Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,3,Mod(2,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.2");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.n (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: | \(1.71662566547\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 2.4 | ||
Character | \(\chi\) | \(=\) | 63.2 |
Dual form | 63.3.n.b.32.4 |
$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.26920 | + | 0.732774i | −0.634601 | + | 0.366387i | −0.782532 | − | 0.622611i | \(-0.786072\pi\) |
0.147931 | + | 0.988998i | \(0.452739\pi\) | |||||||
\(3\) | 1.95453 | + | 2.27592i | 0.651511 | + | 0.758640i | ||||
\(4\) | −0.926086 | + | 1.60403i | −0.231521 | + | 0.401007i | ||||
\(5\) | − | 1.15270i | − | 0.230540i | −0.993334 | − | 0.115270i | \(-0.963227\pi\) | ||
0.993334 | − | 0.115270i | \(-0.0367734\pi\) | |||||||
\(6\) | −4.14843 | − | 1.45637i | −0.691405 | − | 0.242728i | ||||
\(7\) | −2.90907 | + | 6.36689i | −0.415582 | + | 0.909556i | ||||
\(8\) | − | 8.57663i | − | 1.07208i | ||||||
\(9\) | −1.35961 | + | 8.89671i | −0.151068 | + | 0.988523i | ||||
\(10\) | 0.844669 | + | 1.46301i | 0.0844669 | + | 0.146301i | ||||
\(11\) | 0.241349i | 0.0219408i | 0.999940 | + | 0.0109704i | \(0.00349206\pi\) | ||||
−0.999940 | + | 0.0109704i | \(0.996508\pi\) | |||||||
\(12\) | −5.46070 | + | 1.02743i | −0.455058 | + | 0.0856189i | ||||
\(13\) | 7.70332 | + | 13.3426i | 0.592563 | + | 1.02635i | 0.993886 | + | 0.110413i | \(0.0352174\pi\) |
−0.401322 | + | 0.915937i | \(0.631449\pi\) | |||||||
\(14\) | −0.973295 | − | 10.2126i | −0.0695210 | − | 0.729468i | ||||
\(15\) | 2.62345 | − | 2.25299i | 0.174897 | − | 0.150199i | ||||
\(16\) | 2.58039 | + | 4.46937i | 0.161274 | + | 0.279335i | ||||
\(17\) | 10.9102 | − | 6.29901i | 0.641777 | − | 0.370530i | −0.143522 | − | 0.989647i | \(-0.545843\pi\) |
0.785299 | + | 0.619117i | \(0.212509\pi\) | |||||||
\(18\) | −4.79366 | − | 12.2880i | −0.266314 | − | 0.682667i | ||||
\(19\) | 13.7090 | − | 23.7446i | 0.721525 | − | 1.24972i | −0.238864 | − | 0.971053i | \(-0.576775\pi\) |
0.960389 | − | 0.278664i | \(-0.0898917\pi\) | |||||||
\(20\) | 1.84896 | + | 1.06750i | 0.0924482 | + | 0.0533750i | ||||
\(21\) | −20.1764 | + | 5.82348i | −0.960781 | + | 0.277309i | ||||
\(22\) | −0.176854 | − | 0.306320i | −0.00803882 | − | 0.0139236i | ||||
\(23\) | − | 20.3881i | − | 0.886438i | −0.896413 | − | 0.443219i | \(-0.853836\pi\) | ||
0.896413 | − | 0.443219i | \(-0.146164\pi\) | |||||||
\(24\) | 19.5197 | − | 16.7633i | 0.813322 | − | 0.698471i | ||||
\(25\) | 23.6713 | 0.946851 | ||||||||
\(26\) | −19.5541 | − | 11.2896i | −0.752082 | − | 0.434215i | ||||
\(27\) | −22.9056 | + | 14.2945i | −0.848355 | + | 0.529427i | ||||
\(28\) | −7.51862 | − | 10.5625i | −0.268522 | − | 0.377233i | ||||
\(29\) | 16.9161 | + | 9.76653i | 0.583315 | + | 0.336777i | 0.762450 | − | 0.647048i | \(-0.223997\pi\) |
−0.179135 | + | 0.983825i | \(0.557330\pi\) | |||||||
\(30\) | −1.67876 | + | 4.78190i | −0.0559586 | + | 0.159397i | ||||
\(31\) | 1.36337 | − | 2.36142i | 0.0439796 | − | 0.0761749i | −0.843198 | − | 0.537604i | \(-0.819330\pi\) |
0.887177 | + | 0.461429i | \(0.152663\pi\) | |||||||
\(32\) | 23.1603 | + | 13.3716i | 0.723758 | + | 0.417862i | ||||
\(33\) | −0.549290 | + | 0.471724i | −0.0166452 | + | 0.0142947i | ||||
\(34\) | −9.23150 | + | 15.9894i | −0.271515 | + | 0.470277i | ||||
\(35\) | 7.33912 | + | 3.35329i | 0.209689 | + | 0.0958082i | ||||
\(36\) | −13.0114 | − | 10.4200i | −0.361429 | − | 0.289444i | ||||
\(37\) | −11.4455 | + | 19.8242i | −0.309338 | + | 0.535789i | −0.978218 | − | 0.207582i | \(-0.933441\pi\) |
0.668880 | + | 0.743371i | \(0.266774\pi\) | |||||||
\(38\) | 40.1823i | 1.05743i | ||||||||
\(39\) | −15.3102 | + | 43.6106i | −0.392568 | + | 1.11822i | ||||
\(40\) | −9.88629 | −0.247157 | ||||||||
\(41\) | −61.9933 | + | 35.7918i | −1.51203 | + | 0.872972i | −0.512130 | + | 0.858908i | \(0.671144\pi\) |
−0.999901 | + | 0.0140641i | \(0.995523\pi\) | |||||||
\(42\) | 21.3406 | − | 22.1759i | 0.508110 | − | 0.527998i | ||||
\(43\) | 14.8972 | − | 25.8028i | 0.346447 | − | 0.600064i | −0.639168 | − | 0.769067i | \(-0.720721\pi\) |
0.985616 | + | 0.169003i | \(0.0540546\pi\) | |||||||
\(44\) | −0.387130 | − | 0.223510i | −0.00879841 | − | 0.00507977i | ||||
\(45\) | 10.2552 | + | 1.56722i | 0.227894 | + | 0.0348272i | ||||
\(46\) | 14.9398 | + | 25.8766i | 0.324779 | + | 0.562534i | ||||
\(47\) | −25.9734 | + | 14.9958i | −0.552626 | + | 0.319059i | −0.750180 | − | 0.661233i | \(-0.770033\pi\) |
0.197555 | + | 0.980292i | \(0.436700\pi\) | |||||||
\(48\) | −5.12846 | + | 14.6083i | −0.106843 | + | 0.304339i | ||||
\(49\) | −32.0746 | − | 37.0435i | −0.654584 | − | 0.755989i | ||||
\(50\) | −30.0436 | + | 17.3457i | −0.600872 | + | 0.346914i | ||||
\(51\) | 35.6604 | + | 12.5191i | 0.699223 | + | 0.245473i | ||||
\(52\) | −28.5358 | −0.548764 | ||||||||
\(53\) | 90.5906 | − | 52.3025i | 1.70926 | − | 0.986840i | 0.773778 | − | 0.633457i | \(-0.218365\pi\) |
0.935479 | − | 0.353383i | \(-0.114969\pi\) | |||||||
\(54\) | 18.5971 | − | 34.9273i | 0.344392 | − | 0.646801i | ||||
\(55\) | 0.278203 | 0.00505824 | ||||||||
\(56\) | 54.6065 | + | 24.9500i | 0.975116 | + | 0.445536i | ||||
\(57\) | 80.8355 | − | 15.2091i | 1.41817 | − | 0.266827i | ||||
\(58\) | −28.6266 | −0.493563 | ||||||||
\(59\) | −75.0951 | − | 43.3562i | −1.27280 | − | 0.734850i | −0.297284 | − | 0.954789i | \(-0.596081\pi\) |
−0.975514 | + | 0.219939i | \(0.929414\pi\) | |||||||
\(60\) | 1.18432 | + | 6.29455i | 0.0197386 | + | 0.104909i | ||||
\(61\) | −8.94224 | − | 15.4884i | −0.146594 | − | 0.253908i | 0.783372 | − | 0.621553i | \(-0.213498\pi\) |
−0.929967 | + | 0.367644i | \(0.880164\pi\) | |||||||
\(62\) | 3.99616i | 0.0644542i | ||||||||
\(63\) | −52.6892 | − | 34.5377i | −0.836336 | − | 0.548217i | ||||
\(64\) | −59.8365 | −0.934945 | ||||||||
\(65\) | 15.3800 | − | 8.87963i | 0.236615 | − | 0.136610i | ||||
\(66\) | 0.351493 | − | 1.00122i | 0.00532565 | − | 0.0151700i | ||||
\(67\) | 9.02196 | − | 15.6265i | 0.134656 | − | 0.233231i | −0.790810 | − | 0.612062i | \(-0.790340\pi\) |
0.925466 | + | 0.378831i | \(0.123674\pi\) | |||||||
\(68\) | 23.3337i | 0.343143i | ||||||||
\(69\) | 46.4016 | − | 39.8491i | 0.672487 | − | 0.577524i | ||||
\(70\) | −11.7720 | + | 1.12192i | −0.168172 | + | 0.0160274i | ||||
\(71\) | 74.2118i | 1.04524i | 0.852567 | + | 0.522618i | \(0.175045\pi\) | ||||
−0.852567 | + | 0.522618i | \(0.824955\pi\) | |||||||
\(72\) | 76.3038 | + | 11.6609i | 1.05978 | + | 0.161957i | ||||
\(73\) | 13.0598 | + | 22.6203i | 0.178902 | + | 0.309867i | 0.941505 | − | 0.337000i | \(-0.109412\pi\) |
−0.762603 | + | 0.646867i | \(0.776079\pi\) | |||||||
\(74\) | − | 33.5479i | − | 0.453349i | ||||||
\(75\) | 46.2663 | + | 53.8739i | 0.616884 | + | 0.718319i | ||||
\(76\) | 25.3914 | + | 43.9791i | 0.334097 | + | 0.578673i | ||||
\(77\) | −1.53664 | − | 0.702101i | −0.0199564 | − | 0.00911819i | ||||
\(78\) | −12.5250 | − | 66.5695i | −0.160577 | − | 0.853455i | ||||
\(79\) | −11.2561 | − | 19.4962i | −0.142483 | − | 0.246788i | 0.785948 | − | 0.618292i | \(-0.212175\pi\) |
−0.928431 | + | 0.371505i | \(0.878842\pi\) | |||||||
\(80\) | 5.15184 | − | 2.97442i | 0.0643980 | − | 0.0371802i | ||||
\(81\) | −77.3029 | − | 24.1921i | −0.954357 | − | 0.298668i | ||||
\(82\) | 52.4546 | − | 90.8541i | 0.639691 | − | 1.10798i | ||||
\(83\) | −77.0996 | − | 44.5135i | −0.928911 | − | 0.536307i | −0.0424438 | − | 0.999099i | \(-0.513514\pi\) |
−0.886467 | + | 0.462792i | \(0.846848\pi\) | |||||||
\(84\) | 9.34404 | − | 37.7565i | 0.111239 | − | 0.449483i | ||||
\(85\) | −7.26088 | − | 12.5762i | −0.0854221 | − | 0.147955i | ||||
\(86\) | 43.6652i | 0.507735i | ||||||||
\(87\) | 10.8353 | + | 57.5887i | 0.124543 | + | 0.661939i | ||||
\(88\) | 2.06996 | 0.0235223 | ||||||||
\(89\) | −49.7459 | − | 28.7208i | −0.558942 | − | 0.322706i | 0.193779 | − | 0.981045i | \(-0.437926\pi\) |
−0.752721 | + | 0.658340i | \(0.771259\pi\) | |||||||
\(90\) | −14.1644 | + | 5.52565i | −0.157382 | + | 0.0613961i | ||||
\(91\) | −107.360 | + | 10.2318i | −1.17978 | + | 0.112438i | ||||
\(92\) | 32.7030 | + | 18.8811i | 0.355468 | + | 0.205229i | ||||
\(93\) | 8.03915 | − | 1.51256i | 0.0864425 | − | 0.0162641i | ||||
\(94\) | 21.9770 | − | 38.0653i | 0.233798 | − | 0.404950i | ||||
\(95\) | −27.3705 | − | 15.8023i | −0.288110 | − | 0.166340i | ||||
\(96\) | 14.8348 | + | 78.8461i | 0.154530 | + | 0.821313i | ||||
\(97\) | 73.9883 | − | 128.152i | 0.762766 | − | 1.32115i | −0.178653 | − | 0.983912i | \(-0.557174\pi\) |
0.941419 | − | 0.337238i | \(-0.109493\pi\) | |||||||
\(98\) | 67.8536 | + | 23.5122i | 0.692384 | + | 0.239920i | ||||
\(99\) | −2.14721 | − | 0.328140i | −0.0216890 | − | 0.00331455i | ||||
\(100\) | −21.9216 | + | 37.9694i | −0.219216 | + | 0.379694i | ||||
\(101\) | 84.1369i | 0.833039i | 0.909127 | + | 0.416519i | \(0.136750\pi\) | ||||
−0.909127 | + | 0.416519i | \(0.863250\pi\) | |||||||
\(102\) | −54.4339 | + | 10.2417i | −0.533666 | + | 0.100409i | ||||
\(103\) | 58.9675 | 0.572500 | 0.286250 | − | 0.958155i | \(-0.407591\pi\) | ||||
0.286250 | + | 0.958155i | \(0.407591\pi\) | |||||||
\(104\) | 114.434 | − | 66.0686i | 1.10033 | − | 0.635275i | ||||
\(105\) | 6.71274 | + | 23.2574i | 0.0639308 | + | 0.221499i | ||||
\(106\) | −76.6518 | + | 132.765i | −0.723130 | + | 1.25250i | ||||
\(107\) | −76.9320 | − | 44.4167i | −0.718990 | − | 0.415109i | 0.0953906 | − | 0.995440i | \(-0.469590\pi\) |
−0.814381 | + | 0.580331i | \(0.802923\pi\) | |||||||
\(108\) | −1.71629 | − | 49.9792i | −0.0158916 | − | 0.462770i | ||||
\(109\) | 94.4610 | + | 163.611i | 0.866615 | + | 1.50102i | 0.865435 | + | 0.501021i | \(0.167042\pi\) |
0.00117990 | + | 0.999999i | \(0.499624\pi\) | |||||||
\(110\) | −0.353096 | + | 0.203860i | −0.00320996 | + | 0.00185327i | ||||
\(111\) | −67.4889 | + | 12.6980i | −0.608008 | + | 0.114396i | ||||
\(112\) | −35.9625 | + | 3.42736i | −0.321094 | + | 0.0306014i | ||||
\(113\) | 101.115 | − | 58.3790i | 0.894827 | − | 0.516629i | 0.0193087 | − | 0.999814i | \(-0.493853\pi\) |
0.875518 | + | 0.483185i | \(0.160520\pi\) | |||||||
\(114\) | −91.4516 | + | 78.5376i | −0.802207 | + | 0.688926i | ||||
\(115\) | −23.5014 | −0.204360 | ||||||||
\(116\) | −31.3316 | + | 18.0893i | −0.270100 | + | 0.155942i | ||||
\(117\) | −129.178 | + | 50.3936i | −1.10409 | + | 0.430714i | ||||
\(118\) | 127.081 | 1.07696 | ||||||||
\(119\) | 8.36656 | + | 87.7884i | 0.0703072 | + | 0.737718i | ||||
\(120\) | −19.3231 | − | 22.5004i | −0.161026 | − | 0.187503i | ||||
\(121\) | 120.942 | 0.999519 | ||||||||
\(122\) | 22.6990 | + | 13.1053i | 0.186057 | + | 0.107420i | ||||
\(123\) | −202.627 | − | 71.1354i | −1.64738 | − | 0.578336i | ||||
\(124\) | 2.52519 | + | 4.37376i | 0.0203644 | + | 0.0352722i | ||||
\(125\) | − | 56.1034i | − | 0.448827i | ||||||
\(126\) | 92.1815 | + | 5.22598i | 0.731599 | + | 0.0414760i | ||||
\(127\) | −33.5427 | −0.264116 | −0.132058 | − | 0.991242i | \(-0.542159\pi\) | ||||
−0.132058 | + | 0.991242i | \(0.542159\pi\) | |||||||
\(128\) | −16.6965 | + | 9.63973i | −0.130441 | + | 0.0753104i | ||||
\(129\) | 87.8421 | − | 16.5274i | 0.680947 | − | 0.128120i | ||||
\(130\) | −13.0135 | + | 22.5401i | −0.100104 | + | 0.173385i | ||||
\(131\) | 71.4985i | 0.545790i | 0.962044 | + | 0.272895i | \(0.0879812\pi\) | ||||
−0.962044 | + | 0.272895i | \(0.912019\pi\) | |||||||
\(132\) | −0.247968 | − | 1.31793i | −0.00187855 | − | 0.00998434i | ||||
\(133\) | 111.299 | + | 156.358i | 0.836836 | + | 1.17563i | ||||
\(134\) | 26.4442i | 0.197345i | ||||||||
\(135\) | 16.4773 | + | 26.4033i | 0.122054 | + | 0.195580i | ||||
\(136\) | −54.0243 | − | 93.5729i | −0.397238 | − | 0.688036i | ||||
\(137\) | − | 216.764i | − | 1.58222i | −0.611677 | − | 0.791108i | \(-0.709505\pi\) | ||
0.611677 | − | 0.791108i | \(-0.290495\pi\) | |||||||
\(138\) | −29.6926 | + | 84.5785i | −0.215164 | + | 0.612887i | ||||
\(139\) | 53.7032 | + | 93.0167i | 0.386354 | + | 0.669185i | 0.991956 | − | 0.126583i | \(-0.0404009\pi\) |
−0.605602 | + | 0.795768i | \(0.707068\pi\) | |||||||
\(140\) | −12.1754 | + | 8.66672i | −0.0869673 | + | 0.0619051i | ||||
\(141\) | −84.8950 | − | 29.8037i | −0.602092 | − | 0.211374i | ||||
\(142\) | −54.3804 | − | 94.1897i | −0.382961 | − | 0.663307i | ||||
\(143\) | −3.22021 | + | 1.85919i | −0.0225189 | + | 0.0130013i | ||||
\(144\) | −43.2710 | + | 16.8804i | −0.300493 | + | 0.117225i | ||||
\(145\) | 11.2579 | − | 19.4992i | 0.0776406 | − | 0.134477i | ||||
\(146\) | −33.1511 | − | 19.1398i | −0.227062 | − | 0.131094i | ||||
\(147\) | 21.6171 | − | 145.402i | 0.147055 | − | 0.989128i | ||||
\(148\) | −21.1990 | − | 36.7178i | −0.143237 | − | 0.248093i | ||||
\(149\) | − | 157.089i | − | 1.05429i | −0.849777 | − | 0.527143i | \(-0.823263\pi\) | ||
0.849777 | − | 0.527143i | \(-0.176737\pi\) | |||||||
\(150\) | −98.1986 | − | 34.4741i | −0.654657 | − | 0.229827i | ||||
\(151\) | −120.482 | −0.797897 | −0.398948 | − | 0.916973i | \(-0.630625\pi\) | ||||
−0.398948 | + | 0.916973i | \(0.630625\pi\) | |||||||
\(152\) | −203.649 | − | 117.577i | −1.33980 | − | 0.773532i | ||||
\(153\) | 41.2069 | + | 105.629i | 0.269326 | + | 0.690387i | ||||
\(154\) | 2.46479 | − | 0.234904i | 0.0160051 | − | 0.00152535i | ||||
\(155\) | −2.72201 | − | 1.57156i | −0.0175614 | − | 0.0101391i | ||||
\(156\) | −55.7740 | − | 64.9450i | −0.357526 | − | 0.416314i | ||||
\(157\) | −3.87777 | + | 6.71650i | −0.0246992 | + | 0.0427802i | −0.878111 | − | 0.478457i | \(-0.841196\pi\) |
0.853412 | + | 0.521238i | \(0.174529\pi\) | |||||||
\(158\) | 28.5726 | + | 16.4964i | 0.180839 | + | 0.104408i | ||||
\(159\) | 296.098 | + | 103.950i | 1.86225 | + | 0.653773i | ||||
\(160\) | 15.4134 | − | 26.6969i | 0.0963340 | − | 0.166855i | ||||
\(161\) | 129.809 | + | 59.3104i | 0.806265 | + | 0.368387i | ||||
\(162\) | 115.840 | − | 25.9409i | 0.715064 | − | 0.160129i | ||||
\(163\) | 129.964 | − | 225.104i | 0.797323 | − | 1.38100i | −0.124031 | − | 0.992278i | \(-0.539582\pi\) |
0.921354 | − | 0.388725i | \(-0.127084\pi\) | |||||||
\(164\) | − | 132.585i | − | 0.808447i | ||||||
\(165\) | 0.543757 | + | 0.633168i | 0.00329550 | + | 0.00383738i | ||||
\(166\) | 130.473 | 0.785983 | ||||||||
\(167\) | 97.3809 | − | 56.2229i | 0.583119 | − | 0.336664i | −0.179253 | − | 0.983803i | \(-0.557368\pi\) |
0.762372 | + | 0.647139i | \(0.224035\pi\) | |||||||
\(168\) | 49.9459 | + | 173.046i | 0.297297 | + | 1.03003i | ||||
\(169\) | −34.1824 | + | 59.2057i | −0.202263 | + | 0.350330i | ||||
\(170\) | 18.4310 | + | 10.6412i | 0.108418 | + | 0.0625951i | ||||
\(171\) | 192.610 | + | 154.248i | 1.12638 | + | 0.902036i | ||||
\(172\) | 27.5922 | + | 47.7911i | 0.160420 | + | 0.277855i | ||||
\(173\) | 12.1128 | − | 6.99333i | 0.0700162 | − | 0.0404239i | −0.464583 | − | 0.885529i | \(-0.653796\pi\) |
0.534599 | + | 0.845106i | \(0.320463\pi\) | |||||||
\(174\) | −55.9517 | − | 65.1519i | −0.321561 | − | 0.374436i | ||||
\(175\) | −68.8614 | + | 150.712i | −0.393494 | + | 0.861214i | ||||
\(176\) | −1.07868 | + | 0.622774i | −0.00612884 | + | 0.00353849i | ||||
\(177\) | −48.1006 | − | 255.651i | −0.271755 | − | 1.44436i | ||||
\(178\) | 84.1834 | 0.472940 | ||||||||
\(179\) | −44.1214 | + | 25.4735i | −0.246488 | + | 0.142310i | −0.618155 | − | 0.786056i | \(-0.712120\pi\) |
0.371667 | + | 0.928366i | \(0.378786\pi\) | |||||||
\(180\) | −12.0111 | + | 14.9983i | −0.0667284 | + | 0.0833239i | ||||
\(181\) | −239.784 | −1.32477 | −0.662387 | − | 0.749161i | \(-0.730457\pi\) | ||||
−0.662387 | + | 0.749161i | \(0.730457\pi\) | |||||||
\(182\) | 128.764 | − | 91.6569i | 0.707494 | − | 0.503609i | ||||
\(183\) | 17.7725 | − | 50.6244i | 0.0971174 | − | 0.276636i | ||||
\(184\) | −174.861 | −0.950332 | ||||||||
\(185\) | 22.8514 | + | 13.1932i | 0.123521 | + | 0.0713148i | ||||
\(186\) | −9.09493 | + | 7.81062i | −0.0488975 | + | 0.0419926i | ||||
\(187\) | 1.52026 | + | 2.63317i | 0.00812973 | + | 0.0140811i | ||||
\(188\) | − | 55.5494i | − | 0.295476i | ||||||
\(189\) | −24.3778 | − | 187.421i | −0.128983 | − | 0.991647i | ||||
\(190\) | 46.3182 | 0.243780 | ||||||||
\(191\) | −159.211 | + | 91.9205i | −0.833566 | + | 0.481259i | −0.855072 | − | 0.518509i | \(-0.826487\pi\) |
0.0215064 | + | 0.999769i | \(0.493154\pi\) | |||||||
\(192\) | −116.952 | − | 136.183i | −0.609127 | − | 0.709286i | ||||
\(193\) | −76.3985 | + | 132.326i | −0.395847 | + | 0.685628i | −0.993209 | − | 0.116344i | \(-0.962882\pi\) |
0.597362 | + | 0.801972i | \(0.296216\pi\) | |||||||
\(194\) | 216.867i | 1.11787i | ||||||||
\(195\) | 50.2700 | + | 17.6480i | 0.257795 | + | 0.0905028i | ||||
\(196\) | 89.1226 | − | 17.1431i | 0.454707 | − | 0.0874650i | ||||
\(197\) | 386.007i | 1.95943i | 0.200402 | + | 0.979714i | \(0.435775\pi\) | ||||
−0.200402 | + | 0.979714i | \(0.564225\pi\) | |||||||
\(198\) | 2.96570 | − | 1.15694i | 0.0149783 | − | 0.00584315i | ||||
\(199\) | −22.8387 | − | 39.5577i | −0.114767 | − | 0.198782i | 0.802920 | − | 0.596087i | \(-0.203279\pi\) |
−0.917687 | + | 0.397305i | \(0.869946\pi\) | |||||||
\(200\) | − | 203.020i | − | 1.01510i | ||||||
\(201\) | 53.1983 | − | 10.0092i | 0.264668 | − | 0.0497972i | ||||
\(202\) | −61.6533 | − | 106.787i | −0.305214 | − | 0.528647i | ||||
\(203\) | −111.393 | + | 79.2916i | −0.548732 | + | 0.390599i | ||||
\(204\) | −53.1056 | + | 45.6065i | −0.260322 | + | 0.223561i | ||||
\(205\) | 41.2573 | + | 71.4597i | 0.201255 | + | 0.348584i | ||||
\(206\) | −74.8417 | + | 43.2099i | −0.363309 | + | 0.209757i | ||||
\(207\) | 181.387 | + | 27.7199i | 0.876265 | + | 0.133912i | ||||
\(208\) | −39.7552 | + | 68.8579i | −0.191131 | + | 0.331048i | ||||
\(209\) | 5.73074 | + | 3.30864i | 0.0274198 | + | 0.0158308i | ||||
\(210\) | −25.5622 | − | 24.5993i | −0.121725 | − | 0.117140i | ||||
\(211\) | −169.338 | − | 293.302i | −0.802550 | − | 1.39006i | −0.917933 | − | 0.396736i | \(-0.870143\pi\) |
0.115383 | − | 0.993321i | \(-0.463190\pi\) | |||||||
\(212\) | 193.746i | 0.913898i | ||||||||
\(213\) | −168.900 | + | 145.049i | −0.792957 | + | 0.680982i | ||||
\(214\) | 130.190 | 0.608362 | ||||||||
\(215\) | −29.7429 | − | 17.1721i | −0.138339 | − | 0.0798700i | ||||
\(216\) | 122.599 | + | 196.453i | 0.567588 | + | 0.909504i | ||||
\(217\) | 11.0688 | + | 15.5500i | 0.0510082 | + | 0.0716588i | ||||
\(218\) | −239.780 | − | 138.437i | −1.09991 | − | 0.635032i | ||||
\(219\) | −25.9561 | + | 73.9351i | −0.118521 | + | 0.337603i | ||||
\(220\) | −0.257640 | + | 0.446245i | −0.00117109 | + | 0.00202839i | ||||
\(221\) | 168.090 | + | 97.0467i | 0.760587 | + | 0.439125i | ||||
\(222\) | 76.3522 | − | 65.5703i | 0.343929 | − | 0.295362i | ||||
\(223\) | 43.8681 | − | 75.9817i | 0.196718 | − | 0.340725i | −0.750745 | − | 0.660593i | \(-0.770305\pi\) |
0.947462 | + | 0.319868i | \(0.103638\pi\) | |||||||
\(224\) | −152.510 | + | 108.560i | −0.680849 | + | 0.484643i | ||||
\(225\) | −32.1837 | + | 210.597i | −0.143039 | + | 0.935985i | ||||
\(226\) | −85.5572 | + | 148.189i | −0.378572 | + | 0.655706i | ||||
\(227\) | 352.696i | 1.55373i | 0.629668 | + | 0.776864i | \(0.283191\pi\) | ||||
−0.629668 | + | 0.776864i | \(0.716809\pi\) | |||||||
\(228\) | −50.4647 | + | 143.747i | −0.221336 | + | 0.630470i | ||||
\(229\) | −380.791 | −1.66284 | −0.831421 | − | 0.555644i | \(-0.812472\pi\) | ||||
−0.831421 | + | 0.555644i | \(0.812472\pi\) | |||||||
\(230\) | 29.8280 | − | 17.2212i | 0.129687 | − | 0.0748747i | ||||
\(231\) | −1.40549 | − | 4.86955i | −0.00608438 | − | 0.0210803i | ||||
\(232\) | 83.7640 | − | 145.083i | 0.361052 | − | 0.625360i | ||||
\(233\) | 271.555 | + | 156.782i | 1.16547 | + | 0.672885i | 0.952609 | − | 0.304197i | \(-0.0983882\pi\) |
0.212862 | + | 0.977082i | \(0.431722\pi\) | |||||||
\(234\) | 127.026 | − | 158.618i | 0.542847 | − | 0.677855i | ||||
\(235\) | 17.2856 | + | 29.9396i | 0.0735558 | + | 0.127402i | ||||
\(236\) | 139.089 | − | 80.3030i | 0.589360 | − | 0.340267i | ||||
\(237\) | 22.3713 | − | 63.7241i | 0.0943937 | − | 0.268878i | ||||
\(238\) | −74.9479 | − | 105.290i | −0.314907 | − | 0.442396i | ||||
\(239\) | 199.851 | − | 115.384i | 0.836195 | − | 0.482777i | −0.0197741 | − | 0.999804i | \(-0.506295\pi\) |
0.855969 | + | 0.517027i | \(0.172961\pi\) | |||||||
\(240\) | 16.8390 | + | 5.91158i | 0.0701624 | + | 0.0246316i | ||||
\(241\) | −180.856 | −0.750442 | −0.375221 | − | 0.926935i | \(-0.622433\pi\) | ||||
−0.375221 | + | 0.926935i | \(0.622433\pi\) | |||||||
\(242\) | −153.499 | + | 88.6229i | −0.634295 | + | 0.366210i | ||||
\(243\) | −96.0317 | − | 223.219i | −0.395192 | − | 0.918598i | ||||
\(244\) | 33.1251 | 0.135759 | ||||||||
\(245\) | −42.7000 | + | 36.9724i | −0.174286 | + | 0.150908i | ||||
\(246\) | 309.301 | − | 58.1947i | 1.25732 | − | 0.236564i | ||||
\(247\) | 422.419 | 1.71020 | ||||||||
\(248\) | −20.2531 | − | 11.6931i | −0.0816655 | − | 0.0471496i | ||||
\(249\) | −49.3846 | − | 262.475i | −0.198332 | − | 1.05412i | ||||
\(250\) | 41.1111 | + | 71.2065i | 0.164444 | + | 0.284826i | ||||
\(251\) | 161.864i | 0.644878i | 0.946590 | + | 0.322439i | \(0.104503\pi\) | ||||
−0.946590 | + | 0.322439i | \(0.895497\pi\) | |||||||
\(252\) | 104.194 | − | 52.5301i | 0.413468 | − | 0.208453i | ||||
\(253\) | 4.92064 | 0.0194492 | ||||||||
\(254\) | 42.5725 | − | 24.5792i | 0.167608 | − | 0.0967687i | ||||
\(255\) | 14.4308 | − | 41.1058i | 0.0565914 | − | 0.161199i | ||||
\(256\) | 133.800 | − | 231.749i | 0.522658 | − | 0.905270i | ||||
\(257\) | − | 75.6745i | − | 0.294453i | −0.989103 | − | 0.147227i | \(-0.952965\pi\) | ||
0.989103 | − | 0.147227i | \(-0.0470347\pi\) | |||||||
\(258\) | −99.3784 | + | 85.3450i | −0.385188 | + | 0.330795i | ||||
\(259\) | −92.9227 | − | 130.542i | −0.358775 | − | 0.504024i | ||||
\(260\) | 32.8932i | 0.126512i | ||||||||
\(261\) | −109.889 | + | 137.219i | −0.421032 | + | 0.525744i | ||||
\(262\) | −52.3922 | − | 90.7460i | −0.199970 | − | 0.346359i | ||||
\(263\) | 11.6465i | 0.0442833i | 0.999755 | + | 0.0221417i | \(0.00704849\pi\) | ||||
−0.999755 | + | 0.0221417i | \(0.992952\pi\) | |||||||
\(264\) | 4.04580 | + | 4.71106i | 0.0153250 | + | 0.0178449i | ||||
\(265\) | −60.2892 | − | 104.424i | −0.227506 | − | 0.394052i | ||||
\(266\) | −255.836 | − | 116.893i | −0.961791 | − | 0.439448i | ||||
\(267\) | −31.8637 | − | 169.353i | −0.119340 | − | 0.634282i | ||||
\(268\) | 16.7102 | + | 28.9429i | 0.0623516 | + | 0.107996i | ||||
\(269\) | 265.976 | − | 153.562i | 0.988760 | − | 0.570861i | 0.0838565 | − | 0.996478i | \(-0.473276\pi\) |
0.904903 | + | 0.425617i | \(0.139943\pi\) | |||||||
\(270\) | −40.2607 | − | 21.4369i | −0.149114 | − | 0.0793961i | ||||
\(271\) | 169.039 | − | 292.784i | 0.623759 | − | 1.08038i | −0.365020 | − | 0.931000i | \(-0.618938\pi\) |
0.988779 | − | 0.149383i | \(-0.0477287\pi\) | |||||||
\(272\) | 56.3052 | + | 32.5078i | 0.207004 | + | 0.119514i | ||||
\(273\) | −233.125 | − | 224.344i | −0.853939 | − | 0.821774i | ||||
\(274\) | 158.839 | + | 275.117i | 0.579703 | + | 1.00408i | ||||
\(275\) | 5.71304i | 0.0207747i | ||||||||
\(276\) | 20.9473 | + | 111.333i | 0.0758959 | + | 0.403381i | ||||
\(277\) | −132.022 | −0.476614 | −0.238307 | − | 0.971190i | \(-0.576592\pi\) | ||||
−0.238307 | + | 0.971190i | \(0.576592\pi\) | |||||||
\(278\) | −136.320 | − | 78.7046i | −0.490361 | − | 0.283110i | ||||
\(279\) | 19.1552 | + | 15.3401i | 0.0686568 | + | 0.0549824i | ||||
\(280\) | 28.7599 | − | 62.9450i | 0.102714 | − | 0.224803i | ||||
\(281\) | −64.2832 | − | 37.1139i | −0.228766 | − | 0.132078i | 0.381237 | − | 0.924477i | \(-0.375498\pi\) |
−0.610003 | + | 0.792399i | \(0.708832\pi\) | |||||||
\(282\) | 129.588 | − | 24.3819i | 0.459533 | − | 0.0864607i | ||||
\(283\) | 5.65152 | − | 9.78873i | 0.0199701 | − | 0.0345891i | −0.855868 | − | 0.517195i | \(-0.826976\pi\) |
0.875838 | + | 0.482606i | \(0.160310\pi\) | |||||||
\(284\) | −119.038 | − | 68.7264i | −0.419147 | − | 0.241994i | ||||
\(285\) | −17.5316 | − | 93.1791i | −0.0615144 | − | 0.326944i | ||||
\(286\) | 2.72473 | − | 4.71937i | 0.00952702 | − | 0.0165013i | ||||
\(287\) | −47.5399 | − | 498.826i | −0.165644 | − | 1.73807i | ||||
\(288\) | −150.452 | + | 187.870i | −0.522403 | + | 0.652326i | ||||
\(289\) | −65.1449 | + | 112.834i | −0.225415 | + | 0.390430i | ||||
\(290\) | 32.9979i | 0.113786i | ||||||||
\(291\) | 436.275 | − | 82.0849i | 1.49923 | − | 0.282079i | ||||
\(292\) | −48.3781 | −0.165678 | ||||||||
\(293\) | −144.131 | + | 83.2139i | −0.491913 | + | 0.284006i | −0.725368 | − | 0.688361i | \(-0.758330\pi\) |
0.233454 | + | 0.972368i | \(0.424997\pi\) | |||||||
\(294\) | 79.1102 | + | 200.385i | 0.269082 | + | 0.681580i | ||||
\(295\) | −49.9767 | + | 86.5621i | −0.169412 | + | 0.293431i | ||||
\(296\) | 170.025 | + | 98.1639i | 0.574408 | + | 0.331635i | ||||
\(297\) | −3.44997 | − | 5.52824i | −0.0116161 | − | 0.0186136i | ||||
\(298\) | 115.110 | + | 199.377i | 0.386276 | + | 0.669050i | ||||
\(299\) | 272.029 | − | 157.056i | 0.909796 | − | 0.525271i | ||||
\(300\) | −129.262 | + | 24.3205i | −0.430872 | + | 0.0810684i | ||||
\(301\) | 120.946 | + | 169.911i | 0.401815 | + | 0.564489i | ||||
\(302\) | 152.916 | − | 88.2864i | 0.506346 | − | 0.292339i | ||||
\(303\) | −191.489 | + | 164.448i | −0.631976 | + | 0.542734i | ||||
\(304\) | 141.498 | 0.465454 | ||||||||
\(305\) | −17.8535 | + | 10.3077i | −0.0585361 | + | 0.0337958i | ||||
\(306\) | −129.702 | − | 103.869i | −0.423863 | − | 0.339443i | ||||
\(307\) | −382.982 | −1.24750 | −0.623749 | − | 0.781625i | \(-0.714391\pi\) | ||||
−0.623749 | + | 0.781625i | \(0.714391\pi\) | |||||||
\(308\) | 2.54925 | − | 1.81461i | 0.00827679 | − | 0.00589159i | ||||
\(309\) | 115.254 | + | 134.205i | 0.372990 | + | 0.434321i | ||||
\(310\) | 4.60638 | 0.0148593 | ||||||||
\(311\) | −135.109 | − | 78.0053i | −0.434435 | − | 0.250821i | 0.266799 | − | 0.963752i | \(-0.414034\pi\) |
−0.701234 | + | 0.712931i | \(0.747367\pi\) | |||||||
\(312\) | 374.032 | + | 131.310i | 1.19882 | + | 0.420864i | ||||
\(313\) | −58.2651 | − | 100.918i | −0.186150 | − | 0.322422i | 0.757813 | − | 0.652472i | \(-0.226268\pi\) |
−0.943964 | + | 0.330050i | \(0.892935\pi\) | |||||||
\(314\) | − | 11.3661i | − | 0.0361978i | ||||||
\(315\) | −39.8116 | + | 60.7349i | −0.126386 | + | 0.192809i | ||||
\(316\) | 41.6966 | 0.131951 | ||||||||
\(317\) | −162.694 | + | 93.9313i | −0.513229 | + | 0.296313i | −0.734160 | − | 0.678976i | \(-0.762424\pi\) |
0.220931 | + | 0.975290i | \(0.429091\pi\) | |||||||
\(318\) | −451.980 | + | 85.0398i | −1.42132 | + | 0.267421i | ||||
\(319\) | −2.35714 | + | 4.08269i | −0.00738916 | + | 0.0127984i | ||||
\(320\) | 68.9736i | 0.215542i | ||||||||
\(321\) | −49.2772 | − | 261.905i | −0.153512 | − | 0.815903i | ||||
\(322\) | −208.214 | + | 19.8436i | −0.646629 | + | 0.0616261i | ||||
\(323\) | − | 345.412i | − | 1.06939i | ||||||
\(324\) | 110.394 | − | 101.592i | 0.340722 | − | 0.313556i | ||||
\(325\) | 182.348 | + | 315.835i | 0.561069 | + | 0.971801i | ||||
\(326\) | 380.936i | 1.16851i | ||||||||
\(327\) | −187.739 | + | 534.769i | −0.574125 | + | 1.63538i | ||||
\(328\) | 306.974 | + | 531.694i | 0.935895 | + | 1.62102i | ||||
\(329\) | −19.9179 | − | 208.994i | −0.0605406 | − | 0.635239i | ||||
\(330\) | −1.15411 | − | 0.405166i | −0.00349729 | − | 0.00122778i | ||||
\(331\) | 31.7161 | + | 54.9338i | 0.0958189 | + | 0.165963i | 0.909950 | − | 0.414718i | \(-0.136120\pi\) |
−0.814131 | + | 0.580681i | \(0.802786\pi\) | |||||||
\(332\) | 142.802 | − | 82.4466i | 0.430125 | − | 0.248333i | ||||
\(333\) | −160.809 | − | 128.781i | −0.482909 | − | 0.386728i | ||||
\(334\) | −82.3973 | + | 142.716i | −0.246698 | + | 0.427294i | ||||
\(335\) | −18.0127 | − | 10.3996i | −0.0537692 | − | 0.0310437i | ||||
\(336\) | −78.0902 | − | 75.1488i | −0.232411 | − | 0.223657i | ||||
\(337\) | 88.4049 | + | 153.122i | 0.262329 | + | 0.454367i | 0.966860 | − | 0.255306i | \(-0.0821761\pi\) |
−0.704531 | + | 0.709673i | \(0.748843\pi\) | |||||||
\(338\) | − | 100.192i | − | 0.296426i | ||||||
\(339\) | 330.499 | + | 116.027i | 0.974924 | + | 0.342262i | ||||
\(340\) | 26.8968 | 0.0791082 | ||||||||
\(341\) | 0.569926 | + | 0.329047i | 0.00167134 | + | 0.000964948i | ||||
\(342\) | −357.490 | − | 54.6323i | −1.04529 | − | 0.159743i | ||||
\(343\) | 329.159 | − | 96.4535i | 0.959648 | − | 0.281206i | ||||
\(344\) | −221.301 | − | 127.768i | −0.643316 | − | 0.371419i | ||||
\(345\) | −45.9342 | − | 53.4872i | −0.133142 | − | 0.155035i | ||||
\(346\) | −10.2491 | + | 17.7519i | −0.0296216 | + | 0.0513060i | ||||
\(347\) | 210.706 | + | 121.651i | 0.607223 | + | 0.350580i | 0.771878 | − | 0.635771i | \(-0.219318\pi\) |
−0.164655 | + | 0.986351i | \(0.552651\pi\) | |||||||
\(348\) | −102.408 | − | 35.9520i | −0.294277 | − | 0.103310i | ||||
\(349\) | −209.668 | + | 363.156i | −0.600768 | + | 1.04056i | 0.391937 | + | 0.919992i | \(0.371805\pi\) |
−0.992705 | + | 0.120568i | \(0.961528\pi\) | |||||||
\(350\) | −23.0391 | − | 241.744i | −0.0658261 | − | 0.690698i | ||||
\(351\) | −367.175 | − | 195.504i | −1.04608 | − | 0.556990i | ||||
\(352\) | −3.22722 | + | 5.58970i | −0.00916823 | + | 0.0158798i | ||||
\(353\) | − | 347.861i | − | 0.985443i | −0.870187 | − | 0.492722i | \(-0.836002\pi\) | ||
0.870187 | − | 0.492722i | \(-0.163998\pi\) | |||||||
\(354\) | 248.384 | + | 289.226i | 0.701649 | + | 0.817023i | ||||
\(355\) | 85.5440 | 0.240969 | ||||||||
\(356\) | 92.1379 | − | 53.1958i | 0.258814 | − | 0.149426i | ||||
\(357\) | −183.447 | + | 190.627i | −0.513856 | + | 0.533969i | ||||
\(358\) | 37.3326 | − | 64.6620i | 0.104281 | − | 0.180620i | ||||
\(359\) | −392.233 | − | 226.456i | −1.09257 | − | 0.630796i | −0.158311 | − | 0.987389i | \(-0.550605\pi\) |
−0.934260 | + | 0.356593i | \(0.883938\pi\) | |||||||
\(360\) | 13.4415 | − | 87.9555i | 0.0373375 | − | 0.244321i | ||||
\(361\) | −195.372 | − | 338.394i | −0.541196 | − | 0.937379i | ||||
\(362\) | 304.334 | − | 175.708i | 0.840703 | − | 0.485380i | ||||
\(363\) | 236.384 | + | 275.254i | 0.651197 | + | 0.758274i | ||||
\(364\) | 83.0125 | − | 181.684i | 0.228056 | − | 0.499132i | ||||
\(365\) | 26.0744 | − | 15.0541i | 0.0714368 | − | 0.0412440i | ||||
\(366\) | 14.5394 | + | 77.2758i | 0.0397251 | + | 0.211136i | ||||
\(367\) | −3.19960 | −0.00871826 | −0.00435913 | − | 0.999990i | \(-0.501388\pi\) | ||||
−0.00435913 | + | 0.999990i | \(0.501388\pi\) | |||||||
\(368\) | 91.1218 | − | 52.6092i | 0.247613 | − | 0.142960i | ||||
\(369\) | −234.143 | − | 600.199i | −0.634534 | − | 1.62656i | ||||
\(370\) | −38.6706 | −0.104515 | ||||||||
\(371\) | 69.4700 | + | 728.932i | 0.187251 | + | 1.96478i | ||||
\(372\) | −5.01875 | + | 14.2958i | −0.0134913 | + | 0.0384295i | ||||
\(373\) | −149.443 | −0.400652 | −0.200326 | − | 0.979729i | \(-0.564200\pi\) | ||||
−0.200326 | + | 0.979729i | \(0.564200\pi\) | |||||||
\(374\) | −3.85903 | − | 2.22801i | −0.0103183 | − | 0.00595725i | ||||
\(375\) | 127.687 | − | 109.656i | 0.340498 | − | 0.292416i | ||||
\(376\) | 128.613 | + | 222.764i | 0.342056 | + | 0.592459i | ||||
\(377\) | 300.939i | 0.798247i | ||||||||
\(378\) | 168.278 | + | 220.012i | 0.445179 | + | 0.582042i | ||||
\(379\) | 431.217 | 1.13778 | 0.568888 | − | 0.822415i | \(-0.307374\pi\) | ||||
0.568888 | + | 0.822415i | \(0.307374\pi\) | |||||||
\(380\) | 50.6948 | − | 29.2686i | 0.133407 | − | 0.0770227i | ||||
\(381\) | −65.5604 | − | 76.3406i | −0.172074 | − | 0.200369i | ||||
\(382\) | 134.714 | − | 233.331i | 0.352654 | − | 0.610815i | ||||
\(383\) | 179.770i | 0.469373i | 0.972071 | + | 0.234687i | \(0.0754064\pi\) | ||||
−0.972071 | + | 0.234687i | \(0.924594\pi\) | |||||||
\(384\) | −54.5731 | − | 19.1587i | −0.142117 | − | 0.0498925i | ||||
\(385\) | −0.809312 | + | 1.77129i | −0.00210211 | + | 0.00460075i | ||||
\(386\) | − | 223.931i | − | 0.580133i | ||||||
\(387\) | 209.305 | + | 167.618i | 0.540841 | + | 0.433122i | ||||
\(388\) | 137.039 | + | 237.359i | 0.353193 | + | 0.611749i | ||||
\(389\) | 337.148i | 0.866703i | 0.901225 | + | 0.433352i | \(0.142669\pi\) | ||||
−0.901225 | + | 0.433352i | \(0.857331\pi\) | |||||||
\(390\) | −76.7347 | + | 14.4376i | −0.196756 | + | 0.0370194i | ||||
\(391\) | −128.425 | − | 222.438i | −0.328452 | − | 0.568896i | ||||
\(392\) | −317.708 | + | 275.092i | −0.810480 | + | 0.701766i | ||||
\(393\) | −162.725 | + | 139.746i | −0.414058 | + | 0.355588i | ||||
\(394\) | −282.856 | − | 489.921i | −0.717908 | − | 1.24345i | ||||
\(395\) | −22.4733 | + | 12.9750i | −0.0568945 | + | 0.0328480i | ||||
\(396\) | 2.51485 | − | 3.14030i | 0.00635062 | − | 0.00793005i | ||||
\(397\) | −266.853 | + | 462.203i | −0.672174 | + | 1.16424i | 0.305113 | + | 0.952316i | \(0.401306\pi\) |
−0.977286 | + | 0.211923i | \(0.932027\pi\) | |||||||
\(398\) | 57.9737 | + | 33.4711i | 0.145663 | + | 0.0840983i | ||||
\(399\) | −138.321 | + | 558.915i | −0.346670 | + | 1.40079i | ||||
\(400\) | 61.0811 | + | 105.796i | 0.152703 | + | 0.264489i | ||||
\(401\) | − | 606.232i | − | 1.51180i | −0.654687 | − | 0.755900i | \(-0.727199\pi\) | ||
0.654687 | − | 0.755900i | \(-0.272801\pi\) | |||||||
\(402\) | −60.1849 | + | 51.6861i | −0.149714 | + | 0.128572i | ||||
\(403\) | 42.0099 | 0.104243 | ||||||||
\(404\) | −134.958 | − | 77.9180i | −0.334054 | − | 0.192866i | ||||
\(405\) | −27.8863 | + | 89.1071i | −0.0688550 | + | 0.220018i | ||||
\(406\) | 83.2769 | − | 182.263i | 0.205115 | − | 0.448923i | ||||
\(407\) | −4.78455 | − | 2.76236i | −0.0117556 | − | 0.00678712i | ||||
\(408\) | 107.372 | − | 305.846i | 0.263167 | − | 0.749623i | ||||
\(409\) | 196.056 | − | 339.580i | 0.479355 | − | 0.830268i | −0.520364 | − | 0.853944i | \(-0.674204\pi\) |
0.999720 | + | 0.0236765i | \(0.00753715\pi\) | |||||||
\(410\) | −104.728 | − | 60.4645i | −0.255433 | − | 0.147474i | ||||
\(411\) | 493.336 | − | 423.671i | 1.20033 | − | 1.03083i | ||||
\(412\) | −54.6090 | + | 94.5855i | −0.132546 | + | 0.229577i | ||||
\(413\) | 494.501 | − | 351.996i | 1.19734 | − | 0.852291i | ||||
\(414\) | −250.529 | + | 97.7334i | −0.605142 | + | 0.236071i | ||||
\(415\) | −51.3107 | + | 88.8728i | −0.123640 | + | 0.214151i | ||||
\(416\) | 412.023i | 0.990439i | ||||||||
\(417\) | −106.734 | + | 304.028i | −0.255956 | + | 0.729085i | ||||
\(418\) | −9.69795 | −0.0232008 | ||||||||
\(419\) | −577.328 | + | 333.321i | −1.37787 | + | 0.795515i | −0.991903 | − | 0.126997i | \(-0.959466\pi\) |
−0.385969 | + | 0.922512i | \(0.626133\pi\) | |||||||
\(420\) | −43.5220 | − | 10.7709i | −0.103624 | − | 0.0256450i | ||||
\(421\) | 235.637 | − | 408.136i | 0.559708 | − | 0.969443i | −0.437812 | − | 0.899067i | \(-0.644246\pi\) |
0.997520 | − | 0.0703769i | \(-0.0224202\pi\) | |||||||
\(422\) | 429.848 | + | 248.173i | 1.01860 | + | 0.588087i | ||||
\(423\) | −98.0992 | − | 251.466i | −0.231913 | − | 0.594483i | ||||
\(424\) | −448.579 | − | 776.962i | −1.05797 | − | 1.83246i | ||||
\(425\) | 258.259 | − | 149.106i | 0.607667 | − | 0.350837i | ||||
\(426\) | 108.080 | − | 307.862i | 0.253708 | − | 0.722681i | ||||
\(427\) | 124.627 | − | 11.8774i | 0.291866 | − | 0.0278159i | ||||
\(428\) | 142.491 | − | 82.2673i | 0.332923 | − | 0.192213i | ||||
\(429\) | −10.5254 | − | 3.69509i | −0.0245346 | − | 0.00861326i | ||||
\(430\) | 50.3329 | 0.117053 | ||||||||
\(431\) | −204.379 | + | 117.998i | −0.474197 | + | 0.273778i | −0.717995 | − | 0.696048i | \(-0.754940\pi\) |
0.243798 | + | 0.969826i | \(0.421607\pi\) | |||||||
\(432\) | −122.993 | − | 65.4880i | −0.284706 | − | 0.151593i | ||||
\(433\) | 388.304 | 0.896776 | 0.448388 | − | 0.893839i | \(-0.351998\pi\) | ||||
0.448388 | + | 0.893839i | \(0.351998\pi\) | |||||||
\(434\) | −25.4431 | − | 11.6251i | −0.0586247 | − | 0.0267860i | ||||
\(435\) | 66.3826 | − | 12.4898i | 0.152604 | − | 0.0287123i | ||||
\(436\) | −349.916 | −0.802559 | ||||||||
\(437\) | −484.107 | − | 279.500i | −1.10780 | − | 0.639587i | ||||
\(438\) | −21.2343 | − | 112.858i | −0.0484800 | − | 0.257668i | ||||
\(439\) | 175.658 | + | 304.248i | 0.400132 | + | 0.693049i | 0.993741 | − | 0.111704i | \(-0.0356309\pi\) |
−0.593610 | + | 0.804753i | \(0.702298\pi\) | |||||||
\(440\) | − | 2.38605i | − | 0.00542283i | ||||||
\(441\) | 373.174 | − | 234.994i | 0.846200 | − | 0.532866i | ||||
\(442\) | −284.453 | −0.643559 | ||||||||
\(443\) | 46.0205 | − | 26.5700i | 0.103884 | − | 0.0599773i | −0.447158 | − | 0.894455i | \(-0.647564\pi\) |
0.551042 | + | 0.834478i | \(0.314230\pi\) | |||||||
\(444\) | 42.1325 | − | 120.013i | 0.0948931 | − | 0.270300i | ||||
\(445\) | −33.1065 | + | 57.3421i | −0.0743966 | + | 0.128859i | ||||
\(446\) | 128.581i | 0.288299i | ||||||||
\(447\) | 357.521 | − | 307.035i | 0.799823 | − | 0.686878i | ||||
\(448\) | 174.069 | − | 380.972i | 0.388546 | − | 0.850385i | ||||
\(449\) | 526.389i | 1.17236i | 0.810181 | + | 0.586179i | \(0.199369\pi\) | ||||
−0.810181 | + | 0.586179i | \(0.800631\pi\) | |||||||
\(450\) | −113.472 | − | 290.873i | −0.252160 | − | 0.646384i | ||||
\(451\) | −8.63832 | − | 14.9620i | −0.0191537 | − | 0.0331752i | ||||
\(452\) | 216.256i | 0.478442i | ||||||||
\(453\) | −235.487 | − | 274.208i | −0.519838 | − | 0.605316i | ||||
\(454\) | −258.447 | − | 447.643i | −0.569266 | − | 0.985997i | ||||
\(455\) | 11.7942 | + | 123.754i | 0.0259214 | + | 0.271987i | ||||
\(456\) | −130.443 | − | 693.296i | −0.286060 | − | 1.52039i | ||||
\(457\) | 369.881 | + | 640.652i | 0.809367 | + | 1.40186i | 0.913303 | + | 0.407280i | \(0.133523\pi\) |
−0.103936 | + | 0.994584i | \(0.533144\pi\) | |||||||
\(458\) | 483.300 | − | 279.033i | 1.05524 | − | 0.609243i | ||||
\(459\) | −159.863 | + | 300.239i | −0.348286 | + | 0.654116i | ||||
\(460\) | 21.7643 | − | 37.6968i | 0.0473136 | − | 0.0819496i | ||||
\(461\) | 284.624 | + | 164.328i | 0.617406 | + | 0.356460i | 0.775858 | − | 0.630907i | \(-0.217317\pi\) |
−0.158452 | + | 0.987367i | \(0.550650\pi\) | |||||||
\(462\) | 5.35213 | + | 5.15053i | 0.0115847 | + | 0.0111483i | ||||
\(463\) | 3.64605 | + | 6.31515i | 0.00787484 | + | 0.0136396i | 0.869936 | − | 0.493165i | \(-0.164160\pi\) |
−0.862061 | + | 0.506804i | \(0.830827\pi\) | |||||||
\(464\) | 100.806i | 0.217254i | ||||||||
\(465\) | −1.74353 | − | 9.26674i | −0.00374953 | − | 0.0199285i | ||||
\(466\) | −459.543 | −0.986145 | ||||||||
\(467\) | 446.593 | + | 257.841i | 0.956303 | + | 0.552122i | 0.895033 | − | 0.445999i | \(-0.147152\pi\) |
0.0612697 | + | 0.998121i | \(0.480485\pi\) | |||||||
\(468\) | 38.7975 | − | 253.874i | 0.0829007 | − | 0.542466i | ||||
\(469\) | 73.2467 | + | 102.900i | 0.156176 | + | 0.219404i | ||||
\(470\) | −43.8779 | − | 25.3329i | −0.0933572 | − | 0.0538998i | ||||
\(471\) | −22.8654 | + | 4.30211i | −0.0485466 | + | 0.00913400i | ||||
\(472\) | −371.850 | + | 644.063i | −0.787817 | + | 1.36454i | ||||
\(473\) | 6.22747 | + | 3.59543i | 0.0131659 | + | 0.00760133i | ||||
\(474\) | 18.3016 | + | 97.2718i | 0.0386110 | + | 0.205215i | ||||
\(475\) | 324.509 | − | 562.066i | 0.683177 | − | 1.18330i | ||||
\(476\) | −148.563 | − | 67.8794i | −0.312107 | − | 0.142604i | ||||
\(477\) | 342.152 | + | 877.070i | 0.717301 | + | 1.83872i | ||||
\(478\) | −169.100 | + | 292.890i | −0.353767 | + | 0.612742i | ||||
\(479\) | − | 289.661i | − | 0.604720i | −0.953194 | − | 0.302360i | \(-0.902226\pi\) | ||
0.953194 | − | 0.302360i | \(-0.0977745\pi\) | |||||||
\(480\) | 90.8859 | − | 17.1001i | 0.189346 | − | 0.0356253i | ||||
\(481\) | −352.674 | −0.733209 | ||||||||
\(482\) | 229.543 | − | 132.527i | 0.476231 | − | 0.274952i | ||||
\(483\) | 118.730 | + | 411.358i | 0.245817 | + | 0.851673i | ||||
\(484\) | −112.002 | + | 193.994i | −0.231410 | + | 0.400814i | ||||
\(485\) | −147.720 | − | 85.2864i | −0.304578 | − | 0.175848i | ||||
\(486\) | 285.453 | + | 212.941i | 0.587352 | + | 0.438150i | ||||
\(487\) | −252.275 | − | 436.953i | −0.518018 | − | 0.897234i | −0.999781 | − | 0.0209323i | \(-0.993337\pi\) |
0.481763 | − | 0.876302i | \(-0.339997\pi\) | |||||||
\(488\) | −132.838 | + | 76.6943i | −0.272210 | + | 0.157161i | ||||
\(489\) | 766.335 | − | 144.185i | 1.56715 | − | 0.294858i | ||||
\(490\) | 27.1025 | − | 78.2149i | 0.0553113 | − | 0.159622i | ||||
\(491\) | −311.614 | + | 179.910i | −0.634651 | + | 0.366416i | −0.782551 | − | 0.622586i | \(-0.786082\pi\) |
0.147900 | + | 0.989002i | \(0.452749\pi\) | |||||||
\(492\) | 301.753 | − | 259.142i | 0.613320 | − | 0.526712i | ||||
\(493\) | 246.078 | 0.499144 | ||||||||
\(494\) | −536.134 | + | 309.537i | −1.08529 | + | 0.626594i | ||||
\(495\) | −0.378248 | + | 2.47509i | −0.000764137 | + | 0.00500019i | ||||
\(496\) | 14.0721 | 0.0283711 | ||||||||
\(497\) | −472.498 | − | 215.887i | −0.950701 | − | 0.434381i | ||||
\(498\) | 255.014 | + | 296.946i | 0.512076 | + | 0.596278i | ||||
\(499\) | −647.042 | −1.29668 | −0.648338 | − | 0.761352i | \(-0.724536\pi\) | ||||
−0.648338 | + | 0.761352i | \(0.724536\pi\) | |||||||
\(500\) | 89.9914 | + | 51.9566i | 0.179983 | + | 0.103913i | ||||
\(501\) | 318.293 | + | 111.742i | 0.635315 | + | 0.223037i | ||||
\(502\) | −118.610 | − | 205.438i | −0.236275 | − | 0.409240i | ||||
\(503\) | − | 183.191i | − | 0.364198i | −0.983280 | − | 0.182099i | \(-0.941711\pi\) | ||
0.983280 | − | 0.182099i | \(-0.0582891\pi\) | |||||||
\(504\) | −296.217 | + | 451.896i | −0.587732 | + | 0.896619i | ||||
\(505\) | 96.9847 | 0.192049 | ||||||||
\(506\) | −6.24528 | + | 3.60571i | −0.0123425 | + | 0.00712592i | ||||
\(507\) | −201.558 | + | 37.9230i | −0.397550 | + | 0.0747988i | ||||
\(508\) | 31.0635 | − | 53.8035i | 0.0611485 | − | 0.105912i | ||||
\(509\) | 867.180i | 1.70369i | 0.523792 | + | 0.851846i | \(0.324517\pi\) | ||||
−0.523792 | + | 0.851846i | \(0.675483\pi\) | |||||||
\(510\) | 11.8056 | + | 62.7460i | 0.0231483 | + | 0.123031i | ||||
\(511\) | −182.013 | + | 17.3465i | −0.356189 | + | 0.0339462i | ||||
\(512\) | 315.064i | 0.615359i | ||||||||
\(513\) | 25.4065 | + | 739.848i | 0.0495254 | + | 1.44220i | ||||
\(514\) | 55.4523 | + | 96.0462i | 0.107884 | + | 0.186860i | ||||
\(515\) | − | 67.9719i | − | 0.131984i | ||||||
\(516\) | −54.8388 | + | 156.207i | −0.106277 | + | 0.302727i | ||||
\(517\) | −3.61921 | − | 6.26865i | −0.00700040 | − | 0.0121251i | ||||
\(518\) | 213.596 | + | 97.5931i | 0.412347 | + | 0.188404i | ||||
\(519\) | 39.5911 | + | 13.8991i | 0.0762835 | + | 0.0267805i | ||||
\(520\) | −76.1573 | − | 131.908i | −0.146456 | − | 0.253670i | ||||
\(521\) | −60.2047 | + | 34.7592i | −0.115556 | + | 0.0667163i | −0.556664 | − | 0.830738i | \(-0.687919\pi\) |
0.441108 | + | 0.897454i | \(0.354586\pi\) | |||||||
\(522\) | 38.9211 | − | 254.683i | 0.0745614 | − | 0.487898i | ||||
\(523\) | −356.425 | + | 617.347i | −0.681502 | + | 1.18040i | 0.293021 | + | 0.956106i | \(0.405339\pi\) |
−0.974523 | + | 0.224290i | \(0.927994\pi\) | |||||||
\(524\) | −114.686 | − | 66.2137i | −0.218866 | − | 0.126362i | ||||
\(525\) | −477.601 | + | 137.849i | −0.909717 | + | 0.262570i | ||||
\(526\) | −8.53426 | − | 14.7818i | −0.0162248 | − | 0.0281022i | ||||
\(527\) | − | 34.3515i | − | 0.0651831i | ||||||
\(528\) | −3.52569 | − | 1.23775i | −0.00667744 | − | 0.00234422i | ||||
\(529\) | 113.326 | 0.214227 | ||||||||
\(530\) | 153.038 | + | 88.3566i | 0.288751 | + | 0.166711i | ||||
\(531\) | 487.827 | − | 609.152i | 0.918695 | − | 1.14718i | ||||
\(532\) | −353.876 | + | 33.7257i | −0.665180 | + | 0.0633941i | ||||
\(533\) | −955.109 | − | 551.432i | −1.79195 | − | 1.03458i | ||||
\(534\) | 164.539 | + | 191.594i | 0.308126 | + | 0.358791i | ||||
\(535\) | −51.1992 | + | 88.6796i | −0.0956994 | + | 0.165756i | ||||
\(536\) | −134.023 | − | 77.3781i | −0.250042 | − | 0.144362i | ||||
\(537\) | −144.212 | − | 50.6280i | −0.268552 | − | 0.0942793i | ||||
\(538\) | −225.052 | + | 389.801i | −0.418312 | + | 0.724537i | ||||
\(539\) | 8.94040 | − | 7.74117i | 0.0165870 | − | 0.0143621i | ||||
\(540\) | −57.6110 | + | 1.97837i | −0.106687 | + | 0.00366366i | ||||
\(541\) | 180.101 | − | 311.944i | 0.332904 | − | 0.576607i | −0.650176 | − | 0.759784i | \(-0.725305\pi\) |
0.983080 | + | 0.183177i | \(0.0586381\pi\) | |||||||
\(542\) | 495.468i | 0.914148i | ||||||||
\(543\) | −468.666 | − | 545.729i | −0.863105 | − | 1.00503i | ||||
\(544\) | 336.911 | 0.619322 | ||||||||
\(545\) | 188.595 | − | 108.885i | 0.346046 | − | 0.199790i | ||||
\(546\) | 460.277 | + | 113.910i | 0.842998 | + | 0.208626i | ||||
\(547\) | −47.0212 | + | 81.4432i | −0.0859620 | + | 0.148891i | −0.905801 | − | 0.423704i | \(-0.860730\pi\) |
0.819839 | + | 0.572595i | \(0.194063\pi\) | |||||||
\(548\) | 347.695 | + | 200.742i | 0.634479 | + | 0.366317i | ||||
\(549\) | 149.954 | − | 58.4983i | 0.273140 | − | 0.106554i | ||||
\(550\) | −4.18636 | − | 7.25099i | −0.00761157 | − | 0.0131836i | ||||
\(551\) | 463.805 | − | 267.778i | 0.841752 | − | 0.485986i | ||||
\(552\) | −341.772 | − | 397.970i | −0.619151 | − | 0.720959i | ||||
\(553\) | 156.875 | − | 14.9508i | 0.283680 | − | 0.0270358i | ||||
\(554\) | 167.562 | − | 96.7422i | 0.302459 | − | 0.174625i | ||||
\(555\) | 14.6370 | + | 77.7945i | 0.0263729 | + | 0.140170i | ||||
\(556\) | −198.935 | −0.357797 | ||||||||
\(557\) | −516.609 | + | 298.264i | −0.927484 | + | 0.535483i | −0.886015 | − | 0.463657i | \(-0.846537\pi\) |
−0.0414691 | + | 0.999140i | \(0.513204\pi\) | |||||||
\(558\) | −35.5527 | − | 5.43322i | −0.0637145 | − | 0.00973696i | ||||
\(559\) | 459.033 | 0.821168 | ||||||||
\(560\) | 3.95072 | + | 41.4540i | 0.00705486 | + | 0.0740250i | ||||
\(561\) | −3.02148 | + | 8.60660i | −0.00538588 | + | 0.0153415i | ||||
\(562\) | 108.784 | 0.193567 | ||||||||
\(563\) | −627.192 | − | 362.110i | −1.11402 | − | 0.643179i | −0.174151 | − | 0.984719i | \(-0.555718\pi\) |
−0.939867 | + | 0.341540i | \(0.889051\pi\) | |||||||
\(564\) | 126.426 | − | 108.573i | 0.224159 | − | 0.192505i | ||||
\(565\) | −67.2936 | − | 116.556i | −0.119104 | − | 0.206294i | ||||
\(566\) | 16.5652i | 0.0292671i | ||||||||
\(567\) | 378.908 | − | 421.803i | 0.668269 | − | 0.743920i | ||||
\(568\) | 636.487 | 1.12058 | ||||||||
\(569\) | 284.852 | − | 164.459i | 0.500619 | − | 0.289032i | −0.228350 | − | 0.973579i | \(-0.573333\pi\) |
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(570\) | 90.5303 | + | 105.416i | 0.158825 | + | 0.184941i | ||||
\(571\) | −3.75701 | + | 6.50734i | −0.00657971 | + | 0.0113964i | −0.869297 | − | 0.494291i | \(-0.835428\pi\) |
0.862717 | + | 0.505687i | \(0.168761\pi\) | |||||||
\(572\) | − | 6.88707i | − | 0.0120403i | ||||||
\(573\) | −520.387 | − | 182.690i | −0.908179 | − | 0.318830i | ||||
\(574\) | 425.864 | + | 598.274i | 0.741923 | + | 1.04229i | ||||
\(575\) | − | 482.612i | − | 0.839325i | ||||||
\(576\) | 81.3543 | − | 532.348i | 0.141240 | − | 0.924215i | ||||
\(577\) | −367.284 | − | 636.154i | −0.636540 | − | 1.10252i | −0.986187 | − | 0.165638i | \(-0.947032\pi\) |
0.349647 | − | 0.936882i | \(-0.386302\pi\) | |||||||
\(578\) | − | 190.946i | − | 0.330356i | ||||||
\(579\) | −450.487 | + | 84.7588i | −0.778043 | + | 0.146388i | ||||
\(580\) | 20.8515 | + | 36.1159i | 0.0359509 | + | 0.0622688i | ||||
\(581\) | 507.701 | − | 361.392i | 0.873839 | − | 0.622017i | ||||
\(582\) | −493.571 | + | 423.873i | −0.848061 | + | 0.728304i | ||||
\(583\) | 12.6232 | + | 21.8639i | 0.0216521 | + | 0.0375025i | ||||
\(584\) | 194.006 | − | 112.009i | 0.332202 | − | 0.191797i | ||||
\(585\) | 58.0887 | + | 148.904i | 0.0992970 | + | 0.254537i | ||||
\(586\) | 121.954 | − | 211.230i | 0.208112 | − | 0.360461i | ||||
\(587\) | 125.855 | + | 72.6624i | 0.214404 | + | 0.123786i | 0.603356 | − | 0.797472i | \(-0.293830\pi\) |
−0.388953 | + | 0.921258i | \(0.627163\pi\) | |||||||
\(588\) | 213.209 | + | 169.329i | 0.362601 | + | 0.287974i | ||||
\(589\) | −37.3807 | − | 64.7453i | −0.0634647 | − | 0.109924i | ||||
\(590\) | − | 146.486i | − | 0.248282i | ||||||
\(591\) | −878.521 | + | 754.463i | −1.48650 | + | 1.27659i | ||||
\(592\) | −118.135 | −0.199553 | ||||||||
\(593\) | −248.428 | − | 143.430i | −0.418934 | − | 0.241872i | 0.275687 | − | 0.961247i | \(-0.411095\pi\) |
−0.694621 | + | 0.719376i | \(0.744428\pi\) | |||||||
\(594\) | 8.42965 | + | 4.48840i | 0.0141913 | + | 0.00755623i | ||||
\(595\) | 101.194 | − | 9.64414i | 0.170074 | − | 0.0162086i | ||||
\(596\) | 251.974 | + | 145.477i | 0.422776 | + | 0.244090i | ||||
\(597\) | 45.3913 | − | 129.296i | 0.0760323 | − | 0.216576i | ||||
\(598\) | −230.173 | + | 398.671i | −0.384905 | + | 0.666674i | ||||
\(599\) | 605.878 | + | 349.804i | 1.01148 | + | 0.583980i | 0.911626 | − | 0.411022i | \(-0.134828\pi\) |
0.0998576 | + | 0.995002i | \(0.468161\pi\) | |||||||
\(600\) | 462.057 | − | 396.809i | 0.770095 | − | 0.661348i | ||||
\(601\) | 58.2075 | − | 100.818i | 0.0968511 | − | 0.167751i | −0.813529 | − | 0.581525i | \(-0.802456\pi\) |
0.910380 | + | 0.413774i | \(0.135790\pi\) | |||||||
\(602\) | −278.012 | − | 127.025i | −0.461813 | − | 0.211005i | ||||
\(603\) | 126.758 | + | 101.512i | 0.210212 | + | 0.168345i | ||||
\(604\) | 111.577 | − | 193.257i | 0.184730 | − | 0.319962i | ||||
\(605\) | − | 139.410i | − | 0.230429i | ||||||
\(606\) | 122.534 | − | 349.036i | 0.202202 | − | 0.575967i | ||||
\(607\) | 642.310 | 1.05817 | 0.529086 | − | 0.848568i | \(-0.322535\pi\) | ||||
0.529086 | + | 0.848568i | \(0.322535\pi\) | |||||||
\(608\) | 635.007 | − | 366.621i | 1.04442 | − | 0.602996i | ||||
\(609\) | −398.182 | − | 98.5426i | −0.653829 | − | 0.161811i | ||||
\(610\) | 15.1065 | − | 26.1652i | 0.0247647 | − | 0.0428937i | ||||
\(611\) | −400.163 | − | 231.034i | −0.654932 | − | 0.378125i | ||||
\(612\) | −207.593 | − | 31.7248i | −0.339205 | − | 0.0518378i | ||||
\(613\) | 257.842 | + | 446.595i | 0.420623 | + | 0.728540i | 0.996000 | − | 0.0893481i | \(-0.0284783\pi\) |
−0.575378 | + | 0.817888i | \(0.695145\pi\) | |||||||
\(614\) | 486.081 | − | 280.639i | 0.791663 | − | 0.457067i | ||||
\(615\) | −81.9978 | + | 233.569i | −0.133330 | + | 0.379786i | ||||
\(616\) | −6.02166 | + | 13.1792i | −0.00977542 | + | 0.0213948i | ||||
\(617\) | 352.937 | − | 203.768i | 0.572021 | − | 0.330257i | −0.185935 | − | 0.982562i | \(-0.559531\pi\) |
0.757956 | + | 0.652305i | \(0.226198\pi\) | |||||||
\(618\) | −244.623 | − | 85.8785i | −0.395829 | − | 0.138962i | ||||
\(619\) | −42.3520 | −0.0684201 | −0.0342100 | − | 0.999415i | \(-0.510892\pi\) | ||||
−0.0342100 | + | 0.999415i | \(0.510892\pi\) | |||||||
\(620\) | 5.04163 | − | 2.91079i | 0.00813167 | − | 0.00469482i | ||||
\(621\) | 291.438 | + | 467.001i | 0.469305 | + | 0.752015i | ||||
\(622\) | 228.641 | 0.367590 | ||||||||
\(623\) | 327.576 | − | 233.176i | 0.525805 | − | 0.374279i | ||||
\(624\) | −234.418 | + | 44.1055i | −0.375670 | + | 0.0706820i | ||||
\(625\) | 527.112 | 0.843378 | ||||||||
\(626\) | 147.900 | + | 85.3902i | 0.236262 | + | 0.136406i | ||||
\(627\) | 3.67071 | + | 19.5095i | 0.00585440 | + | 0.0311157i | ||||
\(628\) | −7.18230 | − | 12.4401i | −0.0114368 | − | 0.0198091i | ||||
\(629\) | 288.382i | 0.458476i | ||||||||
\(630\) | 6.02399 | − | 106.258i | 0.00956190 | − | 0.168663i | ||||
\(631\) | −534.410 | −0.846926 | −0.423463 | − | 0.905914i | \(-0.639186\pi\) | ||||
−0.423463 | + | 0.905914i | \(0.639186\pi\) | |||||||
\(632\) | −167.212 | + | 96.5399i | −0.264576 | + | 0.152753i | ||||
\(633\) | 336.555 | − | 958.668i | 0.531683 | − | 1.51448i | ||||
\(634\) | 137.661 | − | 238.435i | 0.217130 | − | 0.376081i | ||||
\(635\) | 38.6648i | 0.0608894i | ||||||||
\(636\) | −440.951 | + | 378.684i | −0.693319 | + | 0.595414i | ||||
\(637\) | 247.173 | − | 713.315i | 0.388027 | − | 1.11980i | ||||
\(638\) | − | 6.90900i | − | 0.0108292i | ||||||
\(639\) | −660.241 | − | 100.899i | −1.03324 | − | 0.157902i | ||||
\(640\) | 11.1117 | + | 19.2461i | 0.0173621 | + | 0.0300720i | ||||
\(641\) | − | 350.735i | − | 0.547169i | −0.961848 | − | 0.273584i | \(-0.911791\pi\) | ||
0.961848 | − | 0.273584i | \(-0.0882093\pi\) | |||||||
\(642\) | 254.460 | + | 296.301i | 0.396355 | + | 0.461528i | ||||
\(643\) | −329.068 | − | 569.963i | −0.511770 | − | 0.886412i | −0.999907 | − | 0.0136450i | \(-0.995657\pi\) |
0.488137 | − | 0.872767i | \(-0.337677\pi\) | |||||||
\(644\) | −215.349 | + | 153.290i | −0.334393 | + | 0.238028i | ||||
\(645\) | −19.0512 | − | 101.256i | −0.0295367 | − | 0.156986i | ||||
\(646\) | 253.109 | + | 438.397i | 0.391809 | + | 0.678634i | ||||
\(647\) | −482.718 | + | 278.697i | −0.746087 | + | 0.430753i | −0.824278 | − | 0.566185i | \(-0.808419\pi\) |
0.0781915 | + | 0.996938i | \(0.475085\pi\) | |||||||
\(648\) | −207.487 | + | 662.999i | −0.320196 | + | 1.02315i | ||||
\(649\) | 10.4640 | − | 18.1241i | 0.0161232 | − | 0.0279262i | ||||
\(650\) | −462.871 | − | 267.239i | −0.712110 | − | 0.411137i | ||||
\(651\) | −13.7561 | + | 55.5845i | −0.0211308 | + | 0.0853833i | ||||
\(652\) | 240.715 | + | 416.930i | 0.369194 | + | 0.639464i | ||||
\(653\) | − | 182.445i | − | 0.279395i | −0.990194 | − | 0.139697i | \(-0.955387\pi\) | ||
0.990194 | − | 0.139697i | \(-0.0446130\pi\) | |||||||
\(654\) | −153.586 | − | 816.300i | −0.234841 | − | 1.24816i | ||||
\(655\) | 82.4164 | 0.125827 | ||||||||
\(656\) | −319.934 | − | 184.714i | −0.487704 | − | 0.281576i | ||||
\(657\) | −219.002 | + | 85.4347i | −0.333337 | + | 0.130038i | ||||
\(658\) | 178.425 | + | 250.660i | 0.271162 | + | 0.380942i | ||||
\(659\) | −10.7149 | − | 6.18625i | −0.0162593 | − | 0.00938733i | 0.491848 | − | 0.870681i | \(-0.336321\pi\) |
−0.508108 | + | 0.861294i | \(0.669655\pi\) | |||||||
\(660\) | −1.51918 | + | 0.285833i | −0.00230179 | + | 0.000433081i | ||||
\(661\) | 265.629 | − | 460.083i | 0.401860 | − | 0.696041i | −0.592091 | − | 0.805871i | \(-0.701697\pi\) |
0.993950 | + | 0.109830i | \(0.0350307\pi\) | |||||||
\(662\) | −80.5081 | − | 46.4814i | −0.121613 | − | 0.0702136i | ||||
\(663\) | 107.666 | + | 572.240i | 0.162393 | + | 0.863106i | ||||
\(664\) | −381.776 | + | 661.255i | −0.574963 | + | 0.995866i | ||||
\(665\) | 180.234 | − | 128.295i | 0.271029 | − | 0.192924i | ||||
\(666\) | 298.466 | + | 45.6120i | 0.448146 | + | 0.0684865i | ||||
\(667\) | 199.121 | − | 344.887i | 0.298532 | − | 0.517072i | ||||
\(668\) | 208.269i | 0.311780i | ||||||||
\(669\) | 258.670 | − | 48.6685i | 0.386651 | − | 0.0727482i | ||||
\(670\) | 30.4823 | 0.0454959 | ||||||||
\(671\) | 3.73811 | − | 2.15820i | 0.00557096 | − | 0.00321639i | ||||
\(672\) | −545.160 | − | 134.917i | −0.811250 | − | 0.200769i | ||||
\(673\) | −29.8818 | + | 51.7568i | −0.0444009 | + | 0.0769046i | −0.887372 | − | 0.461055i | \(-0.847471\pi\) |
0.842971 | + | 0.537959i | \(0.180805\pi\) | |||||||
\(674\) | −224.407 | − | 129.561i | −0.332948 | − | 0.192228i | ||||
\(675\) | −542.205 | + | 338.370i | −0.803266 | + | 0.501289i | ||||
\(676\) | −63.3117 | − | 109.659i | −0.0936564 | − | 0.162218i | ||||
\(677\) | −797.131 | + | 460.224i | −1.17745 | + | 0.679799i | −0.955422 | − | 0.295243i | \(-0.904599\pi\) |
−0.222023 | + | 0.975041i | \(0.571266\pi\) | |||||||
\(678\) | −504.491 | + | 94.9197i | −0.744088 | + | 0.140000i | ||||
\(679\) | 600.690 | + | 843.878i | 0.884668 | + | 1.24282i | ||||
\(680\) | −107.862 | + | 62.2739i | −0.158620 | + | 0.0915793i | ||||
\(681\) | −802.708 | + | 689.356i | −1.17872 | + | 1.01227i | ||||
\(682\) | −0.964468 | −0.00141418 | ||||||||
\(683\) | 487.711 | − | 281.580i | 0.714071 | − | 0.412269i | −0.0984954 | − | 0.995138i | \(-0.531403\pi\) |
0.812567 | + | 0.582868i | \(0.198070\pi\) | |||||||
\(684\) | −425.792 | + | 166.105i | −0.622503 | + | 0.242844i | ||||
\(685\) | −249.864 | −0.364764 | ||||||||
\(686\) | −347.091 | + | 363.618i | −0.505963 | + | 0.530055i | ||||
\(687\) | −744.267 | − | 866.648i | −1.08336 | − | 1.26150i | ||||
\(688\) | 153.763 | 0.223492 | ||||||||
\(689\) | 1395.70 | + | 805.807i | 2.02569 | + | 1.16953i | ||||
\(690\) | 97.4937 | + | 34.2267i | 0.141295 | + | 0.0496038i | ||||
\(691\) | −210.654 | − | 364.864i | −0.304854 | − | 0.528023i | 0.672375 | − | 0.740211i | \(-0.265274\pi\) |
−0.977229 | + | 0.212188i | \(0.931941\pi\) | |||||||
\(692\) | 25.9057i | 0.0374360i | ||||||||
\(693\) | 8.33562 | − | 12.7165i | 0.0120283 | − | 0.0183499i | ||||
\(694\) | −356.572 | −0.513792 | ||||||||
\(695\) | 107.220 | − | 61.9038i | 0.154274 | − | 0.0890702i | ||||
\(696\) | 493.917 | − | 92.9302i | 0.709651 | − | 0.133520i | ||||
\(697\) | −450.907 | + | 780.993i | −0.646925 | + | 1.12051i | ||||
\(698\) | − | 614.557i | − | 0.880454i | ||||||
\(699\) | 173.939 | + | 924.472i | 0.248840 | + | 1.32256i | ||||
\(700\) | −177.975 | − | 250.028i | −0.254250 | − | 0.357183i | ||||
\(701\) | 523.850i | 0.747289i | 0.927572 | + | 0.373645i | \(0.121892\pi\) | ||||
−0.927572 | + | 0.373645i | \(0.878108\pi\) | |||||||
\(702\) | 609.279 | − | 20.9228i | 0.867918 | − | 0.0298045i | ||||
\(703\) | 313.812 | + | 543.539i | 0.446390 | + | 0.773170i | ||||
\(704\) | − | 14.4415i | − | 0.0205134i | ||||||
\(705\) | −34.3547 | + | 97.8585i | −0.0487301 | + | 0.138806i | ||||
\(706\) | 254.904 | + | 441.506i | 0.361053 | + | 0.625363i | ||||
\(707\) | −535.691 | − | 244.760i | −0.757695 | − | 0.346196i | ||||
\(708\) | 454.617 | + | 159.600i | 0.642114 | + | 0.225424i | ||||
\(709\) | −33.9678 | − | 58.8340i | −0.0479095 | − | 0.0829817i | 0.841076 | − | 0.540917i | \(-0.181923\pi\) |
−0.888986 | + | 0.457935i | \(0.848589\pi\) | |||||||
\(710\) | −108.573 | + | 62.6844i | −0.152919 | + | 0.0882878i | ||||
\(711\) | 188.756 | − | 73.6354i | 0.265480 | − | 0.103566i | ||||
\(712\) | −246.328 | + | 426.652i | −0.345966 | + | 0.599230i | ||||
\(713\) | −48.1449 | − | 27.7964i | −0.0675243 | − | 0.0389852i | ||||
\(714\) | 93.1443 | − | 376.369i | 0.130454 | − | 0.527127i | ||||
\(715\) | 2.14309 | + | 3.71194i | 0.00299733 | + | 0.00519152i | ||||
\(716\) | − | 94.3626i | − | 0.131791i | ||||||
\(717\) | 653.218 | + | 229.322i | 0.911044 | + | 0.319836i | ||||
\(718\) | 663.764 | 0.924462 | ||||||||
\(719\) | −766.286 | − | 442.415i | −1.06577 | − | 0.615321i | −0.138745 | − | 0.990328i | \(-0.544307\pi\) |
−0.927022 | + | 0.375008i | \(0.877640\pi\) | |||||||
\(720\) | 19.4580 | + | 49.8785i | 0.0270250 | + | 0.0692757i | ||||
\(721\) | −171.541 | + | 375.440i | −0.237921 | + | 0.520721i | ||||
\(722\) | 495.932 | + | 286.327i | 0.686887 | + | 0.396574i | ||||
\(723\) | −353.490 | − | 411.615i | −0.488921 | − | 0.569315i | ||||
\(724\) | 222.061 | − | 384.620i | 0.306714 | − | 0.531244i | ||||
\(725\) | 400.426 | + | 231.186i | 0.552312 | + | 0.318878i | ||||
\(726\) | −501.718 | − | 176.136i | −0.691072 | − | 0.242611i | ||||
\(727\) | −228.413 | + | 395.623i | −0.314186 | + | 0.544186i | −0.979264 | − | 0.202588i | \(-0.935065\pi\) |
0.665078 | + | 0.746774i | \(0.268398\pi\) | |||||||
\(728\) | 87.7545 | + | 920.788i | 0.120542 | + | 1.26482i | ||||
\(729\) | 320.332 | − | 654.850i | 0.439413 | − | 0.898285i | ||||
\(730\) | −22.0625 | + | 38.2133i | −0.0302225 | + | 0.0523470i | ||||
\(731\) | − | 375.351i | − | 0.513477i | ||||||
\(732\) | 64.7441 | + | 75.3901i | 0.0884482 | + | 0.102992i | ||||
\(733\) | −105.338 | −0.143709 | −0.0718543 | − | 0.997415i | \(-0.522892\pi\) | ||||
−0.0718543 | + | 0.997415i | \(0.522892\pi\) | |||||||
\(734\) | 4.06094 | − | 2.34458i | 0.00553261 | − | 0.00319426i | ||||
\(735\) | −167.605 | − | 24.9180i | −0.228034 | − | 0.0339021i | ||||
\(736\) | 272.621 | − | 472.193i | 0.370409 | − | 0.641567i | ||||
\(737\) | 3.77144 | + | 2.17744i | 0.00511728 | + | 0.00295446i | ||||
\(738\) | 736.985 | + | 590.200i | 0.998624 | + | 0.799729i | ||||
\(739\) | 169.442 | + | 293.482i | 0.229285 | + | 0.397133i | 0.957596 | − | 0.288113i | \(-0.0930279\pi\) |
−0.728311 | + | 0.685246i | \(0.759695\pi\) | |||||||
\(740\) | −42.3246 | + | 24.4361i | −0.0571955 | + | 0.0330218i | ||||
\(741\) | 825.631 | + | 961.390i | 1.11421 | + | 1.29742i | ||||
\(742\) | −622.314 | − | 874.256i | −0.838698 | − | 1.17824i | ||||
\(743\) | 200.529 | − | 115.776i | 0.269891 | − | 0.155822i | −0.358947 | − | 0.933358i | \(-0.616864\pi\) |
0.628838 | + | 0.777536i | \(0.283531\pi\) | |||||||
\(744\) | −12.9727 | − | 68.9488i | −0.0174364 | − | 0.0926732i | ||||
\(745\) | −181.076 | −0.243055 | ||||||||
\(746\) | 189.673 | − | 109.508i | 0.254254 | − | 0.146793i | ||||
\(747\) | 500.849 | − | 625.412i | 0.670480 | − | 0.837231i | ||||
\(748\) | −5.63156 | −0.00752883 | ||||||||
\(749\) | 506.597 | − | 360.606i | 0.676364 | − | 0.481450i | ||||
\(750\) | −81.7073 | + | 232.741i | −0.108943 | + | 0.310321i | ||||
\(751\) | −122.582 | −0.163225 | −0.0816127 | − | 0.996664i | \(-0.526007\pi\) | ||||
−0.0816127 | + | 0.996664i | \(0.526007\pi\) | |||||||
\(752\) | −134.043 | − | 77.3898i | −0.178249 | − | 0.102912i | ||||
\(753\) | −368.390 | + | 316.369i | −0.489230 | + | 0.420145i | ||||
\(754\) | −220.520 | − | 381.952i | −0.292467 | − | 0.506568i | ||||
\(755\) | 138.880i | 0.183947i | ||||||||
\(756\) | 323.205 | + | 134.465i | 0.427519 | + | 0.177864i | ||||
\(757\) | 162.273 | 0.214363 | 0.107181 | − | 0.994239i | \(-0.465817\pi\) | ||||
0.107181 | + | 0.994239i | \(0.465817\pi\) | |||||||
\(758\) | −547.301 | + | 315.984i | −0.722033 | + | 0.416866i | ||||
\(759\) | 9.61755 | + | 11.1990i | 0.0126713 | + | 0.0147549i | ||||
\(760\) | −135.531 | + | 234.746i | −0.178330 | + | 0.308877i | ||||
\(761\) | − | 347.668i | − | 0.456857i | −0.973561 | − | 0.228429i | \(-0.926641\pi\) | ||
0.973561 | − | 0.228429i | \(-0.0733588\pi\) | |||||||
\(762\) | 139.150 | + | 48.8506i | 0.182611 | + | 0.0641084i | ||||
\(763\) | −1316.49 | + | 125.466i | −1.72541 | + | 0.164438i | ||||
\(764\) | − | 340.505i | − | 0.445687i | ||||||
\(765\) | 121.759 | − | 47.4992i | 0.159162 | − | 0.0620904i | ||||
\(766\) | −131.731 | − | 228.164i | −0.171972 | − | 0.297865i | ||||
\(767\) | − | 1335.95i | − | 1.74178i | ||||||
\(768\) | 788.960 | − | 148.442i | 1.02729 | − | 0.193284i | ||||
\(769\) | 21.9448 | + | 38.0094i | 0.0285367 | + | 0.0494271i | 0.879941 | − | 0.475083i | \(-0.157582\pi\) |
−0.851404 | + | 0.524510i | \(0.824249\pi\) | |||||||
\(770\) | −0.270774 | − | 2.84116i | −0.000351654 | − | 0.00368982i | ||||
\(771\) | 172.229 | − | 147.908i | 0.223384 | − | 0.191839i | ||||
\(772\) | −141.503 | − | 245.091i | −0.183294 | − | 0.317475i | ||||
\(773\) | 31.3486 | − | 18.0991i | 0.0405545 | − | 0.0234141i | −0.479586 | − | 0.877495i | \(-0.659213\pi\) |
0.520140 | + | 0.854081i | \(0.325880\pi\) | |||||||
\(774\) | −388.477 | − | 59.3677i | −0.501908 | − | 0.0767024i | ||||
\(775\) | 32.2727 | − | 55.8979i | 0.0416421 | − | 0.0721263i | ||||
\(776\) | −1099.11 | − | 634.571i | −1.41638 | − | 0.817746i | ||||
\(777\) | 115.483 | − | 466.634i | 0.148627 | − | 0.600558i | ||||
\(778\) | −247.053 | − | 427.908i | −0.317549 | − | 0.550010i | ||||
\(779\) | 1962.68i | 2.51948i | ||||||||
\(780\) | −74.8622 | + | 64.2908i | −0.0959772 | + | 0.0824241i | ||||
\(781\) | −17.9109 | −0.0229333 | ||||||||
\(782\) | 325.994 | + | 188.213i | 0.416872 | + | 0.240681i | ||||
\(783\) | −527.082 | + | 18.1001i | −0.673157 | + | 0.0231164i | ||||
\(784\) | 82.7958 | − | 238.940i | 0.105607 | − | 0.304770i | ||||
\(785\) | 7.74211 | + | 4.46991i | 0.00986256 | + | 0.00569415i | ||||
\(786\) | 104.128 | − | 296.606i | 0.132479 | − | 0.377362i | ||||
\(787\) | 334.824 | − | 579.932i | 0.425443 | − | 0.736890i | −0.571018 | − | 0.820937i | \(-0.693451\pi\) |
0.996462 | + | 0.0840478i | \(0.0267848\pi\) | |||||||
\(788\) | −619.166 | − | 357.476i | −0.785744 | − | 0.453649i | ||||
\(789\) | −26.5065 | + | 22.7635i | −0.0335951 | + | 0.0288511i | ||||
\(790\) | 19.0154 | − | 32.9357i | 0.0240702 | − | 0.0416908i | ||||
\(791\) | 77.5410 | + | 813.620i | 0.0980291 | + | 1.02860i | ||||
\(792\) | −2.81434 | + | 18.4158i | −0.00355346 | + | 0.0232523i | ||||
\(793\) | 137.770 | − | 238.625i | 0.173733 | − | 0.300914i | ||||
\(794\) | − | 782.171i | − | 0.985102i | ||||||
\(795\) | 119.823 | − | 341.313i | 0.150721 | − | 0.429325i | ||||
\(796\) | 84.6022 | 0.106284 | ||||||||
\(797\) | 12.4445 | − | 7.18485i | 0.0156142 | − | 0.00901487i | −0.492173 | − | 0.870498i | \(-0.663797\pi\) |
0.507787 | + | 0.861483i | \(0.330464\pi\) | |||||||
\(798\) | −234.001 | − | 810.734i | −0.293234 | − | 1.01596i | ||||
\(799\) | −188.917 | + | 327.214i | −0.236442 | + | 0.409529i | ||||
\(800\) | 548.233 | + | 316.523i | 0.685291 | + | 0.395653i | ||||
\(801\) | 323.156 | − | 403.525i | 0.403440 | − | 0.503777i | ||||
\(802\) | 444.231 | + | 769.431i | 0.553904 | + | 0.959390i | ||||
\(803\) | −5.45938 | + | 3.15197i | −0.00679873 | + | 0.00392525i | ||||
\(804\) | −33.2111 | + | 94.6010i | −0.0413074 | + | 0.117663i | ||||
\(805\) | 68.3671 | − | 149.631i | 0.0849281 | − | 0.185877i | ||||
\(806\) | −53.3190 | + | 30.7837i | −0.0661526 | + | 0.0381932i | ||||
\(807\) | 869.353 | + | 305.200i | 1.07727 | + | 0.378190i | ||||
\(808\) | 721.611 | 0.893084 | ||||||||
\(809\) | −134.305 | + | 77.5408i | −0.166013 | + | 0.0958478i | −0.580705 | − | 0.814114i | \(-0.697223\pi\) |
0.414691 | + | 0.909962i | \(0.363890\pi\) | |||||||
\(810\) | −29.9021 | − | 133.529i | −0.0369161 | − | 0.164851i | ||||
\(811\) | −758.588 | −0.935374 | −0.467687 | − | 0.883894i | \(-0.654913\pi\) | ||||
−0.467687 | + | 0.883894i | \(0.654913\pi\) | |||||||
\(812\) | −24.0268 | − | 252.108i | −0.0295897 | − | 0.310477i | ||||
\(813\) | 996.743 | − | 187.537i | 1.22601 | − | 0.230672i | ||||
\(814\) | 8.09674 | 0.00994685 | ||||||||
\(815\) | −259.477 | − | 149.809i | −0.318377 | − | 0.183815i | ||||
\(816\) | 36.0651 | + | 191.684i | 0.0441975 | + | 0.234906i | ||||
\(817\) | −408.451 | − | 707.459i | −0.499941 | − | 0.865922i | ||||
\(818\) | 574.660i | 0.702518i | ||||||||
\(819\) | 54.9384 | − | 969.063i | 0.0670799 | − | 1.18323i | ||||
\(820\) | −152.831 | −0.186379 | ||||||||
\(821\) | 195.171 | − | 112.682i | 0.237724 | − | 0.137250i | −0.376406 | − | 0.926455i | \(-0.622840\pi\) |
0.614130 | + | 0.789205i | \(0.289507\pi\) | |||||||
\(822\) | −315.688 | + | 899.228i | −0.384048 | + | 1.09395i | ||||
\(823\) | −299.847 | + | 519.350i | −0.364334 | + | 0.631045i | −0.988669 | − | 0.150112i | \(-0.952037\pi\) |
0.624335 | + | 0.781157i | \(0.285370\pi\) | |||||||
\(824\) | − | 505.743i | − | 0.613766i | ||||||
\(825\) | −13.0024 | + | 11.1663i | −0.0157605 | + | 0.0135349i | ||||
\(826\) | −369.688 | + | 809.111i | −0.447564 | + | 0.979553i | ||||
\(827\) | 634.083i | 0.766727i | 0.923598 | + | 0.383363i | \(0.125234\pi\) | ||||
−0.923598 | + | 0.383363i | \(0.874766\pi\) | |||||||
\(828\) | −212.443 | + | 265.278i | −0.256574 | + | 0.320385i | ||||
\(829\) | −376.723 | − | 652.503i | −0.454431 | − | 0.787097i | 0.544225 | − | 0.838940i | \(-0.316824\pi\) |
−0.998655 | + | 0.0518425i | \(0.983491\pi\) | |||||||
\(830\) | − | 150.397i | − | 0.181201i | ||||||
\(831\) | −258.041 | − | 300.471i | −0.310519 | − | 0.361578i | ||||
\(832\) | −460.940 | − | 798.371i | −0.554014 | − | 0.959581i | ||||
\(833\) | −583.278 | − | 202.114i | −0.700214 | − | 0.242633i | ||||
\(834\) | −87.3173 | − | 464.085i | −0.104697 | − | 0.556457i | ||||
\(835\) | −64.8082 | − | 112.251i | −0.0776146 | − | 0.134432i | ||||
\(836\) | −10.6143 | + | 6.12817i | −0.0126965 | + | 0.00733035i | ||||
\(837\) | 2.52670 | + | 73.5785i | 0.00301876 | + | 0.0879074i | ||||
\(838\) | 488.497 | − | 846.102i | 0.582932 | − | 1.00967i | ||||
\(839\) | 953.473 | + | 550.488i | 1.13644 | + | 0.656124i | 0.945547 | − | 0.325487i | \(-0.105528\pi\) |
0.190893 | + | 0.981611i | \(0.438862\pi\) | |||||||
\(840\) | 199.470 | − | 57.5727i | 0.237464 | − | 0.0685389i | ||||
\(841\) | −229.730 | − | 397.904i | −0.273163 | − | 0.473132i | ||||
\(842\) | 690.675i | 0.820279i | ||||||||
\(843\) | −41.1753 | − | 218.844i | −0.0488438 | − | 0.259601i | ||||
\(844\) | 627.286 | 0.743230 | ||||||||
\(845\) | 68.2465 | + | 39.4021i | 0.0807651 | + | 0.0466297i | ||||
\(846\) | 308.776 | + | 247.277i | 0.364983 | + | 0.292289i | ||||
\(847\) | −351.828 | + | 770.023i | −0.415381 | + | 0.909118i | ||||
\(848\) | 467.518 | + | 269.922i | 0.551318 | + | 0.318304i | ||||
\(849\) | 33.3244 | − | 6.26997i | 0.0392514 | − | 0.00738512i | ||||
\(850\) | −218.521 | + | 378.490i | −0.257084 | + | 0.445283i | ||||
\(851\) | 404.177 | + | 233.352i | 0.474944 | + | 0.274209i | ||||
\(852\) | −76.2472 | − | 405.248i | −0.0894920 | − | 0.475643i | ||||
\(853\) | 161.623 | − | 279.939i | 0.189476 | − | 0.328181i | −0.755600 | − | 0.655033i | \(-0.772655\pi\) |
0.945076 | + | 0.326852i | \(0.105988\pi\) | |||||||
\(854\) | −149.473 | + | 106.398i | −0.175027 | + | 0.124588i | ||||
\(855\) | 177.802 | − | 222.022i | 0.207956 | − | 0.259675i | ||||
\(856\) | −380.946 | + | 659.817i | −0.445030 | + | 0.770815i | ||||
\(857\) | 1303.35i | 1.52083i | 0.649439 | + | 0.760414i | \(0.275004\pi\) | ||||
−0.649439 | + | 0.760414i | \(0.724996\pi\) | |||||||
\(858\) | 16.0665 | − | 3.02290i | 0.0187255 | − | 0.00352319i | ||||
\(859\) | −175.654 | −0.204486 | −0.102243 | − | 0.994759i | \(-0.532602\pi\) | ||||
−0.102243 | + | 0.994759i | \(0.532602\pi\) | |||||||
\(860\) | 55.0889 | − | 31.8056i | 0.0640568 | − | 0.0369832i | ||||
\(861\) | 1042.37 | − | 1083.17i | 1.21065 | − | 1.25803i | ||||
\(862\) | 172.932 | − | 299.527i | 0.200617 | − | 0.347479i | ||||
\(863\) | −289.608 | − | 167.205i | −0.335582 | − | 0.193749i | 0.322734 | − | 0.946490i | \(-0.395398\pi\) |
−0.658317 | + | 0.752741i | \(0.728731\pi\) | |||||||
\(864\) | −721.640 | + | 24.7813i | −0.835232 | + | 0.0286820i | ||||
\(865\) | −8.06122 | − | 13.9624i | −0.00931933 | − | 0.0161416i | ||||
\(866\) | −492.836 | + | 284.539i | −0.569094 | + | 0.328567i | ||||
\(867\) | −384.129 | + | 72.2736i | −0.443056 | + | 0.0833606i | ||||
\(868\) | −35.1932 | + | 3.35404i | −0.0405452 | + | 0.00386410i | ||||
\(869\) | 4.70539 | − | 2.71666i | 0.00541472 | − | 0.00312619i | ||||
\(870\) | −75.1006 | + | 64.4955i | −0.0863226 | + | 0.0741328i | ||||
\(871\) | 277.996 | 0.319169 | ||||||||
\(872\) | 1403.23 | − | 810.157i | 1.60921 | − | 0.929080i | ||||
\(873\) | 1039.53 | + | 832.489i | 1.19076 | + | 0.953596i | ||||
\(874\) | 819.240 | 0.937345 | ||||||||
\(875\) | 357.204 | + | 163.209i | 0.408234 | + | 0.186524i | ||||
\(876\) | −94.5564 | − | 110.105i | −0.107941 | − | 0.125690i | ||||
\(877\) | 791.230 | 0.902200 | 0.451100 | − | 0.892473i | \(-0.351032\pi\) | ||||
0.451100 | + | 0.892473i | \(0.351032\pi\) | |||||||
\(878\) | −445.891 | − | 257.435i | −0.507848 | − | 0.293206i | ||||
\(879\) | −471.096 | − | 165.385i | −0.535945 | − | 0.188152i | ||||
\(880\) | 0.717872 | + | 1.24339i | 0.000815764 | + | 0.00141294i | ||||
\(881\) | − | 307.622i | − | 0.349174i | −0.984642 | − | 0.174587i | \(-0.944141\pi\) | ||
0.984642 | − | 0.174587i | \(-0.0558591\pi\) | |||||||
\(882\) | −301.436 | + | 571.707i | −0.341764 | + | 0.648193i | ||||
\(883\) | −1744.35 | −1.97548 | −0.987742 | − | 0.156094i | \(-0.950110\pi\) | ||||
−0.987742 | + | 0.156094i | \(0.950110\pi\) | |||||||
\(884\) | −311.331 | + | 179.747i | −0.352184 | + | 0.203334i | ||||
\(885\) | −294.689 | + | 55.4456i | −0.332982 | + | 0.0626504i | ||||
\(886\) | −38.9395 | + | 67.4452i | −0.0439498 | + | 0.0761233i | ||||
\(887\) | − | 176.500i | − | 0.198986i | −0.995038 | − | 0.0994928i | \(-0.968278\pi\) | ||
0.995038 | − | 0.0994928i | \(-0.0317220\pi\) | |||||||
\(888\) | 108.906 | + | 578.827i | 0.122642 | + | 0.651832i | ||||
\(889\) | 97.5782 | − | 213.563i | 0.109762 | − | 0.240228i | ||||
\(890\) | − | 97.0382i | − | 0.109032i | ||||||
\(891\) | 5.83874 | − | 18.6570i | 0.00655302 | − | 0.0209394i | ||||
\(892\) | 81.2511 | + | 140.731i | 0.0910887 | + | 0.157770i | ||||
\(893\) | 822.306i | 0.920835i | ||||||||
\(894\) | −228.779 | + | 651.671i | −0.255905 | + | 0.728938i | ||||
\(895\) | 29.3634 | + | 50.8588i | 0.0328082 | + | 0.0568255i | ||||
\(896\) | −12.8038 | − | 134.348i | −0.0142900 | − | 0.149941i | ||||
\(897\) | 889.136 | + | 312.145i | 0.991233 | + | 0.347988i | ||||
\(898\) | −385.724 | − | 668.094i | −0.429537 | − | 0.743980i | ||||
\(899\) | 46.1258 | − | 26.6307i | 0.0513079 | − | 0.0296226i | ||||
\(900\) | −307.998 | − | 246.654i | −0.342220 | − | 0.274060i | ||||
\(901\) | 658.908 | − | 1141.26i | 0.731308 | − | 1.26666i | ||||
\(902\) | 21.9275 | + | 12.6599i | 0.0243099 | + | 0.0140353i | ||||
\(903\) | −150.310 | + | 607.361i | −0.166457 | + | 0.672603i | ||||
\(904\) | −500.696 | − | 867.230i | −0.553867 | − | 0.959325i | ||||
\(905\) | 276.400i | 0.305414i | ||||||||
\(906\) | 499.813 | + | 175.467i | 0.551670 | + | 0.193672i | ||||
\(907\) | 1694.96 | 1.86876 | 0.934379 | − | 0.356280i | \(-0.115955\pi\) | ||||
0.934379 | + | 0.356280i | \(0.115955\pi\) | |||||||
\(908\) | −565.735 | − | 326.627i | −0.623056 | − | 0.359721i | ||||
\(909\) | −748.542 | − | 114.393i | −0.823478 | − | 0.125845i | ||||
\(910\) | −105.653 | − | 148.426i | −0.116102 | − | 0.163106i | ||||
\(911\) | 893.443 | + | 515.830i | 0.980728 | + | 0.566224i | 0.902490 | − | 0.430711i | \(-0.141737\pi\) |
0.0782381 | + | 0.996935i | \(0.475071\pi\) | |||||||
\(912\) | 276.562 | + | 322.038i | 0.303248 | + | 0.353112i | ||||
\(913\) | 10.7433 | − | 18.6079i | 0.0117670 | − | 0.0203810i | ||||
\(914\) | −938.906 | − | 542.078i | −1.02725 | − | 0.593083i | ||||
\(915\) | −58.3548 | − | 20.4864i | −0.0637758 | − | 0.0223895i | ||||
\(916\) | 352.645 | − | 610.798i | 0.384983 | − | 0.666811i | ||||
\(917\) | −455.223 | − | 207.994i | −0.496427 | − | 0.226820i | ||||
\(918\) | −17.1085 | − | 498.207i | −0.0186368 | − | 0.542710i | ||||
\(919\) | 362.145 | − | 627.254i | 0.394064 | − | 0.682539i | −0.598917 | − | 0.800811i | \(-0.704402\pi\) |
0.992981 | + | 0.118272i | \(0.0377354\pi\) | |||||||
\(920\) | 201.563i | 0.219090i | ||||||||
\(921\) | −748.550 | − | 871.635i | −0.812758 | − | 0.946401i | ||||
\(922\) | −481.661 | −0.522409 | ||||||||
\(923\) | −990.174 | + | 571.677i | −1.07278 | + | 0.619369i | ||||
\(924\) | 9.11250 | + | 2.25517i | 0.00986201 | + | 0.00244066i | ||||
\(925\) | −270.930 | + | 469.264i | −0.292897 | + | 0.507312i | ||||
\(926\) | −9.25515 | − | 5.34346i | −0.00999476 | − | 0.00577048i | ||||
\(927\) | −80.1729 | + | 524.617i | −0.0864864 | + | 0.565930i | ||||
\(928\) | 261.188 | + | 452.391i | 0.281453 | + | 0.487490i | ||||
\(929\) | −1267.59 | + | 731.841i | −1.36446 | + | 0.787773i | −0.990214 | − | 0.139556i | \(-0.955433\pi\) |
−0.374248 | + | 0.927328i | \(0.622099\pi\) | |||||||
\(930\) | 9.00331 | + | 10.4837i | 0.00968098 | + | 0.0112728i | ||||
\(931\) | −1319.29 | + | 253.772i | −1.41707 | + | 0.272580i | ||||
\(932\) | −502.966 | + | 290.387i | −0.539663 | + | 0.311575i | ||||
\(933\) | −86.5414 | − | 459.961i | −0.0927561 | − | 0.492992i | ||||
\(934\) | −755.756 | −0.809161 | ||||||||
\(935\) | 3.03525 | − | 1.75240i | 0.00324626 | − | 0.00187423i | ||||
\(936\) | 432.207 | + | 1107.92i | 0.461760 | + | 1.18367i | ||||
\(937\) | 282.325 | 0.301308 | 0.150654 | − | 0.988587i | \(-0.451862\pi\) | ||||
0.150654 | + | 0.988587i | \(0.451862\pi\) | |||||||
\(938\) | −168.368 | − | 76.9281i | −0.179496 | − | 0.0820129i | ||||
\(939\) | 115.800 | − | 329.854i | 0.123323 | − | 0.351282i | ||||
\(940\) | −64.0319 | −0.0681190 | ||||||||
\(941\) | 255.008 | + | 147.229i | 0.270997 | + | 0.156460i | 0.629341 | − | 0.777129i | \(-0.283325\pi\) |
−0.358344 | + | 0.933590i | \(0.616658\pi\) | |||||||
\(942\) | 25.8683 | − | 22.2154i | 0.0274611 | − | 0.0235833i | ||||
\(943\) | 729.727 | + | 1263.92i | 0.773836 | + | 1.34032i | ||||
\(944\) | − | 447.503i | − | 0.474050i | ||||||
\(945\) | −216.041 | + | 28.1003i | −0.228614 | + | 0.0297358i | ||||
\(946\) | −10.5385 | −0.0111401 | ||||||||
\(947\) | 763.933 | − | 441.057i | 0.806687 | − | 0.465741i | −0.0391168 | − | 0.999235i | \(-0.512454\pi\) |
0.845804 | + | 0.533493i | \(0.179121\pi\) | |||||||
\(948\) | 81.4974 | + | 94.8981i | 0.0859677 | + | 0.100103i | ||||
\(949\) | −201.208 | + | 348.503i | −0.212021 | + | 0.367231i | ||||
\(950\) | 951.166i | 1.00123i | ||||||||
\(951\) | −531.770 | − | 186.686i | −0.559169 | − | 0.196305i | ||||
\(952\) | 752.929 | − | 71.7569i | 0.790892 | − | 0.0753749i | ||||
\(953\) | − | 347.203i | − | 0.364326i | −0.983268 | − | 0.182163i | \(-0.941690\pi\) | ||
0.983268 | − | 0.182163i | \(-0.0583099\pi\) | |||||||
\(954\) | −1076.95 | − | 862.457i | −1.12888 | − | 0.904043i | ||||
\(955\) | 105.957 | + | 183.523i | 0.110950 | + | 0.192170i | ||||
\(956\) | 427.421i | 0.447093i | ||||||||
\(957\) | −13.8990 | + | 2.61508i | −0.0145235 | + | 0.00273258i | ||||
\(958\) | 212.256 | + | 367.638i | 0.221561 | + | 0.383756i | ||||
\(959\) | 1380.11 | + | 630.581i | 1.43911 | + | 0.657540i | ||||
\(960\) | −156.978 | + | 134.811i | −0.163519 | + | 0.140428i | ||||
\(961\) | 476.782 | + | 825.811i | 0.496132 | + | 0.859325i | ||||
\(962\) | 447.614 | − | 258.430i | 0.465295 | − | 0.268638i | ||||
\(963\) | 499.760 | − | 624.052i | 0.518962 | − | 0.648029i | ||||
\(964\) | 167.489 | − | 290.099i | 0.173743 | − | 0.300932i | ||||
\(965\) | 152.532 | + | 88.0647i | 0.158065 | + | 0.0912587i | ||||
\(966\) | −452.124 | − | 435.094i | −0.468037 | − | 0.450408i | ||||
\(967\) | 774.207 | + | 1340.97i | 0.800627 | + | 1.38673i | 0.919204 | + | 0.393782i | \(0.128834\pi\) |
−0.118577 | + | 0.992945i | \(0.537833\pi\) | |||||||
\(968\) | − | 1037.27i | − | 1.07156i | ||||||
\(969\) | 786.129 | − | 675.119i | 0.811279 | − | 0.696717i | ||||
\(970\) | 249.983 | 0.257714 | ||||||||
\(971\) | 859.844 | + | 496.431i | 0.885525 | + | 0.511258i | 0.872476 | − | 0.488657i | \(-0.162513\pi\) |
0.0130486 | + | 0.999915i | \(0.495846\pi\) | |||||||
\(972\) | 446.984 | + | 52.6828i | 0.459860 | + | 0.0542004i | ||||
\(973\) | −748.454 | + | 71.3304i | −0.769223 | + | 0.0733098i | ||||
\(974\) | 640.375 | + | 369.721i | 0.657470 | + | 0.379590i | ||||
\(975\) | −362.411 | + | 1032.32i | −0.371704 | + | 1.05879i | ||||
\(976\) | 46.1489 | − | 79.9323i | 0.0472837 | − | 0.0818978i | ||||
\(977\) | −206.132 | − | 119.011i | −0.210985 | − | 0.121812i | 0.390784 | − | 0.920482i | \(-0.372204\pi\) |
−0.601769 | + | 0.798670i | \(0.705537\pi\) | |||||||
\(978\) | −866.978 | + | 744.551i | −0.886481 | + | 0.761299i | ||||
\(979\) | 6.93173 | − | 12.0061i | 0.00708042 | − | 0.0122636i | ||||
\(980\) | −19.7609 | − | 102.732i | −0.0201642 | − | 0.104828i | ||||
\(981\) | −1584.03 | + | 617.945i | −1.61471 | + | 0.629913i | ||||
\(982\) | 263.667 | − | 456.685i | 0.268500 | − | 0.465056i | ||||
\(983\) | 632.857i | 0.643801i | 0.946773 | + | 0.321901i | \(0.104322\pi\) | ||||
−0.946773 | + | 0.321901i | \(0.895678\pi\) | |||||||
\(984\) | −610.102 | + | 1737.86i | −0.620023 | + | 1.76612i | ||||
\(985\) | 444.951 | 0.451727 | ||||||||
\(986\) | −312.323 | + | 180.320i | −0.316757 | + | 0.182880i | ||||
\(987\) | 436.722 | − | 453.816i | 0.442475 | − | 0.459793i | ||||
\(988\) | −391.196 | + | 677.571i | −0.395947 | + | 0.685801i | ||||
\(989\) | −526.069 | − | 303.726i | −0.531920 | − | 0.307104i | ||||
\(990\) | −1.33361 | − | 3.41856i | −0.00134708 | − | 0.00345309i | ||||
\(991\) | 589.789 | + | 1021.54i | 0.595145 | + | 1.03082i | 0.993526 | + | 0.113602i | \(0.0362389\pi\) |
−0.398381 | + | 0.917220i | \(0.630428\pi\) | |||||||
\(992\) | 63.1519 | − | 36.4608i | 0.0636612 | − | 0.0367548i | ||||
\(993\) | −63.0349 | + | 179.553i | −0.0634792 | + | 0.180819i | ||||
\(994\) | 757.892 | − | 72.2299i | 0.762467 | − | 0.0726659i | ||||
\(995\) | −45.5982 | + | 26.3261i | −0.0458274 | + | 0.0264584i | ||||
\(996\) | 466.752 | + | 163.860i | 0.468626 | + | 0.164519i | ||||
\(997\) | −1492.30 | −1.49679 | −0.748394 | − | 0.663254i | \(-0.769175\pi\) | ||||
−0.748394 | + | 0.663254i | \(0.769175\pi\) | |||||||
\(998\) | 821.226 | − | 474.135i | 0.822872 | − | 0.475085i | ||||
\(999\) | −21.2117 | − | 617.693i | −0.0212329 | − | 0.618311i |
(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 | 63.3.n.b.2.4 | yes | 22 | |
3.2 | odd | 2 | 189.3.n.b.170.8 | 22 | |||
7.2 | even | 3 | 441.3.r.g.344.8 | 22 | |||
7.3 | odd | 6 | 441.3.j.f.263.4 | 22 | |||
7.4 | even | 3 | 63.3.j.b.11.4 | ✓ | 22 | ||
7.5 | odd | 6 | 441.3.r.f.344.8 | 22 | |||
7.6 | odd | 2 | 441.3.n.f.128.4 | 22 | |||
9.4 | even | 3 | 189.3.j.b.44.4 | 22 | |||
9.5 | odd | 6 | 63.3.j.b.23.8 | yes | 22 | ||
21.11 | odd | 6 | 189.3.j.b.116.8 | 22 | |||
63.4 | even | 3 | 189.3.n.b.179.8 | 22 | |||
63.5 | even | 6 | 441.3.r.f.50.8 | 22 | |||
63.23 | odd | 6 | 441.3.r.g.50.8 | 22 | |||
63.32 | odd | 6 | inner | 63.3.n.b.32.4 | yes | 22 | |
63.41 | even | 6 | 441.3.j.f.275.8 | 22 | |||
63.59 | even | 6 | 441.3.n.f.410.4 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.3.j.b.11.4 | ✓ | 22 | 7.4 | even | 3 | ||
63.3.j.b.23.8 | yes | 22 | 9.5 | odd | 6 | ||
63.3.n.b.2.4 | yes | 22 | 1.1 | even | 1 | trivial | |
63.3.n.b.32.4 | yes | 22 | 63.32 | odd | 6 | inner | |
189.3.j.b.44.4 | 22 | 9.4 | even | 3 | |||
189.3.j.b.116.8 | 22 | 21.11 | odd | 6 | |||
189.3.n.b.170.8 | 22 | 3.2 | odd | 2 | |||
189.3.n.b.179.8 | 22 | 63.4 | even | 3 | |||
441.3.j.f.263.4 | 22 | 7.3 | odd | 6 | |||
441.3.j.f.275.8 | 22 | 63.41 | even | 6 | |||
441.3.n.f.128.4 | 22 | 7.6 | odd | 2 | |||
441.3.n.f.410.4 | 22 | 63.59 | even | 6 | |||
441.3.r.f.50.8 | 22 | 63.5 | even | 6 | |||
441.3.r.f.344.8 | 22 | 7.5 | odd | 6 | |||
441.3.r.g.50.8 | 22 | 63.23 | odd | 6 | |||
441.3.r.g.344.8 | 22 | 7.2 | even | 3 |