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lfunc_lfunctions • Show schema
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{'Lhash': '2330261502380608747167490634214', 'a10': [-537.4370548741737, 0.0], 'a2': [-16.0, 0.0], 'a3': [191.7771400370551, 0.0], 'a4': [256.0, 0.0], 'a5': [33.589815929635854, 0.0], 'a6': [-3068.4342405928815, 0.0], 'a7': [0.0, 0.0], 'a8': [-4096.0, 0.0], 'a9': [17095.471440792237, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 50.47351194405958, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [16.0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7], 'central_character': '98.1', 'coefficient_field': 'CDF', 'conductor': 98, 'conductor_radical': 14, 'degree': 2, 'euler_factors': [[[1.0, 0], [16.0, 0]], [[1.0, 0], [-191.7771400370551, 0], [19683.0, 0]], [[1.0, 0], [-33.589815929635854, 0], [1953125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [51540.38258992365, 0], [2357947691.0, 0]], [[1.0, 0], [-113302.54119292006, 0], [10604499373.0, 0]], [[1.0, 0], [461666.50342259224, 0], [118587876497.0, 0]], [[1.0, 0], 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'4.14284049513747639397573803476', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 50.47351194405958, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 98, 'conductor_radical': 14, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/98/10/a/k/1/4'], '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': '2-98-1.1-c9-0-27', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 1, 'prelabel': '2-98-1.1-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.104471264215205, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '1.83825219816964197246404820960', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2330261502380608747167490634214', 'Lhash_array': ['2330261502380608747167490634214'], 'label': '2-98-1.1-c9-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/98/10/a/k/1/4'}