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lfunc_lfunctions • Show schema
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{'Lhash': '2133268341092693009060114730667', 'a10': [-1.2732876357429541, -2.8725899192152076], 'a2': [-0.21892808841808553, -1.397165162785561], 'a3': [-0.9659258262890683, -0.25881904510252074], 'a4': [-1.9041409842032058, 0.6117573965859723], 'a5': [2.1461204950980326, -0.5750512535213991], 'a6': [-0.15014465857954137, 1.4062206731164326], 'a7': [2.5364866239253887, -0.7524862833617528], 'a8': [1.271596068336451, 2.5264685707507386], 'a9': [0.8660254037844386, 0.5], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.682973507915022, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.21892808841808553, 1.397165162785561]]], [3, [[1.0, 0], [0.9659258262890683, 0.25881904510252074]]], [7, [[1.0, 0], [-2.5364866239253887, 0.7524862833617528]]]], 'bad_primes': [2, 3, 7], 'central_character': '336.37', 'coefficient_field': 'CDF', 'conductor': 336, 'conductor_radical': 42, 'conjugate': '1444889995125942155682335495763', 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['1.68285199463370798350691457352234', '4.05568465002703855698177835867271', '5.18734065821111264424136446306305', '6.05784393738491448151943350933525', '6.71385802472838815248700860832032', '8.114165706134014874631093895491451', '8.875955293062258752302442276096354', '9.871463751278645622701265271918399', '10.78508953748847597781384165670885', '11.64514457280061642256956353136755'], 'prelabel': '2-336-112.37-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6379784821282062, 'root_angle': 0.5651279277403016, 'root_number': '-0.20318082553088426 + 0.9791412319663535*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.28256396387', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.68285199463370798350691457352', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.05568465002703855698177835867', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.18734065821111264424136446306', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.682973507915022, 'bad_primes': [2, 3, 7], 'central_character': '112.37', 'conductor': 336, 'conductor_radical': 42, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/336/2/bq/b/37/15'], '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': '2-336-112.37-c1-0-14', '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': '2-336-112.37-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6379784821282062, 'root_angle': 0.2825639638701508, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.68285199463370798350691457352', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2133268341092693009060114730667', 'Lhash_array': ['2133268341092693009060114730667'], 'label': '2-336-112.37-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/336/2/bq/b/37/15'}