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lfunc_lfunctions • Show schema
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{'Lhash': '808786203863585487674164246492', 'a10': [0.146972056182888, 0.4038024056533009], 'a2': [-1.8668755332131224, 1.566494571373019], 'a3': [-1.403449857947569, -1.0150509820826483], 'a4': [0.6840226590347809, -3.879285270390516], 'a5': [0.0603077842789526, -0.16569427552376273], 'a6': [4.2101380549930685, -0.3035227402550538], 'a7': [0.34005894171685136, 0.5889993646216902], 'a8': [2.3628612212261486, 4.092595686397934], 'a9': [0.9393430075461027, 2.849146313226866], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.403449857947569, 1.0150509820826483]]], [19, [[1.0, 0], [0.12243735727892689, -4.357179029319607]]]], 'bad_primes': [3, 19], 'central_character': '171.110', 'coefficient_field': 'CDF', 'conductor': 171, 'conductor_radical': 57, 'conjugate': '2043483252678612378040725051770', 'degree': 2, 'euler_factors': [[[1.0, 0], 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{'__RealLiteral__': 0, 'data': '-0.332607241026', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.63801981691009384345949693835', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.85959993701283800515640726211', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.37235876670099440361746848143', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'bad_primes': [3, 19], 'central_character': '171.110', 'conductor': 171, 'conductor_radical': 57, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/171/2/x/a/110/2'], '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': '2-171-171.110-c1-0-2', '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': '2-171-171.110-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': -0.3326072410257649, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.63801981691009384345949693835', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '808786203863585487674164246492', 'Lhash_array': ['808786203863585487674164246492'], 'label': '2-171-171.110-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/171/2/x/a/110/2'}