-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2190787735517819726293123638711,3900523319090803013467044302415', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -1, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.008069734733433876, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 1]], [3, [1]], [5, [1, 0, 1]]], 'bad_primes': [2, 3, 5], 'central_character': '180.1', 'coefficient_field': '1.1.1.1', 'conductor': 32400, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1, 0, 1], [1], [1, 0, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 4, 6, 4, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, -4, 6, -4, 1], [1, 0, 2, 0, 1]], 'euler_factors_factorization': [[[[1, 0, 1], 1]], [1], [[[1, 0, 1], 1]], [[[1, 0, 1], 2]], [[[1, -1], 2], [[1, 1], 2]], [[[1, -1], 2], [[1, 1], 2]], [[[1, 0, 1], 2]], [[[1, -1], 2], [[1, 1], 2]], [[[1, 0, 1], 2]], [[[1, 0, 1], 2]], [[[1, -1], 2], [[1, 1], 2]], [[[1, -1], 2], [[1, 1], 2]], [[[1, 0, 1], 2]], [[[1, 0, 1], 2]], [[[1, 0, 1], 2]], [[[1, 0, 1], 2]], [[[1, -1], 2], [[1, 1], 2]], [[[1, 1], 4]], [[[1, 0, 1], 2]], [[[1, -1], 2], [[1, 1], 2]], [[[1, -1], 2], [[1, 1], 2]], [[[1, -1], 2], [[1, 1], 2]], [[[1, 0, 1], 2]], [[[1, 0, 1], 2]], [[[1, -1], 2], [[1, 1], 2]], [[[1, 0, 1], 2]], [[[1, 0, 1], 2]], [[[1, 0, 1], 2]], [[[1, -1], 4]], [[[1, 0, 1], 2]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 1, 'label': '4-180e2-1.1-c0e2-0-1', 'leading_term': '0.384380277330429107174179257521637291482380796243315222430883922500000000000000000000000000', '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/180/1/f/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.041015625', 'prec': 37}, 'plot_values': [0.38438027733042907, 0.38778440441292383, 0.3944635046323776, 0.4069709523127117, 0.4248832956346873, 0.447544824957628, 0.4750130772525022, 0.5073423879683379, 0.5443641909033532, 0.5858919964261402, 0.6317391479150268, 0.6816739098518626, 0.7353974785230377, 0.792558587513732, 0.852740196687424, 0.9154565833211344, 0.9801437858205039, 1.0461576854332497, 1.1127693246112826, 1.179162267330889, 1.2444318706784443, 1.307585817602783, 1.3675461496329613, 1.4231560371714556, 1.4731831781541005, 1.5163358393262358, 1.551266234082851, 1.5765982641426548, 1.5909296912727122, 1.5928724474930582, 1.5810541253850616, 1.5541677688083346, 1.510977027312902, 1.4503669480873584, 1.371360240984469, 1.273158102400904, 1.1551737840509424, 1.01705443033625, 0.8587325819105371, 0.680426432271781, 0.4827002904920051, 0.2664504151165563, 0.03295535897099816, -0.2161390963745821, -0.478799953041918, -0.7526131357549645, -1.0348060802812875, -1.322244369615535, -1.6114970248449216, -1.8988331655250272, -2.1803184021726194, -2.4518269323760467, -2.7091530509018114, -2.948047988744916, -3.164337479114423, -3.353978709763445, -3.5131838812775067, -3.6384814191795174, -3.7268483577175577, -3.7757572650758577, -3.783314564118391, -3.7482811765644355, -3.6702025386273243, -3.5494006681973453, -3.3870744639599524, -3.1852646393468085, -2.946906098875757, -2.675763294256046, -2.376428460399574, -2.054218020830418, -1.7151237302878317, -1.3656604399385155, -1.0127813057806092, -0.6636802314665107, -0.32567650395595577, -0.005993043469313103, 0.28838855840175753, 0.5509420099019058, 0.775765113168357, 0.9577569173721894, 1.0927890573991677, 1.177831095744962, 1.2110876683821077, 1.1920689608772514, 1.1216552134682405, 1.0021105546599296, 0.8370512315718137, 0.6313946052110098, 0.3912312070883694, 0.12369708165153968, -0.1632329808550854, -0.4609476899098189, -0.7604672058381657, -1.0526910175738249, -1.328714468597735, -1.5800725349752331, -1.7990874314897813, -1.9790587501570234, -2.1146038763280237, -2.20176695866177, -2.2382894568891745, -2.223634891664512, -2.1591240006680215, -2.0478794251737864, -1.8947867349308378, -1.7063548286800143, -1.4905101781809822, -1.2563576316362561, -1.0138578840600412, -0.773482532728233, -0.5458376177990619, -0.34124606635317145, -0.16936613633448924, -0.03877465541244883, 0.043381589302678956, 0.07171563966405398, 0.04287269362658901, -0.044290755991263996, -0.18857084965018725, -0.3864083479923592, -0.6319518818771412, -0.9172067674101974, -1.2323312204892856, -1.5659125137676806, -1.9054777968453187, -2.2378596765192333, -2.5498559889579986, -2.8286273461351534, -3.062420907155602, -3.2409096571531295, -3.3559006557987816, -3.4015071782451587, -3.374766721859669, -3.2755587076041075, -3.107049623565506, -2.875332383733595, -2.5896052339006626, -2.2615840647235648, -1.9053452386541887, -1.5366018266022123, -1.1722175190487039, -0.8294349009962707, -0.5251633555715376, -0.27523340802144736, -0.0936307162875405, 0.00815246417200654, 0.02175127568748275, -0.05760504739914387, -0.23073832379883988, -0.49432345696454844, -0.840905862684202, -1.2590168240357473, -1.7336124720693729, -2.246466986629958, -2.7770394974788086, -3.303029462996304, -3.8016156885896755, -4.250017993392625, -4.626966727837048, -4.913122418661745, -5.092561796538374, -5.152934253126483, -5.086732259443325, -4.891092081489248, -4.568662592159749, -4.12699373772497, -3.578898805678544, -2.9414469550209095, -2.235786327738122, -1.485865967356505, -0.7177467177892309, 0.0417219984105031, 0.7660108351515152, 1.430010582296491, 2.0113890886967516, 2.4912346175526223, 2.8554206473058548, 3.0946460496393424, 3.2055571308493267, 3.190132295457966, 3.0563793025813557, 2.8170995249649216, 2.490097604068446, 2.096449934477927, 1.6602833173449745, 1.2067698184632538, 0.7616141744037024, 0.34907575602111884, -0.008644244392498312, -0.29304346018055516, -0.48980742020574836, -0.5898754842426954, -0.5895882151312509, -0.49105768201955824, -0.30183638622667164, -0.034579071079993376, 0.2937515338697172, 0.6628529580672092, 1.050169418447787, 1.4323097334160222, 1.7861761849463473, 2.090524880788329, 2.326925982369127, 2.4810439079589752, 2.543316006489209, 2.5095514623537616, 2.3812587746322462, 2.1653641328599487, 1.8741127674689153, 1.523990943474097, 1.135147937049253, 0.7298402308961142, 0.3314207760549542, -0.0372895156303344, -0.3552204063671184, -0.6044121497438891, -0.7710775998192241, -0.846456518057016, -0.8273734811976504, -0.7164343561191545, -0.5218947775788884, -0.2571433950308243, 0.060102050837680956, 0.4089166790491448, 0.7664899343266172, 1.1095352759250334, 1.4159049241118917, 1.6658361937897257, 1.843573416260402, 1.9380380082848423, 1.9441080567110895, 1.8624973321773854, 1.7003419627181886, 1.4703097124939912, 1.1903023638512191, 0.8819730849397752, 0.5696324311655764, 0.27844703490219835, 0.03289259547111378, -0.1450143547013173, -0.23725502654662634, -0.23113754105589557, -0.12039829224708201, 0.09426871462340405, 0.40486958559856107, 0.7965358675666101, 1.2481338189396192, 1.7335017721435557, 2.2230139969273686, 2.685260214866976, 3.089277480905513, 3.406254302904828, 3.61184190877286, 3.68753419708501, 3.6223611508019675, 3.4136555539239684, 3.06760838827934, 2.599178035866501, 2.0313669998389368, 1.3941339139623667, 0.722629306763416, 0.05523828250997308, -0.5687995413087366, -1.1117105583499989, -1.5397267573209956, -1.825041372691075, -1.9480193976441549, -1.898158203898868, -1.67544624440743, -1.29004568701903, -0.7623663242368384, -0.12155478251060053, 0.595809204281822, 1.3481128660126827, 2.0910126696293094, 2.7802867579422017, 3.374424730591776, 3.837351587900108, 4.1405844092989, 4.265113462446075, 4.202651686440049, 3.9560467844532408, 3.5394005414497154, 2.976811638842647, 2.3013087807977453, 1.5522981509468217, 0.7734440093065309, 0.009601763619787273, -0.6959150373324334, -1.304097310146092, -1.7828067127213791, -2.108657929331863, -2.268553194275835, -2.2603665076192008, -2.0929078564465273, -1.785280226059675, -1.3653131892258836, -0.8676766396348372, -0.33131884069571155, 0.20322383372615183, 0.6966822633384864, 1.113722987587755, 1.425467916931307, 1.6112259220741585, 1.660142560486935, 1.571417545955352, 1.3546581589822206, 1.0285718946874123, 0.6198641381097343, 0.16083567389795148, -0.3128227084488154, -0.7649563942820385, -1.1613975882784362, -1.472840247634788, -1.6765433510428402, -1.7585446106380387, -1.7140016512332061, -1.5480863992781586, -1.2749862077735892, -0.9170562060673041, -0.5029319248366395, -0.06511638347483854, 0.36222657291084065, 0.7464416434181244, 1.0583638393706918, 1.2751432661730207, 1.3814907192436827, 1.3712791920487655, 1.2475573567191771, 1.0226433985312529, 0.7165976118926395, 0.35609490050086473, -0.02849371501690608, -0.40482826209772244, -0.7422431380975768, -1.0133204611749331, -1.1973159587554263, -1.2808470111364694, -1.2602443134190953, -1.1408425521967431, -0.937742051458484, -0.6736361401579276, -0.37790947366697863, -0.08347377989805731, 0.17540767194409584, 0.3664276890666685, 0.4618697283371681, 0.4411739142929127, 0.2929719602451786, 0.016285270719326325, -0.3789699484562233, -0.8723882928768416, -1.4345187443963816, -2.028677260360784, -2.614090828692309, -3.148475022897316, -3.5921116577270147, -3.9101818738760272, -4.076785104376007, -4.075957610443788, -3.904653974760391, -3.5717708994189774, -3.099320497776931, -2.519497818808648, -1.8737015000673447, -1.2083816970896248, -0.5722379838828778, -0.011930973599782327, 0.4314960265159762, 0.7259817871578509, 0.8513910690340932, 0.8011432588189712, 0.5833120452672946, 0.22011169971110212, -0.25340810916978646, -0.7918522107446976, -1.342986606818474, -1.8513651177833588, -2.263218025087125, -2.529894441832795, -2.612905208929859, -2.485865893741548, -2.1383177089869587, -1.5753784805738844, -0.8191982863551189, 0.09371116218146487, 1.1138290912007653, 2.182971729256119, 3.2379526628156383, 4.215479176723602, 5.0568773067090325, 5.712146452088711, 6.144300188801381, 6.331210692537571, 6.268429827059046, 5.967964346272323, 5.458975863514339, 4.783598473165129, 3.995500684288242, 3.153874654533422, 2.320461352958208, 1.5534177202782886, 0.903967494173753, 0.4117717086528418, 0.1026149430861142, -0.013656476175686945, 0.05665069961485019, 0.2919254262655932, 0.6573497118547496, 1.108246069432169, 1.5938089190905387, 2.061785640606296, 2.462690543638696, 2.7540935739118373, 2.904173538017311, 2.8939404650302656, 2.7192187915067776, 2.3899324638249855, 1.9299733844205411, 1.373868436823735, 0.7645374697753169, 0.14862553661309794, -0.42709706238453393, -0.9201670292805905, -1.2959517587767178, -1.530595892478313, -1.6129407547737418, -1.545284815877004, -1.3428246445458667, -1.032150747401666, -0.6483696900197374, -0.23193997712185024, 0.17552324352136003, 0.5348041946833396, 0.813271345703053, 0.9872843565810347, 1.0451280213505179, 0.987142958066686, 0.8265371698138293, 0.587065901056189, 0.30147528340291824, 0.007550570695146194, -0.2552181002136363, -0.4498357101542829, -0.5455777945514979, -0.5210262616822905, -0.3667229299041748, -0.08602038843566058, 0.3045140854597242, 0.776727399258421, 1.2930181794038482, 1.809793187406976, 2.281604969144452, 2.66494013560466, 2.923206511724261, 3.029072156021238, 2.968885241506053, 2.742240201709643, 2.364446780484804, 1.8632149261228739, 1.278637684146965, 0.6570870126474407, 0.049540926807668834, -0.494797033458527], 'positive_zeros': ['1.72822679618767786561111164746698', '3.07697035633363634318314595900529', '3.66834307526012773911986557906858', '4.65105749693461699670374546515450', '4.78133270384470936549343138358675', '5.94207158086714460524284264873672', '6.00544160009276436343889004619707', '7.01138108804813254061843343096739', '7.70984593560360609597004373017168', '8.002705591916857497167492234650906', '8.731949602901659574138655814885801', '9.098082573711693085294217039422640', '9.768152071362591591297198359402497', '9.951066944493501011919944634999216', '10.70856199700068145277697392096374', '11.12243734817267578579130886343014', '11.77201509376005350156308605147273', '12.24786515957334543450342310497947', '12.68773874131481316135968972331543', '13.61416047276907475538878389671946'], 'prelabel': '4-180e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.2997193725369457, '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': 625580576926617290, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.72822679618767786561111164747', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.07697035633363634318314595901', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.66834307526012773911986557907', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.008069734733433876, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 32400, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'euler11': [1, 0, -2, 0, 1], 'euler13': [1, 0, -2, 0, 1], 'euler17': [1, 0, 2, 0, 1], 'euler19': [1, 0, -2, 0, 1], 'euler2': [1, 0, 1, 0, 0], 'euler23': [1, 0, 2, 0, 1], 'euler29': [1, 0, 2, 0, 1], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, -2, 0, 1], 'euler37': [1, 0, -2, 0, 1], 'euler41': [1, 0, 2, 0, 1], 'euler43': [1, 0, 2, 0, 1], 'euler47': [1, 0, 2, 0, 1], 'euler5': [1, 0, 1, 0, 0], 'euler53': [1, 0, 2, 0, 1], 'euler59': [1, 0, -2, 0, 1], 'euler61': [1, 4, 6, 4, 1], 'euler67': [1, 0, 2, 0, 1], 'euler7': [1, 0, 2, 0, 1], 'euler71': [1, 0, -2, 0, 1], 'euler73': [1, 0, -2, 0, 1], 'euler79': [1, 0, -2, 0, 1], 'euler83': [1, 0, 2, 0, 1], 'euler89': [1, 0, 2, 0, 1], 'euler97': [1, 0, -2, 0, 1], 'euler_factors': [[1, 0, 1, 0, 0], [1, 0, 0, 0, 0], [1, 0, 1, 0, 0], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 4, 6, 4, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, 0, 2, 0, 1], [1, 0, 2, 0, 1], [1, 0, -2, 0, 1]], 'index': 1, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/180/1/f/a', 'ArtinRepresentation/2.180.8t11.b'], 'is_instance_Artin': True, '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': '4-180e2-1.1-c0e2-0-1', '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': '4-180e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.2997193725369457, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e2-0', 'trace_hash': 625580576926617290, 'z1': {'__RealLiteral__': 0, 'data': '1.72822679618767786561111164747', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 24602915
{'Lhash': '2190787735517819726293123638711,3900523319090803013467044302415', 'Lhash_array': ['2190787735517819726293123638711', '3900523319090803013467044302415'], 'label': '4-180e2-1.1-c0e2-0-1', 'type': 'Artin', 'url': 'ArtinRepresentation/2.180.8t11.b'}
-
id: 19801971
{'Lhash': '2190787735517819726293123638711,3900523319090803013467044302415', 'Lhash_array': ['2190787735517819726293123638711', '3900523319090803013467044302415'], 'label': '4-180e2-1.1-c0e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/180/1/f/a'}