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lfunc_lfunctions • Show schema
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{'Lhash': '2235456008638926475326400404315', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [-0.5, -0.8660254037844386], 'a5': [0.5, -0.8660254037844386], 'a6': [0.0, 0.0], 'a7': [-0.5, -0.8660254037844386], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.261137286923597, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0.5, 0.8660254037844386]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [7, 19], 'central_character': '2527.1152', 'coefficient_field': 'CDF', 'conductor': 2527, 'conductor_radical': 133, 'conjugate': '1240046284542087351413954316067', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-0.5, 0.8660254037844386], [-0.5, -0.8660254037844386]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [-0.5, 0.8660254037844386], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 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'7.12036365109043479879896475291471', '7.68236527385182617986736640424600', '8.552382183417946714269682844097596', '9.572606047885828759493346665559647'], 'prelabel': '2-2527-133.88-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.123003689630447, 'root_angle': 0.5879262411162229, 'root_number': '-0.27272900678581514933226890521225 + 0.96209089428058864371161070339262*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.29396312055811147', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.76346385055665352594223022210', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.82445315478393322423230371854', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.57914796134275968253036637996', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.261137286923597, 'bad_primes': [7, 19], 'central_character': '133.88', 'conductor': 2527, 'conductor_radical': 133, 'degree': 2, 'index': 0, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2527/1/n/a/1152/1', 'ArtinRepresentation/2.2527.6t5.c.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': '2-2527-133.88-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': '2-2527-133.88-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.123003689630447, 'root_angle': 0.29396312055811147, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.76346385055665352594223022210', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24600261
{'Lhash': '2235456008638926475326400404315', 'Lhash_array': ['2235456008638926475326400404315'], 'label': '2-2527-133.88-c0-0-0', 'type': 'Artin', 'url': 'ArtinRepresentation/2.2527.6t5.c.a'}
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id: 19886500
{'Lhash': '2235456008638926475326400404315', 'Lhash_array': ['2235456008638926475326400404315'], 'label': '2-2527-133.88-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2527/1/n/a/1152/1'}