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lfunc_lfunctions • Show schema
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{'Lhash': '1356473108810856615699167412310', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.17364817766693036, 0.984807753012208], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.17364817766693036, 0.984807753012208], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.3638183942094588, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.323', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '2861090202602302203719342304156', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-0.17364817766693036, -0.984807753012208]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.766044443118978, -0.6427876096865394]], [[1.0, 0], [0.17364817766693036, -0.984807753012208], [-0.9396926207859084, -0.3420201433256687]], [[1.0, 0], [0, 0], [-0.766044443118978, 0.6427876096865394]], [[1.0, 0], 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0.6031736020495747, 'root_angle': -0.42592592592592593, 'root_number': '0.23061587074244017845019834929328 - 0.97304487057982383883288517278498*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.21296296296296297', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.07006860452449239445642996379', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.63873397899260259435274010216', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.02644344698241976310623600268', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.3638183942094588, 'bad_primes': [3], 'central_character': '27.11', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 0, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/1/f/a/323/1', 'ArtinRepresentation/2.729.18t16.a.a'], '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': '2-3e6-27.11-c0-0-0', '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': '2-3e6-27.11-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6031736020495747, 'root_angle': -0.21296296296296297, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.07006860452449239445642996379', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24603596
{'Lhash': '1356473108810856615699167412310', 'Lhash_array': ['1356473108810856615699167412310'], 'label': '2-3e6-27.11-c0-0-0', 'type': 'Artin', 'url': 'ArtinRepresentation/2.729.18t16.a.a'}
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id: 19805353
{'Lhash': '1356473108810856615699167412310', 'Lhash_array': ['1356473108810856615699167412310'], 'label': '2-3e6-27.11-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/1/f/a/323/1'}