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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_67.40', 'a10': [-0.6548607339452851, 0.7557495743542583], 'a2': [-0.14231483827328514, 0.9898214418809327], 'a3': [-0.6548607339452851, -0.7557495743542583], 'a4': [-0.9594929736144974, -0.28173255684142967], 'a5': [0.8412535328311812, 0.5406408174555976], 'a6': [0.8412535328311812, -0.5406408174555976], 'a7': [-0.14231483827328514, 0.9898214418809327], 'a8': [0.41541501300188644, -0.9096319953545183], 'a9': [-0.14231483827328514, 0.9898214418809327], 'algebraic': True, 'analytic_conductor': 0.311146691911923, 'analytic_normalization': 0, 'bad_lfactors': [[67, [1]]], 'bad_primes': [67], 'central_character': '67.40', 'coeff_info': ['x^11 - 1', '0.841253532831181 + 0.540640817455598*I', '\\\\zeta_{11}'], 'conductor': 67, 'conductor_radical': 67, 'conjugate': 'dirichlet_L_67.62', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^3', 'a^7', 'a^6', 'a^1', 'a^10', 'a^3', 'a^9', 'a^3', 'a^4', 'a^1', 'a^2', 'a^2', 'a^6', 'a^8', 'a^1', 'a^5', 'a^6', 'a^8', 'a^7', 'a^10', 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{'__RealLiteral__': 0, 'data': '2.0068113406', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '4.79539015326', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '6.41739294708', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.311146691911923, 'bad_primes': [67], 'central_character': '67.40', 'conductor': 67, 'conductor_radical': 67, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/67/40'], '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': '1-67-67.40-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': '1-67-67.40-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.311146691911923, 'root_angle': 0.23918553834329415, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.0068113406', 'prec': 40}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_67.40', 'Lhash_array': ['dirichlet_L_67.40'], 'label': '1-67-67.40-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/67/40'}
Lfunction data - 1-67-67.40-r0-0-0