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lfunc_lfunctions • Show schema
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{'Lhash': '566827177322510223121864823265', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.7071067811865476, 1.5811388300841898], 'a4': [0.0, 0.0], 'a5': [0.0, -2.23606797749979], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.0, -2.23606797749979], '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], [0.7071067811865476, -1.5811388300841898]]], [19, [[1.0, 0], [3.0, -3.1622776601683795]]]], 'bad_primes': [2, 3, 19], 'central_character': '912.113', 'coefficient_field': 'CDF', 'conductor': 912, 'conductor_radical': 114, 'conjugate': '1803693622612572571726215123792', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.7071067811865476, -1.5811388300841898]], [[1.0, 0], [0, 2.23606797749979], [-5.0, 0]], [[1.0, 0], [1.0, 0], [7.0, 0]], [[1.0, 0], [0, 2.23606797749979], [-11.0, 0]], [[1.0, 0], [0, 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'4.62411563386382750183457771525887', '5.62277476298258352768183391929999', '6.74268050916995412554314943872137', '6.98132831895399362915872014491659', '7.916194677846779579613007855674872', '8.937099936863126864208714465677746', '10.05128273705276275378165049658300'], 'prelabel': '2-912-57.56-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.698584196266771, 'root_angle': -0.6245202116822072, 'root_number': '-0.3812904350580137 - 0.9244553013170894*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.312260105841', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.44714780020650638930014820179', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.35457229626279657845647034775', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.98842393226924914420396648086', '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': '57.56', 'conductor': 912, 'conductor_radical': 114, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/912/2/f/f/113/2'], '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': '2-912-57.56-c1-0-5', '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': '2-912-57.56-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.698584196266771, 'root_angle': -0.3122601058411036, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.44714780020650638930014820179', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '566827177322510223121864823265', 'Lhash_array': ['566827177322510223121864823265'], 'label': '2-912-57.56-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/912/2/f/f/113/2'}