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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_181.16', 'a10': [-0.9975640502598242, 0.0697564737441253], 'a2': [0.9902680687415704, 0.13917310096006544], 'a3': [0.03489949670250097, 0.9993908270190958], 'a4': [0.9612616959383189, 0.27563735581699916], 'a5': [-0.9781476007338057, 0.20791169081775934], 'a6': [-0.10452846326765347, 0.9945218953682733], 'a7': [-0.5, 0.8660254037844386], 'a8': [0.9135454576426009, 0.4067366430758002], 'a9': [-0.9975640502598242, 0.0697564737441253], 'algebraic': True, 'analytic_conductor': 0.8405604662098218, 'analytic_normalization': 0, 'bad_lfactors': [[181, [1]]], 'bad_primes': [181], 'central_character': '181.16', 'coeff_info': ['x^45 - 1', '0.990268068741570 + 0.139173100960065*I', '\\\\zeta_{45}'], 'conductor': 181, 'conductor_radical': 181, 'conjugate': 'dirichlet_L_181.34', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 'a^11', 'a^2', 'a^21', 'a^12', 'a^15', 'a^3', 'a^22', 'a^22', 'a^17', 'a^13', 'a^29', 'a^16', 'a^32', 'a^4', 'a^40', 'a^23', 'a^0', 'a^23', 'a^26', 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'186.90416336955863458396989522142', '187.57248961621604454408818522011', '188.115185325359249983416380751682', '188.94321408148207722606097063144', '189.69653451379722983058859223209', '191.01842130336057838148554087623', '191.530753755554616050684374496', '192.184351221586804975455292827383', '193.30468283790060419924997930724', '193.57246507040632009917720008254', '194.02365460277606550230241718836', '195.11350049664084003907348135610', '195.639360871355876037955703326664', '196.47065573359214242989557453211', '197.0365984409116114237221083752', '198.00747801705593570157838727135', '198.77802177442616964832663580782', '199.01506204404879189305838246841'], 'prelabel': '1-181-181.16-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8405604662098218, 'root_angle': 0.6611024683255445, 'root_number': '-0.484785872295697003961866048861+0.874632870421927463066680265098*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.330551234163', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(45)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.21237775117211415596392986680+0.844384758339531620695030911551*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.82792742675', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.3526623928', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '4.88729326704', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8405604662098218, 'bad_primes': [181], 'central_character': '181.16', 'conductor': 181, 'conductor_radical': 181, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/181/16'], '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': '1-181-181.16-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': '1-181-181.16-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8405604662098218, 'root_angle': 0.33055123416277227, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.82792742675', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_181.16', 'Lhash_array': ['dirichlet_L_181.16'], 'label': '1-181-181.16-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/181/16'}