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lfunc_lfunctions • Show schema
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{'Lhash': '5758146369451586010722017568325', 'a10': [2.19670654164398, -29.31301165957674], 'a2': [3.2732574646308787, -4.104535035605503], 'a3': [-9.590322269946935, 1.4455085001034336], 'a4': [-4.35282595710078, -19.070976590814773], 'a5': [4.626273205614966, -3.1541396649687], 'a6': [-25.458453675379452, 44.09533524789583], 'a7': [0.41010379523441554, 0.7103206097228308], 'a8': [-54.685458989737505, -26.33512906729758], 'a9': [64.08432066134303, -19.767395010784682], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.537082130246848, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[43, [[1.0, 0], [-94.52216800369742, -265.65496373281036]]]], 'bad_primes': [43], 'central_character': '43.24', 'coefficient_field': 'CDF', 'conductor': 43, 'conductor_radical': 43, 'conjugate': '1349631370190284862896985082320', 'degree': 2, 'euler_factors': [[[1.0, 0], [-3.2732574646308787, 4.104535035605503], [-1.7801674716505151, 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'-0.9167834938041944 + 0.3993845583997642*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.434611916972', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.54237655740066081904099571010', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.58042938366954707334120762664', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.61813636974391116760670183104', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.537082130246848, 'bad_primes': [43], 'central_character': '43.24', 'conductor': 43, 'conductor_radical': 43, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/43/4/g/a/24/10'], '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': '2-43-43.24-c3-0-9', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-43-43.24-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.592822064841785, 'root_angle': 0.4346119169717, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '4.54237655740066081904099571010', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '5758146369451586010722017568325', 'Lhash_array': ['5758146369451586010722017568325'], 'label': '2-43-43.24-c3-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/43/4/g/a/24/10'}