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lfunc_lfunctions • Show schema
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{'Lhash': '2680465988716709274787373502143', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -1.0], 'a4': [0, 0], 'a5': [-1.6751308705666461, -1.4811943040920157], 'a6': [0, 0], 'a7': [0, -1.0], 'a8': [0, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.0193554789367, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [1.6751308705666461, 1.4811943040920157]]], [23, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '1380.829', 'coefficient_field': 'CDF', 'conductor': 1380, 'conductor_radical': 690, 'conjugate': '126624344755058181140333067796', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [1.6751308705666461, 1.4811943040920157]], [[1.0, 0], [0, 1.0], [-7.0, 0]], [[1.0, 0], [1.6751308705666461, 0], [11.0, 0]], [[1.0, 0], [0, 0.8690674370412765], [-13.0, 0]], [[1.0, 0], [0, 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['2.11451482627319769464167510977818', '3.25801566857281240583196657946303', '3.97890346019327622627674007502750', '5.01295195184554566015188705111789', '5.90298994368192753163919035632332', '6.88121085099408559555584303724598', '7.68990592615887585851002756719153', '8.499293571920891904724609941434346', '9.231903607320071452735468939437135', '10.24855552245154405640493815643995'], 'prelabel': '2-1380-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3195414561256347, 'root_angle': -0.7695336070209555, 'root_number': '-0.74914129955908445453105880718175956359649879110032479350 - 0.66241023036704836934394295657888095753754327898659579537*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.38476680351047776', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.11451482627319769464167510978', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.25801566857281240583196657946', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.97890346019327622627674007503', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 11.0193554789367, 'bad_primes': [2, 3, 5, 23], 'central_character': '5.4', 'conductor': 1380, 'conductor_radical': 690, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1380/2/f/a/829/1'], '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': '2-1380-5.4-c1-0-19', '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': '2-1380-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3195414561256347, 'root_angle': -0.38476680351047776, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.11451482627319769464167510978', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2680465988716709274787373502143', 'Lhash_array': ['2680465988716709274787373502143'], 'label': '2-1380-5.4-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1380/2/f/a/829/1'}