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lfunc_lfunctions • Show schema
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{'Lhash': '1180668139086158427395577097325', 'a10': [2.466773785762759, 0.0], 'a2': [0.8478227041629287, 0.0], 'a3': [-1.0, 0.0], 'a4': [-1.281196662305859, 0.0], 'a5': [2.9095396639539763, 0.0], 'a6': [-0.8478227041629287, 0.0], 'a7': [4.442263126753135, 0.0], 'a8': [-2.7818730271265295, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 44.53256920726809, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [11, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11, 13], 'central_character': '5577.1', 'coefficient_field': 'CDF', 'conductor': 5577, 'conductor_radical': 429, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8478227041629287, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-2.9095396639539763, 0], [5.0, 0]], [[1.0, 0], [-4.442263126753135, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.033399827619829, 0], [17.0, 0]], [[1.0, 0], 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'2.72196709062270928604284440960153', '4.14967056297365204683233716189429', '4.51189916887813730503160464459986', '5.33210898208764476308840077860292', '5.76654811506372379251429657529995', '6.35613934911350242640243295097318', '7.39551700194010206352485020281812', '8.242091011626567305310186471726703'], 'prelabel': '2-5577-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.67327275085232, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.931382936965114407020189465529', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.83569944059681080578080656030', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.72196709062270928604284440960', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 44.53256920726809, 'bad_primes': [3, 11, 13], 'central_character': '1.1', 'conductor': 5577, 'conductor_radical': 429, 'degree': 2, 'index': 114, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5577/2/a/u/1/3'], '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': '2-5577-1.1-c1-0-114', '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': '2-5577-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.67327275085232, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.931382936965114407020189465529', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1180668139086158427395577097325', 'Lhash_array': ['1180668139086158427395577097325'], 'label': '2-5577-1.1-c1-0-114', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5577/2/a/u/1/3'}