Lfunction data - 32-567e16-1.1-c1e16-0-0

Formats: - HTML - YAML - JSON - 2026-03-02T21:55:46.882045

• lfunc_lfunctions •

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

  
  {'Lhash': '34130188740801886788700212259,869854715466114466508230506732,880904549432483298721535967969,896975176690344823916771777402,1075099520949293198146981506845,1552596227700637580622614665052,1610291640447675939637481317066,1772289676918710435264521011494,1871229787705308903168193207501,2060738638426483987427234125935,2087651353880796734615205128553,2323920609809933710762209894996,2542634665423618807386008213471,2891860290966885174691084588583,3119054871315492433553380819973,3328502514683524782501609271631', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 5, 'a5': 0, 'a6': 0, 'a7': 6, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 31171855510.889465, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [7, [1, -6, 25, -114, 508, -1728, 5227, -16224, 47623, -113568, 256123, -592704, 1219708, -1915998, 2941225, -4941258, 5764801]]], 'bad_primes': [3, 7], 'central_character': '567.1', 'coefficient_field': '1.1.1.1', 'conductor': 114111375997743384649195776508234722433546881, 'conductor_radical': 21, 'degree': 32, 'euler_factors': [[1, 0, -5, 0, 11, 0, -22, 0, 35, 0, -22, 0, -30, 0, 264, 0, -815, 0, 1056, 0, -480, 0, -1408, 0, 8960, 0, -22528, 0, 45056, 0, -81920, 0, 65536], [1], [1, 0, -20, 0, 158, 0, -1006, 0, 8963, 0, -61399, 0, 293727, 0, -1729137, 0, 10444771, 0, -43228425, 0, 183579375, 0, -959359375, 0, 3501171875, 0, -9824218750, 0, 38574218750, 0, -122070312500, 0, 152587890625], [1, -6, 25, -114, 508, -1728, 5227, -16224, 47623, -113568, 256123, -592704, 1219708, -1915998, 2941225, -4941258, 5764801], [1, 0, -53, 0, 1301, 0, -24310, 0, 438422, 0, -6939277, 0, 93358746, 0, -1178831562, 0, 13833581305, 0, -142638619002, 0, 1366865400186, 0, -12293352501397, 0, 93979649325782, 0, -630538792050310, 0, 4083095318114021, 0, -20126741179911773, 0, 45949729863572161], [1, -12, 134, -888, 6105, -30876, 179098, -823572, 4484276, -19211160, 95146260, -368856120, 1678874623, -6083817792, 26395513124, -90966061620, 369996806871, -1182558801060, 4460841717956, -13366147689024, 47950338107503, -136953695363160, 459252824084340, -1205471799849720, 3657961694642996, -8733568757620356, 24690180173172202, -55334744326286412, 142234809672746505, -268953094653920664, 527608435683704726, -614230716169089084, 665416609183179841], [1, 0, -82, 0, 3429, 0, -97574, 0, 2107148, 0, -35018028, 0, 442861075, 0, -4531943836, 0, 55716215391, 0, -1309731768604, 0, 36988199845075, 0, -845250067093932, 0, 14698953340288268, 0, -196708588842410726, 0, 1997811651460850469, 0, -13806981777870876178, 0, 48661191875666868481], [1, 24, 260, 1860, 10686, 47166, 107086, -419166, -6879541, -51420516, -276786939, -1114492218, -2822472485, 1822505070, 73990037195, 552542496228, 2810170911123, 10498307428332, 26710403427395, 12500562275130, -367827436717685, -2759593066497582, -13021685394548259, -45963346057197324, -116839118266644181, -135259711527232314, 656551361282877886, 5494379551193397354, 23651483225140996446, 78218549239798129740, 207741738303549871460, 364347048716995159176, 288441413567621167681], [1, 0, -52, 0, 150, 0, 14626, 0, 624335, 0, -12478623, 0, -438951857, 0, 2082575939, 0, 287649733203, 0, 1101682671731, 0, -122836726614737, 0, -1847284049300847, 0, 48892288995413135, 0, 605904153010830274, 0, 3287193664803048150, 0, -602827488876014990068, 0, 6132610415680998648961], [1, 0, 280, 0, 39620, 0, 3737168, 0, 262509098, 0, 14548474088, 0, 657722898576, 0, 24729928393512, 0, 781194417693235, 0, 20797869778943592, 0, 465194909427731856, 0, 8653771672506606248, 0, 131319234644127619178, 0, 1572253609658045570768, 0, 14018141710600683404420, 0, 83316305149223849774680, 0, 250246473680347348787521], [1, 20, 62, -592, 3993, 63748, -324158, -3584180, 11230028, 57146320, -1099785196, -3941857864, 35484532311, 90132924080, -1223837154900, 752142514188, 58822158018199, 23316417939828, -1176107505858900, 2685149941267280, 32770710764387031, -112852044008993464, -976063409759306476, 1572244650023721520, 9577990231411478348, -94764364955833784780, -265689066251122490558, 1619739585192015166588, 3145137495667679195673, -14455187408087465213872, 46930523983689371859902, 469305239836893718599020, 727423121747185263828481], [1, -4, -196, 260, 21774, 11002, -1641314, -2280458, 93818327, 140015056, -4667204695, -4202897350, 221711706075, 53066357330, -10011159522405, -92340382656, 401193533075251, -3416594158272, -13705277386172445, 2687970197836490, 415523432769228075, -291445533113813950, -11974770342170290255, 13291892092962114448, 329534945988741810167, -296372289209601705266, -7892396850630629413586, 1957449674817623463826, 143337196975160928208494, 63327998296181139403220, -1766364014015021626739044, -1333785071807261228353972, 12337511914217166362274241], [1, 0, 274, 0, 37841, 0, 3616646, 0, 273427556, 0, 17420877956, 0, 965828738463, 0, 47347608344316, 0, 2060739655855303, 0, 79591329626795196, 0, 2729201181827945343, 0, 82750986260739011396, 0, 2183298590241295058276, 0, 48545007103425440467046, 0, 853825036456156847491121, 0, 10392608251406863111792114, 0, 63759030914653054346432641], [1, -20, 526, -6928, 109937, -1136500, 14215266, -127050948, 1379372148, -11085538656, 107579120964, -785905304304, 6925030209399, -46488750751176, 377038314636420, -2341844065443996, 17543733667749351, -100699294814091828, 697143843762740580, -3696181105973750232, 23675300204923510599, -115534715131172238672, 680046680105730859236, -3013255720846879452192, 16122377923168687656948, -63854867804372019277164, 307212969737630933145234, -1056142334909044606505500, 4393041930958655861796737, -11904133853027710560163504, 38863697963016852980626174, -63541407315959113238286140, 136614025729312093462315201], [1, 0, -187, 0, 17658, 0, -1097501, 0, 46137122, 0, -883107198, 0, -54170427851, 0, 6798567948140, 0, -400845896701047, 0, 15018036597441260, 0, -264334407546395531, 0, -9519202645831838142, 0, 1098584237690639991842, 0, -57727600227955714607549, 0, 2051709208737813994579578, 0, -47996726417093805545527003, 0, 566977372488557307219621121], [1, 0, -136, 0, 11898, 0, -982454, 0, 65260463, 0, -3934825011, 0, 227355327775, 0, -12350790854677, 0, 663083591655843, 0, -34693371510787693, 0, 1793942894057409775, 0, -87212882523225397419, 0, 4063096222482079320143, 0, -171818894810479757042246, 0, 5844998442846527787918618, 0, -187672691639771552500573384, 0, 3876269050118516845397872321], [1, 0, -412, 0, 92526, 0, -14617286, 0, 1798129247, 0, -181339187307, 0, 15440137281895, 0, -1128686492503633, 0, 71461191506541507, 0, -3928957680405146473, 0, 187093717334280479095, 0, -7648983690634513694787, 0, 264020104206138203676287, 0, -7471139762386919341857686, 0, 164622020320031004162131406, 0, -2551675119711427115634657532, 0, 21559177407076402401757871041], [1, 36, 458, 2136, 4581, 101244, 205534, -19237608, -259070596, -2084437056, -16420374612, -94639746252, -82112767277, 2391348337452, 32333281143140, 638769415441428, 7239849135563583, 38964934341927108, 120312139133623940, 542790636983192412, -1136920319787344957, -79932379612017813852, -845983847158100122932, -6550849624880703994176, -49665727835764135049476, -224967398428674813574728, 146616222005718912513934, 4405523074652210049394284, 12159572651257242191268501, 345851053955078286084593016, 4523589300279483687561497978, 21689524243261454536866920436, 36751693856637464631913392961], [1, -18, -25, 498, 21465, -77334, -372626, -15207210, -70258, 522690522, 14456179755, -11746976322, -252467626262, -9019369794816, -18089573469178, 87121202733900, 7145095613367393, 5837120583171300, -81204095303140042, -2712692717598244608, -5087505685388339702, -15859887663666716454, 1307682632981550788595, 3167876512677736848606, -28529502889774483378, -413735481936680480967870, -679236759758904661695074, -9444811698072796633096722, 175642061287944278608001865, 273024598971979911485422326, -918305629072422393048358225, -44299063546453656240652800774, 164890958756244164895763202881], [1, 0, 422, 0, 88767, 0, 13696474, 0, 1783062743, 0, 197270735778, 0, 18780300283168, 0, 1592056496650616, 0, 120384303819988383, 0, 8025556799615755256, 0, 477238999880074885408, 0, 25270437262466372825538, 0, 1151419062725002815782423, 0, 44585358660074511612585274, 0, 1456638307838462881953170847, 0, 34908350913530678807493147782, 0, 416997623116370028124580469121], [1, 32, 80, -5956, 1902, 1405666, 2145574, -160863194, 419706635, 20362342396, -73674153571, -1424225986954, 15803979253215, 105018878113286, -1523386397874453, -1680917453035836, 144926371035107203, -122706974071616028, -8118126114272960037, 40854128906996179862, 448805211591799594815, -2952522435566725997722, -11149421028164251428019, 224950911230916458736412, 338476651430655512927435, -9470271473739922692894122, 9220874241940380999195526, 440994935196133917835464082, 43559695384424472069312942, -9957535666037406604664792548, 9763601123179727093895632720, 285097152796848031141752475424, 650377879817809571042122834561], [1, -32, 4, 7004, 42998, -2012542, -7832466, 293719086, 2551107411, -42512614356, -399580429395, 3686139563154, 60485393470035, -282988338874782, -6212474403083781, 6532193094162084, 578303058890079675, 516043254438804636, -38772052749645877221, -139524287610483642498, 2355910974974734322835, 11342459330410080322446, -97132989857619143439795, -816408376856300508698604, 3870307528246017984623571, 35202701227655924543536434, -74159950495787971389027666, -1505368959426678025248000418, 2540816791339925247095200118, 32696278518001815852405408356, 1475160481394713565014293124, -932301424241458973089033254368, 2301619141096101839813550846721], [1, 0, 1106, 0, 588057, 0, 199446598, 0, 48280461356, 0, 8842976735556, 0, 1267446926365087, 0, 144990400379398868, 0, 13377759444102660759, 0, 998838868213678801652, 0, 60150903081897662038927, 0, 2891126115616059417808164, 0, 108741708076207950219399596, 0, 3094621629216088596089616502, 0, 62857417280773844837266047177, 0, 814419981222669953584128636674, 0, 5072820298953863752478356399681], [1, 0, 4, 0, 10610, 0, -307510, 0, -23884909, 0, -1439051407, 0, 120404885691, 0, 39552324252603, 0, 7282335141246355, 0, 313293960404868363, 0, 7554472355602173531, 0, -715181626010103432127, 0, -94025065394612885795629, 0, -9588690695663901119143510, 0, 2620568181827431308620357810, 0, 7825643946561765653376759364, 0, 15496731425178936435099327730561], [1, -28, 1286, -28048, 761097, -13824068, 283936306, -4458422660, 75799851020, -1051953765872, 15453031592924, -192095689823008, 2496107817288063, -28011310651778320, 326354731921222764, -3318512907126253500, 34927887494891105479, -321895751991246589500, 3070671672646784986476, -25565166926490474649360, 220978630362991587272703, -1649591050413301803233056, 12871942708189082849522396, -84996059632748134510359536, 594076298832916753520350220, -3389431378741302675920617220, 20938148254582118041853634994, -98883752367850336142914091204, 528081339426544875710554819977, -1887706382496404368130705066896, 8395474528143413922181988428934, -17731033295830102809211726728604, 61425365346268570446197767595521], [1, 0, -212, 0, 29990, 0, 1151906, 0, -596922157, 0, 99293990441, 0, -2310347801433, 0, -678778859519817, 0, 145008714016048243, 0, -6924223145961653217, 0, -240415718666586354633, 0, 105402571686704574405041, 0, -6463811604454276130607757, 0, 127242085399391894230757906, 0, 33793482653657771922629417990, 0, -2436885332063759301538561217012, 0, 117257864492369852051862561201601], [1, 82, 3223, 82190, 1567565, 24593306, 337971114, 4180280094, 46906294014, 489459159042, 5050201898751, 54859021437318, 631982333551566, 7476290449377420, 88096131293097594, 1001455290678110508, 10610413156797229017, 103149894939845382324, 934611856888472374746, 8169544433876840024340, 71130168417664612229646, 635966412937506799247274, 6030205175138747886735279, 60197302789859075023217454, 594194898857062298851600254, 5454317367546393825372230802, 45420491584977947481982472586, 340428871582907317826757871382, 2234972864589030498620944877165, 12069878590858407095214879334370, 48750766832080235369161555879687, 127753328161262695602835402097374, 160470643909878751793805444097921], [1, 0, -476, 0, 121046, 0, -19956088, 0, 2200786145, 0, -123821203816, 0, -8244177549498, 0, 3091482592406172, 0, -427465385739478556, 0, 35394384200458263228, 0, -1080643503761355590298, 0, -185822238769152421455784, 0, 37813603391045681848270145, 0, -3925664559539000705735881912, 0, 272618783077351821737509985846, 0, -12273822554957934003326255060924, 0, 295216374856540727739668685278401], [1, -16, -220, -2596, 126318, 784366, -2815250, -385731170, -1256719801, 15435936364, 749387486621, 2269823294510, -26382924682101, -1223702061917794, -4051528569446601, 40733674268333616, 1618493596605186667, 4439970495248364144, -48136210933595066481, -1584729657543338846026, -3724165129926886776261, 34924044943231236575990, 1256797836874937504558261, 2821749553982893454911516, -25040929265449325195637721, -837766935794418948120955130, -666472058489545804304665250, 20239987378237814827449215494, 355290189905251665648098681358, -795882877312414955259334340884, -7351799459919765264683681623420, -58279719355000321007310639778384, 397030588105939686862303733490241], [1, 0, 1354, 0, 897161, 0, 385346966, 0, 119888512556, 0, 28612504264412, 0, 5413681476610215, 0, 827843091990785844, 0, 103360484179101055063, 0, 10570728441630344442036, 0, 882686478055878781392615, 0, 59569853399825049746850908, 0, 3187169200006880709540114476, 0, 130808624458906766624558898134, 0, 3888765079091073865826139664841, 0, 74940549481434715339790522964106, 0, 706732552679793116819634555191041]], 'euler_factors_factorization': [[[[1, 0, -4, 0, 14, 0, -39, 0, 77, 0, -156, 0, 224, 0, -256, 0, 256], 1], [[1, 0, -1, 0, -7, 0, 3, 0, 29, 0, 12, 0, -112, 0, -64, 0, 256], 1]], [1], [[[1, 0, -20, 0, 158, 0, -1006, 0, 8963, 0, -61399, 0, 293727, 0, -1729137, 0, 10444771, 0, -43228425, 0, 183579375, 0, -959359375, 0, 3501171875, 0, -9824218750, 0, 38574218750, 0, -122070312500, 0, 152587890625], 1]], [[[1, -3, 8, -33, 123, -231, 392, -1029, 2401], 2]], [[[1, 0, -53, 0, 1301, 0, -24310, 0, 438422, 0, -6939277, 0, 93358746, 0, -1178831562, 0, 13833581305, 0, -142638619002, 0, 1366865400186, 0, -12293352501397, 0, 93979649325782, 0, -630538792050310, 0, 4083095318114021, 0, -20126741179911773, 0, 45949729863572161], 1]], [[[1, -3, 20, -15, 231, -195, 3380, -6591, 28561], 4]], [[[1, 0, -82, 0, 3429, 0, -97574, 0, 2107148, 0, -35018028, 0, 442861075, 0, -4531943836, 0, 55716215391, 0, -1309731768604, 0, 36988199845075, 0, -845250067093932, 0, 14698953340288268, 0, -196708588842410726, 0, 1997811651460850469, 0, -13806981777870876178, 0, 48661191875666868481], 1]], [[[1, 12, 58, 234, 853, -225, -20609, -148827, -769679, -2827713, -7439849, -1543275, 111163813, 579407166, 2728661098, 10726460868, 16983563041], 2]], [[[1, 0, -52, 0, 150, 0, 14626, 0, 624335, 0, -12478623, 0, -438951857, 0, 2082575939, 0, 287649733203, 0, 1101682671731, 0, -122836726614737, 0, -1847284049300847, 0, 48892288995413135, 0, 605904153010830274, 0, 3287193664803048150, 0, -602827488876014990068, 0, 6132610415680998648961], 1]], [[[1, 0, 140, 0, 10010, 0, 467184, 0, 15748739, 0, 392901744, 0, 7079882810, 0, 83275264940, 0, 500246412961], 2]], [[[1, 10, -19, -106, 2876, 1100, -124053, -225804, 1496959, -6999924, -119214933, 32770100, 2656046396, -3034690006, -16862569939, 275126141110, 852891037441], 2]], [[[1, -2, -100, -70, 5747, 9995, -228417, -195273, 7862563, -7225101, -312702873, 506276735, 10770803267, -4854076990, -256572640900, -189863754266, 3512479453921], 2]], [[[1, 0, 137, 0, 9536, 0, 501891, 0, 22487063, 0, 843678771, 0, 26946456896, 0, 650764281017, 0, 7984925229121], 2]], [[[1, -5, 94, -197, 4069, -8471, 173806, -397535, 3418801], 4]], [[[1, 0, -187, 0, 17658, 0, -1097501, 0, 46137122, 0, -883107198, 0, -54170427851, 0, 6798567948140, 0, -400845896701047, 0, 15018036597441260, 0, -264334407546395531, 0, -9519202645831838142, 0, 1098584237690639991842, 0, -57727600227955714607549, 0, 2051709208737813994579578, 0, -47996726417093805545527003, 0, 566977372488557307219621121], 1]], [[[1, 0, -136, 0, 11898, 0, -982454, 0, 65260463, 0, -3934825011, 0, 227355327775, 0, -12350790854677, 0, 663083591655843, 0, -34693371510787693, 0, 1793942894057409775, 0, -87212882523225397419, 0, 4063096222482079320143, 0, -171818894810479757042246, 0, 5844998442846527787918618, 0, -187672691639771552500573384, 0, 3876269050118516845397872321], 1]], [[[1, 0, -412, 0, 92526, 0, -14617286, 0, 1798129247, 0, -181339187307, 0, 15440137281895, 0, -1128686492503633, 0, 71461191506541507, 0, -3928957680405146473, 0, 187093717334280479095, 0, -7648983690634513694787, 0, 264020104206138203676287, 0, -7471139762386919341857686, 0, 164622020320031004162131406, 0, -2551675119711427115634657532, 0, 21559177407076402401757871041], 1]], [[[1, 18, 67, -138, 2530, 14328, -334169, -4214598, -32506397, -257090478, -1243442849, 3252183768, 35029977730, -116554289538, 3451865082187, 56569371048378, 191707312997281], 2]], [[[1, -9, -53, -228, 7276, 14733, 305920, -2410548, -28627265, -161506716, 1373274880, 4431141279, 146619556396, -307828524396, -4794294254957, -54546404447907, 406067677556641], 2]], [[[1, 0, 211, 0, 22123, 0, 2180284, 0, 186777883, 0, 10990811644, 0, 562182618763, 0, 27029159907331, 0, 645753531245761], 2]], [[[1, 16, -88, -1570, 22199, 209489, -1557975, -2216535, 190716007, -161807055, -8302448775, 81494782313, 630412551959, -3254722401010, -13317411913432, 176758376305552, 806460091894081], 2]], [[[1, -16, -126, 1486, 37337, -221643, -3862157, 1655231, 447741333, 130763249, -24103721837, -109278643077, 1454279174297, 4572505808914, -30629019395646, -307262543778544, 1517108809906561], 2]], [[[1, 0, 553, 0, 141124, 0, 21681727, 0, 2192243959, 0, 149365417303, 0, 6697508092804, 0, 180798026473057, 0, 2252292232139041], 2]], [[[1, 0, 4, 0, 10610, 0, -307510, 0, -23884909, 0, -1439051407, 0, 120404885691, 0, 39552324252603, 0, 7282335141246355, 0, 313293960404868363, 0, 7554472355602173531, 0, -715181626010103432127, 0, -94025065394612885795629, 0, -9588690695663901119143510, 0, 2620568181827431308620357810, 0, 7825643946561765653376759364, 0, 15496731425178936435099327730561], 1]], [[[1, -7, 248, -1461, 30281, -141717, 2333432, -6388711, 88529281], 4]], [[[1, 0, -212, 0, 29990, 0, 1151906, 0, -596922157, 0, 99293990441, 0, -2310347801433, 0, -678778859519817, 0, 145008714016048243, 0, -6924223145961653217, 0, -240415718666586354633, 0, 105402571686704574405041, 0, -6463811604454276130607757, 0, 127242085399391894230757906, 0, 33793482653657771922629417990, 0, -2436885332063759301538561217012, 0, 117257864492369852051862561201601], 1]], [[[1, 41, 771, 9484, 97718, 978051, 8571760, 57863054, 421695387, 5959894562, 90937801840, 1068742735077, 10998246989558, 109945553206612, 920614320623859, 5042482848241967, 12667700813876161], 2]], [[[1, 0, -476, 0, 121046, 0, -19956088, 0, 2200786145, 0, -123821203816, 0, -8244177549498, 0, 3091482592406172, 0, -427465385739478556, 0, 35394384200458263228, 0, -1080643503761355590298, 0, -185822238769152421455784, 0, 37813603391045681848270145, 0, -3925664559539000705735881912, 0, 272618783077351821737509985846, 0, -12273822554957934003326255060924, 0, 295216374856540727739668685278401], 1]], [[[1, -8, -142, -2434, 33605, 315395, 2925267, -42882789, -353010881, -4674224001, 34755097227, 408445671455, 4743620000405, -37450107062266, -238148215739422, -1462431296653352, 19925626416901921], 2]], [[[1, 0, 677, 0, 219416, 0, 44128851, 0, 5997333623, 0, 563481298419, 0, 35775199761176, 0, 1409481336516293, 0, 26584441929064321], 2]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 0, 'label': '32-567e16-1.1-c1e16-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/567/2/e/g', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0078125', 'prec': 30}, 'plot_values': [0.5965931511796908, 0.5553099098473501, 0.4114110914123092, 0.1657458270118216, -0.18038563680020747, -0.6252316763033872, -1.1665904018010502, -1.8018122317975014, -2.5278040208882855, -3.3410348318341825, -4.23754344102672, -5.2129476642100085, -6.262455585830304, -7.380878770673983, -8.562647530464387, -9.801828310761872, -11.092143254800924, -12.427015460734033, -13.799655632751202, -15.203004797005065, -16.629738682890245, -18.0723002371061, -19.522934748446488, -20.973727495875615, -22.416643808742414, -23.843571403286223, -25.246364834013022, -26.616891872215238, -27.947081597032017, -29.22897395718419, -30.454770534077003, -31.616886209575917, -32.70800141467996, -33.72106193120199, -34.649170643670686, -35.48579645176062, -36.224884787641415, -36.86091526760873, -37.38895751111432, -37.80472447729087, -38.10462265072884, -38.28579839635002, -38.34617979847246, -38.284513302290655, -38.100394487678685, -37.79429232609159, -37.36756630195047, -36.82247582073249, -36.16218137742937, -35.39072941984422, -34.51302121437617, -33.534823767965385, -32.46274260795855, -31.30417431864071, -30.0672485879872, -28.760759978067878, -27.394089789455386, -25.97711855288214, -24.5201298481542, -23.033706318596877, -21.528618916472645, -20.01571057804357, -18.505775683228848, -17.00943680094751, -15.537020353940335, -14.098444767181054, -12.703131547791614, -11.35984567085202, -10.076569221039147, -8.860396721911588, -7.717441852095566, -6.652757550364497, -5.670271381569255, -4.772737861804093, -3.9617092242229504, -3.237525847586586, -2.599327269904547, -2.0450843724150123, -1.571652948616616, -1.1748484741520877, -0.8495414720765455, -0.5897749333850228, -0.38889985630541807, -0.2397106420128489, -0.13460942364447015, -0.06578522358421157, -0.02540044289106706, -0.0057808607418602925, 0.000394940507632296, -8.900608112107163e-05, -0.001161422379902158, 0.0023744262834309578, 0.014696797550130068, 0.038843463525809876, 0.0766153870526312, 0.12850942502598606, 0.1936828796008788, 0.2699513613788181, 0.35382046395544275, 0.4405593519575179, 0.5243115231601959, 0.5982409394802993, 0.6547117273980693, 0.6854981065757505, 0.6820202566121781, 0.6356009472757189, 0.5377369645774599, 0.3803786902527559, 0.15621066057484154, -0.14107443552115775, -0.5165160399293699, -0.9736479918909801, -1.5142902483072438, -2.1383714300054506, -2.8437788183762707, -3.62628916510504, -4.4795497929307055, -5.395112655950777, -6.362527334349795, -7.369492798477639, -8.402066078336413, -9.444924257609166, -10.481674527303909, -11.495205435366573, -12.468071007697974, -13.382898143690106, -14.222806653111734, -14.971830543306664, -15.6153287219276, -16.14037815269559, -16.536151483193716, -16.79422538799044, -16.908828373457926, -16.877025008668344, -16.69882693623556, -16.377225898699454, -15.918146318898373, -15.330317419209383, -14.625067377320937, -13.816044512979296, -12.918872896104547, -11.950751977426645, -10.93001178741056, -9.87563685324791, -8.806773182009264, -7.742245924068311, -6.70010664541282, -5.697125986609898, -4.74836755913407, -3.866834799163154, -3.0631872806827203, -2.345535127078217, -1.7193174383004766, -1.1872676931176125, -0.7494660007726562, -0.40347497867731114, -0.1445530406483543, 0.03406388996750671, 0.14082366608463692, 0.1854756324260471, 0.17865969373852306, 0.13148360263421324, 0.05510513193458818, -0.03967509078905358, -0.14278505107080022, -0.24520279735173353, -0.339217775241236, -0.4186238138562878, -0.47883859689556735, -0.5169476994878307, -0.5316745608608492, -0.5232809469266481, -0.49340539403329875, -0.4448496835919803, -0.381325461572245, -0.3071745933997129, -0.22707766664154727, -0.14576568139833748, -0.0677479859014193, 0.0029344833885714366, 0.0629119678163782, 0.10963791430104951, 0.14148553326647456, 0.15778646208876365, 0.15881227578972082, 0.14570264269097427, 0.12034670803611515, 0.08522665711476961, 0.043234237135404474, -0.0025277912363686245, -0.048946807129484265, -0.09309184743540486, -0.13238417832881502, -0.16473759531571452, -0.1886622826139108, -0.20332295647345675, -0.20854973397225973, -0.2048040633914269, -0.1931036256938307, -0.17491282342050612, -0.15200761656565187, -0.12632500973169386, -0.09980834249174327, -0.07425962949165682, -0.051209529349482766, -0.03181413109506119, -0.016785719860294382, -0.006362148506644648, -0.00031656319129495694, 0.001993813122859398, 0.001544229427232329, -0.0004693753390893383, -0.002761213405716027, -0.004093679941830316, -0.0034105965463112147, 4.609028014083989e-05, 0.00664687116552053, 0.016321317706682704, 0.02854699168661495, 0.04238358728276427, 0.05655169200062224, 0.06955185100998398, 0.07981606527595816, 0.0858807143149565, 0.08656742140269717, 0.081157041852732, 0.06954179068239558, 0.05233784136020733, 0.03094598455150337, 0.007550816709833731, -0.014947558072323067, -0.03307041341743875, -0.042961768059589324, -0.04064486838483791, -0.022319478880783575, 0.015318569388218675, 0.0747573181028238, 0.1573717076341315, 0.2631735784070969, 0.39063113889080314, 0.5365772914569735, 0.6962219768020561, 0.8632803843182211, 1.030215554406548, 1.1885859407983623, 1.3294840255566718, 1.444043565729724, 1.5239867710002983, 1.562178044582904, 1.5531482529800564, 1.4935531228638361, 1.38253145199557, 1.2219333620756077, 1.016395642505066, 0.7732499973029772, 0.5022602234786586, 0.21519540254170963, -0.0747418620215989, -0.3536115704569755, -0.6075235722586914, -0.8234416793202873, -0.989963734272704, -1.0980296694702742, -1.1415096284789807, -1.1176303811504213, -1.0272074956018338, -0.8746625208350722, -0.6678180678610356, -0.41747828243125995, -0.13681680239428534, 0.15939212885295054, 0.45565215044384, 0.7366769530598256, 0.9883140261634636, 1.1984063009181039, 1.3575376275374336, 1.4595779364129664, 1.5020020055489145, 1.4859623708239214, 1.4161107127814085, 1.3001800820620852, 1.1483577991493092, 0.9724944784331985, 0.7852071744820025, 0.5989431126125075, 0.42507410168888143, 0.2730901281378719, 0.149953771672015, 0.05966533882303916, 0.003073511459087842, -0.02205495667889241, -0.02071441562601427, -0.00010294348989560182, 0.031118238663367288, 0.06368429906536685, 0.08863199364720036, 0.09817236313777788, 0.0864542452648057, 0.05014983703104503, -0.011192557509683957, -0.09506453031214201, -0.19619570295278596, -0.30702293677441883, -0.41839523225148323, -0.520456751898402, -0.6036340056729902, -0.6596439526915026, -0.6824135675646634, -0.6688255172517027, -0.6192151883679705, -0.537560197213718, -0.4313297081688168, -0.3109903561893258, -0.18919672053282566, -0.07972449593955978, 0.0037689293150962155, 0.04905136390420107, 0.046572902194054404, -0.009446403328033974, -0.12020966299875292, -0.2819097026014713, -0.48573483922437966, -0.7183525185894571, -0.9628491192946875, -1.2000579881086808, -1.4101796380270604, -1.5745618290896528, -1.6774836011456378, -1.707776213365554, -1.6601170350673105, -1.5358503925325329, -1.3432216451420564, -1.0969555233635861, -0.81716400970276, -0.5276287715309395, -0.2535636100567519, -0.01901842433420756, 0.15586869041084725, 0.2575443896064938, 0.2813562635450645, 0.23324022420987794, 0.13058749964828764, 0.002135723083051761, -0.1132034031578593, -0.1685840912123623, -0.11244837939945532, 0.10744536466048346, 0.539444604514458, 1.22319972398068, 2.1850059587920154, 3.4336792381621133, 4.9573443355652875, 6.721472093262287, 8.668431362121488, 10.71877011735531, 12.774291513942238, 14.722729246565184, 16.443815721141203, 17.81640161287386, 18.726178590090075, 19.073487073262605, 18.780657133881743, 17.79833723467623, 16.110313696022935, 13.736411560944008, 10.733189763089804, 7.192292123621274, 3.2364802865040856, -0.9864568213831617, -5.3115745313870555, -9.566085533244838, -13.579390714793274, -17.192898828511957, -20.26908849162582, -22.699205604757655, -24.40906497265303, -25.362562624674617, -25.562673976524902, -25.04989953406979, -23.898309677177256, -22.20951808012612, -20.10506520017211, -17.717806635218714, -15.182966673012954, -12.629529535667226, -10.172659697051495, -7.907653403521677, -5.905382160816968, -4.210188771881333, -2.8400787855249487, -1.7889575811659535, -1.0305802057017432, -0.5237458899661919, -0.21817982548711623, -0.060508857746769826, 0.00024201598136979716, 0.008131473182493855, -0.0028592036754523913, -0.010406276735645516, -0.0037934350178129373, 0.017641078149241908, 0.04727091273534269, 0.07474393753899165, 0.08983510752081623, 0.08604755961161546, 0.06345778104870456, 0.03039227401478629, 0.003661700309004928, 0.00725144250242969, 0.06955718285539604, 0.21944078583014617, 0.48154545180404773, 0.8714313818794414, 1.3911591231949856, 2.025947486063061, 2.74246281838877, 3.489159746131489, 4.198930546062323, 4.794130721522602, 5.193447569623517, 5.320213636869653, 5.111467986626184, 4.526883397186832, 3.556629423476491, 2.2272622037080065, 0.6048440846608388, -1.2053056125241572, -3.0625567133328184, -4.798617402555885, -6.2285469267180975, -7.164453299345023, -7.430897510051397, -6.880794706059025, -5.410564926729536, -2.9732277575189903, 0.41279644081145783, 4.65939147151765, 9.60959663937508, 15.043927784524058, 20.691950065013852, 26.248432665689446, 31.393003688129685, 35.811888844110875, 39.22009188531281, 41.38228095918392, 42.13069537274739, 41.3785813820787, 39.1279908253926, 35.47120810688398, 30.585804838057204, 24.723594639482958, 18.192340152069338, 11.334026313089712, 4.501112597205633, -1.9676153373128475, -7.7696872652518385, -12.658319334574275, -16.457043160054774, -19.068537789500056, -20.47711115418196, -20.74482086168903, -20.001760616454884, -18.431520799249885, -16.253217525674728, -13.701740467914126, -11.008120820483086, -8.381651195249907, -5.99414430737821, -3.969241235865397, -2.3771083539946303, -1.2344867835234277, -0.509743188144915, -0.1321148567901077, -0.00398159529409206, -0.014763607637728516, -0.05495687840949552, -0.028879510568319656, 0.13509676212310284, 0.47774027687603354, 1.006093716043963, 1.694631778450618, 2.490084786585914, 3.3192025954660336, 4.098605597691621, 4.745398662640615, 5.187302571367927, 5.3711868645248035, 5.269101868515264, 4.88122514890316, 4.235508020725509, 3.384188649960219, 2.3976872942885854, 1.356678467192391, 0.34331492647966244, -0.567358354945905, -1.3148200512637125, -1.8585078817959855, -2.180735840829246, -2.286874200141335, -2.202779033561174, -1.9700016794856476, -1.639482758530493, -1.2645840349742818, -0.8943766906422708, -0.5680439690292367, -0.3110886883449174, -0.1337832567051011, -0.03199319741029772, 0.009817039319875723, 0.013884836724970519, 0.0034811116422926404, -0.002859689227442224, 0.0036869623186400204, 0.018870531665457164, 0.024226403517927816, -0.011526643885388026, -0.1285892339896757, -0.3700624346464146, -0.774499803256821, -1.3679605899576435, -2.1566241535444957, -3.1210282272661525, -4.212863720484273, -5.3550066311399895, -6.445118533656442, -7.362738433854025, -7.979366286436799, -8.170651172681367, -7.829491804115805, -6.878792337835623, -5.282573024831495, -3.0530729890070587, -0.25379591222787434, 3.0020854046286365, 6.558147007823913, 10.225520723873728, 13.797183287588233, 17.064432641503327, 19.833997213832635, 21.944124584015444, 23.27806996717796, 23.773647219988394, 23.42789186971707, 22.29637705221975, 20.487267208626285, 18.150736014154553, 15.464752173316109, 12.618692700430985, 9.79675251010974, 7.162722366855142, 4.8475695523598805, 2.940938432485128, 1.4872347510501203, 0.48644445746484, -0.10067656066515951, -0.3438637278088564, -0.33222956678861754, -0.16215509043091042, 0.07438924971385069, 0.29979202013621337, 0.45798815280234123, 0.518251782619807, 0.4753957970580252, 0.3464737289712503, 0.1648286698054676, -0.02747346960397929, -0.18769104073488235, -0.2797963862361787, -0.2802259267828278, -0.18128639835219187, 0.008126266355903244, 0.26444547424202186, 0.553567070938425, 0.8364715950399673, 1.0754180962298876, 1.2397351075985164, 1.310319585899842, 1.28219434153313, 1.1647802563569993, 0.9796493505684947, 0.7563718640072882, 0.527192168992166, 0.32143084843002523, 0.1605836154783112, 0.054986339281120004, 0.0026726477587971833, -0.009301348866552555, -0.0012026614549018662, 0.004812802181915527, -0.008985962146054871, -0.04984369949367576, -0.10991233487414238, -0.16418807421728984, -0.17178827845380176, -0.08094239595059123, 0.1625155046900108, 0.6040145677958391, 1.2678277432287077, 2.145101017535319, 3.1842414220267554, 4.285495805869278, 5.3012116642673925, 6.0426906332255985, 6.2937804023965445, 5.830485727932812, 4.445017193979864, 1.9719480649791614, -1.6863803291218566, -6.538290574238079, -12.488011490599265, -19.33033884179675, -26.75622205697772, -34.36954348533574, -41.714306605772805, -48.31017190809162, -53.693198403955144, -57.45786672890335, -59.29607916615174, -59.028918309416966, -56.627513522515216, -52.2203712161563, -46.085876274051145, -38.63022811514218, -30.352665984852518, -21.801282506392397, -13.523696475417504, -6.017131880066759, 0.3152274556172371, 5.197115532635191, 8.498371477449187, 10.238475491168346, 10.574257622747204, 9.773402537938386, 8.177006075085572, 6.155711547897516, 4.064708821272215, 2.203017199288021, 0.7819641644637783, -0.09333839041582014, -0.4273124016297472, -0.32171588314344657, 0.05037844037708602, 0.4809444941320917, 0.7689687531711011, 0.7618386090088906, 0.39020621693906804, -0.30882916998238735, -1.1840426425619885, -1.979863789445536, -2.3634003585284034, -1.966268732185436, -0.43678511478560716, 2.5034806773633203, 7.005682903731279, 13.049214968781268, 20.41305424760842, 28.66774277341203, 37.19118125614487, 45.20977730885316, 51.858102969961, 56.25335013769466, 57.57791334162295, 55.16159348101148, 48.55495690431386, 37.58606409334592, 22.394307650877618, 3.4373106918586886, -18.530500794684457, -42.506208585824375, -67.30945819749715, -91.66984904399057, -114.32263491656272, -134.10392583269007, -150.03785036144575, -161.41054360965634, -167.81430761097886, -169.16400010184313, -165.68666170034606, -157.88601313929382, -146.48646943392686, -132.3630425815189, -116.46447939518592, -99.73714160953676, -83.05650988972667, -67.17189598566665, -52.66816090777069, -39.94618913180937, -29.22180318333052, -20.54095046687108, -13.807706884517167, -8.820321467667954, -5.309635785784908, -2.9774356149475443, -1.5297921254019984, -0.7024217146735829, -0.27677746547183696, -0.08693548160404838, -0.018490345546386077, -0.0014960630608334884, 9.122889521169908e-05, 6.207412549192929e-06, 0.00020003988294626273, -0.001174403062250567, -0.005018553789002706, -0.009709441008972544, -0.011957856117601211, -0.00894617860603127, -0.0004450862844175061, 0.010245588463263301, 0.01729603139381795, 0.015496696665977592, 0.005165203388577025, -0.002126056790011039, 0.02168971043925169, 0.12448896067064288, 0.374065182051237, 0.8541670124584997, 1.6562399897413722, 2.8673961184774535, 4.555884638234634, 6.755959029124125, 9.45457510556567, 12.582746312592732, 16.0122824491011, 19.559669777909928, 22.997618489237038, 26.073573766225596, 28.533568558046902, 30.14893720580597, 30.742823523966216, 30.213200090500496, 28.54931682266892, 25.839111827578638, 22.26608610496461, 18.09535676168888, 13.649915266350668, 9.279363613210483, 5.324414930873378, 2.0807883654492003, -0.23277507081010884, -1.4977899354542814, -1.708589234145017, -0.9727883584090411, 0.5004707594857558, 2.4232229875381694, 4.459815634775814, 6.263015402066347, 7.511086969183291, 7.941772035108684, 7.379496660101197, 5.7529512409496855, 3.1013189894608963, -0.43126322551817964, -4.6119271203973415, -9.144342975708442, -13.701411776675222, -17.9586598482979, -21.62522789351366, -24.469549647281752, -26.337328369347997, -27.160449389190134, -26.95658175134705, -25.820282938226896, -23.90730474653569, -21.414412803309077, -18.557323758118056, -15.549323445254768, -12.58278883459318, -9.815263947933003, -7.361136288894173, -5.28900117566336, -3.623474992128647, -2.3517858421712026, -1.4332417113619584, -0.8098010331492962, -0.4162632607205156, -0.18890171959692068, -0.071778363658582, -0.020435611098839936, -0.003083487250899594, 0.0002662019340016373, 5.944832677528449e-05, 0.0001252996984784358, 0.0005980148781794174, 0.0003253084981580028, -0.0015331980531084457, -0.004787060789338629, -0.008248958074233951, -0.01026245675246907, -0.009410705625277158, -0.005117377326021314, 0.002062390322134675, 0.01054174325217685, 0.018147764833302823, 0.02276794980189002, 0.022998623759928755, 0.018598906322725726, 0.01060932577666325, 0.0010877132641149377, -0.007476825554276744, -0.012914879694863598, -0.014075903845710645, -0.01125110703084252, -0.006144855224542097, -0.0013289732935308132, 0.0007584266246402494, -0.0009197612302875349, -0.0047556836000124045, -0.0056111862338277, 0.005397883655419479, 0.04023374220315007, 0.11232911234699491, 0.23417771793525546, 0.41445487844375173, 0.6551566077952613, 0.9493284014911878, 1.2799387045592954, 1.6203574641961436, 1.9367239673586543, 2.1918365951598817, 2.35025102325183, 2.383929264691168, 2.2775607101847357, 2.0326434828811015, 1.6695113179295331, 1.2267331748542285, 0.7576733014752928, 0.32443019678149854, -0.010189872754704754, -0.19163547407212747, -0.18223472291321052, 0.031857477077823826, 0.4365902336931761, 0.9897107194005553, 1.6246997461482602, 2.258496243435093, 2.802038775676662, 3.1722792326795024, 3.3039930275896836, 3.159659934148317, 2.735890518792743, 2.0653112104454903, 1.2134413759873282, 0.27081346007960055, -0.6587009442024163, -1.4717972399572086, -2.079922932803511, -2.4216724982336473, -2.4715118923595822, -2.243490051644063, -1.7892119963649444, -1.189685991243189, -0.5428403622627119, 0.05149666397682277, 0.5069846221031876, 0.764195591747545, 0.7999973710737539, 0.6313846169992982, 0.3130543175522084, -0.07104777794709397, -0.42106505682397544, -0.6375384190429364, -0.6382689606669322, -0.3731645113822918, 0.16527487228615212, 0.9375977687755827, 1.860199175317744, 2.815186022090527, 3.665762621274326, 4.275021362460263, 4.525496891982505, 4.336685758019378, 3.677997465972959, 2.5752335734784757, 1.109596841743777, -0.590718930485753, -2.3652675408234494, -4.040444397127385, -5.450364429873402, -6.456721821251387, -6.964996709873683, -6.935061848692362, -6.385068774488427, -5.386884116988309, -4.05506649748223, -2.5312367202553006, -0.966042651485598, 0.498754963058302, 1.7457185660284704, 2.6928315939460044, 3.299132167424287, 3.564606468501092, 3.524897362813818, 3.242073960361084, 2.7931608097575906, 2.258287595990284, 1.7101862848402993, 1.2063945569564698, 0.7849113358915845, 0.4633316256622507, 0.2413024233508859, 0.10525826447625306, 0.03420496914552496, 0.005357332856521723, -0.0013458870157002948, -0.0004561945573179156, -0.00012781896311754714, -0.002884065467439546, -0.0074840270754210035, -0.011185150807381555, -0.01172271795938029, -0.008509651283592972, -0.0028463100481401853, 0.0027544810011909185, 0.005757578652771047, 0.00479317050963868, 0.0003391492339261021, -0.005420574702463324, -0.00957703812618727, -0.009979882402577776, -0.006579885005176286, -0.0018162931601750372, 0.0007272202671543915, -0.00010388614311922616, 0.002766895943881988, 0.03202826098155239, 0.13361411321009595, 0.38269964352469726, 0.8858767640735282, 1.7774549248968305, 3.208596447884604, 5.328758428587613, 8.26026509175736, 12.06832729096826, 16.73013064618279, 22.107630648820844, 27.929141068765578, 33.78452405784848, 39.13771537953957, 43.3584914220418, 45.772974074175316, 45.7296540540829, 42.6750525722528, 36.23093042484229, 26.26356820046782, 12.935844182685337, -3.2685868804089737, -21.559698435250198, -40.88676881765182, -60.01501748161837, -77.62794055855012, -92.44567714084586, -103.34721605988652, -109.48309623306939, -110.36567672129212, -105.92607376368785, -96.5302929684157, -82.95154797774079, -66.30072857046186, -47.921855398153916, -29.263524124911882, -11.74045314332947, 3.402425985911346, 15.20772706896353, 23.08344346918707, 26.8380133696475, 26.671593502463466, 23.12668401085474, 17.005859767448243, 9.267835111618766, 0.9150265857555355, -7.113998594379963, -14.035242890992087, -19.284065757008964, -22.54874442158862, -23.771743673068215, -23.121705287408535, -20.943108566610928, -17.692651373534705, -13.867035520270807, -9.936798929453772, -6.294233734851823, -3.219864374261308, -0.86923259623609, 0.7213551276254745, 1.613987761127923, 1.9387312418201534, 1.8597538621541083, 1.5437104569015847, 1.1348517041621584, 0.7395264789114949, 0.42074993708977865, 0.20167081992773409, 0.07538508794132605, 0.017795018080928576, 0.00018992513586902195, -0.0011527907501182925, -8.710135694682798e-07, -0.0001511153315261201, 0.0005684742990977787, 0.004128594173524788, 0.006233898071010651, -0.007495571748817485, -0.06159150498448449, -0.18653492986800888, -0.41088683393445113, -0.7513663484437421, -1.2031755815909067, -1.7330731534079933, -2.277415398935098, -2.7466452818204816, -3.035847507896255, -3.0403232008297865, -2.673897850105922, -1.886846204133705, -0.6801345999895942, 0.8869360404390042, 2.6976680565270947, 4.588124296798129, 6.365614054932987, 7.833161663282002, 8.816484851451401, 9.189416106899449, 8.893757833070943, 7.950281539561679, 6.459018266893388, 4.588420587711585, 2.5534679374973215, 0.5875919978483437, -1.0876810698738184, -2.291144019637114, -2.904313574701082, -2.8847359740144256, -2.2685318085430355, -1.1621698197629882, 0.27493527465450074, 1.8540984431306806, 3.383599321659478, 4.693558466971803, 5.655950946160485, 6.197194727598952, 6.30218687513457, 6.010001060981633, 5.401462351230777, 4.582475943591169, 3.6661052449001814, 2.7561911760030537, 1.934862435903152, 1.2553684689531237, 0.7406006937767659, 0.3866530358382472, 0.16998542911619502, 0.0563149202852876, 0.009316647347407604, -0.002457772427801643, -0.0014405521583286632, 4.256674473626804e-05, -0.001760912782258145, -0.005237116889150715, -0.007078899538086373, -0.005257878495851648, -0.00047035996350152997, 0.0042402752192702035, 0.005416161754937553, 0.001934119091651163, -0.002429227774353579, 0.0023904207336829194, 0.03223909456171159, 0.10611144950495566, 0.2417354032839369, 0.4502559742153741, 0.7312621760408842, 1.0694900562957423, 1.434330653310367, 1.782791790396913, 2.0655792752917552, 2.2354653720992923, 2.256453996085118, 2.1118847397328175, 1.8096641706336176, 1.3832369290640136, 0.887664081618092, 0.39112976120675264, -0.03683305384753406, -0.33831944512664575, -0.4787252453664992, -0.454655120315882, -0.2961570781082625, -0.062361380596010076, 0.16915357506838433, 0.3176500181754647, 0.3161712055424896, 0.12682139870150627, -0.24875976907830377, -0.7662155530087721, -1.3438122654643645, -1.875945452474134, -2.2528212822770968, -2.38294610055922, -2.214219329263179, -1.749323396308556, -1.05181348015001, -0.24075884231127428, 0.5262358009969272, 1.0796205527088525, 1.2701779061374054, 1.0017934874830148, 0.2576495865592551, -0.8855124967600622, -2.2583548653587995, -3.6163232015458164, -4.671858778626208, -5.137201788248071, -4.771464345301293, -3.4245257247301555, -1.0703666937636502, 2.1762429380969968, 6.06342231072814, 10.226853583702606, 14.23275562710298, 17.63343483279714, 20.027905955493488, 21.119171335447124, 20.755392014197103, 18.951254767392626, 15.886440383168813, 11.881163202747906, 7.352603826325769, 2.758930530096742, -1.4606151025849903, -4.940677764526542, -7.431897112106931, -8.824486955285549, -9.150663121924753, -8.566679363737377, -7.318377761432689, -5.696564606616621, -3.9899821281632626, -2.4432077611151466, -1.2247509987971634, -0.4120083472610575, 0.006671935682954836, 0.11516129632209786, 0.04236800520928986, -0.06949017811799696, -0.09507196544522502, 0.050707452978746924, 0.3996695303519963, 0.9290975135349892, 1.5712696003838795, 2.2309427571518357, 2.8066810748206894, 3.2115462630113196, 3.3891913242335954, 3.322661846549049, 3.0346579579606687, 2.580022240086478, 2.0327803715789643, 1.4708864316894545, 0.9619811126543863, 0.5529254791119285, 0.26479981720125356, 0.09372709305388148, 0.016599543188287907, -0.00017087771450526327, 0.00879296682357749, 0.015763790332018746, 0.004730191284568033, -0.027558553558715605, -0.0739937624970214, -0.12182158153129359, -0.15801405944869207, -0.17368609279284924, -0.1664576215945326, -0.1403814540176142, -0.10382571108711387, -0.06628330111031602, -0.03531434957699859, -0.014652741077228255, -0.003992442472467446, -0.00029193327339632486, 0.00016176553471142804, -3.0149347573168955e-05, -2.140138382619237e-05, -4.6616630047929565e-06, 0.00017029581255556124, 0.0015208906809908722, 0.0037848060481524655, -0.0005170739139839321, -0.035000059719479296, -0.1474117498712273, -0.40896625271290815, -0.8935326268916043, -1.622657601234898, -2.4623170881824157, -2.960763313188105, -2.1245486141593233, 1.8582500171587781, 11.923319669551512, 32.42292288293667, 69.34983368018752, 130.42817970415507, 225.01765079331068, 363.7610296806931, 557.9411186414659, 818.5441573432531, 1155.062804826586, 1574.1171230255704, 2078.0152072682085, 2663.4107359814943, 3320.236206266019, 4031.092372333644, 4771.252716058067, 5509.39570622256, 6209.109482169029, 6831.129175524709, 7336.175165650727, 7688.326343018364, 7858.825623118284, 7828.640149191679, 7590.553874067463, 7150.476224928602, 6527.633578001734, 5753.556049719826, 4869.898811132118, 3925.2665798511534, 2971.3265421960014, 2058.583894646215, 1232.24339614787, 528.5821524526777, -27.788705425329184, -425.48862365106237, -666.60184172658, -765.5904727964346, -747.0478305936648, -642.3901696752836, -486.03353316369044, -311.5499808582965, -148.22568907270244, -18.387483589408145, 64.24414310636809, 95.05329865919292, 77.90122761420366, 23.532072645913477, -52.71939952565903, -133.57880676555666, -202.47878610721048, -245.86224570233927, -254.87002761580467, -226.24311890332524, -162.37132489418002, -70.51114706183456, 38.59195490572923, 152.4357268477054, 258.58071613982946, 346.2973550238729, 407.8280293996022, 439.12487597499245, 440.01071432279986, 413.797200764194, 366.46854909494755, 305.59125041177816, 239.13432060132175, 174.3794139025344, 117.0687939752806, 70.89057311858633, 37.332579589377126, 15.873062045931036, 4.464393480709071, 0.17658060592225713, -0.12980019404625298, 0.7841541223119932, 0.9520413783316255, -0.5996305208288139, -3.8751816299998634, -8.120206177313175, -12.154506034539624, -14.748358835599952, -14.96339318833715, -12.39375474075127, -7.26800561592771, -0.4015766423270592, 6.982094794720772, 13.512019656280904, 17.95478165511839, 19.466404532094888, 17.761895487581203, 13.172016443974018, 6.579737886009718, -0.7481363298577997, -7.399668395644003, -12.080494744832977, -13.851363009572799, -12.29747669579083, -7.600301904870609, -0.500932564808261, 7.836138135591475, 16.032723950154452, 22.742535463632876, 26.88500439409684, 27.825904940518857, 25.477151490234526, 20.30201332355627, 13.228525549620194, 5.489102597127333, -1.5842499315494012, -6.7738502252134145, -9.16438741984204, -8.2761303958369, -4.124754589632614, 2.797912074474884, 11.614920002109644, 21.208683041896627, 30.394300305390093, 38.09611793023445, 43.4902342276841, 46.09650661637731, 45.81272218529642, 42.891161898305754, 37.86715428192271, 31.455631021744864, 24.434862617085077, 17.536305762160303, 11.356253016236431, 6.29960595944204, 2.5597189032065426, 0.1320468876553513, -1.1457133987366743, -1.537481669198655, -1.3482434178295164, -0.8694828612153152, -0.3376910067377926, 0.08855576383376094, 0.3327738558337866, 0.38935022101839506, 0.3022925481232223, 0.14009346204545137, -0.02764958905200291, -0.14768238113058105, -0.19242838925506528, -0.1610843321548731, -0.07406070160021266, 0.036565487361484926, 0.13757568903844172, 0.20345090504588262, 0.2217316473282158, 0.19419924802678992, 0.1342154050943957, 0.06153629255920939, -0.0037410740003644325, -0.046492674231748084, -0.05993423449725594, -0.0464617599251237, -0.016064168291163482, 0.017026705737033156, 0.038441414013061774, 0.03745897038823886, 0.009589351747773988, -0.042557303329309126, -0.11017153380953774, -0.18055281076899704, -0.24018122931096847, -0.2777966389697002, -0.28666582501143106, -0.26567124397388286, -0.21911283357775732, -0.15539596684447515, -0.08501295070073747, -0.01833279446491187, 0.03630695583713044, 0.07384139098493407, 0.09288190541573277, 0.09531949155783935, 0.08533654380155047, 0.06813687443749313, 0.04871916635431469, 0.030956688871763564, 0.017131589666615304, 0.00793534661516621, 0.002832778374387839, 0.000625555751346848, 1.169995146006831e-05, -1.1629082688680478e-05, 2.2859782515333478e-05, -3.4859003646589904e-07, 1.818819948795626e-05, 0.00015010213412734613, 0.00026063775072578994, -3.754368228630155e-05, -0.0012846913607463804, -0.003969541331819348, -0.00829892646355473, -0.014030152884209054, -0.02043588841337193, -0.026430787864880633, -0.030826308916957815, -0.032642706491650984, -0.031387481300556117, -0.027215531956938523, -0.020919418033923297, -0.013746635468127768, -0.007090675983229839, -0.002139420983642897, 0.00042248369291636185, 0.0005749922399023991, -0.001056724852248024, -0.003396362372194764, -0.005230242199844885, -0.00555227087882882, -0.0038435388013682405, -0.00020843487229626876, 0.004672497161831455, 0.009750895860483996, 0.013914083596801453, 0.016293127843746986, 0.01648654106764745, 0.014638869742387596, 0.011358965495638156, 0.007511651099890779, 0.003953791393258116, 0.001299951168169591, -0.00021056472655400256, -0.0007102364284904958, -0.0005766192941388711, -0.00023927384367132616, -9.163678077855222e-07, 5.247593517491494e-05, 1.3026449659999728e-05, -6.834039534164957e-07, -3.827367475735249e-05, -0.00045423764558854776, -0.0018925178527572255, -0.005073933299418492, -0.010422083853279402, -0.017651387322044198, -0.025503921535719672, -0.03182855691191873, -0.03412719623926881, -0.030550696855566623, -0.02113909284049421, -0.008918770875246647, -0.00035923343870267226, -0.004712756549232755, -0.031978401776346914, -0.08963113067748975, -0.1787062435226563, -0.2903041903788549, -0.4039181241337123, -0.489049780118321, -0.5112664713786768, -0.44312662988939855, -0.2793189575623, -0.054077464083396, 0.14230363010660313, 0.151927441089984, -0.2529438906953091, -1.3590952550796536, -3.486435759193518, -6.947876560583434, -11.99861468509902, -18.780885782773392, -27.272560649823564, -37.24893648126173, -48.2665821161676, -59.67593049837835, -70.66561916014264, -80.3368005022939, -87.80047751949542, -92.28623041650327, -93.2473732709226, -90.44637072195972, -84.00571726239691, -74.41349363691833, -62.48149087164888, -49.25800535043308, -35.88681574752187, -23.459156525837216, -12.876090659328733, -4.739613895980617, 0.7100938950752114, 3.600920095554659, 4.377292098791484, 3.699190970265026, 2.308527690221443, 0.8855954532932232, -0.07952926631137927, -0.3778549715621137, -0.1179652920923534, 0.29926552697241543, 0.26432475093791435, -0.9128226463765565, -3.8535888317578104, -8.968588924492343, -16.349050763150938, -25.712401830456233, -36.412985537363575, -47.517259335341485, -57.931331778963404, -66.55937316807731, -72.46595996560256, -75.01476475386708, -73.96028272279426, -69.47769724399743, -62.12698144052628, -52.75888817663357, -42.38168304878956, -32.012090201856125, -22.527746374831633, -14.559860716162, -8.438671174220426, -4.194921064259462, -1.6113776435041853, -0.30935269120495, 0.1503764023211731, 0.17393080072029057, 0.0662219416008706, -0.0004845463234422872, 0.020672281848794275, 0.08990881716688313, 0.13674020446618693, 0.11516169897498632, 0.04090304009314115, -0.001393648433960871, 0.11498651140157655, 0.5037015537703408, 1.1961970986609571, 2.078278380232084, 2.8531918937735115, 3.048057897842137, 2.072143204468711, -0.675770347307264, -5.665557353360083, -13.08414635968272, -22.70476281035257, -33.80786508463118, -45.1785980701664, -55.193973383838966, -62.00010607724961, -63.76310990615411, -58.934994592307035, -46.51063221216493, -26.23402297813185, 1.284575050845604, 34.564552316999475, 71.3709402177937, 108.93900129244048, 144.2787837066215, 174.51813016104745, 197.23619407602638, 210.74060900720278, 214.24990646471036, 207.95717687208938, 192.96892805761007, 171.13627394112956, 144.8043437417458, 116.48445004551668, 88.55125246133626, 62.99474681386055, 41.24980216244289, 24.11789779214873, 11.78060720730833, 3.8908813366048185, -0.2816802010910133, -1.68038018298462, -1.2944421240710033, -0.019411892371847237, 1.4391155629945243, 2.6119838870737127, 3.2658940287327796, 3.365968952196278, 3.015959398561617, 2.389876366002503, 1.6710299771917068, 1.008359624897715, 0.4937783190114282, 0.1592428272067933, -0.011497225418229874, -0.0633815070354572, -0.04960863673571321, -0.015571067515659377, 0.010010646331216616, 0.016487978677904743, 0.007002509175985893, -0.008573098630909343, -0.02048668815239586, -0.023557069595397714, -0.018321021082465097, -0.009304963585435392, -0.0017924077258028683, 0.0011841846350800049, 0.00024558327065548436, -0.0010932337493663477, 0.0010774006347029194, 0.008017542678508752, 0.016246996265854442, 0.017626843001261567, 0.002051026724752576, -0.03784575543326009, -0.10149594127782385, -0.1767629684125826, -0.23975289875429162, -0.2591374793138242, -0.20468058096840464, -0.0578984633231456, 0.17810774433750443, 0.47307161341274523, 0.7711490459801565, 1.001096987494016, 1.0943142520832594, 1.0076786049450153, 0.7461841286465334, 0.3794179948237224, 0.046298115849146164, -0.05568367290771887, 0.30254882988976906, 1.3413440337744458, 3.2251011450025335, 6.017376826976236, 9.649634546907587, 13.910208284692676, 18.457781336635485, 22.859575962599262, 26.649134653748586, 29.394497850898965, 30.76503631938777, 30.5848634729852, 28.862792155763827, 25.792884066919513, 21.725007419595215, 17.11042153881033, 12.432121104748616, 8.132528853920597, 4.5515178433533565, 1.8857072189811004, 0.17475356377284065, -0.6841374777290337, -0.8954000274184184, -0.7106296942500118, -0.37307503734730063, -0.07244397282392698, 0.08177667226917698, 0.06500043964973207, -0.07810112005238268, -0.2634256616168345, -0.4025395346511569, -0.4336059944394759, -0.3404490418659442, -0.1556006796685654, 0.05239060884287627, 0.20291038872188266, 0.23109639830216294, 0.11084224564055321, -0.1342445174106987, -0.43552225044003395, -0.6987604424881603, -0.8331848492046419, -0.7820014559032932, -0.5454629469545507, -0.18913447610585807, 0.16632481293875767, 0.3727001905889219, 0.29309005222209006, -0.15743327077331934, -0.980191513096651, -2.0796661681341133, -3.273926841671625, -4.328363360103948, -5.00735446490648, -5.131285643170972, -4.624896618876926, -3.5441559104075107, -2.0731416093634345, -0.48922036791150536, 0.8974627146885321, 1.81737358525193, 2.1108910531294374, 1.7762207877417424, 0.9824540401126047, 0.04167044025984081, -0.6566292622479043, -0.7361638676008969, 0.0700410793511709, 1.8410320700403011, 4.426994594094218, 7.457757122072658, 10.402588000447036, 12.671368527180526, 13.73706490401905, 13.25332870360406, 11.14060942775528, 7.619776152017145, 3.18296432781781, -1.494986999758611, -5.6875313296956485, -8.762423939839753, -10.310630522348239, -10.22849268675611, -8.733207341768212, -6.305660954886378, -3.5706763109616713, -1.1452742466850814, 0.5105337164873869, 1.204857798021822, 1.058495227990808, 0.4689736510633478, -0.001368071794194984, 0.20986899501891088, 1.485041874201024, 3.875057879746767, 7.017445054904806, 10.151638529707181, 12.238637759542145, 12.168185271832375, 9.01500650306593, 2.287059149152966, -7.90146077176606, -20.767386941630328, -34.92947648023358, -48.609252751702996, -59.92894614356869, -67.25085530966673, -69.49025676834452, -66.3356210924308, -58.32578339458055, -46.761306804794465, -33.46139306625906, -20.411468986817447, -9.372788476159295, -1.537939287845686, 2.688581141597171, 3.7299355102831067, 2.671141017334699, 0.9086468740735534, -0.3074662763837933, -0.3398665572032199, 0.4673293162778693, 0.6107674768550617, -2.4987553770271895, -12.198700989880859, -32.012789766346096, -64.95267442891807, -112.80548712724949, -175.54212027496027, -250.96883684617018, -334.70875731532175, -420.5588184248313, -501.22545838251875, -569.2304579800349, -617.8951955182646, -642.2546825265588, -639.7462716076272, -610.5630070695482, -557.6174032267159, -486.12586671516164, -402.8854860382394, -315.3627362506719, -230.7397636031171, -155.06442592671414, -92.62599694499723, -45.63465872636991, -14.228198507824446, 3.2251009313991763, 9.609716616384778, 8.43783951262332, 3.2167615984972597, -3.06932635150035, -8.291093238419222, -11.293757408434846, -11.82143452942382, -10.296601177296784, -7.524655013560978, -4.396636607178304, -1.6511105913454727, 0.26676267751596655, 1.238699365622495, 1.4150795030449197, 1.099588313708974, 0.6193083086681811, 0.21942827101299026, 0.009233289917483026, -0.03246236039573238, -0.003473112532443882, -0.0005285491439018426, -0.0476530555366302, -0.057036973047421655, 0.16234099757443926, 0.8484777249449271, 2.1979915981373077, 4.272266934737841, 6.9285286493345595, 9.801593696602595, 12.349828089043893, 13.961997718022669, 14.105024341205477, 12.479223790884985, 9.13499775323477, 4.520672135857893, -0.55874233511164, -5.073171567757931, -7.969023975297446, -8.402269582279773, -5.95430775841726, -0.7817899813373738, 6.337774330110912, 14.083251710388097, 20.783999994231568, 24.70035104431896, 24.340615585810937, 18.754894233793344, 7.7477195632659726, -8.037048339489166, -27.179252321961805, -47.68119713156871, -67.26787987585398, -83.7352479258252, -95.2845187526685, -100.78415304537207, -99.91563007751118, -93.18164341370523, -81.78114654773147, -67.37973280413581, -51.821533442412694, -36.836967448005545, -23.798080853369733, -13.560854817216173, -6.414577155439621, -2.136740450907539, -0.13202957317987135, 0.3832639830606272, 0.1934404007938075, -0.0706443021502683, -0.02574518705468257, 0.440322770707493, 1.2108475108371424, 2.0295730281013147, 2.6106844924021497, 2.7411759174418617, 2.3519301691890417, 1.543206311779701, 0.5619853916987966, -0.25996845347686653, -0.5899728861693173, -0.17870167230327932, 1.0772057476045767, 3.1078078559989493, 5.681662388188611, 8.452128297152335, 11.026245683654547, 13.04019970899137, 14.22513533899374, 14.450400533785086, 13.737124677551982, 12.241894965200231, 10.216589079124198, 7.95483129265736, 5.7372658334737245, 3.7867545585618316, 2.2413108458243767, 1.1474982214354637, 0.47221815624505004, 0.12862554005483218, 0.00710586021200546, 0.003319887547110886, 0.037642694314772365, 0.06342267937327781, 0.06471629184094502, 0.04670270082455811, 0.02330140011955229, 0.006426665493043484, 1.5224339106554613e-05, -5.1459141174576827e-05, -0.0011087528084195205, -0.006517756944720263, -0.009342265356518397, 0.010296060525775107, 0.08271812198099118, 0.24133203766776282, 0.5123211474947258, 0.9043091284102593, 1.401110759346963, 1.9599635489282705, 2.5162445213670996, 2.9939920778014293, 3.320025381639459, 3.438480952191631, 3.322413138400926, 2.979766672656543, 2.4523477201341137, 1.8080554371311772, 1.1281320937280364, 0.4920593388549151, -0.03602068321251466, -0.41638449693948987, -0.637127636796635, -0.7118324964319627, -0.6727060509515688, -0.5612538474252101, -0.41884166831080916, -0.27919283762842123, -0.16411486207165366, -0.08278144379980851, -0.033983217779901084, -0.010130276369599352, -0.001572112830693796, -2.9054856106523205e-06, -0.0002334532230381088, -0.00025041249868367876, -4.311510118460711e-05, -2.8222044741200044e-06, 0.00029754138078494987, 0.0024362671750000875, 0.008533357647874756, 0.020066135322095557, 0.036721108988570825, 0.05587917047381415, 0.07307334860876928, 0.08335602190140039, 0.08311606007644139, 0.07164684632827964, 0.05178404823623704, 0.02922126220554545, 0.010590219166334717, 0.0009008468899725207, 0.0013088084313089413, 0.008217844180516172, 0.01434991441948249, 0.011783366651464722, -0.003786251708691851, -0.028922757506768176, -0.05007661729146558, -0.04432660517656898, 0.016153274526406778, 0.15638787037818186, 0.3892952286847393, 0.7072814183431607, 1.0774941746304012, 1.4429721507089976, 1.7306469405497396, 1.8653952756365848, 1.787446325561685, 1.468963905409679, 0.9254456071477646, 0.21831770968621528, -0.5530782274000208, -1.2693786546956125, -1.815602960190042, -2.1066439424426053, -2.107553112727793, -1.8430223874215308, -1.3927064058252916, -0.8724065771609089, -0.4048855830343382, -0.08724816204108755, 0.03651728947638176, -0.010414969116491944, -0.14261075144181512, -0.23627855311636808, -0.16744191580301193, 0.14459602576073838, 0.6999680046719041, 1.3984017905884054, 2.0449699686312544, 2.3840179220926165, 2.1569625805272388, 1.1729660238476318, -0.6233416206468849, -3.1045043394066214, -5.948249831048577, -8.669558939811342, -10.696521435889386, -11.480407915501884, -10.616668362179958, -7.949578389825144, -3.63747028213207, 1.8391174561032722, 7.733336064555972, 13.145890543718016, 17.178194865173687, 19.09671738518169, 18.476353387431693, 15.293107941210463, 9.9451408398133, 3.1947780573699123, -3.9601925309140764, -10.462949200261548, -15.387454082427999, -18.104903299148006, -18.398488180892763, -16.492720319240316, -12.994530833645811, -8.759924683445124, -4.713896544099547, -1.6606726285325317, -0.12298775280427976, -0.24274437355785575, -1.7624117781901891, -4.089665786677713, -6.430586859346344, -7.962810984078074, -8.01223267092182, -6.1967492617141575, -2.508165934868191, 2.6852181569114895, 8.715658795899916, 14.748396644702868, 19.94126053933282, 23.59859640205447, 25.289174893276453, 24.906871062942322, 22.665948998605433, 19.03673122485457, 14.639254011305137, 10.119794884226273, 6.036616015346017, 2.776956349145896, 0.5185604513757325, -0.7618960019381684, -1.2416201548382104, -1.1816810935270108, -0.852935902524492, -0.4756995464454949, -0.18560616856177417, -0.029116724332892, 0.01605934164487449, 0.006297956352490695, -0.0037339372489731534, 0.013710979305759053, 0.051939020063607996, 0.08073010105220792, 0.07017689554119245, 0.017550318752167574, -0.033989381041726587, 0.00618513813031025, 0.25674356854332797, 0.8269837560126815, 1.7710540777787072, 3.0464879414842314, 4.490129102613954, 5.821297097305666, 6.675888285651537, 6.667568100698053, 5.4650995867306875, 2.869941619291555, -1.123181985624941, -6.297512655403971, -12.226009312386779, -18.32405356597204, -23.934824024097004, -28.431873696677528, -31.32086769149206, -32.322890588154756, -31.410370349593222, -28.7990439894179, -24.900240126489443, -20.243563113669342, -15.386269948733919, -10.827064452428171, -6.939724468511639, -3.9366742744156444, -1.8656691148130602, -0.635793196195056, -0.06349726070547776, 0.07351595021427597, -0.013299622368201593, -0.159207677606281, -0.2634598633258991, -0.2881079738052079, -0.24236820416893737, -0.16008696301827718, -0.07808125144219263, -0.021119526327197862, 0.0038163592676192497, 0.00469493681845274, -0.0036969020408178003, -0.008761690289814654, -0.006023668089186209, 0.0001948092243525495, 0.0011378673058995523, -0.009380017157994453, -0.028972643649134693, -0.04519020939265091, -0.04054614206370163, -0.0036612012312915217, 0.05653352432783318, 0.09841637003775114, 0.042355013739400205, -0.2236031543135605, -0.8258061893328267, -1.8770900599939, -3.4444252404953803, -5.519799315777459, -8.002325208278142, -10.697789734711625, -13.338293534816188, -15.620062441483102, -17.253020988546393, -18.012441211993906, -17.782591439959266, -16.58335728696251, -14.566757056341636, -11.989899335432511, -9.16954446717836, -6.426988049734703, -4.0346897879957515, -2.1754274038877193, -0.9216958150048489, -0.2383470725045452, -0.006211573670300896, -0.05989874405241128, -0.23019636575817812, -0.3810790024192716, -0.43331907594538954, -0.37050727476833295, -0.22789576418588034, -0.06875061723848505, 0.04375322992649616, 0.07097924663866995, 0.013063113822546796, -0.09040552217620429, -0.17263844236740228, -0.160690206327557, 0.001111479562379171, 0.33217400546875936, 0.8064948557705766, 1.355946135268495, 1.8851336316696066, 2.2938533493068882, 2.501181505131131, 2.464882791413943, 2.191418668827978, 1.7343639550023509, 1.17983086379679, 0.6252403923053775, 0.15712790338076082, -0.16662833619765255, -0.32607353813176004, -0.3383747720304335, -0.24814003289391662, -0.1122741614813969, 0.016078156541491643, 0.10014850925081768, 0.12574938026920832, 0.10019938868843083, 0.04527715450103684, -0.012874875594369891, -0.053374060481334855, -0.06675686561233876, -0.05600018222144441, -0.032776583684562856, -0.01099901486618682, -0.0004560448232645677, -0.003082852470308725, -0.013228318060389922, -0.02160520400581646, -0.021061182861555578, -0.011463554679776842, -0.0011999117722997022, -0.004050543126858617, -0.032096596213298814, -0.08722664663463821, -0.1549575127214162, -0.20413172691893272, -0.19441285612865375, -0.09068951196534474, 0.11957229746016595, 0.4122869807436064, 0.7228647961322915, 0.957627798313346, 1.0217465654098703, 0.8595730225951735, 0.49787047656838695, 0.07870991945929362, -0.13178622770971365, 0.23074993347089676, 1.5654800691625335, 4.212084268477026, 8.342780554381717, 13.866592072526265, 20.37767493813608, 27.163664052134152, 33.28479735207029, 37.720220695603174, 39.55999880680951, 38.20787448769419, 33.55214997175221, 26.06309752344035, 16.78585900827215, 7.2165794151210445, -0.9267732203449345, -6.003598972397863, -6.765877795789335, -2.626561639150009, 6.177778041442098, 18.572634897286374, 32.80154865089814, 46.72748603650959, 58.21145106659647, 65.49679741568416, 67.52356683673402, 64.10989916254306, 55.9641480943597, 44.525875404007024, 31.669177444004486, 19.330332956308695, 9.13737704384885, 2.1183947235294673, -1.4519465813216326, -2.038323264692938, -0.6706029118778414, 1.3474144987492205, 2.779159888120333, 2.7670758386666394, 1.0325923773641126, -2.0823372178741284, -5.738899126082753, -8.857858288815523, -10.444788436542353, -9.903606008056084, -7.2601098397680515, -3.2375039660437204, 0.8403987013986453, 3.3030373413954877, 2.492250254693914, -2.850395857672923, -13.253651586479773, -28.319343041955857, -46.70697289304958, -66.31035850875504, -84.59462166224164, -99.0270578606666, -107.51647868397438, -108.77497486847732, -102.53329953262364, -89.57203758252044, -71.56835762831223, -50.794265240001664, -29.729420192789426, -10.66455559702546, 4.631560119563523, 15.126226475454834, 20.589990786030487, 21.520032580723868, 18.94888903517525, 14.186786575382378, 8.56067835946182, 3.197352040675518, -1.1169671252840951, -3.9877640173496567, -5.381295563227391, -5.534040067503631, -4.833052003142587, -3.697847152406124, -2.4878355891284607, -1.4485959505839598, -0.6986248026642545, -0.24852275164987186, -0.038877490152439124, 0.017972095711389, 0.0039949513002393335, -0.024087951881046274, -0.03900314178799311, -0.03641449633967405, -0.023890900288606586, -0.010846497033648768, -0.0027114582660420984, 0.00012437340819069324, 0.00017146163590776395, -5.4523700820876225e-05, 0.00029868257047256555, 0.0006434485522015617, 0.00033433000834762026, -0.0002622082107868851, -0.00015305103843810526, 0.0005732876054197101, -0.0005527989962208754, -0.006514282651582948, -0.013444238691869606, 0.002395757738218033, 0.10008459542541695, 0.38532518712455555, 1.0089768326984196, 2.1452148871245345, 3.946209570156451, 6.4778797497133445, 9.65043854976383, 13.165465352189536, 16.505094592232343, 18.986056625655124, 19.890541067757496, 18.668588817487677, 15.184193759979157, 9.950106418140455, 4.296303147858648, 0.4125783255158133, 1.2195176987443124, 10.050754538387979, 30.16692040058319, 64.16161802709712, 113.35349072004166, 177.2777001282606, 253.38867333633337, 337.0614518750893, 421.93370697822695, 500.57150797220027, 565.379894387684, 609.6524185235955, 628.6319064514307, 620.1782482292872, 585.08388496977, 526.9795633254872, 451.82126308003984, 367.04334269533865, 280.5206652849827, 199.51353974444604, 129.7679106687714, 74.91001407615923, 36.21667081183245, 12.771359958527956, 1.9464243634403018, 0.09685370364396093, 3.321318941887511, 8.146077098090796, 12.016196565175287, 13.52981045303619, 12.404089603169345, 9.222439780001565, 5.053686699656781, 1.0481345271556888, -1.8950921053047103, -3.325257247009055, -3.278759972426985, -2.1778755694032226, -0.6399690051466098, 0.7365270557034703, 1.5458153798524852, 1.6635122972038228, 1.2348575010837377, 0.5774112001518122, 0.03705731954678745, -0.15166234549283333, 0.04636622512483642, 0.45631534864795514, 0.7622036847472706, 0.6324989156443486, -0.13727962741706623, -1.5104604623554618, -3.161827881088752, -4.516979349166598, -4.874379114125042, -3.582480859952351, -0.22753110266354, 5.217749252344989, 12.32684539167704, 20.25723006914003, 27.89448319814885, 34.070172036509014, 37.79849802148993, 38.47946823936286, 36.02274505952778, 30.864814791619448, 23.87696197077609, 16.18635110771376, 8.951451025799352, 3.1418464642513237, -0.6305217159045573, -2.195299871282902, -1.8101374233792624, -0.059429768583913675, 2.3056675281295176, 4.545965230958833, 6.09119456494163, 6.63886766818103, 6.177975116187846, 4.941937109405389, 3.31089340834985, 1.693320114571086, 0.4184942284854485, -0.33504864915872157, -0.5618446905751578, -0.40335693375007564, -0.08636695781705254, 0.15343973211562711, 0.14053079975056937, -0.1965039701798491, -0.8151480162886512, -1.5823580905560082, -2.321680014083974, -2.8669273955047765, -3.10674603139768, -3.009055168937746, -2.6209837297638945, -2.0473743900219064, -1.4165998377575943, -0.8449583469066051, -0.4099029507526027, -0.1384744896285135, -0.011989065677279679, 0.016997189255574287, 0.002666846122195694, -0.013286504392318425, -0.012191428829017609, 0.0019750537807373763, 0.011989407608827548, 0.0008182032661340646, -0.036988378760723604, -0.09072877699942934, -0.13757720781549032, -0.15341732010395484, -0.12586345007080732, -0.06375489304068455, 0.0015409437955190464, 0.0248032484742658, -0.03635537905368423, -0.20209841938611367, -0.45530602825601135, -0.7372625685886219, -0.9575540097115044, -1.0172146381074043, -0.8393675796979372, -0.39733662187016733, 0.2685152808051951, 1.0516350506227585, 1.7994854762706478, 2.348981567880056, 2.568149566648148, 2.392504782568096, 1.8454226738046222, 1.035786683210195, 0.1324268640447184, -0.6784119600067623, -1.2410887937449204, -1.4704739613518099, -1.3719829646496615, -1.0355483337613622, -0.604815648393138, -0.22972790703022916, -0.01877710885069295, -0.006420321576634016, -0.14640835295350507, -0.33384101502642494, -0.44946164469538885, -0.4119429665623549, -0.22019422927638319, 0.03052945018891048, 0.16782524453105493, -0.0049739206576615526, -0.635238295274435, -1.7484157210271718, -3.200843078387359, -4.678167123686174, -5.748393858950811, -5.9620392321297615, -4.976522002568698, -2.6719825406496422, 0.776075847770052, 4.893847747422311, 8.986031498338061, 12.281373463583344, 14.115757997323879, 14.107981288400085, 12.280553084184055, 9.087736581965814, 5.334091352132129, 1.9944228272629787, -0.026511273643922383, -0.13632530857382288, 1.7650572409030438, 5.225355605789841, 9.3274910438009, 12.911607244311542, 14.884230880608758, 14.540985112438376, 11.819658688689142, 7.411291095848153, 2.6868727565557013, -0.5599680632845462, -0.5081239204561016, 4.241839402351135, 14.268177292880319, 29.07768872329846, 47.07588512482639, 65.78120003152296, 82.25085584252572, 93.63661443149502, 97.74855901489873, 93.50485278477646, 81.16843580761359, 62.31697122612828, 39.55078861733414, 16.001253156955322, -5.254430195529398, -21.746601527071572, -32.01866067565203, -35.80438031445002, -33.95030174310562, -28.11521859308907, -20.32857165023779, -12.518948070255036, -6.123212457134981, -1.8641706275893803, 0.25802525032026424, 0.786657119423962, 0.5085291173563948, 0.12628954169958442, -0.0020989474076890265, 0.015300872754478305, -0.3470136287429228, -1.8314923204753841, -5.106564206604786, -10.473301865651692, -17.660621944200578, -25.777780410420892, -33.45121112943022, -39.12432365859997, -41.45332485717654, -39.67514550186006, -33.8587399833554, -24.968064643022398, -14.707101657940013, -5.172835186662578, 1.6088843239357666, 4.157718699823831, 1.9098870430533477, -4.6070486040075815, -13.844983480956584, -23.544395158991005, -31.21816850570743, -34.703740479181384, -32.65844358852751, -24.884475652315643, -12.40459832201875, 2.7441524247951126, 17.936329591138154, 30.510084060413593, 38.32623308951856, 40.213998195395334, 36.20956699375519, 27.539874213599415, 16.35931116372263, 5.299229407000237, -3.072017610849553, -6.764794194199243, -4.754569549793683, 2.835685528611251, 14.786800586810202, 29.06006465086174, 43.26403082510536, 55.11250549527532, 62.81965244856761, 65.3726145160994, 62.63613163476687, 55.2875093310832, 44.61382450579119, 32.22638141656936, 19.756595781745474, 8.592508641227742, -0.30114757016694127, -6.4591044855263915, -9.891195250847675, -10.979961457228645, -10.33424453647133, -8.634897918349287, -6.50500315270076, -4.424786512595304, -2.692400789670101, -1.4313780698300893, -0.6306316468959443, -0.19850882169779838, -0.014475920087757718, 0.03253278670698458, 0.02344018944666014, 0.004541074713969573, -0.005980336964095978, -0.00686938614775839, -0.0032796588351104478, 3.9006915354296686e-05, 0.0012616907141294867, 0.0009391163478440267, 0.00030310427241725873, 1.6119747107392505e-05, 1.4050419078648301e-06, 3.443038778931275e-06, -2.4262700803979685e-06, -0.00032103963525040215, -0.0031027953174699785, -0.014286178742208555, -0.04467764127386638, -0.10893311411057302, -0.22185796276548814, -0.3925479559758542, -0.6180441369280208, -0.8788924004014044, -1.1389162782566988, -1.3506530421720193, -1.4663146431369216, -1.4506244160222324, -1.2925535306994749, -1.012298096657593, -0.6606152831605379, -0.3096722687193513, -0.03696439137791355, 0.09397174852161254, 0.05105272597160365, -0.15558218108408903, -0.4729838906780582, -0.8158938481744538, -1.0862675728886233, -1.1971861158356134, -1.0950901147575156, -0.7744749836444241, -0.28077648402327915, 0.30012995461482056, 0.8624605701752622, 1.3056412833501447, 1.5575261596390655, 1.5898285973659663, 1.4220895865435323, 1.1136446701432514, 0.7462380167851944, 0.4023004724546741, 0.14483661354479044, 0.004142923368721651, -0.025545065540987174, 0.020727146847679807, 0.09291658329827442, 0.14315535180127328, 0.14061088552049705, 0.07980511274999455, -0.019770051047307356, -0.12200002411321394, -0.1873507392144336, -0.18654738417149036, -0.11044814768855377, 0.02678681221844599, 0.19194287226932685, 0.34282322489440237, 0.44083360387945947, 0.4621266931191145, 0.4039486505486676, 0.2844376183487086, 0.136218116296977, -0.003938446873304453, -0.10601718257752203, -0.15477849944949748, -0.15233622207207653, -0.11494153387453825, -0.06547610302402163, -0.024474373421011494, -0.00285527063241407, 0.0011683872144231193, 6.436907666942749e-05, 0.010731116071098399, 0.04643004054129176, 0.10999004890944873, 0.1909772744887861, 0.2681509641949635, 0.3166160586096885, 0.31728533338801357, 0.26517233936410767, 0.1730139967688253, 0.06840957575333116, -0.015294541060587294, -0.05192958424438636, -0.03516512172958042, 0.013591235179362914, 0.04555106173351502, -0.0055751310497133295, -0.20578294232107205, -0.5993612816221986, -1.1898325198840494, -1.9292767826153674, -2.7203512123090645, -3.4321545329097924, -3.927672835483925, -4.0972431612916465, -3.8858637487522243, -3.3091903575918242, -2.453791466558889, -1.4606301962246255, -0.4953030472439449, 0.2879866333778347, 0.7800324049509708, 0.9396132503436506, 0.8002694640674023, 0.45930739561036427, 0.05192127288608131, -0.2829720896857269, -0.4365800433779124, -0.35536285751616453, -0.05140088431583145, 0.4044156783699119, 0.9041812895754032, 1.3327336037738424, 1.5970840523609808, 1.647975526313361, 1.4885988075660428, 1.1692278834098457, 0.7703316578571783, 0.3795674178742327, 0.06925869826178704, -0.1197064829889252, -0.1838473219817621, -0.15229708443031478, -0.07363229863768414, 0.001154149286198605, 0.034312221321486265, 0.011269781579618419, -0.05766445952252156, -0.14365470858744653, -0.21091536087559679, -0.22942087327541125, -0.18471341568001767, -0.08203033192801311, 0.05604072308296574, 0.19711720266919952, 0.3090327555980265, 0.3690272314858052, 0.3693717881603052, 0.3180263366563291, 0.23459598758121297, 0.14330120675780741, 0.06545973319384647, 0.01389165107439344, -0.009186242566103484, -0.010546140923221085, -0.0016940078537775074, 0.006202823729633041, 0.006327332364184316, -0.0021129800568064406, -0.014833322242586197, -0.02532382852601415, -0.02824355371998197, -0.02191316319117592, -0.008945631344194203, 0.005114207721074124, 0.014428041850671392, 0.015549366530342924, 0.008937402038530627, -0.0013917960562544853, -0.009916100271837057, -0.012351483062761081, -0.007771951459112581, 0.000956535873986618, 0.008738534251572486, 0.011165533415425375, 0.007401440889991263, 0.0014777649054943894, 0.0009856741512616286, 0.01328097281750769, 0.04061687531279788, 0.07653107427318556, 0.10584124555657219, 0.10952618785187584, 0.07380607271432162, 0.0004923011903622806, -0.08622564405512059, -0.14122989622518575, -0.11085605107502156, 0.04471807471237132, 0.32438818038839506, 0.6632908652287319, 0.9245296411068906, 0.9137724491453822, 0.41952840756121246, -0.7260938402786326, -2.5797608269386365, -5.03215792954328, -7.78708634562342, -10.390184491915209, -12.312824393440732, -13.081169174441694, -12.40901103449984, -10.305117156440998, -7.118789082302384, -3.4969969427477428, -0.24849049441986512, 1.8634100049629396, 2.35272448744429, 1.2047046265532366, -1.0321191093777928, -3.30266356886537, -4.264349488853576, -2.6385699297519896, 2.378674811835819, 10.751423783034152, 21.39645153773677, 32.229073879478996, 40.50170123250349, 43.389972956424394, 38.72158277512906, 25.69007990033682, 5.375063085369356, -19.088967173075552, -42.79112463575735, -59.7737109397937, -64.11223166247083, -51.152368144935075, -18.651974224403837, 32.43075938396874, 97.71062487450044, 169.81486658108963, 239.4539098599033, 296.9799377426544, 334.16099530290245, 345.6978355532902, 330.2012011826959, 290.4344611800597, 232.76731320904963, 165.951271916207, 99.46987025540949, 41.80451215459127, -1.0288122174392467, -26.37942465634846, -35.13166839615609, -31.138343706841965, -20.071592152559226, -7.9681591882669665, 0.19490948986792891, 1.5763503503942755, -4.040107951541204, -14.431652989574992, -25.706991029535722, -33.442734938381015, -33.8939535892907, -24.986207055803252, -6.86400335012393, 18.11279040883717, 45.897607287754205, 71.6625794403535, 90.85285428384981, 100.14067914714477, 98.0684943499967, 85.25559803467425, 64.15405022053352, 38.440131083050204, 12.18730647005171, -10.948929315884014, -28.356386200008163, -38.791277316417194, -42.37422478727142, -40.30856283974633, -34.42931948352658, -26.713650608042162, -18.87023669119599, -12.084626301296593, -6.944284244905041, -3.5172581353258274, -1.524895785030546, -0.5384978408590305, -0.14118290480091478, -0.0222173133161308, -0.0008582527948034471, 3.205955218422142e-05, -5.156526101482465e-06, -4.132891359639962e-05, 0.0010795314506774603, 0.005569239248767007, 0.011273652255807452, 0.011729732506079907, 0.004660870869597934, -3.344653551699523e-05, 0.01128460584894043, 0.02019239585526767, -0.07845609353365267, -0.5120619493718027, -1.580397725108046, -3.4427070874048886, -5.681193723144321, -6.630904538214772, -2.546683118994798, 13.228503454543777, 50.84803323053872, 124.01256307610004, 249.22631159831602, 444.10107231938173, 724.7265171127818, 1102.3481961153266, 1579.820447403281, 2148.4765325757953, 2786.130608291656, 3456.8580619627337, 4113.2597418797395, 4701.866899656231, 5168.835446772802, 5466.505828405436, 5559.947390961976, 5432.230238221214, 5087.507082950949, 4551.307762745091, 3867.8915448031335, 3094.9882062631696, 2296.6984332295865, 1535.6345568180857, 865.5048732762849, 325.25533085850685, -64.40155288337056, -301.664410238953, -401.6340701084173, -392.2005662813914, -308.2948715836645, -185.80809853400936, -56.39362924700761, 56.13142862618386, 137.45210570131502, 182.55135523084732, 194.02625461272086, 179.51920833617143, 148.91531469416972, 111.87592435570178, 76.09697241079151, 46.4526160713526, 24.966369637707444, 11.38937188097921, 4.085456559775813, 0.9279168676311992, -0.010463727168207022, -0.08151725047361302, 0.0033592077343539725, 0.021150512931443884, -0.001596681116203575, 0.0028493378490320057, 0.03510312811192943, 0.03027266954668653, -0.07035274349361648, -0.24125485726853563, -0.3451321387031349, -0.18129892987069074, 0.40602490536685104, 1.4100049159239272, 2.5978235027305088, 3.5514155644595955, 3.8216075408407066, 3.157696791751203, 1.735907942105969, 0.2934533074459365, 0.08962963545391459, 2.6597267450105697, 9.390448457675951, 21.009271221550552, 37.12514769252748, 55.96852110511991, 74.4476882520592, 88.57024054356336, 94.18749264002747, 87.92875402188298, 68.13081707210493, 35.53057719675381, -6.530100796318993, -52.40798484391335, -94.95147449371879, -126.65742052207396, -140.97581487915778, -133.50858702787613, -102.86519177753443, -51.00459917079993, 17.00433838230016, 93.75695988437998, 170.67093148872743, 239.30834722657175, 292.61888710858557, 325.8879546184323, 337.25765196890296, 327.78021427528364, 300.90143795037505, 261.63603576087155, 215.62601307465945, 168.2513089891545, 123.9376932050931, 85.74658407755821, 55.264155098277605, 32.74789765464268, 17.448698616594193, 8.010540201983412, 2.857059129465066, 0.4984185811897073, -0.2754701605570746, -0.317343518560869, -0.13819879025197526, 0.01921531377869269, 0.08578101876782321, 0.07923690595343395, 0.04187965843600843, 0.006916655435265072, -0.01161506978803649, -0.014833902449443631, -0.010266123086556408, -0.004735398698052459, -0.0013809088855952863, -0.00019424187277523327, -4.22692412334092e-06, 7.312808724529147e-08, -2.5469213526138495e-06, 0.00010922463995846752, 0.0008381727695827241, 0.00266135731120851, 0.004906481424561975, 0.004818138519766748, -0.0020897374873009287, -0.019869527665077668, -0.04873329219624502, -0.08204949841865249, -0.10584082362812187, -0.10232521933270897, -0.057518246266381454, 0.029081015611181035, 0.13636343432356898, 0.2192086755254867, 0.21486855674772087, 0.05854172366104067, -0.29493294447030555, -0.8497017900027022, -1.5558905798388922, -2.3109668719293244, -2.9778673382976484, -3.4170356340378203, -3.52439244104358, -3.2640838975847557, -2.684921262001416, -1.9131292110648794, -1.1206175207764484, -0.4757176054022711, -0.08985595671462981, 0.02324241448187593, -0.03908539132175027, -0.0908597381908136, 0.08602754017560606, 0.6637931851394734, 1.6904261544247219, 3.035614878100974, 4.380871758453751, 5.263212159843149, 5.167725673773016, 3.650418255968507, 0.4626706354918615, -4.354462779094324, -10.432838892558168, -17.111073919148854, -23.53725931118343, -28.821105344668716, -32.20314405317129, -33.20327460062634, -31.71365432690223, -28.01138237123688, -22.697248431846717, -16.572752785508232, -10.48400897333009, -5.168188453254231, -1.1348025233838954, 1.3959677430894122, 2.490275493790977, 2.4405885131151845, 1.6684557050925362, 0.6162126659135303, -0.34676860417508487, -0.9843611062355561, -1.2121205841495108, -1.0768567983790613, -0.7095976766199878, -0.2685384441642698, 0.11218217686887196, 0.3532887762814063, 0.4373335048259904, 0.39590351671006213, 0.2857516648956416, 0.16385113058740902, 0.06943370286591394, 0.017031074582469417, 2.6647329375322678e-05, 0.0007715629045629787, 0.0018845929246225535, -0.0059049704707986395, -0.021707607115565776, -0.03776183159136343, -0.04545148466411748, -0.04068536163242256, -0.026042211829763122, -0.008972616468215356, 0.00262526068199595, 0.004899595562893063, 0.00011190105338817, -0.0049152145666162715, -0.003222599243945908, 0.007398617629833297, 0.02201706608994568, 0.030661031768223216, 0.02466779370157502, 0.004408988189416636, -0.016308673773445307, -0.013800652624038645, 0.031814307023627864, 0.11515654687248351, 0.18350094681534806, 0.12428334674074284, -0.22739762330676064, -1.0546140157021977, -2.498368547769217, -4.581025758495848, -7.131645505487044, -9.736436019390661, -11.736753756750781, -12.289565526629882, -10.491918253356802, -5.554420820908912, 3.006963787482143, 15.202008368205844, 30.464189953255893, 47.66054503018431, 65.21982385555513, 81.34903502399693, 94.30567192861857, 102.67478283289391, 105.59647400981191, 102.8986833922805, 95.10944945810495, 83.34802060324228, 69.11922158402604, 54.05476282621147, 39.65431942890113, 27.07636080428367, 17.014912864789476, 9.67731414278771, 4.855477090601821, 2.0611271567790226, 0.6852886772970878, 0.14988725501392688, 0.011116270071730237, -0.0007102017251144731, 0.0006781308037080031, 0.0014929039513524706, 0.02104504983434168, 0.05917705616335724, 0.07395090575856074, -0.0072742765791827604, -0.25257920838239656, -0.6833326508547263, -1.2440999651406695, -1.7986694801371481, -2.156699605946827, -2.124565514943686, -1.565392027480558, -0.4491238706981251, 1.123834022008671, 2.9341062586196323, 4.688226973907386, 6.085252161064772, 6.8870603478426995, 6.973279987925892, 6.366310376934222, 5.2205041663268705, 3.7796253690368835, 2.315222353032832, 1.063148081698842, 0.1749537910657444, -0.3045603097854004, -0.4299405280688436, -0.32162224351894086, -0.12189874706274176, 0.04668160733892015, 0.10976995682450273, 0.05073531126443626, -0.09825507730113067, -0.27776757431808263, -0.42654563950325824, -0.5023357558896894, -0.49237220794899966, -0.4120347227371599, -0.2943203730560252, -0.1754342034633789, -0.08226949337762351, -0.02592003873128585, -0.002395663852932632, 0.0011955410864940544, -0.0014699486673385729, -0.001956516583813963, 0.001214757198966788, 0.004950246158527379, 0.005858739490462036, 0.0034916261458863927, 0.0004924267723113088, -0.00036233438746311874, -2.853146754933081e-05, -0.004524125097982659, -0.020871518398435093, -0.04734233277724783, -0.06140929534420098, -0.012208905540413172, 0.1743972725322671, 0.5726676667753887, 1.215740780129477, 2.043941367869186, 2.8575793547428194, 3.2932964232949207, 2.841702118673896, 0.9164074990117109, -3.0283752823830175, -9.349831076862248, -18.069818785968497, -28.76840066688239, -40.55434862192773, -52.13649419850037, -61.998141159177706, -68.65544307750233, -70.95966894601102, -68.33689875347805, -60.93086398989689, -49.61238518648641, -35.84252522761756, -21.41368349403971, -8.122293495239552, 2.5558384483104692, 9.71603775735551, 13.146640812896617, 13.298457508106184, 11.114785057507154, 7.768453793485852, 4.3739562170244675, 1.7466067201405289, 0.2657737495584683, -0.13092691793427802, 0.16876219772170398, 0.6470941942150742, 0.8641434374500105, 0.6126782150178217, -0.025892525651456333, -0.7379297252118409, -1.1234512455002275, -0.8791601864209366, 0.047525355163487173, 1.3932522267574838, 2.6368302260426755, 3.177504697013568, 2.590679741804362, 0.8883224204009955, -1.2995887678914047, -2.6933087798777953, -1.5164568910343565, 4.183694385352684, 16.10800132130925, 35.26124981324355, 61.59557576473427, 93.83163491525454, 129.51207115218045, 165.2922740540282, 197.42141691980564, 222.32444061075776, 237.17276906496508, 240.3332373521649, 231.61032536657612, 212.24014917619286, 184.65540632981336, 152.07151517660566, 117.90949966217448, 85.28173768372412, 56.605941018211105, 33.38722751165966, 16.181674439714268, 4.717947692557839, -1.8729886486433915, -4.782220933922203, -5.2607121486644495, -4.415435506698943, -3.0874116109591703, -1.813276608560626, -0.8543908504359062, -0.2673988272638693, 0.011626792992919625, 0.09228272802039533, 0.07762832580852991, 0.03826122444182683, 0.008564706183321105, -0.0038307521342589848, -0.004568363252480455, -0.0016188918499241104, 0.00031219466303334547, 0.00045888536213453977, 8.461488592249363e-06, -8.41083604100314e-05, 1.3471064501631469e-05, -0.000444307901025723, -0.0016634802065821118, -0.002718773161719041, -0.0020739279008865088, 0.0010766742413743458, 0.005640317837890738, 0.00872046423404715, 0.007485761769670619, 0.0023468711344204777, 6.282155348211099e-05, 0.01501958819516513, 0.06732876997657879, 0.17750626357499052, 0.35892008572078393, 0.6103838489526778, 0.911703458367717, 1.2243953978038031, 1.4982914089898551, 1.6827881858985774, 1.7399316218308927, 1.655642777727205, 1.4439359165434447, 1.1436933654263621, 0.8088534314276608, 0.49477007092346137, 0.2448271394044199, 0.08124479461320308, 0.002589423565539087, -0.011723526064822494, 0.008093510102749165, 0.03323660813500436, 0.045062446207712506, 0.03879411823604854, 0.021398344035041473, 0.005056374506587264, -0.0007252848417497544, 0.005120166662032114, 0.014098852887861432, 0.012215189140172611, -0.01240865711742089, -0.06154110919991747, -0.12202038926070204, -0.16662820117665883, -0.1611285172700208, -0.0755800461329363, 0.1037810938996563, 0.3663623914168604, 0.6760688203658151, 0.9783153254508719, 1.213578240046144, 1.3335219928044435, 1.3147805956369185, 1.1659664247725032, 0.924241889871336, 0.6438415995620939, 0.38048421269680394, 0.17660729967775987, 0.05195791297909294, 0.002046956688960119, 0.0042005726775568054, 0.028408892368759934, 0.04876104398918826, 0.05142121335233392, 0.036718404073782275, 0.01533715139231292, 0.0008680317270845695, 0.002234202479455542, 0.019282430051292796, 0.04324787867292958, 0.06157959287270578, 0.06448909016961288, 0.049837681496794954, 0.023950674901107714, -0.0019540507034285014, -0.017778789118478213, -0.019746968581797374, -0.011888641168556131, -0.002860571221112767, 0.0001621295456948581, -0.0032650726533906813, -0.006404234230063879, -0.0013626872691472945, 0.01069166588404204, 0.011293364287761246, -0.03392613862274502, -0.15942200278741814, -0.3722580130086195, -0.6250202388843982, -0.8078012239102225, -0.7767402334367834, -0.42418133342719927, 0.2273666137802927, 0.9521337030649468, 1.3324396052133616, 0.9143833557806229, -0.47112290139997076, -2.279493757630857, -2.8822354817074394, 0.464569081392108, 10.954328294750542, 30.506353953704224, 56.744306146324995, 78.68466966711428, 71.5079303707908, -8.782332126274913, -229.59857717082923, -683.4185712291692, -1485.3298984284602, -2765.2623514424495, -4654.375568480919, -7266.06838254983, -10673.272585878361, -14884.88452048169, -19825.123223381008, -25320.031547255636, -31097.04374785211, -36804.95374796068, -42037.952572468, -46371.214203722084, -49405.16763702967, -50811.70866378269, -50376.12317437524, -48028.59299379456, -43860.24197422516, -38120.63839048703, -31196.22430598903, -23571.899900032975, -15780.503962529518, -8346.778653504245, -1733.2659618595287, 3704.704617437007, 7749.891429104444, 10338.19239439822, 11549.141713380206, 11577.657796693387, 10695.307798161755, 9207.475427472116, 7412.864747035209, 5570.613322263347, 3878.4308612967975, 2463.0147062195974, 1381.9229720803519, 634.4490826909752, 178.0597408665245, -53.29119576197659, -132.24337763760275, -124.87017447085564, -82.49305006267376, -38.54372813111874, -9.612315728189417, 0.7043709751782593, -3.250344227505881, -14.013173605996881, -24.624872277103886, -30.652091965823764, -30.6929992850174, -25.784966654204347, -18.26985489964119, -10.632926413816888, -4.6717568400414775, -1.144191250109546, 0.14348414372467996, -0.030401593739405923, -0.7472695374456492, -1.301739257947594, -1.3685271213807753, -0.9803838796460007, -0.3830461958813649, 0.14377089559866404, 0.4224979860636901, 0.4301172470060495, 0.2680309591676149, 0.08250016965396913, -0.018731557031818877, -0.015664098742193967, 0.025609058099674533, -0.0023010159026534954, -0.1855801174869682, -0.5394221686122779, -0.9932431651354232, -1.4168945333307803, -1.6742389930255395, -1.6792389239531949, -1.4306001155088466, -1.0112658938818677, -0.5543549573366993, -0.19080178819358554, -0.0006569045396847646, 0.012521806094774124, -0.08498466260287522, -0.19160019240443296, -0.2172448592204217, -0.12221245431755466, 0.06810681703849268, 0.27825519105820007, 0.4201665125169325, 0.4358490101757311, 0.32541865590939484, 0.14722792767884327, -0.010846025763662736, -0.07608856818133576, -0.03012341784632745, 0.07812823879113129, 0.1556837112380594, 0.11782304485588037, -0.05434314260345696, -0.2838124637893104, -0.42355990649444814, -0.3482854365247355, -0.09395146374679379, 0.001348553996035028, -0.7809886039350972, -3.4968417578361843, -9.343278936123337, -19.32156319750866, -33.8223559499481, -52.238027111672594, -72.72508900323638, -92.22459328220724, -106.79890976278487, -112.2686172820988, -105.05066151439826, -83.03019447769512, -46.26400805982917, 2.6734876088978874, 58.82830995311048, 115.51465492973635, 165.39555685656396, 201.82753543295917, 220.0526300778851, 218.04817616889966, 196.87358162104036, 160.43420388249837, 114.71614020168587, 66.65738170044237, 22.89371101073892, -11.36386810268956, -33.10215540807054, -41.796398048428394, -39.196046931879614, -28.692282786776012, -14.4370593685472, -0.42282971677384573, 10.27965276057856, 15.986181960455191, 16.48543210745283, 12.78093478565592, 6.613544109242844, -0.08890318389383149, -5.695701225428651, -9.19091530657364, -10.280978276514398, -9.306761177984495, -7.019623077223428, -4.303658385800777, -1.9245754211854527, -0.3637088799234896, 0.23750091769915913, 0.031124284108735252, -0.6514583342084903, -1.4362382883451008, -2.0231155900932354, -2.2522847780898507, -2.1130696480705278, -1.7067154852657898, -1.18558795962929, -0.6930723006585175, -0.3225172870563037, -0.10326971231955027, -0.011299997603691773, 0.005487416047399221, -0.0003062776262717958, 0.004861477632089529, 0.02892568553817672, 0.05982286357440014, 0.07805445985578188, 0.06943278711526968, 0.03258203188254679, -0.020956598845622076, -0.07270255185337943, -0.10567854547325393, -0.11126656690243832, -0.09172930307674984, -0.05789339259261159, -0.023622228631935336, 0.00014058829550757628, 0.009157755880137161, 0.006195896968320726, -0.0017769594534323644, -0.0077599235256313225, -0.008101796205280539, -0.0035699772664602994, 0.0021193691505395373, 0.005196316458405501, 0.004343732329344841, 0.0013249791725273106, -0.0006418342139715822, 0.00022296637775839727, 0.00201440203136848, -0.000558619844446304, -0.01249787553635833, -0.03236650577830248, -0.04623649827255529, -0.025096906068468258, 0.0715294990149311, 0.28503929716062054, 0.6423789354281426, 1.1406934346212145, 1.7385445943725057, 2.3574899881467886, 2.8955758220894032, 3.2504354511700515, 3.3458586708284375, 3.153862478717855, 2.704962343489033, 2.0825610975036692, 1.402235790391801, 0.781656822123208, 0.3102121312253769, 0.027862673842370442, -0.08002778590574956, -0.07040243566443408, -0.017307016778400516, 0.016982491621494154, 0.0037103057377595927, -0.046242065395731544, -0.09452103320846714, -0.10111597438743833, -0.053724498787895925, 0.011470736811577108, 0.007451070868755977, -0.1838139460542093, -0.6735790488336869, -1.521938734739007, -2.701982002639181, -4.086416843945846, -5.464415776204556, -6.58699102299337, -7.2294670487930075, -7.253784317473316, -6.651690594322984, -5.546105835109482, -4.156550229025362, -2.7392990494860516, -1.5201536204730632, -0.6406534322448684, -0.1337736675847593, 0.06497135822366847, 0.07716156362517686, 0.027848950614466017, -0.0011283724203102077, 0.0061925548844332795, 0.008871787027360838, -0.05533333790842943, -0.2239197154054343, -0.47466677526872564, -0.7204439858365581, -0.8413861637249922, -0.7445880750409223, -0.42747736013275306, -0.015100814151676203, 0.25297565494080426, 0.09406175598304471, -0.7025950505297622, -2.152745569178445, -3.993144180392201, -5.679647561256718, -6.489753134179177, -5.719101618679059, -2.9258969491962667, 1.849307594354275, 7.968273816356442, 14.247082926410489, 19.189565046859798, 21.361456730706838, 19.814278152187526, 14.437249505020574, 6.118750476240579, -3.361546469253451, -11.719794892928423, -16.762900692720308, -17.048535668893855, -12.428469843068214, -4.301888709759683, 4.535470688040099, 10.461564470875954, 9.917560423575013, 0.4116420635945346, -18.64612439176589, -45.503228998666906, -76.15461999558333, -104.98980463586966, -125.88055686312066, -133.47800815351064, -124.4254455371299, -98.20075464571437, -57.38027822035673, -7.24637915843614, 45.186918290107585, 92.51926251366409, 128.3820339566362, 148.61470330572968, 151.94427950244443, 140.0422245628954, 116.97460822175218, 88.11446726786735, 58.89868004309478, 33.73380249314197, 15.274584836482019, 4.1953527230206324, -0.5562546077093253, -1.1486885919351912, -0.09653016549856405, 0.4564226121757124, -0.7709683345947848, -4.022377753738771, -8.643577976528736, -13.450542257883901, -17.189808535825673, -18.94855353682164, -18.405320546510502, -15.859025772803818, -12.065250447682462, -7.959987220450149, -4.3716447854233635, -1.8115232326552784, -0.3954482464990585, 0.09954156059292235, 0.0830669016311766, -0.031346436584988195, 0.026197134637687493, 0.3147455834524678, 0.7072906835712935, 0.985549193807246, 0.9600774396588867, 0.5662833646438418, -0.10000698952718748, -0.8181604612121218, -1.3309072134786335, -1.4473022801969277, -1.118774490616797, -0.4584601276201035, 0.30319852701188715, 0.908714947717341, 1.1740219264854883, 1.0592741880703198, 0.6810142802208033, 0.2587910308747131, 0.014614615291601114, 0.06293780612047294, 0.3348922673973814, 0.5705001543749509, 0.3890943966328156, -0.5806722377716949, -2.5530335698387563, -5.470489695710532, -8.965580551319988, -12.41959514872813, -15.108044733028823, -16.39377196102498, -15.910856524300163, -13.682155747106759, -10.131153952503318, -5.979793566529877, -2.0587883858522744, 0.9152854176424535, 2.5300697837587305, 2.7770677895228957, 2.0297830253765166, 0.908843227432976, 0.0786331351692926, 0.03869571921907604, 0.9728120616876125, 2.6999733442026175, 4.739895923717773, 6.470880865617936, 7.3301350230891735, 6.994330430357704, 5.484716784195765, 3.1644221616315855, 0.6286159946241786, -1.4789623037851791, -2.666847491434936, -2.7523576019298415, -1.924061034919271, -0.6856240490349731, 0.29577922087377784, 0.38893026098158945, -0.8126989294426763, -3.3668366038159374, -6.956546715402829, -10.967268986484175, -14.642481976696473, -17.272991165733988, -18.367761044256493, -17.761994024326036, -15.637760383246526, -12.457686503069235, -8.835585251078752, -5.383541526463985, -2.5764065692300213, -0.6646340488952038, 0.34007007320940724, 0.6159922609413456, 0.4436691178406337, 0.10962411106298721, -0.1703343212280336, -0.2903356737344642, -0.2521878408814438, -0.13064505263492265, -0.023524217078609164, -0.005701018821877086, -0.10149694951720929, -0.28148738285893515, -0.4805677712490222, -0.6273608073451014, -0.6726018612903893, -0.6054570975089277, -0.4535096189935854, -0.26876373121433805, -0.10658033897067513, -0.0060637002442422835, 0.02123505382823684, -0.008692551799986651, -0.06217546991622074, -0.10275602725518396, -0.105068453797893, -0.06277318999662754, 0.011600931366260756, 0.09380456578468262, 0.15843454031329754, 0.18853730551372438, 0.18076758775173088, 0.14436077783882392, 0.09552607152372654, 0.050272739707676505, 0.018754943992005113, 0.003122328385077826, -0.0009151277076630933, -0.00020691206166101146, -0.000143445910795372, -0.0023864427172558475, -0.00512245217691613, -0.0052652713988840276, -0.0011014534717111945, 0.00621761649856604, 0.01317686889799838, 0.016035814533184527, 0.013255627459973404, 0.006634810683655685, 0.000238754644930667, -0.0024131883922515794, -0.001175732123457776, -6.211254569960471e-07, -0.00431418151969572, -0.015744951148319156, -0.02703521844685737, -0.02111650007308061, 0.022539264498924176, 0.11436719587340156, 0.23876843327336064, 0.34508456441712265, 0.35669410750490393, 0.20680373989808443, -0.09861639818487483, -0.4035336798796801, -0.33351898907011973, 0.7324914660382215, 3.619869582485718, 9.226518963708283, 18.304284836501818, 31.183579715434195, 47.49759775236986, 65.9796505557709, 84.40801609728518, 99.753437676897, 108.5462123360473, 107.42931477627118, 93.81234541164949, 66.50877708299205, 26.20683017983976, -24.423547711683753, -80.9574025832854, -137.76823429758804, -188.83178917665097, -228.63839468243668, -253.0444012157324, -259.90150563803167, -249.34564011074823, -223.69544897113514, -186.9889192305756, -144.25792275882952, -100.6885882246311, -60.83046113551938, -27.99715787818228, -3.953020241943638, 11.093732317745866, 18.227831911377397, 19.360657761126745, 16.70722076856463, 12.325761442157445, 7.800766281178846, 4.103440868742789, 1.6171446935899487, 0.2801809491346691, -0.21860152842914324, -0.25353425290332005, -0.12958037370585695, -0.022248064360675238, 0.01648063842360977, 0.010417626704606444, 0.000446661932851661, 0.0011450950222484308, -0.013143290078171981, -0.09345764428890807, -0.28469996304483586, -0.5942985698976169, -0.9757291635122245, -1.334253366782678, -1.5530246399470669, -1.5300354885404708, -1.2127272008184724, -0.6183156230066919, 0.16685175694768314, 1.008408105269596, 1.7584875247175298, 2.2927615758064555, 2.5395323084178685, 2.493431506362521, 2.207067013999863, 1.769761480955943, 1.281112188996948, 0.8269621408881453, 0.4637531545385367, 0.2137152112744978, 0.06975595824154172, 0.0063752045982839334, -0.007967653905549262, -0.0009047314332716112, 0.009241896848271798, 0.014178686359597743, 0.013066565736782536, 0.008694480926479503, 0.004199646778510053, 0.0013093360300561142, 0.00014187671883884092, -4.846420314556745e-05, -1.5295661302523412e-06, -2.814393424323601e-06, 4.8333511822436036e-05, 0.0003057260281784767, 0.0007188747990706379, 0.0010395042929559535, 0.0010367840266123655, 0.0007062814351556211, 0.0002807664958385062, 2.703902043349871e-05, 7.622961383430431e-06, 4.698282295287105e-05, -1.2712493193790522e-06, 0.00013390333862068758, 0.0012506978622279228, 0.004150619737469534, 0.008517140914265359, 0.0118290548100809, 0.009406986533161294, -0.003362517451108561, -0.026387876549003392, -0.04902549054247544, -0.04578703110437541, 0.022781430046042734, 0.20105553610420726, 0.5205884010181833, 0.9770222064668018, 1.5091108801792148, 1.9898977265736666, 2.2391690487407043, 2.0599420970914526, 1.2947303739978957, -0.11160706039181098, -2.0622424358288187, -4.29277212712755, -6.4041861869847665, -7.9459189472408625, -8.533614898235534, -7.970656377245426, -6.334013324288365, -3.9882238589485013, -1.5078489881995996, 0.4841862794357011, 1.524386820053333, 1.500603860220914, 0.757414962296725, 0.05602463190448839, 0.377472399521099, 2.6078119020692396, 7.186716851903023, 13.826723339432522, 21.406100737851208, 28.1011393383696, 31.760284988713188, 30.44891576481482, 23.030845282987965, 9.62156339761581, -8.2373961638996, -27.771944947362776, -45.52925159177273, -58.180665345440666, -63.38299220786057, -60.42004478869769, -50.42543785273912, -36.109751469889936, -21.042306242820093, -8.670581440439046, -1.3471872796035365, 0.3527373906861821, -2.1897489933614165, -6.039476765275144, -7.59943680809606, -3.7515719301683252, 7.08423465173191, 24.299049023293932, 45.075507107412015, 65.05377505432936, 79.54514571770433, 84.8974246302556, 79.61238873525811, 64.87897406164907, 44.337817445811844, 23.11916242553523, 6.4146541737183895, -2.0085114110568147, -0.9116453735911888, 8.033392067553097, 20.719938059152295, 31.8233123099661, 36.41500107085099, 31.49845467185256, 16.99709554923228, -4.12370826723394, -26.678865399495557, -44.827101986145244, -53.856823467441586, -51.646897098371156, -39.346647607353624, -21.047794596034798, -2.5275997379568507, 10.567983525771306, 14.54798688121883, 8.93328315768173, -3.2723467135795934, -16.426988947590722, -24.000726181919436, -20.729691440686604, -4.521717236624914, 22.49784057974157, 54.184391820932774, 81.82405853733137, 96.4469852327273, 91.35628591998835, 64.14746563504818, 17.627287472756, -40.651698135689784, -100.13385547704216, -149.811993783409, -180.89192090168743, -188.84595413145013, -174.30964737045213, -142.6084999059248, -102.09104462510768, -61.77792269333915, -29.017139077727307, -7.801645465953857, 1.7893646166923884, 2.9253823206612766, 0.4746781344582628, -0.8767532544287167, 1.7769909681273035, 8.738557449805006, 17.880465826230395, 25.70477902468254, 28.888900120673217, 25.75672939155577, 17.134948514156154, 6.252001683405363, -2.3452091077264874, -4.54072150413219, 1.5060218208841423, 14.066934221663457, 27.71900601265154, 34.64480576160598, 27.06029356761557, 0.06080881248598652, -46.03907307753762, -104.71662502095289, -164.07983260730379, -209.4602223263983, -227.12387857642142, -208.07398373820482, -150.8317949397889, -62.33996286707124, 43.338476621369104, 148.21064999281376, 234.6628868434399, 289.8029751890461, 307.6647961791458, 289.59498555870533, 243.17641346477748, 180.09090484881474, 113.51499695816774, 55.61616950310696, 15.583343285801943, -1.5607628017087494, 4.693614046344633, 30.74202110142376, 69.81380567491614, 113.22972776039094, 151.73557087351313], 'positive_zeros': ['0.02692397158543296147048926900598', '0.68619437825336471599434631607214', '0.69491116027861631629233463245379', '0.70758864984472242576688756719904', '0.848103981298735577522859941001361', '1.22478246562665312628652339677808', '1.27029612115338170958390381798401', '1.39809003884794846660408727703205', '1.47614002420573172837877414546218', '1.62563614773303150125020108311900', '1.64686653680827616898102988237038', '1.67962559926462854111824903477169', '1.79159921881837028356358531596235', '1.83325011591643007466950379242055', '2.00578508381240041867726752870164', '2.10520050949947398169414904178508', '2.25842871290572638777445837503163', '2.28127552690483562784297006026541', '2.33471820724337585353745447733925', '2.46050044921994584994125605386203', '2.48345813995628448060801416548916', '2.62572550676365949860183203482893', '2.67201319597907113378013633940630', '2.70012229300031914122176498920497', '2.87320330182179210669973616218349', '3.08586475292292406127240128570576', '3.09975994635783296249191891156865', '3.11899727321998119919676028993533', '3.18258797816224937803177385089146', '3.18372922226579937695695020301357', '3.32299023482943864578219838519380', '3.39759012981726221520036219870822', '3.54442734790450551571233406248083', '3.69631517297824351070651649362299', '3.69965209453097757671568926641787', '3.72090169189119196445488702546436', '3.85437564566033959001911822084151', '3.96586057341497644931323163677800', '3.98720552177829917556720610065292', '3.99735810439214277190157776092491', '4.02198796240277814553631478567928', '4.15690507806590389127221330873686', '4.32630844143813285626157650749854', '4.35698592983613903476626537349948', '4.41290467765206819997848263654215', '4.45285420372676828085228860088277', '4.57106638287454337767529987459114', '4.58687226035444973878667569070515', '4.59828815005179662239372060629329', '4.64391823298403364483246958232483', '4.73890233202447965427104432941354', '4.89799490439169556537283862125962', '4.98322859248273049317550703446408', '5.00690456919640407739328344782701', '5.04377372336568548520017354712441', '5.08740062583580726887674099996584', '5.20442330910704329902035238741455', '5.45724030645110693132418523144908', '5.46353696298908915805260289452245', '5.46855281463627861861516463701241', '5.47923339412488166226449037205713', '5.52375886919741236716929790023094', '5.55843951532002473047011411574652', '5.56484173657085013348049975795309', '5.77245399428676177185374715262501', '5.80235060419873928139586845029298', '5.87412802022948566756514645090576', '6.09163611903928612930408125871142', '6.10371160406115555260904367354881', '6.10588438461454665153010739583637', '6.12706941460400532770704589759162', '6.17763829320418665201814393964604', '6.23528190799873408384716248043848', '6.28456788687308062718394777076126', '6.29434019602034139178898233973872', '6.31788629103186443684107934571478', '6.46845661121683462124057026006001', '6.49137072146763547642723601489856', '6.58816119590991287946766299050359', '6.66331277950201310453804574105169', '6.70952037232760111936762230148126', '6.74796466564479736261787165812298', '6.83331216711751306428161952162468', '6.92694109612625626463266819119538', '7.05898654734397779687637113070651', '7.07350210043332575035330976142313', '7.07710768472990176243181961941711', '7.12872122025009841186282994764043', '7.15672425014332638194147157786985', '7.19946085815776074033992042765640', '7.21027908130710528503494963016842', '7.21519328289225071336763875978942', '7.38913845813680964102179905384650', '7.51372442264753520807481906862089', '7.57900281853232361879479745431239', '7.68353494050093008581130108698572', '7.77368236378115869499906450694572', '7.78905575898734090438604795742673', '7.79358905459681405138358119264078', '7.80184305754911631656153885338254', '7.82557936631710895745030958917022', '7.933283396821627961407420748194833', '8.033804165809849795398338573126894', '8.084518241731738478966449539544996', '8.230969955003856152059665021996828', '8.248574893009051591658499478227748', '8.250978634363536774382127888784997', '8.289772088724781405544398818394095', '8.315470860970177108658044580290854', '8.326533606272062263839739701805714', '8.460168848099577410334838224151755', '8.501985730782897115390500461089924', '8.534306261913143556326549607355414', '8.611705351717827410868237054541893', '8.650441539090874686138066183631759', '8.713739201457723557986293555397395', '8.817472969513100316484949902159424', '8.913872687796202343189649448677795', '8.932455243395180005684043253677717', '8.951390477051303252379892370134484', '9.092300668377523490104933086289281', '9.094326454606083495736008949069711', '9.118712013280243512347807772655800', '9.220753435852796573981523580349739', '9.232634757751393513827349539658572', '9.246427918667106115385209005905972', '9.247690744055262978854226996564675', '9.252901163398461859266344335799597', '9.280938580515427781257789817351863', '9.348905945223813436282449404450322', '9.608927287394928812672227262154258', '9.681079614183927899138788936976766', '9.713508706636215716253762138512557', '9.778560947602953004094598724136112', '9.914937135912519136317531298097384', '9.923167570087439705044760173234181', '9.943233139257572878594777427277173', '10.00823409196570542997067722007832', '10.06951222806047199704195765351302', '10.11768031574285479886751084188999', '10.19338736311867262044126075988315', '10.23152877811182990524707837596546', '10.35995627907347649306168641301234', '10.40436193567645414334625932504791', '10.44392334173372659653908200007380', '10.48182390528799860243115972118261', '10.53853881322182835490760064709546', '10.57395988860449781186231381240205', '10.60326633351614945220489364695437', '10.68986082259552018576136970485775', '10.78958789824989485583737429728857', '10.79852873796803815743191098573266', '10.81238265963602489240057257341671', '10.81769901025726592951364884891612', '10.84331966763799627996189629842770', '10.97229057865159340487617402648445', '11.01599296895566861059864754772870', '11.10001061909337177850664281810919', '11.13285971758240644712963354524783', '11.36363274327175625302856661093880'], 'prelabel': '32-567e16-1.1-c1e16-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.1277964645629526, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e16-0', 'trace_hash': 1128853891659322367, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.02692397158543296147048926901', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.68619437825336471599434631607', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.69491116027861631629233463245', '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': 31171855510.889465, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 114111375997743384649195776508234722433546881, 'conductor_radical': 21, 'degree': 32, 'dirichlet_coefficients': [1, 0, 0, 5, 0, 0, 6, 0, 0, 0, 0, 0, 12, 0, 0, 14, 0, 0, -24, 0, 0, 0, 0, 0, 20, 0, 0, 30, 0, 0, -20, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 11, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, 0, -36, 0, 0, 37, 0, 0, 18, 0, 0, 0, 0, 0, -32, 0, 0, -120, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 28, 0, 0, 100], 'euler11': [1, 0, -53, 0, 1301, 0, -24310, 0, 438422, 0, -6939277, 0, 93358746, 0, -1178831562, 0, 13833581305, 0, -142638619002, 0, 1366865400186, 0, -12293352501397, 0, 93979649325782, 0, -630538792050310, 0, 4083095318114021, 0, -20126741179911773, 0, 45949729863572161], 'euler13': [1, -12, 134, -888, 6105, -30876, 179098, -823572, 4484276, -19211160, 95146260, -368856120, 1678874623, -6083817792, 26395513124, -90966061620, 369996806871, -1182558801060, 4460841717956, -13366147689024, 47950338107503, -136953695363160, 459252824084340, -1205471799849720, 3657961694642996, -8733568757620356, 24690180173172202, -55334744326286412, 142234809672746505, -268953094653920664, 527608435683704726, -614230716169089084, 665416609183179841], 'euler17': [1, 0, -82, 0, 3429, 0, -97574, 0, 2107148, 0, -35018028, 0, 442861075, 0, -4531943836, 0, 55716215391, 0, -1309731768604, 0, 36988199845075, 0, -845250067093932, 0, 14698953340288268, 0, -196708588842410726, 0, 1997811651460850469, 0, -13806981777870876178, 0, 48661191875666868481], 'euler19': [1, 24, 260, 1860, 10686, 47166, 107086, -419166, -6879541, -51420516, -276786939, -1114492218, -2822472485, 1822505070, 73990037195, 552542496228, 2810170911123, 10498307428332, 26710403427395, 12500562275130, -367827436717685, -2759593066497582, -13021685394548259, -45963346057197324, -116839118266644181, -135259711527232314, 656551361282877886, 5494379551193397354, 23651483225140996446, 78218549239798129740, 207741738303549871460, 364347048716995159176, 288441413567621167681], 'euler2': [1, 0, -5, 0, 11, 0, -22, 0, 35, 0, -22, 0, -30, 0, 264, 0, -815, 0, 1056, 0, -480, 0, -1408, 0, 8960, 0, -22528, 0, 45056, 0, -81920, 0, 65536], 'euler23': [1, 0, -52, 0, 150, 0, 14626, 0, 624335, 0, -12478623, 0, -438951857, 0, 2082575939, 0, 287649733203, 0, 1101682671731, 0, -122836726614737, 0, -1847284049300847, 0, 48892288995413135, 0, 605904153010830274, 0, 3287193664803048150, 0, -602827488876014990068, 0, 6132610415680998648961], 'euler29': [1, 0, 280, 0, 39620, 0, 3737168, 0, 262509098, 0, 14548474088, 0, 657722898576, 0, 24729928393512, 0, 781194417693235, 0, 20797869778943592, 0, 465194909427731856, 0, 8653771672506606248, 0, 131319234644127619178, 0, 1572253609658045570768, 0, 14018141710600683404420, 0, 83316305149223849774680, 0, 250246473680347348787521], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 20, 62, -592, 3993, 63748, -324158, -3584180, 11230028, 57146320, -1099785196, -3941857864, 35484532311, 90132924080, -1223837154900, 752142514188, 58822158018199, 23316417939828, -1176107505858900, 2685149941267280, 32770710764387031, -112852044008993464, -976063409759306476, 1572244650023721520, 9577990231411478348, -94764364955833784780, -265689066251122490558, 1619739585192015166588, 3145137495667679195673, -14455187408087465213872, 46930523983689371859902, 469305239836893718599020, 727423121747185263828481], 'euler37': [1, -4, -196, 260, 21774, 11002, -1641314, -2280458, 93818327, 140015056, -4667204695, -4202897350, 221711706075, 53066357330, -10011159522405, -92340382656, 401193533075251, -3416594158272, -13705277386172445, 2687970197836490, 415523432769228075, -291445533113813950, -11974770342170290255, 13291892092962114448, 329534945988741810167, -296372289209601705266, -7892396850630629413586, 1957449674817623463826, 143337196975160928208494, 63327998296181139403220, -1766364014015021626739044, -1333785071807261228353972, 12337511914217166362274241], 'euler41': [1, 0, 274, 0, 37841, 0, 3616646, 0, 273427556, 0, 17420877956, 0, 965828738463, 0, 47347608344316, 0, 2060739655855303, 0, 79591329626795196, 0, 2729201181827945343, 0, 82750986260739011396, 0, 2183298590241295058276, 0, 48545007103425440467046, 0, 853825036456156847491121, 0, 10392608251406863111792114, 0, 63759030914653054346432641], 'euler43': [1, -20, 526, -6928, 109937, -1136500, 14215266, -127050948, 1379372148, -11085538656, 107579120964, -785905304304, 6925030209399, -46488750751176, 377038314636420, -2341844065443996, 17543733667749351, -100699294814091828, 697143843762740580, -3696181105973750232, 23675300204923510599, -115534715131172238672, 680046680105730859236, -3013255720846879452192, 16122377923168687656948, -63854867804372019277164, 307212969737630933145234, -1056142334909044606505500, 4393041930958655861796737, -11904133853027710560163504, 38863697963016852980626174, -63541407315959113238286140, 136614025729312093462315201], 'euler47': [1, 0, -187, 0, 17658, 0, -1097501, 0, 46137122, 0, -883107198, 0, -54170427851, 0, 6798567948140, 0, -400845896701047, 0, 15018036597441260, 0, -264334407546395531, 0, -9519202645831838142, 0, 1098584237690639991842, 0, -57727600227955714607549, 0, 2051709208737813994579578, 0, -47996726417093805545527003, 0, 566977372488557307219621121], 'euler5': [1, 0, -20, 0, 158, 0, -1006, 0, 8963, 0, -61399, 0, 293727, 0, -1729137, 0, 10444771, 0, -43228425, 0, 183579375, 0, -959359375, 0, 3501171875, 0, -9824218750, 0, 38574218750, 0, -122070312500, 0, 152587890625], 'euler53': [1, 0, -136, 0, 11898, 0, -982454, 0, 65260463, 0, -3934825011, 0, 227355327775, 0, -12350790854677, 0, 663083591655843, 0, -34693371510787693, 0, 1793942894057409775, 0, -87212882523225397419, 0, 4063096222482079320143, 0, -171818894810479757042246, 0, 5844998442846527787918618, 0, -187672691639771552500573384, 0, 3876269050118516845397872321], 'euler59': [1, 0, -412, 0, 92526, 0, -14617286, 0, 1798129247, 0, -181339187307, 0, 15440137281895, 0, -1128686492503633, 0, 71461191506541507, 0, -3928957680405146473, 0, 187093717334280479095, 0, -7648983690634513694787, 0, 264020104206138203676287, 0, -7471139762386919341857686, 0, 164622020320031004162131406, 0, -2551675119711427115634657532, 0, 21559177407076402401757871041], 'euler61': [1, 36, 458, 2136, 4581, 101244, 205534, -19237608, -259070596, -2084437056, -16420374612, -94639746252, -82112767277, 2391348337452, 32333281143140, 638769415441428, 7239849135563583, 38964934341927108, 120312139133623940, 542790636983192412, -1136920319787344957, -79932379612017813852, -845983847158100122932, -6550849624880703994176, -49665727835764135049476, -224967398428674813574728, 146616222005718912513934, 4405523074652210049394284, 12159572651257242191268501, 345851053955078286084593016, 4523589300279483687561497978, 21689524243261454536866920436, 36751693856637464631913392961], 'euler67': [1, -18, -25, 498, 21465, -77334, -372626, -15207210, -70258, 522690522, 14456179755, -11746976322, -252467626262, -9019369794816, -18089573469178, 87121202733900, 7145095613367393, 5837120583171300, -81204095303140042, -2712692717598244608, -5087505685388339702, -15859887663666716454, 1307682632981550788595, 3167876512677736848606, -28529502889774483378, -413735481936680480967870, -679236759758904661695074, -9444811698072796633096722, 175642061287944278608001865, 273024598971979911485422326, -918305629072422393048358225, -44299063546453656240652800774, 164890958756244164895763202881], 'euler7': [1, -6, 25, -114, 508, -1728, 5227, -16224, 47623, -113568, 256123, -592704, 1219708, -1915998, 2941225, -4941258, 5764801, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler71': [1, 0, 422, 0, 88767, 0, 13696474, 0, 1783062743, 0, 197270735778, 0, 18780300283168, 0, 1592056496650616, 0, 120384303819988383, 0, 8025556799615755256, 0, 477238999880074885408, 0, 25270437262466372825538, 0, 1151419062725002815782423, 0, 44585358660074511612585274, 0, 1456638307838462881953170847, 0, 34908350913530678807493147782, 0, 416997623116370028124580469121], 'euler73': [1, 32, 80, -5956, 1902, 1405666, 2145574, -160863194, 419706635, 20362342396, -73674153571, -1424225986954, 15803979253215, 105018878113286, -1523386397874453, -1680917453035836, 144926371035107203, -122706974071616028, -8118126114272960037, 40854128906996179862, 448805211591799594815, -2952522435566725997722, -11149421028164251428019, 224950911230916458736412, 338476651430655512927435, -9470271473739922692894122, 9220874241940380999195526, 440994935196133917835464082, 43559695384424472069312942, -9957535666037406604664792548, 9763601123179727093895632720, 285097152796848031141752475424, 650377879817809571042122834561], 'euler79': [1, -32, 4, 7004, 42998, -2012542, -7832466, 293719086, 2551107411, -42512614356, -399580429395, 3686139563154, 60485393470035, -282988338874782, -6212474403083781, 6532193094162084, 578303058890079675, 516043254438804636, -38772052749645877221, -139524287610483642498, 2355910974974734322835, 11342459330410080322446, -97132989857619143439795, -816408376856300508698604, 3870307528246017984623571, 35202701227655924543536434, -74159950495787971389027666, -1505368959426678025248000418, 2540816791339925247095200118, 32696278518001815852405408356, 1475160481394713565014293124, -932301424241458973089033254368, 2301619141096101839813550846721], 'euler83': [1, 0, 1106, 0, 588057, 0, 199446598, 0, 48280461356, 0, 8842976735556, 0, 1267446926365087, 0, 144990400379398868, 0, 13377759444102660759, 0, 998838868213678801652, 0, 60150903081897662038927, 0, 2891126115616059417808164, 0, 108741708076207950219399596, 0, 3094621629216088596089616502, 0, 62857417280773844837266047177, 0, 814419981222669953584128636674, 0, 5072820298953863752478356399681], 'euler89': [1, 0, 4, 0, 10610, 0, -307510, 0, -23884909, 0, -1439051407, 0, 120404885691, 0, 39552324252603, 0, 7282335141246355, 0, 313293960404868363, 0, 7554472355602173531, 0, -715181626010103432127, 0, -94025065394612885795629, 0, -9588690695663901119143510, 0, 2620568181827431308620357810, 0, 7825643946561765653376759364, 0, 15496731425178936435099327730561], 'euler97': [1, -28, 1286, -28048, 761097, -13824068, 283936306, -4458422660, 75799851020, -1051953765872, 15453031592924, -192095689823008, 2496107817288063, -28011310651778320, 326354731921222764, -3318512907126253500, 34927887494891105479, -321895751991246589500, 3070671672646784986476, -25565166926490474649360, 220978630362991587272703, -1649591050413301803233056, 12871942708189082849522396, -84996059632748134510359536, 594076298832916753520350220, -3389431378741302675920617220, 20938148254582118041853634994, -98883752367850336142914091204, 528081339426544875710554819977, -1887706382496404368130705066896, 8395474528143413922181988428934, -17731033295830102809211726728604, 61425365346268570446197767595521], 'euler_factors': [[1, 0, -5, 0, 11, 0, -22, 0, 35, 0, -22, 0, -30, 0, 264, 0, -815, 0, 1056, 0, -480, 0, -1408, 0, 8960, 0, -22528, 0, 45056, 0, -81920, 0, 65536], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -20, 0, 158, 0, -1006, 0, 8963, 0, -61399, 0, 293727, 0, -1729137, 0, 10444771, 0, -43228425, 0, 183579375, 0, -959359375, 0, 3501171875, 0, -9824218750, 0, 38574218750, 0, -122070312500, 0, 152587890625], [1, -6, 25, -114, 508, -1728, 5227, -16224, 47623, -113568, 256123, -592704, 1219708, -1915998, 2941225, -4941258, 5764801, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -53, 0, 1301, 0, -24310, 0, 438422, 0, -6939277, 0, 93358746, 0, -1178831562, 0, 13833581305, 0, -142638619002, 0, 1366865400186, 0, -12293352501397, 0, 93979649325782, 0, -630538792050310, 0, 4083095318114021, 0, -20126741179911773, 0, 45949729863572161], [1, -12, 134, -888, 6105, -30876, 179098, -823572, 4484276, -19211160, 95146260, -368856120, 1678874623, -6083817792, 26395513124, -90966061620, 369996806871, -1182558801060, 4460841717956, -13366147689024, 47950338107503, -136953695363160, 459252824084340, -1205471799849720, 3657961694642996, -8733568757620356, 24690180173172202, -55334744326286412, 142234809672746505, -268953094653920664, 527608435683704726, -614230716169089084, 665416609183179841], [1, 0, -82, 0, 3429, 0, -97574, 0, 2107148, 0, -35018028, 0, 442861075, 0, -4531943836, 0, 55716215391, 0, -1309731768604, 0, 36988199845075, 0, -845250067093932, 0, 14698953340288268, 0, -196708588842410726, 0, 1997811651460850469, 0, -13806981777870876178, 0, 48661191875666868481], [1, 24, 260, 1860, 10686, 47166, 107086, -419166, -6879541, -51420516, -276786939, -1114492218, -2822472485, 1822505070, 73990037195, 552542496228, 2810170911123, 10498307428332, 26710403427395, 12500562275130, -367827436717685, -2759593066497582, -13021685394548259, -45963346057197324, -116839118266644181, -135259711527232314, 656551361282877886, 5494379551193397354, 23651483225140996446, 78218549239798129740, 207741738303549871460, 364347048716995159176, 288441413567621167681], [1, 0, -52, 0, 150, 0, 14626, 0, 624335, 0, -12478623, 0, -438951857, 0, 2082575939, 0, 287649733203, 0, 1101682671731, 0, -122836726614737, 0, -1847284049300847, 0, 48892288995413135, 0, 605904153010830274, 0, 3287193664803048150, 0, -602827488876014990068, 0, 6132610415680998648961], [1, 0, 280, 0, 39620, 0, 3737168, 0, 262509098, 0, 14548474088, 0, 657722898576, 0, 24729928393512, 0, 781194417693235, 0, 20797869778943592, 0, 465194909427731856, 0, 8653771672506606248, 0, 131319234644127619178, 0, 1572253609658045570768, 0, 14018141710600683404420, 0, 83316305149223849774680, 0, 250246473680347348787521], [1, 20, 62, -592, 3993, 63748, -324158, -3584180, 11230028, 57146320, -1099785196, -3941857864, 35484532311, 90132924080, -1223837154900, 752142514188, 58822158018199, 23316417939828, -1176107505858900, 2685149941267280, 32770710764387031, -112852044008993464, -976063409759306476, 1572244650023721520, 9577990231411478348, -94764364955833784780, -265689066251122490558, 1619739585192015166588, 3145137495667679195673, -14455187408087465213872, 46930523983689371859902, 469305239836893718599020, 727423121747185263828481], [1, -4, -196, 260, 21774, 11002, -1641314, -2280458, 93818327, 140015056, -4667204695, -4202897350, 221711706075, 53066357330, -10011159522405, -92340382656, 401193533075251, -3416594158272, -13705277386172445, 2687970197836490, 415523432769228075, -291445533113813950, -11974770342170290255, 13291892092962114448, 329534945988741810167, -296372289209601705266, -7892396850630629413586, 1957449674817623463826, 143337196975160928208494, 63327998296181139403220, -1766364014015021626739044, -1333785071807261228353972, 12337511914217166362274241], [1, 0, 274, 0, 37841, 0, 3616646, 0, 273427556, 0, 17420877956, 0, 965828738463, 0, 47347608344316, 0, 2060739655855303, 0, 79591329626795196, 0, 2729201181827945343, 0, 82750986260739011396, 0, 2183298590241295058276, 0, 48545007103425440467046, 0, 853825036456156847491121, 0, 10392608251406863111792114, 0, 63759030914653054346432641], [1, -20, 526, -6928, 109937, -1136500, 14215266, -127050948, 1379372148, -11085538656, 107579120964, -785905304304, 6925030209399, -46488750751176, 377038314636420, -2341844065443996, 17543733667749351, -100699294814091828, 697143843762740580, -3696181105973750232, 23675300204923510599, -115534715131172238672, 680046680105730859236, -3013255720846879452192, 16122377923168687656948, -63854867804372019277164, 307212969737630933145234, -1056142334909044606505500, 4393041930958655861796737, -11904133853027710560163504, 38863697963016852980626174, -63541407315959113238286140, 136614025729312093462315201], [1, 0, -187, 0, 17658, 0, -1097501, 0, 46137122, 0, -883107198, 0, -54170427851, 0, 6798567948140, 0, -400845896701047, 0, 15018036597441260, 0, -264334407546395531, 0, -9519202645831838142, 0, 1098584237690639991842, 0, -57727600227955714607549, 0, 2051709208737813994579578, 0, -47996726417093805545527003, 0, 566977372488557307219621121], [1, 0, -136, 0, 11898, 0, -982454, 0, 65260463, 0, -3934825011, 0, 227355327775, 0, -12350790854677, 0, 663083591655843, 0, -34693371510787693, 0, 1793942894057409775, 0, -87212882523225397419, 0, 4063096222482079320143, 0, -171818894810479757042246, 0, 5844998442846527787918618, 0, -187672691639771552500573384, 0, 3876269050118516845397872321], [1, 0, -412, 0, 92526, 0, -14617286, 0, 1798129247, 0, -181339187307, 0, 15440137281895, 0, -1128686492503633, 0, 71461191506541507, 0, -3928957680405146473, 0, 187093717334280479095, 0, -7648983690634513694787, 0, 264020104206138203676287, 0, -7471139762386919341857686, 0, 164622020320031004162131406, 0, -2551675119711427115634657532, 0, 21559177407076402401757871041], [1, 36, 458, 2136, 4581, 101244, 205534, -19237608, -259070596, -2084437056, -16420374612, -94639746252, -82112767277, 2391348337452, 32333281143140, 638769415441428, 7239849135563583, 38964934341927108, 120312139133623940, 542790636983192412, -1136920319787344957, -79932379612017813852, -845983847158100122932, -6550849624880703994176, -49665727835764135049476, -224967398428674813574728, 146616222005718912513934, 4405523074652210049394284, 12159572651257242191268501, 345851053955078286084593016, 4523589300279483687561497978, 21689524243261454536866920436, 36751693856637464631913392961], [1, -18, -25, 498, 21465, -77334, -372626, -15207210, -70258, 522690522, 14456179755, -11746976322, -252467626262, -9019369794816, -18089573469178, 87121202733900, 7145095613367393, 5837120583171300, -81204095303140042, -2712692717598244608, -5087505685388339702, -15859887663666716454, 1307682632981550788595, 3167876512677736848606, -28529502889774483378, -413735481936680480967870, -679236759758904661695074, -9444811698072796633096722, 175642061287944278608001865, 273024598971979911485422326, -918305629072422393048358225, -44299063546453656240652800774, 164890958756244164895763202881], [1, 0, 422, 0, 88767, 0, 13696474, 0, 1783062743, 0, 197270735778, 0, 18780300283168, 0, 1592056496650616, 0, 120384303819988383, 0, 8025556799615755256, 0, 477238999880074885408, 0, 25270437262466372825538, 0, 1151419062725002815782423, 0, 44585358660074511612585274, 0, 1456638307838462881953170847, 0, 34908350913530678807493147782, 0, 416997623116370028124580469121], [1, 32, 80, -5956, 1902, 1405666, 2145574, -160863194, 419706635, 20362342396, -73674153571, -1424225986954, 15803979253215, 105018878113286, -1523386397874453, -1680917453035836, 144926371035107203, -122706974071616028, -8118126114272960037, 40854128906996179862, 448805211591799594815, -2952522435566725997722, -11149421028164251428019, 224950911230916458736412, 338476651430655512927435, -9470271473739922692894122, 9220874241940380999195526, 440994935196133917835464082, 43559695384424472069312942, -9957535666037406604664792548, 9763601123179727093895632720, 285097152796848031141752475424, 650377879817809571042122834561], [1, -32, 4, 7004, 42998, -2012542, -7832466, 293719086, 2551107411, -42512614356, -399580429395, 3686139563154, 60485393470035, -282988338874782, -6212474403083781, 6532193094162084, 578303058890079675, 516043254438804636, -38772052749645877221, -139524287610483642498, 2355910974974734322835, 11342459330410080322446, -97132989857619143439795, -816408376856300508698604, 3870307528246017984623571, 35202701227655924543536434, -74159950495787971389027666, -1505368959426678025248000418, 2540816791339925247095200118, 32696278518001815852405408356, 1475160481394713565014293124, -932301424241458973089033254368, 2301619141096101839813550846721], [1, 0, 1106, 0, 588057, 0, 199446598, 0, 48280461356, 0, 8842976735556, 0, 1267446926365087, 0, 144990400379398868, 0, 13377759444102660759, 0, 998838868213678801652, 0, 60150903081897662038927, 0, 2891126115616059417808164, 0, 108741708076207950219399596, 0, 3094621629216088596089616502, 0, 62857417280773844837266047177, 0, 814419981222669953584128636674, 0, 5072820298953863752478356399681], [1, 0, 4, 0, 10610, 0, -307510, 0, -23884909, 0, -1439051407, 0, 120404885691, 0, 39552324252603, 0, 7282335141246355, 0, 313293960404868363, 0, 7554472355602173531, 0, -715181626010103432127, 0, -94025065394612885795629, 0, -9588690695663901119143510, 0, 2620568181827431308620357810, 0, 7825643946561765653376759364, 0, 15496731425178936435099327730561], [1, -28, 1286, -28048, 761097, -13824068, 283936306, -4458422660, 75799851020, -1051953765872, 15453031592924, -192095689823008, 2496107817288063, -28011310651778320, 326354731921222764, -3318512907126253500, 34927887494891105479, -321895751991246589500, 3070671672646784986476, -25565166926490474649360, 220978630362991587272703, -1649591050413301803233056, 12871942708189082849522396, -84996059632748134510359536, 594076298832916753520350220, -3389431378741302675920617220, 20938148254582118041853634994, -98883752367850336142914091204, 528081339426544875710554819977, -1887706382496404368130705066896, 8395474528143413922181988428934, -17731033295830102809211726728604, 61425365346268570446197767595521]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/567/2/e/g'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '32-567e16-1.1-c1e16-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '32-567e16-1.1-c1e16-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.1277964645629526, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e16-0', 'trace_hash': 1128853891659322367, 'z1': {'__RealLiteral__': 0, 'data': '0.02692397158543296147048926901', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '34130188740801886788700212259,869854715466114466508230506732,880904549432483298721535967969,896975176690344823916771777402,1075099520949293198146981506845,1552596227700637580622614665052,1610291640447675939637481317066,1772289676918710435264521011494,1871229787705308903168193207501,2060738638426483987427234125935,2087651353880796734615205128553,2323920609809933710762209894996,2542634665423618807386008213471,2891860290966885174691084588583,3119054871315492433553380819973,3328502514683524782501609271631', 'Lhash_array': ['34130188740801886788700212259', '869854715466114466508230506732', '880904549432483298721535967969', '896975176690344823916771777402', '1075099520949293198146981506845', '1552596227700637580622614665052', '1610291640447675939637481317066', '1772289676918710435264521011494', '1871229787705308903168193207501', '2060738638426483987427234125935', '2087651353880796734615205128553', '2323920609809933710762209894996', '2542634665423618807386008213471', '2891860290966885174691084588583', '3119054871315492433553380819973', '3328502514683524782501609271631'], 'factors': ['2-567-7.2-c1-0-0', '2-567-7.2-c1-0-4', '2-567-7.2-c1-0-5', '2-567-7.4-c1-0-3', '2-567-7.2-c1-0-9', '2-567-7.4-c1-0-8', '2-567-7.2-c1-0-14', '2-567-7.4-c1-0-10', '2-567-7.4-c1-0-12', '2-567-7.2-c1-0-18', '2-567-7.4-c1-0-17', '2-567-7.4-c1-0-19', '2-567-7.2-c1-0-22', '2-567-7.4-c1-0-23', '2-567-7.2-c1-0-25', '2-567-7.4-c1-0-26'], 'label': '32-567e16-1.1-c1e16-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/567/2/e/g'}