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lfunc_lfunctions • Show schema
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{'Lhash': '2253331285067816898387144584251', 'a10': [-0.2803801369048046, -0.5538610804419064], 'a2': [-1.1840363575050463, -0.7733420356518724], 'a3': [0.5, 0.8660254037844386], 'a4': [0.8038841917876361, 1.8313301739975616], 'a5': [0.38015216571741023, 0.21948095520996602], 'a6': [0.07771566993636934, -1.4120765824297], 'a7': [2.0235040548828316, 1.7045325869201617], 'a8': [0.46441649440985106, -2.7900389459145662], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6707433769787555, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.1840363575050463, 0.7733420356518724]]], [3, [[1.0, 0], [-0.5, -0.8660254037844386]]], [7, [[1.0, 0], [-2.0235040548828316, -1.7045325869201617]]]], 'bad_primes': [2, 3, 7], 'central_character': '84.19', 'coefficient_field': 'CDF', 'conductor': 84, 'conductor_radical': 42, 'conjugate': '2952279558263235800291195383662', 'degree': 2, 'euler_factors': 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'8.625627145943266633493381068038985', '9.515565619828406398793387636789967', '10.94594719852831285667298096024209', '11.85012995652094919708135537700024', '13.65202769915119487663106068878356', '14.20771852109056533605840313278153'], 'prelabel': '2-84-28.19-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8189892410641031, 'root_angle': -0.03515393494953041, 'root_number': '0.9939077716161812 - 0.11021497865969543*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0175769674748', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.77756495730142384033954453433', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.67762246919378936523647647867', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.53513172287902680440732507763', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6707433769787555, 'bad_primes': [2, 3, 7], 'central_character': '28.19', 'conductor': 84, 'conductor_radical': 42, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/84/2/o/b/19/1'], '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': '2-84-28.19-c1-0-1', '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': '2-84-28.19-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8189892410641031, 'root_angle': -0.017576967474765205, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.77756495730142384033954453433', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2253331285067816898387144584251', 'Lhash_array': ['2253331285067816898387144584251'], 'label': '2-84-28.19-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/84/2/o/b/19/1'}