Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,3,Mod(13,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.13");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.v (of order \(8\), degree \(4\), 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: | \(6.10355792167\) |
Analytic rank: | \(0\) |
Dimension: | \(240\) |
Relative dimension: | \(60\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 13.8 | ||
Character | \(\chi\) | \(=\) | 224.13 |
Dual form | 224.3.v.b.69.8 |
$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{7}{8}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.89176 | + | 0.649047i | −0.945878 | + | 0.324523i | ||||
\(3\) | 5.08830 | + | 2.10764i | 1.69610 | + | 0.702548i | 0.999883 | − | 0.0152817i | \(-0.00486452\pi\) |
0.696218 | + | 0.717830i | \(0.254865\pi\) | |||||||
\(4\) | 3.15748 | − | 2.45567i | 0.789369 | − | 0.613919i | ||||
\(5\) | 0.976625 | + | 2.35778i | 0.195325 | + | 0.471556i | 0.990950 | − | 0.134234i | \(-0.0428572\pi\) |
−0.795625 | + | 0.605790i | \(0.792857\pi\) | |||||||
\(6\) | −10.9938 | − | 0.684602i | −1.83230 | − | 0.114100i | ||||
\(7\) | −5.09544 | − | 4.79964i | −0.727919 | − | 0.685663i | ||||
\(8\) | −4.37933 | + | 6.69489i | −0.547416 | + | 0.836861i | ||||
\(9\) | 15.0847 | + | 15.0847i | 1.67608 | + | 1.67608i | ||||
\(10\) | −3.37785 | − | 3.82647i | −0.337785 | − | 0.382647i | ||||
\(11\) | 2.51817 | + | 6.07940i | 0.228925 | + | 0.552673i | 0.996047 | − | 0.0888278i | \(-0.0283121\pi\) |
−0.767122 | + | 0.641501i | \(0.778312\pi\) | |||||||
\(12\) | 21.2419 | − | 5.84038i | 1.77016 | − | 0.486698i | ||||
\(13\) | −9.18830 | + | 22.1825i | −0.706792 | + | 1.70635i | 0.00107294 | + | 0.999999i | \(0.499658\pi\) |
−0.707865 | + | 0.706348i | \(0.750342\pi\) | |||||||
\(14\) | 12.7545 | + | 5.77257i | 0.911036 | + | 0.412326i | ||||
\(15\) | 14.0555i | 0.937033i | ||||||||
\(16\) | 3.93933 | − | 15.5075i | 0.246208 | − | 0.969217i | ||||
\(17\) | 12.9448 | 0.761457 | 0.380729 | − | 0.924687i | \(-0.375673\pi\) | ||||
0.380729 | + | 0.924687i | \(0.375673\pi\) | |||||||
\(18\) | −38.3273 | − | 18.7459i | −2.12929 | − | 1.04144i | ||||
\(19\) | 5.85517 | − | 14.1356i | 0.308167 | − | 0.743981i | −0.691598 | − | 0.722283i | \(-0.743093\pi\) |
0.999765 | − | 0.0216978i | \(-0.00690718\pi\) | |||||||
\(20\) | 8.87361 | + | 5.04637i | 0.443681 | + | 0.252318i | ||||
\(21\) | −15.8112 | − | 35.1614i | −0.752914 | − | 1.67435i | ||||
\(22\) | −8.70958 | − | 9.86633i | −0.395890 | − | 0.448470i | ||||
\(23\) | 3.80500 | + | 3.80500i | 0.165435 | + | 0.165435i | 0.784969 | − | 0.619535i | \(-0.212679\pi\) |
−0.619535 | + | 0.784969i | \(0.712679\pi\) | |||||||
\(24\) | −36.3938 | + | 24.8355i | −1.51641 | + | 1.03481i | ||||
\(25\) | 13.0723 | − | 13.0723i | 0.522893 | − | 0.522893i | ||||
\(26\) | 2.98453 | − | 47.9275i | 0.114790 | − | 1.84337i | ||||
\(27\) | 25.9936 | + | 62.7541i | 0.962726 | + | 2.32423i | ||||
\(28\) | −27.8751 | − | 2.64202i | −0.995538 | − | 0.0943578i | ||||
\(29\) | 10.4805 | − | 25.3022i | 0.361398 | − | 0.872491i | −0.633699 | − | 0.773580i | \(-0.718464\pi\) |
0.995096 | − | 0.0989110i | \(-0.0315359\pi\) | |||||||
\(30\) | −9.12267 | − | 26.5895i | −0.304089 | − | 0.886318i | ||||
\(31\) | 26.1430i | 0.843323i | 0.906753 | + | 0.421661i | \(0.138553\pi\) | ||||
−0.906753 | + | 0.421661i | \(0.861447\pi\) | |||||||
\(32\) | 2.61283 | + | 31.8932i | 0.0816510 | + | 0.996661i | ||||
\(33\) | 36.2413i | 1.09822i | ||||||||
\(34\) | −24.4883 | + | 8.40176i | −0.720245 | + | 0.247111i | ||||
\(35\) | 6.34017 | − | 16.7014i | 0.181148 | − | 0.477182i | ||||
\(36\) | 84.6728 | + | 10.5865i | 2.35202 | + | 0.294069i | ||||
\(37\) | −22.3665 | + | 9.26451i | −0.604500 | + | 0.250392i | −0.663875 | − | 0.747844i | \(-0.731089\pi\) |
0.0593748 | + | 0.998236i | \(0.481089\pi\) | |||||||
\(38\) | −1.90187 | + | 30.5414i | −0.0500492 | + | 0.803722i | ||||
\(39\) | −93.5057 | + | 93.5057i | −2.39758 | + | 2.39758i | ||||
\(40\) | −20.0620 | − | 3.78710i | −0.501551 | − | 0.0946776i | ||||
\(41\) | −1.69723 | + | 1.69723i | −0.0413957 | + | 0.0413957i | −0.727502 | − | 0.686106i | \(-0.759319\pi\) |
0.686106 | + | 0.727502i | \(0.259319\pi\) | |||||||
\(42\) | 52.7323 | + | 56.2546i | 1.25553 | + | 1.33939i | ||||
\(43\) | −23.2062 | − | 56.0247i | −0.539679 | − | 1.30290i | −0.924947 | − | 0.380095i | \(-0.875891\pi\) |
0.385269 | − | 0.922804i | \(-0.374109\pi\) | |||||||
\(44\) | 22.8801 | + | 13.0118i | 0.520002 | + | 0.295722i | ||||
\(45\) | −20.8344 | + | 50.2986i | −0.462986 | + | 1.11775i | ||||
\(46\) | −9.66776 | − | 4.72851i | −0.210169 | − | 0.102794i | ||||
\(47\) | 63.8209 | 1.35789 | 0.678946 | − | 0.734188i | \(-0.262437\pi\) | ||||
0.678946 | + | 0.734188i | \(0.262437\pi\) | |||||||
\(48\) | 52.7287 | − | 70.6041i | 1.09852 | − | 1.47092i | ||||
\(49\) | 2.92694 | + | 48.9125i | 0.0597334 | + | 0.998214i | ||||
\(50\) | −16.2451 | + | 33.2142i | −0.324902 | + | 0.664284i | ||||
\(51\) | 65.8669 | + | 27.2830i | 1.29151 | + | 0.534960i | ||||
\(52\) | 25.4612 | + | 92.6042i | 0.489638 | + | 1.78085i | ||||
\(53\) | −29.7801 | − | 71.8955i | −0.561889 | − | 1.35652i | −0.908254 | − | 0.418419i | \(-0.862584\pi\) |
0.346365 | − | 0.938100i | \(-0.387416\pi\) | |||||||
\(54\) | −89.9039 | − | 101.844i | −1.66489 | − | 1.88601i | ||||
\(55\) | −11.8746 | + | 11.8746i | −0.215902 | + | 0.215902i | ||||
\(56\) | 54.4476 | − | 13.0942i | 0.972279 | − | 0.233824i | ||||
\(57\) | 59.5858 | − | 59.5858i | 1.04536 | − | 1.04536i | ||||
\(58\) | −3.40427 | + | 54.6680i | −0.0586943 | + | 0.942552i | ||||
\(59\) | −25.6143 | − | 61.8384i | −0.434141 | − | 1.04811i | −0.977939 | − | 0.208892i | \(-0.933014\pi\) |
0.543798 | − | 0.839216i | \(-0.316986\pi\) | |||||||
\(60\) | 34.5157 | + | 44.3799i | 0.575262 | + | 0.739665i | ||||
\(61\) | −46.9261 | − | 19.4374i | −0.769280 | − | 0.318646i | −0.0366990 | − | 0.999326i | \(-0.511684\pi\) |
−0.732581 | + | 0.680680i | \(0.761684\pi\) | |||||||
\(62\) | −16.9680 | − | 49.4562i | −0.273678 | − | 0.797680i | ||||
\(63\) | −4.46202 | − | 149.264i | −0.0708257 | − | 2.36928i | ||||
\(64\) | −25.6430 | − | 58.6382i | −0.400672 | − | 0.916222i | ||||
\(65\) | −61.2750 | −0.942693 | ||||||||
\(66\) | −23.5223 | − | 68.5596i | −0.356398 | − | 1.03878i | ||||
\(67\) | −0.333590 | + | 0.805357i | −0.00497895 | + | 0.0120203i | −0.926349 | − | 0.376665i | \(-0.877071\pi\) |
0.921371 | + | 0.388685i | \(0.127071\pi\) | |||||||
\(68\) | 40.8728 | − | 31.7881i | 0.601071 | − | 0.467473i | ||||
\(69\) | 11.3414 | + | 27.3806i | 0.164368 | + | 0.396820i | ||||
\(70\) | −1.15408 | + | 35.7100i | −0.0164869 | + | 0.510142i | ||||
\(71\) | 48.5986 | − | 48.5986i | 0.684488 | − | 0.684488i | −0.276520 | − | 0.961008i | \(-0.589181\pi\) |
0.961008 | + | 0.276520i | \(0.0891813\pi\) | |||||||
\(72\) | −167.051 | + | 34.9295i | −2.32016 | + | 0.485132i | ||||
\(73\) | −69.1076 | + | 69.1076i | −0.946679 | + | 0.946679i | −0.998649 | − | 0.0519698i | \(-0.983450\pi\) |
0.0519698 | + | 0.998649i | \(0.483450\pi\) | |||||||
\(74\) | 36.2989 | − | 32.0431i | 0.490525 | − | 0.433015i | ||||
\(75\) | 94.0679 | − | 38.9642i | 1.25424 | − | 0.519522i | ||||
\(76\) | −16.2249 | − | 59.0113i | −0.213486 | − | 0.776465i | ||||
\(77\) | 16.3478 | − | 43.0635i | 0.212309 | − | 0.559266i | ||||
\(78\) | 116.200 | − | 237.580i | 1.48975 | − | 3.04589i | ||||
\(79\) | − | 104.667i | − | 1.32490i | −0.749107 | − | 0.662449i | \(-0.769517\pi\) | ||
0.749107 | − | 0.662449i | \(-0.230483\pi\) | |||||||
\(80\) | 40.4105 | − | 5.85692i | 0.505131 | − | 0.0732115i | ||||
\(81\) | 182.100i | 2.24815i | ||||||||
\(82\) | 2.10916 | − | 4.31231i | 0.0257214 | − | 0.0525892i | ||||
\(83\) | −22.3992 | + | 54.0765i | −0.269870 | + | 0.651524i | −0.999477 | − | 0.0323427i | \(-0.989703\pi\) |
0.729607 | + | 0.683867i | \(0.239703\pi\) | |||||||
\(84\) | −136.268 | − | 72.1941i | −1.62224 | − | 0.859454i | ||||
\(85\) | 12.6422 | + | 30.5209i | 0.148732 | + | 0.359070i | ||||
\(86\) | 80.2631 | + | 90.9231i | 0.933291 | + | 1.05725i | ||||
\(87\) | 106.656 | − | 106.656i | 1.22593 | − | 1.22593i | ||||
\(88\) | −51.7288 | − | 9.76483i | −0.587827 | − | 0.110964i | ||||
\(89\) | 47.9956 | + | 47.9956i | 0.539277 | + | 0.539277i | 0.923317 | − | 0.384040i | \(-0.125467\pi\) |
−0.384040 | + | 0.923317i | \(0.625467\pi\) | |||||||
\(90\) | 6.76738 | − | 108.675i | 0.0751932 | − | 1.20750i | ||||
\(91\) | 153.286 | − | 68.9291i | 1.68447 | − | 0.757462i | ||||
\(92\) | 21.3581 | + | 2.67036i | 0.232153 | + | 0.0290257i | ||||
\(93\) | −55.1002 | + | 133.024i | −0.592475 | + | 1.43036i | ||||
\(94\) | −120.734 | + | 41.4227i | −1.28440 | + | 0.440668i | ||||
\(95\) | 39.0470 | 0.411021 | ||||||||
\(96\) | −53.9246 | + | 167.789i | −0.561714 | + | 1.74780i | ||||
\(97\) | − | 8.86586i | − | 0.0914006i | −0.998955 | − | 0.0457003i | \(-0.985448\pi\) | ||
0.998955 | − | 0.0457003i | \(-0.0145519\pi\) | |||||||
\(98\) | −37.2835 | − | 90.6308i | −0.380444 | − | 0.924804i | ||||
\(99\) | −53.7202 | + | 129.692i | −0.542628 | + | 1.31002i | ||||
\(100\) | 9.17420 | − | 73.3770i | 0.0917420 | − | 0.733770i | ||||
\(101\) | −31.1848 | − | 75.2869i | −0.308761 | − | 0.745415i | −0.999746 | − | 0.0225455i | \(-0.992823\pi\) |
0.690985 | − | 0.722869i | \(-0.257177\pi\) | |||||||
\(102\) | −142.312 | − | 8.86202i | −1.39522 | − | 0.0868825i | ||||
\(103\) | −2.67598 | − | 2.67598i | −0.0259804 | − | 0.0259804i | 0.693997 | − | 0.719978i | \(-0.255848\pi\) |
−0.719978 | + | 0.693997i | \(0.755848\pi\) | |||||||
\(104\) | −108.271 | − | 158.659i | −1.04107 | − | 1.52557i | ||||
\(105\) | 67.4613 | − | 71.6188i | 0.642488 | − | 0.682084i | ||||
\(106\) | 103.000 | + | 116.680i | 0.971700 | + | 1.10076i | ||||
\(107\) | −69.2179 | − | 167.107i | −0.646897 | − | 1.56175i | −0.817199 | − | 0.576355i | \(-0.804475\pi\) |
0.170303 | − | 0.985392i | \(-0.445525\pi\) | |||||||
\(108\) | 236.178 | + | 134.313i | 2.18683 | + | 1.24364i | ||||
\(109\) | −1.47397 | − | 0.610540i | −0.0135227 | − | 0.00560128i | 0.375912 | − | 0.926655i | \(-0.377330\pi\) |
−0.389435 | + | 0.921054i | \(0.627330\pi\) | |||||||
\(110\) | 14.7567 | − | 30.1710i | 0.134151 | − | 0.274282i | ||||
\(111\) | −133.334 | −1.20121 | ||||||||
\(112\) | −94.5028 | + | 60.1100i | −0.843775 | + | 0.536696i | ||||
\(113\) | 42.7926i | 0.378695i | 0.981910 | + | 0.189348i | \(0.0606373\pi\) | ||||
−0.981910 | + | 0.189348i | \(0.939363\pi\) | |||||||
\(114\) | −74.0478 | + | 151.396i | −0.649542 | + | 1.32803i | ||||
\(115\) | −5.25530 | + | 12.6874i | −0.0456983 | + | 0.110325i | ||||
\(116\) | −29.0420 | − | 105.628i | −0.250362 | − | 0.910586i | ||||
\(117\) | −473.220 | + | 196.014i | −4.04461 | + | 1.67533i | ||||
\(118\) | 88.5920 | + | 100.358i | 0.750780 | + | 0.850494i | ||||
\(119\) | −65.9592 | − | 62.1302i | −0.554279 | − | 0.522103i | ||||
\(120\) | −94.0999 | − | 61.5536i | −0.784166 | − | 0.512947i | ||||
\(121\) | 54.9420 | − | 54.9420i | 0.454066 | − | 0.454066i | ||||
\(122\) | 101.388 | + | 6.31363i | 0.831052 | + | 0.0517511i | ||||
\(123\) | −12.2132 | + | 5.05885i | −0.0992939 | + | 0.0411289i | ||||
\(124\) | 64.1987 | + | 82.5460i | 0.517732 | + | 0.665693i | ||||
\(125\) | 102.533 | + | 42.4706i | 0.820264 | + | 0.339764i | ||||
\(126\) | 105.321 | + | 279.476i | 0.835878 | + | 2.21806i | ||||
\(127\) | 204.737 | 1.61210 | 0.806051 | − | 0.591846i | \(-0.201601\pi\) | ||||
0.806051 | + | 0.591846i | \(0.201601\pi\) | |||||||
\(128\) | 86.5692 | + | 94.2856i | 0.676322 | + | 0.736607i | ||||
\(129\) | − | 333.981i | − | 2.58900i | ||||||
\(130\) | 115.917 | − | 39.7703i | 0.891672 | − | 0.305926i | ||||
\(131\) | 192.258 | + | 79.6357i | 1.46761 | + | 0.607906i | 0.966314 | − | 0.257367i | \(-0.0828549\pi\) |
0.501301 | + | 0.865273i | \(0.332855\pi\) | |||||||
\(132\) | 88.9968 | + | 114.431i | 0.674218 | + | 0.866901i | ||||
\(133\) | −97.6806 | + | 43.9245i | −0.734441 | + | 0.330260i | ||||
\(134\) | 0.108356 | − | 1.74005i | 0.000808628 | − | 0.0129855i | ||||
\(135\) | −122.574 | + | 122.574i | −0.907959 | + | 0.907959i | ||||
\(136\) | −56.6894 | + | 86.6637i | −0.416834 | + | 0.637233i | ||||
\(137\) | 16.3266 | + | 16.3266i | 0.119172 | + | 0.119172i | 0.764178 | − | 0.645006i | \(-0.223145\pi\) |
−0.645006 | + | 0.764178i | \(0.723145\pi\) | |||||||
\(138\) | −39.2265 | − | 44.4363i | −0.284250 | − | 0.322002i | ||||
\(139\) | 28.4103 | − | 11.7679i | 0.204391 | − | 0.0846613i | −0.278140 | − | 0.960541i | \(-0.589718\pi\) |
0.482530 | + | 0.875879i | \(0.339718\pi\) | |||||||
\(140\) | −20.9942 | − | 68.3036i | −0.149959 | − | 0.487883i | ||||
\(141\) | 324.740 | + | 134.512i | 2.30312 | + | 0.953985i | ||||
\(142\) | −60.3940 | + | 123.480i | −0.425310 | + | 0.869574i | ||||
\(143\) | −157.994 | −1.10485 | ||||||||
\(144\) | 293.349 | − | 174.502i | 2.03715 | − | 1.21182i | ||||
\(145\) | 69.8927 | 0.482019 | ||||||||
\(146\) | 85.8806 | − | 175.589i | 0.588223 | − | 1.20266i | ||||
\(147\) | −88.1970 | + | 255.051i | −0.599980 | + | 1.73504i | ||||
\(148\) | −47.8711 | + | 84.1773i | −0.323453 | + | 0.568766i | ||||
\(149\) | −17.4326 | − | 42.0860i | −0.116997 | − | 0.282456i | 0.854523 | − | 0.519414i | \(-0.173850\pi\) |
−0.971520 | + | 0.236958i | \(0.923850\pi\) | |||||||
\(150\) | −152.664 | + | 134.765i | −1.01776 | + | 0.898434i | ||||
\(151\) | 6.67074 | + | 6.67074i | 0.0441771 | + | 0.0441771i | 0.728850 | − | 0.684673i | \(-0.240055\pi\) |
−0.684673 | + | 0.728850i | \(0.740055\pi\) | |||||||
\(152\) | 68.9947 | + | 101.104i | 0.453913 | + | 0.665160i | ||||
\(153\) | 195.268 | + | 195.268i | 1.27626 | + | 1.27626i | ||||
\(154\) | −2.97573 | + | 92.0761i | −0.0193229 | + | 0.597897i | ||||
\(155\) | −61.6395 | + | 25.5319i | −0.397674 | + | 0.164722i | ||||
\(156\) | −65.6226 | + | 524.862i | −0.420657 | + | 3.36450i | ||||
\(157\) | 2.83630 | + | 1.17483i | 0.0180656 | + | 0.00748301i | 0.391698 | − | 0.920094i | \(-0.371888\pi\) |
−0.373632 | + | 0.927577i | \(0.621888\pi\) | |||||||
\(158\) | 67.9337 | + | 198.004i | 0.429960 | + | 1.25319i | ||||
\(159\) | − | 428.592i | − | 2.69555i | ||||||
\(160\) | −72.6453 | + | 37.3081i | −0.454033 | + | 0.233176i | ||||
\(161\) | −1.12551 | − | 37.6508i | −0.00699074 | − | 0.233856i | ||||
\(162\) | −118.192 | − | 344.489i | −0.729578 | − | 2.12648i | ||||
\(163\) | −72.9396 | + | 176.092i | −0.447482 | + | 1.08032i | 0.525780 | + | 0.850620i | \(0.323773\pi\) |
−0.973262 | + | 0.229697i | \(0.926227\pi\) | |||||||
\(164\) | −1.19112 | + | 9.52679i | −0.00726291 | + | 0.0580902i | ||||
\(165\) | −85.4490 | + | 35.3941i | −0.517873 | + | 0.214510i | ||||
\(166\) | 7.27569 | − | 116.838i | 0.0438294 | − | 0.703842i | ||||
\(167\) | −1.99765 | − | 1.99765i | −0.0119620 | − | 0.0119620i | 0.701100 | − | 0.713062i | \(-0.252692\pi\) |
−0.713062 | + | 0.701100i | \(0.752692\pi\) | |||||||
\(168\) | 304.644 | + | 48.1291i | 1.81336 | + | 0.286483i | ||||
\(169\) | −288.138 | − | 288.138i | −1.70496 | − | 1.70496i | ||||
\(170\) | −43.7254 | − | 49.5328i | −0.257208 | − | 0.291369i | ||||
\(171\) | 301.556 | − | 124.908i | 1.76348 | − | 0.730459i | ||||
\(172\) | −210.851 | − | 119.910i | −1.22588 | − | 0.697150i | ||||
\(173\) | −70.0181 | + | 169.039i | −0.404729 | + | 0.977101i | 0.581773 | + | 0.813351i | \(0.302359\pi\) |
−0.986502 | + | 0.163750i | \(0.947641\pi\) | |||||||
\(174\) | −132.543 | + | 270.992i | −0.761740 | + | 1.55743i | ||||
\(175\) | −129.352 | + | 3.86676i | −0.739153 | + | 0.0220958i | ||||
\(176\) | 104.196 | − | 15.1017i | 0.592023 | − | 0.0858053i | ||||
\(177\) | − | 368.638i | − | 2.08270i | ||||||
\(178\) | −121.947 | − | 59.6446i | −0.685098 | − | 0.335082i | ||||
\(179\) | 175.891 | + | 72.8566i | 0.982634 | + | 0.407020i | 0.815400 | − | 0.578897i | \(-0.196517\pi\) |
0.167233 | + | 0.985917i | \(0.446517\pi\) | |||||||
\(180\) | 57.7329 | + | 209.979i | 0.320739 | + | 1.16655i | ||||
\(181\) | −116.575 | + | 48.2870i | −0.644062 | + | 0.266779i | −0.680714 | − | 0.732549i | \(-0.738330\pi\) |
0.0366527 | + | 0.999328i | \(0.488330\pi\) | |||||||
\(182\) | −245.242 | + | 229.887i | −1.34748 | + | 1.26312i | ||||
\(183\) | −197.807 | − | 197.807i | −1.08091 | − | 1.08091i | ||||
\(184\) | −42.1374 | + | 8.81070i | −0.229008 | + | 0.0478842i | ||||
\(185\) | −43.6874 | − | 43.6874i | −0.236148 | − | 0.236148i | ||||
\(186\) | 17.8976 | − | 287.411i | 0.0962234 | − | 1.54522i | ||||
\(187\) | 32.5971 | + | 78.6965i | 0.174316 | + | 0.420837i | ||||
\(188\) | 201.513 | − | 156.723i | 1.07188 | − | 0.833635i | ||||
\(189\) | 168.748 | − | 444.520i | 0.892848 | − | 2.35196i | ||||
\(190\) | −73.8675 | + | 25.3433i | −0.388776 | + | 0.133386i | ||||
\(191\) | 165.116 | 0.864482 | 0.432241 | − | 0.901758i | \(-0.357723\pi\) | ||||
0.432241 | + | 0.901758i | \(0.357723\pi\) | |||||||
\(192\) | −6.89080 | − | 352.415i | −0.0358896 | − | 1.83550i | ||||
\(193\) | −262.848 | −1.36191 | −0.680953 | − | 0.732327i | \(-0.738434\pi\) | ||||
−0.680953 | + | 0.732327i | \(0.738434\pi\) | |||||||
\(194\) | 5.75435 | + | 16.7720i | 0.0296616 | + | 0.0864538i | ||||
\(195\) | −311.786 | − | 129.146i | −1.59890 | − | 0.662287i | ||||
\(196\) | 129.355 | + | 147.253i | 0.659974 | + | 0.751288i | ||||
\(197\) | −82.6273 | + | 34.2253i | −0.419428 | + | 0.173733i | −0.582408 | − | 0.812897i | \(-0.697889\pi\) |
0.162980 | + | 0.986629i | \(0.447889\pi\) | |||||||
\(198\) | 17.4493 | − | 280.212i | 0.0881278 | − | 1.41521i | ||||
\(199\) | 117.305 | + | 117.305i | 0.589475 | + | 0.589475i | 0.937489 | − | 0.348014i | \(-0.113144\pi\) |
−0.348014 | + | 0.937489i | \(0.613144\pi\) | |||||||
\(200\) | 30.2697 | + | 144.766i | 0.151349 | + | 0.723829i | ||||
\(201\) | −3.39481 | + | 3.39481i | −0.0168896 | + | 0.0168896i | ||||
\(202\) | 107.859 | + | 122.184i | 0.533954 | + | 0.604871i | ||||
\(203\) | −174.844 | + | 78.6232i | −0.861303 | + | 0.387306i | ||||
\(204\) | 274.971 | − | 75.6024i | 1.34790 | − | 0.370600i | ||||
\(205\) | −5.65924 | − | 2.34413i | −0.0276060 | − | 0.0114348i | ||||
\(206\) | 6.79914 | + | 3.32546i | 0.0330055 | + | 0.0161430i | ||||
\(207\) | 114.795i | 0.554564i | ||||||||
\(208\) | 307.799 | + | 229.871i | 1.47980 | + | 1.10515i | ||||
\(209\) | 100.681 | 0.481725 | ||||||||
\(210\) | −81.1363 | + | 179.271i | −0.386363 | + | 0.853671i | ||||
\(211\) | −362.717 | − | 150.242i | −1.71904 | − | 0.712049i | −0.999852 | − | 0.0172322i | \(-0.994515\pi\) |
−0.719187 | − | 0.694817i | \(-0.755485\pi\) | |||||||
\(212\) | −270.582 | − | 153.878i | −1.27633 | − | 0.725841i | ||||
\(213\) | 349.713 | − | 144.856i | 1.64185 | − | 0.680075i | ||||
\(214\) | 239.404 | + | 271.200i | 1.11871 | + | 1.26729i | ||||
\(215\) | 109.430 | − | 109.430i | 0.508978 | − | 0.508978i | ||||
\(216\) | −533.966 | − | 100.797i | −2.47207 | − | 0.466651i | ||||
\(217\) | 125.477 | − | 133.210i | 0.578235 | − | 0.613871i | ||||
\(218\) | 3.18467 | + | 0.198315i | 0.0146086 | + | 0.000909700i | ||||
\(219\) | −497.295 | + | 205.986i | −2.27075 | + | 0.940576i | ||||
\(220\) | −8.33362 | + | 66.6539i | −0.0378801 | + | 0.302972i | ||||
\(221\) | −118.940 | + | 287.148i | −0.538192 | + | 1.29931i | ||||
\(222\) | 252.235 | − | 86.5399i | 1.13619 | − | 0.389819i | ||||
\(223\) | − | 27.1084i | − | 0.121562i | −0.998151 | − | 0.0607812i | \(-0.980641\pi\) | ||
0.998151 | − | 0.0607812i | \(-0.0193592\pi\) | |||||||
\(224\) | 139.762 | − | 175.050i | 0.623938 | − | 0.781474i | ||||
\(225\) | 394.385 | 1.75282 | ||||||||
\(226\) | −27.7744 | − | 80.9530i | −0.122895 | − | 0.358199i | ||||
\(227\) | −197.820 | − | 81.9397i | −0.871454 | − | 0.360968i | −0.0982775 | − | 0.995159i | \(-0.531333\pi\) |
−0.773176 | + | 0.634191i | \(0.781333\pi\) | |||||||
\(228\) | 41.8175 | − | 334.464i | 0.183410 | − | 1.46695i | ||||
\(229\) | −151.031 | − | 364.622i | −0.659526 | − | 1.59224i | −0.798537 | − | 0.601946i | \(-0.794392\pi\) |
0.139011 | − | 0.990291i | \(-0.455608\pi\) | |||||||
\(230\) | 1.70702 | − | 27.4124i | 0.00742182 | − | 0.119184i | ||||
\(231\) | 173.945 | − | 184.665i | 0.753009 | − | 0.799416i | ||||
\(232\) | 123.498 | + | 180.973i | 0.532319 | + | 0.780055i | ||||
\(233\) | 235.935 | + | 235.935i | 1.01260 | + | 1.01260i | 0.999920 | + | 0.0126786i | \(0.00403584\pi\) |
0.0126786 | + | 0.999920i | \(0.495964\pi\) | |||||||
\(234\) | 767.994 | − | 677.952i | 3.28203 | − | 2.89723i | ||||
\(235\) | 62.3291 | + | 150.476i | 0.265230 | + | 0.640322i | ||||
\(236\) | −232.732 | − | 132.353i | −0.986151 | − | 0.560818i | ||||
\(237\) | 220.601 | − | 532.577i | 0.930805 | − | 2.24716i | ||||
\(238\) | 165.104 | + | 74.7246i | 0.693715 | + | 0.313969i | ||||
\(239\) | 184.016i | 0.769942i | 0.922929 | + | 0.384971i | \(0.125789\pi\) | ||||
−0.922929 | + | 0.384971i | \(0.874211\pi\) | |||||||
\(240\) | 217.965 | + | 55.3691i | 0.908188 | + | 0.230705i | ||||
\(241\) | −253.749 | −1.05290 | −0.526449 | − | 0.850207i | \(-0.676477\pi\) | ||||
−0.526449 | + | 0.850207i | \(0.676477\pi\) | |||||||
\(242\) | −68.2769 | + | 139.597i | −0.282136 | + | 0.576846i | ||||
\(243\) | −149.860 | + | 361.795i | −0.616709 | + | 1.48887i | ||||
\(244\) | −195.900 | + | 53.8619i | −0.802868 | + | 0.220746i | ||||
\(245\) | −112.466 | + | 54.6702i | −0.459047 | + | 0.223144i | ||||
\(246\) | 19.8209 | − | 17.4970i | 0.0805726 | − | 0.0711261i | ||||
\(247\) | 259.765 | + | 259.765i | 1.05168 | + | 1.05168i | ||||
\(248\) | −175.024 | − | 114.489i | −0.705744 | − | 0.461648i | ||||
\(249\) | −227.948 | + | 227.948i | −0.915455 | + | 0.915455i | ||||
\(250\) | −221.533 | − | 13.7952i | −0.886131 | − | 0.0551809i | ||||
\(251\) | 110.097 | + | 265.797i | 0.438632 | + | 1.05895i | 0.976422 | + | 0.215872i | \(0.0692593\pi\) |
−0.537790 | + | 0.843079i | \(0.680741\pi\) | |||||||
\(252\) | −380.634 | − | 460.342i | −1.51045 | − | 1.82675i | ||||
\(253\) | −13.5505 | + | 32.7138i | −0.0535593 | + | 0.129303i | ||||
\(254\) | −387.312 | + | 132.884i | −1.52485 | + | 0.523165i | ||||
\(255\) | 181.945i | 0.713510i | ||||||||
\(256\) | −224.963 | − | 122.178i | −0.878763 | − | 0.477258i | ||||
\(257\) | − | 19.7298i | − | 0.0767695i | −0.999263 | − | 0.0383848i | \(-0.987779\pi\) | ||
0.999263 | − | 0.0383848i | \(-0.0122213\pi\) | |||||||
\(258\) | 216.769 | + | 631.811i | 0.840191 | + | 2.44888i | ||||
\(259\) | 158.433 | + | 60.1444i | 0.611712 | + | 0.232218i | ||||
\(260\) | −193.475 | + | 150.472i | −0.744133 | + | 0.578737i | ||||
\(261\) | 539.773 | − | 223.581i | 2.06810 | − | 0.856633i | ||||
\(262\) | −415.392 | − | 25.8671i | −1.58546 | − | 0.0987296i | ||||
\(263\) | 123.704 | − | 123.704i | 0.470357 | − | 0.470357i | −0.431673 | − | 0.902030i | \(-0.642077\pi\) |
0.902030 | + | 0.431673i | \(0.142077\pi\) | |||||||
\(264\) | −242.631 | − | 158.712i | −0.919057 | − | 0.601183i | ||||
\(265\) | 140.430 | − | 140.430i | 0.529924 | − | 0.529924i | ||||
\(266\) | 156.279 | − | 146.494i | 0.587514 | − | 0.550728i | ||||
\(267\) | 143.059 | + | 345.374i | 0.535800 | + | 1.29354i | ||||
\(268\) | 0.924393 | + | 3.36209i | 0.00344923 | + | 0.0125451i | ||||
\(269\) | −89.1653 | + | 215.264i | −0.331470 | + | 0.800238i | 0.667006 | + | 0.745052i | \(0.267575\pi\) |
−0.998476 | + | 0.0551865i | \(0.982425\pi\) | |||||||
\(270\) | 152.324 | − | 311.438i | 0.564165 | − | 1.15347i | ||||
\(271\) | 211.034 | 0.778724 | 0.389362 | − | 0.921085i | \(-0.372696\pi\) | ||||
0.389362 | + | 0.921085i | \(0.372696\pi\) | |||||||
\(272\) | 50.9937 | − | 200.741i | 0.187477 | − | 0.738017i | ||||
\(273\) | 925.246 | − | 27.6587i | 3.38918 | − | 0.101314i | ||||
\(274\) | −41.4827 | − | 20.2892i | −0.151397 | − | 0.0740483i | ||||
\(275\) | 112.390 | + | 46.5536i | 0.408692 | + | 0.169286i | ||||
\(276\) | 103.048 | + | 58.6028i | 0.373363 | + | 0.212329i | ||||
\(277\) | 119.315 | + | 288.051i | 0.430738 | + | 1.03989i | 0.979050 | + | 0.203620i | \(0.0652708\pi\) |
−0.548312 | + | 0.836274i | \(0.684729\pi\) | |||||||
\(278\) | −46.1074 | + | 40.7016i | −0.165854 | + | 0.146409i | ||||
\(279\) | −394.360 | + | 394.360i | −1.41348 | + | 1.41348i | ||||
\(280\) | 84.0481 | + | 115.587i | 0.300172 | + | 0.412812i | ||||
\(281\) | −169.721 | + | 169.721i | −0.603989 | + | 0.603989i | −0.941369 | − | 0.337380i | \(-0.890459\pi\) |
0.337380 | + | 0.941369i | \(0.390459\pi\) | |||||||
\(282\) | −701.634 | − | 43.6919i | −2.48806 | − | 0.154936i | ||||
\(283\) | −10.3304 | − | 24.9398i | −0.0365032 | − | 0.0881265i | 0.904577 | − | 0.426311i | \(-0.140187\pi\) |
−0.941080 | + | 0.338185i | \(0.890187\pi\) | |||||||
\(284\) | 34.1067 | − | 272.792i | 0.120094 | − | 0.960534i | ||||
\(285\) | 198.683 | + | 82.2973i | 0.697134 | + | 0.288762i | ||||
\(286\) | 298.886 | − | 102.546i | 1.04506 | − | 0.358551i | ||||
\(287\) | 16.7942 | − | 0.502035i | 0.0585163 | − | 0.00174925i | ||||
\(288\) | −441.685 | + | 520.513i | −1.53363 | + | 1.80734i | ||||
\(289\) | −121.433 | −0.420183 | ||||||||
\(290\) | −132.220 | + | 45.3636i | −0.455931 | + | 0.156426i | ||||
\(291\) | 18.6861 | − | 45.1122i | 0.0642133 | − | 0.155025i | ||||
\(292\) | −48.4999 | + | 387.911i | −0.166095 | + | 1.32846i | ||||
\(293\) | 1.20658 | + | 2.91294i | 0.00411802 | + | 0.00994178i | 0.925925 | − | 0.377707i | \(-0.123287\pi\) |
−0.921807 | + | 0.387649i | \(0.873287\pi\) | |||||||
\(294\) | 1.30747 | − | 539.737i | 0.00444719 | − | 1.83584i | ||||
\(295\) | 120.786 | − | 120.786i | 0.409444 | − | 0.409444i | ||||
\(296\) | 35.9254 | − | 190.314i | 0.121370 | − | 0.642951i | ||||
\(297\) | −316.051 | + | 316.051i | −1.06415 | + | 1.06415i | ||||
\(298\) | 60.2939 | + | 68.3018i | 0.202329 | + | 0.229201i | ||||
\(299\) | −119.366 | + | 49.4430i | −0.399217 | + | 0.165361i | ||||
\(300\) | 201.334 | − | 354.029i | 0.671113 | − | 1.18010i | ||||
\(301\) | −150.653 | + | 396.852i | −0.500507 | + | 1.31844i | ||||
\(302\) | −16.9490 | − | 8.28979i | −0.0561226 | − | 0.0274496i | ||||
\(303\) | − | 448.809i | − | 1.48122i | ||||||
\(304\) | −196.143 | − | 146.484i | −0.645206 | − | 0.481855i | ||||
\(305\) | − | 129.624i | − | 0.424998i | ||||||
\(306\) | −496.138 | − | 242.662i | −1.62137 | − | 0.793012i | ||||
\(307\) | 105.156 | − | 253.869i | 0.342528 | − | 0.826936i | −0.654931 | − | 0.755689i | \(-0.727302\pi\) |
0.997459 | − | 0.0712470i | \(-0.0226979\pi\) | |||||||
\(308\) | −54.1323 | − | 176.117i | −0.175754 | − | 0.571808i | ||||
\(309\) | −7.97619 | − | 19.2562i | −0.0258129 | − | 0.0623179i | ||||
\(310\) | 100.035 | − | 88.3070i | 0.322695 | − | 0.284861i | ||||
\(311\) | −308.259 | + | 308.259i | −0.991187 | + | 0.991187i | −0.999962 | − | 0.00877417i | \(-0.997207\pi\) |
0.00877417 | + | 0.999962i | \(0.497207\pi\) | |||||||
\(312\) | −216.518 | − | 1035.50i | −0.693968 | − | 3.31892i | ||||
\(313\) | 49.9640 | + | 49.9640i | 0.159629 | + | 0.159629i | 0.782402 | − | 0.622773i | \(-0.213994\pi\) |
−0.622773 | + | 0.782402i | \(0.713994\pi\) | |||||||
\(314\) | −6.12810 | − | 0.381607i | −0.0195162 | − | 0.00121531i | ||||
\(315\) | 347.575 | − | 156.296i | 1.10341 | − | 0.496177i | ||||
\(316\) | −257.028 | − | 330.483i | −0.813379 | − | 1.04583i | ||||
\(317\) | −80.6419 | + | 194.687i | −0.254391 | + | 0.614154i | −0.998549 | − | 0.0538495i | \(-0.982851\pi\) |
0.744158 | + | 0.668003i | \(0.232851\pi\) | |||||||
\(318\) | 278.176 | + | 810.791i | 0.874768 | + | 2.54966i | ||||
\(319\) | 180.214 | 0.564935 | ||||||||
\(320\) | 113.212 | − | 117.728i | 0.353789 | − | 0.367900i | ||||
\(321\) | − | 996.178i | − | 3.10336i | ||||||
\(322\) | 26.5663 | + | 70.4956i | 0.0825040 | + | 0.218930i | ||||
\(323\) | 75.7939 | − | 182.983i | 0.234656 | − | 0.566509i | ||||
\(324\) | 447.179 | + | 574.978i | 1.38018 | + | 1.77462i | ||||
\(325\) | 169.865 | + | 410.090i | 0.522661 | + | 1.26181i | ||||
\(326\) | 23.6921 | − | 380.464i | 0.0726752 | − | 1.16707i | ||||
\(327\) | −6.21322 | − | 6.21322i | −0.0190007 | − | 0.0190007i | ||||
\(328\) | −3.93002 | − | 18.7954i | −0.0119818 | − | 0.0573032i | ||||
\(329\) | −325.195 | − | 306.317i | −0.988436 | − | 0.931056i | ||||
\(330\) | 138.676 | − | 122.417i | 0.420231 | − | 0.370962i | ||||
\(331\) | −143.604 | − | 346.691i | −0.433849 | − | 1.04740i | −0.978035 | − | 0.208440i | \(-0.933161\pi\) |
0.544186 | − | 0.838965i | \(-0.316839\pi\) | |||||||
\(332\) | 62.0693 | + | 225.751i | 0.186956 | + | 0.679972i | ||||
\(333\) | −477.145 | − | 197.640i | −1.43287 | − | 0.593513i | ||||
\(334\) | 5.07564 | + | 2.48250i | 0.0151965 | + | 0.00743264i | ||||
\(335\) | −2.22465 | −0.00664074 | ||||||||
\(336\) | −607.550 | + | 106.680i | −1.80818 | + | 0.317499i | ||||
\(337\) | 438.012i | 1.29974i | 0.760046 | + | 0.649869i | \(0.225176\pi\) | ||||
−0.760046 | + | 0.649869i | \(0.774824\pi\) | |||||||
\(338\) | 732.102 | + | 358.072i | 2.16598 | + | 1.05938i | ||||
\(339\) | −90.1915 | + | 217.742i | −0.266052 | + | 0.642305i | ||||
\(340\) | 114.867 | + | 65.3241i | 0.337844 | + | 0.192130i | ||||
\(341\) | −158.934 | + | 65.8326i | −0.466082 | + | 0.193057i | ||||
\(342\) | −489.398 | + | 432.020i | −1.43099 | + | 1.26322i | ||||
\(343\) | 219.848 | − | 263.279i | 0.640957 | − | 0.767577i | ||||
\(344\) | 476.706 | + | 89.9877i | 1.38577 | + | 0.261592i | ||||
\(345\) | −53.4812 | + | 53.4812i | −0.155018 | + | 0.155018i | ||||
\(346\) | 22.7432 | − | 365.225i | 0.0657317 | − | 1.05556i | ||||
\(347\) | 10.4450 | − | 4.32648i | 0.0301010 | − | 0.0124682i | −0.367582 | − | 0.929991i | \(-0.619814\pi\) |
0.397683 | + | 0.917523i | \(0.369814\pi\) | |||||||
\(348\) | 74.8517 | − | 598.678i | 0.215091 | − | 1.72034i | ||||
\(349\) | −34.0581 | − | 14.1073i | −0.0975877 | − | 0.0404221i | 0.333356 | − | 0.942801i | \(-0.391819\pi\) |
−0.430943 | + | 0.902379i | \(0.641819\pi\) | |||||||
\(350\) | 242.192 | − | 91.2703i | 0.691977 | − | 0.260772i | ||||
\(351\) | −1630.88 | −4.64639 | ||||||||
\(352\) | −187.312 | + | 96.1969i | −0.532136 | + | 0.273287i | ||||
\(353\) | 549.398i | 1.55637i | 0.628036 | + | 0.778184i | \(0.283859\pi\) | ||||
−0.628036 | + | 0.778184i | \(0.716141\pi\) | |||||||
\(354\) | 239.264 | + | 697.374i | 0.675886 | + | 1.96998i | ||||
\(355\) | 162.048 | + | 67.1223i | 0.456472 | + | 0.189077i | ||||
\(356\) | 269.407 | + | 33.6835i | 0.756761 | + | 0.0946165i | ||||
\(357\) | −204.672 | − | 455.156i | −0.573312 | − | 1.27495i | ||||
\(358\) | −380.031 | − | 23.6652i | −1.06154 | − | 0.0661038i | ||||
\(359\) | −24.9930 | + | 24.9930i | −0.0696183 | + | 0.0696183i | −0.741059 | − | 0.671440i | \(-0.765676\pi\) |
0.671440 | + | 0.741059i | \(0.265676\pi\) | |||||||
\(360\) | −245.503 | − | 359.758i | −0.681952 | − | 0.999327i | ||||
\(361\) | 89.7324 | + | 89.7324i | 0.248566 | + | 0.248566i | ||||
\(362\) | 189.191 | − | 167.010i | 0.522628 | − | 0.461353i | ||||
\(363\) | 395.360 | − | 163.763i | 1.08915 | − | 0.451139i | ||||
\(364\) | 314.731 | − | 594.064i | 0.864646 | − | 1.63204i | ||||
\(365\) | −230.433 | − | 95.4483i | −0.631322 | − | 0.261502i | ||||
\(366\) | 502.588 | + | 245.816i | 1.37319 | + | 0.671630i | ||||
\(367\) | −334.565 | −0.911620 | −0.455810 | − | 0.890077i | \(-0.650650\pi\) | ||||
−0.455810 | + | 0.890077i | \(0.650650\pi\) | |||||||
\(368\) | 73.9951 | − | 44.0168i | 0.201074 | − | 0.119611i | ||||
\(369\) | −51.2043 | −0.138765 | ||||||||
\(370\) | 111.001 | + | 54.2907i | 0.300003 | + | 0.146732i | ||||
\(371\) | −193.330 | + | 509.273i | −0.521105 | + | 1.37270i | ||||
\(372\) | 152.685 | + | 555.327i | 0.410444 | + | 1.49281i | ||||
\(373\) | −16.1104 | − | 38.8939i | −0.0431913 | − | 0.104273i | 0.900812 | − | 0.434210i | \(-0.142972\pi\) |
−0.944003 | + | 0.329937i | \(0.892972\pi\) | |||||||
\(374\) | −112.743 | − | 127.717i | −0.301453 | − | 0.341490i | ||||
\(375\) | 432.206 | + | 432.206i | 1.15255 | + | 1.15255i | ||||
\(376\) | −279.493 | + | 427.274i | −0.743332 | + | 1.13637i | ||||
\(377\) | 464.969 | + | 464.969i | 1.23334 | + | 1.23334i | ||||
\(378\) | −30.7167 | + | 950.448i | −0.0812612 | + | 2.51441i | ||||
\(379\) | 264.383 | − | 109.511i | 0.697580 | − | 0.288947i | −0.00557400 | − | 0.999984i | \(-0.501774\pi\) |
0.703154 | + | 0.711037i | \(0.251774\pi\) | |||||||
\(380\) | 123.290 | − | 95.8868i | 0.324448 | − | 0.252334i | ||||
\(381\) | 1041.76 | + | 431.513i | 2.73429 | + | 1.13258i | ||||
\(382\) | −312.359 | + | 107.168i | −0.817695 | + | 0.280545i | ||||
\(383\) | − | 443.315i | − | 1.15748i | −0.815512 | − | 0.578741i | \(-0.803544\pi\) | ||
0.815512 | − | 0.578741i | \(-0.196456\pi\) | |||||||
\(384\) | 241.770 | + | 662.211i | 0.629608 | + | 1.72451i | ||||
\(385\) | 117.500 | − | 3.51247i | 0.305195 | − | 0.00912331i | ||||
\(386\) | 497.244 | − | 170.601i | 1.28820 | − | 0.441970i | ||||
\(387\) | 495.058 | − | 1195.18i | 1.27922 | − | 3.08831i | ||||
\(388\) | −21.7717 | − | 27.9937i | −0.0561125 | − | 0.0721488i | ||||
\(389\) | −234.282 | + | 97.0428i | −0.602268 | + | 0.249467i | −0.662918 | − | 0.748692i | \(-0.730682\pi\) |
0.0606509 | + | 0.998159i | \(0.480682\pi\) | |||||||
\(390\) | 673.645 | + | 41.9490i | 1.72729 | + | 0.107562i | ||||
\(391\) | 49.2549 | + | 49.2549i | 0.125972 | + | 0.125972i | ||||
\(392\) | −340.282 | − | 194.608i | −0.868065 | − | 0.496450i | ||||
\(393\) | 810.421 | + | 810.421i | 2.06214 | + | 2.06214i | ||||
\(394\) | 134.097 | − | 118.375i | 0.340347 | − | 0.300444i | ||||
\(395\) | 246.782 | − | 102.220i | 0.624764 | − | 0.258786i | ||||
\(396\) | 148.861 | + | 541.419i | 0.375912 | + | 1.36722i | ||||
\(397\) | 227.661 | − | 549.622i | 0.573453 | − | 1.38444i | −0.325144 | − | 0.945664i | \(-0.605413\pi\) |
0.898597 | − | 0.438774i | \(-0.144587\pi\) | |||||||
\(398\) | −298.050 | − | 145.777i | −0.748869 | − | 0.366273i | ||||
\(399\) | −589.606 | + | 17.6253i | −1.47771 | + | 0.0441737i | ||||
\(400\) | −151.223 | − | 254.215i | −0.378057 | − | 0.635538i | ||||
\(401\) | − | 595.500i | − | 1.48504i | −0.669826 | − | 0.742518i | \(-0.733631\pi\) | ||
0.669826 | − | 0.742518i | \(-0.266369\pi\) | |||||||
\(402\) | 4.21877 | − | 8.62555i | 0.0104944 | − | 0.0214566i | ||||
\(403\) | −579.918 | − | 240.210i | −1.43900 | − | 0.596054i | ||||
\(404\) | −283.346 | − | 161.137i | −0.701350 | − | 0.398853i | ||||
\(405\) | −429.353 | + | 177.844i | −1.06013 | + | 0.439120i | ||||
\(406\) | 279.733 | − | 262.218i | 0.688997 | − | 0.645857i | ||||
\(407\) | −112.645 | − | 112.645i | −0.276770 | − | 0.276770i | ||||
\(408\) | −471.109 | + | 321.490i | −1.15468 | + | 0.787967i | ||||
\(409\) | −369.737 | − | 369.737i | −0.904002 | − | 0.904002i | 0.0917776 | − | 0.995780i | \(-0.470745\pi\) |
−0.995780 | + | 0.0917776i | \(0.970745\pi\) | |||||||
\(410\) | 12.2273 | + | 0.761418i | 0.0298228 | + | 0.00185712i | ||||
\(411\) | 48.6641 | + | 117.486i | 0.118404 | + | 0.285853i | ||||
\(412\) | −15.0207 | − | 1.87801i | −0.0364580 | − | 0.00455828i | ||||
\(413\) | −166.286 | + | 438.033i | −0.402629 | + | 1.06061i | ||||
\(414\) | −74.5071 | − | 217.164i | −0.179969 | − | 0.524550i | ||||
\(415\) | −149.376 | −0.359943 | ||||||||
\(416\) | −731.478 | − | 235.085i | −1.75836 | − | 0.565107i | ||||
\(417\) | 169.363 | 0.406146 | ||||||||
\(418\) | −190.463 | + | 65.3464i | −0.455653 | + | 0.156331i | ||||
\(419\) | −496.820 | − | 205.790i | −1.18573 | − | 0.491145i | −0.299367 | − | 0.954138i | \(-0.596775\pi\) |
−0.886362 | + | 0.462993i | \(0.846775\pi\) | |||||||
\(420\) | 37.1348 | − | 391.798i | 0.0884163 | − | 0.932852i | ||||
\(421\) | 293.755 | − | 121.677i | 0.697754 | − | 0.289019i | −0.00547243 | − | 0.999985i | \(-0.501742\pi\) |
0.703227 | + | 0.710966i | \(0.251742\pi\) | |||||||
\(422\) | 783.686 | + | 48.8015i | 1.85708 | + | 0.115643i | ||||
\(423\) | 962.721 | + | 962.721i | 2.27594 | + | 2.27594i | ||||
\(424\) | 611.749 | + | 115.480i | 1.44280 | + | 0.272358i | ||||
\(425\) | 169.218 | − | 169.218i | 0.398161 | − | 0.398161i | ||||
\(426\) | −567.554 | + | 501.012i | −1.33229 | + | 1.17609i | ||||
\(427\) | 145.816 | + | 324.270i | 0.341490 | + | 0.759415i | ||||
\(428\) | −628.914 | − | 357.659i | −1.46943 | − | 0.835653i | ||||
\(429\) | −803.922 | − | 332.996i | −1.87394 | − | 0.776213i | ||||
\(430\) | −135.990 | + | 278.041i | −0.316256 | + | 0.646606i | ||||
\(431\) | 5.12246i | 0.0118851i | 0.999982 | + | 0.00594253i | \(0.00189158\pi\) | ||||
−0.999982 | + | 0.00594253i | \(0.998108\pi\) | |||||||
\(432\) | 1075.56 | − | 155.886i | 2.48971 | − | 0.360848i | ||||
\(433\) | −684.828 | −1.58159 | −0.790795 | − | 0.612082i | \(-0.790332\pi\) | ||||
−0.790795 | + | 0.612082i | \(0.790332\pi\) | |||||||
\(434\) | −150.912 | + | 333.441i | −0.347724 | + | 0.768298i | ||||
\(435\) | 355.635 | + | 147.309i | 0.817552 | + | 0.338641i | ||||
\(436\) | −6.15332 | + | 1.69183i | −0.0141131 | + | 0.00388035i | ||||
\(437\) | 76.0651 | − | 31.5072i | 0.174062 | − | 0.0720988i | ||||
\(438\) | 807.065 | − | 712.443i | 1.84261 | − | 1.62658i | ||||
\(439\) | 20.8767 | − | 20.8767i | 0.0475552 | − | 0.0475552i | −0.682929 | − | 0.730484i | \(-0.739294\pi\) |
0.730484 | + | 0.682929i | \(0.239294\pi\) | |||||||
\(440\) | −27.4963 | − | 131.502i | −0.0624916 | − | 0.298868i | ||||
\(441\) | −693.679 | + | 781.983i | −1.57297 | + | 1.77320i | ||||
\(442\) | 38.6340 | − | 620.411i | 0.0874073 | − | 1.40364i | ||||
\(443\) | 188.599 | − | 78.1204i | 0.425732 | − | 0.176344i | −0.159521 | − | 0.987194i | \(-0.550995\pi\) |
0.585253 | + | 0.810851i | \(0.300995\pi\) | |||||||
\(444\) | −420.999 | + | 327.425i | −0.948195 | + | 0.737443i | ||||
\(445\) | −66.2895 | + | 160.037i | −0.148965 | + | 0.359634i | ||||
\(446\) | 17.5946 | + | 51.2825i | 0.0394498 | + | 0.114983i | ||||
\(447\) | − | 250.888i | − | 0.561270i | ||||||
\(448\) | −150.780 | + | 421.864i | −0.336562 | + | 0.941661i | ||||
\(449\) | 111.048 | 0.247323 | 0.123661 | − | 0.992324i | \(-0.460536\pi\) | ||||
0.123661 | + | 0.992324i | \(0.460536\pi\) | |||||||
\(450\) | −746.080 | + | 255.974i | −1.65796 | + | 0.568832i | ||||
\(451\) | −14.5920 | − | 6.04421i | −0.0323548 | − | 0.0134018i | ||||
\(452\) | 105.085 | + | 135.117i | 0.232488 | + | 0.298930i | ||||
\(453\) | 19.8832 | + | 48.0023i | 0.0438923 | + | 0.105965i | ||||
\(454\) | 427.410 | + | 26.6155i | 0.941431 | + | 0.0586246i | ||||
\(455\) | 312.223 | + | 294.098i | 0.686204 | + | 0.646369i | ||||
\(456\) | 137.974 | + | 659.866i | 0.302575 | + | 1.44707i | ||||
\(457\) | 144.681 | + | 144.681i | 0.316588 | + | 0.316588i | 0.847455 | − | 0.530867i | \(-0.178134\pi\) |
−0.530867 | + | 0.847455i | \(0.678134\pi\) | |||||||
\(458\) | 522.371 | + | 591.750i | 1.14055 | + | 1.29203i | ||||
\(459\) | 336.481 | + | 812.338i | 0.733075 | + | 1.76980i | ||||
\(460\) | 14.5627 | + | 52.9656i | 0.0316580 | + | 0.115143i | ||||
\(461\) | 220.262 | − | 531.760i | 0.477792 | − | 1.15349i | −0.482850 | − | 0.875703i | \(-0.660398\pi\) |
0.960642 | − | 0.277790i | \(-0.0896018\pi\) | |||||||
\(462\) | −209.205 | + | 462.239i | −0.452825 | + | 1.00052i | ||||
\(463\) | 756.952i | 1.63489i | 0.576009 | + | 0.817443i | \(0.304609\pi\) | ||||
−0.576009 | + | 0.817443i | \(0.695391\pi\) | |||||||
\(464\) | −351.088 | − | 262.200i | −0.756654 | − | 0.565087i | ||||
\(465\) | −367.453 | −0.790221 | ||||||||
\(466\) | −599.465 | − | 293.199i | −1.28641 | − | 0.629182i | ||||
\(467\) | −263.945 | + | 637.220i | −0.565193 | + | 1.36450i | 0.340373 | + | 0.940291i | \(0.389447\pi\) |
−0.905566 | + | 0.424206i | \(0.860553\pi\) | |||||||
\(468\) | −1012.83 | + | 1780.98i | −2.16418 | + | 3.80552i | ||||
\(469\) | 5.56521 | − | 2.50254i | 0.0118661 | − | 0.00533590i | ||||
\(470\) | −215.577 | − | 244.209i | −0.458675 | − | 0.519593i | ||||
\(471\) | 11.9558 | + | 11.9558i | 0.0253839 | + | 0.0253839i | ||||
\(472\) | 526.174 | + | 99.3258i | 1.11478 | + | 0.210436i | ||||
\(473\) | 282.160 | − | 282.160i | 0.596532 | − | 0.596532i | ||||
\(474\) | −71.6552 | + | 1150.69i | −0.151171 | + | 2.42761i | ||||
\(475\) | −108.245 | − | 261.327i | −0.227884 | − | 0.550161i | ||||
\(476\) | −360.836 | − | 34.2003i | −0.758060 | − | 0.0718494i | ||||
\(477\) | 635.299 | − | 1533.75i | 1.33186 | − | 3.21540i | ||||
\(478\) | −119.435 | − | 348.114i | −0.249864 | − | 0.728271i | ||||
\(479\) | 381.484i | 0.796417i | 0.917295 | + | 0.398209i | \(0.130368\pi\) | ||||
−0.917295 | + | 0.398209i | \(0.869632\pi\) | |||||||
\(480\) | −448.274 | + | 36.7246i | −0.933904 | + | 0.0765096i | ||||
\(481\) | − | 581.270i | − | 1.20846i | ||||||
\(482\) | 480.030 | − | 164.695i | 0.995913 | − | 0.341690i | ||||
\(483\) | 73.6275 | − | 193.951i | 0.152438 | − | 0.401554i | ||||
\(484\) | 38.5584 | − | 308.398i | 0.0796662 | − | 0.637185i | ||||
\(485\) | 20.9038 | − | 8.65862i | 0.0431005 | − | 0.0178528i | ||||
\(486\) | 48.6774 | − | 781.694i | 0.100159 | − | 1.60842i | ||||
\(487\) | 72.7819 | − | 72.7819i | 0.149449 | − | 0.149449i | −0.628423 | − | 0.777872i | \(-0.716299\pi\) |
0.777872 | + | 0.628423i | \(0.216299\pi\) | |||||||
\(488\) | 335.636 | − | 229.042i | 0.687778 | − | 0.469348i | ||||
\(489\) | −742.277 | + | 742.277i | −1.51795 | + | 1.51795i | ||||
\(490\) | 177.275 | − | 176.419i | 0.361787 | − | 0.360038i | ||||
\(491\) | 40.6981 | + | 98.2539i | 0.0828882 | + | 0.200110i | 0.959890 | − | 0.280378i | \(-0.0904597\pi\) |
−0.877002 | + | 0.480488i | \(0.840460\pi\) | |||||||
\(492\) | −26.1398 | + | 45.9647i | −0.0531298 | + | 0.0934243i | ||||
\(493\) | 135.668 | − | 327.532i | 0.275189 | − | 0.664364i | ||||
\(494\) | −660.011 | − | 322.812i | −1.33605 | − | 0.653466i | ||||
\(495\) | −358.250 | −0.723737 | ||||||||
\(496\) | 405.412 | + | 102.986i | 0.817363 | + | 0.207633i | ||||
\(497\) | −480.887 | + | 14.3754i | −0.967580 | + | 0.0289242i | ||||
\(498\) | 283.273 | − | 579.171i | 0.568822 | − | 1.16299i | ||||
\(499\) | −121.759 | − | 50.4340i | −0.244005 | − | 0.101070i | 0.257330 | − | 0.966324i | \(-0.417157\pi\) |
−0.501335 | + | 0.865253i | \(0.667157\pi\) | |||||||
\(500\) | 428.039 | − | 117.688i | 0.856079 | − | 0.235376i | ||||
\(501\) | −5.95433 | − | 14.3750i | −0.0118849 | − | 0.0286926i | ||||
\(502\) | −380.790 | − | 431.364i | −0.758546 | − | 0.859292i | ||||
\(503\) | −265.041 | + | 265.041i | −0.526920 | + | 0.526920i | −0.919653 | − | 0.392733i | \(-0.871530\pi\) |
0.392733 | + | 0.919653i | \(0.371530\pi\) | |||||||
\(504\) | 1018.85 | + | 623.805i | 2.02153 | + | 1.23771i | ||||
\(505\) | 147.054 | − | 147.054i | 0.291196 | − | 0.291196i | ||||
\(506\) | 4.40145 | − | 70.6814i | 0.00869852 | − | 0.139687i | ||||
\(507\) | −858.841 | − | 2073.43i | −1.69397 | − | 4.08960i | ||||
\(508\) | 646.452 | − | 502.767i | 1.27254 | − | 0.989700i | ||||
\(509\) | −238.605 | − | 98.8333i | −0.468771 | − | 0.194171i | 0.135778 | − | 0.990739i | \(-0.456647\pi\) |
−0.604549 | + | 0.796568i | \(0.706647\pi\) | |||||||
\(510\) | −118.091 | − | 344.196i | −0.231551 | − | 0.674893i | ||||
\(511\) | 683.824 | − | 20.4418i | 1.33821 | − | 0.0400036i | ||||
\(512\) | 504.875 | + | 85.1191i | 0.986084 | + | 0.166248i | ||||
\(513\) | 1039.27 | 2.02586 | ||||||||
\(514\) | 12.8055 | + | 37.3239i | 0.0249135 | + | 0.0726146i | ||||
\(515\) | 3.69595 | − | 8.92280i | 0.00717659 | − | 0.0173258i | ||||
\(516\) | −820.149 | − | 1054.54i | −1.58944 | − | 2.04368i | ||||
\(517\) | 160.712 | + | 387.993i | 0.310855 | + | 0.750470i | ||||
\(518\) | −338.754 | − | 10.9479i | −0.653965 | − | 0.0211349i | ||||
\(519\) | −712.546 | + | 712.546i | −1.37292 | + | 1.37292i | ||||
\(520\) | 268.343 | − | 410.229i | 0.516045 | − | 0.788902i | ||||
\(521\) | −304.312 | + | 304.312i | −0.584092 | + | 0.584092i | −0.936025 | − | 0.351933i | \(-0.885524\pi\) |
0.351933 | + | 0.936025i | \(0.385524\pi\) | |||||||
\(522\) | −876.004 | + | 773.299i | −1.67817 | + | 1.48142i | ||||
\(523\) | 655.653 | − | 271.580i | 1.25364 | − | 0.519274i | 0.345687 | − | 0.938350i | \(-0.387646\pi\) |
0.907951 | + | 0.419076i | \(0.137646\pi\) | |||||||
\(524\) | 802.608 | − | 220.674i | 1.53170 | − | 0.421134i | ||||
\(525\) | −666.331 | − | 252.952i | −1.26920 | − | 0.481814i | ||||
\(526\) | −153.728 | + | 314.307i | −0.292258 | + | 0.597542i | ||||
\(527\) | 338.415i | 0.642154i | ||||||||
\(528\) | 562.010 | + | 142.766i | 1.06441 | + | 0.270390i | ||||
\(529\) | − | 500.044i | − | 0.945263i | ||||||
\(530\) | −174.513 | + | 356.805i | −0.329271 | + | 0.673216i | ||||
\(531\) | 546.430 | − | 1319.20i | 1.02906 | − | 2.48437i | ||||
\(532\) | −200.560 | + | 378.562i | −0.376992 | + | 0.711584i | ||||
\(533\) | −22.0541 | − | 53.2433i | −0.0413773 | − | 0.0998937i | ||||
\(534\) | −494.796 | − | 560.512i | −0.926584 | − | 1.04965i | ||||
\(535\) | 326.402 | − | 326.402i | 0.610096 | − | 0.610096i | ||||
\(536\) | −3.93088 | − | 5.76027i | −0.00733372 | − | 0.0107468i | ||||
\(537\) | 741.433 | + | 741.433i | 1.38069 | + | 1.38069i | ||||
\(538\) | 28.9626 | − | 465.100i | 0.0538337 | − | 0.864497i | ||||
\(539\) | −289.988 | + | 140.964i | −0.538012 | + | 0.261529i | ||||
\(540\) | −86.0231 | + | 688.029i | −0.159302 | + | 1.27413i | ||||
\(541\) | −36.8197 | + | 88.8907i | −0.0680586 | + | 0.164308i | −0.954249 | − | 0.299013i | \(-0.903342\pi\) |
0.886190 | + | 0.463321i | \(0.153342\pi\) | |||||||
\(542\) | −399.225 | + | 136.971i | −0.736578 | + | 0.252714i | ||||
\(543\) | −694.942 | −1.27982 | ||||||||
\(544\) | 33.8225 | + | 412.849i | 0.0621737 | + | 0.758915i | ||||
\(545\) | − | 4.07157i | − | 0.00747078i | ||||||
\(546\) | −1732.39 | + | 652.851i | −3.17287 | + | 1.19570i | ||||
\(547\) | −158.179 | + | 381.878i | −0.289176 | + | 0.698132i | −0.999986 | − | 0.00525185i | \(-0.998328\pi\) |
0.710811 | + | 0.703383i | \(0.248328\pi\) | |||||||
\(548\) | 91.6438 | + | 11.4581i | 0.167233 | + | 0.0209089i | ||||
\(549\) | −414.658 | − | 1001.07i | −0.755298 | − | 1.82345i | ||||
\(550\) | −242.831 | − | 15.1215i | −0.441510 | − | 0.0274936i | ||||
\(551\) | −296.298 | − | 296.298i | −0.537746 | − | 0.537746i | ||||
\(552\) | −232.978 | − | 43.9791i | −0.422061 | − | 0.0796724i | ||||
\(553\) | −502.363 | + | 533.324i | −0.908433 | + | 0.964419i | ||||
\(554\) | −412.672 | − | 467.481i | −0.744896 | − | 0.843828i | ||||
\(555\) | −130.217 | − | 314.372i | −0.234626 | − | 0.566436i | ||||
\(556\) | 60.8066 | − | 106.923i | 0.109364 | − | 0.192308i | ||||
\(557\) | 911.509 | + | 377.560i | 1.63646 | + | 0.677845i | 0.995934 | − | 0.0900898i | \(-0.0287154\pi\) |
0.640528 | + | 0.767935i | \(0.278715\pi\) | |||||||
\(558\) | 490.075 | − | 1001.99i | 0.878270 | − | 1.79568i | ||||
\(559\) | 1455.99 | 2.60464 | ||||||||
\(560\) | −234.020 | − | 164.112i | −0.417893 | − | 0.293057i | ||||
\(561\) | 469.135i | 0.836247i | ||||||||
\(562\) | 210.914 | − | 431.227i | 0.375291 | − | 0.767308i | ||||
\(563\) | 84.5886 | − | 204.215i | 0.150246 | − | 0.362726i | −0.830780 | − | 0.556601i | \(-0.812105\pi\) |
0.981026 | + | 0.193874i | \(0.0621054\pi\) | |||||||
\(564\) | 1355.68 | − | 372.738i | 2.40368 | − | 0.660884i | ||||
\(565\) | −100.895 | + | 41.7923i | −0.178576 | + | 0.0739686i | ||||
\(566\) | 35.7297 | + | 40.4751i | 0.0631267 | + | 0.0715108i | ||||
\(567\) | 874.016 | − | 927.881i | 1.54147 | − | 1.63647i | ||||
\(568\) | 112.533 | + | 538.192i | 0.198121 | + | 0.947521i | ||||
\(569\) | 437.146 | − | 437.146i | 0.768271 | − | 0.768271i | −0.209531 | − | 0.977802i | \(-0.567194\pi\) |
0.977802 | + | 0.209531i | \(0.0671937\pi\) | |||||||
\(570\) | −429.275 | − | 26.7317i | −0.753114 | − | 0.0468977i | ||||
\(571\) | −174.532 | + | 72.2933i | −0.305659 | + | 0.126608i | −0.530241 | − | 0.847847i | \(-0.677899\pi\) |
0.224581 | + | 0.974455i | \(0.427899\pi\) | |||||||
\(572\) | −498.863 | + | 387.982i | −0.872138 | + | 0.678291i | ||||
\(573\) | 840.161 | + | 348.006i | 1.46625 | + | 0.607341i | ||||
\(574\) | −31.4446 | + | 11.8499i | −0.0547816 | + | 0.0206445i | ||||
\(575\) | 99.4805 | 0.173010 | ||||||||
\(576\) | 497.724 | − | 1271.36i | 0.864103 | − | 2.20722i | ||||
\(577\) | − | 92.1486i | − | 0.159703i | −0.996807 | − | 0.0798515i | \(-0.974555\pi\) | ||
0.996807 | − | 0.0798515i | \(-0.0254446\pi\) | |||||||
\(578\) | 229.721 | − | 78.8156i | 0.397442 | − | 0.136359i | ||||
\(579\) | −1337.45 | − | 553.990i | −2.30993 | − | 0.956805i | ||||
\(580\) | 220.685 | − | 171.634i | 0.380491 | − | 0.295920i | ||||
\(581\) | 373.682 | − | 168.035i | 0.643170 | − | 0.289217i | ||||
\(582\) | −6.06959 | + | 97.4694i | −0.0104288 | + | 0.167473i | ||||
\(583\) | 362.090 | − | 362.090i | 0.621081 | − | 0.621081i | ||||
\(584\) | −160.023 | − | 765.312i | −0.274011 | − | 1.31047i | ||||
\(585\) | −924.317 | − | 924.317i | −1.58003 | − | 1.58003i | ||||
\(586\) | −4.17319 | − | 4.72745i | −0.00712148 | − | 0.00806731i | ||||
\(587\) | −539.361 | + | 223.411i | −0.918843 | + | 0.380597i | −0.791435 | − | 0.611253i | \(-0.790666\pi\) |
−0.127408 | + | 0.991850i | \(0.540666\pi\) | |||||||
\(588\) | 347.841 | + | 1021.90i | 0.591567 | + | 1.73793i | ||||
\(589\) | 369.548 | + | 153.072i | 0.627416 | + | 0.259884i | ||||
\(590\) | −150.102 | + | 306.893i | −0.254410 | + | 0.520157i | ||||
\(591\) | −492.568 | −0.833448 | ||||||||
\(592\) | 55.5602 | + | 383.344i | 0.0938517 | + | 0.647540i | ||||
\(593\) | 446.001 | 0.752110 | 0.376055 | − | 0.926597i | \(-0.377280\pi\) | ||||
0.376055 | + | 0.926597i | \(0.377280\pi\) | |||||||
\(594\) | 392.760 | − | 803.024i | 0.661212 | − | 1.35189i | ||||
\(595\) | 82.0720 | − | 216.195i | 0.137936 | − | 0.363354i | ||||
\(596\) | −158.392 | − | 90.0767i | −0.265759 | − | 0.151135i | ||||
\(597\) | 349.648 | + | 844.124i | 0.585675 | + | 1.41394i | ||||
\(598\) | 193.720 | − | 171.008i | 0.323947 | − | 0.285967i | ||||
\(599\) | 262.791 | + | 262.791i | 0.438716 | + | 0.438716i | 0.891580 | − | 0.452864i | \(-0.149598\pi\) |
−0.452864 | + | 0.891580i | \(0.649598\pi\) | |||||||
\(600\) | −151.093 | + | 800.410i | −0.251822 | + | 1.33402i | ||||
\(601\) | −21.0456 | − | 21.0456i | −0.0350177 | − | 0.0350177i | 0.689381 | − | 0.724399i | \(-0.257883\pi\) |
−0.724399 | + | 0.689381i | \(0.757883\pi\) | |||||||
\(602\) | 27.4228 | − | 848.527i | 0.0455529 | − | 1.40951i | ||||
\(603\) | −17.1807 | + | 7.11648i | −0.0284920 | + | 0.0118018i | ||||
\(604\) | 37.4439 | + | 4.68154i | 0.0619932 | + | 0.00775090i | ||||
\(605\) | 183.199 | + | 75.8834i | 0.302808 | + | 0.125427i | ||||
\(606\) | 291.298 | + | 849.037i | 0.480690 | + | 1.40105i | ||||
\(607\) | 261.327i | 0.430523i | 0.976556 | + | 0.215261i | \(0.0690604\pi\) | ||||
−0.976556 | + | 0.215261i | \(0.930940\pi\) | |||||||
\(608\) | 466.129 | + | 149.806i | 0.766659 | + | 0.246391i | ||||
\(609\) | −1055.37 | + | 31.5486i | −1.73296 | + | 0.0518040i | ||||
\(610\) | 84.1323 | + | 245.218i | 0.137922 | + | 0.401996i | ||||
\(611\) | −586.406 | + | 1415.71i | −0.959747 | + | 2.31704i | ||||
\(612\) | 1096.07 | + | 137.040i | 1.79096 | + | 0.223921i | ||||
\(613\) | −776.638 | + | 321.694i | −1.26695 | + | 0.524786i | −0.912034 | − | 0.410114i | \(-0.865489\pi\) |
−0.354911 | + | 0.934900i | \(0.615489\pi\) | |||||||
\(614\) | −34.1567 | + | 548.510i | −0.0556297 | + | 0.893339i | ||||
\(615\) | −23.8553 | − | 23.8553i | −0.0387892 | − | 0.0387892i | ||||
\(616\) | 216.713 | + | 298.036i | 0.351807 | + | 0.483824i | ||||
\(617\) | −69.8903 | − | 69.8903i | −0.113274 | − | 0.113274i | 0.648198 | − | 0.761472i | \(-0.275523\pi\) |
−0.761472 | + | 0.648198i | \(0.775523\pi\) | |||||||
\(618\) | 27.5872 | + | 31.2511i | 0.0446394 | + | 0.0505682i | ||||
\(619\) | 243.628 | − | 100.914i | 0.393583 | − | 0.163027i | −0.177110 | − | 0.984191i | \(-0.556675\pi\) |
0.570693 | + | 0.821164i | \(0.306675\pi\) | |||||||
\(620\) | −131.927 | + | 231.983i | −0.212786 | + | 0.374166i | ||||
\(621\) | −139.874 | + | 337.685i | −0.225240 | + | 0.543777i | ||||
\(622\) | 383.077 | − | 783.226i | 0.615879 | − | 1.25921i | ||||
\(623\) | −14.1970 | − | 474.920i | −0.0227881 | − | 0.762312i | ||||
\(624\) | 1081.69 | + | 1818.39i | 1.73347 | + | 2.91408i | ||||
\(625\) | − | 178.949i | − | 0.286318i | ||||||
\(626\) | −126.949 | − | 62.0907i | −0.202793 | − | 0.0991864i | ||||
\(627\) | 512.293 | + | 212.199i | 0.817055 | + | 0.338435i | ||||
\(628\) | 11.8405 | − | 3.25551i | 0.0188544 | − | 0.00518394i | ||||
\(629\) | −289.529 | + | 119.927i | −0.460301 | + | 0.190663i | ||||
\(630\) | −556.084 | + | 521.266i | −0.882673 | + | 0.827406i | ||||
\(631\) | −722.309 | − | 722.309i | −1.14471 | − | 1.14471i | −0.987578 | − | 0.157127i | \(-0.949777\pi\) |
−0.157127 | − | 0.987578i | \(-0.550223\pi\) | |||||||
\(632\) | 700.733 | + | 458.371i | 1.10875 | + | 0.725270i | ||||
\(633\) | −1528.96 | − | 1528.96i | −2.41541 | − | 2.41541i | ||||
\(634\) | 26.1940 | − | 420.640i | 0.0413154 | − | 0.663470i | ||||
\(635\) | 199.951 | + | 482.725i | 0.314884 | + | 0.760197i | ||||
\(636\) | −1052.48 | − | 1353.27i | −1.65485 | − | 2.12778i | ||||
\(637\) | −1111.90 | − | 384.496i | −1.74552 | − | 0.603604i | ||||
\(638\) | −340.921 | + | 116.967i | −0.534359 | + | 0.183335i | ||||
\(639\) | 1466.19 | 2.29451 | ||||||||
\(640\) | −137.759 | + | 296.193i | −0.215249 | + | 0.462801i | ||||
\(641\) | −685.507 | −1.06943 | −0.534717 | − | 0.845031i | \(-0.679582\pi\) | ||||
−0.534717 | + | 0.845031i | \(0.679582\pi\) | |||||||
\(642\) | 646.566 | + | 1884.52i | 1.00711 | + | 2.93540i | ||||
\(643\) | 336.431 | + | 139.354i | 0.523220 | + | 0.216725i | 0.628631 | − | 0.777704i | \(-0.283616\pi\) |
−0.105411 | + | 0.994429i | \(0.533616\pi\) | |||||||
\(644\) | −96.0118 | − | 116.118i | −0.149087 | − | 0.180307i | ||||
\(645\) | 787.454 | − | 326.174i | 1.22086 | − | 0.505697i | ||||
\(646\) | −24.6192 | + | 395.352i | −0.0381103 | + | 0.612000i | ||||
\(647\) | −262.641 | − | 262.641i | −0.405936 | − | 0.405936i | 0.474383 | − | 0.880319i | \(-0.342671\pi\) |
−0.880319 | + | 0.474383i | \(0.842671\pi\) | |||||||
\(648\) | −1219.14 | − | 797.477i | −1.88139 | − | 1.23067i | ||||
\(649\) | 311.439 | − | 311.439i | 0.479876 | − | 0.479876i | ||||
\(650\) | −587.510 | − | 665.539i | −0.903861 | − | 1.02391i | ||||
\(651\) | 919.225 | − | 413.352i | 1.41202 | − | 0.634950i | ||||
\(652\) | 202.119 | + | 735.121i | 0.309998 | + | 1.12749i | ||||
\(653\) | 639.834 | + | 265.028i | 0.979838 | + | 0.405862i | 0.814366 | − | 0.580352i | \(-0.197085\pi\) |
0.165472 | + | 0.986214i | \(0.447085\pi\) | |||||||
\(654\) | 15.7866 | + | 7.72123i | 0.0241385 | + | 0.0118062i | ||||
\(655\) | 531.075i | 0.810802i | ||||||||
\(656\) | 19.6338 | + | 33.0056i | 0.0299295 | + | 0.0503134i | ||||
\(657\) | −2084.94 | −3.17342 | ||||||||
\(658\) | 814.004 | + | 368.411i | 1.23709 | + | 0.559895i | ||||
\(659\) | −695.726 | − | 288.179i | −1.05573 | − | 0.437297i | −0.213796 | − | 0.976878i | \(-0.568583\pi\) |
−0.841934 | + | 0.539581i | \(0.818583\pi\) | |||||||
\(660\) | −182.887 | + | 321.591i | −0.277101 | + | 0.487259i | ||||
\(661\) | 595.117 | − | 246.506i | 0.900329 | − | 0.372928i | 0.115982 | − | 0.993251i | \(-0.462998\pi\) |
0.784347 | + | 0.620323i | \(0.212998\pi\) | |||||||
\(662\) | 496.682 | + | 562.649i | 0.750275 | + | 0.849923i | ||||
\(663\) | −1210.41 | + | 1210.41i | −1.82566 | + | 1.82566i | ||||
\(664\) | −263.943 | − | 386.779i | −0.397504 | − | 0.582499i | ||||
\(665\) | −198.962 | − | 187.412i | −0.299191 | − | 0.281822i | ||||
\(666\) | 1030.92 | + | 64.1971i | 1.54793 | + | 0.0963921i | ||||
\(667\) | 136.153 | − | 56.3966i | 0.204128 | − | 0.0845527i | ||||
\(668\) | −11.2131 | − | 1.40196i | −0.0167861 | − | 0.00209874i | ||||
\(669\) | 57.1349 | − | 137.936i | 0.0854034 | − | 0.206182i | ||||
\(670\) | 4.20849 | − | 1.44390i | 0.00628133 | − | 0.00215508i | ||||
\(671\) | − | 334.229i | − | 0.498106i | ||||||
\(672\) | 1080.10 | − | 596.140i | 1.60729 | − | 0.887113i | ||||
\(673\) | −124.014 | −0.184271 | −0.0921355 | − | 0.995746i | \(-0.529369\pi\) | ||||
−0.0921355 | + | 0.995746i | \(0.529369\pi\) | |||||||
\(674\) | −284.290 | − | 828.612i | −0.421795 | − | 1.22939i | ||||
\(675\) | 1160.14 | + | 480.546i | 1.71873 | + | 0.711920i | ||||
\(676\) | −1617.36 | − | 202.216i | −2.39255 | − | 0.299136i | ||||
\(677\) | 235.888 | + | 569.484i | 0.348431 | + | 0.841188i | 0.996806 | + | 0.0798661i | \(0.0254493\pi\) |
−0.648374 | + | 0.761322i | \(0.724551\pi\) | |||||||
\(678\) | 29.2959 | − | 470.452i | 0.0432093 | − | 0.693882i | ||||
\(679\) | −42.5529 | + | 45.1754i | −0.0626700 | + | 0.0665323i | ||||
\(680\) | −259.698 | − | 49.0232i | −0.381909 | − | 0.0720929i | ||||
\(681\) | −833.869 | − | 833.869i | −1.22448 | − | 1.22448i | ||||
\(682\) | 257.936 | − | 227.695i | 0.378205 | − | 0.333863i | ||||
\(683\) | −473.632 | − | 1143.45i | −0.693459 | − | 1.67416i | −0.737693 | − | 0.675137i | \(-0.764085\pi\) |
0.0442338 | − | 0.999021i | \(-0.485915\pi\) | |||||||
\(684\) | 645.421 | − | 1134.92i | 0.943598 | − | 1.65924i | ||||
\(685\) | −22.5496 | + | 54.4396i | −0.0329191 | + | 0.0794738i | ||||
\(686\) | −245.019 | + | 640.751i | −0.357171 | + | 0.934039i | ||||
\(687\) | − | 2173.63i | − | 3.16394i | ||||||
\(688\) | −960.218 | + | 139.170i | −1.39567 | + | 0.202282i | ||||
\(689\) | 1868.45 | 2.71183 | ||||||||
\(690\) | 66.4615 | − | 135.885i | 0.0963210 | − | 0.196935i | ||||
\(691\) | 318.457 | − | 768.824i | 0.460864 | − | 1.11262i | −0.507179 | − | 0.861841i | \(-0.669312\pi\) |
0.968043 | − | 0.250784i | \(-0.0806883\pi\) | |||||||
\(692\) | 194.023 | + | 705.677i | 0.280380 | + | 1.01976i | ||||
\(693\) | 896.202 | − | 403.000i | 1.29322 | − | 0.581529i | ||||
\(694\) | −16.9514 | + | 14.9639i | −0.0244256 | + | 0.0215619i | ||||
\(695\) | 55.4924 | + | 55.4924i | 0.0798452 | + | 0.0798452i | ||||
\(696\) | 246.969 | + | 1181.13i | 0.354840 | + | 1.69703i | ||||
\(697\) | −21.9702 | + | 21.9702i | −0.0315211 | + | 0.0315211i | ||||
\(698\) | 73.5859 | + | 4.58232i | 0.105424 | + | 0.00656493i | ||||
\(699\) | 703.243 | + | 1697.78i | 1.00607 | + | 2.42887i | ||||
\(700\) | −398.930 | + | 329.855i | −0.569899 | + | 0.471221i | ||||
\(701\) | −488.956 | + | 1180.44i | −0.697512 | + | 1.68394i | 0.0315568 | + | 0.999502i | \(0.489953\pi\) |
−0.729069 | + | 0.684441i | \(0.760047\pi\) | |||||||
\(702\) | 3085.23 | − | 1058.52i | 4.39491 | − | 1.50786i | ||||
\(703\) | 370.410i | 0.526899i | ||||||||
\(704\) | 291.912 | − | 303.555i | 0.414647 | − | 0.431186i | ||||
\(705\) | 897.034i | 1.27239i | ||||||||
\(706\) | −356.585 | − | 1039.33i | −0.505078 | − | 1.47213i | ||||
\(707\) | −202.449 | + | 533.295i | −0.286350 | + | 0.754308i | ||||
\(708\) | −905.256 | − | 1163.97i | −1.27861 | − | 1.64402i | ||||
\(709\) | −463.982 | + | 192.187i | −0.654417 | + | 0.271068i | −0.685087 | − | 0.728461i | \(-0.740236\pi\) |
0.0306702 | + | 0.999530i | \(0.490236\pi\) | |||||||
\(710\) | −350.120 | − | 21.8026i | −0.493127 | − | 0.0307078i | ||||
\(711\) | 1578.87 | − | 1578.87i | 2.22063 | − | 2.22063i | ||||
\(712\) | −531.514 | + | 111.137i | −0.746508 | + | 0.156091i | ||||
\(713\) | −99.4742 | + | 99.4742i | −0.139515 | + | 0.139515i | ||||
\(714\) | 682.607 | + | 728.202i | 0.956033 | + | 1.01989i | ||||
\(715\) | −154.301 | − | 372.516i | −0.215806 | − | 0.521001i | ||||
\(716\) | 734.285 | − | 201.889i | 1.02554 | − | 0.281968i | ||||
\(717\) | −387.841 | + | 936.331i | −0.540922 | + | 1.30590i | ||||
\(718\) | 31.0590 | − | 63.5022i | 0.0432576 | − | 0.0884431i | ||||
\(719\) | 713.239 | 0.991987 | 0.495994 | − | 0.868326i | \(-0.334804\pi\) | ||||
0.495994 | + | 0.868326i | \(0.334804\pi\) | |||||||
\(720\) | 697.931 | + | 521.231i | 0.969348 | + | 0.723931i | ||||
\(721\) | 0.791548 | + | 26.4790i | 0.00109785 | + | 0.0367254i | ||||
\(722\) | −227.992 | − | 111.511i | −0.315779 | − | 0.154448i | ||||
\(723\) | −1291.15 | − | 534.812i | −1.78582 | − | 0.739712i | ||||
\(724\) | −249.506 | + | 438.736i | −0.344622 | + | 0.605989i | ||||
\(725\) | −193.754 | − | 467.764i | −0.267247 | − | 0.645192i | ||||
\(726\) | −641.634 | + | 566.407i | −0.883793 | + | 0.780175i | ||||
\(727\) | −118.043 | + | 118.043i | −0.162370 | + | 0.162370i | −0.783616 | − | 0.621246i | \(-0.786627\pi\) |
0.621246 | + | 0.783616i | \(0.286627\pi\) | |||||||
\(728\) | −209.819 | + | 1328.10i | −0.288213 | + | 1.82431i | ||||
\(729\) | −366.191 | + | 366.191i | −0.502319 | + | 0.502319i | ||||
\(730\) | 497.873 | + | 31.0034i | 0.682017 | + | 0.0424704i | ||||
\(731\) | −300.399 | − | 725.227i | −0.410942 | − | 0.992102i | ||||
\(732\) | −1110.32 | − | 138.821i | −1.51683 | − | 0.189647i | ||||
\(733\) | 92.9778 | + | 38.5127i | 0.126846 | + | 0.0525411i | 0.445203 | − | 0.895429i | \(-0.353131\pi\) |
−0.318358 | + | 0.947971i | \(0.603131\pi\) | |||||||
\(734\) | 632.914 | − | 217.148i | 0.862281 | − | 0.295842i | ||||
\(735\) | −687.489 | + | 41.1395i | −0.935359 | + | 0.0559722i | ||||
\(736\) | −111.412 | + | 131.295i | −0.151375 | + | 0.178390i | ||||
\(737\) | −5.73613 | −0.00778308 | ||||||||
\(738\) | 96.8661 | − | 33.2340i | 0.131255 | − | 0.0450325i | ||||
\(739\) | −270.592 | + | 653.266i | −0.366159 | + | 0.883987i | 0.628213 | + | 0.778042i | \(0.283787\pi\) |
−0.994372 | + | 0.105945i | \(0.966213\pi\) | |||||||
\(740\) | −245.224 | − | 30.6599i | −0.331384 | − | 0.0414323i | ||||
\(741\) | 774.271 | + | 1869.25i | 1.04490 | + | 2.52261i | ||||
\(742\) | 35.1912 | − | 1088.90i | 0.0474275 | − | 1.46752i | ||||
\(743\) | −296.350 | + | 296.350i | −0.398856 | + | 0.398856i | −0.877829 | − | 0.478973i | \(-0.841009\pi\) |
0.478973 | + | 0.877829i | \(0.341009\pi\) | |||||||
\(744\) | −649.276 | − | 951.443i | −0.872683 | − | 1.27882i | ||||
\(745\) | 82.2044 | − | 82.2044i | 0.110341 | − | 0.110341i | ||||
\(746\) | 55.7208 | + | 63.1213i | 0.0746927 | + | 0.0846130i | ||||
\(747\) | −1153.62 | + | 477.843i | −1.54433 | + | 0.639683i | ||||
\(748\) | 296.178 | + | 168.434i | 0.395959 | + | 0.225180i | ||||
\(749\) | −449.357 | + | 1183.70i | −0.599943 | + | 1.58038i | ||||
\(750\) | −1098.15 | − | 537.107i | −1.46420 | − | 0.716142i | ||||
\(751\) | 240.176i | 0.319809i | 0.987133 | + | 0.159904i | \(0.0511186\pi\) | ||||
−0.987133 | + | 0.159904i | \(0.948881\pi\) | |||||||
\(752\) | 251.411 | − | 989.701i | 0.334324 | − | 1.31609i | ||||
\(753\) | 1584.50i | 2.10425i | ||||||||
\(754\) | −1181.39 | − | 577.821i | −1.56684 | − | 0.766341i | ||||
\(755\) | −9.21333 | + | 22.2430i | −0.0122031 | + | 0.0294609i | ||||
\(756\) | −558.776 | − | 1817.95i | −0.739122 | − | 2.40470i | ||||
\(757\) | −110.643 | − | 267.117i | −0.146160 | − | 0.352863i | 0.833797 | − | 0.552072i | \(-0.186163\pi\) |
−0.979957 | + | 0.199209i | \(0.936163\pi\) | |||||||
\(758\) | −429.070 | + | 378.765i | −0.566056 | + | 0.499690i | ||||
\(759\) | −137.898 | + | 137.898i | −0.181684 | + | 0.181684i | ||||
\(760\) | −171.000 | + | 261.415i | −0.225000 | + | 0.343968i | ||||
\(761\) | 224.784 | + | 224.784i | 0.295379 | + | 0.295379i | 0.839201 | − | 0.543822i | \(-0.183023\pi\) |
−0.543822 | + | 0.839201i | \(0.683023\pi\) | |||||||
\(762\) | −2250.83 | − | 140.163i | −2.95385 | − | 0.183941i | ||||
\(763\) | 4.58017 | + | 10.1855i | 0.00600284 | + | 0.0133493i | ||||
\(764\) | 521.350 | − | 405.472i | 0.682396 | − | 0.530722i | ||||
\(765\) | −269.696 | + | 651.103i | −0.352544 | + | 0.851116i | ||||
\(766\) | 287.732 | + | 838.644i | 0.375630 | + | 1.09484i | ||||
\(767\) | 1607.08 | 2.09528 | ||||||||
\(768\) | −887.175 | − | 1095.82i | −1.15518 | − | 1.42685i | ||||
\(769\) | 1086.61i | 1.41301i | 0.707706 | + | 0.706507i | \(0.249730\pi\) | ||||
−0.707706 | + | 0.706507i | \(0.750270\pi\) | |||||||
\(770\) | −220.001 | + | 82.9077i | −0.285716 | + | 0.107672i | ||||
\(771\) | 41.5834 | − | 100.391i | 0.0539343 | − | 0.130209i | ||||
\(772\) | −829.936 | + | 645.469i | −1.07505 | + | 0.836100i | ||||
\(773\) | −405.851 | − | 979.811i | −0.525034 | − | 1.26754i | −0.934742 | − | 0.355327i | \(-0.884369\pi\) |
0.409708 | − | 0.912217i | \(-0.365631\pi\) | |||||||
\(774\) | −160.804 | + | 2582.30i | −0.207757 | + | 3.33630i | ||||
\(775\) | 341.750 | + | 341.750i | 0.440968 | + | 0.440968i | ||||
\(776\) | 59.3559 | + | 38.8265i | 0.0764896 | + | 0.0500341i | ||||
\(777\) | 679.394 | + | 639.955i | 0.874382 | + | 0.823622i | ||||
\(778\) | 380.219 | − | 335.641i | 0.488713 | − | 0.431415i | ||||
\(779\) | 14.0538 | + | 33.9289i | 0.0180408 | + | 0.0435544i | ||||
\(780\) | −1301.60 | + | 357.869i | −1.66872 | + | 0.458807i | ||||
\(781\) | 417.830 | + | 173.071i | 0.534994 | + | 0.221602i | ||||
\(782\) | −125.147 | − | 61.2095i | −0.160034 | − | 0.0782730i | ||||
\(783\) | 1860.25 | 2.37579 | ||||||||
\(784\) | 770.039 | + | 147.293i | 0.982193 | + | 0.187874i | ||||
\(785\) | 7.83473i | 0.00998055i | ||||||||
\(786\) | −2059.12 | − | 1007.12i | −2.61975 | − | 1.28132i | ||||
\(787\) | 65.6039 | − | 158.382i | 0.0833595 | − | 0.201248i | −0.876704 | − | 0.481031i | \(-0.840263\pi\) |
0.960063 | + | 0.279783i | \(0.0902626\pi\) | |||||||
\(788\) | −176.847 | + | 310.972i | −0.224426 | + | 0.394634i | ||||
\(789\) | 890.167 | − | 368.719i | 1.12822 | − | 0.467325i | ||||
\(790\) | −400.505 | + | 353.549i | −0.506968 | + | 0.447530i | ||||
\(791\) | 205.389 | − | 218.047i | 0.259657 | − | 0.275660i | ||||
\(792\) | −633.015 | − | 927.614i | −0.799261 | − | 1.17123i | ||||
\(793\) | 862.341 | − | 862.341i | 1.08744 | − | 1.08744i | ||||
\(794\) | −73.9485 | + | 1187.51i | −0.0931341 | + | 1.49561i | ||||
\(795\) | 1010.53 | − | 418.574i | 1.27110 | − | 0.526508i | ||||
\(796\) | 658.453 | + | 82.3253i | 0.827203 | + | 0.103424i | ||||
\(797\) | −627.827 | − | 260.054i | −0.787738 | − | 0.326292i | −0.0477041 | − | 0.998862i | \(-0.515190\pi\) |
−0.740034 | + | 0.672570i | \(0.765190\pi\) | |||||||
\(798\) | 1103.95 | − | 416.024i | 1.38340 | − | 0.521334i | ||||
\(799\) | 826.147 | 1.03398 | ||||||||
\(800\) | 451.074 | + | 382.762i | 0.563842 | + | 0.478453i | ||||
\(801\) | 1448.00i | 1.80774i | ||||||||
\(802\) | 386.507 | + | 1126.54i | 0.481929 | + | 1.40466i | ||||
\(803\) | −594.157 | − | 246.108i | −0.739922 | − | 0.306486i | ||||
\(804\) | −2.38249 | + | 19.0556i | −0.00296330 | + | 0.0237010i | ||||
\(805\) | 87.6731 | − | 39.4244i | 0.108911 | − | 0.0489744i | ||||
\(806\) | 1252.97 | + | 78.0246i | 1.55455 | + | 0.0968047i | ||||
\(807\) | −907.401 | + | 907.401i | −1.12441 | + | 1.12441i | ||||
\(808\) | 640.606 | + | 120.927i | 0.792829 | + | 0.149662i | ||||
\(809\) | 15.9686 | + | 15.9686i | 0.0197387 | + | 0.0197387i | 0.716907 | − | 0.697169i | \(-0.245557\pi\) |
−0.697169 | + | 0.716907i | \(0.745557\pi\) | |||||||
\(810\) | 696.801 | − | 615.107i | 0.860249 | − | 0.759391i | ||||
\(811\) | 164.217 | − | 68.0210i | 0.202487 | − | 0.0838730i | −0.279135 | − | 0.960252i | \(-0.590048\pi\) |
0.481622 | + | 0.876379i | \(0.340048\pi\) | |||||||
\(812\) | −358.995 | + | 677.612i | −0.442111 | + | 0.834498i | ||||
\(813\) | 1073.81 | + | 444.785i | 1.32079 | + | 0.547091i | ||||
\(814\) | 286.210 | + | 139.985i | 0.351609 | + | 0.171972i | ||||
\(815\) | −486.420 | −0.596835 | ||||||||
\(816\) | 682.561 | − | 913.953i | 0.836472 | − | 1.12004i | ||||
\(817\) | −927.821 | −1.13564 | ||||||||
\(818\) | 939.428 | + | 459.475i | 1.14844 | + | 0.561706i | ||||
\(819\) | 3352.06 | + | 1272.51i | 4.09287 | + | 1.55373i | ||||
\(820\) | −23.6253 | + | 6.49570i | −0.0288114 | + | 0.00792159i | ||||
\(821\) | 180.317 | + | 435.323i | 0.219630 | + | 0.530235i | 0.994838 | − | 0.101471i | \(-0.0323550\pi\) |
−0.775208 | + | 0.631706i | \(0.782355\pi\) | |||||||
\(822\) | −168.314 | − | 190.669i | −0.204762 | − | 0.231957i | ||||
\(823\) | −396.044 | − | 396.044i | −0.481220 | − | 0.481220i | 0.424301 | − | 0.905521i | \(-0.360520\pi\) |
−0.905521 | + | 0.424301i | \(0.860520\pi\) | |||||||
\(824\) | 29.6344 | − | 6.19639i | 0.0359640 | − | 0.00751989i | ||||
\(825\) | 473.758 | + | 473.758i | 0.574252 | + | 0.574252i | ||||
\(826\) | 30.2685 | − | 936.579i | 0.0366447 | − | 1.13387i | ||||
\(827\) | −1305.85 | + | 540.901i | −1.57902 | + | 0.654052i | −0.988258 | − | 0.152794i | \(-0.951173\pi\) |
−0.590763 | + | 0.806845i | \(0.701173\pi\) | |||||||
\(828\) | 281.899 | + | 362.462i | 0.340457 | + | 0.437756i | ||||
\(829\) | 425.833 | + | 176.386i | 0.513671 | + | 0.212770i | 0.624434 | − | 0.781077i | \(-0.285330\pi\) |
−0.110763 | + | 0.993847i | \(0.535330\pi\) | |||||||
\(830\) | 282.583 | − | 96.9521i | 0.340462 | − | 0.116810i | ||||
\(831\) | 1717.16i | 2.06638i | ||||||||
\(832\) | 1536.36 | − | 30.0405i | 1.84658 | − | 0.0361064i | ||||
\(833\) | 37.8885 | + | 633.161i | 0.0454844 | + | 0.760097i | ||||
\(834\) | −320.393 | + | 109.924i | −0.384164 | + | 0.131804i | ||||
\(835\) | 2.75907 | − | 6.66099i | 0.00330428 | − | 0.00797723i | ||||
\(836\) | 317.897 | − | 247.239i | 0.380259 | − | 0.295740i | ||||
\(837\) | −1640.58 | + | 679.551i | −1.96007 | + | 0.811889i | ||||
\(838\) | 1073.43 | + | 66.8443i | 1.28094 | + | 0.0797665i | ||||
\(839\) | −84.6245 | − | 84.6245i | −0.100864 | − | 0.100864i | 0.654874 | − | 0.755738i | \(-0.272722\pi\) |
−0.755738 | + | 0.654874i | \(0.772722\pi\) | |||||||
\(840\) | 184.045 | + | 765.288i | 0.219101 | + | 0.911057i | ||||
\(841\) | 64.3150 | + | 64.3150i | 0.0764745 | + | 0.0764745i | ||||
\(842\) | −476.738 | + | 420.844i | −0.566197 | + | 0.499814i | ||||
\(843\) | −1221.30 | + | 505.880i | −1.44876 | + | 0.600095i | ||||
\(844\) | −1514.22 | + | 416.328i | −1.79410 | + | 0.493280i | ||||
\(845\) | 397.964 | − | 960.769i | 0.470963 | − | 1.13700i | ||||
\(846\) | −2446.08 | − | 1196.38i | −2.89135 | − | 1.41416i | ||||
\(847\) | −543.655 | + | 16.2517i | −0.641859 | + | 0.0191874i | ||||
\(848\) | −1232.23 | + | 178.594i | −1.45310 | + | 0.210606i | ||||
\(849\) | − | 148.674i | − | 0.175117i | ||||||
\(850\) | −210.289 | + | 429.950i | −0.247399 | + | 0.505824i | ||||
\(851\) | −120.356 | − | 49.8531i | −0.141429 | − | 0.0585818i | ||||
\(852\) | 748.493 | − | 1316.16i | 0.878513 | − | 1.54479i | ||||
\(853\) | −1272.11 | + | 526.927i | −1.49134 | + | 0.617733i | −0.971608 | − | 0.236596i | \(-0.923968\pi\) |
−0.519732 | + | 0.854329i | \(0.673968\pi\) | |||||||
\(854\) | −486.315 | − | 518.798i | −0.569455 | − | 0.607492i | ||||
\(855\) | 589.014 | + | 589.014i | 0.688905 | + | 0.688905i | ||||
\(856\) | 1421.89 | + | 268.410i | 1.66109 | + | 0.313563i | ||||
\(857\) | 623.149 | + | 623.149i | 0.727129 | + | 0.727129i | 0.970047 | − | 0.242918i | \(-0.0781046\pi\) |
−0.242918 | + | 0.970047i | \(0.578105\pi\) | |||||||
\(858\) | 1736.95 | + | 108.163i | 2.02442 | + | 0.126064i | ||||
\(859\) | −260.001 | − | 627.697i | −0.302678 | − | 0.730730i | −0.999904 | − | 0.0138783i | \(-0.995582\pi\) |
0.697225 | − | 0.716852i | \(-0.254418\pi\) | |||||||
\(860\) | 76.7984 | − | 614.248i | 0.0893005 | − | 0.714242i | ||||
\(861\) | 86.5120 | + | 32.8416i | 0.100479 | + | 0.0381436i | ||||
\(862\) | −3.32472 | − | 9.69045i | −0.00385698 | − | 0.0112418i | ||||
\(863\) | 231.692 | 0.268473 | 0.134236 | − | 0.990949i | \(-0.457142\pi\) | ||||
0.134236 | + | 0.990949i | \(0.457142\pi\) | |||||||
\(864\) | −1933.51 | + | 992.984i | −2.23786 | + | 1.14929i | ||||
\(865\) | −466.937 | −0.539812 | ||||||||
\(866\) | 1295.53 | − | 444.485i | 1.49599 | − | 0.513263i | ||||
\(867\) | −617.888 | − | 255.938i | −0.712673 | − | 0.295199i | ||||
\(868\) | 69.0703 | − | 728.738i | 0.0795741 | − | 0.839560i | ||||
\(869\) | 636.312 | − | 263.569i | 0.732235 | − | 0.303302i | ||||
\(870\) | −768.385 | − | 47.8487i | −0.883202 | − | 0.0549985i | ||||
\(871\) | −14.7997 | − | 14.7997i | −0.0169916 | − | 0.0169916i | ||||
\(872\) | 10.5425 | − | 7.19433i | 0.0120900 | − | 0.00825038i | ||||
\(873\) | 133.739 | − | 133.739i | 0.153195 | − | 0.153195i | ||||
\(874\) | −123.447 | + | 108.974i | −0.141244 | + | 0.124684i | ||||
\(875\) | −318.607 | − | 708.527i | −0.364122 | − | 0.809746i | ||||
\(876\) | −1064.36 | + | 1871.59i | −1.21502 | + | 2.13652i | ||||
\(877\) | 1256.51 | + | 520.462i | 1.43273 | + | 0.593457i | 0.958024 | − | 0.286686i | \(-0.0925538\pi\) |
0.474708 | + | 0.880143i | \(0.342554\pi\) | |||||||
\(878\) | −25.9437 | + | 53.0436i | −0.0295486 | + | 0.0604142i | ||||
\(879\) | 17.3650i | 0.0197554i | ||||||||
\(880\) | 137.367 | + | 230.923i | 0.156099 | + | 0.262412i | ||||
\(881\) | 438.344 | 0.497552 | 0.248776 | − | 0.968561i | \(-0.419972\pi\) | ||||
0.248776 | + | 0.968561i | \(0.419972\pi\) | |||||||
\(882\) | 804.728 | − | 1929.55i | 0.912390 | − | 2.18770i | ||||
\(883\) | 1424.76 | + | 590.156i | 1.61355 | + | 0.668353i | 0.993248 | − | 0.116012i | \(-0.0370109\pi\) |
0.620300 | + | 0.784365i | \(0.287011\pi\) | |||||||
\(884\) | 329.589 | + | 1198.74i | 0.372839 | + | 1.35604i | ||||
\(885\) | 869.169 | − | 360.022i | 0.982112 | − | 0.406804i | ||||
\(886\) | −306.080 | + | 270.194i | −0.345463 | + | 0.304960i | ||||
\(887\) | 829.089 | − | 829.089i | 0.934711 | − | 0.934711i | −0.0632842 | − | 0.997996i | \(-0.520157\pi\) |
0.997996 | + | 0.0632842i | \(0.0201575\pi\) | |||||||
\(888\) | 583.913 | − | 892.655i | 0.657560 | − | 1.00524i | ||||
\(889\) | −1043.22 | − | 982.663i | −1.17348 | − | 1.10536i | ||||
\(890\) | 21.5321 | − | 345.776i | 0.0241933 | − | 0.388512i | ||||
\(891\) | −1107.06 | + | 458.560i | −1.24249 | + | 0.514657i | ||||
\(892\) | −66.5694 | − | 85.5942i | −0.0746294 | − | 0.0959576i | ||||
\(893\) | 373.682 | − | 902.149i | 0.418457 | − | 1.01025i | ||||
\(894\) | 162.838 | + | 474.619i | 0.182145 | + | 0.530893i | ||||
\(895\) | 485.867i | 0.542868i | ||||||||
\(896\) | 11.4294 | − | 895.927i | 0.0127560 | − | 0.999919i | ||||
\(897\) | −711.579 | −0.793287 | ||||||||
\(898\) | −210.076 | + | 72.0753i | −0.233937 | + | 0.0802621i | ||||
\(899\) | 661.477 | + | 273.993i | 0.735792 | + | 0.304775i | ||||
\(900\) | 1245.26 | − | 968.481i | 1.38362 | − | 1.07609i | ||||
\(901\) | −385.496 | − | 930.671i | −0.427854 | − | 1.03293i | ||||
\(902\) | 31.5275 | + | 1.96327i | 0.0349529 | + | 0.00217658i | ||||
\(903\) | −1602.99 | + | 1701.78i | −1.77518 | + | 1.88458i | ||||
\(904\) | −286.491 | − | 187.403i | −0.316915 | − | 0.207304i | ||||
\(905\) | −227.700 | − | 227.700i | −0.251603 | − | 0.251603i | ||||
\(906\) | −68.7699 | − | 77.9035i | −0.0759049 | − | 0.0859862i | ||||
\(907\) | −140.440 | − | 339.051i | −0.154840 | − | 0.373816i | 0.827356 | − | 0.561678i | \(-0.189844\pi\) |
−0.982195 | + | 0.187862i | \(0.939844\pi\) | |||||||
\(908\) | −825.830 | + | 227.059i | −0.909504 | + | 0.250065i | ||||
\(909\) | 665.267 | − | 1606.10i | 0.731867 | − | 1.76688i | ||||
\(910\) | −781.533 | − | 353.714i | −0.858827 | − | 0.388697i | ||||
\(911\) | − | 189.744i | − | 0.208281i | −0.994563 | − | 0.104141i | \(-0.966791\pi\) | ||
0.994563 | − | 0.104141i | \(-0.0332092\pi\) | |||||||
\(912\) | −689.297 | − | 1158.75i | −0.755808 | − | 1.27056i | ||||
\(913\) | −385.158 | −0.421860 | ||||||||
\(914\) | −367.605 | − | 179.796i | −0.402194 | − | 0.196713i | ||||
\(915\) | 273.202 | − | 659.569i | 0.298582 | − | 0.720840i | ||||
\(916\) | −1372.27 | − | 780.402i | −1.49811 | − | 0.851968i | ||||
\(917\) | −597.414 | − | 1328.55i | −0.651487 | − | 1.44880i | ||||
\(918\) | −1163.79 | − | 1318.35i | −1.26774 | − | 1.43611i | ||||
\(919\) | −929.998 | − | 929.998i | −1.01197 | − | 1.01197i | −0.999928 | − | 0.0120403i | \(-0.996167\pi\) |
−0.0120403 | − | 0.999928i | \(-0.503833\pi\) | |||||||
\(920\) | −61.9261 | − | 90.7460i | −0.0673110 | − | 0.0986370i | ||||
\(921\) | 1070.13 | − | 1070.13i | 1.16192 | − | 1.16192i | ||||
\(922\) | −71.5453 | + | 1148.92i | −0.0775979 | + | 1.24612i | ||||
\(923\) | 631.501 | + | 1524.58i | 0.684183 | + | 1.65176i | ||||
\(924\) | 95.7500 | − | 1010.23i | 0.103626 | − | 1.09332i | ||||
\(925\) | −171.274 | + | 413.491i | −0.185161 | + | 0.447018i | ||||
\(926\) | −491.297 | − | 1431.97i | −0.530559 | − | 1.54640i | ||||
\(927\) | − | 80.7328i | − | 0.0870904i | ||||||
\(928\) | 834.352 | + | 268.147i | 0.899086 | + | 0.288951i | ||||
\(929\) | − | 1718.82i | − | 1.85019i | −0.379741 | − | 0.925093i | \(-0.623987\pi\) | ||
0.379741 | − | 0.925093i | \(-0.376013\pi\) | |||||||
\(930\) | 695.131 | − | 238.494i | 0.747452 | − | 0.256445i | ||||
\(931\) | 708.547 | + | 245.017i | 0.761060 | + | 0.263176i | ||||
\(932\) | 1324.34 | + | 165.580i | 1.42097 | + | 0.177661i | ||||
\(933\) | −2218.22 | + | 918.816i | −2.37751 | + | 0.984797i | ||||
\(934\) | 85.7343 | − | 1376.78i | 0.0917926 | − | 1.47407i | ||||
\(935\) | −153.714 | + | 153.714i | −0.164400 | + | 0.164400i | ||||
\(936\) | 760.093 | − | 4026.56i | 0.812065 | − | 4.30188i | ||||
\(937\) | 668.936 | − | 668.936i | 0.713912 | − | 0.713912i | −0.253439 | − | 0.967351i | \(-0.581562\pi\) |
0.967351 | + | 0.253439i | \(0.0815618\pi\) | |||||||
\(938\) | −8.90376 | + | 8.34627i | −0.00949228 | + | 0.00889794i | ||||
\(939\) | 148.926 | + | 359.538i | 0.158600 | + | 0.382895i | ||||
\(940\) | 566.322 | + | 322.064i | 0.602470 | + | 0.342621i | ||||
\(941\) | 39.9194 | − | 96.3740i | 0.0424223 | − | 0.102417i | −0.901248 | − | 0.433303i | \(-0.857348\pi\) |
0.943670 | + | 0.330887i | \(0.107348\pi\) | |||||||
\(942\) | −30.3773 | − | 14.8576i | −0.0322477 | − | 0.0157724i | ||||
\(943\) | −12.9159 | −0.0136966 | ||||||||
\(944\) | −1059.86 | + | 153.612i | −1.12273 | + | 0.162724i | ||||
\(945\) | 1212.88 | − | 36.2572i | 1.28347 | − | 0.0383674i | ||||
\(946\) | −350.642 | + | 716.911i | −0.370658 | + | 0.757834i | ||||
\(947\) | −1123.92 | − | 465.541i | −1.18682 | − | 0.491596i | −0.300100 | − | 0.953908i | \(-0.597020\pi\) |
−0.886717 | + | 0.462312i | \(0.847020\pi\) | |||||||
\(948\) | −611.295 | − | 2223.32i | −0.644826 | − | 2.34528i | ||||
\(949\) | −897.998 | − | 2167.96i | −0.946258 | − | 2.28447i | ||||
\(950\) | 374.386 | + | 424.110i | 0.394091 | + | 0.446431i | ||||
\(951\) | −820.661 | + | 820.661i | −0.862946 | + | 0.862946i | ||||
\(952\) | 704.812 | − | 169.501i | 0.740349 | − | 0.178047i | ||||
\(953\) | 897.266 | − | 897.266i | 0.941517 | − | 0.941517i | −0.0568645 | − | 0.998382i | \(-0.518110\pi\) |
0.998382 | + | 0.0568645i | \(0.0181103\pi\) | |||||||
\(954\) | −206.357 | + | 3313.81i | −0.216307 | + | 3.47360i | ||||
\(955\) | 161.257 | + | 389.308i | 0.168855 | + | 0.407652i | ||||
\(956\) | 451.884 | + | 581.027i | 0.472682 | + | 0.607769i | ||||
\(957\) | 916.985 | + | 379.828i | 0.958187 | + | 0.396894i | ||||
\(958\) | −247.601 | − | 721.674i | −0.258456 | − | 0.753313i | ||||
\(959\) | −4.82937 | − | 161.553i | −0.00503584 | − | 0.168460i | ||||
\(960\) | 824.188 | − | 360.425i | 0.858530 | − | 0.375442i | ||||
\(961\) | 277.543 | 0.288806 | ||||||||
\(962\) | 377.272 | + | 1099.62i | 0.392174 | + | 1.14306i | ||||
\(963\) | 1476.63 | − | 3564.89i | 1.53336 | − | 3.70186i | ||||
\(964\) | −801.205 | + | 623.124i | −0.831126 | + | 0.646394i | ||||
\(965\) | −256.704 | − | 619.738i | −0.266014 | − | 0.642216i | ||||
\(966\) | −13.4022 | + | 414.695i | −0.0138739 | + | 0.429291i | ||||
\(967\) | −858.178 | + | 858.178i | −0.887464 | + | 0.887464i | −0.994279 | − | 0.106815i | \(-0.965935\pi\) |
0.106815 | + | 0.994279i | \(0.465935\pi\) | |||||||
\(968\) | 127.221 | + | 608.439i | 0.131427 | + | 0.628553i | ||||
\(969\) | 771.324 | − | 771.324i | 0.796000 | − | 0.796000i | ||||
\(970\) | −33.9249 | + | 29.9475i | −0.0349742 | + | 0.0308737i | ||||
\(971\) | −776.670 | + | 321.707i | −0.799867 | + | 0.331316i | −0.744903 | − | 0.667173i | \(-0.767504\pi\) |
−0.0549635 | + | 0.998488i | \(0.517504\pi\) | |||||||
\(972\) | 415.270 | + | 1510.37i | 0.427232 | + | 1.55388i | ||||
\(973\) | −201.245 | − | 76.3964i | −0.206829 | − | 0.0785163i | ||||
\(974\) | −90.4467 | + | 184.924i | −0.0928611 | + | 0.189861i | ||||
\(975\) | 2444.68i | 2.50736i | ||||||||
\(976\) | −486.282 | + | 651.134i | −0.498240 | + | 0.667146i | ||||
\(977\) | 405.987i | 0.415545i | 0.978177 | + | 0.207772i | \(0.0666214\pi\) | ||||
−0.978177 | + | 0.207772i | \(0.933379\pi\) | |||||||
\(978\) | 922.435 | − | 1885.98i | 0.943185 | − | 1.92840i | ||||
\(979\) | −170.924 | + | 412.646i | −0.174590 | + | 0.421498i | ||||
\(980\) | −220.858 | + | 448.801i | −0.225365 | + | 0.457960i | ||||
\(981\) | −13.0247 | − | 31.4443i | −0.0132769 | − | 0.0320533i | ||||
\(982\) | −140.762 | − | 159.457i | −0.143342 | − | 0.162380i | ||||
\(983\) | 371.887 | − | 371.887i | 0.378318 | − | 0.378318i | −0.492177 | − | 0.870495i | \(-0.663799\pi\) |
0.870495 | + | 0.492177i | \(0.163799\pi\) | |||||||
\(984\) | 19.6170 | − | 103.920i | 0.0199359 | − | 0.105610i | ||||
\(985\) | −161.392 | − | 161.392i | −0.163849 | − | 0.163849i | ||||
\(986\) | −44.0675 | + | 707.665i | −0.0446932 | + | 0.717713i | ||||
\(987\) | −1009.09 | − | 2244.03i | −1.02238 | − | 2.27359i | ||||
\(988\) | 1458.10 | + | 182.304i | 1.47581 | + | 0.184518i | ||||
\(989\) | 124.874 | − | 301.474i | 0.126263 | − | 0.304827i | ||||
\(990\) | 677.721 | − | 232.521i | 0.684567 | − | 0.234869i | ||||
\(991\) | −1349.78 | −1.36204 | −0.681020 | − | 0.732265i | \(-0.738463\pi\) | ||||
−0.681020 | + | 0.732265i | \(0.738463\pi\) | |||||||
\(992\) | −833.783 | + | 68.3073i | −0.840507 | + | 0.0688581i | ||||
\(993\) | − | 2066.74i | − | 2.08130i | ||||||
\(994\) | 900.391 | − | 339.313i | 0.905826 | − | 0.341361i | ||||
\(995\) | −162.017 | + | 391.144i | −0.162831 | + | 0.393110i | ||||
\(996\) | −159.975 | + | 1279.51i | −0.160617 | + | 1.28465i | ||||
\(997\) | 574.550 | + | 1387.09i | 0.576279 | + | 1.39126i | 0.896130 | + | 0.443792i | \(0.146367\pi\) |
−0.319851 | + | 0.947468i | \(0.603633\pi\) | |||||||
\(998\) | 263.071 | + | 16.3819i | 0.263599 | + | 0.0164147i | ||||
\(999\) | −1162.77 | − | 1162.77i | −1.16394 | − | 1.16394i |
(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 | 224.3.v.b.13.8 | yes | 240 | |
7.6 | odd | 2 | inner | 224.3.v.b.13.7 | ✓ | 240 | |
32.5 | even | 8 | inner | 224.3.v.b.69.7 | yes | 240 | |
224.69 | odd | 8 | inner | 224.3.v.b.69.8 | yes | 240 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.v.b.13.7 | ✓ | 240 | 7.6 | odd | 2 | inner | |
224.3.v.b.13.8 | yes | 240 | 1.1 | even | 1 | trivial | |
224.3.v.b.69.7 | yes | 240 | 32.5 | even | 8 | inner | |
224.3.v.b.69.8 | yes | 240 | 224.69 | odd | 8 | inner |