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lfunc_lfunctions • Show schema
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{'Lhash': '2532823665651131380329847843949', 'a10': [12.807764064044152, 0.0], 'a2': [2.5615528128088303, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.4384471871911697, 0.0], 'a5': [5.0, 0.0], 'a6': [0.0, 0.0], 'a7': [6.246211251235321, 0.0], 'a8': [-24.177080940897135, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.20594545284162, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-5.0, 0]]], [11, [[1.0, 0], [-11.0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '495.1', 'coefficient_field': 'CDF', 'conductor': 495, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.5615528128088303, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-5.0, 0]], [[1.0, 0], [-6.246211251235321, 0], [343.0, 0]], [[1.0, 0], [-11.0, 0]], [[1.0, 0], [49.12310562561766, 0], [2197.0, 0]], [[1.0, 0], [82.70832376358854, 0], [4913.0, 0]], [[1.0, 0], [130.35416188179425, 0], 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'5.00070831600848173878349309544694', '6.27472499112418587661656578340977', '7.00130698532024725838238632289966', '8.527017468236425571268673193361870', '9.077248386688530555116035978632718', '10.13245662428900951426411017863327'], 'prelabel': '2-495-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.4042525341476795, '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': '1.99804556965075284609601186932', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.21493357478241499562303704031', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.57726716946648769513464080531', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.20594545284162, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 495, 'conductor_radical': 165, 'degree': 2, 'index': 44, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/495/4/a/d/1/2'], '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': '2-495-1.1-c3-0-44', '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': '2-495-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.4042525341476795, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.99804556965075284609601186932', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2532823665651131380329847843949', 'Lhash_array': ['2532823665651131380329847843949'], 'label': '2-495-1.1-c3-0-44', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/495/4/a/d/1/2'}