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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_59.54', 'a10': [0.16178199655276473, 0.9868265225415261], 'a2': [-0.7960930657056438, -0.6051742151937651], 'a3': [0.46840844069979015, 0.8835120444460229], 'a4': [0.2675283385292208, 0.9635499925192229], 'a5': [-0.7259954919231308, -0.6876994588534233], 'a6': [0.16178199655276473, -0.9868265225415261], 'a7': [0.6473862847818277, -0.7621620551276365], 'a8': [0.37013815533991434, -0.9289767198167914], 'a9': [-0.5611870653623824, 0.8276889981568906], 'algebraic': True, 'analytic_conductor': 6.340430562882876, 'analytic_normalization': 0, 'bad_lfactors': [[59, [1]]], 'bad_primes': [59], 'central_character': '59.54', 'coeff_info': ['x^58 - 1', '0.994137957154360 + 0.108119018423942*I', '\\\\zeta_{58}'], 'conductor': 59, 'conductor_radical': 59, 'conjugate': 'dirichlet_L_59.47', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^35', 'a^10', 'a^12', 'a^36', 'a^45', 'a^50', 'a^47', 'a^20', 'a^13', 'a^5', 'a^22', 'a^9', 'a^27', 'a^46', 'a^24', 'a^8', 'a^55', 'a^54', 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{'__RealLiteral__': 0, 'data': '3.60969626599', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.52653110237', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.340430562882876, 'bad_primes': [59], 'central_character': '59.54', 'conductor': 59, 'conductor_radical': 59, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/59/54'], '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': '1-59-59.54-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-59-59.54-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.340430562882876, 'root_angle': 0.029476455094801565, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.34416088849', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_59.54', 'Lhash_array': ['dirichlet_L_59.54'], 'label': '1-59-59.54-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/59/54'}