-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1294922538764531033515856948593', 'a10': [78.4629983750201, 0.0], 'a2': [-5.510469827545792, 0.0], 'a3': [3.0, 0.0], 'a4': [22.36527772029255, 0.0], 'a5': [-14.23889447371592, 0.0], 'a6': [-16.531409482637375, 0.0], 'a7': [3.4397694044136298, 0.0], 'a8': [-79.15942944198791, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 118.77084484155591, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-3.0, 0]]], [11, [[1.0, 0], [-11.0, 0]]], [61, [[1.0, 0], [-61.0, 0]]]], 'bad_primes': [3, 11, 61], 'central_character': '2013.1', 'coefficient_field': 'CDF', 'conductor': 2013, 'conductor_radical': 2013, 'degree': 2, 'euler_factors': [[[1.0, 0], [5.510469827545792, 0], [8.0, 0]], [[1.0, 0], [-3.0, 0]], [[1.0, 0], [14.23889447371592, 0], [125.0, 0]], [[1.0, 0], [-3.4397694044136298, 0], [343.0, 0]], [[1.0, 0], [-11.0, 0]], [[1.0, 0], [2.0013429267053233, 0], [2197.0, 0]], [[1.0, 0], [9.450087295738136, 0], [4913.0, 0]], [[1.0, 0], [-151.18653943482173, 0], [6859.0, 0]], [[1.0, 0], [109.9578896069143, 0], [12167.0, 0]], [[1.0, 0], [75.26637785260228, 0], [24389.0, 0]], [[1.0, 0], [61.48086036051698, 0], [29791.0, 0]], [[1.0, 0], [-61.26743688818119, 0], [50653.0, 0]], [[1.0, 0], [422.58161939222487, 0], [68921.0, 0]], [[1.0, 0], [218.72021594528542, 0], [79507.0, 0]], [[1.0, 0], [-426.1188923305957, 0], [103823.0, 0]], [[1.0, 0], [-562.7751592036348, 0], [148877.0, 0]], [[1.0, 0], [-142.96686925720695, 0], [205379.0, 0]], [[1.0, 0], [-61.0, 0]], [[1.0, 0], [408.3990088110968, 0], [300763.0, 0]], [[1.0, 0], [-220.2327240195105, 0], [357911.0, 0]], [[1.0, 0], [-84.80215493639582, 0], [389017.0, 0]], [[1.0, 0], [-1038.454984749838, 0], [493039.0, 0]], [[1.0, 0], [210.2368859164793, 0], [571787.0, 0]], [[1.0, 0], [-1211.521936400441, 0], [704969.0, 0]], [[1.0, 0], [1410.5762281149098, 0], [912673.0, 0]], [[1.0, 0], [325.16916664948104, 0], [1030301.0, 0]], [[1.0, 0], [802.2020758713278, 0], [1092727.0, 0]], [[1.0, 0], [-2188.541427921629, 0], [1225043.0, 0]], [[1.0, 0], [357.2384399805425, 0], [1295029.0, 0]], [[1.0, 0], [1346.1679972699508, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 168, 'label': '2-2013-1.1-c3-0-168', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/2013/4/a/a/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [4.800959052256154e-61, 0.10618049799537944, 0.21015496966743993, 0.3097499586940509, 0.40285711301567173, 0.48746562646942176, 0.5616944897318333, 0.6238243934885166, 0.6723290530472209, 0.7059056392132044, 0.7235039097995873, 0.7243535447623896, 0.7079891010002987, 0.6742719257616641, 0.6234083056192522, 0.5559630860229025, 0.4728679789140072, 0.3754237864962404, 0.26529581090042337, 0.14450179412267883, 0.015391841193451208, -0.11938007810823972, -0.25689327885376767, -0.3940061869231897, -0.5274106352374703, -0.6536941715524127, -0.7694096509091689, -0.871151109028273, -0.9556346353665646, -1.0197826948363755, -1.0608100944850156, -1.076309565262153, -1.0643347389613027, -1.02347815590973, -0.9529418488943588, -0.8525980212181165, -0.7230373785925055, -0.5656027912145889, -0.3824061574790115, -0.1763266158827237, 0.049011393996659915, 0.28928129034724653, 0.5395192965582091, 0.7942111846704646, 1.047400211140683, 1.2928149943005982, 1.5240154165731215, 1.7345539672376133, 1.9181492934422868, 2.0688681195358556, 2.1813111495153157, 2.2507981062787663, 2.2735467054717575, 2.246840130538901, 2.169177486368177, 2.0404017758315574, 1.861800177012829, 1.6361718049924088, 1.3678587217801867, 1.0627367069917293, 0.7281632100861046, 0.37288095652861314, 0.006876853438738865, -0.3588028920523998, -0.7122791986148937, -1.0411044820670792, -1.3325600326003029, -1.5739801742591926, -1.7530957999228058, -1.8583888363733994, -1.879448341902132, -1.807318312231077, -1.6348269036614713, -1.3568867035451069, -0.9707559082380407, -0.4762508198145495, 0.12409905244943337, 0.8249608092632343, 1.6181789328058842, 2.4928312924556053, 3.435362681097865, 4.429796016583595, 5.4580190615681685, 6.500142179946911, 7.534920330862361, 8.540230276683477, 9.493591925431826, 10.372720915400839, 11.15609805065633, 11.823540074477942, 12.356755578080534, 12.739869626958521, 12.959900975976517, 13.007176550441038, 12.875669190614023, 12.563246470737488, 12.071820672226321, 11.407392658648726, 10.57998539576175, 9.603466097182286, 8.495259357262603, 7.275957050361344, 5.968834117248792, 4.599282510246099, 3.1941784163638514, 1.7812003158901035, 0.38811736660147317, -0.9579310507580591, -2.2311430959348315, -3.4077280122478757, -4.466524635279848, -5.389545478684312, -6.162429114267102, -6.774786293826115, -7.220428535578539, -7.497471616601527, -7.608310453715986, -7.559466082601038, -7.361309711984036, -7.027672984434604, -6.575357465693828, -6.023559864629355, -5.393232421559624, -4.706400176765435, -3.985458348637991, -3.2524737437392592, -2.5285139506168828, -1.8330270292884863, -1.1832925259861957, -0.5939619782659689, -0.07670372077611545, 0.36003712257041953, 0.7111569233458376, 0.9748881825807587, 1.152673277317698, 1.2489246721095872, 1.2706832517269149, 1.2271902756579187, 1.129391681234371, 0.9893959347828205, 0.8199082425039439, 0.633664612336751, 0.44288897024665813, 0.2587952846701025, 0.09115448742748188, -0.05205701600663508, -0.16491415705290738, -0.2436965018347378, -0.2869338316784846, -0.2953446043633761, -0.2716726610451117, -0.22043206426919315, -0.1475740240652183, -0.06009330649215369, 0.03440583719272165, 0.12816245813832408, 0.21370793247697317, 0.28428906433654827, 0.3342444822977858, 0.3593158958909319, 0.3568790175527717, 0.3260829359158173, 0.2678912677324614, 0.1850233081528342, 0.08179841237085159, -0.036108263963049864, -0.16198600102108388, -0.2884681088240752, -0.4079510900145291, -0.513031364183627, -0.5969364047903054, -0.6539271489564089, -0.6796497204886001, -0.67141682009497, -0.6284024899955606, -0.5517382055458626, -0.44450318906246544, -0.31160724648163696, -0.15957003281377358, 0.003793821846945568, 0.1697691301815602, 0.32919498344586484, 0.4729572290696106, 0.5924932526647297, 0.680282414183602, 0.7302955240476021, 0.7383781650070977, 0.7025454348335932, 0.6231696994806357, 0.5030480352740448, 0.34734197117853527, 0.16338863722634842, -0.0396108357198314, -0.25101317754969804, -0.45924641612350064, -0.6523907849226078, -0.8187986612871653, -0.9477221057438056, -1.0299151277304126, -1.058178028790751, -1.0278131155977244, -0.9369646894642308, -0.7868213759002929, -0.5816653425756881, -0.3287604758380884, -0.038079789863167464, 0.27811917423290955, 0.6058538711383719, 0.9300863687700867, 1.2354715108405907, 1.5071467569958692, 1.7315232484613698, 1.897036047810446, 1.9948120454842397, 2.019216766136261, 1.968246186110028, 1.843736517870495, 1.6513734482352116, 1.400492157143709, 1.103670132733177, 0.7761258154499452, 0.43494689068275266, 0.0981820382433995, -0.21616141047682463, -0.4911646608629437, -0.7120357170759102, -0.8670830156739311, -0.9485695967219988, -0.9533967115473196, -0.8835722880587975, -0.7464287621373068, -0.5545660746860815, -0.3255086398815014, -0.08107921642811139, 0.15349281376684606, 0.35069695796539696, 0.4820558274753169, 0.5195714000049304, 0.4372374776888408, 0.21254621467171322, -0.17208633877106694, -0.7280500370120914, -1.459495737822991, -2.3625776123454973, -3.4250331789313786, -4.626137260559391, -5.937049449487985, -7.321556488004562, -8.737192086708724, -10.136698010030438, -11.469772689194896, -12.685038074234399, -13.73214273350411, -14.56391005836617, -15.138435382532009, -15.421035241632621, -15.385956028647188], 'positive_zeros': ['1.02151376612087870116059231705133', '2.02052045007240309065834296704690', '3.14938708006563969994882659249204', '3.84955820229746410396464182078131', '5.39723078379573740767680068920432', '6.60982308758460280721997598592286', '7.34364434361250691075502037357325', '7.80199488306511633076162787991057', '8.363850031546220674722195722028744'], 'prelabel': '2-2013-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.898203743808239, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.02151376612087870116059231705', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.02052045007240309065834296705', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.14938708006563969994882659249', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 118.77084484155591, 'bad_primes': [3, 11, 61], 'central_character': '1.1', 'conductor': 2013, 'conductor_radical': 2013, 'degree': 2, 'index': 168, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2013/4/a/a/1/3'], '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': '2-2013-1.1-c3-0-168', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-2013-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.898203743808239, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.02151376612087870116059231705', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1294922538764531033515856948593', 'Lhash_array': ['1294922538764531033515856948593'], 'label': '2-2013-1.1-c3-0-168', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2013/4/a/a/1/3'}