Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(191,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.u (of order \(4\), 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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 191.8 | ||
Character | \(\chi\) | \(=\) | 1110.191 |
Dual form | 1110.2.u.e.401.8 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | −1.59695 | + | 0.670623i | −0.922002 | + | 0.387184i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | −0.707107 | + | 0.707107i | −0.316228 | + | 0.316228i | ||||
\(6\) | 1.60342 | + | 0.655016i | 0.654593 | + | 0.267409i | ||||
\(7\) | 3.28633 | 1.24212 | 0.621058 | − | 0.783765i | \(-0.286703\pi\) | ||||
0.621058 | + | 0.783765i | \(0.286703\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 2.10053 | − | 2.14191i | 0.700177 | − | 0.713970i | ||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −1.74571 | −0.526352 | −0.263176 | − | 0.964748i | \(-0.584770\pi\) | ||||
−0.263176 | + | 0.964748i | \(0.584770\pi\) | |||||||
\(12\) | −0.670623 | − | 1.59695i | −0.193592 | − | 0.461001i | ||||
\(13\) | −3.25667 | − | 3.25667i | −0.903238 | − | 0.903238i | 0.0924765 | − | 0.995715i | \(-0.470522\pi\) |
−0.995715 | + | 0.0924765i | \(0.970522\pi\) | |||||||
\(14\) | −2.32379 | − | 2.32379i | −0.621058 | − | 0.621058i | ||||
\(15\) | 0.655016 | − | 1.60342i | 0.169124 | − | 0.414001i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −1.24108 | + | 1.24108i | −0.301005 | + | 0.301005i | −0.841407 | − | 0.540402i | \(-0.818272\pi\) |
0.540402 | + | 0.841407i | \(0.318272\pi\) | |||||||
\(18\) | −2.99986 | + | 0.0292590i | −0.707073 | + | 0.00689642i | ||||
\(19\) | 0.258976 | + | 0.258976i | 0.0594133 | + | 0.0594133i | 0.736189 | − | 0.676776i | \(-0.236623\pi\) |
−0.676776 | + | 0.736189i | \(0.736623\pi\) | |||||||
\(20\) | −0.707107 | − | 0.707107i | −0.158114 | − | 0.158114i | ||||
\(21\) | −5.24812 | + | 2.20389i | −1.14523 | + | 0.480928i | ||||
\(22\) | 1.23440 | + | 1.23440i | 0.263176 | + | 0.263176i | ||||
\(23\) | 1.64920 | − | 1.64920i | 0.343881 | − | 0.343881i | −0.513943 | − | 0.857824i | \(-0.671816\pi\) |
0.857824 | + | 0.513943i | \(0.171816\pi\) | |||||||
\(24\) | −0.655016 | + | 1.60342i | −0.133705 | + | 0.327297i | ||||
\(25\) | − | 1.00000i | − | 0.200000i | ||||||
\(26\) | 4.60563i | 0.903238i | ||||||||
\(27\) | −1.91804 | + | 4.82920i | −0.369127 | + | 0.929379i | ||||
\(28\) | 3.28633i | 0.621058i | ||||||||
\(29\) | 0.378286 | + | 0.378286i | 0.0702459 | + | 0.0702459i | 0.741357 | − | 0.671111i | \(-0.234183\pi\) |
−0.671111 | + | 0.741357i | \(0.734183\pi\) | |||||||
\(30\) | −1.59695 | + | 0.670623i | −0.291563 | + | 0.122438i | ||||
\(31\) | 3.64796 | − | 3.64796i | 0.655193 | − | 0.655193i | −0.299046 | − | 0.954239i | \(-0.596668\pi\) |
0.954239 | + | 0.299046i | \(0.0966683\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | 2.78782 | − | 1.17071i | 0.485297 | − | 0.203795i | ||||
\(34\) | 1.75515 | 0.301005 | ||||||||
\(35\) | −2.32379 | + | 2.32379i | −0.392792 | + | 0.392792i | ||||
\(36\) | 2.14191 | + | 2.10053i | 0.356985 | + | 0.350088i | ||||
\(37\) | −4.68494 | + | 3.87960i | −0.770200 | + | 0.637802i | ||||
\(38\) | − | 0.366248i | − | 0.0594133i | ||||||
\(39\) | 7.38476 | + | 3.01676i | 1.18251 | + | 0.483068i | ||||
\(40\) | 1.00000i | 0.158114i | ||||||||
\(41\) | 9.92643 | 1.55025 | 0.775124 | − | 0.631809i | \(-0.217687\pi\) | ||||
0.775124 | + | 0.631809i | \(0.217687\pi\) | |||||||
\(42\) | 5.26937 | + | 2.15260i | 0.813081 | + | 0.332153i | ||||
\(43\) | −4.35358 | − | 4.35358i | −0.663914 | − | 0.663914i | 0.292386 | − | 0.956300i | \(-0.405551\pi\) |
−0.956300 | + | 0.292386i | \(0.905551\pi\) | |||||||
\(44\) | − | 1.74571i | − | 0.263176i | ||||||
\(45\) | 0.0292590 | + | 2.99986i | 0.00436168 | + | 0.447192i | ||||
\(46\) | −2.33232 | −0.343881 | ||||||||
\(47\) | − | 2.28468i | − | 0.333255i | −0.986020 | − | 0.166627i | \(-0.946712\pi\) | ||
0.986020 | − | 0.166627i | \(-0.0532877\pi\) | |||||||
\(48\) | 1.59695 | − | 0.670623i | 0.230501 | − | 0.0967961i | ||||
\(49\) | 3.79996 | 0.542852 | ||||||||
\(50\) | −0.707107 | + | 0.707107i | −0.100000 | + | 0.100000i | ||||
\(51\) | 1.14965 | − | 2.81424i | 0.160983 | − | 0.394072i | ||||
\(52\) | 3.25667 | − | 3.25667i | 0.451619 | − | 0.451619i | ||||
\(53\) | − | 9.35271i | − | 1.28469i | −0.766414 | − | 0.642347i | \(-0.777961\pi\) | ||
0.766414 | − | 0.642347i | \(-0.222039\pi\) | |||||||
\(54\) | 4.77102 | − | 2.05850i | 0.649253 | − | 0.280126i | ||||
\(55\) | 1.23440 | − | 1.23440i | 0.166447 | − | 0.166447i | ||||
\(56\) | 2.32379 | − | 2.32379i | 0.310529 | − | 0.310529i | ||||
\(57\) | −0.587249 | − | 0.239898i | −0.0777831 | − | 0.0317753i | ||||
\(58\) | − | 0.534977i | − | 0.0702459i | ||||||
\(59\) | −0.666775 | + | 0.666775i | −0.0868068 | + | 0.0868068i | −0.749177 | − | 0.662370i | \(-0.769551\pi\) |
0.662370 | + | 0.749177i | \(0.269551\pi\) | |||||||
\(60\) | 1.60342 | + | 0.655016i | 0.207001 | + | 0.0845622i | ||||
\(61\) | −0.134354 | + | 0.134354i | −0.0172022 | + | 0.0172022i | −0.715656 | − | 0.698453i | \(-0.753872\pi\) |
0.698453 | + | 0.715656i | \(0.253872\pi\) | |||||||
\(62\) | −5.15899 | −0.655193 | ||||||||
\(63\) | 6.90303 | − | 7.03902i | 0.869701 | − | 0.886833i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 4.60563 | 0.571258 | ||||||||
\(66\) | −2.79911 | − | 1.14347i | −0.344546 | − | 0.140751i | ||||
\(67\) | − | 8.70321i | − | 1.06327i | −0.846975 | − | 0.531633i | \(-0.821579\pi\) | ||
0.846975 | − | 0.531633i | \(-0.178421\pi\) | |||||||
\(68\) | −1.24108 | − | 1.24108i | −0.150503 | − | 0.150503i | ||||
\(69\) | −1.52770 | + | 3.73968i | −0.183914 | + | 0.450205i | ||||
\(70\) | 3.28633 | 0.392792 | ||||||||
\(71\) | − | 7.14239i | − | 0.847645i | −0.905745 | − | 0.423823i | \(-0.860688\pi\) | ||
0.905745 | − | 0.423823i | \(-0.139312\pi\) | |||||||
\(72\) | −0.0292590 | − | 2.99986i | −0.00344821 | − | 0.353537i | ||||
\(73\) | − | 13.7212i | − | 1.60595i | −0.596014 | − | 0.802974i | \(-0.703250\pi\) | ||
0.596014 | − | 0.802974i | \(-0.296750\pi\) | |||||||
\(74\) | 6.05605 | + | 0.569464i | 0.704001 | + | 0.0661988i | ||||
\(75\) | 0.670623 | + | 1.59695i | 0.0774368 | + | 0.184400i | ||||
\(76\) | −0.258976 | + | 0.258976i | −0.0297066 | + | 0.0297066i | ||||
\(77\) | −5.73698 | −0.653790 | ||||||||
\(78\) | −3.08864 | − | 7.35498i | −0.349720 | − | 0.832788i | ||||
\(79\) | 6.38622 | + | 6.38622i | 0.718506 | + | 0.718506i | 0.968299 | − | 0.249793i | \(-0.0803627\pi\) |
−0.249793 | + | 0.968299i | \(0.580363\pi\) | |||||||
\(80\) | 0.707107 | − | 0.707107i | 0.0790569 | − | 0.0790569i | ||||
\(81\) | −0.175546 | − | 8.99829i | −0.0195051 | − | 0.999810i | ||||
\(82\) | −7.01905 | − | 7.01905i | −0.775124 | − | 0.775124i | ||||
\(83\) | − | 14.6153i | − | 1.60423i | −0.597166 | − | 0.802117i | \(-0.703707\pi\) | ||
0.597166 | − | 0.802117i | \(-0.296293\pi\) | |||||||
\(84\) | −2.20389 | − | 5.24812i | −0.240464 | − | 0.572617i | ||||
\(85\) | − | 1.75515i | − | 0.190373i | ||||||
\(86\) | 6.15689i | 0.663914i | ||||||||
\(87\) | −0.857793 | − | 0.350418i | −0.0919650 | − | 0.0375688i | ||||
\(88\) | −1.23440 | + | 1.23440i | −0.131588 | + | 0.131588i | ||||
\(89\) | 0.495164 | + | 0.495164i | 0.0524872 | + | 0.0524872i | 0.732863 | − | 0.680376i | \(-0.238184\pi\) |
−0.680376 | + | 0.732863i | \(0.738184\pi\) | |||||||
\(90\) | 2.10053 | − | 2.14191i | 0.221415 | − | 0.225777i | ||||
\(91\) | −10.7025 | − | 10.7025i | −1.12193 | − | 1.12193i | ||||
\(92\) | 1.64920 | + | 1.64920i | 0.171941 | + | 0.171941i | ||||
\(93\) | −3.37922 | + | 8.27203i | −0.350409 | + | 0.857770i | ||||
\(94\) | −1.61551 | + | 1.61551i | −0.166627 | + | 0.166627i | ||||
\(95\) | −0.366248 | −0.0375762 | ||||||||
\(96\) | −1.60342 | − | 0.655016i | −0.163648 | − | 0.0668523i | ||||
\(97\) | 4.16187 | + | 4.16187i | 0.422573 | + | 0.422573i | 0.886089 | − | 0.463515i | \(-0.153412\pi\) |
−0.463515 | + | 0.886089i | \(0.653412\pi\) | |||||||
\(98\) | −2.68698 | − | 2.68698i | −0.271426 | − | 0.271426i | ||||
\(99\) | −3.66692 | + | 3.73915i | −0.368539 | + | 0.375799i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 18.6620 | 1.85694 | 0.928471 | − | 0.371406i | \(-0.121124\pi\) | ||||
0.928471 | + | 0.371406i | \(0.121124\pi\) | |||||||
\(102\) | −2.80289 | + | 1.17704i | −0.277528 | + | 0.116545i | ||||
\(103\) | 6.60999 | − | 6.60999i | 0.651301 | − | 0.651301i | −0.302005 | − | 0.953306i | \(-0.597656\pi\) |
0.953306 | + | 0.302005i | \(0.0976559\pi\) | |||||||
\(104\) | −4.60563 | −0.451619 | ||||||||
\(105\) | 2.15260 | − | 5.26937i | 0.210072 | − | 0.514237i | ||||
\(106\) | −6.61336 | + | 6.61336i | −0.642347 | + | 0.642347i | ||||
\(107\) | − | 10.8073i | − | 1.04479i | −0.852705 | − | 0.522393i | \(-0.825040\pi\) | ||
0.852705 | − | 0.522393i | \(-0.174960\pi\) | |||||||
\(108\) | −4.82920 | − | 1.91804i | −0.464690 | − | 0.184563i | ||||
\(109\) | 8.67304 | + | 8.67304i | 0.830726 | + | 0.830726i | 0.987616 | − | 0.156890i | \(-0.0501467\pi\) |
−0.156890 | + | 0.987616i | \(0.550147\pi\) | |||||||
\(110\) | −1.74571 | −0.166447 | ||||||||
\(111\) | 4.87990 | − | 9.33738i | 0.463179 | − | 0.886265i | ||||
\(112\) | −3.28633 | −0.310529 | ||||||||
\(113\) | 11.6207 | + | 11.6207i | 1.09318 | + | 1.09318i | 0.995187 | + | 0.0979919i | \(0.0312419\pi\) |
0.0979919 | + | 0.995187i | \(0.468758\pi\) | |||||||
\(114\) | 0.245614 | + | 0.584882i | 0.0230039 | + | 0.0547792i | ||||
\(115\) | 2.33232i | 0.217490i | ||||||||
\(116\) | −0.378286 | + | 0.378286i | −0.0351230 | + | 0.0351230i | ||||
\(117\) | −13.8162 | + | 0.134756i | −1.27731 | + | 0.0124582i | ||||
\(118\) | 0.942963 | 0.0868068 | ||||||||
\(119\) | −4.07859 | + | 4.07859i | −0.373884 | + | 0.373884i | ||||
\(120\) | −0.670623 | − | 1.59695i | −0.0612192 | − | 0.145781i | ||||
\(121\) | −7.95249 | −0.722954 | ||||||||
\(122\) | 0.190005 | 0.0172022 | ||||||||
\(123\) | −15.8521 | + | 6.65689i | −1.42933 | + | 0.600231i | ||||
\(124\) | 3.64796 | + | 3.64796i | 0.327597 | + | 0.327597i | ||||
\(125\) | 0.707107 | + | 0.707107i | 0.0632456 | + | 0.0632456i | ||||
\(126\) | −9.85852 | + | 0.0961548i | −0.878267 | + | 0.00856615i | ||||
\(127\) | −8.70788 | −0.772700 | −0.386350 | − | 0.922352i | \(-0.626264\pi\) | ||||
−0.386350 | + | 0.922352i | \(0.626264\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 9.87207 | + | 4.03286i | 0.869188 | + | 0.355073i | ||||
\(130\) | −3.25667 | − | 3.25667i | −0.285629 | − | 0.285629i | ||||
\(131\) | 7.38432 | + | 7.38432i | 0.645171 | + | 0.645171i | 0.951822 | − | 0.306651i | \(-0.0992084\pi\) |
−0.306651 | + | 0.951822i | \(0.599208\pi\) | |||||||
\(132\) | 1.17071 | + | 2.78782i | 0.101898 | + | 0.242649i | ||||
\(133\) | 0.851082 | + | 0.851082i | 0.0737982 | + | 0.0737982i | ||||
\(134\) | −6.15410 | + | 6.15410i | −0.531633 | + | 0.531633i | ||||
\(135\) | −2.05850 | − | 4.77102i | −0.177167 | − | 0.410624i | ||||
\(136\) | 1.75515i | 0.150503i | ||||||||
\(137\) | 9.66267i | 0.825537i | 0.910836 | + | 0.412769i | \(0.135438\pi\) | ||||
−0.910836 | + | 0.412769i | \(0.864562\pi\) | |||||||
\(138\) | 3.72460 | − | 1.56410i | 0.317059 | − | 0.133145i | ||||
\(139\) | − | 9.40917i | − | 0.798076i | −0.916934 | − | 0.399038i | \(-0.869344\pi\) | ||
0.916934 | − | 0.399038i | \(-0.130656\pi\) | |||||||
\(140\) | −2.32379 | − | 2.32379i | −0.196396 | − | 0.196396i | ||||
\(141\) | 1.53216 | + | 3.64853i | 0.129031 | + | 0.307262i | ||||
\(142\) | −5.05043 | + | 5.05043i | −0.423823 | + | 0.423823i | ||||
\(143\) | 5.68521 | + | 5.68521i | 0.475421 | + | 0.475421i | ||||
\(144\) | −2.10053 | + | 2.14191i | −0.175044 | + | 0.178492i | ||||
\(145\) | −0.534977 | −0.0444274 | ||||||||
\(146\) | −9.70237 | + | 9.70237i | −0.802974 | + | 0.802974i | ||||
\(147\) | −6.06837 | + | 2.54834i | −0.500511 | + | 0.210184i | ||||
\(148\) | −3.87960 | − | 4.68494i | −0.318901 | − | 0.385100i | ||||
\(149\) | − | 7.23397i | − | 0.592630i | −0.955090 | − | 0.296315i | \(-0.904242\pi\) | ||
0.955090 | − | 0.296315i | \(-0.0957578\pi\) | |||||||
\(150\) | 0.655016 | − | 1.60342i | 0.0534818 | − | 0.130919i | ||||
\(151\) | − | 15.0674i | − | 1.22617i | −0.790018 | − | 0.613084i | \(-0.789929\pi\) | ||
0.790018 | − | 0.613084i | \(-0.210071\pi\) | |||||||
\(152\) | 0.366248 | 0.0297066 | ||||||||
\(153\) | 0.0513539 | + | 5.26519i | 0.00415172 | + | 0.425666i | ||||
\(154\) | 4.05666 | + | 4.05666i | 0.326895 | + | 0.326895i | ||||
\(155\) | 5.15899i | 0.414380i | ||||||||
\(156\) | −3.01676 | + | 7.38476i | −0.241534 | + | 0.591254i | ||||
\(157\) | 8.06347 | 0.643535 | 0.321768 | − | 0.946819i | \(-0.395723\pi\) | ||||
0.321768 | + | 0.946819i | \(0.395723\pi\) | |||||||
\(158\) | − | 9.03148i | − | 0.718506i | ||||||
\(159\) | 6.27214 | + | 14.9359i | 0.497413 | + | 1.18449i | ||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 5.41980 | − | 5.41980i | 0.427140 | − | 0.427140i | ||||
\(162\) | −6.23862 | + | 6.48688i | −0.490152 | + | 0.509657i | ||||
\(163\) | 2.23140 | − | 2.23140i | 0.174777 | − | 0.174777i | −0.614298 | − | 0.789074i | \(-0.710561\pi\) |
0.789074 | + | 0.614298i | \(0.210561\pi\) | |||||||
\(164\) | 9.92643i | 0.775124i | ||||||||
\(165\) | −1.14347 | + | 2.79911i | −0.0890189 | + | 0.217910i | ||||
\(166\) | −10.3346 | + | 10.3346i | −0.802117 | + | 0.802117i | ||||
\(167\) | −0.575837 | + | 0.575837i | −0.0445596 | + | 0.0445596i | −0.729035 | − | 0.684476i | \(-0.760031\pi\) |
0.684476 | + | 0.729035i | \(0.260031\pi\) | |||||||
\(168\) | −2.15260 | + | 5.26937i | −0.166077 | + | 0.406540i | ||||
\(169\) | 8.21183i | 0.631679i | ||||||||
\(170\) | −1.24108 | + | 1.24108i | −0.0951863 | + | 0.0951863i | ||||
\(171\) | 1.09869 | − | 0.0107161i | 0.0840191 | − | 0.000819478i | ||||
\(172\) | 4.35358 | − | 4.35358i | 0.331957 | − | 0.331957i | ||||
\(173\) | −16.6885 | −1.26880 | −0.634400 | − | 0.773005i | \(-0.718753\pi\) | ||||
−0.634400 | + | 0.773005i | \(0.718753\pi\) | |||||||
\(174\) | 0.358768 | + | 0.854334i | 0.0271981 | + | 0.0647669i | ||||
\(175\) | − | 3.28633i | − | 0.248423i | ||||||
\(176\) | 1.74571 | 0.131588 | ||||||||
\(177\) | 0.617655 | − | 1.51196i | 0.0464258 | − | 0.113646i | ||||
\(178\) | − | 0.700267i | − | 0.0524872i | ||||||
\(179\) | 0.0776850 | + | 0.0776850i | 0.00580645 | + | 0.00580645i | 0.710004 | − | 0.704198i | \(-0.248693\pi\) |
−0.704198 | + | 0.710004i | \(0.748693\pi\) | |||||||
\(180\) | −2.99986 | + | 0.0292590i | −0.223596 | + | 0.00218084i | ||||
\(181\) | 14.4452 | 1.07370 | 0.536852 | − | 0.843677i | \(-0.319614\pi\) | ||||
0.536852 | + | 0.843677i | \(0.319614\pi\) | |||||||
\(182\) | 15.1356i | 1.12193i | ||||||||
\(183\) | 0.124456 | − | 0.304657i | 0.00920006 | − | 0.0225209i | ||||
\(184\) | − | 2.33232i | − | 0.171941i | ||||||
\(185\) | 0.569464 | − | 6.05605i | 0.0418678 | − | 0.445249i | ||||
\(186\) | 8.23868 | − | 3.45974i | 0.604090 | − | 0.253680i | ||||
\(187\) | 2.16656 | − | 2.16656i | 0.158435 | − | 0.158435i | ||||
\(188\) | 2.28468 | 0.166627 | ||||||||
\(189\) | −6.30331 | + | 15.8703i | −0.458498 | + | 1.15440i | ||||
\(190\) | 0.258976 | + | 0.258976i | 0.0187881 | + | 0.0187881i | ||||
\(191\) | −8.90023 | + | 8.90023i | −0.643998 | + | 0.643998i | −0.951536 | − | 0.307538i | \(-0.900495\pi\) |
0.307538 | + | 0.951536i | \(0.400495\pi\) | |||||||
\(192\) | 0.670623 | + | 1.59695i | 0.0483980 | + | 0.115250i | ||||
\(193\) | −14.5654 | − | 14.5654i | −1.04844 | − | 1.04844i | −0.998765 | − | 0.0496763i | \(-0.984181\pi\) |
−0.0496763 | − | 0.998765i | \(-0.515819\pi\) | |||||||
\(194\) | − | 5.88577i | − | 0.422573i | ||||||
\(195\) | −7.35498 | + | 3.08864i | −0.526701 | + | 0.221182i | ||||
\(196\) | 3.79996i | 0.271426i | ||||||||
\(197\) | − | 3.22806i | − | 0.229990i | −0.993366 | − | 0.114995i | \(-0.963315\pi\) | ||
0.993366 | − | 0.114995i | \(-0.0366851\pi\) | |||||||
\(198\) | 5.23688 | − | 0.0510778i | 0.372169 | − | 0.00362994i | ||||
\(199\) | 15.7523 | − | 15.7523i | 1.11665 | − | 1.11665i | 0.124424 | − | 0.992229i | \(-0.460292\pi\) |
0.992229 | − | 0.124424i | \(-0.0397081\pi\) | |||||||
\(200\) | −0.707107 | − | 0.707107i | −0.0500000 | − | 0.0500000i | ||||
\(201\) | 5.83657 | + | 13.8986i | 0.411680 | + | 0.980334i | ||||
\(202\) | −13.1960 | − | 13.1960i | −0.928471 | − | 0.928471i | ||||
\(203\) | 1.24317 | + | 1.24317i | 0.0872536 | + | 0.0872536i | ||||
\(204\) | 2.81424 | + | 1.14965i | 0.197036 | + | 0.0804916i | ||||
\(205\) | −7.01905 | + | 7.01905i | −0.490231 | + | 0.490231i | ||||
\(206\) | −9.34793 | −0.651301 | ||||||||
\(207\) | −0.0682413 | − | 6.99661i | −0.00474310 | − | 0.486298i | ||||
\(208\) | 3.25667 | + | 3.25667i | 0.225810 | + | 0.225810i | ||||
\(209\) | −0.452098 | − | 0.452098i | −0.0312723 | − | 0.0312723i | ||||
\(210\) | −5.24812 | + | 2.20389i | −0.362155 | + | 0.152083i | ||||
\(211\) | −13.6945 | −0.942766 | −0.471383 | − | 0.881929i | \(-0.656245\pi\) | ||||
−0.471383 | + | 0.881929i | \(0.656245\pi\) | |||||||
\(212\) | 9.35271 | 0.642347 | ||||||||
\(213\) | 4.78985 | + | 11.4061i | 0.328195 | + | 0.781531i | ||||
\(214\) | −7.64195 | + | 7.64195i | −0.522393 | + | 0.522393i | ||||
\(215\) | 6.15689 | 0.419896 | ||||||||
\(216\) | 2.05850 | + | 4.77102i | 0.140063 | + | 0.324626i | ||||
\(217\) | 11.9884 | − | 11.9884i | 0.813826 | − | 0.813826i | ||||
\(218\) | − | 12.2655i | − | 0.830726i | ||||||
\(219\) | 9.20176 | + | 21.9122i | 0.621798 | + | 1.48069i | ||||
\(220\) | 1.23440 | + | 1.23440i | 0.0832235 | + | 0.0832235i | ||||
\(221\) | 8.08356 | 0.543759 | ||||||||
\(222\) | −10.0531 | + | 3.15192i | −0.674722 | + | 0.211543i | ||||
\(223\) | −17.3050 | −1.15883 | −0.579413 | − | 0.815034i | \(-0.696718\pi\) | ||||
−0.579413 | + | 0.815034i | \(0.696718\pi\) | |||||||
\(224\) | 2.32379 | + | 2.32379i | 0.155264 | + | 0.155264i | ||||
\(225\) | −2.14191 | − | 2.10053i | −0.142794 | − | 0.140035i | ||||
\(226\) | − | 16.4341i | − | 1.09318i | ||||||
\(227\) | −0.729623 | + | 0.729623i | −0.0484268 | + | 0.0484268i | −0.730905 | − | 0.682479i | \(-0.760902\pi\) |
0.682479 | + | 0.730905i | \(0.260902\pi\) | |||||||
\(228\) | 0.239898 | − | 0.587249i | 0.0158876 | − | 0.0388915i | ||||
\(229\) | 18.8546 | 1.24595 | 0.622973 | − | 0.782243i | \(-0.285925\pi\) | ||||
0.622973 | + | 0.782243i | \(0.285925\pi\) | |||||||
\(230\) | 1.64920 | − | 1.64920i | 0.108745 | − | 0.108745i | ||||
\(231\) | 9.16170 | − | 3.84735i | 0.602796 | − | 0.253137i | ||||
\(232\) | 0.534977 | 0.0351230 | ||||||||
\(233\) | 3.88220 | 0.254332 | 0.127166 | − | 0.991881i | \(-0.459412\pi\) | ||||
0.127166 | + | 0.991881i | \(0.459412\pi\) | |||||||
\(234\) | 9.86484 | + | 9.67426i | 0.644885 | + | 0.632426i | ||||
\(235\) | 1.61551 | + | 1.61551i | 0.105384 | + | 0.105384i | ||||
\(236\) | −0.666775 | − | 0.666775i | −0.0434034 | − | 0.0434034i | ||||
\(237\) | −14.4813 | − | 5.91576i | −0.940658 | − | 0.384270i | ||||
\(238\) | 5.76799 | 0.373884 | ||||||||
\(239\) | −8.52789 | + | 8.52789i | −0.551623 | + | 0.551623i | −0.926909 | − | 0.375286i | \(-0.877545\pi\) |
0.375286 | + | 0.926909i | \(0.377545\pi\) | |||||||
\(240\) | −0.655016 | + | 1.60342i | −0.0422811 | + | 0.103500i | ||||
\(241\) | 14.3656 | + | 14.3656i | 0.925369 | + | 0.925369i | 0.997402 | − | 0.0720330i | \(-0.0229487\pi\) |
−0.0720330 | + | 0.997402i | \(0.522949\pi\) | |||||||
\(242\) | 5.62326 | + | 5.62326i | 0.361477 | + | 0.361477i | ||||
\(243\) | 6.31480 | + | 14.2521i | 0.405094 | + | 0.914275i | ||||
\(244\) | −0.134354 | − | 0.134354i | −0.00860111 | − | 0.00860111i | ||||
\(245\) | −2.68698 | + | 2.68698i | −0.171665 | + | 0.171665i | ||||
\(246\) | 15.9162 | + | 6.50197i | 1.01478 | + | 0.414550i | ||||
\(247\) | − | 1.68680i | − | 0.107329i | ||||||
\(248\) | − | 5.15899i | − | 0.327597i | ||||||
\(249\) | 9.80134 | + | 23.3399i | 0.621134 | + | 1.47911i | ||||
\(250\) | − | 1.00000i | − | 0.0632456i | ||||||
\(251\) | −13.7487 | − | 13.7487i | −0.867811 | − | 0.867811i | 0.124418 | − | 0.992230i | \(-0.460294\pi\) |
−0.992230 | + | 0.124418i | \(0.960294\pi\) | |||||||
\(252\) | 7.03902 | + | 6.90303i | 0.443416 | + | 0.434850i | ||||
\(253\) | −2.87902 | + | 2.87902i | −0.181002 | + | 0.181002i | ||||
\(254\) | 6.15740 | + | 6.15740i | 0.386350 | + | 0.386350i | ||||
\(255\) | 1.17704 | + | 2.80289i | 0.0737092 | + | 0.175524i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −14.8299 | + | 14.8299i | −0.925062 | + | 0.925062i | −0.997382 | − | 0.0723195i | \(-0.976960\pi\) |
0.0723195 | + | 0.997382i | \(0.476960\pi\) | |||||||
\(258\) | −4.12895 | − | 9.83227i | −0.257057 | − | 0.612131i | ||||
\(259\) | −15.3963 | + | 12.7496i | −0.956678 | + | 0.792224i | ||||
\(260\) | 4.60563i | 0.285629i | ||||||||
\(261\) | 1.60485 | − | 0.0156529i | 0.0993380 | − | 0.000968891i | ||||
\(262\) | − | 10.4430i | − | 0.645171i | ||||||
\(263\) | 9.08600 | 0.560267 | 0.280134 | − | 0.959961i | \(-0.409621\pi\) | ||||
0.280134 | + | 0.959961i | \(0.409621\pi\) | |||||||
\(264\) | 1.14347 | − | 2.79911i | 0.0703756 | − | 0.172273i | ||||
\(265\) | 6.61336 | + | 6.61336i | 0.406256 | + | 0.406256i | ||||
\(266\) | − | 1.20361i | − | 0.0737982i | ||||||
\(267\) | −1.12282 | − | 0.458686i | −0.0687156 | − | 0.0280711i | ||||
\(268\) | 8.70321 | 0.531633 | ||||||||
\(269\) | − | 19.1471i | − | 1.16742i | −0.811962 | − | 0.583710i | \(-0.801601\pi\) | ||
0.811962 | − | 0.583710i | \(-0.198399\pi\) | |||||||
\(270\) | −1.91804 | + | 4.82920i | −0.116728 | + | 0.293895i | ||||
\(271\) | −29.7365 | −1.80636 | −0.903180 | − | 0.429261i | \(-0.858774\pi\) | ||||
−0.903180 | + | 0.429261i | \(0.858774\pi\) | |||||||
\(272\) | 1.24108 | − | 1.24108i | 0.0752513 | − | 0.0752513i | ||||
\(273\) | 24.2687 | + | 9.91407i | 1.46881 | + | 0.600027i | ||||
\(274\) | 6.83254 | − | 6.83254i | 0.412769 | − | 0.412769i | ||||
\(275\) | 1.74571i | 0.105270i | ||||||||
\(276\) | −3.73968 | − | 1.52770i | −0.225102 | − | 0.0919569i | ||||
\(277\) | −0.963857 | + | 0.963857i | −0.0579126 | + | 0.0579126i | −0.735470 | − | 0.677557i | \(-0.763039\pi\) |
0.677557 | + | 0.735470i | \(0.263039\pi\) | |||||||
\(278\) | −6.65329 | + | 6.65329i | −0.399038 | + | 0.399038i | ||||
\(279\) | −0.150947 | − | 15.4762i | −0.00903697 | − | 0.926539i | ||||
\(280\) | 3.28633i | 0.196396i | ||||||||
\(281\) | −14.7139 | + | 14.7139i | −0.877757 | + | 0.877757i | −0.993302 | − | 0.115546i | \(-0.963138\pi\) |
0.115546 | + | 0.993302i | \(0.463138\pi\) | |||||||
\(282\) | 1.49650 | − | 3.66330i | 0.0891153 | − | 0.218146i | ||||
\(283\) | 0.747604 | − | 0.747604i | 0.0444404 | − | 0.0444404i | −0.684537 | − | 0.728978i | \(-0.739996\pi\) |
0.728978 | + | 0.684537i | \(0.239996\pi\) | |||||||
\(284\) | 7.14239 | 0.423823 | ||||||||
\(285\) | 0.584882 | − | 0.245614i | 0.0346454 | − | 0.0145489i | ||||
\(286\) | − | 8.04010i | − | 0.475421i | ||||||
\(287\) | 32.6215 | 1.92559 | ||||||||
\(288\) | 2.99986 | − | 0.0292590i | 0.176768 | − | 0.00172411i | ||||
\(289\) | 13.9195i | 0.818792i | ||||||||
\(290\) | 0.378286 | + | 0.378286i | 0.0222137 | + | 0.0222137i | ||||
\(291\) | −9.43736 | − | 3.85527i | −0.553228 | − | 0.226000i | ||||
\(292\) | 13.7212 | 0.802974 | ||||||||
\(293\) | 27.9875i | 1.63505i | 0.575893 | + | 0.817525i | \(0.304654\pi\) | ||||
−0.575893 | + | 0.817525i | \(0.695346\pi\) | |||||||
\(294\) | 6.09293 | + | 2.48904i | 0.355347 | + | 0.145163i | ||||
\(295\) | − | 0.942963i | − | 0.0549014i | ||||||
\(296\) | −0.569464 | + | 6.05605i | −0.0330994 | + | 0.352001i | ||||
\(297\) | 3.34834 | − | 8.43038i | 0.194290 | − | 0.489180i | ||||
\(298\) | −5.11519 | + | 5.11519i | −0.296315 | + | 0.296315i | ||||
\(299\) | −10.7418 | −0.621213 | ||||||||
\(300\) | −1.59695 | + | 0.670623i | −0.0922002 | + | 0.0387184i | ||||
\(301\) | −14.3073 | − | 14.3073i | −0.824658 | − | 0.824658i | ||||
\(302\) | −10.6543 | + | 10.6543i | −0.613084 | + | 0.613084i | ||||
\(303\) | −29.8024 | + | 12.5152i | −1.71210 | + | 0.718978i | ||||
\(304\) | −0.258976 | − | 0.258976i | −0.0148533 | − | 0.0148533i | ||||
\(305\) | − | 0.190005i | − | 0.0108796i | ||||||
\(306\) | 3.68674 | − | 3.75937i | 0.210757 | − | 0.214909i | ||||
\(307\) | − | 3.09733i | − | 0.176774i | −0.996086 | − | 0.0883870i | \(-0.971829\pi\) | ||
0.996086 | − | 0.0883870i | \(-0.0281712\pi\) | |||||||
\(308\) | − | 5.73698i | − | 0.326895i | ||||||
\(309\) | −6.12304 | + | 14.9887i | −0.348328 | + | 0.852675i | ||||
\(310\) | 3.64796 | − | 3.64796i | 0.207190 | − | 0.207190i | ||||
\(311\) | −6.12907 | − | 6.12907i | −0.347548 | − | 0.347548i | 0.511648 | − | 0.859195i | \(-0.329035\pi\) |
−0.859195 | + | 0.511648i | \(0.829035\pi\) | |||||||
\(312\) | 7.35498 | − | 3.08864i | 0.416394 | − | 0.174860i | ||||
\(313\) | −14.4360 | − | 14.4360i | −0.815969 | − | 0.815969i | 0.169552 | − | 0.985521i | \(-0.445768\pi\) |
−0.985521 | + | 0.169552i | \(0.945768\pi\) | |||||||
\(314\) | −5.70174 | − | 5.70174i | −0.321768 | − | 0.321768i | ||||
\(315\) | 0.0961548 | + | 9.85852i | 0.00541771 | + | 0.555465i | ||||
\(316\) | −6.38622 | + | 6.38622i | −0.359253 | + | 0.359253i | ||||
\(317\) | −16.7549 | −0.941048 | −0.470524 | − | 0.882387i | \(-0.655935\pi\) | ||||
−0.470524 | + | 0.882387i | \(0.655935\pi\) | |||||||
\(318\) | 6.12617 | − | 14.9963i | 0.343539 | − | 0.840952i | ||||
\(319\) | −0.660378 | − | 0.660378i | −0.0369741 | − | 0.0369741i | ||||
\(320\) | 0.707107 | + | 0.707107i | 0.0395285 | + | 0.0395285i | ||||
\(321\) | 7.24765 | + | 17.2588i | 0.404524 | + | 0.963294i | ||||
\(322\) | −7.66476 | −0.427140 | ||||||||
\(323\) | −0.642819 | −0.0357674 | ||||||||
\(324\) | 8.99829 | − | 0.175546i | 0.499905 | − | 0.00975255i | ||||
\(325\) | −3.25667 | + | 3.25667i | −0.180648 | + | 0.180648i | ||||
\(326\) | −3.15568 | −0.174777 | ||||||||
\(327\) | −19.6668 | − | 8.03411i | −1.08758 | − | 0.444288i | ||||
\(328\) | 7.01905 | − | 7.01905i | 0.387562 | − | 0.387562i | ||||
\(329\) | − | 7.50821i | − | 0.413941i | ||||||
\(330\) | 2.78782 | − | 1.17071i | 0.153465 | − | 0.0644457i | ||||
\(331\) | 2.35068 | + | 2.35068i | 0.129205 | + | 0.129205i | 0.768752 | − | 0.639547i | \(-0.220878\pi\) |
−0.639547 | + | 0.768752i | \(0.720878\pi\) | |||||||
\(332\) | 14.6153 | 0.802117 | ||||||||
\(333\) | −1.53112 | + | 18.1839i | −0.0839047 | + | 0.996474i | ||||
\(334\) | 0.814356 | 0.0445596 | ||||||||
\(335\) | 6.15410 | + | 6.15410i | 0.336234 | + | 0.336234i | ||||
\(336\) | 5.24812 | − | 2.20389i | 0.286308 | − | 0.120232i | ||||
\(337\) | 7.13984i | 0.388932i | 0.980909 | + | 0.194466i | \(0.0622974\pi\) | ||||
−0.980909 | + | 0.194466i | \(0.937703\pi\) | |||||||
\(338\) | 5.80664 | − | 5.80664i | 0.315840 | − | 0.315840i | ||||
\(339\) | −26.3507 | − | 10.7646i | −1.43118 | − | 0.584652i | ||||
\(340\) | 1.75515 | 0.0951863 | ||||||||
\(341\) | −6.36828 | + | 6.36828i | −0.344862 | + | 0.344862i | ||||
\(342\) | −0.784470 | − | 0.769315i | −0.0424193 | − | 0.0415998i | ||||
\(343\) | −10.5164 | −0.567831 | ||||||||
\(344\) | −6.15689 | −0.331957 | ||||||||
\(345\) | −1.56410 | − | 3.72460i | −0.0842085 | − | 0.200526i | ||||
\(346\) | 11.8005 | + | 11.8005i | 0.634400 | + | 0.634400i | ||||
\(347\) | 21.1695 | + | 21.1695i | 1.13644 | + | 1.13644i | 0.989084 | + | 0.147356i | \(0.0470762\pi\) |
0.147356 | + | 0.989084i | \(0.452924\pi\) | |||||||
\(348\) | 0.350418 | − | 0.857793i | 0.0187844 | − | 0.0459825i | ||||
\(349\) | 6.55526 | 0.350895 | 0.175447 | − | 0.984489i | \(-0.443863\pi\) | ||||
0.175447 | + | 0.984489i | \(0.443863\pi\) | |||||||
\(350\) | −2.32379 | + | 2.32379i | −0.124212 | + | 0.124212i | ||||
\(351\) | 21.9735 | − | 9.48068i | 1.17286 | − | 0.506041i | ||||
\(352\) | −1.23440 | − | 1.23440i | −0.0657939 | − | 0.0657939i | ||||
\(353\) | 4.68774 | + | 4.68774i | 0.249503 | + | 0.249503i | 0.820767 | − | 0.571264i | \(-0.193547\pi\) |
−0.571264 | + | 0.820767i | \(0.693547\pi\) | |||||||
\(354\) | −1.50587 | + | 0.632372i | −0.0800360 | + | 0.0336102i | ||||
\(355\) | 5.05043 | + | 5.05043i | 0.268049 | + | 0.268049i | ||||
\(356\) | −0.495164 | + | 0.495164i | −0.0262436 | + | 0.0262436i | ||||
\(357\) | 3.77813 | − | 9.24852i | 0.199960 | − | 0.489483i | ||||
\(358\) | − | 0.109863i | − | 0.00580645i | ||||||
\(359\) | − | 13.7603i | − | 0.726242i | −0.931742 | − | 0.363121i | \(-0.881711\pi\) | ||
0.931742 | − | 0.363121i | \(-0.118289\pi\) | |||||||
\(360\) | 2.14191 | + | 2.10053i | 0.112889 | + | 0.110708i | ||||
\(361\) | − | 18.8659i | − | 0.992940i | ||||||
\(362\) | −10.2143 | − | 10.2143i | −0.536852 | − | 0.536852i | ||||
\(363\) | 12.6998 | − | 5.33312i | 0.666565 | − | 0.279916i | ||||
\(364\) | 10.7025 | − | 10.7025i | 0.560963 | − | 0.560963i | ||||
\(365\) | 9.70237 | + | 9.70237i | 0.507845 | + | 0.507845i | ||||
\(366\) | −0.303429 | + | 0.127422i | −0.0158605 | + | 0.00666043i | ||||
\(367\) | 22.8151 | 1.19094 | 0.595468 | − | 0.803379i | \(-0.296966\pi\) | ||||
0.595468 | + | 0.803379i | \(0.296966\pi\) | |||||||
\(368\) | −1.64920 | + | 1.64920i | −0.0859703 | + | 0.0859703i | ||||
\(369\) | 20.8508 | − | 21.2615i | 1.08545 | − | 1.10683i | ||||
\(370\) | −4.68494 | + | 3.87960i | −0.243559 | + | 0.201691i | ||||
\(371\) | − | 30.7361i | − | 1.59574i | ||||||
\(372\) | −8.27203 | − | 3.37922i | −0.428885 | − | 0.175205i | ||||
\(373\) | 33.4109i | 1.72995i | 0.501813 | + | 0.864976i | \(0.332667\pi\) | ||||
−0.501813 | + | 0.864976i | \(0.667333\pi\) | |||||||
\(374\) | −3.06398 | −0.158435 | ||||||||
\(375\) | −1.60342 | − | 0.655016i | −0.0828002 | − | 0.0338249i | ||||
\(376\) | −1.61551 | − | 1.61551i | −0.0833137 | − | 0.0833137i | ||||
\(377\) | − | 2.46391i | − | 0.126898i | ||||||
\(378\) | 15.6791 | − | 6.76490i | 0.806447 | − | 0.347949i | ||||
\(379\) | 17.5721 | 0.902618 | 0.451309 | − | 0.892368i | \(-0.350957\pi\) | ||||
0.451309 | + | 0.892368i | \(0.350957\pi\) | |||||||
\(380\) | − | 0.366248i | − | 0.0187881i | ||||||
\(381\) | 13.9061 | − | 5.83970i | 0.712431 | − | 0.299177i | ||||
\(382\) | 12.5868 | 0.643998 | ||||||||
\(383\) | 10.0177 | − | 10.0177i | 0.511883 | − | 0.511883i | −0.403220 | − | 0.915103i | \(-0.632109\pi\) |
0.915103 | + | 0.403220i | \(0.132109\pi\) | |||||||
\(384\) | 0.655016 | − | 1.60342i | 0.0334261 | − | 0.0818242i | ||||
\(385\) | 4.05666 | − | 4.05666i | 0.206746 | − | 0.206746i | ||||
\(386\) | 20.5986i | 1.04844i | ||||||||
\(387\) | −18.4698 | + | 0.180145i | −0.938872 | + | 0.00915726i | ||||
\(388\) | −4.16187 | + | 4.16187i | −0.211287 | + | 0.211287i | ||||
\(389\) | 0.842156 | − | 0.842156i | 0.0426990 | − | 0.0426990i | −0.685435 | − | 0.728134i | \(-0.740388\pi\) |
0.728134 | + | 0.685435i | \(0.240388\pi\) | |||||||
\(390\) | 7.38476 | + | 3.01676i | 0.373942 | + | 0.152760i | ||||
\(391\) | 4.09356i | 0.207020i | ||||||||
\(392\) | 2.68698 | − | 2.68698i | 0.135713 | − | 0.135713i | ||||
\(393\) | −16.7445 | − | 6.84034i | −0.844650 | − | 0.345049i | ||||
\(394\) | −2.28258 | + | 2.28258i | −0.114995 | + | 0.114995i | ||||
\(395\) | −9.03148 | −0.454423 | ||||||||
\(396\) | −3.73915 | − | 3.66692i | −0.187900 | − | 0.184270i | ||||
\(397\) | 7.83011i | 0.392982i | 0.980506 | + | 0.196491i | \(0.0629546\pi\) | ||||
−0.980506 | + | 0.196491i | \(0.937045\pi\) | |||||||
\(398\) | −22.2772 | −1.11665 | ||||||||
\(399\) | −1.92989 | − | 0.788385i | −0.0966156 | − | 0.0394686i | ||||
\(400\) | 1.00000i | 0.0500000i | ||||||||
\(401\) | −13.4140 | − | 13.4140i | −0.669863 | − | 0.669863i | 0.287821 | − | 0.957684i | \(-0.407069\pi\) |
−0.957684 | + | 0.287821i | \(0.907069\pi\) | |||||||
\(402\) | 5.70074 | − | 13.9549i | 0.284327 | − | 0.696007i | ||||
\(403\) | −23.7604 | −1.18359 | ||||||||
\(404\) | 18.6620i | 0.928471i | ||||||||
\(405\) | 6.48688 | + | 6.23862i | 0.322336 | + | 0.310000i | ||||
\(406\) | − | 1.75811i | − | 0.0872536i | ||||||
\(407\) | 8.17856 | − | 6.77266i | 0.405396 | − | 0.335708i | ||||
\(408\) | −1.17704 | − | 2.80289i | −0.0582723 | − | 0.138764i | ||||
\(409\) | −6.10615 | + | 6.10615i | −0.301930 | + | 0.301930i | −0.841768 | − | 0.539839i | \(-0.818485\pi\) |
0.539839 | + | 0.841768i | \(0.318485\pi\) | |||||||
\(410\) | 9.92643 | 0.490231 | ||||||||
\(411\) | −6.48001 | − | 15.4308i | −0.319635 | − | 0.761147i | ||||
\(412\) | 6.60999 | + | 6.60999i | 0.325651 | + | 0.325651i | ||||
\(413\) | −2.19124 | + | 2.19124i | −0.107824 | + | 0.107824i | ||||
\(414\) | −4.89910 | + | 4.99561i | −0.240778 | + | 0.245521i | ||||
\(415\) | 10.3346 | + | 10.3346i | 0.507304 | + | 0.507304i | ||||
\(416\) | − | 4.60563i | − | 0.225810i | ||||||
\(417\) | 6.31001 | + | 15.0260i | 0.309002 | + | 0.735828i | ||||
\(418\) | 0.639363i | 0.0312723i | ||||||||
\(419\) | 10.4867i | 0.512308i | 0.966636 | + | 0.256154i | \(0.0824554\pi\) | ||||
−0.966636 | + | 0.256154i | \(0.917545\pi\) | |||||||
\(420\) | 5.26937 | + | 2.15260i | 0.257119 | + | 0.105036i | ||||
\(421\) | −23.4161 | + | 23.4161i | −1.14123 | + | 1.14123i | −0.153004 | + | 0.988226i | \(0.548895\pi\) |
−0.988226 | + | 0.153004i | \(0.951105\pi\) | |||||||
\(422\) | 9.68345 | + | 9.68345i | 0.471383 | + | 0.471383i | ||||
\(423\) | −4.89357 | − | 4.79904i | −0.237934 | − | 0.233337i | ||||
\(424\) | −6.61336 | − | 6.61336i | −0.321173 | − | 0.321173i | ||||
\(425\) | 1.24108 | + | 1.24108i | 0.0602011 | + | 0.0602011i | ||||
\(426\) | 4.67838 | − | 11.4522i | 0.226668 | − | 0.554863i | ||||
\(427\) | −0.441531 | + | 0.441531i | −0.0213672 | + | 0.0213672i | ||||
\(428\) | 10.8073 | 0.522393 | ||||||||
\(429\) | −12.8917 | − | 5.26639i | −0.622415 | − | 0.254264i | ||||
\(430\) | −4.35358 | − | 4.35358i | −0.209948 | − | 0.209948i | ||||
\(431\) | −17.7076 | − | 17.7076i | −0.852946 | − | 0.852946i | 0.137549 | − | 0.990495i | \(-0.456077\pi\) |
−0.990495 | + | 0.137549i | \(0.956077\pi\) | |||||||
\(432\) | 1.91804 | − | 4.82920i | 0.0922817 | − | 0.232345i | ||||
\(433\) | 6.23639 | 0.299702 | 0.149851 | − | 0.988709i | \(-0.452121\pi\) | ||||
0.149851 | + | 0.988709i | \(0.452121\pi\) | |||||||
\(434\) | −16.9542 | −0.813826 | ||||||||
\(435\) | 0.854334 | − | 0.358768i | 0.0409622 | − | 0.0172016i | ||||
\(436\) | −8.67304 | + | 8.67304i | −0.415363 | + | 0.415363i | ||||
\(437\) | 0.854206 | 0.0408622 | ||||||||
\(438\) | 8.98762 | − | 22.0009i | 0.429445 | − | 1.05124i | ||||
\(439\) | 4.50777 | − | 4.50777i | 0.215144 | − | 0.215144i | −0.591304 | − | 0.806449i | \(-0.701387\pi\) |
0.806449 | + | 0.591304i | \(0.201387\pi\) | |||||||
\(440\) | − | 1.74571i | − | 0.0832235i | ||||||
\(441\) | 7.98194 | − | 8.13917i | 0.380092 | − | 0.387580i | ||||
\(442\) | −5.71594 | − | 5.71594i | −0.271880 | − | 0.271880i | ||||
\(443\) | −13.6288 | −0.647524 | −0.323762 | − | 0.946139i | \(-0.604948\pi\) | ||||
−0.323762 | + | 0.946139i | \(0.604948\pi\) | |||||||
\(444\) | 9.33738 | + | 4.87990i | 0.443132 | + | 0.231590i | ||||
\(445\) | −0.700267 | −0.0331958 | ||||||||
\(446\) | 12.2365 | + | 12.2365i | 0.579413 | + | 0.579413i | ||||
\(447\) | 4.85127 | + | 11.5523i | 0.229457 | + | 0.546406i | ||||
\(448\) | − | 3.28633i | − | 0.155264i | ||||||
\(449\) | −7.59604 | + | 7.59604i | −0.358479 | + | 0.358479i | −0.863252 | − | 0.504773i | \(-0.831576\pi\) |
0.504773 | + | 0.863252i | \(0.331576\pi\) | |||||||
\(450\) | 0.0292590 | + | 2.99986i | 0.00137928 | + | 0.141415i | ||||
\(451\) | −17.3287 | −0.815975 | ||||||||
\(452\) | −11.6207 | + | 11.6207i | −0.546590 | + | 0.546590i | ||||
\(453\) | 10.1045 | + | 24.0620i | 0.474753 | + | 1.13053i | ||||
\(454\) | 1.03184 | 0.0484268 | ||||||||
\(455\) | 15.1356 | 0.709569 | ||||||||
\(456\) | −0.584882 | + | 0.245614i | −0.0273896 | + | 0.0115019i | ||||
\(457\) | 11.5653 | + | 11.5653i | 0.541001 | + | 0.541001i | 0.923822 | − | 0.382822i | \(-0.125048\pi\) |
−0.382822 | + | 0.923822i | \(0.625048\pi\) | |||||||
\(458\) | −13.3322 | − | 13.3322i | −0.622973 | − | 0.622973i | ||||
\(459\) | −3.61297 | − | 8.37384i | −0.168639 | − | 0.390857i | ||||
\(460\) | −2.33232 | −0.108745 | ||||||||
\(461\) | 15.5874 | − | 15.5874i | 0.725979 | − | 0.725979i | −0.243837 | − | 0.969816i | \(-0.578406\pi\) |
0.969816 | + | 0.243837i | \(0.0784062\pi\) | |||||||
\(462\) | −9.19879 | − | 3.75781i | −0.427966 | − | 0.174829i | ||||
\(463\) | −10.8674 | − | 10.8674i | −0.505049 | − | 0.505049i | 0.407954 | − | 0.913003i | \(-0.366243\pi\) |
−0.913003 | + | 0.407954i | \(0.866243\pi\) | |||||||
\(464\) | −0.378286 | − | 0.378286i | −0.0175615 | − | 0.0175615i | ||||
\(465\) | −3.45974 | − | 8.23868i | −0.160442 | − | 0.382060i | ||||
\(466\) | −2.74513 | − | 2.74513i | −0.127166 | − | 0.127166i | ||||
\(467\) | 24.9944 | − | 24.9944i | 1.15660 | − | 1.15660i | 0.171404 | − | 0.985201i | \(-0.445170\pi\) |
0.985201 | − | 0.171404i | \(-0.0548303\pi\) | |||||||
\(468\) | −0.134756 | − | 13.8162i | −0.00622911 | − | 0.638656i | ||||
\(469\) | − | 28.6016i | − | 1.32070i | ||||||
\(470\) | − | 2.28468i | − | 0.105384i | ||||||
\(471\) | −12.8770 | + | 5.40755i | −0.593341 | + | 0.249167i | ||||
\(472\) | 0.942963i | 0.0434034i | ||||||||
\(473\) | 7.60009 | + | 7.60009i | 0.349452 | + | 0.349452i | ||||
\(474\) | 6.05672 | + | 14.4229i | 0.278194 | + | 0.662464i | ||||
\(475\) | 0.258976 | − | 0.258976i | 0.0118827 | − | 0.0118827i | ||||
\(476\) | −4.07859 | − | 4.07859i | −0.186942 | − | 0.186942i | ||||
\(477\) | −20.0327 | − | 19.6457i | −0.917232 | − | 0.899513i | ||||
\(478\) | 12.0603 | 0.551623 | ||||||||
\(479\) | 10.7474 | − | 10.7474i | 0.491062 | − | 0.491062i | −0.417579 | − | 0.908641i | \(-0.637121\pi\) |
0.908641 | + | 0.417579i | \(0.137121\pi\) | |||||||
\(480\) | 1.59695 | − | 0.670623i | 0.0728907 | − | 0.0306096i | ||||
\(481\) | 27.8919 | + | 2.62274i | 1.27176 | + | 0.119587i | ||||
\(482\) | − | 20.3160i | − | 0.925369i | ||||||
\(483\) | −5.02054 | + | 12.2898i | −0.228442 | + | 0.559206i | ||||
\(484\) | − | 7.95249i | − | 0.361477i | ||||||
\(485\) | −5.88577 | −0.267259 | ||||||||
\(486\) | 5.61255 | − | 14.5430i | 0.254590 | − | 0.659685i | ||||
\(487\) | 5.16144 | + | 5.16144i | 0.233887 | + | 0.233887i | 0.814313 | − | 0.580426i | \(-0.197114\pi\) |
−0.580426 | + | 0.814313i | \(0.697114\pi\) | |||||||
\(488\) | 0.190005i | 0.00860111i | ||||||||
\(489\) | −2.06702 | + | 5.05988i | −0.0934739 | + | 0.228816i | ||||
\(490\) | 3.79996 | 0.171665 | ||||||||
\(491\) | − | 22.5148i | − | 1.01608i | −0.861334 | − | 0.508039i | \(-0.830371\pi\) | ||
0.861334 | − | 0.508039i | \(-0.169629\pi\) | |||||||
\(492\) | −6.65689 | − | 15.8521i | −0.300116 | − | 0.714666i | ||||
\(493\) | −0.938964 | −0.0422888 | ||||||||
\(494\) | −1.19275 | + | 1.19275i | −0.0536643 | + | 0.0536643i | ||||
\(495\) | −0.0510778 | − | 5.23688i | −0.00229578 | − | 0.235380i | ||||
\(496\) | −3.64796 | + | 3.64796i | −0.163798 | + | 0.163798i | ||||
\(497\) | − | 23.4722i | − | 1.05287i | ||||||
\(498\) | 9.57323 | − | 23.4344i | 0.428987 | − | 1.05012i | ||||
\(499\) | −17.6251 | + | 17.6251i | −0.789008 | + | 0.789008i | −0.981332 | − | 0.192323i | \(-0.938398\pi\) |
0.192323 | + | 0.981332i | \(0.438398\pi\) | |||||||
\(500\) | −0.707107 | + | 0.707107i | −0.0316228 | + | 0.0316228i | ||||
\(501\) | 0.533416 | − | 1.30575i | 0.0238313 | − | 0.0583368i | ||||
\(502\) | 19.4436i | 0.867811i | ||||||||
\(503\) | 5.33267 | − | 5.33267i | 0.237772 | − | 0.237772i | −0.578155 | − | 0.815927i | \(-0.696227\pi\) |
0.815927 | + | 0.578155i | \(0.196227\pi\) | |||||||
\(504\) | −0.0961548 | − | 9.85852i | −0.00428308 | − | 0.439133i | ||||
\(505\) | −13.1960 | + | 13.1960i | −0.587216 | + | 0.587216i | ||||
\(506\) | 4.07155 | 0.181002 | ||||||||
\(507\) | −5.50704 | − | 13.1139i | −0.244576 | − | 0.582410i | ||||
\(508\) | − | 8.70788i | − | 0.386350i | ||||||
\(509\) | −42.0833 | −1.86531 | −0.932654 | − | 0.360772i | \(-0.882513\pi\) | ||||
−0.932654 | + | 0.360772i | \(0.882513\pi\) | |||||||
\(510\) | 1.14965 | − | 2.81424i | 0.0509073 | − | 0.124617i | ||||
\(511\) | − | 45.0925i | − | 1.99477i | ||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −1.74737 | + | 0.753921i | −0.0771485 | + | 0.0332864i | ||||
\(514\) | 20.9726 | 0.925062 | ||||||||
\(515\) | 9.34793i | 0.411919i | ||||||||
\(516\) | −4.03286 | + | 9.87207i | −0.177537 | + | 0.434594i | ||||
\(517\) | 3.98839i | 0.175409i | ||||||||
\(518\) | 19.9022 | + | 1.87145i | 0.874451 | + | 0.0822266i | ||||
\(519\) | 26.6507 | − | 11.1917i | 1.16984 | − | 0.491259i | ||||
\(520\) | 3.25667 | − | 3.25667i | 0.142815 | − | 0.142815i | ||||
\(521\) | −31.4829 | −1.37929 | −0.689645 | − | 0.724147i | \(-0.742234\pi\) | ||||
−0.689645 | + | 0.724147i | \(0.742234\pi\) | |||||||
\(522\) | −1.14587 | − | 1.12374i | −0.0501534 | − | 0.0491846i | ||||
\(523\) | −23.0706 | − | 23.0706i | −1.00880 | − | 1.00880i | −0.999961 | − | 0.00884384i | \(-0.997185\pi\) |
−0.00884384 | − | 0.999961i | \(-0.502815\pi\) | |||||||
\(524\) | −7.38432 | + | 7.38432i | −0.322586 | + | 0.322586i | ||||
\(525\) | 2.20389 | + | 5.24812i | 0.0961855 | + | 0.229047i | ||||
\(526\) | −6.42478 | − | 6.42478i | −0.280134 | − | 0.280134i | ||||
\(527\) | 9.05480i | 0.394433i | ||||||||
\(528\) | −2.78782 | + | 1.17071i | −0.121324 | + | 0.0509488i | ||||
\(529\) | 17.5603i | 0.763492i | ||||||||
\(530\) | − | 9.35271i | − | 0.406256i | ||||||
\(531\) | 0.0275902 | + | 2.82875i | 0.00119731 | + | 0.122757i | ||||
\(532\) | −0.851082 | + | 0.851082i | −0.0368991 | + | 0.0368991i | ||||
\(533\) | −32.3271 | − | 32.3271i | −1.40024 | − | 1.40024i | ||||
\(534\) | 0.469615 | + | 1.11829i | 0.0203222 | + | 0.0483933i | ||||
\(535\) | 7.64195 | + | 7.64195i | 0.330390 | + | 0.330390i | ||||
\(536\) | −6.15410 | − | 6.15410i | −0.265816 | − | 0.265816i | ||||
\(537\) | −0.176157 | − | 0.0719622i | −0.00760173 | − | 0.00310540i | ||||
\(538\) | −13.5390 | + | 13.5390i | −0.583710 | + | 0.583710i | ||||
\(539\) | −6.63364 | −0.285731 | ||||||||
\(540\) | 4.77102 | − | 2.05850i | 0.205312 | − | 0.0885836i | ||||
\(541\) | 23.9583 | + | 23.9583i | 1.03005 | + | 1.03005i | 0.999534 | + | 0.0305122i | \(0.00971385\pi\) |
0.0305122 | + | 0.999534i | \(0.490286\pi\) | |||||||
\(542\) | 21.0268 | + | 21.0268i | 0.903180 | + | 0.903180i | ||||
\(543\) | −23.0683 | + | 9.68728i | −0.989957 | + | 0.415721i | ||||
\(544\) | −1.75515 | −0.0752513 | ||||||||
\(545\) | −12.2655 | −0.525397 | ||||||||
\(546\) | −10.1503 | − | 24.1709i | −0.434392 | − | 1.03442i | ||||
\(547\) | −2.23881 | + | 2.23881i | −0.0957245 | + | 0.0957245i | −0.753347 | − | 0.657623i | \(-0.771562\pi\) |
0.657623 | + | 0.753347i | \(0.271562\pi\) | |||||||
\(548\) | −9.66267 | −0.412769 | ||||||||
\(549\) | 0.00555936 | + | 0.569987i | 0.000237268 | + | 0.0243265i | ||||
\(550\) | 1.23440 | − | 1.23440i | 0.0526352 | − | 0.0526352i | ||||
\(551\) | 0.195934i | 0.00834708i | ||||||||
\(552\) | 1.56410 | + | 3.72460i | 0.0665727 | + | 0.158530i | ||||
\(553\) | 20.9872 | + | 20.9872i | 0.892468 | + | 0.892468i | ||||
\(554\) | 1.36310 | 0.0579126 | ||||||||
\(555\) | 3.15192 | + | 10.0531i | 0.133791 | + | 0.426732i | ||||
\(556\) | 9.40917 | 0.399038 | ||||||||
\(557\) | −20.2197 | − | 20.2197i | −0.856737 | − | 0.856737i | 0.134215 | − | 0.990952i | \(-0.457149\pi\) |
−0.990952 | + | 0.134215i | \(0.957149\pi\) | |||||||
\(558\) | −10.8366 | + | 11.0501i | −0.458751 | + | 0.467788i | ||||
\(559\) | 28.3563i | 1.19935i | ||||||||
\(560\) | 2.32379 | − | 2.32379i | 0.0981979 | − | 0.0981979i | ||||
\(561\) | −2.00696 | + | 4.91285i | −0.0847337 | + | 0.207421i | ||||
\(562\) | 20.8086 | 0.877757 | ||||||||
\(563\) | 8.96911 | − | 8.96911i | 0.378003 | − | 0.378003i | −0.492378 | − | 0.870381i | \(-0.663872\pi\) |
0.870381 | + | 0.492378i | \(0.163872\pi\) | |||||||
\(564\) | −3.64853 | + | 1.53216i | −0.153631 | + | 0.0645155i | ||||
\(565\) | −16.4341 | −0.691387 | ||||||||
\(566\) | −1.05727 | −0.0444404 | ||||||||
\(567\) | −0.576902 | − | 29.5713i | −0.0242276 | − | 1.24188i | ||||
\(568\) | −5.05043 | − | 5.05043i | −0.211911 | − | 0.211911i | ||||
\(569\) | 1.66794 | + | 1.66794i | 0.0699235 | + | 0.0699235i | 0.741204 | − | 0.671280i | \(-0.234255\pi\) |
−0.671280 | + | 0.741204i | \(0.734255\pi\) | |||||||
\(570\) | −0.587249 | − | 0.239898i | −0.0245972 | − | 0.0100482i | ||||
\(571\) | −23.6993 | −0.991783 | −0.495892 | − | 0.868384i | \(-0.665159\pi\) | ||||
−0.495892 | + | 0.868384i | \(0.665159\pi\) | |||||||
\(572\) | −5.68521 | + | 5.68521i | −0.237710 | + | 0.237710i | ||||
\(573\) | 8.24457 | − | 20.1820i | 0.344422 | − | 0.843113i | ||||
\(574\) | −23.0669 | − | 23.0669i | −0.962794 | − | 0.962794i | ||||
\(575\) | −1.64920 | − | 1.64920i | −0.0687762 | − | 0.0687762i | ||||
\(576\) | −2.14191 | − | 2.10053i | −0.0892462 | − | 0.0875221i | ||||
\(577\) | 10.0160 | + | 10.0160i | 0.416973 | + | 0.416973i | 0.884159 | − | 0.467186i | \(-0.154732\pi\) |
−0.467186 | + | 0.884159i | \(0.654732\pi\) | |||||||
\(578\) | 9.84254 | − | 9.84254i | 0.409396 | − | 0.409396i | ||||
\(579\) | 33.0282 | + | 13.4924i | 1.37261 | + | 0.560726i | ||||
\(580\) | − | 0.534977i | − | 0.0222137i | ||||||
\(581\) | − | 48.0306i | − | 1.99265i | ||||||
\(582\) | 3.94713 | + | 9.39931i | 0.163614 | + | 0.389614i | ||||
\(583\) | 16.3271i | 0.676201i | ||||||||
\(584\) | −9.70237 | − | 9.70237i | −0.401487 | − | 0.401487i | ||||
\(585\) | 9.67426 | − | 9.86484i | 0.399982 | − | 0.407861i | ||||
\(586\) | 19.7902 | − | 19.7902i | 0.817525 | − | 0.817525i | ||||
\(587\) | 13.1493 | + | 13.1493i | 0.542729 | + | 0.542729i | 0.924328 | − | 0.381599i | \(-0.124626\pi\) |
−0.381599 | + | 0.924328i | \(0.624626\pi\) | |||||||
\(588\) | −2.54834 | − | 6.06837i | −0.105092 | − | 0.250255i | ||||
\(589\) | 1.88947 | 0.0778543 | ||||||||
\(590\) | −0.666775 | + | 0.666775i | −0.0274507 | + | 0.0274507i | ||||
\(591\) | 2.16481 | + | 5.15506i | 0.0890483 | + | 0.212051i | ||||
\(592\) | 4.68494 | − | 3.87960i | 0.192550 | − | 0.159451i | ||||
\(593\) | − | 10.4729i | − | 0.430072i | −0.976606 | − | 0.215036i | \(-0.931013\pi\) | ||
0.976606 | − | 0.215036i | \(-0.0689870\pi\) | |||||||
\(594\) | −8.32881 | + | 3.59354i | −0.341735 | + | 0.147445i | ||||
\(595\) | − | 5.76799i | − | 0.236465i | ||||||
\(596\) | 7.23397 | 0.296315 | ||||||||
\(597\) | −14.5919 | + | 35.7196i | −0.597206 | + | 1.46191i | ||||
\(598\) | 7.59559 | + | 7.59559i | 0.310607 | + | 0.310607i | ||||
\(599\) | − | 26.9297i | − | 1.10032i | −0.835060 | − | 0.550159i | \(-0.814567\pi\) | ||
0.835060 | − | 0.550159i | \(-0.185433\pi\) | |||||||
\(600\) | 1.60342 | + | 0.655016i | 0.0654593 | + | 0.0267409i | ||||
\(601\) | 3.63775 | 0.148387 | 0.0741934 | − | 0.997244i | \(-0.476362\pi\) | ||||
0.0741934 | + | 0.997244i | \(0.476362\pi\) | |||||||
\(602\) | 20.2336i | 0.824658i | ||||||||
\(603\) | −18.6415 | − | 18.2813i | −0.759139 | − | 0.744474i | ||||
\(604\) | 15.0674 | 0.613084 | ||||||||
\(605\) | 5.62326 | − | 5.62326i | 0.228618 | − | 0.228618i | ||||
\(606\) | 29.9231 | + | 12.2239i | 1.21554 | + | 0.496563i | ||||
\(607\) | −8.68800 | + | 8.68800i | −0.352635 | + | 0.352635i | −0.861089 | − | 0.508454i | \(-0.830217\pi\) |
0.508454 | + | 0.861089i | \(0.330217\pi\) | |||||||
\(608\) | 0.366248i | 0.0148533i | ||||||||
\(609\) | −2.81899 | − | 1.15159i | −0.114231 | − | 0.0466648i | ||||
\(610\) | −0.134354 | + | 0.134354i | −0.00543982 | + | 0.00543982i | ||||
\(611\) | −7.44045 | + | 7.44045i | −0.301008 | + | 0.301008i | ||||
\(612\) | −5.26519 | + | 0.0513539i | −0.212833 | + | 0.00207586i | ||||
\(613\) | − | 9.16353i | − | 0.370112i | −0.982728 | − | 0.185056i | \(-0.940753\pi\) | ||
0.982728 | − | 0.185056i | \(-0.0592466\pi\) | |||||||
\(614\) | −2.19014 | + | 2.19014i | −0.0883870 | + | 0.0883870i | ||||
\(615\) | 6.50197 | − | 15.9162i | 0.262185 | − | 0.641804i | ||||
\(616\) | −4.05666 | + | 4.05666i | −0.163447 | + | 0.163447i | ||||
\(617\) | 35.6832 | 1.43655 | 0.718275 | − | 0.695759i | \(-0.244932\pi\) | ||||
0.718275 | + | 0.695759i | \(0.244932\pi\) | |||||||
\(618\) | 14.9282 | − | 6.26894i | 0.600502 | − | 0.252174i | ||||
\(619\) | 13.9865i | 0.562167i | 0.959683 | + | 0.281083i | \(0.0906937\pi\) | ||||
−0.959683 | + | 0.281083i | \(0.909306\pi\) | |||||||
\(620\) | −5.15899 | −0.207190 | ||||||||
\(621\) | 4.80107 | + | 11.1275i | 0.192660 | + | 0.446532i | ||||
\(622\) | 8.66781i | 0.347548i | ||||||||
\(623\) | 1.62727 | + | 1.62727i | 0.0651952 | + | 0.0651952i | ||||
\(624\) | −7.38476 | − | 3.01676i | −0.295627 | − | 0.120767i | ||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 20.4155i | 0.815969i | ||||||||
\(627\) | 1.02517 | + | 0.418793i | 0.0409412 | + | 0.0167250i | ||||
\(628\) | 8.06347i | 0.321768i | ||||||||
\(629\) | 0.999493 | − | 10.6293i | 0.0398524 | − | 0.423816i | ||||
\(630\) | 6.90303 | − | 7.03902i | 0.275023 | − | 0.280441i | ||||
\(631\) | −0.282325 | + | 0.282325i | −0.0112392 | + | 0.0112392i | −0.712704 | − | 0.701465i | \(-0.752530\pi\) |
0.701465 | + | 0.712704i | \(0.252530\pi\) | |||||||
\(632\) | 9.03148 | 0.359253 | ||||||||
\(633\) | 21.8695 | − | 9.18382i | 0.869233 | − | 0.365024i | ||||
\(634\) | 11.8475 | + | 11.8475i | 0.470524 | + | 0.470524i | ||||
\(635\) | 6.15740 | − | 6.15740i | 0.244349 | − | 0.244349i | ||||
\(636\) | −14.9359 | + | 6.27214i | −0.592245 | + | 0.248707i | ||||
\(637\) | −12.3752 | − | 12.3752i | −0.490325 | − | 0.490325i | ||||
\(638\) | 0.933915i | 0.0369741i | ||||||||
\(639\) | −15.2983 | − | 15.0028i | −0.605193 | − | 0.593502i | ||||
\(640\) | − | 1.00000i | − | 0.0395285i | ||||||
\(641\) | − | 25.2386i | − | 0.996866i | −0.866928 | − | 0.498433i | \(-0.833909\pi\) | ||
0.866928 | − | 0.498433i | \(-0.166091\pi\) | |||||||
\(642\) | 7.07898 | − | 17.3287i | 0.279385 | − | 0.683909i | ||||
\(643\) | −21.1632 | + | 21.1632i | −0.834596 | + | 0.834596i | −0.988142 | − | 0.153546i | \(-0.950931\pi\) |
0.153546 | + | 0.988142i | \(0.450931\pi\) | |||||||
\(644\) | 5.41980 | + | 5.41980i | 0.213570 | + | 0.213570i | ||||
\(645\) | −9.83227 | + | 4.12895i | −0.387145 | + | 0.162577i | ||||
\(646\) | 0.454542 | + | 0.454542i | 0.0178837 | + | 0.0178837i | ||||
\(647\) | 26.0237 | + | 26.0237i | 1.02310 | + | 1.02310i | 0.999727 | + | 0.0233686i | \(0.00743914\pi\) |
0.0233686 | + | 0.999727i | \(0.492561\pi\) | |||||||
\(648\) | −6.48688 | − | 6.23862i | −0.254829 | − | 0.245076i | ||||
\(649\) | 1.16400 | − | 1.16400i | 0.0456909 | − | 0.0456909i | ||||
\(650\) | 4.60563 | 0.180648 | ||||||||
\(651\) | −11.1052 | + | 27.1846i | −0.435249 | + | 1.06545i | ||||
\(652\) | 2.23140 | + | 2.23140i | 0.0873885 | + | 0.0873885i | ||||
\(653\) | 17.4422 | + | 17.4422i | 0.682567 | + | 0.682567i | 0.960578 | − | 0.278011i | \(-0.0896751\pi\) |
−0.278011 | + | 0.960578i | \(0.589675\pi\) | |||||||
\(654\) | 8.22554 | + | 19.5875i | 0.321644 | + | 0.765932i | ||||
\(655\) | −10.4430 | −0.408042 | ||||||||
\(656\) | −9.92643 | −0.387562 | ||||||||
\(657\) | −29.3896 | − | 28.8218i | −1.14660 | − | 1.12445i | ||||
\(658\) | −5.30910 | + | 5.30910i | −0.206970 | + | 0.206970i | ||||
\(659\) | −10.4238 | −0.406055 | −0.203028 | − | 0.979173i | \(-0.565078\pi\) | ||||
−0.203028 | + | 0.979173i | \(0.565078\pi\) | |||||||
\(660\) | −2.79911 | − | 1.14347i | −0.108955 | − | 0.0445094i | ||||
\(661\) | 16.8687 | − | 16.8687i | 0.656115 | − | 0.656115i | −0.298343 | − | 0.954459i | \(-0.596434\pi\) |
0.954459 | + | 0.298343i | \(0.0964340\pi\) | |||||||
\(662\) | − | 3.32436i | − | 0.129205i | ||||||
\(663\) | −12.9091 | + | 5.42102i | −0.501347 | + | 0.210535i | ||||
\(664\) | −10.3346 | − | 10.3346i | −0.401059 | − | 0.401059i | ||||
\(665\) | −1.20361 | −0.0466741 | ||||||||
\(666\) | 13.9407 | − | 11.7753i | 0.540189 | − | 0.456285i | ||||
\(667\) | 1.24773 | 0.0483125 | ||||||||
\(668\) | −0.575837 | − | 0.575837i | −0.0222798 | − | 0.0222798i | ||||
\(669\) | 27.6353 | − | 11.6051i | 1.06844 | − | 0.448680i | ||||
\(670\) | − | 8.70321i | − | 0.336234i | ||||||
\(671\) | 0.234543 | − | 0.234543i | 0.00905442 | − | 0.00905442i | ||||
\(672\) | −5.26937 | − | 2.15260i | −0.203270 | − | 0.0830383i | ||||
\(673\) | 37.8385 | 1.45857 | 0.729284 | − | 0.684211i | \(-0.239853\pi\) | ||||
0.729284 | + | 0.684211i | \(0.239853\pi\) | |||||||
\(674\) | 5.04863 | − | 5.04863i | 0.194466 | − | 0.194466i | ||||
\(675\) | 4.82920 | + | 1.91804i | 0.185876 | + | 0.0738254i | ||||
\(676\) | −8.21183 | −0.315840 | ||||||||
\(677\) | 11.3003 | 0.434306 | 0.217153 | − | 0.976138i | \(-0.430323\pi\) | ||||
0.217153 | + | 0.976138i | \(0.430323\pi\) | |||||||
\(678\) | 11.0211 | + | 26.2445i | 0.423262 | + | 1.00791i | ||||
\(679\) | 13.6773 | + | 13.6773i | 0.524885 | + | 0.524885i | ||||
\(680\) | −1.24108 | − | 1.24108i | −0.0475931 | − | 0.0475931i | ||||
\(681\) | 0.675873 | − | 1.65448i | 0.0258995 | − | 0.0633997i | ||||
\(682\) | 9.00611 | 0.344862 | ||||||||
\(683\) | −5.37507 | + | 5.37507i | −0.205671 | + | 0.205671i | −0.802425 | − | 0.596753i | \(-0.796457\pi\) |
0.596753 | + | 0.802425i | \(0.296457\pi\) | |||||||
\(684\) | 0.0107161 | + | 1.09869i | 0.000409739 | + | 0.0420095i | ||||
\(685\) | −6.83254 | − | 6.83254i | −0.261058 | − | 0.261058i | ||||
\(686\) | 7.43620 | + | 7.43620i | 0.283915 | + | 0.283915i | ||||
\(687\) | −30.1099 | + | 12.6443i | −1.14877 | + | 0.482411i | ||||
\(688\) | 4.35358 | + | 4.35358i | 0.165979 | + | 0.165979i | ||||
\(689\) | −30.4587 | + | 30.4587i | −1.16038 | + | 1.16038i | ||||
\(690\) | −1.52770 | + | 3.73968i | −0.0581587 | + | 0.142367i | ||||
\(691\) | 35.6614i | 1.35663i | 0.734773 | + | 0.678313i | \(0.237289\pi\) | ||||
−0.734773 | + | 0.678313i | \(0.762711\pi\) | |||||||
\(692\) | − | 16.6885i | − | 0.634400i | ||||||
\(693\) | −12.0507 | + | 12.2881i | −0.457768 | + | 0.466786i | ||||
\(694\) | − | 29.9382i | − | 1.13644i | ||||||
\(695\) | 6.65329 | + | 6.65329i | 0.252374 | + | 0.252374i | ||||
\(696\) | −0.854334 | + | 0.358768i | −0.0323835 | + | 0.0135991i | ||||
\(697\) | −12.3195 | + | 12.3195i | −0.466633 | + | 0.466633i | ||||
\(698\) | −4.63527 | − | 4.63527i | −0.175447 | − | 0.175447i | ||||
\(699\) | −6.19970 | + | 2.60349i | −0.234494 | + | 0.0984732i | ||||
\(700\) | 3.28633 | 0.124212 | ||||||||
\(701\) | −7.81125 | + | 7.81125i | −0.295027 | + | 0.295027i | −0.839062 | − | 0.544035i | \(-0.816896\pi\) |
0.544035 | + | 0.839062i | \(0.316896\pi\) | |||||||
\(702\) | −22.2415 | − | 8.83378i | −0.839451 | − | 0.333410i | ||||
\(703\) | −2.21802 | − | 0.208565i | −0.0836540 | − | 0.00786618i | ||||
\(704\) | 1.74571i | 0.0657939i | ||||||||
\(705\) | −3.66330 | − | 1.49650i | −0.137968 | − | 0.0563615i | ||||
\(706\) | − | 6.62946i | − | 0.249503i | ||||||
\(707\) | 61.3296 | 2.30654 | ||||||||
\(708\) | 1.51196 | + | 0.617655i | 0.0568231 | + | 0.0232129i | ||||
\(709\) | 27.9441 | + | 27.9441i | 1.04946 | + | 1.04946i | 0.998711 | + | 0.0507522i | \(0.0161619\pi\) |
0.0507522 | + | 0.998711i | \(0.483838\pi\) | |||||||
\(710\) | − | 7.14239i | − | 0.268049i | ||||||
\(711\) | 27.0932 | − | 0.264252i | 1.01607 | − | 0.00991024i | ||||
\(712\) | 0.700267 | 0.0262436 | ||||||||
\(713\) | − | 12.0324i | − | 0.450617i | ||||||
\(714\) | −9.21123 | + | 3.86815i | −0.344722 | + | 0.144762i | ||||
\(715\) | −8.04010 | −0.300683 | ||||||||
\(716\) | −0.0776850 | + | 0.0776850i | −0.00290323 | + | 0.00290323i | ||||
\(717\) | 7.89966 | − | 19.3376i | 0.295018 | − | 0.722178i | ||||
\(718\) | −9.73002 | + | 9.73002i | −0.363121 | + | 0.363121i | ||||
\(719\) | 14.9574i | 0.557817i | 0.960318 | + | 0.278908i | \(0.0899726\pi\) | ||||
−0.960318 | + | 0.278908i | \(0.910027\pi\) | |||||||
\(720\) | −0.0292590 | − | 2.99986i | −0.00109042 | − | 0.111798i | ||||
\(721\) | 21.7226 | − | 21.7226i | 0.808992 | − | 0.808992i | ||||
\(722\) | −13.3402 | + | 13.3402i | −0.496470 | + | 0.496470i | ||||
\(723\) | −32.5751 | − | 13.3073i | −1.21148 | − | 0.494904i | ||||
\(724\) | 14.4452i | 0.536852i | ||||||||
\(725\) | 0.378286 | − | 0.378286i | 0.0140492 | − | 0.0140492i | ||||
\(726\) | −12.7512 | − | 5.20901i | −0.473241 | − | 0.193324i | ||||
\(727\) | −7.87230 | + | 7.87230i | −0.291967 | + | 0.291967i | −0.837857 | − | 0.545890i | \(-0.816192\pi\) |
0.545890 | + | 0.837857i | \(0.316192\pi\) | |||||||
\(728\) | −15.1356 | −0.560963 | ||||||||
\(729\) | −19.6423 | − | 18.5252i | −0.727491 | − | 0.686117i | ||||
\(730\) | − | 13.7212i | − | 0.507845i | ||||||
\(731\) | 10.8062 | 0.399684 | ||||||||
\(732\) | 0.304657 | + | 0.124456i | 0.0112605 | + | 0.00460003i | ||||
\(733\) | 2.19338i | 0.0810144i | 0.999179 | + | 0.0405072i | \(0.0128974\pi\) | ||||
−0.999179 | + | 0.0405072i | \(0.987103\pi\) | |||||||
\(734\) | −16.1327 | − | 16.1327i | −0.595468 | − | 0.595468i | ||||
\(735\) | 2.48904 | − | 6.09293i | 0.0918095 | − | 0.224741i | ||||
\(736\) | 2.33232 | 0.0859703 | ||||||||
\(737\) | 15.1933i | 0.559652i | ||||||||
\(738\) | −29.7779 | + | 0.290438i | −1.09614 | + | 0.0106912i | ||||
\(739\) | − | 53.7157i | − | 1.97597i | −0.154565 | − | 0.987983i | \(-0.549398\pi\) | ||
0.154565 | − | 0.987983i | \(-0.450602\pi\) | |||||||
\(740\) | 6.05605 | + | 0.569464i | 0.222625 | + | 0.0209339i | ||||
\(741\) | 1.13121 | + | 2.69375i | 0.0415560 | + | 0.0989573i | ||||
\(742\) | −21.7337 | + | 21.7337i | −0.797869 | + | 0.797869i | ||||
\(743\) | −6.02994 | −0.221217 | −0.110609 | − | 0.993864i | \(-0.535280\pi\) | ||||
−0.110609 | + | 0.993864i | \(0.535280\pi\) | |||||||
\(744\) | 3.45974 | + | 8.23868i | 0.126840 | + | 0.302045i | ||||
\(745\) | 5.11519 | + | 5.11519i | 0.187406 | + | 0.187406i | ||||
\(746\) | 23.6251 | − | 23.6251i | 0.864976 | − | 0.864976i | ||||
\(747\) | −31.3046 | − | 30.6998i | −1.14537 | − | 1.12325i | ||||
\(748\) | 2.16656 | + | 2.16656i | 0.0792173 | + | 0.0792173i | ||||
\(749\) | − | 35.5165i | − | 1.29774i | ||||||
\(750\) | 0.670623 | + | 1.59695i | 0.0244877 | + | 0.0583125i | ||||
\(751\) | 45.2316i | 1.65052i | 0.564750 | + | 0.825262i | \(0.308973\pi\) | ||||
−0.564750 | + | 0.825262i | \(0.691027\pi\) | |||||||
\(752\) | 2.28468i | 0.0833137i | ||||||||
\(753\) | 31.1763 | + | 12.7359i | 1.13613 | + | 0.464121i | ||||
\(754\) | −1.74224 | + | 1.74224i | −0.0634488 | + | 0.0634488i | ||||
\(755\) | 10.6543 | + | 10.6543i | 0.387748 | + | 0.387748i | ||||
\(756\) | −15.8703 | − | 6.30331i | −0.577198 | − | 0.229249i | ||||
\(757\) | −37.4148 | − | 37.4148i | −1.35986 | − | 1.35986i | −0.874077 | − | 0.485787i | \(-0.838533\pi\) |
−0.485787 | − | 0.874077i | \(-0.661467\pi\) | |||||||
\(758\) | −12.4254 | − | 12.4254i | −0.451309 | − | 0.451309i | ||||
\(759\) | 2.66693 | − | 6.52840i | 0.0968034 | − | 0.236966i | ||||
\(760\) | −0.258976 | + | 0.258976i | −0.00939406 | + | 0.00939406i | ||||
\(761\) | 0.131478 | 0.00476608 | 0.00238304 | − | 0.999997i | \(-0.499241\pi\) | ||||
0.00238304 | + | 0.999997i | \(0.499241\pi\) | |||||||
\(762\) | −13.9624 | − | 5.70380i | −0.505804 | − | 0.206627i | ||||
\(763\) | 28.5025 | + | 28.5025i | 1.03186 | + | 1.03186i | ||||
\(764\) | −8.90023 | − | 8.90023i | −0.321999 | − | 0.321999i | ||||
\(765\) | −3.75937 | − | 3.68674i | −0.135920 | − | 0.133294i | ||||
\(766\) | −14.1672 | −0.511883 | ||||||||
\(767\) | 4.34294 | 0.156814 | ||||||||
\(768\) | −1.59695 | + | 0.670623i | −0.0576251 | + | 0.0241990i | ||||
\(769\) | 20.5578 | − | 20.5578i | 0.741334 | − | 0.741334i | −0.231500 | − | 0.972835i | \(-0.574363\pi\) |
0.972835 | + | 0.231500i | \(0.0743634\pi\) | |||||||
\(770\) | −5.73698 | −0.206746 | ||||||||
\(771\) | 13.7374 | − | 33.6279i | 0.494740 | − | 1.21108i | ||||
\(772\) | 14.5654 | − | 14.5654i | 0.524221 | − | 0.524221i | ||||
\(773\) | − | 6.89204i | − | 0.247889i | −0.992289 | − | 0.123945i | \(-0.960445\pi\) | ||
0.992289 | − | 0.123945i | \(-0.0395545\pi\) | |||||||
\(774\) | 13.1875 | + | 12.9327i | 0.474015 | + | 0.464857i | ||||
\(775\) | −3.64796 | − | 3.64796i | −0.131039 | − | 0.131039i | ||||
\(776\) | 5.88577 | 0.211287 | ||||||||
\(777\) | 16.0369 | − | 30.6857i | 0.575322 | − | 1.10084i | ||||
\(778\) | −1.19099 | −0.0426990 | ||||||||
\(779\) | 2.57071 | + | 2.57071i | 0.0921053 | + | 0.0921053i | ||||
\(780\) | −3.08864 | − | 7.35498i | −0.110591 | − | 0.263351i | ||||
\(781\) | 12.4685i | 0.446160i | ||||||||
\(782\) | 2.89458 | − | 2.89458i | 0.103510 | − | 0.103510i | ||||
\(783\) | −2.55238 | + | 1.10125i | −0.0912147 | + | 0.0393554i | ||||
\(784\) | −3.79996 | −0.135713 | ||||||||
\(785\) | −5.70174 | + | 5.70174i | −0.203504 | + | 0.203504i | ||||
\(786\) | 7.00332 | + | 16.6770i | 0.249800 | + | 0.594849i | ||||
\(787\) | 33.5868 | 1.19724 | 0.598619 | − | 0.801034i | \(-0.295716\pi\) | ||||
0.598619 | + | 0.801034i | \(0.295716\pi\) | |||||||
\(788\) | 3.22806 | 0.114995 | ||||||||
\(789\) | −14.5099 | + | 6.09328i | −0.516568 | + | 0.216927i | ||||
\(790\) | 6.38622 | + | 6.38622i | 0.227212 | + | 0.227212i | ||||
\(791\) | 38.1893 | + | 38.1893i | 1.35786 | + | 1.35786i | ||||
\(792\) | 0.0510778 | + | 5.23688i | 0.00181497 | + | 0.186085i | ||||
\(793\) | 0.875092 | 0.0310754 | ||||||||
\(794\) | 5.53672 | − | 5.53672i | 0.196491 | − | 0.196491i | ||||
\(795\) | −14.9963 | − | 6.12617i | −0.531865 | − | 0.217273i | ||||
\(796\) | 15.7523 | + | 15.7523i | 0.558326 | + | 0.558326i | ||||
\(797\) | −9.89671 | − | 9.89671i | −0.350559 | − | 0.350559i | 0.509758 | − | 0.860318i | \(-0.329735\pi\) |
−0.860318 | + | 0.509758i | \(0.829735\pi\) | |||||||
\(798\) | 0.807169 | + | 1.92211i | 0.0285735 | + | 0.0680421i | ||||
\(799\) | 2.83546 | + | 2.83546i | 0.100311 | + | 0.100311i | ||||
\(800\) | 0.707107 | − | 0.707107i | 0.0250000 | − | 0.0250000i | ||||
\(801\) | 2.10070 | − | 0.0204891i | 0.0742246 | − | 0.000723948i | ||||
\(802\) | 18.9703i | 0.669863i | ||||||||
\(803\) | 23.9533i | 0.845293i | ||||||||
\(804\) | −13.8986 | + | 5.83657i | −0.490167 | + | 0.205840i | ||||
\(805\) | 7.66476i | 0.270147i | ||||||||
\(806\) | 16.8012 | + | 16.8012i | 0.591795 | + | 0.591795i | ||||
\(807\) | 12.8405 | + | 30.5771i | 0.452007 | + | 1.07636i | ||||
\(808\) | 13.1960 | − | 13.1960i | 0.464235 | − | 0.464235i | ||||
\(809\) | −28.6463 | − | 28.6463i | −1.00715 | − | 1.00715i | −0.999974 | − | 0.00717696i | \(-0.997715\pi\) |
−0.00717696 | − | 0.999974i | \(-0.502285\pi\) | |||||||
\(810\) | −0.175546 | − | 8.99829i | −0.00616805 | − | 0.316168i | ||||
\(811\) | 36.8856 | 1.29523 | 0.647615 | − | 0.761968i | \(-0.275767\pi\) | ||||
0.647615 | + | 0.761968i | \(0.275767\pi\) | |||||||
\(812\) | −1.24317 | + | 1.24317i | −0.0436268 | + | 0.0436268i | ||||
\(813\) | 47.4878 | − | 19.9419i | 1.66547 | − | 0.699394i | ||||
\(814\) | −10.5721 | − | 0.994119i | −0.370552 | − | 0.0348439i | ||||
\(815\) | 3.15568i | 0.110539i | ||||||||
\(816\) | −1.14965 | + | 2.81424i | −0.0402458 | + | 0.0985181i | ||||
\(817\) | − | 2.25495i | − | 0.0788906i | ||||||
\(818\) | 8.63540 | 0.301930 | ||||||||
\(819\) | −45.4047 | + | 0.442854i | −1.58657 | + | 0.0154746i | ||||
\(820\) | −7.01905 | − | 7.01905i | −0.245116 | − | 0.245116i | ||||
\(821\) | 11.4259i | 0.398768i | 0.979921 | + | 0.199384i | \(0.0638942\pi\) | ||||
−0.979921 | + | 0.199384i | \(0.936106\pi\) | |||||||
\(822\) | −6.32920 | + | 15.4933i | −0.220756 | + | 0.540391i | ||||
\(823\) | 28.0646 | 0.978272 | 0.489136 | − | 0.872208i | \(-0.337312\pi\) | ||||
0.489136 | + | 0.872208i | \(0.337312\pi\) | |||||||
\(824\) | − | 9.34793i | − | 0.325651i | ||||||
\(825\) | −1.17071 | − | 2.78782i | −0.0407590 | − | 0.0970595i | ||||
\(826\) | 3.09889 | 0.107824 | ||||||||
\(827\) | 13.4411 | − | 13.4411i | 0.467392 | − | 0.467392i | −0.433677 | − | 0.901069i | \(-0.642784\pi\) |
0.901069 | + | 0.433677i | \(0.142784\pi\) | |||||||
\(828\) | 6.99661 | − | 0.0682413i | 0.243149 | − | 0.00237155i | ||||
\(829\) | −13.4477 | + | 13.4477i | −0.467058 | + | 0.467058i | −0.900960 | − | 0.433902i | \(-0.857136\pi\) |
0.433902 | + | 0.900960i | \(0.357136\pi\) | |||||||
\(830\) | − | 14.6153i | − | 0.507304i | ||||||
\(831\) | 0.892852 | − | 2.18562i | 0.0309727 | − | 0.0758183i | ||||
\(832\) | −3.25667 | + | 3.25667i | −0.112905 | + | 0.112905i | ||||
\(833\) | −4.71605 | + | 4.71605i | −0.163401 | + | 0.163401i | ||||
\(834\) | 6.16316 | − | 15.0869i | 0.213413 | − | 0.522415i | ||||
\(835\) | − | 0.814356i | − | 0.0281820i | ||||||
\(836\) | 0.452098 | − | 0.452098i | 0.0156361 | − | 0.0156361i | ||||
\(837\) | 10.6198 | + | 24.6136i | 0.367073 | + | 0.850772i | ||||
\(838\) | 7.41520 | − | 7.41520i | 0.256154 | − | 0.256154i | ||||
\(839\) | 0.547494 | 0.0189016 | 0.00945080 | − | 0.999955i | \(-0.496992\pi\) | ||||
0.00945080 | + | 0.999955i | \(0.496992\pi\) | |||||||
\(840\) | −2.20389 | − | 5.24812i | −0.0760413 | − | 0.181077i | ||||
\(841\) | − | 28.7138i | − | 0.990131i | ||||||
\(842\) | 33.1153 | 1.14123 | ||||||||
\(843\) | 13.6299 | − | 33.3649i | 0.469440 | − | 1.14915i | ||||
\(844\) | − | 13.6945i | − | 0.471383i | ||||||
\(845\) | −5.80664 | − | 5.80664i | −0.199754 | − | 0.199754i | ||||
\(846\) | 0.0668475 | + | 6.85371i | 0.00229826 | + | 0.235635i | ||||
\(847\) | −26.1345 | −0.897993 | ||||||||
\(848\) | 9.35271i | 0.321173i | ||||||||
\(849\) | −0.692529 | + | 1.69525i | −0.0237675 | + | 0.0581808i | ||||
\(850\) | − | 1.75515i | − | 0.0602011i | ||||||
\(851\) | −1.32817 | + | 14.1246i | −0.0455291 | + | 0.484185i | ||||
\(852\) | −11.4061 | + | 4.78985i | −0.390766 | + | 0.164097i | ||||
\(853\) | 13.4325 | − | 13.4325i | 0.459918 | − | 0.459918i | −0.438710 | − | 0.898629i | \(-0.644565\pi\) |
0.898629 | + | 0.438710i | \(0.144565\pi\) | |||||||
\(854\) | 0.624418 | 0.0213672 | ||||||||
\(855\) | −0.769315 | + | 0.784470i | −0.0263100 | + | 0.0268283i | ||||
\(856\) | −7.64195 | − | 7.64195i | −0.261196 | − | 0.261196i | ||||
\(857\) | −17.0482 | + | 17.0482i | −0.582355 | + | 0.582355i | −0.935550 | − | 0.353195i | \(-0.885095\pi\) |
0.353195 | + | 0.935550i | \(0.385095\pi\) | |||||||
\(858\) | 5.39187 | + | 12.8397i | 0.184076 | + | 0.438339i | ||||
\(859\) | 15.3183 | + | 15.3183i | 0.522652 | + | 0.522652i | 0.918371 | − | 0.395719i | \(-0.129505\pi\) |
−0.395719 | + | 0.918371i | \(0.629505\pi\) | |||||||
\(860\) | 6.15689i | 0.209948i | ||||||||
\(861\) | −52.0951 | + | 21.8767i | −1.77540 | + | 0.745557i | ||||
\(862\) | 25.0423i | 0.852946i | ||||||||
\(863\) | 55.5383i | 1.89055i | 0.326279 | + | 0.945274i | \(0.394205\pi\) | ||||
−0.326279 | + | 0.945274i | \(0.605795\pi\) | |||||||
\(864\) | −4.77102 | + | 2.05850i | −0.162313 | + | 0.0700315i | ||||
\(865\) | 11.8005 | − | 11.8005i | 0.401230 | − | 0.401230i | ||||
\(866\) | −4.40979 | − | 4.40979i | −0.149851 | − | 0.149851i | ||||
\(867\) | −9.33470 | − | 22.2287i | −0.317023 | − | 0.754928i | ||||
\(868\) | 11.9884 | + | 11.9884i | 0.406913 | + | 0.406913i | ||||
\(869\) | −11.1485 | − | 11.1485i | −0.378187 | − | 0.378187i | ||||
\(870\) | −0.857793 | − | 0.350418i | −0.0290819 | − | 0.0118803i | ||||
\(871\) | −28.3435 | + | 28.3435i | −0.960382 | + | 0.960382i | ||||
\(872\) | 12.2655 | 0.415363 | ||||||||
\(873\) | 17.6565 | − | 0.172212i | 0.597581 | − | 0.00582849i | ||||
\(874\) | −0.604015 | − | 0.604015i | −0.0204311 | − | 0.0204311i | ||||
\(875\) | 2.32379 | + | 2.32379i | 0.0785583 | + | 0.0785583i | ||||
\(876\) | −21.9122 | + | 9.20176i | −0.740344 | + | 0.310899i | ||||
\(877\) | 2.26286 | 0.0764112 | 0.0382056 | − | 0.999270i | \(-0.487836\pi\) | ||||
0.0382056 | + | 0.999270i | \(0.487836\pi\) | |||||||
\(878\) | −6.37495 | −0.215144 | ||||||||
\(879\) | −18.7691 | − | 44.6949i | −0.633066 | − | 1.50752i | ||||
\(880\) | −1.23440 | + | 1.23440i | −0.0416117 | + | 0.0416117i | ||||
\(881\) | −0.256382 | −0.00863772 | −0.00431886 | − | 0.999991i | \(-0.501375\pi\) | ||||
−0.00431886 | + | 0.999991i | \(0.501375\pi\) | |||||||
\(882\) | −11.3993 | + | 0.111183i | −0.383836 | + | 0.00374373i | ||||
\(883\) | 40.6712 | − | 40.6712i | 1.36869 | − | 1.36869i | 0.506389 | − | 0.862305i | \(-0.330980\pi\) |
0.862305 | − | 0.506389i | \(-0.169020\pi\) | |||||||
\(884\) | 8.08356i | 0.271880i | ||||||||
\(885\) | 0.632372 | + | 1.50587i | 0.0212570 | + | 0.0506192i | ||||
\(886\) | 9.63702 | + | 9.63702i | 0.323762 | + | 0.323762i | ||||
\(887\) | −6.83977 | −0.229657 | −0.114828 | − | 0.993385i | \(-0.536632\pi\) | ||||
−0.114828 | + | 0.993385i | \(0.536632\pi\) | |||||||
\(888\) | −3.15192 | − | 10.0531i | −0.105771 | − | 0.337361i | ||||
\(889\) | −28.6170 | −0.959782 | ||||||||
\(890\) | 0.495164 | + | 0.495164i | 0.0165979 | + | 0.0165979i | ||||
\(891\) | 0.306452 | + | 15.7084i | 0.0102665 | + | 0.526251i | ||||
\(892\) | − | 17.3050i | − | 0.579413i | ||||||
\(893\) | 0.591678 | − | 0.591678i | 0.0197997 | − | 0.0197997i | ||||
\(894\) | 4.73837 | − | 11.5991i | 0.158475 | − | 0.387932i | ||||
\(895\) | −0.109863 | −0.00367232 | ||||||||
\(896\) | −2.32379 | + | 2.32379i | −0.0776322 | + | 0.0776322i | ||||
\(897\) | 17.1541 | − | 7.20368i | 0.572760 | − | 0.240524i | ||||
\(898\) | 10.7424 | 0.358479 | ||||||||
\(899\) | 2.75994 | 0.0920493 | ||||||||
\(900\) | 2.10053 | − | 2.14191i | 0.0700177 | − | 0.0713970i | ||||
\(901\) | 11.6074 | + | 11.6074i | 0.386700 | + | 0.386700i | ||||
\(902\) | 12.2532 | + | 12.2532i | 0.407988 | + | 0.407988i | ||||
\(903\) | 32.4429 | + | 13.2533i | 1.07963 | + | 0.441042i | ||||
\(904\) | 16.4341 | 0.546590 | ||||||||
\(905\) | −10.2143 | + | 10.2143i | −0.339535 | + | 0.339535i | ||||
\(906\) | 9.86938 | − | 24.1594i | 0.327888 | − | 0.802641i | ||||
\(907\) | −38.3472 | − | 38.3472i | −1.27330 | − | 1.27330i | −0.944347 | − | 0.328952i | \(-0.893305\pi\) |
−0.328952 | − | 0.944347i | \(-0.606695\pi\) | |||||||
\(908\) | −0.729623 | − | 0.729623i | −0.0242134 | − | 0.0242134i | ||||
\(909\) | 39.2002 | − | 39.9724i | 1.30019 | − | 1.32580i | ||||
\(910\) | −10.7025 | − | 10.7025i | −0.354784 | − | 0.354784i | ||||
\(911\) | −0.756551 | + | 0.756551i | −0.0250657 | + | 0.0250657i | −0.719529 | − | 0.694463i | \(-0.755642\pi\) |
0.694463 | + | 0.719529i | \(0.255642\pi\) | |||||||
\(912\) | 0.587249 | + | 0.239898i | 0.0194458 | + | 0.00794382i | ||||
\(913\) | 25.5140i | 0.844391i | ||||||||
\(914\) | − | 16.3558i | − | 0.541001i | ||||||
\(915\) | 0.127422 | + | 0.303429i | 0.00421243 | + | 0.0100311i | ||||
\(916\) | 18.8546i | 0.622973i | ||||||||
\(917\) | 24.2673 | + | 24.2673i | 0.801377 | + | 0.801377i | ||||
\(918\) | −3.36644 | + | 8.47595i | −0.111109 | + | 0.279748i | ||||
\(919\) | −9.32372 | + | 9.32372i | −0.307561 | + | 0.307561i | −0.843963 | − | 0.536402i | \(-0.819783\pi\) |
0.536402 | + | 0.843963i | \(0.319783\pi\) | |||||||
\(920\) | 1.64920 | + | 1.64920i | 0.0543724 | + | 0.0543724i | ||||
\(921\) | 2.07714 | + | 4.94630i | 0.0684441 | + | 0.162986i | ||||
\(922\) | −22.0440 | −0.725979 | ||||||||
\(923\) | −23.2604 | + | 23.2604i | −0.765626 | + | 0.765626i | ||||
\(924\) | 3.84735 | + | 9.16170i | 0.126569 | + | 0.301398i | ||||
\(925\) | 3.87960 | + | 4.68494i | 0.127560 | + | 0.154040i | ||||
\(926\) | 15.3688i | 0.505049i | ||||||||
\(927\) | −0.273512 | − | 28.0425i | −0.00898330 | − | 0.921036i | ||||
\(928\) | 0.534977i | 0.0175615i | ||||||||
\(929\) | 34.5104 | 1.13225 | 0.566124 | − | 0.824320i | \(-0.308442\pi\) | ||||
0.566124 | + | 0.824320i | \(0.308442\pi\) | |||||||
\(930\) | −3.37922 | + | 8.27203i | −0.110809 | + | 0.271251i | ||||
\(931\) | 0.984101 | + | 0.984101i | 0.0322526 | + | 0.0322526i | ||||
\(932\) | 3.88220i | 0.127166i | ||||||||
\(933\) | 13.8981 | + | 5.67756i | 0.455005 | + | 0.185875i | ||||
\(934\) | −35.3475 | −1.15660 | ||||||||
\(935\) | 3.06398i | 0.100203i | ||||||||
\(936\) | −9.67426 | + | 9.86484i | −0.316213 | + | 0.322442i | ||||
\(937\) | 20.9824 | 0.685464 | 0.342732 | − | 0.939433i | \(-0.388648\pi\) | ||||
0.342732 | + | 0.939433i | \(0.388648\pi\) | |||||||
\(938\) | −20.2244 | + | 20.2244i | −0.660350 | + | 0.660350i | ||||
\(939\) | 32.7347 | + | 13.3725i | 1.06826 | + | 0.436395i | ||||
\(940\) | −1.61551 | + | 1.61551i | −0.0526922 | + | 0.0526922i | ||||
\(941\) | 17.7672i | 0.579195i | 0.957149 | + | 0.289597i | \(0.0935214\pi\) | ||||
−0.957149 | + | 0.289597i | \(0.906479\pi\) | |||||||
\(942\) | 12.9291 | + | 5.28170i | 0.421254 | + | 0.172087i | ||||
\(943\) | 16.3706 | − | 16.3706i | 0.533101 | − | 0.533101i | ||||
\(944\) | 0.666775 | − | 0.666775i | 0.0217017 | − | 0.0217017i | ||||
\(945\) | −6.76490 | − | 15.6791i | −0.220062 | − | 0.510042i | ||||
\(946\) | − | 10.7481i | − | 0.349452i | ||||||
\(947\) | −15.2535 | + | 15.2535i | −0.495672 | + | 0.495672i | −0.910088 | − | 0.414416i | \(-0.863986\pi\) |
0.414416 | + | 0.910088i | \(0.363986\pi\) | |||||||
\(948\) | 5.91576 | − | 14.4813i | 0.192135 | − | 0.470329i | ||||
\(949\) | −44.6855 | + | 44.6855i | −1.45055 | + | 1.45055i | ||||
\(950\) | −0.366248 | −0.0118827 | ||||||||
\(951\) | 26.7568 | − | 11.2362i | 0.867649 | − | 0.364359i | ||||
\(952\) | 5.76799i | 0.186942i | ||||||||
\(953\) | −52.8076 | −1.71061 | −0.855303 | − | 0.518128i | \(-0.826629\pi\) | ||||
−0.855303 | + | 0.518128i | \(0.826629\pi\) | |||||||
\(954\) | 0.273651 | + | 28.0568i | 0.00885979 | + | 0.908372i | ||||
\(955\) | − | 12.5868i | − | 0.407300i | ||||||
\(956\) | −8.52789 | − | 8.52789i | −0.275812 | − | 0.275812i | ||||
\(957\) | 1.49746 | + | 0.611729i | 0.0484059 | + | 0.0197744i | ||||
\(958\) | −15.1991 | −0.491062 | ||||||||
\(959\) | 31.7547i | 1.02541i | ||||||||
\(960\) | −1.60342 | − | 0.655016i | −0.0517501 | − | 0.0211405i | ||||
\(961\) | 4.38477i | 0.141444i | ||||||||
\(962\) | −17.8680 | − | 21.5771i | −0.576088 | − | 0.695674i | ||||
\(963\) | −23.1483 | − | 22.7011i | −0.745945 | − | 0.731534i | ||||
\(964\) | −14.3656 | + | 14.3656i | −0.462685 | + | 0.462685i | ||||
\(965\) | 20.5986 | 0.663093 | ||||||||
\(966\) | 12.2403 | − | 5.14016i | 0.393824 | − | 0.165382i | ||||
\(967\) | 28.9785 | + | 28.9785i | 0.931887 | + | 0.931887i | 0.997824 | − | 0.0659365i | \(-0.0210035\pi\) |
−0.0659365 | + | 0.997824i | \(0.521003\pi\) | |||||||
\(968\) | −5.62326 | + | 5.62326i | −0.180738 | + | 0.180738i | ||||
\(969\) | 1.02655 | − | 0.431089i | 0.0329777 | − | 0.0138486i | ||||
\(970\) | 4.16187 | + | 4.16187i | 0.133629 | + | 0.133629i | ||||
\(971\) | 49.8195i | 1.59878i | 0.600809 | + | 0.799392i | \(0.294845\pi\) | ||||
−0.600809 | + | 0.799392i | \(0.705155\pi\) | |||||||
\(972\) | −14.2521 | + | 6.31480i | −0.457137 | + | 0.202547i | ||||
\(973\) | − | 30.9216i | − | 0.991302i | ||||||
\(974\) | − | 7.29938i | − | 0.233887i | ||||||
\(975\) | 3.01676 | − | 7.38476i | 0.0966137 | − | 0.236502i | ||||
\(976\) | 0.134354 | − | 0.134354i | 0.00430056 | − | 0.00430056i | ||||
\(977\) | 7.20803 | + | 7.20803i | 0.230605 | + | 0.230605i | 0.812945 | − | 0.582340i | \(-0.197863\pi\) |
−0.582340 | + | 0.812945i | \(0.697863\pi\) | |||||||
\(978\) | 5.03948 | − | 2.11627i | 0.161145 | − | 0.0676709i | ||||
\(979\) | −0.864412 | − | 0.864412i | −0.0276267 | − | 0.0276267i | ||||
\(980\) | −2.68698 | − | 2.68698i | −0.0858324 | − | 0.0858324i | ||||
\(981\) | 36.7948 | − | 0.358878i | 1.17477 | − | 0.0114581i | ||||
\(982\) | −15.9204 | + | 15.9204i | −0.508039 | + | 0.508039i | ||||
\(983\) | −55.4821 | −1.76961 | −0.884803 | − | 0.465966i | \(-0.845707\pi\) | ||||
−0.884803 | + | 0.465966i | \(0.845707\pi\) | |||||||
\(984\) | −6.50197 | + | 15.9162i | −0.207275 | + | 0.507391i | ||||
\(985\) | 2.28258 | + | 2.28258i | 0.0727291 | + | 0.0727291i | ||||
\(986\) | 0.663948 | + | 0.663948i | 0.0211444 | + | 0.0211444i | ||||
\(987\) | 5.03517 | + | 11.9903i | 0.160271 | + | 0.381654i | ||||
\(988\) | 1.68680 | 0.0536643 | ||||||||
\(989\) | −14.3598 | −0.456615 | ||||||||
\(990\) | −3.66692 | + | 3.73915i | −0.116542 | + | 0.118838i | ||||
\(991\) | −30.6865 | + | 30.6865i | −0.974790 | + | 0.974790i | −0.999690 | − | 0.0249001i | \(-0.992073\pi\) |
0.0249001 | + | 0.999690i | \(0.492073\pi\) | |||||||
\(992\) | 5.15899 | 0.163798 | ||||||||
\(993\) | −5.33035 | − | 2.17751i | −0.169154 | − | 0.0691012i | ||||
\(994\) | −16.5974 | + | 16.5974i | −0.526437 | + | 0.526437i | ||||
\(995\) | 22.2772i | 0.706233i | ||||||||
\(996\) | −23.3399 | + | 9.80134i | −0.739554 | + | 0.310567i | ||||
\(997\) | 18.2859 | + | 18.2859i | 0.579121 | + | 0.579121i | 0.934661 | − | 0.355540i | \(-0.115703\pi\) |
−0.355540 | + | 0.934661i | \(0.615703\pi\) | |||||||
\(998\) | 24.9257 | 0.789008 | ||||||||
\(999\) | −9.74944 | − | 30.0657i | −0.308459 | − | 0.951238i |
(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 | 1110.2.u.e.191.8 | ✓ | 40 | |
3.2 | odd | 2 | inner | 1110.2.u.e.191.19 | yes | 40 | |
37.31 | odd | 4 | inner | 1110.2.u.e.401.19 | yes | 40 | |
111.68 | even | 4 | inner | 1110.2.u.e.401.8 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.u.e.191.8 | ✓ | 40 | 1.1 | even | 1 | trivial | |
1110.2.u.e.191.19 | yes | 40 | 3.2 | odd | 2 | inner | |
1110.2.u.e.401.8 | yes | 40 | 111.68 | even | 4 | inner | |
1110.2.u.e.401.19 | yes | 40 | 37.31 | odd | 4 | inner |