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lfunc_lfunctions • Show schema
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{'Lhash': '2671910541994803726860302023537', 'a10': [0.0, 0.0], 'a2': [0.12235889361317802, -0.5360893402981712], 'a3': [1.7774321220634877, -0.8559661966389808], 'a4': [1.5295176538697508, 0.7365768811217108], 'a5': [0.0, 0.0], 'a6': [-0.24138972574551437, -1.0575974905328194], 'a7': [-1.941115139200393, -4.030767119760106], 'a8': [1.2677051048209351, -1.5896519212979932], 'a9': [0.5561174131783098, -0.6973491792091827], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.78915414654283, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [29, [[1.0, 0], [-3.780140505217658, -3.835431887129895]]]], 'bad_primes': [5, 29], 'central_character': '725.149', 'coefficient_field': 'CDF', 'conductor': 725, 'conductor_radical': 145, 'conjugate': '1535925237258799344933583098721', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.12235889361317802, 0.5360893402981712], [-1.8019377358048383, -0.8677674782351162]], [[1.0, 0], 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'data': '2.10776576882758514605329242917', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.81541937946615817285472348030', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.99534878373735619115876030893', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.78915414654283, 'bad_primes': [5, 29], 'central_character': '145.4', 'conductor': 725, 'conductor_radical': 145, 'degree': 2, 'index': 39, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/725/2/p/a/149/3'], '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': '2-725-145.4-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': '2-725-145.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.406066114333276, 'root_angle': 0.22107260178576507, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.10776576882758514605329242917', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2671910541994803726860302023537', 'Lhash_array': ['2671910541994803726860302023537'], 'label': '2-725-145.4-c1-0-39', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/725/2/p/a/149/3'}