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lfunc_lfunctions • Show schema
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{'Lhash': '2573255490203472170320665388515', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.8660254037844386, 0.5], 'a4': [0.0, 0.0], 'a5': [0.5, 0.8660254037844386], 'a6': [0.0, 0.0], 'a7': [0.0, -1.0], 'a8': [0.0, 0.0], 'a9': [4.582907173931562e-80, 2.6459426907612794e-80], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.2235811256595851, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 7], 'central_character': '448.319', 'coefficient_field': 'CDF', 'conductor': 448, 'conductor_radical': 14, 'conjugate': '2885414085973525556260846540234', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.8660254037844386, -0.5], [0.5, 0.8660254037844386]], [[1.0, 0], [-0.5, -0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0.8660254037844386, 0.5], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0.5, 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-0.20328579555789794, 0.40879460549926677, 0.9680177030629777, 1.4317820137796038], 'positive_zeros': ['2.02994065536684953209698623130349', '2.73398387896804476451503107402372', '4.64136410754007343002297009940797', '5.44163912864693047746632767644162', '6.65694898352044507335700182880852', '7.87796513082127025455064011611284', '8.564727706205373841052505983396901', '9.197753547314721500721906544337786', '10.13465358453283239459952849932807', '11.37366971238623890730623490037983'], 'prelabel': '2-448-28.11-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.47284365879176715, 'root_angle': -0.14649371361272057, 'root_number': '0.89595321966310477774725020770463 - 0.44414843034206066891807967048929*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.07324685680636027', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.02994065536684953209698623130', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.2235811256595851, 'bad_primes': [2, 7], 'central_character': '28.11', 'conductor': 448, 'conductor_radical': 14, 'degree': 2, 'index': 1, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/448/1/r/a/319/2', 'ArtinRepresentation/2.448.16t60.a.d'], 'is_instance_Artin': True, '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': '2-448-28.11-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': '2-448-28.11-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.47284365879176715, 'root_angle': -0.07324685680636028, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.02994065536684953209698623130', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24603215
{'Lhash': '2573255490203472170320665388515', 'Lhash_array': ['2573255490203472170320665388515'], 'label': '2-448-28.11-c0-0-1', 'type': 'Artin', 'url': 'ArtinRepresentation/2.448.16t60.a.d'}
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id: 19812545
{'Lhash': '2573255490203472170320665388515', 'Lhash_array': ['2573255490203472170320665388515'], 'label': '2-448-28.11-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/448/1/r/a/319/2'}