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lfunc_lfunctions • Show schema
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{'Lhash': '2763837253159599011904433777607', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.19164096485107293, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]]], 'bad_primes': [2, 3], 'central_character': '384.65', 'coefficient_field': '1.1.1.1', 'conductor': 384, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 0, 1], [1, 0, 1], [1, 2, 1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 0, 1], [1, 0, 1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 0, 1], [1, -2, 1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 2, 1], [1, 0, 1], [1, 2, 1], [1, 0, -1], [1, -2, 1], [1, 0, 1], [1, 0, 1], [1, -2, 1], [1, 0, -1], [1, 0, -1]], 'euler_factors_factorization': [[1], [[[1, -1], 1]], [[[1, 0, 1], 1]], [[[1, 0, 1], 1]], [[[1, 1], 2]], [[[1, -1], 1], [[1, 1], 1]], [[[1, -1], 1], [[1, 1], 1]], [[[1, -1], 1], 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6.30822265914561, 6.05681280348199, 5.590384611711799, 4.9329826397334795, 4.120762612365936, 3.1995981407181193, 2.2219713696947077, 1.2433705394053702, 0.3184573058726556, -0.5027130738397108, -1.178136811761461, -1.6767129778857117, -1.9802854687993918, -2.084720185905347, -1.9999351062203505, -1.74888110440668], 'positive_zeros': ['2.18028315741103604715303308093136', '3.22873040444622756373737015809730', '4.56816156008636606652577181447535', '5.69772240246461967573219910016294', '7.17586826676654994203448376032325', '7.923175260352088101919956375328404', '8.645607284808412110813643206624461', '9.846246176532358425912726735900120', '10.37209973055988199399442480591365', '11.51594431833325755850778013774962'], 'prelabel': '2-384-24.5-c0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.4377681633594121, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0-0', 'trace_hash': 336085567881746484, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.18028315741103604715303308093', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.22873040444622756373737015810', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.56816156008636606652577181448', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.19164096485107293, 'bad_primes': [2, 3], 'central_character': '24.5', 'conductor': 384, 'conductor_radical': 6, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0], 'euler11': [1, 2, 1], 'euler13': [1, 0, -1], 'euler17': [1, 0, -1], 'euler19': [1, 0, -1], 'euler2': [1, 0, 0], 'euler23': [1, 0, -1], 'euler29': [1, 0, 1], 'euler3': [1, -1, 0], 'euler31': [1, 0, 1], 'euler37': [1, 0, -1], 'euler41': [1, 0, -1], 'euler43': [1, 0, -1], 'euler47': [1, 0, -1], 'euler5': [1, 0, 1], 'euler53': [1, 0, 1], 'euler59': [1, -2, 1], 'euler61': [1, 0, -1], 'euler67': [1, 0, -1], 'euler7': [1, 0, 1], 'euler71': [1, 0, -1], 'euler73': [1, 2, 1], 'euler79': [1, 0, 1], 'euler83': [1, 2, 1], 'euler89': [1, 0, -1], 'euler97': [1, -2, 1], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 0, 1], [1, 0, 1], [1, 2, 1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 0, 1], [1, 0, 1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 0, 1], [1, -2, 1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 2, 1], [1, 0, 1], [1, 2, 1], [1, 0, -1], [1, -2, 1]], 'index': 1, 'instance_types': ['CMF', 'CMF', 'Artin', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/384/1/h/b/65/1', 'ModularForm/GL2/Q/holomorphic/384/1/h/b', 'ArtinRepresentation/2.384.4t3.b.a', 'ArtinRepresentation/2.384.4t3.b'], 'is_instance_Artin': True, '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': '2-384-24.5-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-384-24.5-c0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.4377681633594121, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0-0', 'trace_hash': 336085567881746484, 'z1': {'__RealLiteral__': 0, 'data': '2.18028315741103604715303308093', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24603138
{'Lhash': '2763837253159599011904433777607', 'Lhash_array': ['2763837253159599011904433777607'], 'label': '2-384-24.5-c0-0-1', 'type': 'Artin', 'url': 'ArtinRepresentation/2.384.4t3.b'}
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id: 24596688
{'Lhash': '2763837253159599011904433777607', 'Lhash_array': ['2763837253159599011904433777607'], 'label': '2-384-24.5-c0-0-1', 'type': 'Artin', 'url': 'ArtinRepresentation/2.384.4t3.b.a'}
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id: 19811909
{'Lhash': '2763837253159599011904433777607', 'Lhash_array': ['2763837253159599011904433777607'], 'label': '2-384-24.5-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/384/1/h/b'}
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id: 24545893
{'Lhash': '2763837253159599011904433777607', 'Lhash_array': ['2763837253159599011904433777607'], 'label': '2-384-24.5-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/384/1/h/b/65/1'}