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lfunc_lfunctions • Show schema
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{'Lhash': '1364037390236819763273752577241', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 2.732050807568877], 'a4': [0.0, 0.0], 'a5': [-0.7320508075688773, 0.0], 'a6': [0.0, 0.0], 'a7': [2.0, -1.7320508075688772], 'a8': [0.0, 0.0], 'a9': [-4.464101615137754, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.154596021106726, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.0, 1.7320508075688772]]]], 'bad_primes': [2, 7], 'central_character': '896.447', 'coefficient_field': 'CDF', 'conductor': 896, 'conductor_radical': 14, 'conjugate': '1797389922018878305197282883772', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -2.732050807568877], [-3.0, 0]], [[1.0, 0], [0.7320508075688773, 0], [5.0, 0]], [[1.0, 0], [-2.0, 1.7320508075688772]], [[1.0, 0], [-5.464101615137754, 0], [11.0, 0]], [[1.0, 0], [-4.732050807568878, 0], [13.0, 0]], [[1.0, 0], [0, -4.0], [-17.0, 0]], 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'5.98146381498554191637788670242085', '6.41324342318245343264630003545572', '7.42965418339472495126761822824292', '8.132151101461361238436766100901251', '8.808766164420323817614450525082852', '9.699593610222403287632702125487198'], 'prelabel': '2-896-56.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6748076605817332, 'root_angle': -0.47718552582850504, 'root_number': '0.07161243393857311 - 0.9974325337111245*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.238592762914', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.07603577041752416904336029184', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.91856583621132483853471710087', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.30848256172512858456214678087', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.154596021106726, 'bad_primes': [2, 7], 'central_character': '56.27', 'conductor': 896, 'conductor_radical': 14, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/896/2/e/f/447/4'], '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': '2-896-56.27-c1-0-11', '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': '2-896-56.27-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6748076605817332, 'root_angle': -0.23859276291425252, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.07603577041752416904336029184', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1364037390236819763273752577241', 'Lhash_array': ['1364037390236819763273752577241'], 'label': '2-896-56.27-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/896/2/e/f/447/4'}