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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1380.59', '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': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.8412535328311812, 0.5406408174555976], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 6.408693057290354, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]], [23, [1]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '1380.59', 'coeff_info': ['x^22 - 1', '0.959492973614497 + 0.281732556841430*I', '\\\\zeta_{22}'], 'conductor': 1380, 'conductor_radical': 690, 'conjugate': 'dirichlet_L_1380.959', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 0, 0, 'a^24', 0, 0, 0, 'a^16', 0, 'a^9', 0, 0, 0, 'a^10', 0, 'a^23', 0, 0, 0, 0, 0, 0, 0, 0, 0, 'a^21', 0, 'a^29', 0, 0, 0, 0, 0, 'a^19', 0, 0, 0, 'a^3', 0, 'a^26', 0, 0, 0, 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'189.524256455694418994974526954058', '190.051095440049324811066064359376', '190.89198241662368597497305510275', '191.260431811923528614604862975450', '191.98955879013492290910502452473', '192.538297292383903107830970219208', '193.054742308559927387020249043551', '193.60216855546766881560714655569', '194.308901754754190887225261416', '195.07100836240461440519640380562', '195.42648857903250809684510797447', '195.859830619474815264418545169265', '196.75376111334782893476139464859', '197.22109130976685797273754703806', '197.753311490017993944027803581217', '198.48345215671025350079004576297', '199.08074524633407615326932100106', '199.45164173553005585897272451593'], 'prelabel': '1-1380-1380.59-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.408693057290354, 'root_angle': 0.23102128355504845, 'root_number': '0.747985421752568033740852219304+0.663715156407952554852935257719*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.115510641778', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(22)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.12394230337436646387245386247+0.129706902532745418619090991104*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.05604957881', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.17177249309', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.96718120945', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.408693057290354, 'bad_primes': [2, 3, 5, 23], 'central_character': '1380.59', 'conductor': 1380, 'conductor_radical': 690, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1380/59'], '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': '1-1380-1380.59-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': '1-1380-1380.59-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.408693057290354, 'root_angle': 0.11551064177752422, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.05604957881', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1380.59', 'Lhash_array': ['dirichlet_L_1380.59'], 'label': '1-1380-1380.59-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1380/59'}