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lfunc_lfunctions • Show schema
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{'Lhash': '1769621560097586784221778216144', 'a10': [0.0, 1.0], 'a2': [0.0, 1.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [0.0, 1.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7680610544421907, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [3, 19], 'central_character': '1539.892', 'coefficient_field': 'CDF', 'conductor': 1539, 'conductor_radical': 57, 'conjugate': '2434607327216246933790070704191', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0], [1.0, 0]], [[1.0, 0], [-1.0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [0, -1.0], [-1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [0, 1.0], [-1.0, 0]], [[1.0, 0], [0, 1.0], [-1.0, 0]], [[1.0, 0], [0, 0], 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'-0.25', 'prec': 17}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.39598526579720145480991906165', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.20964697324240044925406340760', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.09523048201631533229628724228', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7680610544421907, 'bad_primes': [3, 19], 'central_character': '19.18', 'conductor': 1539, 'conductor_radical': 57, 'degree': 2, 'index': 2, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1539/1/c/d/892/2', 'ArtinRepresentation/2.1539.24t21.a.b'], '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': '2-1539-19.18-c0-0-2', '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': '2-1539-19.18-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8763909255818381, 'root_angle': -0.25, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.39598526579720145480991906165', 'prec': 103}}
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lfunc_instances • Show schema
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id: 19819003
{'Lhash': '1769621560097586784221778216144', 'Lhash_array': ['1769621560097586784221778216144'], 'label': '2-1539-19.18-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1539/1/c/d/892/2'}
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id: 24604813
{'Lhash': '1769621560097586784221778216144', 'Lhash_array': ['1769621560097586784221778216144'], 'label': '2-1539-19.18-c0-0-2', 'type': 'Artin', 'url': 'ArtinRepresentation/2.1539.24t21.a.b'}