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lfunc_lfunctions • Show schema
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{'Lhash': '905105621324347407331733489388', 'a10': [0.4679111137620439, 0.0], 'a2': [0.3472963553338607, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.8793852415718169, 0.0], 'a5': [1.3472963553338606, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.6527036446661393, 0.0], 'a8': [-1.3472963553338606, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.94339561671401, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 19], 'central_character': '3249.1', 'coefficient_field': 'CDF', 'conductor': 3249, 'conductor_radical': 57, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.3472963553338607, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.3472963553338606, 0], [5.0, 0]], [[1.0, 0], [0.6527036446661393, 0], [7.0, 0]], [[1.0, 0], [3.943563014047729, 0], [11.0, 0]], [[1.0, 0], [-1.6945927106677214, 0], [13.0, 0]], [[1.0, 0], [-3.8374961755702346, 0], [17.0, 0]], [[1.0, 0], 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'5.03598891302171777081717378595053', '5.47991933697402943491407553552080', '6.12585299449138411813521988457154', '7.23789188937206170387185495945983', '8.001754309133772974814996416618286', '8.661528088526571561060020028085997'], 'prelabel': '2-57e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.0934659728630765, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.71400243975855102173931326550', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.11402975531072306752974516724', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.21557383356775530205009893249', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.94339561671401, 'bad_primes': [3, 19], 'central_character': '1.1', 'conductor': 3249, 'conductor_radical': 57, 'degree': 2, 'index': 28, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3249/2/a/w/1/2'], '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': '2-57e2-1.1-c1-0-28', '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': '2-57e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.0934659728630765, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.71400243975855102173931326550', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '905105621324347407331733489388', 'Lhash_array': ['905105621324347407331733489388'], 'factors': ['2-57e2-1.1-c1-0-28'], 'label': '2-57e2-1.1-c1-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3249/2/a/w/1/2'}