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lfunc_lfunctions • Show schema
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{'Lhash': '1068743702334315225131842203329', 'a10': [0.4239918400972065, 3.9608511031481113], 'a2': [-0.7637013428163183, 1.6094664853100475], 'a3': [-1.715339752036783, -1.5824436250780958], 'a4': [-0.742251875126075, -0.909093508442978], 'a5': [1.9066712291495564, -1.1681630125685885], 'a6': [3.8568972514724353, -1.5522675204199854], 'a7': [1.6175533664853958, 0.4685300463608543], 'a8': [-1.4293859284396648, 0.3523119890897877], 'a9': [0.19686293221713, 2.4385849865046683], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.747358970798196, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-1.9066712291495564, 1.1681630125685885]]], [13, [[1.0, 0], [2.4930079451272027, -2.604786245651002]]]], 'bad_primes': [5, 13], 'central_character': '845.392', 'coefficient_field': 'CDF', 'conductor': 845, 'conductor_radical': 65, 'conjugate': '1378775992999180934641937117527', 'degree': 2, 'euler_factors': [[[1.0, 0], 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2.5975678953201964, 'root_angle': -0.34245260820716844, 'root_number': '0.4749874134544776 - 0.8799925892073326*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.171226304104', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.843090124472703496228105817398', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.28655653345994288741509852120', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.42744182528549519978854584918', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.747358970798196, 'bad_primes': [5, 13], 'central_character': '845.392', 'conductor': 845, 'conductor_radical': 65, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/845/2/bn/a/392/19'], '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': '2-845-845.392-c1-0-15', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-845-845.392-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5975678953201964, 'root_angle': -0.17122630410358422, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.843090124472703496228105817398', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1068743702334315225131842203329', 'Lhash_array': ['1068743702334315225131842203329'], 'label': '2-845-845.392-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/845/2/bn/a/392/19'}