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lfunc_lfunctions • Show schema
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{'Lhash': '450512256682713691072060508306', 'a10': [101.49964029631779, 0.0], 'a2': [-5.045367259725642, 0.0], 'a3': [0.0, 0.0], 'a4': [17.45573078551143, 0.0], 'a5': [-20.117393852878248, 0.0], 'a6': [0.0, 0.0], 'a7': [-15.427894061534943, 0.0], 'a8': [-47.707634521999196, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 89.74190511873151, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '1521.1', 'coefficient_field': 'CDF', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'euler_factors': [[[1.0, 0], [5.045367259725642, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [20.117393852878248, 0], [125.0, 0]], [[1.0, 0], [15.427894061534943, 0], [343.0, 0]], [[1.0, 0], [-26.937202339409712, 0], [1331.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [23.233433378388803, 0], [4913.0, 0]], [[1.0, 0], [-45.079403646627256, 0], 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'2.98224324607426310874782425643555', '3.62210291396119034010953574357914', '4.88794022407451426610746237813657', '6.56455219592156002988103451532261', '6.89191597220384612205881271845463', '7.70029233511396108277612808875754', '8.365598157766889667335448473943504', '9.043574144407916387348949112743951'], 'prelabel': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.35539150661988634740455470305', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.38724509636436461059490329200', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.98224324607426310874782425644', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 89.74190511873151, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/4/a/bk/1/2'], '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': '2-39e2-1.1-c3-0-17', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.35539150661988634740455470305', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '450512256682713691072060508306', 'Lhash_array': ['450512256682713691072060508306'], 'label': '2-39e2-1.1-c3-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/4/a/bk/1/2'}