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lfunc_lfunctions • Show schema
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{'Lhash': '2257455968219620100791086020830', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.0, -1.0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [1.0, -1.0], 'a8': [0, 0], 'a9': [0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.776064323404867, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '1600.1407', 'coefficient_field': 'CDF', 'conductor': 1600, 'conductor_radical': 10, 'conjugate': '1986797419957166613302380441482', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 1.0], [0, 3.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 1.0], [0, -7.0]], [[1.0, 0], [0, -6.0], [-11.0, 0]], [[1.0, 0], [1.0, -1.0], [0, -13.0]], [[1.0, 0], [1.0, 1.0], [0, 17.0]], [[1.0, 0], [4.0, 0], [19.0, 0]], [[1.0, 0], [5.0, 5.0], [0, 23.0]], [[1.0, 0], [0, 8.0], [-29.0, 0]], [[1.0, 0], [0, -2.0], [-31.0, 0]], [[1.0, 0], [5.0, 5.0], [0, 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'-0.8506508083520399321815404970630110722404014037648168819 - 0.5257311121191336060256690848478766072854979322433417815*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4118959044126083', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.78081875858630517063994731620', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.10534604220966593671916779248', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.05225121294251739274196101591', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.776064323404867, 'bad_primes': [2, 5], 'central_character': '20.7', 'conductor': 1600, 'conductor_radical': 10, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1600/2/n/e/1407/1'], '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': '2-40e2-20.7-c1-0-29', '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': '2-40e2-20.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.5743620862197027, 'root_angle': -0.4118959044126083, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.78081875858630517063994731620', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2257455968219620100791086020830', 'Lhash_array': ['2257455968219620100791086020830'], 'label': '2-40e2-20.7-c1-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1600/2/n/e/1407/1'}