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lfunc_lfunctions • Show schema
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{'Lhash': '1739422974340543730957184896413', 'a10': [2.1213203435596424, 1.224744871391589], 'a2': [0.8660254037844386, -0.5], 'a3': [0.0, 0.0], 'a4': [0.5, -0.8660254037844386], 'a5': [1.224744871391589, 2.1213203435596424], 'a6': [0.0, 0.0], 'a7': [-1.0, 2.449489742783178], 'a8': [0.0, -1.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.0183451964044, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, 0.5]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, -2.449489742783178]]]], 'bad_primes': [2, 3, 7], 'central_character': '378.269', 'coefficient_field': 'CDF', 'conductor': 378, 'conductor_radical': 42, 'conjugate': '2586183002827803937902735783765', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, 0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.224744871391589, -2.1213203435596424], [-2.5, 4.330127018922194]], [[1.0, 0], [1.0, -2.449489742783178]], [[1.0, 0], 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False, 'root_analytic_conductor': 1.737338538225754, 'root_angle': -0.08363671556013398, 'root_number': '0.9656787062946326 - 0.25973955457173764*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0418183577801', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.37216278210050611772860377394', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.40981879657180536897900609000', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.39119045265655951491120401214', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.0183451964044, 'bad_primes': [2, 3, 7], 'central_character': '21.17', 'conductor': 378, 'conductor_radical': 42, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/378/2/k/d/269/4'], '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': '2-378-21.17-c1-0-3', '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': '2-378-21.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.737338538225754, 'root_angle': -0.04181835778006699, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.37216278210050611772860377394', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1739422974340543730957184896413', 'Lhash_array': ['1739422974340543730957184896413'], 'label': '2-378-21.17-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/378/2/k/d/269/4'}