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lfunc_lfunctions • Show schema
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{'Lhash': '949159363939411484883030356764', 'a10': [0, 0], 'a2': [0, 0], 'a3': [46.76537180435969, 0], 'a4': [0, 0], 'a5': [0, -402.17597936674116], 'a6': [0, 0], 'a7': [0, -1935.6487284628893], 'a8': [0, 0], 'a9': [2187.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 156.4333862634729, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-46.76537180435969, 0]]]], 'bad_primes': [2, 3], 'central_character': '384.319', 'coefficient_field': 'CDF', 'conductor': 384, 'conductor_radical': 6, 'conjugate': '1280532735703600627376804153374', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-46.76537180435969, 0]], [[1.0, 0], [0, 402.17597936674116], [-390625.0, 0]], [[1.0, 0], [0, 1935.6487284628893], [-5764801.0, 0]], [[1.0, 0], [-20109.348669909243, 0], [214358881.0, 0]], [[1.0, 0], [0, -43789.29954951033], [-815730721.0, 0]], [[1.0, 0], [-101325.2408102013, 0], [6975757441.0, 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'z3': {'__RealLiteral__': 0, 'data': '3.11520600731085162838610410974', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 156.4333862634729, 'bad_primes': [2, 3], 'central_character': '8.3', 'conductor': 384, 'conductor_radical': 6, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/384/9/b/a/319/6'], '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': '2-384-8.3-c8-0-34', 'motivic_weight': 8, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [8], 'order_of_vanishing': 0, 'prelabel': '2-384-8.3-c8-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.507333299447684, 'root_angle': 0.0, 'self_dual': False, 'spectral_label': 'c8-0', 'z1': {'__RealLiteral__': 0, 'data': '0.74875471503624393377991841243', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '949159363939411484883030356764', 'Lhash_array': ['949159363939411484883030356764'], 'label': '2-384-8.3-c8-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/384/9/b/a/319/6'}