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lfunc_lfunctions • Show schema
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{'Lhash': '2614738213486489242813972594655', 'a10': [2.3697612961355916, 0.0], 'a2': [-1.0, 0.0], 'a3': [0.29205844987701945, 0.0], 'a4': [1.0, 0.0], 'a5': [-2.3697612961355916, 0.0], 'a6': [-0.29205844987701945, 0.0], 'a7': [3.965307504351478, 0.0], 'a8': [-1.0, 0.0], 'a9': [-2.9147018618554323, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.295951628744887, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [269, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 269], 'central_character': '538.1', 'coefficient_field': 'CDF', 'conductor': 538, 'conductor_radical': 538, 'conjugate': '2614738213486489242813972594655', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [-0.29205844987701945, 0], [3.0, 0]], [[1.0, 0], [2.3697612961355916, 0], [5.0, 0]], [[1.0, 0], [-3.965307504351478, 0], [7.0, 0]], [[1.0, 0], [4.620299614131987, 0], [11.0, 0]], [[1.0, 0], [3.1670360074095694, 0], [13.0, 0]], 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'5.55230044375907880073276032681659', '7.43694117209567088183996382251455', '7.65558222085611238815612500658044', '8.460022227700454746247557283703640', '9.285294297490040221701412859229808', '10.67151927477544505759243361131020'], 'prelabel': '2-538-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0726677564783236, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.06266475400692312260068191156', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.30413003462160399027029545788', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.83145098301425494316976901471', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.295951628744887, 'bad_primes': [2, 269], 'central_character': '1.1', 'conductor': 538, 'conductor_radical': 538, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/538/2/a/d/1/5'], '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': '2-538-1.1-c1-0-14', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-538-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0726677564783236, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.06266475400692312260068191156', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2614738213486489242813972594655', 'Lhash_array': ['2614738213486489242813972594655'], 'label': '2-538-1.1-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/538/2/a/d/1/5'}