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lfunc_lfunctions • Show schema
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{'Lhash': '1247680732397552627042966905607', 'a10': [21.308892150575037, 0.0], 'a2': [-4.261778430115007, 0.0], 'a3': [0.0, 0.0], 'a4': [10.162755387393535, 0.0], 'a5': [-5.0, 0.0], 'a6': [0.0, 0.0], 'a7': [30.76393299946156, 0.0], 'a8': [-9.217184259608791, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.89577355232496, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [5.0, 0]]]], 'bad_primes': [3, 5], 'central_character': '405.1', 'coefficient_field': 'CDF', 'conductor': 405, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[[1.0, 0], [4.261778430115007, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [5.0, 0]], [[1.0, 0], [-30.76393299946156, 0], [343.0, 0]], [[1.0, 0], [-40.714628597539075, 0], [1331.0, 0]], [[1.0, 0], [-63.21780562563997, 0], [2197.0, 0]], [[1.0, 0], [6.589897817535751, 0], [4913.0, 0]], [[1.0, 0], [-75.38028045062367, 0], [6859.0, 0]], 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'3.76939229706880367161895096057315', '4.97409491770830216879436917775046', '6.48222691434272075392756449812846', '7.47396556948554538029086414219862', '8.407853250042967559280748385751217', '8.658262277153445364084444410767099', '9.842522722574301190127635484123001', '10.81939904212213424802028127587890'], 'prelabel': '2-405-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8883303440259604, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.984246551985948356398853228608', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.77040465006059863744687634367', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.76939229706880367161895096057', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.89577355232496, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 405, 'conductor_radical': 15, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/405/4/a/m/1/2'], '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': '2-405-1.1-c3-0-13', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-405-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8883303440259604, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.984246551985948356398853228608', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1247680732397552627042966905607', 'Lhash_array': ['1247680732397552627042966905607'], 'label': '2-405-1.1-c3-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/405/4/a/m/1/2'}