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lfunc_lfunctions • Show schema
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{'Lhash': '1043431789963723788820396226202', 'a10': [-1.7608767217434456, -3.03825458683459e-61], 'a2': [-0.5, 0.8660254037844386], 'a3': [1.7105333071544737, 0.2721687070829029], 'a4': [-0.5, -0.8660254037844386], 'a5': [0.8804383608717228, 1.524963973962486], 'a6': [-1.0909716680261965, 1.3452809444737328], 'a7': [0.0, 0.0], 'a8': [1.0, 0.0], 'a9': [2.851848389769642, 0.9311072772609503], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.042805458276933, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, -0.8660254037844386]]], [3, [[1.0, 0], [-1.7105333071544737, -0.2721687070829029]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '882.295', 'coefficient_field': 'CDF', 'conductor': 882, 'conductor_radical': 42, 'conjugate': '2471708094398220411638904453724', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [-1.7105333071544737, -0.2721687070829029]], 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'9.008585592590557317805555386990934', '9.617017308396910116800236544235158'], 'prelabel': '2-882-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6538284530611493, 'root_angle': -0.6773251382519764, 'root_number': '-0.5287127968295104 - 0.8488007884472757*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.338662569126', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.823122546367163808942760802401', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.24212920294888074247423571400', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.09647240771912127959814468508', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.042805458276933, 'bad_primes': [2, 3, 7], 'central_character': '9.7', 'conductor': 882, 'conductor_radical': 42, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/882/2/f/m/295/3'], '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': '2-882-9.7-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': '2-882-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6538284530611493, 'root_angle': -0.3386625691259882, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.823122546367163808942760802401', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1043431789963723788820396226202', 'Lhash_array': ['1043431789963723788820396226202'], 'label': '2-882-9.7-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/882/2/f/m/295/3'}