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lfunc_lfunctions • Show schema
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{'Lhash': '1231912384657395407825902567553', 'a10': [87.48822386602833, 0], 'a2': [0, -5.330393086063503], 'a3': [-3.0, 0], 'a4': [-20.413090451953597, 0], 'a5': [0, 16.413090451953597], 'a6': [0, 15.99117925819051], 'a7': [0, 9.679684445740131], 'a8': [0, 66.16665152177433], 'a9': [9.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.913968372910507, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [3.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '507.337', 'coefficient_field': 'CDF', 'conductor': 507, 'conductor_radical': 39, 'conjugate': '91765582530510130822812067059', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 5.330393086063503], [-8.0, 0]], [[1.0, 0], [3.0, 0]], [[1.0, 0], [0, -16.413090451953597], [-125.0, 0]], [[1.0, 0], [0, -9.679684445740131], [-343.0, 0]], [[1.0, 0], [0, -27.588166338040548], [-1331.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [107.92817727552993, 0], 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-0.00954877929905883], 'positive_zeros': ['0.971807518913808236602584366253082', '4.06289993272182890002597716842063', '4.74645235055810286344973248647997', '5.53610999143646727010340213708857', '6.41057129125528092480748131447625', '7.26398602686369633889805688010697', '8.387359070152541623797841371776905', '8.774923041839275523980115450584545', '9.706334558023056170382946291129633', '10.91028655301023965388577866695156'], 'prelabel': '2-507-13.12-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.469366359361064, 'root_angle': -0.8128329581890013, 'root_number': '-0.83205029433784368302751260018549906451952997857967220293 - 0.5547001962252291220183417334569993763463533190531148020*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4064164790945006', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.971807518913808236602584366253', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '4.06289993272182890002597716842', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.74645235055810286344973248648', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.913968372910507, 'bad_primes': [3, 13], 'central_character': '13.12', 'conductor': 507, 'conductor_radical': 39, 'degree': 2, 'index': 39, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/507/4/b/h/337/1'], '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': '2-507-13.12-c3-0-39', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-507-13.12-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.469366359361064, 'root_angle': -0.4064164790945006, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.971807518913808236602584366253', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1231912384657395407825902567553', 'Lhash_array': ['1231912384657395407825902567553'], 'label': '2-507-13.12-c3-0-39', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/507/4/b/h/337/1'}