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lfunc_lfunctions • Show schema
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{'Lhash': '1593603267233336890436711229593', 'a10': [0.0, 0.0], 'a2': [1.9364916731037085, 1.118033988749895], 'a3': [0.0, 0.0], 'a4': [1.5, 2.598076211353316], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.5, 2.598076211353316], 'a8': [0.0, 2.23606797749979], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.5275177946066, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.5, -2.598076211353316]]]], 'bad_primes': [3, 7], 'central_character': '567.458', 'coefficient_field': 'CDF', 'conductor': 567, 'conductor_radical': 21, 'conjugate': '2882290534095226349151789621176', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.9364916731037085, -1.118033988749895], [1.0, 1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [5.0, 0]], [[1.0, 0], [0.5, -2.598076211353316]], [[1.0, 0], [0, -4.47213595499958], [-11.0, 0]], [[1.0, 0], [-1.5, -0.8660254037844386], [6.5, 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0.9938283388902579*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.267691301251', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.25713131595285212076105899498', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.92836040090298976684038372553', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.75634895091802207344630030279', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.5275177946066, 'bad_primes': [3, 7], 'central_character': '63.59', 'conductor': 567, 'conductor_radical': 21, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/567/2/s/e/458/2'], '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': '2-567-63.59-c1-0-11', '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': '2-567-63.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1277964645629526, 'root_angle': -0.26769130125080476, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.25713131595285212076105899498', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1593603267233336890436711229593', 'Lhash_array': ['1593603267233336890436711229593'], 'label': '2-567-63.59-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/567/2/s/e/458/2'}