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lfunc_lfunctions • Show schema
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{'Lhash': '1161713784995321211594221037064', 'a10': [166.41153700190546, -3.705780839286183e-60], 'a2': [-2.0, -3.4641016151377544], 'a3': [-2.4338140417460603, 15.397290320384288], 'a4': [-8.0, 13.856406460551018], 'a5': [-20.801442125238182, 36.02915463161605], 'a6': [58.20540635108025, -22.363601487811103], 'a7': [101.66072216469237, 176.0815359233907], 'a8': [64.0, 0.0], 'a9': [-231.1530984203994, -74.94828277318396], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.8869087566336518, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [2.0, 3.4641016151377544]]], [3, [[1.0, 0], [2.4338140417460603, -15.397290320384288]]]], 'bad_primes': [2, 3], 'central_character': '18.13', 'coefficient_field': 'CDF', 'conductor': 18, 'conductor_radical': 6, 'conjugate': '3889073186355059350149925857566', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.0, 3.4641016151377544]], [[1.0, 0], [2.4338140417460603, -15.397290320384288]], 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['0.916430588039136972737422307562930', '5.04791351640243052345209877504218', '7.33103831796893653089430074620367', '8.016668984762849669723093966123614', '10.25892326133427922183191293679221', '12.05497591550853884360819620927998', '13.42934193235437147742669244323450', '14.65174390824673245448867612688256', '16.40424592337537953139432736475373', '17.42049655817944042852234461490403'], 'prelabel': '2-18-9.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.699090567519475, 'root_angle': -0.4557522828640618, 'root_number': '0.13856105204615599 - 0.9903538937449897*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.227876141432', 'prec': 50}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.916430588039136972737422307563', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '5.04791351640243052345209877504', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.33103831796893653089430074620', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.8869087566336518, 'bad_primes': [2, 3], 'central_character': '9.4', 'conductor': 18, 'conductor_radical': 6, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/18/6/c/b/13/2'], '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': '2-18-9.4-c5-0-1', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-18-9.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.699090567519475, 'root_angle': -0.2278761414320309, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.916430588039136972737422307563', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1161713784995321211594221037064', 'Lhash_array': ['1161713784995321211594221037064'], 'label': '2-18-9.4-c5-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/18/6/c/b/13/2'}