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lfunc_lfunctions • Show schema
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{'Lhash': '1508686630161404071359664744155', 'a10': [-0.5302487364574218, 2.1722882583776277], 'a2': [-0.9510565162951535, -0.30901699437494745], 'a3': [-0.260073510670101, 0.35796047807979386], 'a4': [0.8090169943749475, 0.5877852522924731], 'a5': [-0.1669774724547413, -2.229824774212679], 'a6': [0.35796047807979386, -0.260073510670101], 'a7': [0.0, 0.2734574719946391], 'a8': [-0.5877852522924731, -0.8090169943749475], 'a9': [0.8665535102099988, 2.6669774724547413], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.3917721111704235, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9510565162951535, 0.30901699437494745]]], [5, [[1.0, 0], [0.1669774724547413, 2.229824774212679]]], [11, [[1.0, 0], [0.30901699437494745, -0.9510565162951535]]]], 'bad_primes': [2, 5, 11], 'central_character': '550.529', 'coefficient_field': 'CDF', 'conductor': 550, 'conductor_radical': 110, 'conjugate': 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'sign_arg': {'__RealLiteral__': 0, 'data': '0.0862081911748', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.19014390076396306773597844741', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.91522726636804120375780931004', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.96843081632990997603459638482', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.3917721111704235, 'bad_primes': [2, 5, 11], 'central_character': '25.4', 'conductor': 550, 'conductor_radical': 110, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/550/2/t/a/529/1'], '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': '2-550-25.4-c1-0-12', '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': '2-550-25.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.095655532565031, 'root_angle': 0.08620819117478336, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.19014390076396306773597844741', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1508686630161404071359664744155', 'Lhash_array': ['1508686630161404071359664744155'], 'label': '2-550-25.4-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/550/2/t/a/529/1'}