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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_11.2', 'a10': [-1.0, -1.4081532572346456e-30], 'a2': [0.8090169943749475, 0.5877852522924731], 'a3': [0.30901699437494745, -0.9510565162951535], 'a4': [0.30901699437494745, 0.9510565162951535], 'a5': [-0.8090169943749475, 0.5877852522924731], 'a6': [0.8090169943749475, -0.5877852522924731], 'a7': [-0.30901699437494745, -0.9510565162951535], 'a8': [-0.30901699437494745, 0.9510565162951535], 'a9': [-0.8090169943749475, -0.5877852522924731], 'algebraic': True, 'analytic_conductor': 1.1821141727408753, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]]], 'bad_primes': [11], 'central_character': '11.2', 'coeff_info': ['x^10 - 1', '0.809016994374947 + 0.587785252292473*I', '\\\\zeta_{10}'], 'conductor': 11, 'conductor_radical': 11, 'conjugate': 'dirichlet_L_11.6', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 'a^8', 'a^2', 'a^4', 'a^9', 'a^7', 'a^3', 'a^6', 'a^5', 0, 'a^0', 'a^1', 'a^8', 'a^2', 'a^4', 'a^9', 'a^7', 'a^3', 'a^6', 'a^5', 0, 'a^0', 'a^1', 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'193.862649626523751340703393511206', '194.64278437380620994979248905734', '195.42942126064488450525481038302', '196.35035186823584530162189043433', '197.73929421699079978741153689820', '197.96243431521211576995156099138', '199.72555196792092984235031615681'], 'prelabel': '1-11-11.2-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1821141727408753, 'root_angle': 0.09300173434355702, 'root_number': '0.957620076587575619739038691519+0.288034353708730036260580978186*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0465008671718', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(10)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.41574766342698150628193076547+0.174032883719992697485523555452*I']], 'z1': {'__RealLiteral__': 0, 'data': '3.54704109172', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '6.63073045048', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '7.8864346592', 'prec': 40}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.1821141727408753, 'bad_primes': [11], 'central_character': '11.2', 'conductor': 11, 'conductor_radical': 11, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/11/2'], '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': '1-11-11.2-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': '1-11-11.2-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1821141727408753, 'root_angle': 0.04650086717177851, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.54704109172', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_11.2', 'Lhash_array': ['dirichlet_L_11.2'], 'label': '1-11-11.2-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/11/2'}