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lfunc_lfunctions • Show schema
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{'Lhash': '2844473560313465010903049410245', 'a10': [659.3001664081031, 0.0], 'a2': [9.34907849162148, 0.0], 'a3': [9.0, 0.0], 'a4': [55.405268642499365, 0.0], 'a5': [70.52033705770673, 0.0], 'a6': [84.14170642459332, 0.0], 'a7': [-89.71317395092547, 0.0], 'a8': [218.81769365621346, 0.0], 'a9': [81.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.066483567095666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-9.0, 0]]], [23, [[1.0, 0], [529.0, 0]]]], 'bad_primes': [3, 23], 'central_character': '69.1', 'coefficient_field': 'CDF', 'conductor': 69, 'conductor_radical': 69, 'conjugate': '2844473560313465010903049410245', 'degree': 2, 'euler_factors': [[[1.0, 0], [-9.34907849162148, 0], [32.0, 0]], [[1.0, 0], [-9.0, 0]], [[1.0, 0], [-70.52033705770673, 0], [3125.0, 0]], [[1.0, 0], [89.71317395092547, 0], [16807.0, 0]], [[1.0, 0], [436.76324192728055, 0], [161051.0, 0]], [[1.0, 0], [258.8648767924981, 0], 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.066483567095666, 'bad_primes': [3, 23], 'central_character': '1.1', 'conductor': 69, 'conductor_radical': 69, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/69/6/a/e/1/5'], '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': '2-69-1.1-c5-0-13', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-69-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.326632466488546, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '2.24389398766611432919762071086', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2844473560313465010903049410245', 'Lhash_array': ['2844473560313465010903049410245'], 'label': '2-69-1.1-c5-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/69/6/a/e/1/5'}