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lfunc_lfunctions • Show schema
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{'Lhash': '2136551348455685872294248148075', 'a10': [-0.650309979570227, 1.1170455067147638], 'a2': [0, 0.5780473568143483], 'a3': [0, -0.551887553448663], 'a4': [1.6658612532799455, 0], 'a5': [1.9324463533072183, 1.1250115962022942], 'a6': [0.319017141529737, 0], 'a7': [0, -4.662974575652525], 'a8': [0, 2.1190414079066064], 'a9': [2.695420128348449, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.412997564841117, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-1.9324463533072183, -1.1250115962022942]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 19], 'central_character': '1805.1084', 'coefficient_field': 'CDF', 'conductor': 1805, 'conductor_radical': 95, 'conjugate': '1273380015970015101608178747950', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -0.5780473568143483], [-2.0, 0]], [[1.0, 0], [0, 0.551887553448663], [-3.0, 0]], [[1.0, 0], [-1.9324463533072183, -1.1250115962022942]], [[1.0, 0], [0, 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103}, 'z2': {'__RealLiteral__': 0, 'data': '2.09803389982137216318938034902', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.17235111132651730890723961748', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.412997564841117, 'bad_primes': [5, 19], 'central_character': '5.4', 'conductor': 1805, 'conductor_radical': 95, 'degree': 2, 'index': 125, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1805/2/b/i/1084/10'], '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': '2-1805-5.4-c1-0-125', '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': '2-1805-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7964453854679796, 'root_angle': 0.08390740275776054, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.68544183079392578049080933889', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2136551348455685872294248148075', 'Lhash_array': ['2136551348455685872294248148075'], 'label': '2-1805-5.4-c1-0-125', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1805/2/b/i/1084/10'}