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lfunc_lfunctions • Show schema
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{'Lhash': '1441552324428339473714171305133', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-3.0, 0.0], 'a4': [0.0, 0.0], 'a5': [14.704699910719626, 0.0], 'a6': [0.0, 0.0], 'a7': [-31.40939982143925, 0.0], 'a8': [0.0, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 124.61203393212423, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [3.0, 0]]], [11, [[1.0, 0], [11.0, 0]]]], 'bad_primes': [2, 3, 11], 'central_character': '2112.1', 'coefficient_field': 'CDF', 'conductor': 2112, 'conductor_radical': 66, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [3.0, 0]], [[1.0, 0], [-14.704699910719626, 0], [125.0, 0]], [[1.0, 0], [31.40939982143925, 0], [343.0, 0]], [[1.0, 0], [11.0, 0]], [[1.0, 0], [22.704699910719626, 0], [2197.0, 0]], [[1.0, 0], [46.11409973215888, 0], [4913.0, 0]], [[1.0, 0], [-4.114099732158875, 0], [6859.0, 0]], [[1.0, 0], [-163.52349955359813, 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'4.47796898347901354970849647734700', '5.27846093357250755201574045953831', '6.18984533869279141511714632799327', '6.51720387714690591690413716424609', '7.25474025076188390527265916866632', '8.579543922565863800575491334425612'], 'prelabel': '2-2112-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.162976033841703, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.13718427157199356669876605765', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.51144709292696402862363764563', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.07332731810258926105659995186', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 124.61203393212423, 'bad_primes': [2, 3, 11], 'central_character': '1.1', 'conductor': 2112, 'conductor_radical': 66, 'degree': 2, 'index': 78, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2112/4/a/bd/1/2'], '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': '2-2112-1.1-c3-0-78', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-2112-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.162976033841703, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.13718427157199356669876605765', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1441552324428339473714171305133', 'Lhash_array': ['1441552324428339473714171305133'], 'factors': ['2-2112-1.1-c3-0-78'], 'label': '2-2112-1.1-c3-0-78', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2112/4/a/bd/1/2'}