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lfunc_lfunctions • Show schema
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{'Lhash': '3129069208125109607428900820825', 'a10': [0.975769248229062, 1.690081914396023], 'a2': [0.0, -2.3032665137821264], 'a3': [0.0, 0.0], 'a4': [-3.305036633510071, 0.0], 'a5': [-0.7337760976782444, 0.4236458275194475], 'a6': [0.0, 0.0], 'a7': [-0.35777731568650534, -2.621449101619209], 'a8': [0.0, 3.0058471772227042], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.5397479255428665, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.35777731568650534, 2.621449101619209]]], [13, [[1.0, 0], [2.9232860268708456, -2.1105446702454955]]]], 'bad_primes': [3, 7, 13], 'central_character': '819.550', 'coefficient_field': 'CDF', 'conductor': 819, 'conductor_radical': 273, 'conjugate': '117306760929790292649455377097', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.3032665137821264], [-2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.7337760976782444, -0.4236458275194475], [2.5, 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'9.711312595422040167578232979235154', '10.72904083501557514498404591766262'], 'prelabel': '2-819-91.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5572930855775735, 'root_angle': -0.3927987458431339, 'root_number': '0.33045222088275494 - 0.9438227215497913*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.196399372922', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.46840036802076855308653574056', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.97535707349629238169125239524', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.19146037103840292130380615322', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.5397479255428665, 'bad_primes': [3, 7, 13], 'central_character': '91.4', 'conductor': 819, 'conductor_radical': 273, 'degree': 2, 'index': 44, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/819/2/bm/f/550/1'], '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': '2-819-91.4-c1-0-44', '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': '2-819-91.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5572930855775735, 'root_angle': -0.19639937292156695, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.46840036802076855308653574056', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3129069208125109607428900820825', 'Lhash_array': ['3129069208125109607428900820825'], 'label': '2-819-91.4-c1-0-44', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/819/2/bm/f/550/1'}