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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_4235.2229', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.8799502578106532, 0.4750658309949949], 'a3': [-0.10452846326765347, 0.9945218953682733], 'a4': [0.5486249124420699, 0.8360686009221558], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.5644432188667692, 0.825471896962774], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.08557500847883974, 0.9963317308626913], 'a9': [-0.9781476007338057, -0.20791169081775934], 'algebraic': True, 'analytic_conductor': 19.66725731711931, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [7, [1]], [11, [1]]], 'bad_primes': [5, 7, 11], 'central_character': '4235.2229', 'coeff_info': ['x^330 - 1', '0.999818745523526 + 0.0190388051033467*I', '\\\\zeta_{330}'], 'conductor': 4235, 'conductor_radical': 385, 'conjugate': 'dirichlet_L_4235.19', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^26', 'a^88', 'a^52', 0, 'a^114', 0, 'a^78', 'a^176', 0, 0, 'a^140', 'a^261', 0, 0, 'a^104', 'a^229', 'a^202', 'a^68', 0, 0, 0, 'a^5', 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{'__RealLiteral__': 0, 'data': '2.63132806136', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.17018678731', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.66725731711931, 'bad_primes': [5, 7, 11], 'central_character': '4235.2229', 'conductor': 4235, 'conductor_radical': 385, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4235/2229'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-4235-4235.2229-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-4235-4235.2229-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.66725731711931, 'root_angle': 0.4770600053955439, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.19625713823', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_4235.2229', 'Lhash_array': ['dirichlet_L_4235.2229'], 'label': '1-4235-4235.2229-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4235/2229'}