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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_605.87', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.28173255684142967, 0.9594929736144974], 'a3': [2.9010907910729803e-30, -1.0], 'a4': [-0.8412535328311812, 0.5406408174555976], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.9594929736144974, -0.28173255684142967], 'a7': [0.9096319953545183, -0.41541501300188644], 'a8': [-0.7557495743542583, -0.6548607339452851], 'a9': [-1.0, -1.4081532572346456e-30], 'algebraic': True, 'analytic_conductor': 2.8096081881599018, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]]], 'bad_primes': [5, 11], 'central_character': '605.87', 'coeff_info': ['x^44 - 1', '0.989821441880933 + 0.142314838273285*I', '\\\\zeta_{44}'], 'conductor': 605, 'conductor_radical': 55, 'conjugate': 'dirichlet_L_605.153', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^9', 'a^33', 'a^18', 0, 'a^42', 'a^41', 'a^27', 'a^22', 0, 0, 'a^7', 'a^7', 'a^6', 0, 'a^36', 'a^1', 'a^31', 'a^32', 0, 'a^30', 0, 'a^25', 'a^16', 0, 'a^16', 'a^11', 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'198.294075810676489471506463581756', '198.70445907311977786372769657105', '199.56300993685334853420018800474'], 'prelabel': '1-605-605.87-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8096081881599018, 'root_angle': -0.0345356104781092, 'root_number': '0.994119991476314702994793018883-0.108284082612044057822939095684*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0172678052391', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(44)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.20452364623962021564984487642+0.120564153627043246865747535369*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.856306812923', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.17995881779', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.63017303258', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.8096081881599018, 'bad_primes': [5, 11], 'central_character': '605.87', 'conductor': 605, 'conductor_radical': 55, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/605/87'], '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': '1-605-605.87-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': '1-605-605.87-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8096081881599018, 'root_angle': -0.0172678052390546, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.856306812923', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_605.87', 'Lhash_array': ['dirichlet_L_605.87'], 'label': '1-605-605.87-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/605/87'}