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lfunc_lfunctions • Show schema
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{'Lhash': '1683913280642039688899636801836', 'a10': [0.0, 0.0], 'a2': [0.0, 1.4142135623730951], 'a3': [0.0, 0.0], 'a4': [-1.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 1.0155401550139735e-77], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.22008767057115408, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '441.197', 'coefficient_field': 'CDF', 'conductor': 441, 'conductor_radical': 21, 'conjugate': '2997220221282626419693871096875', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.4142135623730951], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.4142135623730951], [-1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 1.4142135623730951], [-1.0, 0]], [[1.0, 0], [0, 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0.4691350238163359, 'root_angle': -0.6959132760153036, 'root_number': '-0.57735026918962576450914878050208 - 0.81649658092772603273242802490216*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3479566380076518', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.32837335488096312434276989129', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.91671596863141148818752592879', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.64577065757865264279999126722', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.22008767057115408, 'bad_primes': [3, 7], 'central_character': '3.2', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'index': 0, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/1/b/a/197/2', 'ArtinRepresentation/2.441.8t8.a.b'], 'is_instance_Artin': True, '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': '2-21e2-3.2-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': '2-21e2-3.2-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.4691350238163359, 'root_angle': -0.3479566380076518, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.32837335488096312434276989129', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24596774
{'Lhash': '1683913280642039688899636801836', 'Lhash_array': ['1683913280642039688899636801836'], 'label': '2-21e2-3.2-c0-0-0', 'type': 'Artin', 'url': 'ArtinRepresentation/2.441.8t8.a.b'}
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id: 19805535
{'Lhash': '1683913280642039688899636801836', 'Lhash_array': ['1683913280642039688899636801836'], 'label': '2-21e2-3.2-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/1/b/a/197/2'}