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lfunc_lfunctions • Show schema
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{'Lhash': '374501066864878424092115796183', 'a10': [-1.0, 0], 'a2': [0, 1.0], 'a3': [-1.0, 0], 'a4': [-1.0, 0], 'a5': [0, 1.0], 'a6': [0, -1.0], 'a7': [2.0, 0], 'a8': [0, -1.0], 'a9': [1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.863394624362128, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.0]]], [3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [0, -1.0]]], [37, [[1.0, 0], [6.0, -1.0]]]], 'bad_primes': [2, 3, 5, 37], 'central_character': '1110.961', 'coefficient_field': 'CDF', 'conductor': 1110, 'conductor_radical': 1110, 'conjugate': '2156683063541160234128050471328', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [-2.0, 0], [7.0, 0]], [[1.0, 0], [4.0, 0], [11.0, 0]], [[1.0, 0], [0, -2.0], [-13.0, 0]], [[1.0, 0], [0, 2.0], [-17.0, 0]], [[1.0, 0], [0, -6.0], [-19.0, 0]], [[1.0, 0], [0, 0], [-23.0, 0]], [[1.0, 0], [0, 2.0], [-29.0, 0]], 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0.9474315432887466, 'root_number': '-0.98639392383214373335130014787060546952729244780320181402 + 0.1643989873053572888918833579784342449212154079672003024*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4737157716443733', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.29542925061326266326070552891', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.72754324329536463598166408976', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.91158535905479085598150828743', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.863394624362128, 'bad_primes': [2, 3, 5, 37], 'central_character': '37.36', 'conductor': 1110, 'conductor_radical': 1110, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1110/2/h/b/961/2'], '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': '2-1110-37.36-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': '2-1110-37.36-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.9771453817981626, 'root_angle': 0.4737157716443733, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.29542925061326266326070552891', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '374501066864878424092115796183', 'Lhash_array': ['374501066864878424092115796183'], 'label': '2-1110-37.36-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1110/2/h/b/961/2'}