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lfunc_lfunctions • Show schema
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{'Lhash': '1937431036230984827776779886926', 'a10': [-0.9330339224620101, 3.963413875977569e-61], 'a2': [-0.2557276266953869, -0.954388495726191], 'a3': [0.0, 0.0], 'a4': [0.8865900258496306, -0.5118729900851215], 'a5': [0.244406215770672, -0.9121364149417898], 'a6': [0.0, 0.0], 'a7': [2.4678515252785944, -0.9537865847138529], 'a8': [-2.1125729942341427, -2.1125729942341427], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.5397479255428665, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.4678515252785944, 0.9537865847138529]]], [13, [[1.0, 0], [-3.4395737785010603, -1.0813566582066896]]]], 'bad_primes': [3, 7, 13], 'central_character': '819.262', 'coefficient_field': 'CDF', 'conductor': 819, 'conductor_radical': 273, 'conjugate': '1646550473319063372665871146696', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.2557276266953869, 0.954388495726191], [-1.7320508075688772, 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'5.47457013659650278622343171413021', '6.25864355054476003785475423229892', '6.77093303727133738072667077558431', '8.114288763153700273298306436067391', '8.433409022500844569654639229080608', '9.226985575059941485823368483650854', '10.68571355319155877299416166077090'], 'prelabel': '2-819-91.80-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5572930855775735, 'root_angle': 0.4474283938841231, 'root_number': '0.16440874682322865 + 0.9863922971962096*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.223714196942', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.52836360104445761145938577418', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.96487876703632804586411815394', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.97205744808142396039069625440', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.5397479255428665, 'bad_primes': [3, 7, 13], 'central_character': '91.80', 'conductor': 819, 'conductor_radical': 273, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/819/2/gh/c/262/3'], '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': '2-819-91.80-c1-0-25', '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': '2-819-91.80-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5572930855775735, 'root_angle': 0.22371419694206154, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.52836360104445761145938577418', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1937431036230984827776779886926', 'Lhash_array': ['1937431036230984827776779886926'], 'label': '2-819-91.80-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/819/2/gh/c/262/3'}