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lfunc_lfunctions • Show schema
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{'Lhash': '1340415477490320470603553526149', 'a10': [-0.09990042250462965, 0.7588190451025207], 'a2': [0.9659258262890683, 0.25881904510252074], 'a3': [0.0, 0.0], 'a4': [0.8660254037844386, 0.5], 'a5': [0.09990042250462965, 0.7588190451025207], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.7071067811865476, 0.7071067811865476], 'a9': [-0.25881904510252074, 0.9659258262890683], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9659258262890683, -0.25881904510252074]]], [7, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [0.25881904510252074, 0.9659258262890683]]]], 'bad_primes': [2, 7, 17], 'central_character': '3332.263', 'coefficient_field': 'CDF', 'conductor': 3332, 'conductor_radical': 238, 'conjugate': '2359572472890955850756865695190', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.9659258262890683, -0.25881904510252074]], [[1.0, 0], [0, 0], 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'6.78410677624725477064403623971579', '7.88705168490309106426204937911399', '8.718121995825093886757082408792561'], 'prelabel': '2-3332-476.263-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': -0.4607147515929238, 'root_number': '0.12310516722255723037982311441213 - 0.99239363047286141926411758684747*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2303573757964619', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.05740136694526897986230506952', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.11276847089133480192130302580', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.28046304674850454497978475998', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'bad_primes': [2, 7, 17], 'central_character': '476.263', 'conductor': 3332, 'conductor_radical': 238, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3332/1/bp/b/263/1'], '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': '2-3332-476.263-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3332-476.263-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': -0.2303573757964619, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.05740136694526897986230506952', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1340415477490320470603553526149', 'Lhash_array': ['1340415477490320470603553526149'], 'label': '2-3332-476.263-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3332/1/bp/b/263/1'}