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lfunc_lfunctions • Show schema
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{'Lhash': '808926015980048752370542810695', 'a10': [0, 905.3045738795968], 'a2': [0, -10.958439106587024], 'a3': [0, 0], 'a4': [-88.0873876527758, 0], 'a5': [-82.61254774281002, 0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 614.6302222404845], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 70.72926453752447, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '441.440', 'coefficient_field': 'CDF', 'conductor': 441, 'conductor_radical': 21, 'conjugate': '374843762839440132455064069828', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 10.958439106587024], [-32.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [82.61254774281002, 0], [3125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -113.81554023885776], [-161051.0, 0]], [[1.0, 0], [0, 329.28807866980355], [-371293.0, 0]], [[1.0, 0], [-443.2019673165611, 0], [1419857.0, 0]], [[1.0, 0], [0, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 70.72926453752447, 'bad_primes': [3, 7], 'central_character': '21.20', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/6/c/b/440/3'], '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': '2-21e2-21.20-c5-0-29', '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': '2-21e2-21.20-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.410069235001842, 'root_angle': -0.4615494009219044, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.63813010922284791997541466371', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '808926015980048752370542810695', 'Lhash_array': ['808926015980048752370542810695'], 'label': '2-21e2-21.20-c5-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/6/c/b/440/3'}