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lfunc_lfunctions • Show schema
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{'Lhash': '2880336029907867324306014095571', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.7071067811865476, -1.5811388300841898], 'a4': [0.0, 0.0], 'a5': [0.0, -2.23606797749979], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.0, -2.23606797749979], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.282356664340774, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.7071067811865476, 1.5811388300841898]]], [19, [[1.0, 0], [3.0, 3.1622776601683795]]]], 'bad_primes': [2, 3, 19], 'central_character': '912.113', 'coefficient_field': 'CDF', 'conductor': 912, 'conductor_radical': 114, 'conjugate': '713301407112864533306953162084', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.7071067811865476, 1.5811388300841898]], [[1.0, 0], [0, 2.23606797749979], [-5.0, 0]], [[1.0, 0], [1.0, 0], [7.0, 0]], [[1.0, 0], [0, 2.23606797749979], [-11.0, 0]], [[1.0, 0], [0, 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'6.29168550720794500664621359887991', '7.03478316735657042958477977066663', '7.946265843822307648787595259390185', '9.091253803798652752921299459683313', '9.616180599234108856807964177736229', '10.39813385594226099478384383132433'], 'prelabel': '2-912-57.56-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.698584196266771, 'root_angle': 0.8922406844834373, 'root_number': '-0.9432419220070302 + 0.33210642355799697*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.446120342242', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.27218448789381555023435913855', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.10501960608518363710646247425', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.17101021529907217688289906249', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.282356664340774, 'bad_primes': [2, 3, 19], 'central_character': '57.56', 'conductor': 912, 'conductor_radical': 114, 'degree': 2, 'index': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/912/2/f/f/113/3'], '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': '2-912-57.56-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': '2-912-57.56-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.698584196266771, 'root_angle': 0.44612034224171865, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.27218448789381555023435913855', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2880336029907867324306014095571', 'Lhash_array': ['2880336029907867324306014095571'], 'label': '2-912-57.56-c1-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/912/2/f/f/113/3'}