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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1045.454', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.6156614753256583, -0.7880107536067219], 'a3': [0.7193398003386512, 0.6946583704589973], 'a4': [-0.24192189559966773, -0.9702957262759965], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.9902680687415704, -0.13917310096006544], 'a7': [-0.9135454576426009, 0.4067366430758002], 'a8': [-0.9135454576426009, -0.4067366430758002], 'a9': [0.03489949670250097, 0.9993908270190958], 'algebraic': True, 'analytic_conductor': 4.852959597730739, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]], [19, [1]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.454', 'coeff_info': ['x^90 - 1', '0.997564050259824 + 0.0697564737441253*I', '\\\\zeta_{90}'], 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': 'dirichlet_L_1045.389', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^77', 'a^11', 'a^64', 0, 'a^88', 'a^39', 'a^51', 'a^22', 0, 0, 'a^75', 'a^7', 'a^26', 0, 'a^38', 'a^23', 'a^9', 0, 0, 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'189.32128722586916183575822171113', '190.14481253735146347903344258160', '190.57469258134720799295456195256', '191.04059100751946356322280933698', '191.90795502224735209135332924142', '192.255274451004469898203569113513', '192.95959214431815163753562505357', '193.214125560425793836652009714566', '193.91882315592616404751529279049', '194.54970764419622066191149308470', '195.01656959352650491297795419255', '195.89672525771066516899949413442', '196.58118817696350431991703682767', '197.00619011060691955855073166707', '197.3232619858799675243760747807', '198.376570803417127842302273503775', '198.98345779813435148620639172552', '199.56224078845516263637898308631'], 'prelabel': '1-1045-1045.454-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': 0.10481183079936776, 'root_number': '0.790879101161409242415604810129+0.611972423681101341424790654301*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.104811830799', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(90)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.53278649288178977421346993740-0.0566309552731143111625148589747*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.43365164347', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.50863699185', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.26964946477', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.852959597730739, 'bad_primes': [5, 11, 19], 'central_character': '1045.454', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1045/454'], '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': '1-1045-1045.454-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': '1-1045-1045.454-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': 0.10481183079936776, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.43365164347', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1045.454', 'Lhash_array': ['dirichlet_L_1045.454'], 'factors': ['1-1045-1045.454-r0-0-0'], 'label': '1-1045-1045.454-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1045/454'}
Lfunction data - 1-1045-1045.454-r0-0-0