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lfunc_lfunctions • Show schema
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{'Lhash': '3124723835639720114931467297713', 'a10': [-0.2675189107869173, 4.272741883682712e-62], 'a2': [0.2316781727342133, 0.13375945539345865], 'a3': [1.7034779833073845, -0.31330936849543145], 'a4': [-0.9642168161856907, -1.6700725151459173], 'a5': [-0.8660254037844386, 0.5], 'a6': [0.43656675696523495, 0.1552693453284112], 'a7': [-3.308045108835775, -1.9099007340777596], 'a8': [0.0, -1.050930286430685], 'a9': [2.803674479225988, -1.0674312223918154], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.7034779833073845, 0.31330936849543145]]], [5, [[1.0, 0], [0.8660254037844386, -0.5]]], [13, [[1.0, 0], [-3.3717536630737626, -1.2772146395765527]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.376', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '673286192092831347203189063856', 'degree': 2, 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[[1.0, 0], [7.170720163877618, 12.420051650694662], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 50, 'label': '2-585-117.25-c1-0-50', '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/585/2/bt/b/376/30', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.1502648489579836, 1.4057690005034558, 1.6683307091382285, 1.939486420850558, 2.216321063187355, 2.491375140516494, 2.7531508231262176, 2.987043955067017, 3.1765768573090436, 3.3048599314581937, 3.3562268266139332, 3.317967824130233, 3.1820459584048715, 2.9466381290490005, 2.617312954355461, 2.207648196441857, 1.7391097081320963, 1.2400641391664105, 0.7438783993474489, 0.28616498016213476, -0.09864618058545968, -0.3811058379577175, -0.5405038020580922, -0.5681068950499268, 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'7.75254077334507011775125084231254', '8.419690535897490246016315932010839', '9.162572554245959604780285328379655', '9.865357415155112304988189567740024', '10.95912572757438627479639716103776'], 'prelabel': '2-585-117.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.7216860174492753, 'root_number': '-0.6414962680998446 + 0.7671261552143639*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.360843008725', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.46497247354842172013933723950', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.24515309890458308058968546188', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.17700972047524079031417197859', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.671248518244905, 'bad_primes': [3, 5, 13], 'central_character': '117.25', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 50, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/bt/b/376/30'], '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': '2-585-117.25-c1-0-50', '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': '2-585-117.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.36084300872463765, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.46497247354842172013933723950', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3124723835639720114931467297713', 'Lhash_array': ['3124723835639720114931467297713'], 'label': '2-585-117.25-c1-0-50', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/bt/b/376/30'}