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lfunc_lfunctions • Show schema
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{'Lhash': '567739131724172633442691534005', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-3.1859019805353466, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.1055599786182224, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 54.80931594740688, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [11, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 11, 13], 'central_character': '6864.1', 'coefficient_field': 'CDF', 'conductor': 6864, 'conductor_radical': 858, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [3.1859019805353466, 0], [5.0, 0]], [[1.0, 0], [1.1055599786182224, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [6.291461959153569, 0], [17.0, 0]], [[1.0, 0], [3.7440382569720603, 0], [19.0, 0]], [[1.0, 0], [3.2662439824524703, 0], 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'4.72023130585570917220570456471571', '6.06432031103699448321016858176755', '6.67230183754304370464556390725734', '7.44871357579514465479321819017876', '7.901117302951875777942755990484084'], 'prelabel': '2-6864-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.403331408724513, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.44786720538132208449908148316', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.00844397431474141938390203981', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.81200120341979243166919960193', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 54.80931594740688, 'bad_primes': [2, 3, 11, 13], 'central_character': '1.1', 'conductor': 6864, 'conductor_radical': 858, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6864/2/a/ca/1/1'], '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': '2-6864-1.1-c1-0-5', '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': '2-6864-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.403331408724513, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.44786720538132208449908148316', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '567739131724172633442691534005', 'Lhash_array': ['567739131724172633442691534005'], 'label': '2-6864-1.1-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6864/2/a/ca/1/1'}