Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [195,2,Mod(121,195)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(195, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("195.121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 195 = 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 195.bb (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.55708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.191102976.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 6x^{6} + 6x^{4} + 36x^{2} + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 121.2 | ||
Root | \(-2.10121 - 0.563016i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 195.121 |
Dual form | 195.2.bb.b.166.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/195\mathbb{Z}\right)^\times\).
\(n\) | \(106\) | \(131\) | \(157\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.975173 | − | 0.563016i | −0.689551 | − | 0.398113i | 0.113893 | − | 0.993493i | \(-0.463668\pi\) |
−0.803444 | + | 0.595380i | \(0.797001\pi\) | |||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −0.366025 | − | 0.633975i | −0.183013 | − | 0.316987i | ||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | −0.975173 | + | 0.563016i | −0.398113 | + | 0.229850i | ||||
\(7\) | 2.47517 | − | 1.42904i | 0.935527 | − | 0.540127i | 0.0469719 | − | 0.998896i | \(-0.485043\pi\) |
0.888555 | + | 0.458769i | \(0.151710\pi\) | |||||||
\(8\) | 3.07638i | 1.08766i | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −0.563016 | + | 0.975173i | −0.178041 | + | 0.308377i | ||||
\(11\) | −2.66422 | − | 1.53819i | −0.803293 | − | 0.463781i | 0.0413283 | − | 0.999146i | \(-0.486841\pi\) |
−0.844621 | + | 0.535364i | \(0.820174\pi\) | |||||||
\(12\) | −0.732051 | −0.211325 | ||||||||
\(13\) | −3.55507 | − | 0.601205i | −0.986000 | − | 0.166744i | ||||
\(14\) | −3.21829 | −0.860125 | ||||||||
\(15\) | −0.866025 | − | 0.500000i | −0.223607 | − | 0.129099i | ||||
\(16\) | 1.00000 | − | 1.73205i | 0.250000 | − | 0.433013i | ||||
\(17\) | −0.975173 | − | 1.68905i | −0.236514 | − | 0.409654i | 0.723198 | − | 0.690641i | \(-0.242672\pi\) |
−0.959712 | + | 0.280987i | \(0.909338\pi\) | |||||||
\(18\) | 1.12603i | 0.265408i | ||||||||
\(19\) | 6.42652 | − | 3.71035i | 1.47434 | − | 0.851213i | 0.474762 | − | 0.880114i | \(-0.342534\pi\) |
0.999582 | + | 0.0289008i | \(0.00920068\pi\) | |||||||
\(20\) | −0.633975 | + | 0.366025i | −0.141761 | + | 0.0818458i | ||||
\(21\) | − | 2.85808i | − | 0.623685i | ||||||
\(22\) | 1.73205 | + | 3.00000i | 0.369274 | + | 0.639602i | ||||
\(23\) | −4.39627 | + | 7.61457i | −0.916686 | + | 1.58775i | −0.112272 | + | 0.993677i | \(0.535813\pi\) |
−0.804414 | + | 0.594070i | \(0.797520\pi\) | |||||||
\(24\) | 2.66422 | + | 1.53819i | 0.543832 | + | 0.313982i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 3.12832 | + | 2.58784i | 0.613515 | + | 0.507518i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.81195 | − | 1.04613i | −0.342427 | − | 0.197700i | ||||
\(29\) | 3.34120 | − | 5.78712i | 0.620445 | − | 1.07464i | −0.368958 | − | 0.929446i | \(-0.620285\pi\) |
0.989403 | − | 0.145196i | \(-0.0463813\pi\) | |||||||
\(30\) | 0.563016 | + | 0.975173i | 0.102792 | + | 0.178041i | ||||
\(31\) | − | 3.15276i | − | 0.566252i | −0.959083 | − | 0.283126i | \(-0.908629\pi\) | ||
0.959083 | − | 0.283126i | \(-0.0913714\pi\) | |||||||
\(32\) | 3.37810 | − | 1.95035i | 0.597169 | − | 0.344776i | ||||
\(33\) | −2.66422 | + | 1.53819i | −0.463781 | + | 0.267764i | ||||
\(34\) | 2.19615i | 0.376637i | ||||||||
\(35\) | −1.42904 | − | 2.47517i | −0.241552 | − | 0.418381i | ||||
\(36\) | −0.366025 | + | 0.633975i | −0.0610042 | + | 0.105662i | ||||
\(37\) | 7.14650 | + | 4.12603i | 1.17488 | + | 0.678316i | 0.954824 | − | 0.297172i | \(-0.0960436\pi\) |
0.220053 | + | 0.975488i | \(0.429377\pi\) | |||||||
\(38\) | −8.35596 | −1.35551 | ||||||||
\(39\) | −2.29820 | + | 2.77818i | −0.368006 | + | 0.444865i | ||||
\(40\) | 3.07638 | 0.486418 | ||||||||
\(41\) | 2.87710 | + | 1.66109i | 0.449327 | + | 0.259419i | 0.707546 | − | 0.706667i | \(-0.249802\pi\) |
−0.258219 | + | 0.966086i | \(0.583136\pi\) | |||||||
\(42\) | −1.60915 | + | 2.78712i | −0.248297 | + | 0.430063i | ||||
\(43\) | 4.77337 | + | 8.26772i | 0.727932 | + | 1.26082i | 0.957756 | + | 0.287583i | \(0.0928517\pi\) |
−0.229824 | + | 0.973232i | \(0.573815\pi\) | |||||||
\(44\) | 2.25207i | 0.339512i | ||||||||
\(45\) | −0.866025 | + | 0.500000i | −0.129099 | + | 0.0745356i | ||||
\(46\) | 8.57425 | − | 4.95035i | 1.26420 | − | 0.729889i | ||||
\(47\) | − | 1.79759i | − | 0.262205i | −0.991369 | − | 0.131103i | \(-0.958148\pi\) | ||
0.991369 | − | 0.131103i | \(-0.0418518\pi\) | |||||||
\(48\) | −1.00000 | − | 1.73205i | −0.144338 | − | 0.250000i | ||||
\(49\) | 0.584320 | − | 1.01207i | 0.0834743 | − | 0.144582i | ||||
\(50\) | 0.975173 | + | 0.563016i | 0.137910 | + | 0.0796225i | ||||
\(51\) | −1.95035 | −0.273103 | ||||||||
\(52\) | 0.920099 | + | 2.47388i | 0.127595 | + | 0.343066i | ||||
\(53\) | 10.6569 | 1.46384 | 0.731918 | − | 0.681393i | \(-0.238625\pi\) | ||||
0.731918 | + | 0.681393i | \(0.238625\pi\) | |||||||
\(54\) | 0.975173 | + | 0.563016i | 0.132704 | + | 0.0766168i | ||||
\(55\) | −1.53819 | + | 2.66422i | −0.207409 | + | 0.359244i | ||||
\(56\) | 4.39627 | + | 7.61457i | 0.587477 | + | 1.01754i | ||||
\(57\) | − | 7.42071i | − | 0.982896i | ||||||
\(58\) | −6.51649 | + | 3.76230i | −0.855657 | + | 0.494014i | ||||
\(59\) | 4.17256 | − | 2.40903i | 0.543221 | − | 0.313629i | −0.203162 | − | 0.979145i | \(-0.565122\pi\) |
0.746383 | + | 0.665516i | \(0.231789\pi\) | |||||||
\(60\) | 0.732051i | 0.0945074i | ||||||||
\(61\) | 3.13397 | + | 5.42820i | 0.401264 | + | 0.695010i | 0.993879 | − | 0.110476i | \(-0.0352375\pi\) |
−0.592614 | + | 0.805486i | \(0.701904\pi\) | |||||||
\(62\) | −1.77505 | + | 3.07448i | −0.225432 | + | 0.390460i | ||||
\(63\) | −2.47517 | − | 1.42904i | −0.311842 | − | 0.180042i | ||||
\(64\) | −8.39230 | −1.04904 | ||||||||
\(65\) | −0.601205 | + | 3.55507i | −0.0745703 | + | 0.440953i | ||||
\(66\) | 3.46410 | 0.426401 | ||||||||
\(67\) | −5.09097 | − | 2.93927i | −0.621961 | − | 0.359090i | 0.155671 | − | 0.987809i | \(-0.450246\pi\) |
−0.777632 | + | 0.628719i | \(0.783579\pi\) | |||||||
\(68\) | −0.713876 | + | 1.23647i | −0.0865702 | + | 0.149944i | ||||
\(69\) | 4.39627 | + | 7.61457i | 0.529249 | + | 0.916686i | ||||
\(70\) | 3.21829i | 0.384660i | ||||||||
\(71\) | 8.91942 | − | 5.14963i | 1.05854 | − | 0.611148i | 0.133512 | − | 0.991047i | \(-0.457375\pi\) |
0.925028 | + | 0.379899i | \(0.124041\pi\) | |||||||
\(72\) | 2.66422 | − | 1.53819i | 0.313982 | − | 0.181277i | ||||
\(73\) | − | 11.1101i | − | 1.30034i | −0.759787 | − | 0.650172i | \(-0.774697\pi\) | ||
0.759787 | − | 0.650172i | \(-0.225303\pi\) | |||||||
\(74\) | −4.64605 | − | 8.04719i | −0.540092 | − | 0.935467i | ||||
\(75\) | −0.500000 | + | 0.866025i | −0.0577350 | + | 0.100000i | ||||
\(76\) | −4.70454 | − | 2.71617i | −0.539648 | − | 0.311566i | ||||
\(77\) | −8.79254 | −1.00200 | ||||||||
\(78\) | 3.80530 | − | 1.41529i | 0.430865 | − | 0.160250i | ||||
\(79\) | −11.0968 | −1.24849 | −0.624246 | − | 0.781228i | \(-0.714594\pi\) | ||||
−0.624246 | + | 0.781228i | \(0.714594\pi\) | |||||||
\(80\) | −1.73205 | − | 1.00000i | −0.193649 | − | 0.111803i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −1.87044 | − | 3.23970i | −0.206556 | − | 0.357765i | ||||
\(83\) | 6.97707i | 0.765833i | 0.923783 | + | 0.382916i | \(0.125080\pi\) | ||||
−0.923783 | + | 0.382916i | \(0.874920\pi\) | |||||||
\(84\) | −1.81195 | + | 1.04613i | −0.197700 | + | 0.114142i | ||||
\(85\) | −1.68905 | + | 0.975173i | −0.183203 | + | 0.105772i | ||||
\(86\) | − | 10.7499i | − | 1.15920i | ||||||
\(87\) | −3.34120 | − | 5.78712i | −0.358214 | − | 0.620445i | ||||
\(88\) | 4.73205 | − | 8.19615i | 0.504438 | − | 0.873713i | ||||
\(89\) | 0.0805845 | + | 0.0465255i | 0.00854194 | + | 0.00493169i | 0.504265 | − | 0.863549i | \(-0.331764\pi\) |
−0.495723 | + | 0.868481i | \(0.665097\pi\) | |||||||
\(90\) | 1.12603 | 0.118694 | ||||||||
\(91\) | −9.65857 | + | 3.59226i | −1.01249 | + | 0.376571i | ||||
\(92\) | 6.43659 | 0.671061 | ||||||||
\(93\) | −2.73037 | − | 1.57638i | −0.283126 | − | 0.163463i | ||||
\(94\) | −1.01207 | + | 1.75296i | −0.104387 | + | 0.180804i | ||||
\(95\) | −3.71035 | − | 6.42652i | −0.380674 | − | 0.659347i | ||||
\(96\) | − | 3.90069i | − | 0.398113i | ||||||
\(97\) | 4.15483 | − | 2.39879i | 0.421860 | − | 0.243561i | −0.274013 | − | 0.961726i | \(-0.588351\pi\) |
0.695873 | + | 0.718165i | \(0.255018\pi\) | |||||||
\(98\) | −1.13963 | + | 0.657963i | −0.115120 | + | 0.0664643i | ||||
\(99\) | 3.07638i | 0.309188i | ||||||||
\(100\) | 0.366025 | + | 0.633975i | 0.0366025 | + | 0.0633975i | ||||
\(101\) | 1.39627 | − | 2.41841i | 0.138934 | − | 0.240641i | −0.788159 | − | 0.615471i | \(-0.788966\pi\) |
0.927093 | + | 0.374830i | \(0.122299\pi\) | |||||||
\(102\) | 1.90192 | + | 1.09808i | 0.188319 | + | 0.108726i | ||||
\(103\) | −8.35395 | −0.823139 | −0.411570 | − | 0.911378i | \(-0.635019\pi\) | ||||
−0.411570 | + | 0.911378i | \(0.635019\pi\) | |||||||
\(104\) | 1.84953 | − | 10.9368i | 0.181362 | − | 1.07244i | ||||
\(105\) | −2.85808 | −0.278920 | ||||||||
\(106\) | −10.3923 | − | 6.00000i | −1.00939 | − | 0.582772i | ||||
\(107\) | −3.17529 | + | 5.49977i | −0.306967 | + | 0.531683i | −0.977697 | − | 0.210019i | \(-0.932648\pi\) |
0.670730 | + | 0.741701i | \(0.265981\pi\) | |||||||
\(108\) | 0.366025 | + | 0.633975i | 0.0352208 | + | 0.0610042i | ||||
\(109\) | 11.7996i | 1.13020i | 0.825024 | + | 0.565098i | \(0.191162\pi\) | ||||
−0.825024 | + | 0.565098i | \(0.808838\pi\) | |||||||
\(110\) | 3.00000 | − | 1.73205i | 0.286039 | − | 0.165145i | ||||
\(111\) | 7.14650 | − | 4.12603i | 0.678316 | − | 0.391626i | ||||
\(112\) | − | 5.71617i | − | 0.540127i | ||||||
\(113\) | −1.73205 | − | 3.00000i | −0.162938 | − | 0.282216i | 0.772983 | − | 0.634426i | \(-0.218764\pi\) |
−0.935921 | + | 0.352210i | \(0.885430\pi\) | |||||||
\(114\) | −4.17798 | + | 7.23647i | −0.391303 | + | 0.677757i | ||||
\(115\) | 7.61457 | + | 4.39627i | 0.710062 | + | 0.409955i | ||||
\(116\) | −4.89185 | −0.454197 | ||||||||
\(117\) | 1.25688 | + | 3.37939i | 0.116198 | + | 0.312424i | ||||
\(118\) | −5.42529 | −0.499438 | ||||||||
\(119\) | −4.82744 | − | 2.78712i | −0.442531 | − | 0.255495i | ||||
\(120\) | 1.53819 | − | 2.66422i | 0.140417 | − | 0.243209i | ||||
\(121\) | −0.767949 | − | 1.33013i | −0.0698136 | − | 0.120921i | ||||
\(122\) | − | 7.05791i | − | 0.638994i | ||||||
\(123\) | 2.87710 | − | 1.66109i | 0.259419 | − | 0.149776i | ||||
\(124\) | −1.99877 | + | 1.15399i | −0.179495 | + | 0.103631i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 1.60915 | + | 2.78712i | 0.143354 | + | 0.248297i | ||||
\(127\) | −7.48601 | + | 12.9662i | −0.664276 | + | 1.15056i | 0.315205 | + | 0.949024i | \(0.397927\pi\) |
−0.979481 | + | 0.201536i | \(0.935407\pi\) | |||||||
\(128\) | 1.42775 | + | 0.824313i | 0.126197 | + | 0.0728597i | ||||
\(129\) | 9.54674 | 0.840543 | ||||||||
\(130\) | 2.58784 | − | 3.12832i | 0.226969 | − | 0.274372i | ||||
\(131\) | −10.5831 | −0.924649 | −0.462324 | − | 0.886711i | \(-0.652984\pi\) | ||||
−0.462324 | + | 0.886711i | \(0.652984\pi\) | |||||||
\(132\) | 1.95035 | + | 1.12603i | 0.169756 | + | 0.0980085i | ||||
\(133\) | 10.6045 | − | 18.3675i | 0.919526 | − | 1.59267i | ||||
\(134\) | 3.30972 | + | 5.73260i | 0.285916 | + | 0.495221i | ||||
\(135\) | 1.00000i | 0.0860663i | ||||||||
\(136\) | 5.19615 | − | 3.00000i | 0.445566 | − | 0.257248i | ||||
\(137\) | 7.54009 | − | 4.35327i | 0.644193 | − | 0.371925i | −0.142035 | − | 0.989862i | \(-0.545365\pi\) |
0.786228 | + | 0.617937i | \(0.212031\pi\) | |||||||
\(138\) | − | 9.90069i | − | 0.842803i | ||||||
\(139\) | 5.82844 | + | 10.0952i | 0.494362 | + | 0.856260i | 0.999979 | − | 0.00649792i | \(-0.00206837\pi\) |
−0.505617 | + | 0.862758i | \(0.668735\pi\) | |||||||
\(140\) | −1.04613 | + | 1.81195i | −0.0884142 | + | 0.153138i | ||||
\(141\) | −1.55676 | − | 0.898795i | −0.131103 | − | 0.0756922i | ||||
\(142\) | −11.5973 | −0.973223 | ||||||||
\(143\) | 8.54674 | + | 7.07012i | 0.714714 | + | 0.591233i | ||||
\(144\) | −2.00000 | −0.166667 | ||||||||
\(145\) | −5.78712 | − | 3.34120i | −0.480595 | − | 0.277471i | ||||
\(146\) | −6.25519 | + | 10.8343i | −0.517684 | + | 0.896654i | ||||
\(147\) | −0.584320 | − | 1.01207i | −0.0481939 | − | 0.0834743i | ||||
\(148\) | − | 6.04093i | − | 0.496561i | ||||||
\(149\) | 5.91003 | − | 3.41216i | 0.484168 | − | 0.279535i | −0.237984 | − | 0.971269i | \(-0.576486\pi\) |
0.722152 | + | 0.691734i | \(0.243153\pi\) | |||||||
\(150\) | 0.975173 | − | 0.563016i | 0.0796225 | − | 0.0459701i | ||||
\(151\) | 12.6810i | 1.03197i | 0.856598 | + | 0.515984i | \(0.172574\pi\) | ||||
−0.856598 | + | 0.515984i | \(0.827426\pi\) | |||||||
\(152\) | 11.4144 | + | 19.7704i | 0.925834 | + | 1.60359i | ||||
\(153\) | −0.975173 | + | 1.68905i | −0.0788380 | + | 0.136551i | ||||
\(154\) | 8.57425 | + | 4.95035i | 0.690933 | + | 0.398910i | ||||
\(155\) | −3.15276 | −0.253235 | ||||||||
\(156\) | 2.60249 | + | 0.440113i | 0.208366 | + | 0.0352372i | ||||
\(157\) | 7.98333 | 0.637139 | 0.318569 | − | 0.947900i | \(-0.396798\pi\) | ||||
0.318569 | + | 0.947900i | \(0.396798\pi\) | |||||||
\(158\) | 10.8213 | + | 6.24770i | 0.860900 | + | 0.497041i | ||||
\(159\) | 5.32844 | − | 9.22913i | 0.422573 | − | 0.731918i | ||||
\(160\) | −1.95035 | − | 3.37810i | −0.154188 | − | 0.267062i | ||||
\(161\) | 25.1298i | 1.98051i | ||||||||
\(162\) | 0.975173 | − | 0.563016i | 0.0766168 | − | 0.0442347i | ||||
\(163\) | −10.6713 | + | 6.16109i | −0.835843 | + | 0.482574i | −0.855849 | − | 0.517226i | \(-0.826965\pi\) |
0.0200063 | + | 0.999800i | \(0.493631\pi\) | |||||||
\(164\) | − | 2.43201i | − | 0.189908i | ||||||
\(165\) | 1.53819 | + | 2.66422i | 0.119748 | + | 0.207409i | ||||
\(166\) | 3.92820 | − | 6.80385i | 0.304888 | − | 0.528081i | ||||
\(167\) | −19.0020 | − | 10.9708i | −1.47042 | − | 0.848947i | −0.470970 | − | 0.882149i | \(-0.656096\pi\) |
−0.999449 | + | 0.0332022i | \(0.989429\pi\) | |||||||
\(168\) | 8.79254 | 0.678360 | ||||||||
\(169\) | 12.2771 | + | 4.27466i | 0.944393 | + | 0.328820i | ||||
\(170\) | 2.19615 | 0.168437 | ||||||||
\(171\) | −6.42652 | − | 3.71035i | −0.491448 | − | 0.283738i | ||||
\(172\) | 3.49435 | − | 6.05239i | 0.266442 | − | 0.461490i | ||||
\(173\) | 7.52528 | + | 13.0342i | 0.572136 | + | 0.990969i | 0.996346 | + | 0.0854053i | \(0.0272185\pi\) |
−0.424210 | + | 0.905564i | \(0.639448\pi\) | |||||||
\(174\) | 7.52460i | 0.570438i | ||||||||
\(175\) | −2.47517 | + | 1.42904i | −0.187105 | + | 0.108025i | ||||
\(176\) | −5.32844 | + | 3.07638i | −0.401647 | + | 0.231891i | ||||
\(177\) | − | 4.81805i | − | 0.362147i | ||||||
\(178\) | −0.0523892 | − | 0.0907407i | −0.00392673 | − | 0.00680130i | ||||
\(179\) | −0.240387 | + | 0.416363i | −0.0179674 | + | 0.0311204i | −0.874869 | − | 0.484359i | \(-0.839053\pi\) |
0.856902 | + | 0.515480i | \(0.172386\pi\) | |||||||
\(180\) | 0.633975 | + | 0.366025i | 0.0472537 | + | 0.0272819i | ||||
\(181\) | −1.85887 | −0.138169 | −0.0690844 | − | 0.997611i | \(-0.522008\pi\) | ||||
−0.0690844 | + | 0.997611i | \(0.522008\pi\) | |||||||
\(182\) | 11.4413 | + | 1.93486i | 0.848084 | + | 0.143421i | ||||
\(183\) | 6.26795 | 0.463340 | ||||||||
\(184\) | −23.4253 | − | 13.5246i | −1.72694 | − | 0.997046i | ||||
\(185\) | 4.12603 | − | 7.14650i | 0.303352 | − | 0.525421i | ||||
\(186\) | 1.77505 | + | 3.07448i | 0.130153 | + | 0.225432i | ||||
\(187\) | 6.00000i | 0.438763i | ||||||||
\(188\) | −1.13963 | + | 0.657963i | −0.0831158 | + | 0.0479869i | ||||
\(189\) | −2.47517 | + | 1.42904i | −0.180042 | + | 0.103947i | ||||
\(190\) | 8.35596i | 0.606205i | ||||||||
\(191\) | −4.35937 | − | 7.55066i | −0.315433 | − | 0.546346i | 0.664096 | − | 0.747647i | \(-0.268816\pi\) |
−0.979529 | + | 0.201301i | \(0.935483\pi\) | |||||||
\(192\) | −4.19615 | + | 7.26795i | −0.302831 | + | 0.524519i | ||||
\(193\) | 5.58869 | + | 3.22663i | 0.402283 | + | 0.232258i | 0.687468 | − | 0.726214i | \(-0.258722\pi\) |
−0.285186 | + | 0.958472i | \(0.592055\pi\) | |||||||
\(194\) | −5.40224 | −0.387858 | ||||||||
\(195\) | 2.77818 | + | 2.29820i | 0.198950 | + | 0.164577i | ||||
\(196\) | −0.855504 | −0.0611074 | ||||||||
\(197\) | 10.0399 | + | 5.79651i | 0.715310 | + | 0.412984i | 0.813024 | − | 0.582230i | \(-0.197820\pi\) |
−0.0977141 | + | 0.995215i | \(0.531153\pi\) | |||||||
\(198\) | 1.73205 | − | 3.00000i | 0.123091 | − | 0.213201i | ||||
\(199\) | 0.400691 | + | 0.694017i | 0.0284042 | + | 0.0491976i | 0.879878 | − | 0.475199i | \(-0.157624\pi\) |
−0.851474 | + | 0.524397i | \(0.824291\pi\) | |||||||
\(200\) | − | 3.07638i | − | 0.217533i | ||||||
\(201\) | −5.09097 | + | 2.93927i | −0.359090 | + | 0.207320i | ||||
\(202\) | −2.72321 | + | 1.57225i | −0.191605 | + | 0.110623i | ||||
\(203\) | − | 19.0988i | − | 1.34048i | ||||||
\(204\) | 0.713876 | + | 1.23647i | 0.0499813 | + | 0.0865702i | ||||
\(205\) | 1.66109 | − | 2.87710i | 0.116016 | − | 0.200945i | ||||
\(206\) | 8.14655 | + | 4.70341i | 0.567597 | + | 0.327702i | ||||
\(207\) | 8.79254 | 0.611124 | ||||||||
\(208\) | −4.59639 | + | 5.55636i | −0.318702 | + | 0.385265i | ||||
\(209\) | −22.8289 | −1.57911 | ||||||||
\(210\) | 2.78712 | + | 1.60915i | 0.192330 | + | 0.111042i | ||||
\(211\) | 4.14605 | − | 7.18116i | 0.285426 | − | 0.494372i | −0.687287 | − | 0.726386i | \(-0.741198\pi\) |
0.972712 | + | 0.232015i | \(0.0745317\pi\) | |||||||
\(212\) | −3.90069 | − | 6.75620i | −0.267901 | − | 0.464017i | ||||
\(213\) | − | 10.2993i | − | 0.705693i | ||||||
\(214\) | 6.19292 | − | 3.57548i | 0.423339 | − | 0.244415i | ||||
\(215\) | 8.26772 | − | 4.77337i | 0.563854 | − | 0.325541i | ||||
\(216\) | − | 3.07638i | − | 0.209321i | ||||||
\(217\) | −4.50542 | − | 7.80362i | −0.305848 | − | 0.529744i | ||||
\(218\) | 6.64336 | − | 11.5066i | 0.449945 | − | 0.779328i | ||||
\(219\) | −9.62167 | − | 5.55507i | −0.650172 | − | 0.375377i | ||||
\(220\) | 2.25207 | 0.151834 | ||||||||
\(221\) | 2.45135 | + | 6.59097i | 0.164895 | + | 0.443357i | ||||
\(222\) | −9.29209 | −0.623644 | ||||||||
\(223\) | 11.0517 | + | 6.38068i | 0.740074 | + | 0.427282i | 0.822096 | − | 0.569349i | \(-0.192805\pi\) |
−0.0820224 | + | 0.996630i | \(0.526138\pi\) | |||||||
\(224\) | 5.57425 | − | 9.65488i | 0.372445 | − | 0.645094i | ||||
\(225\) | 0.500000 | + | 0.866025i | 0.0333333 | + | 0.0577350i | ||||
\(226\) | 3.90069i | 0.259470i | ||||||||
\(227\) | −14.8189 | + | 8.55568i | −0.983563 | + | 0.567860i | −0.903344 | − | 0.428917i | \(-0.858895\pi\) |
−0.0802192 | + | 0.996777i | \(0.525562\pi\) | |||||||
\(228\) | −4.70454 | + | 2.71617i | −0.311566 | + | 0.179883i | ||||
\(229\) | 6.39993i | 0.422919i | 0.977387 | + | 0.211460i | \(0.0678217\pi\) | ||||
−0.977387 | + | 0.211460i | \(0.932178\pi\) | |||||||
\(230\) | −4.95035 | − | 8.57425i | −0.326416 | − | 0.565369i | ||||
\(231\) | −4.39627 | + | 7.61457i | −0.289253 | + | 0.501002i | ||||
\(232\) | 17.8034 | + | 10.2788i | 1.16885 | + | 0.674836i | ||||
\(233\) | −0.671557 | −0.0439952 | −0.0219976 | − | 0.999758i | \(-0.507003\pi\) | ||||
−0.0219976 | + | 0.999758i | \(0.507003\pi\) | |||||||
\(234\) | 0.676977 | − | 4.00313i | 0.0442553 | − | 0.261693i | ||||
\(235\) | −1.79759 | −0.117262 | ||||||||
\(236\) | −3.05452 | − | 1.76353i | −0.198833 | − | 0.114796i | ||||
\(237\) | −5.54842 | + | 9.61015i | −0.360409 | + | 0.624246i | ||||
\(238\) | 3.13839 | + | 5.43586i | 0.203432 | + | 0.352354i | ||||
\(239\) | 7.12983i | 0.461190i | 0.973050 | + | 0.230595i | \(0.0740673\pi\) | ||||
−0.973050 | + | 0.230595i | \(0.925933\pi\) | |||||||
\(240\) | −1.73205 | + | 1.00000i | −0.111803 | + | 0.0645497i | ||||
\(241\) | −23.3292 | + | 13.4691i | −1.50277 | + | 0.867623i | −0.502772 | + | 0.864419i | \(0.667686\pi\) |
−0.999995 | + | 0.00320355i | \(0.998980\pi\) | |||||||
\(242\) | 1.72947i | 0.111175i | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 2.29423 | − | 3.97372i | 0.146873 | − | 0.254391i | ||||
\(245\) | −1.01207 | − | 0.584320i | −0.0646589 | − | 0.0373308i | ||||
\(246\) | −3.74089 | −0.238510 | ||||||||
\(247\) | −25.0774 | + | 9.32692i | −1.59564 | + | 0.593458i | ||||
\(248\) | 9.69907 | 0.615892 | ||||||||
\(249\) | 6.04232 | + | 3.48853i | 0.382916 | + | 0.221077i | ||||
\(250\) | 0.563016 | − | 0.975173i | 0.0356083 | − | 0.0616753i | ||||
\(251\) | −5.82402 | − | 10.0875i | −0.367609 | − | 0.636718i | 0.621582 | − | 0.783349i | \(-0.286490\pi\) |
−0.989191 | + | 0.146631i | \(0.953157\pi\) | |||||||
\(252\) | 2.09226i | 0.131800i | ||||||||
\(253\) | 23.4253 | − | 13.5246i | 1.47274 | − | 0.850284i | ||||
\(254\) | 14.6003 | − | 8.42949i | 0.916105 | − | 0.528913i | ||||
\(255\) | 1.95035i | 0.122135i | ||||||||
\(256\) | 7.46410 | + | 12.9282i | 0.466506 | + | 0.808013i | ||||
\(257\) | −3.63939 | + | 6.30362i | −0.227019 | + | 0.393209i | −0.956923 | − | 0.290341i | \(-0.906231\pi\) |
0.729904 | + | 0.683550i | \(0.239565\pi\) | |||||||
\(258\) | −9.30972 | − | 5.37497i | −0.579598 | − | 0.334631i | ||||
\(259\) | 23.5851 | 1.46551 | ||||||||
\(260\) | 2.47388 | − | 0.920099i | 0.153424 | − | 0.0570621i | ||||
\(261\) | −6.68240 | −0.413630 | ||||||||
\(262\) | 10.3203 | + | 5.95845i | 0.637593 | + | 0.368114i | ||||
\(263\) | −11.9639 | + | 20.7220i | −0.737724 | + | 1.27778i | 0.215794 | + | 0.976439i | \(0.430766\pi\) |
−0.953518 | + | 0.301336i | \(0.902567\pi\) | |||||||
\(264\) | −4.73205 | − | 8.19615i | −0.291238 | − | 0.504438i | ||||
\(265\) | − | 10.6569i | − | 0.654647i | ||||||
\(266\) | −20.6824 | + | 11.9410i | −1.26812 | + | 0.732150i | ||||
\(267\) | 0.0805845 | − | 0.0465255i | 0.00493169 | − | 0.00284731i | ||||
\(268\) | 4.30340i | 0.262872i | ||||||||
\(269\) | −2.19073 | − | 3.79446i | −0.133571 | − | 0.231352i | 0.791479 | − | 0.611196i | \(-0.209311\pi\) |
−0.925051 | + | 0.379843i | \(0.875978\pi\) | |||||||
\(270\) | 0.563016 | − | 0.975173i | 0.0342641 | − | 0.0593471i | ||||
\(271\) | −2.15488 | − | 1.24412i | −0.130900 | − | 0.0755751i | 0.433120 | − | 0.901336i | \(-0.357413\pi\) |
−0.564020 | + | 0.825761i | \(0.690746\pi\) | |||||||
\(272\) | −3.90069 | −0.236514 | ||||||||
\(273\) | −1.71829 | + | 10.1607i | −0.103996 | + | 0.614953i | ||||
\(274\) | −9.80385 | −0.592272 | ||||||||
\(275\) | 2.66422 | + | 1.53819i | 0.160659 | + | 0.0927563i | ||||
\(276\) | 3.21829 | − | 5.57425i | 0.193719 | − | 0.335530i | ||||
\(277\) | −10.8530 | − | 18.7980i | −0.652096 | − | 1.12946i | −0.982613 | − | 0.185663i | \(-0.940557\pi\) |
0.330518 | − | 0.943800i | \(-0.392777\pi\) | |||||||
\(278\) | − | 13.1260i | − | 0.787247i | ||||||
\(279\) | −2.73037 | + | 1.57638i | −0.163463 | + | 0.0943753i | ||||
\(280\) | 7.61457 | − | 4.39627i | 0.455057 | − | 0.262728i | ||||
\(281\) | − | 29.7270i | − | 1.77336i | −0.462379 | − | 0.886682i | \(-0.653004\pi\) | ||
0.462379 | − | 0.886682i | \(-0.346996\pi\) | |||||||
\(282\) | 1.01207 | + | 1.75296i | 0.0602680 | + | 0.104387i | ||||
\(283\) | 13.9998 | − | 24.2483i | 0.832200 | − | 1.44141i | −0.0640902 | − | 0.997944i | \(-0.520415\pi\) |
0.896290 | − | 0.443468i | \(-0.146252\pi\) | |||||||
\(284\) | −6.52947 | − | 3.76979i | −0.387452 | − | 0.223696i | ||||
\(285\) | −7.42071 | −0.439565 | ||||||||
\(286\) | −4.35395 | − | 11.7065i | −0.257455 | − | 0.692222i | ||||
\(287\) | 9.49508 | 0.560477 | ||||||||
\(288\) | −3.37810 | − | 1.95035i | −0.199056 | − | 0.114925i | ||||
\(289\) | 6.59808 | − | 11.4282i | 0.388122 | − | 0.672247i | ||||
\(290\) | 3.76230 | + | 6.51649i | 0.220930 | + | 0.382662i | ||||
\(291\) | − | 4.79759i | − | 0.281240i | ||||||
\(292\) | −7.04355 | + | 4.06660i | −0.412193 | + | 0.237980i | ||||
\(293\) | −14.6866 | + | 8.47930i | −0.857999 | + | 0.495366i | −0.863342 | − | 0.504620i | \(-0.831633\pi\) |
0.00534246 | + | 0.999986i | \(0.498299\pi\) | |||||||
\(294\) | 1.31593i | 0.0767464i | ||||||||
\(295\) | −2.40903 | − | 4.17256i | −0.140259 | − | 0.242936i | ||||
\(296\) | −12.6932 | + | 21.9853i | −0.737779 | + | 1.27787i | ||||
\(297\) | 2.66422 | + | 1.53819i | 0.154594 | + | 0.0892548i | ||||
\(298\) | −7.68440 | −0.445145 | ||||||||
\(299\) | 20.2070 | − | 24.4273i | 1.16860 | − | 1.41267i | ||||
\(300\) | 0.732051 | 0.0422650 | ||||||||
\(301\) | 23.6298 | + | 13.6427i | 1.36200 | + | 0.786351i | ||||
\(302\) | 7.13963 | − | 12.3662i | 0.410839 | − | 0.711595i | ||||
\(303\) | −1.39627 | − | 2.41841i | −0.0802137 | − | 0.138934i | ||||
\(304\) | − | 14.8414i | − | 0.851213i | ||||||
\(305\) | 5.42820 | − | 3.13397i | 0.310818 | − | 0.179451i | ||||
\(306\) | 1.90192 | − | 1.09808i | 0.108726 | − | 0.0627728i | ||||
\(307\) | − | 15.6072i | − | 0.890752i | −0.895344 | − | 0.445376i | \(-0.853070\pi\) | ||
0.895344 | − | 0.445376i | \(-0.146930\pi\) | |||||||
\(308\) | 3.21829 | + | 5.57425i | 0.183379 | + | 0.317622i | ||||
\(309\) | −4.17698 | + | 7.23474i | −0.237620 | + | 0.411570i | ||||
\(310\) | 3.07448 | + | 1.77505i | 0.174619 | + | 0.100816i | ||||
\(311\) | 24.9941 | 1.41728 | 0.708642 | − | 0.705568i | \(-0.249308\pi\) | ||||
0.708642 | + | 0.705568i | \(0.249308\pi\) | |||||||
\(312\) | −8.54674 | − | 7.07012i | −0.483864 | − | 0.400267i | ||||
\(313\) | 1.16117 | 0.0656331 | 0.0328166 | − | 0.999461i | \(-0.489552\pi\) | ||||
0.0328166 | + | 0.999461i | \(0.489552\pi\) | |||||||
\(314\) | −7.78512 | − | 4.49474i | −0.439340 | − | 0.253653i | ||||
\(315\) | −1.42904 | + | 2.47517i | −0.0805174 | + | 0.139460i | ||||
\(316\) | 4.06173 | + | 7.03512i | 0.228490 | + | 0.395756i | ||||
\(317\) | 8.62570i | 0.484467i | 0.970218 | + | 0.242234i | \(0.0778801\pi\) | ||||
−0.970218 | + | 0.242234i | \(0.922120\pi\) | |||||||
\(318\) | −10.3923 | + | 6.00000i | −0.582772 | + | 0.336463i | ||||
\(319\) | −17.8034 | + | 10.2788i | −0.996798 | + | 0.575502i | ||||
\(320\) | 8.39230i | 0.469144i | ||||||||
\(321\) | 3.17529 | + | 5.49977i | 0.177228 | + | 0.306967i | ||||
\(322\) | 14.1485 | − | 24.5059i | 0.788465 | − | 1.36566i | ||||
\(323\) | −12.5339 | − | 7.23647i | −0.697407 | − | 0.402648i | ||||
\(324\) | 0.732051 | 0.0406695 | ||||||||
\(325\) | 3.55507 | + | 0.601205i | 0.197200 | + | 0.0333489i | ||||
\(326\) | 13.8752 | 0.768475 | ||||||||
\(327\) | 10.2187 | + | 5.89980i | 0.565098 | + | 0.326259i | ||||
\(328\) | −5.11015 | + | 8.85104i | −0.282161 | + | 0.488717i | ||||
\(329\) | −2.56883 | − | 4.44934i | −0.141624 | − | 0.245300i | ||||
\(330\) | − | 3.46410i | − | 0.190693i | ||||||
\(331\) | −22.1899 | + | 12.8113i | −1.21967 | + | 0.704174i | −0.964846 | − | 0.262815i | \(-0.915349\pi\) |
−0.254819 | + | 0.966989i | \(0.582016\pi\) | |||||||
\(332\) | 4.42328 | − | 2.55378i | 0.242759 | − | 0.140157i | ||||
\(333\) | − | 8.25207i | − | 0.452210i | ||||||
\(334\) | 12.3535 | + | 21.3969i | 0.675953 | + | 1.17078i | ||||
\(335\) | −2.93927 | + | 5.09097i | −0.160590 | + | 0.278150i | ||||
\(336\) | −4.95035 | − | 2.85808i | −0.270063 | − | 0.155921i | ||||
\(337\) | −20.1770 | −1.09911 | −0.549556 | − | 0.835457i | \(-0.685203\pi\) | ||||
−0.549556 | + | 0.835457i | \(0.685203\pi\) | |||||||
\(338\) | −9.56560 | − | 11.0807i | −0.520300 | − | 0.602713i | ||||
\(339\) | −3.46410 | −0.188144 | ||||||||
\(340\) | 1.23647 | + | 0.713876i | 0.0670570 | + | 0.0387154i | ||||
\(341\) | −4.84953 | + | 8.39964i | −0.262617 | + | 0.454866i | ||||
\(342\) | 4.17798 | + | 7.23647i | 0.225919 | + | 0.391303i | ||||
\(343\) | 16.6665i | 0.899907i | ||||||||
\(344\) | −25.4346 | + | 14.6847i | −1.37134 | + | 0.791745i | ||||
\(345\) | 7.61457 | − | 4.39627i | 0.409955 | − | 0.236687i | ||||
\(346\) | − | 16.9474i | − | 0.911099i | ||||||
\(347\) | −12.0968 | − | 20.9523i | −0.649393 | − | 1.12478i | −0.983268 | − | 0.182164i | \(-0.941690\pi\) |
0.333876 | − | 0.942617i | \(-0.391643\pi\) | |||||||
\(348\) | −2.44593 | + | 4.23647i | −0.131115 | + | 0.227099i | ||||
\(349\) | 22.2362 | + | 12.8381i | 1.19028 | + | 0.687206i | 0.958369 | − | 0.285532i | \(-0.0921703\pi\) |
0.231907 | + | 0.972738i | \(0.425504\pi\) | |||||||
\(350\) | 3.21829 | 0.172025 | ||||||||
\(351\) | 3.55507 | + | 0.601205i | 0.189756 | + | 0.0320900i | ||||
\(352\) | −12.0000 | −0.639602 | ||||||||
\(353\) | −6.79405 | − | 3.92254i | −0.361611 | − | 0.208776i | 0.308176 | − | 0.951329i | \(-0.400281\pi\) |
−0.669787 | + | 0.742553i | \(0.733615\pi\) | |||||||
\(354\) | −2.71264 | + | 4.69844i | −0.144175 | + | 0.249719i | ||||
\(355\) | −5.14963 | − | 8.91942i | −0.273314 | − | 0.473393i | ||||
\(356\) | − | 0.0681180i | − | 0.00361025i | ||||||
\(357\) | −4.82744 | + | 2.78712i | −0.255495 | + | 0.147510i | ||||
\(358\) | 0.468838 | − | 0.270684i | 0.0247789 | − | 0.0143061i | ||||
\(359\) | 19.7145i | 1.04049i | 0.854017 | + | 0.520245i | \(0.174160\pi\) | ||||
−0.854017 | + | 0.520245i | \(0.825840\pi\) | |||||||
\(360\) | −1.53819 | − | 2.66422i | −0.0810697 | − | 0.140417i | ||||
\(361\) | 18.0334 | − | 31.2348i | 0.949128 | − | 1.64394i | ||||
\(362\) | 1.81272 | + | 1.04658i | 0.0952745 | + | 0.0550068i | ||||
\(363\) | −1.53590 | −0.0806138 | ||||||||
\(364\) | 5.81268 | + | 4.80843i | 0.304667 | + | 0.252030i | ||||
\(365\) | −11.1101 | −0.581532 | ||||||||
\(366\) | −6.11233 | − | 3.52896i | −0.319497 | − | 0.184462i | ||||
\(367\) | 5.58806 | − | 9.67880i | 0.291694 | − | 0.505229i | −0.682516 | − | 0.730870i | \(-0.739114\pi\) |
0.974210 | + | 0.225641i | \(0.0724477\pi\) | |||||||
\(368\) | 8.79254 | + | 15.2291i | 0.458343 | + | 0.793873i | ||||
\(369\) | − | 3.32218i | − | 0.172946i | ||||||
\(370\) | −8.04719 | + | 4.64605i | −0.418353 | + | 0.241536i | ||||
\(371\) | 26.3776 | − | 15.2291i | 1.36946 | − | 0.790657i | ||||
\(372\) | 2.30798i | 0.119663i | ||||||||
\(373\) | 4.37586 | + | 7.57922i | 0.226574 | + | 0.392437i | 0.956790 | − | 0.290778i | \(-0.0939143\pi\) |
−0.730217 | + | 0.683216i | \(0.760581\pi\) | |||||||
\(374\) | 3.37810 | − | 5.85104i | 0.174677 | − | 0.302550i | ||||
\(375\) | 0.866025 | + | 0.500000i | 0.0447214 | + | 0.0258199i | ||||
\(376\) | 5.53006 | 0.285191 | ||||||||
\(377\) | −15.3575 | + | 18.5649i | −0.790949 | + | 0.956142i | ||||
\(378\) | 3.21829 | 0.165531 | ||||||||
\(379\) | −16.2550 | − | 9.38481i | −0.834961 | − | 0.482065i | 0.0205870 | − | 0.999788i | \(-0.493446\pi\) |
−0.855548 | + | 0.517723i | \(0.826780\pi\) | |||||||
\(380\) | −2.71617 | + | 4.70454i | −0.139336 | + | 0.241338i | ||||
\(381\) | 7.48601 | + | 12.9662i | 0.383520 | + | 0.664276i | ||||
\(382\) | 9.81759i | 0.502312i | ||||||||
\(383\) | 5.26083 | − | 3.03734i | 0.268816 | − | 0.155201i | −0.359533 | − | 0.933132i | \(-0.617064\pi\) |
0.628349 | + | 0.777931i | \(0.283731\pi\) | |||||||
\(384\) | 1.42775 | − | 0.824313i | 0.0728597 | − | 0.0420655i | ||||
\(385\) | 8.79254i | 0.448110i | ||||||||
\(386\) | −3.63329 | − | 6.29305i | −0.184930 | − | 0.320308i | ||||
\(387\) | 4.77337 | − | 8.26772i | 0.242644 | − | 0.420272i | ||||
\(388\) | −3.04155 | − | 1.75604i | −0.154411 | − | 0.0891494i | ||||
\(389\) | 9.66572 | 0.490072 | 0.245036 | − | 0.969514i | \(-0.421200\pi\) | ||||
0.245036 | + | 0.969514i | \(0.421200\pi\) | |||||||
\(390\) | −1.41529 | − | 3.80530i | −0.0716658 | − | 0.192689i | ||||
\(391\) | 17.1485 | 0.867237 | ||||||||
\(392\) | 3.11352 | + | 1.79759i | 0.157256 | + | 0.0907920i | ||||
\(393\) | −5.29154 | + | 9.16522i | −0.266923 | + | 0.462324i | ||||
\(394\) | −6.52706 | − | 11.3052i | −0.328829 | − | 0.569548i | ||||
\(395\) | 11.0968i | 0.558343i | ||||||||
\(396\) | 1.95035 | − | 1.12603i | 0.0980085 | − | 0.0565853i | ||||
\(397\) | 21.0718 | − | 12.1658i | 1.05757 | − | 0.610585i | 0.132807 | − | 0.991142i | \(-0.457601\pi\) |
0.924758 | + | 0.380556i | \(0.124268\pi\) | |||||||
\(398\) | − | 0.902382i | − | 0.0452323i | ||||||
\(399\) | −10.6045 | − | 18.3675i | −0.530889 | − | 0.919526i | ||||
\(400\) | −1.00000 | + | 1.73205i | −0.0500000 | + | 0.0866025i | ||||
\(401\) | −7.70454 | − | 4.44822i | −0.384746 | − | 0.222133i | 0.295135 | − | 0.955456i | \(-0.404635\pi\) |
−0.679881 | + | 0.733322i | \(0.737969\pi\) | |||||||
\(402\) | 6.61944 | 0.330148 | ||||||||
\(403\) | −1.89545 | + | 11.2083i | −0.0944193 | + | 0.558324i | ||||
\(404\) | −2.04428 | −0.101707 | ||||||||
\(405\) | 0.866025 | + | 0.500000i | 0.0430331 | + | 0.0248452i | ||||
\(406\) | −10.7530 | + | 18.6247i | −0.533660 | + | 0.924327i | ||||
\(407\) | −12.6932 | − | 21.9853i | −0.629180 | − | 1.08977i | ||||
\(408\) | − | 6.00000i | − | 0.297044i | ||||||
\(409\) | 24.4988 | − | 14.1444i | 1.21139 | − | 0.699394i | 0.248325 | − | 0.968677i | \(-0.420120\pi\) |
0.963061 | + | 0.269283i | \(0.0867866\pi\) | |||||||
\(410\) | −3.23970 | + | 1.87044i | −0.159998 | + | 0.0923746i | ||||
\(411\) | − | 8.70654i | − | 0.429462i | ||||||
\(412\) | 3.05776 | + | 5.29619i | 0.150645 | + | 0.260925i | ||||
\(413\) | 6.88520 | − | 11.9255i | 0.338799 | − | 0.586816i | ||||
\(414\) | −8.57425 | − | 4.95035i | −0.421401 | − | 0.243296i | ||||
\(415\) | 6.97707 | 0.342491 | ||||||||
\(416\) | −13.1819 | + | 4.90269i | −0.646298 | + | 0.240374i | ||||
\(417\) | 11.6569 | 0.570840 | ||||||||
\(418\) | 22.2621 | + | 12.8530i | 1.08888 | + | 0.628663i | ||||
\(419\) | −14.4474 | + | 25.0236i | −0.705801 | + | 1.22248i | 0.260601 | + | 0.965447i | \(0.416079\pi\) |
−0.966402 | + | 0.257036i | \(0.917254\pi\) | |||||||
\(420\) | 1.04613 | + | 1.81195i | 0.0510460 | + | 0.0884142i | ||||
\(421\) | 12.0134i | 0.585498i | 0.956189 | + | 0.292749i | \(0.0945701\pi\) | ||||
−0.956189 | + | 0.292749i | \(0.905430\pi\) | |||||||
\(422\) | −8.08622 | + | 4.66858i | −0.393631 | + | 0.227263i | ||||
\(423\) | −1.55676 | + | 0.898795i | −0.0756922 | + | 0.0437009i | ||||
\(424\) | 32.7846i | 1.59216i | ||||||||
\(425\) | 0.975173 | + | 1.68905i | 0.0473028 | + | 0.0819309i | ||||
\(426\) | −5.79865 | + | 10.0436i | −0.280945 | + | 0.486612i | ||||
\(427\) | 15.5143 | + | 8.95716i | 0.750788 | + | 0.433467i | ||||
\(428\) | 4.64895 | 0.224716 | ||||||||
\(429\) | 10.3963 | − | 3.86663i | 0.501937 | − | 0.186683i | ||||
\(430\) | −10.7499 | −0.518408 | ||||||||
\(431\) | 19.9384 | + | 11.5115i | 0.960401 | + | 0.554488i | 0.896296 | − | 0.443455i | \(-0.146248\pi\) |
0.0641046 | + | 0.997943i | \(0.479581\pi\) | |||||||
\(432\) | −1.00000 | + | 1.73205i | −0.0481125 | + | 0.0833333i | ||||
\(433\) | −13.4397 | − | 23.2783i | −0.645872 | − | 1.11868i | −0.984099 | − | 0.177619i | \(-0.943161\pi\) |
0.338227 | − | 0.941064i | \(-0.390173\pi\) | |||||||
\(434\) | 10.1465i | 0.487047i | ||||||||
\(435\) | −5.78712 | + | 3.34120i | −0.277471 | + | 0.160198i | ||||
\(436\) | 7.48064 | − | 4.31895i | 0.358258 | − | 0.206840i | ||||
\(437\) | 65.2469i | 3.12118i | ||||||||
\(438\) | 6.25519 | + | 10.8343i | 0.298885 | + | 0.517684i | ||||
\(439\) | −15.8272 | + | 27.4135i | −0.755392 | + | 1.30838i | 0.189788 | + | 0.981825i | \(0.439220\pi\) |
−0.945179 | + | 0.326551i | \(0.894113\pi\) | |||||||
\(440\) | −8.19615 | − | 4.73205i | −0.390736 | − | 0.225592i | ||||
\(441\) | −1.16864 | −0.0556495 | ||||||||
\(442\) | 1.32034 | − | 7.80748i | 0.0628021 | − | 0.371364i | ||||
\(443\) | −9.89932 | −0.470331 | −0.235166 | − | 0.971955i | \(-0.575563\pi\) | ||||
−0.235166 | + | 0.971955i | \(0.575563\pi\) | |||||||
\(444\) | −5.23160 | − | 3.02047i | −0.248281 | − | 0.143345i | ||||
\(445\) | 0.0465255 | − | 0.0805845i | 0.00220552 | − | 0.00382007i | ||||
\(446\) | −7.18485 | − | 12.4445i | −0.340212 | − | 0.589265i | ||||
\(447\) | − | 6.82431i | − | 0.322779i | ||||||
\(448\) | −20.7724 | + | 11.9930i | −0.981404 | + | 0.566614i | ||||
\(449\) | −12.9975 | + | 7.50413i | −0.613392 | + | 0.354142i | −0.774292 | − | 0.632829i | \(-0.781894\pi\) |
0.160900 | + | 0.986971i | \(0.448560\pi\) | |||||||
\(450\) | − | 1.12603i | − | 0.0530817i | ||||||
\(451\) | −5.11015 | − | 8.85104i | −0.240627 | − | 0.416779i | ||||
\(452\) | −1.26795 | + | 2.19615i | −0.0596393 | + | 0.103298i | ||||
\(453\) | 10.9821 | + | 6.34052i | 0.515984 | + | 0.297903i | ||||
\(454\) | 19.2679 | 0.904290 | ||||||||
\(455\) | 3.59226 | + | 9.65857i | 0.168408 | + | 0.452801i | ||||
\(456\) | 22.8289 | 1.06906 | ||||||||
\(457\) | −11.2847 | − | 6.51520i | −0.527874 | − | 0.304768i | 0.212276 | − | 0.977210i | \(-0.431912\pi\) |
−0.740150 | + | 0.672441i | \(0.765246\pi\) | |||||||
\(458\) | 3.60326 | − | 6.24104i | 0.168369 | − | 0.291624i | ||||
\(459\) | 0.975173 | + | 1.68905i | 0.0455172 | + | 0.0788380i | ||||
\(460\) | − | 6.43659i | − | 0.300108i | ||||||
\(461\) | 24.8693 | − | 14.3583i | 1.15828 | − | 0.668732i | 0.207388 | − | 0.978259i | \(-0.433504\pi\) |
0.950891 | + | 0.309526i | \(0.100170\pi\) | |||||||
\(462\) | 8.57425 | − | 4.95035i | 0.398910 | − | 0.230311i | ||||
\(463\) | − | 0.460309i | − | 0.0213924i | −0.999943 | − | 0.0106962i | \(-0.996595\pi\) | ||
0.999943 | − | 0.0106962i | \(-0.00340477\pi\) | |||||||
\(464\) | −6.68240 | − | 11.5742i | −0.310222 | − | 0.537321i | ||||
\(465\) | −1.57638 | + | 2.73037i | −0.0731028 | + | 0.126618i | ||||
\(466\) | 0.654884 | + | 0.378098i | 0.0303369 | + | 0.0175150i | ||||
\(467\) | 34.0634 | 1.57627 | 0.788133 | − | 0.615505i | \(-0.211048\pi\) | ||||
0.788133 | + | 0.615505i | \(0.211048\pi\) | |||||||
\(468\) | 1.68240 | − | 2.03377i | 0.0777688 | − | 0.0940111i | ||||
\(469\) | −16.8014 | −0.775816 | ||||||||
\(470\) | 1.75296 | + | 1.01207i | 0.0808580 | + | 0.0466834i | ||||
\(471\) | 3.99166 | − | 6.91376i | 0.183926 | − | 0.318569i | ||||
\(472\) | 7.41108 | + | 12.8364i | 0.341123 | + | 0.590842i | ||||
\(473\) | − | 29.3694i | − | 1.35041i | ||||||
\(474\) | 10.8213 | − | 6.24770i | 0.497041 | − | 0.286967i | ||||
\(475\) | −6.42652 | + | 3.71035i | −0.294869 | + | 0.170243i | ||||
\(476\) | 4.08063i | 0.187036i | ||||||||
\(477\) | −5.32844 | − | 9.22913i | −0.243973 | − | 0.422573i | ||||
\(478\) | 4.01421 | − | 6.95281i | 0.183606 | − | 0.318014i | ||||
\(479\) | 26.7871 | + | 15.4656i | 1.22393 | + | 0.706639i | 0.965755 | − | 0.259458i | \(-0.0835438\pi\) |
0.258180 | + | 0.966097i | \(0.416877\pi\) | |||||||
\(480\) | −3.90069 | −0.178041 | ||||||||
\(481\) | −22.9257 | − | 18.9649i | −1.04532 | − | 0.864723i | ||||
\(482\) | 30.3333 | 1.38165 | ||||||||
\(483\) | 21.7631 | + | 12.5649i | 0.990254 | + | 0.571723i | ||||
\(484\) | −0.562178 | + | 0.973721i | −0.0255535 | + | 0.0442600i | ||||
\(485\) | −2.39879 | − | 4.15483i | −0.108924 | − | 0.188661i | ||||
\(486\) | − | 1.12603i | − | 0.0510779i | ||||||
\(487\) | 14.3223 | − | 8.26901i | 0.649007 | − | 0.374704i | −0.139069 | − | 0.990283i | \(-0.544411\pi\) |
0.788076 | + | 0.615578i | \(0.211078\pi\) | |||||||
\(488\) | −16.6992 | + | 9.64129i | −0.755937 | + | 0.436441i | ||||
\(489\) | 12.3222i | 0.557228i | ||||||||
\(490\) | 0.657963 | + | 1.13963i | 0.0297238 | + | 0.0514831i | ||||
\(491\) | 9.34120 | − | 16.1794i | 0.421562 | − | 0.730167i | −0.574530 | − | 0.818483i | \(-0.694815\pi\) |
0.996093 | + | 0.0883160i | \(0.0281485\pi\) | |||||||
\(492\) | −2.10618 | − | 1.21600i | −0.0949540 | − | 0.0548217i | ||||
\(493\) | −13.0330 | −0.586976 | ||||||||
\(494\) | 29.7060 | + | 5.02364i | 1.33654 | + | 0.226024i | ||||
\(495\) | 3.07638 | 0.138273 | ||||||||
\(496\) | −5.46073 | − | 3.15276i | −0.245194 | − | 0.141563i | ||||
\(497\) | 14.7181 | − | 25.4924i | 0.660195 | − | 1.14349i | ||||
\(498\) | −3.92820 | − | 6.80385i | −0.176027 | − | 0.304888i | ||||
\(499\) | 10.9966i | 0.492277i | 0.969235 | + | 0.246138i | \(0.0791618\pi\) | ||||
−0.969235 | + | 0.246138i | \(0.920838\pi\) | |||||||
\(500\) | 0.633975 | − | 0.366025i | 0.0283522 | − | 0.0163692i | ||||
\(501\) | −19.0020 | + | 10.9708i | −0.848947 | + | 0.490140i | ||||
\(502\) | 13.1161i | 0.585399i | ||||||||
\(503\) | 7.99663 | + | 13.8506i | 0.356552 | + | 0.617567i | 0.987382 | − | 0.158354i | \(-0.0506189\pi\) |
−0.630830 | + | 0.775921i | \(0.717286\pi\) | |||||||
\(504\) | 4.39627 | − | 7.61457i | 0.195826 | − | 0.339180i | ||||
\(505\) | −2.41841 | − | 1.39627i | −0.107618 | − | 0.0621333i | ||||
\(506\) | −30.4583 | −1.35404 | ||||||||
\(507\) | 9.84052 | − | 8.49496i | 0.437033 | − | 0.377274i | ||||
\(508\) | 10.9603 | 0.486284 | ||||||||
\(509\) | 1.23647 | + | 0.713876i | 0.0548055 | + | 0.0316420i | 0.527152 | − | 0.849771i | \(-0.323260\pi\) |
−0.472347 | + | 0.881413i | \(0.656593\pi\) | |||||||
\(510\) | 1.09808 | − | 1.90192i | 0.0486236 | − | 0.0842186i | ||||
\(511\) | −15.8769 | − | 27.4995i | −0.702351 | − | 1.21651i | ||||
\(512\) | − | 20.1069i | − | 0.888608i | ||||||
\(513\) | −6.42652 | + | 3.71035i | −0.283738 | + | 0.163816i | ||||
\(514\) | 7.09808 | − | 4.09808i | 0.313083 | − | 0.180758i | ||||
\(515\) | 8.35395i | 0.368119i | ||||||||
\(516\) | −3.49435 | − | 6.05239i | −0.153830 | − | 0.266442i | ||||
\(517\) | −2.76503 | + | 4.78918i | −0.121606 | + | 0.210628i | ||||
\(518\) | −22.9995 | − | 13.2788i | −1.01054 | − | 0.583436i | ||||
\(519\) | 15.0506 | 0.660646 | ||||||||
\(520\) | −10.9368 | − | 1.84953i | −0.479608 | − | 0.0811075i | ||||
\(521\) | 11.8172 | 0.517719 | 0.258859 | − | 0.965915i | \(-0.416653\pi\) | ||||
0.258859 | + | 0.965915i | \(0.416653\pi\) | |||||||
\(522\) | 6.51649 | + | 3.76230i | 0.285219 | + | 0.164671i | ||||
\(523\) | −14.3063 | + | 24.7792i | −0.625571 | + | 1.08352i | 0.362859 | + | 0.931844i | \(0.381801\pi\) |
−0.988430 | + | 0.151677i | \(0.951533\pi\) | |||||||
\(524\) | 3.87368 | + | 6.70941i | 0.169222 | + | 0.293102i | ||||
\(525\) | 2.85808i | 0.124737i | ||||||||
\(526\) | 23.3337 | − | 13.4717i | 1.01740 | − | 0.587394i | ||||
\(527\) | −5.32516 | + | 3.07448i | −0.231968 | + | 0.133927i | ||||
\(528\) | 6.15276i | 0.267764i | ||||||||
\(529\) | −27.1544 | − | 47.0328i | −1.18063 | − | 2.04491i | ||||
\(530\) | −6.00000 | + | 10.3923i | −0.260623 | + | 0.451413i | ||||
\(531\) | −4.17256 | − | 2.40903i | −0.181074 | − | 0.104543i | ||||
\(532\) | −15.5261 | −0.673140 | ||||||||
\(533\) | −9.22963 | − | 7.63503i | −0.399780 | − | 0.330710i | ||||
\(534\) | −0.104778 | −0.00453420 | ||||||||
\(535\) | 5.49977 | + | 3.17529i | 0.237776 | + | 0.137280i | ||||
\(536\) | 9.04232 | − | 15.6618i | 0.390569 | − | 0.676485i | ||||
\(537\) | 0.240387 | + | 0.416363i | 0.0103735 | + | 0.0179674i | ||||
\(538\) | 4.93367i | 0.212706i | ||||||||
\(539\) | −3.11352 | + | 1.79759i | −0.134109 | + | 0.0774277i | ||||
\(540\) | 0.633975 | − | 0.366025i | 0.0272819 | − | 0.0157512i | ||||
\(541\) | 33.9315i | 1.45883i | 0.684072 | + | 0.729415i | \(0.260208\pi\) | ||||
−0.684072 | + | 0.729415i | \(0.739792\pi\) | |||||||
\(542\) | 1.40092 | + | 2.42647i | 0.0601748 | + | 0.104226i | ||||
\(543\) | −0.929436 | + | 1.60983i | −0.0398859 | + | 0.0690844i | ||||
\(544\) | −6.58846 | − | 3.80385i | −0.282478 | − | 0.163089i | ||||
\(545\) | 11.7996 | 0.505439 | ||||||||
\(546\) | 7.39627 | − | 8.94101i | 0.316531 | − | 0.382640i | ||||
\(547\) | −0.0276116 | −0.00118059 | −0.000590294 | − | 1.00000i | \(-0.500188\pi\) | ||||
−0.000590294 | 1.00000i | \(0.500188\pi\) | ||||||||
\(548\) | −5.51973 | − | 3.18682i | −0.235791 | − | 0.136134i | ||||
\(549\) | 3.13397 | − | 5.42820i | 0.133755 | − | 0.231670i | ||||
\(550\) | −1.73205 | − | 3.00000i | −0.0738549 | − | 0.127920i | ||||
\(551\) | − | 49.5881i | − | 2.11252i | ||||||
\(552\) | −23.4253 | + | 13.5246i | −0.997046 | + | 0.575645i | ||||
\(553\) | −27.4666 | + | 15.8579i | −1.16800 | + | 0.674344i | ||||
\(554\) | 24.4417i | 1.03843i | ||||||||
\(555\) | −4.12603 | − | 7.14650i | −0.175140 | − | 0.303352i | ||||
\(556\) | 4.26672 | − | 7.39017i | 0.180949 | − | 0.313413i | ||||
\(557\) | −34.9572 | − | 20.1826i | −1.48118 | − | 0.855162i | −0.481412 | − | 0.876494i | \(-0.659876\pi\) |
−0.999772 | + | 0.0213318i | \(0.993209\pi\) | |||||||
\(558\) | 3.55011 | 0.150288 | ||||||||
\(559\) | −11.9991 | − | 32.2621i | −0.507507 | − | 1.36454i | ||||
\(560\) | −5.71617 | −0.241552 | ||||||||
\(561\) | 5.19615 | + | 3.00000i | 0.219382 | + | 0.126660i | ||||
\(562\) | −16.7368 | + | 28.9890i | −0.705999 | + | 1.22283i | ||||
\(563\) | 7.06049 | + | 12.2291i | 0.297564 | + | 0.515397i | 0.975578 | − | 0.219653i | \(-0.0704924\pi\) |
−0.678014 | + | 0.735049i | \(0.737159\pi\) | |||||||
\(564\) | 1.31593i | 0.0554105i | ||||||||
\(565\) | −3.00000 | + | 1.73205i | −0.126211 | + | 0.0728679i | ||||
\(566\) | −27.3044 | + | 15.7642i | −1.14769 | + | 0.662618i | ||||
\(567\) | 2.85808i | 0.120028i | ||||||||
\(568\) | 15.8422 | + | 27.4395i | 0.664724 | + | 1.15134i | ||||
\(569\) | −15.5158 | + | 26.8742i | −0.650456 | + | 1.12662i | 0.332556 | + | 0.943084i | \(0.392089\pi\) |
−0.983012 | + | 0.183540i | \(0.941244\pi\) | |||||||
\(570\) | 7.23647 | + | 4.17798i | 0.303102 | + | 0.174996i | ||||
\(571\) | 29.6336 | 1.24013 | 0.620065 | − | 0.784551i | \(-0.287106\pi\) | ||||
0.620065 | + | 0.784551i | \(0.287106\pi\) | |||||||
\(572\) | 1.35395 | − | 8.00626i | 0.0566116 | − | 0.334758i | ||||
\(573\) | −8.71875 | −0.364231 | ||||||||
\(574\) | −9.25934 | − | 5.34589i | −0.386478 | − | 0.223133i | ||||
\(575\) | 4.39627 | − | 7.61457i | 0.183337 | − | 0.317549i | ||||
\(576\) | 4.19615 | + | 7.26795i | 0.174840 | + | 0.302831i | ||||
\(577\) | − | 17.7788i | − | 0.740140i | −0.929004 | − | 0.370070i | \(-0.879334\pi\) | ||
0.929004 | − | 0.370070i | \(-0.120666\pi\) | |||||||
\(578\) | −12.8685 | + | 7.42965i | −0.535260 | + | 0.309033i | ||||
\(579\) | 5.58869 | − | 3.22663i | 0.232258 | − | 0.134094i | ||||
\(580\) | 4.89185i | 0.203123i | ||||||||
\(581\) | 9.97052 | + | 17.2695i | 0.413647 | + | 0.716458i | ||||
\(582\) | −2.70112 | + | 4.67848i | −0.111965 | + | 0.193929i | ||||
\(583\) | −28.3923 | − | 16.3923i | −1.17589 | − | 0.678900i | ||||
\(584\) | 34.1790 | 1.41434 | ||||||||
\(585\) | 3.37939 | − | 1.25688i | 0.139720 | − | 0.0519655i | ||||
\(586\) | 19.0959 | 0.788846 | ||||||||
\(587\) | 4.81687 | + | 2.78102i | 0.198814 | + | 0.114785i | 0.596102 | − | 0.802909i | \(-0.296715\pi\) |
−0.397288 | + | 0.917694i | \(0.630049\pi\) | |||||||
\(588\) | −0.427752 | + | 0.740888i | −0.0176402 | + | 0.0305537i | ||||
\(589\) | −11.6978 | − | 20.2612i | −0.482001 | − | 0.834850i | ||||
\(590\) | 5.42529i | 0.223356i | ||||||||
\(591\) | 10.0399 | − | 5.79651i | 0.412984 | − | 0.238437i | ||||
\(592\) | 14.2930 | − | 8.25207i | 0.587439 | − | 0.339158i | ||||
\(593\) | − | 33.4290i | − | 1.37276i | −0.727241 | − | 0.686382i | \(-0.759198\pi\) | ||
0.727241 | − | 0.686382i | \(-0.240802\pi\) | |||||||
\(594\) | −1.73205 | − | 3.00000i | −0.0710669 | − | 0.123091i | ||||
\(595\) | −2.78712 | + | 4.82744i | −0.114261 | + | 0.197906i | ||||
\(596\) | −4.32644 | − | 2.49787i | −0.177218 | − | 0.102317i | ||||
\(597\) | 0.801382 | 0.0327984 | ||||||||
\(598\) | −33.4583 | + | 12.4440i | −1.36821 | + | 0.508871i | ||||
\(599\) | −8.14349 | −0.332734 | −0.166367 | − | 0.986064i | \(-0.553204\pi\) | ||||
−0.166367 | + | 0.986064i | \(0.553204\pi\) | |||||||
\(600\) | −2.66422 | − | 1.53819i | −0.108766 | − | 0.0627963i | ||||
\(601\) | −11.5588 | + | 20.0204i | −0.471494 | + | 0.816651i | −0.999468 | − | 0.0326092i | \(-0.989618\pi\) |
0.527974 | + | 0.849260i | \(0.322952\pi\) | |||||||
\(602\) | −15.3621 | − | 26.6080i | −0.626113 | − | 1.08446i | ||||
\(603\) | 5.87855i | 0.239393i | ||||||||
\(604\) | 8.03945 | − | 4.64158i | 0.327121 | − | 0.188863i | ||||
\(605\) | −1.33013 | + | 0.767949i | −0.0540774 | + | 0.0312216i | ||||
\(606\) | 3.14450i | 0.127736i | ||||||||
\(607\) | −3.48351 | − | 6.03361i | −0.141391 | − | 0.244897i | 0.786629 | − | 0.617425i | \(-0.211824\pi\) |
−0.928021 | + | 0.372528i | \(0.878491\pi\) | |||||||
\(608\) | 14.4729 | − | 25.0679i | 0.586955 | − | 1.01664i | ||||
\(609\) | −16.5401 | − | 9.54942i | −0.670238 | − | 0.386962i | ||||
\(610\) | −7.05791 | −0.285767 | ||||||||
\(611\) | −1.08072 | + | 6.39056i | −0.0437213 | + | 0.258535i | ||||
\(612\) | 1.42775 | 0.0577135 | ||||||||
\(613\) | −29.7784 | − | 17.1926i | −1.20274 | − | 0.694401i | −0.241574 | − | 0.970382i | \(-0.577664\pi\) |
−0.961163 | + | 0.275982i | \(0.910997\pi\) | |||||||
\(614\) | −8.78712 | + | 15.2197i | −0.354620 | + | 0.614219i | ||||
\(615\) | −1.66109 | − | 2.87710i | −0.0669817 | − | 0.116016i | ||||
\(616\) | − | 27.0492i | − | 1.08984i | ||||||
\(617\) | 13.5177 | − | 7.80446i | 0.544203 | − | 0.314196i | −0.202578 | − | 0.979266i | \(-0.564932\pi\) |
0.746781 | + | 0.665070i | \(0.231598\pi\) | |||||||
\(618\) | 8.14655 | − | 4.70341i | 0.327702 | − | 0.189199i | ||||
\(619\) | − | 16.0626i | − | 0.645610i | −0.946465 | − | 0.322805i | \(-0.895374\pi\) | ||
0.946465 | − | 0.322805i | \(-0.104626\pi\) | |||||||
\(620\) | 1.15399 | + | 1.99877i | 0.0463453 | + | 0.0802724i | ||||
\(621\) | 4.39627 | − | 7.61457i | 0.176416 | − | 0.305562i | ||||
\(622\) | −24.3735 | − | 14.0721i | −0.977290 | − | 0.564238i | ||||
\(623\) | 0.265947 | 0.0106550 | ||||||||
\(624\) | 2.51376 | + | 6.75877i | 0.100631 | + | 0.270568i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −1.13234 | − | 0.653757i | −0.0452574 | − | 0.0261294i | ||||
\(627\) | −11.4144 | + | 19.7704i | −0.455849 | + | 0.789554i | ||||
\(628\) | −2.92210 | − | 5.06123i | −0.116605 | − | 0.201965i | ||||
\(629\) | − | 16.0944i | − | 0.641725i | ||||||
\(630\) | 2.78712 | − | 1.60915i | 0.111042 | − | 0.0641100i | ||||
\(631\) | −31.7588 | + | 18.3359i | −1.26430 | + | 0.729942i | −0.973903 | − | 0.226965i | \(-0.927120\pi\) |
−0.290394 | + | 0.956907i | \(0.593786\pi\) | |||||||
\(632\) | − | 34.1381i | − | 1.35794i | ||||||
\(633\) | −4.14605 | − | 7.18116i | −0.164791 | − | 0.285426i | ||||
\(634\) | 4.85641 | − | 8.41154i | 0.192873 | − | 0.334065i | ||||
\(635\) | 12.9662 | + | 7.48601i | 0.514546 | + | 0.297073i | ||||
\(636\) | −7.80138 | −0.309345 | ||||||||
\(637\) | −2.68576 | + | 3.24670i | −0.106414 | + | 0.128639i | ||||
\(638\) | 23.1485 | 0.916458 | ||||||||
\(639\) | −8.91942 | − | 5.14963i | −0.352847 | − | 0.203716i | ||||
\(640\) | 0.824313 | − | 1.42775i | 0.0325838 | − | 0.0564369i | ||||
\(641\) | 13.3211 | + | 23.0728i | 0.526152 | + | 0.911322i | 0.999536 | + | 0.0304659i | \(0.00969909\pi\) |
−0.473384 | + | 0.880856i | \(0.656968\pi\) | |||||||
\(642\) | − | 7.15097i | − | 0.282226i | ||||||
\(643\) | −1.78484 | + | 1.03048i | −0.0703873 | + | 0.0406381i | −0.534781 | − | 0.844991i | \(-0.679606\pi\) |
0.464393 | + | 0.885629i | \(0.346272\pi\) | |||||||
\(644\) | 15.9317 | − | 9.19815i | 0.627796 | − | 0.362458i | ||||
\(645\) | − | 9.54674i | − | 0.375902i | ||||||
\(646\) | 8.14850 | + | 14.1136i | 0.320598 | + | 0.555293i | ||||
\(647\) | −7.76353 | + | 13.4468i | −0.305216 | + | 0.528649i | −0.977309 | − | 0.211817i | \(-0.932062\pi\) |
0.672093 | + | 0.740466i | \(0.265395\pi\) | |||||||
\(648\) | −2.66422 | − | 1.53819i | −0.104661 | − | 0.0604258i | ||||
\(649\) | −14.8222 | −0.581821 | ||||||||
\(650\) | −3.12832 | − | 2.58784i | −0.122703 | − | 0.101504i | ||||
\(651\) | −9.01084 | −0.353163 | ||||||||
\(652\) | 7.81195 | + | 4.51023i | 0.305940 | + | 0.176634i | ||||
\(653\) | −20.4368 | + | 35.3976i | −0.799754 | + | 1.38521i | 0.120022 | + | 0.992771i | \(0.461703\pi\) |
−0.919776 | + | 0.392444i | \(0.871630\pi\) | |||||||
\(654\) | −6.64336 | − | 11.5066i | −0.259776 | − | 0.449945i | ||||
\(655\) | 10.5831i | 0.413515i | ||||||||
\(656\) | 5.75419 | − | 3.32218i | 0.224663 | − | 0.129710i | ||||
\(657\) | −9.62167 | + | 5.55507i | −0.375377 | + | 0.216724i | ||||
\(658\) | 5.78517i | 0.225530i | ||||||||
\(659\) | −0.917364 | − | 1.58892i | −0.0357354 | − | 0.0618956i | 0.847605 | − | 0.530628i | \(-0.178044\pi\) |
−0.883340 | + | 0.468733i | \(0.844711\pi\) | |||||||
\(660\) | 1.12603 | − | 1.95035i | 0.0438308 | − | 0.0759171i | ||||
\(661\) | 15.0413 | + | 8.68408i | 0.585038 | + | 0.337772i | 0.763133 | − | 0.646242i | \(-0.223660\pi\) |
−0.178095 | + | 0.984013i | \(0.556994\pi\) | |||||||
\(662\) | 28.8519 | 1.12136 | ||||||||
\(663\) | 6.93362 | + | 1.17256i | 0.269280 | + | 0.0455384i | ||||
\(664\) | −21.4641 | −0.832969 | ||||||||
\(665\) | −18.3675 | − | 10.6045i | −0.712262 | − | 0.411225i | ||||
\(666\) | −4.64605 | + | 8.04719i | −0.180031 | + | 0.311822i | ||||
\(667\) | 29.3776 | + | 50.8836i | 1.13751 | + | 1.97022i | ||||
\(668\) | 16.0624i | 0.621472i | ||||||||
\(669\) | 11.0517 | − | 6.38068i | 0.427282 | − | 0.246691i | ||||
\(670\) | 5.73260 | − | 3.30972i | 0.221470 | − | 0.127866i | ||||
\(671\) | − | 19.2826i | − | 0.744396i | ||||||
\(672\) | −5.57425 | − | 9.65488i | −0.215031 | − | 0.372445i | ||||
\(673\) | −4.75396 | + | 8.23410i | −0.183252 | + | 0.317401i | −0.942986 | − | 0.332832i | \(-0.891996\pi\) |
0.759734 | + | 0.650234i | \(0.225329\pi\) | |||||||
\(674\) | 19.6761 | + | 11.3600i | 0.757894 | + | 0.437570i | ||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | −1.78371 | − | 9.34801i | −0.0686041 | − | 0.359539i | ||||
\(677\) | 20.7375 | 0.797008 | 0.398504 | − | 0.917167i | \(-0.369530\pi\) | ||||
0.398504 | + | 0.917167i | \(0.369530\pi\) | |||||||
\(678\) | 3.37810 | + | 1.95035i | 0.129735 | + | 0.0749026i | ||||
\(679\) | 6.85596 | − | 11.8749i | 0.263107 | − | 0.455715i | ||||
\(680\) | −3.00000 | − | 5.19615i | −0.115045 | − | 0.199263i | ||||
\(681\) | 17.1114i | 0.655709i | ||||||||
\(682\) | 9.45827 | − | 5.46073i | 0.362176 | − | 0.209102i | ||||
\(683\) | 14.4521 | − | 8.34393i | 0.552995 | − | 0.319272i | −0.197334 | − | 0.980336i | \(-0.563228\pi\) |
0.750329 | + | 0.661065i | \(0.229895\pi\) | |||||||
\(684\) | 5.43233i | 0.207710i | ||||||||
\(685\) | −4.35327 | − | 7.54009i | −0.166330 | − | 0.288092i | ||||
\(686\) | 9.38352 | − | 16.2527i | 0.358264 | − | 0.620532i | ||||
\(687\) | 5.54250 | + | 3.19996i | 0.211460 | + | 0.122086i | ||||
\(688\) | 19.0935 | 0.727932 | ||||||||
\(689\) | −37.8860 | − | 6.40698i | −1.44334 | − | 0.244086i | ||||
\(690\) | −9.90069 | −0.376913 | ||||||||
\(691\) | 19.6119 | + | 11.3229i | 0.746073 | + | 0.430745i | 0.824273 | − | 0.566192i | \(-0.191584\pi\) |
−0.0782005 | + | 0.996938i | \(0.524917\pi\) | |||||||
\(692\) | 5.50889 | − | 9.54167i | 0.209416 | − | 0.362720i | ||||
\(693\) | 4.39627 | + | 7.61457i | 0.167001 | + | 0.289253i | ||||
\(694\) | 27.2429i | 1.03413i | ||||||||
\(695\) | 10.0952 | − | 5.82844i | 0.382931 | − | 0.221085i | ||||
\(696\) | 17.8034 | − | 10.2788i | 0.674836 | − | 0.389616i | ||||
\(697\) | − | 6.47941i | − | 0.245425i | ||||||
\(698\) | −14.4561 | − | 25.0387i | −0.547171 | − | 0.947728i | ||||
\(699\) | −0.335778 | + | 0.581585i | −0.0127003 | + | 0.0219976i | ||||
\(700\) | 1.81195 | + | 1.04613i | 0.0684854 | + | 0.0395400i | ||||
\(701\) | −9.33818 | −0.352698 | −0.176349 | − | 0.984328i | \(-0.556429\pi\) | ||||
−0.176349 | + | 0.984328i | \(0.556429\pi\) | |||||||
\(702\) | −3.12832 | − | 2.58784i | −0.118071 | − | 0.0976719i | ||||
\(703\) | 61.2361 | 2.30956 | ||||||||
\(704\) | 22.3590 | + | 12.9090i | 0.842685 | + | 0.486524i | ||||
\(705\) | −0.898795 | + | 1.55676i | −0.0338506 | + | 0.0586309i | ||||
\(706\) | 4.41691 | + | 7.65032i | 0.166233 | + | 0.287923i | ||||
\(707\) | − | 7.98133i | − | 0.300169i | ||||||
\(708\) | −3.05452 | + | 1.76353i | −0.114796 | + | 0.0662775i | ||||
\(709\) | 24.6318 | − | 14.2212i | 0.925068 | − | 0.534088i | 0.0398194 | − | 0.999207i | \(-0.487322\pi\) |
0.885248 | + | 0.465119i | \(0.153988\pi\) | |||||||
\(710\) | 11.5973i | 0.435239i | ||||||||
\(711\) | 5.54842 | + | 9.61015i | 0.208082 | + | 0.360409i | ||||
\(712\) | −0.143130 | + | 0.247908i | −0.00536402 | + | 0.00929075i | ||||
\(713\) | 24.0069 | + | 13.8604i | 0.899064 | + | 0.519075i | ||||
\(714\) | 6.27679 | 0.234903 | ||||||||
\(715\) | 7.07012 | − | 8.54674i | 0.264407 | − | 0.319630i | ||||
\(716\) | 0.351951 | 0.0131530 | ||||||||
\(717\) | 6.17461 | + | 3.56491i | 0.230595 | + | 0.133134i | ||||
\(718\) | 11.0996 | − | 19.2250i | 0.414233 | − | 0.717472i | ||||
\(719\) | 15.9484 | + | 27.6235i | 0.594776 | + | 1.03018i | 0.993578 | + | 0.113145i | \(0.0360926\pi\) |
−0.398802 | + | 0.917037i | \(0.630574\pi\) | |||||||
\(720\) | 2.00000i | 0.0745356i | ||||||||
\(721\) | −20.6775 | + | 11.9381i | −0.770070 | + | 0.444600i | ||||
\(722\) | −35.1714 | + | 20.3062i | −1.30894 | + | 0.755720i | ||||
\(723\) | 26.9383i | 1.00184i | ||||||||
\(724\) | 0.680394 | + | 1.17848i | 0.0252867 | + | 0.0437978i | ||||
\(725\) | −3.34120 | + | 5.78712i | −0.124089 | + | 0.214928i | ||||
\(726\) | 1.49777 | + | 0.864736i | 0.0555873 | + | 0.0320934i | ||||
\(727\) | 4.68029 | 0.173583 | 0.0867913 | − | 0.996227i | \(-0.472339\pi\) | ||||
0.0867913 | + | 0.996227i | \(0.472339\pi\) | |||||||
\(728\) | −11.0512 | − | 29.7134i | −0.409583 | − | 1.10125i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 10.8343 | + | 6.25519i | 0.400996 | + | 0.231515i | ||||
\(731\) | 9.30972 | − | 16.1249i | 0.344332 | − | 0.596401i | ||||
\(732\) | −2.29423 | − | 3.97372i | −0.0847971 | − | 0.146873i | ||||
\(733\) | 14.1306i | 0.521926i | 0.965349 | + | 0.260963i | \(0.0840401\pi\) | ||||
−0.965349 | + | 0.260963i | \(0.915960\pi\) | |||||||
\(734\) | −10.8986 | + | 6.29233i | −0.402276 | + | 0.232254i | ||||
\(735\) | −1.01207 | + | 0.584320i | −0.0373308 | + | 0.0215530i | ||||
\(736\) | 34.2970i | 1.26420i | ||||||||
\(737\) | 9.04232 | + | 15.6618i | 0.333078 | + | 0.576908i | ||||
\(738\) | −1.87044 | + | 3.23970i | −0.0688520 | + | 0.119255i | ||||
\(739\) | −10.2955 | − | 5.94409i | −0.378725 | − | 0.218657i | 0.298539 | − | 0.954398i | \(-0.403501\pi\) |
−0.677263 | + | 0.735741i | \(0.736834\pi\) | |||||||
\(740\) | −6.04093 | −0.222069 | ||||||||
\(741\) | −4.46137 | + | 26.3812i | −0.163892 | + | 0.969136i | ||||
\(742\) | −34.2970 | −1.25908 | ||||||||
\(743\) | 20.7932 | + | 12.0050i | 0.762830 | + | 0.440420i | 0.830311 | − | 0.557301i | \(-0.188163\pi\) |
−0.0674812 | + | 0.997721i | \(0.521496\pi\) | |||||||
\(744\) | 4.84953 | − | 8.39964i | 0.177793 | − | 0.307946i | ||||
\(745\) | −3.41216 | − | 5.91003i | −0.125012 | − | 0.216527i | ||||
\(746\) | − | 9.85473i | − | 0.360807i | ||||||
\(747\) | 6.04232 | − | 3.48853i | 0.221077 | − | 0.127639i | ||||
\(748\) | 3.80385 | − | 2.19615i | 0.139082 | − | 0.0802993i | ||||
\(749\) | 18.1505i | 0.663205i | ||||||||
\(750\) | −0.563016 | − | 0.975173i | −0.0205584 | − | 0.0356083i | ||||
\(751\) | 7.93491 | − | 13.7437i | 0.289549 | − | 0.501513i | −0.684153 | − | 0.729338i | \(-0.739828\pi\) |
0.973702 | + | 0.227825i | \(0.0731614\pi\) | |||||||
\(752\) | −3.11352 | − | 1.79759i | −0.113538 | − | 0.0655513i | ||||
\(753\) | −11.6480 | −0.424478 | ||||||||
\(754\) | 25.4285 | − | 9.45750i | 0.926052 | − | 0.344422i | ||||
\(755\) | 12.6810 | 0.461510 | ||||||||
\(756\) | 1.81195 | + | 1.04613i | 0.0659001 | + | 0.0380474i | ||||
\(757\) | −18.0819 | + | 31.3188i | −0.657198 | + | 1.13830i | 0.324140 | + | 0.946009i | \(0.394925\pi\) |
−0.981338 | + | 0.192291i | \(0.938408\pi\) | |||||||
\(758\) | 10.5676 | + | 18.3036i | 0.383832 | + | 0.664817i | ||||
\(759\) | − | 27.0492i | − | 0.981823i | ||||||
\(760\) | 19.7704 | − | 11.4144i | 0.717148 | − | 0.414046i | ||||
\(761\) | −12.6597 | + | 7.30905i | −0.458912 | + | 0.264953i | −0.711587 | − | 0.702598i | \(-0.752023\pi\) |
0.252675 | + | 0.967551i | \(0.418690\pi\) | |||||||
\(762\) | − | 16.8590i | − | 0.610737i | ||||||
\(763\) | 16.8621 | + | 29.2060i | 0.610449 | + | 1.05733i | ||||
\(764\) | −3.19128 | + | 5.52746i | −0.115457 | + | 0.199977i | ||||
\(765\) | 1.68905 | + | 0.975173i | 0.0610677 | + | 0.0352574i | ||||
\(766\) | −6.84029 | −0.247150 | ||||||||
\(767\) | −16.2821 | + | 6.05571i | −0.587912 | + | 0.218659i | ||||
\(768\) | 14.9282 | 0.538675 | ||||||||
\(769\) | −15.8994 | − | 9.17950i | −0.573346 | − | 0.331021i | 0.185139 | − | 0.982712i | \(-0.440727\pi\) |
−0.758484 | + | 0.651691i | \(0.774060\pi\) | |||||||
\(770\) | 4.95035 | − | 8.57425i | 0.178398 | − | 0.308995i | ||||
\(771\) | 3.63939 | + | 6.30362i | 0.131070 | + | 0.227019i | ||||
\(772\) | − | 4.72412i | − | 0.170025i | ||||||
\(773\) | −7.38753 | + | 4.26519i | −0.265711 | + | 0.153408i | −0.626937 | − | 0.779070i | \(-0.715692\pi\) |
0.361226 | + | 0.932478i | \(0.382358\pi\) | |||||||
\(774\) | −9.30972 | + | 5.37497i | −0.334631 | + | 0.193199i | ||||
\(775\) | 3.15276i | 0.113250i | ||||||||
\(776\) | 7.37960 | + | 12.7818i | 0.264912 | + | 0.458841i | ||||
\(777\) | 11.7925 | − | 20.4253i | 0.423055 | − | 0.732753i | ||||
\(778\) | −9.42575 | − | 5.44196i | −0.337930 | − | 0.195104i | ||||
\(779\) | 24.6530 | 0.883284 | ||||||||
\(780\) | 0.440113 | − | 2.60249i | 0.0157586 | − | 0.0931843i | ||||
\(781\) | −31.6844 | −1.13376 | ||||||||
\(782\) | −16.7227 | − | 9.65488i | −0.598004 | − | 0.345258i | ||||
\(783\) | −3.34120 | + | 5.78712i | −0.119405 | + | 0.206815i | ||||
\(784\) | −1.16864 | − | 2.02414i | −0.0417371 | − | 0.0722909i | ||||
\(785\) | − | 7.98333i | − | 0.284937i | ||||||
\(786\) | 10.3203 | − | 5.95845i | 0.368114 | − | 0.212531i | ||||
\(787\) | −2.96679 | + | 1.71288i | −0.105755 | + | 0.0610574i | −0.551944 | − | 0.833881i | \(-0.686114\pi\) |
0.446190 | + | 0.894938i | \(0.352781\pi\) | |||||||
\(788\) | − | 8.48668i | − | 0.302326i | ||||||
\(789\) | 11.9639 | + | 20.7220i | 0.425925 | + | 0.737724i | ||||
\(790\) | 6.24770 | − | 10.8213i | 0.222283 | − | 0.385006i | ||||
\(791\) | −8.57425 | − | 4.95035i | −0.304865 | − | 0.176014i | ||||
\(792\) | −9.46410 | −0.336292 | ||||||||
\(793\) | −7.87805 | − | 21.1818i | −0.279758 | − | 0.752189i | ||||
\(794\) | −27.3982 | −0.972327 | ||||||||
\(795\) | −9.22913 | − | 5.32844i | −0.327324 | − | 0.188980i | ||||
\(796\) | 0.293326 | − | 0.508056i | 0.0103967 | − | 0.0180076i | ||||
\(797\) | 14.0505 | + | 24.3361i | 0.497693 | + | 0.862030i | 0.999996 | − | 0.00266150i | \(-0.000847184\pi\) |
−0.502303 | + | 0.864692i | \(0.667514\pi\) | |||||||
\(798\) | 23.8820i | 0.845414i | ||||||||
\(799\) | −3.03622 | + | 1.75296i | −0.107414 | + | 0.0620153i | ||||
\(800\) | −3.37810 | + | 1.95035i | −0.119434 | + | 0.0689551i | ||||
\(801\) | − | 0.0930509i | − | 0.00328779i | ||||||
\(802\) | 5.00884 | + | 8.67556i | 0.176868 | + | 0.306345i | ||||
\(803\) | −17.0895 | + | 29.5999i | −0.603076 | + | 1.04456i | ||||
\(804\) | 3.72685 | + | 2.15170i | 0.131436 | + | 0.0758845i | ||||
\(805\) | 25.1298 | 0.885710 | ||||||||
\(806\) | 8.15884 | − | 9.86284i | 0.287383 | − | 0.347404i | ||||
\(807\) | −4.38147 | −0.154235 | ||||||||
\(808\) | 7.43996 | + | 4.29546i | 0.261737 | + | 0.151114i | ||||
\(809\) | −18.0846 | + | 31.3235i | −0.635822 | + | 1.10128i | 0.350518 | + | 0.936556i | \(0.386005\pi\) |
−0.986340 | + | 0.164720i | \(0.947328\pi\) | |||||||
\(810\) | −0.563016 | − | 0.975173i | −0.0197824 | − | 0.0342641i | ||||
\(811\) | − | 13.9825i | − | 0.490993i | −0.969397 | − | 0.245497i | \(-0.921049\pi\) | ||
0.969397 | − | 0.245497i | \(-0.0789510\pi\) | |||||||
\(812\) | −12.1082 | + | 6.99066i | −0.424914 | + | 0.245324i | ||||
\(813\) | −2.15488 | + | 1.24412i | −0.0755751 | + | 0.0436333i | ||||
\(814\) | 28.5860i | 1.00194i | ||||||||
\(815\) | 6.16109 | + | 10.6713i | 0.215814 | + | 0.373800i | ||||
\(816\) | −1.95035 | + | 3.37810i | −0.0682757 | + | 0.118257i | ||||
\(817\) | 61.3523 | + | 35.4218i | 2.14645 | + | 1.23925i | ||||
\(818\) | −31.8540 | −1.11375 | ||||||||
\(819\) | 7.94028 | + | 6.56844i | 0.277456 | + | 0.229520i | ||||
\(820\) | −2.43201 | −0.0849294 | ||||||||
\(821\) | 3.67156 | + | 2.11977i | 0.128138 | + | 0.0739806i | 0.562699 | − | 0.826662i | \(-0.309763\pi\) |
−0.434561 | + | 0.900643i | \(0.643096\pi\) | |||||||
\(822\) | −4.90192 | + | 8.49038i | −0.170974 | + | 0.296136i | ||||
\(823\) | 16.8201 | + | 29.1332i | 0.586310 | + | 1.01552i | 0.994711 | + | 0.102716i | \(0.0327534\pi\) |
−0.408400 | + | 0.912803i | \(0.633913\pi\) | |||||||
\(824\) | − | 25.6999i | − | 0.895299i | ||||||
\(825\) | 2.66422 | − | 1.53819i | 0.0927563 | − | 0.0535529i | ||||
\(826\) | −13.4285 | + | 7.75296i | −0.467238 | + | 0.269760i | ||||
\(827\) | − | 6.94609i | − | 0.241539i | −0.992681 | − | 0.120770i | \(-0.961464\pi\) | ||
0.992681 | − | 0.120770i | \(-0.0385362\pi\) | |||||||
\(828\) | −3.21829 | − | 5.57425i | −0.111843 | − | 0.193719i | ||||
\(829\) | 6.68271 | − | 11.5748i | 0.232100 | − | 0.402009i | −0.726326 | − | 0.687351i | \(-0.758774\pi\) |
0.958426 | + | 0.285341i | \(0.0921069\pi\) | |||||||
\(830\) | −6.80385 | − | 3.92820i | −0.236165 | − | 0.136350i | ||||
\(831\) | −21.7061 | −0.752975 | ||||||||
\(832\) | 29.8353 | + | 5.04550i | 1.03435 | + | 0.174921i | ||||
\(833\) | −2.27925 | −0.0789714 | ||||||||
\(834\) | −11.3675 | − | 6.56302i | −0.393624 | − | 0.227259i | ||||
\(835\) | −10.9708 | + | 19.0020i | −0.379661 | + | 0.657591i | ||||
\(836\) | 8.35596 | + | 14.4729i | 0.288997 | + | 0.500557i | ||||
\(837\) | 3.15276i | 0.108975i | ||||||||
\(838\) | 28.1774 | − | 16.2682i | 0.973371 | − | 0.561976i | ||||
\(839\) | 17.3830 | − | 10.0361i | 0.600127 | − | 0.346483i | −0.168965 | − | 0.985622i | \(-0.554042\pi\) |
0.769091 | + | 0.639139i | \(0.220709\pi\) | |||||||
\(840\) | − | 8.79254i | − | 0.303372i | ||||||
\(841\) | −7.82721 | − | 13.5571i | −0.269904 | − | 0.467487i | ||||
\(842\) | 6.76375 | − | 11.7152i | 0.233094 | − | 0.403731i | ||||
\(843\) | −25.7443 | − | 14.8635i | −0.886682 | − | 0.511926i | ||||
\(844\) | −6.07023 | −0.208946 | ||||||||
\(845\) | 4.27466 | − | 12.2771i | 0.147053 | − | 0.422345i | ||||
\(846\) | 2.02414 | 0.0695915 | ||||||||
\(847\) | −3.80161 | − | 2.19486i | −0.130625 | − | 0.0754164i | ||||
\(848\) | 10.6569 | − | 18.4583i | 0.365959 | − | 0.633860i | ||||
\(849\) | −13.9998 | − | 24.2483i | −0.480471 | − | 0.832200i | ||||
\(850\) | − | 2.19615i | − | 0.0753274i | ||||||
\(851\) | −62.8359 | + | 36.2783i | −2.15399 | + | 1.24360i | ||||
\(852\) | −6.52947 | + | 3.76979i | −0.223696 | + | 0.129151i | ||||
\(853\) | − | 54.6353i | − | 1.87068i | −0.353755 | − | 0.935338i | \(-0.615095\pi\) | ||
0.353755 | − | 0.935338i | \(-0.384905\pi\) | |||||||
\(854\) | −10.0861 | − | 17.4696i | −0.345138 | − | 0.597796i | ||||
\(855\) | −3.71035 | + | 6.42652i | −0.126891 | + | 0.219782i | ||||
\(856\) | −16.9194 | − | 9.76840i | −0.578292 | − | 0.333877i | ||||
\(857\) | 3.66436 | 0.125172 | 0.0625860 | − | 0.998040i | \(-0.480065\pi\) | ||||
0.0625860 | + | 0.998040i | \(0.480065\pi\) | |||||||
\(858\) | −12.3151 | − | 2.08264i | −0.420432 | − | 0.0711000i | ||||
\(859\) | 28.1460 | 0.960330 | 0.480165 | − | 0.877178i | \(-0.340577\pi\) | ||||
0.480165 | + | 0.877178i | \(0.340577\pi\) | |||||||
\(860\) | −6.05239 | − | 3.49435i | −0.206385 | − | 0.119156i | ||||
\(861\) | 4.74754 | − | 8.22298i | 0.161796 | − | 0.280238i | ||||
\(862\) | −12.9623 | − | 22.4513i | −0.441497 | − | 0.764696i | ||||
\(863\) | − | 50.4623i | − | 1.71776i | −0.512180 | − | 0.858878i | \(-0.671162\pi\) | ||
0.512180 | − | 0.858878i | \(-0.328838\pi\) | |||||||
\(864\) | −3.37810 | + | 1.95035i | −0.114925 | + | 0.0663521i | ||||
\(865\) | 13.0342 | − | 7.52528i | 0.443175 | − | 0.255867i | ||||
\(866\) | 30.2671i | 1.02852i | ||||||||
\(867\) | −6.59808 | − | 11.4282i | −0.224082 | − | 0.388122i | ||||
\(868\) | −3.29820 | + | 5.71264i | −0.111948 | + | 0.193900i | ||||
\(869\) | 29.5644 | + | 17.0690i | 1.00291 | + | 0.579028i | ||||
\(870\) | 7.52460 | 0.255108 | ||||||||
\(871\) | 16.3317 | + | 13.5101i | 0.553378 | + | 0.457771i | ||||
\(872\) | −36.3000 | −1.22927 | ||||||||
\(873\) | −4.15483 | − | 2.39879i | −0.140620 | − | 0.0811869i | ||||
\(874\) | 36.7351 | − | 63.6270i | 1.24258 | − | 2.15221i | ||||
\(875\) | 1.42904 | + | 2.47517i | 0.0483104 | + | 0.0836761i | ||||
\(876\) | 8.13319i | 0.274795i | ||||||||
\(877\) | −20.0993 | + | 11.6043i | −0.678705 | + | 0.391851i | −0.799367 | − | 0.600843i | \(-0.794832\pi\) |
0.120662 | + | 0.992694i | \(0.461498\pi\) | |||||||
\(878\) | 30.8685 | − | 17.8220i | 1.04176 | − | 0.601462i | ||||
\(879\) | 16.9586i | 0.572000i | ||||||||
\(880\) | 3.07638 | + | 5.32844i | 0.103705 | + | 0.179622i | ||||
\(881\) | −8.55758 | + | 14.8222i | −0.288312 | + | 0.499371i | −0.973407 | − | 0.229083i | \(-0.926427\pi\) |
0.685095 | + | 0.728454i | \(0.259761\pi\) | |||||||
\(882\) | 1.13963 | + | 0.657963i | 0.0383732 | + | 0.0221548i | ||||
\(883\) | 21.3589 | 0.718783 | 0.359391 | − | 0.933187i | \(-0.382984\pi\) | ||||
0.359391 | + | 0.933187i | \(0.382984\pi\) | |||||||
\(884\) | 3.28125 | − | 3.96655i | 0.110361 | − | 0.133410i | ||||
\(885\) | −4.81805 | −0.161957 | ||||||||
\(886\) | 9.65355 | + | 5.57348i | 0.324317 | + | 0.187245i | ||||
\(887\) | −17.1600 | + | 29.7220i | −0.576177 | + | 0.997968i | 0.419735 | + | 0.907646i | \(0.362123\pi\) |
−0.995913 | + | 0.0903216i | \(0.971210\pi\) | |||||||
\(888\) | 12.6932 | + | 21.9853i | 0.425957 | + | 0.737779i | ||||
\(889\) | 42.7913i | 1.43517i | ||||||||
\(890\) | −0.0907407 | + | 0.0523892i | −0.00304164 | + | 0.00175609i | ||||
\(891\) | 2.66422 | − | 1.53819i | 0.0892548 | − | 0.0515313i | ||||
\(892\) | − | 9.34196i | − | 0.312792i | ||||||
\(893\) | −6.66969 | − | 11.5522i | −0.223193 | − | 0.386581i | ||||
\(894\) | −3.84220 | + | 6.65488i | −0.128502 | + | 0.222573i | ||||
\(895\) | 0.416363 | + | 0.240387i | 0.0139175 | + | 0.00803526i | ||||
\(896\) | 4.71191 | 0.157414 | ||||||||
\(897\) | −11.0512 | − | 29.7134i | −0.368987 | − | 0.992102i | ||||
\(898\) | 16.8998 | 0.563953 | ||||||||
\(899\) | −18.2454 | − | 10.5340i | −0.608518 | − | 0.351328i | ||||
\(900\) | 0.366025 | − | 0.633975i | 0.0122008 | − | 0.0211325i | ||||
\(901\) | −10.3923 | − | 18.0000i | −0.346218 | − | 0.599667i | ||||
\(902\) | 11.5084i | 0.383187i | ||||||||
\(903\) | 23.6298 | − | 13.6427i | 0.786351 | − | 0.454000i | ||||
\(904\) | 9.22913 | − | 5.32844i | 0.306956 | − | 0.177221i | ||||
\(905\) | 1.85887i | 0.0617910i | ||||||||
\(906\) | −7.13963 | − | 12.3662i | −0.237198 | − | 0.410839i | ||||
\(907\) | 29.4542 | − | 51.0161i | 0.978010 | − | 1.69396i | 0.308387 | − | 0.951261i | \(-0.400211\pi\) |
0.669623 | − | 0.742701i | \(-0.266456\pi\) | |||||||
\(908\) | 10.8482 | + | 6.26319i | 0.360009 | + | 0.207851i | ||||
\(909\) | −2.79254 | −0.0926229 | ||||||||
\(910\) | 1.93486 | − | 11.4413i | 0.0641398 | − | 0.379275i | ||||
\(911\) | −55.5007 | −1.83882 | −0.919410 | − | 0.393299i | \(-0.871334\pi\) | ||||
−0.919410 | + | 0.393299i | \(0.871334\pi\) | |||||||
\(912\) | −12.8530 | − | 7.42071i | −0.425607 | − | 0.245724i | ||||
\(913\) | 10.7321 | − | 18.5885i | 0.355179 | − | 0.615188i | ||||
\(914\) | 7.33633 | + | 12.7069i | 0.242664 | + | 0.420307i | ||||
\(915\) | − | 6.26795i | − | 0.207212i | ||||||
\(916\) | 4.05739 | − | 2.34254i | 0.134060 | − | 0.0773996i | ||||
\(917\) | −26.1950 | + | 15.1237i | −0.865034 | + | 0.499428i | ||||
\(918\) | − | 2.19615i | − | 0.0724838i | ||||||
\(919\) | −27.3656 | − | 47.3985i | −0.902707 | − | 1.56353i | −0.823967 | − | 0.566638i | \(-0.808244\pi\) |
−0.0787401 | − | 0.996895i | \(-0.525090\pi\) | |||||||
\(920\) | −13.5246 | + | 23.4253i | −0.445893 | + | 0.772309i | ||||
\(921\) | −13.5163 | − | 7.80362i | −0.445376 | − | 0.257138i | ||||
\(922\) | −32.3358 | −1.06492 | ||||||||
\(923\) | −34.8052 | + | 12.9449i | −1.14563 | + | 0.426087i | ||||
\(924\) | 6.43659 | 0.211748 | ||||||||
\(925\) | −7.14650 | − | 4.12603i | −0.234975 | − | 0.135663i | ||||
\(926\) | −0.259162 | + | 0.448881i | −0.00851658 | + | 0.0147511i | ||||
\(927\) | 4.17698 | + | 7.23474i | 0.137190 | + | 0.237620i | ||||
\(928\) | − | 26.0660i | − | 0.855657i | ||||||
\(929\) | 14.8799 | − | 8.59092i | 0.488194 | − | 0.281859i | −0.235631 | − | 0.971843i | \(-0.575716\pi\) |
0.723825 | + | 0.689984i | \(0.242382\pi\) | |||||||
\(930\) | 3.07448 | − | 1.77505i | 0.100816 | − | 0.0582063i | ||||
\(931\) | − | 8.67213i | − | 0.284218i | ||||||
\(932\) | 0.245807 | + | 0.425750i | 0.00805167 | + | 0.0139459i | ||||
\(933\) | 12.4970 | − | 21.6455i | 0.409135 | − | 0.708642i | ||||
\(934\) | −33.2177 | − | 19.1782i | −1.08692 | − | 0.627531i | ||||
\(935\) | 6.00000 | 0.196221 | ||||||||
\(936\) | −10.3963 | + | 3.86663i | −0.339813 | + | 0.126385i | ||||
\(937\) | 39.6401 | 1.29499 | 0.647493 | − | 0.762071i | \(-0.275817\pi\) | ||||
0.647493 | + | 0.762071i | \(0.275817\pi\) | |||||||
\(938\) | 16.3842 | + | 9.45945i | 0.534965 | + | 0.308862i | ||||
\(939\) | 0.580584 | − | 1.00560i | 0.0189467 | − | 0.0328166i | ||||
\(940\) | 0.657963 | + | 1.13963i | 0.0214604 | + | 0.0371705i | ||||
\(941\) | 33.3796i | 1.08815i | 0.839038 | + | 0.544073i | \(0.183118\pi\) | ||||
−0.839038 | + | 0.544073i | \(0.816882\pi\) | |||||||
\(942\) | −7.78512 | + | 4.49474i | −0.253653 | + | 0.146447i | ||||
\(943\) | −25.2970 | + | 14.6052i | −0.823784 | + | 0.475612i | ||||
\(944\) | − | 9.63611i | − | 0.313629i | ||||||
\(945\) | 1.42904 | + | 2.47517i | 0.0464867 | + | 0.0805174i | ||||
\(946\) | −16.5354 | + | 28.6402i | −0.537613 | + | 0.931174i | ||||
\(947\) | −17.8054 | − | 10.2800i | −0.578599 | − | 0.334054i | 0.181978 | − | 0.983303i | \(-0.441750\pi\) |
−0.760576 | + | 0.649249i | \(0.775084\pi\) | |||||||
\(948\) | 8.12345 | 0.263837 | ||||||||
\(949\) | −6.67948 | + | 39.4974i | −0.216825 | + | 1.28214i | ||||
\(950\) | 8.35596 | 0.271103 | ||||||||
\(951\) | 7.47007 | + | 4.31285i | 0.242234 | + | 0.139854i | ||||
\(952\) | 8.57425 | − | 14.8510i | 0.277893 | − | 0.481325i | ||||
\(953\) | −27.4376 | − | 47.5234i | −0.888792 | − | 1.53943i | −0.841305 | − | 0.540561i | \(-0.818212\pi\) |
−0.0474871 | − | 0.998872i | \(-0.515121\pi\) | |||||||
\(954\) | 12.0000i | 0.388514i | ||||||||
\(955\) | −7.55066 | + | 4.35937i | −0.244333 | + | 0.141066i | ||||
\(956\) | 4.52013 | − | 2.60970i | 0.146191 | − | 0.0844036i | ||||
\(957\) | 20.5576i | 0.664532i | ||||||||
\(958\) | −17.4147 | − | 30.1632i | −0.562644 | − | 0.974528i | ||||
\(959\) | 12.4420 | − | 21.5502i | 0.401773 | − | 0.695892i | ||||
\(960\) | 7.26795 | + | 4.19615i | 0.234572 | + | 0.135430i | ||||
\(961\) | 21.0601 | 0.679359 | ||||||||
\(962\) | 11.6790 | + | 31.4016i | 0.376547 | + | 1.01243i | ||||
\(963\) | 6.35059 | 0.204645 | ||||||||
\(964\) | 17.0782 | + | 9.86009i | 0.550051 | + | 0.317572i | ||||
\(965\) | 3.22663 | − | 5.58869i | 0.103869 | − | 0.179906i | ||||
\(966\) | −14.1485 | − | 24.5059i | −0.455221 | − | 0.788465i | ||||
\(967\) | 10.9215i | 0.351211i | 0.984461 | + | 0.175605i | \(0.0561883\pi\) | ||||
−0.984461 | + | 0.175605i | \(0.943812\pi\) | |||||||
\(968\) | 4.09197 | − | 2.36250i | 0.131521 | − | 0.0759337i | ||||
\(969\) | −12.5339 | + | 7.23647i | −0.402648 | + | 0.232469i | ||||
\(970\) | 5.40224i | 0.173456i | ||||||||
\(971\) | −15.7356 | − | 27.2548i | −0.504978 | − | 0.874648i | −0.999983 | − | 0.00575765i | \(-0.998167\pi\) |
0.495005 | − | 0.868890i | \(-0.335166\pi\) | |||||||
\(972\) | 0.366025 | − | 0.633975i | 0.0117403 | − | 0.0203347i | ||||
\(973\) | 28.8528 | + | 16.6582i | 0.924979 | + | 0.534037i | ||||
\(974\) | −18.6223 | −0.596698 | ||||||||
\(975\) | 2.29820 | − | 2.77818i | 0.0736012 | − | 0.0889730i | ||||
\(976\) | 12.5359 | 0.401264 | ||||||||
\(977\) | −27.3260 | − | 15.7767i | −0.874235 | − | 0.504740i | −0.00548205 | − | 0.999985i | \(-0.501745\pi\) |
−0.868753 | + | 0.495245i | \(0.835078\pi\) | |||||||
\(978\) | 6.93759 | − | 12.0163i | 0.221840 | − | 0.384238i | ||||
\(979\) | −0.143130 | − | 0.247908i | −0.00457445 | − | 0.00792318i | ||||
\(980\) | 0.855504i | 0.0273281i | ||||||||
\(981\) | 10.2187 | − | 5.89980i | 0.326259 | − | 0.188366i | ||||
\(982\) | −18.2186 | + | 10.5185i | −0.581378 | + | 0.335659i | ||||
\(983\) | − | 43.6214i | − | 1.39131i | −0.718377 | − | 0.695654i | \(-0.755115\pi\) | ||
0.718377 | − | 0.695654i | \(-0.244885\pi\) | |||||||
\(984\) | 5.11015 | + | 8.85104i | 0.162906 | + | 0.282161i | ||||
\(985\) | 5.79651 | − | 10.0399i | 0.184692 | − | 0.319896i | ||||
\(986\) | 12.7094 | + | 7.33778i | 0.404750 | + | 0.233683i | ||||
\(987\) | −5.13766 | −0.163534 | ||||||||
\(988\) | 15.0920 | + | 12.4846i | 0.480141 | + | 0.397187i | ||||
\(989\) | −83.9401 | −2.66914 | ||||||||
\(990\) | −3.00000 | − | 1.73205i | −0.0953463 | − | 0.0550482i | ||||
\(991\) | −8.99740 | + | 15.5840i | −0.285812 | + | 0.495041i | −0.972806 | − | 0.231623i | \(-0.925597\pi\) |
0.686994 | + | 0.726663i | \(0.258930\pi\) | |||||||
\(992\) | −6.14896 | − | 10.6503i | −0.195230 | − | 0.338148i | ||||
\(993\) | 25.6227i | 0.813110i | ||||||||
\(994\) | −28.7053 | + | 16.5730i | −0.910477 | + | 0.525664i | ||||
\(995\) | 0.694017 | − | 0.400691i | 0.0220018 | − | 0.0127028i | ||||
\(996\) | − | 5.10757i | − | 0.161840i | ||||||
\(997\) | 12.1045 | + | 20.9657i | 0.383355 | + | 0.663990i | 0.991539 | − | 0.129806i | \(-0.0414353\pi\) |
−0.608185 | + | 0.793796i | \(0.708102\pi\) | |||||||
\(998\) | 6.19128 | − | 10.7236i | 0.195982 | − | 0.339450i | ||||
\(999\) | −7.14650 | − | 4.12603i | −0.226105 | − | 0.130542i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 195.2.bb.b.121.2 | ✓ | 8 | |
3.2 | odd | 2 | 585.2.bu.d.316.3 | 8 | |||
5.2 | odd | 4 | 975.2.w.i.199.3 | 8 | |||
5.3 | odd | 4 | 975.2.w.h.199.2 | 8 | |||
5.4 | even | 2 | 975.2.bc.j.901.3 | 8 | |||
13.6 | odd | 12 | 2535.2.a.bj.1.3 | 4 | |||
13.7 | odd | 12 | 2535.2.a.bk.1.2 | 4 | |||
13.10 | even | 6 | inner | 195.2.bb.b.166.2 | yes | 8 | |
39.20 | even | 12 | 7605.2.a.ch.1.3 | 4 | |||
39.23 | odd | 6 | 585.2.bu.d.361.3 | 8 | |||
39.32 | even | 12 | 7605.2.a.ci.1.2 | 4 | |||
65.23 | odd | 12 | 975.2.w.i.49.3 | 8 | |||
65.49 | even | 6 | 975.2.bc.j.751.3 | 8 | |||
65.62 | odd | 12 | 975.2.w.h.49.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
195.2.bb.b.121.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
195.2.bb.b.166.2 | yes | 8 | 13.10 | even | 6 | inner | |
585.2.bu.d.316.3 | 8 | 3.2 | odd | 2 | |||
585.2.bu.d.361.3 | 8 | 39.23 | odd | 6 | |||
975.2.w.h.49.2 | 8 | 65.62 | odd | 12 | |||
975.2.w.h.199.2 | 8 | 5.3 | odd | 4 | |||
975.2.w.i.49.3 | 8 | 65.23 | odd | 12 | |||
975.2.w.i.199.3 | 8 | 5.2 | odd | 4 | |||
975.2.bc.j.751.3 | 8 | 65.49 | even | 6 | |||
975.2.bc.j.901.3 | 8 | 5.4 | even | 2 | |||
2535.2.a.bj.1.3 | 4 | 13.6 | odd | 12 | |||
2535.2.a.bk.1.2 | 4 | 13.7 | odd | 12 | |||
7605.2.a.ch.1.3 | 4 | 39.20 | even | 12 | |||
7605.2.a.ci.1.2 | 4 | 39.32 | even | 12 |