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lfunc_lfunctions • Show schema
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{'Lhash': '1231056172610039776378102353001', 'a10': [0.0, -11.74734012447073], 'a2': [0.0, 1.7320508075688772], 'a3': [0.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-6.782329983125268, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 11.74734012447073], 'a8': [0.0, 8.660254037844387], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.6975546171669396, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-6.782329983125268, -8.660254037844387]]]], 'bad_primes': [3, 11], 'central_character': '99.10', 'coefficient_field': 'CDF', 'conductor': 99, 'conductor_radical': 33, 'conjugate': '3531012256840299209813562038575', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.7320508075688772], [-4.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [6.782329983125268, 0], [25.0, 0]], [[1.0, 0], [0, -11.74734012447073], [-49.0, 0]], [[1.0, 0], [-6.782329983125268, -8.660254037844387]], [[1.0, 0], [0, 11.74734012447073], 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'7.49332802505999476441806615288047', '9.013320073132737747242718233618026', '10.60506399923170267341093856448324', '11.08600616678118909678308822060365', '11.95671064374631123944258757419144', '13.06514820196499564056444740709220'], 'prelabel': '2-99-11.10-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6424233976557139, 'root_angle': -0.7114804717232609, 'root_number': '-0.616575453011388 - 0.7872958216222169*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.355740235862', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.971132086703070137351424888201', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.50240115117172536100578564413', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.19172701595080439185364153819', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.6975546171669396, 'bad_primes': [3, 11], 'central_character': '11.10', 'conductor': 99, 'conductor_radical': 33, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/99/3/c/c/10/3'], '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': '2-99-11.10-c2-0-1', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-99-11.10-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6424233976557139, 'root_angle': -0.35574023586163045, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.971132086703070137351424888201', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1231056172610039776378102353001', 'Lhash_array': ['1231056172610039776378102353001'], 'label': '2-99-11.10-c2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/99/3/c/c/10/3'}