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lfunc_lfunctions • Show schema
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{'Lhash': '1029086229502198409773756115579', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.5, -0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [0.5, 0.8660254037844386], 'a6': [0.0, 0.0], 'a7': [0.5, 2.598076211353316], 'a8': [0.0, 0.0], 'a9': [1.0, 1.7320508075688772], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.471622513191703, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.5, -0.8660254037844386]]], [7, [[1.0, 0], [-0.5, -2.598076211353316]]]], 'bad_primes': [2, 5, 7], 'central_character': '560.81', 'coefficient_field': 'CDF', 'conductor': 560, 'conductor_radical': 70, 'conjugate': '2711899385425552991226987360871', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.5, 0.8660254037844386], [-1.5, -2.598076211353316]], [[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [-0.5, -2.598076211353316]], [[1.0, 0], [3.0, -5.196152422706632], [-5.5, -9.526279441628825]], 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'data': '2.80063679728376044789761690869', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.88345065625122588213397001023', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.471622513191703, 'bad_primes': [2, 5, 7], 'central_character': '7.4', 'conductor': 560, 'conductor_radical': 70, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/560/2/q/g/81/1'], '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': '2-560-7.4-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': '2-560-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.114621127576215, 'root_angle': -0.1868396197206128, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.811805894555582142530315413422', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1029086229502198409773756115579', 'Lhash_array': ['1029086229502198409773756115579'], 'factors': ['2-560-7.4-c1-0-3'], 'label': '2-560-7.4-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/560/2/q/g/81/1'}