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lfunc_lfunctions • Show schema
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{'Lhash': '961269195021426405558470753999', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.5, 0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [1.336411850500474, 2.314733224903964], 'a6': [0.0, 0.0], 'a7': [0.0, 3.935687225712214], '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], [-4.244816969317151, -0.990721402311041]]]], 'bad_primes': [2, 3, 19], 'central_character': '912.31', 'coefficient_field': 'CDF', 'conductor': 912, 'conductor_radical': 114, 'conjugate': '3027106634289831482285493551465', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [-1.336411850500474, -2.314733224903964], [-2.5, 4.330127018922194]], [[1.0, 0], [0, -3.935687225712214], [-7.0, 0]], [[1.0, 0], [0, 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'2-912-76.31-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.698584196266771, 'root_angle': -0.7291876700438473, 'root_number': '-0.6593954231042185 - 0.751796299531468*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.364593835022', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.75830768734567576895811671950', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.83710953731770869445486813751', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.37403017923393060480696825084', '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': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/912/2/bb/f/31/3'], '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': '2-912-76.31-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': '2-912-76.31-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.698584196266771, 'root_angle': -0.36459383502192366, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.75830768734567576895811671950', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '961269195021426405558470753999', 'Lhash_array': ['961269195021426405558470753999'], 'label': '2-912-76.31-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/912/2/bb/f/31/3'}