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lfunc_lfunctions • Show schema
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{'Lhash': '1008294645983269421126710897280', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -252.0], 'a4': [0, 0], 'a5': [0, 4830.0], 'a6': [0, 0], 'a7': [16744.0, 0], 'a8': [0, 0], 'a9': [113643.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 196.6958542232548, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '5.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]]], 'bad_primes': [2], 'central_character': '256.129', 'coefficient_field': 'CDF', 'conductor': 256, 'conductor_radical': 2, 'conjugate': '630628603366107369661291119652', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 252.0], [-177147.0, 0]], [[1.0, 0], [0, -4830.0], [-48828125.0, 0]], [[1.0, 0], [-16744.0, 0], [1977326743.0, 0]], [[1.0, 0], [0, -534612.0], [-285311670611.0, 0]], [[1.0, 0], [0, -577738.0], [-1792160394037.0, 0]], [[1.0, 0], [6905934.0, 0], [34271896307633.0, 0]], [[1.0, 0], [0, 10661420.0], [-116490258898219.0, 0]], [[1.0, 0], [18643272.0, 0], [952809757913927.0, 0]], 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'1.77606892777127041953409347500', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.27673451371320770854529727683', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 196.6958542232548, 'bad_primes': [2], 'central_character': '8.5', 'conductor': 256, 'conductor_radical': 2, 'degree': 2, 'index': 53, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/256/12/b/e/129/1'], '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': '2-2e8-8.5-c11-0-53', 'motivic_weight': 11, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [11], 'order_of_vanishing': 0, 'prelabel': '2-2e8-8.5-c11-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 14.024829917801313, 'root_angle': 0.125, 'self_dual': False, 'spectral_label': 'c11-0', 'z1': {'__RealLiteral__': 0, 'data': '0.795404227159861550504585360639', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1008294645983269421126710897280', 'Lhash_array': ['1008294645983269421126710897280'], 'factors': ['2-2e8-8.5-c11-0-53'], 'label': '2-2e8-8.5-c11-0-53', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/256/12/b/e/129/1'}