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  • lfunc_lfunctions • Show schema
    {'Lhash': '2162901678716042499205871756527', 'a10': [1.5, 2.598076211353316], 'a2': [0.5, 0.8660254037844386], 'a3': [-1.5, 0.8660254037844386], 'a4': [0.5, -0.8660254037844386], 'a5': [3.0, 0.0], 'a6': [-1.5, -0.8660254037844386], 'a7': [-0.5, 0.8660254037844386], 'a8': [3.0, 0.0], 'a9': [1.5, -2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[3, [[1.0, 0], [1.5, -0.8660254037844386]]], [19, [[1.0, 0], [4.0, -1.7320508075688772]]]], 'bad_primes': [3, 19], 'central_character': '171.106', 'coefficient_field': 'CDF', 'conductor': 171, 'conductor_radical': 57, 'conjugate': '2665251492689007872973939742990', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, -0.8660254037844386], [-1.0, 1.7320508075688772]], [[1.0, 0], [1.5, -0.8660254037844386]], [[1.0, 0], [-3.0, 0], [5.0, 0]], [[1.0, 0], [0.5, -0.8660254037844386], [-3.5, -6.06217782649107]], 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2.670422272645354, 1.2727388383824747, -0.2726589280250542, -1.6377003627114295, -2.5241519474742904, -2.7376961002280886], 'positive_zeros': ['1.70622857617598332888309681539952', '3.23968468519268185190959903963865', '5.15664700952504823783882866984742', '6.03159128952584862550636425224313', '7.21270551016907254918314328735242', '8.424272868385385424520672541082239', '10.18966887567098193450825032112833', '10.67139776607494661805316815598008', '11.61409407938119411404578755455134', '12.88175615714191337441196109689425'], 'prelabel': '2-171-171.106-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': -0.15446893415994545, 'root_number': '0.5648400337006948 - 0.8252004219151842*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.15446893416', 'prec': 37}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.70622857617598332888309681540', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.23968468519268185190959903964', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '5.15664700952504823783882866985', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'bad_primes': [3, 19], 'central_character': '171.106', 'conductor': 171, 'conductor_radical': 57, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/171/2/g/a/106/1'], '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': '2-171-171.106-c1-0-5', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-171-171.106-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': -0.15446893415994545, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.70622857617598332888309681540', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '2162901678716042499205871756527', 'Lhash_array': ['2162901678716042499205871756527'], 'factors': ['2-171-171.106-c1-0-5'], 'label': '2-171-171.106-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/171/2/g/a/106/1'}