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lfunc_lfunctions • Show schema
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{'Lhash': '2133522559237594299070011059353', 'a10': [-3.922730369634611, 0.1489477556202073], 'a2': [-1.3351103672545233, -0.46634783933185775], 'a3': [-0.9888308262251285, -0.14904226617617444], 'a4': [1.5650393855010156, 1.2452516700774199], 'a5': [2.583908260218262, -1.0141092624341963], 'a6': [1.2506927487536423, 0.660126994005743], 'a7': [1.5145570505066404, -2.1693586473334987], 'a8': [-1.508779882979062, -2.3924011504590297], 'a9': [0.9555728057861407, 0.2947551744109042], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.6952036388512886, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.3351103672545233, 0.46634783933185775]]], [3, [[1.0, 0], [0.9888308262251285, 0.14904226617617444]]], [7, [[1.0, 0], [-1.5145570505066404, 2.1693586473334987]]]], 'bad_primes': [2, 3, 7], 'central_character': '588.187', 'coefficient_field': 'CDF', 'conductor': 588, 'conductor_radical': 42, 'conjugate': 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'-0.1381758204102373 + 0.9904077153647168*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.272061951554', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.68305253738961842149096190485', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.56100997496850809623527782336', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.86713922208741295868960829266', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.6952036388512886, 'bad_primes': [2, 3, 7], 'central_character': '196.187', 'conductor': 588, 'conductor_radical': 42, 'degree': 2, 'index': 39, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/588/2/ba/b/187/3'], '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': '2-588-196.187-c1-0-39', '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': '2-588-196.187-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.166841858293145, 'root_angle': 0.2720619515539834, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.68305253738961842149096190485', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2133522559237594299070011059353', 'Lhash_array': ['2133522559237594299070011059353'], 'label': '2-588-196.187-c1-0-39', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/588/2/ba/b/187/3'}