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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_529.371', 'a10': [-0.8060875299907577, 0.5917963281344345], 'a2': [-0.9661931299194909, -0.2578193858040505], 'a3': [-0.1668503692778238, -0.9859822281724219], 'a4': [0.8670583286072443, 0.4982066386478726], 'a5': [0.6262596677501294, -0.7796145384415926], 'a6': [-0.09299565196035955, 0.9956665148112934], 'a7': [-0.616530879230335, -0.7873307278110452], 'a8': [-0.7092984707601008, -0.7049082772796631], 'a9': [-0.9443219085437077, 0.3290229977438802], 'algebraic': True, 'analytic_conductor': 2.4566656719613023, 'analytic_normalization': 0, 'bad_lfactors': [[23, [1]]], 'bad_primes': [23], 'central_character': '529.371', 'coeff_info': ['x^253 - 1', '0.999691634078213 + 0.0248321717542501*I', '\\\\zeta_{253}'], 'conductor': 529, 'conductor_radical': 23, 'conjugate': 'dirichlet_L_529.77', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^137', 'a^183', 'a^21', 'a^217', 'a^67', 'a^163', 'a^158', 'a^113', 'a^101', 'a^28', 'a^204', 'a^244', 'a^47', 'a^147', 'a^42', 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'a^178'], [1, 'a^102'], [1, 'a^150'], [1, 'a^85'], [1, 'a^124']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-23e2-529.371-r0-0-0', 'leading_term': '0.311666780803476758990916401722-0.870980809042981231448916067533*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/529/371', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.9250641880310626, 0.6206809466016411, 0.23502202715129591, -0.15641416334474417, -0.2069434091010765, 0.2763516254053725, 1.038488799175157, 1.4195516170153128, 0.7835971566357326, -0.9005373436400728, -2.773131963471819, -3.4412186968916716, -1.8910613166666543, 1.632818660780321, 5.504175347400075, 7.616162482294938, 6.786864780749696, 3.640997888553247, 0.2159275669724539, -1.5010628052370123, -0.9940382984704186, 0.5519656155555863, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.4566656719613023, 'bad_primes': [23], 'central_character': '529.371', 'conductor': 529, 'conductor_radical': 23, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/529/371'], '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': '1-23e2-529.371-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': '1-23e2-529.371-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4566656719613023, 'root_angle': -0.3906169444921808, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.796491976926', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_529.371', 'Lhash_array': ['dirichlet_L_529.371'], 'label': '1-23e2-529.371-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/529/371'}