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{'Lhash': 'dirichlet_L_1580.907', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.23931566428755777, -0.970941817426052], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.23931566428755777, 0.970941817426052], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.8854560256532099, 0.46472317204376856], 'algebraic': True, 'analytic_conductor': 7.337489152549826, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [79, [1]]], 'bad_primes': [2, 5, 79], 'central_character': '1580.907', 'coeff_info': ['x^52 - 1', '0.992708874098054 + 0.120536680255323*I', '\\\\zeta_{52}'], 'conductor': 1580, 'conductor_radical': 790, 'conjugate': 'dirichlet_L_1580.763', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^37', 0, 0, 0, 'a^63', 0, 'a^22', 0, 'a^46', 0, 'a^23', 0, 0, 0, 'a^49', 0, 'a^40', 0, 'a^48', 0, 'a^65', 0, 0, 0, 'a^59', 0, 'a^30', 0, 'a^70', 0, 'a^31', 0, 0, 0, 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'primitive': True, 'rational': False, 'root_analytic_conductor': 7.337489152549826, 'root_angle': -0.09955604608504276, 'root_number': '0.810653439235225017793302579581-0.585526260261742094752681470024*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.099556046085', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(52)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.997745937330925973072211376278-0.220710317563572135698806989214*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.785598804275', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.86515383607', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.62709028331', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.337489152549826, 'bad_primes': [2, 5, 79], 'central_character': '1580.907', 'conductor': 1580, 'conductor_radical': 790, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1580/907'], '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': '1-1580-1580.907-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': '1-1580-1580.907-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.337489152549826, 'root_angle': -0.09955604608504276, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.785598804275', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1580.907', 'Lhash_array': ['dirichlet_L_1580.907'], 'factors': ['1-1580-1580.907-r0-0-0'], 'label': '1-1580-1580.907-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1580/907'}