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lfunc_lfunctions • Show schema
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{'Lhash': '2135109372591446823794901058518', 'a10': [1.0872594422280726, 0.6277295316493401], 'a2': [0.5, 0.8660254037844386], 'a3': [-1.3101405179265084, -1.1329306348083543], 'a4': [-0.5, 0.8660254037844386], 'a5': [1.0872594422280726, -0.6277295316493401], 'a6': [0.3260764515064112, -1.7010802884558351], 'a7': [1.1420830297093678, -2.3865553321156985], 'a8': [-1.0, 0.0], 'a9': [0.43293635342547904, 2.96859665732525], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.359831950361911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, -0.8660254037844386]]], [3, [[1.0, 0], [1.3101405179265084, 1.1329306348083543]]], [7, [[1.0, 0], [-1.1420830297093678, 2.3865553321156985]]], [13, [[1.0, 0], [0.6576492009290591, 3.545066646555093]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.311', 'coefficient_field': 'CDF', 'conductor': 546, 'conductor_radical': 546, 'conjugate': '1031905766936958584031937772240', 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'5.40317346189444405507196175868682', '5.89021707269638724534620375105795', '7.05004758642213421071939676971296', '8.756583752530527931126793105638768', '9.214334153614561924329557075432263', '10.50083490127244028411219917798138', '10.69915198566393046406473177631248'], 'prelabel': '2-546-273.38-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.2702937205839963, 'root_number': '0.660619418567618 + 0.7507209760033233*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.135146860292', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.68430431240835531386615989220', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.12086064032729403717962892042', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.30533334238521434909720216028', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.359831950361911, 'bad_primes': [2, 3, 7, 13], 'central_character': '273.38', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/2/bg/b/311/5'], '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': '2-546-273.38-c1-0-27', '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': '2-546-273.38-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.13514686029199816, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.68430431240835531386615989220', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2135109372591446823794901058518', 'Lhash_array': ['2135109372591446823794901058518'], 'label': '2-546-273.38-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/bg/b/311/5'}