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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_189.164', 'a10': [-1.0, -1.4081532572346456e-30], 'a2': [-0.766044443118978, 0.6427876096865394], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.17364817766693036, -0.984807753012208], 'a5': [0.766044443118978, 0.6427876096865394], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.5, 0.8660254037844386], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.8777123100202007, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '189.164', 'coeff_info': ['x^18 - 1', '0.939692620785908 + 0.342020143325669*I', '\\\\zeta_{18}'], 'conductor': 189, 'conductor_radical': 21, 'conjugate': 'dirichlet_L_189.68', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^7', 0, 'a^14', 'a^2', 0, 0, 'a^3', 0, 'a^9', 'a^7', 0, 'a^17', 0, 0, 'a^10', 'a^0', 0, 'a^9', 'a^16', 0, 'a^14', 'a^17', 0, 'a^4', 'a^6', 0, 0, 'a^1', 0, 'a^5', 'a^17', 0, 'a^7', 0, 0, 'a^12', 'a^16', 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'190.12355040043303930905220814793', '190.96479171350674543989555513406', '191.64120359768405821496795225025', '192.32655726788465283688703094227', '193.28680238591702491337214556569', '193.88104798027686688354253562102', '194.760206492510628711302604312018', '195.55919370105807728671242085434', '196.55582813943920144456512677036', '196.83977714394385547842726011140', '197.57335230039874528764435620587', '198.47017397979810535939141899169', '198.79640919661519635596444332185', '199.59767236251583434545538689871'], 'prelabel': '1-189-189.164-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8777123100202007, 'root_angle': 0.41071627647826264, 'root_number': '0.276829501679642886829705797695+0.960919053302514444475291667133*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.205358138239', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(18)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.782676322547016487398884384085+0.335693061011084682312480094782*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.5079110242', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.9043826998', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '4.97082395494', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8777123100202007, 'bad_primes': [3, 7], 'central_character': '189.164', 'conductor': 189, 'conductor_radical': 21, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/189/164'], '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': '1-189-189.164-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': '1-189-189.164-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8777123100202007, 'root_angle': 0.20535813823913132, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.5079110242', 'prec': 40}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_189.164', 'Lhash_array': ['dirichlet_L_189.164'], 'label': '1-189-189.164-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/189/164'}