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lfunc_lfunctions • Show schema
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{'Lhash': '1316410309032943896593383052007', 'a10': [-9.238245095853235e-61, 1.4185836995976868], 'a2': [0.5556320787951069, -0.32079433026274634], 'a3': [0.0, 0.0], 'a4': [-0.7941819953425521, 1.3755635663897297], 'a5': [-1.1055242921810657, 1.9148242430592264], 'a6': [0.0, 0.0], 'a7': [-0.9061609023903838, 2.4857337787822424], 'a8': [0.0, 2.3022536462615673], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5091725982022, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.9061609023903838, -2.4857337787822424]]]], 'bad_primes': [3, 7], 'central_character': '189.125', 'coefficient_field': 'CDF', 'conductor': 189, 'conductor_radical': 21, 'conjugate': '3594611751858869167302148126062', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5556320787951069, 0.32079433026274634], [1.0, -1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.1055242921810657, -1.9148242430592264], 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'12.47489133484027218838111942784973'], 'prelabel': '2-189-63.41-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2284838615961546, 'root_angle': -0.4119166229699742, 'root_number': '0.273203916470656 - 0.9619561424644549*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.205958311485', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.03846462802600001614286503433', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.88902011780119719378323057258', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.61884076897991055353850629959', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.5091725982022, 'bad_primes': [3, 7], 'central_character': '63.41', 'conductor': 189, 'conductor_radical': 21, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/189/2/o/a/125/3'], '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': '2-189-63.41-c1-0-1', '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': '2-189-63.41-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2284838615961546, 'root_angle': -0.2059583114849871, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.03846462802600001614286503433', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1316410309032943896593383052007', 'Lhash_array': ['1316410309032943896593383052007'], 'label': '2-189-63.41-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/189/2/o/a/125/3'}