Lfunction data - 36-87e18-1.1-c1e18-0-0

Formats: - HTML - YAML - JSON - 2025-01-19T13:22:47.888161

• lfunc_lfunctions •

  Column	Type
  A10	numeric
  A2	numeric
  A3	numeric
  A4	numeric
  A5	numeric
  A6	numeric
  A7	numeric
  A8	numeric
  A9	numeric
  Lhash	text
  a10	jsonb
  a2	jsonb
  a3	jsonb
  a4	jsonb
  a5	jsonb
  a6	jsonb
  a7	jsonb
  a8	jsonb
  a9	jsonb
  accuracy	smallint
  algebraic	boolean
  analytic_conductor	double precision
  analytic_normalization	numeric
  bad_lfactors	jsonb
  bad_primes	bigint[]
  central_character	text
  coeff_info	jsonb
  coefficient_field	text
  conductor	numeric
  conductor_radical	integer
  conjugate	text
  credit	text
  degree	smallint
  dirichlet_coefficients	jsonb
  euler_factors	jsonb
  euler_factors_factorization	jsonb
  gamma_factors	jsonb
  group	text
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  label	text
  leading_term	text
  load_key	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  origin	text
  plot_delta	numeric
  plot_values	jsonb
  positive_zeros	jsonb
  precision	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  root_number	text
  self_dual	boolean
  sign_arg	numeric
  spectral_label	text
  st_group	text
  symmetry_type	text
  trace_hash	bigint
  types	jsonb
  values	jsonb
  z1	numeric
  z2	numeric
  z3	numeric

  
  {'Lhash': '426735551420417918750031183525,1065590478541186173827787051040,2286232357456574903818092486375,2422649266003650366130043853912,2452687214327100868508124450595,2658655794920918447948215736221,2948235394119547648459605919357,3074325182394385580040063028793,3078427358371524545707329371085,3222566588514582221815983204510,3286945439882013084100250076825,3421775313888983752102268377459,3637457581613351487941650147358,3831863756060468619526555280920,4043165374641679341604942725515,4625703310903716780121595501841,4648983842726490537904049447509,5422888444450870127294313622356', 'a10': 14, 'a2': -2, 'a3': 3, 'a4': 2, 'a5': -7, 'a6': -6, 'a7': -4, 'a8': -1, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.001420150834673389, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -3, 6, -10, 15, -21, 28, -33, 36, -37, 36, -33, 28, -21, 15, -10, 6, -3, 1]], [29, [1, 10, -36, -578, 1016, 21063, -22778, -592636, 552441, 19185875, 16020789, -498406876, -555532642, 14897459703, 20839327384, -343807879538, -620995547124, 5002464129610, 14507145975869]]], 'bad_primes': [3, 29], 'central_character': '87.1', 'coefficient_field': '1.1.1.1', 'conductor': 81535464022367037427533666993843729, 'conductor_radical': 87, 'degree': 36, 'euler_factors': [[1, 2, 2, 1, -4, -15, -14, -22, -30, 4, 42, 72, 232, 163, 54, 107, -307, -860, -451, -1720, -1228, 856, 864, 5216, 14848, 9216, 10752, 2048, -30720, -45056, -57344, -122880, -65536, 32768, 131072, 262144, 262144], [1, -3, 6, -10, 15, -21, 28, -33, 36, -37, 36, -33, 28, -21, 15, -10, 6, -3, 1], [1, 7, 15, -1, -57, -198, -610, -727, 2083, 10771, 26002, 37370, -7745, -222133, -680461, -964364, 607712, 6539033, 18434481, 32695165, 15192800, -120545500, -425288125, -694165625, -121015625, 2919531250, 10157031250, 21037109375, 20341796875, -35498046875, -148925781250, -241699218750, -347900390625, -30517578125, 2288818359375, 5340576171875, 3814697265625], [1, 4, -11, -55, 66, 374, 119, -613, -7208, -12134, 88572, 142848, -536011, -791002, 184498, 3122533, 33800345, -9073301, -365501233, -63513107, 1656216905, 1071028819, 442979698, -13294370614, -63061158139, 117641470464, 510599954172, -489650667338, -2036081594792, -1212101293459, 1647113176919, 36236489892218, 44762722808034, -261115883046865, -365562236265611, 930522055948828, 1628413597910449], [1, 6, -26, -169, 460, 1938, -7939, -6352, 93064, -220713, -588046, 5323182, 330459, -60022879, 69159966, 445746144, -1248237636, -1751031277, 14689255023, -19261344047, -151036753956, 593288117664, 1012571062206, -9666744685829, 585428276499, 103733757898122, -126052882536526, -520429708723683, 2413840483067464, -1812299731721072, -24915982882788019, 66905016134938278, 174684923448290860, -705954940631245019, -1194692976452876186, 3032682170995762626, 5559917313492231481], [1, 11, 33, 19, 484, 3635, 5989, -7910, 21400, 328794, 368440, -4176168, -17362703, -14359812, 51809026, -472892417, -4553078857, -4550813008, 32473776559, -59160569104, -769470326833, -1038944640149, 1479717591586, -5331697676916, -83806451104727, -262048348742856, 300547826845240, 3486695766846162, 2950171725568600, -14175988716832670, 139532231798538709, 1100951012462839655, 1905690170678455876, 972531967267724383, 21958748103044934753, 95154575113194717263, 112455406951957393129], [1, 32, 636, 9168, 107716, 1075374, 9488972, 75394932, 549525638, 3708760934, 23410558147, 138909905608, 779417417940, 4146983519552, 21000151016102, 101355659628906, 467303236083537, 2058962915267918, 8680483977882271, 35002369559554606, 135050635228142193, 497960355756815178, 1753953613015855142, 5888123579120544064, 18813241705328587860, 57000106333741978184, 163306375191898421827, 439814083598090368198, 1107840334348345211462, 2583927291625041115956, 5528486095650559695692, 10651125697558189095438, 18136985965672430468164, 26242694536241991190224, 30948518032924128353916, 26471688380362776453664, 14063084452067724991009], [1, -2, -33, -43, 907, 88, -15761, 6234, 526856, -253857, -10948627, -451388, 217872346, -111041419, -4764832328, 840233774, 92916967495, 27457863777, -1750903420621, 521699411763, 33543025265695, 5763163455866, -620957713817288, -274949546544481, 10249996463106826, -403482976523732, -185946696866894707, -81916530895083603, 3230189044320003656, 726200273971497246, -34884056439401763521, 3700662544678621192, 724699064005075897747, -652788462284616326857, -9518566647731498533473, -10960773715569604371878, 104127350297911241532841], [1, 6, 13, 198, 1726, 5684, 22852, 237892, 1222151, 1544926, 12854897, 112304298, 15330732, -1458953602, 1302687861, -5767597954, -381323450868, -1440526017186, -596591623839, -33132098395278, -201720105509172, -70174364306318, 364545473710101, -9390325803557486, 2269498540640748, 382376531637871206, 1006679649755771057, 2782647576663386738, 50629452106272338999, 226665818929659921884, 500792997520528375492, 2864942681246880604972, 20009235496153882170334, 52793776621949466630186, 79723935403852982436493, 846300237363977813556618, 3244150909895248285300369], [1, 10, -36, -578, 1016, 21063, -22778, -592636, 552441, 19185875, 16020789, -498406876, -555532642, 14897459703, 20839327384, -343807879538, -620995547124, 5002464129610, 14507145975869], [1, -8, -88, 1175, 2935, -95354, 83734, 5121343, -15576190, -214533311, 1072347695, 7530307288, -53974915502, -225699026103, 2357070708448, 5305263707573, -90443497568807, -63546541686843, 3016759237501459, -1969942792292133, -86916201163623527, 158049111112307243, 2176804297736605408, -6461571498855728553, -47902936189688962862, 207178438551994940968, 914595738086015048495, -5672179683717723611681, -12766685927387482728190, 130125525294064606408033, 65954155537750425687574, -2328310709646574591222214, 2221630449873037200142135, 27571682840417505967692425, -64013234713752303216906328, -180400934193301945429463288, 699053619999045038539170241], [1, -20, 240, -2269, 18773, -118409, 546048, -1505305, -5399881, 140220268, -1319930786, 9027617334, -54653437317, 266050494186, -662544800951, -2763918353713, 51970413618945, -511474898941224, 3657434064135413, -18924571260825288, 71147496244335705, -140000756370624589, -1241715626695127111, 18448994028662734002, -140225767466853004653, 857008659555029023422, -4636229766422796311906, 18223269983811962020636, -25965783389516066875969, -267820285652730656990965, 3594607776884939585119488, -28840788270201971290753373, 169183426709714290810061597, -756589581982668931783790617, 2961002859412119926945817840, -9129758816520703108082938340, 16890053810563300749953435929], [1, 68, 2732, 79524, 1854184, 36327930, 617718564, 9305428128, 126117160274, 1554895353522, 17591274618651, 183830881240028, 1783865333241028, 16139473243016116, 136587032944522846, 1083862880259016814, 8079512830930672073, 56646447878895865730, 373822238115621121535, 2322504363034730494930, 13581661068794459754713, 74700913570331697837694, 385962310800347821835806, 1869858056076996981535316, 8473546284801085377999748, 35801849792805998012108668, 140465012514862268074935771, 509044648616214199916880642, 1692827675521788632282917874, 5121047251387382357517548448, 13937886827170129140112107684, 33607080743682653075019235530, 70327766197177310482026091624, 123667638401387060825505105924, 174189672458832144474453975212, 177760178190052715517854203108, 107178930967531784356353269521], [1, 3, -45, -679, 3799, 35953, -41985, -2376026, 4654921, 80879753, -124963966, -2923869730, 12841489201, 78049687599, -1079976447261, -329598473085, 54748168547443, 44776368685846, -3261703262426839, 1925383853491378, 101229363644222107, -26205385799569095, -3692224557872354061, 11473963050565398357, 81175715329333933849, -794762209066399091110, -1460603862091321925566, 40649566313076713439779, 100599742861235429639329, -2208026086620851403622382, -1677705099023069270195985, 61776750060321200601841579, 280690472550382175804940751, -2157230778376811894439814453, -6147631157819044205804184045, 17623209319081260056638660929, 252599333573498060811820806649], [1, -19, 117, 59, -4860, 58233, -513325, 3488486, -28131034, 128623658, 1140129796, -17807857568, 124898306503, -813503687318, 3483040291028, -99284260941, -110224753873477, 2037787357356288, -20438556318603675, 95776005795745536, -243486481306510693, -10307989823677443, 16996125530363802068, -186573008862472521226, 1346305740023277984487, -9021872369860810213984, 27147957404171089930756, 143946655229748501461686, -1479667977296631126640666, 8624092811591565742843258, -59643993066901028925561325, 318010395886519920165283191, -1247401552872063609365033340, 711737552698401726084205237, 66336352581161204944695671157, -506310793632281675347121661053, 1252453015827223091648143056289], [1, 1, -138, -503, 10974, 37822, -525687, -1664660, 25250021, 95315685, -995167016, -10282486106, 12539948599, 691255727491, 356576543387, -20781271975832, 56568783466599, 358216320273226, -8202609795566856, 18985464974480978, 158901712757676591, -3093853427945940664, 2813560440640799147, 289080029747172398063, 277939949287333608271, -12078950973937375604722, -61958790323757938868776, 314519227090680691356105, 4415912299366082163024029, -15429793350188712463862020, -258248419602005602054763367, 984760896670288520904090806, 15143530279815095714274208206, -36787987400181395721417542971, -534925128916355324664906380298, 205442259656281392806087233013, 10888439761782913818722623349689], [1, -20, 626, -8564, 162947, -1696940, 24910254, -200626000, 2553583107, -15538477748, 196388922244, -873378871340, 13492483071388, -48723839974648, 997354137368668, -3769558106468820, 75923921551419957, -297399023618888648, 4995624294128214432, -17546542393514430232, 264291170920492870317, -774188074348459782780, 12085300127339740245148, -34833857138463399171752, 569120136093304538563708, -2173535624969833364187460, 28835871393727490507416324, -134609767759186812941797372, 1305179106933204373858412907, -6050055275113974421304534000, 44320259604490992818815797774, -178132284747536166266458604260, 1009193703232082316046894516667, -3129369412105123901163634027036, 13496045056829827903500427271666, -25439829340350154834074287828380, 75047496554032956760519149093721], [1, -24, 136, 1099, -14763, -26612, 1514090, -5581559, -104473494, 980262005, 936281331, -49133146846, 54221391570, 3713982961879, -19803841436352, -185670567383233, 2005909869108029, 1472327064254111, -96825153288065495, 89811950919500771, 7463990622950975909, -42143691055213609573, -274200839716941412032, 3136816271580027409579, 2793506392060769536770, -154412845261434291339766, 179491978175527854061011, 11463327095724511189112705, -74525426401554695438277894, -242875498469368208200852499, 4018923238494232226452242890, -4308889629144449133559545572, -145811678690013139038144966483, 662132976204009403778242932199, 4998230364502695189940221442696, -53804479806117248221121207294904, 136753052840548005895349735207881], [1, 14, -32, -682, 5796, 60182, 497107, 2601082, -46571706, -89197296, 2836640474, -2020680604, 17069214395, -670507002066, -16280748321974, 27121309354516, -177525510497970, -6590984722833208, -10231191562009335, -441595976429824936, -796912016625387330, 8157086365392295708, -328075329406645032854, -905268337908607471062, 1544053519067506122755, -12246762387313889255092, 1151868009340349288087834, -2426749301680501690863312, -84892666319270095984961994, 317670490356720019810283806, 4067686846525325716561285027, 32994310070947178781155996834, 212899977044150407604331370884, -1678442296593410753118067229326, -5276510680199813276664422492192, 154667719313357026672225884302378, 740195513856780056217081017732809], [1, 28, 134, -5058, -92230, -295310, 9519255, 138484508, 374996946, -9994700294, -127252903162, -320416895110, 6864434010851, 77716662201882, 144679893780110, -3606790368380910, -29546900140126224, 49009998494139752, 1914476521633020253, 3479709893083922392, -148945923606376295184, -1290909947537579879010, 3676559307854039464910, 140218683006387791838582, 879335945746981894826771, -2914230161804015633368010, -82174011578136365755996282, -458242023610141741359715114, 1220706390114900666197812146, 32006856912306117389384321668, 156207954477258744593679310455, -344061982119843293459742389410, -7629377262452451437002590094630, -29706675742571825383860957926958, 55877681497593583768693782862214, 828991274755343615911665972612548, 2102085018129621311776010144838961], [1, -43, 888, -13358, 184502, -2351213, 25832040, -252404694, 2354167993, -20333166464, 148975109506, -914346534322, 4423731769883, 1268511191925, -426612869319200, 6611832777671515, -74648373280790749, 776591982937366054, -7215964915516431616, 56691214754427721942, -397801181213333901421, 2572115351671439750755, -12115055076628147527200, 2629714517382288486525, 669462024705312397054187, -10101150549210337082947234, 120142480502139539928233986, -1197045772539021280138869632, 10117333174178184095506128457, -79186088070516048274825921638, 591606621218858222646358932840, -3930874295827872547880074023029, 22517549180361325103474150351318, -119010242720634249999735298959806, 577535557278214899085405077090168, -2041536164748104243501223577686979, 3465863721549107204083472585375569], [1, -9, -82, 1665, 6709, -152438, -404348, 22461545, -7157894, -1870541243, 8126850221, 158962023876, -597143483446, -11689720137657, 119565726907184, 729473769567002, -10369364506544525, -2028724400936535, 902286961401370031, -160269227673986265, -64715203885344380525, 359659017873545099078, 4657094747858696281904, -35969928152096632717143, -145158089971834524805366, 3052692238770337911532284, 12329316067070182252199981, -224187353324860676816830517, -67772916562178213818954694, 16801096634885385082457458055, -23893534302635380571478905468, -711615548933061222859648149482, 2474212917419283326920223142229, 48508808480063412193538761516335, -188732769569880350864711169431122, -1636451209319328408107434652018631, 14364405059580771582276370834385761], [1, -8, -234, 2464, 21170, -394800, 600379, 37896208, -446353614, -1105697210, 61509840758, -252712240386, -4304401003813, 47969845142298, 8400474449334, -4216300370766766, 35323954454545452, 147533091486972446, -4237337014813148067, 12245246593418713018, 243346722237363618828, -2410825740099616830842, 398672412968791208214, 188955169653927940417614, -1407282471316520612655997, -6857612240817371616476022, 138538136539352781624833078, -206699318686007227159375630, -6925641058882183248915514686, 48803927305854356773028175536, 64174515956129627212248051019, -3502614529583543189121919712400, 15588852624307344409924053560930, 150595532730389401037429761070048, -1187039949955204118079935397525354, -3368352678505365531645628649388184, 34946659039493167390823397237402409], [1, 6, -156, -694, -3404, -25746, 3035191, 13236946, -278777232, -1416799932, -11405650892, 7940957862, 4209032266621, 13140194419338, -249945404179812, -1607993216703362, -17507012849570242, 71140627461568478, 3552231900008687859, 6331515844079594542, -138673048781445886882, -1133585369986152405778, -15682134785892171838692, 73375626809001427224762, 2091810289561808529312781, 351239166585405961198998, -44899357623193154843906252, -496384928948529592002205788, -8692753571075206517890572432, 36734816118107667719574506594, 749663049987651560889984207511, -565952328787020276718646198274, -6659622998524062571023622218764, -120839681000833504336617229719206, -2417490102327914083875495125967516, 8275254581045552056343041008119574, 122749609618842355502421774953773681], [1, 81, 3185, 82471, 1613811, 25949863, 362302042, 4544285207, 52100768296, 547505111492, 5193536282736, 42479546681972, 263323717596387, 516943190734146, -18045629276362598, -399707182302942667, -5752758554039954081, -68393514389764220053, -713679846716078529478, -6634170895807129345141, -54127705234961927948129, -364801953193973592718891, -1597566585028931096232038, 4439167072373361330315522, 219341284991620276196591523, 3432274497311254838805678836, 40703995735930769263860445296, 416230390528348920648370173764, 3842036357123275923733182142504, 32505335845995079373468210842871, 251380504214748340191289956773722, 1746496078508531494067076532350151, 10535543657649806349277167129460659, 52224858819300157456375011251239303, 195639788627865396871139889791734385, 482619095525632157995775859998008497, 577951262543040979328274795306257089], [1, -39, 434, 966, -36241, 59286, -1656630, 25146290, 475185757, -7503849405, 22723154442, 6504064092, -2831460280241, 70992109077851, -520512122231737, 2631411805510787, -26325798732532727, -225834355311260806, 6786806820977667669, -22809269886437341406, -268549472870566348127, 2711146214629569356887, -54164700164795567146537, 746134201186168443103351, -3005652143102175984574841, 697323704540298028248492, 246059201605421947242468042, -8206849582689804299774113905, 52490070086247215137091592757, 280549197890665830365995565290, -1866732149667524998338965412630, 6747299822376799642771116211086, -416580949619446702108768854083641, 1121496010887418584971279545749966, 50889913189688515790508351561494834, -461878728235444847232286628573106339, 1196147475686664860781049986817531801], [1, 3, -555, -1989, 130341, 701213, -16445017, -155249442, 1280828755, 22520254467, -98604809392, -2351159201568, 10908652470453, 221971753397473, -700525340261737, -20111271880842799, -47391146532751967, 921145767473930680, 11968838362646706853, 94878014049814860040, -502772673565965617903, -21976129788537709222873, -78844744209283269940297, 2573260989406033920342439, 13025501534381153966957637, -289162925546168723029019616, -1249096224187142124097704112, 29383824121552357485541302261, 172132674297943939598941568995, -2149015360274703117601220925774, -23446662022120489142931817858297, 102975493081051176718054643906699, 1971524573273400545532698217472629, -3098797191618920750659019692337523, -89061207369982707245562021474346155, 49585428968152534304285882226257589, 1702433061239903677780481956434843889], [1, -124, 7254, -266896, 6940534, -135376194, 2029560825, -22946196128, 170202760268, -89370562588, -21899273546516, 431819837454616, -5383194759612495, 48317238309052100, -271251910835973500, -382065501096947662, 35739041401827919554, -600796160663818953902, 7066434258251432469877, -64285189191028628067514, 409176285009527850973746, -468046667660308054699466, -35555592242866982826573500, 677674262130053643314694700, -8078723765664952596246753255, 69340829616054892832662793288, -376270291559825506411089453716, -164304134109080605320473784116, 33481459087562670084169157882732, -482983457178757121641637269710304, 4570959819349389505979823375570825, -32623564425539168606642027613703158, 178964039396328591428239467107174566, -736374482090759757671089845103402928, 2141499583209346439023556643009520854, -3916930861596582375649924116273824468, 3379932275732534791891466777752413049], [1, -16, 17, 2300, -41513, 592601, -2350525, -62477265, 1170165288, -11001490403, 70901597525, 395041770537, -15776021922053, 182687619895402, -1444563205012733, 6632232806970009, 75744055034094015, -1903822076834794409, 22445306458064600228, -207516606374992590581, 899915117860070992215, 8588933819777563785261, -203911885467863371864013, 2810875482347313495653698, -26457968114105132162276573, 72215181089832607101986253, 1412758744644687860141345525, -23894063070124763935240293767, 277020679607982314566507504488, -1612179843372633681209376630885, -6611238886200238061064117172525, 181679887896076431009875496819029, -1387251140816587342876425796513793, 8377709657281296144800904468142700, 6749519997800974676659163469334097, -692421345656758813887857711206980304, 4717120417286669419611030657597553321], [1, -63, 1963, -42284, 769277, -13416133, 230083746, -3749624164, 56784667451, -808293066032, 11107062590959, -149323652357232, 1950294068765376, -24473653839415064, 294913786040415681, -3445992037100024799, 39395422338475460678, -440057502202628953031, 4763053522396806389749, -49726497748897071692503, 503040147839993157397382, -4972211572355514482402703, 48084914536408416130067841, -450911207997488268479609752, 4060418154569012128016865984, -35129964289616130210830066544, 295275060451832233292824073839, -2428146268542015404165191602736, 19275938037674249024161884279899, -143830376600840191379414384469668, 997303312015636602808168878056226, -6571236839623071409627128065162549, 42577578348175519580833112359127453, -264455568650551965943375464882282988, 1387316000910433888316942631840013483, -5031229042527447198638978398405020879, 9024267965168278308669913635234402529]], 'euler_factors_factorization': [[[[1, 2, 2, 1, -4, -15, -14, -22, -30, 4, 42, 72, 232, 163, 54, 107, -307, -860, -451, -1720, -1228, 856, 864, 5216, 14848, 9216, 10752, 2048, -30720, -45056, -57344, -122880, -65536, 32768, 131072, 262144, 262144], 1]], [[[1, -1, 1, -1, 1, -1, 1], 3]], [[[1, 7, 15, -1, -57, -198, -610, -727, 2083, 10771, 26002, 37370, -7745, -222133, -680461, -964364, 607712, 6539033, 18434481, 32695165, 15192800, -120545500, -425288125, -694165625, -121015625, 2919531250, 10157031250, 21037109375, 20341796875, -35498046875, -148925781250, -241699218750, -347900390625, -30517578125, 2288818359375, 5340576171875, 3814697265625], 1]], [[[1, 4, -11, -55, 66, 374, 119, -613, -7208, -12134, 88572, 142848, -536011, -791002, 184498, 3122533, 33800345, -9073301, -365501233, -63513107, 1656216905, 1071028819, 442979698, -13294370614, -63061158139, 117641470464, 510599954172, -489650667338, -2036081594792, -1212101293459, 1647113176919, 36236489892218, 44762722808034, -261115883046865, -365562236265611, 930522055948828, 1628413597910449], 1]], [[[1, 6, -26, -169, 460, 1938, -7939, -6352, 93064, -220713, -588046, 5323182, 330459, -60022879, 69159966, 445746144, -1248237636, -1751031277, 14689255023, -19261344047, -151036753956, 593288117664, 1012571062206, -9666744685829, 585428276499, 103733757898122, -126052882536526, -520429708723683, 2413840483067464, -1812299731721072, -24915982882788019, 66905016134938278, 174684923448290860, -705954940631245019, -1194692976452876186, 3032682170995762626, 5559917313492231481], 1]], [[[1, 11, 33, 19, 484, 3635, 5989, -7910, 21400, 328794, 368440, -4176168, -17362703, -14359812, 51809026, -472892417, -4553078857, -4550813008, 32473776559, -59160569104, -769470326833, -1038944640149, 1479717591586, -5331697676916, -83806451104727, -262048348742856, 300547826845240, 3486695766846162, 2950171725568600, -14175988716832670, 139532231798538709, 1100951012462839655, 1905690170678455876, 972531967267724383, 21958748103044934753, 95154575113194717263, 112455406951957393129], 1]], [[[1, 16, 190, 1544, 11104, 66663, 376150, 1868520, 8820919, 37225411, 149955623, 540002280, 1848024950, 5567760423, 15766092128, 37268406536, 77964347870, 111612119056, 118587876497], 2]], [[[1, -2, -33, -43, 907, 88, -15761, 6234, 526856, -253857, -10948627, -451388, 217872346, -111041419, -4764832328, 840233774, 92916967495, 27457863777, -1750903420621, 521699411763, 33543025265695, 5763163455866, -620957713817288, -274949546544481, 10249996463106826, -403482976523732, -185946696866894707, -81916530895083603, 3230189044320003656, 726200273971497246, -34884056439401763521, 3700662544678621192, 724699064005075897747, -652788462284616326857, -9518566647731498533473, -10960773715569604371878, 104127350297911241532841], 1]], [[[1, 6, 13, 198, 1726, 5684, 22852, 237892, 1222151, 1544926, 12854897, 112304298, 15330732, -1458953602, 1302687861, -5767597954, -381323450868, -1440526017186, -596591623839, -33132098395278, -201720105509172, -70174364306318, 364545473710101, -9390325803557486, 2269498540640748, 382376531637871206, 1006679649755771057, 2782647576663386738, 50629452106272338999, 226665818929659921884, 500792997520528375492, 2864942681246880604972, 20009235496153882170334, 52793776621949466630186, 79723935403852982436493, 846300237363977813556618, 3244150909895248285300369], 1]], [[[1, 10, -36, -578, 1016, 21063, -22778, -592636, 552441, 19185875, 16020789, -498406876, -555532642, 14897459703, 20839327384, -343807879538, -620995547124, 5002464129610, 14507145975869], 1]], [[[1, -8, -88, 1175, 2935, -95354, 83734, 5121343, -15576190, -214533311, 1072347695, 7530307288, -53974915502, -225699026103, 2357070708448, 5305263707573, -90443497568807, -63546541686843, 3016759237501459, -1969942792292133, -86916201163623527, 158049111112307243, 2176804297736605408, -6461571498855728553, -47902936189688962862, 207178438551994940968, 914595738086015048495, -5672179683717723611681, -12766685927387482728190, 130125525294064606408033, 65954155537750425687574, -2328310709646574591222214, 2221630449873037200142135, 27571682840417505967692425, -64013234713752303216906328, -180400934193301945429463288, 699053619999045038539170241], 1]], [[[1, -20, 240, -2269, 18773, -118409, 546048, -1505305, -5399881, 140220268, -1319930786, 9027617334, -54653437317, 266050494186, -662544800951, -2763918353713, 51970413618945, -511474898941224, 3657434064135413, -18924571260825288, 71147496244335705, -140000756370624589, -1241715626695127111, 18448994028662734002, -140225767466853004653, 857008659555029023422, -4636229766422796311906, 18223269983811962020636, -25965783389516066875969, -267820285652730656990965, 3594607776884939585119488, -28840788270201971290753373, 169183426709714290810061597, -756589581982668931783790617, 2961002859412119926945817840, -9129758816520703108082938340, 16890053810563300749953435929], 1]], [[[1, 34, 788, 12970, 175640, 1971845, 19301782, 164588816, 1253221727, 8463182695, 51382090807, 276673799696, 1330298117222, 5571962699045, 20348983143640, 61608852005770, 153466367818228, 271487457790114, 327381934393961], 2]], [[[1, 3, -45, -679, 3799, 35953, -41985, -2376026, 4654921, 80879753, -124963966, -2923869730, 12841489201, 78049687599, -1079976447261, -329598473085, 54748168547443, 44776368685846, -3261703262426839, 1925383853491378, 101229363644222107, -26205385799569095, -3692224557872354061, 11473963050565398357, 81175715329333933849, -794762209066399091110, -1460603862091321925566, 40649566313076713439779, 100599742861235429639329, -2208026086620851403622382, -1677705099023069270195985, 61776750060321200601841579, 280690472550382175804940751, -2157230778376811894439814453, -6147631157819044205804184045, 17623209319081260056638660929, 252599333573498060811820806649], 1]], [[[1, -19, 117, 59, -4860, 58233, -513325, 3488486, -28131034, 128623658, 1140129796, -17807857568, 124898306503, -813503687318, 3483040291028, -99284260941, -110224753873477, 2037787357356288, -20438556318603675, 95776005795745536, -243486481306510693, -10307989823677443, 16996125530363802068, -186573008862472521226, 1346305740023277984487, -9021872369860810213984, 27147957404171089930756, 143946655229748501461686, -1479667977296631126640666, 8624092811591565742843258, -59643993066901028925561325, 318010395886519920165283191, -1247401552872063609365033340, 711737552698401726084205237, 66336352581161204944695671157, -506310793632281675347121661053, 1252453015827223091648143056289], 1]], [[[1, 1, -138, -503, 10974, 37822, -525687, -1664660, 25250021, 95315685, -995167016, -10282486106, 12539948599, 691255727491, 356576543387, -20781271975832, 56568783466599, 358216320273226, -8202609795566856, 18985464974480978, 158901712757676591, -3093853427945940664, 2813560440640799147, 289080029747172398063, 277939949287333608271, -12078950973937375604722, -61958790323757938868776, 314519227090680691356105, 4415912299366082163024029, -15429793350188712463862020, -258248419602005602054763367, 984760896670288520904090806, 15143530279815095714274208206, -36787987400181395721417542971, -534925128916355324664906380298, 205442259656281392806087233013, 10888439761782913818722623349689], 1]], [[[1, -10, 263, -1652, 30369, -110304, 2000488, -1128580, 96017121, 142377228, 5665010139, -3928586980, 410858224952, -1336593387744, 21711536036331, -69682241574932, 654515340507397, -1468304376043210, 8662995818654939], 2]], [[[1, -24, 136, 1099, -14763, -26612, 1514090, -5581559, -104473494, 980262005, 936281331, -49133146846, 54221391570, 3713982961879, -19803841436352, -185670567383233, 2005909869108029, 1472327064254111, -96825153288065495, 89811950919500771, 7463990622950975909, -42143691055213609573, -274200839716941412032, 3136816271580027409579, 2793506392060769536770, -154412845261434291339766, 179491978175527854061011, 11463327095724511189112705, -74525426401554695438277894, -242875498469368208200852499, 4018923238494232226452242890, -4308889629144449133559545572, -145811678690013139038144966483, 662132976204009403778242932199, 4998230364502695189940221442696, -53804479806117248221121207294904, 136753052840548005895349735207881], 1]], [[[1, 14, -32, -682, 5796, 60182, 497107, 2601082, -46571706, -89197296, 2836640474, -2020680604, 17069214395, -670507002066, -16280748321974, 27121309354516, -177525510497970, -6590984722833208, -10231191562009335, -441595976429824936, -796912016625387330, 8157086365392295708, -328075329406645032854, -905268337908607471062, 1544053519067506122755, -12246762387313889255092, 1151868009340349288087834, -2426749301680501690863312, -84892666319270095984961994, 317670490356720019810283806, 4067686846525325716561285027, 32994310070947178781155996834, 212899977044150407604331370884, -1678442296593410753118067229326, -5276510680199813276664422492192, 154667719313357026672225884302378, 740195513856780056217081017732809], 1]], [[[1, 28, 134, -5058, -92230, -295310, 9519255, 138484508, 374996946, -9994700294, -127252903162, -320416895110, 6864434010851, 77716662201882, 144679893780110, -3606790368380910, -29546900140126224, 49009998494139752, 1914476521633020253, 3479709893083922392, -148945923606376295184, -1290909947537579879010, 3676559307854039464910, 140218683006387791838582, 879335945746981894826771, -2914230161804015633368010, -82174011578136365755996282, -458242023610141741359715114, 1220706390114900666197812146, 32006856912306117389384321668, 156207954477258744593679310455, -344061982119843293459742389410, -7629377262452451437002590094630, -29706675742571825383860957926958, 55877681497593583768693782862214, 828991274755343615911665972612548, 2102085018129621311776010144838961], 1]], [[[1, -43, 888, -13358, 184502, -2351213, 25832040, -252404694, 2354167993, -20333166464, 148975109506, -914346534322, 4423731769883, 1268511191925, -426612869319200, 6611832777671515, -74648373280790749, 776591982937366054, -7215964915516431616, 56691214754427721942, -397801181213333901421, 2572115351671439750755, -12115055076628147527200, 2629714517382288486525, 669462024705312397054187, -10101150549210337082947234, 120142480502139539928233986, -1197045772539021280138869632, 10117333174178184095506128457, -79186088070516048274825921638, 591606621218858222646358932840, -3930874295827872547880074023029, 22517549180361325103474150351318, -119010242720634249999735298959806, 577535557278214899085405077090168, -2041536164748104243501223577686979, 3465863721549107204083472585375569], 1]], [[[1, -9, -82, 1665, 6709, -152438, -404348, 22461545, -7157894, -1870541243, 8126850221, 158962023876, -597143483446, -11689720137657, 119565726907184, 729473769567002, -10369364506544525, -2028724400936535, 902286961401370031, -160269227673986265, -64715203885344380525, 359659017873545099078, 4657094747858696281904, -35969928152096632717143, -145158089971834524805366, 3052692238770337911532284, 12329316067070182252199981, -224187353324860676816830517, -67772916562178213818954694, 16801096634885385082457458055, -23893534302635380571478905468, -711615548933061222859648149482, 2474212917419283326920223142229, 48508808480063412193538761516335, -188732769569880350864711169431122, -1636451209319328408107434652018631, 14364405059580771582276370834385761], 1]], [[[1, -8, -234, 2464, 21170, -394800, 600379, 37896208, -446353614, -1105697210, 61509840758, -252712240386, -4304401003813, 47969845142298, 8400474449334, -4216300370766766, 35323954454545452, 147533091486972446, -4237337014813148067, 12245246593418713018, 243346722237363618828, -2410825740099616830842, 398672412968791208214, 188955169653927940417614, -1407282471316520612655997, -6857612240817371616476022, 138538136539352781624833078, -206699318686007227159375630, -6925641058882183248915514686, 48803927305854356773028175536, 64174515956129627212248051019, -3502614529583543189121919712400, 15588852624307344409924053560930, 150595532730389401037429761070048, -1187039949955204118079935397525354, -3368352678505365531645628649388184, 34946659039493167390823397237402409], 1]], [[[1, 6, -156, -694, -3404, -25746, 3035191, 13236946, -278777232, -1416799932, -11405650892, 7940957862, 4209032266621, 13140194419338, -249945404179812, -1607993216703362, -17507012849570242, 71140627461568478, 3552231900008687859, 6331515844079594542, -138673048781445886882, -1133585369986152405778, -15682134785892171838692, 73375626809001427224762, 2091810289561808529312781, 351239166585405961198998, -44899357623193154843906252, -496384928948529592002205788, -8692753571075206517890572432, 36734816118107667719574506594, 749663049987651560889984207511, -565952328787020276718646198274, -6659622998524062571023622218764, -120839681000833504336617229719206, -2417490102327914083875495125967516, 8275254581045552056343041008119574, 122749609618842355502421774953773681], 1]], [[[1, 81, 3185, 82471, 1613811, 25949863, 362302042, 4544285207, 52100768296, 547505111492, 5193536282736, 42479546681972, 263323717596387, 516943190734146, -18045629276362598, -399707182302942667, -5752758554039954081, -68393514389764220053, -713679846716078529478, -6634170895807129345141, -54127705234961927948129, -364801953193973592718891, -1597566585028931096232038, 4439167072373361330315522, 219341284991620276196591523, 3432274497311254838805678836, 40703995735930769263860445296, 416230390528348920648370173764, 3842036357123275923733182142504, 32505335845995079373468210842871, 251380504214748340191289956773722, 1746496078508531494067076532350151, 10535543657649806349277167129460659, 52224858819300157456375011251239303, 195639788627865396871139889791734385, 482619095525632157995775859998008497, 577951262543040979328274795306257089], 1]], [[[1, -39, 434, 966, -36241, 59286, -1656630, 25146290, 475185757, -7503849405, 22723154442, 6504064092, -2831460280241, 70992109077851, -520512122231737, 2631411805510787, -26325798732532727, -225834355311260806, 6786806820977667669, -22809269886437341406, -268549472870566348127, 2711146214629569356887, -54164700164795567146537, 746134201186168443103351, -3005652143102175984574841, 697323704540298028248492, 246059201605421947242468042, -8206849582689804299774113905, 52490070086247215137091592757, 280549197890665830365995565290, -1866732149667524998338965412630, 6747299822376799642771116211086, -416580949619446702108768854083641, 1121496010887418584971279545749966, 50889913189688515790508351561494834, -461878728235444847232286628573106339, 1196147475686664860781049986817531801], 1]], [[[1, 3, -555, -1989, 130341, 701213, -16445017, -155249442, 1280828755, 22520254467, -98604809392, -2351159201568, 10908652470453, 221971753397473, -700525340261737, -20111271880842799, -47391146532751967, 921145767473930680, 11968838362646706853, 94878014049814860040, -502772673565965617903, -21976129788537709222873, -78844744209283269940297, 2573260989406033920342439, 13025501534381153966957637, -289162925546168723029019616, -1249096224187142124097704112, 29383824121552357485541302261, 172132674297943939598941568995, -2149015360274703117601220925774, -23446662022120489142931817858297, 102975493081051176718054643906699, 1971524573273400545532698217472629, -3098797191618920750659019692337523, -89061207369982707245562021474346155, 49585428968152534304285882226257589, 1702433061239903677780481956434843889], 1]], [[[1, -124, 7254, -266896, 6940534, -135376194, 2029560825, -22946196128, 170202760268, -89370562588, -21899273546516, 431819837454616, -5383194759612495, 48317238309052100, -271251910835973500, -382065501096947662, 35739041401827919554, -600796160663818953902, 7066434258251432469877, -64285189191028628067514, 409176285009527850973746, -468046667660308054699466, -35555592242866982826573500, 677674262130053643314694700, -8078723765664952596246753255, 69340829616054892832662793288, -376270291559825506411089453716, -164304134109080605320473784116, 33481459087562670084169157882732, -482983457178757121641637269710304, 4570959819349389505979823375570825, -32623564425539168606642027613703158, 178964039396328591428239467107174566, -736374482090759757671089845103402928, 2141499583209346439023556643009520854, -3916930861596582375649924116273824468, 3379932275732534791891466777752413049], 1]], [[[1, -16, 17, 2300, -41513, 592601, -2350525, -62477265, 1170165288, -11001490403, 70901597525, 395041770537, -15776021922053, 182687619895402, -1444563205012733, 6632232806970009, 75744055034094015, -1903822076834794409, 22445306458064600228, -207516606374992590581, 899915117860070992215, 8588933819777563785261, -203911885467863371864013, 2810875482347313495653698, -26457968114105132162276573, 72215181089832607101986253, 1412758744644687860141345525, -23894063070124763935240293767, 277020679607982314566507504488, -1612179843372633681209376630885, -6611238886200238061064117172525, 181679887896076431009875496819029, -1387251140816587342876425796513793, 8377709657281296144800904468142700, 6749519997800974676659163469334097, -692421345656758813887857711206980304, 4717120417286669419611030657597553321], 1]], [[[1, -63, 1963, -42284, 769277, -13416133, 230083746, -3749624164, 56784667451, -808293066032, 11107062590959, -149323652357232, 1950294068765376, -24473653839415064, 294913786040415681, -3445992037100024799, 39395422338475460678, -440057502202628953031, 4763053522396806389749, -49726497748897071692503, 503040147839993157397382, -4972211572355514482402703, 48084914536408416130067841, -450911207997488268479609752, 4060418154569012128016865984, -35129964289616130210830066544, 295275060451832233292824073839, -2428146268542015404165191602736, 19275938037674249024161884279899, -143830376600840191379414384469668, 997303312015636602808168878056226, -6571236839623071409627128065162549, 42577578348175519580833112359127453, -264455568650551965943375464882282988, 1387316000910433888316942631840013483, -5031229042527447198638978398405020879, 9024267965168278308669913635234402529], 1]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 0, 'label': '36-87e18-1.1-c1e18-0-0', '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}, {'__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, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/87/2/g/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.00694444444444', 'prec': 54}, 'plot_values': [0.03191987091431375, 0.03202131700526266, 0.03209501595143393, 0.0321421867421364, 0.03216404945446492, 0.03216181288784713, 0.03213666263742617, 0.032089749573489965, 0.032022178679361205, 0.03193499818563672, 0.0318291889242617, 0.031705653811471626, 0.03156520735391854, 0.03140856505707129, 0.031236332598954565, 0.03104899461514186, 0.030846902922265, 0.030630263986722514, 0.03039912542227066, 0.030153032433624067, 0.029890049380830064, 0.029607776183210862, 0.02930367558343266, 0.028975065896899965, 0.028619113657578587, 0.028232826198483812, 0.02781304420997956, 0.027356434324515712, 0.02685948178249887, 0.026318483240661047, 0.025729539791577778, 0.025088550270903166, 0.02439120493744683, 0.023632979620424432, 0.02280913043807214, 0.021914689202328932, 0.020944459635449133, 0.0198930602866713, 0.018755038200205573, 0.017524686955289998, 0.01619598282303309, 0.014762571325885827, 0.013217753652229483, 0.011554472988606294, 0.009765300842549526, 0.007842423440617544, 0.005777628299222265, 0.0035622910802948922, 0.001187362859893822, -0.001356642044316883, -0.004079657521037877, -0.006992076201213129, -0.010104758870112135, -0.013429042517233276, -0.016976746756224605, -0.020760152223672432, -0.024791891097916335, -0.029084959652946104, -0.033652717376938444, -0.038508862599285903, -0.04366740247962275, -0.04914261672273988, -0.05494901433109261, -0.06110128265149306, -0.06761422791450697, -0.07450270640403232, -0.08178154533052985, -0.08946545241443196, -0.09756891311643852, -0.10610607437879697, -0.1150906136663866, -0.12453559201863885, -0.13445328974322823, -0.1448550183061295, -0.15575090704414266, -0.16714970429421833, -0.17905854050179537, -0.19148266091507074, -0.2044251321473489, -0.21788652078420648, -0.23186454213922356, -0.24635367719168666, -0.2613447556727736, -0.27682450320424906, -0.2927750503366131, -0.3091734012831209, -0.32599086010328393, -0.34319241205574336, -0.3607360578171609, -0.37857209825255494, -0.39664236742493236, -0.414879352257339, -0.4332051384131612, -0.45153066249141677, -0.4697547948229728, -0.48776330557774955, -0.5054277717397094, -0.5226044239330466, -0.5391329323326667, -0.5548351311776424, -0.5695136817301405, -0.582950673886632, -0.5949061670553148, -0.6051166713657523, -0.6132935707758768, -0.6191214901896627, -0.6222566092977768, -0.6223249265049189, -0.6189204770127505, -0.6116036288239429, -0.5998997122776009, -0.5832970427430137, -0.5612450102823107, -0.5331522571401428, -0.498384863264149, -0.4562645511447945, -0.4060669223875528, -0.34701973959196375, -0.2783012683059957, -0.1990386950444382, -0.10830663860003711, -0.005125773128006776, 0.11153841726032493, 0.2427767314104577, 0.38973716932892344, 0.553625652261847, 0.7357065200719581, 0.9373020311494534, 1.1597896152182192, 1.404602870384198, 1.673231331424922, 1.9672192229561014, 2.2881638085095792, 2.637713305987174, 3.0175643399699266, 3.429458901605696, 3.8751807872924244, 4.3565514881417, 4.875425503270263, 5.433685051347241, 6.033234156544202, 6.675992087113452, 7.3638861272773255, 8.098843665965333, 8.88278358920285, 9.717604594262538, 10.605167075443127, 11.547287709183234, 12.54572994702272, 13.602191683732293, 14.718292260094744, 15.895558826444155, 17.135412100085123, 18.43915155711145, 19.807940106893692, 21.242788305570915, 22.74453817322193, 24.313846687955603, 25.951169038892225, 27.656741728843976, 29.430565626373447, 31.27238907573396, 33.18169118189209, 35.15766113985752, 37.19916869174978, 39.30476020484633, 41.47264829532344, 43.70069834070552, 45.98641609190294, 48.326936551408785, 50.719014287308276, 53.15901535461102, 55.64291099593357, 58.16627329260863, 60.724272934772706, 63.31167927477165, 65.92286282222719, 68.55180033123715, 71.19208262035716, 73.8369252541727, 76.47918220136322, 79.11136056414638, 81.72563577642623, 84.3138833567353, 86.86770827946818, 89.37847529593623, 91.83734247780299, 94.23529792878844, 96.56319958039293, 98.81181795594986, 100.97188175479658, 103.03412607500911, 104.98934305926088, 106.82843471424684, 108.54246762010155, 110.12272921268918, 111.56078528894379, 112.84853835398299, 113.97828639893349, 114.94279080770025, 115.73536524608471, 116.3499109186156, 116.78096349482395, 117.02374617314597, 117.07422003031593, 116.92913112367478, 116.58605381650543, 116.04342980469669, 115.30060233700645, 114.35784514110324, 113.21638559357933, 111.87842170429504, 110.34713252375903, 108.62668162668072, 106.72221337521965, 104.63984172155469, 102.38663137090604, 99.97059270473436, 97.40071091646925, 94.68683637876192, 91.83961063160798, 88.87040661611782, 85.79126184135387, 82.61480489135985, 79.3541757619321, 76.02294059706892, 72.63500147232722, 69.204501945423, 65.74572916225279, 62.273013368005024, 58.800625727131845, 55.3426754016524, 51.913006873614385, 48.52509852368214, 45.191963492966686, 41.92607179240295, 38.73930498705938, 35.64280280322949, 32.646863514687375, 29.760871859232427, 26.993235513878993, 24.351330888182517, 21.841458900516677, 19.468811296478314, 17.23744795306007, 15.150285488033997, 13.209097362547963, 11.414525527827347, 9.766103525816508, 8.262290810431347, 6.900517912773265, 5.677241932197503, 4.588011697607129, 3.627545770214379, 2.7898214619376684, 2.0681448421754474, 1.455243362030769, 0.9433683085642333, 0.5244003911530228, 0.18995705301290453, -0.06849992578429873, -0.2595579732712016, -0.39174984237017846, -0.47345368610992306, -0.5127984191912842, -0.517575614206421, -0.4951590811574553, -0.4524331604576211, -0.39573062391518965, -0.3307809272156979, -0.2626693933580924, -0.19580801911446657, -0.13391813092385532, -0.08002246744628541, -0.036449638063299074, -0.004850331267696576, 0.013775627998612958, 0.019042134511270556, 0.011130501936590775, -0.009264915276839215, -0.04099796711064768, -0.08253750197798161, -0.1320383075913692, -0.18741473947066123, -0.24641554815890737, -0.3066984148898664, -0.3659027327505853, -0.42171922599025363, -0.47195508316102197, -0.5145933099579303, -0.5478454573221918, -0.5701974292313055, -0.5804461974631081, -0.5777271818451932, -0.5615320784068333, -0.5317169910050888, -0.4885009407907508, -0.4324550434549397, -0.36448285177960893, -0.2857925559612962, -0.19786191207988724, -0.10239692587511504, -0.001285451042518418, 0.10345303453488992, 0.20972013733707154, 0.3153923625469839, 0.41837464671799335, 0.5166521421777674, 0.6083391604240881, 0.6917248962911753, 0.7653132399867709, 0.8278560907122396, 0.8783795626171342, 0.9162025015985403, 0.9409469438633451, 0.9525403681973726, 0.9512098177082787, 0.9374681874822087, 0.9120931861973133, 0.8760996765333482, 0.8307062758061327, 0.7772972497260173, 0.7173808542452726, 0.6525453695888671, 0.5844141240887863, 0.5146012369661727, 0.4446695700583541, 0.3760887601231327, 0.31019831975097234, 0.24817626532961634, 0.19101366638924636, 0.1394957740797067, 0.09419017324271967, 0.0554421755260168, 0.023377437188762788, -0.0020884480723754417, -0.02123385642932728, -0.03450922691718755, -0.0425102141003475, -0.04594693450766061, -0.04561046717177769, -0.042337856368011094, -0.03697691046281112, -0.03035212018353109, -0.023232968375283877, -0.016305521814140248, -0.01014860785942719, -0.005215487494722119, -0.0018216641374417509, -0.00013925284278780412, -0.0001980786118196552, -0.0018934058635645874, -0.004999933103521758, -0.009191427109798115, -0.014065129280661358, -0.01916985255615955, -0.02403650931916957, -0.02820967671722845, -0.03127872248236355, -0.03290698657969808, -0.03285754512895811, -0.031014191624780703, -0.027396444842654945, -0.022167381747037248, -0.015633592624675778, -0.00823683323246648, -0.0005372557914091873, 0.006811524791832092, 0.013094898053055174, 0.017576256236700897, 0.019541169397630096, 0.018345064165031472, 0.013462461432024292, 0.004535617113810126, -0.008579728895581099, -0.02577384763703776, -0.046650080029485286, -0.07050165448822206, -0.0963002373747552, -0.12269790253297971, -0.1480439952817227, -0.17041754502875112, -0.18767523216793497, -0.1975145888157639, -0.1975514011461987, -0.18540963248136344, -0.1588215601751204, -0.11573523183627771, -0.0544258215646129, 0.02639297210434494, 0.12746167621166293, 0.24887633544694301, 0.39000280180786673, 0.5494083836799929, 0.7248149598788829, 0.9130772430126175, 1.1101892937193782, 1.3113216298031678, 1.5108913241750785, 1.702665898775808, 1.8798981000228445, 2.0354904909472173, 2.1621870783955925, 2.252787844681967, 2.300380973273136, 2.2985865798241267, 2.2418049226456613, 2.1254614075723968, 1.9462402544918918, 1.7022984846345057, 1.3934519408820567, 1.0213253821324646, 0.5894593030987699, 0.10336701973406928, -0.42946328476361595, -0.9996245619012731, -1.5959088559060541, -2.2054953411067517, -2.814193999974287, -3.4067441334670643, -3.967163506896385, -4.47914065004524, -4.9264610772575885, -5.293456641446827, -5.5654659455852915, -5.729292760676406, -5.773648787163491, -5.689566884219944, -5.470771104088605, -5.113990519591131, -4.619204921405816, -3.9898119727115637, -3.2327073128734907, -2.3582759173849106, -1.3802914680797977, -0.31568446982447684, 0.8157729970569603, 1.99186704075382, 3.188423104845685, 4.379857379474005, 5.539784880445092, 6.6416684665694365, 7.659491356012604, 8.568434484738635, 9.34553937830976, 9.970337120159085, 10.42542451473501, 10.696969663122475, 10.775130872488086, 10.654375069736151, 10.333684625733035, 9.816656177381995, 9.111497237050072, 8.230822460954506, 7.191347334915976, 6.013478995770037, 4.72080410925814, 3.3394882430780832, 1.8976040044130573, 0.42440751318902453, -1.050415527298657, -2.4975118850409794, -3.8886084017941323, -5.197222998283815, -6.399318093719845, -7.4738772989121145, -8.403388723341111, -9.174221270582523, -9.776883782951717, -10.206171978114558, -10.461219907766356, -10.545360406153534, -10.465871984830695, -10.233625785974098, -9.862637804633646, -9.36954326576006, -8.773012307585836, -8.093127679098911, -7.35074595554065, -6.566863790308609, -5.762009962087655, -4.955682479497894, -4.165847836988335, -3.4085167655374855, -2.6974076023470515, -2.04370484514057, -1.455916701412897, -0.9398367471594447, -0.49860353699271415, -0.13281417040197374, 0.15925971101735678, 0.38138289927154323, 0.5390171481899096, 0.6389478938350746, 0.6888943049450572, 0.6971195524477752, 0.6720572225648377, 0.6219681800645385, 0.5546400072291797, 0.4771385143907543, 0.39561787244644403, 0.31519280211437817, 0.23987312016447399, 0.17255793956523557, 0.11508409026490686, 0.06832133084487382, 0.03230447722321986, 0.006389312213114235, -0.010574926259555507, -0.020069203144504756, -0.023735895810721344, -0.023227141778614305, -0.020078081342437555, -0.015610532495851547, -0.010870166932528024, -0.006597692254970384, -0.003232047461957604, -0.0009413444627387027, 0.00032461517681114336, 0.0007678242767844048, 0.0006699373768623327, 0.0003230447220906098, -2.8676924809328633e-05, -0.00022969926887163832, -0.0002313876063169062, -8.528113851282024e-05, 8.832277420496591e-05, 0.00015316976374804407, 2.48604737820231e-05, -0.0002555639272494103, -0.00045396001079595164, -9.489188821499783e-05, 0.0015524832671910756, 0.005439739102338127, 0.012641941643061054, 0.024186129311036315, 0.04079695025347509, 0.06255509223484354, 0.08846924326821211, 0.11596813641881723, 0.14032550860974363, 0.15403735812806085, 0.14617772337327134, 0.10176374066119928, 0.0011658743614696768, -0.18039706299570446, -0.47323680410444646, -0.9134070950036005, -1.5427084304113148, -2.4084509345817504, -3.5629466191439114, -5.062710679373133, -6.967361800277026, -9.338223332063778, -12.23664026117418, -15.722040661783224, -19.849784207106403, -24.66885374414826, -30.219458258676532, -36.53064064052843, -43.61802003394413, -51.48165214558681, -60.10415738492446, -69.44921645623832, -79.46050987548912, -90.0611770186113, -101.15385686194244, -112.62135575491934, -124.32796784731103, -136.12145180477984, -147.83564394408705, -159.29366376352613, -170.31164396834964, -180.7028944644143, -190.2823893820291, -198.87144891754585, -206.30247447850783, -212.42376849461382, -217.1045119021757, -220.23825353429467, -221.7461093711352, -221.57944575447692, -219.721773337665, -216.18977008148474, -211.03337965821393, -204.3349624173341, -196.20750846834716, -186.79195522424328, -176.25368365199327, -164.7782972276019, -152.56681398478486, -139.8304239806652, -126.78498104062089, -113.64540805130221, -100.62019884707709, -87.9062983354116, -75.6845327618462, -64.11497032424222, -53.333392358581605, -43.44874183798806, -34.541488720159506, -26.662944852941724, -19.835525730519475, -14.053921485041391, -9.287106518033875, -5.481087456724815, -2.5622638547472194, -0.44125624310766587, 0.9829574634635528, 1.8187630980565754, 2.1776548034229135, 2.1701621205252066, 1.9021055090899102, 1.4713041225558856, 0.9648317673130009, 0.45692586909233196, 0.007584086916557681, -0.33813950133484866, -0.5501553872193862, -0.6127242063961711, -0.5232794426887617, -0.29078056191832613, 0.06629454616495396, 0.5221990824428011, 1.0462861936363639, 1.6053766116813581, 2.166012197940194, 2.6964952219728886, 3.1686301298891424, 3.559104698491286, 3.8504696971788404, 4.031709071700173, 4.0984172352483235, 4.05252409132591, 3.9016873136445787, 3.6584136682175026, 3.3389740672117476, 2.9621916678037667, 2.548183629089162, 2.1171338406021616, 1.6881664542370864, 1.2783790217364677, 0.9020802722688668, 0.570261993477991, 0.2903181071856737, 0.06600786859244716, -0.1023548740824418, -0.21751738867040663, -0.2847500039185936, -0.31120350129036634, -0.3052148467471053, -0.2756031675472176, -0.23101220159885735, -0.17934309419856181, -0.12730896476744857, -0.08013205678559833, -0.041392266862477704, -0.013023883595160895, 0.004553700819963322, 0.012194954602140587, 0.011707626886484595, 0.005487812802220945, -0.003852708988552638, -0.013831789758449366, -0.022384146651734764, -0.02806653951833272, -0.03016548094036699, -0.02870183728697235, -0.024336762290707616, -0.018191943518225978, -0.011606840851421505, -0.005861955364348307, -0.0019005425082905425, -8.193630639381761e-05, 2.6540058949470264e-06, -0.0003737801424890681, 0.0009159859229582424, 0.00672917540572782, 0.020417174657233993, 0.045491978007777815, 0.08521939734494992, 0.14217258974848554, 0.2177861466211124, 0.31195460358946686, 0.42271928405903414, 0.5460839144151926, 0.6759933536460139, 0.804495695655579, 0.9220945373179148, 1.0182837333671595, 1.0822402555722939, 1.1036352361143145, 1.0735096328239964, 0.9851504684761804, 0.8348973363162033, 0.622807649681402, 0.35311343957246866, 0.03441248068230797, -0.3204481548326959, -0.6948180899417853, -1.0690177582368545, -1.4214138363990423, -1.7297435733032982, -1.9726147659364752, -2.131094162559108, -2.190244857721256, -2.1405016397659073, -1.9787705031142808, -1.709142692993248, -1.3431344025600718, -0.8993909199023884, -0.40282881493683165, 0.11677026184186678, 0.6266578920085604, 1.0934104870160006, 1.485476072756898, 1.7758053351880585, 1.9443726144360058, 1.9803811877191213, 1.883949861437332, 1.6670957821117742, 1.3538601742209135, 0.9794719978103096, 0.588518824389142, 0.23214213107793688, -0.03563526947232041, -0.1622679786229104, -0.10148248277376537, 0.1818031647732766, 0.7067893263955638, 1.4727132774540974, 2.4557548707758143, 3.607281121938718, 4.853726881638047, 6.098327251124433, 7.224811601707083, 8.103043501687091, 8.596451832449393, 8.570953735357959, 7.904963762333185, 6.499948141336988, 4.290531743615702, 1.2536977463964711, -2.5836950412500377, -7.139851083915511, -12.276101787346763, -17.798638004288318, -23.46428112323788, -28.990443656202537, -34.069175549997304, -38.384913569810365, -41.63526236410406, -43.55385358613378, -43.934071375749326, -42.652216635105425, -39.6885262813134, -35.14438276681082, -29.25411529263378, -22.38977846936129, -15.057064507674887, -7.882118852621732, -1.5885700723260099, 3.0353992012532105, 5.179498474293909, 4.0622817157608635, -1.0109806695853332, -10.585648623775745, -24.992913760408115, -44.28590310381643, -68.18003104913406, -96.0011038114496, -126.64467940010255, -158.55001151791035, -189.69155171765863, -217.59045316342707, -239.3485758606823, -251.7075869392156, -251.126579766915, -233.88058086927327, -196.1780573217099, -134.2936358800077, -44.7118422837986, 75.72311894424308, 229.65714035380805, 419.0815460105453, 645.2001544068809, 908.3141463880881, 1207.7304517188713, 1541.6987381451163, 1907.3812053832298, 2300.858280854446, 2717.172023109002, 3150.407611801516, 3593.8174639066942, 4039.9987148744494, 4481.073219612728, 4908.891616691551, 5315.257327285359, 5692.158955924735, 6032.002907195359, 6327.837855753155, 6573.562872808434, 6764.111518661456, 6895.605040687579, 6965.46893735666, 6972.508515967562, 6916.940627834282, 6800.380443765578, 6625.783862938869, 6397.347855091593, 6120.372645494331, 5801.106701769558, 5446.591489876867, 5064.387400530338, 4662.326205839336, 4248.279762603594, 3829.9368012295336, 3414.595632703206, 3008.979710752944, 2619.08182322081, 2250.041314960584, 1906.057231881273, 1590.3386945874095, 1305.0922342847716, 1051.5443247875223, 829.9959884204328, 639.9051973914582, 479.9918814610895, 348.3597197608127, 242.62998382296928, 160.0799105321627, 97.77053785289796, 52.675996148117754, 21.802722738826773, 2.2924188910636905, -8.494019020016067, -12.913208940766559, -12.99710594511714, -10.431338985554566, -6.5525109320658945, -2.362122679856211, 1.445813449702392, 4.446790443841853, 6.440941560013398, 7.404741623628076, 7.442492864069337, 6.740422078809879, 5.525711507598868, 4.032193840482375, 2.473642994975876, 1.025175545243918, -0.18736389876102105, -1.090736446474991, -1.6614871865530483, -1.9183936640143127, -1.9117732542586814, -1.7112644758512887, -1.3935970973905276, -1.031657295198883, -0.6858616500344459, -0.3985063567103715, -0.1913867409011739, -0.06661799274575174, -0.010259601080426888, 0.0019222622694455484, -0.0025903636002979004, -0.0004400249746613956, 0.020862807751466993, 0.0576924041231544, 0.08725721104910181, 0.06721489695621945, -0.06185251690802631, -0.3712009750858706, -0.9363061434066788, -1.8274991909836202, -3.099690515406689, -4.782144388367571, -6.869314976141063, -9.313715246768938, -12.021666881814832, -14.852580063612022, -17.622151480767037, -20.109566541794077, -22.068513012814, -23.241495977729894, -23.376222064988696, -22.24330651839858, -19.65408501856065, -15.477213204219355, -9.652799714950287, -2.2029357394820317, 6.762312868596146, 17.04410849235896, 28.359565681752954, 40.351957575718934, 52.60599366063923, 64.66740286413632, 76.06574390000483, 86.33911784582912, 95.05929435647006, 101.85569541955813, 106.43691400380894, 108.60851360749484, 108.28425028354219, 105.49163203109188, 100.37124459695065, 93.16961649272682, 84.22600009742371, 73.95382813458744, 62.81794051717799, 51.30894359297534, 39.916244742562256, 29.10138826561841, 19.2732981371925, 10.766910881102078, 3.8264655091594806, -1.4055786510741897, -4.893382056279618, -6.706102731494663, -7.010059224060714, -6.055211395482136, -4.15639662459833, -1.6713440509903945, 1.0232279892507568, 3.5559942492117074, 5.584368326419629, 6.8153939456299035, 7.022949598288364, 6.060293999034749, 3.8672952212841256, 0.472036222115249, -4.013149355550423, -9.400808086105652, -15.441946388575301, -21.8430795428184, -28.285578573034456, -34.4460311931191, -40.01651173766201, -44.72382272171705, -48.34478753951874, -50.71804566199421, -51.75177155782607, -51.42684073394401, -49.795434420521495, -46.97536428469209, -43.140658199072966, -38.5091618974139, -33.328067313727544, -27.8583687812158, -22.35926993441658, -17.073518627907433, -12.214540340593178, -7.956082069436252, -4.424881343791012, -1.6966534809785276, 0.20455146472457755, 1.3038072285180429, 1.6697690059775967, 1.4067430948285138, 0.6451387704472474, -0.4689642134441917, -1.7843929988445084, -3.154906401315368, -4.448055655742573, -5.552391088825772, -6.38267088732844, -6.882887551963422, -7.027088456247671, -6.818117998786354, -6.284540350922471, -5.476105941906986, -4.458196183211997, -3.3057167540863426, -2.0969191398106966, -0.9075479040411478, 0.1943589472738692, 1.152522193323256, 1.925208934345859, 2.4867006802439713, 2.827468579169167, 2.953173951547721, 2.882686738007621, 2.645367737409259, 2.277890484878168, 1.8208851114146907, 1.3156711424165624, 0.8013120698159814, 0.31217598032202926, -0.12387140295605135, -0.4865768524234098, -0.7637092806822758, -0.950823203205992, -1.0504829283612664, -1.0710386937862995, -1.025113091057468, -0.9279734457822083, -0.7959372380667136, -0.6449360591403415, -0.4893341071447108, -0.34106308471417085, -0.20910003430969995, -0.09928134396461417, -0.014417579188974185, 0.04534804643238205, 0.08200865956266162, 0.09906688924305826, 0.10088667627656887, 0.09208921844352212, 0.07704444311114872, 0.05949258785618837, 0.042311268649119466, 0.027423022557224907, 0.015832581280481848, 0.007764182262037576, 0.0028628538934386523, 0.00042252111093560324, -0.00039343371746916416, -0.0003670764847461711, -9.5275370597158e-05, 7.763103616166218e-05, 6.495032339104084e-05, -9.738065734913902e-06, 0.000103635809633857, 0.0006810391369068757, 0.0019269938672837742, 0.0038981591256871504, 0.006460793350400808, 0.009288804216322446, 0.011902338516583996, 0.013740051280486264, 0.014252790464020719, 0.013003187099326257, 0.00975463458015799, 0.0045346247835349645, -0.002338895995165322, -0.010274115242043155, -0.018464551162430322, -0.02598416842562121, -0.031906193034376924, -0.035429479137595955, -0.03599453109118885, -0.03337201098744565, -0.027709743419388606, -0.019529518429336833, -0.009671752489494975, 0.0008066138693983507, 0.01076868480399648, 0.019150099433981375, 0.025106042793128985, 0.02813071383727253, 0.028129773756715565, 0.025431971639162547, 0.0207342979219673, 0.01498481565500932, 0.009217617360514211, 0.004363839617443297, 0.0010700064688060008, -0.00044103066543791074, -0.00043154572381312297, 0.00039722235064680193, 0.0010791107546431178, 0.0006913224022582256, -0.0012136154502026394, -0.00408121513101747, -0.005780449281051168, -0.0020424329416468, 0.014016085871527372, 0.05220894506020932, 0.12536466489360015, 0.24911827738493314, 0.4413702992763796, 0.7213986509834093, 1.1086407464825663, 1.6211969544452358, 2.274140188332408, 3.0777463009818518, 4.035783047905421, 5.144008787363099, 6.389033575754596, 7.74768355000977, 9.186984200539476, 10.66488750220973, 12.131866473594727, 13.532953136650425, 14.810392886577601, 15.906782242401844, 16.76846521697355, 17.348963912542686, 17.61219929712197, 17.535256490463542, 17.11046658575332, 16.346613827162518, 15.26913103571941, 13.919214181895445, 12.351864268909308, 10.63294553113695, 8.835427089872468, 7.035044262854509, 5.305669730356236, 3.714728184415638, 2.3189582925693206, 1.1608016565346257, 0.26587054782852637, -0.3583825966486984, -0.7226996711745879, -0.8547347163518207, -0.796533847654921, -0.6009519020033011, -0.32726495289604757, -0.036304211158171756, 0.21452063993221987, 0.37592584050476663, 0.4108176159011622, 0.2973916744885671, 0.03101400383873135, -0.375279783239935, -0.8917233844810535, -1.4741548072618051, -2.067626932129084, -2.610906534119639, -3.0415331786294906, -3.3010621591480023, -3.3400733112103747, -3.1225488957202945, -2.6292707094022982, -1.8599612367399603, -0.8339902799617972, 0.41042039665021113, 1.8184449634641953, 3.3221909732301005, 4.845262140463318, 6.308001344439624, 7.633014656179974, 8.750554262742178, 9.60334831969719, 10.150564397508376, 10.370675838782844, 10.262529756336162, 9.844950257385817, 9.154924581159436, 8.244482362791942, 7.1765252817254455, 6.019941870085962, 4.844392629696706, 3.7151702597151215, 2.688527616640701, 1.8078234177154353, 1.100766433404165, 0.5779488143927207, 0.23275564101028856, 0.04262910100824903, -0.028439487493585092, -0.026410070691061924, -0.0029818319604510966, -0.011008158104291208, -0.09991352842811603, -0.31150434030007085, -0.6764880967365856, -1.2119503489136778, -1.9199578244023328, -2.787363297225329, -3.7867922532029894, -4.87870086056251, -6.014316087384471, -7.1392077350883625, -8.197202796793261, -9.134337144718701, -9.902548364869853, -10.462844926280567, -10.787737411421675, -10.862782475002781, -10.687232418134425, -10.273844966851595, -9.647345136042972, -8.84226360502866, -7.9003013831035025, -6.867378089675448, -5.790597719433693, -4.7153556125603, -3.6827834454505832, -2.727688728412076, -1.8770957399757888, -1.149440701162507, -0.5544199998710694, -0.09344076801615832, 0.23941824449430968, 0.456058048921607, 0.5727636234317169, 0.6085066312385904, 0.5832895164628172, 0.5166551554163006, 0.42641580706700294, 0.3277078811695586, 0.23240845276369548, 0.1489049367664827, 0.08218357798574805, 0.034179943717288615, 0.004319965743978955, -0.00982633319246168, -0.011854874103494829, -0.005869590438872129, 0.004088536625504972, 0.01448715858279309, 0.02260254110414071, 0.026670743643960867, 0.02590201180370408, 0.020382123245753912, 0.010892347162463678, -0.0013173981483888702, -0.014771125791382674, -0.0279918902994196, -0.03968647261136627, -0.04887540526189589, -0.05496260085689322, -0.05774690358316061, -0.057384363378499746, -0.054314420477141946, -0.04916528439850802, -0.04265369430523605, -0.035492303859187925, -0.028314665530246957, -0.0216238087694862, -0.015766328492029913, -0.01093026550069847, -0.007162275684138545, -0.004397912268299265, -0.0024982148503990024, -0.0012862402472602842, -0.0005789061225304041, -0.00021069746246013264, -4.7888499628898976e-05, 6.25378334648562e-06, 1.349597198218413e-05, 7.360369052224884e-06, 1.8646521129231154e-06, -2.5188648114043244e-08, 1.9657919524575348e-07, 6.091367660011104e-07, 4.6503438929957545e-07, 7.226069555134308e-08, -6.357066049432399e-08, 5.5419881708294715e-08, -1.0838757327234235e-07, -9.686281826322274e-07, -1.9520389252930312e-06, -1.2183568911710963e-06, 3.267894444857966e-06, 1.0932197027296962e-05, 1.4379311261957107e-05, -5.01378243059245e-06, -7.967368436119767e-05, -0.00025407436827858354, -0.0005762979236297957, -0.0010815461650886054, -0.001768145113793044, -0.0025693312645079414, -0.003327411562569339, -0.0037802699801274277, -0.0035730155949416174, -0.0023091047550488175, 0.0003451916844162038, 0.004492209017363426, 0.009765454077044032, 0.015026611053627415, 0.01801204973234261, 0.01495631514706898, 0.00023272145249153293, -0.03393760289792842, -0.09764906616394654, -0.20328562081137402, -0.365247897886127, -0.5993880248138477, -0.9221269972299102, -1.3492574651196818, -1.8944689027406934, -2.5676698022357765, -3.3732193199621037, -4.308214623366709, -5.361005647805982, -6.510152073469326, -7.724067929871504, -8.961256557476563, -10.171404734967638, -11.297398844835918, -12.278222672503965, -13.052636616821928, -13.563453422164882, -13.762145432771545, -13.61345096655824, -13.099600696118145, -12.22376594262047, -11.012344821441545, -9.515752055674211, -7.807463811127888, -5.981186581012081, -4.146162056978679, -2.4207780596858184, -0.924800449632078, 0.229313654965726, 0.9451995475067246, 1.150873878881647, 0.8059004542359127, -0.09322273610043105, -1.510013576731603, -3.3677076131318278, -5.551937477297312, -7.916394709258774, -10.291241434935822, -12.493804772010169, -14.340874877986922, -15.66175756899703, -16.311121454192737, -16.18064062741679, -15.208474859160457, -13.385751282373901, -10.759498644874748, -7.431499219917316, -3.552223831014771, 0.688542881305683, 5.074003264651324, 9.374829657906286, 13.364758393798008, 16.836113619351405, 19.614064019593116, 21.568497841535567, 22.622577543539393, 22.757292404383385, 22.01164569379026, 20.478466897856745, 18.296199595040296, 15.637351127695487, 12.694571731510505, 9.665532692058191, 6.737964865846649, 4.075980005828124, 1.808252962345246, 0.02029342994021629, -1.249031444919638, -2.0067041342176597, -2.300716305127297, -2.2117744964098445, -1.8424602923725968, -1.304983211986793, -0.708787745919135, -0.14928039046461752, 0.30117340859427133, 0.5990593960660296, 0.7317269562636958, 0.7153803277175416, 0.589234661142496, 0.40642309573551055, 0.2225978219055726, 0.08342406586848641, 0.012316523630281581, -7.232526669677372e-05, -0.003323247262091135, -0.09065568693500664, -0.3976003222879771, -1.0957094245222718, -2.381548382948086, -4.46167617157926, -7.534735976327469, -11.77210106224876, -17.298724205667863, -24.17590099829694, -32.3875696884362, -41.83153770867875, -52.316665189221744, -63.566577452827374, -75.23009444145444, -86.89835740512818, -98.12657461126501, -108.45920801289083, -117.45694400995993, -124.72342032396962, -129.92974821228228, -132.8350301867691, -133.30137909286708, -131.30236782885095, -126.92434349891296, -120.36058250201619, -111.89879865650583, -101.90300120194145, -90.7910949546076, -79.00989104974768, -67.00933444596681, -55.217746742936704, -44.019911892648985, -33.73927227994887, -24.623978769425182, -16.83951090762426, -10.467407877635633, -5.5094955360930955, -1.8968578391143667, 0.4975008742637114, 1.843551337579682, 2.3380203611666937, 2.18835020461048, 1.5979915108818086, 0.7539645462640719, -0.18265406469682016, -1.0829677047377217, -1.8531726778403759, -2.4343783068635574, -2.7997923786151637, -2.9499067521186366, -2.906408121285267, -2.7054036851255687, -2.3907543337106087, -2.008097619038682, -1.599967533932228, -1.2022589765492069, -0.8421148908884448, -0.53716176737315, -0.29589764813161173, -0.11895441106905004, -0.0009161303177407161, 0.06762401937545887, 0.09805051910491364, 0.10197723810519918, 0.08990982991373701, 0.0703852266301564, 0.049581842382114126, 0.03133565618332573, 0.017458130103868253, 0.00823425111352584, 0.0029820226637511734, 0.0005723848581668818, -0.00016108020081220933, -0.00015824993878200906, -1.6516047247119878e-05, 1.9334251655136854e-06, -0.00011869247575676673, -0.0002706167403712318, -0.0003364773128045487, -0.00026420247591429566, -8.949094807292357e-05, 9.010141377449085e-05, 0.00017160974050629222, 0.0001081491087513386, -5.01112410754498e-05, -0.00015383046475747492, 3.0257456229337456e-06, 0.0006053381907639115, 0.0017263799681698155, 0.0032558568561083506, 0.004878213306898415, 0.006124635186160184, 0.006505402888875071, 0.005706542096521987, 0.0038102751848377607, 0.001477904202254113, 2.2056759783365712e-05, 0.0012976041766889514, 0.007360222641090542, 0.019879151929977405, 0.0393437041841811, 0.06416566492956928, 0.08984310054820303, 0.10840435907443859, 0.10837934071315701, 0.07553928298370528, -0.005385684221023225, -0.14788676695873557, -0.3597532710110809, -0.6382003488168275, -0.9643778154819758, -1.2977668644655167, -1.5711271839118635, -1.6867679355817247, -1.5149598591080011, -0.895264006237104, 0.3585862629088097, 2.449851708010012, 5.585932969614837, 9.961826640700076, 15.740662536620915, 23.03286673282742, 31.87669935999232, 42.219572333747, 53.90298516619872, 66.65321335627104, 80.07919921485768, 93.67887016934854, 106.85455092568839, 118.93745343085398, 129.22047165206854, 136.9977376631815, 141.60867915277188, 142.4837250571246, 139.1883991063583, 131.46237256732607, 119.25015194795236, 102.72046761518084, 82.27209323840135, 58.525581132957676, 32.29939967115203, 4.5645234839533, -23.608417522050928, -51.10868390360741, -76.84894443582768, -99.82835006803052, -119.19068268618902, -134.27338854410837, -144.64393814443804, -150.12088117486485, -150.77811483218179, -146.9321640040878, -139.1135770462478, -128.0247622321877, -114.48762405629921, -99.38511707486417, -83.60125250176964, -67.9649540600022, -53.201583848890955, -39.88967099922403, -28.4351077273778, -19.061662696903994, -11.81645499702286, -6.588905991820056, -3.140612153317154, -1.1427809596435117, -0.21740673225912102, 0.021736027510153088, -0.06805772894610732, -0.18865574786833247, -0.12216852861714785, 0.25834821687409887, 0.9887210313111794, 2.0231357020903027, 3.25148916162655, 4.522177561896212, 5.667588148867031, 6.529271079871995, 6.979829155210135, 6.939329661876417, 6.384758466520837, 5.351893539200904, 3.9298595939395753, 2.2494330185790314, 0.46681341185037395, -1.2549978707956193, -2.7649069967892563, -3.940321041469495, -4.699767208003513, -5.010221090107503, -4.8884969118492805, -4.396770973015115, -3.6329937895457203, -2.7175358101447316, -1.7777998163860838, -0.9325726591209046, -0.2781772633945114, 0.12194564176472442, 0.24309146235869328, 0.10002317214630332, -0.25733617524231656, -0.7525505901837637, -1.294441317940106, -1.7904036112807098, -2.159531208209059, -2.343860539287269, -2.3163019359377386, -2.084251898417735, -1.6884263813972067, -1.1970542392455592, -0.6961509087362598, -0.2770883026361372, -0.02300906940261295, 0.004174398270678486, -0.22554710184089133, -0.7032978356732754, -1.3789880499885916, -2.164062345266337, -2.9391527006655624, -3.5658826496579223, -3.90157239729586, -3.815239037567326, -3.203112143319284, -2.00191263293546, -0.19836875370015267, 2.1661584104481384, 4.996541376446745, 8.150251703760434, 11.448635480055167, 14.692105397575727, 17.678027546949203, 20.21839170307624, 22.155987268509765, 23.3775896645119, 23.822820407730973, 23.487901827998215, 22.424079377995938, 20.73104546722088, 18.54620678086845, 16.031037727549815, 13.356015100506399, 10.685710117383383, 8.165520559272505, 5.911274404182096, 4.002561189482414, 2.4801954408647804, 1.34774226077172, 0.5766023452599005, 0.1137486067566695, -0.10898474313894423, -0.1651208943944587, -0.12458228272050115, -0.04653964430829684, 0.025285965994128985, 0.06458851998211035, 0.06180439887739585, 0.021231570462679185, -0.04337434639794547, -0.11389511112275447, -0.17277911151234196, -0.20704258819979834, -0.2107766555921176, -0.1858606790984291, -0.14088073532674014, -0.08853903768336967, -0.04207709738131627, -0.011385445578308858, 0.00048150430196497825, -0.00029264892357831415, 0.0025386808760117867, 0.034283658627181204, 0.1265176621635368, 0.31281295548767823, 0.6235518032141883, 1.080548674510816, 1.692272627249384, 2.4504146416669372, 3.3283908539812304, 4.282130363901437, 5.253196971450218, 6.173977582040383, 6.97437898543952, 7.589249602794065, 7.965621229639017, 8.068844386687688, 7.886756435910167, 7.4313786550949645, 6.7378801551784475, 5.860892442748707, 4.868607032188986, 3.8353789562038085, 2.8337581324527807, 1.9269500760621763, 1.1626545221278326, 0.5690496570044717, 0.15340258539923288, -0.09657010194580146, -0.2088473750162151, -0.2213612154811703, -0.17524673368110968, -0.10812082197307714, -0.04843809793093705, -0.011828749450700263, -5.8228017037727375e-05, -0.0028690562564896356, -0.0024870162638714914, 0.019826118819369295, 0.07614086553632694, 0.1643525065131208, 0.2620800510916498, 0.32315707550561706, 0.2776296793133074, 0.03575894819774421, -0.5039940098349075, -1.4435812295412278, -2.871687754419981, -4.849292469589991, -7.39626582420569, -10.48085270758971, -14.013891449783063, -17.84954007673679, -21.791650714804515, -25.606314620724167, -29.039834601312002, -31.840462108351247, -33.78180851677642, -34.685516929630396, -34.440718188955586, -33.018011807070316, -30.47619660234267, -26.960682761355198, -22.69337522352719, -17.954735943667604, -13.059607768172324, -8.32911458674929, -4.061453142867562, -0.5045968144730254, 2.1662487118299953, 3.864217801504762, 4.596875944315087, 4.462124807111176, 3.634788555688743, 2.345371026954338, 0.8533142756123768, -0.5823070696778496, -1.731440887876612, -2.4179239912250754, -2.5378487680059636, -2.0694499077279667, -1.073485128353864, 0.31584580161132914, 1.9083333781562908, 3.4814907670138493, 4.807826790958734, 5.6825059251030865, 5.948198954569086, 5.514267647360627, 4.368052867523559, 2.576880866365665, 0.280755431006334, -2.323280454046644, -5.003197487271279, -7.51781496440919, -9.643384982378096, -11.197851810926268, -12.060029973927783, -12.181579508924452, -11.590530586282338, -10.386116494101723, -8.72569367798611, -6.805439487893061, -4.837215853665878, -3.024390055882423, -1.539473959949032, -0.5061098095884747, 0.01251072207104473, 0.017433221808085136, -0.4300356772399047, -1.219233890910205, -2.206365041242424, -3.233832227640751, -4.150182692681335, -4.82818269887402, -5.1788719149264235, -5.1600363729654735, -4.778307820900461, -4.0849431820081366, -3.166150916820383, -2.1295073181178905, -1.0884601315317153, -0.14709406228246388, 0.6127797405571677, 1.1406123091512743, 1.4210975077306585, 1.4726258538512194, 1.3408868799789806, 1.0888759895768492, 0.7850279825724172, 0.4914384939075234, 0.254084959929147, 0.09662805757156899, 0.01880901378408049, -0.00026354334758897527, 0.0055795644027079915, 0.0004621955428997784, -0.04121006358854241, -0.12307657050963436, -0.2179096180365981, -0.26328059994970926, -0.16305612524330573, 0.20478464865412901, 0.9745593232272601, 2.2749174921330075, 4.208628438705904, 6.832755836701926, 10.14201169212751, 14.057873973360069, 18.42548710171973, 23.019499556211375, 27.55892707057599, 31.72999159482902, 35.21481781089339, 37.72300951959369, 39.02259553054767, 38.966710042065934, 37.512689120233745, 34.731002184371256, 30.802641769608453, 26.004677478923636, 20.68418779412281, 15.22467428828238, 10.008299380367454, 5.377949997585592, 1.6033928385817007, -1.1446144560871683, -2.8092587241671616, -3.4498925352925647, -3.2312454507277617, -2.4008508722158814, -1.2573104883615815, -0.1131202423325245, 0.7435477999317808, 1.0835615917728372, 0.7638903907574818, -0.2562427448036047, -1.9120759851992266, -4.043354124043199, -6.416457158002662, -8.755723760473636, -10.779981045549391, -12.239697102686593, -12.950095350749923, -12.816056484330636, -11.845633032214032, -10.150394423935984, -7.932440078951677, -5.459569267254158, -3.0315791757216086, -0.9417954794157885, 0.5614177778727457, 1.308352696240491, 1.2325580028528071, 0.38309601734941345, -1.0773328893814171, -2.8886082705714102, -4.722035446347143, -6.218152750878355, -7.029187199253458, -6.861214330270563, -5.511063277019878, -2.8936076180776698, 0.9438046872022202, 5.821537556280283, 11.442532864177076, 17.420228857411526, 23.316411885499075, 28.684764291906138, 33.11525464893687, 36.274468932678076, 37.93750224670431, 38.00805241168572, 36.52524883525847, 33.657089017770204, 29.67748411078119, 24.934322056755832, 19.812058454383013, 14.692728049248148, 9.919757046199747, 5.768413465318517, 2.4257596684236318, -0.018297143737160213, -1.5686579224584625, -2.3125396102220668, -2.399127552257122, -2.0144570166191733, -1.3549753404303815, -0.6031480832929925, 0.09203909027601012, 0.6276813627267104, 0.9517176202297182, 1.060073442706024, 0.987370130761301, 0.7931439493410294, 0.5462124466903766, 0.3098243954914966, 0.12988794363524503, 0.02792338362964522, -0.00047559464660221673, 0.018169140718817655, 0.04334203008163691, 0.031239833463392572, -0.05405976297422674, -0.23113407518448809, -0.49531435117469264, -0.8175904453849122, -1.1487339771601885, -1.428133969123368, -1.5959875464626525, -1.606813828118599, -1.4417083211894142, -1.1170139046198395, -0.6874068374141951, -0.24212090608140477, 0.10596363037624733, 0.23753404183959714, 0.048465333613600586, -0.5269182219368362, -1.4942423912150564, -2.7825567671177986, -4.235941038632243, -5.6154986227789205, -6.612822160603801, -6.874610230834421, -6.036644201275365, -3.763984411528, 0.20691696227405357, 6.029665025097093, 13.717128406643637, 23.122227158127803, 33.933491559216215, 45.68686037061649, 57.79347032844701, 69.58142368270292, 80.34792522068479, 89.41694173429829, 96.19680368464654, 100.23203257473546, 101.24416202850422, 99.15737842902078, 94.1063248775701, 86.42522389691051, 76.61937963554449, 65.32190865626406, 53.24074694235148, 41.10078152040454, 29.581550957313663, 19.26494217614468, 10.595367392528027, 3.854579701270365, -0.8473303054841183, -3.564931918686765, -4.496229932622928, -3.9503329367948603, -2.308048417431, 0.020130658721354337, 2.6342609430340302, 5.179565123232583, 7.372513202292042, 9.016624084508823, 10.007512369323905, 10.327919721620363, 10.03456972693109, 9.239384665915432, 8.087215034742128, 6.733687681613226, 5.325749823382976, 3.9867128963378, 2.806855984388486, 1.8398078718740698, 1.1041672042302755, 0.5892305293876677, 0.2633355698494247, 0.08321332508000129, 0.002863262732234749, -0.019223836374863437, -0.015237237192003004, -0.0058736525194292045, -0.0006315929433489691, -2.5250326747251594e-05, 0.0010518282813441662, 0.009650704743998578, 0.031539718499695446, 0.0689907602876435, 0.11986466733656398, 0.17798829408200667, 0.23456256886079066, 0.28016654654803036, 0.30685022931499334, 0.3098419607912126, 0.2885187700582602, 0.24646956344618284, 0.19068243772760923, 0.13006846209731446, 0.07366109560285142, 0.028881082989381135, 0.00022488880740112517, -0.011369642902717735, -0.008380603562254533, 0.004149574031056279, 0.019963033700641324, 0.03310185303502222, 0.03923962385046226, 0.03653414222247892, 0.025823636598026792, 0.010146802312488996, -0.0062703429368941134, -0.0192870056282651, -0.02603831273203423, -0.02571756285837915, -0.019721842536997877, -0.011097728494208474, -0.0034211651968782406, 0.0005697743233477503, 0.00014654752193418185, -0.00289928045382135, -0.004770255488130895, -0.0013409762680904908, 0.009180860721543898, 0.02314491575970081, 0.028742226004797804, 0.004704281409070173, -0.07858715900423824, -0.2548666991014902, -0.5544677523864744, -0.9941440251062218, -1.5657777688770196, -2.2264482751631616, -2.8930872083719352, -3.445341824857331, -3.7401328422664157, -3.6406074824506662, -3.060702795253548, -2.024401435929497, -0.7361679358758721, 0.3437668539698824, 0.428209775945943, -1.6537251707161444, -7.487122898627382, -19.06408183001229, -38.729175353213584, -69.07123908900721, -112.75994769810168, -172.33155221970858, -249.93466845422637, -347.0534756220009, -464.23134555912225, -600.8220032494675, -754.7971203090675, -922.6382300884497, -1099.3367405196084, -1278.5186347767103, -1452.7148453327668, -1613.798881703657, -1753.4518549748268, -1863.7057811097238, -1937.526704724821, -1969.3793544048185, -1955.723425908783, -1895.3936279555976, -1789.8224176056551, -1643.0755843560703, -1461.6857231122185, -1254.2859485872934, -1031.0644012667244, -803.0774422954494, -581.4741742370677, -376.6954578155843, -197.71565541339643, -51.39413647960699, 58.004060244169494, 129.0789269595179, 163.3208167985526, 164.8713848533975, 140.0569581284371, 96.7393489641684, 43.54395246661422, -10.963263772011556, -59.07323507984796, -94.63137375077096, -113.57032428705315, -114.22875535402292, -97.42765477656545, -66.29905955415201, -25.88618562122524, 17.443844693230385, 56.71525447888748, 85.11502995740943, 96.74245147666831, 87.25784643645171, 54.36943008347461, -1.8905527770239616, -79.12389988041888, -172.75890033780917, -276.4548819916704, -382.67622094905977, -483.3774708647017, -570.7316677082641, -637.8311762015597, -679.2947641028708, -691.7253132628397, -673.9784689588537, -627.221871983069, -554.7853911267622, -461.82286820115803, -354.82332211451114, -241.0235605272, -127.77208457077435, -21.903166008349658, 70.79067153989027, 145.95715089781467, 200.92831272215483, 234.79801757130758, 248.337578480426, 243.769513961094, 224.43170179069884, 194.37245266486352, 157.92063906579412, 119.27395012694271, 82.14302715432957, 49.48050945346753, 23.313028542846666, 4.682233909284886, -6.310668609020223, -10.372761967749366, -8.823219635223397, -3.3567745640951476, 4.201026367200152, 12.117968296894338, 18.937221324598752, 23.60282204054741, 25.522016993485117, 24.565676014451157, 21.014768539596876, 15.466032756005973, 8.713045883931027, 1.6197877337269053, -4.997393855879613, -10.466405541513408, -14.32570574345043, -16.35605326141859, -16.57815052477907, -15.220858618344932, -12.667460906280063, -9.388215244604766, -5.871107834773039, -2.5596229563575963, 0.1956540746281955, 2.1672411119109527, 3.261284653623197, 3.5096330041942077, 3.0469077442035215, 2.077532160641505, 0.8383560708271856, -0.43762237110531427, -1.5517829135127643, -2.361362375808547, -2.7902267418749593, -2.8289370978901562, -2.52557102215041, -1.9698554146624914, -1.27371793970167, -0.5514392204292823, 0.09746880571665457, 0.6005776050075974, 0.9189538572464683, 1.0475683998560292, 1.0105007504129038, 0.8524056296235449, 0.62807588481802, 0.39198554887429027, 0.1894569953599806, 0.0506357297711792, -0.012131163094534658, -0.0035289548925711207, 0.05832149478125418, 0.14734010248168025, 0.23569088720888343, 0.29956552589075264, 0.3235918932392203, 0.303200606606756, 0.24472973164606707, 0.16346512750932768, 0.08013877993951772, 0.01662441659923762, -0.00835472562628528, 0.017243887265498966, 0.0965805429137613, 0.2233647376339176, 0.38293097679921895, 0.5546960970287675, 0.7155226767078959, 0.8433919154512577, 0.9207728546705071, 0.9371587156852439, 0.8904055201747638, 0.7867307739849055, 0.6394405266319143, 0.4665812886992914, 0.2880545294245443, 0.12267036038572568, -0.014405981257083507, -0.1134457888103403, -0.17096569999626862, -0.18950564394969477, -0.17649629360456856, -0.14247355181829618, -0.0989836178377036, -0.05654664799268997, -0.023010046719493044, -0.0025339457166230024, 0.0046709513614751775, 0.00186727074711704, -0.005285696210580795, -0.010177926769836174, -0.006782218919896715, 0.009004312765725794, 0.03844554622528624, 0.07962211253133059, 0.12769421858684407, 0.17570265952874553, 0.21575096956051745, 0.2403544291737283, 0.24372292357598377, 0.2227652667705012, 0.17765696908172007, 0.11189080225184796, 0.03181608678035713, -0.05424610243369668, -0.13716143611611137, -0.20822820222268318, -0.26031969177358855, -0.2887621177945125, -0.29183942319596434, -0.2708353001740715, -0.22966005166093378, -0.17415213316642486, -0.11117935739782381, -0.04768657566490684, 0.010168827440900573, 0.057679249850189955, 0.09197479240147396, 0.11211375770501274, 0.11890028670781941, 0.11449214527217064, 0.10188569267744783, 0.08437228035583728, 0.06505144066042567, 0.046464594359443695, 0.030383824317604766, 0.017759451995537846, 0.008803226075611821, 0.0031657213713962014, 0.0001577000294788545, -0.0010330450028061004, -0.0011665936427536726, -0.000838791420726373, -0.0004363571298121527, -0.00014894896770850695, -1.8553288167431906e-05, -3.4109841635783374e-06, -3.6390447294117966e-05, -6.460603447019152e-05, -6.576854057410815e-05, -4.47246460714059e-05, -1.8880270197707997e-05, -2.6498253880094124e-06, 1.1713937665726292e-06, -8.245014423621835e-09, 2.3044740312246984e-06, 7.343202351377409e-06, 1.218403102043089e-06, -3.498805784845369e-05, -0.00010478254815002746, -0.00016945965387727086, -0.0001263642522839251, 0.00019410985411308728, 0.00100162564160938, 0.0024855746837102997, 0.004729262171303502, 0.00761913096668685, 0.010779396401464835, 0.013565548306325094, 0.015143358372417603, 0.014662153332940409, 0.011503853699446304, 0.005557729028515769, -0.002559412102145328, -0.011435332764648773, -0.019028781962570098, -0.02312509189469278, -0.0220758379975666, -0.01573468838482603, -0.006408527994306789, 0.00044344873454672123, -0.003911417124001938, -0.030687380547694938, -0.09159856054585191, -0.1955461741777612, -0.34404474208703434, -0.5257274683995493, -0.7105685059125607, -0.8447395533230027, -0.8472263095732422, -0.6094672224450721, 0.0007437267764732598, 1.1308446603712325, 2.9301633372144993, 5.532053390848546, 9.032753629501858, 13.46893562459952, 18.79655087079875, 24.874013092258085, 31.45285204185845, 38.178677704218636, 44.604565286861686, 50.21783181227304, 54.47970296138541, 56.87569925941578, 56.97288611954137, 54.47864505005204, 49.29455233338379, 41.55911933144844, 31.67262249113406, 20.292951458501726, 8.306270528472355, -3.2283593798966455, -13.158327476756645, -20.33505216917173, -23.72147803569667, -22.499296822433898, -16.164797249112294, -4.602511935048673, 11.872677744410856, 32.51167188618557, 56.16862647851056, 81.37870035958528, 106.47065951997922, 129.70489938450092, 149.4242174045935, 164.204553924875, 172.99436519004541, 175.21099742090277, 170.79267140868095, 160.20141238138137, 144.37484344158378, 124.63157885965757, 102.54006139193247, 79.76476199236755, 57.90621090179825, 38.35203548991616, 22.154932904569588, 9.950423686171284, 1.9226541682258913, -2.1790383084060054, -2.975967664421132, -1.3570401580599314, 1.6500169540960983, 5.0169554589850245, 7.845959087087696, 9.477952998473022, 9.563612341303266, 8.088650292899112, 5.351147283029292, 1.8947324318659025, -1.5929497927462495, -4.402636771729407, -5.930189048914561, -5.790564656462682, -3.9034730209242277, -0.5386682787551076, 3.686123618414536, 7.855715109298609, 10.851372821616684, 11.477588029748132, 8.606894926135618, 1.325087905580062, -10.943054640553841, -28.341030138525426, -50.53144165238734, -76.69753275980177, -105.5958956205272, -135.65500997015602, -165.1091205970894, -192.15310392439798, -215.10183553227853, -232.53735907311173, -243.42884720534803, -247.2136857223084, -243.83256343421513, -233.71664357799014, -217.73010208866054, -197.0759395889973, -173.1764966676681, -147.54417846586304, -121.65549922773185, -96.82642661073693, -74.12249486717785, -54.30441965462852, -37.80847987859686, -24.7597160468211, -15.012645282122058, -8.211778170436716, -3.8629417995184543, -1.4063115361088525, -0.2830277789484967, 0.01090399003273424, -0.11262696253575367, -0.35301850168262455, -0.523071773642011, -0.536984532054634, -0.3884737347834416, -0.12385863444693197, 0.18524043350665736, 0.4657082176499845, 0.6603836599042621, 0.7379000598420419, 0.6950562193414762, 0.5529833370900127, 0.34912381106269874, 0.12734879038156832, -0.07157139042320225, -0.2173863538457991, -0.29459490401759536, -0.3031626682796637, -0.256107362394956, -0.17486399206786807, -0.08363768971737608, -0.003987525429535953, 0.04931480535036671, 0.07048139770418792, 0.0627486916428731, 0.03646925825692421, 0.005877765473590594, -0.014639833886471339, -0.013947381006310945, 0.013447444384073495, 0.0664154525594745, 0.1377296714707093, 0.21586259123772789, 0.28758749941302875, 0.34078594879655216, 0.3668647613658357, 0.3623078416261918, 0.32909821658862604, 0.2739965225267139, 0.20690059029137758, 0.13868893669011226, 0.07903679356069158, 0.034664423190656005, 0.008358312007957006, -0.0010542553531746664, 0.002136352564287524, 0.011963605107943287, 0.022441975237192092, 0.029027437968550326, 0.029537538478035728, 0.024335177843317866, 0.015772881399560342, 0.0070870429093218565, 0.0010793227271958107, -0.0010110519620570738, -7.389332424515867e-05, 0.001105693085055113, -0.0010827348735467416, -0.009365872003415062, -0.02364528032795964, -0.0393667817567521, -0.04675995419865788, -0.031377565549290685, 0.023881836733236267, 0.1354114363763468, 0.3146807902003544, 0.56394213258383, 0.8727949063135397, 1.2165308472429546, 1.5569710887514856, 1.8461164366045428, 2.0324173499907676, 2.0689176082143717, 1.9220393542844296, 1.579461226493557, 1.0554796878798471, 0.3924824097368589, -0.3422650342516792, -1.0646172704435282, -1.6858387717255463, -2.126986890681078, -2.333070104194202, -2.2843814942522074, -2.0025400893835075, -1.5494326582403681, -1.0183263589762637, -0.5177749632582447, -0.15035890132584145, 0.010463743845266514, -0.058694384339814214, -0.31668099923644555, -0.6535442880784254, -0.898922417655315, -0.8436192193149304, -0.27263161110012574, 0.9944149908001741, 3.061494250906936, 5.920267564493058, 9.42725358654811, 13.300173207913344, 17.137216006263426, 20.45967184611926, 22.77451911982069, 23.649713547502678, 22.791699396043096, 20.11266765130038, 15.774794878286999, 10.200388703243124, 4.04054619513954, -1.89969832288769, -6.775290923543524, -9.842959328385238, -10.613683826273059, -8.994232168283919, -5.39438863910367, -0.7785195646152647, 3.355711835953295, 5.080468375301047, 2.2217907230087404, -7.387404921629637, -25.60828772558998, -53.683164985923355, -91.94689317830179, -139.60281829177833, -194.6004032930068, -253.64365263993997, -312.3468802283218, -365.538429554125, -407.6953117866972, -433.4744040490333, -438.29099955128885, -418.8873505964903, -373.82335645383284, -303.80873482436414, -211.86099573000814, -103.25357505828227, 14.75935975829098, 133.42887617903924, 243.1728149143967, 334.3577444414544, 398.13120762597725, 427.22597665497585, 416.65780276114646, 364.24612117807794, 270.9027210258454, 140.65503238459044, -19.60376908709438, -200.61884710545323, -391.48779230782947, -580.5387388529911, -756.329327893697, -908.5091033329966, -1028.5707662718671, -1110.436495371327, -1150.8199639334812, -1149.3411885960968, -1108.3955900048686, -1032.8017136812184, -929.2716381504049, -805.7623377952401, -670.7739646424368, -532.6617101280198, -399.0219155631954, -276.2014284088998, -168.96341647962922, -80.32487628728141, -11.56295275429363, 37.628554584545846, 68.86876662062431, 84.74302781366627, 88.41095550040772, 83.22670234752094, 72.40915656041862, 58.786834309069384, 44.63059792452449, 31.57588800430757, 20.626162877464463, 12.221650229970416, 6.352890806145372, 2.6970308370704164, 0.7561467623393611, -0.01950304074327119, -0.13528417041247606, 0.010732860128032796, 0.15678139931488735, 0.17656475371302685, 0.05592042889602177, -0.1439061633683854, -0.3268652646725493, -0.3986721337995723, -0.2938113188945892, 0.009799811634956154, 0.4885913117114878, 1.0814866940893941, 1.7049053847128919, 2.2705308727783136, 2.701973607011324, 2.9473098024662403, 2.985716886961702, 2.8277819372976145, 2.510280474307862, 2.087117398518273, 1.6185801143785434, 1.1610956557355627, 0.7591968112942431, 0.44056477457286786, 0.21503835921552641, 0.07695027296171776, 0.00970922003730025, -0.00864731169120879, -0.00017518035107018194, 0.017005686698971883, 0.030944408849775916, 0.03622114772917554, 0.03277816142867635, 0.023837670303980953, 0.013621688866775604, 0.005506189175001535, 0.0010178371258659467, -0.00021735923692693093, 0.00024042941630383847, 0.0007196874371812565, 0.00037529094006395693, -0.0004543023799306386, -0.0007251219059453425, 2.2013252074697545e-05, -0.0001284718050285311, -0.007217826696834517, -0.03248547703484265, -0.09218410141762265, -0.2057796066775169, -0.3925237059559515, -0.6667888578040341, -1.0329290339326505, -1.4806893608467784, -1.9822642450152457, -2.49196024842616, -2.949061321375887, -3.2839679972097953, -3.4270950971872014, -3.3194377808945643, -2.923031117785334, -2.2296678658830906, -1.2662288717356007, -0.09535887333547005, 1.1891060163863247, 2.471738926070007, 3.629089872986827, 4.545434096121123, 5.128436000567017, 5.322327637661714, 5.1164504714791414, 4.547624856192706, 3.69571046888436, 2.6727685330645867, 1.6072672698143162, 0.6256149501012781, -0.16618853130166866, -0.6979341340096132, -0.9450679873656175, -0.9313536246590722, -0.7238992926431913, -0.4212664686262899, -0.13648714819073474, 0.022332859529972025, -0.029287574709040386, -0.3372570194530883, -0.9002103263824476, -1.6685764284555944, -2.551694627134015, -3.43194373014667, -4.183673980645268, -4.693893911890734, -4.881309115799706, -4.710508348063333, -4.198887141311793, -3.4149840464826, -2.4678223384173243, -1.4895361999964982, -0.613981084551438, 0.0452544375520044, 0.41378000761563205, 0.46905146812353804, 0.2444762866372677, -0.1759222731785105, -0.6716386857797292, -1.106494634879876, -1.3528300366552277, -1.3151131504562867, -0.9489672406518754, -0.27222539515786615, 0.6341846868659354, 1.6361311812858799, 2.5657231772519586, 3.2473806938890406, 3.527018666206805, 3.2992742028656994, 2.5284090451625216, 1.2593757173055773, -0.3831165690776005, -2.2079178882057775, -3.9816290179063434, -5.460452881070507, -6.425223323046622, -6.71450383624817, -6.250774840148012, -5.05560263721547, -3.251192156865957, -1.0476581507961624, 1.282572645436301, 3.4398982883346334, 5.137609435379444, 6.141288477979576, 6.299852857203566, 5.5655626435292325, 4.000381515622093, 1.767737987905683, -0.8890517922502347, -3.6786014702940903, -6.2990392483995965, -8.476162329058887, -9.99698060430836, -10.73421344351168, -10.658656761670446, -9.838097296927026, -8.423360127814167, -6.623859833664799, -4.67643352758838, -2.812071313537397, -1.2254050275804171, -0.05083546644176765, 0.6517899675098242, 0.898574076359631, 0.771443740538779, 0.39891889285314264, -0.06881774107678038, -0.4864867971892669, -0.737821130213112, -0.7536957102593717, -0.5218175254398224, -0.08688642369273812, 0.45839336300437045, 0.9897241850186165, 1.3722871890666708, 1.483129818623471, 1.2314533742931955, 0.5738197147174594, -0.47790345678277096, -1.8570581144001073, -3.4506037186652003, -5.114038759552853, -6.690406282795539, -8.030463241030285, -9.01111412171602, -9.549624524794487, -9.61188243372442, -9.21392981948482, -8.41699008698459, -7.3171167094551235, -6.031260361772906, -4.681914089606402, -3.3825187762312345, -2.2255173856039843, -1.274404573099901, -0.5604284157476793, -0.08391741328576684, 0.18055688804428494, 0.2765685481227156, 0.2566528088963948, 0.17333194606278668, 0.07171179200681757, -0.01547441020348295, -0.0699916086158009, -0.08750931373877913, -0.07481683890895603, -0.045656350660320685, -0.01609739497645469, -0.0003252105547088052, -0.0075249981587244726, -0.04026277502895041, -0.0944481680684648, -0.16067279053523095, -0.22649703522151748, -0.27913917255504306, -0.3080084086658227, -0.30660949245300695, -0.2735362314565635, -0.21245966780259784, -0.13121046009587334, -0.04021065787195119, 0.049398969529575544, 0.1275721994678846, 0.1867982118362477, 0.22295958110563718, 0.23552660490074173, 0.22713684613533244, 0.20271420565712525, 0.1683458876933183, 0.13015078449518816, 0.09334178232299287, 0.06161866355277242, 0.036944991276753665, 0.019678391120475303, 0.008959784443479658, 0.0032349212941875823, 0.0007691125907119713, 4.789284416662769e-05, 3.7023693774997288e-06, 6.115737792351525e-05, 3.9302172394256244e-05, -2.156675524105061e-05, -3.352228482378781e-05, 2.5959750789173673e-05, 9.293256431967226e-05, 8.309459065542712e-05, 8.062721097877651e-06, 8.5494627292289e-05, 0.0007859047009057749, 0.0027771258627335518, 0.006759834479836417, 0.013225938216860115, 0.02220425197680913, 0.033074072936389795, 0.044522603278376906, 0.054694467238634005, 0.061535369148813426, 0.06327680738439934, 0.05895748084004028, 0.04884301739623683, 0.034599972631166404, 0.01910866542207612, 0.005861357983909927, -0.002020951704895592, -0.0030233693327309814, 0.0014930986296569236, 0.0062607926053219465, 0.0015986760036942797, -0.026332717055964044, -0.09440391543465859, -0.22055021182258425, -0.4211289325114289, -0.7079190684548873, -1.0851906042844242, -1.5473204361149966, -2.077408086043439, -2.647244291842228, -3.2188185516231647, -3.7473391999747454, -4.185511921558678, -4.488614626946949, -4.619752273756397, -4.5546020106344605, -4.284983230660433, -3.8207106313566386, -3.189397688674382, -2.4342432367627707, -1.6099443683570451, -0.7764626328987894, 0.007391515213933069, 0.689983727598077, 1.2318713900042166, 1.6092084095091108, 1.8151702035786639, 1.859308310144217, 1.7650265273827543, 1.5656156745219671, 1.2994571921799545, 1.0050839632114217, 0.71676208248344, 0.4611378502670763, 0.2553021980322574, 0.10639257334831269, 0.012617421151881667, -0.03461586183773409, -0.04792544328635702, -0.041009784310337506, -0.02605620646165599, -0.011895712372822848, -0.003110137055855146, -0.00011148116001118108, -4.1205284652370905e-05, 0.001791269978894386, 0.010278135047932997, 0.02903625865012123, 0.059364980161661, 0.0998098564934422, 0.1463712670474691, 0.19326795720027715, 0.234063730160944, 0.2629075930053824, 0.27563160585000285, 0.2704989508361061, 0.24847520018305166, 0.2129509726151757, 0.16903412999352446, 0.12257466277947211, 0.07912328992814964, 0.043028363103016914, 0.016834576354403434, 0.0010760779442447552, -0.005528225098791389, -0.005550329939125461, -0.0021340081831247104, 0.0017548710512083781, 0.003949784360897966, 0.0034559381409199033, 0.0005137671649691136, -0.003635991587691415, -0.00721073187727803, -0.008447641353586157, -0.006131594176624881, 3.4581230394446434e-05, 0.009303177283296707, 0.020021328846127607, 0.029998299281523175, 0.037009719776369486, 0.03931825607202462, 0.036088174785645515, 0.027597091997957342, 0.015195631016046235, 0.001023951610982491, -0.012449980018850296, -0.022964474921469347, -0.028947728344136222, -0.029839225495120084, -0.02617406496000816, -0.019409833230367542, -0.011535654141123505, -0.004554719923868265, 3.485155294866499e-05, 0.0016338891916334274, 0.0007127699339534217, -0.0012896592484314539, -0.0023242732634047533, -0.00027054882245990976, 0.006466804739813664, 0.018446386698121046, 0.03489453268342854, 0.05371322616512708, 0.07181330506750003, 0.08572001514749705, 0.09233063400486703, 0.08965965235963361, 0.07739728952285824, 0.05713640193202784, 0.03218557120286214, 0.006968235980290728, -0.013872643879524993, -0.026482944764916302, -0.02871013521956864, -0.020712897242016897, -0.005112019176776553, 0.013384232642955395, 0.028838151311774106, 0.03527500129364659, 0.02797880236285351, 0.004622540937518365, -0.034019131421211234, -0.08395474236337748, -0.13852330290462198, -0.18953234813635114, -0.228784578855008, -0.24969517007893866, -0.2486716997173915, -0.2259566007220473, -0.18565051377058878, -0.13494552953906613, -0.0827055349415498, -0.0376701253975742, -0.006660016802589549, 0.006821671322572518, 0.0032674324474062737, -0.013056373198034944, -0.0352149453598814, -0.055373022960814096, -0.06683403835620574, -0.06586445268512443, -0.0528262434285047, -0.03226099712115609, -0.011785379779719437, 6.838952755905575e-05, -0.003342760218935834, -0.023946708709574226, -0.05684648336601622, -0.08960149153648726, -0.1033210743719904, -0.07564503247107031, 0.014728154919138852, 0.18270095532299027, 0.43165097374183875, 0.7496591497280436, 1.1081211010963914, 1.4634335358592627, 1.7619251415541406, 1.947577010138932, 1.9714644553815346, 1.801373231318089, 1.4298088242815299, 0.8787017108240985, 0.19958279357568717, -0.5313855619877562, -1.2235955218953658, -1.7853930796748387, -2.1386591638496713, -2.2321330544381164, -2.0510208217351957, -1.6209453962233291, -1.00521092422352, -0.29552478829525214, 0.4024615610990875, 0.9863988216173583, 1.3742431947440021, 1.5178982638698162, 1.4108878053597609, 1.0884999766983419, 0.6202533044127144, 0.09604527297509, -0.3913450523828423, -0.7639836802992301, -0.9730506773112922, -1.0064242757750623, -0.8881222699491332, -0.6698648975636298, -0.41680989609760516, -0.19092531358723613, -0.03612464759960853, 0.031028800404957705, 0.02254975087389385, -0.028231402379475027, -0.0804397110455527, -0.10181085729779736, -0.08184320003428187, -0.03668749549363259, -0.002287277215363485, -0.01557915036450426, -0.08782758488053753, -0.17845083053779798, -0.18076962307364358, 0.06860722702303167, 0.7484730322169119, 1.9790644744416641, 3.726197118737706, 5.708349250529214, 7.346095475738005, 7.805290183632266, 6.191446500755793, 1.949544072282958, -4.491555807655443, -10.81903398256924, -11.70983558691412, 2.442398018798503, 46.81367330056534, 143.26483655074819, 321.0617838420884, 616.9663475151951, 1074.494150222831, 1742.1637163829605, 2670.6488246871627, 3908.8596772080105, 5499.111577595923, 7471.682408379399, 9839.195200151604, 12591.371331427745, 15690.765508584493, 19070.10039317821, 22631.756248646674, 26249.835875723038, 29775.02229428969, 33042.1897943772, 35880.440050672674, 38124.94251837519, 39630.14085273445, 40283.82774008443, 40017.05308656493, 38811.85084246509, 36705.71289282823, 33791.7239213478, 30214.028285769156, 26158.728826199902, 21840.766113430072, 17487.749026518282, 13322.057837801316, 9542.778397517968, 6309.119660744293, 3726.8996039380995, 1839.455813263564, 623.9631643216558, -6.345326477557037, -194.11133963549577, -124.55233866622706, -8.11384010654879, -60.68859562231028, -483.16774704395044, -1442.3637188858945, -3055.0888996858434, -5376.83597822255, -8396.05409710638, -12034.47224356312, -16153.343515504013, -20564.929792496045, -25048.071056623274, -29366.332955648537, -33287.03198841284, -36599.41468716835, -39130.41197960022, -40756.68186280891, -41412.05740450678, -41090.42520654163, -39844.3846224304, -37776.557193232664, -35028.386882406885, -31767.248369024703, -28172.71425608599, -24423.240573082225, -20684.367794378515, -17099.2811138559, -13782.263576385232, -10815.246346279, -8247.34782311943, -6097.028063166135, -4356.289352798763, -2996.2402019677793, -1973.310546885066, -1235.453142570157, -727.7749144811795, -397.1914849835203, -195.86587300920957, -83.37795585797257, -27.685031798359105, -5.049155475883154, 0.799428737378904, -0.029297397302409905, -2.079014212513522, -3.0707032264513283, -2.6196282240423248, -1.239957584490731, 0.3331809673924284, 1.5265315396670454, 2.074034883382057, 1.999551876196384, 1.512866169272833, 0.8832622044764029, 0.3357481646444952, -0.006769211385726592, -0.13188756002241916, -0.1077485656302318, -0.033997695664216454, 0.0060016916014965565, -0.023730184656170408, -0.10486939723242815, -0.18094738080104078, -0.188401416526652, -0.090277044721422, 0.10003173753549613, 0.3145616591057982, 0.4501248411129786, 0.408733634201921, 0.150625569743621, -0.25269355293023577, -0.579282193890533, -0.443599197868398, 0.6830245497369274, 3.417198389643689, 8.37997304955108, 16.097036383079836, 26.898276004312407, 40.83349610838213, 57.61918464708596, 76.62676253590115, 96.91650639959879, 117.31439539534189, 136.5226457949122, 153.2497004096472, 166.34268450093387, 174.90518260204445, 178.38555825012563, 176.62546334538268, 169.8639020406096, 158.6983056600601, 144.01204218368846, 126.87977594573708, 108.44487210909034, 89.80815337125021, 71.9363167677784, 55.595755536388616, 41.31611638320426, 29.383603307324837, 19.860289921475857, 12.622984365728994, 7.413750886457992, 3.8940509969273327, 1.695447396824338, 0.4615947185506232, -0.12157058069177738, -0.30832615127382973, -0.2873433276486658, -0.18520058447544532, -0.07617580207557015, 0.004849664187396154, 0.04911917661604009, 0.062310322439127076, 0.05565455089012782, 0.0402208211443418, 0.024056402541932722, 0.011485208840416638, 0.0037272215213539784, 7.244275103524479e-05, -0.0009572706889925475, -0.0007773036597333376, -0.00033251668554895196, -4.4099414395360595e-05, 3.5886538128815375e-05, 1.3626885407376207e-05, -7.205099703190833e-06, 6.734922232174153e-06, 3.0880363711454755e-05, 3.184227244343295e-05, 7.383306412958287e-06, -9.18305469709437e-06, 2.080517384500283e-05, 9.934854555448631e-05, 0.00016785153321826154, 0.0001216732948635885, -0.00013716593376279768, -0.0006316426306758518, -0.0012615731448511656, -0.0018090228564203326, -0.0020118061066516564, -0.0016903481431552417, -0.0008843852308357465, 6.032462703907665e-05, 0.0005100474520748863, -0.0003078730061438503, -0.0030445121946470863, -0.007927704142361361, -0.0145223343012607, -0.02165582126651597, -0.027579142131600298, -0.03036845178100876, -0.028491156287089994, -0.021387072816559393, -0.009875610188281064, 0.003786630004017926, 0.016300193085383455, 0.024149165169193795, 0.024696539055268446, 0.017261507881392177, 0.0038295552966173636, -0.010921077615276258, -0.02045398217084137, -0.018020282838160644, 0.0012002614097410549, 0.03802210661526094, 0.08795184502884092, 0.14124989366588528, 0.1846774059337685, 0.2048143416219397, 0.19231760326207756, 0.14603175764433884, 0.07561743362227685, 0.0014520856493354217, -0.04894968205739278, -0.04788363944759387, 0.023436638481450993, 0.16589756388745378, 0.3566558941680308, 0.5495740428296088, 0.684214680251119, 0.7038834452491594, 0.5805597535382893, 0.3415027391979387, 0.08944905461244367, 0.006496003040476256, 0.3321820750427907, 1.3091192508466636, 3.095208951158568, 5.649691211843203, 8.610091108938411, 11.186983807361907, 12.111368230671781, 9.673078130217228, 1.8859899319476963, -13.194675990722514, -36.99638889478641, -69.81420529053176, -110.10711822102718, -153.78855957274305, -193.62198092140153, -218.84923723296677, -215.17478054171136, -165.2153448083652, -49.489075317112444, 152.03876126357378, 457.9069571653561, 882.7382624990931, 1434.6564525453946, 2112.8130595981374, 2905.336829969402, 3788.0266010511036, 4724.076547974505, 5665.049502156377, 6553.202403613964, 7325.126552090394, 7916.507906696589, 8267.656909842624, 8329.460206127607, 8069.302301786505, 7475.139817347439, 6558.263143224987, 5354.2613163351525, 3921.806444262474, 2339.2159380338776, 698.9840063672834, -899.2984208203384, -2357.02059040725, -3584.871919000613, -4510.588158559311, -5085.330658740825, -5288.018096380594, -5127.122266114031, -4639.692891022629, -3887.6642730789545, -2951.7871776954544, -1923.7647811483694, -897.2884932038413, 40.844496371958876, 818.5650646401881, 1384.606543424, 1712.236253196046, 1800.3287783587134, 1671.7607983990447, 1369.3982452588039, 950.2002734908067, 478.1529340854431, 16.848595919387062, -377.464539367564, -661.6233613126151, -809.5072967510274, -813.8629715562888, -685.9025176731834, -452.83805641886585, -153.73883714117667, 165.78678557948675, 459.37128966340833, 685.3037521707267, 811.0361446602421, 816.3461973494809, 694.9005396562892, 454.16504043097757, 113.80250049003637, -297.14097864740575, -743.8469919022886, -1189.664446414752, -1599.9136657790227, -1945.1491220540877, -2203.5750931854363, -2362.434769416407, -2418.328050071612, -2376.5394866073266, -2249.59732294659, -2055.333176370227, -1814.4250668844925, -1548.0615310124872, -1275.942356650296, -1014.7506613909554, -777.1878785109141, -571.5831645669199, -402.0197497978915, -268.8698733745223, -169.60084402500476, -99.70770315763623, -53.6402514385443, -25.61898283375137, -10.269728757307405, -3.044357111113742, -0.42922346740397405, 0.02986267273450969, -0.16002349494670912, -0.24269761786451904, 0.015851074791419163, 0.5462852720726402, 1.155202399086271, 1.649862409795829, 1.9067071648049867, 1.8920253616689682, 1.6489326551681474, 1.266513957605139, 0.8452660166221779, 0.4690595841786585, 0.18901716232893628, 0.020146939799839725, -0.05186271008976879, -0.05816534691124683, -0.033378359326622246, -0.005132228234003315, 0.011325997184219248, 0.013209878336317411, 0.006219190178381626, -0.0012753623995176685, -0.0036119057787233903, -0.0010579767445535937, -8.256287586591169e-05, -0.01090908041186836, -0.04339774309557921, -0.10273249351608153, -0.1863535970702263, -0.2831385546385811, -0.37514441110166025, -0.4414862740843056, -0.4633373620047547, -0.428739795803814, -0.33597332393473395, -0.19460930508583263, -0.0239701677849283, 0.15067644639799557, 0.3032635974329417, 0.41208185921924173, 0.46382388836552735, 0.455682756856752, 0.3951548233916669, 0.29774403949433453, 0.18322842792720792, 0.0714259937412464, -0.02156674649885241, -0.08588693876052243, -0.11875647327097734, -0.12369221901765534, -0.10848333631572193, -0.08259332574128571, -0.05470331731219163, -0.030980551596337478, -0.014383046603273905, -0.004977519421305771, -0.0009648762513058585, 4.6021739018474846e-05, 4.192374200549061e-06, -7.257946059383056e-05, -2.8718986526449017e-07, 4.263244392011919e-05, -1.4117767103308854e-06, 8.935679664968236e-05, 0.0005291647133947206, 0.001030446265085873, 0.0007348977896678641, -0.0005105995993495622, 0.001422105450580858, 0.02145580982700441, 0.09469940284540232, 0.28766125417009747, 0.7091112663500817, 1.5174531625451435, 2.921002606100252, 5.167770667481752, 8.522409153153085, 13.229870863924857, 19.467864052074965, 27.292967647348927, 36.58782327934733, 47.01858749764477, 58.01232235412234, 68.7628901090244, 78.27110531334797, 85.42058465082198, 89.08541744771125, 88.26019944204656, 82.19801732495172, 70.53853963706906, 53.40798617460082, 31.472554792316853, 5.925352431991289, -21.588285346466385, -49.1052057256532, -74.52779994504971, -95.83699193877182, -111.31024390660119, -119.71779112074172, -120.47172919018584, -113.7075411428498, -100.28560698792684, -81.71016301118536, -59.97373055879988, -37.344746768214, -16.12362547252914, 1.6033239664401042, 14.18240519566376, 20.557184502576717, 20.359497675667953, 13.91800881078007, 2.1857241465745356, -13.39954504878978, -31.100947936350195, -49.08939436480061, -65.6451242106528, -79.33025610940619, -89.11399257501756, -94.43966264983406, -95.23113898231408, -91.84414474509907, -84.97448078263086, -75.53946388700578, -64.55047555688475, -52.99350358077498, -41.73132981258815, -31.43669387012414, -22.559469149177442, -15.32378815455373, -9.754660629107912, -5.723162838697567, -2.999795780427245, -1.307075499656444, -0.364388507202752, 0.07919690105307062, 0.22567862010321277, 0.22149781261420481, 0.1608617083231657, 0.09543076552472549, 0.046726900865238924, 0.018224554845992086, 0.0050955210331355945, 0.0007013967851142812, -9.09590883242384e-05, -2.8736577683647877e-05, -1.2183858097626832e-06, -1.5640326137148608e-05, 3.671114179553459e-05, 8.725247713648463e-05, -5.7463616168792586e-06, -0.00021905869655343405, -0.00026494452607098325, 0.00023433689014250802, 0.0013671429676421914, 0.0025942527509330592, 0.00276521765570882, 0.0007185122252342503, -0.0035286694182701567, -0.007293358798586721, -0.004007956586324959, 0.017024412639807, 0.06926859332219716, 0.1656840587197049, 0.3138070725338072, 0.5099990464519399, 0.7341493956471074, 0.9464037548237334, 1.087389679082755, 1.0829315625040699, 0.8534237903068983, 0.3270058489239111, -0.5453384969286232, -1.775420023639921, -3.3272184663856192, -5.112738436955249, -6.996226711651981, -8.80725319568492, -10.361493515039307, -11.486411749835684, -12.047768966707997, -11.972758327987348, -11.26585945995085, -10.00972040224721, -8.35354031120875, -6.490487807648751, -4.627461542145459, -2.9525412148601293, -1.6061300846607083, -0.6612724224052764, -0.116979217301615, 0.09411415232491574, 0.08533547965226886, -0.012902431539260758, -0.08421482453018245, -0.052652155583196, 0.10177988919104976, 0.3424935278406145, 0.5913588558459548, 0.7565000924529071, 0.766581243497889, 0.6032252062701521, 0.3225085432590598, 0.05803213172749575, 0.0016133632929011472, 0.36251721936776043, 1.3114866623560266, 2.920543172208166, 5.11250788870297, 7.6345670690641, 10.067517412778853, 11.876679894287335, 12.502570157280768, 11.48050226315371, 8.569989366378472, 3.868805370577517, -2.1155983529136324, -8.462477651783859, -13.92050517143041, -17.075726569497238, -16.594437240570496, -11.516565867185895, -1.561315300889184, 12.60126394069562, 29.161169406812913, 45.10509561027689, 56.30982933115563, 57.80504909002877, 44.19594797108849, 10.212858472697956, -48.665909506027575, -135.58731767218833, -251.76967601144847, -396.0960305830043, -564.917044269874, -752.1247209258495, -949.5657352858962, -1147.6018999775201, -1335.8395267542246, -1503.968667582857, -1642.61338086802, -1744.1049489601658, -1803.099012387839, -1816.975822814321, -1785.9878041588893, -1713.1470988076715, -1603.874162225431, -1465.4532907674281, -1306.3593500995123, -1135.5299869713995, -961.6584855643824, -792.5746070194641, -634.765748401797, -493.08444918812353, -370.6414092779182, -268.78441846454115, -187.30133246910776, -124.74585129057998, -78.81414990716354, -46.72413057775729, -25.557207775721725, -12.534232418245198, -5.210323571151088, -1.5860295503214932, -0.14279141085500058, 0.1819125001907526, 0.06052476208677902, -0.13717796195604223, -0.2525196042822682, -0.2553114130336118, -0.17826785949234264, -0.07162503743789536, 0.02292109204463175, 0.08263650791465511, 0.1034544727755292, 0.09401219110392267, 0.0682216779747639, 0.039160862738084376, 0.015570129215917872, 0.0009989624796182689, -0.005139989980081134, -0.005648619198169886, -0.0036847648690162514, -0.001549141745720359, -0.0002840268748662557, 8.558514074866613e-05, 1.0377014119547788e-05, -8.521969870450122e-05, -5.476783835226449e-05, 9.44975701197847e-07, -6.714702219638683e-05, -0.00026494498971005645, -0.00040986686822321023, -0.00026331325959696067, 0.0002465730665129971, 0.000870578294488184, 0.0010949689142942345, 0.00044485935585585897, -0.0010884856022933445, -0.0027624675268484015, -0.0032581271482859738, -0.0015388500387290688, 0.00163453165941343, 0.0019179662377013474, -0.009925301891028582, -0.04788509179984788, -0.1281866238416224, -0.2638688153069784, -0.4567070156209224, -0.687683523918992, -0.9081631491000565, -1.0346417704993225, -0.9500760393166267, -0.5141839079688435, 0.41633961421468507, 1.958891931775468, 4.171029070063946, 7.017610161597644, 10.34672870764058, 13.882442707956805, 17.240872801670516, 19.97291003422771, 21.631802198207247, 21.857917620706324, 20.467025888282784, 17.524195917471438, 13.382432690287802, 8.66267278436475, 4.16780640063096, 0.7268134807476628, -1.0229107959451613, -0.8932383582533444, 0.5910306567800384, 1.9656027002552388, 0.684080419447128, -6.89685241968821, -25.37110344644972, -59.95989696566095, -116.01873813287708, -198.40756644748868, -310.7821233322211, -454.88513248512464, -629.9283523600747, -832.1721440617331, -1054.8261636553184, -1288.2136852071085, -1520.2629793086596, -1737.314728638763, -1925.1768426199512, -2070.332087530221, -2161.17930934714, -2189.1774064911615, -2149.7647386073145, -2042.9455912923895, -1873.46793345171, -1650.559465600064, -1387.2369199819348, -1099.250997538251, -803.7704093473425, -517.9381201506002, -257.44732776495397, -35.28525952298073, 139.24031583560702, 261.10015980691577, 329.66569987767065, 348.407557654102, 324.2361797898499, 266.5758146115833, 186.28521225761602, 94.54637558296572, 1.8364620846737452, -82.92074470743468, -152.95540152197506, -203.96916501219076, -234.1690058072669, -244.04765940407944, -235.96562156965575, -213.605214392478, -181.37295633027918, -143.82568337818688, -105.17242949993116, -68.8789509614112, -37.45054213077715, -12.369612224265289, 5.839609560277427, 17.4519812162577, 23.32602301028215, 24.66973843577367, 22.820060634811384, 19.059913346135744, 14.486994489202198, 9.938629648367908, 5.968710674187974, 2.8667038057040046, 0.7053680584791479, -0.5969038955921483, -1.2117622339552414, -1.3443206004597446, -1.1903845012215695, -0.9092812306219116, -0.6119990749555151, -0.36187340649945604, -0.18339144786429987, -0.07465858204746507, -0.019864086372642815, 0.0006842516262874526, 0.004071922754487053, 0.0018292104118047417, -0.0002458287996696145, -0.000610811274360963, 4.934429388917383e-05, 0.0005718289143459654, 0.0003444095889153825, -0.0004500961072720012, -0.0011597534657964285, -0.0012164470689476185, -0.0005867502357626336, 9.070276915405888e-05, -0.00027085359424636543, -0.0027288757463217127, -0.0077816897737564925, -0.01499902735663626, -0.02296257983576146, -0.029556438550269216, -0.032529356110958106, -0.030161662223019286, -0.021834622296148576, -0.008326680795290623, 0.00826107647571287, 0.02494300086382309, 0.03854172754459424, 0.0464568004522403, 0.047309352078219555, 0.04129616895675243, 0.0301626705137301, 0.016801251974609948, 0.00457806344928053, -0.0034448764917030723, -0.005203071369604217, -7.488327929091155e-05, 0.011019236306669058, 0.025874341628873313, 0.04153961017100867, 0.05499796927538839, 0.06381984508185416, 0.06663963362727132, 0.06335549543186145, 0.055026776542785774, 0.04351907595329657, 0.031005358205052864, 0.01945848761203125, 0.010260201201309712, 0.00401094932683379, 0.0005678593187391451, -0.0007389829060531337, -0.0007964533119623656, -0.0004061890859406612, -7.952188914354602e-05, 2.0234809558389184e-05, -9.122047551890475e-06, 1.3663425680303016e-05, 0.0001727349845589336, 0.00036533051793691224, 0.0003709703628098774, 9.647234469375472e-05, -5.034619931931915e-05, 0.0012358549207108606, 0.006435989733397278, 0.019226092204462347, 0.04414412462948712, 0.08590743462071852, 0.1484574786868022, 0.23389278945332287, 0.34151204667014384, 0.46719551349605937, 0.6033125632702421, 0.7392557177301545, 0.8625837033790856, 0.9606308253910243, 1.0223337783638862, 1.0399635904984537, 1.0104456282041387, 0.9360087777088784, 0.8240173704940303, 0.6859857327694634, 0.5359271587262538, 0.3883161615118495, 0.25603368494329914, 0.14862937866056578, 0.07112211820046674, 0.02374548002957036, 0.002544199741522411, 0.0006253516426064831, 0.0097809933944538, 0.0221457051228419, 0.03156917374803798, 0.03446436274042579, 0.030016524659916267, 0.019779444182194326, 0.006812440348146318, -0.005401608009975057, -0.01398754730460943, -0.017420851539175497, -0.015828357708284477, -0.010808267668004181, -0.004850598445037341, -0.0005336701861972841, 0.0002782455180797057, -0.002995523905517367, -0.009473320923112254, -0.017075633546854836, -0.023169595509557425, -0.025430589855989935, -0.02269831294548142, -0.015598942633567163, -0.006754638279719776, -0.0004949909304899367, -0.002100754008888592, -0.016721701554828137, -0.04819224370866901, -0.09800163041811458, -0.16465220650246254, -0.2435638432200794, -0.3275787056796925, -0.4080119639701337, -0.47599803709716815, -0.5238922081488862, -0.5464674273049975, -0.5416819686690092, -0.5108885439168321, -0.45846979226352014, -0.3909972679266185, -0.31609748657286485, -0.2412523938932864, -0.17275609047644222, -0.1149992463388194, -0.07017137557557451, -0.038378888411442214, -0.01809448846191769, -0.006798131741337184, -0.0016510242570728368, -6.242570169060665e-05, -5.599451719176495e-05, -0.0004042928972402885, -0.0005585791306338407, -0.00044484521820966147, -0.0002163789857329415, -4.361266601023051e-05, 7.951396444996644e-06, -2.490079060802556e-07, 6.519282352353025e-05, 0.0003220863819579382, 0.0007996336576969483, 0.001412858048406498, 0.001992936372059135, 0.0023570487302410747, 0.0023852972778010736, 0.002070550966926416, 0.0015198058931953002, 0.0009073076533713556, 0.0004012105991130688, 9.782552550159378e-05, -6.181496987582729e-06, 8.482301525575747e-06, 4.265788031117917e-05, 3.979573213979202e-05, 1.0213406808286778e-05, -1.2291983040924822e-06, 1.5983098722720814e-05, -1.987175480541809e-06, -0.00011307739644363825, -9.964147227818435e-05, 0.0009674964098031009, 0.005142061162989175, 0.015588177860119536, 0.035527682600128126, 0.06542270436966693, 0.09774713851033752, 0.10907078020115288, 0.04975728703867041, -0.16751413267225423, -0.6781599408978042, -1.6718323397933563, -3.390432585286526, -6.114091330764055, -10.132000114065814, -15.696746683182512, -22.963524784626987, -31.919018378832085, -42.30844398692134, -53.57252975956313, -64.80836571291469, -74.76834000217943, -81.90920601236486, -84.49844188085032, -80.77853371248138, -69.17654361867297, -48.52692970325192, -18.29372376692394, 21.24047740634791, 68.85217467580883, 122.34945894374857, 178.65860585927965, 234.03086709980838, 284.35950424195414, 325.5802548487131, 354.1132304781855, 367.2932656143429, 363.7311752989963, 343.55171758215704, 308.46571591372066, 261.65294136743364, 207.45687769656115, 150.92631514583414, 97.24955798320485, 51.103708678690424, 16.09768506178123, -5.6370008417150075, -13.660139585635179, -9.210014206353337, 5.0352307846999995, 25.388031747941636, 47.71072361249655, 68.02069406345919, 83.05051041215954, 90.67828948514281, 90.16322757822178, 82.15175406372741, 68.4567411104108, 51.6498647854994, 34.53943866746377, 19.628457662968533, 8.649290346075691, 2.259635218182118, -0.01673757144648118, 0.4042961079741718, 1.5829566602017366, 1.6211057427309234, -0.7252517104612491, -5.503982567641783, -11.207827874379497, -14.686275556622071, -11.375259050838222, 4.159626029482448, 37.42440690478929, 93.0481233749903, 173.82344608031894, 279.889079475099, 408.19673560818404, 552.3752357658083, 703.0690513271691, 848.7330212913176, 976.7863437768444, 1074.991772302661, 1132.8829249399614, 1143.0497051432135, 1102.1067260811335, 1011.2099448967219, 876.0465651148892, 706.2938819529658, 514.6138311167956, 315.3113120783222, 122.82723418560666, -49.744127950405826, -191.93163369343, -296.8081900417725, -361.45840299698926, -386.9573741809341, -377.89879955328536, -341.5586982421342, -286.79971400807847, -222.89586906071276, -158.43900800637115, -100.45918800524379, -53.84991542810212, -21.138500946942784, -2.5900911521509538, 3.4111500535258346, -0.20739402398962276, -9.859574821224179, -21.9328659058021, -33.3130614144068, -41.74162389060527, -45.97938373288758, -45.78355896173976, -41.73363328014365, -34.95923678710044, -26.826678577663998, -18.65044920565281, -11.472820073970865, -5.936464922675643, -2.2555619954250137, -0.27254618126029284, 0.425644303853165, 0.36464954672969824, 0.04562207541439259, -0.15975070507106268, -0.06623377862465517, 0.319935429918755, 0.8409140551072253, 1.2567479761493412, 1.3251630676423667, 0.8726666515348723, -0.15787154151419, -1.6914622400619868, -3.5373517544137556, -5.430456900075487, -7.0867108264071135, -8.2593631290363, -8.784375412050862, -8.606489873038347, -7.782354066882194, -6.4621348117088715, -4.855290348675342, -3.188807356898548, -1.666868438782829, -0.43966059499122956, 0.4136797217645134, 0.8864490906884527, 1.0319519187081025, 0.9417579029576354, 0.7205033082784605, 0.462997282840494, 0.2381579092483822, 0.08217719764496761, 0.0005874618747795543, -0.02301916689725244, -0.0150632184448821, -0.0005324909232680304, 0.004973391646672216, -0.0019436861323849544, -0.014821066687167893, -0.02334395487562444, -0.020544967206388643, -0.008458045130330943, 2.1887744939662415e-07, -0.015980421560066446, -0.07759908895523446, -0.19618172287629512, -0.36294395535004303, -0.5419912462533273, -0.6689117647234726, -0.6561965305458731, -0.40527215054249516, 0.1766372042836004, 1.1577943253199972, 2.564963010926757, 4.371615918091876, 6.493974548584217, 8.796150055188914, 11.104011557170285, 13.225816029104308, 14.976397302230621, 16.201062896062112, 16.7953995529322, 16.717917958111496, 15.993722805153654, 14.709485833351298, 13.001060329579232, 11.031604385146656, 8.969279023051694, 6.967323365006254, 5.148641102273924, 3.596600955879658, 2.352536800059335, 1.4192875798982265, 0.769240242337346, 0.3548534770492369, 0.11957989869737023, 0.007418482213008553, -0.030097411102614224, -0.02998644964079233, -0.01684226256231677, -0.0041615529905419555, 0.002924384665136899, 0.004452174615845493, 0.0027391725527683613, 0.0002932237123809918, -0.0013012501250044028, -0.0016252300091232708, -0.0010917172359615015, -0.00038986346239696604, -3.7692220951703956e-06, 2.151296140244076e-05, 3.6099879602745364e-05, 0.0005465282768574759, 0.0019225624250010175, 0.004185145048775991, 0.006957923770293614, 0.009589867542703025, 0.01138904048631144, 0.011870171917874282, 0.010920897172601413, 0.008828627138509423, 0.006165603596399515, 0.0035819679324141703, 0.0015888517220384887, 0.0004127904666056185, -2.914116469571304e-05, -3.31801769068328e-05, 6.102436871283389e-05, 3.877945650488639e-05, -9.600413497459584e-05, -0.00014352397476167454, 0.00016044217653978768, 0.0009600129277603694, 0.0021251231877895023, 0.0032063985913419893, 0.003539100390672779, 0.0024767487573301764, -0.000323852401774474, -0.004679101125025644, -0.009822990403152633, -0.014570356932948062, -0.017669569728556808, -0.018233218198336745, -0.016085294508662754, -0.011872672079658664, -0.006864038866928259, -0.0024824522861411997, 0.0002544582240917471, 0.0011360603102197149, 0.0007769049713760453, 0.00017698508182319218, 2.8088727911483748e-06, 4.8756241974352744e-05, -0.00047169246951246066, -0.0011878498802689662, 0.002872595580205194, 0.0259895729642454, 0.09634329892522131, 0.2581989480276515, 0.5687601757974273, 1.0868233942554277, 1.8513954565243862, 2.8505866066145322, 3.9842413226265303, 5.027484536546376, 5.605884767314521, 5.195279166426567, 3.1594093663818263, -1.164513948844579, -8.328832777151815, -18.593594543067248, -31.718766252377378, -46.76228211070923, -61.92639305075876, -74.50206039801778, -80.9598037470955, -77.19871218485615, -58.966562305509484, -22.432312619611956, 35.142111183740745, 114.71250275360897, 214.84980078665012, 331.33845503367434, 457.0830088006235, 582.4041888244296, 695.761389522071, 784.8794936290552, 838.1914974951356, 846.44389972899, 804.2600573731227, 711.4282113403882, 573.6840411205304, 402.83175579014153, 216.07291057338543, 34.236328535180995, -120.55658355686445, -227.58596882438925, -270.29137529386225, -238.71443634699307, -131.25914375316592, 44.53046910001049, 272.358436796206, 528.7605903343305, 785.7440981569929, 1014.1812849905858, 1187.5271415786292, 1285.3552063052775, 1296.201075465351, 1219.2722604590047, 1064.7221208594585, 852.3985473919764, 609.1841662289515, 365.06248472288587, 148.64073710076636, -17.22006377149319, -119.03394832975918, -155.0151887702019, -135.71499363617707, -82.82445180507712, -26.265521903600746, 0.05310764491779154, -36.76623090610639, -163.56331169436245, -396.75015112869204, -739.2599087730348, -1179.2770259359968, -1690.9622976742216, -2237.1043391498274, -2773.379146747841, -3253.7165217943234, -3635.8378171000713, -3886.2828747205085, -3984.2716228142626, -3923.8895694683492, -3714.3485375192536, -3378.3515130498404, -2948.8552974628083, -2464.7378160822623, -1966.008477085668, -1489.23323375483, -1063.7797803526398, -709.3365580281493, -434.9484127035327, -239.57627047144615, -113.96489129963192, -43.425017542398216, -11.029010497647304, -0.6946414436317893, 0.3088549009836776, -0.22856043498910256, 0.033077292377631996, -1.4733400729017647, -10.82180831437933, -35.6529166851011, -83.07284870819397, -157.76776288206202, -260.6460350605773, -388.21148852735536, -532.7364658377056, -683.1677828951758, -826.5832290675501, -949.9384654172288, -1041.8137604663539, -1093.8884345233382, -1101.9515297666007, -1066.335304725059, -991.58102883281, -885.6115175728343, -758.5564415217893, -621.4090666378023, -484.7178976489138, -357.4890495734293, -246.42374012771987, -155.55093313085771, -86.24958500079147, -37.59870721655311, -6.954336860260023, 9.365466149441282, 15.403263143510879, 14.987274057448785, 11.32093209789808, 6.7619015390673765, 2.780869829698119, 0.06297404575168865, -1.3005681148840875, -1.584480435636197, -1.2160810524903998, -0.6106920363203051, -0.07158915484289899, 0.24635826296189808, 0.32264408433784925, 0.2266719073691636, 0.06376445847686822, -0.07133243197689426, -0.12311256674690153, -0.08323321521075432, 0.01889528964125668, 0.13551398546200238, 0.22147778637568638, 0.2497853528073381, 0.21781716218836608, 0.1439983257263861, 0.057619683807208145, -0.013302183697490994, -0.05170707822079608, -0.05575325553260157, -0.036874520256353946, -0.013037921716556954, -0.00011776290143846759, -0.004730814662046827, -0.021176626666989475, -0.03358318472742574, -0.022492771028175217, 0.02646954194684165, 0.11502449862789145, 0.22873434550408794, 0.33933848221999174, 0.41285497261540544, 0.42144692693835345, 0.3555690938501091, 0.231972757666655, 0.09447870462961772, 0.0061661512257199635, 0.033989423672508415, 0.22920797094833945, 0.6086332021782476, 1.1420803544423155, 1.7503656250798914, 2.3158736177690553, 2.7046432925722064, 2.7958168457299934, 2.5119571125516735, 1.8428202786532577, 0.8560205597406066, -0.30941983768088177, -1.4668622946627965, -2.4192191733715216, -3.0020530382701445, -3.1227953148548724, -2.785887460371199, -2.0967688384247367, -1.2418232226443116, -0.44666151947045407, 0.07970483375366164, 0.20337215527524607, -0.08631609484249711, -0.6509196224519491, -1.2074513091876213, -1.3656016877594521, -0.6931790869869261, 1.2009498287868048, 4.581571189541546, 9.516231879274633, 15.83376270635631, 23.123486861884203, 30.78078365176732, 38.08392353609138, 44.29413065755415, 48.76263554951872, 51.02561571461, 50.87071718143238, 48.36400185942381, 43.833361112974124, 37.81227463058924, 30.954761440328937, 23.937141882766944, 17.363931909756253, 11.693571843225143, 7.195162788875296, 3.9409300170410235, 1.8321032745520283, 0.6497319092079551, 0.11785168349126326, -0.03484482091132327, -0.02686876032756152, 0.0024759651216482376, -0.0045160335449150575, -0.041906165658311574, -0.0704857010709945, -0.05061596145561737, 0.031930865866484234, 0.15385634185594926, 0.25843807602487107, 0.2736868389935778, 0.13845965234406066, -0.1718359371507327, -0.6283591452374601, -1.1469957631871444, -1.6038616171346107, -1.8657365835367319, -1.8288021064393025, -1.4560334934219732, -0.8011785927045132, -0.012468323503482114, 0.6871911917429806, 1.0415777585005743, 0.816645927797394, -0.14121069912019638, -1.8570911836619386, -4.201461593463684, -6.893828882626426, -9.538227706827838, -11.685909341309241, -12.914596146890426, -12.90953935944143, -11.53034093525908, -8.84945945227298, -5.1532456792575, -0.903293007373934, 3.337405399976939, 7.0003463938564865, 9.609491003073865, 10.863250706467566, 10.68503003773243, 9.232796295768715, 6.8660730445437395, 4.076960715073977, 1.3986410264475744, -0.6910263498038797, -1.852551614921343, -1.9391743185307864, -1.0130890628122857, 0.6782747617329387, 2.7598973358887, 4.808245322056407, 6.435455382702284, 7.361831639753974, 7.462856315241508, 6.7822839304276625, 5.5101253108334465, 3.932105999730646, 2.362839682805143, 1.0777925357387306, 0.2586587716306351, -0.03678447466134068, 0.12492302564058333, 0.5807809925504211, 1.119712038043867, 1.5393463958370095, 1.6974449289175078, 1.545636263360088, 1.1373195438026011, 0.6075781187502624, 0.12946021642886146, -0.14339963660600602, -0.13435723230794155, 0.11270215746092252, 0.4153802002259959, 0.4663451999952458, -0.12197425294209963, -1.7486240101953636, -4.743640000167615, -9.291123799785503, -15.371101801998561, -22.732351618532764, -30.90293924700135, -39.238418771441964, -47.00080342903108, -53.45581854773786, -57.97263381537262, -60.109834679693954, -59.6738661527522, -56.74217461667083, -51.64882532069587, -44.9270873409468, -37.229935278930526, -29.24105681967774, -21.58947334080443, -14.780344384137726, -9.150793628003381, -4.854679590250469, -1.8751097372529566, -0.05909203664649441, 0.834247886125379, 1.081592883520507, 0.9485056881065592, 0.6544272761265856, 0.3532332492135964, 0.12959877354646923, 0.0084832018315279, -0.026935805955451263, -0.01432637283401591, 0.006701159570808371, 0.007938137796863502, -0.021286997376013462, -0.07485557377972288, -0.13562312308995061, -0.1835013089148165, -0.20309591478093664, -0.18874954579981434, -0.1458801871679515, -0.08867530291342868, -0.03519823682944582, -0.001566753282354281, 0.0030321651449441225, -0.02090354754220468, -0.06335686136892865, -0.10773037951822574, -0.13567639368365592, -0.13246007027190176, -0.09127834747903668, -0.015477341097259312, 0.08183830968236665, 0.18065670524427987, 0.25861697108617493, 0.2961385524407111, 0.2808969822216091, 0.21062845891734067, 0.09367952715027511, -0.0527374534588731, -0.20610157332834575, -0.3430935994650234, -0.4440408462552879, -0.4963603499790283, -0.49635017249608965, -0.4490882621949653, -0.36665067113994737, -0.26518004787695904, -0.16135709272491458, -0.06931154765271069, 0.001464975949485038, 0.046944706715196786, 0.06816247159010493, 0.06988801395160503, 0.058828502330622465, 0.04184281951902731, 0.02455671779944105, 0.010598724536173778, 0.0014848253108643691, -0.0029827546560251337, -0.00403439203607634, -0.0032188844530256747, -0.0018533887659121424, -0.0007396289046646654, -0.00014540300800036052, 2.920110321324042e-05, 1.858199741556474e-05, -5.108328862349931e-08, 6.259845944378852e-06, -4.970465970759227e-05, -0.0002809951234055622, -0.0007254806593433854, -0.0012947709232812524, -0.001799149270886126, -0.002035009786872825, -0.001889697248368006, -0.001408367105807442, -0.0007831798239188685, -0.0002609568858312015, -6.829298468023731e-06, 9.653500688529254e-06, 3.779382728917118e-05, 0.0004409406399246203, 0.0014808412940251882, 0.0030714317029106007, 0.004626399161462181, 0.00511662564262004, 0.0033863158553014937, -0.0013351763830038177, -0.008906081445608916, -0.017979284949229665, -0.02616745832841587, -0.03074858970598151, -0.02976335349964317, -0.02311032963717826, -0.013093542776418738, -0.003926195361912323, -4.683615782051902e-06, -0.0033083840251767046, -0.01091308443931132, -0.014103895005031945, -0.0005458770918098754, 0.04012437876943255, 0.10771642819558067, 0.1811444078911192, 0.20828492906083426, 0.09831500156318335, -0.28130049749479447, -1.1015273628478273, -2.561375167571801, -4.870576477224649, -8.22646389717921, -12.786961020929711, -18.642103859024598, -25.786675937475668, -34.09638109114652, -43.309549501179035], 'positive_zeros': ['0.33663499338349850951616216263253', '0.840602669496891280351210769258179', '1.80351932704876151773841839122470', '1.91113329301265944928779355276910', '1.93482905611807858650630086515738', '2.09730961705240444748345141327293', '2.32574764180977286338758692199365', '2.42521494632738723457307893262129', '2.42845099258208896765894669284536', '2.54215679615060119698579005785637', '2.59294275511740168070333641520652', '2.69930477157737553204957959417055', '2.86944808053454088208169353824229', '3.02280751128944763674251069582839', '3.18949509739808649516602472934451', '3.39878355710959014789584512321033', '3.52307780115957818715897757022720', '3.59486991487819349566625928273394', '3.62433848994998155292623325915582', '3.64903650112333742707224865203190', '3.66740160253107730561586249301293', '3.68821588661257684820173630755927', '3.77783770503437198700932372241988', '4.21712110329007367991069909982700', '4.27790468720207800230934456506184', '4.31830425762404274827130986333218', '4.48162903083060553061157483700598', '4.56719057115337065583188079934928', '4.59451425935125874738159811681987', '4.67441406496771689143352280681161', '4.68060400702176963914707979818494', '4.69151722685619570225598728960736', '4.84097997171007912815234348814316', '4.94289481757606924129502933645064', '5.03357936346255450219982332669566', '5.05181233627449719491525356056531', '5.15520813837550531855458318983434', '5.28678870161059551461664721660223', '5.31148973087099081828135633611724', '5.42641800393009191105941480259927', '5.79281001245314802768439148892100', '5.83750007089789818103747118500967', '5.90853433365689050427506205141558', '5.99677699763847541971715031520960', '6.00361210190932933877974384582318', '6.01415881187197505451899146134200', '6.04617873448739441364004847164991', '6.18236823293577027874684331002411', '6.35899788416307813139331277133691', '6.40708763929686860673538073045867', '6.45914288867065132690537763409194', '6.63102492328295062507112919442680', '6.66394405070562912935527997122573', '6.76954759821916524734056361812441', '6.85902930013229628673272700306129', '6.95977393484443984075993531816358', '7.05101291507953887870061642382480', '7.07236362740617034961699628308910', '7.08879819042059365802511269525375', '7.09332890571311192474067950347796', '7.17835237114699243479607450892134', '7.25640684521460144674291903024516', '7.33727245897799606280269382786690', '7.35118704892474149938195512249571', '7.37124917646129727597585952061283', '7.39727395962489050433871042774491', '7.65538138934954537305403392103775', '7.70229613149571380523816029498900', '7.73673413998218321588103746074599', '7.82421778983140250247807195448837', '7.989095101302902548308098827480867', '8.008697569370666197617668340365541', '8.010582384727180109768103075881476', '8.223933758845294494959907695022074', '8.314037887750172186842692903275566', '8.337579529425072061015132709781328', '8.388187763864793944217306503595290', '8.547074224549717038125896281475036', '8.576070669138318105499200333447058', '8.580606293894004414992790591931411', '8.605981583085119117281117588125687', '8.615049088521025700493071100411959', '8.623092770098183662905856474211925', '8.648507334275361163928768731747105', '8.672680076593385096086781910153538', '8.749281084830674980893654728294178', '8.791730475458109670612653961113464', '9.012293052843298308445987640551692', '9.041094055793296856686353436234606', '9.151671938806780205743081172052204', '9.277870869383365607802339168101950', '9.335428144864701899625525865973859', '9.400053005328048438913470314269602', '9.402907339106312293078091655613329', '9.408569874164116857878163937354724', '9.678802075328873372790333170407114', '9.720875159998078997906835981996190', '9.833408095384208736425607964525850', '9.913861828082166033268532562154267', '9.931916942921962243781696739185503', '9.937692601084918336223512194281731', '9.975440516733443496364393678535147', '9.997920265924044007766611695230250', '10.01382899820837782735571331020684', '10.08377564760850675841894361234239', '10.08496482764488674377084844213059', '10.15242427152875456195570961638909', '10.22060011920424518086121041235876', '10.39695854605230818572181306643072', '10.57431105887403485800104486571117', '10.57970530246585255993190735620065', '10.60024006133918225112399872516834', '10.69629314685900320849090979998261', '10.78204111084409700682967660388462', '10.80094571347772997344294808152484', '10.89013865084419211115554209392451', '10.89611068764399141558334075870655', '10.97287172402162558728539641906324', '11.14166482605076096030060578329783', '11.17089615573558642086859872206279', '11.19694399901726266972220934251693', '11.27008733233902995908185165607577', '11.27699900407404653424500684347453', '11.28268786247941478890160201829197', '11.46898762746772847264017701162827', '11.52106907446574385740040894748650', '11.52254472677245687643893826720218', '11.53627588225444625585037759735447', '11.58396300389461956135187849472033', '11.75114440425857549769520759626293', '11.80263783270728393119184326481872', '11.84577863036101994033090550882347', '11.91049142222315017987804321053830', '12.02050504283647730236679127649013', '12.02825511134601057031413111394001', '12.12620799498255366611452399803969', '12.20746569336512079093491929639466', '12.20951197224154527463370358443639', '12.22238145556166435774378668696439', '12.26080821337876697931680632070093', '12.42730590728811132991081768202140', '12.47299811079381710247712652746586', '12.49862358696200197818924384934535', '12.60117652900676482200157105995156', '12.62707780425592769190633463340280', '12.68595656100089856444479119597006', '12.81938882166421447036056916605822', '12.86705748010902315276593109137069', '12.93638418520070515313129313396976', '12.93836797014185057406395240496179', '12.96174536832155259188761446268053', '13.04612654294961150131848483168579', '13.06333603176451627867364086827974', '13.13164540119560641575419823775163', '13.29710577721514152244328050244370', '13.33328786289006017623822044689032', '13.46572944405036329529590712506146', '13.49621310297348168381822310242601', '13.49940833364045067197241688193654', '13.50330128522437668413479190720514', '13.61813415860792534176184067111475', '13.63692981013337820844174188838873', '13.68477986512241917689039189820771', '13.73437766346699013638322099364427', '13.74349436034626932759294383638663', '13.76510114089098072099725010068221', '13.79229880352355306982404814771722', '13.88625020839372426783470706554678', '13.89833404375414612127693639093487', '14.12796569723191849447857700651273', '14.17912554245879296819183477160234', '14.23330579335308102454371215832317', '14.27757045370274437708462084493396', '14.39736827457890762328597777299836', '14.49547890865336996274585757183864', '14.59190111820962048798259125435199', '14.66609146321388820445480692163392', '14.77663531250962499054413475816582', '14.84494962934818121891519417654126', '15.14261221794553540389408834196634'], 'prelabel': '36-87e18-1.1-c1e18-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.8334857512790124, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e18-0', 'trace_hash': 1557918283118283475, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.33663499338349850951616216263', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.840602669496891280351210769258', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.80351932704876151773841839122', 'prec': 103}}
• lfunc_search •

  Column	Type
  algebraic	boolean
  analytic_conductor	double precision
  bad_primes	bigint[]
  central_character	text
  conductor	numeric
  conductor_radical	bigint
  degree	smallint
  dirichlet_coefficients	numeric[]
  euler11	numeric[]
  euler13	numeric[]
  euler17	numeric[]
  euler19	numeric[]
  euler2	numeric[]
  euler23	numeric[]
  euler29	numeric[]
  euler3	numeric[]
  euler31	numeric[]
  euler37	numeric[]
  euler41	numeric[]
  euler43	numeric[]
  euler47	numeric[]
  euler5	numeric[]
  euler53	numeric[]
  euler59	numeric[]
  euler61	numeric[]
  euler67	numeric[]
  euler7	numeric[]
  euler71	numeric[]
  euler73	numeric[]
  euler79	numeric[]
  euler83	numeric[]
  euler89	numeric[]
  euler97	numeric[]
  euler_factors	numeric[]
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  is_instance_Artin	boolean
  is_instance_BMF	boolean
  is_instance_CMF	boolean
  is_instance_DIR	boolean
  is_instance_ECNF	boolean
  is_instance_ECQ	boolean
  is_instance_G2Q	boolean
  is_instance_HMF	boolean
  is_instance_MaassGL3	boolean
  is_instance_MaassGL4	boolean
  is_instance_MaassGSp4	boolean
  is_instance_NF	boolean
  label	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  self_dual	boolean
  spectral_label	text
  trace_hash	bigint
  z1	numeric

  
  {'algebraic': True, 'analytic_conductor': 0.001420150834673389, 'bad_primes': [3, 29], 'central_character': '1.1', 'conductor': 81535464022367037427533666993843729, 'conductor_radical': 87, 'degree': 36, 'dirichlet_coefficients': [1, -2, 3, 2, -7, -6, -4, -1, 3, 14, -6, 6, -11, 8, -21, 4, -32, -6, 2, -14, -12, 12, -6, -3, 34, 22, 1, -8, -10, 42, 8, -1, -18, 64, 28, 6, 20, -4, -33, 7, -68, 24, -3, -12, -21, 12, 19, 12, 27, -68, -96, -22, -1, -2, 42, 4, 6, 20, 20, -42, 24, -16, -12, -13, 77, 36, -14, -64, -18, -56, -28, -3, 43, -40, 102, 4, 24, 66, 9, -28, 0, 136, 8, -24, 224, 6, -30, 6, -6, 42, 44, -12, 24, -38, -14, -3, -81, -54, -18, 68], 'euler11': [1, 6, -26, -169, 460, 1938, -7939, -6352, 93064, -220713, -588046, 5323182, 330459, -60022879, 69159966, 445746144, -1248237636, -1751031277, 14689255023, -19261344047, -151036753956, 593288117664, 1012571062206, -9666744685829, 585428276499, 103733757898122, -126052882536526, -520429708723683, 2413840483067464, -1812299731721072, -24915982882788019, 66905016134938278, 174684923448290860, -705954940631245019, -1194692976452876186, 3032682170995762626, 5559917313492231481], 'euler13': [1, 11, 33, 19, 484, 3635, 5989, -7910, 21400, 328794, 368440, -4176168, -17362703, -14359812, 51809026, -472892417, -4553078857, -4550813008, 32473776559, -59160569104, -769470326833, -1038944640149, 1479717591586, -5331697676916, -83806451104727, -262048348742856, 300547826845240, 3486695766846162, 2950171725568600, -14175988716832670, 139532231798538709, 1100951012462839655, 1905690170678455876, 972531967267724383, 21958748103044934753, 95154575113194717263, 112455406951957393129], 'euler17': [1, 32, 636, 9168, 107716, 1075374, 9488972, 75394932, 549525638, 3708760934, 23410558147, 138909905608, 779417417940, 4146983519552, 21000151016102, 101355659628906, 467303236083537, 2058962915267918, 8680483977882271, 35002369559554606, 135050635228142193, 497960355756815178, 1753953613015855142, 5888123579120544064, 18813241705328587860, 57000106333741978184, 163306375191898421827, 439814083598090368198, 1107840334348345211462, 2583927291625041115956, 5528486095650559695692, 10651125697558189095438, 18136985965672430468164, 26242694536241991190224, 30948518032924128353916, 26471688380362776453664, 14063084452067724991009], 'euler19': [1, -2, -33, -43, 907, 88, -15761, 6234, 526856, -253857, -10948627, -451388, 217872346, -111041419, -4764832328, 840233774, 92916967495, 27457863777, -1750903420621, 521699411763, 33543025265695, 5763163455866, -620957713817288, -274949546544481, 10249996463106826, -403482976523732, -185946696866894707, -81916530895083603, 3230189044320003656, 726200273971497246, -34884056439401763521, 3700662544678621192, 724699064005075897747, -652788462284616326857, -9518566647731498533473, -10960773715569604371878, 104127350297911241532841], 'euler2': [1, 2, 2, 1, -4, -15, -14, -22, -30, 4, 42, 72, 232, 163, 54, 107, -307, -860, -451, -1720, -1228, 856, 864, 5216, 14848, 9216, 10752, 2048, -30720, -45056, -57344, -122880, -65536, 32768, 131072, 262144, 262144], 'euler23': [1, 6, 13, 198, 1726, 5684, 22852, 237892, 1222151, 1544926, 12854897, 112304298, 15330732, -1458953602, 1302687861, -5767597954, -381323450868, -1440526017186, -596591623839, -33132098395278, -201720105509172, -70174364306318, 364545473710101, -9390325803557486, 2269498540640748, 382376531637871206, 1006679649755771057, 2782647576663386738, 50629452106272338999, 226665818929659921884, 500792997520528375492, 2864942681246880604972, 20009235496153882170334, 52793776621949466630186, 79723935403852982436493, 846300237363977813556618, 3244150909895248285300369], 'euler29': [1, 10, -36, -578, 1016, 21063, -22778, -592636, 552441, 19185875, 16020789, -498406876, -555532642, 14897459703, 20839327384, -343807879538, -620995547124, 5002464129610, 14507145975869, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler3': [1, -3, 6, -10, 15, -21, 28, -33, 36, -37, 36, -33, 28, -21, 15, -10, 6, -3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, -8, -88, 1175, 2935, -95354, 83734, 5121343, -15576190, -214533311, 1072347695, 7530307288, -53974915502, -225699026103, 2357070708448, 5305263707573, -90443497568807, -63546541686843, 3016759237501459, -1969942792292133, -86916201163623527, 158049111112307243, 2176804297736605408, -6461571498855728553, -47902936189688962862, 207178438551994940968, 914595738086015048495, -5672179683717723611681, -12766685927387482728190, 130125525294064606408033, 65954155537750425687574, -2328310709646574591222214, 2221630449873037200142135, 27571682840417505967692425, -64013234713752303216906328, -180400934193301945429463288, 699053619999045038539170241], 'euler37': [1, -20, 240, -2269, 18773, -118409, 546048, -1505305, -5399881, 140220268, -1319930786, 9027617334, -54653437317, 266050494186, -662544800951, -2763918353713, 51970413618945, -511474898941224, 3657434064135413, -18924571260825288, 71147496244335705, -140000756370624589, -1241715626695127111, 18448994028662734002, -140225767466853004653, 857008659555029023422, -4636229766422796311906, 18223269983811962020636, -25965783389516066875969, -267820285652730656990965, 3594607776884939585119488, -28840788270201971290753373, 169183426709714290810061597, -756589581982668931783790617, 2961002859412119926945817840, -9129758816520703108082938340, 16890053810563300749953435929], 'euler41': [1, 68, 2732, 79524, 1854184, 36327930, 617718564, 9305428128, 126117160274, 1554895353522, 17591274618651, 183830881240028, 1783865333241028, 16139473243016116, 136587032944522846, 1083862880259016814, 8079512830930672073, 56646447878895865730, 373822238115621121535, 2322504363034730494930, 13581661068794459754713, 74700913570331697837694, 385962310800347821835806, 1869858056076996981535316, 8473546284801085377999748, 35801849792805998012108668, 140465012514862268074935771, 509044648616214199916880642, 1692827675521788632282917874, 5121047251387382357517548448, 13937886827170129140112107684, 33607080743682653075019235530, 70327766197177310482026091624, 123667638401387060825505105924, 174189672458832144474453975212, 177760178190052715517854203108, 107178930967531784356353269521], 'euler43': [1, 3, -45, -679, 3799, 35953, -41985, -2376026, 4654921, 80879753, -124963966, -2923869730, 12841489201, 78049687599, -1079976447261, -329598473085, 54748168547443, 44776368685846, -3261703262426839, 1925383853491378, 101229363644222107, -26205385799569095, -3692224557872354061, 11473963050565398357, 81175715329333933849, -794762209066399091110, -1460603862091321925566, 40649566313076713439779, 100599742861235429639329, -2208026086620851403622382, -1677705099023069270195985, 61776750060321200601841579, 280690472550382175804940751, -2157230778376811894439814453, -6147631157819044205804184045, 17623209319081260056638660929, 252599333573498060811820806649], 'euler47': [1, -19, 117, 59, -4860, 58233, -513325, 3488486, -28131034, 128623658, 1140129796, -17807857568, 124898306503, -813503687318, 3483040291028, -99284260941, -110224753873477, 2037787357356288, -20438556318603675, 95776005795745536, -243486481306510693, -10307989823677443, 16996125530363802068, -186573008862472521226, 1346305740023277984487, -9021872369860810213984, 27147957404171089930756, 143946655229748501461686, -1479667977296631126640666, 8624092811591565742843258, -59643993066901028925561325, 318010395886519920165283191, -1247401552872063609365033340, 711737552698401726084205237, 66336352581161204944695671157, -506310793632281675347121661053, 1252453015827223091648143056289], 'euler5': [1, 7, 15, -1, -57, -198, -610, -727, 2083, 10771, 26002, 37370, -7745, -222133, -680461, -964364, 607712, 6539033, 18434481, 32695165, 15192800, -120545500, -425288125, -694165625, -121015625, 2919531250, 10157031250, 21037109375, 20341796875, -35498046875, -148925781250, -241699218750, -347900390625, -30517578125, 2288818359375, 5340576171875, 3814697265625], 'euler53': [1, 1, -138, -503, 10974, 37822, -525687, -1664660, 25250021, 95315685, -995167016, -10282486106, 12539948599, 691255727491, 356576543387, -20781271975832, 56568783466599, 358216320273226, -8202609795566856, 18985464974480978, 158901712757676591, -3093853427945940664, 2813560440640799147, 289080029747172398063, 277939949287333608271, -12078950973937375604722, -61958790323757938868776, 314519227090680691356105, 4415912299366082163024029, -15429793350188712463862020, -258248419602005602054763367, 984760896670288520904090806, 15143530279815095714274208206, -36787987400181395721417542971, -534925128916355324664906380298, 205442259656281392806087233013, 10888439761782913818722623349689], 'euler59': [1, -20, 626, -8564, 162947, -1696940, 24910254, -200626000, 2553583107, -15538477748, 196388922244, -873378871340, 13492483071388, -48723839974648, 997354137368668, -3769558106468820, 75923921551419957, -297399023618888648, 4995624294128214432, -17546542393514430232, 264291170920492870317, -774188074348459782780, 12085300127339740245148, -34833857138463399171752, 569120136093304538563708, -2173535624969833364187460, 28835871393727490507416324, -134609767759186812941797372, 1305179106933204373858412907, -6050055275113974421304534000, 44320259604490992818815797774, -178132284747536166266458604260, 1009193703232082316046894516667, -3129369412105123901163634027036, 13496045056829827903500427271666, -25439829340350154834074287828380, 75047496554032956760519149093721], 'euler61': [1, -24, 136, 1099, -14763, -26612, 1514090, -5581559, -104473494, 980262005, 936281331, -49133146846, 54221391570, 3713982961879, -19803841436352, -185670567383233, 2005909869108029, 1472327064254111, -96825153288065495, 89811950919500771, 7463990622950975909, -42143691055213609573, -274200839716941412032, 3136816271580027409579, 2793506392060769536770, -154412845261434291339766, 179491978175527854061011, 11463327095724511189112705, -74525426401554695438277894, -242875498469368208200852499, 4018923238494232226452242890, -4308889629144449133559545572, -145811678690013139038144966483, 662132976204009403778242932199, 4998230364502695189940221442696, -53804479806117248221121207294904, 136753052840548005895349735207881], 'euler67': [1, 14, -32, -682, 5796, 60182, 497107, 2601082, -46571706, -89197296, 2836640474, -2020680604, 17069214395, -670507002066, -16280748321974, 27121309354516, -177525510497970, -6590984722833208, -10231191562009335, -441595976429824936, -796912016625387330, 8157086365392295708, -328075329406645032854, -905268337908607471062, 1544053519067506122755, -12246762387313889255092, 1151868009340349288087834, -2426749301680501690863312, -84892666319270095984961994, 317670490356720019810283806, 4067686846525325716561285027, 32994310070947178781155996834, 212899977044150407604331370884, -1678442296593410753118067229326, -5276510680199813276664422492192, 154667719313357026672225884302378, 740195513856780056217081017732809], 'euler7': [1, 4, -11, -55, 66, 374, 119, -613, -7208, -12134, 88572, 142848, -536011, -791002, 184498, 3122533, 33800345, -9073301, -365501233, -63513107, 1656216905, 1071028819, 442979698, -13294370614, -63061158139, 117641470464, 510599954172, -489650667338, -2036081594792, -1212101293459, 1647113176919, 36236489892218, 44762722808034, -261115883046865, -365562236265611, 930522055948828, 1628413597910449], 'euler71': [1, 28, 134, -5058, -92230, -295310, 9519255, 138484508, 374996946, -9994700294, -127252903162, -320416895110, 6864434010851, 77716662201882, 144679893780110, -3606790368380910, -29546900140126224, 49009998494139752, 1914476521633020253, 3479709893083922392, -148945923606376295184, -1290909947537579879010, 3676559307854039464910, 140218683006387791838582, 879335945746981894826771, -2914230161804015633368010, -82174011578136365755996282, -458242023610141741359715114, 1220706390114900666197812146, 32006856912306117389384321668, 156207954477258744593679310455, -344061982119843293459742389410, -7629377262452451437002590094630, -29706675742571825383860957926958, 55877681497593583768693782862214, 828991274755343615911665972612548, 2102085018129621311776010144838961], 'euler73': [1, -43, 888, -13358, 184502, -2351213, 25832040, -252404694, 2354167993, -20333166464, 148975109506, -914346534322, 4423731769883, 1268511191925, -426612869319200, 6611832777671515, -74648373280790749, 776591982937366054, -7215964915516431616, 56691214754427721942, -397801181213333901421, 2572115351671439750755, -12115055076628147527200, 2629714517382288486525, 669462024705312397054187, -10101150549210337082947234, 120142480502139539928233986, -1197045772539021280138869632, 10117333174178184095506128457, -79186088070516048274825921638, 591606621218858222646358932840, -3930874295827872547880074023029, 22517549180361325103474150351318, -119010242720634249999735298959806, 577535557278214899085405077090168, -2041536164748104243501223577686979, 3465863721549107204083472585375569], 'euler79': [1, -9, -82, 1665, 6709, -152438, -404348, 22461545, -7157894, -1870541243, 8126850221, 158962023876, -597143483446, -11689720137657, 119565726907184, 729473769567002, -10369364506544525, -2028724400936535, 902286961401370031, -160269227673986265, -64715203885344380525, 359659017873545099078, 4657094747858696281904, -35969928152096632717143, -145158089971834524805366, 3052692238770337911532284, 12329316067070182252199981, -224187353324860676816830517, -67772916562178213818954694, 16801096634885385082457458055, -23893534302635380571478905468, -711615548933061222859648149482, 2474212917419283326920223142229, 48508808480063412193538761516335, -188732769569880350864711169431122, -1636451209319328408107434652018631, 14364405059580771582276370834385761], 'euler83': [1, -8, -234, 2464, 21170, -394800, 600379, 37896208, -446353614, -1105697210, 61509840758, -252712240386, -4304401003813, 47969845142298, 8400474449334, -4216300370766766, 35323954454545452, 147533091486972446, -4237337014813148067, 12245246593418713018, 243346722237363618828, -2410825740099616830842, 398672412968791208214, 188955169653927940417614, -1407282471316520612655997, -6857612240817371616476022, 138538136539352781624833078, -206699318686007227159375630, -6925641058882183248915514686, 48803927305854356773028175536, 64174515956129627212248051019, -3502614529583543189121919712400, 15588852624307344409924053560930, 150595532730389401037429761070048, -1187039949955204118079935397525354, -3368352678505365531645628649388184, 34946659039493167390823397237402409], 'euler89': [1, 6, -156, -694, -3404, -25746, 3035191, 13236946, -278777232, -1416799932, -11405650892, 7940957862, 4209032266621, 13140194419338, -249945404179812, -1607993216703362, -17507012849570242, 71140627461568478, 3552231900008687859, 6331515844079594542, -138673048781445886882, -1133585369986152405778, -15682134785892171838692, 73375626809001427224762, 2091810289561808529312781, 351239166585405961198998, -44899357623193154843906252, -496384928948529592002205788, -8692753571075206517890572432, 36734816118107667719574506594, 749663049987651560889984207511, -565952328787020276718646198274, -6659622998524062571023622218764, -120839681000833504336617229719206, -2417490102327914083875495125967516, 8275254581045552056343041008119574, 122749609618842355502421774953773681], 'euler97': [1, 81, 3185, 82471, 1613811, 25949863, 362302042, 4544285207, 52100768296, 547505111492, 5193536282736, 42479546681972, 263323717596387, 516943190734146, -18045629276362598, -399707182302942667, -5752758554039954081, -68393514389764220053, -713679846716078529478, -6634170895807129345141, -54127705234961927948129, -364801953193973592718891, -1597566585028931096232038, 4439167072373361330315522, 219341284991620276196591523, 3432274497311254838805678836, 40703995735930769263860445296, 416230390528348920648370173764, 3842036357123275923733182142504, 32505335845995079373468210842871, 251380504214748340191289956773722, 1746496078508531494067076532350151, 10535543657649806349277167129460659, 52224858819300157456375011251239303, 195639788627865396871139889791734385, 482619095525632157995775859998008497, 577951262543040979328274795306257089], 'euler_factors': [[1, 2, 2, 1, -4, -15, -14, -22, -30, 4, 42, 72, 232, 163, 54, 107, -307, -860, -451, -1720, -1228, 856, 864, 5216, 14848, 9216, 10752, 2048, -30720, -45056, -57344, -122880, -65536, 32768, 131072, 262144, 262144], [1, -3, 6, -10, 15, -21, 28, -33, 36, -37, 36, -33, 28, -21, 15, -10, 6, -3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 7, 15, -1, -57, -198, -610, -727, 2083, 10771, 26002, 37370, -7745, -222133, -680461, -964364, 607712, 6539033, 18434481, 32695165, 15192800, -120545500, -425288125, -694165625, -121015625, 2919531250, 10157031250, 21037109375, 20341796875, -35498046875, -148925781250, -241699218750, -347900390625, -30517578125, 2288818359375, 5340576171875, 3814697265625], [1, 4, -11, -55, 66, 374, 119, -613, -7208, -12134, 88572, 142848, -536011, -791002, 184498, 3122533, 33800345, -9073301, -365501233, -63513107, 1656216905, 1071028819, 442979698, -13294370614, -63061158139, 117641470464, 510599954172, -489650667338, -2036081594792, -1212101293459, 1647113176919, 36236489892218, 44762722808034, -261115883046865, -365562236265611, 930522055948828, 1628413597910449], [1, 6, -26, -169, 460, 1938, -7939, -6352, 93064, -220713, -588046, 5323182, 330459, -60022879, 69159966, 445746144, -1248237636, -1751031277, 14689255023, -19261344047, -151036753956, 593288117664, 1012571062206, -9666744685829, 585428276499, 103733757898122, -126052882536526, -520429708723683, 2413840483067464, -1812299731721072, -24915982882788019, 66905016134938278, 174684923448290860, -705954940631245019, -1194692976452876186, 3032682170995762626, 5559917313492231481], [1, 11, 33, 19, 484, 3635, 5989, -7910, 21400, 328794, 368440, -4176168, -17362703, -14359812, 51809026, -472892417, -4553078857, -4550813008, 32473776559, -59160569104, -769470326833, -1038944640149, 1479717591586, -5331697676916, -83806451104727, -262048348742856, 300547826845240, 3486695766846162, 2950171725568600, -14175988716832670, 139532231798538709, 1100951012462839655, 1905690170678455876, 972531967267724383, 21958748103044934753, 95154575113194717263, 112455406951957393129], [1, 32, 636, 9168, 107716, 1075374, 9488972, 75394932, 549525638, 3708760934, 23410558147, 138909905608, 779417417940, 4146983519552, 21000151016102, 101355659628906, 467303236083537, 2058962915267918, 8680483977882271, 35002369559554606, 135050635228142193, 497960355756815178, 1753953613015855142, 5888123579120544064, 18813241705328587860, 57000106333741978184, 163306375191898421827, 439814083598090368198, 1107840334348345211462, 2583927291625041115956, 5528486095650559695692, 10651125697558189095438, 18136985965672430468164, 26242694536241991190224, 30948518032924128353916, 26471688380362776453664, 14063084452067724991009], [1, -2, -33, -43, 907, 88, -15761, 6234, 526856, -253857, -10948627, -451388, 217872346, -111041419, -4764832328, 840233774, 92916967495, 27457863777, -1750903420621, 521699411763, 33543025265695, 5763163455866, -620957713817288, -274949546544481, 10249996463106826, -403482976523732, -185946696866894707, -81916530895083603, 3230189044320003656, 726200273971497246, -34884056439401763521, 3700662544678621192, 724699064005075897747, -652788462284616326857, -9518566647731498533473, -10960773715569604371878, 104127350297911241532841], [1, 6, 13, 198, 1726, 5684, 22852, 237892, 1222151, 1544926, 12854897, 112304298, 15330732, -1458953602, 1302687861, -5767597954, -381323450868, -1440526017186, -596591623839, -33132098395278, -201720105509172, -70174364306318, 364545473710101, -9390325803557486, 2269498540640748, 382376531637871206, 1006679649755771057, 2782647576663386738, 50629452106272338999, 226665818929659921884, 500792997520528375492, 2864942681246880604972, 20009235496153882170334, 52793776621949466630186, 79723935403852982436493, 846300237363977813556618, 3244150909895248285300369], [1, 10, -36, -578, 1016, 21063, -22778, -592636, 552441, 19185875, 16020789, -498406876, -555532642, 14897459703, 20839327384, -343807879538, -620995547124, 5002464129610, 14507145975869, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -8, -88, 1175, 2935, -95354, 83734, 5121343, -15576190, -214533311, 1072347695, 7530307288, -53974915502, -225699026103, 2357070708448, 5305263707573, -90443497568807, -63546541686843, 3016759237501459, -1969942792292133, -86916201163623527, 158049111112307243, 2176804297736605408, -6461571498855728553, -47902936189688962862, 207178438551994940968, 914595738086015048495, -5672179683717723611681, -12766685927387482728190, 130125525294064606408033, 65954155537750425687574, -2328310709646574591222214, 2221630449873037200142135, 27571682840417505967692425, -64013234713752303216906328, -180400934193301945429463288, 699053619999045038539170241], [1, -20, 240, -2269, 18773, -118409, 546048, -1505305, -5399881, 140220268, -1319930786, 9027617334, -54653437317, 266050494186, -662544800951, -2763918353713, 51970413618945, -511474898941224, 3657434064135413, -18924571260825288, 71147496244335705, -140000756370624589, -1241715626695127111, 18448994028662734002, -140225767466853004653, 857008659555029023422, -4636229766422796311906, 18223269983811962020636, -25965783389516066875969, -267820285652730656990965, 3594607776884939585119488, -28840788270201971290753373, 169183426709714290810061597, -756589581982668931783790617, 2961002859412119926945817840, -9129758816520703108082938340, 16890053810563300749953435929], [1, 68, 2732, 79524, 1854184, 36327930, 617718564, 9305428128, 126117160274, 1554895353522, 17591274618651, 183830881240028, 1783865333241028, 16139473243016116, 136587032944522846, 1083862880259016814, 8079512830930672073, 56646447878895865730, 373822238115621121535, 2322504363034730494930, 13581661068794459754713, 74700913570331697837694, 385962310800347821835806, 1869858056076996981535316, 8473546284801085377999748, 35801849792805998012108668, 140465012514862268074935771, 509044648616214199916880642, 1692827675521788632282917874, 5121047251387382357517548448, 13937886827170129140112107684, 33607080743682653075019235530, 70327766197177310482026091624, 123667638401387060825505105924, 174189672458832144474453975212, 177760178190052715517854203108, 107178930967531784356353269521], [1, 3, -45, -679, 3799, 35953, -41985, -2376026, 4654921, 80879753, -124963966, -2923869730, 12841489201, 78049687599, -1079976447261, -329598473085, 54748168547443, 44776368685846, -3261703262426839, 1925383853491378, 101229363644222107, -26205385799569095, -3692224557872354061, 11473963050565398357, 81175715329333933849, -794762209066399091110, -1460603862091321925566, 40649566313076713439779, 100599742861235429639329, -2208026086620851403622382, -1677705099023069270195985, 61776750060321200601841579, 280690472550382175804940751, -2157230778376811894439814453, -6147631157819044205804184045, 17623209319081260056638660929, 252599333573498060811820806649], [1, -19, 117, 59, -4860, 58233, -513325, 3488486, -28131034, 128623658, 1140129796, -17807857568, 124898306503, -813503687318, 3483040291028, -99284260941, -110224753873477, 2037787357356288, -20438556318603675, 95776005795745536, -243486481306510693, -10307989823677443, 16996125530363802068, -186573008862472521226, 1346305740023277984487, -9021872369860810213984, 27147957404171089930756, 143946655229748501461686, -1479667977296631126640666, 8624092811591565742843258, -59643993066901028925561325, 318010395886519920165283191, -1247401552872063609365033340, 711737552698401726084205237, 66336352581161204944695671157, -506310793632281675347121661053, 1252453015827223091648143056289], [1, 1, -138, -503, 10974, 37822, -525687, -1664660, 25250021, 95315685, -995167016, -10282486106, 12539948599, 691255727491, 356576543387, -20781271975832, 56568783466599, 358216320273226, -8202609795566856, 18985464974480978, 158901712757676591, -3093853427945940664, 2813560440640799147, 289080029747172398063, 277939949287333608271, -12078950973937375604722, -61958790323757938868776, 314519227090680691356105, 4415912299366082163024029, -15429793350188712463862020, -258248419602005602054763367, 984760896670288520904090806, 15143530279815095714274208206, -36787987400181395721417542971, -534925128916355324664906380298, 205442259656281392806087233013, 10888439761782913818722623349689], [1, -20, 626, -8564, 162947, -1696940, 24910254, -200626000, 2553583107, -15538477748, 196388922244, -873378871340, 13492483071388, -48723839974648, 997354137368668, -3769558106468820, 75923921551419957, -297399023618888648, 4995624294128214432, -17546542393514430232, 264291170920492870317, -774188074348459782780, 12085300127339740245148, -34833857138463399171752, 569120136093304538563708, -2173535624969833364187460, 28835871393727490507416324, -134609767759186812941797372, 1305179106933204373858412907, -6050055275113974421304534000, 44320259604490992818815797774, -178132284747536166266458604260, 1009193703232082316046894516667, -3129369412105123901163634027036, 13496045056829827903500427271666, -25439829340350154834074287828380, 75047496554032956760519149093721], [1, -24, 136, 1099, -14763, -26612, 1514090, -5581559, -104473494, 980262005, 936281331, -49133146846, 54221391570, 3713982961879, -19803841436352, -185670567383233, 2005909869108029, 1472327064254111, -96825153288065495, 89811950919500771, 7463990622950975909, -42143691055213609573, -274200839716941412032, 3136816271580027409579, 2793506392060769536770, -154412845261434291339766, 179491978175527854061011, 11463327095724511189112705, -74525426401554695438277894, -242875498469368208200852499, 4018923238494232226452242890, -4308889629144449133559545572, -145811678690013139038144966483, 662132976204009403778242932199, 4998230364502695189940221442696, -53804479806117248221121207294904, 136753052840548005895349735207881], [1, 14, -32, -682, 5796, 60182, 497107, 2601082, -46571706, -89197296, 2836640474, -2020680604, 17069214395, -670507002066, -16280748321974, 27121309354516, -177525510497970, -6590984722833208, -10231191562009335, -441595976429824936, -796912016625387330, 8157086365392295708, -328075329406645032854, -905268337908607471062, 1544053519067506122755, -12246762387313889255092, 1151868009340349288087834, -2426749301680501690863312, -84892666319270095984961994, 317670490356720019810283806, 4067686846525325716561285027, 32994310070947178781155996834, 212899977044150407604331370884, -1678442296593410753118067229326, -5276510680199813276664422492192, 154667719313357026672225884302378, 740195513856780056217081017732809], [1, 28, 134, -5058, -92230, -295310, 9519255, 138484508, 374996946, -9994700294, -127252903162, -320416895110, 6864434010851, 77716662201882, 144679893780110, -3606790368380910, -29546900140126224, 49009998494139752, 1914476521633020253, 3479709893083922392, -148945923606376295184, -1290909947537579879010, 3676559307854039464910, 140218683006387791838582, 879335945746981894826771, -2914230161804015633368010, -82174011578136365755996282, -458242023610141741359715114, 1220706390114900666197812146, 32006856912306117389384321668, 156207954477258744593679310455, -344061982119843293459742389410, -7629377262452451437002590094630, -29706675742571825383860957926958, 55877681497593583768693782862214, 828991274755343615911665972612548, 2102085018129621311776010144838961], [1, -43, 888, -13358, 184502, -2351213, 25832040, -252404694, 2354167993, -20333166464, 148975109506, -914346534322, 4423731769883, 1268511191925, -426612869319200, 6611832777671515, -74648373280790749, 776591982937366054, -7215964915516431616, 56691214754427721942, -397801181213333901421, 2572115351671439750755, -12115055076628147527200, 2629714517382288486525, 669462024705312397054187, -10101150549210337082947234, 120142480502139539928233986, -1197045772539021280138869632, 10117333174178184095506128457, -79186088070516048274825921638, 591606621218858222646358932840, -3930874295827872547880074023029, 22517549180361325103474150351318, -119010242720634249999735298959806, 577535557278214899085405077090168, -2041536164748104243501223577686979, 3465863721549107204083472585375569], [1, -9, -82, 1665, 6709, -152438, -404348, 22461545, -7157894, -1870541243, 8126850221, 158962023876, -597143483446, -11689720137657, 119565726907184, 729473769567002, -10369364506544525, -2028724400936535, 902286961401370031, -160269227673986265, -64715203885344380525, 359659017873545099078, 4657094747858696281904, -35969928152096632717143, -145158089971834524805366, 3052692238770337911532284, 12329316067070182252199981, -224187353324860676816830517, -67772916562178213818954694, 16801096634885385082457458055, -23893534302635380571478905468, -711615548933061222859648149482, 2474212917419283326920223142229, 48508808480063412193538761516335, -188732769569880350864711169431122, -1636451209319328408107434652018631, 14364405059580771582276370834385761], [1, -8, -234, 2464, 21170, -394800, 600379, 37896208, -446353614, -1105697210, 61509840758, -252712240386, -4304401003813, 47969845142298, 8400474449334, -4216300370766766, 35323954454545452, 147533091486972446, -4237337014813148067, 12245246593418713018, 243346722237363618828, -2410825740099616830842, 398672412968791208214, 188955169653927940417614, -1407282471316520612655997, -6857612240817371616476022, 138538136539352781624833078, -206699318686007227159375630, -6925641058882183248915514686, 48803927305854356773028175536, 64174515956129627212248051019, -3502614529583543189121919712400, 15588852624307344409924053560930, 150595532730389401037429761070048, -1187039949955204118079935397525354, -3368352678505365531645628649388184, 34946659039493167390823397237402409], [1, 6, -156, -694, -3404, -25746, 3035191, 13236946, -278777232, -1416799932, -11405650892, 7940957862, 4209032266621, 13140194419338, -249945404179812, -1607993216703362, -17507012849570242, 71140627461568478, 3552231900008687859, 6331515844079594542, -138673048781445886882, -1133585369986152405778, -15682134785892171838692, 73375626809001427224762, 2091810289561808529312781, 351239166585405961198998, -44899357623193154843906252, -496384928948529592002205788, -8692753571075206517890572432, 36734816118107667719574506594, 749663049987651560889984207511, -565952328787020276718646198274, -6659622998524062571023622218764, -120839681000833504336617229719206, -2417490102327914083875495125967516, 8275254581045552056343041008119574, 122749609618842355502421774953773681], [1, 81, 3185, 82471, 1613811, 25949863, 362302042, 4544285207, 52100768296, 547505111492, 5193536282736, 42479546681972, 263323717596387, 516943190734146, -18045629276362598, -399707182302942667, -5752758554039954081, -68393514389764220053, -713679846716078529478, -6634170895807129345141, -54127705234961927948129, -364801953193973592718891, -1597566585028931096232038, 4439167072373361330315522, 219341284991620276196591523, 3432274497311254838805678836, 40703995735930769263860445296, 416230390528348920648370173764, 3842036357123275923733182142504, 32505335845995079373468210842871, 251380504214748340191289956773722, 1746496078508531494067076532350151, 10535543657649806349277167129460659, 52224858819300157456375011251239303, 195639788627865396871139889791734385, 482619095525632157995775859998008497, 577951262543040979328274795306257089]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/87/2/g/b'], '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': '36-87e18-1.1-c1e18-0-0', '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}, {'__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, 1, 1], 'order_of_vanishing': 0, 'prelabel': '36-87e18-1.1-c1e18-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.8334857512790124, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e18-0', 'trace_hash': 1557918283118283475, 'z1': {'__RealLiteral__': 0, 'data': '0.33663499338349850951616216263', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '426735551420417918750031183525,1065590478541186173827787051040,2286232357456574903818092486375,2422649266003650366130043853912,2452687214327100868508124450595,2658655794920918447948215736221,2948235394119547648459605919357,3074325182394385580040063028793,3078427358371524545707329371085,3222566588514582221815983204510,3286945439882013084100250076825,3421775313888983752102268377459,3637457581613351487941650147358,3831863756060468619526555280920,4043165374641679341604942725515,4625703310903716780121595501841,4648983842726490537904049447509,5422888444450870127294313622356', 'Lhash_array': ['426735551420417918750031183525', '1065590478541186173827787051040', '2286232357456574903818092486375', '2422649266003650366130043853912', '2452687214327100868508124450595', '2658655794920918447948215736221', '2948235394119547648459605919357', '3074325182394385580040063028793', '3078427358371524545707329371085', '3222566588514582221815983204510', '3286945439882013084100250076825', '3421775313888983752102268377459', '3637457581613351487941650147358', '3831863756060468619526555280920', '4043165374641679341604942725515', '4625703310903716780121595501841', '4648983842726490537904049447509', '5422888444450870127294313622356'], 'label': '36-87e18-1.1-c1e18-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/87/2/g/b'}