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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_847.54', 'a10': [-0.9954719225730846, -0.09505604330418266], 'a2': [0.8888354486549235, 0.4582265217274104], 'a3': [0.5, -0.8660254037844386], 'a4': [0.5800569095711982, 0.8145759520503357], 'a5': [-0.9283679330160726, 0.3716624556603275], 'a6': [0.8412535328311812, -0.5406408174555976], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.14231483827328514, 0.9898214418809327], 'a9': [-0.5, -0.8660254037844386], 'algebraic': True, 'analytic_conductor': 3.933451463423862, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '847.54', 'coeff_info': ['x^66 - 1', '0.995471922573085 + 0.0950560433041827*I', '\\\\zeta_{66}'], 'conductor': 847, 'conductor_radical': 77, 'conjugate': 'dirichlet_L_847.549', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^5', 'a^55', 'a^10', 'a^29', 'a^60', 0, 'a^15', 'a^44', 'a^34', 0, 'a^65', 'a^54', 0, 'a^18', 'a^20', 'a^58', 'a^49', 'a^8', 'a^39', 0, 0, 'a^20', 'a^4', 'a^58', 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'191.68289420048650797868943086739', '192.24044715368181929598137066023', '193.32420745898338663713147625495', '193.77680583706254801756932714473', '194.64523974815149304556592252377', '194.86795622169343542051778723159', '195.69258731818729417888292156644', '195.91524847891893536044769588817', '196.72232784247349584757236816485', '197.1468198882513485249912254486', '197.90566705439230708393762200861', '198.43756810217348554012964573202', '198.8886705743618471598993152438', '199.905430097298830857171031066090'], 'prelabel': '1-847-847.54-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.933451463423862, 'root_angle': 0.038166490586322634, 'root_number': '0.992820175511979051269884213123+0.119616466660586125932288402004*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0190832452932', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(66)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.85280299861046241476896345694+0.127222830234032842071941805854*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.08256538252', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.65565257077', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.24379797984', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.933451463423862, 'bad_primes': [7, 11], 'central_character': '847.54', 'conductor': 847, 'conductor_radical': 77, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/847/54'], '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': '1-847-847.54-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': '1-847-847.54-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.933451463423862, 'root_angle': 0.019083245293161317, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.08256538252', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_847.54', 'Lhash_array': ['dirichlet_L_847.54'], 'label': '1-847-847.54-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/847/54'}
Lfunction data - 1-847-847.54-r0-0-0