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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_475.306', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.9612616959383189, 0.27563735581699916], 'a3': [-0.9902680687415704, -0.13917310096006544], 'a4': [0.848048096156426, -0.5299192642332049], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.9902680687415704, -0.13917310096006544], 'a7': [-0.5, 0.8660254037844386], 'a8': [-0.6691306063588582, 0.7431448254773942], 'a9': [0.9612616959383189, 0.27563735581699916], 'algebraic': True, 'analytic_conductor': 51.04583927744689, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [19, [1]]], 'bad_primes': [5, 19], 'central_character': '475.306', 'coeff_info': ['x^90 - 1', '0.997564050259824 + 0.0697564737441253*I', '\\\\zeta_{90}'], 'conductor': 475, 'conductor_radical': 95, 'conjugate': 'dirichlet_L_475.371', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^41', 'a^47', 'a^82', 0, 'a^88', 'a^30', 'a^33', 'a^4', 0, 'a^6', 'a^39', 'a^79', 'a^71', 0, 'a^74', 'a^68', 'a^45', 0, 0, 'a^77', 'a^47', 'a^46', 'a^80', 0, 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'0.831688752749422194399426446564-0.555242126058632619197744236710*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0936872040028', 'prec': 54}, 'spectral_label': 'r1-0', 'st_group': 'mu(90)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.548582085679310552756126089062+0.0292670883408670278850825408588*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.445342082507', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.56983255252', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.88274176597', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 51.04583927744689, 'bad_primes': [5, 19], 'central_character': '475.306', 'conductor': 475, 'conductor_radical': 95, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/475/306'], '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': '1-475-475.306-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': '1-475-475.306-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 51.04583927744689, 'root_angle': -0.09368720400279251, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.445342082507', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_475.306', 'Lhash_array': ['dirichlet_L_475.306'], 'label': '1-475-475.306-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/475/306'}