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lfunc_lfunctions • Show schema
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{'A10': 1, 'A2': 1, 'A3': 1, 'A4': 1, 'A5': 1, 'A6': 1, 'A7': 1, 'A8': 1, 'A9': 1, 'Lhash': '17917892809981029483707922301037', 'a10': 1, 'a2': 1, 'a3': 1, 'a4': 1, 'a5': 1, 'a6': 1, 'a7': 1, 'a8': 1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.004643980476297358, 'analytic_normalization': 0, 'bad_lfactors': [], 'bad_primes': [], 'central_character': '1.1', 'coefficient_field': '1.1.1.1', 'conductor': 1, 'conductor_radical': 1, 'degree': 1, 'dirichlet_coefficients': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'euler_factors': [[1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, 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'43.3270732809149995194961221654068', '48.0051508811671597279424727494277', '49.7738324776723021819167846785638', '52.9703214777144606441472966088808', '56.4462476970633948043677594767060', '59.3470440026023530796536486749922', '60.8317785246098098442599018245241', '65.1125440480816066608750542531836', '67.0798105294941737144788288965221', '69.5464017111739792529268575265547', '72.0671576744819075825221079698261', '75.7046906990839331683269167620305', '77.1448400688748053726826648563047', '79.3373750202493679227635928771161', '82.9103808540860301831648374947706', '84.7354929805170501057353112068276', '87.4252746131252294065316678509191', '88.8091112076344654236823480795095', '92.4918992705584842962597252418105', '94.6513440405198869665979258152080', '95.8706342282453097587410292192467', '98.8311942181936922333244201386224', '101.3178510057313912287854479402924'], 'prelabel': '1-1-1.1-r0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.004643980476297358, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'r0-0', 'types': ['DIR'], 'z1': {'__RealLiteral__': 0, 'data': '14.1347251417346937904572519835625', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '21.0220396387715549926284795938969', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '25.0108575801456887632137909925628', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.004643980476297358, 'bad_primes': [], 'central_character': '1.1', 'conductor': 1, 'conductor_radical': 1, 'degree': 1, 'dirichlet_coefficients': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'euler11': [1, -1], 'euler13': [1, -1], 'euler17': [1, -1], 'euler19': [1, -1], 'euler2': [1, -1], 'euler23': [1, -1], 'euler29': [1, -1], 'euler3': [1, -1], 'euler31': [1, -1], 'euler37': [1, -1], 'euler41': [1, -1], 'euler43': [1, -1], 'euler47': [1, -1], 'euler5': [1, -1], 'euler53': [1, -1], 'euler59': [1, -1], 'euler61': [1, -1], 'euler67': [1, -1], 'euler7': [1, -1], 'euler71': [1, -1], 'euler73': [1, -1], 'euler79': [1, -1], 'euler83': [1, -1], 'euler89': [1, -1], 'euler97': [1, -1], 'euler_factors': [[1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1]], 'index': 0, 'instance_types': ['NF', 'DIR', 'Artin', 'Artin'], 'instance_urls': ['NumberField/1.1.1.1', 'Character/Dirichlet/1/1', 'ArtinRepresentation/1.1.1t1.a.a', 'ArtinRepresentation/1.1.1t1.a'], 'is_instance_Artin': True, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': True, 'label': '1-1-1.1-r0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-1-1.1-r0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.004643980476297358, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '14.1347251417346937904572519835625', 'prec': 113}}
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lfunc_instances • Show schema
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id: 24629728
{'Lhash': '17917892809981029483707922301037', 'Lhash_array': ['17917892809981029483707922301037'], 'label': '1-1-1.1-r0-0-0', 'type': 'Artin', 'url': 'ArtinRepresentation/1.1.1t1.a'}
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id: 24629727
{'Lhash': '17917892809981029483707922301037', 'Lhash_array': ['17917892809981029483707922301037'], 'label': '1-1-1.1-r0-0-0', 'type': 'Artin', 'url': 'ArtinRepresentation/1.1.1t1.a.a'}
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id: 24629726
{'Lhash': '17917892809981029483707922301037', 'Lhash_array': ['17917892809981029483707922301037'], 'label': '1-1-1.1-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1/1'}
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id: 24629725
{'Lhash': '17917892809981029483707922301037', 'Lhash_array': ['17917892809981029483707922301037'], 'label': '1-1-1.1-r0-0-0', 'type': 'NF', 'url': 'NumberField/1.1.1.1'}