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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3503.1099', 'a10': [0.44061076977588376, 0.8976982508379434], 'a2': [0.9639628606958532, -0.2660368455666751], 'a3': [-0.42713243271719675, -0.90418907586914], 'a4': [0.8584487936018661, -0.5128992774059061], 'a5': [0.18591160716291458, 0.9825664732332883], 'a6': [-0.6522874112781212, -0.757971723145453], 'a7': [0.7910710346563412, 0.6117242991150064], 'a8': [0.6910626489868646, -0.7227948638273916], 'a9': [-0.6351157698421788, 0.7724169592245995], 'algebraic': True, 'analytic_conductor': 16.267863608469646, 'analytic_normalization': 0, 'bad_lfactors': [[31, [1]], [113, [1]]], 'bad_primes': [31, 113], 'central_character': '3503.1099', 'coeff_info': ['x^840 - 1', '0.999972025061270 + 0.00747991275773291*I', '\\\\zeta_{840}'], 'conductor': 3503, 'conductor_radical': 3503, 'conjugate': 'dirichlet_L_3503.51', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^804', 'a^571', 'a^768', 'a^185', 'a^535', 'a^88', 'a^732', 'a^302', 'a^149', 'a^758', 'a^499', 'a^746', 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'192.551428652615704155470149161111', '193.27019212989328894587799470387', '193.80041673427657476778491545705', '194.411563191535265710237207737648', '194.82952220895883733972555611164', '194.97285326782267804696479193767', '195.723734301549013109176867926782', '196.359257760275577313376102764708', '196.600878586406078260536880789319', '197.3263312110778919042653391375', '197.736009895801419360908961984', '198.563298730648116982738729040084', '198.9286499935744458158665356616', '199.83452251473881447096041608842'], 'prelabel': '1-3503-3503.1099-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 16.267863608469646, 'root_angle': -0.26065974904458666, 'root_number': '-0.0669271138444388374707482108507-0.997757867136337604178644029701*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(840)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.81512439706879683561933836572-0.839119177858115245106163624783*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.759477987967', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.72287433835', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.43630188546', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 16.267863608469646, 'bad_primes': [31, 113], 'central_character': '3503.1099', 'conductor': 3503, 'conductor_radical': 3503, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3503/1099'], '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': '1-3503-3503.1099-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': '1-3503-3503.1099-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 16.267863608469646, 'root_angle': -0.26065974904458666, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.759477987967', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3503.1099', 'Lhash_array': ['dirichlet_L_3503.1099'], 'factors': ['1-3503-3503.1099-r0-0-0'], 'label': '1-3503-3503.1099-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3503/1099'}
Lfunction data - 1-3503-3503.1099-r0-0-0