Lfunction data - 12-325e6-1.1-c5e6-0-0

Formats: - HTML - YAML - JSON - 2025-01-05T01:51:17.527687

• lfunc_lfunctions •

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

  
  {'Lhash': '166827921382442672072369091303,641465323682029133149675131387,877532569208157957839023914094,1494615567664465785238684503276,2215616346990914970926550324480,2501146588257245809977251586427', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 106, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 586, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 20056884899.17553, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[5, [1]], [13, [1, 0, 85683, 0, 2447192163, 0, 23298085122481]]], 'bad_primes': [5, 13], 'central_character': '325.1', 'coefficient_field': '1.1.1.1', 'conductor': 1178420166015625, 'conductor_radical': 65, 'degree': 12, 'euler_factors': [[1, 0, -106, 0, 6393, 0, -249500, 0, 6546432, 0, -111149056, 0, 1073741824], [1, 0, -586, 0, 265111, 0, -71295948, 0, 15654539439, 0, -2043255658986, 0, 205891132094649], [1], [1, 0, -34250, 0, 1157349791, 0, -19859968898444, 0, 326922670392822959, 0, -2732885120693211034250, 0, 22539340290692258087863249], [1, 1232, 1533018, 1108015792, 763270341223, 375622040193824, 174680409810547436, 60494305195255549024, 19797266925651104627023, 4628456938815632719960592, 1031337851731523280185298618, 133483577222544745555534869232, 17449402268886407318558803753801], [1, 0, 85683, 0, 2447192163, 0, 23298085122481], [1, 0, -5346778, 0, 14107385735535, 0, -24198875660122621868, 0, 28440403594119789431755215, 0, -21730543071972294516181387391578, 0, 8193465725814765556554001028792218849], [1, -6720, 31250826, -100911094976, 262745629662903, -545029703700931968, 948407997263357310924, -1349547504304173945032832, 1610910864410902117324056303, -1531944151554416560539232245824, 1174717719866387126503830242976426, -625474051025080921686016581084953280, 230466617897195215045509519405933293401], [1, 0, -17947666, 0, 177782686483887, 0, -1253587896647997806492, 0, 7364916455217389312852973663, 0, -30800991664745489930959534486550866, 0, 71094348791151363024389554286420996798449], [1, 4612, 131921418, 482045086052, 7042281580277959, 19961981960590772680, 195148564889431593430508, 409443186328989466464609320, 2962738799759707474458470569759, 4159658032394916927156228217543348, 23349375464163380915482048063156008618, 16743230114168916954646246295799613414388, 74462898441675122902293018227199467668020601], [1, 12760, 167910146, 1244683984008, 10450368214644415, 61240217726415691184, 392180300656518420143356, 1753255440562431511676104784, 8565417398087613561214146876415, 29206835781800741288454913092223608, 112800445775429313562701881511643743746, 245410432171524132339764126624278030782760, 550618520345910837374536871905139185678862401], [1, 0, -196213586, 0, 17914233453773591, 0, -1223984481650948142160988, 0, 86142103029660718643345693225759, 0, -4536945437462014600678303752414303678386, 0, 111186413610993811950185637819224232932533011049], [1, -16572, 489905298, -8010514375212, 130619696802950943, -1578862855768603860984, 20340377189916719427358396, -182921052369361378407538361784, 1753263689381413282944695856664143, -12457137407107673281308813371247758412, 88265151399264716481618828639270461215698, -345916551403803868286648532881000771081548572, 2418330769289520463963038742566759257517431737201], [1, 0, -639846330, 0, 198848638114826151, 0, -36858506514033930319814956, 0, 4297413825639225551941868481595599, 0, -298844174856232312504764112577452156866330, 0, 10093776109231555797740541116805209814919811290249], [1, 0, -1108811578, 0, 563976871326771567, 0, -165805033841770318627302380, 0, 29664694032866565986339077657416783, 0, -3067714300314185045442991215736929551118778, 0, 145524373433240498178471282244561013997462983607649], [1, 0, -424381554, 0, 113706106857181431, 0, -92370448163726687599165852, 0, 19885773393363177605857762390993119, 0, -12979976039754971180698565568602448391907154, 0, 5349042986438842598594824161669986924013455633256649], [1, 9504, 1548993978, 55121314533984, 1901220925433216967, 46576371046987319537088, 2159598359041497346262910892, 33298579420731305481941642901312, 971745866714666697150307031895850767, 20141867778803728598609074944453269219616, 404659706507307522493448932897605651396852378, 1775034173700782156809723550817383930796713126496, 133524312114275664899926313757566191470823300027804201], [1, 173788, 13987461770, 736131572343804, 31158192001037904775, 1165410926535887141321720, 37289516992468680224644505068, 984301757697193023313788962957720, 22226475404171517369644701041842319775, 443509544016141948004462200304016669599404, 7117633354659731069655004175281473442069065770, 74690550527093080427424806121656387186278246295788, 362990325539372200679554918670984996723331903112927801], [1, 0, 931485438, 0, 2776490132958986535, 0, 1498115174788945756272087236, 0, 5061091178322587256420622208123089215, 0, 3095081746170594583468360151295763467567350238, 0, 6056811824360306133893955506189170373758117309785601849], [1, 246504, 30535322994, 2586968736727800, 172299665606582864655, 9552551508405710682335184, 444066844817728055922846464860, 17234993808404906429083376192785584, 560877375306987900943386022113811850655, 15193800201293676375631330890159296711017800, 323570926591748552203005672034076395498111308594, 4712839925243251039429183800771620484016976418108504, 34494548241361273407325608100987789752280917290697963601], [1, 0, -6548382410, 0, 25607390713292226047, 0, -63691833893054242739842055180, 0, 110050983760755679891762079570603883503, 0, -120945923687001181337476118133334103580925734410, 0, 79375377473505188618758459764796980252025727125812230449], [1, -221392, 33948733178, -3588114028256496, 315773132652330229423, -22357126481480166296067104, 1366437433861442662975072893292, -68794139103090900692897410896598496, 2989827199428213037165478471127495395023, -104537619340134055832483499178679929622386704, 3043444586235974256400034082206349732347337056378, -61071587025539496032335215612978262091801503869122608, 848814400041653188432880077486808325583024422374372061601], [1, 0, -16170291778, 0, 125928700530667663815, 0, -610163173518072274815142114364, 0, 1953914904085151085694935617274090247935, 0, -3892957871604027876272947019463195052506012068578, 0, 3735448655171776399347824699993039078892536706537925477849], [1, -224420, 40008769650, -4716322634372980, 525034534510445293375, -46656918386908305111102920, 3904538532642753220214920378748, -260535005979637159052229255237491080, 16371479808664870020298149976041558943375, -821208822240117598829994057588674663759760020, 38900513039327957447702598068067060833385088249650, -1218461255679973467021774555407633036732716975788120580, 30317975617236256833580920126868226118402514553481681430801], [1, 0, -29962994618, 0, 403220134089351116879, 0, -3766810890872216526526746302828, 0, 29734425532729564646674796801536214781071, 0, -162937069704129744432198240224195346398029543941818, 0, 401007068543157803727680343536350900670553508041935397795649], [1, -60996, 29692547418, -3397818090368964, 585989035690082546679, -52206765074224452033479112, 8463190499319397335309329504524, -548698347762195715503519283804235112, 64729645407164115843014146869859114775679, -3944761318912939415712920581554410225676014964, 362305506201263191886449107239209354570052401583418, -7822322196807118149470350277908459499596075213940550996, 1347848915332905650585522351309777516867383425202804564353001], [1, 0, 1049208270, 0, 358305211697360122575, 0, 154417955968324373640910152740, 0, 48153224280444533736086173396865080406175, 0, 18949868439550596873479963552958004960996757376270, 0, 2427262471189660338642479878258204290900786637085454027093649], [1, 0, -48676959930, 0, 1071761881332419678247, 0, -16420384265097308172004842788140, 0, 210831783955428741295760064620261459287503, 0, -1883644755221833274135092075690446290942498367099930, 0, 7612255042662029206648128983778031607830320888857736765034249], [1, 608852, 242776674410, 66051411614605428, 14139194824003558370599, 2374987684587276522899271016, 328091598759884520803424160963756, 36542129440984691778831967849648611784, 3347261621432690826361219795752266238687199, 240591108243800810367854081594408586860720216772, 13606202082288085007617663213451386107044795872662410, 525017990624779757474264187243852060850320894013746574148, 13267678469131246220534960856572201266909465533192540861850201], [1, 0, -50557104538, 0, 1863498391425694772655, 0, -38999060455685902460893986615596, 0, 632577087070618204566908660091862885654095, 0, -5825739527216683969059554006700158000593023218630938, 0, 39115897957341730208009052194412390955771656152457329084502049]], 'euler_factors_factorization': [[[[1, 0, -106, 0, 6393, 0, -249500, 0, 6546432, 0, -111149056, 0, 1073741824], 1]], [[[1, 0, -586, 0, 265111, 0, -71295948, 0, 15654539439, 0, -2043255658986, 0, 205891132094649], 1]], [1], [[[1, 0, -34250, 0, 1157349791, 0, -19859968898444, 0, 326922670392822959, 0, -2732885120693211034250, 0, 22539340290692258087863249], 1]], [[[1, 616, 576781, 198710800, 92891156831, 15977453554216, 4177248169415651], 2]], [[[1, 0, 28561], 3]], [[[1, 0, -5346778, 0, 14107385735535, 0, -24198875660122621868, 0, 28440403594119789431755215, 0, -21730543071972294516181387391578, 0, 8193465725814765556554001028792218849], 1]], [[[1, -3360, 9980613, -16920687808, 24712985868687, -20600382626211360, 15181127029874798299], 2]], [[[1, 0, -17947666, 0, 177782686483887, 0, -1253587896647997806492, 0, 7364916455217389312852973663, 0, -30800991664745489930959534486550866, 0, 71094348791151363024389554286420996798449], 1]], [[[1, 2306, 63301891, 95048382380, 1298394518282759, 970150879990263506, 8629188747598184440949], 2]], [[[1, 6380, 63602873, 216555662264, 1820896255150823, 5229228470937510380, 23465261991844685929951], 2]], [[[1, 0, -196213586, 0, 17914233453773591, 0, -1223984481650948142160988, 0, 86142103029660718643345693225759, 0, -4536945437462014600678303752414303678386, 0, 111186413610993811950185637819224232932533011049], 1]], [[[1, -8286, 210623751, -2260028786820, 24402067631229951, -111220155043922794686, 1555098314991537910888601], 2]], [[[1, 0, -639846330, 0, 198848638114826151, 0, -36858506514033930319814956, 0, 4297413825639225551941868481595599, 0, -298844174856232312504764112577452156866330, 0, 10093776109231555797740541116805209814919811290249], 1]], [[[1, 0, -1108811578, 0, 563976871326771567, 0, -165805033841770318627302380, 0, 29664694032866565986339077657416783, 0, -3067714300314185045442991215736929551118778, 0, 145524373433240498178471282244561013997462983607649], 1]], [[[1, 0, -424381554, 0, 113706106857181431, 0, -92370448163726687599165852, 0, 19885773393363177605857762390993119, 0, -12979976039754971180698565568602448391907154, 0, 5349042986438842598594824161669986924013455633256649], 1]], [[[1, 4752, 763206237, 23933901228768, 545634683979652863, 2428826811684647937552, 365409786560616989860302899], 2]], [[[1, 86894, 3218447267, 88402029353204, 2718288656671759367, 61985218966034520731294, 602486784535040403801858901], 2]], [[[1, 0, 931485438, 0, 2776490132958986535, 0, 1498115174788945756272087236, 0, 5061091178322587256420622208123089215, 0, 3095081746170594583468360151295763467567350238, 0, 6056811824360306133893955506189170373758117309785601849], 1]], [[[1, 123252, 7672133745, 347878540025160, 13842288887526549495, 401215278149069877785652, 5873205959385493353867330551], 2]], [[[1, 0, -6548382410, 0, 25607390713292226047, 0, -63691833893054242739842055180, 0, 110050983760755679891762079570603883503, 0, -120945923687001181337476118133334103580925734410, 0, 79375377473505188618758459764796980252025727125812230449], 1]], [[[1, -110696, 10847564381, -593275027409072, 33378567392120524019, -1048100289242461477761896, 29134419507545592909032289199], 2]], [[[1, 0, -16170291778, 0, 125928700530667663815, 0, -610163173518072274815142114364, 0, 1953914904085151085694935617274090247935, 0, -3892957871604027876272947019463195052506012068578, 0, 3735448655171776399347824699993039078892536706537925477849], 1]], [[[1, -112210, 13708842775, -819892069403740, 76550993032594130975, -3498900793341505461868210, 174120577810999285787632895849], 2]], [[[1, 0, -29962994618, 0, 403220134089351116879, 0, -3766810890872216526526746302828, 0, 29734425532729564646674796801536214781071, 0, -162937069704129744432198240224195346398029543941818, 0, 401007068543157803727680343536350900670553508041935397795649], 1]], [[[1, -30498, 14381209707, -1260310911540396, 151147959346526763207, -3368876558079091514628498, 1160968955369998535166956051501], 2]], [[[1, 0, 1049208270, 0, 358305211697360122575, 0, 154417955968324373640910152740, 0, 48153224280444533736086173396865080406175, 0, 18949868439550596873479963552958004960996757376270, 0, 2427262471189660338642479878258204290900786637085454027093649], 1]], [[[1, 0, -48676959930, 0, 1071761881332419678247, 0, -16420384265097308172004842788140, 0, 210831783955428741295760064620261459287503, 0, -1883644755221833274135092075690446290942498367099930, 0, 7612255042662029206648128983778031607830320888857736765034249], 1]], [[[1, 304426, 75050742467, 10178308481043772, 1154748701927569227383, 72068705400137988108072826, 3642482459687520062956914986149], 2]], [[[1, 0, -50557104538, 0, 1863498391425694772655, 0, -38999060455685902460893986615596, 0, 632577087070618204566908660091862885654095, 0, -5825739527216683969059554006700158000593023218630938, 0, 39115897957341730208009052194412390955771656152457329084502049], 1]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 0, 'label': '12-325e6-1.1-c5e6-0-0', 'leading_term': '7.1708443679163334461685695785310545244509094332861609761861742276601949400067425602965002', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5, 5, 5, 5, 5, 5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/325/6/b/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.010416666666666666', 'prec': 67}, 'plot_values': [7.170844367916331, 7.112462489121586, 6.953251599854761, 6.6940301848939825, 6.33673967389592, 5.88450781619085, 5.341695804596212, 4.714082246696953, 4.00921866376971, 3.23569746056232, 2.4028458458515054, 1.5205929787853196, 0.5993324666609922, -0.35023084313883274, -1.3172151384381974, -2.290577845080983, -3.2592220484020547, -4.212128215215835, -5.138485856802079, -6.0278317327198, -6.870213489742129, -7.65630676945646, -8.377520820020411, -9.02609973328101, -9.595213153586466, -10.079033314071006, -10.472791276405934, -10.772829197958007, -10.976641265622757, -11.08289966062929, -11.091466212949122, -11.003391321194723, -10.820898752802183, -10.547342776908637, -10.187159200457502, -9.745805854524178, -9.229690756772609, -8.646086167223352, -8.003023501953722, -7.309192700954353, -6.573834295256307, -5.806623378405235, -5.017548553997227, -4.216782347095475, -3.414537380324594, -2.6209512410965097, -1.8459674454288428, -1.099214878850269, -0.3898913582606485, 0.27335356978037506, 0.8825407840503741, 1.430435791784028, 1.9106253377526508, 2.3175901079320314, 2.646766465568478, 2.894601417939756, 3.0586008363989263, 3.137330613674769, 3.130419464240637, 3.038554888076906, 2.8634666026988094, 2.607898264028714, 2.2755611108140044, 1.8710661808676428, 1.3998573269473171, 0.868137305328499, 0.28278552696214304, -0.34873740703745265, -1.0185117319912658, -1.7182566255044798, -2.4394303139154756, -3.173335729055723, -3.911226783595086, -4.644426834077591, -5.364478274724174, -6.063216382613531, -6.732851422650735, -7.366055671091672, -7.956043645574428, -8.4966628632206, -8.982516553459192, -9.408969025901328, -9.772168973698674, -10.069079501640896, -10.29749780376236, -10.456084847169338, -10.54442510742951, -10.56295084081031, -10.51289534765504, -10.396257332955809, -10.21575673859277, -9.974801791723646, -9.677482590316284, -9.3284390519552, -8.932766777567233, -8.49593926427738, -8.023727566617609, -7.522133194018576, -6.997343087740325, -6.455590860625572, -5.903059193157354, -5.34580199062357, -4.789670826732355, -4.240255567486978, -3.702841799091642, -3.1823153164546314, -2.683103430676702, -2.2091352996284654, -1.763810639664683, -1.3499808015239583, -0.9699405153724342, -0.6254020367655468, -0.31749506352598444, -0.04678024301593502, 0.18672958318969687, 0.3835406905494411, 0.5446457612333507, 0.671488214727477, 0.7659150105929846, 0.8301242658037766, 0.866609853868545, 0.878105156873492, 0.8675289084622402, 0.8379233305240614, 0.7923934228353452, 0.7340491630826187, 0.665950587056946, 0.5910576947550388, 0.5121865117869023, 0.43196238455144836, 0.35278163385782113, 0.27678068597795213, 0.20581172431719533, 0.14142551095680586, 0.08486115152658048, 0.037039070795282084, -0.001437248576582879, -0.03027247954598066, -0.04946472521606899, -0.05928542055417151, -0.06025486485087573, -0.05311341881981048, -0.03878858431505204, -0.018359376230967752, 0.006981102197838694, 0.0359638835661605, 0.06728223749226779, 0.09963010412188988, 0.1317387180574041, 0.1624107305990403, 0.19055127698378244, 0.2151953701393935, 0.23553125837417963, 0.2509192193344538, 0.2609050651992775, 0.2652283307587485, 0.2638250753834678, 0.2568254011617315, 0.24454590858199546, 0.2274765062080018, 0.20626264687282397, 0.18168342054735515, 0.15462596158472602, 0.12605680008433276, 0.09699074611464903, 0.0684580241205773, 0.04147076465567795, 0.0169895247539828, -0.00410938649104859, -0.02106506175811414, -0.03326090952217441, -0.040249840518474744, -0.04177580326004461, -0.03779103983387666, -0.028468474221165323, -0.01420878707200178, 0.004358401754973921, 0.026379056345175598, 0.050784714512225854, 0.07630811296896241, 0.10150428838356385, 0.12477713912597967, 0.14441133483107857, 0.15860644556098305, 0.1655147571250764, 0.16328206680314142, 0.1500904417177162, 0.12420218134578694, 0.08400313374929372, 0.028043455092612295, -0.04492228203890197, -0.13589723506362514, -0.2456077901396114, -0.3744746299178549, -0.5225943548902349, -0.6897210051878976, -0.8752530186309305, -1.0782273338946975, -1.2973201421530676, -1.5308591578763455, -1.7768566600215525, -2.0330249675507512, -2.2968011872854843, -2.5653813432191863, -2.8357598266026276, -3.104782896126654, -3.369229793477204, -3.625844456769268, -3.8713798068623815, -4.102650977484653, -4.316588580391561, -4.5103049767781025, -4.681189896222812, -4.826920884378233, -4.945490779246064, -5.035243230376775, -5.094902727799873, -5.123615240035266, -5.121015722237304, -5.0871865894705675, -5.022639907375798, -4.928308819345184, -4.805531915066993, -4.656047183278605, -4.482008606901416, -4.285893800643976, -4.070442953956962, -3.8386108311563176, -3.5935155655859656, -3.3383982818111755, -3.076601344991044, -2.8114620205267653, -2.5462421165979836, -2.284074691924626, -2.0279141567624, -1.7804988547058527, -1.544328540870687, -1.321593780454629, -1.1141390110073432, -0.9234429685383309, -0.7506067764509818, -0.5963533933277559, -0.46103714481146957, -0.34463663767541447, -0.24677086336619247, -0.1667270401902891, -0.10349445921727222, -0.055804182361340215, -0.022172129220555586, -0.0009406214722186702, 0.009671926217017951, 0.011519256371096574, 0.006476099521382102, -0.0036109722249780727, -0.016969053908251295, -0.03194262067163295, -0.04703271747998865, -0.06092988136333016, -0.07254024253454239, -0.08100418980328272, -0.08570761342589993, -0.08628647487528737, -0.08262262684022201, -0.07483168630966835, -0.06324369841047232, -0.04837746007753398, -0.030909698513255535, -0.01163852699715591, 0.008556779461982121, 0.02875812410824438, 0.04805175580030237, 0.06557071936566806, 0.08053526825590801, 0.09229095713495493, 0.10034152079408581, 0.10437554755656442, 0.10428604480178634, 0.10018205497261684, 0.09239187511882484, 0.08145695555489013, 0.06811613285045227, 0.05328052087734552, 0.03799944314900645, 0.023418125172382905, 0.010728114836811542, 0.001110962495346797, -0.004322834796226825, -0.004597974724365036, 0.0010601844635317538, 0.013160860920542404, 0.031885955448803925, 0.057032571937671, 0.08796245643653884, 0.12356037266141104, 0.16220326613291716, 0.201742240510489, 0.23949918354426036, 0.27227667055365723, 0.29638408360179685, 0.30768045980621506, 0.3016339904876301, 0.2733980548849403, 0.21790171030813327, 0.12995164796523156, 0.004348066102266547, -0.1639883551021964, -0.3798810099299709, -0.6477587305244585, -0.9715257484401115, -1.3544231664243078, -1.7988930159129473, -2.30645085886801, -2.877568911017778, -3.5115842313985697, -4.2066600009607535, -4.9597127507226375, -5.766367092165115, -6.6209428684309035, -7.5164684154265355, -8.444748457840081, -9.396534790591948, -10.361578412048598, -11.328733357825346, -12.286107685211379, -13.221237745818138, -14.121331619633157, -14.973647502860228, -15.765610289601765, -16.484998702684813, -17.12017906121352, -17.660338788001418, -18.095781905638265, -18.418359575730783, -18.621485323424412, -18.70023765202777, -18.651500630736443, -18.4740756480463, -18.168835485229998, -17.738985597753793, -17.18982564829025, -16.528619593982246, -15.764501893030907, -14.908345331387363, -13.97265756473863, -12.971549364860017, -11.920248165972293, -10.834745025483064, -9.73149170305763, -8.62708175614143, -7.537965156203656, -6.4802125931003545, -5.468991640338593, -4.518191787375419, -3.6401215429910105, -2.8452316024931177, -2.141888623905001, -1.536195611215597, -1.0317279086494386, -0.6294049598654747, -0.32744204371591684, -0.12135749263589206, -0.004038056804301577, 0.03414763053186908, 0.005190182753855734, -0.07680447877966598, -0.1959141614231819, -0.33474351088405807, -0.4748037984293042, -0.5969259852607324, -0.6817151516440064, -0.7100161276974498, -0.6633802246043063, -0.5245251667372872, -0.27778388611022675, 0.09045123743776036, 0.5913412074571562, 1.2332642594514718, 2.021532113707004, 2.9581678448144446, 4.0417408238954815, 5.267249444325177, 6.626140663363923, 8.10639760039631, 9.692695996790617, 11.366635808582695, 13.107039511968837, 14.890316597224468, 16.69092706918403, 18.481878679480868, 20.235258399845264, 21.922793501864444, 23.51644127967232, 24.989021969530373, 26.314794785437673, 27.470012077070226, 28.43344639983485, 29.186871933090575, 29.71551486214248, 30.008498488014936, 30.059063905127196, 29.864739063279984, 29.427441232218126, 28.75348702175701, 27.853537827854943, 26.742506930773995, 25.439193689619596, 23.96589077562986, 22.347942779615813, 20.613235449911144, 18.791645010742794, 16.91446546631559, 15.0136766323601, 13.121249809699087, 11.268472000083376, 9.485281201134338, 7.799631712725326, 6.236898952130362, 4.81930990928247, 3.56546750204948, 2.489960199727185, 1.6030591781700967, 0.9105083705652567, 0.41341549680867395, 0.10826825317391045, -0.01295163747649916, 0.03744412446600434, 0.2431603709718912, 0.5843251991332762, 1.0380050984536535, 1.5787711528179729, 2.1793119094253695, 2.8110919087203112, 3.4450401615791626, 4.052271665824971, 4.604851250944552, 5.076428997121742, 5.442857095675418, 5.682773394427857, 5.778123547318066, 5.714628664168166, 5.482188956179439, 5.075056379562948, 4.491958534279858, 3.7361438335202313, 2.8153251614604975, 1.7415189005245821, 0.5307348868180891, -0.7974426018561798, -2.2203056058799255, -3.7125356066604955, -5.246774031608682, -6.794282290252412, -8.325772435351265, -9.812021483967149, -11.224490738445377, -12.535957249215246, -13.72111298677006, -14.75720093485813, -15.624787187471663, -16.307979584397536, -16.794667546044305, -17.07674826873871, -17.150263119243885, -17.015536931465018, -16.677406365733635, -16.14476510611871, -15.430204470296006, -14.549672846738583, -13.522068494981024, -12.368851625379335, -11.113723258369706, -9.781774834636142, -8.398820478645634, -6.990814197565299, -5.583280609560492, -4.20080965160997, -2.8666180649640447, -1.601897169086438, -0.4253715954483572, 0.647019974976017, 1.6023670596971809, 2.4309464293696195, 3.12632468025618, 3.685411197171955, 4.1083666219627695, 4.398423832139156, 4.561640835671967, 4.606608420238611, 4.544144020448248, 4.386858122584645, 4.148700524178861, 3.8445053016376245, 3.489536029555483, 3.099056628488314, 2.68794532261543, 2.2702537285986932, 1.858844624506631, 1.465099096733282, 1.0986843367835828, 0.7673914254207729, 0.4770424845931413, 0.23142818371974935, 0.03233613708241046, -0.12035006876163401, -0.22849453850710894, -0.2955025286746821, -0.3260744373026223, -0.32592841592928745, -0.3014950245029543, -0.2596005329496229, -0.20715089428280234, -0.1508273858196019, -0.09680365379095017, -0.05049047981262194, -0.01632109005633253, 0.0024170764969645123, 0.0036997574683153315, -0.01317078600931272, -0.047558470725610244, -0.09754151578051352, -0.16001289138567304, -0.2308286987065005, -0.30499862678013606, -0.3769123622508223, -0.4405955978744339, -0.4899767500751572, -0.5191604828952855, -0.5226986034222493, -0.495847687384853, -0.4348043853544484, -0.33690678364593185, -0.20078927392346613, -0.026495151402458565, 0.18446008272075656, 0.4290788407962379, 0.7029315769194135, 1.0002795067330659, 1.3142244998634338, 1.6369046828093194, 1.959733701928087, 2.2736732841121445, 2.569544027667069, 2.838383450939523, 3.071729817791364, 3.2619141155266163, 3.402346748202649, 3.487777721575326, 3.5145372049186125, 3.480758421079522, 3.3864430508201107, 3.233504776991625, 3.0257706292823996, 2.7689216507377754, 2.4703815499914694, 2.139148403130841, 1.785506495254509, 1.4207300547711292, 1.0567613487420333, 0.7058593318137684, 0.38022450721227197, 0.09159442201400066, -0.14913926224463972, -0.3322809705653631, -0.44965461664146206, -0.4948904814223537, -0.46367552723463634, -0.35396279026107363, -0.16605356891556197, 0.09737128542817397, 0.43127766244758886, 0.828371195137234, 1.2792574533447176, 1.7726918673399055, 2.2958990123607665, 2.8349141429687976, 3.374957641029152, 3.900835838212625, 4.397381081430875, 4.849970488341779, 5.244914896736846, 5.56982760906889, 5.813974695052387, 5.9685814415683796, 6.0271266374174415, 5.9856689606150315, 5.8428671674234645, 5.599980323985088, 5.260832694300226, 4.831709169451619, 4.321223748603722, 3.740194075752513, 3.1012069868679717, 2.4182223399620715, 1.7061843494329296, 0.9806108885330044, 0.25719551566896254, -0.4485659653402471, -1.121895794709852, -1.7491498060641897, -2.318164631476438, -2.818556049776894, -3.241956050896693, -3.5821961469100945, -3.8354638500514926, -4.000347073052663, -4.077797558262515, -4.07102604781377, -3.9853377469170113, -3.827924106068411, -3.607581702107582, -3.334384776583173, -3.0193310186014255, -2.6739705060445322, -2.3100322456860964, -1.9390609738850488, -1.5720544440661146, -1.2191361722919105, -0.889271194957834, -0.5900303923151795, -0.32740873659424147, -0.10570038494491296, 0.07255693121776453, 0.20657525509915348, 0.2972491001526621, 0.3470302154698851, 0.3597511714154383, 0.3404041432054795, 0.2948748654219811, 0.22965629877455915, 0.15154848919862932, 0.06735378245235604, -0.016421923471373556, -0.0938514526389501, -0.15983737692466335, -0.21032565698393083, -0.24247602763271528, -0.25478289624016554, -0.24714158768784888, -0.2208537858708581, -0.1785786236823731, -0.12423302699912513, -0.06284200233868047, -0.0003436265267781423, 0.05664697670942681, 0.10110579843045123, 0.12586982265712698, 0.12392041267460188, 0.08867004042796907, 0.014240741024467292, -0.1042808651542148, -0.270646524793831, -0.48727208781204645, -0.7550949721038901, -1.0734781422958188, -1.4401622445962503, -1.851297105352887, -2.301617411442316, -2.784522764391208, -3.2922095548434793, -3.815860367686483, -4.345865019744529, -4.87212797383317, -5.384549721904359, -5.873171171306356, -6.328379331461307, -6.7411543149155735, -7.1032995459475705, -7.4077331069043915, -7.648930998824879, -7.822827574420337, -7.926810776648119, -7.959757390607586, -7.922029314955581, -7.81551658470626, -7.643798228544138, -7.411737675199791, -7.125229459697961, -6.7910137811059075, -6.416477856456218, -6.009513822552682, -5.5784710348698185, -5.131701148968659, -4.6772870409441225, -4.222863644288843, -3.7754632343421877, -3.34142338196272, -2.9263650766566753, -2.5349692997248106, -2.1709053440355564, -1.8368344139034534, -1.5344424536201688, -1.2645122555871247, -1.0270272306292818, -0.8212038562427445, -0.6455960440579429, -0.49822531681369125, -0.376713000823429, -0.2784126366637924, -0.20053560015293728, -0.14024672381903966, -0.09476403249932737, -0.061445982901478055, -0.03785995618996579, -0.02183185580868352, -0.01147670310377551, -0.005210534985212915, -0.0017488782489244942, -9.175018682478617e-05, 0.0005024780695193153, 0.0005512358207242004, 0.00038675482276774576, 0.00019680281539950095, 6.450656540914188e-05, 4.874780569076958e-06, -3.923869908382613e-06, 4.116987343789164e-06, 1.8419776110724713e-07, -2.945457596641995e-05, -8.05043110982664e-05, -0.00013363549092770518, -0.00016197454479377973, -0.00014134674995113267, -6.134611923557811e-05, 6.472486159011682e-05, 0.00019276983586063523, 0.0002451437353704357, 0.00011330266160912084, -0.0003335879768627839, -0.0012342529494010818, -0.002715925386296029, -0.004871169088956847, -0.007732734231028952, -0.011248746848521491, -0.015261260113704144, -0.01949231255128303, -0.023537401309486856, -0.02686975611218894, -0.028857747002307636, -0.02879659139944496, -0.025956243765363516, -0.019647031111815906, -0.009289220025591075, 0.0055081036017233746, 0.024862853112464955, 0.048536858163312005, 0.07585933712952071, 0.10566684419672209, 0.13627745952007841, 0.1654924464006109, 0.19063548445734826, 0.20863817615406977, 0.21618192513083231, 0.2099130406132016, 0.18670267975120736, 0.14396119255468673, 0.08000955960637372, -0.0054985893040518236, -0.11110337316440773, -0.2330172243880224, -0.36464903191237497, -0.496125432962549, -0.6138294493304268, -0.6999842156749371, -0.7323051718031343, -0.6837814923348997, -0.5226087192280547, -0.21223432127944594, 0.2884462277728679, 1.0247242050675018, 2.0454909102513326, 3.4023033437340406, 5.148429183232654, 7.3377231159325875, 10.023315269740323, 13.256154613635834, 17.083339173235327, 21.546094147281227, 26.67820154041388, 32.504371506535655, 39.03859516660701, 46.28259819760307, 54.22434500913003, 62.836547455629855, 72.07605842749832, 81.88341950821979, 92.18265882859419, 102.88146141053527, 113.8717341057422, 125.03071145251926, 136.222624302779, 147.30063938974905, 158.1091492209544, 168.48640238628124, 178.26762891154164, 187.28901640178813, 195.39084304036294, 202.42080564907678, 208.2374946747127, 212.71378244610935, 215.74043848431097, 217.23043942820897, 217.1206251722908, 215.37344637609993, 211.97856095824187, 206.95386911864298, 200.34640717362643, 192.23351601498814, 182.72050741693965, 171.93856006633544, 160.0424530263778, 147.20771865809473, 133.627607422517, 119.51010146609809, 105.07238343695602, 90.53593584652658, 76.12187238949588, 62.046239313474246, 48.51550756445924, 35.72230189349691, 23.840706825046993, 13.022509824484867, 3.394126706555456, -4.94586403270562, -11.92857540097719, -17.51610397558147, -21.70166609059219, -24.508986621325786, -25.990999060831097, -26.227843986573376, -25.324285463426325, -23.40657617275854, -20.618328861042986, -17.11629395879505, -13.065979925366763, -8.637138754871469, -3.999195785720451, 0.6834052781158279, 5.255429102015477, 9.574581831527476, 13.514803418989114, 16.969034190693304, 19.85150416445397, 22.09958463172467, 23.67418283245647, 24.55963878892619, 24.763081765385248, 24.313167190870807, 23.258308742098812, 21.664380658163594, 19.611440131877057, 17.190473327177074, 14.500047324190247, 11.64286429751938, 8.722261044339707, 5.8385473969266855, 3.0858169909478055, 0.5492325937777096, -1.6973142191443762, -3.5931019846791146, -5.092131156826391, -6.164452914041483, -6.796098369264368, -6.9886483174951355, -6.758446080846127, -6.135375988680324, -5.161362251249153, -3.8886400308308073, -2.3770477946127295, -0.691496561001145, 1.100483353182925, 2.9311618918629225, 4.734919371012766, 6.450505185534812, 8.023136886820383, 9.406070186812252, 10.561773227916307, 11.462719372235323, 12.09186082807824, 12.44290604453209, 12.519801244094761, 12.335886912025268, 11.912812900986559, 11.279214841488601, 10.469278759049134, 9.521295548267256, 8.475716461026943, 7.373380001472406, 6.253904306278102, 5.154230361680617, 4.107389030681158, 3.1415157914738043, 2.2789510258264474, 1.5357440890423788, 0.9214895155359374, 0.4394496928801639, 0.08694192546514053, -0.14405217214596389, -0.26607034843896343, -0.2951772711735117, -0.24987152873426702, -0.14994934743455898, -0.015381299975697413, 0.13474971044601006, 0.28321637885256745, 0.41544867882541875, 0.5201422643661284, 0.5896527339615547, 0.6201634996484129, 0.6116255679220346, 0.5674619748092409, 0.4940679485713715, 0.40013575925250566, 0.29583875153133904, 0.19191630217987077, 0.09870603518196192, 0.025181583175500618, -0.02195727237789917, -0.03909668403780327, -0.02637847909370171, 0.011812567732444589, 0.06658163082828017, 0.12448614139855686, 0.1677325774482484, 0.17461523494303774, 0.12018971012524936, -0.022838790500852715, -0.2830691515036698, -0.6892412683309697, -1.2689671054460414, -2.0474091934545506, -3.045957779259559, -4.281013265651361, -5.763094514209187, -7.495899411047521, -9.475545485028503, -11.690066505321203, -14.119161182344444, -16.73440230309335, -19.50030051510562, -22.374680269322678, -25.309408169853892, -28.25148312445462, -31.14431906242964, -33.929547896910556, -36.5498419053684, -38.949720035518745, -41.07675534096415, -42.883035409107364, -44.32652084897953, -45.37273328904823, -45.99725032193302, -46.18509905652299, -45.930684415941286, -45.23791418548032, -44.1200691420657, -42.59986400578942, -40.71002985977409, -38.4908737846659, -35.988643864888424, -33.25423012655436, -30.341779544143655, -27.30755356949524, -24.209156472474913, -21.102906687549282, -18.042164836808112, -15.076144522100533, -12.248897239363643, -9.59860614455944, -7.157156805157103, -4.949150578371098, -2.9916515682062648, -1.2943169573438227, 0.14026585174763392, 1.3160532164797585, 2.2429188598345253, 2.935954165547327, 3.414527033428877, 3.7012662691025415, 3.82103640247391, 3.7999604577797568, 3.6645456984035207, 3.440743786700404, 3.1531496238910277, 2.8243557187038095, 2.474452592657568, 2.1206919016494234, 1.7773098445654276, 1.4554077596727966, 1.163009797649235, 0.905252344891047, 0.6846685115878703, 0.5015468260961489, 0.35433788168832303, 0.2400720822895626, 0.15479253915370103, 0.09397115014701352, 0.052886249696407574, 0.02694731390361392, 0.011956324747765004, 0.004299865367740641, 0.0010688224947188582, 0.00010798753516014734, 1.459275681910339e-06, 2.7159170758894984e-06, -7.936671809489886e-05, -2.5427090929503224e-05, 0.0006327932870077048, 0.002448041933101936, 0.0059032393155897854, 0.011278940430703618, 0.01855282140570003, 0.027336435424971772, 0.03685282102680766, 0.0459560799322066, 0.05319097647814468, 0.05688818073919929, 0.05528601606797458, 0.04666601809737002, 0.02949746900782822, 0.002580131424712419, -0.03482547054677465, -0.08289453273799408, -0.14118499563709316, -0.20860571999340113, -0.28342215886870464, -0.36330542960746515, -0.44542147799235904, -0.5265723258619222, -0.6034115311161454, -0.6725970457037489, -0.7309625412632972, -0.775699276641866, -0.8045264396873391, -0.8158624485661652, -0.809009983315916, -0.7841564679580802, -0.7423636857738641, -0.6855303181190262, -0.6163058610383999, -0.537975651945423, -0.4543240747211976, -0.36934438758398974, -0.2869803735952247, -0.210882464162616, -0.14417053840915178, -0.08922109087253029, -0.04748296362440581, -0.019303287815615095, -0.0038463193756367365, 0.0009135843180985479, -0.0018696534197497451, -0.008043695529757085, -0.012653751594537436, -0.010209926709093025, 0.004992192955960997, 0.038517691865923846, 0.09542143819054309, 0.17987499060349835, 0.2948006097265224, 0.44155636822765193, 0.6196857160891589, 0.8267428603378044, 1.0582076771964553, 1.3074965239548475, 1.5660759489113176, 1.8237065233194547, 2.0687826939665213, 2.288760366989051, 2.4706603520360613, 2.6016343493897542, 2.669586634406128, 2.6637811058011414, 2.5754267953080006, 2.3982196914586917, 2.1288118048997386, 1.7671900411111667, 1.3169456004519244, 0.7853617591377708, 0.18336942489903693, -0.4746414273715615, -1.1711601707401278, -1.8860478286411841, -2.597198830532476, -3.281255211377961, -3.914397503525557, -4.473193740028524, -4.935467969290108, -5.28118526930917, -5.493348905272224, -5.558619985815356, -5.467871742085321, -5.216634991826351, -4.805385286653578, -4.239676480390386, -3.530094468406192, -2.6918730419164434, -1.744423737116646, -0.7107397068806488, 0.38333467716889164, 1.5099648618468917, 2.6403533689908247, 3.745705446876074, 4.7981601406622305, 5.77169576785531, 6.6429684368318815, 7.392105829498059, 8.003483342911707, 8.46601161085411, 8.773334206062142, 8.923906075285366, 8.92090291343317, 8.772006590863118, 8.489070768669917, 8.087364813162383, 7.584852090430709, 7.001449392635816, 6.358246186572144, 5.676709605145263, 4.977851981463364, 4.281447141519351, 3.6054122776891417, 2.965306168453916, 2.3739476246519224, 1.8411292044283418, 1.373387577068542, 0.9741277474444944, 0.6438403341510779, 0.38039471303544803, 0.1794182342062519, 0.03471006428920206, -0.0613391202079251, -0.11710558432771495, -0.14119473876670163, -0.14198124075953011, -0.12721079376472336, -0.10368873642453628, -0.07705527641987966, -0.05158628354656469, -0.030153178821984945, -0.014292281378709363, -0.004355918086225032, 0.00026971090257758054, 0.0009007653569227818, -0.000741504670696687, -0.0028451182503904274, -0.003804449622954047, -0.002478458352333099, 0.001606755353649264, 0.008122886936668499, 0.015884187097379127, 0.022880067653167042, 0.026391590579185175, 0.023183738619368538, 0.009761057652421194, -0.01732744772514018, -0.06115539550229353, -0.12408527497629641, -0.20745726282137042, -0.3113240245831723, -0.4342531902876693, -0.5732177049272169, -0.7235897727913103, -0.8792445556656523, -1.032775915605988, -1.175819933494807, -1.2994808429733364, -1.3948513863573395, -1.453556588126671, -1.4683280115612134, -1.4335776613363937, -1.345934136824095, -1.2047136059625219, -1.0122897361543282, -0.7742850535987648, -0.49962970284051267, -0.2004597684387843, 0.10816125426125604, 0.4087063039203488, 0.6818462035886945, 0.9072160417199372, 1.0642866373683018, 1.133322712963675, 1.096385796449264, 0.9383468158177468, 0.6478372040795516, 0.21800504370743273, -0.35283451414248534, -1.060712416942827, -1.895727852238079, -2.8420518317863435, -3.8783754994061876, -4.978426248072484, -6.1116844380273285, -7.244335964159117, -8.340409505920993, -9.363207778400817, -10.277230722739414, -11.049316405198674, -11.649863161221019, -12.054081286089183, -12.243106033598133, -12.205128590929009, -11.93669575949429, -11.442434348518075, -10.73482689297053, -9.833887060697753, -8.766541097216505, -7.565888741379898, -6.270396020935575, -4.921789988677809, -3.563278188582272, -2.2378856513691496, -0.9867860676656355, 0.15227072819183066, 1.1464748766388164, 1.9696089203588951, 2.6031201405013924, 3.0368051958779754, 3.269159298260724, 3.3074183759467704, 3.167372934783906, 2.87256069144949, 2.4531046502295686, 1.944312164942826, 1.3850687156195431, 0.8161259439651527, 0.2783333916392568, -0.18939577899247823, -0.5519038372485223, -0.779381490187407, -0.8487139148671237, -0.7445372854252914, -0.46002616579763467, 0.0027334745071027856, 0.6328373628313111, 1.411052199180541, 2.3106719388787225, 3.2986786680785567, 4.337131427837887, 5.384909187393975, 6.399565686071051, 7.339212929509326, 8.164368660086605, 8.839679917965825, 9.335439624892345, 9.628882912377797, 9.705152164420998, 9.557899211072348, 9.18950907014573, 8.610912711679356, 7.840931790776699, 6.905407547083558, 5.8360431346054416, 4.668994799280342, 3.4432942356854297, 2.1990885900795765, 0.9756517412883445, -0.19002898304589552, -1.2646159930863383, -2.2196593779618015, -3.0325849812701207, -3.6875148490284437, -4.175983067558562, -4.496538672456696, -4.654291361527072, -4.6603039035202825, -4.530742591093813, -4.285924289254748, -3.9493224956608275, -3.5458821048375184, -3.100646251402794, -2.637569683971316, -2.1784613748769055, -1.7421377597318397, -1.3437964013386114, -0.9944103646496264, -0.7005731018382222, -0.46464864581881793, -0.28515410107587297, -0.1573453252984291, -0.07395380365620696, -0.02602259939885977, -0.003829041501988918, 0.002208616761502377, 0.0007060687526410659, -0.0013785546091104066, 0.0007414917153418352, 0.009380701556340364, 0.024320571884761114, 0.04299081575840552, 0.06087942034085423, 0.07214723304623187, 0.07041433896061278, 0.049643312788950976, 0.00506076588443668, -0.06594764644715864, -0.16303824537329642, -0.2822706668992164, -0.4156995560166946, -0.5512678216058445, -0.6729977715816524, -0.7615002922696247, -0.7948030356383307, -0.7494871390596445, -0.6021122553116975, -0.3307701232668001, 0.0832651236601408, 0.6538674067413627, 1.3884708590157486, 2.2866690360175115, 3.3391739510151535, 4.527205070944148, 5.822304991099177, 7.1866643197591005, 8.573992909387021, 9.931039726503652, 11.199982169395023, 12.320890328097732, 13.234584973912078, 13.885839558036533, 14.226744271033722, 14.22026951931245, 13.84412841592324, 13.093288403113139, 11.982176438685464, 10.54640196183962, 8.843724666734214, 6.954303483352291, 4.980188803835205, 3.0428744970668107, 1.2802134053329701, -0.1574248847929396, -1.111812569917193, -1.4222012233716639, -0.9312861839490856, 0.5083706570655525, 3.028033911722265, 6.736687258287878, 11.715325663978746, 18.01194743441865, 25.63770564909269, 34.56394150706022, 44.72040902306977, 55.994865593180556, 68.23407090248804, 81.24675465152167, 94.80955695793214, 108.67146736527687, 122.55971763360432, 136.18701443599517, 149.2594917917928, 161.48637375903039, 172.59270447266806, 182.32465107962523, 190.4559960275688, 196.79503259457044, 201.190521150857, 203.53815713170982, 203.78883343952106, 201.9449989212432, 198.05875394172662, 192.23013941418742, 184.6039992188364, 175.3669744472563, 164.74543443582846, 152.99285456181593, 140.38046150640727, 127.1891645095351, 113.70138379011905, 100.193858771993, 86.93163370302638, 74.1571904389803, 62.08365252273314, 50.89020492863, 40.718773184368324, 31.672273740002577, 23.814234666819125, 17.168151839100315, 11.719582344184651, 7.419734525122999, 4.189982583297321, 1.9271316815453394, 0.50920439807963, -0.1985245238889239, -0.33723739377969164, -0.048509649798920154, 0.5312721757481667, 1.2758866435964498, 2.0736331985320193, 2.830514373538737, 3.4723621269202747, 3.9459391703833204, 4.219019798521614, 4.2795992722742, 4.134392718376895, 3.806081234674507, 3.330130988732052, 2.7513252754390165, 2.1201186014336146, 1.4890236292276788, 0.9091615005430218, 0.42690581284091805, 0.08117151397895227, -0.09865855900916565, -0.09415248011189367, 0.10142890887307002, 0.48304316073198356, 1.0344964837737813, 1.7296979465462388, 2.5344034783059466, 3.4083360733901236, 4.307557926191717, 5.186986947082676, 6.002897926618993, 6.715246378149592, 7.289715996495651, 7.699395284521644, 7.926019332820832, 7.96073239250009, 7.804260680233392, 7.466593697083363, 6.966197788971455, 6.328805783079145, 5.585842220517338, 4.772548868385686, 3.9260463379333927, 3.083351142258677, 2.2794395729716523, 1.5454664947723002, 0.9072050587416088, 0.38379556066406734, -0.012952003998886196, -0.27893536160695426, -0.4177586779395577, -0.44032875103025654, -0.364065104232271, -0.21172065950130983, -0.009980168230091003, 0.2120532468785058, 0.4244692045162755, 0.5981858100332722, 0.7065430751742366, 0.7267315793849093, 0.640855167174983, 0.4367883935885376, 0.10877165115326883, -0.34229728870891535, -0.9089603346093222, -1.5779077820765577, -2.3306537011363226, -3.1443810640772902, -3.992996053005187, -4.848303757837027, -5.681452850433197, -6.464913957079924, -7.173257965698722, -7.783982097543003, -8.278341790057866, -8.641998453071306, -8.865713692517085, -8.946317163993358, -8.885886117722693, -8.691162191532422, -8.37304451271187, -7.945946924611212, -7.42724220243213, -6.836911805858829, -6.195930315754478, -5.525185091419578, -4.844684366865705, -4.172869533041138, -3.5261379571465947, -2.9185785464232112, -2.361279645041303, -1.8621291555766097, -1.425877623795352, -1.0543335462840449, -0.7466869735017243, -0.49991505510100276, -0.3091211326042838, -0.16802255189499182, -0.06946653161548759, -0.005916436559466017, 0.03011337454575099, 0.04569509409289188, 0.0471989011075973, 0.04007889753414196, 0.028747857307812468, 0.016537100919456826, 0.005732167718798301, -0.0023294798945050093, -0.007117843218551616, -0.008736429131624826, -0.0077338127800711184, -0.004917529072339217, -0.0011841253913469274, 0.002623517457470143, 0.005822838603971026, 0.007958941244575107, 0.008831961789422327, 0.008487084171737732, 0.007172782239177862, 0.005274866147643293, 0.003235721981934538, 0.0014696633259572009, 0.0002835185454992274, -0.00018903152474803643, -3.22628986146673e-05, 0.0004327831226204448, 0.0006571936645366678, -0.00010052423547603311, -0.0027152394937827247, -0.008116680675185546, -0.017198113699643622, -0.030721052759382392, -0.04922368438673886, -0.07294059540394454, -0.10174142626974453, -0.1350946704917842, -0.17207905663649337, -0.21148813135265646, -0.2518782782559111, -0.29163641120739364, -0.32907156291354717, -0.36251259561080046, -0.39033356445613165, -0.41080546612296376, -0.42238675760600075, -0.4239314015298287, -0.4148196953415474, -0.3950608302840955, -0.3656646234796802, -0.32937737901001785, -0.2892192241116873, -0.24785620765288427, -0.20742882421447445], 'positive_zeros': ['0.13160402507789351749944687784295', '0.50602691590769484350880232678020', '0.69225113690646767743213188588494', '1.17904378966520690069092343914393', '1.41622499796912474082293003719070', '1.49729564351410859940226877167927', '1.74781311710972457969136815358699', '1.83107112656120550957677172220169', '1.97305676170305622553623191301834', '2.59439118495206476384264718432749', '2.63213673373330264577622190552470', '2.78728132722754434436462039182968', '2.97031795652319445311268804564728', '2.99868734844195749244487282668447', '3.16697511899316000262628465123079', '3.76098703836354212517163431540840', '3.78214763469832472882748376347023', '3.89358309487180517708316339659602', '4.41416057933997276156081313444423', '4.42326549095289092694903424622032', '4.65009716430432302613886380304400', '4.98317167694896253399841079879002', '5.23113297508819732677710988639808', '5.36248492467707382710155723170979', '5.37853881216288424252125835570109', '5.54307827789356718982146436673637', '5.83703545538146828027550499330169', '5.91314089536925104845374446175229', '6.20167149478335900954636946866859', '6.46419197231763001970302948202808', '6.57083384638764173341653711543456', '6.68755879985508062624401432222265', '6.75149923094796152809336867777427', '7.36556494460005664744165162751185', '7.42921783309942903585018455990939', '7.44263473023951420515527309468612', '7.45845076867573038457068387026647', '7.52621151723656881452324087281378', '7.56614132331726483778499188374421', '7.72565167751501040056209538205146', '7.87439955395656975289081220225781', '7.984132886096665421498958917169078', '8.556125996126927397198270932439730', '8.706805259074778708858391296260688', '8.919081058627703981566489061272891', '9.045738676594913244141566878022425', '9.326263076499379606515669277876125', '9.386512769192577315888347835040592', '9.536024327785707647445825287029915', '9.570244405500798458566399488830510', '9.634163226772909111833362091099976', '10.12389129293202384626023075800682', '10.43439538348392186585854557270142', '10.43666230240860933508718463174933', '10.44847047681204504476452141635742', '10.46965591068427910740718575785629', '10.61540972051220710732810171701225', '10.92260517958753307560318100737283', '10.93304022419773690427016114817369', '10.97673409997179872287533198323068'], 'prelabel': '12-325e6-1.1-c5e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.219746632619368, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5e6-0', 'trace_hash': 867434457435040404, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.13160402507789351749944687784', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.50602691590769484350880232678', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.69225113690646767743213188588', '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': 20056884899.17553, 'bad_primes': [5, 13], 'central_character': '1.1', 'conductor': 1178420166015625, 'conductor_radical': 65, 'degree': 12, 'dirichlet_coefficients': [1, 0, 0, 106, 0, 0, 0, 0, 586, 0, -1232, 0, 0, 0, 0, 4843, 0, 0, 6720, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4612, 0, -12760, 0, 0, 0, 0, 62116, 0, 0, 0, 0, 16572, 0, 0, -130592, 0, 0, 0, 0, 34250, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9504, 0, -173788, 0, 0, 85200, 0, 0, 0, 0, 0, 0, -246504, 0, 0, 0, 0, 712320, 0, 0, 221392, 0, 78285, 0, 0, 0, 0, 0, 0, 0, 224420, 0, 0, 0, 0, 0, 0, 0, 0, 0, -721952, 0], 'euler11': [1, 1232, 1533018, 1108015792, 763270341223, 375622040193824, 174680409810547436, 60494305195255549024, 19797266925651104627023, 4628456938815632719960592, 1031337851731523280185298618, 133483577222544745555534869232, 17449402268886407318558803753801], 'euler13': [1, 0, 85683, 0, 2447192163, 0, 23298085122481, 0, 0, 0, 0, 0, 0], 'euler17': [1, 0, -5346778, 0, 14107385735535, 0, -24198875660122621868, 0, 28440403594119789431755215, 0, -21730543071972294516181387391578, 0, 8193465725814765556554001028792218849], 'euler19': [1, -6720, 31250826, -100911094976, 262745629662903, -545029703700931968, 948407997263357310924, -1349547504304173945032832, 1610910864410902117324056303, -1531944151554416560539232245824, 1174717719866387126503830242976426, -625474051025080921686016581084953280, 230466617897195215045509519405933293401], 'euler2': [1, 0, -106, 0, 6393, 0, -249500, 0, 6546432, 0, -111149056, 0, 1073741824], 'euler23': [1, 0, -17947666, 0, 177782686483887, 0, -1253587896647997806492, 0, 7364916455217389312852973663, 0, -30800991664745489930959534486550866, 0, 71094348791151363024389554286420996798449], 'euler29': [1, 4612, 131921418, 482045086052, 7042281580277959, 19961981960590772680, 195148564889431593430508, 409443186328989466464609320, 2962738799759707474458470569759, 4159658032394916927156228217543348, 23349375464163380915482048063156008618, 16743230114168916954646246295799613414388, 74462898441675122902293018227199467668020601], 'euler3': [1, 0, -586, 0, 265111, 0, -71295948, 0, 15654539439, 0, -2043255658986, 0, 205891132094649], 'euler31': [1, 12760, 167910146, 1244683984008, 10450368214644415, 61240217726415691184, 392180300656518420143356, 1753255440562431511676104784, 8565417398087613561214146876415, 29206835781800741288454913092223608, 112800445775429313562701881511643743746, 245410432171524132339764126624278030782760, 550618520345910837374536871905139185678862401], 'euler37': [1, 0, -196213586, 0, 17914233453773591, 0, -1223984481650948142160988, 0, 86142103029660718643345693225759, 0, -4536945437462014600678303752414303678386, 0, 111186413610993811950185637819224232932533011049], 'euler41': [1, -16572, 489905298, -8010514375212, 130619696802950943, -1578862855768603860984, 20340377189916719427358396, -182921052369361378407538361784, 1753263689381413282944695856664143, -12457137407107673281308813371247758412, 88265151399264716481618828639270461215698, -345916551403803868286648532881000771081548572, 2418330769289520463963038742566759257517431737201], 'euler43': [1, 0, -639846330, 0, 198848638114826151, 0, -36858506514033930319814956, 0, 4297413825639225551941868481595599, 0, -298844174856232312504764112577452156866330, 0, 10093776109231555797740541116805209814919811290249], 'euler47': [1, 0, -1108811578, 0, 563976871326771567, 0, -165805033841770318627302380, 0, 29664694032866565986339077657416783, 0, -3067714300314185045442991215736929551118778, 0, 145524373433240498178471282244561013997462983607649], 'euler5': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, 0, -424381554, 0, 113706106857181431, 0, -92370448163726687599165852, 0, 19885773393363177605857762390993119, 0, -12979976039754971180698565568602448391907154, 0, 5349042986438842598594824161669986924013455633256649], 'euler59': [1, 9504, 1548993978, 55121314533984, 1901220925433216967, 46576371046987319537088, 2159598359041497346262910892, 33298579420731305481941642901312, 971745866714666697150307031895850767, 20141867778803728598609074944453269219616, 404659706507307522493448932897605651396852378, 1775034173700782156809723550817383930796713126496, 133524312114275664899926313757566191470823300027804201], 'euler61': [1, 173788, 13987461770, 736131572343804, 31158192001037904775, 1165410926535887141321720, 37289516992468680224644505068, 984301757697193023313788962957720, 22226475404171517369644701041842319775, 443509544016141948004462200304016669599404, 7117633354659731069655004175281473442069065770, 74690550527093080427424806121656387186278246295788, 362990325539372200679554918670984996723331903112927801], 'euler67': [1, 0, 931485438, 0, 2776490132958986535, 0, 1498115174788945756272087236, 0, 5061091178322587256420622208123089215, 0, 3095081746170594583468360151295763467567350238, 0, 6056811824360306133893955506189170373758117309785601849], 'euler7': [1, 0, -34250, 0, 1157349791, 0, -19859968898444, 0, 326922670392822959, 0, -2732885120693211034250, 0, 22539340290692258087863249], 'euler71': [1, 246504, 30535322994, 2586968736727800, 172299665606582864655, 9552551508405710682335184, 444066844817728055922846464860, 17234993808404906429083376192785584, 560877375306987900943386022113811850655, 15193800201293676375631330890159296711017800, 323570926591748552203005672034076395498111308594, 4712839925243251039429183800771620484016976418108504, 34494548241361273407325608100987789752280917290697963601], 'euler73': [1, 0, -6548382410, 0, 25607390713292226047, 0, -63691833893054242739842055180, 0, 110050983760755679891762079570603883503, 0, -120945923687001181337476118133334103580925734410, 0, 79375377473505188618758459764796980252025727125812230449], 'euler79': [1, -221392, 33948733178, -3588114028256496, 315773132652330229423, -22357126481480166296067104, 1366437433861442662975072893292, -68794139103090900692897410896598496, 2989827199428213037165478471127495395023, -104537619340134055832483499178679929622386704, 3043444586235974256400034082206349732347337056378, -61071587025539496032335215612978262091801503869122608, 848814400041653188432880077486808325583024422374372061601], 'euler83': [1, 0, -16170291778, 0, 125928700530667663815, 0, -610163173518072274815142114364, 0, 1953914904085151085694935617274090247935, 0, -3892957871604027876272947019463195052506012068578, 0, 3735448655171776399347824699993039078892536706537925477849], 'euler89': [1, -224420, 40008769650, -4716322634372980, 525034534510445293375, -46656918386908305111102920, 3904538532642753220214920378748, -260535005979637159052229255237491080, 16371479808664870020298149976041558943375, -821208822240117598829994057588674663759760020, 38900513039327957447702598068067060833385088249650, -1218461255679973467021774555407633036732716975788120580, 30317975617236256833580920126868226118402514553481681430801], 'euler97': [1, 0, -29962994618, 0, 403220134089351116879, 0, -3766810890872216526526746302828, 0, 29734425532729564646674796801536214781071, 0, -162937069704129744432198240224195346398029543941818, 0, 401007068543157803727680343536350900670553508041935397795649], 'euler_factors': [[1, 0, -106, 0, 6393, 0, -249500, 0, 6546432, 0, -111149056, 0, 1073741824], [1, 0, -586, 0, 265111, 0, -71295948, 0, 15654539439, 0, -2043255658986, 0, 205891132094649], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -34250, 0, 1157349791, 0, -19859968898444, 0, 326922670392822959, 0, -2732885120693211034250, 0, 22539340290692258087863249], [1, 1232, 1533018, 1108015792, 763270341223, 375622040193824, 174680409810547436, 60494305195255549024, 19797266925651104627023, 4628456938815632719960592, 1031337851731523280185298618, 133483577222544745555534869232, 17449402268886407318558803753801], [1, 0, 85683, 0, 2447192163, 0, 23298085122481, 0, 0, 0, 0, 0, 0], [1, 0, -5346778, 0, 14107385735535, 0, -24198875660122621868, 0, 28440403594119789431755215, 0, -21730543071972294516181387391578, 0, 8193465725814765556554001028792218849], [1, -6720, 31250826, -100911094976, 262745629662903, -545029703700931968, 948407997263357310924, -1349547504304173945032832, 1610910864410902117324056303, -1531944151554416560539232245824, 1174717719866387126503830242976426, -625474051025080921686016581084953280, 230466617897195215045509519405933293401], [1, 0, -17947666, 0, 177782686483887, 0, -1253587896647997806492, 0, 7364916455217389312852973663, 0, -30800991664745489930959534486550866, 0, 71094348791151363024389554286420996798449], [1, 4612, 131921418, 482045086052, 7042281580277959, 19961981960590772680, 195148564889431593430508, 409443186328989466464609320, 2962738799759707474458470569759, 4159658032394916927156228217543348, 23349375464163380915482048063156008618, 16743230114168916954646246295799613414388, 74462898441675122902293018227199467668020601], [1, 12760, 167910146, 1244683984008, 10450368214644415, 61240217726415691184, 392180300656518420143356, 1753255440562431511676104784, 8565417398087613561214146876415, 29206835781800741288454913092223608, 112800445775429313562701881511643743746, 245410432171524132339764126624278030782760, 550618520345910837374536871905139185678862401], [1, 0, -196213586, 0, 17914233453773591, 0, -1223984481650948142160988, 0, 86142103029660718643345693225759, 0, -4536945437462014600678303752414303678386, 0, 111186413610993811950185637819224232932533011049], [1, -16572, 489905298, -8010514375212, 130619696802950943, -1578862855768603860984, 20340377189916719427358396, -182921052369361378407538361784, 1753263689381413282944695856664143, -12457137407107673281308813371247758412, 88265151399264716481618828639270461215698, -345916551403803868286648532881000771081548572, 2418330769289520463963038742566759257517431737201], [1, 0, -639846330, 0, 198848638114826151, 0, -36858506514033930319814956, 0, 4297413825639225551941868481595599, 0, -298844174856232312504764112577452156866330, 0, 10093776109231555797740541116805209814919811290249], [1, 0, -1108811578, 0, 563976871326771567, 0, -165805033841770318627302380, 0, 29664694032866565986339077657416783, 0, -3067714300314185045442991215736929551118778, 0, 145524373433240498178471282244561013997462983607649], [1, 0, -424381554, 0, 113706106857181431, 0, -92370448163726687599165852, 0, 19885773393363177605857762390993119, 0, -12979976039754971180698565568602448391907154, 0, 5349042986438842598594824161669986924013455633256649], [1, 9504, 1548993978, 55121314533984, 1901220925433216967, 46576371046987319537088, 2159598359041497346262910892, 33298579420731305481941642901312, 971745866714666697150307031895850767, 20141867778803728598609074944453269219616, 404659706507307522493448932897605651396852378, 1775034173700782156809723550817383930796713126496, 133524312114275664899926313757566191470823300027804201], [1, 173788, 13987461770, 736131572343804, 31158192001037904775, 1165410926535887141321720, 37289516992468680224644505068, 984301757697193023313788962957720, 22226475404171517369644701041842319775, 443509544016141948004462200304016669599404, 7117633354659731069655004175281473442069065770, 74690550527093080427424806121656387186278246295788, 362990325539372200679554918670984996723331903112927801], [1, 0, 931485438, 0, 2776490132958986535, 0, 1498115174788945756272087236, 0, 5061091178322587256420622208123089215, 0, 3095081746170594583468360151295763467567350238, 0, 6056811824360306133893955506189170373758117309785601849], [1, 246504, 30535322994, 2586968736727800, 172299665606582864655, 9552551508405710682335184, 444066844817728055922846464860, 17234993808404906429083376192785584, 560877375306987900943386022113811850655, 15193800201293676375631330890159296711017800, 323570926591748552203005672034076395498111308594, 4712839925243251039429183800771620484016976418108504, 34494548241361273407325608100987789752280917290697963601], [1, 0, -6548382410, 0, 25607390713292226047, 0, -63691833893054242739842055180, 0, 110050983760755679891762079570603883503, 0, -120945923687001181337476118133334103580925734410, 0, 79375377473505188618758459764796980252025727125812230449], [1, -221392, 33948733178, -3588114028256496, 315773132652330229423, -22357126481480166296067104, 1366437433861442662975072893292, -68794139103090900692897410896598496, 2989827199428213037165478471127495395023, -104537619340134055832483499178679929622386704, 3043444586235974256400034082206349732347337056378, -61071587025539496032335215612978262091801503869122608, 848814400041653188432880077486808325583024422374372061601], [1, 0, -16170291778, 0, 125928700530667663815, 0, -610163173518072274815142114364, 0, 1953914904085151085694935617274090247935, 0, -3892957871604027876272947019463195052506012068578, 0, 3735448655171776399347824699993039078892536706537925477849], [1, -224420, 40008769650, -4716322634372980, 525034534510445293375, -46656918386908305111102920, 3904538532642753220214920378748, -260535005979637159052229255237491080, 16371479808664870020298149976041558943375, -821208822240117598829994057588674663759760020, 38900513039327957447702598068067060833385088249650, -1218461255679973467021774555407633036732716975788120580, 30317975617236256833580920126868226118402514553481681430801], [1, 0, -29962994618, 0, 403220134089351116879, 0, -3766810890872216526526746302828, 0, 29734425532729564646674796801536214781071, 0, -162937069704129744432198240224195346398029543941818, 0, 401007068543157803727680343536350900670553508041935397795649]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/325/6/b/d'], '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': '12-325e6-1.1-c5e6-0-0', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5, 5, 5, 5, 5, 5], 'order_of_vanishing': 0, 'prelabel': '12-325e6-1.1-c5e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.219746632619368, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5e6-0', 'trace_hash': 867434457435040404, 'z1': {'__RealLiteral__': 0, 'data': '0.13160402507789351749944687784', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '166827921382442672072369091303,641465323682029133149675131387,877532569208157957839023914094,1494615567664465785238684503276,2215616346990914970926550324480,2501146588257245809977251586427', 'Lhash_array': ['166827921382442672072369091303', '641465323682029133149675131387', '877532569208157957839023914094', '1494615567664465785238684503276', '2215616346990914970926550324480', '2501146588257245809977251586427'], 'label': '12-325e6-1.1-c5e6-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/325/6/b/d'}