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lfunc_lfunctions • Show schema
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{'Lhash': '1394652509286262470013786146666', 'a10': [0.0, 0.0], 'a2': [1.0, 0.0], 'a3': [-0.5, 1.5388417685876268], 'a4': [1.0, 0.0], 'a5': [0.0, 0.0], 'a6': [-0.5, 1.5388417685876268], 'a7': [0.0, 0.0], 'a8': [1.0, 0.0], 'a9': [-1.3090169943749475, -0.9510565162951535], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.0021225453670688, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [251, [[1.0, 0], [0.8090169943749475, 0.5877852522924731]]]], 'bad_primes': [2, 251], 'central_character': '2008.1619', 'coefficient_field': 'CDF', 'conductor': 2008, 'conductor_radical': 502, 'conjugate': '2397776807461284340587574803038', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.5, -1.5388417685876268], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [-0.19098300562505258, 0.5877852522924731], 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'data': '-0.2719557282036941', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.10018684094431658516196510905', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.28945656651594676027275666223', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.96872576047878490064981224139', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.0021225453670688, 'bad_primes': [2, 251], 'central_character': '2008.1619', 'conductor': 2008, 'conductor_radical': 502, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2008/1/j/a/1619/1'], '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': '2-2008-2008.1619-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-2008-2008.1619-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.001060710130544, 'root_angle': -0.2719557282036941, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.10018684094431658516196510905', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1394652509286262470013786146666', 'Lhash_array': ['1394652509286262470013786146666'], 'label': '2-2008-2008.1619-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2008/1/j/a/1619/1'}