-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '975577999195139873841176088940,1909162456887664133678849027932', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8644315128125628, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [19, [1, -2, 1]]], 'bad_primes': [2, 3, 19], 'central_character': '2736.1', 'coefficient_field': '1.1.1.1', 'conductor': 7485696, 'conductor_radical': 114, 'degree': 4, 'euler_factors': [[1], [1], [1, 0, -1, 0, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, 1, 0, 1, 1], [1, 0, -1, 0, 1], [1, -2, 1], [1, 0, 1, 0, 1], [1, 0, -1, 0, 1], [1, 0, 1, 0, 1], [1, 2, 3, 2, 1], [1, 0, -1, 0, 1], [1, -3, 4, -3, 1], [1, 0, 1, 0, 1], [1, 0, -1, 0, 1], [1, 0, 1, 0, 1], [1, -1, 0, -1, 1], [1, 3, 4, 3, 1], [1, 0, 1, 0, 1], [1, 1, 0, 1, 1], [1, 3, 4, 3, 1], [1, 0, -2, 0, 1], [1, 0, -1, 0, 1], [1, -2, 3, -2, 1], [1, 0, -1, 0, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, -2, 3, -2, 1], [1, 0, 2, 0, 1]], 'euler_factors_factorization': [[1], [1], [[[1, 0, -1, 0, 1], 1]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, -1], 2], [[1, 1], 2]], [[[1, 1], 2], [[1, -1, 1], 1]], [[[1, 0, -1, 0, 1], 1]], [[[1, -1], 2]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, 0, -1, 0, 1], 1]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, 1, 1], 2]], [[[1, 0, -1, 0, 1], 1]], [[[1, -1], 2], [[1, -1, 1], 1]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, 0, -1, 0, 1], 1]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, -1], 2], [[1, 1, 1], 1]], [[[1, 1], 2], [[1, 1, 1], 1]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, 1], 2], [[1, -1, 1], 1]], [[[1, 1], 2], [[1, 1, 1], 1]], [[[1, -1], 2], [[1, 1], 2]], [[[1, 0, -1, 0, 1], 1]], [[[1, -1, 1], 2]], [[[1, 0, -1, 0, 1], 1]], [[[1, -1, 1], 1], [[1, 1, 1], 1]], [[[1, -1], 2], [[1, 1], 2]], [[[1, -1, 1], 2]], [[[1, 0, 1], 2]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 3, 'label': '4-2736e2-1.1-c0e2-0-3', 'leading_term': '1.29686738662494366863146174759655045299565711107580650338540484000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2736/1/bk/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.025390625', 'prec': 37}, 'plot_values': [1.2968673866249434, 1.298828141953266, 1.301850185155416, 1.3076881107294798, 1.3159213721959142, 1.3256739865048774, 1.3364944925408906, 1.3479627819104154, 1.3594091349809538, 1.3700717476551352, 1.3791554395500734, 1.38582320750516, 1.3891855416413628, 1.388321592679003, 1.38230724426768, 1.3702159044063627, 1.3511515142144077, 1.3242456453570108, 1.288700411226766, 1.243779523270498, 1.188855974298168, 1.123398840323927, 1.0470238245257206, 0.9594755402040379, 0.8606784324363739, 0.750714216914711, 0.6298709487339867, 0.49861503831911524, 0.3576361367819749, 0.20781328099686422, 0.05025323119712391, -0.1137493874280952, -0.2826826312085197, -0.45486273546179246, -0.6284156980548506, -0.801327437096804, -0.9714381823475136, -1.1364956390205727, -1.2941633501267817, -1.4420745436349411, -1.577854799059012, -1.6991736653148724, -1.8037809451492248, -1.889552734503902, -1.9545394900583803, -1.9970029294687461, -2.01547285794211, -2.00877144454564, -1.9760746617858338, -1.916920861477273, -1.8312717477468994, -1.7195029374177926, -1.5824587643736368, -1.4214236136789984, -1.2381646553982524, -1.034884142606168, -0.8142444823239755, -0.5793033014418796, -0.33351613005442304, -0.08065774661690024, 0.17520082623010141, 0.4297795344809521, 0.6786393605857024, 0.9172715045160696, 1.1411735870444148, 1.345933180711751, 1.5273267108076354, 1.6813892490991718, 1.804530181960067, 1.8935814007813843, 1.9459215825041025, 1.959495901192636, 1.932939069388532, 1.8655614680156791, 1.7574601660580134, 1.6094688544543392, 1.423246086066581, 1.2011894531063014, 0.9464913819193985, 0.6630213817077025, 0.3553419023590094, 0.028565906062977875, -0.3116715501984615, -0.6593700528905708, -1.0082369498644896, -1.3518455815226582, -1.6837491798691837, -1.997626326447956, -2.2874273523250106, -2.5474925789707923, -2.772719025939346, -2.9586382538487723, -3.1015881883112444, -3.1987401225965755, -3.24825879957412, -3.249272224656315, -3.2020031241507803, -3.10768038391431, -2.9686267815214262, -2.788116669802167, -2.5704084311974067, -2.3205589157348485, -2.0443941510631296, -1.7482963985499744, -1.439112831364625, -1.1239352599527643, -0.8099531500501146, -0.5042485239745635, -0.21360609918266046, 0.05565383376085251, 0.297889988051101, 0.5082485171860853, 0.6828805136427447, 0.81897550415726, 0.9149587898996397, 0.9704402583258078, 0.9863699037255513, 0.9649002193273951, 0.9094824311313855, 0.8246494362948049, 0.716041988502133, 0.5901275973088178, 0.4541545230450986, 0.3158292420053241, 0.18320575394783212, 0.06434920785449677, -0.03282240328588131, -0.10085882925671617, -0.1329580984499866, -0.12324307720674406, -0.06693295244342028, 0.039447590153715455, 0.19793977353971506, 0.4090242466473839, 0.6715678164219353, 0.9827845511095946, 1.3382847520387864, 1.7321168561537186, 2.1569362690178044, 2.6041097325836553, 3.064009421426164, 3.5261515040032863, 3.979607046706422, 4.413139563235733, 4.815710373519722, 5.1765771279342525, 5.485859056339515, 5.7345604513331265, 5.915152355653681, 6.021491902987563, 6.049372760464796, 5.996322538048864, 5.862075550052941, 5.648245082226906, 5.358678930699631, 4.999019512721839, 4.576914626188978, 4.101494221775874, 3.5834246405699433, 3.034344248698574, 2.466767209851164, 1.8935292061962026, 1.3275643665750374, 0.7814154877683473, 0.26692274863845133, -0.2051505967331854, -0.6254687416115366, -0.9863412372496615, -1.2820596829001674, -1.5089340556411444, -1.6655654856042972, -1.752695519320356, -1.7733748551411308, -1.7326413389229518, -1.6375603773183762, -1.496767604468749, -1.3203764508101683, -1.1194376819370366, -0.9057306509690627, -0.6912019400485064, -0.4876762144564005, -0.3063383669925167, -0.1574147513253005, -0.049756916093404255, 0.009448047870249093, 0.01494836608244678, -0.03637017230475249, -0.145382027609617, -0.31065616186476863, -0.5285215941105065, -0.7931702029003601, -1.0968645517758353, -1.4302185160986445, -1.7825005158688463, -2.1420758045538046, -2.4967432195427035, -2.834298508324378, -3.1428364824988066, -3.411374952147251, -3.630058011510693, -3.7907681897667307, -3.887180344363799, -3.915287691969994, -3.873277800541555, -3.7619070200257165, -3.5841973964127773, -3.3456128680546087, -3.053604685935927, -2.7175692102343745, -2.3482953219036844, -1.9577140940223416, -1.5583206604749194, -1.1627560018658496, -0.7832845973133511, -0.43127345539286266, -0.11680380911174768, 0.1518717133768564, 0.3685201436135588, 0.5294081760477407, 0.6332580222851231, 0.6815892164390434, 0.6784333318296139, 0.6304837894001198, 0.5465976115310178, 0.4377304639310871, 0.31628462631688903, 0.19584256611447426, 0.09044324206830627, 0.014163189939840367, -0.01958578380902519, 0.001450644226857608, 0.08777818284445198, 0.24768468493360074, 0.48683241645143704, 0.8079139601162049, 1.2104704562919848, 1.6907628001919457, 2.2418208940777986, 2.853594127125128, 3.5131969386304003, 4.205365196326384, 4.912827706316631, 5.617051907553073, 6.298645292222573, 6.938331351301249, 7.517273766460888, 8.01818846383013, 8.425489340033891, 8.726420375651875, 8.910944360868452, 8.972774159856916, 8.908962475687119, 8.720724816087722, 8.41273347797565, 7.9936549091636895, 7.475197879482091, 6.872330375172373, 6.2021728800339035, 5.483908158953099, 4.737638868893402, 3.984049929887333, 3.243360287735972, 2.5348344737500117, 1.8759489135143292, 1.2818705367656649, 0.7649294275111606, 0.33418420054505504, -0.004750948487897377, -0.24995253920632954, -0.4030105120549582, -0.4690200464912027, -0.4561105965637442, -0.37516398586586497, -0.23915041220528058, -0.06260410019182787, 0.13910479215908775, 0.3504602381810411, 0.5564560630842791, 0.7433426921071707, 0.8990888724164519, 1.0140628783177696, 1.0812137220292024, 1.0965733077721165, 1.059120385445695, 0.9710197807587871, 0.8371885071933747, 0.6652340136250369, 0.46479486940915676, 0.24719418615863054, 0.024667893068672963, -0.1901974409479593, -0.3852148115480368, -0.5492630857903689, -0.6728845426177601, -0.7489205056665915, -0.7728514844806257, -0.7432678948747753, -0.6618938147179727, -0.5337838814266006, -0.3670289162814512, -0.17261661027989447, 0.036124128533223485, 0.24400091390580175, 0.4346686600736708, 0.591384437429049, 0.6977365266134851, 0.738559546241943, 0.7005390218328773, 0.5731327333204574, 0.3489287798957314, 0.024407671809947427, -0.4000236949748002, -0.9195772119511276, -1.525390550279275, -2.2044832244566304, -2.9403551162933788, -3.7133926360788414, -4.501649527024443, -5.281668604748894, -6.029293624877267, -6.72080181291708, -7.33357995960465, -7.847408699715354, -8.244850701181864, -8.512499475376789, -8.640971092723994, -8.625933863336314, -8.467660629940523, -8.17169102474057, -7.747977944542296, -7.21109558637155, -6.579087675069477, -5.873211539408515, -5.116653512984208, -4.3338782854711, -3.5494076008151847, -2.7869107065384635, -2.0682396112162262, -1.4124383384177854, -0.8351911126677488, -0.3479373002128173, 0.04217626892938839, 0.3329134107651346, 0.5264832392937122, 0.6297861133944804, 0.6535112883635027, 0.6119818097856775, 0.5219633101477189, 0.4021613873029156, 0.2719356367172105, 0.1505759854024757, 0.05612701107247848, 0.004619042463523179, 0.009181323668023348, 0.07941956330481362, 0.22093704834414613, 0.43502906571978417, 0.7186494292293998, 1.0645372106669337, 1.4615774766004719, 1.895397033362295, 2.348989241129682, 2.803727788107239, 3.2400714579070566, 3.6388651516017028, 3.9819221189488587, 4.253425225201281, 4.440205435173572, 4.533035105942269, 4.526478858618734, 4.4198893096809515, 4.2167892324367395, 3.925435759164303, 3.5577851207230258, 3.1295737702243085, 2.6590010070379635, 2.166368998101346, 1.6726775415832065, 1.198951361018329, 0.764963042561156, 0.3884380231297175, 0.08410133067293003, -0.1370243945885658, -0.2681120849051033, -0.30694172994831764, -0.2558845001334469, -0.12188420151361741, 0.08401824636712384, 0.3471857853908257, 0.6501808362385314, 0.9737017090882221, 1.2974950477571343, 1.6015888594230618, 1.8670944629071964, 2.0775318542413412, 2.2193150176691425, 2.2829401584469684, 2.263011240102748, 2.1590828309002394, 1.975175634565015, 1.7201301767420278, 1.4066666621820505, 1.051201465132107, 0.6726008643828691, 0.29152061263822604, -0.07093061406407673, -0.39416915588480655, -0.659324158879255, -0.8503041192032023, -0.9546224074317998, -0.9642986573629689, -0.8761786506875938, -0.6924428783262139, -0.42037872333742365, -0.07234165773604088, 0.33494998590735914, 0.7810491156328597, 1.2427917556942694, 1.6954550487527802, 2.1138374800015662, 2.4737611776745903, 2.7529624103230375, 2.9326836643905647, 2.9981496806139822, 2.939969052998951, 2.754052075967189, 2.442571285026178, 2.013290628662118, 1.4799145142616483, 0.8609208200534266, 0.17924327600095366, -0.5391914765295522, -1.266375761418711, -1.9737097128903622, -2.633320843829932, -3.219292055996358, -3.7091249909442214, -4.0844616268366325, -4.33240315030864, -4.445571466540711, -4.4230294364713725, -4.26965355373676, -3.996487391208778, -3.619529752391151, -3.159473629494804, -2.6401282672624804, -2.087626013163834, -1.5287683126469118, -0.9898953790349806, -0.49545995762749634, -0.06682597133925125, 0.27867352225202713, 0.5287279908613268, 0.6763502886524435, 0.7204235299529903, 0.6653350625276033, 0.520940043999722, 0.30163887343650614, 0.025746265345015052, -0.28576507512349464, -0.6103701283925438, -0.9252937368589967, -1.2088648947613403, -1.4415730044418935, -1.6073861561618195, -1.6943281304576678, -1.6954787654064596, -1.6089468768702682, -1.4383349868874626, -1.192118812242203, -0.8834711562002823, -0.5291919264524803, -0.14892302636083346, 0.23612498105197813, 0.6044032050625113, 0.9352065532965176, 1.210087662441081, 1.4136696325601816, 1.5349402327796466, 1.5674953567842653, 1.5104347699842693, 1.367960057944682, 1.1496798301042943, 0.8696281681765193, 0.5459179423791694, 0.1993752565416586, -0.1473736606741882, -0.47136882580019707, -0.7505798228785703, -0.9651642195073268, -1.098779428867792, -1.1393678839916663, -1.080195282183167, -0.9200015695984747, -0.6634942554124107, -0.3208469511314295, 0.09251389625515673, 0.5569275487811781, 1.0494235008292632, 1.5450090398502454, 2.0181881749420807, 2.4441420986001714, 2.8004735141728143, 3.0681412820151834, 3.2334681418016076, 3.2878163075544222, 3.2282099886136004, 3.058477700097169, 2.7926713296967502, 2.4474075881183843, 2.0340081929880887, 1.5777319552124829], 'positive_zeros': ['0.76959534355878156740201573646075', '1.50606362395437365325097187521705', '2.05880563793082294983593070623204', '2.76213216514709892984274457454328', '3.18985694617474133857687924156054', '3.31808992649296495843495233732744', '4.17810278864933120319254758078703', '4.66579629539841551547516813597859', '4.70815618028868880075134397474422', '5.46945916640562172902027589447542', '5.79609977516594648501204724340809', '5.83912396319886297117849941602533', '6.77888406630811769064961417941269', '6.96516226400799493069668125762204', '7.34073364062009789488295651084539', '7.63823020565407308784191310789303', '7.87273262613030846417016401448323', '8.655110398597480460679181888037184', '8.943994934304339261617236592803762', '8.952910772874176106280888074192586'], 'prelabel': '4-2736e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.1685212341091173, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c0e2-0', 'trace_hash': 2140838749342573235, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.76959534355878156740201573646', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.50606362395437365325097187522', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.05880563793082294983593070623', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.8644315128125628, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 7485696, 'conductor_radical': 114, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0], 'euler11': [1, 0, -2, 0, 1], 'euler13': [1, 1, 0, 1, 1], 'euler17': [1, 0, -1, 0, 1], 'euler19': [1, -2, 1, 0, 0], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 1, 0, 1], 'euler29': [1, 0, -1, 0, 1], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, 1, 0, 1], 'euler37': [1, 2, 3, 2, 1], 'euler41': [1, 0, -1, 0, 1], 'euler43': [1, -3, 4, -3, 1], 'euler47': [1, 0, 1, 0, 1], 'euler5': [1, 0, -1, 0, 1], 'euler53': [1, 0, -1, 0, 1], 'euler59': [1, 0, 1, 0, 1], 'euler61': [1, -1, 0, -1, 1], 'euler67': [1, 3, 4, 3, 1], 'euler7': [1, 0, 1, 0, 1], 'euler71': [1, 0, 1, 0, 1], 'euler73': [1, 1, 0, 1, 1], 'euler79': [1, 3, 4, 3, 1], 'euler83': [1, 0, -2, 0, 1], 'euler89': [1, 0, -1, 0, 1], 'euler97': [1, -2, 3, -2, 1], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, -1, 0, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, 1, 0, 1, 1], [1, 0, -1, 0, 1], [1, -2, 1, 0, 0], [1, 0, 1, 0, 1], [1, 0, -1, 0, 1], [1, 0, 1, 0, 1], [1, 2, 3, 2, 1], [1, 0, -1, 0, 1], [1, -3, 4, -3, 1], [1, 0, 1, 0, 1], [1, 0, -1, 0, 1], [1, 0, 1, 0, 1], [1, -1, 0, -1, 1], [1, 3, 4, 3, 1], [1, 0, 1, 0, 1], [1, 1, 0, 1, 1], [1, 3, 4, 3, 1], [1, 0, -2, 0, 1], [1, 0, -1, 0, 1], [1, -2, 3, -2, 1]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2736/1/bk/b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-2736e2-1.1-c0e2-0-3', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0], 'order_of_vanishing': 0, 'prelabel': '4-2736e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.1685212341091173, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e2-0', 'trace_hash': 2140838749342573235, 'z1': {'__RealLiteral__': 0, 'data': '0.76959534355878156740201573646', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '975577999195139873841176088940,1909162456887664133678849027932', 'Lhash_array': ['975577999195139873841176088940', '1909162456887664133678849027932'], 'label': '4-2736e2-1.1-c0e2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2736/1/bk/b'}