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lfunc_lfunctions • Show schema
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{'Lhash': '1494195546438026127747419613355', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-0.9441521672688893, 1.4520938967716444], 'a4': [0, 0], 'a5': [-0.637560027189452, 1.1042863599671258], 'a6': [0, 0], 'a7': [1.7356001116539197, -1.002049191668935], 'a8': [0, 0], 'a9': [-1.2171533700829185, -2.74199519942975], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.198766312851504, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.9441521672688893, -1.4520938967716444]]]], 'bad_primes': [2, 3], 'central_character': '1152.959', 'coefficient_field': 'CDF', 'conductor': 1152, 'conductor_radical': 6, 'conjugate': '855037230521619050279994837796', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.9441521672688893, -1.4520938967716444]], [[1.0, 0], [0.637560027189452, -1.1042863599671258], [-2.5, -4.330127018922194]], [[1.0, 0], [-1.7356001116539197, 1.002049191668935], [3.5, 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'8.846214921407233643136016892238324', '9.771161053553807487575403516353040'], 'prelabel': '2-1152-72.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.032946803498456, 'root_angle': 0.06146602567349103, 'root_number': '0.9814138218494359113724437014421921684410835786225118212 + 0.1919033878879778175584242651108437883119161300129148604*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.030733012836745517', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.17871245134030567290490751132', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.16022269672046176718377690021', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.66222438220490972827590385774', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.198766312851504, 'bad_primes': [2, 3], 'central_character': '72.59', 'conductor': 1152, 'conductor_radical': 6, 'degree': 2, 'index': 26, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1152/2/p/g/959/4'], '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': '2-1152-72.59-c1-0-26', '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': '2-1152-72.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.032946803498456, 'root_angle': 0.030733012836745514, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.17871245134030567290490751132', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1494195546438026127747419613355', 'Lhash_array': ['1494195546438026127747419613355'], 'label': '2-1152-72.59-c1-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1152/2/p/g/959/4'}