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lfunc_lfunctions • Show schema
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{'Lhash': '1682330624140102680353083251400', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-0.5, 0.8660254037844386], 'a6': [0.0, 0.0], 'a7': [0.5, -2.598076211353316], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.024460261872533, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.5, 2.598076211353316]]]], 'bad_primes': [2, 3, 7], 'central_character': '504.289', 'coefficient_field': 'CDF', 'conductor': 504, 'conductor_radical': 42, 'conjugate': '1534987587599522210763885920903', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.5, -0.8660254037844386], [-2.5, -4.330127018922194]], [[1.0, 0], [-0.5, 2.598076211353316]], [[1.0, 0], [-1.5, -2.598076211353316], [-5.5, 9.526279441628825]], [[1.0, 0], [-4.0, 0], [13.0, 0]], [[1.0, 0], [0, 0], [-8.5, 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0.8601311516368817, 0.6321552511476786, -0.09408894344685255], 'positive_zeros': ['1.32712485904019117575690321371842', '3.01535134390573336343941041426376', '4.12653489596136534809295839707145', '5.50403315614617341918933317590960', '6.06227841437955689729721380516317', '7.39915350766115575884578249705049', '8.573070825867855166115179036694924', '8.840257192656848746535689843757154', '10.00263326156933108535713621077384', '11.16629336353761874326569095686399'], 'prelabel': '2-504-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0061057454363, 'root_angle': 0.04034590610789225, 'root_number': '0.9919779164085226 + 0.12641128651274003*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0201729530539', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.32712485904019117575690321372', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.01535134390573336343941041426', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.12653489596136534809295839707', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.024460261872533, 'bad_primes': [2, 3, 7], 'central_character': '7.2', 'conductor': 504, 'conductor_radical': 42, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/504/2/s/d/289/1'], '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': '2-504-7.2-c1-0-4', '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': '2-504-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0061057454363, 'root_angle': 0.020172953053946126, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.32712485904019117575690321372', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1682330624140102680353083251400', 'Lhash_array': ['1682330624140102680353083251400'], 'label': '2-504-7.2-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/504/2/s/d/289/1'}