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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_59.22', 'a10': [0.6473862847818277, 0.7621620551276365], 'a2': [-0.9476531711828025, 0.31930153013597995], 'a3': [-0.8568571761675893, 0.5155538571770217], 'a4': [0.7960930657056438, -0.6051742151937651], 'a5': [-0.37013815533991434, -0.9289767198167914], 'a6': [0.6473862847818277, -0.7621620551276365], 'a7': [0.907575419670957, 0.4198891015602646], 'a8': [-0.5611870653623824, 0.8276889981568906], 'a9': [0.46840844069979015, -0.8835120444460229], 'algebraic': True, 'analytic_conductor': 0.2739948481015441, 'analytic_normalization': 0, 'bad_lfactors': [[59, [1]]], 'bad_primes': [59], 'central_character': '59.22', 'coeff_info': ['x^29 - 1', '0.976620555710087 + 0.214970440211024*I', '\\\\zeta_{29}'], 'conductor': 59, 'conductor_radical': 59, 'conjugate': 'dirichlet_L_59.51', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^13', 'a^12', 'a^26', 'a^20', 'a^25', 'a^2', 'a^10', 'a^24', 'a^4', 'a^6', 'a^9', 'a^5', 'a^15', 'a^3', 'a^23', 'a^27', 'a^8', 'a^1', 'a^17', 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'4.52663778727', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.70999647624', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.2739948481015441, 'bad_primes': [59], 'central_character': '59.22', 'conductor': 59, 'conductor_radical': 59, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/59/22'], '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': '1-59-59.22-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': '1-59-59.22-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.2739948481015441, 'root_angle': 0.09246156352616469, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.41508389211', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_59.22', 'Lhash_array': ['dirichlet_L_59.22'], 'label': '1-59-59.22-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/59/22'}