-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1057283928076988805297245918187', 'a10': [-0.5506185588486056, -0.9885445096227085], 'a2': [-0.5506107502802738, 1.302623430495473], 'a3': [-0.3888455021906114, 0.14999426189798934], 'a4': [-1.393655603351588, -1.434476928795553], 'a5': [-0.4922623712581618, 0.6307759350753244], 'a6': [0.01871647371608716, -0.5891077150776569], 'a7': [1.2421278188591078, -3.4715146932131717], 'a8': [2.635945015347999, -1.025570024943221], 'a9': [-2.094150830093331, 1.8980276763541877], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.088340583489558, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5506107502802738, -1.302623430495473]]]], 'bad_primes': [2], 'central_character': '512.157', 'coefficient_field': 'CDF', 'conductor': 512, 'conductor_radical': 2, 'conjugate': '1612783520492116226149230457811', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5506107502802738, -1.302623430495473]], [[1.0, 0], [0.3888455021906114, -0.14999426189798934], [2.222853376064877, -2.0146768645410553]], [[1.0, 0], [0.4922623712581618, -0.6307759350753244], [-1.2149008995163195, -4.8501562659727195]], [[1.0, 0], [-1.2421278188591078, 3.4715146932131717], [-5.411073173539159, -4.440752989145518]], [[1.0, 0], [-0.5853808412036205, -2.606819264177542], [-9.943882224357877, 4.703106027733103]], [[1.0, 0], [0.6898923071912062, -0.19091891378296655], [11.150471930003537, -6.683335674511882]], [[1.0, 0], [-4.646269159535091, 1.409430340692044], [14.134983409143269, -9.444693961333238]], [[1.0, 0], [-2.7983691309759435, -5.55940463827562], [-11.318286785356234, 15.260943098132254]], [[1.0, 0], [-8.056386520764706, 1.1950520505482636], [22.009627721840804, -6.676547576852634]], [[1.0, 0], [0.14684422845725775, 0.846284141231285], [-27.3047778903076, 9.769805748374381]], [[1.0, 0], [3.059518315996107, -4.578892742700386], [-11.863186403317783, -28.64026550784989]], [[1.0, 0], [5.102565697089368, -4.401503440039035], [5.429027554848385, -36.599530868696895]], [[1.0, 0], [-0.39490507759312077, 1.5765494430988274], [-36.158771838282554, -19.327266209865904]], [[1.0, 0], [-1.8174336883906173, -4.100064704287515], [-28.877035058421793, 31.86089839026324]], [[1.0, 0], [-0.9675087512126711, -1.1789128243898601], [-9.169245134758029, 46.09690817895183]], [[1.0, 0], [-1.416510708029468, 8.163552362145213], [-49.9018354547001, -17.855162229787663]], [[1.0, 0], [2.67727338796031, -9.674422916009407], [-50.605987990016054, -30.33206190740008]], [[1.0, 0], [-10.531089309702061, -0.2585237318592204], [60.926522828515516, 2.993128133972499]], [[1.0, 0], [-2.366494307619471, 2.253089881070943], [3.287534179937007, -66.91929556574655]], [[1.0, 0], [-5.790223012258787, 0.28445541605494956], [70.65811559372598, -6.959216963398803]], [[1.0, 0], [4.88756568739575, 13.659831009519838], [-56.4297630954798, 46.31070974394612]], [[1.0, 0], [2.027254552091082, -0.1996671457976501], [77.48203715185521, -15.412135439274133]], [[1.0, 0], [-6.42180102575564, -5.539483660589232], [12.178629379795025, 82.10165032707683]], [[1.0, 0], [-0.6096280128375662, -0.09042977331530072], [85.16768988016659, 25.83533627564715]], [[1.0, 0], [15.111447281912739, -3.005853753378161], [89.61631465359481, -37.12029293941371]], [[1.0, 0], [-2.40750728960657, 0.7953329791172131], [81.12396067954514, -60.165629753735764]], [[1.0, 0], [-4.69079988512264, -2.811557251660328], [48.55386389307776, 90.83789022788056]], [[1.0, 0], [-8.983542477141205, -8.553043455988115], [5.250241153033728, 106.87111381395344]], [[1.0, 0], [3.165526364536477, -9.582185069858891], [-87.5496209313903, -64.93122418967523]], [[1.0, 0], [-0.7881068494514556, 0.421251887350897], [62.77943633121505, -93.95606619018761]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 21, 'label': '2-2e9-512.157-c1-0-21', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/512/2/o/a/157/23', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.9749147154081865, 0.8832715879600269, 0.7775749571628386, 0.6542912662944551, 0.5094289860672045, 0.3399200578325579, 0.14478228017044803, -0.07403565673159854, -0.311153448638282, -0.5576116165923465, -0.8010936588856878, -1.0265399876201438, -1.2171647723758825, -1.3558567574429428, -1.426899669159737, -1.4178936786553267, -1.3217047642943367, -1.1382228394223433, -0.8756815131804636, -0.5512909561054661, -0.19096721769131872, 0.17199015951903884, 0.49931650390386245, 0.7512080984889781, 0.8905190423186338, 0.8873448203165923, 0.7234843342167401, 0.3961935300067344, -0.0793686894317111, -0.669532875496104, -1.3237247020139982, -1.978422316596853, -2.563306051269247, -3.009114819178597, -3.2564116895035733, -3.2642125891644933, -3.017294595539493, -2.531012832931447, -1.8526399437343837, -1.058598750233629, -0.24745937950577668, 0.47083789337336845, 0.9884707820544751, 1.214347574428079, 1.0879049965707193, 0.5900478654007328, -0.2506201936999481, -1.3576283404139786, -2.613124763865427, -3.87067434869294, -4.973043394715924, -5.772772542312071, -6.152723868581525, -6.043559255364185, -5.4353410914289295, -4.3811499338067525, -2.991714743828943, -1.4214023483695049, 0.15269105687212617, 1.5555945728621385, 2.639511095452987, 3.305084587906426, 3.5153481260246604, 3.2998828635994104, 2.7482729821962066, 1.9937395586652542, 1.1895702871784863, 0.48231423358060327, -0.013588793922647783, -0.23519325660131246, -0.18085798841300685, 0.09143767109051931, 0.47709129340166906, 0.8468592237849989, 1.0737091801875769, 1.0593761465756806, 0.7553749158626427, 0.1741808442073974, -0.6118569452823319, -1.483891779656177, -2.2997591930965706, -2.9223857471077066, -3.2476371109222653, -3.225769083291743, -2.8718315068965374, -2.2625980671143124, -1.5204246056398825, -0.7872891785001532, -0.1945158916875799, 0.16519343239929624, 0.2571050144497266, 0.11060423622380187, -0.18956426110090713, -0.5253063454585143, -0.7756227450704669, -0.8484810451933054, -0.706441895651978, -0.3794691762808329, 0.03892514515992894, 0.41225190264549383, 0.5943336813342842, 0.4679594279595303, -0.02026601089059161, -0.8377929534672867, -1.863222766093683, -2.9049892337241325, -3.738975951554578, -4.157676343718192, -4.020174136043326, -3.291200609822875, -2.059215050018428, -0.5276425028483297, 1.0207351849705657, 2.279980147156219, 2.986335300145777, 2.978394616584065, 2.238128051968043, 0.9023873932603905, -0.7592582256504311, -2.3969934352206854, -3.653068132290854, -4.238488425836039, -3.997015780936676, -2.9417053565795577, -1.2550445010064222, 0.7481372865928462, 2.6872704523813726, 4.197482958203253, 5.007529754239973, 4.99646264263311, 4.216099588412327, 2.874310041959784, 1.2833665759548047, -0.21410613142495952, -1.323767800814284, -1.8640127941866675, -1.8011170367458904, -1.2473516586291211, -0.4236190825430182, 0.40298974156906, 0.9901739405501778, 1.1815331957606876, 0.9423170270349337, 0.36124784081616074, -0.38102179673386477, -1.0673532109890251, -1.5077018921044023, -1.5930753062059615, -1.3249766835659011, -0.8124047096139972, -0.23763584764070855, 0.1991604945987407, 0.34040274353980954, 0.11910472462005597, -0.4196590824266636, -1.1303321593524152, -1.8084686120360736, -2.250520384347451, -2.3145007667034085, -1.9636556274753167, -1.2799367876011043, -0.44270555279997, 0.32173405936698135, 0.8054127349406724, 0.8796953093772346, 0.5337272560903585, -0.12166884404082194, -0.8866009197678448, -1.5322398649039453, -1.8709143677899915, -1.8150289240063175, -1.4063538781309621, -0.805618139012571, -0.24410682136069076, 0.04929145516121405, -0.07601467329908726, -0.6370147760539999, -1.5007855133469807, -2.414559718636671, -3.0757410063875654, -3.222841724377951, -2.720835145819863, -1.614543118339208, -0.13177424781004263, 1.3680451246421683, 2.4879527226782256, 2.9050743691386467, 2.468040771261952, 1.2509468941868975, -0.4541412625011979, -2.20705940252276, -3.5346364014671345, -4.060027561951802, -3.609998988927103, -2.2689320739421817, -0.36261922893679366, 1.6254324319495486, 3.183081003481719, 3.908448976140718, 3.6196361226079397, 2.404032273887401, 0.5929658188674906, -1.3312929279672139, -2.869726763724145, -3.6436757109743634, -3.49584886894282, -2.5269276220845653, -1.0583918817505653, 0.46621276624137936, 1.6115613747897506, 2.0736955835418067, 1.760292814953913, 0.805928587135623, -0.47978443026074136, -1.7130572433396032, -2.5534038522209728, -2.80138497595011, -2.447634117789582, -1.6603937032776552, -0.7185690882856525, 0.08568438477499722, 0.5419780904097131, 0.5834613981709657, 0.29652914388993223, -0.12241203642313267, -0.44616005842742323, -0.5031679431211946, -0.2406327773939734, 0.25772592489688084, 0.8049969255172316, 1.1832048107448152, 1.228090556784982, 0.8956685675207324, 0.28578762442421113, -0.3871197247992156, -0.8671890473373329, -0.949262788768578, -0.557501536289598, 0.21835471174868173, 1.1438927893772128, 1.9132091248658345, 2.2508073296818316, 2.0076073494434694, 1.217191273254556, 0.09107546907629797, -1.047603366100134, -1.870993996804078, -2.1579576098646425, -1.8709469486120718, -1.1698942327567594, -0.35576092053776737, 0.23897371141106083, 0.37592931962717463, 0.007975823995510459, -0.6889675264729773, -1.3653273622493154, -1.6165645354941618], 'positive_zeros': ['0.834049956578440528398753678655778', '2.56507507620876251579173127936879', '3.48132148722739059740303892853479', '5.04036171967758547589170358335222', '5.71715471467861290158664446685674', '7.23748107747240451263123102835891', '8.495401881210655359457980237693914', '8.840559311333233732959003340470878', '9.655060219991567550899273606526990', '11.05633112658029865166821216313610'], 'prelabel': '2-2e9-512.157-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0219645356656377, 'root_angle': -0.50666997298516, 'root_number': '-0.020952804710052196 - 0.9997804658897784*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.253334986493', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.834049956578440528398753678656', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.56507507620876251579173127937', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.48132148722739059740303892853', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.088340583489558, 'bad_primes': [2], 'central_character': '512.157', 'conductor': 512, 'conductor_radical': 2, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/512/2/o/a/157/23'], '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': '2-2e9-512.157-c1-0-21', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-2e9-512.157-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0219645356656377, 'root_angle': -0.25333498649258, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.834049956578440528398753678656', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1057283928076988805297245918187', 'Lhash_array': ['1057283928076988805297245918187'], 'label': '2-2e9-512.157-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/512/2/o/a/157/23'}