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{'Lhash': 'dirichlet_L_2028.1043', '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': [0.3546048870425356, -0.9350162426854148], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.9199794436588242, -0.3919666098600751], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 9.417992405931042, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [13, [1]]], 'bad_primes': [2, 3, 13], 'central_character': '2028.1043', 'coeff_info': ['x^78 - 1', '0.996757308134210 + 0.0804665687167259*I', '\\\\zeta_{78}'], 'conductor': 2028, 'conductor_radical': 78, 'conjugate': 'dirichlet_L_2028.35', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^63', 0, 'a^73', 0, 0, 0, 'a^110', 0, 0, 0, 0, 0, 'a^73', 0, 'a^91', 0, 0, 0, 'a^104', 0, 'a^48', 0, 0, 0, 'a^59', 0, 'a^69', 0, 0, 0, 'a^58', 0, 'a^56', 0, 0, 0, 'a^23', 0, 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'196.250123534886249707676367985848', '196.93064225618622717080190528421', '197.72468483231361605574920590718', '198.118663921358906822150111428993', '198.741980279555923088187821528663', '199.25417188291981044376911015235', '199.9908616724975908512296947619'], 'prelabel': '1-2028-2028.1043-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.417992405931042, 'root_angle': -0.15581854043392504, 'root_number': '0.557822253330656665203812128845-0.829960441038673058865859964808*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.155818540434', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(78)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.23165457647443621475450654855-0.277276940126780078665719101841*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.77072939235', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.6570044432', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.47379220946', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.417992405931042, 'bad_primes': [2, 3, 13], 'central_character': '2028.1043', 'conductor': 2028, 'conductor_radical': 78, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2028/1043'], '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': '1-2028-2028.1043-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': '1-2028-2028.1043-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.417992405931042, 'root_angle': -0.15581854043392504, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.77072939235', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_2028.1043', 'Lhash_array': ['dirichlet_L_2028.1043'], 'factors': ['1-2028-2028.1043-r0-0-0'], 'label': '1-2028-2028.1043-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2028/1043'}