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lfunc_lfunctions • Show schema
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{'Lhash': '983018712321584268476017249640', 'a10': [-0.6529576155681158, 0.0], 'a2': [1.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-0.6529576155681158, 0.0], 'a6': [-1.0, 0.0], 'a7': [-3.8965776147090603, 0.0], 'a8': [1.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 31.956130888916427, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [23, [[1.0, 0], [1.0, 0]]], [29, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 23, 29], 'central_character': '4002.1', 'coefficient_field': 'CDF', 'conductor': 4002, 'conductor_radical': 4002, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0.6529576155681158, 0], [5.0, 0]], [[1.0, 0], [3.8965776147090603, 0], [7.0, 0]], [[1.0, 0], [-5.432458978110464, 0], [11.0, 0]], [[1.0, 0], [-3.143349716109209, 0], [13.0, 0]], [[1.0, 0], [-4.779501362542348, 0], [17.0, 0]], [[1.0, 0], 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'4.50075422738214119321475005848763', '5.74479431948903609799879438951342', '6.24230625122690068411531527642777', '6.61725892538844719689741717266697', '7.43058332928863645183539403112712', '8.514145209929140007297474725741337'], 'prelabel': '2-4002-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.6529754014073355, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.77546503125119835742745990205', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.01520868188976670209533314902', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.41908874728328934385418670915', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 31.956130888916427, 'bad_primes': [2, 3, 23, 29], 'central_character': '1.1', 'conductor': 4002, 'conductor_radical': 4002, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4002/2/a/bk/1/4'], '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': '2-4002-1.1-c1-0-17', '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': '2-4002-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.6529754014073355, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.77546503125119835742745990205', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '983018712321584268476017249640', 'Lhash_array': ['983018712321584268476017249640'], 'label': '2-4002-1.1-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4002/2/a/bk/1/4'}