-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1270392159442171155745917860996,1415507358859874084698725531093,1459068626227221787685406718718,1561504248625316361218179574561,1764346546224360172197376590208,1931357193332749219551807346134,2317399753391531909358967921640,2480947226949888874413374237479', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -118, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 626315468010290.9, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '441.1', 'coefficient_field': '1.1.1.1', 'conductor': 1430568690241985328321, 'conductor_radical': 21, 'degree': 16, 'euler_factors': [[1, 0, 118, 0, 7329, 0, 347864, 0, 12928016, 0, 356212736, 0, 7685013504, 0, 126701535232, 0, 1099511627776], [1], [1, 0, 13696, 0, 96678756, 0, 474668448896, 0, 1726257864895526, 0, 4635434071250000000, 0, 9220004653930664062500, 0, 12755393981933593750000000, 0, 9094947017729282379150390625], [1], [1, 0, 1187736, 0, 632475284284, 0, 196968753081795816, 0, 39212142376366900126950, 0, 5108862181812065363177269416, 0, 425497744297030451227292130697084, 0, 20725283253238065882915759335324584536, 0, 452592555681759518058893560348969204658401], [1, 0, 2840192, 0, 3576259172004, 0, 2606307168346742656, 0, 1202118358013343154181606, 0, 359301575523519693247876610944, 0, 67966676013521222054804052130527204, 0, 7441290667129424476913159135120963105408, 0, 361188648084531445929920877641340156544317601], [1, 0, 4015872, 0, 10924993475716, 0, 21937050776253166848, 0, 36263664388467106611525510, 0, 44224960558766385019787899114752, 0, 44401701601424791118986444180593021316, 0, 32903909591259194185129629219497865493571328, 0, 16517976926780506002833800829531584028976727363201], [1, 0, 15214488, 0, 111300185318908, 0, 499736263830315607656, 0, 1498483400493801114061906470, 0, 3063916144969586343088235265324456, 0, 4183771011957698048321810597612833003708, 0, 3506431592397461832967324036887339221249993688, 0, 1413006104539009638843035501053457425807904438071201], [1, 0, 38163256, 0, 699446036548572, 0, 7979756161797717331208, 0, 61712614932671651932620913670, 0, 330573458118897841008099365383257992, 0, 1200358394326696043964731847329320274202972, 0, 2713191833070000001848712803958581824594389589944, 0, 2945190837423705167875564697729320458241471826430830401], [1, 0, 42210904, 0, 637579767132924, 0, 21813627071864992587944, 0, 738018312441664797771226227110, 0, 9177150693646685841840372038845376744, 0, 112848160646215140275582423936644957955662524, 0, 3143146257683298212016891972258566918585921458833304, 0, 31327079986910989416247938623974919746509417027114485440801], [1, 0, -40260616, 0, 3885926233187100, 0, -103066241041063506882104, 0, 5036668636781866257046238205254, 0, -84476006590037210042244234207218485304, 0, 2610528439144706358691801484659155979792547100, 0, -22168240810134903393774677177613997181169378443499016, 0, 451302514611022222119906091571193923850834154614488607763201], [1, 19136, 437777256, 6077088467008, 93285117391646396, 1022985398841059479488, 11791613314410175238784280, 106451612492828156564349135680, 1000255490283666733242507353967462, 7381776039283338497187494197581085760, 56700967509267004882812434400622932613720, 341110663412750571305184190869772799334331584, 2156983603230912585791206375284044659058964019196, 9744031074594601088595620071058940318963507438811456, 48674883055101922428532277215109808741909134706448901544, 147540586204356218708402428433613045476328598576604920768448, 534649250915012063273309653845946926220190993810950712361813601], [1, 0, 173596416, 0, 11491494839757124, 0, 2673635180001687354813696, 0, 566501870036624280108779416204230, 0, 35887294140800639263866767084470722084096, 0, 2070397148134192625798747550745677120234005392324, 0, 419813554251183618902640682178736047839847207102747471616, 0, 32460430015431999968619493682032835511850959272235390105491169601], [1, 41184, 1917102744, 49989503472480, 1307512314736623676, 24483442620824640696672, 447322153309046138625736680, 6312737956105614096102143621088, 86253610940133323867337199871810022, 928025777994088671826828502698528845984, 9667294804578675922566997442273567865553320, 77785620003336599481610646829798721021644086304, 610681691042642415216259626600563735308549428567676, 3432339296749551468520373735926230123576568215246308640, 19350805876329459351237500375072092249678502364498538343256, 61111714839162692841781851185550474961735925784450921553891488, 218141463858908869909615270212837010053304269297195114305378988001], [1, 0, 1399898360, 0, 930350136456357532, 0, 381905954056396390555411400, 0, 105565729022425147098984582778044358, 0, 20087921779063229049659347091010607677158600, 0, 2573970613703694052452923944610297950926662127314332, 0, 203719331709220942885624935321258082414985474913054718555640, 0, 7654455761751330268890575447204214294134057054403947260546060444801], [1, 0, -429356568, 0, 754267242567238204, 0, -227120053615418724534607464, 0, 202671147277215934252218256112552166, 0, -39720451646080277010499598238411560184797736, 0, 23069736758857343655913548818846976420472402962823804, 0, -2296646738741852000024875324618102734299294096515341477820632, 0, 935480596774678503001801362972812283024661354043792689825893575512801], [1, 0, 2241608536, 0, 3923072134349249340, 0, 4134762873678020477262045224, 0, 3584661460369030015309939946211975014, 0, 2113346575662339896951032984220787592268718824, 0, 1024864680586100861061513154320671478074721605389001340, 0, 299309237798888537896750410689974609386007904290014934298259736, 0, 68246512894550079052163515422746832731983773500978660478681746942325601], [1, 0, 4378091776, 0, 9919688276098981924, 0, 14347996635747417226408450816, 0, 14427780262678331637351707978428492390, 0, 10235041696673306594061247890159605141290652416, 0, 5047713824192221638847094330887147899800498999597466724, 0, 1589204959011488195998181000773788263973806352337138004839864576, 0, 258936575725713381876605656162686020810913039245684608619946288452090401], [1, 42336, 9039868248, 327593961146592, 38188063338457064956, 1175174860497534714587616, 96655973945132836444101572520, 2493955708024349255000180447550816, 159760782356354874179957048472564359334, 3367152217149635296512488911768853339937312, 176188163342958196310530019539181037236813781480, 2892174767965283383732264753058542206216583600867488, 126888916282194159549211687363452570077077931884817562556, 1469623049874672937647654037004774449844043207504976280067744, 54752780895145684331347604979524248743198297100990041842345190552, 346200680370000544778799634076263654135884574379696782939897975081248, 11040585568500089406404363834296492635119570897676624567608785151541319201], [1, 0, 1373084344, 0, 13726970932748754780, 0, 13570273501915838717144926856, 0, 68189811981699367994392981957922807174, 0, 44174545302551810728839540567808396824394434056, 0, 145459365367783064790408231437585297866279272866456226780, 0, 47363924143565897763502327393745905044020565821816270653214962744, 0, 112288155707690524284921569184047598526949432199996966253201749159632164801], [1, 0, 9148617728, 0, 42350893504763527236, 0, 137329185205740019515844344832, 0, 331563523792361883439793317778834919110, 0, 590189453512331985612692760529367431227947219968, 0, 782203544814580180689821122453887633740291121957030026436, 0, 726174985520801418897557478354196363854548475095296257884942799872, 0, 341125672472605815737240060891364026523290350856811222245874647291144654401], [1, 251072, 34185820792, 3747763195142848, 365244380233998074012, 30218813515090232657132480, 2166926410856781613720260571208, 141808586784327973139210262481499584, 8384779126878446767770966324442297288390, 436353019397863222662707055975167914063038016, 20517057508727702236103455771605172783108395988808, 880407589968927283564331304711311707386806769416083520, 32743520232343531676398911926443403852358410519007562086812, 1033830699046399157658175168506252781864747173473465474947193152, 29017416965492953235181845649391103162434861820649598431423370607992, 655762348268337446377863195074589237233287060755459526268255432839454528, 8036809082503641618612682084624530392577487756904348192905795828229186428801], [1, 0, 11370719128, 0, 98334521353313919996, 0, 551725998946145421653997716072, 0, 2573924686208101506377840949326027215910, 0, 8560603323700685657060944626080118571955543932328, 0, 23673793534982544139943561609995381031492139228082205137596, 0, 42474737475023594029803277041401710921214868185472911888416164595672, 0, 57959375186337998161464929843210464026538099255933595673241672975683189751201], [1, 0, 33866865792, 0, 553368297612803154628, 0, 5570940042424748932903383260544, 0, 37599272765314860558238652471626139840070, 0, 173711492149522450195079946342343342405131523138944, 0, 538039806401233909088016002222394233570957615760071145436228, 0, 1026774811314068672139327900708517827221047061818090911347436002059392, 0, 945366624540204596465924137849354245846140921259572676085974614185475142494401], [1, 0, 31825821824, 0, 520164682838485697796, 0, 6594768168373290663450998972800, 0, 66036870545936076959057435767152664496390, 0, 486314115863713911449644550776329830388068082467200, 0, 2828626119178542155522887202032773409537931575323440983016196, 0, 12762379513619095515752317630215013831882958070400787090362887436443776, 0, 29571228739913279498948663112125511966004786122340140758535526194999034006060801], [1, 0, 24756769408, 0, 647604834278228515428, 0, 8854318632260096693620388445056, 0, 119357816519832870451655974415130341068070, 0, 978067626663517731706335386727859738749511828701056, 0, 7902009686084480873614126852413798584077657775494488492571428, 0, 33368384793719660746165997034606128760868641974067048234577142469793408, 0, 148886373358822087497126463801738296202951256788286744534662595050969228887804001], [1, 0, -2061475400, 0, 23099506246333743196, 0, -299759510947205779871691783800, 0, 36529193767045341013515388973979886710406, 0, -40285171662613347044533073865722162262660987006200, 0, 417202777468196734256368031536454242826709041502658333349596, 0, -5003741873700693522467141664024282993866415493000391174684490909734600, 0, 326203779199907436766740454433356067287204248224700781926823975402404198696196801], [1, 0, 91705003160, 0, 3914909197768913285692, 0, 101145463200824623576925663988200, 0, 1725812274466285130496571533389263372268518, 0, 19896843521918394045851072356249899920290051255461800, 0, 151494632946505957729932890751778222581440863465596652225901692, 0, 698081872742047323207678961465451977334659457856512758827913982053226840, 0, 1497445783920694873253605954725085018527510926336074313466818706592456466757996001], [1, 344640, 175048372392, 41594639249507520, 11666214670149094159228, 2065981080791758988565253440, 403492225834881294166900688704344, 54917833881049032519079408850686257600, 8055966379080573568685547460105972352396070, 844978947606008785753246697529969532475921822400, 95521283842181699861871695848304049468983621995153944, 7525299848830247390338262638306791398610779024920274602560, 653822591165966576194939358122410526868588170263711387444909628, 35867392928887537961313453010980587440797260369205828770744854572480, 2322485521441806865135246385476393988005142309603976729421830610768050792, 70354699034374561248910649136011870375789573921802374931938803920372447639360, 3140942005398926371772028385862838092239539909405451295670621541688111654708253601], [1, 0, 80850198920, 0, 3498877064828649350812, 0, 102825358842627136204766728988600, 0, 2209200172303898559436609445647385426237638, 0, 34904760998423278582362402455077455491926524531721400, 0, 403178674959982427914311031787535080600650966884223884074304412, 0, 3162528130785500561734504847078904321286947322024016903293892150797587080, 0, 13278155163351753706317696533924544108513274407835339859871275831776558989263625601]], 'euler_factors_factorization': [[[[1, 0, 59, 0, 1924, 0, 60416, 0, 1048576], 2]], [1], [[[1, 0, 6848, 0, 24891826, 0, 66875000000, 0, 95367431640625], 2]], [1], [[[1, 0, 593868, 0, 139898041430, 0, 15403406472946668, 0, 672749994932560009201], 2]], [[[1, 0, 1420096, 0, 779793261394, 0, 195772292840797504, 0, 19004963774880799438801], 2]], [[[1, 0, 2007936, 0, 3446593247810, 0, 4047986728491963264, 0, 4064231406647572522401601], 2]], [[[1, 0, 7607244, 0, 26715012021686, 0, 46640517003259110444, 0, 37589973457545958193355601], 2]], [[[1, 0, 19081628, 0, 167668754709094, 0, 790485276316678740572, 0, 1716155831334586342923895201], 2]], [[[1, 0, 21105452, 0, 96069831504310, 0, 8879216318470193795852, 0, 176994576151109753197786640401], 2]], [[[1, 0, -20130308, 0, 1740348466506118, 0, -16499369862435914216708, 0, 671790528819082282036142601601], 2]], [[[1, 4784, 75114330, 331741490288, 4808584372417849], 4]], [[[1, 0, 86798208, 0, 1978782963872930, 0, 1165062774715744613697408, 0, 180167782956420929503029846064801], 2]], [[[1, 10296, 320264262, 1513598929128, 21611482313284249], 4]], [[[1, 0, 699949180, 0, 220210640936842566, 0, 36816719477180809416909820, 0, 2766668711962335809450748011342401], 2]], [[[1, 0, -214678284, 0, 354090238473026774, 0, -37544542031169194138927916, 0, 30585627290848204916791848989276401], 2]], [[[1, 0, 1120804268, 0, 1333434963591116758, 0, 572861838545661969378299468, 0, 261240335504588722483367157995242801], 2]], [[[1, 0, 2189045888, 0, 2563883188164636690, 0, 1561540367509580399945794688, 0, 508858109619679129936596364708525201], 2]], [[[1, 10584, 2091935478, 14289724132488, 1822837804551761449], 4]], [[[1, 0, 686542172, 0, 6627815389407138598, 0, 2234861977899316633196508572, 0, 10596610576391421032662867140133202401], 2]], [[[1, 0, 4574308864, 0, 10713295960747278370, 0, 19658667926968338246155700736, 0, 18469587772135192290560825407466407201], 2]], [[[1, 62768, 2636722462, 193140676052432, 9468276082626847201], 4]], [[[1, 0, 5685359564, 0, 33005603990673824950, 0, 88214273159098713343054536236, 0, 240747534123068430155382383568465195601], 2]], [[[1, 0, 16933432896, 0, 133313573984734103906, 0, 528013562015948189556749138496, 0, 972299657790850297934682879408841327201], 2]], [[[1, 0, 15912910912, 0, 133471974572618513026, 0, 1173456443563837659380849946688, 0, 5437943429267472574499737549036572950401], 2]], [[[1, 0, 12378384704, 0, 247190213199003673906, 0, 1367343762089002361692359888704, 0, 12201900399479668244827490915525641902001], 2]], [[[1, 0, -1030737700, 0, 11018543020066226598, 0, -138522527783748773684544547300, 0, 18061112346694138117573133075817258818401], 2]], [[[1, 0, 45852501580, 0, 906228648312505394646, 0, 9019881071821893846698593453420, 0, 38696844624861790832365403138487376998001], 2]], [[[1, 86160, 32626774698, 1325678399541840, 236736367459211723401], 4]], [[[1, 0, 40425099460, 0, 932344199238878529606, 0, 13722572436127847244202259881540, 0, 115230877647233745723406127208308085892801], 2]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 0, 'label': '16-21e16-1.1-c5e8-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5, 5, 5, 5, 5, 5, 5, 5], 'order_of_vanishing': 8, 'origin': 'ModularForm/GL2/Q/holomorphic/441/6/a/be', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0078125', 'prec': 30}, 'plot_values': [0.0, 5.810608918834215e-13, 1.4856505807432997e-10, 3.7996038473971624e-09, 3.7842164996739835e-08, 2.2470855251150908e-07, 9.617635071311765e-07, 3.283037555781665e-06, 9.494637731125874e-06, 2.4187948783307142e-05, 5.5743360356654576e-05, 0.00011844105362016901, 0.0002352941560257035, 0.00044171294080042257, 0.0007900966028003536, 0.0013554315081067945, 0.002241953027549159, 0.0035909057596441043, 0.005589397468609414, 0.008480305887892213, 0.012573164079364044, 0.018255906473208596, 0.02600731420603926, 0.03640995791619157, 0.050163463585414764, 0.06809779744181134, 0.09118621911282702, 0.12055753216993936, 0.15750728774638184, 0.20350754860908143, 0.26021478731512965, 0.32947567790784776, 0.413330864943334, 0.5140150578629817, 0.6339542128661311, 0.775758524493141, 0.9422113967300005, 1.1362541674248485, 1.3609663811141546, 1.6195438677478529, 1.915271551706754, 2.2514894315281033, 2.631557301538987, 3.0588123790186006, 3.536523245321969, 4.067840510457942, 4.655746936817372, 5.303012949382437, 6.012136295248718, 6.7852844394506295, 7.624243810848811, 8.530359714949704, 9.50447900982457, 10.546897044261616, 11.657326370412814, 12.834858595975236, 14.07790940503448, 15.384187111570334, 16.750679865988094, 18.173626238692435, 19.648498683731063, 21.17001253117178, 22.732177557747786, 24.32828506385297, 25.950921217938657, 27.59200996575051, 29.24288579619855, 30.894329498656727, 32.53662710032047, 34.15970410090793, 35.75321983850448, 37.30660251197819, 38.809140628451054, 40.25009528763338, 41.61884584181607, 42.90496441563064, 44.09834247858799, 45.18939555437354, 46.169089508256995, 47.02901445729792, 47.761483340417314, 48.3596418659239, 48.81760667967071, 49.13050152473233, 49.294606790572004, 49.30741848332088, 49.16759490814431, 48.874982048983846, 48.430630837222836, 47.83681941530361, 47.097096921428474, 46.216239590624006, 45.20029506688558, 44.056414916887014, 42.792749914060586, 41.418370031694636, 39.94317391886268, 38.377805134336214, 36.73359256279358, 35.022456862704615, 33.256752876198654, 31.44905132329247, 29.612003727452922, 27.75821131370001, 25.900095631054075, 24.049784667952835, 22.219042877716404, 20.419159189289058, 18.660748589073503, 16.953633318302195, 15.30675808029543, 13.728117752088208, 12.22469838422386, 10.802440662810024, 9.466251477500983, 8.219942766734965, 7.066189391865324, 6.006545490670436, 5.041476694719828, 4.170405968835249, 3.3917721184520153, 2.7031061559570957, 2.101122586839709, 1.581778213129441, 1.1403655915281243, 0.771620562364726, 0.4698334342173171, 0.2289619795211616, 0.04274441263746155, -0.09518903344765971, -0.1912091769948262, -0.2515893368544147, -0.28240783065880654, -0.2894579389220829, -0.2781679603229713, -0.2535324126628197, -0.2200556881640717, -0.1817088149611472, -0.14189591274156627, -0.10343575722525479, -0.06855641548045278, -0.03890282213094894, -0.01555686712005767, 0.0009308658131881479, 0.010498730935592601, 0.013522940736356511, 0.010758168841854642, 0.0032712370520445355, -0.007629945185509308, -0.020470399340724005, -0.033683210087164496, -0.045683898325534586, -0.05494236388897538, -0.06005104950384381, -0.05978701476794283, -0.053166507702984665, -0.03949070360976951, -0.018381482975965008, 0.010193622675546785, 0.045907530894058926, 0.08807176913896762, 0.135647379586664, 0.18726755540736012, 0.24127175800453138, 0.2957505681282484, 0.3486002541075087, 0.39758569671109845, 0.4404103019114129, 0.4747922297413925, 0.49854378853907766, 0.5096522419820374, 0.506359991323322, 0.48724209798212037, 0.45127909085116025, 0.39792356598367307, 0.32715801943041145, 0.23954131953032198, 0.13624315148651672, 0.019064801580845284, -0.10955493993866927, -0.24654942252226064, -0.38824964286450475, -0.5304256845225543, -0.6683457935703508, -0.7968506109126392, -0.9104418753120651, -1.0033846539083506, -1.069820941014521, -1.1038929875442947, -1.0998746753424895, -1.0523079108053688, -0.956140591441587, -0.8068641393802385, -0.6006475043975132, -0.3344645115348085, -0.00621112216046872, 0.3851895990810028, 0.8396979369466326, 1.3560870334899018, 1.9318920128596215, 2.5633811096945838, 3.2455507989500134, 3.9721467039779768, 4.735709715940377, 5.527652592156604, 6.338360360562257, 7.157310000895927, 7.973216380480762, 8.774200003940058, 9.547974414696222, 10.282050967145294, 10.9639599417814, 11.581492270275813, 12.122919264505072, 12.57722042329692, 12.93431253903188, 13.185271377547158, 13.3225410544423, 13.340126737719368, 13.233786662179412, 13.00117749151693, 12.641951439021968, 12.157840736244975, 11.5527088144132, 10.832565088453675, 10.005539677005531, 9.08182008988644, 8.073566499907853, 6.994747751536362, 5.860956292627599, 4.689194960270237, 3.497631584088326, 2.3053246889965777, 1.131921340673729, -0.0026705734120118954, -1.0786156319573312, -2.0764947893528913, -2.9776484203812514, -3.764516160725188, -4.420967691175111, -4.932618381917769, -5.287128592960554, -5.4744820471708975, -5.487195796905439, -5.320502677456996, -4.9724969929728235, -4.444234591795981, -3.739784390948104, -2.8662294732331235, -1.8336140296216232, -0.6548010912032287, 0.6546966747911206, 2.0769253766928, 3.5917479589734778, 5.177145016272529, 6.80955414847363, 8.464251360147541, 10.115804477895741, 11.7385388055208, 13.306934619634339, 14.796051747041513, 16.1819629296317, 17.442176654219825, 18.556044702671855, 19.50520647056899, 20.273972517949442, 20.849622717220292, 21.22259953602606, 21.3866853025988, 21.33914053287146, 21.080783254663956, 20.616037505808062, 19.952980489899836, 19.103151769864056, 18.081372348898917, 16.905448347571415, 15.59585659841853, 14.17539544119363, 12.668794674095375, 11.102352460837167, 9.503449785323214, 7.899980995320476, 6.319850277307158, 4.790434290750129, 3.338075376509727, 1.9875978216423351, 0.761860047916414, -0.31865482910818793, -1.236287935214032, -1.9765558875150542, -2.528433928004963, -2.8845681923535986, -3.0414162230505055, -2.9993182407764345, -2.7625078330457624, -2.3390576941911267, -1.7407301587827935, -0.9827543813806987, -0.08353467174035893, 0.9357101063823382, 2.051355706015382, 3.2378184230170333, 4.468024532811475, 5.713960830502884, 6.947231729401015, 8.139621256360115, 9.263666327055862, 10.293192755513742, 11.203827037184599, 11.97347404745397, 12.582771395289088, 13.015491281644374, 13.258868698211218, 13.303868746620719, 13.145395169586788, 12.782376968554072, 12.217795174390664, 11.458658616760525, 10.51586454004868, 9.403983095351885, 8.140974027209756, 6.747840024245682, 5.248221104837582, 3.6679113202363682, 2.034373880898486, 0.37620102662617616, -1.2774783726572219, -2.8975761934988276, -4.455619180110986, -5.924312591423481, -7.278091074334112, -8.493613922730164, -9.550205497136965, -10.430279896519282, -11.119683642501888, -11.607960793222162, -11.888542074669498, -11.958860312225385, -11.820396409689035, -11.478611330653532, -10.942810400831917, -10.225925702737833, -9.344223480749468, -8.316944585971507, -7.165885680956431, -5.91493285990083, -4.589560299068336, -3.2162885936291135, -1.8221090420886974, -0.4339113371435543, 0.9220783953117823, 2.2208413372420077, 3.439080115842423, 4.555694150600214, 5.552205637428732, 6.413127069762379, 7.126266003598543, 7.682949091552054, 8.078167758078038, 8.310643156130256, 8.38280941332539, 8.300718595469434, 8.073873381555561, 7.714968681251899, 7.239567279904082, 6.665716533930396, 6.013512467574221, 5.304621050911285, 4.561767426235142, 3.8082059989334605, 3.067178449049002, 2.3613721465156154, 1.712397546525672, 1.1402928453549102, 0.663066300288818, 0.2962862591537606, 0.052727901244202, -0.057915965939973085, -0.029251406210019586, 0.14167947534349176, 0.4543366812121828, 0.9046991035100463, 1.4853600871216552, 2.1856996219055356, 2.9921312382810967, 3.888419820170395, 4.856065088041223, 5.874718203690796, 6.922641375032541, 7.9772008629006645, 9.015380006676489, 10.014303246857187, 10.951762815871426, 11.80672173130751, 12.559801116987911, 13.193696953556012, 13.693562986616326, 14.047345098815217, 14.246054426638551, 14.283978800175136, 14.158812122177798, 13.871703061474145, 13.427228954213506, 12.833284991360248, 12.100914304716255, 11.244072915332138, 10.279332105117879, 9.225522238484716, 8.103327220829927, 6.934836268382716, 5.743044225601719, 4.551383232371743, 3.383241965671866, 2.2614808513069775, 1.2079589524933245, 0.24309117111124276, -0.6145581826110319, -1.348656351430785, -1.9454555194238838, -2.394008650873191, -2.6863524692505045, -2.817635463998874, -2.786158892518832, -2.593375143269267, -2.243824680996394, -1.7450130026732238, -1.1072242555039447, -0.34324286455148173, 0.5319450382958478, 1.501535504494799, 2.547291987028252, 3.649886696808952, 4.78929199890717, 5.945190124563629, 7.09741652169609, 8.226332811695016, 9.313210661432944, 10.340670935069248, 11.292894989824246, 12.155843888996115, 12.917464492308858, 13.567872140923967, 14.099535275167257, 14.507279273273953, 14.788373564363559, 14.94248435941927, 14.9714747037127, 14.879263534251216, 14.671654573952086, 14.356157955228733, 13.941826715638033, 13.4389630387733, 12.858914676124337, 12.213691901779548, 11.515663289001706, 10.777293878436966, 10.010897167693237, 9.228419776073054, 8.441270149686488, 7.660126381009094, 6.894745081402587, 6.153779028251035, 5.444688876606424, 4.773690467557447, 4.145734013061178, 3.5645189885198656, 3.0325494235666084, 2.551184768928729, 2.120685130503115, 1.7403118054568336, 1.4084516021386708, 1.1227506939937422, 0.8802537489914315, 0.6775456379986085, 0.5108947296697779, 0.3763738688677662, 0.2699782887781633, 0.18774099648365472, 0.12583365175077013, 0.08065115644888855, 0.048879092884682424, 0.027543940900599178, 0.014045893775404217, 0.006174300294142059, 0.002109774496152762, 0.0004125929908210087, -1.039972973331683e-06, 0.0001074213294041817, 0.00025783744074984197, 0.00020536825703015334, -0.00010810762064922326, -0.0006029462842632879, -0.0011090079123465455, -0.0014093414191533053, -0.001278709986410118, -0.0005157481067853806, 0.0010320719217008052, 0.003451053806138633, 0.006751488640192142, 0.010865391408319824, 0.015651014255202454, 0.020903186641972795, 0.02636833211415866, 0.031762830445299504, 0.03679328022471074, 0.041177245493127, 0.04466308843290722, 0.047047630914341755, 0.04819038182694903, 0.04802344649422337, 0.04655649524683624, 0.04387645693622135, 0.04014192196717258, 0.035572527606089754, 0.03043396605015833, 0.02501952705787185, 0.01962929978051383, 0.014548395893053017, 0.01002569129379785, 0.006254650570648772, 0.003357814722090903, 0.0013764451405284233, 0.00026665971867858847, -9.681199811918671e-05, 9.152591408969524e-05, 0.0005889986960500975, 0.0011348375976279526, 0.001488944214706567, 0.001478562151304941, 0.0010516634072771638, 0.00033542031391812463, -0.0003021969170923538, -0.00018998352499798577, 0.0017071615894839183, 0.006844394060743925, 0.017145805670177806, 0.035043049887332936, 0.06350108773600073, 0.10602927714204033, 0.1666746748034881, 0.24999575925232453, 0.36101602068522015, 0.5051588614407552, 0.6881588971648516, 0.9159521390849925, 1.1945491236518946, 1.5298993197450934, 1.9277308545810017, 2.393379259795774, 2.931622564957595, 3.5465108721024237, 4.241182448976334, 5.0176922112207345, 5.876862420858161, 6.818183394615197, 7.839678649204201, 8.937816224219894, 10.107497664075785, 11.342005057251942, 12.63299362247799, 13.970531140645608, 15.343203425047324, 16.738333527292124, 18.142079087142154, 19.539676751796858, 20.91568205482838, 22.25413894296497, 23.53883417680659, 24.75357093760636, 25.882503723014572, 26.91059401681058, 27.823810972046857, 28.60949518137247, 29.256486372631922, 29.75530029421014, 30.09832002131886, 30.279955208272543, 30.296828222582885, 30.148052685902062, 29.835214818942205, 29.362283880603492, 28.735402634632752, 27.96276853550682, 27.05448309538575, 26.02236638456275, 24.879796912772395, 23.641661532528676, 22.32399255421582, 20.943467018301686, 19.517062127667472, 18.06175655621066, 16.594240025032253, 15.130637002382798, 13.68628895319073, 12.27566650178894, 10.911988464188983, 9.606935312718354, 8.370520225783457, 7.211003896289378, 6.134849921226454, 5.146719933430857, 4.249529807997931, 3.4445609777350783, 2.7314529754972514, 2.108318510986094, 1.571912941756769, 1.1178220426509078, 0.7406622781065657, 0.4342878938419629, 0.1920031907034485, 0.006765519883930136, -0.12863872510807367, -0.22140816478013503, -0.27855448772749747, -0.3067531166704811, -0.3122187525722615, -0.3006078235135546, -0.2769487079961507, -0.24559445985553438, -0.21020229110973734, -0.1737358476137223, -0.13848935539979187, -0.10613082633762534, -0.07776077171533877, -0.0539829525465199, -0.03498202123938359, -0.02060531962141864, -0.01044530804918791, -0.003919531787950806, -0.00034487471894248563, 0.000996528789142644, 0.0008016383850011602, -0.0002976117777091627, -0.0017663988882375189, -0.003186941550303397, -0.004266837381964345, -0.004836918303748832, -0.004840146420128473, -0.0043134705620497165, -0.003364817551375521, -0.002147436417373511, -0.000833808577663317, 0.0004087065347222407, 0.0014386414102191816, 0.0021561109546683983, 0.0025123574105765344, 0.0025125913040461405, 0.002212112614923763, 0.0017062262881573692, 0.0011150046116528783, 0.0005644481195253983, 0.00016600469544110683, -3.299247061804211e-06, 8.233987264171831e-05, 0.00038628617171085306, 0.0008062693994769672, 0.0011814202740388798, 0.0013113671086734948, 0.0009887082199788503, 4.55106368823363e-05, -0.0015861704640526227, -0.0038005880569509857, -0.006233111793175186, -0.008165975163623171, -0.008428296277761505, -0.0052944595717050805, 0.0036145201384484285, 0.021421744420355736, 0.0520716784155281, 0.10038885268075669, 0.17211283955660175, 0.2739034707853319, 0.4133120937504834, 0.5987158566899669, 0.8392157520063181, 1.1444905719663703, 1.5246114711665966, 1.9898275369725282, 2.550303306413253, 3.2158232793478425, 3.9954705940236566, 4.897293300981711, 5.927987350418385, 7.092543895251089, 8.393950017331631, 9.83290212899298, 11.40750078861874, 13.113010426448733, 14.941670905923722, 16.882599383993448, 18.921849138982065, 21.0424273095127, 23.22452533299908, 25.445631742811212, 27.6807646156684, 29.902814487276842, 32.082960029553696, 34.19121781745353, 36.19722746715853, 38.07090411358023, 39.78303248318366, 41.30569763942363, 42.612884810637006, 43.68107106492077, 44.48978519396366, 45.022220589812605, 45.2660957196744, 45.21402865165177, 44.86339836521029, 44.216382061678566, 43.27998416443885, 42.065959758336206, 40.5906322451973, 38.87471958345101, 36.943458197544686, 34.825712746987435, 32.55300945213486, 30.158864307581542, 27.678081340883807, 25.146026597527552, 22.5978954815519, 20.068108594751802, 17.58988760886334, 15.194111951758115, 12.908605417312701, 10.757649427569735, 8.761595889268897, 6.9365876132682445, 5.294393063305388, 3.8424086872847014, 2.5837287490582588, 1.5171421326937895, 0.6374064154842289, -0.06434583108863379, -0.600122745914276, -0.9845277292077973, -1.23417494820993, -1.367088494121316, -1.4020701640841577, -1.3581083816600834, -1.2537930857061803, -1.1067777878408775, -0.9333123043941254, -0.7478586760147881, -0.5628063366179942, -0.38826916744655443, -0.23197642008712244, -0.09927409767692352, 0.006779282225480792, 0.08522998814701178, 0.13697166689719859, 0.16442813879048612, 0.17119464605689835, 0.16165473925934595, 0.1405882739873238, 0.11279106597773864, 0.08272678194585945, 0.05422827992809169, 0.03026290509434273, 0.012773666911258436, 0.0026033710080682667, -0.000492388280155577, 0.002258076001823959, 0.008832042089091987, 0.016680479765223286, 0.0230626928469522, 0.02543224201910923, 0.02185631326062183, 0.011447909098717382, -0.005211792866565025, -0.025683794075051666, -0.04533707680133826, -0.05709092402690434, -0.051252843063340874, -0.015468197105607715, 0.06520526743542115, 0.20809047722527982, 0.43254911946725355, 0.7595066727059689, 1.2108553327766023, 1.8087463604890783, 2.5747909713217347, 3.529195845104299, 4.689857047065228, 6.0714442576421295, 7.684513860751986, 9.534698339413437, 11.621966989983688, 13.940012514200006, 16.475820650449155, 19.209413941412876, 22.113768038136858, 25.1549597461957, 28.29257116304286, 31.480400645409812, 34.667238598833656, 37.79790065240318, 40.81453236015349, 43.65791858154621, 46.26894265722247, 48.59014696646967, 50.56739182492483, 52.15163931146961, 53.30029018237173, 53.97859596697748, 54.160859280444924, 53.83132687016756, 52.9849349741071, 51.62778573866526, 49.77740006877901, 47.46277540437737, 44.72365703155415, 41.60967877160884, 38.179162917352976, 34.49772477209899, 30.636667108991364, 26.67118185364054, 22.67844656248751, 18.73565379642309, 14.91769501757385, 11.29506360535433, 7.931981944272462, 4.884675970488704, 2.1998651084706107, -0.08648298899517841, -1.950095573120206, -3.3790498173636427, -4.374051236319558, -4.948145584041502, -5.126112078946874, -4.94352553941764, -4.44549071849697, -3.6850845257601694, -2.7215576720528762, -1.618303056325753, -0.4406001063609357, 0.7465974706500403, 1.8808301881057226, 2.9042080336765848, 3.765326136727629, 4.420959007250929, 4.8375246173064586, 4.992332947170808, 4.874166503809817, 4.483501178044578, 3.8323594077571186, 2.9437592236458476, 1.8507751669288104, 0.5952396216755641, -0.7738566374435565, -2.2022492363970456, -3.6326641989286625, -5.007104605414505, -6.269148379863462, -7.366213268509448, -8.251712231858088, -8.88706227248636, -9.243525090637428, -9.303504948151295, -9.061567844537816, -8.525012143791209, -7.7139760899061525, -6.66108866003846, -5.410672908663384, -4.017601304807963, -2.5456121077747835, -1.0651816192161985, 0.3488053598901238, 1.6195922399115303, 2.6712139444464236, 3.431203058866442, 3.833246140670924, 3.8197183932270757, 3.3440446015521808, 2.372750342185136, 0.8870592808575877, -1.1159535756421328, -3.62268374655706, -6.602831839948491, -10.009791550811237, -13.78160254429355, -17.84236110468933, -22.104027872606128, -26.46879590774685, -30.831766729042123, -35.08386327318143, -39.11496991145584, -42.81732287890886, -46.08860024211083, -48.83489243593271, -50.973475094515244, -52.43533899435528, -53.167305605043865, -53.13368961576686, -52.317687248289126, -50.72200973801022, -48.36867339599395, -45.29843095522388, -41.569680744402554, -37.256815393523574, -32.44813552547655, -27.24343844723037, -21.751367454879603, -16.08616407866783, -10.36444047838353, -4.70198990371206, 0.7893431404382878, 6.004644723562849, 10.848626600716106, 15.237990006306752, 19.103441728236763, 22.39121686435293, 25.064068732938505, 27.101750579799916, 28.501002545533925, 29.274950383098304, 29.452055165087604, 29.074680678420748, 28.197168611834933, 26.88363770874669, 25.205576028413333, 23.239304534624104, 21.06340096721344, 18.756083431324804, 16.392759196319446, 14.043771224611922, 11.772414886438389, 9.633298869278208, 7.671080721508272, 5.919610584927784, 4.401496743206046, 3.1280740202616886, 2.0997991788195094, 1.3070662142991123, 0.7313377813053682, 0.3465540217052685, 0.12076480633285396, 0.01791812266878336, -0.00026698885545858327, 0.02758484098253375, 0.06432493712238901, 0.07595509242863929, 0.0331065492089775, -0.08772414743097245, -0.30322438104528104, -0.6226307308094648, -1.0474383228613984, -1.5714888359886416, -2.181347478637601, -2.856976193201417, -3.5726824309799228, -4.298298080105483, -5.000540343019193, -5.644498151831029, -6.195242890735957, -6.619381577257129, -6.886443830716086, -6.970217565981322, -6.849924135599574, -6.511186712035206, -5.946756884396865, -5.1569619078769, -4.149771505247337, -2.940570104460588, -1.5517216713641362, -0.011888920915371273, 1.6448712245242978, 3.3802021979544916, 5.152694944715526, 6.919385683692512, 8.63749250752212, 10.265611346218156, 11.764954264486086, 13.100548040533342, 14.242288487876165, 15.165817225563636, 15.85325133040746, 16.293897404521562, 16.48452742815159, 16.42896191318975, 16.137646904154458, 15.627109048934042, 14.9192282092398, 14.040363825128768, 13.020481310603342, 11.892071888359542, 10.688986054435674, 9.445067446859772, 8.193010101482349, 6.963371449391573, 5.783708037156154, 4.677875392080253, 3.6654999970324424, 2.7615339387335, 1.9760859889794697, 1.3143577253212417, 0.776836396998739, 0.35967110898472165, 0.05518628548314874, -0.14749649859433417, -0.2617602374269789, -0.30273014242723706, -0.2864934621364504, -0.2293343234108951, -0.1470076188024679, -0.054089316504563036, 0.03657365879305369, 0.11430070223216411, 0.1708880031318217, 0.20077902818496712, 0.2010999353525173, 0.1715662126794105, 0.11426898235916591, 0.033359594438819966, -0.06534340293951468, -0.1748111918422163, -0.2873005901670723, -0.3948551369428865, -0.48979376396459, -0.5651583549573903, -0.6151007329707129, -0.635194321375734, -0.6226592640003381, -0.5764904597528132, -0.4974852354396728, -0.3881769348412554, -0.2526848382425507, -0.09647205065471588, 0.07395838337704566, 0.2514130019313229, 0.42838738668760545, 0.5974522711011316, 0.7516263927112439, 0.8847175495665061, 0.9916151922280835, 1.0685243108091063, 1.1131259805954319, 1.124660324852207, 1.1039221994466721, 1.0531772318748227, 0.9760040520836829, 0.8770722065249115, 0.7618681641970697, 0.6363790297123124, 0.5067591867775972, 0.3789968201399805, 0.25859727130448545, 0.15029919549469328, 0.057839131076956464, -0.016222673102427056, -0.07060596653261471, -0.10533664183969915, -0.12169135295557448, -0.12206440228826285, -0.10976653643992076, -0.08876357965610066, -0.06336740984899991, -0.0378949815521032, -0.01631287978208224, -0.0018860468145961125, 0.0031458679239712646, -0.002151037978156561, -0.01718146186593961, -0.03966973667659506, -0.06559243461594151, -0.08920284337056876, -0.1031518706773484, -0.09869998766341287, -0.06600855480907038, 0.005491927215936411, 0.12666936158282016, 0.3082095986209216, 0.560106341378221, 0.8911446558652136, 1.308441483725896, 1.8170298901271718, 2.4194600229846657, 3.115485783946396, 3.9018406813693334, 4.772114207772285, 5.71673758744913, 6.7231435527521395, 7.7762195957725275, 8.858560195905, 9.950847417728731, 11.032354835171656, 12.081513626361204, 13.076522717151416, 13.995993586442076, 14.819863268693227, 15.530164894706921, 16.11128459242503, 16.550383734061594, 16.837775896199478, 16.967207997529787, 16.936036790503, 16.74538912138867, 16.400420153380054, 15.909947540160434, 15.285923863628396, 14.542996624720605, 13.698038575215163, 12.76962436141372, 11.777479803198721, 10.742066060587822, 9.683958136501676, 8.623154182207726, 7.578438350474868, 6.5668987343379195, 5.603556772772131, 4.701082839976734, 3.8696248011096546, 3.1167418534195312, 2.447296403607536, 1.8635443918642163, 1.3652581305279803, 0.9499645944011378, 0.6132538848379134, 0.34912726007759565, 0.15037026874088236, 0.00891887983760409, -0.08376752906267744, -0.13634197385672184, -0.1572532766315407, -0.15446329243446408, -0.1352150432116034, -0.10586040070199818, -0.07174892817442553, -0.037166432201216924, -0.005331898171706891, 0.02155399076837608, 0.0422186288798921, 0.05619501409087244, 0.06367650033464704, 0.06535907339083169, 0.062282124957286494, 0.05567524237799311, 0.046819079505818276, 0.03692770822150864, 0.027056641327273326, 0.018039362631744237, 0.010452976330500751, 0.00461152921489281, 0.0005838365001654021, -0.0017682760140415857, -0.0027369334962908318, -0.0027066067920107116, -0.0020903036368169156, -0.001269590726873396, -0.0005439092611194493, -9.356216374973549e-05, 4.0520516451331446e-05, -4.135375614671308e-05, -0.00011407573780510864, 0.0001392020161132875, 0.0010805462171979672, 0.0030617254359586966, 0.006365150813733725, 0.011147246282260069, 0.017390444988911735, 0.024869773950833014, 0.03313931570759375, 0.04154276757942201, 0.04925047652675861, 0.0553237890342908, 0.05880540967135684, 0.05883315857411934, 0.05477218357508279, 0.04635878373357626, 0.033847513235294086, 0.018151869287227694, 0.0009674946091989077, -0.015131738761981395, -0.026629383108317594, -0.029046364211518325, -0.01697250646241268, 0.015845473396432542, 0.07635666637835611, 0.17200061793094612, 0.31046114590391743, 0.4993821132229781, 0.7460319062803168, 1.056943957397562, 1.4375440296713793, 1.8917790740787006, 2.421767119006384, 3.0275248951286153, 3.7068385618730564, 4.455056346966522, 5.264971155547802, 6.126810934913852, 7.028321990112699, 7.95494900362661, 8.890133816633575, 9.815975904492214, 10.713760252262585, 11.564273625719927, 12.348345984018518, 13.047427746000386, 13.64417457138189, 14.123019502386622, 14.470862559398782, 14.678025136980187, 14.73820733214718, 14.648592355811482, 14.40998758819409, 14.026852374826545, 13.507209447779848, 12.862456563715691, 12.107397703792687, 11.259778920038483, 10.339296990695813, 9.366947689641433, 8.364372821289324, 7.353193491723294, 6.35435240924517, 5.38755434545521, 4.470833759561515, 3.6197539677107455, 2.846898704520521, 2.1615923891340514, 1.5697529650150865, 1.073870467345045, 0.673110657605506, 0.3635621545158578, 0.13850539202808376, -0.011214325856504921, -0.09666709300714164, -0.13026312309364207, -0.12515447361598292, -0.09463929997379388, -0.051593834280795614, -0.007954374029604853, 0.025752066650957382, 0.040794416812369776, 0.03052009262033102, -0.00947377021572506, -0.08128162344317548, -0.18473977648790313, -0.3175692557243103, -0.47560930967667925, -0.6531429998556464, -0.843283486317757, -1.0383949862131525, -1.2305280974783288, -1.4118485748961402, -1.5750352276491755, -1.7136273242580289, -1.8223353330692635, -1.8972727506940386, -1.9361075582706069, -1.9381142277441363, -1.9041430841196378, -1.8365121851990118, -1.7388283975333165, -1.6157555956945222, -1.472739534640318, -1.3157045387525736, -1.1507432835009488, -0.9838067568474246, -0.8204233035566225, -0.6654588231987596, -0.5229282042826121, -0.39586691036343286, -0.28626500067871585, -0.19506489505836266, -0.12221961505734236, -0.06680403067881205, -0.027170696766873066, -0.0011369338961407494, 0.013809220521562244, 0.02030067209458849, 0.020895945577289986, 0.01790891182784521, 0.013274840697952369, 0.008461575697423203, 0.004431054286042893, 0.001653008242902553, 0.00016934807702847853, -0.0002970636332716073, -0.00019845864565787617, 5.23709772291939e-06, 2.3344330853756357e-05, -9.421770855048168e-05, 0.0001935542029913976, 0.0020338883250301688, 0.007247675810113952, 0.018339376138181245, 0.03844279747941624, 0.07120055944946253, 0.1205812017162589, 0.19063943484900894, 0.2852382052175931, 0.40773805230548593, 0.5606733069055299, 0.7454367166039317, 0.9619930377622279, 1.2086482380646018, 1.481908495232617, 1.7764465941581329, 2.0851655242360967, 2.3993221365077, 2.7087809955398754, 3.0023744976728364, 3.268358246487608, 3.494959404485251, 3.671051525273685, 3.7868729261796554, 3.8345302359176947, 3.80851279820106, 3.7061654413528533, 3.5280558855917747, 3.2782091468099614, 2.9642023870086454, 2.5972061082915023, 2.191604890165524, 1.7643448506958213, 1.3342525768041458, 0.9212159069542286, 0.5452502888030589, 0.22548759224986023, -0.020858311135933356, -0.17953802932787594, -0.24033647227450025, -0.19790356101919784, -0.052374336251444324, 0.19023898675398887, 0.5179165946073655, 0.9127839289575858, 1.3515189425627903, 1.8061357898779948, 2.2451232833482493, 2.634792523357937, 2.940821595618456, 3.129935960329669, 3.171654279374301, 3.040012910958623, 2.715229278694188, 2.185344730857157, 1.4473681806511152, 0.50807335184621, -0.615595300040806, -1.8965782294142484, -3.29824489480829, -4.775433673037017, -6.27596287858222, -7.742556774216413, -9.115376232523108, -10.334777397484833, -11.344229768065418, -12.093310563805371, -12.540666216470626, -12.656854370783115, -12.426771804511787, -11.851621616698406, -10.950374925517353, -9.76050953865397, -8.337986679087269, -6.756438066693453, -5.105599352101165, -3.4888754005568106, -2.0200943939650906, -0.8196649522926378, -0.010201440427526546, 0.28822330310850486, -0.03697505405897782, -1.0859321788500738, -2.941542473693435, -5.665042543309833, -9.292199777388955, -13.830294788832338, -19.25602226720279, -25.514430174010904, -32.518995148364475, -40.153017296158836, -48.27213250316191, -56.70776801483404, -65.27175172745288, -73.76195289329792, -81.96843181051125, -89.6801026328344, -96.6918766669557, -102.8122275342873, -107.8693532041749, -111.7170966052051, -114.24035077955655, -115.35963754092612, -115.0341365632388, -113.26353331902578, -110.08912577426122, -105.59261984011671, -99.8928815283934, -93.14207695615978, -85.52066765797656, -77.23140332490425, -68.49232996793654, -59.529419717883, -50.56896560258155, -41.82922842615403, -33.51295822179473, -25.800692233091223, -18.844915010775463, -12.765310527388793, -7.645357956403772, -3.530222392520868, -0.4261715004537475, 1.698266595107562, 2.9096861152576516, 3.3058421596466734, 3.010485748198034, 2.167169572900668, 0.9324176110296619, -0.5316161249902657, -2.064754549567029, -3.5160932203592306, -4.7507859326641695, -5.656075578699667, -6.146331814779823, -6.166844118531014, -5.696271790675406, -4.747532535104228, -3.3670354366606756, -1.632551338642441, 0.3502813363850554, 2.4526800967280606, 4.528541287440298, 6.421264787931512, 7.970998372339731, 9.021934585326916, 9.429446708726154, 9.066843176469709, 7.831455297291913, 5.649817888764488, 2.48176665601865, -1.676474189867732, -6.791264868809063, -12.79232871000811, -19.574571185671623, -27.001223731007475, -34.90820385061229, -43.10952173750864, -51.40366071830244, -59.581207332248646, -67.43229789050478, -74.75377083830013, -81.3560532167824, -87.06948927180791, -91.74988791805279, -95.28311738318241, -97.58931536956221, -98.62621469924888, -98.38871547287778, -96.90785773868272, -94.24883115595304, -90.50784330919032, -85.80799791514129, -80.2945694396057, -74.13023656972958, -67.48886260321187, -60.548274469350766, -53.48397019361996, -46.463436324044956, -39.64104856455043, -33.15373338366337, -27.117731972537488, -21.62596145053963, -16.746237842912887, -12.520564037366963, -8.965715496368578, -6.074826468681161, -3.8197788961904267, -2.154255864501497, -1.0172714716894522, -0.33695133531188004, -0.03453027330382227, -0.02832527865342948, -0.23750459705494684, -0.5854755340044798, -1.0027662205099006, -1.429317545160655, -1.816125582275648, -2.126197404468654, -2.3348421736992737, -2.4293046367495696, -2.407828479487396, -2.2782471445870978, -2.0562162903736763, -1.7632098251772903, -1.4243598971677531, -1.0663214356397748, -0.7152657785378684, -0.3950887395738416, -0.12593321023610438, 0.07691790322729504, 0.20374550412773804, 0.25068232389673223, 0.21959132228721337, 0.11757567391895772, -0.04382285776401275, -0.24966823057417545, -0.4828357134771082, -0.725296553319004, -0.959403457476605, -1.1690637216427755, -1.3407442361338526, -1.464252463207291, -1.5332460522750049, -1.545464665842503, -1.5026703533447263, -1.410323064255759, -1.2769828053684489, -1.113497068906329, -0.9320703010923282, -0.7452591337616091, -0.5649631809386919, -0.401517734038979, -0.2629053668385795, -0.15414571945251937, -0.07690790159722938, -0.029391774701749345, -0.006478368671303135, -0.00013985844096778296, -8.518166278185252e-05, 0.00540752343725901, 0.028527604062989872, 0.08089398990786231, 0.17251210628352762, 0.3107956203186999, 0.49972064901159635, 0.7391865475472114, 1.024671698893126, 1.3471276155056702, 1.6931964891430034, 2.0457088089426825, 2.384458906464324, 2.6872322022677384, 2.9310319412601826, 3.093476853313807, 3.154328801072987, 3.096846409648995, 2.909027153227549, 2.5846002594651862, 2.1238122232707517, 1.533900789785212, 0.8292122026562692, 0.03093614851787176, -0.8335912507839339, -1.7319960818750624, -2.6283812771459347, -3.4850211639368442, -4.264210800471567, -4.930211445869589, -5.451199146134884, -5.80118044265129, -5.96188309441651, -5.924011940434266, -5.688125055819686, -5.26509390872049, -4.676079271455728, -3.952007393613444, -3.132553023399033, -2.264715413241062, -1.4010350957702613, -0.5970558080600364, 0.09126911087349161, 0.6102056858498258, 0.9108534255284921, 0.9516252411860007, 0.7004785437796395, 0.1368119156935659, -0.747081439399812, -1.945144139928763, -3.437341697832521, -5.190079898223407, -7.157234191513495, -9.281754410107668, -11.497787563473427, -13.733280051571928, -15.912978966128541, -17.96157303085984, -19.80685414952687, -21.382781810439283, -22.632309121446962, -23.50984815210836, -23.983345351287138, -24.03578607402927, -23.66609164337019, -22.88905758689283, -21.734660407312383, -20.246750792217902, -18.48114398813385, -16.503216456909502, -14.385125693618685, -12.202629891505724, -10.031878822780486, -7.945976046911859, -6.011810519108292, -4.287238282691295, -2.818695610174165, -1.6393518247143495, -0.7678646521754174, -0.20781438372456953, 0.05216457292231166, 0.037590148304278266, -0.21333352902192118, -0.6517581104378964, -1.2207083701849069, -1.8579650691447278, -2.499144116579411, -3.0808473679325625, -3.5437481961716446, -3.835451854828739, -3.913013532947476, -3.7450034572398545, -3.313037491632569, -2.6126600346523885, -1.653568011553673, -0.4591920939123992, 0.934404364704701, 2.4801254901150944, 4.121931513454891, 5.797336681494681, 7.4401959105603765, 8.983607227553689, 10.362829484860326, 11.518150326069511, 12.397628929367277, 12.95915196752037, 13.1721421573102, 13.018756551969341, 12.494514305862033, 11.608434812752865, 10.382608057550156, 8.851270439952296, 7.059405621101687, 5.0606718172302685, 2.9151051154967567, 0.6865039881832287, -1.5598811962358468, -3.759720941069438, -5.8519327396935505, -7.780842317478476, -9.498175285191634, -10.964549315701339, -12.150676582830448, -13.037887578552905, -13.618069622159922, -13.893399344740525, -13.87570962757607, -13.585573863208394, -13.0511915289316, -12.306717279741326, -11.390451335990939, -10.343051746343374, -9.205886022316873, -8.019488114438639, -6.822165405023927, -5.648820218429796, -4.529999548495155, -3.490876229211728, -2.5507612482490183, -1.723156113069227, -1.0159050327934065, -0.4315535024535279, 0.032114726827814744, 0.38140369359039655, 0.6260002845213661, 0.7782810682906726, 0.8522269822067642, 0.862529166001851, 0.8238373872873122, 0.7501138078623106, 0.6541094067876497, 0.5469770769092409, 0.4380620344172903, 0.3347174766624819, 0.24223445795611237, 0.16396052364293628, 0.10150683687408374, 0.055016502262850216, 0.023469748389644864, 0.0050042123669881665, -0.002775168846479076, -0.0025173922067987676, 0.003131307570953038, 0.011735366912560177, 0.021220328965761683, 0.029965360571757433, 0.03684131457162802, 0.04120024509593322, 0.04282872181572198, 0.041873127063323454, 0.03874574333343867, 0.034024289489180404, 0.02835507326551635, 0.022368098248590717, 0.016610149760385454, 0.011499507121833688, 0.00730333403759882, 0.004135926422395328, 0.0019753809144378892, 0.0006938902227363942, 9.599147208953894e-05, -4.1096893222124575e-05, 6.947214333148599e-05, 0.0002531982626705194, 0.0003921998347912009, 0.0004306885580908428, 0.00036835620582271783, 0.00024388109054295534, 0.00011234573379574274, 2.156850710376914e-05, -6.939358222456133e-06, 1.342501460249621e-05, 4.147474423404402e-05, 3.5214965562128176e-05, 1.1588317551545085e-06, 6.633213160982841e-05, 0.0005708767532838205, 0.0021766704117526276, 0.005985115135480517, 0.013655089559551735, 0.02751107442913635, 0.05062960648845304, 0.0868921254848794, 0.14099297792993912, 0.21839438942602798, 0.3252282405428045, 0.46812941927786855, 0.6540076880048273, 0.8897764074246475, 1.1820158744681655, 1.5365954701872695, 1.9582741774404637, 2.4503427995378093, 3.014279001325585, 3.6493834789969513, 4.35252002851706, 5.11801135554351, 5.9375064924536884, 6.799965074629281, 7.691829180274205, 8.597472060355987, 9.499460040993077, 10.378960446271734, 11.216344102072485, 11.992011367977016, 12.686903421800013, 13.2831148778235, 13.764824753915759, 14.118940986028528, 14.335346906261291, 14.407289028767988, 14.331744970012515, 14.109816646272467, 13.746480171518332, 13.250460647322736, 12.634242171543315, 11.913271798412607, 11.105298436991601, 10.229750362704054, 9.307119319039511, 8.358393539132058, 7.404148655955416, 6.463998894177805, 5.55592241612275, 4.6955500853195735, 3.8957900708104214, 3.1665902174065406, 2.5148478945679056, 1.9444545527559545, 1.4563755983716202, 1.0489285571425844, 0.7180467549980802, 0.4577074732414969, 0.2604280857687575, 0.1177743657920925, 0.020855166753136763, -0.03922313575421517, -0.07095485255027546, -0.08210750576498882, -0.07947234186098869, -0.06869700080689949, -0.05421133824990263, -0.039239646919905856, -0.025887771350707172, -0.015289338743948949, -0.007791278843031224, -0.0031637677779733104, -0.0008151335509607318, 6.7857641402105125e-06, 4.237972151387296e-05, -0.00011124319575668238, -8.385223674864794e-05, 0.0002345387068182804, 0.0007082136926565528, 0.0010117069462330568, 0.0007165160118641444, -0.0006049625155457619, -0.0032733789512723755, -0.007409572866714528, -0.01286902325411758, -0.01921526250360887, -0.02574073812944767, -0.03153842826615258, -0.03562251319938794, -0.03709113405195195, -0.035319146855312004, -0.03016432979369432, -0.022167173465376486, -0.01272188093424536, -0.00419591164640952, 2.2232796029039556e-05, -0.004434955719261364, -0.022769015570642856, -0.06076088016194392, -0.1244075639531127, -0.21946085892869618, -0.3508884804707664, -0.5222782266382688, -0.7352183387504593, -0.9886932042593515, -1.2785364299802595, -1.5969855662825672, -1.9323837647440374, -2.2690640040274643, -2.587462591097056, -2.8644220567769656, -3.0737398161009453, -3.186963950213755, -3.1744164429880635, -3.0064005874190105, -2.654490520171345, -2.0929729058273003, -1.3003278571737635, -0.26058397654433063, 1.035399325476061, 2.588812081676431, 4.3920273550984845, 6.428329149408007, 8.671905515522328, 11.087916189371622, 13.633282918375974, 16.257671346847896, 18.904809249631217, 21.514142751610553, 24.022988874873803, 26.369461547002373, 28.494109589655796, 30.341958608037896, 31.86498315655886, 33.023609002166936, 33.78808363264833, 34.13965329988592, 34.07213774010033, 33.592147488929065, 32.71793589552717, 31.478759444375637, 29.914117497609777, 28.071685570753637, 26.005284761928706, 23.77302955267803, 21.435661675656494, 19.053415523873763, 16.683639954659725, 14.378960573482725, 12.185799151471107, 10.142756393207717, 8.279680719613175, 6.6174428008415065, 5.167762203369986, 3.933377329022812, 2.9089201837300362, 2.08212457009921, 1.4352590641680028, 0.9466230737353458, 0.5921787089651255, 0.3471404901838632, 0.18736740436673494, 0.09061249957726449, 0.037495529719807894, 0.012140288014116185, 0.00246035516112839, 0.00010180763738073216, 7.340120493135369e-05, 0.00011288350806536607, -0.00014057291551385445, -8.520339969822599e-05, 0.0008866803716796369, 0.002509718321284404, 0.002934874350945681, -0.001732849581008348, -0.017584499900197323, -0.05270108408577506, -0.11657712277232299, -0.21918856737245507, -0.3697487962387577, -0.5752242511372276, -0.8387091383291189, -1.1578083172881417, -1.5231291004102852, -1.916958028260289, -2.3122890529819373, -2.6723019392778706, -2.950380583608198, -3.090746857779317, -3.029675756546624, -2.6972295934996438, -2.020456656697224, -0.9271192612179183, 0.6501337775340215, 2.7692414646332626, 5.474083351775663, 8.790091638853493, 12.723641831208143, 17.264242106206954, 22.383906672149067, 28.03768559651363, 34.164826039901605, 40.6904182377914], 'positive_zeros': ['1.00216270888322709782583949528494', '1.11663841645720387559669160234722', '1.15100219726518430637131665897830', '1.23180965507702294376864588329904', '1.39182401357811451403857198434334', '1.52357218383758525566708223434188', '1.82810606721939338471105041918400', '1.95712227525724835287858217205927', '2.23976325241379451568608829320128', '2.32879932055782628513131329921581', '2.54083322087813541063759708801092', '2.72903553659885590859757714765551', '2.94014478315800471154889557590389', '2.95507197048260548174376292431355', '3.24429887335336888039556620315954', '3.33911309168299900069244889817388', '3.79672849118677358618601427159683', '3.79877785017424152885525445251487', '3.82601017729652787981938778258034', '3.87029792190206528835159351968026', '4.08208364268789818599596325033423', '4.09165414951758407511774919519333', '4.14421316306443043148758387149732', '4.15776924691665043330608042822439', '4.76595998783021677919650717204078', '4.91530832616257503357688675428300', '4.93573759170980716997775427705504', '5.01294500451344411470168572756422', '5.09323251893312900939946692630341', '5.09675233204216599307800723459863', '5.14871096353512985023412379023636', '5.20065512487099792416893349620166', '5.72575961773120948029758651443987', '5.84318245635476395236018109378816', '5.94204535024031199336278227730952', '5.94842316693436551340659894989439', '6.00561658218954213287009737421731', '6.04884527078206248051322163018026', '6.43717613634165881415478287496041', '6.52632119035924993493150907776286', '6.62845880276585683863269949105183', '6.77145294748344876401375215055486', '6.83964779423897521399275548135598', '7.07698100560862656146132187988798', '7.32456497746855877960317003147512', '7.32830282067222861140296078051283', '7.36215894237170455214857026045391', '7.53911855263057160498065521025776', '7.79867245308999391725144581146709', '7.85613657410137569135252668592897', '7.916837171262653904383861167192391', '8.027919406858157817466543334811264', '8.193413070485824763929049720462865', '8.275075147501063938340219028313367', '8.287242680885506287228500480921540', '8.351100452497072129242880882526970', '8.750612711784064299887338665389431', '8.821741291716433464569823895716617', '8.931213736669705426329326406696296', '8.987727541843118663172708516952177', '8.997274057166563329212249890212147', '9.013102509203953611807720118463451', '9.148878605908269900699617995335188', '9.184419401335940598036294588218165', '9.577388713198222770160435735172012', '9.626586493775397396849260093301407', '9.654850934421136744203856651008422', '9.914512127507345336400521554630307', '9.986020396809120544915260008141037', '10.00752096759768812248312097245374', '10.01726790493519846061698238014310', '10.02873813497300779314461214194957'], 'prelabel': '16-21e16-1.1-c5e8-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.410069235001842, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c5e8-0', 'trace_hash': 1813158258039843533, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.00216270888322709782583949528', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.11663841645720387559669160235', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.15100219726518430637131665898', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 626315468010290.9, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 1430568690241985328321, 'conductor_radical': 21, 'degree': 16, 'dirichlet_coefficients': [1, 0, 0, -118, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6595, 0, 0, 0, 0, 0, 0, 0, 0, -13696, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -19136, 0, 0, 0, 0, 0, -41184, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -261252, 0, 0, -42336, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -251072, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1616128], 'euler11': [1, 0, 1187736, 0, 632475284284, 0, 196968753081795816, 0, 39212142376366900126950, 0, 5108862181812065363177269416, 0, 425497744297030451227292130697084, 0, 20725283253238065882915759335324584536, 0, 452592555681759518058893560348969204658401], 'euler13': [1, 0, 2840192, 0, 3576259172004, 0, 2606307168346742656, 0, 1202118358013343154181606, 0, 359301575523519693247876610944, 0, 67966676013521222054804052130527204, 0, 7441290667129424476913159135120963105408, 0, 361188648084531445929920877641340156544317601], 'euler17': [1, 0, 4015872, 0, 10924993475716, 0, 21937050776253166848, 0, 36263664388467106611525510, 0, 44224960558766385019787899114752, 0, 44401701601424791118986444180593021316, 0, 32903909591259194185129629219497865493571328, 0, 16517976926780506002833800829531584028976727363201], 'euler19': [1, 0, 15214488, 0, 111300185318908, 0, 499736263830315607656, 0, 1498483400493801114061906470, 0, 3063916144969586343088235265324456, 0, 4183771011957698048321810597612833003708, 0, 3506431592397461832967324036887339221249993688, 0, 1413006104539009638843035501053457425807904438071201], 'euler2': [1, 0, 118, 0, 7329, 0, 347864, 0, 12928016, 0, 356212736, 0, 7685013504, 0, 126701535232, 0, 1099511627776], 'euler23': [1, 0, 38163256, 0, 699446036548572, 0, 7979756161797717331208, 0, 61712614932671651932620913670, 0, 330573458118897841008099365383257992, 0, 1200358394326696043964731847329320274202972, 0, 2713191833070000001848712803958581824594389589944, 0, 2945190837423705167875564697729320458241471826430830401], 'euler29': [1, 0, 42210904, 0, 637579767132924, 0, 21813627071864992587944, 0, 738018312441664797771226227110, 0, 9177150693646685841840372038845376744, 0, 112848160646215140275582423936644957955662524, 0, 3143146257683298212016891972258566918585921458833304, 0, 31327079986910989416247938623974919746509417027114485440801], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 0, -40260616, 0, 3885926233187100, 0, -103066241041063506882104, 0, 5036668636781866257046238205254, 0, -84476006590037210042244234207218485304, 0, 2610528439144706358691801484659155979792547100, 0, -22168240810134903393774677177613997181169378443499016, 0, 451302514611022222119906091571193923850834154614488607763201], 'euler37': [1, 19136, 437777256, 6077088467008, 93285117391646396, 1022985398841059479488, 11791613314410175238784280, 106451612492828156564349135680, 1000255490283666733242507353967462, 7381776039283338497187494197581085760, 56700967509267004882812434400622932613720, 341110663412750571305184190869772799334331584, 2156983603230912585791206375284044659058964019196, 9744031074594601088595620071058940318963507438811456, 48674883055101922428532277215109808741909134706448901544, 147540586204356218708402428433613045476328598576604920768448, 534649250915012063273309653845946926220190993810950712361813601], 'euler41': [1, 0, 173596416, 0, 11491494839757124, 0, 2673635180001687354813696, 0, 566501870036624280108779416204230, 0, 35887294140800639263866767084470722084096, 0, 2070397148134192625798747550745677120234005392324, 0, 419813554251183618902640682178736047839847207102747471616, 0, 32460430015431999968619493682032835511850959272235390105491169601], 'euler43': [1, 41184, 1917102744, 49989503472480, 1307512314736623676, 24483442620824640696672, 447322153309046138625736680, 6312737956105614096102143621088, 86253610940133323867337199871810022, 928025777994088671826828502698528845984, 9667294804578675922566997442273567865553320, 77785620003336599481610646829798721021644086304, 610681691042642415216259626600563735308549428567676, 3432339296749551468520373735926230123576568215246308640, 19350805876329459351237500375072092249678502364498538343256, 61111714839162692841781851185550474961735925784450921553891488, 218141463858908869909615270212837010053304269297195114305378988001], 'euler47': [1, 0, 1399898360, 0, 930350136456357532, 0, 381905954056396390555411400, 0, 105565729022425147098984582778044358, 0, 20087921779063229049659347091010607677158600, 0, 2573970613703694052452923944610297950926662127314332, 0, 203719331709220942885624935321258082414985474913054718555640, 0, 7654455761751330268890575447204214294134057054403947260546060444801], 'euler5': [1, 0, 13696, 0, 96678756, 0, 474668448896, 0, 1726257864895526, 0, 4635434071250000000, 0, 9220004653930664062500, 0, 12755393981933593750000000, 0, 9094947017729282379150390625], 'euler53': [1, 0, -429356568, 0, 754267242567238204, 0, -227120053615418724534607464, 0, 202671147277215934252218256112552166, 0, -39720451646080277010499598238411560184797736, 0, 23069736758857343655913548818846976420472402962823804, 0, -2296646738741852000024875324618102734299294096515341477820632, 0, 935480596774678503001801362972812283024661354043792689825893575512801], 'euler59': [1, 0, 2241608536, 0, 3923072134349249340, 0, 4134762873678020477262045224, 0, 3584661460369030015309939946211975014, 0, 2113346575662339896951032984220787592268718824, 0, 1024864680586100861061513154320671478074721605389001340, 0, 299309237798888537896750410689974609386007904290014934298259736, 0, 68246512894550079052163515422746832731983773500978660478681746942325601], 'euler61': [1, 0, 4378091776, 0, 9919688276098981924, 0, 14347996635747417226408450816, 0, 14427780262678331637351707978428492390, 0, 10235041696673306594061247890159605141290652416, 0, 5047713824192221638847094330887147899800498999597466724, 0, 1589204959011488195998181000773788263973806352337138004839864576, 0, 258936575725713381876605656162686020810913039245684608619946288452090401], 'euler67': [1, 42336, 9039868248, 327593961146592, 38188063338457064956, 1175174860497534714587616, 96655973945132836444101572520, 2493955708024349255000180447550816, 159760782356354874179957048472564359334, 3367152217149635296512488911768853339937312, 176188163342958196310530019539181037236813781480, 2892174767965283383732264753058542206216583600867488, 126888916282194159549211687363452570077077931884817562556, 1469623049874672937647654037004774449844043207504976280067744, 54752780895145684331347604979524248743198297100990041842345190552, 346200680370000544778799634076263654135884574379696782939897975081248, 11040585568500089406404363834296492635119570897676624567608785151541319201], 'euler7': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler71': [1, 0, 1373084344, 0, 13726970932748754780, 0, 13570273501915838717144926856, 0, 68189811981699367994392981957922807174, 0, 44174545302551810728839540567808396824394434056, 0, 145459365367783064790408231437585297866279272866456226780, 0, 47363924143565897763502327393745905044020565821816270653214962744, 0, 112288155707690524284921569184047598526949432199996966253201749159632164801], 'euler73': [1, 0, 9148617728, 0, 42350893504763527236, 0, 137329185205740019515844344832, 0, 331563523792361883439793317778834919110, 0, 590189453512331985612692760529367431227947219968, 0, 782203544814580180689821122453887633740291121957030026436, 0, 726174985520801418897557478354196363854548475095296257884942799872, 0, 341125672472605815737240060891364026523290350856811222245874647291144654401], 'euler79': [1, 251072, 34185820792, 3747763195142848, 365244380233998074012, 30218813515090232657132480, 2166926410856781613720260571208, 141808586784327973139210262481499584, 8384779126878446767770966324442297288390, 436353019397863222662707055975167914063038016, 20517057508727702236103455771605172783108395988808, 880407589968927283564331304711311707386806769416083520, 32743520232343531676398911926443403852358410519007562086812, 1033830699046399157658175168506252781864747173473465474947193152, 29017416965492953235181845649391103162434861820649598431423370607992, 655762348268337446377863195074589237233287060755459526268255432839454528, 8036809082503641618612682084624530392577487756904348192905795828229186428801], 'euler83': [1, 0, 11370719128, 0, 98334521353313919996, 0, 551725998946145421653997716072, 0, 2573924686208101506377840949326027215910, 0, 8560603323700685657060944626080118571955543932328, 0, 23673793534982544139943561609995381031492139228082205137596, 0, 42474737475023594029803277041401710921214868185472911888416164595672, 0, 57959375186337998161464929843210464026538099255933595673241672975683189751201], 'euler89': [1, 0, 33866865792, 0, 553368297612803154628, 0, 5570940042424748932903383260544, 0, 37599272765314860558238652471626139840070, 0, 173711492149522450195079946342343342405131523138944, 0, 538039806401233909088016002222394233570957615760071145436228, 0, 1026774811314068672139327900708517827221047061818090911347436002059392, 0, 945366624540204596465924137849354245846140921259572676085974614185475142494401], 'euler97': [1, 0, 31825821824, 0, 520164682838485697796, 0, 6594768168373290663450998972800, 0, 66036870545936076959057435767152664496390, 0, 486314115863713911449644550776329830388068082467200, 0, 2828626119178542155522887202032773409537931575323440983016196, 0, 12762379513619095515752317630215013831882958070400787090362887436443776, 0, 29571228739913279498948663112125511966004786122340140758535526194999034006060801], 'euler_factors': [[1, 0, 118, 0, 7329, 0, 347864, 0, 12928016, 0, 356212736, 0, 7685013504, 0, 126701535232, 0, 1099511627776], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 13696, 0, 96678756, 0, 474668448896, 0, 1726257864895526, 0, 4635434071250000000, 0, 9220004653930664062500, 0, 12755393981933593750000000, 0, 9094947017729282379150390625], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1187736, 0, 632475284284, 0, 196968753081795816, 0, 39212142376366900126950, 0, 5108862181812065363177269416, 0, 425497744297030451227292130697084, 0, 20725283253238065882915759335324584536, 0, 452592555681759518058893560348969204658401], [1, 0, 2840192, 0, 3576259172004, 0, 2606307168346742656, 0, 1202118358013343154181606, 0, 359301575523519693247876610944, 0, 67966676013521222054804052130527204, 0, 7441290667129424476913159135120963105408, 0, 361188648084531445929920877641340156544317601], [1, 0, 4015872, 0, 10924993475716, 0, 21937050776253166848, 0, 36263664388467106611525510, 0, 44224960558766385019787899114752, 0, 44401701601424791118986444180593021316, 0, 32903909591259194185129629219497865493571328, 0, 16517976926780506002833800829531584028976727363201], [1, 0, 15214488, 0, 111300185318908, 0, 499736263830315607656, 0, 1498483400493801114061906470, 0, 3063916144969586343088235265324456, 0, 4183771011957698048321810597612833003708, 0, 3506431592397461832967324036887339221249993688, 0, 1413006104539009638843035501053457425807904438071201], [1, 0, 38163256, 0, 699446036548572, 0, 7979756161797717331208, 0, 61712614932671651932620913670, 0, 330573458118897841008099365383257992, 0, 1200358394326696043964731847329320274202972, 0, 2713191833070000001848712803958581824594389589944, 0, 2945190837423705167875564697729320458241471826430830401], [1, 0, 42210904, 0, 637579767132924, 0, 21813627071864992587944, 0, 738018312441664797771226227110, 0, 9177150693646685841840372038845376744, 0, 112848160646215140275582423936644957955662524, 0, 3143146257683298212016891972258566918585921458833304, 0, 31327079986910989416247938623974919746509417027114485440801], [1, 0, -40260616, 0, 3885926233187100, 0, -103066241041063506882104, 0, 5036668636781866257046238205254, 0, -84476006590037210042244234207218485304, 0, 2610528439144706358691801484659155979792547100, 0, -22168240810134903393774677177613997181169378443499016, 0, 451302514611022222119906091571193923850834154614488607763201], [1, 19136, 437777256, 6077088467008, 93285117391646396, 1022985398841059479488, 11791613314410175238784280, 106451612492828156564349135680, 1000255490283666733242507353967462, 7381776039283338497187494197581085760, 56700967509267004882812434400622932613720, 341110663412750571305184190869772799334331584, 2156983603230912585791206375284044659058964019196, 9744031074594601088595620071058940318963507438811456, 48674883055101922428532277215109808741909134706448901544, 147540586204356218708402428433613045476328598576604920768448, 534649250915012063273309653845946926220190993810950712361813601], [1, 0, 173596416, 0, 11491494839757124, 0, 2673635180001687354813696, 0, 566501870036624280108779416204230, 0, 35887294140800639263866767084470722084096, 0, 2070397148134192625798747550745677120234005392324, 0, 419813554251183618902640682178736047839847207102747471616, 0, 32460430015431999968619493682032835511850959272235390105491169601], [1, 41184, 1917102744, 49989503472480, 1307512314736623676, 24483442620824640696672, 447322153309046138625736680, 6312737956105614096102143621088, 86253610940133323867337199871810022, 928025777994088671826828502698528845984, 9667294804578675922566997442273567865553320, 77785620003336599481610646829798721021644086304, 610681691042642415216259626600563735308549428567676, 3432339296749551468520373735926230123576568215246308640, 19350805876329459351237500375072092249678502364498538343256, 61111714839162692841781851185550474961735925784450921553891488, 218141463858908869909615270212837010053304269297195114305378988001], [1, 0, 1399898360, 0, 930350136456357532, 0, 381905954056396390555411400, 0, 105565729022425147098984582778044358, 0, 20087921779063229049659347091010607677158600, 0, 2573970613703694052452923944610297950926662127314332, 0, 203719331709220942885624935321258082414985474913054718555640, 0, 7654455761751330268890575447204214294134057054403947260546060444801], [1, 0, -429356568, 0, 754267242567238204, 0, -227120053615418724534607464, 0, 202671147277215934252218256112552166, 0, -39720451646080277010499598238411560184797736, 0, 23069736758857343655913548818846976420472402962823804, 0, -2296646738741852000024875324618102734299294096515341477820632, 0, 935480596774678503001801362972812283024661354043792689825893575512801], [1, 0, 2241608536, 0, 3923072134349249340, 0, 4134762873678020477262045224, 0, 3584661460369030015309939946211975014, 0, 2113346575662339896951032984220787592268718824, 0, 1024864680586100861061513154320671478074721605389001340, 0, 299309237798888537896750410689974609386007904290014934298259736, 0, 68246512894550079052163515422746832731983773500978660478681746942325601], [1, 0, 4378091776, 0, 9919688276098981924, 0, 14347996635747417226408450816, 0, 14427780262678331637351707978428492390, 0, 10235041696673306594061247890159605141290652416, 0, 5047713824192221638847094330887147899800498999597466724, 0, 1589204959011488195998181000773788263973806352337138004839864576, 0, 258936575725713381876605656162686020810913039245684608619946288452090401], [1, 42336, 9039868248, 327593961146592, 38188063338457064956, 1175174860497534714587616, 96655973945132836444101572520, 2493955708024349255000180447550816, 159760782356354874179957048472564359334, 3367152217149635296512488911768853339937312, 176188163342958196310530019539181037236813781480, 2892174767965283383732264753058542206216583600867488, 126888916282194159549211687363452570077077931884817562556, 1469623049874672937647654037004774449844043207504976280067744, 54752780895145684331347604979524248743198297100990041842345190552, 346200680370000544778799634076263654135884574379696782939897975081248, 11040585568500089406404363834296492635119570897676624567608785151541319201], [1, 0, 1373084344, 0, 13726970932748754780, 0, 13570273501915838717144926856, 0, 68189811981699367994392981957922807174, 0, 44174545302551810728839540567808396824394434056, 0, 145459365367783064790408231437585297866279272866456226780, 0, 47363924143565897763502327393745905044020565821816270653214962744, 0, 112288155707690524284921569184047598526949432199996966253201749159632164801], [1, 0, 9148617728, 0, 42350893504763527236, 0, 137329185205740019515844344832, 0, 331563523792361883439793317778834919110, 0, 590189453512331985612692760529367431227947219968, 0, 782203544814580180689821122453887633740291121957030026436, 0, 726174985520801418897557478354196363854548475095296257884942799872, 0, 341125672472605815737240060891364026523290350856811222245874647291144654401], [1, 251072, 34185820792, 3747763195142848, 365244380233998074012, 30218813515090232657132480, 2166926410856781613720260571208, 141808586784327973139210262481499584, 8384779126878446767770966324442297288390, 436353019397863222662707055975167914063038016, 20517057508727702236103455771605172783108395988808, 880407589968927283564331304711311707386806769416083520, 32743520232343531676398911926443403852358410519007562086812, 1033830699046399157658175168506252781864747173473465474947193152, 29017416965492953235181845649391103162434861820649598431423370607992, 655762348268337446377863195074589237233287060755459526268255432839454528, 8036809082503641618612682084624530392577487756904348192905795828229186428801], [1, 0, 11370719128, 0, 98334521353313919996, 0, 551725998946145421653997716072, 0, 2573924686208101506377840949326027215910, 0, 8560603323700685657060944626080118571955543932328, 0, 23673793534982544139943561609995381031492139228082205137596, 0, 42474737475023594029803277041401710921214868185472911888416164595672, 0, 57959375186337998161464929843210464026538099255933595673241672975683189751201], [1, 0, 33866865792, 0, 553368297612803154628, 0, 5570940042424748932903383260544, 0, 37599272765314860558238652471626139840070, 0, 173711492149522450195079946342343342405131523138944, 0, 538039806401233909088016002222394233570957615760071145436228, 0, 1026774811314068672139327900708517827221047061818090911347436002059392, 0, 945366624540204596465924137849354245846140921259572676085974614185475142494401], [1, 0, 31825821824, 0, 520164682838485697796, 0, 6594768168373290663450998972800, 0, 66036870545936076959057435767152664496390, 0, 486314115863713911449644550776329830388068082467200, 0, 2828626119178542155522887202032773409537931575323440983016196, 0, 12762379513619095515752317630215013831882958070400787090362887436443776, 0, 29571228739913279498948663112125511966004786122340140758535526194999034006060801]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/6/a/be'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '16-21e16-1.1-c5e8-0-0', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5, 5, 5, 5, 5, 5, 5, 5], 'order_of_vanishing': 8, 'prelabel': '16-21e16-1.1-c5e8-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.410069235001842, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5e8-0', 'trace_hash': 1813158258039843533, 'z1': {'__RealLiteral__': 0, 'data': '1.00216270888322709782583949528', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1270392159442171155745917860996,1415507358859874084698725531093,1459068626227221787685406718718,1561504248625316361218179574561,1764346546224360172197376590208,1931357193332749219551807346134,2317399753391531909358967921640,2480947226949888874413374237479', 'Lhash_array': ['1270392159442171155745917860996', '1415507358859874084698725531093', '1459068626227221787685406718718', '1561504248625316361218179574561', '1764346546224360172197376590208', '1931357193332749219551807346134', '2317399753391531909358967921640', '2480947226949888874413374237479'], 'label': '16-21e16-1.1-c5e8-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/6/a/be'}