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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_115.19', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.6548607339452851, -0.7557495743542583], 'a3': [-0.8412535328311812, 0.5406408174555976], 'a4': [-0.14231483827328514, -0.9898214418809327], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.14231483827328514, 0.9898214418809327], 'a7': [-0.9594929736144974, 0.28173255684142967], 'a8': [-0.8412535328311812, -0.5406408174555976], 'a9': [0.41541501300188644, -0.9096319953545183], 'algebraic': True, 'analytic_conductor': 12.358466351381878, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [23, [1]]], 'bad_primes': [5, 23], 'central_character': '115.19', 'coeff_info': ['x^22 - 1', '0.959492973614497 + 0.281732556841430*I', '\\\\zeta_{22}'], 'conductor': 115, 'conductor_radical': 115, 'conjugate': 'dirichlet_L_115.109', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^19', 'a^9', 'a^16', 0, 'a^6', 'a^10', 'a^13', 'a^18', 0, 'a^3', 'a^3', 'a^1', 'a^7', 0, 'a^10', 'a^6', 'a^15', 'a^5', 0, 'a^19', 'a^0', 0, 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'1-115-115.19-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.358466351381878, 'root_angle': 0.23150081901437505, 'root_number': '0.746984683080717620856479663672+0.664841246646746382608774307407*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.115750409507', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(22)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.02398008191555948240944078839-0.0859884753926177550215358045727*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.41539139717', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.42400368573', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.35473671512', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.358466351381878, 'bad_primes': [5, 23], 'central_character': '115.19', 'conductor': 115, 'conductor_radical': 115, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/115/19'], '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': '1-115-115.19-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-115-115.19-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.358466351381878, 'root_angle': 0.11575040950718753, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.41539139717', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_115.19', 'Lhash_array': ['dirichlet_L_115.19'], 'label': '1-115-115.19-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/115/19'}