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lfunc_lfunctions • Show schema
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{'Lhash': '1326358884513316988469159618326', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.0, 1.7320508075688772], 'a4': [0.0, 0.0], 'a5': [0.0, 1.7320508075688772], 'a6': [0.0, 0.0], 'a7': [12.0, 6.928203230275509], 'a8': [0.0, 0.0], 'a9': [11.5, -19.91858428704209], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.272397281194053, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-45.5, 11.258330249197702]]]], 'bad_primes': [2, 13], 'central_character': '208.49', 'coefficient_field': 'CDF', 'conductor': 208, 'conductor_radical': 26, 'conjugate': '1838466768974716830897598870124', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, -1.7320508075688772], [-13.5, 23.382685902179844]], [[1.0, 0], [0, -1.7320508075688772], [-125.0, 0]], [[1.0, 0], [-12.0, -6.928203230275509], [171.5, 297.04671349806245]], [[1.0, 0], [12.0, -6.928203230275509], [665.5, -1152.6798124370878]], 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['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.04631267028510669576583039583', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.60138688882169316357273968957', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.34095374656694777953470558090', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.272397281194053, 'bad_primes': [2, 13], 'central_character': '13.10', 'conductor': 208, 'conductor_radical': 26, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/208/4/w/b/49/1'], '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': '2-208-13.10-c3-0-8', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-208-13.10-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.503198150432552, 'root_angle': -0.11989762151858327, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.04631267028510669576583039583', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1326358884513316988469159618326', 'Lhash_array': ['1326358884513316988469159618326'], 'label': '2-208-13.10-c3-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/208/4/w/b/49/1'}