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lfunc_lfunctions • Show schema
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{'Lhash': '1362265165775780028832146522009', 'a10': [1.579740493728931e-61, -6.9030188176798735], 'a2': [1.6159183452446992, 1.9257764932842611], 'a3': [-1.4926061551872998, 0.87870749712119], 'a4': [-0.7501266482539983, 4.254179622653669], 'a5': [-2.1034931841840248, -1.7650403550327376], 'a6': [-4.10412391082095, -1.4545062826889175], 'a7': [-0.12250845888664329, 2.6429134827877396], 'a8': [-5.050500733555285, 2.9159079580605463], 'a9': [1.4557462690060277, -2.6231284376246293], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5091725982022, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.4926061551872998, -0.87870749712119]]], [7, [[1.0, 0], [0.12250845888664329, -2.6429134827877396]]]], 'bad_primes': [3, 7], 'central_character': '189.131', 'coefficient_field': 'CDF', 'conductor': 189, 'conductor_radical': 21, 'conjugate': '4841933195121373918817932122335', 'degree': 2, 'euler_factors': [[[1.0, 0], 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{'__RealLiteral__': 0, 'data': '-0.45798319192', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.07463773182493354436306605014', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.22127902250597008593504479968', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.08582595493178479288428070155', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.5091725982022, 'bad_primes': [3, 7], 'central_character': '189.131', 'conductor': 189, 'conductor_radical': 21, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/189/2/ba/a/131/21'], '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': '2-189-189.131-c1-0-2', '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': '2-189-189.131-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2284838615961546, 'root_angle': -0.4579831919202464, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.07463773182493354436306605014', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1362265165775780028832146522009', 'Lhash_array': ['1362265165775780028832146522009'], 'factors': ['2-189-189.131-c1-0-2'], 'label': '2-189-189.131-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/189/2/ba/a/131/21'}