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lfunc_lfunctions • Show schema
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{'Lhash': '564011447208473089728115951202', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-2.6445290431015778, 0.0], 'a6': [0.0, 0.0], 'a7': [0.18096854854533745, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 43.69413998604465, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 19], 'central_character': '5472.1', 'coefficient_field': 'CDF', 'conductor': 5472, 'conductor_radical': 114, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.6445290431015778, 0], [5.0, 0]], [[1.0, 0], [-0.18096854854533745, 0], [7.0, 0]], [[1.0, 0], [0.6445290431015779, 0], [11.0, 0]], [[1.0, 0], [3.948603217264576, 0], [13.0, 0]], [[1.0, 0], [5.568018953001083, 0], [17.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [4.463560494556241, 0], [23.0, 0]], 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[113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-5472-1.1-c1-0-3', 'leading_term': '0.76294029567339126048367060737217', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/5472/2/a/bt/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.7629402956733913, 0.7529948562446626, 0.7231415477207166, 0.6733375293653115, 0.6035379050873411, 0.5137334627580703, 0.4039996878646324, 0.27455368990470547, 0.1258152794514733, -0.041531685569477644, -0.22648144750318427, -0.4276554578580038, -0.6432615033682499, -0.8710654296236715, -1.1083775393091309, -1.3520552311860246, -1.5985229349303764, -1.8438098850275981, -2.08360575970774, -2.3133336841729912, -2.528239559710121, -2.7234961345416058, -2.8943196860558476, -3.0360966495351778, 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'4.93833320088255168787101420148941', '6.22236001032281473313944073310960', '6.74103353067535340049920296752529', '7.59362774709974973570775509592701', '8.110338566745507572195447948303564'], 'prelabel': '2-5472-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.610154308792242, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.44492658079988899345149422603', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.99577781044041123888215544026', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.83081853277788718274860662447', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 43.69413998604465, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 5472, 'conductor_radical': 114, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5472/2/a/bt/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': '2-5472-1.1-c1-0-3', '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': '2-5472-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.610154308792242, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.44492658079988899345149422603', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '564011447208473089728115951202', 'Lhash_array': ['564011447208473089728115951202'], 'label': '2-5472-1.1-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5472/2/a/bt/1/2'}