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lfunc_lfunctions • Show schema
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{'Lhash': '3007904280151112882345933593617', 'a10': [3.7987761972900023, -6.579673380289577], 'a2': [1.8267839950181866, 1.05469423127505], 'a3': [-1.130824202928435, 1.958644973900628], 'a4': [1.224759842969737, 2.1213462750936647], 'a5': [0.0, -3.6017796292462445], 'a6': [-4.131543110177726, 2.385347526829654], 'a7': [-0.8660254037844386, 0.5], 'a8': [0.0, 0.9482116392098715], 'a9': [-1.057526755857461, -1.8316900715086102], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0.8660254037844386, -0.5]]], [13, [[1.0, 0], [1.17348727575741, -3.4092415012192157]]]], 'bad_primes': [7, 13], 'central_character': '91.43', 'coefficient_field': 'CDF', 'conductor': 91, 'conductor_radical': 91, 'conjugate': '5068001065665056102816571400111', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.8267839950181866, -1.05469423127505], [1.0, 1.7320508075688772]], [[1.0, 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'11.93724755004018094311959272544772', '12.81055390391385226140366309788936', '13.61120391086656579978546598347219'], 'prelabel': '2-91-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': -0.3985604639663612, 'root_number': '0.3133149117090877 - 0.9496492858422664*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.199280231983', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.37281809325816280058643494239', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.74834103153718575203641713323', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.82471067815063300170082587770', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'bad_primes': [7, 13], 'central_character': '13.4', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/91/2/q/a/43/6'], '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': '2-91-13.4-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': '2-91-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': -0.1992802319831806, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.37281809325816280058643494239', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3007904280151112882345933593617', 'Lhash_array': ['3007904280151112882345933593617'], 'label': '2-91-13.4-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/2/q/a/43/6'}