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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_49.23', 'a10': [0.07473009358642425, -0.9972037971811801], 'a2': [-0.9888308262251285, -0.14904226617617444], 'a3': [0.8262387743159949, -0.5633200580636221], 'a4': [0.9555728057861407, 0.2947551744109042], 'a5': [0.07473009358642425, 0.9972037971811801], 'a6': [-0.9009688679024191, 0.4338837391175581], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.9009688679024191, -0.4338837391175581], 'a9': [0.36534102436639504, -0.9308737486442042], 'algebraic': True, 'analytic_conductor': 0.22755504333857055, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]]], 'bad_primes': [7], 'central_character': '49.23', 'coeff_info': ['x^21 - 1', '0.955572805786141 + 0.294755174410904*I', '\\\\zeta_{21}'], 'conductor': 49, 'conductor_radical': 7, 'conjugate': 'dirichlet_L_49.32', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^11', 'a^19', 'a^1', 'a^5', 'a^9', 0, 'a^12', 'a^17', 'a^16', 'a^4', 'a^20', 'a^18', 0, 'a^3', 'a^2', 'a^13', 'a^7', 'a^14', 'a^6', 0, 'a^15', 'a^8', 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.22755504333857055, 'bad_primes': [7], 'central_character': '49.23', 'conductor': 49, 'conductor_radical': 7, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/49/23'], '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': '1-7e2-49.23-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': '1-7e2-49.23-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.22755504333857055, 'root_angle': -0.034013605442176874, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.97689286096', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_49.23', 'Lhash_array': ['dirichlet_L_49.23'], 'label': '1-7e2-49.23-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/49/23'}