-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1339302986308033688892944524169,2318973886116365061683168954537', 'a10': 40000000, 'a2': 256, 'a3': -1844, 'a4': 49152, 'a5': 156250, 'a6': -472064, 'a7': -984932, 'a8': 8388608, 'a9': -2190662, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 203.6143639770104, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '7.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -256, 16384]], [5, [1, -156250, 6103515625]]], 'bad_primes': [2, 5], 'central_character': '10.1', 'coefficient_field': '1.1.1.1', 'conductor': 100, 'conductor_radical': 10, 'degree': 4, 'euler_factors': [[1, -256, 16384], [1, 1844, 5590998, 26459384508, 205891132094649], [1, -156250, 6103515625], [1, 984932, 5451061620942, 4676025253111178876, 22539340290692258087863249], [1, -111552144, 8012222290532086, -465980989318391096205744, 17449402268886407318558803753801], [1, -289313596, 103772781935696718, -14808774772377875578032172, 2619995643649944960380551432833049], [1, -1421739348, 6225862099428528262, -4069619482953735921139922964, 8193465725814765556554001028792218849], [1, -6159406120, 39410443325042817798, -93506726736308255476626189880, 230466617897195215045509519405933293401], [1, 4330165884, -110893604430382042322, 1154574800080213868555696271588, 71094348791151363024389554286420996798449], [1, 164295941940, 14378922315721959469198, 1417740693464692625359568262501060, 74462898441675122902293018227199467668020601], [1, 282710965016, 46132800803772415026366, 6633886862067677481247884587594216, 550618520345910837374536871905139185678862401], [1, -790105159228, 738354877323120993260382, -263457616634051386638801478851563404, 111186413610993811950185637819224232932533011049], [1, 374717265276, 1942836306701256663750646, 582722187828944719049654749801518876, 2418330769289520463963038742566759257517431737201], [1, 923824433204, 6564997984212119216826918, 2935055229932521336549907313893449628, 10093776109231555797740541116805209814919811290249], [1, -4796717212428, 21879753149460807012252382, -57864470673894987744975128142753882804, 145524373433240498178471282244561013997462983607649], [1, 2768921292084, -8450722799243656501655522, 202511017107912887111184835775995849188, 5349042986438842598594824161669986924013455633256649], [1, 20737233989880, 458638788293084545621082998, 7577588246099622663115284590055100662120, 133524312114275664899926313757566191470823300027804201], [1, -577887725164, 970479592507275682166682126, -348169717356327514399884217293395084764, 362990325539372200679554918670984996723331903112927801], [1, -86553258077668, 6334155289139017871596250742, -213012682207512108953694140372980190139724, 6056811824360306133893955506189170373758117309785601849], [1, -73838906689464, 2819240503294930412702700526, -433671106803069335101594346757002397014664, 34494548241361273407325608100987789752280917290697963601], [1, -39973727021476, 12190632960617917120884352758, -356137367515663628462906877217920669068932, 79375377473505188618758459764796980252025727125812230449], [1, -421665304874800, 102094352521841419715212891998, -12284973883999532913048229247733698087285200, 848814400041653188432880077486808325583024422374372061601], [1, 721146660038964, 249448014272784276512084181238, 44075270067089610955702069724953552942375548, 3735448655171776399347824699993039078892536706537925477849], [1, -363712836623220, 249128072608318548772726423798, -63329889270112648731165429164700991115013780, 30317975617236256833580920126868226118402514553481681430801], [1, -289030099396948, 1180620298639861253894467877862, -183028654139441753815707540651440598330782164, 401007068543157803727680343536350900670553508041935397795649], [1, -173447027446524, 1727804743405189608917910174046, -201366614266622432746696701689397221467432524, 1347848915332905650585522351309777516867383425202804564353001], [1, 2829741424568204, 5011535724613460788552936928718, 4408644936882692121558391437328648490657467028, 2427262471189660338642479878258204290900786637085454027093649], [1, -3633609228600228, 8488075404698571101559943038982, -10025242468342342978692406022616368956184225004, 7612255042662029206648128983778031607830320888857736765034249], [1, -4378927451306860, 12075162363217609725981794567598, -15950166433629414653374995669640099808848682140, 13267678469131246220534960856572201266909465533192540861850201], [1, -190316489700036, 12164628625138439664299808022438, -1190290783918265455639215479052967635865173252, 39115897957341730208009052194412390955771656152457329084502049]], 'euler_factors_factorization': [[[[1, -128], 2]], [[[1, 1844, 5590998, 26459384508, 205891132094649], 1]], [[[1, -78125], 2]], [[[1, 984932, 5451061620942, 4676025253111178876, 22539340290692258087863249], 1]], [[[1, -111552144, 8012222290532086, -465980989318391096205744, 17449402268886407318558803753801], 1]], [[[1, -289313596, 103772781935696718, -14808774772377875578032172, 2619995643649944960380551432833049], 1]], [[[1, -1421739348, 6225862099428528262, -4069619482953735921139922964, 8193465725814765556554001028792218849], 1]], [[[1, -6159406120, 39410443325042817798, -93506726736308255476626189880, 230466617897195215045509519405933293401], 1]], [[[1, 4330165884, -110893604430382042322, 1154574800080213868555696271588, 71094348791151363024389554286420996798449], 1]], [[[1, 164295941940, 14378922315721959469198, 1417740693464692625359568262501060, 74462898441675122902293018227199467668020601], 1]], [[[1, 282710965016, 46132800803772415026366, 6633886862067677481247884587594216, 550618520345910837374536871905139185678862401], 1]], [[[1, -790105159228, 738354877323120993260382, -263457616634051386638801478851563404, 111186413610993811950185637819224232932533011049], 1]], [[[1, 374717265276, 1942836306701256663750646, 582722187828944719049654749801518876, 2418330769289520463963038742566759257517431737201], 1]], [[[1, 923824433204, 6564997984212119216826918, 2935055229932521336549907313893449628, 10093776109231555797740541116805209814919811290249], 1]], [[[1, -4796717212428, 21879753149460807012252382, -57864470673894987744975128142753882804, 145524373433240498178471282244561013997462983607649], 1]], [[[1, 2768921292084, -8450722799243656501655522, 202511017107912887111184835775995849188, 5349042986438842598594824161669986924013455633256649], 1]], [[[1, 20737233989880, 458638788293084545621082998, 7577588246099622663115284590055100662120, 133524312114275664899926313757566191470823300027804201], 1]], [[[1, -577887725164, 970479592507275682166682126, -348169717356327514399884217293395084764, 362990325539372200679554918670984996723331903112927801], 1]], [[[1, -86553258077668, 6334155289139017871596250742, -213012682207512108953694140372980190139724, 6056811824360306133893955506189170373758117309785601849], 1]], [[[1, -73838906689464, 2819240503294930412702700526, -433671106803069335101594346757002397014664, 34494548241361273407325608100987789752280917290697963601], 1]], [[[1, -39973727021476, 12190632960617917120884352758, -356137367515663628462906877217920669068932, 79375377473505188618758459764796980252025727125812230449], 1]], [[[1, -421665304874800, 102094352521841419715212891998, -12284973883999532913048229247733698087285200, 848814400041653188432880077486808325583024422374372061601], 1]], [[[1, 721146660038964, 249448014272784276512084181238, 44075270067089610955702069724953552942375548, 3735448655171776399347824699993039078892536706537925477849], 1]], [[[1, -363712836623220, 249128072608318548772726423798, -63329889270112648731165429164700991115013780, 30317975617236256833580920126868226118402514553481681430801], 1]], [[[1, -289030099396948, 1180620298639861253894467877862, -183028654139441753815707540651440598330782164, 401007068543157803727680343536350900670553508041935397795649], 1]], [[[1, -173447027446524, 1727804743405189608917910174046, -201366614266622432746696701689397221467432524, 1347848915332905650585522351309777516867383425202804564353001], 1]], [[[1, 2829741424568204, 5011535724613460788552936928718, 4408644936882692121558391437328648490657467028, 2427262471189660338642479878258204290900786637085454027093649], 1]], [[[1, -3633609228600228, 8488075404698571101559943038982, -10025242468342342978692406022616368956184225004, 7612255042662029206648128983778031607830320888857736765034249], 1]], [[[1, -4378927451306860, 12075162363217609725981794567598, -15950166433629414653374995669640099808848682140, 13267678469131246220534960856572201266909465533192540861850201], 1]], [[[1, -190316489700036, 12164628625138439664299808022438, -1190290783918265455639215479052967635865173252, 39115897957341730208009052194412390955771656152457329084502049], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 0, 'label': '4-10e2-1.1-c15e2-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 15, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [15, 15], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/10/16/a/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.087890625', 'prec': 37}, 'plot_values': [7.8021494277761665, 7.67785170285558, 7.442448751260678, 7.015501077930173, 6.423194716851253, 5.713208031653461, 4.912943602992551, 4.049251468402761, 3.1580445385410134, 2.2760336408862623, 1.4375709350716375, 0.6738764665699927, 0.012555414072298784, -0.5242879100370763, -0.9208808841621768, -1.1684731521852554, -1.2655677165164088, -1.2178831265771854, -1.0379260449956333, -0.7442529905772355, -0.3603355722763009, 0.08659560914074381, 0.5672816526934151, 1.0516635991245962, 1.5109645194400116, 1.9186227143807628, 2.25239937610366, 2.4947052972712846, 2.634390989144996, 2.6662789849948463, 2.5923525066407813, 2.4204746017065264, 2.164817714263791, 1.8439325793380252, 1.4804312418385484, 1.0987230289475067, 0.7241412344833628, 0.3807531546589814, 0.09026386920065857, -0.12969419791809295, -0.2664765591396755, -0.3133523746120636, -0.2698619637831289, -0.14183577038968506, 0.059055680751029856, 0.3160840120943074, 0.608766676940899, 0.914127533690184, 1.2086669823310252, 1.4696297889023737, 1.6772531904296, 1.8155392944519957, 1.874284341670938, 1.8489596816715594, 1.7420527978206177, 1.5618911441290537, 1.3229975933675058, 1.0439928618970913, 0.7469513083889879, 0.4548093481985087, 0.19002912853809667, -0.027867502616089345, -0.18375653398561212, -0.26861254750403374, -0.280405158406614, -0.22457627616758943, -0.11379387872591325, 0.032899322696283706, 0.19174296722013948, 0.33610974485638484, 0.43938615329319936, 0.47710949485266946, 0.43041930793349814, 0.28757059483587766, 0.04698604060263799, -0.28267918245724666, -0.6808846612161366, -1.117030738685801, -1.5508856362175005, -1.9361521149049488, -2.223031812822293, -2.362755562303428, -2.3115784373454757, -2.035054509578276, -1.5120937096056357, -0.7376955289586542, 0.27461188196389213, 1.492466157175666, 2.865318437743032, 4.326645436997772, 5.798408869912727, 7.194901852424589, 8.430644227485468, 9.424160476345888, 10.107812351991935, 10.429467746889074, 10.362021567832155, 9.901264007314964, 9.0727793640212, 7.925339904802628, 6.533608427702611, 4.987798316919127, 3.3919654707812064, 1.85202238952571, 0.4709585034934504, -0.66193121206786, -1.4763682044545259, -1.9279492504520626, -2.0011375048022084, -1.7106596303873784, -1.1000046328048994, -0.23762157850223012, 0.7896495537822306, 1.8834623712455012, 2.944265587870403, 3.877961320301933, 4.607098322797951, 5.073986377540017, 5.249476629483204, 5.13048241627387, 4.74388058198405, 4.138519596149163, 3.383655262115199, 2.557713492814271, 1.7428702924447723, 1.014182763584319, 0.4335202226602257, 0.042572971467229374, -0.1403836007006411, -0.12167813050260703, 0.06960063440303071, 0.385689142765602, 0.7670532248948843, 1.1489418161882932, 1.4710164513741504, 1.6824926209543936, 1.7508646887997363, 1.6624255166572997, 1.4268394974767549, 1.0720103762198787, 0.6432094025540516, 0.1939801144168904, -0.2188251519344248, -0.5444446839409093, -0.7438528688686404, -0.7955852037612637, -0.6982616614660158, -0.4706820263001142, -0.14898739233683408, 0.21824154500566542, 0.5776021198581437, 0.8774136690535284, 1.0768711625856855, 1.149912180395346, 1.0916161844605141, 0.9163834282485714, 0.6585580065052193, 0.36492769276838255, 0.08962892836921478, -0.11583292478044246, -0.21000512185684606, -0.1691563110002928, 0.008096103738517836, 0.2991729433726616, 0.6597993163449388, 1.0288639076604942, 1.3382001331639886, 1.5204196476682217, 1.5226305181195632, 1.311463568962555, 0.8845743433627513, 0.267949865036366, -0.4802337856091708, -1.2810572813960674, -2.040099734856872, -2.6637038404904656, -3.069511596462754, -3.2003592022996505, -3.032708512797795, -2.5815659379987146, -1.8998091568034077, -1.0720678049704593, -0.20256782250978803, 0.597800475776906, 1.23091020150311, 1.6224088011861344, 1.7393729256469928, 1.5908259236838738, 1.234620953768429, 0.7641653756318285, 0.30103996294118657, -0.02756040553667027, -0.10563773447282168, 0.1502114039028919, 0.7758650032280513, 1.7501488642687424, 2.993603124177358, 4.375318475473849, 5.730743821820701, 6.879707254228623, 7.658232936886529, 7.9349158557058495, 7.643208471480341, 6.782539909942645, 5.436154589455195, 3.7506735532739772, 1.9318266367810641, 0.20797873784220897, -1.1915422459566967, -2.073749138869398, -2.305821236340512, -1.836482175078423, -0.7043842104529419, 0.9650235971834956, 2.9763503134627336, 5.086758725054909, 7.043951469956546, 8.611434015428216, 9.611463902082876, 9.934285489841646, 9.5669034426889, 8.57630312260823, 7.113066294377934, 5.373547773670522, 3.581959400768004, 1.9487499737570957, 0.647082622769587, -0.21322497770015714, -0.5964172861049418, -0.541403684087285, -0.15005868497026278, 0.4322693738865934, 1.0460172607970226, 1.5400532444334083, 1.8027407247172658, 1.7701145243119305, 1.4425676421947056, 0.8713701779176034, 0.15484851585456297, -0.5893556264182365, -1.2411486591823309, -1.7034987208595551, -1.916970305379957, -1.8688031997225991, -1.592761294526284, -1.1593349565355235, -0.6600677651618816, -0.18932581005995588, 0.1761127611542019, 0.3883040465196688, 0.43922110676282156, 0.3558470755541057, 0.19528101157014174, 0.02716085389418507, -0.08131815709095905, -0.08262208908403987, 0.04007239097244277, 0.26826762714270963, 0.5523642133585803, 0.8213621483023172, 1.001925628131731, 1.0319199629337306, 0.8819705258373509, 0.5582546048931734, 0.11160686309446483, -0.3772940145818885, -0.8068312821449732, -1.0796938404297116, -1.1207322991021649, -0.8961042502067688, -0.42263899626055684, 0.2322476050475615, 0.9619053207711166, 1.6383468466561577, 2.140767014250867, 2.3749544845673984, 2.3010117282401352, 1.9349148234202709, 1.3563883228715303, 0.685718070552704, 0.06728403626040624, -0.3658230400739114, -0.5172109246059676, -0.35096493310043453, 0.09882164094711696, 0.732597652637503, 1.406418177558258, 1.9598617286378042, 2.258685221416881, 2.2209157923033858, 1.8525878243682286, 1.2447708004452935, 0.5752454269635772, 0.06922115052753124, -0.03613592968249161, 0.4538646962374777, 1.6461882263313667, 3.5264117424729604, 5.944459767729526, 8.625097511624428, 11.208983231572818, 13.297574871801306, 14.536794043830655, 14.656771302227513, 13.553958823255764, 11.28348920473615, 8.09398406470296, 4.359822735717953, 0.5545565785216197, -2.847480935086453, -5.430001980139828, -6.910513184147414, -7.179042542557212, -6.311408568004485, -4.550181215476784, -2.25819133346277, 0.15366076559773692, 2.2888872951382426, 3.8476460199813234, 4.652266437509438, 4.690516379452039, 4.080661803555035, 3.0573944868789797, 1.8984328662243612, 0.8777324123537436, 0.20256658842099148, -0.019360919644987845, 0.20510410695723233, 0.767020602085471, 1.4863656872350286, 2.1625659166136333, 2.614364934342162, 2.7309579739795957, 2.480328706498181, 1.925822225913608, 1.1922581523596705, 0.44403964270910923, -0.16500783382473247, -0.5232910112730088, -0.5891960333432245, -0.3977688406834598, -0.048278256293498, 0.32394730998142107, 0.5825422907373659, 0.629931973792576, 0.4287040609502312, 0.0184432489331331, -0.4987866447381024, -0.9786945149313709, -1.2739792085965402, -1.27142085724812, -0.922211249061958, -0.25850095392235084, 0.6096884268848883, 1.5197917445082239, 2.2854133079698173, 2.749337468281842, 2.8041859379473792, 2.435492293618362, 1.7055501064602356, 0.7586643813499123, -0.2283653951170084, -1.0726163147716417, -1.6339533219867106, -1.8394422756274, -1.697060711382586, -1.2888964548066364, -0.7456098976980406, -0.2107863838940379, 0.19381715263312263, 0.4016329194342878, 0.40906623460036995, 0.2773452381638143, 0.10469016030741464, -0.0013082351046460263, 0.03932793797799086, 0.2543229044397539, 0.6081871885048079, 1.0118281988743973, 1.3459269985738644, 1.5024498870141485, 1.4139166527924618, 1.0903030130962204, 0.6161044872584389, 0.1466139626413173, -0.13574918723225401, -0.06329419047374137, 0.46590926643947533, 1.4521223882137384, 2.7810056730065886, 4.2403455674402215, 5.556666002665707, 6.467142315957972, 6.765883004459303, 6.380806339486005, 5.371093734448868, 3.948679230831145, 2.405981015223655, 1.069423326540363, 0.20089730057552882, -0.06344956729698613, 0.23686818952332503, 0.8857676666658897, 1.5279141989703742, 1.7546147982081812, 1.189610039257816, -0.3920209829129302, -3.017959213183204, -6.459505291356015, -10.286383062778242, -13.916623090744258, -16.746961831112152, -18.26734483430517, -18.17243237101799, -16.434004102194177, -13.311224521674788, -9.301646762902816, -5.055300300407707, -1.2222769869932268, 1.637411500068197, 3.208003411100134, 3.412682933580566, 2.4709040133492, 0.7785802895004883, -1.144033011885695, -2.807408161594555, -3.8356965699421726, -4.0490827712332305, -3.4831703255026807, -2.355761643724427, -0.997730097499335, 0.24030448593545245, 1.084174037149762, 1.3913181847973681, 1.190092518778791, 0.6458274629717181, 0.018001991887903482, -0.425862155618485, -0.48059472247158747, -0.06047571002126145, 0.7808665263096517, 1.8662944012278775, 2.9513128253730563, 3.7801830635532867, 4.169889915420256, 4.0353629273227165, 3.4306592418695687, 2.5072042532593644, 1.4891581310683542, 0.5978721069832033, 0.004359813895681006, -0.21483454807007138, -0.08766986394350552, 0.27037456835477497, 0.6991167699686679, 1.038482057949363, 1.1826520516658794, 1.095218635813246, 0.8245154984958522, 0.4690548159513599, 0.14966749090251466, -0.038860998426009936, -0.055517669592202175, 0.07401067284738394, 0.2697777238752549, 0.4269713454992231, 0.4590297265134497, 0.3269253164003431, 0.06481514758031537, -0.23316571190098487, -0.4348387925717471, -0.41783812113600716, -0.1127239715009903, 0.465695790922207, 1.2111664594673752, 1.9469457143758313, 2.477403117398962, 2.636211488361842, 2.3539114791676434, 1.6699198126276844, 0.7494814112601931, -0.1718597342888391, -0.8377056342798332, -1.051929160123347, -0.7348052684509014, 0.04645157051459956, 1.0911461435664176, 2.112181354876752, 2.8272984913991963, 3.0244133057481886, 2.6534673866180563, 1.8208997210009004, 0.7964747119514134, -0.08492814052630442, -0.5006748173339668, -0.25288480283717524, 0.6662704552926351, 2.0511881811801977, 3.5254397226879237, 4.624743953710643, 4.936907612801568, 4.194085833990312, 2.3947014787485092, -0.2159010156567042, -3.153943849958911, -5.833225392886361, -7.680306707262519, -8.3046619340049, -7.585361383356689, -5.672208666579941, -3.0445089501740843, -0.36869061929943236], 'positive_zeros': ['1.05652376614415983558783477406535', '1.82934783898564328314299555812443', '3.37231254108050711152341656899732', '3.84406424235310651912738150050598', '5.34866802695151667810779327678542', '5.87007184809743479809345747409827', '6.51792103893196097256117846195459', '7.53656591567008018063511862389040', '9.174544246965007758659248960165670', '9.777170891710757936159813134058858', '11.17589325978277518626815501111286', '11.40073356157614210382640980135000', '12.43223860759449504643554059911549', '13.04406072003805975213607098352551', '13.92042686494785765624038293957279', '14.23529056334680800000275933122524', '15.06216042430586010407602211658455', '16.01719778423616035572737560115771', '16.77683200436030348164112878374799', '16.92643205475262515583626570642751'], 'prelabel': '4-10e2-1.1-c15e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.7774793857798947, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c15e2-0', 'trace_hash': 2189003928865665278, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.05652376614415983558783477407', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.82934783898564328314299555812', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.37231254108050711152341656900', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 203.6143639770104, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 100, 'conductor_radical': 10, 'degree': 4, 'dirichlet_coefficients': [1, 256, -1844, 49152, 156250, -472064, -984932, 8388608, -2190662, 40000000, 111552144, -90636288, 289313596, -252142592, -288125000, 1342177280, 1421739348, -560809472, 6159406120, 7680000000, 1816214608, 28557348864, -4330165884, -15468593152, 18310546875, 74064280576, -12110003468, -48411377664, -164295941940, -73760000000, -282710965016, 206158430208, -205702153536, 363965273088, -153895625000, -107675418624, 790105159228, 1576807966720, -533494271024, 1310720000000, -374717265276, 464950939648, -923824433204, 5483010981888, -342290937500, -1108522466304, 4796717212428, -2474974904320, -4480970576318, 4687500000000, -2621687357712, 14220341870592, -2768921292084, -3100160887808, 17430022500000, -8262208454656, -11357944885280, -42059761136640, -20737233989880, -14161920000000, 577887725164, -72374007044096, 2157653104984, 30786325577728, 45205249375000, -52659751305216, 86553258077668, 69881332432896, 7984825890096, -39397280000000, 73838906689464, -18376604778496, 39973727021476, 202266920762368, -33764648437500, 302747129610240, -109871276294208, -136574533382144, 421665304874800, 209715200000000, -122521193806229, -95927619910656, -721146660038964, 89270580412416, 222146773125000, -236499054900224, 302961716937360, 935767207575552, 363712836623220, -87626480000000, -284954218735472, -212836313530368, 521319019489504, 1227959606381568, 962407206250000, -380156145303552, 289030099396948, -1147128467537408, -244373042879328, 900000000000000], 'euler11': [1, -111552144, 8012222290532086, -465980989318391096205744, 17449402268886407318558803753801], 'euler13': [1, -289313596, 103772781935696718, -14808774772377875578032172, 2619995643649944960380551432833049], 'euler17': [1, -1421739348, 6225862099428528262, -4069619482953735921139922964, 8193465725814765556554001028792218849], 'euler19': [1, -6159406120, 39410443325042817798, -93506726736308255476626189880, 230466617897195215045509519405933293401], 'euler2': [1, -256, 16384, 0, 0], 'euler23': [1, 4330165884, -110893604430382042322, 1154574800080213868555696271588, 71094348791151363024389554286420996798449], 'euler29': [1, 164295941940, 14378922315721959469198, 1417740693464692625359568262501060, 74462898441675122902293018227199467668020601], 'euler3': [1, 1844, 5590998, 26459384508, 205891132094649], 'euler31': [1, 282710965016, 46132800803772415026366, 6633886862067677481247884587594216, 550618520345910837374536871905139185678862401], 'euler37': [1, -790105159228, 738354877323120993260382, -263457616634051386638801478851563404, 111186413610993811950185637819224232932533011049], 'euler41': [1, 374717265276, 1942836306701256663750646, 582722187828944719049654749801518876, 2418330769289520463963038742566759257517431737201], 'euler43': [1, 923824433204, 6564997984212119216826918, 2935055229932521336549907313893449628, 10093776109231555797740541116805209814919811290249], 'euler47': [1, -4796717212428, 21879753149460807012252382, -57864470673894987744975128142753882804, 145524373433240498178471282244561013997462983607649], 'euler5': [1, -156250, 6103515625, 0, 0], 'euler53': [1, 2768921292084, -8450722799243656501655522, 202511017107912887111184835775995849188, 5349042986438842598594824161669986924013455633256649], 'euler59': [1, 20737233989880, 458638788293084545621082998, 7577588246099622663115284590055100662120, 133524312114275664899926313757566191470823300027804201], 'euler61': [1, -577887725164, 970479592507275682166682126, -348169717356327514399884217293395084764, 362990325539372200679554918670984996723331903112927801], 'euler67': [1, -86553258077668, 6334155289139017871596250742, -213012682207512108953694140372980190139724, 6056811824360306133893955506189170373758117309785601849], 'euler7': [1, 984932, 5451061620942, 4676025253111178876, 22539340290692258087863249], 'euler71': [1, -73838906689464, 2819240503294930412702700526, -433671106803069335101594346757002397014664, 34494548241361273407325608100987789752280917290697963601], 'euler73': [1, -39973727021476, 12190632960617917120884352758, -356137367515663628462906877217920669068932, 79375377473505188618758459764796980252025727125812230449], 'euler79': [1, -421665304874800, 102094352521841419715212891998, -12284973883999532913048229247733698087285200, 848814400041653188432880077486808325583024422374372061601], 'euler83': [1, 721146660038964, 249448014272784276512084181238, 44075270067089610955702069724953552942375548, 3735448655171776399347824699993039078892536706537925477849], 'euler89': [1, -363712836623220, 249128072608318548772726423798, -63329889270112648731165429164700991115013780, 30317975617236256833580920126868226118402514553481681430801], 'euler97': [1, -289030099396948, 1180620298639861253894467877862, -183028654139441753815707540651440598330782164, 401007068543157803727680343536350900670553508041935397795649], 'euler_factors': [[1, -256, 16384, 0, 0], [1, 1844, 5590998, 26459384508, 205891132094649], [1, -156250, 6103515625, 0, 0], [1, 984932, 5451061620942, 4676025253111178876, 22539340290692258087863249], [1, -111552144, 8012222290532086, -465980989318391096205744, 17449402268886407318558803753801], [1, -289313596, 103772781935696718, -14808774772377875578032172, 2619995643649944960380551432833049], [1, -1421739348, 6225862099428528262, -4069619482953735921139922964, 8193465725814765556554001028792218849], [1, -6159406120, 39410443325042817798, -93506726736308255476626189880, 230466617897195215045509519405933293401], [1, 4330165884, -110893604430382042322, 1154574800080213868555696271588, 71094348791151363024389554286420996798449], [1, 164295941940, 14378922315721959469198, 1417740693464692625359568262501060, 74462898441675122902293018227199467668020601], [1, 282710965016, 46132800803772415026366, 6633886862067677481247884587594216, 550618520345910837374536871905139185678862401], [1, -790105159228, 738354877323120993260382, -263457616634051386638801478851563404, 111186413610993811950185637819224232932533011049], [1, 374717265276, 1942836306701256663750646, 582722187828944719049654749801518876, 2418330769289520463963038742566759257517431737201], [1, 923824433204, 6564997984212119216826918, 2935055229932521336549907313893449628, 10093776109231555797740541116805209814919811290249], [1, -4796717212428, 21879753149460807012252382, -57864470673894987744975128142753882804, 145524373433240498178471282244561013997462983607649], [1, 2768921292084, -8450722799243656501655522, 202511017107912887111184835775995849188, 5349042986438842598594824161669986924013455633256649], [1, 20737233989880, 458638788293084545621082998, 7577588246099622663115284590055100662120, 133524312114275664899926313757566191470823300027804201], [1, -577887725164, 970479592507275682166682126, -348169717356327514399884217293395084764, 362990325539372200679554918670984996723331903112927801], [1, -86553258077668, 6334155289139017871596250742, -213012682207512108953694140372980190139724, 6056811824360306133893955506189170373758117309785601849], [1, -73838906689464, 2819240503294930412702700526, -433671106803069335101594346757002397014664, 34494548241361273407325608100987789752280917290697963601], [1, -39973727021476, 12190632960617917120884352758, -356137367515663628462906877217920669068932, 79375377473505188618758459764796980252025727125812230449], [1, -421665304874800, 102094352521841419715212891998, -12284973883999532913048229247733698087285200, 848814400041653188432880077486808325583024422374372061601], [1, 721146660038964, 249448014272784276512084181238, 44075270067089610955702069724953552942375548, 3735448655171776399347824699993039078892536706537925477849], [1, -363712836623220, 249128072608318548772726423798, -63329889270112648731165429164700991115013780, 30317975617236256833580920126868226118402514553481681430801], [1, -289030099396948, 1180620298639861253894467877862, -183028654139441753815707540651440598330782164, 401007068543157803727680343536350900670553508041935397795649]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/10/16/a/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': '4-10e2-1.1-c15e2-0-0', 'motivic_weight': 15, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [15, 15], 'order_of_vanishing': 0, 'prelabel': '4-10e2-1.1-c15e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.7774793857798947, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c15e2-0', 'trace_hash': 2189003928865665278, 'z1': {'__RealLiteral__': 0, 'data': '1.05652376614415983558783477407', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1339302986308033688892944524169,2318973886116365061683168954537', 'Lhash_array': ['1339302986308033688892944524169', '2318973886116365061683168954537'], 'label': '4-10e2-1.1-c15e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/10/16/a/d'}