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lfunc_lfunctions • Show schema
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{'Lhash': '2083232343567685293809137189937', 'a10': [0.5, -0.8660254037844386], 'a2': [0.8660254037844386, 0.5], 'a3': [0.0, 0.0], 'a4': [0.5, 0.8660254037844386], 'a5': [0.0, -1.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [3.9689140359382235e-80, 1.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.808485320465464, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, -0.5]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 3, 5], 'central_character': '1620.379', 'coefficient_field': 'CDF', 'conductor': 1620, 'conductor_radical': 30, 'conjugate': '1827161757496012085506770534725', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [-1.5, 0.8660254037844386], [0.5, -0.8660254037844386]], 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'3.88156644436308382415282703005130', '4.02082850120711028131731895035687', '5.65183261391244173302746590621644', '6.13121024246363087341627813573886', '6.87417665803887921583664907983751', '7.78597927458104807636715313656461', '8.914939898645643276668562489691223', '9.750539564565347596011197610112328'], 'prelabel': '2-1620-180.79-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8991581176108371, 'root_angle': -0.1111111111111111, 'root_number': '0.93969262078590838405410927732446 - 0.34202014332566873304409961468239*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.05555555555555555', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.64338055233249409097346739135', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.59586186248190910979691187596', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.88156644436308382415282703005', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.808485320465464, 'bad_primes': [2, 3, 5], 'central_character': '180.79', 'conductor': 1620, 'conductor_radical': 30, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1620/1/p/e/379/2'], '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': '2-1620-180.79-c0-0-8', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1620-180.79-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8991581176108371, 'root_angle': -0.05555555555555555, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.64338055233249409097346739135', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2083232343567685293809137189937', 'Lhash_array': ['2083232343567685293809137189937'], 'label': '2-1620-180.79-c0-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1620/1/p/e/379/2'}