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lfunc_lfunctions • Show schema
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{'Lhash': '884561153260051686893556377738', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.5, -0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [-0.6759696007767309, -1.1708136929173483], 'a6': [0.0, 0.0], 'a7': [0.0, 1.4573473167334163], 'a8': [0.0, 0.0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.282356664340774, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.5, 0.8660254037844386]]], [19, [[1.0, 0], [-2.438069399204956, -3.613283493536092]]]], 'bad_primes': [2, 3, 19], 'central_character': '912.31', 'coefficient_field': 'CDF', 'conductor': 912, 'conductor_radical': 114, 'conjugate': '1572590882229834849481236823495', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0.6759696007767309, 1.1708136929173483], [-2.5, 4.330127018922194]], [[1.0, 0], [0, -1.4573473167334163], [-7.0, 0]], [[1.0, 0], [0, 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'10.16596685776051519587379878442411'], 'prelabel': '2-912-76.31-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.698584196266771, 'root_angle': -0.15778200812858825, 'root_number': '0.8796422517246313 - 0.47563589959213587*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0788910040643', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.69779571208406653154871227506', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.80040300193354369364332505204', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.57607587867932585985733948714', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.282356664340774, 'bad_primes': [2, 3, 19], 'central_character': '76.31', 'conductor': 912, 'conductor_radical': 114, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/912/2/bb/e/31/2'], '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': '2-912-76.31-c1-0-1', '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': '2-912-76.31-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.698584196266771, 'root_angle': -0.07889100406429413, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.69779571208406653154871227506', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '884561153260051686893556377738', 'Lhash_array': ['884561153260051686893556377738'], 'label': '2-912-76.31-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/912/2/bb/e/31/2'}