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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_3528.277', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.8262387743159949, -0.5633200580636221], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 16.38396312037708, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1]]], 'bad_primes': [2, 3, 7], 'central_character': '3528.277', 'coeff_info': ['x^42 - 1', '0.988830826225129 + 0.149042266176174*I', '\\\\zeta_{42}'], 'conductor': 3528, 'conductor_radical': 42, 'conjugate': 'dirichlet_L_3528.1885', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^25', 0, 0, 0, 0, 0, 'a^41', 0, 'a^41', 0, 0, 0, 'a^16', 0, 'a^35', 0, 0, 0, 'a^40', 0, 'a^8', 0, 0, 0, 'a^37', 0, 'a^0', 0, 0, 0, 0, 0, 'a^23', 0, 0, 0, 'a^32', 0, 'a^31', 0, 0, 0, 'a^6', 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'root_analytic_conductor': 16.38396312037708, 'root_angle': -0.24943310657596374, 'root_number': '0.708364979689479431910223487655-0.705846339899502058693456918208*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(42)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.07007907137856898137797242727-0.174339900029541695524764601611*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.705985165295', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.34819127046', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.57853308373', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 16.38396312037708, 'bad_primes': [2, 3, 7], 'central_character': '3528.277', 'conductor': 3528, 'conductor_radical': 42, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3528/277'], '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': '1-3528-3528.277-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': '1-3528-3528.277-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 16.38396312037708, 'root_angle': -0.12471655328798187, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.705985165295', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_3528.277', 'Lhash_array': ['dirichlet_L_3528.277'], 'label': '1-3528-3528.277-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3528/277'}