593298357948, 0, 145164479770038246, 0, -8273990663189924508, 0, 409820631885709625120, 0, -17386918303075846697876, 0, 615743444912579289965036, 0, -17471990683136736440674716, 0, 371778734736017107679072544, 0, -5254474907748221226599818612, 0, 36751693856637464631913392961], [1, 0, 440, -384, 103256, -204288, 16810088, -51498624, 2145056668, -8382078336, 230189227448, -998146574592, 21528530047720, -93761161331328, 1768500126721704, -7326918670005504, 126982101380577414, -490903550890368768, 7938797068853729256, -28199888165494203264, 433824013943741494120, -1347622750822707481344, 20822545107678048574712, -50801359447721700582528, 871038179402146724732188, -1401099085217860468652928, 30642063904241910512697512, -24949720590890106273851904, 844914823216770297318790616, -210524991978394148615265408, 16162179071674634117651104760, 0, 164890958756244164895763202881], [1, 0, -556, 0, 159568, 0, -31261348, 0, 4675032076, 0, -566675658188, 0, 57715565878768, 0, -5048338414984420, 0, 383759996279289574, 0, -25448673949936461220, 0, 1466649548845737089008, 0, -72591312705002348395148, 0, 3018918471764200914029836, 0, -101763301472875647663118948, 0, 2618460255558572951068567888, 0, -45992993146737102883806137836, 0, 416997623116370028124580469121], [1, 0, -484, 0, 118496, 0, -19741196, 0, 2519941548, 0, -263032335940, 0, 23581346703712, 0, -1898951836350284, 0, 142510808022168230, 0, -10119514335910663436, 0, 669668766796568970592, 0, -39805795048468227526660, 0, 2032232292367792727177388, 0, -84840273838840553446208204, 0, 2713801085316909696280392416, 0, -59069786795237348918068577956, 0, 650377879817809571042122834561], [1, 4, 390, -1192, 68245, -733040, 10443766, -148070804, 1691400502, -20859036532, 230955075130, -2554721106112, 26034380550683, -265360741457144, 2617960752313162, -23151724856456284, 227694068962749618, -1828986263660046436, 16338693055186444042, -130833194607288820616, 1014041231233927455323, -7861020927222287610688, 56142281553013088292730, -400575039099493663360588, 2566038602664579848493622, -17746522177829464519458476, 98884459830351457484998966, -548309382869093941705462160, 4032700170356602597516441045, -5564529410830691675623536088, 143828146935984572588893579590, 116537678030182371636129156796, 2301619141096101839813550846721], [1, 20, 1052, 19348, 549888, 9078916, 186325460, 2742193252, 45343893036, 595522850820, 8359936336636, 98328379003972, 1204950715864128, 12731008103047540, 138344927981317204, 1314718662957128596, 12780679604563617638, 109121649025441673468, 953058208863294218356, 7279424930217243753980, 57184937862659579009088, 387319481256953566433996, 2733200707240843913446684, 16160138445339553288444140, 102127698059926356583618476, 512626306521806747743960556, 2891033511585076758577511540, 11692113271068124108257846572, 58777532575396888379654611968, 171652953187392081112286987324, 774656257003841583336802283708, 1222366337097316566862254554140, 5072820298953863752478356399681], [1, -24, 1104, -21736, 568792, -9605400, 185994096, -2762913896, 43792315484, -580961162104, 7934230025424, -94888815252104, 1149110187837160, -12461695108494072, 135963207869162864, -1341461948429341064, 13290404171910305606, -119390113410211354696, 1076964569531639045744, -8785108738939957443768, 72097748340834361475560, -529864785412926658330696, 3943163880816747371392464, -25696687722317735273833016, 172392338910088309267322204, -968004576355996803160564264, 5799615810099243629438019696, -26656647442761449016533040600, 140486165624692583307520316632, -477803923658613871465722588584, 2159877729251047320331985584464, -4178893867463982858903189500376, 15496731425178936435099327730561], [1, 0, -686, 0, 252221, 0, -64043882, 0, 12508641022, 0, -1992015843950, 0, 268648339369171, 0, -31445973528756858, 0, 3242273163197169378, 0, -295875164932073276922, 0, 23783244326196702196051, 0, -1659293431385365494829550, 0, 98035643365824562896294142, 0, -4722750376681181191328682218, 0, 175001614132630367872415536061, 0, -4478456863379768235316363967534, 0, 61425365346268570446197767595521], [1, 40, 1296, 33304, 726776, 14138376, 249195696, 4039008888, 61089060316, 867101462664, 11646992260112, 148651491635512, 1809361010727496, 21065021779070824, 234869709385716528, 2510948889286178712, 25766421187307622022, 253605837817904049912, 2395905905443694302128, 21703313003998449038024, 188282832330068535485896, 1562342116712791980591512, 12363516978002771605127312, 92965013198577102524767464, 661506986036988418921793116, 4417404537046837297738688088, 27526707935884439407028091696, 157737385764525916151713151976, 818949388099192425703265017976, 3790305861155027077266964448504, 14897185803559585164122525175696, 46438758214799941406678242060040, 117257864492369852051862561201601], [1, 0, -926, 0, 434613, 0, -137874674, 0, 33046146750, 0, -6323835745814, 0, 996531478133819, 0, -131654809913299098, 0, 14719420841814619618, 0, -1396725878370190130682, 0, 112160495808193564344539, 0, -7550990595161388198479606, 0, 418618700080446052732626750, 0, -18529203268533114360381267026, 0, 619654216314878370017922520533, 0, -14006580852158330112269190426494, 0, 160470643909878751793805444097921], [1, 0, -904, 0, 394520, 0, -109874904, 0, 21771228316, 0, -3260052122504, 0, 389540306424872, 0, -40477237870737560, 0, 4176245231749945350, 0, -463423896382074324440, 0, 51060787939589958236072, 0, -4892459168851507170909896, 0, 374070236105165670017695516, 0, -21614056653566069001031779096, 0, 888534625676824023196821370520, 0, -23309948717819269619762467594696, 0, 295216374856540727739668685278401], [1, -36, 1294, -33408, 794877, -16177448, 309025614, -5331392500, 86996477398, -1317046342748, 18981547514994, -256933665088840, 3326997957159459, -40758832370765232, 478701384280063602, -5339439679818559372, 57180137375814570098, -581998925100222971548, 5687451146631435655362, -52783869926279727631728, 469632913283386016194899, -3953242919259430606533160, 31833955441330145509449954, -240761223847189087941886412, 1733459308218999695459281558, -11579215540819132459194182500, 73157601310212522779992193214, -417447139896551585617796610632, 2235722543749241820131443939437, -10242240048248520348730293397632, 43241947732437164784094018275934, -131129368548750722266448939501364, 397030588105939686862303733490241], [1, 0, -1032, 0, 526616, 0, -174927384, 0, 42322376412, 0, -7969089135240, 0, 1229728138853544, 0, -163082597417657688, 0, 19333546408187818438, 0, -2082401686426071018072, 0, 200503927787511914697384, 0, -16591259091810258223841160, 0, 1125116758024815596321196252, 0, -59380279333080245882959925016, 0, 2282629216930545303380216444696, 0, -57118646281270772696206661520648, 0, 706732552679793116819634555191041]], 'euler_factors_factorization': [[1], [[[1, 0, 1, 2, 2, -2, -9, 20, -70, 60, -81, -54, 162, 486, 729, 0, 6561], 1]], [[[1, 1], 16]], [[[1, -2, 4, -34, 20, 54, -196, 1590, -4714, 11130, -9604, 18522, 48020, -571438, 470596, -1647086, 5764801], 1]], [[[1, 0, -98, 0, 4677, 0, -145778, 0, 3365990, 0, -61993422, 0, 956138939, 0, -12739504414, 0, 149122019666, 0, -1541480034094, 0, 13998830205899, 0, -109825128671742, 0, 721529849857190, 0, -3781105883484578, 0, 14678429517924117, 0, -37215483691157618, 0, 45949729863572161], 1]], [[[1, 0, -62, 0, 2189, 0, -56298, 0, 1188526, 0, -21616414, 0, 350156979, 0, -5148156634, 0, 69670246018, 0, -870038471146, 0, 10000833477219, 0, -104338301642926, 0, 969517170907246, 0, -7761157374115002, 0, 50999508333110909, 0, -244117335913355918, 0, 665416609183179841], 1]], [[[1, 0, 57, -98, 1646, -4282, 41047, -81412, 839106, -1384004, 11862583, -21037466, 137475566, -139145986, 1375841433, 0, 6975757441], 2]], [[[1, 0, -192, 0, 18200, 0, -1136320, 0, 52494236, 0, -1907281216, 0, 56456539944, 0, -1389647467328, 0, 28750954230662, 0, -501662735705408, 0, 7357472742042024, 0, -89729725121471296, 0, 891539166395131676, 0, -6966853210064432320, 0, 40282331527004130200, 0, -153409283670313751232, 0, 288441413567621167681], 1]], [[[1, 0, -176, 0, 16600, 0, -1097616, 0, 56000348, 0, -2314599984, 0, 79690491368, 0, -2321865829264, 0, 57730745485894, 0, -1228267023680656, 0, 22300666794912488, 0, -342643866310825776, 0, 4385442427958877788, 0, -45470401532280560784, 0, 363782765571537328600, 0, -2040339193118819966384, 0, 6132610415680998648961], 1]], [[[1, 0, -222, 0, 26333, 0, -2171770, 0, 137753198, 0, -7082097518, 0, 304034253475, 0, -11089366548570, 0, 346812558599170, 0, -9326157267347370, 0, 215037650832051475, 0, -4212596765302617278, 0, 68910543173406399278, 0, -913679348064377525770, 0, 9317004686149616256653, 0, -66057927654027480892782, 0, 250246473680347348787521], 1]], [[[1, 0, -236, 0, 29072, 0, -2456356, 0, 159264268, 0, -8416386060, 0, 375234642352, 0, -14382750977508, 0, 478150921280358, 0, -13821823689385188, 0, 346537072139561392, 0, -7469573608967086860, 0, 135835066761801458188, 0, -2013298860495012421156, 0, 22898932450300718651792, 0, -178638768712107931595756, 0, 727423121747185263828481], 1]], [[[1, -6, 84, -770, 7124, -50334, 405452, -2547786, 16833206, -94268082, 555063788, -2549568102, 13351522964, -53394846890, 215521018356, -569591262798, 3512479453921], 2]], [[[1, 16, 308, 3264, 37460, 303968, 2637964, 17639760, 127095446, 723230160, 4434417484, 20949778528, 105853007060, 378154640064, 1463032106228, 3116068382096, 7984925229121], 2]], [[[1, -16, 348, -4144, 51940, -484528, 4416132, -33077136, 236220694, -1422316848, 8165428068, -38523367696, 177572523940, -609202987792, 2199834341052, -4349097777712, 11688200277601], 2]], [[[1, 2, 177, 154, 17046, 6450, 1195423, 419226, 64751346, 19703622, 2640689407, 669658350, 83179042326, 35319131078, 1907921113233, 1013246240926, 23811286661761], 2]], [[[1, 0, -336, 0, 57368, 0, -6570480, 0, 562971676, 0, -38226667216, 0, 2167136874280, 0, -110899294229232, 0, 5697668480853766, 0, -311516117489912688, 0, 17099752330905728680, 0, -847269656933529046864, 0, 35050442258125031611036, 0, -1149094626287196178193520, 0, 28182540819399866039444888, 0, -463661944051200306177887184, 0, 3876269050118516845397872321], 1]], [[[1, -12, 328, -3436, 51916, -473868, 5241336, -40917388, 367036742, -2414125892, 18245090616, -97322535972, 629084913676, -2456479891364, 13835215034248, -29863817817828, 146830437604321], 2]], [[[1, 0, -532, 0, 140064, 0, -24493116, 0, 3211893356, 0, -337476552116, 0, 29598825516320, 0, -2223593298357948, 0, 145164479770038246, 0, -8273990663189924508, 0, 409820631885709625120, 0, -17386918303075846697876, 0, 615743444912579289965036, 0, -17471990683136736440674716, 0, 371778734736017107679072544, 0, -5254474907748221226599818612, 0, 36751693856637464631913392961], 1]], [[[1, 0, 220, -192, 27428, -59904, 2352452, -7304256, 167339734, -489385152, 10560157028, -18016906752, 552704946788, -259224020544, 19900844077180, 0, 406067677556641], 2]], [[[1, 0, -556, 0, 159568, 0, -31261348, 0, 4675032076, 0, -566675658188, 0, 57715565878768, 0, -5048338414984420, 0, 383759996279289574, 0, -25448673949936461220, 0, 1466649548845737089008, 0, -72591312705002348395148, 0, 3018918471764200914029836, 0, -101763301472875647663118948, 0, 2618460255558572951068567888, 0, -45992993146737102883806137836, 0, 416997623116370028124580469121], 1]], [[[1, 0, -484, 0, 118496, 0, -19741196, 0, 2519941548, 0, -263032335940, 0, 23581346703712, 0, -1898951836350284, 0, 142510808022168230, 0, -10119514335910663436, 0, 669668766796568970592, 0, -39805795048468227526660, 0, 2032232292367792727177388, 0, -84840273838840553446208204, 0, 2713801085316909696280392416, 0, -59069786795237348918068577956, 0, 650377879817809571042122834561], 1]], [[[1, 2, 193, -982, 17462, -211918, 1793391, -19574326, 178160242, -1546371754, 11192553231, -104483838802, 680146314422, -3021669383818, 46915878915553, 38407817972318, 1517108809906561], 2]], [[[1, 10, 476, 4914, 112516, 1075234, 16779076, 138590858, 1685572758, 11503041214, 115591054564, 614804823158, 5339820445636, 19356445719702, 155623617723644, 271360509896270, 2252292232139041], 2]], [[[1, -12, 480, -5108, 107900, -1056060, 15486496, -137556996, 1596396230, -12242572644, 122668534816, -744489562140, 6769887803900, -28523375665492, 238551019661280, -530776018746348, 3936588805702081], 2]], [[[1, 0, -686, 0, 252221, 0, -64043882, 0, 12508641022, 0, -1992015843950, 0, 268648339369171, 0, -31445973528756858, 0, 3242273163197169378, 0, -295875164932073276922, 0, 23783244326196702196051, 0, -1659293431385365494829550, 0, 98035643365824562896294142, 0, -4722750376681181191328682218, 0, 175001614132630367872415536061, 0, -4478456863379768235316363967534, 0, 61425365346268570446197767595521], 1]], [[[1, 20, 448, 7692, 109196, 1439252, 17309568, 188592556, 1985382982, 19047848156, 176574903168, 1482862774852, 11362979547596, 80843693053692, 475561027469248, 2144270704214020, 10828567056280801], 2]], [[[1, 0, -926, 0, 434613, 0, -137874674, 0, 33046146750, 0, -6323835745814, 0, 996531478133819, 0, -131654809913299098, 0, 14719420841814619618, 0, -1396725878370190130682, 0, 112160495808193564344539, 0, -7550990595161388198479606, 0, 418618700080446052732626750, 0, -18529203268533114360381267026, 0, 619654216314878370017922520533, 0, -14006580852158330112269190426494, 0, 160470643909878751793805444097921], 1]], [[[1, 0, -904, 0, 394520, 0, -109874904, 0, 21771228316, 0, -3260052122504, 0, 389540306424872, 0, -40477237870737560, 0, 4176245231749945350, 0, -463423896382074324440, 0, 51060787939589958236072, 0, -4892459168851507170909896, 0, 374070236105165670017695516, 0, -21614056653566069001031779096, 0, 888534625676824023196821370520, 0, -23309948717819269619762467594696, 0, 295216374856540727739668685278401], 1]], [[[1, -18, 485, -7974, 136294, -1768042, 24793123, -275111310, 3135176338, -29987132790, 294567094363, -2289665663218, 19239010395334, -122689874163726, 813393553757885, -3290470417470042, 19925626416901921], 2]], [[[1, 0, -1032, 0, 526616, 0, -174927384, 0, 42322376412, 0, -7969089135240, 0, 1229728138853544, 0, -163082597417657688, 0, 19333546408187818438, 0, -2082401686426071018072, 0, 200503927787511914697384, 0, -16591259091810258223841160, 0, 1125116758024815596321196252, 0, -59380279333080245882959925016, 0, 2282629216930545303380216444696, 0, -57118646281270772696206661520648, 0, 706732552679793116819634555191041], 1]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 0, 'label': '32-840e16-1.1-c1e16-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__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}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/840/2/f/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.010986328125', 'prec': 47}, 'plot_values': [0.2606110516147656, 0.2521618348916749, 0.23011356690393472, 0.19512429607002982, 0.14810575388336134, 0.09022259610253493, 0.022884775343216913, -0.052267625559292596, -0.13338758434234743, -0.21845260193215152, -0.3053043972206841, -0.39169646130283525, -0.47534872738756223, -0.5540082146924261, -0.6255140948469413, -0.6878652262571119, -0.7392878274629912, -0.7783199329906012, -0.8039378351801887, -0.8155570578661611, -0.8130371590181593, -0.7966870874042594, -0.7672541823087204, -0.7258968571197242, -0.6741416444312996, -0.613825919334926, -0.5470282336423821, -0.4759887609374545, -0.40302284482555956, -0.33043103595530804, -0.2604092750026943, -0.19496300985169124, -0.1358290110725992, -0.08440713598668585, -0.041707267504503445, -0.008321489265935959, 0.015594748293500283, 0.030322823084891398, 0.03655907915505175, 0.035371040153759616, 0.028133075096982235, 0.016444179735446512, 0.002031793481955737, -0.013353283379784663, -0.028044861275257446, -0.04056554986762067, -0.04972019716130876, -0.05467175370811489, -0.05499336303822161, -0.050691876437889846, -0.042200486658569444, -0.030335966839433404, -0.01622135324924845, -0.001179796170795998, 0.013392953125564051, 0.026167337315188152, 0.03601788877190876, 0.042146733773712614, 0.04417892330836238, 0.04221672921436083, 0.03684229421846104, 0.02906163127768579, 0.02018784875127281, 0.01166742607862329, 0.004860041459284549, 0.000789463504159436, -0.00011107970885694379, 0.0017709577743440907, 0.005059245227458411, 0.007316866913284723, 0.005103385051163971, -0.005813262259656041, -0.030074418313646982, -0.07217657380313022, -0.13576160015156058, -0.22278727529138756, -0.3326346686487604, -0.46122871951699934, -0.6002652070856259, -0.7366490865083501, -0.8522536759349456, -0.9241091384383091, -0.9251377599872725, -0.8254805461447552, -0.5944087721071305, -0.20278926511102013, 0.3739968817414488, 1.1528461468373834, 2.139659949521394, 3.326285187704764, 4.687983480059622, 6.181761535504703, 7.745885434224272, 9.300861315242187, 10.752091907997364, 11.9943129641503, 12.917779369747835, 13.41605700005743, 13.395230558118461, 12.783610883199737, 11.54125787309888, 9.668583936901406, 7.21315015612314, 4.273796609116552, 1.0013423792614826, -2.4047332070249037, -5.703961987221039, -8.6269228726483, -10.891283615636585, -12.221096991925968, -12.368216952671212, -11.1343629573878, -8.39210589452612, -4.1031250895160545, 1.667840756188277, 8.747083397491867, 16.85393307353503, 25.61128196938702, 34.564795417433665, 43.21005132871551, 51.026071843770666, 57.512992973828005, 62.23103185082436, 64.83752649948818, 65.1186974968366, 63.012953560252186, 58.62304847497086, 52.21518049262935, 44.204162398667194, 35.12557103352257, 25.596505838811378, 16.26310243372641, 7.7448920532986625, 0.580223452204588, -4.822703175030035, -8.22423269194956, -9.576881377300408, -9.031224188306805, -6.922687807828246, -3.7397507294672176, -0.07597433260911564, 3.429919229178054, 6.1602442576045435, 7.584192412751332, 7.316379982622142, 5.161776327155039, 1.141969594272557, -4.502933731823334, -11.336870879793514, -18.772652097118254, -26.13471375800719, -32.733135279013865, -37.94072357546994, -41.26431983965076, -42.40184442211768, -41.27797772660621, -38.0536692578084, -33.10764875827722, -26.991461345812493, -20.362875990566884, -13.905413233688881, -8.244004747177943, -3.8671476904488675, -1.064902272912541, 0.10536995144215354, -0.178912932017589, -1.5364665110137858, -3.4427228124821947, -5.312489303783959, -6.593609116671244, -6.858363104626429, -5.87884236535355, -3.673862291401581, -0.5181384140628645, 3.0908872648222716, 6.507501193155982, 9.046375369438138, 10.11295974115642, 9.339121449716256, 6.702467815411632, 2.6102345392851607, -2.0679189236599256, -6.028846998675334, -7.629831832799578, -5.042380318651457, 3.547499255315671, 19.71314771886414, 44.56093155605231, 78.53163259314194, 121.2562547631056, 171.48833282503657, 227.1271431556283, 285.3362482859967, 342.755283487189, 395.79886937726906, 440.97532536004127, 475.20940481088877, 496.1361898354135, 502.32997939584897, 493.4418407766372, 470.2297634660275, 434.477714465049, 388.81282339446534, 336.4418078348607, 280.8370805510288, 225.40856774280311, 173.1983893688947, 126.63205928925645, 87.35220452459282, 56.15168881055685, 33.00568740734061, 17.184121227213083, 7.447452593665971, 2.283361163092198, 0.14675154062114357, -0.3292447482644595, -0.17737571379316677, -0.012041638342825076, -0.02191390620113104, -0.03306169763976975, 0.37374705646144946, 1.7149826838628115, 4.452173445281739, 8.861300497788681, 14.944615391651556, 22.39800411636447, 30.638187009067792, 38.88230402708878, 46.26392647602945, 51.964684066449905, 55.3387051380689, 56.009158260263334, 53.92157982995837, 49.346380132460794, 42.83158906377729, 35.11507461180992, 27.011815248931274, 19.295345768186035, 12.592730584803954, 7.309414311339039, 3.5946569256082492, 1.3510195535059504, 0.2836778322114189, -0.02105710972223581, -0.003524752063506525, -0.04258598861151929, -0.38700865526051, -1.1173936521099228, -2.14364692421061, -3.236396169306398, -4.084737593595553, -4.368304396466954, -3.8295791187185753, -2.332897893754321, 0.10047735882761283, 3.287121427453805, 6.906335320192262, 10.550269683473669, 13.791014986451716, 16.249644110250866, 17.65434561802271, 17.87874605316191, 16.95474278775033, 15.059043746142976, 12.477301898867834, 9.553428030866185, 6.633755555778484, 4.015937652074528, 1.9108643737338769, 0.4229070903522846, -0.4499267449378871, -0.7980710685508485, -0.7698830823811248, -0.535509071947825, -0.2524829757833199, -0.039216076090709366, 0.03955603619390159, -0.025983011206932544, -0.20104427307507636, -0.4241894104948244, -0.6279429539124449, -0.7571743109891754, -0.7814907692005909, -0.6996950955260683, -0.5363985463744727, -0.3326733124940477, -0.1338007356554023, 0.02248655405232951, 0.1143664100122989, 0.1391527027824845, 0.1110949531734002, 0.05479987541218664, -0.0033099565932029193, -0.042928498051407665, -0.05501732195184657, -0.04291609450539102, -0.019361444615738008, -0.0005260276015173883, 0.000993855794753013, -0.017954215338557265, -0.04821407930475693, -0.06947006119329995, -0.055290932012128736, 0.019166038309451502, 0.1688341114233551, 0.3921213002204107, 0.6680354531470369, 0.958232075531616, 1.2136960023129575, 1.3846675608635648, 1.4315570681495304, 1.3342579749045362, 1.0975790531288747, 0.751390313600613, 0.34530710920802526, -0.06097383913151263, -0.4095357965680145, -0.6556180337422158, -0.775929048970259, -0.7720414115431103, -0.6681811758084757, -0.5040942375068892, -0.3247589447652443, -0.1692903289169122, -0.06226197780013802, -0.009341007920248669, 0.0019585905976910807, -0.0031498140225654464, 0.00477868027384596, 0.05018165515696832, 0.14495619133294702, 0.2845795692226377, 0.4488449757971859, 0.6069550726108058, 0.7255780521008275, 0.7777022058723667, 0.7499217824043576, 0.6462303561799526, 0.4872759868455, 0.30499333358136066, 0.134386655017938, 0.00466151905472982, -0.06796821847622794, -0.08391069073872111, -0.05933958698522396, -0.02112421984140323, 0.0010655741114731425, -0.01665050316735833, -0.08538492958067735, -0.1999896641985402, -0.3399950683983779, -0.47474767201794404, -0.5713942073145765, -0.6036191735543194, -0.5588515225345877, -0.44175696561579625, -0.2732082718789448, -0.08509681750922193, 0.08759024497530245, 0.21528494441993498, 0.2806878490653652, 0.2821874417184566, 0.2330452439312155, 0.1567039002159079, 0.07962152967939289, 0.0236833833573223, 0.0003178004049853594, 0.007930354035827102, 0.033311663355533226, 0.05654219183232265, 0.057929346541256296, 0.024845451348999077, -0.043575192153407445, -0.13525202629163546, -0.22785120580969795, -0.29461246493210197, -0.31168183476180544, -0.26490271441479324, -0.15417408511486655, 0.00583421920248526, 0.1888094295809, 0.3629139695697142, 0.4982384681925683, 0.5736036514981631, 0.5809517316445653, 0.5263302785710371, 0.42737832099660494, 0.30779905509431915, 0.1910834603552624, 0.09517871802287527, 0.029370988383992557, -0.006051936702575739, -0.017660169075482814, -0.01526651003217311, -0.008169972956403149, -0.0024718719165575864, -0.00017455248613829397, -7.21878500000872e-05, 0.00020821919616200506, 0.002035080253734445, 0.00446547249048486, 0.0043882658827768236, -0.0019459801396326207, -0.01672342473569151, -0.038754542141696366, -0.06300925708623428, -0.08193783914465623, -0.0882564907277774, -0.0781682065054487, -0.05362558618939556, -0.02241315435821772, 0.004461361799542438, 0.017525318834882134, 0.014175571726834743, 0.0024130919148211767, 0.0009451992835088945, 0.034605148019050666, 0.12565184535031157, 0.28328548611190213, 0.4951463304806409, 0.7246315532372147, 0.9165200268532543, 1.0109369777326591, 0.9626653381484895, 0.7601864678348551, 0.4375954580679379, 0.07339244310674103, -0.22675031845639657, -0.3613627240288972, -0.2715550031465824, 0.02485705532700047, 0.4161500944607985, 0.706751697033397, 0.6588190697535667, 0.06066721817596735, -1.1940731341510848, -3.0380607655209144, -5.194894927587374, -7.1943722875388225, -8.44497080465975, -8.355538842422876, -6.4833085110341395, -2.6743370362177155, 2.841126136465299, 9.430014464637072, 16.131203128552514, 21.81882133016228, 25.426189805388155, 26.183588208506194, 23.815340329479746, 18.64595066322159, 11.565580172289534, 3.861856424128719, -3.0480671867148197, -7.927359359180074, -9.998736634575135, -9.124397869766163, -5.839408810160479, -1.225694318839857, 3.346947384723784, 6.552158879706153, 7.429882095285684, 5.619817948503151, 1.4453026211073683, -4.175426638295681, -9.969806335072686, -14.64353473959499, -17.210289748465538, -17.231143073918016, -14.902349050904785, -10.969951451620002, -6.497405631659414, -2.5530178748281447, 0.09363786674513402, 1.1795632601679746, 1.0006328888420155, 0.29300728603238574, -0.021868031338129694, 0.8468549535617074, 3.2783811186418648, 7.082428970338519, 11.519561563743633, 15.504783315921095, 17.93512542278899, 18.042879833676192, 15.668399761407256, 11.365985551773361, 6.302751957198759, 1.9697431226018567, -0.2197684998775234, 0.6659717015849189, 4.78726895701229, 11.444606933715901, 19.22521391279787, 26.352037213880788, 31.14370251761996, 32.45941530240132, 30.00610303914204, 24.419497540679032, 17.06803343325877, 9.662334362521147, 3.7863075406281794, 0.4833007490880879, 0.014181691095164073, 1.8507840068614323, 4.89673322329139, 7.859799347289427, 9.656145892930361, 9.720465346041143, 8.128978091054819, 5.504441967682931, 2.7441690093296747, 0.6705260627273881, -0.27102460211431806, -0.15800775245535262, 0.47429519966765515, 0.883957900243458, 0.4597201200183765, -0.9905612102075926, -3.122642704342209, -5.17180192571983, -6.274057233495873, -5.875598741237533, -4.057698415273587, -1.6073419217445086, 0.2668379220081869, 0.552199299675978, -0.7773406877580881, -2.070047326730559, 0.28361880840711623, 11.470272414295307, 37.139246119910595, 81.70503507210368, 146.43651640198922, 227.8561246303459, 316.9969469900266, 399.9355854454793, 459.7466247771839, 479.66561512985874, 446.88797484801347, 356.1686941731499, 212.30562477312463, 30.732780984269375, -164.1896380578867, -343.09178661799353, -477.1115620414633, -543.9932833721333, -533.026420632855, -447.7907323001101, -306.0530808986872, -136.68554272255793, 25.840822626213654, 148.27126653964558, 205.2543826592262, 184.4613718997426, 89.02295864892334, -63.24832020523914, -243.67441872876617, -418.7190359779819, -556.8590184875645, -634.817966707669, -641.8666105065258, -581.3316287709298, -468.75539014026674, -327.65103961330675, -183.9756591166748, -60.60613411490022, 26.96932198242961, 72.90787398397453, 80.91928410899948, 62.087613008397675, 31.322874552582817, 3.4022444454362795, -10.443052378335912, -4.6678375428087255, 20.068015205547574, 57.92524557171852, 100.02484335109285, 137.0754764602053, 161.70987309047504, 169.98255162504347, 161.80640372873674, 140.3925009741391, 110.9987020045434, 79.41558138718318, 50.61094216623284, 27.83903921517622, 12.345162217176826, 3.616909039484489, -0.000708012436890801, -0.5691078891552015, 0.0766403016826486, 0.7107825452875115, 0.8083686632309747, 0.3990872999121453, -0.20327177332771418, -0.6680560775177725, -0.8191880441683929, -0.6769853643554131, -0.39351651487385286, -0.14052635526078647, -0.014858512424032293, -0.0053600854224080665, -0.02975012048437733, -0.015741555248311632, 0.01874933302181195, -0.07023689309059859, -0.5213590294128599, -1.5768447332512123, -3.3665245553897893, -5.817053533501923, -8.625929790713872, -11.315732345780468, -13.354900353027618, -14.306205147547614, -13.953611844312004, -12.365399715346497, -9.873265429639805, -6.9755621224811595, -4.1976945961690495, -1.9554657955303807, -0.46384718594219837, 0.2840123477630118, 0.467992858500877, 0.3465763634536809, 0.1547271385333979, 0.03135639457350398, -0.0005745550361188406, -0.0009497843835256477, -0.04762478178571495, -0.17219417059567685, -0.3264476183313862, -0.395345648273114, -0.25210464283465295, 0.1674188374643318, 0.8033743262529898, 1.4528726714927378, 1.8078384990857836, 1.5432219936477878, 0.4290949688959495, -1.5712328155890667, -4.253366622753261, -7.197444540844447, -9.864834305160402, -11.735367455846767, -12.44440517672974, -11.878496975793247, -10.201230718775665, -7.802700301269755, -5.189401461814343, -2.8488030425756534, -1.129011400001455, -0.16734517696659665, 0.11509487875706884, -0.04311927563693081, -0.3396616725446206, -0.5108372876890962, -0.4082831300592977, -0.028388045042061823, 0.5098129317182156, 1.0239972281592782, 1.340851032825968, 1.356003684945371, 1.0635805632476005, 0.5496269255981302, -0.04373452174110143, -0.5678096229212032, -0.9124622500728896, -1.0327319963286083, -0.9509479662935778, -0.737427065304717, -0.4796240622724069, -0.25201490672413007, -0.09676273050298968, -0.019686344068610744, 0.00015798093341015578, -0.006250105505135451, -0.013562257315044656, -0.01077176999567547, -0.0011120875036004592, 0.004710056382311015, -0.002604164513510589, -0.024583037593125676, -0.053844383311255774, -0.07803945080957864, -0.08633020912445823, -0.07488410177251373, -0.048641592474792536, -0.018623886524675504, 0.00371201845837175, 0.012161448676418853, 0.008592538222126356, 0.0015250555317973882, 0.0013220990565698581, 0.014437788005647134, 0.03956947330493232, 0.06762138577861083, 0.08556399765786495, 0.08242737734041077, 0.0546470521098453, 0.00825036200125236, -0.04319518099582704, -0.0840066102850756, -0.10275574694526461, -0.09670307815396358, -0.07230449321138115, -0.041621559585240935, -0.016386709611704586, -0.0027845354043649585, 0.0004837707637860331, -3.0240829383271214e-05, 0.0023123555040601433, 0.008940414690977316, 0.01367828340484208, 0.004990383167733617, -0.027708588535265023, -0.08653123916024087, -0.16036784544986696, -0.22618592939861834, -0.2572000266756013, -0.23545046998954217, -0.16368710083561866, -0.07058862703885549, -0.004969499127270416, -0.020046242141563662, -0.1527228329141967, -0.4056068448803424, -0.739407627244183, -1.0801058306779985, -1.3399119581063037, -1.445529039011065, -1.3637883658613392, -1.1148765791166786, -0.7673511803382708, -0.41569036148141825, -0.1478731052690897, -0.014804974181310016, -0.013414419742825737, -0.09070821705480236, -0.1682012035285869, -0.1771426309487813, -0.09037861170422186, 0.06206280089225431, 0.20050021770884124, 0.2242379422951296, 0.05105595319886156, -0.34720591806227796, -0.9266887877370695, -1.578640196470769, -2.1599063129351115, -2.536415906884387, -2.6244208264217006, -2.415054268455035, -1.9740003577267282, -1.4171851070576311, -0.8714656763609123, -0.43580397666120774, -0.1566862860909792, -0.02489767476131158, 0.007905870950429921, 0.0017991646913658797, 0.0025741831426654934, 0.027343350478520077, 0.06594118103855227, 0.0949722372064959, 0.09596161668446873, 0.06789925672222898, 0.027907320204012417, 0.0001114325846725625, -0.000956928433177193, 0.017098158953772608, 0.023763760300889853, -0.021884511772802644, -0.1505008617891711, -0.3631904392383667, -0.6233795503056954, -0.865108407475073, -1.015774995780381, -1.024526066731531, -0.8842169309121588, -0.6368489954422241, -0.35907098428432055, -0.13297495743458723, -0.014243114632237881, -0.01147922188163835, -0.08614842350386998, -0.17369102423270374, -0.21592252913116208, -0.18855695397372801, -0.11047360146159399, -0.030241744085674052, 0.0034689684845988092, -0.027332652922016382, -0.09432401103110229, -0.13217171672771583, -0.07069201201735399, 0.1241234732259401, 0.4204129232125519, 0.7192171977410112, 0.8870173136773168, 0.8114190036364822, 0.45665810171827964, -0.10775027112096218, -0.7237995268910837, -1.2032478248518756, -1.4033646041308494, -1.2862279969275532, -0.9329699098627429, -0.504245318920029, -0.16410076934147366, -0.00396129148838339, -0.005960713426802528, -0.06684046351617218, -0.07171825624776836, 0.02381757051148217, 0.15725690772488923, 0.20510355982553832, 0.1032192229232922, -0.02099446042532776, 0.1966530724671819, 1.227458902200361, 3.3235530437462346, 6.079493024729208, 8.07235369693729, 6.825037654194392, -0.7045696397711546, -17.05897785032992, -42.826245776569706, -75.22440296309317, -107.31032342588361, -128.37448186674797, -125.83363456772994, -88.48648823292613, -10.488637883997042, 105.16186740174022, 245.22773833847995, 387.39269398700264, 504.1783123915639, 569.0059512471654, 563.0048556362103, 480.7421746741733, 333.12526920429576, 146.33743233405318, -43.31339913320716, -197.59566355569038, -285.6081450933483, -291.6358321348002, -219.3855969778547, -91.27474751741917, 57.157887323980354, 186.36043726653267, 263.40081257498366, 270.3575105033273, 208.20335376098896, 95.33566265657444, -38.5640364682599, -161.31968599058658, -247.00557851262025, -282.1276808108239, -267.6580468184029, -216.7087520003223, -148.98364508140875, -84.05040313920593, -35.66377962576294, -8.820673068648107, -0.1619406720911196, -1.1486490221916537, -2.5132782163215612, 1.8347381854752585, 12.822906909384457, 26.653487536266894, 37.19825655810651, 39.169702687651466, 30.681896663641623, 14.161584317969572, -4.692251273142076, -19.378118241110354, -25.385537793592963, -22.090378538060023, -12.920690431483548, -3.6997879340699553, 0.1398991524637127, -3.731434803407986, -13.132537774697573, -21.96556413382939, -22.66609389600371, -9.6018950336798, 17.9094518941393, 54.21241598875105, 88.24075869925336, 106.60675389125923, 97.88980903047405, 56.680494851520955, -14.037327456104672, -103.05108979676486, -193.66183511561866, -268.1611954384479, -312.6581195688419, -320.79303710836643, -294.7874390619286, -243.91761573087877, -181.20900613363057, -119.55223737877532, -68.50711667627586, -32.66601940378505, -11.80498233694259, -2.4155469220692285, 0.1892523113737879, 0.0477383131666457, -0.4252827340954689, -0.4428881145181339, -0.18715663803414279, -0.015335225089727286, -0.0016219573961460344, -0.0014750631163999114, -0.06893471078578564, -0.8173422437977813, -3.3246629761854405, -8.44287144216082, -15.749746133309074, -22.69242992639062, -24.54643486649468, -15.57905414580079, 8.675627428089937, 48.672262375332146, 98.66857277605808, 146.15882570656572, 173.5952370691634, 162.34195259810895, 97.9941128006375, -24.50069601224082, -197.81991089055046, -402.32343514695924, -609.4216944338921, -787.5144369763678, -908.9523947216152, -956.1472544283155, -925.1978426318726, -826.1295637844047, -679.8230742994612, -512.6272339788318, -350.23115503671903, -212.45102310390584, -110.17583230672489, -44.97452277057139, -11.050480277351292, 1.398555108239609, 2.59646083191738, 0.4817525039283569, -0.5240268643112446, 0.6959672974551062, 3.129393296825239, 5.1012046681648755, 5.435306792900309, 3.979932995464041, 1.4863249324042742, -0.9193213949728799, -2.3293191924918317, -2.428216042418764, -1.5220352770966858, -0.2779123534271414, 0.6505271754785874, 0.9174418817856677, 0.5738715466819038, -0.05266634780358251, -0.5841054978312543, -0.7903784144727117, -0.6672013765570033, -0.37812517118874794, -0.11935209624284884, 0.0018846924729431357, 0.005517599734368914, -0.0179327921193382, -0.00781276762665203, 0.004573749215350745, -0.06340603589183597, -0.1980754336011336, -0.10341764411492395, 0.9067479657812844, 3.834914972094978, 9.71302490181844, 19.168870371699008, 31.9954450947824, 46.902280765390586, 61.585733681053064, 73.15303185980483, 78.80894437411025, 76.61129738322896, 66.06188396217107, 48.33948786136144, 26.08942736377582, 2.8222994698842916, -17.904285759576272, -33.288921457651796, -41.86025610619846, -43.632145412739355, -39.864415179223705, -32.56065089681634, -23.878834212313926, -15.628243798873228, -8.969236553855545, -4.350412056446495, -1.6411421956596997, -0.37017001512286424, 0.027606141453511892, 0.029487673977843184, -0.06009325132406419, -0.10736581551489928, -0.09470732755641677, -0.05426415458550228, -0.01900131140566625, -0.002085576941842131, 0.0006927177325672227, -0.0009179081579326978, -0.0010784683519901345, 3.879501474398176e-05, -0.00022083847991602126, -0.0026601951141193825, -0.004910836896152126, -0.0036651968986050948, 0.0019132850120955446, 0.00867748604097214, 0.011319962396136127, 0.006365273446832849, -0.004558213007074215, -0.014746122727780855, -0.0161803310510673, -0.004767352507833435, 0.01630233308578173, 0.03737342535402073, 0.047181992000299766, 0.03915904541895793, 0.015602579510668419, -0.012796759644390553, -0.03205397369604631, -0.03199629251517111, -0.011572954434335724, 0.020531113460554334, 0.0503441555010135, 0.06571065393562493, 0.06217450026031497, 0.04447640628118681, 0.022978823407968568, 0.007211800920398261, 0.0006824572429186222, 6.881470055095669e-07, -0.0014164350922990108, -0.007695502171381137, -0.016863061118031215, -0.022016902937737844, -0.017069600973007866, -0.0035743189472558765, 0.006312949672158828, -0.005799502158606509, -0.05335776709771523, -0.13191106204595718, -0.21194289813705655, -0.24376065681584444, -0.17554826343204796, 0.022505117787208383, 0.3386533836580837, 0.7146446496575021, 1.05991803305596, 1.281049262414777, 1.3152372714943334, 1.1539724685371675, 0.8465718382151185, 0.4816690282666835, 0.15430118746099583, -0.0674734462263316, -0.16249407262288898, -0.1554423112256826, -0.09718245204904659, -0.03745476082664104, -0.0037870200094725567, 0.0036002760001725533, 0.0003744891670039917, 2.2970744294401593e-06, 0.002519056011313239, -0.0005966714095252997, -0.006328022058603271, 0.023602886120958184, 0.17320716745439238, 0.5563394363220846, 1.273364444559209, 2.354396278971679, 3.7138831637548595, 5.141569310006575, 6.342889176310045, 7.022665850381376, 6.98609901114969, 6.208899517485625, 4.852815319976752, 3.2186666849338166, 1.6523835920747072, 0.43891175566440055, -0.27677321294272156, -0.5140013898347555, -0.42119496962634, -0.1999957111082799, -0.022422691830772314, 0.02543703127721878, -0.04587874089139248, -0.16162646513172435, -0.2371909369191097, -0.22574268319727586, -0.13718925677103008, -0.023106713851344853, 0.05881216694054931, 0.07864130659531737, 0.04800884054073321, 0.008194988249169272, 0.001635874596304261, 0.04461707249020068, 0.11733426039454861, 0.17688646595465252, 0.18519317658661366, 0.13485749619155582, 0.05672259804217664, 0.00314157763735848, 0.015342853625549616, 0.0937268779904098, 0.19052434430313273, 0.23239564025200785, 0.16149956705728458, -0.027915481535860785, -0.27896443542654337, -0.4956362891457431, -0.5895903197315642, -0.5257370899825994, -0.34137230527050055, -0.12704173491422638, 0.021772049583434535, 0.0559080010164849, -0.002833522724705109, -0.07959876817866884, -0.09842539161267558, -0.03752853990626528, 0.04934498588278741, 0.06760648481933437, -0.038145904407725334, -0.20138694604997384, -0.20255374361622525, 0.2743091670137847, 1.503860929349554, 3.5550401740865563, 6.181141120940386, 8.833829325461467, 10.8199931826186, 11.551575899573285, 10.784739827501827, 8.73601534923106, 6.010275606366582, 3.3615165769939135, 1.3910343730885038, 0.32886699615201687, 0.008592252929814614, 0.03863052777551687, 0.07112568447118799, 0.009740609905990148, 0.018823175124055194, 0.29853774918924714, 0.7305162267560318, 0.6063264922317572, -1.3388649946164295, -6.479432665883098, -15.537467762409362, -27.815188250026175, -40.837231364631904, -50.75939926922314, -53.654504267979796, -47.11173760448257, -31.55534620754839, -10.680608524043766, 9.346191325242565, 21.792769501360972, 21.76103471312043, 8.192942945023024, -15.349710213075552, -41.559058705187425, -61.720419498022714, -68.73621596067365, -59.7275582027243, -37.19966650968005, -8.261690913521777, 17.861623752917534, 33.124920348097945, 33.56988989567333, 20.577380862429514, 0.020735878276983744, -20.24906807930512, -33.49867900225887, -36.50591123366707, -30.322623843341066, -19.21485360614341, -8.380791362194733, -1.5472812710138075, 0.4629372014102642, -0.39440731051610056, -0.893146387441912, 1.4142979428288989, 6.6994238529981684, 12.71833343493792, 16.118032460311582, 14.48411761731542, 8.012136794147386, -0.18310316408530491, -5.469364427658394, -4.301184892595124, 3.1611904329578655, 11.770192155970921, 12.332393174134973, -5.272043519654863, -47.84444634044534, -115.18496954435349, -198.60978422520867, -282.53964306781677, -348.9118309716521, -383.0810661827657, -378.281110755784, -337.3415528998418, -271.250161460806, -195.23734160807678, -123.97652664113522, -67.67023250880852, -30.256154856944796, -10.00166017494561, -1.7996495119404758, 0.06501425170416074, -0.14529814599031318, -0.35563128774711283, -0.2038857327150222, -0.016050763217662203, 0.01104607102762305, 0.003575871984142532, 0.10201411157962247, 0.150915092510507, -0.16073516799531384, -0.7224253175495533, -0.5731561709782272, 1.548607723880484, 5.224585545301106, 5.462834449680368, -9.458493847263954, -57.11854222893719, -155.2055886327226, -310.7639400709116, -506.87848598754607, -691.6897234317057, -775.8439929708504, -643.0865059993693, -173.33984049299275, 725.1750280064512, 2082.6841044677462, 3843.559697976002, 5859.882804448782, 7907.583543645514, 9723.677320951261, 11056.783617268826, 11718.695159314635, 11623.780951273384, 10805.916380434728, 9408.641586793381, 7651.541777810254, 5782.178747905476, 4026.980862094391, 2552.3477036621225, 1441.1797651769716, 696.2881666037424, 261.73728157315753, 51.871865463236894, -21.223721986567455, -28.506876822175226, -15.665548067739174, -4.494928802433177, -0.1940016832914497, -0.13823883604528558, -0.6702387222945568, -0.3488455745616686, 0.005917149679623565, -1.046691567620212, -3.9486631264187335, -7.629388566850337, -10.204647684794326, -10.225011796407337, -7.611847643571565, -3.735427634945237, -0.6501112520392068, 0.028922191356040225, -2.027241418847519, -5.723565798991242, -9.140322067897692, -10.516088753487685, -9.094638712735152, -5.425528833479405, -1.0134519599947103, 2.457429289378309, 3.9090372510658318, 3.2818671757923603, 1.4002029706347932, -0.562484012020978, -1.6934153313357434, -1.7177046442343362, -0.995353791812741, -0.2016787271871541, 0.09562132753083573, -0.27156339283854275, -1.0434562967184386, -1.7433737512983194, -1.9790017682852377, -1.6549110946423815, -0.9879745649722887, -0.3408411370030133, 0.008091586531477976, 0.013338883014373, -0.1547384246843733, -0.26352137854782276, -0.19344706675390066, -0.0143041587028624, 0.08936681007580378, -0.0054151014700534236, -0.20335665326306065, -0.17390215501907022, 0.4831931534235848, 1.9594478256053276, 4.000737117007919, 5.871062536034102, 6.589584054642742, 5.372771963653203, 2.08951467589073, -2.5084973629948815, -6.94612183337861, -9.533929916366326, -9.031929521083402, -5.190427476907638, 1.0706932930250543, 7.935598753145907, 13.320577404832202, 15.609699073979336, 14.208399218841121, 9.704784731100224, 3.5931054756978167, -2.3091593140504583, -6.505266527248449, -8.27311429315287, -7.7776131422131245, -5.840584428945057, -3.49905076405637, -1.5798290432446345, -0.45656981045685907, -0.047370871806617976, 1.0402121935530427e-06, 0.05768242345662717, 0.32754792635068786, 0.7834947006220788, 1.2424966349373743, 1.5009700309043579, 1.4543946546473607, 1.1425241980229326, 0.7108902477898646, 0.32386685035837504, 0.08351744986730082, -0.00401186801944129, -0.0050776843817464095, -0.0020434872570642432, -0.04171838375770956, -0.11617855468134042, -0.1803084338568819, -0.18901661187234034, -0.1287750280014964, -0.025458097841589762, 0.07299474709476036, 0.12548135447544362, 0.11946036422558755, 0.07337629493341447, 0.02081693681250003, -0.01147415520871792, -0.01720267333652157, -0.008267271988461304, -0.0005297133014183771, 0.00013497243291385878, 0.0007536663507260365, 0.011345628488842581, 0.03013561786659578, 0.03598591800577916, -0.0040784139351100895, -0.11440846420238045, -0.2890394673535371, -0.48332014076904867, -0.6272025997844543, -0.656322622021804, -0.5457085206559676, -0.32745881006369704, -0.08085150823495586, 0.10261610494569161, 0.16202614149654526, 0.09373676889658175, -0.050934343900124086, -0.19453415716323022, -0.27258340560178485, -0.2621518879224344, -0.18598831751678635, -0.09249400539711292, -0.025148432460829748, 7.40418000551737e-05, -0.003176416106392101, -0.00914031843911279, -0.0037480544598773305, 0.002710662237360337, -0.01573060635675426, -0.07486880636653605, -0.1541703381175481, -0.18973050754286566, -0.09597305308090705, 0.19110139186164096, 0.6705296545239319, 1.2574700013928963, 1.802945383905497, 2.147283370141321, 2.184304974971527, 1.90621280882372, 1.4071983588555195, 0.8434052866740108, 0.3681842375687856, 0.073501979605696, -0.03545732745939247, -0.02319011884749478, 0.02354052636237701, 0.04427949474291914, 0.027406871331695445, -0.0013584966434169185, -0.012147283196883402, -0.0022194147231882474, -0.004945400629715268, -0.07102509761658854, -0.23394598726891017, -0.48148229983470753, -0.7516760315454739, -0.957413215701776, -1.0269002781508705, -0.9379049330662006, -0.7271189602472479, -0.47012864122320414, -0.24383282229910014, -0.09359174896601813, -0.021986924504701327, -0.0016325016100886443, -1.815806508015484e-05, 0.0011773551982727781, 0.003328521225286842, 0.002064164743262637, -0.0009278225187145274, 0.001678737645035409, 0.010048241324751593, 0.008349686965664729, -0.016621278324646466, -0.017721998889221845, 0.19184861765066816, 0.9917016160794587, 2.9262204257686193, 6.564354678808256, 12.267227286663799, 19.939957169202287, 28.876394339631123, 37.79182022935927, 45.07687255952773, 49.21736780791308, 49.2466286113897, 45.066367946937554, 37.50807945898849, 28.099469946614324, 18.613412362303446, 10.562211839585657, 4.821331436590074, 1.5028844347277241, 0.09691926206565389, -0.18828856556982734, -0.07544712189273149, 0.0004945567020826692, -0.07495810125478808, -0.21061556264939954, -0.2755498567719717, -0.21893393097359937, -0.09367112590140134, 0.0023789081165613733, 0.009181822761181516, -0.05079822379966834, -0.09409141378653618, -0.04420085602759667, 0.10476862501809935, 0.2759036310726451, 0.3600946333422891, 0.2945818116671045, 0.1142251452760401, -0.0624232852639857, -0.10700847935027018, 0.03133788255187708, 0.28409433176187865, 0.49935233868591505, 0.5383964500463142, 0.3730683833584274, 0.1174956547679617, -0.03524942234774221, 0.059942994830348734, 0.38877714872264035, 0.7617130961581946, 0.9206718160572301, 0.7106566818193121, 0.2103130430798293, -0.27112158926971014, -0.3518355808402469, 0.18336260210338282, 1.1995566561484805, 2.209530046410084, 2.5892808812450725, 1.9224211514020693, 0.29186707613072876, -1.663767953286207, -3.005939654145343, -2.972705082671538, -1.4407396361125475, 0.8955434218451988, 2.7881387328356753, 3.059715032889047, 1.2609634622557537, -1.9919058261674418, -5.20815947223326, -6.687257398178209, -5.350851677738149, -1.3292867063838485, 4.0087150395966535, 8.627948081683353, 10.743275563340505, 9.640689035032393, 5.996925948146766, 1.5340372317339044, -1.8218475393635671, -2.855846014939451, -1.5934417049606293, 0.8349136096487246, 2.889572021168304, 3.464630481397568, 2.414475290257798, 0.5039719440755537, -1.1385380265794394, -1.7093351774016186, -1.1456853515364214, -0.048157052587399427, 0.7959966730929285, 0.9467951797582772, 0.5421801898727647, 0.08846356010318057, -0.00447456182589858, 0.23814800277583664, 0.436040517104004, 0.300286923566135, 0.012573433872985195, -0.013672433775342318, -0.21625916700490197, -3.3723375242208626, -15.416990815054477, -44.38211137629674, -96.90836787479698, -173.13230973077833, -262.2057684789565, -341.41729783796944, -381.14809674778445, -355.58711994339404, -255.96778119196858, -100.53501521014445, 65.42010797780901, 183.15197492388418, 203.59872625039657, 112.40252492570184, -53.68297883775173, -208.30754825334262, -238.71137001250904, -46.123455806022974, 408.98364511754966, 1073.4470389257378, 1794.8928675589086, 2349.62873723293, 2500.859156361137, 2071.5416160592004, 1008.9658099380863, -582.7322274402462, -2459.697740517131, -4294.302178509324, -5756.120040648624, -6593.8358917715395, -6693.308489564879, -6096.229309290331, -4976.857334683095, -3587.1609787567986, -2189.1096593870625, -994.4867465514153, -127.6421242690836, 382.5136229152224, 584.7001504676276, 572.1128871306831, 446.8388076751408, 292.64193502471653, 161.50246279834775, 73.43317751292129, 25.937438382147032, 6.170266341581754, 0.6038495108233785, -0.006854455812969524, 0.07556172594272717, -0.10848513032223941, -0.2885839665445805, -0.24207365819184815, -0.08134884332343645, 0.0034368258779180236, -0.0009466281315655865, 0.054761023898137015, 0.2790979249802563, 0.5879857695928123, 0.758078134456423, 0.6294376635484176, 0.26758388402456995, -0.06411008827330511, -0.10865896559594905, 0.1656500959882164, 0.514857191837129, 0.5986134480614528, 0.27429186191512983, -0.21120161788660421, -0.299190040264712, 0.5428518928564038, 2.4216274340155954, 4.826059057452128, 6.805970731367158, 7.456986415660326, 6.438656248200096, 4.184029203067087, 1.6609804526970118, -0.16729954811511671, -0.8493859203313004, -0.6100940049020276, -0.0876438177649585, 0.15766840624557238, 0.01082026021209553, -0.21929640344141724, -0.18949582756041747, 0.038262955353925425, -0.08043535771227955, -1.0933701895036112, -2.7545562620641717, -3.521543768839857, -0.968319362537828, 6.761065841135456, 19.106431705799462, 32.079723100594336, 39.256010303953374, 35.06890082853504, 19.31730632027509, 0.5385362402618323, -4.433012918251081, 23.654919998882832, 95.83959618438942, 202.97103363499542, 307.71770322690975, 345.79687922538744, 239.1602716008197, -80.73426177383831, -647.2581450614058, -1439.0037944655053, -2373.76210856343, -3320.100213305934, -4124.641899978104, -4647.841404414917, -4797.946838183445, -4553.1568602507705, -3965.59505998733, -3146.387827123471, -2236.863658880983, -1374.7636700989576, -665.1664635113084, -163.51564805144778, 126.28619148001832, 240.64724917707218, 237.49409501325604, 176.33001197133217, 103.49812928876132, 45.83048648003529, 11.96054218938222, -1.6480662388923872, -3.502572161094931, -1.4773647464489565, -0.06976372846663173, -0.30792917403995307, -1.197366860796978, -1.4225389984387982, -0.4206697805119505, 1.4303418608041374, 3.254992376113052, 4.286452314883773, 4.251636803333761, 3.3843935802961234, 2.179556598612263, 1.098013309726549, 0.3847159563864409, 0.04998991294740551, -0.03523423746474245, -0.019737912904003986, 0.0030967174219837584, 0.006546369868975237, 0.0008138346246805454, -0.0011619860429947018, 0.0012867124679998305, 0.0017233969485380277, -0.0019375397928985106, -0.0033289010282743525, 0.006126388795428521, 0.02807981327923214, 0.05416414081763765, 0.07134112791398112, 0.0708839250583558, 0.053893304905238686, 0.029702659566407573, 0.00918529758255631, -0.0016903875708888373, -0.003779044422759518, -0.0018598117651326387, -0.00013563860028194646, 0.00018688526985171007, 1.584258283412841e-05, -2.442078394771155e-05, -0.0007396556617495536, -0.003174429508666472, -0.0066573163723252895, -0.008663245872551302, -0.007165598695990452, -0.0031564125551472927, -0.00012986218367301927, -0.00011276104492222345, -0.0004329826018335403, 0.0024722045096851357, -0.0002577648874547281, -0.046208907555635524, -0.2061262663832601, -0.5616068053511146, -1.1535683653233737, -1.919889943751679, -2.6589476627719315, -3.057147401160572, -2.784273739223971, -1.6307709708945222, 0.3688573077296275, 2.8891935122922634, 5.380047614305687, 7.233652351960845, 7.992238062622748, 7.510985829476665, 6.005773374992188, 3.9638166712665845, 1.9560328143861774, 0.43326455918160317, -0.4072214772124496, -0.6355181643625923, -0.4929550655062034, -0.24633212276762764, -0.06921628333389786, -0.004033178627645364, -0.0036539803191083914, -0.007715184075860698, 0.0007981030259698479, -0.009988711949744896, -0.08219605348433756, -0.22077367869630557, -0.37513548881453196, -0.46463405104870276, -0.4306569312364079, -0.2786340198977304, -0.07921272026759377, 0.07448777032543705, 0.12559498354136947, 0.0872404359977025, 0.025262471602858577, 7.583809970184538e-06, 0.009059161817435952, -0.02519364675962825, -0.20741833010992383, -0.5865885726420663, -1.0928415413139985, -1.5428501498693898, -1.7237429499087336, -1.5148584045640152, -0.9754918288560214, -0.3376927563128832, 0.10550971788927795, 0.16157412004346963, -0.1439729428236532, -0.5731695407049753, -0.8170376315534511, -0.6965304507700704, -0.3044453219620737, 0.00500454823655064, -0.2082792074216616, -1.2118138712700979, -2.8978879308130754, -4.759218875674454, -6.079829709071285, -6.264822991951292, -5.151073120440868, -3.1367077640186265, -1.0479588723170041, 0.2096842655403302, 0.05744342484568749, -1.492676771428535, -3.8515386300217536, -6.122278311095159, -7.485276046548902, -7.518874414961615, -6.321196665231457, -4.402214765569426, -2.4223317327031584, -0.9128848306419743, -0.10259824925668909, 0.09363180536270924, -0.04884344606087486, -0.23801603280302872, -0.2974847934374536, -0.20541801477116398, -0.04599186518992993, 0.07808720254357446, 0.11426220513752246, 0.07644472241519205, 0.015941030265830245, -0.021425919429181185, -0.021403545525981733, 0.0007482941037652862, 0.020670976403013432, 0.024643048861180707, 0.015390897940143325, 0.0041271964062263794, -0.0010701230059464819, -0.00038586021097689966, 0.001342015520020035, 0.0011366665756139115, 0.00011499333117940229, 9.798137911986508e-05, 0.0001841637992568467, -0.0004231448377865458, 0.006082665027804027, 0.041415243930818794, 0.13313445781336108, 0.2921865353119133, 0.48923451301889126, 0.6509324565376947, 0.6898208074169585, 0.5596121022406382, 0.3042456231224936, 0.06209833450341797, 0.006613115489010543, 0.2445931146158149, 0.7300538781632401, 1.2584318048527088, 1.564841529817207, 1.4770634688780333, 1.029573828869081, 0.45640795953502156, 0.04820456948189467, -0.0529282847735355, 0.007018688411569814, -0.17312699232344222, -1.031531928607142, -2.7455392685736983, -5.030434318021011, -7.180820973091809, -8.372613482927315, -8.083568865153616, -6.396937521309945, -3.9902343672180827, -1.7725699395407875, -0.3949269938758326, 0.06427605336710182, 0.027240842410278333, -0.016335708917598803, -0.025991241181451394, -0.6285305056111314, -2.7888999678978474, -7.012339987321758, -12.502603842922552, -16.85154431041924, -16.65664099743174, -8.996986546968255, 6.833561176294367, 28.236359511863284, 49.655781804700524, 64.46178496107638, 67.53267105858905, 57.396069122384006, 36.923596388691855, 12.228038824063686, -9.740875078487518, -23.801713719220572, -28.192667021058664, -24.628264051273344, -16.924174278081637, -9.018395883073723, -3.404056293689182, -0.6296043167361376, 0.1438012935671861, 0.10613766740181717, 0.006181869570849468, 2.6985234227495082e-05, -0.0005510026417995187, 0.03908221542998075, 0.2870322976927294, 0.7489187805528291, 1.0828909401055253, 0.8874436932244743, 0.28732600172856715, -0.008642164025280055, -0.1591326749766818, -4.3437732839897265, -24.208694662492654, -79.62361676294955, -193.47662291513515, -379.22990745662923, -624.3881823324919, -876.7133162185274, -1041.704376431745, -997.8052963669539, -629.56306468185, 129.16202823083856, 1256.5196453495255, 2624.920790011684, 4015.7306831551696, 5167.261002136097, 5844.127321703811, 5906.210608174846, 5353.087094821061, 4326.696012601949, 3069.2791434996047, 1850.5653325422613, 888.3468819420557, 288.36190876835076, 31.982642718024696, 8.18259052187, 71.67256171198792, 102.20557980305982, 42.76400442960579, -94.41758722559749, -250.73689062036087, -358.6189646660917, -375.3246811062774, -299.4814765006276, -166.26196999965413, -27.111378491703316, 74.20356890052172, 117.7927501021111, 110.2183101437226, 74.73642585475534, 36.49467109232533, 11.071246598507638, 1.0118179428745584, -0.08504744314665633, -0.16854367086120478, -3.0268306085804944, -7.162911183784964, -8.807564801996, -6.128134269149741, -1.3760876666626913, 0.49578929577991443, -4.373067422682414, -15.36990262185355, -27.03502696273195, -32.30031299295239, -27.288730577537567, -14.543800555461806, -2.4716261963534993, -1.0055580407622766, -15.78405239497591, -44.116468547530445, -75.14705451292814, -94.40235019349903, -90.54866777882776, -60.97165297207321, -13.35927953677572, 37.49886557632391, 76.07787477205228, 92.51200468140166, 86.0443207822135, 64.14348968213496, 37.8389346126225, 16.40620036527342, 4.07109396864157, -0.14612993722628084, -0.10041751638765714, 0.49500338434609387, 0.00017954116142395493, -1.0824740918515916, -1.4309887356582935, -0.40602494806803335, 1.3516276387965056, 2.5113272205871646, 2.228227855365866, 0.9197026382361394, 0.001406875303971593, 0.7470887518602928, 3.129163270918538, 5.555270949202555, 5.816735352219518, 2.7112030135303975, -2.7405060767817537, -7.414385025783282, -7.684857320113272, -1.6916864674227128, 9.08156654431697, 20.011721908075813, 25.451432086412932, 21.74058363849756, 9.451985434172306, -6.507351945250014, -19.197865145216372, -23.246304918438117, -17.679344250209944, -6.383577024270935, 4.018114486555372, 7.737156426564086, 2.939095467695902, -7.236779611824908, -16.29458265608015, -17.791687003679456, -8.771278763434022, 8.551809475265973, 27.70983311676948, 41.0250378528008, 43.226118188349275, 33.82963762083323, 17.151701576146646, 0.014480160400587519, -11.600678133686422, -15.086391329187999, -11.808020888887576, -5.7396864330611, -1.070577358613118, -0.09980522209429495, -2.4182627833932795, -5.599829795453813, -6.837970624033392, -4.563106344409703, 0.7860773710530855, 7.125804677993875, 11.898124406623827, 13.354137384880929, 11.29210047106719, 6.955241900030521, 2.237599079846749, -1.258382873226697, -2.823288696908427, -2.6940183043258696, -1.6673963861677927, -0.5735451848046326, 0.09819521129754304, 0.2835320141034941, 0.18784036012554087, 0.05268359884148953, -0.0010473933089526107, 0.009487521005334005, 0.011178444277401616, -0.03356101428986998, -0.09550541492304579, -0.11554702993189055, -0.06379813576242849, 0.03219454142760069, 0.10873459055827249, 0.11456528739346798, 0.04708730481990199, -0.049231513987366436, -0.11703354102338463, -0.12487649089896091, -0.08301678579519679, -0.028586987511800128, 0.004563944656219667, 0.007381505792379105, -0.00541528563649686, -0.013623611625098455, -0.009351091424059006, 0.00018989093941132798, 0.004330521067014258, 0.001367950065745521, -0.0007234797209737103, 0.004919283592672145, 0.014160957051272235, 0.015346634501516031, 0.005257902438984985, 0.0010125539516555536, 0.02885095866800655, 0.0882952521115877, 0.11825808133544116, 0.0080885584482437, -0.31886523688076523, -0.7699381668088614, -0.9736088322416072, -0.2964011242914628, 1.9668223175912283, 6.273337923743198, 12.514286322917636, 19.861755398444732, 26.89411111259804, 31.993736194522757, 33.880151951743464, 32.06449966967265, 27.03145906114935, 20.06712923650232, 12.804426398169932, 6.677896577983659, 2.510014621225445, 0.3787735206938373, -0.21977138839212432, -0.02908404592909466, 0.3142811415684541, 0.47286914122587753, 0.4046659079882158, 0.23028200806510427, 0.0807002504557295, 0.010644001122230297, -0.0007055933007766679, 0.002383775001895529, -0.00041154881276177886, 0.002066268535016529, 0.024631208022846997, 0.055140717801514534, 0.052229242661826644, -0.02382809981090875, -0.17162362096650766, -0.3349300146229701, -0.4319642665270101, -0.4086861210625838, -0.2777956983614554, -0.11358258631912556, -0.0032058881714191645, 0.013673959632221636, -0.025154610006805727, -0.028307629443835275, 0.08384416973885973, 0.31387205901581006, 0.5665997401204844, 0.6913422563608369, 0.5658116231069881, 0.17258479494117798, -0.3790154685072666, -0.9014646467161659, -1.2190550134849867, -1.2480804773421466, -1.025412906880231, -0.6753661888746794, -0.3395395374930586, -0.11137574860614931, -0.008545517764386322, 0.009969931525716961, 0.00147007587961209, 0.0018614330303296737, 0.013658492898458255, 0.02015968716357683, 0.009146039403828278, -0.01365719873567062, -0.02998010539260303, -0.026014917767944724, -0.004795689652189588, 0.016382371991581348, 0.020376770747808422, 0.004115582006818421, -0.019089172544743422, -0.030164108146401435, -0.019014002940235763, 0.008165991764067265, 0.03421103697107657, 0.044114340405588315, 0.03537588814948791, 0.017845080986389997, 0.004231354933621481, -7.25593479083462e-06, 0.0011986756817072514, 0.001289638369046957, -0.0009114152831042416, -0.0009588963349611532, 0.002538126143804365, -0.0008175208933000967, -0.030633086684476923, -0.09930606566892354, -0.19332064714690564, -0.27076886772972175, -0.2845332365170991, -0.21897660740848857, -0.11013772360490662, -0.02386288517327138, 0.0017842084963615, 0.0016996856287868811, 0.05082037152747922, 0.12279044876433329, -0.10594304633727031, -1.3738241737414636, -4.730752629211832, -11.156096362150885, -20.995768468557095, -33.46256088507806, -46.4903206872999, -57.12670305967522, -62.41712182920726, -60.47680597474495, -51.3019953327338, -36.92942183755945, -20.812706841174155, -6.634918136515117, 2.9489384372741654, 7.121016295034934, 6.91448100799139, 4.4252742880231875, 1.7394669936365563, 0.11600074786938329, -0.25322645838166985, 0.07804725956305589, 0.3989497510357868, 0.32413997012082196, -0.06655211249392795, -0.42466179778453567, -0.4617688140750891, -0.16538108793235887, 0.2244618308157911, 0.4221421022387949, 0.31157936472829184, 0.009667933153608496, -0.25073814259430666, -0.3066175478643246, -0.17250611694111817, 0.0009629933423928765, 0.06748702672133226, 0.002139108099293939, -0.09818504527493785, -0.12167301664290824, -0.055321960221917106, -0.00011032590744239894, -0.06988192113953537, -0.2648379028398288, -0.4445692412235275, -0.44439467115772785, -0.24068403566627095, 0.001389292461006564, 0.0780770025451924, -0.026098356742881596, -0.08076994753458938, 0.13600455941859418, 0.4430692232725466, 0.19021532010498074, -1.04154741019802, -2.0568184147806527, 1.1195349882371843, 14.717517051491683, 43.830555958846, 86.41192084678596, 127.04163763838184, 134.53328064430906, 67.38283871870951, -111.62438950223952, -415.9466905829082, -818.9555045950126, -1249.7729528618597, -1607.0361307613027, -1789.1801910058293, -1731.7389933500413, -1436.9714557573097, -981.904056267482, -498.244492987716, -129.0495600003361, 22.308103773936583, -69.49837545887078, -342.56672856922154, -672.6876061845732, -923.1140957432892, -999.1664390450667, -880.5776121079098, -620.3571161459602, -314.43518259903783, -57.953586874050785, 91.50461834693915, 128.8093957614683, 91.0633747261855, 31.011009576294114, -10.67792215687912, -20.66251375344919, -10.386030142722195, -0.45618870429049074, -3.141218531584187, -13.859190076667643, -16.067039034528875, 4.730624658542014, 47.807143578605924, 93.93174372638133, 114.48576719574439, 87.75615156156461, 12.801278488437205, -87.40185923714722, -175.7545196543326, -218.741994144003, -202.64131963249451, -139.6910519941953, -61.1879041847882, -1.4915412556587664, 18.419261153853498, -0.6413746939334449, -39.43491539418737, -72.71782064659631, -83.06489205034485, -68.28939165028842, -39.49263534212484, -12.352061477035813, 2.4009978290275047, 3.8063105766598415, -1.1821846054713103, -4.000364691318061, -0.6097737990540796, 6.4663487551127625, 11.08013281105118, 8.872400787688736, 1.115365327024539, -5.877058544727896, -5.534290156677718, 3.2055390891491977, 13.305683375450718, 12.459324935131528, -9.933146434281742, -55.589991436501, -114.27687145206481, -166.9615749780624, -193.89197177154034, -183.57219230461945, -138.09422314564864, -72.20185345205769, -6.711706234977282, 40.292899301024725, 60.19983254889841, 55.62240748800909, 37.02567759436918, 16.54692750624973, 2.3868673346962654, -3.301074046604761, -3.022529708641, -0.8148440136082852, 0.48046935428683435, 0.24029225580674946, -0.5993685152106402, -0.9073589769817951, -0.33008510781404676, 0.6411801540936115, 1.2711236323923474, 1.2149912005323404, 0.6947090351832518, 0.18974220637326056, 0.0009063733278818174, 0.07235701581963376, 0.16255114477043717, 0.12877393716160884, 0.030303490048998398, -0.01285009003736399, 0.004240835577116528, -0.0021831067425988828, -0.022192137447443715, -0.0011551704823034483, -0.5127676580120031, -3.915901740755113, -15.025587090739444, -39.84155948918167, -81.38788279236414, -133.37548439743952, -174.61459827806067, -168.50709036107745, -69.86002259232049, 161.15287116504837, 541.7337738473559, 1052.517839229032, 1633.5451947331942, 2193.7313209539484, 2632.372448208943, 2866.2269868623184, 2852.9963273000585, 2602.9145093347106, 2174.4121550485947, 1655.711815850822, 1139.272741551403, 698.150288266563, 371.92983484472876, 165.05811442767254, 55.54361853809533, 10.178423115193123, -1.953426674185808, -2.012381772794474, -0.3946379921455865, 0.0820568594936776, -0.08589230624451585, -0.11576563449681712, 0.01524588503889286, -0.08024071914981883, -0.5366376955078951, -1.0217048943151468, -1.0616123860922384, -0.5011185289514918, 0.3413680386073854, 0.9385959469866523, 0.9780937921414897, 0.5762996697159121, 0.13296508395078735, -0.020812539952901644, 0.12366337023615752, 0.29790338811454636, 0.24189945247757405, -0.030973091376164063, -0.23664342129075855, -0.11445967340804762, 0.22454593531465225, 0.22312238018244399, -0.7677075700448632, -2.8847562564816993, -5.33736647749639, -6.572382753947937, -5.054700187812989, -0.2866656573863727, 6.535651474320063, 12.70103802573996, 15.038589570251679, 11.398828867221097, 1.8320268615618511, -11.161925284578821, -23.498455080340527, -31.125274937641926, -31.655067214367488, -25.27081639886543, -14.518567616441194, -3.135635173965558, 5.504124857652923, 9.63923415468142, 9.485680284850195, 6.660719536551641, 3.1686886637586245, 0.5041811674107345, -0.7643164899897592, -0.8811474279879618, -0.4713663245318821, -0.09160971581461369, 0.015546591787189222, -0.0881320404609941, -0.20686874441071348, -0.19296772246118685, -0.03363070137290746, 0.17635574206537463, 0.32265020851733744, 0.34723343466776296, 0.2684227033095529, 0.1494186604613868, 0.05057988881225609, -0.0009364266609546401, -0.012117490822038163, -0.005507612918568608, 0.0005175915299897536, 0.00018048621234412679, -0.0031394900942258003, -0.004772084509760092, -0.0035577982259880456, -0.0013704379790736763, -0.00011870756506697811, 3.00637176208826e-05, -3.430760890650954e-05, 5.068985936009914e-05, -0.0003291689438301119, -0.001789729984185126, -0.003914040320154467, -0.005398824134378868, -0.0052128913919595185, -0.0035323942677346902, -0.0015238340814307688, -0.00026838337447283433, 5.5903844879009e-05, -2.610946097437961e-06, 2.9846811159317563e-05, 0.00011317685503648514, 5.3227865444358366e-05, 1.1868069659931163e-05, 0.0002308903484314473, 0.00011903951532105343, -0.0018178951237329036, -0.0060833806103706605, -0.0096099128173574, -0.006054482788298069, 0.008343226909356101, 0.025585355766753085, 0.021458706546845206, -0.03532392664916684, -0.15935904753621377, -0.32281976197810236, -0.450089627755255, -0.44977583312641983, -0.27777323701405715, 0.005264491901322598, 0.2338984986521551, 0.2279748510936463, -0.048792725142815595, -0.3456602119963295, -0.10070845860112705, 1.4001387816922226, 4.707608755354448, 9.862578699416163, 16.19354985726889, 22.39502057660803, 26.904491555289233, 28.448934188980747, 26.532709493377695, 21.64583488379646, 15.089611929801293, 8.491649418340781, 3.2258504077038554, -0.015763137239700915, -1.3155182018456804, -1.2876101606270247, -0.6930394021516413, -0.1141625888000901, 0.18726582576646442, 0.22363799510459154, 0.133719683745652, 0.04331882898335618, 0.002043544689498304, -0.0027987240446488634, 0.00030167394547535504, -0.0009144020938007372, -0.0022082834730020135, 0.00046530067370713607, 0.0016952905583249038, -0.006000605531178145, -0.020076386805308533, -0.027800882053693673, -0.019702925679986927, -0.0014834839509336446, 0.010640516020476547, 0.007997735021513519, -6.508585792597552e-05, -0.00043451402101866087, -0.004526446043814359, -0.05231933952032375, -0.16003287696747023, -0.23133814996543978, -0.018901229415738036, 0.7572996559529742, 2.1056070008626775, 3.403393328277422, 3.2455184737512384, -0.25315053487310135, -8.657776678552928, -22.18970306048797, -39.00126537607567, -55.268848719938255, -66.30136044125129, -68.33860675041778, -60.26068029965078, -44.327753626934594, -25.444416093934155, -9.157807053169666, 0.7045376926632694, 3.5753646585831063, 2.042461038230636, 0.12862323661315292, 0.8873527022977915, 4.732814642996242, 9.470781522308332, 11.924745440808273, 10.113636538185013, 4.6344538246567195, -1.601111053211095, -5.127957745494375, -4.124061310218329, 0.31031695469089743, 4.62794165628686, 4.870239433488991, -0.8809889015418865, -11.083866504187583, -21.26137306971199, -26.29684731487655, -23.154438823920774, -12.500267205316407, 1.6015782190307064, 13.685638059452627, 19.45645337543957, 17.59928494362841, 10.006825961571248, 0.49521034240202777, -7.159681404435998, -10.808379374718326, -10.439816452059286, -7.593780259972841, -4.2169999822931405, -1.6744287795539983, -0.37169174107019803, 0.009371628774936205, 0.00043410670418620833, -0.04402087375805753, -0.032634398732382545, -0.007498122798470135, -0.00010181027616421315, -9.835523304537956e-05, -0.013911522344958403, -0.10415192058237141, -0.3394859190678053, -0.6941356979915659, -1.0060470807444437, -1.0636107499240324, -0.7733999288572944, -0.2705819241692242, 0.1412276782250691, 0.20084357501247654, -0.11188847454939056, -0.5587486079619918, -0.8231058609575397, -0.7438475746458233, -0.4163233342795844, -0.08594731289042508, 0.06366890143267237, 0.03904875409819752, -0.02347261791227264, -0.026878231045210775, -0.0013364277812022215, -0.013376747612181238, -0.030698258814214213, 0.00485898515710754, -0.11563338408534364, -0.8326194631293007, -1.4825667455104483, 2.95980348092164, 26.32716019899299, 94.3357056558343, 242.6615189813752, 507.314293954196, 907.9152371860348, 1429.0916196815822, 2008.7450195371553, 2541.8894167005324, 2903.8775616401513, 2988.3810956302677, 2747.092779572414, 2214.3036113250178, 1503.8402786142246, 775.0972176592875, 176.71839410880406, -200.7331494542083, -345.8320557807325, -315.35381877694147, -199.4128230612531, -80.69835012433646, -6.358555170819253, 17.504777819933565, 11.366200224231106, 0.06849336472324777, -3.2580763848137417, 0.21008010841400326, 3.266621897721066, 2.3945064839534624, 0.2904800839485043, 0.21624566500305423, 0.009476556569898988, -3.6501330278197117, 3.0072394779059253, 74.08375699252417, 313.41822558376475, 852.5637820190323, 1794.306827632841, 3140.3844188353623, 4738.811333525514, 6286.532873154879, 7403.014741681181, 7757.012627741554, 7198.041329584585, 5833.037998992747, 4007.30002834797, 2186.543437554134, 780.5510688236652, -0.1755388284869628, -199.0244806918067, -61.67750820993214, 93.57110070337652, 22.532143678727703, -346.05605921526035, -898.8573324151206, -1410.765584557275, -1661.6991494199212, -1540.2899437760857, -1088.4697358176588, -472.47065928328215, 98.73214149001666, 464.50249297346033, 570.9041936164766, 470.40740435304133, 274.26033770116476, 91.12675351518259, -16.911287847684253, -45.102451078849356, -27.137825340040347, -3.689791955502404, 2.508049734531363, -6.081012332154026, -11.424360330568472, 3.218623026504172, 40.676384804731704, 88.15963575327072, 125.59245302985006, 137.5005415478415, 120.99798000115997, 85.5578025608075, 46.395408685998085, 16.347017777442865, 0.8305210148054083, -2.267486790641293, 0.9412660382078504, 4.634488370434254, 5.863696088274926, 4.666632664785013, 2.5636196628033114, 0.9153038320020679, 0.15785937120224988, 0.0006906454152046192, 0.014489955577656357, 0.00731173189077907, 0.0022247514816333747, 0.03574398955956777, 0.06551409508215351, 0.04613967769679402, 0.0076499696238118645, -0.001404242041282732, 0.0003979953289178763, 0.11026580662817143, 1.1678360413034798, 5.566766517328098, 17.55552774796008, 42.303346216972095, 83.58126056047149, 140.85360208260863, 207.3140545236611, 270.4740885255027, 316.0434860027452, 332.7341096087774, 316.2560096120912, 270.8373748324711, 207.57247575121428, 140.41647035073146, 81.62356250453202, 38.483600966960175, 12.410865250275446, 0.2668737293271294, -3.1257390638776803, -2.5911312216984346, -1.2459540724954525, -0.3678911230798089, -0.05149247057948203, -0.00022915148164022854, -0.0002658193614408541, 7.296905795110924e-05, 0.003117226047531152, 0.03591894696120803, 0.11484074013627155, 0.18773525174382918, 0.16015347496760746, 0.00663460109261924, -0.14164785239125127, -0.04435384573020053, 0.4670334705261223, 1.308049422432345, 2.1238975291884064, 2.4882578367130463, 2.194439666442272, 1.4169275067357503, 0.5948615393993266, 0.10432937853989115, -0.012078216016245712, 0.0004961638195243263, 0.0266215761178419, 0.6399936430857015, 3.398471058692897, 10.539625389404685, 24.051443931022504, 44.478476115650146, 70.05926111622344, 96.71957288191, 119.07740412570305, 132.1286197652961, 132.93053402570226, 121.62933358957146, 101.41678792607215, 77.04732386481285, 53.18218685393911, 33.16468822285811, 18.514155546161, 9.124628195167933, 3.888245299123352, 1.3873854532569299, 0.39347673133682703, 0.08079036660088748, 0.009834260876703147, 0.0003758359199733201, 2.630544058129759e-06, -7.993165648499213e-06, -4.0426823322515793e-07, -3.856101272018106e-07, 6.281971823463949e-06, -0.00017870826689833383, -0.0010936056247836346, -0.0028153063753843218, -0.004362694998177314, -0.0044609491503736646, -0.0029296007172141506, -0.0009640928846623155, 0.00011565021882633999, 0.0001530960602402336, -5.750711907900437e-05, -3.1562749282629845e-05, -1.041861850105271e-05, -3.227734813225164e-05, -0.00014212987992681883, -0.004543637595022922, -0.027597565059262877, -0.0930888358054259, -0.2176891472422581, -0.3796883796553264, -0.4906455133413529, -0.3980154057218402, 0.06158709991794292, 0.9677193137986033, 2.2242980463333315, 3.531853175315447, 4.465406299255388, 4.6456584830145635, 3.930067490473906, 2.5206742392132684, 0.9134831404420445, -0.3068172815651012, -0.7356679012103006, -0.32997477713895634, 0.6011632086754163, 1.5731553437793406, 2.165230520056676, 2.1957605100032405, 1.7554510147968334, 1.105509293977776, 0.5175880254750137, 0.14902553120173723, 0.008885510756392054, 0.008348778004737321, 0.04371595633771287, 0.05563873993534349, 0.03877649904232182, 0.014804626620880047, 0.0010714282536494794, -0.0013776324761924099, -6.258936526118694e-05, 0.0002607454989637923, -1.6671402613842829e-06, 6.835303775459395e-05, -3.2065661223887356e-05, 0.0013033307632484656, 0.006108447475345782, -0.0031891973254791106, -0.09790440820201904, -0.42101961728612547, -1.1495272293315086, -2.388964467041719, -4.0431824255483555, -5.751532300735899, -6.983809628824004, -7.256677940740455, -6.373219916305975, -4.5527505052389, -2.3610966381148035, -0.46345195738972084, 0.6722621860976968, 0.9603779076920047, 0.6737122418544378, 0.23804344193190866, -0.021558665520893423, -0.028066164095449188, 0.08269455902583778, 0.13082191749437816, 0.05886256235841981, -0.028176820198205395, 0.02817503032476315, 0.27985453922828624, 0.6037337953842121, 0.7878250695266846, 0.7025611803256181, 0.4109614734797994, 0.11686611434751724, -0.01264014302647366, 0.006722175572225121, 0.0197066879213693, -0.018042226317344517, 0.2460062670145195, 1.618609760532858, 5.026082981606195, 10.88469110266287, 18.53579194859397, 26.1827265284251, 31.477996510910646, 32.534045544600346, 28.84499138574753, 21.597397677603766, 13.162132172677744, 6.0129178144394695, 1.6426545596749564, 0.04747354579379589, 0.01777494538882198, 0.012801694065698813, -0.9212777376600378, -2.713632228818992, -4.507387414509236, -5.345655545295814, -4.824749481636784, -3.3013951627519003, -1.5773336930813884, -0.36359875352447957, 0.09719473276501465, 0.039643206179561075, -0.11876354164227809, -0.11856436901246054, -0.0011822528331210769, 0.011943004848093283, -0.23152722952701854, -0.6514686636737164, -0.9833241580051555, -0.9871446876272799, -0.6415930339280779, -0.1647987610367256, 0.1534580440913493, 0.17169923901580839, -0.012990871181473858, -0.17267059711033583, -0.1478969442152083, 0.032309205819628095, 0.20236389281184328, 0.22539286064689104, 0.11724482585052728, 0.013384867766337377, 0.00454710315483045, -0.007219776415997489, -0.28139203660802825, -1.0277893146119181, -2.1673136189534534, -3.2767053692817703, -3.81120530017604, -3.477391112770905, -2.4446940691465984, -1.234525094255645, -0.3662581686509263, -0.025401359678283154, -0.006667741306732652, 0.034855594348150214, 0.24646337472470511, 0.45720464794413945, 0.3994948540526385, 0.08898822674587765, -0.008586198337208603, 0.729079694357757, 2.4669403641298184, 4.47861872496074, 5.392559727613571, 4.154766642367148, 1.0777337209395619, -1.9248975062016611, -2.3651371393785183, 1.0161845973803347, 6.913555103602588, 11.766273182326378, 11.880575251004526, 6.169437100892307, -2.418878713371657, -8.129867368301204, -5.917074448920255, 4.906536321337971, 19.524663790585368, 30.211945085288917, 31.28935087576731, 23.028677231313218, 11.271879262360983, 2.796702934794758, 0.05958806430604861, 0.12135880405624265, 0.03382221095786126, 5.85631045252527, 38.16735378334928, 127.0120008275842, 294.8890325199121, 535.0701395958134, 798.8377243334465, 1003.9495629928314, 1066.4749099230803, 943.5096749899303, 664.088373056794, 326.4540680919014, 53.504194023466084, -69.56836467041693, -41.8037562264602, 51.55170657091155, 88.23587960140992, -13.47552940095278, -231.50332780959982, -431.13937013543665, -424.6168251185523, -75.25957622930001, 606.7991344581658, 1433.3091835101802, 2098.8376865898445, 2314.5211764751743, 1953.5545310985003, 1131.6144493007992, 167.3400824423081, -553.4777758777127, -745.6057026653634, -345.52928329999185, 469.0922555067366, 1366.618493779519, 2009.7909571039434, 2194.009441278417, 1914.319400906324, 1338.484046837094, 709.5786190465328, 231.85191115916385, -5.3685308100992675, -36.800692541492296, 28.71575690662933, 81.51213700729518, 65.98928648408675, -7.625562797438325, -90.2648751641734, -135.06188945015313, -125.86977775447694, -80.03201826521443, -30.145905184262602, -0.9285145779947053, 3.310067726458897, -4.952349076511632, -10.21726847530135, -6.299724691455989, 1.300719698808703, 3.0666948155647313, -4.209827980702914, -13.152146759263392, -10.767567641373121, 11.437815047172116, 49.64599341381324, 87.8343749913525, 105.9872219837092, 91.34630587710791, 45.868312213764916, -14.410991839478715, -67.45448323261255, -95.88678362246598, -94.34621341946152, -70.0572175831283, -37.27270912322148, -9.45976048385882, 6.328864517920728, 10.521373752478741, 8.022829110645429, 3.9879721591395363, 1.2481225996138547, 0.17599821001566918, -0.009802096063711548, 0.0015620378717298513, 0.0007330235333466753, 0.0003302085546517929, 0.0004501189376822464, 0.1207955938668989, 0.816936055851252, 2.654433177217225, 5.529613839297, 7.93486715448159, 7.176194874333212, 0.9163394475143206, -10.77424403662493, -24.33080283263099, -33.721833873692475, -33.462265122710456, -22.02795711156689, -3.4991302726149547, 13.929121764344602, 22.096220696599566, 17.456988553448394, 3.3446968279689915, -11.667458486309568, -18.632340537085984, -13.629647098698305, -0.5012372156135243, 10.875606694483595, 9.9528108686597, -8.672793249184995, -42.1764289674729, -80.65129542776062, -111.65548201228667, -125.65685098298707, -119.68593703324744, -97.71373227358434, -68.05649051870806, -39.47186544266313, -17.923665986686274, -5.279515803633003, -0.02048300039190013, 0.9177545704290476, 0.3443682679092381, -0.14567109251532967, -0.16308880968789483, 0.04751769153776605, 0.19040171243349707, 0.1794028552405792, 0.09299237489017978, 0.025038301703741432, 0.0018278059189301115, -1.811138858678332e-06, -0.0003311361919013333, 0.004533006881492063, 0.020644986562042954, 0.033480544362613655, 0.016654516483749396, -0.03637669214995742, -0.09512742018091017, -0.11310898554161539, -0.07023371634771064, 0.004792259947164408, 0.05656661134023049, 0.0518945574986997, 0.010310377243129606, -0.015138458061315745, 0.006661940448161478, 0.043413896769885024, 0.016003335550895656, -0.13088430701205767, -0.36017784514587275, -0.54167621060431, -0.537358879355938, -0.31838648149112886, -0.02035646712614622, 0.12342903664269983, -0.059973202221059556, -0.5499282263665148, -1.1249861145943236, -1.48931780434704, -1.4498531616579806, -1.0281165666394283, -0.4374104689188236, 0.05285107077011613, 0.2722869218386518, 0.22589184579841545, 0.053800964362296186, -0.08325057963105502, -0.10701887751869801, -0.04741775615731303, 0.011944046071630693, 0.013686185074391694, -0.03294431229262252, -0.075665823302597, -0.07430623905605027, -0.03462916040524603, 0.00458649159802458, 0.012221431459002384, -0.007511950242880264, -0.02425578681761522, -0.014767379034660336, 0.014149363982445087, 0.03495771964995631, 0.029495306161767106, 0.007265422345756396, -0.0077311515930060136, -0.005864854825866858, -0.00023477513060082063, -0.0010134292377822008, 0.006083931032822546, 0.013113494674282064, -0.14580120075482772, -0.9424669778049738, -3.15926027968311, -7.618501717695199, -14.65729425980308, -23.57921891042695, -32.44234292694382, -38.46504038778536, -39.03594253184939, -32.93908222154096, -21.17551153346255, -6.858945407048226, 5.904729807590565, 13.71804831157338, 15.320143802867332, 11.90550019215036, 6.284901106307386, 1.4045876240593327, -0.982353978139054, -0.8515978652989427, 0.5080114054868425, 1.4994168403359793, 1.182920795792556, -0.31633252734414985, -2.0915182552243294, -3.1480158726924006, -3.030743545416981, -2.01735148128546, -0.8272655758335486, -0.09891193240590725, -0.005214670592388102, -0.2517300903225738, -0.37687018095930946, -0.09918166450192532, 0.5210992471665132, 1.1739415676488187, 1.5363568034740458, 1.4740856481954785, 1.0871967530163453, 0.6043486754038158, 0.2267705528155314, 0.0318718233289669, -0.019973781553596835, -0.011901055080990396, -0.0012564566652330793, -0.00010053578062099578, 0.0012000015627413724, 0.005942039038219154, 0.0070674396185794065, 0.001991842384655345, 0.0005969805570500453, 0.011307188480377203, 0.018344151465446056, -0.020822065949719616, -0.14312295741856063, -0.33197668323432084, -0.4963087034574586, -0.5069831118342799, -0.27825306731373306, 0.1594940549000025, 0.6539921177323477, 1.0101590936021339, 1.1004113370347195, 0.9292385559875547, 0.6147405929591946, 0.30707185292948985, 0.1038509896479021, 0.016594164254163046, -0.0013717419294395974, -0.000278973212934782, 5.993757950877166e-05, 0.0024886339353518546, 0.0020410544520998394, -0.02908323203002733, -0.12069560653160119, -0.2656379619246491, -0.40366469288741036, -0.45409657833179123, -0.3774009378070638, -0.21315362804457827, -0.05606695146654661, 0.01710465510541417, 0.010346061021242109, 0.0017056892288719585, 0.061332571521386346, 0.1559230267864716, 0.1269725398815285, -0.21472896055766155, -0.9260825187981695, -1.816966395401512, -2.489160369594052, -2.537591614623788, -1.801857892399142, -0.4957436241661267, 0.8845320073802433, 1.8147119931511988, 2.0050011256665554, 1.5181851994123499, 0.6894674891392771, -0.08205560173560335, -0.53403158441678, -0.6244388454776347, -0.4791517223526342, -0.2694061671986598, -0.11006323187376245, -0.030120937393093957, -0.004481711334263979, -0.000188186039931524, -1.6285248495427303e-07, -3.853324976261047e-07, 3.77977155598503e-05, 1.1139341411526555e-05, -0.0007145649109051599, -0.0014204106308808868, -0.00022728408637009916, 0.00042208334738879613, 0.0007720718788116723, 0.05031403018810734, 0.31058700018893154, 1.0048621304750984, 2.0654309169601586, 2.4258522953681383, -0.7111445435324619, -11.865726683968536, -35.73293341047481, -74.13535616462669, -122.66016320717297, -169.19511156260808, -196.51581278418635, -189.33327680895306, -143.4005381139421, -71.89039655650417, -4.097835662683858, 25.48637952755173, -5.5880160429941945, -92.40354708463185, -198.77423267435992, -270.107896710555, -259.7737569070107, -156.85266684560983, 0.4941330022641424, 137.08244766739534, 176.6126166671602, 82.4306425947878, -119.51621388041883, -349.6023425068089, -512.378911363177, -543.9175708483946, -442.9638081312658, -268.45414644272415, -104.61586992095864, -13.567658520998275, -3.0640886614599188, -28.629347623588654, -28.96713647489207, 27.159813243367505, 112.74830210732293, 153.04387277579048, 70.85104593182544, -159.97028546341406, -485.6465743268985, -787.8263211327778, -937.5707697773778, -859.9403778432863, -574.1657893997232, -187.0723493928, 157.3506516789796, 345.7199182097662, 344.9644675243624, 209.15750879879056, 42.490919754489546, -59.08970862000773, -55.01351804697154, 28.57294753578889, 126.0323858532762, 176.19521600386867, 155.85526736810917, 86.30165670568753, 14.01301447494319, -19.32875585865367, 0.8900975603198075, 58.54023473564179, 120.32727225693925, 156.0091643516114, 153.0135512560039, 118.76074068112678, 72.20499401704969, 31.735433220013206, 6.873973134145314, -2.8762069436206588, -3.635909089990005, -1.637129819377708, -0.1998364884388754, 0.1586073219095503, 0.07132276051772021, 0.0047548174387310365, -2.246454515919025e-05, -0.0015425166571460239, 0.023809114001871124, 0.06278386719209425, 0.026016104342366543, 0.020556435740416282, 0.5448501697582602, 1.9734462935677684, 3.4120041892600015, 2.20749624850334, -4.260365843998678, -14.30166093574533, -17.489079190374536, 5.821024020679157, 77.84760236711516, 210.37455150066748, 391.09568775743276, 577.7869307802515, 706.7491175562435, 715.2643211069764, 569.6299146126553, 285.4169597637283, -71.54806987594203, -406.44219763297025, -630.7478364189541, -696.2182557491683, -610.9007245649709, -429.2440143468782, -224.57895411934587, -58.69346575392811, 37.74443043842816, 67.52846152432663, 54.921491253027334, 28.36603790879025, 7.297339324610081, -2.0427403966994855, -2.850977187677123, -0.9604663418437202, 0.07640435801334244, -0.06173926348358792, -0.298218800430841, -0.12886884974017176, 0.022921402763629663, -0.21784826447981626, -0.35705426485546604, 0.6094471162892341, 2.981254787717664, 5.53183100296505, 6.05047602282319, 3.0293323568861483, -2.7956276595217115, -8.389135968710018, -10.13124403009678, -6.223109591480277, 1.9148661558908968, 10.321210506937703, 14.868476296703264, 13.743987321707088, 8.329456300013872, 1.9910755533523183, -2.2010022434807652, -3.1881827355228674, -2.0256315978050345, -0.5819112644321258, -0.006997303915557302, -0.13300792876080378, -0.09558869967139529, 0.5443111125815139, 1.2465820654581057, 1.017950313961936, -0.4545459211123994, -2.128115636596539, -2.1388311061972782, 0.7205653471392887, 5.7719530687782, 10.54614085140036, 12.256494730835138, 9.649979876216834, 3.9068991411785645, -2.0790020708535852, -5.547538545645647, -5.546968543877737, -3.278005132955434, -0.9347195300696786, 0.021694643003991133, -0.18559154301455436, -0.199576255682504, 0.8861987017536558, 2.2540672420368675, 1.5990018376916946, -3.1092425819069542, -11.640588915462033, -20.90802226928723, -26.445913659070445, -25.14524886897399, -17.434507223981946, -7.349108868019433, -0.2948009702084153, 0.13911592137313408, -5.71258882693496, -13.913103283121485, -19.440442860328883, -19.23976242589318, -13.849152251420076, -6.6522517447911405, -1.420209379829681, 0.06531536913176328, -1.296133535579352, -3.1131086573570386, -3.473659274813615, -2.19887292223828, -0.5689995548070103, 0.07297659127523365, -0.3974781681404864, -0.8167907466422165, 0.019854126943324436, 1.7895844672568448, 2.1222010767286004, -2.171832221996427, -12.722965357890628, -27.689207977490785, -41.92051270833842, -49.358259425490445, -46.27983588239597, -33.50070343256067, -16.224047853968337, -1.5940255895729358, 4.704191514448719, 0.9892996025313908, -9.96927912762236, -22.64894019535729, -31.553049470605007, -33.58353338253404, -28.927337780227873, -20.290951919230857, -11.17232891829728, -4.209630594732496, -0.3658932480856548, 0.8916819343161686, 0.7608060821244457, 0.2967496483063095, 0.026954088978581293, 0.004388729270370324, 0.07408926761951835, 0.10582884039449532, 0.07601522154785947, 0.02736513042656727, -0.0007018572533345975, -0.003474547643103609, 0.00217612916765872, 0.0033235417481872176, 0.0006733315122379991, 0.00037021167320466916, 0.0035966633063919933, 0.005924984640886486, 0.003955189493594851, -0.0004441330429048911, -0.0028763667779670866, -0.0018419646025279615, -0.00010443900012249976, -0.000772093859178712, -0.003224976579038567, -0.003993117788765769, -0.0016057200979789127, 0.0006320235261059661, -0.002002927722318299, -0.00935660995689555, -0.01479871417819145, -0.011680091591423046, -0.0016413765603349936, 0.0055453216297814585, 0.0021710784311743617, -0.007692011678293997, -0.011375387462928816, -0.0038121770983923337, -0.0008640938419876178, -0.03112926561890423, -0.10502156469305385, -0.18527915181528334, -0.19244549958887974, -0.05718626025126232, 0.21071278913584565, 0.49542009754293626, 0.6320504323985231, 0.5268374694483466, 0.2525671844784641, 0.01848314011745815, -0.004014108803422522, 0.10095005286733473, -0.09723042859673339, -1.2167264333622538, -3.6854568983394964, -7.3441701587543085, -11.294619715944382, -14.153133225176814, -14.64140593188099, -12.227301315834943, -7.461816062208976, -1.8014318061631907, 3.015417606679704, 5.721786305100479, 6.0164727672495655, 4.5230413772997995, 2.3346850706375997, 0.4501057758027809, -0.6069357966822353, -0.8455501368962265, -0.6029765390605246, -0.25805607766560484, -0.03539369127547871, 0.03003169508794937, 0.011083903725052467, -0.014736347426975665, -0.017797637346738556, -0.007893656436674059, -0.0009909304776516857, 1.007168346501301e-05, 0.0005746895976021977, 0.0025061538171416322, 0.002190121340689455, -0.001649841473154197, -0.003972790141519394, -1.9347768475863503e-05, 0.005890926674049387, 0.0026518232447666867, -0.01302569861596576, -0.024903217377115507, -0.005406888525034626, 0.057430489032776866, 0.1377383400936934, 0.18058866790273584, 0.1433221050559614, 0.037623748265713845, -0.06950408763062847, -0.10757620685352684, -0.06480756740573343, -0.0013973534927149917, 0.007981097767899164, -0.04127960550337475, -0.0526544992410347, 0.10204244885841612, 0.45260246876464133, 0.8504355554600304, 1.0335957403728142, 0.8226763031547809, 0.30722989766896763, -0.15056222999708507, -0.15330335073315676, 0.39473292273602567, 1.125769150927151, 1.406970367109498, 0.807383348119955, -0.4809187626678923, -1.6022025841111804, -1.4812654356229096, 0.4835138236239586, 3.9254622456409245, 7.575471336234782, 9.90220879485981, 9.953828909432538, 7.87344939831692, 4.760367316536071, 1.9797318221680897, 0.38875241164379293, -0.015210445172904461, 0.15843614630956482, 0.28871768385514335, 0.1771078977894586, 0.017625340026636408, 0.03246973417414566, 0.16621470739033278, 0.1336059083024767, -0.23839545751169605, -0.7279329727303949, -0.817233037383965, -0.15032370409292722, 1.0397606128000791, 1.9705237238801792, 1.8878604505319174, 0.7491869177336364, -0.617436629224689, -1.1444867262800869, -0.48520986350505774, 0.5536324802784112, 0.5957371856833369, -1.068603806787355, -3.635531284308212, -5.22308423217778, -4.466643664148207, -1.9777393555654552, -0.05063701172959644, -0.07295290849675105, 0.9413974188940379, 11.815197812459521, 44.212067939015604, 105.33595115872093, 189.96460800309342, 277.5792039053832, 338.27274329580854, 345.73128085085983, 290.8142558198857, 187.9172577767114, 69.7819403512247, -27.115756856443145, -78.8967731884477, -83.47915018173715, -57.9483004975947, -26.39689734186292, -6.051499691988129, -0.0604915220928619, -0.5651692320591141, 1.2838830957019003, 6.256322415369058, 5.864494341068803, -10.019608101520454, -42.65540745507044, -79.38107118391227, -98.70533120851323, -83.07750794816214, -31.192329630384446, 38.57743200221151, 96.59433138459588, 117.6027640390211, 94.25692991976881, 40.42271556243731, -17.439540147969673, -55.138229814119, -62.67494633536776, -46.59129935922374, -22.610420225659716, -4.523307758956539, 2.6560393584773965, 2.2127917339075385, 0.22295707214299773, 0.09478338165626884, 1.084480846931021, 0.9642924683829518, -0.2849925220198257, 0.6361995729392358, 7.731111719094908, 21.545769719298477, 37.16692221709294, 46.565654102962974, 44.01404395372754, 30.59834517351109, 13.986349300084619, 2.787929084440922, 0.01374667672530775, 0.5706405932914318, -5.210445897673703, -24.36328342090168, -55.439475118980496, -88.17993615977934, -109.06771798161228, -109.13963780299778, -89.00305476167458, -58.01337826248856, -28.504330658933867, -9.06314651984333, -1.0628902279251293, -0.06617629492041434, -0.31662795699325386, 1.2417428549689475, 4.019851564108466, 5.751685360797136, 5.127622033654827, 2.8772965835564093, 0.7931444286744427, -0.018970513087959155, 0.07501001426913192, 0.057485746854013246, -0.24365427565135786, 0.4417126270368468, 3.772887112164709, 9.921232087086015, 16.61472311447318, 20.243759202662474, 18.432762159132473, 11.874814606360875, 3.919057641903759, -1.7442245099432052, -3.467395481509963, -2.294014025936154, -0.5763806566782353, 0.07316986504792533, -0.26738596892385347, -0.5827052263035719, -0.34553965684310206, -0.014447010891496853, -0.11328510317881016, -0.1984323168688086, 0.37130033311719024, -0.410292169446198, -9.526272429533197, -36.8952582110039, -87.72891396169591, -153.46320146415664, -209.33188016851855, -224.6026755431271, -182.90853167241315, -99.98394721933836, -22.610255261105888, -1.2266726074292722, -47.07279636613969, -101.87299431880024, -50.07225818918843, 216.63938036970907, 708.2306043926761, 1274.6881735294055, 1631.3822028491486, 1483.5735777319483, 704.1462431305232, -522.1643466594044, -1677.1888102376001, -2052.134031450667, -1018.7118239620247, 1678.231349641516, 5739.336281947615, 10336.664670264003, 14356.615125260842, 16772.364349709576, 16996.952294258608, 15073.104407930814, 11626.231833161499, 7613.042354490432, 3973.6670400844177, 1319.8912660149144, -176.90914797676766, -710.8839703216775, -659.363067431482, -392.7105451905858, -153.06581286669183, -28.019863533982544, 3.313577484238483, -1.0005835636089422, 0.34630024803212667, 14.38550387944438, 26.356322959475076, 22.011540108680034, 1.345132979733215, -22.877339400643585, -36.354060115909334, -33.439170910221385, -19.17923292078432, -3.8291690200350947, 4.698026432531133, 5.0341869375809445, 1.3377838742918964, -0.9779065899430334, 0.8009254916248444, 5.528457160944414, 9.88947162159572, 11.132402012668482, 8.800018843349813, 4.566033913411623, 0.7447604262415836, -1.228972864020947, -1.3639270686451084, -0.6060156197259191, 0.0777795860970441, 0.27747504658830724, 0.12969120606354342, -0.04598732779463418, -0.0737353719986578, 0.006539584360048196, 0.07128783910670047, 0.061658025174021844, 0.01525729637658103, -0.007151719751198588, 0.002254401878750364, -0.0024786869081680056, -0.05866551002625534, -0.14288581144173831, -0.18460092783088158, -0.12921926797010724, 0.010923288813143655, 0.1620739545814187, 0.24306552162790537, 0.22095869815887614, 0.12612255955006713, 0.021847142468238094, -0.04160601061868404, -0.053080545337051685, -0.03370049942363894, -0.01132941235506055, -0.00027518908699946575, 0.001061035960097727, -6.850761055207244e-05, -9.070246097939424e-05, 4.246544330385163e-05, -0.0007822904403721194, -0.0015284868340190367, -0.0009183022955386048, 0.00025350370326583763, 6.847620496454073e-05, -0.001559900712771531, -0.002212243773823392, -0.00011359088003071918, 0.0026131979240599486, 0.0014513695910605983, -0.004687527810237054, -0.010125444552149932, -0.007804743236668254, -0.0005401259543527148, -0.005974729037518695, -0.04509214632032518, -0.11999719645905658, -0.20102009724539666, -0.2393701171980233, -0.2009575997417002, -0.09612217218432936, 0.021359545034996215, 0.08990290472699726, 0.08452746642771118, 0.033359286531559285, -0.009783366348012515, -0.014701326530127068, -0.0008906684016959431, -0.01104480603512867, -0.04973598097374403, -0.04520303092892294, 0.11413909532449293, 0.4777002886433746, 0.9453414705593125, 1.2838385542961583, 1.2658239641050013, 0.8478907874944548, 0.2527413082042477, -0.1300607101420122, 0.01623209173156715, 0.7098977451482977, 1.6237267120380874, 2.268114687283559, 2.2929051438155343, 1.703382567174669, 0.8387856866783953, 0.13037769410204486, -0.1814819498042568, -0.15621024529219094, -0.02937793743325096, 0.014427013680082684, -0.023977079129407823, -0.025896250210004655, 0.04054150019097091, -0.03297277645052835, -0.6352161601358037, -2.0642072546843115, -4.22525042450691, -6.53466048022117, -8.144028569762941, -8.378575313925177, -7.119642242499462, -4.88249067535409, -2.528129966991209, -0.7846634202518561, 0.07363035588772292, 0.23132101370094207, 0.08546015724514922, -0.043945873072505186, -0.055424525155116616, -0.012324056304400817, 0.005428276960019479, -7.954438801599833e-05, 0.03566559169713577, 0.14939027192687723, 0.2926466786432715, 0.36652057904439594, 0.31254805517374395, 0.1687171972649654, 0.03403447796034262, -0.022454363112619124, -0.01322909365321473, 0.002919450036419429, -0.0006543031409958029, 0.013463317030681491, 0.0894341646786011, 0.1894893070792252, 0.18742327787956928, -0.00026495806398471903, -0.23105757898081983, -0.09015592969064645, 0.8792285785513275, 2.7376987411205387, 4.800318354798974, 5.724395610232236, 4.151716779489346, -0.41401031691597334, -7.058440417420558, -13.654904998238557, -17.79125489766113, -17.939866650411563, -14.206089761766876, -8.227228531628135, -2.2991311623194313, 1.7446095315480685, 3.2678430194427195, 2.8330995365855847, 1.592143405445287, 0.5311482731421632, 0.03960105347901802, -0.026776679011370208, 0.020503293887325635, 0.01802835340503909, -0.006487249216430041, -0.0005858167876704929, -0.03577335078554031, -0.2737693581764607, -0.7850370308784678, -1.4044415979366287, -1.7831312255622522, -1.6238094922613653, -0.9194435078642952, 0.0034646172172874625, 0.6877523167174344, 0.849454866364503, 0.5537297359387998, 0.13282988830346504, -0.08266038944284217, -0.0036359580047017914, 0.19461872309813055, 0.25465676631580475, 0.05641747169787518, -0.29973349965835355, -0.5918675144114754, -0.6558331598526933, -0.495498578319371, -0.2500502316695237, -0.06787754849993272, -0.0022129286427887687, -0.005810102205748282, -0.006046460768676132, 0.022551573316507346, 0.05206887340216727, 0.05049344294110366, 0.022835507679004576, 0.0006375539266452853, 0.0012438000091057819, 0.010169029838431879, 0.0071221338002507, -7.318151817215632e-05, 0.017873021631544188, 0.06570120722742648, 0.09698941857247091, 0.057953449150075456, -0.02854089464241147, -0.04117125508906846, 0.13287255263582068, 0.43916656579980756, 0.6351828018650015, 0.5115843293769666, 0.17671518544483295, -0.00036348565557430543, -0.04760238438053575, -1.355131067803813, -7.066574643348638, -20.976889558897323, -44.85356016783838, -75.47094714181395, -103.59819704254127, -116.7222228343348, -105.21826811017799, -69.02408135717113, -20.46664845014301, 19.797088799573718, 32.85292777601923, 12.537274129667491, -29.78880092368654, -71.01890224056196, -89.12158088803396, -75.25158641265533, -37.84893513677663, 3.5086787730011766, 30.233950945525024, 34.94505772561099, 23.53851723550938, 8.673217985806783, 0.08464862514925009, -1.0396152388818365, 0.08041621141123105, -0.8290393516939416, -1.3010857831759366, 6.597830060929187, 28.563515229320256, 60.475007074532186, 88.02319684234568, 95.18187708209503, 75.80804061158048, 39.31084789120173, 5.134700278179014, -10.611862097908725, -6.254918349710259, 5.806147065506016, 11.10430767801145, 6.364137985152936, 0.623545174276095, -0.04393695002073055, -12.347976562704082, -78.34765203148248, -237.733995948149, -482.55388656650734, -729.904883262791, -846.8474953864707, -730.8073094314008, -405.11616741289043, -63.9417963067415, -17.344532537748755, -543.0551910046227, -1715.4153405483448, -3311.3137992121483, -4862.512542183367, -5845.025770397908, -5914.308261736145, -5066.114611898261, -3631.3774579393375, -2081.2014718061096, -816.0671600747679, -35.346931899061616, 278.24577291462384, 281.9214968478484, 162.9065744225404, 53.671156928294984, 2.598876344440628, -4.481636980094877, -0.06994629592322837, -0.37018610455679696, -0.16948331673842518, 2.076955169874396], 'positive_zeros': ['0.06919659456630221999986211040272', '0.38795809214759296185524800453587', '0.46291499561039230991169190515237', '0.58315902034624030749907114461156', '0.71899627596063368056906150782498', '0.72658477238687432999552042430690', '0.77556119170702829497037050778326', '0.938164448712390297720542419552183', '1.14583788040039758560325152889196', '1.24952910940782362175057982107036', '1.46221662182827388756188409947476', '1.53832270122617932133760352359855', '1.60648478446009938114882649162934', '1.79961419355137801256099355184506', '1.81020181298446147648591396873809', '1.90226210185634149410349710259987', '1.98368019499029006343151863336806', '2.02891325124552686417288108057845', '2.35273297174532368519890566741596', '2.38658102409015489042688663434430', '2.39019901346728191423073886203283', '2.40829690165591560128071970863861', '2.66750718454268042433328053452910', '2.68160227957977986441458489735731', '2.68707936948050471281288720202345', '2.79014808527691718620720427124365', '2.95978116199134906243254516331275', '3.02452661063759508520748932154479', '3.04073079486781060823388146596151', '3.15120005178773055263402939297702', '3.20730275930757782446825296562268', '3.26346759233213273611853090601315', '3.27501804023252710216422520891567', '3.32683784684726783596257239056761', '3.45894292124834570965558104458177', '3.57586121240277547787388123295109', '3.58642622222238096937649617602438', '3.60073153012744232305999107347028', '3.74681784150146819797263116341711', '3.79984683999888403227597371553714', '3.80546572596685752094594654909556', '3.92730627599264169870478752053062', '4.02162017218439937021668123841924', '4.02503420624257316163214860654686', '4.08055367327982574544049421179924', '4.16337260788216421648868819798014', '4.29305211936899193041505067916327', '4.35524758266156414288052288920403', '4.35682322317945702668588882484843', '4.36958136703626759597259408912780', '4.41426088617325270736457436288785', '4.51324682926109036519088744995471', '4.55136610119154681044345792894944', '4.55832209228267404384179871976292', '4.68246840100156647863877413813655', '4.72339516056644651074057013950555', '4.76878270519552572628334823125395', '4.86172080827249501623645611823457', '4.97171799998362589399181888296092', '5.03454256415504180219918431242836', '5.08968265333015286728069670843084', '5.19588970597340144588337356539046', '5.23612395186630115687946802744128', '5.24154902579640364196532285871794', '5.36999342353919551020662877213697', '5.37969986232507492939809537647808', '5.51920335478964666350990030173890', '5.52592222549360184469242612454031', '5.63110323532818199563872650842647', '5.65009022059041341457675100323854', '5.68435243659446275101357690682907', '5.76565657243741865039199746634754', '5.78455276637135214607316986183921', '5.81120619740894001725240220864066', '5.95633761413534131207647221100165', '6.05162088767524856418218469831351', '6.10421639166490800091241363389799', '6.22523712741743606207520783856045', '6.28595388831260866205518655318439', '6.30897215305578201364196047326542', '6.47098608432775628309175873861685', '6.49185442709334186826003712057577', '6.53311199845977827856667058871075', '6.60813898157879924552833438652775', '6.61001927037586537634666545643408', '6.63993252256361041806843910530330', '6.65265738581809805224699708894173', '6.82811534417320639126991066623028', '6.88700455085706306601667331051158', '6.89213560891623889231671075085902', '6.89837302654336437758562066097746', '6.96186672403596277456841907342589', '7.02306883068255739022646631615225', '7.16697645828224028833458264630034', '7.18328428118801857901900285864535', '7.22959593117187213759123561479055', '7.30511702057320591424095685229482', '7.41508461746613729913972185350512', '7.41789824430256023605689080212657', '7.46089915960105977871474083920269', '7.47962362156145399496183290498911', '7.56721526818227919605848117924802', '7.60836866820702843702196710367017', '7.60855026808282788636928410277933', '7.69226673643722195665580839411968', '7.78452248163665675050631348463202', '7.79834780348741089876755280913078', '7.80142853057962309491527825359689', '7.84671319264885741403525334092414', '7.945304046313029879318131345524181', '7.949027791769712921174113797068016', '8.091188239990849912392269507494225', '8.091482614078441564975858883799779', '8.147727941174846249909021329743404', '8.186856364193000473441104535677459', '8.333094633250994532064926309031238', '8.352564638673099466353948452517956', '8.357327999556646576948280692357984', '8.437580702896492805360736286940848', '8.449292682702860148275056079340727', '8.478099730729241772089812284109002', '8.607262063493942543596979925299416', '8.608549119653354044248579550370311', '8.687056340320522304070851428357043', '8.693792443396182053175093192541673', '8.739208306750984584709761484254161', '8.809115145836417708913151314283873', '8.899675014341982307450732207589820', '8.908729016414686623749450657691162', '8.940849627724705044518885498184673', '8.983608850729234043953058713619803', '8.991338849744893581816243052929008', '9.062707102677606836145568551347021', '9.152771236887339371481678755152896', '9.258925813227803652091482834353339', '9.323144487045560099674323654678754', '9.390171287138012329220018075983532', '9.504162203493995076476140298897825', '9.508079579152799531925485986946467', '9.533222612228566749188043920346350', '9.610280112189693807920091963391287', '9.676915376490492217797539291601153', '9.681010138293761537067149865732135', '9.738111067384084621860188564405178', '9.808906311527400990318616110566459', '9.962477331645066832330826965642050', '9.976496877391420366119557533018451', '10.02278914733658797890103766710854', '10.02944477023613127542288983676340', '10.04263212244091890593797531936704', '10.04572526313083908190897696202706', '10.13732882930392760080815446675637', '10.21541946830974330032270878937993', '10.39066613509118468210359755135246', '10.41801466912819117227766174928835', '10.43260578822125057401775569502457', '10.49832338704051757660043172446151', '10.58985148501001489186468817713286', '10.65626675004050815937369406591431', '10.66994831129025115176620414454482'], 'prelabel': '32-840e16-1.1-c1e16-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.5898713809352687, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e16-0', 'trace_hash': 409932047586885907, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.06919659456630221999986211040', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.38795809214759296185524800454', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.46291499561039230991169190515', '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': 16784263508638.938, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 61442457392708813112505175900160000000000000000, 'conductor_radical': 210, 'degree': 32, 'dirichlet_coefficients': [1, 0, 0, 0, -16, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 136, 0, -2, 0, 0, 0, 0, 0, 0, 0, -32, 0, 12, 0, 0, 0, -32, 0, 32, 0, 16, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -1, 0, -20, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -98, 0, 4677, 0, -145778, 0, 3365990, 0, -61993422, 0, 956138939, 0, -12739504414, 0, 149122019666, 0, -1541480034094, 0, 13998830205899, 0, -109825128671742, 0, 721529849857190, 0, -3781105883484578, 0, 14678429517924117, 0, -37215483691157618, 0, 45949729863572161], 'euler13': [1, 0, -62, 0, 2189, 0, -56298, 0, 1188526, 0, -21616414, 0, 350156979, 0, -5148156634, 0, 69670246018, 0, -870038471146, 0, 10000833477219, 0, -104338301642926, 0, 969517170907246, 0, -7761157374115002, 0, 50999508333110909, 0, -244117335913355918, 0, 665416609183179841], 'euler17': [1, 0, 114, -196, 6541, -19736, 279342, -973588, 9906158, -34190532, 288802250, -983850976, 7042955907, -23427311044, 148964955926, -463899371944, 2734099308930, -7886289323048, 43050872262614, -115098379159172, 588234720308547, -1396927695230432, 6970984236730250, -14029697530044036, 69102955380221678, -115455733502961236, 563151768139224558, -676390145527444888, 3810932053719866701, -1941297294449563652, 19195072227771705906, 0, 48661191875666868481], 'euler19': [1, 0, -192, 0, 18200, 0, -1136320, 0, 52494236, 0, -1907281216, 0, 56456539944, 0, -1389647467328, 0, 28750954230662, 0, -501662735705408, 0, 7357472742042024, 0, -89729725121471296, 0, 891539166395131676, 0, -6966853210064432320, 0, 40282331527004130200, 0, -153409283670313751232, 0, 288441413567621167681], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, -176, 0, 16600, 0, -1097616, 0, 56000348, 0, -2314599984, 0, 79690491368, 0, -2321865829264, 0, 57730745485894, 0, -1228267023680656, 0, 22300666794912488, 0, -342643866310825776, 0, 4385442427958877788, 0, -45470401532280560784, 0, 363782765571537328600, 0, -2040339193118819966384, 0, 6132610415680998648961], 'euler29': [1, 0, -222, 0, 26333, 0, -2171770, 0, 137753198, 0, -7082097518, 0, 304034253475, 0, -11089366548570, 0, 346812558599170, 0, -9326157267347370, 0, 215037650832051475, 0, -4212596765302617278, 0, 68910543173406399278, 0, -913679348064377525770, 0, 9317004686149616256653, 0, -66057927654027480892782, 0, 250246473680347348787521], 'euler3': [1, 0, 1, 2, 2, -2, -9, 20, -70, 60, -81, -54, 162, 486, 729, 0, 6561, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 0, -236, 0, 29072, 0, -2456356, 0, 159264268, 0, -8416386060, 0, 375234642352, 0, -14382750977508, 0, 478150921280358, 0, -13821823689385188, 0, 346537072139561392, 0, -7469573608967086860, 0, 135835066761801458188, 0, -2013298860495012421156, 0, 22898932450300718651792, 0, -178638768712107931595756, 0, 727423121747185263828481], 'euler37': [1, -12, 204, -2548, 30544, -315516, 3204644, -29388068, 260621516, -2160117596, 17303305260, -130636973540, 956432790256, -6653840316492, 44780826644644, -287677700045588, 1792998139554726, -10644074901686756, 61304951676517636, -337036973551269276, 1792509034618975216, -9058884675767897780, 44395547268570611340, -205064018216303332268, 915427720199743164236, -3819324446496028941236, 15409801057562625290756, -56135856353368231668108, 201069686066378037622864, -620614383302575166151556, 1838460504382981693136556, -4001355215421783685061916, 12337511914217166362274241], 'euler41': [1, 32, 872, 16384, 274232, 3817280, 48731960, 551477536, 5831203740, 56373518304, 515488156008, 4384273868096, 35539636596616, 270512950758784, 1970604382806776, 13541976868055776, 89216269810380230, 555221051590286816, 3312585967498190456, 18644023079246152064, 100426519048890224776, 507945314501177663296, 2448622476038870429928, 10978983623412782617824, 46561725859670732112540, 180543782510495265560096, 654112496595974399435960, 2100760006189800848860480, 6187631072050019941364792, 15156889228329183302795264, 33074286113966367275484392, 49763146079729213148435232, 63759030914653054346432641], 'euler43': [1, -32, 952, -19424, 357592, -5515360, 77660136, -975180704, 11318069276, -120359053216, 1193913076408, -11001602170720, 95153617423464, -770195411016672, 5873756113211176, -42078669686599968, 284532009262738694, -1809382796523798624, 10860575053327464424, -61235926543702540704, 325311282400956146664, -1617328405622967388960, 7547158004923444847992, -32715830679326621670112, 132287860453650549086876, -490118617133769360277472, 1678350655611249383997864, -5125389518930002869279520, 14289244296054719220386392, -33375562350059216212560032, 70338860191619855584707448, -101666251705534581181257824, 136614025729312093462315201], 'euler47': [1, 4, 358, 1016, 66037, 135600, 8474646, 13153612, 846912054, 1034902316, 69207254810, 68533780576, 4751856535867, 3963078874536, 278875561511018, 206074401591908, 14105075484489906, 9685496874819676, 616036115377838762, 411458737990951128, 23187544052796018427, 15717880385939184032, 745999901925960982490, 524305440706305692308, 20166065695094811767094, 14720608020570233244404, 445759025605848181437654, 335224789565392068286800, 7672936970065637261300917, 5548375701418512508164232, 91886781055184932541704102, 48253393403281472954861372, 566977372488557307219621121], 'euler5': [1, 16, 120, 560, 1820, 4368, 8008, 11440, 12870, 11440, 8008, 4368, 1820, 560, 120, 16, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, 0, -336, 0, 57368, 0, -6570480, 0, 562971676, 0, -38226667216, 0, 2167136874280, 0, -110899294229232, 0, 5697668480853766, 0, -311516117489912688, 0, 17099752330905728680, 0, -847269656933529046864, 0, 35050442258125031611036, 0, -1149094626287196178193520, 0, 28182540819399866039444888, 0, -463661944051200306177887184, 0, 3876269050118516845397872321], 'euler59': [1, -24, 800, -14744, 293880, -4447736, 67718496, -875251000, 11106099164, -125700063288, 1385158876704, -13954407369016, 136513206958408, -1236675854856728, 10872242802330464, -89065877344947160, 708055161210923142, -5254886763351882440, 37846277194912345184, -253987250394619939912, 1654179809982741721288, -9976344906254198119784, 58426740596942843199264, -312823649143523471224872, 1630713400327103620887644, -7582295753273554014689000, 34612057813922471511052896, -134125430647644513356770024, 522870537272233874836988280, -1547716717336896552283914376, 4954708970313450709970208800, -8769834877454807756647269576, 21559177407076402401757871041], 'euler61': [1, 0, -532, 0, 140064, 0, -24493116, 0, 3211893356, 0, -337476552116, 0, 29598825516320, 0, -2223593298357948, 0, 145164479770038246, 0, -8273990663189924508, 0, 409820631885709625120, 0, -17386918303075846697876, 0, 615743444912579289965036, 0, -17471990683136736440674716, 0, 371778734736017107679072544, 0, -5254474907748221226599818612, 0, 36751693856637464631913392961], 'euler67': [1, 0, 440, -384, 103256, -204288, 16810088, -51498624, 2145056668, -8382078336, 230189227448, -998146574592, 21528530047720, -93761161331328, 1768500126721704, -7326918670005504, 126982101380577414, -490903550890368768, 7938797068853729256, -28199888165494203264, 433824013943741494120, -1347622750822707481344, 20822545107678048574712, -50801359447721700582528, 871038179402146724732188, -1401099085217860468652928, 30642063904241910512697512, -24949720590890106273851904, 844914823216770297318790616, -210524991978394148615265408, 16162179071674634117651104760, 0, 164890958756244164895763202881], 'euler7': [1, -2, 4, -34, 20, 54, -196, 1590, -4714, 11130, -9604, 18522, 48020, -571438, 470596, -1647086, 5764801, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler71': [1, 0, -556, 0, 159568, 0, -31261348, 0, 4675032076, 0, -566675658188, 0, 57715565878768, 0, -5048338414984420, 0, 383759996279289574, 0, -25448673949936461220, 0, 1466649548845737089008, 0, -72591312705002348395148, 0, 3018918471764200914029836, 0, -101763301472875647663118948, 0, 2618460255558572951068567888, 0, -45992993146737102883806137836, 0, 416997623116370028124580469121], 'euler73': [1, 0, -484, 0, 118496, 0, -19741196, 0, 2519941548, 0, -263032335940, 0, 23581346703712, 0, -1898951836350284, 0, 142510808022168230, 0, -10119514335910663436, 0, 669668766796568970592, 0, -39805795048468227526660, 0, 2032232292367792727177388, 0, -84840273838840553446208204, 0, 2713801085316909696280392416, 0, -59069786795237348918068577956, 0, 650377879817809571042122834561], 'euler79': [1, 4, 390, -1192, 68245, -733040, 10443766, -148070804, 1691400502, -20859036532, 230955075130, -2554721106112, 26034380550683, -265360741457144, 2617960752313162, -23151724856456284, 227694068962749618, -1828986263660046436, 16338693055186444042, -130833194607288820616, 1014041231233927455323, -7861020927222287610688, 56142281553013088292730, -400575039099493663360588, 2566038602664579848493622, -17746522177829464519458476, 98884459830351457484998966, -548309382869093941705462160, 4032700170356602597516441045, -5564529410830691675623536088, 143828146935984572588893579590, 116537678030182371636129156796, 2301619141096101839813550846721], 'euler83': [1, 20, 1052, 19348, 549888, 9078916, 186325460, 2742193252, 45343893036, 595522850820, 8359936336636, 98328379003972, 1204950715864128, 12731008103047540, 138344927981317204, 1314718662957128596, 12780679604563617638, 109121649025441673468, 953058208863294218356, 7279424930217243753980, 57184937862659579009088, 387319481256953566433996, 2733200707240843913446684, 16160138445339553288444140, 102127698059926356583618476, 512626306521806747743960556, 2891033511585076758577511540, 11692113271068124108257846572, 58777532575396888379654611968, 171652953187392081112286987324, 774656257003841583336802283708, 1222366337097316566862254554140, 5072820298953863752478356399681], 'euler89': [1, -24, 1104, -21736, 568792, -9605400, 185994096, -2762913896, 43792315484, -580961162104, 7934230025424, -94888815252104, 1149110187837160, -12461695108494072, 135963207869162864, -1341461948429341064, 13290404171910305606, -119390113410211354696, 1076964569531639045744, -8785108738939957443768, 72097748340834361475560, -529864785412926658330696, 3943163880816747371392464, -25696687722317735273833016, 172392338910088309267322204, -968004576355996803160564264, 5799615810099243629438019696, -26656647442761449016533040600, 140486165624692583307520316632, -477803923658613871465722588584, 2159877729251047320331985584464, -4178893867463982858903189500376, 15496731425178936435099327730561], 'euler97': [1, 0, -686, 0, 252221, 0, -64043882, 0, 12508641022, 0, -1992015843950, 0, 268648339369171, 0, -31445973528756858, 0, 3242273163197169378, 0, -295875164932073276922, 0, 23783244326196702196051, 0, -1659293431385365494829550, 0, 98035643365824562896294142, 0, -4722750376681181191328682218, 0, 175001614132630367872415536061, 0, -4478456863379768235316363967534, 0, 61425365346268570446197767595521], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 2, 2, -2, -9, 20, -70, 60, -81, -54, 162, 486, 729, 0, 6561, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 16, 120, 560, 1820, 4368, 8008, 11440, 12870, 11440, 8008, 4368, 1820, 560, 120, 16, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -2, 4, -34, 20, 54, -196, 1590, -4714, 11130, -9604, 18522, 48020, -571438, 470596, -1647086, 5764801, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -98, 0, 4677, 0, -145778, 0, 3365990, 0, -61993422, 0, 956138939, 0, -12739504414, 0, 149122019666, 0, -1541480034094, 0, 13998830205899, 0, -109825128671742, 0, 721529849857190, 0, -3781105883484578, 0, 14678429517924117, 0, -37215483691157618, 0, 45949729863572161], [1, 0, -62, 0, 2189, 0, -56298, 0, 1188526, 0, -21616414, 0, 350156979, 0, -5148156634, 0, 69670246018, 0, -870038471146, 0, 10000833477219, 0, -104338301642926, 0, 969517170907246, 0, -7761157374115002, 0, 50999508333110909, 0, -244117335913355918, 0, 665416609183179841], [1, 0, 114, -196, 6541, -19736, 279342, -973588, 9906158, -34190532, 288802250, -983850976, 7042955907, -23427311044, 148964955926, -463899371944, 2734099308930, -7886289323048, 43050872262614, -115098379159172, 588234720308547, -1396927695230432, 6970984236730250, -14029697530044036, 69102955380221678, -115455733502961236, 563151768139224558, -676390145527444888, 3810932053719866701, -1941297294449563652, 19195072227771705906, 0, 48661191875666868481], [1, 0, -192, 0, 18200, 0, -1136320, 0, 52494236, 0, -1907281216, 0, 56456539944, 0, -1389647467328, 0, 28750954230662, 0, -501662735705408, 0, 7357472742042024, 0, -89729725121471296, 0, 891539166395131676, 0, -6966853210064432320, 0, 40282331527004130200, 0, -153409283670313751232, 0, 288441413567621167681], [1, 0, -176, 0, 16600, 0, -1097616, 0, 56000348, 0, -2314599984, 0, 79690491368, 0, -2321865829264, 0, 57730745485894, 0, -1228267023680656, 0, 22300666794912488, 0, -342643866310825776, 0, 4385442427958877788, 0, -45470401532280560784, 0, 363782765571537328600, 0, -2040339193118819966384, 0, 6132610415680998648961], [1, 0, -222, 0, 26333, 0, -2171770, 0, 137753198, 0, -7082097518, 0, 304034253475, 0, -11089366548570, 0, 346812558599170, 0, -9326157267347370, 0, 215037650832051475, 0, -4212596765302617278, 0, 68910543173406399278, 0, -913679348064377525770, 0, 9317004686149616256653, 0, -66057927654027480892782, 0, 250246473680347348787521], [1, 0, -236, 0, 29072, 0, -2456356, 0, 159264268, 0, -8416386060, 0, 375234642352, 0, -14382750977508, 0, 478150921280358, 0, -13821823689385188, 0, 346537072139561392, 0, -7469573608967086860, 0, 135835066761801458188, 0, -2013298860495012421156, 0, 22898932450300718651792, 0, -178638768712107931595756, 0, 727423121747185263828481], [1, -12, 204, -2548, 30544, -315516, 3204644, -29388068, 260621516, -2160117596, 17303305260, -130636973540, 956432790256, -6653840316492, 44780826644644, -287677700045588, 1792998139554726, -10644074901686756, 61304951676517636, -337036973551269276, 1792509034618975216, -9058884675767897780, 44395547268570611340, -205064018216303332268, 915427720199743164236, -3819324446496028941236, 15409801057562625290756, -56135856353368231668108, 201069686066378037622864, -620614383302575166151556, 1838460504382981693136556, -4001355215421783685061916, 12337511914217166362274241], [1, 32, 872, 16384, 274232, 3817280, 48731960, 551477536, 5831203740, 56373518304, 515488156008, 4384273868096, 35539636596616, 270512950758784, 1970604382806776, 13541976868055776, 89216269810380230, 555221051590286816, 3312585967498190456, 18644023079246152064, 100426519048890224776, 507945314501177663296, 2448622476038870429928, 10978983623412782617824, 46561725859670732112540, 180543782510495265560096, 654112496595974399435960, 2100760006189800848860480, 6187631072050019941364792, 15156889228329183302795264, 33074286113966367275484392, 49763146079729213148435232, 63759030914653054346432641], [1, -32, 952, -19424, 357592, -5515360, 77660136, -975180704, 11318069276, -120359053216, 1193913076408, -11001602170720, 95153617423464, -770195411016672, 5873756113211176, -42078669686599968, 284532009262738694, -1809382796523798624, 10860575053327464424, -61235926543702540704, 325311282400956146664, -1617328405622967388960, 7547158004923444847992, -32715830679326621670112, 132287860453650549086876, -490118617133769360277472, 1678350655611249383997864, -5125389518930002869279520, 14289244296054719220386392, -33375562350059216212560032, 70338860191619855584707448, -101666251705534581181257824, 136614025729312093462315201], [1, 4, 358, 1016, 66037, 135600, 8474646, 13153612, 846912054, 1034902316, 69207254810, 68533780576, 4751856535867, 3963078874536, 278875561511018, 206074401591908, 14105075484489906, 9685496874819676, 616036115377838762, 411458737990951128, 23187544052796018427, 15717880385939184032, 745999901925960982490, 524305440706305692308, 20166065695094811767094, 14720608020570233244404, 445759025605848181437654, 335224789565392068286800, 7672936970065637261300917, 5548375701418512508164232, 91886781055184932541704102, 48253393403281472954861372, 566977372488557307219621121], [1, 0, -336, 0, 57368, 0, -6570480, 0, 562971676, 0, -38226667216, 0, 2167136874280, 0, -110899294229232, 0, 5697668480853766, 0, -311516117489912688, 0, 17099752330905728680, 0, -847269656933529046864, 0, 35050442258125031611036, 0, -1149094626287196178193520, 0, 28182540819399866039444888, 0, -463661944051200306177887184, 0, 3876269050118516845397872321], [1, -24, 800, -14744, 293880, -4447736, 67718496, -875251000, 11106099164, -125700063288, 1385158876704, -13954407369016, 136513206958408, -1236675854856728, 10872242802330464, -89065877344947160, 708055161210923142, -5254886763351882440, 37846277194912345184, -253987250394619939912, 1654179809982741721288, -9976344906254198119784, 58426740596942843199264, -312823649143523471224872, 1630713400327103620887644, -7582295753273554014689000, 34612057813922471511052896, -134125430647644513356770024, 522870537272233874836988280, -1547716717336896552283914376, 4954708970313450709970208800, -8769834877454807756647269576, 21559177407076402401757871041], [1, 0, -532, 0, 140064, 0, -24493116, 0, 3211893356, 0, -337476552116, 0, 29598825516320, 0, -2223593298357948, 0, 145164479770038246, 0, -8273990663189924508, 0, 409820631885709625120, 0, -17386918303075846697876, 0, 615743444912579289965036, 0, -17471990683136736440674716, 0, 371778734736017107679072544, 0, -5254474907748221226599818612, 0, 36751693856637464631913392961], [1, 0, 440, -384, 103256, -204288, 16810088, -51498624, 2145056668, -8382078336, 230189227448, -998146574592, 21528530047720, -93761161331328, 1768500126721704, -7326918670005504, 126982101380577414, -490903550890368768, 7938797068853729256, -28199888165494203264, 433824013943741494120, -1347622750822707481344, 20822545107678048574712, -50801359447721700582528, 871038179402146724732188, -1401099085217860468652928, 30642063904241910512697512, -24949720590890106273851904, 844914823216770297318790616, -210524991978394148615265408, 16162179071674634117651104760, 0, 164890958756244164895763202881], [1, 0, -556, 0, 159568, 0, -31261348, 0, 4675032076, 0, -566675658188, 0, 57715565878768, 0, -5048338414984420, 0, 383759996279289574, 0, -25448673949936461220, 0, 1466649548845737089008, 0, -72591312705002348395148, 0, 3018918471764200914029836, 0, -101763301472875647663118948, 0, 2618460255558572951068567888, 0, -45992993146737102883806137836, 0, 416997623116370028124580469121], [1, 0, -484, 0, 118496, 0, -19741196, 0, 2519941548, 0, -263032335940, 0, 23581346703712, 0, -1898951836350284, 0, 142510808022168230, 0, -10119514335910663436, 0, 669668766796568970592, 0, -39805795048468227526660, 0, 2032232292367792727177388, 0, -84840273838840553446208204, 0, 2713801085316909696280392416, 0, -59069786795237348918068577956, 0, 650377879817809571042122834561], [1, 4, 390, -1192, 68245, -733040, 10443766, -148070804, 1691400502, -20859036532, 230955075130, -2554721106112, 26034380550683, -265360741457144, 2617960752313162, -23151724856456284, 227694068962749618, -1828986263660046436, 16338693055186444042, -130833194607288820616, 1014041231233927455323, -7861020927222287610688, 56142281553013088292730, -400575039099493663360588, 2566038602664579848493622, -17746522177829464519458476, 98884459830351457484998966, -548309382869093941705462160, 4032700170356602597516441045, -5564529410830691675623536088, 143828146935984572588893579590, 116537678030182371636129156796, 2301619141096101839813550846721], [1, 20, 1052, 19348, 549888, 9078916, 186325460, 2742193252, 45343893036, 595522850820, 8359936336636, 98328379003972, 1204950715864128, 12731008103047540, 138344927981317204, 1314718662957128596, 12780679604563617638, 109121649025441673468, 953058208863294218356, 7279424930217243753980, 57184937862659579009088, 387319481256953566433996, 2733200707240843913446684, 16160138445339553288444140, 102127698059926356583618476, 512626306521806747743960556, 2891033511585076758577511540, 11692113271068124108257846572, 58777532575396888379654611968, 171652953187392081112286987324, 774656257003841583336802283708, 1222366337097316566862254554140, 5072820298953863752478356399681], [1, -24, 1104, -21736, 568792, -9605400, 185994096, -2762913896, 43792315484, -580961162104, 7934230025424, -94888815252104, 1149110187837160, -12461695108494072, 135963207869162864, -1341461948429341064, 13290404171910305606, -119390113410211354696, 1076964569531639045744, -8785108738939957443768, 72097748340834361475560, -529864785412926658330696, 3943163880816747371392464, -25696687722317735273833016, 172392338910088309267322204, -968004576355996803160564264, 5799615810099243629438019696, -26656647442761449016533040600, 140486165624692583307520316632, -477803923658613871465722588584, 2159877729251047320331985584464, -4178893867463982858903189500376, 15496731425178936435099327730561], [1, 0, -686, 0, 252221, 0, -64043882, 0, 12508641022, 0, -1992015843950, 0, 268648339369171, 0, -31445973528756858, 0, 3242273163197169378, 0, -295875164932073276922, 0, 23783244326196702196051, 0, -1659293431385365494829550, 0, 98035643365824562896294142, 0, -4722750376681181191328682218, 0, 175001614132630367872415536061, 0, -4478456863379768235316363967534, 0, 61425365346268570446197767595521]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/840/2/f/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '32-840e16-1.1-c1e16-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__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}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '32-840e16-1.1-c1e16-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.5898713809352687, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e16-0', 'trace_hash': 409932047586885907, 'z1': {'__RealLiteral__': 0, 'data': '0.06919659456630221999986211040', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '87717104635722446327634384947,491795308374294949828230219296,586814472040161990286951018984,739241882170417767736408228542,911436060783358951294433041251,921055622832912684281894117204,983140610181135308943532121551,1189264726523047498974737578243,1452522076853806133284546891711,1583966325543472539599151724287,1853579778324305314990553073068,1950055695554077421810848597881,2281282012634645338768954217501,2294703414763981657709945441992,2411403695209604549801728054917,2571953100752400533705368020987', 'Lhash_array': ['87717104635722446327634384947', '491795308374294949828230219296', '586814472040161990286951018984', '739241882170417767736408228542', '911436060783358951294433041251', '921055622832912684281894117204', '983140610181135308943532121551', '1189264726523047498974737578243', '1452522076853806133284546891711', '1583966325543472539599151724287', '1853579778324305314990553073068', '1950055695554077421810848597881', '2281282012634645338768954217501', '2294703414763981657709945441992', '2411403695209604549801728054917', '2571953100752400533705368020987'], 'factors': ['2-840-21.20-c1-0-0', '2-840-21.20-c1-0-1', '2-840-21.20-c1-0-2', '2-840-21.20-c1-0-4', '2-840-21.20-c1-0-7', '2-840-21.20-c1-0-8', '2-840-21.20-c1-0-11', '2-840-21.20-c1-0-13', '2-840-21.20-c1-0-14', '2-840-21.20-c1-0-16', '2-840-21.20-c1-0-20', '2-840-21.20-c1-0-22', '2-840-21.20-c1-0-27', '2-840-21.20-c1-0-28', '2-840-21.20-c1-0-29', '2-840-21.20-c1-0-30'], 'label': '32-840e16-1.1-c1e16-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/840/2/f/a'}