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lfunc_lfunctions • Show schema
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{'Lhash': '2543638615436455637423617053462', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, -3.4641016151377544], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.9826650861278985, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [1.0, 3.4641016151377544]]]], 'bad_primes': [2, 3, 13], 'central_character': '624.337', 'coefficient_field': 'CDF', 'conductor': 624, 'conductor_radical': 78, 'conjugate': '1091030209730495903424604500817', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-5.0, 0]], [[1.0, 0], [0, 3.4641016151377544], [-7.0, 0]], [[1.0, 0], [0, 3.4641016151377544], [-11.0, 0]], [[1.0, 0], [1.0, 3.4641016151377544]], [[1.0, 0], [6.0, 0], [17.0, 0]], [[1.0, 0], [0, -3.4641016151377544], [-19.0, 0]], 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'prelabel': '2-624-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.232188407399317, 'root_angle': 0.4105438124889666, 'root_number': '0.2773500981126145 + 0.9607689228305228*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.205271906244', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.00657706072832352684294701813', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.75771868111859403138891802347', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.36860633865166102426951112563', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.9826650861278985, 'bad_primes': [2, 3, 13], 'central_character': '13.12', 'conductor': 624, 'conductor_radical': 78, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/624/2/c/e/337/1'], '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': '2-624-13.12-c1-0-11', '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': '2-624-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.232188407399317, 'root_angle': 0.2052719062444833, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.00657706072832352684294701813', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2543638615436455637423617053462', 'Lhash_array': ['2543638615436455637423617053462'], 'label': '2-624-13.12-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/624/2/c/e/337/1'}