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lfunc_lfunctions • Show schema
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{'Lhash': '2446233468444445254281287277252', 'a10': [70.07522378597733, 0.0], 'a2': [4.050375149299158, 0.0], 'a3': [-0.8412552107517293, 0.0], 'a4': [8.405538850060175, 0.0], 'a5': [17.300921816613098, 0.0], 'a6': [-3.4073991998472297, 0.0], 'a7': [0.0, 0.0], 'a8': [1.6425844803590888, 0.0], 'a9': [-26.292289670383063, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 124.31702438209554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [43, [[1.0, 0], [43.0, 0]]]], 'bad_primes': [7, 43], 'central_character': '2107.1', 'coefficient_field': 'CDF', 'conductor': 2107, 'conductor_radical': 301, 'degree': 2, 'euler_factors': [[[1.0, 0], [-4.050375149299158, 0], [8.0, 0]], [[1.0, 0], [0.8412552107517293, 0], [27.0, 0]], [[1.0, 0], [-17.300921816613098, 0], [125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-64.60671470175483, 0], [1331.0, 0]], [[1.0, 0], [30.93275108311111, 0], [2197.0, 0]], [[1.0, 0], 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'4.28225089863606070897602089768267', '5.31672602126874730224355342021249', '5.84582159313404238555844193189075', '6.44354034664440874950564754941015', '6.99991062010605316763465962296267', '8.666409266505331234855683872443897'], 'prelabel': '2-2107-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.149754453892495, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.92973794829902050083479299028', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.26454270227070968636203066623', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.60346155041178611904708653376', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 124.31702438209554, 'bad_primes': [7, 43], 'central_character': '1.1', 'conductor': 2107, 'conductor_radical': 301, 'degree': 2, 'index': 416, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2107/4/a/h/1/27'], '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': '2-2107-1.1-c3-0-416', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-2107-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.149754453892495, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.92973794829902050083479299028', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2446233468444445254281287277252', 'Lhash_array': ['2446233468444445254281287277252'], 'label': '2-2107-1.1-c3-0-416', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2107/4/a/h/1/27'}