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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_4235.2949', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.9283679330160726, 0.3716624556603275], 'a3': [0.5, -0.8660254037844386], 'a4': [0.7237340381050702, -0.690079011482112], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.14231483827328514, 0.9898214418809327], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.41541501300188644, 0.9096319953545183], 'a9': [-0.5, -0.8660254037844386], 'algebraic': True, 'analytic_conductor': 19.66725731711931, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [7, [1]], [11, [1]]], 'bad_primes': [5, 7, 11], 'central_character': '4235.2949', 'coeff_info': ['x^66 - 1', '0.995471922573085 + 0.0950560433041827*I', '\\\\zeta_{66}'], 'conductor': 4235, 'conductor_radical': 385, 'conjugate': 'dirichlet_L_4235.3224', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^29', 'a^55', 'a^58', 0, 'a^18', 0, 'a^21', 'a^44', 0, 0, 'a^47', 'a^3', 0, 0, 'a^50', 'a^13', 'a^7', 'a^20', 0, 0, 0, 'a^17', 'a^10', 0, 'a^32', 'a^33', 0, 'a^42', 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{'__RealLiteral__': 0, 'data': '1.67929080761', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.17091523152', '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': '4235.2949', 'conductor': 4235, 'conductor_radical': 385, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4235/2949'], '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': '1-4235-4235.2949-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': '1-4235-4235.2949-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 19.66725731711931, 'root_angle': 0.07413606330383257, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.882700772544', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_4235.2949', 'Lhash_array': ['dirichlet_L_4235.2949'], 'label': '1-4235-4235.2949-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4235/2949'}