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lfunc_lfunctions • Show schema
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{'Lhash': '739456706881835496517727194432', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [2.9530872497325364, 0.0], 'a4': [0.0, 0.0], 'a5': [4.895747256496971, 0.0], 'a6': [0.0, 0.0], 'a7': [4.462350891693439, 0.0], 'a8': [0.0, 0.0], 'a9': [-18.279275695467124, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 136.41241593327237, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 17], 'central_character': '2312.1', 'coefficient_field': 'CDF', 'conductor': 2312, 'conductor_radical': 34, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.9530872497325364, 0], [27.0, 0]], [[1.0, 0], [-4.895747256496971, 0], [125.0, 0]], [[1.0, 0], [-4.462350891693439, 0], [343.0, 0]], [[1.0, 0], [60.386455943898895, 0], [1331.0, 0]], [[1.0, 0], [56.19383171410101, 0], [2197.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-134.84523222927626, 0], [6859.0, 0]], [[1.0, 0], 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 136.41241593327237, 'bad_primes': [2, 17], 'central_character': '1.1', 'conductor': 2312, 'conductor_radical': 34, 'degree': 2, 'index': 51, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2312/4/a/k/1/6'], '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': '2-2312-1.1-c3-0-51', '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': '2-2312-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.679572592063135, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.58332848716255313965586445695', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '739456706881835496517727194432', 'Lhash_array': ['739456706881835496517727194432'], 'label': '2-2312-1.1-c3-0-51', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2312/4/a/k/1/6'}