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lfunc_lfunctions • Show schema
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{'Lhash': '1079359504042986012494527937382', 'a10': [0.5, -0.8660254037844386], 'a2': [-0.30901699437494745, -0.5352331346596348], 'a3': [0.0, 0.0], 'a4': [0.30901699437494745, -0.5352331346596348], 'a5': [0.8090169943749475, 1.4012585384440734], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-1.0, 1.6656746703541308e-80], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.9318806639023525, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [79, [[1.0, 0], [0.5, 0.8660254037844386]]]], 'bad_primes': [7, 79], 'central_character': '3871.3791', 'coefficient_field': 'CDF', 'conductor': 3871, 'conductor_radical': 553, 'conjugate': '1718243093253851549932620437593', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.30901699437494745, 0.5352331346596348], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [-0.8090169943749475, -1.4012585384440734], [-0.5, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.9318806639023525, 'bad_primes': [7, 79], 'central_character': '553.473', 'conductor': 3871, 'conductor_radical': 553, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3871/1/m/c/3791/1'], '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': '2-3871-553.473-c0-0-4', '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': '2-3871-553.473-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3899210998838576, 'root_angle': -0.020172953053946126, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.851464515418252297395622892466', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1079359504042986012494527937382', 'Lhash_array': ['1079359504042986012494527937382'], 'factors': ['2-3871-553.473-c0-0-4'], 'label': '2-3871-553.473-c0-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3871/1/m/c/3791/1'}