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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_2205.1073', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.6801727377709194, -0.7330518718298263], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.07473009358642425, -0.9972037971811801], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.7818314824680298, -0.6234898018587335], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 10.239976950235675, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]], [7, [1]]], 'bad_primes': [3, 5, 7], 'central_character': '2205.1073', 'coeff_info': ['x^84 - 1', '0.997203797181180 + 0.0747300935864243*I', '\\\\zeta_{84}'], 'conductor': 2205, 'conductor_radical': 105, 'conjugate': 'dirichlet_L_2205.1607', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^73', 0, 'a^62', 0, 0, 0, 'a^51', 0, 0, 'a^66', 0, 'a^73', 0, 0, 'a^40', 'a^1', 0, 'a^14', 0, 0, 'a^55', 'a^27', 0, 0, 'a^62', 0, 0, 'a^8', 0, 'a^56', 'a^29', 0, 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'1.49770210611', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.61581466827', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.239976950235675, 'bad_primes': [3, 5, 7], 'central_character': '2205.1073', 'conductor': 2205, 'conductor_radical': 105, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2205/1073'], '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': '1-2205-2205.1073-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': '1-2205-2205.1073-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.239976950235675, 'root_angle': -0.35737847200462525, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.722678103287', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_2205.1073', 'Lhash_array': ['dirichlet_L_2205.1073'], 'factors': ['1-2205-2205.1073-r0-0-0'], 'label': '1-2205-2205.1073-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2205/1073'}