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lfunc_lfunctions • Show schema
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{'Lhash': '3847879331407938628275777914342', 'a10': [1.0, -1.0], 'a2': [0.0, 1.0], 'a3': [0.0, 0.0], 'a4': [-1.0, 0.0], 'a5': [-1.0, -1.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, -1.0], 'a9': [0.0, 1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.033936420859044164, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.0]]], [17, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 17], 'central_character': '68.47', 'coefficient_field': 'CDF', 'conductor': 68, 'conductor_radical': 34, 'conjugate': '5356635858368639559690519274117', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [1.0, 1.0], [0, 1.0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [-1.0, -1.0], [0, 1.0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [1.0, 1.0], [0, 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'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.14449478259434234', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.03544157255568814852703229915', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.29878395807902601847606510864', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.52495137986341477590907454457', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.033936420859044164, 'bad_primes': [2, 17], 'central_character': '68.47', 'conductor': 68, 'conductor_radical': 34, 'degree': 2, 'index': 0, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/68/1/f/a/47/1', 'ArtinRepresentation/2.68.8t17.a.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': '2-68-68.47-c0-0-0', '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': '2-68-68.47-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.18421840532108663, 'root_angle': -0.14449478259434237, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.03544157255568814852703229915', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24596358
{'Lhash': '3847879331407938628275777914342', 'Lhash_array': ['3847879331407938628275777914342'], 'label': '2-68-68.47-c0-0-0', 'type': 'Artin', 'url': 'ArtinRepresentation/2.68.8t17.a.b'}
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id: 19807609
{'Lhash': '3847879331407938628275777914342', 'Lhash_array': ['3847879331407938628275777914342'], 'label': '2-68-68.47-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/68/1/f/a/47/1'}