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lfunc_lfunctions • Show schema
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{'Lhash': '2437962812869548801776784411784', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, -0.29684755576436084], 'a4': [0.0, 0.0], 'a5': [-2.1827050350568387, 0.48559111394003474], 'a6': [0.0, 0.0], 'a7': [0.0, -3.4603733388820523], 'a8': [0.0, 0.0], 'a9': [2.911881528636725, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.346236985957799, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [2.1827050350568387, -0.48559111394003474]]], [23, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 5, 23], 'central_character': '920.369', 'coefficient_field': 'CDF', 'conductor': 920, 'conductor_radical': 230, 'conjugate': '220265285164241618769383550735', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0.29684755576436084], [-3.0, 0]], [[1.0, 0], [2.1827050350568387, -0.48559111394003474]], [[1.0, 0], [0, 3.4603733388820523], [-7.0, 0]], [[1.0, 0], [3.113765815632711, 0], [11.0, 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'4.20536789393233861694088457739136', '5.26363236497416633775524954072300', '5.97878144254988785448240980899645', '7.30443184459368379912695629106131', '8.041002781000399550607530065178801', '8.647462180996254382467119972603120', '9.595226168958733005010241451429206', '10.68929968896938138917532155888870'], 'prelabel': '2-920-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.710394249174426, 'root_angle': 0.9303197015552495, 'root_number': '-0.9761353666436307 + 0.21716294800795255*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.465159850778', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.92321355145543647751025490044', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.23324062318899175647603202648', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.20536789393233861694088457739', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.346236985957799, 'bad_primes': [2, 5, 23], 'central_character': '5.4', 'conductor': 920, 'conductor_radical': 230, 'degree': 2, 'index': 28, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/920/2/e/c/369/8'], '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': '2-920-5.4-c1-0-28', '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': '2-920-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.710394249174426, 'root_angle': 0.46515985077762473, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.92321355145543647751025490044', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2437962812869548801776784411784', 'Lhash_array': ['2437962812869548801776784411784'], 'label': '2-920-5.4-c1-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/920/2/e/c/369/8'}