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lfunc_lfunctions • Show schema
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{'Lhash': '2594795472313862752037052383890', 'a10': [0.8153517417195804, 1.6430926097888803], 'a2': [-0.695663295883592, -0.43469867284588687], 'a3': [-2.6247323355034355, 0.7526298860575495], 'a4': [-0.5817578085125081, -1.192780269661948], 'a5': [-1.904355376119653, -1.1719345551028757], 'a6': [2.1530971599419257, 0.6173906757037413], 'a7': [2.448997888373533, -4.241788770291853], 'a8': [-0.28528417032792686, 2.714297569520409], 'a9': [3.778623799181042, -2.3611462045034184], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.79289409601082, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [1.904355376119653, 1.1719345551028757]]], [19, [[1.0, 0], [-2.9284895427407833, 3.228614098658723]]]], 'bad_primes': [5, 19], 'central_character': '475.6', 'coefficient_field': 'CDF', 'conductor': 475, 'conductor_radical': 95, 'conjugate': '348100644662724420882942054361', 'degree': 2, 'euler_factors': [[[1.0, 0], 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1.9475353901818626, 'root_angle': -0.7850356156931746, 'root_number': '-0.7805003608537705 - 0.6251553300637643*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.392517807847', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.04693270515289664662800548746', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.07627303172884069110566102452', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.96347756198043149213654464990', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.79289409601082, 'bad_primes': [5, 19], 'central_character': '475.6', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'index': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/2/bc/a/6/20'], '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': '2-475-475.6-c1-0-36', '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': '2-475-475.6-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': -0.3925178078465873, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.04693270515289664662800548746', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2594795472313862752037052383890', 'Lhash_array': ['2594795472313862752037052383890'], 'label': '2-475-475.6-c1-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/bc/a/6/20'}