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lfunc_lfunctions • Show schema
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{'Lhash': '2137063689885446514990053045721', 'a10': [0.8467460949375999, 5.629116640587864], 'a2': [-2.2046745713132565, 1.2728694572232315], 'a3': [0.0, 0.0], 'a4': [2.240393310263528, -3.8804750423138534], 'a5': [0.8175444385565523, -2.0812546915227004], 'a6': [0.0, 0.0], 'a7': [-2.5448608327047726, -1.4692760868122356], 'a8': [0.0, 6.315435038313856], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.8175444385565523, 2.0812546915227004]]], [13, [[1.0, 0], [-3.6048388692084083, -0.07167096374575402]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.289', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '472795079680254967308240163404', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.2046745713132565, -1.2728694572232315], [1.0, -1.7320508075688772]], [[1.0, 0], [0, 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'9.450923285590722863616013138783923', '9.935006492626439300998563809625709', '10.82888550802467557010647423223852'], 'prelabel': '2-585-65.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.5400954692099585, 'root_number': '-0.12563078829018787 + 0.9920770660758095*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.270047734605', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.68584599691798898852558225611', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.87450166157146223744966424214', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.57727177497259332258716230240', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.671248518244905, 'bad_primes': [3, 5, 13], 'central_character': '65.29', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/bs/a/289/1'], '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': '2-585-65.29-c1-0-23', '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': '2-585-65.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': 0.2700477346049793, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.68584599691798898852558225611', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2137063689885446514990053045721', 'Lhash_array': ['2137063689885446514990053045721'], 'label': '2-585-65.29-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/bs/a/289/1'}