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lfunc_lfunctions • Show schema
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{'Lhash': '1147983453962708177205617902899', 'a10': [0.0, 0.0], 'a2': [0.17364817766693036, 0.984807753012208], 'a3': [-1.4396926207859084, 1.2080455471101075], 'a4': [-0.9396926207859084, 0.3420201433256687], 'a5': [0.0, 0.0], 'a6': [-1.4396926207859084, -1.2080455471101075], 'a7': [0.0, 0.0], 'a8': [-0.5, -0.8660254037844386], 'a9': [0.4396926207859084, -2.493620766483186], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.441299756484111, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.17364817766693036, -0.984807753012208]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 19], 'central_character': '2888.2555', 'coefficient_field': 'CDF', 'conductor': 2888, 'conductor_radical': 38, 'conjugate': '830041639599140624063873310983', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.17364817766693036, -0.984807753012208]], [[1.0, 0], [1.4396926207859084, -1.2080455471101075], [0.17364817766693036, -0.984807753012208]], 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'5.78174463730179939181739265694194', '6.23089341703450122113155051270999', '7.17136436638907362084785214342131', '7.969303771140136466558771894528890', '8.710741924869237087602087911078915'], 'prelabel': '2-2888-152.123-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.200541443051472, 'root_angle': -0.507374408005585, 'root_number': '-0.023165313640611571057882979835263 - 0.99973164811559911698739102960153*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2536872040027925', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.905599266671765704664414227366', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.83720065416355188228658964347', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.74211724122067830910684810425', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.441299756484111, 'bad_primes': [2, 19], 'central_character': '152.123', 'conductor': 2888, 'conductor_radical': 38, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2888/1/u/b/2555/1'], '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': '2-2888-152.123-c0-0-2', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-2888-152.123-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.200541443051472, 'root_angle': -0.2536872040027925, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.905599266671765704664414227366', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1147983453962708177205617902899', 'Lhash_array': ['1147983453962708177205617902899'], 'label': '2-2888-152.123-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2888/1/u/b/2555/1'}