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lfunc_lfunctions • Show schema
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{'Lhash': '2529213469093468197290179202262', 'a10': [-4.0, 10.583005244258363], 'a2': [-0.7071067811865476, 1.8708286933869707], 'a3': [-1.4142135623730951, 2.6457513110645907], 'a4': [-3.0, -2.6457513110645907], 'a5': [5.656854249492381, 0.0], 'a6': [-3.9497474683058327, -4.516580004451561], 'a7': [4.0, 0.0], 'a8': [7.0710678118654755, -3.7416573867739413], 'a9': [-5.0, -7.483314773547883], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6539526344647126, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, -1.8708286933869707]]], [3, [[1.0, 0], [1.4142135623730951, -2.6457513110645907]]]], 'bad_primes': [2, 3], 'central_character': '24.5', 'coefficient_field': 'CDF', 'conductor': 24, 'conductor_radical': 6, 'conjugate': '6315694238498967508496959491192', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7071067811865476, -1.8708286933869707]], [[1.0, 0], [1.4142135623730951, -2.6457513110645907]], 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'positive_zeros': ['1.99519762672624888677905786602553', '5.38400542037203543276090817067073', '7.55293857840674426208737803386275', '9.292175672440491200167963865655737', '10.79036843865912096372979466727456', '11.94041167474267908976916677817614', '13.30585491727059322223027458989126', '14.01171933621875929984920208097365', '16.59151766647779599834726882433768', '17.73030614622155761934021313831978'], 'prelabel': '2-24-24.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8086733793471333, 'root_angle': -0.4986670063002111, 'root_number': '0.004187710974514036 - 0.9999912314999537*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.24933350315', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.99519762672624888677905786603', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.38400542037203543276090817067', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.55293857840674426208737803386', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6539526344647126, 'bad_primes': [2, 3], 'central_character': '24.5', 'conductor': 24, 'conductor_radical': 6, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/24/3/h/c/5/2'], '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': '2-24-24.5-c2-0-0', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-24-24.5-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8086733793471333, 'root_angle': -0.24933350315010555, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.99519762672624888677905786603', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2529213469093468197290179202262', 'Lhash_array': ['2529213469093468197290179202262'], 'label': '2-24-24.5-c2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/24/3/h/c/5/2'}