Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [288,2,Mod(37,288)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(288, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("288.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 288 = 2^{5} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 288.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: | \(2.29969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 37.1 | ||
Character | \(\chi\) | \(=\) | 288.37 |
Dual form | 288.2.v.c.109.1 |
$q$-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 \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41364 | − | 0.0402136i | −0.999596 | − | 0.0284353i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.99677 | + | 0.113695i | 0.998383 | + | 0.0568477i | ||||
\(5\) | −1.51282 | − | 0.626632i | −0.676556 | − | 0.280239i | 0.0178305 | − | 0.999841i | \(-0.494324\pi\) |
−0.694386 | + | 0.719602i | \(0.744324\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.32530 | − | 1.32530i | −0.500915 | − | 0.500915i | 0.410807 | − | 0.911722i | \(-0.365247\pi\) |
−0.911722 | + | 0.410807i | \(0.865247\pi\) | |||||||
\(8\) | −2.81814 | − | 0.241022i | −0.996363 | − | 0.0852141i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.11339 | + | 0.946670i | 0.668313 | + | 0.299363i | ||||
\(11\) | −0.938971 | + | 2.26688i | −0.283110 | + | 0.683489i | −0.999905 | − | 0.0137954i | \(-0.995609\pi\) |
0.716794 | + | 0.697285i | \(0.245609\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.73458 | + | 1.96113i | −1.31314 | + | 0.543919i | −0.925798 | − | 0.378018i | \(-0.876606\pi\) |
−0.387339 | + | 0.921937i | \(0.626606\pi\) | |||||||
\(14\) | 1.82020 | + | 1.92679i | 0.486469 | + | 0.514956i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.97415 | + | 0.454046i | 0.993537 | + | 0.113512i | ||||
\(17\) | − | 5.78108i | − | 1.40212i | −0.713103 | − | 0.701059i | \(-0.752711\pi\) | ||
0.713103 | − | 0.701059i | \(-0.247289\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.04283 | + | 0.431956i | −0.239243 | + | 0.0990975i | −0.499083 | − | 0.866554i | \(-0.666330\pi\) |
0.259841 | + | 0.965651i | \(0.416330\pi\) | |||||||
\(20\) | −2.94951 | − | 1.42324i | −0.659531 | − | 0.318246i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.41853 | − | 3.16679i | 0.302431 | − | 0.675162i | ||||
\(23\) | −4.29232 | + | 4.29232i | −0.895011 | + | 0.895011i | −0.994990 | − | 0.0999784i | \(-0.968123\pi\) |
0.0999784 | + | 0.994990i | \(0.468123\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.63956 | − | 1.63956i | −0.327913 | − | 0.327913i | ||||
\(26\) | 6.77187 | − | 2.58194i | 1.32807 | − | 0.506360i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.49563 | − | 2.79699i | −0.471629 | − | 0.528581i | ||||
\(29\) | 0.389398 | + | 0.940091i | 0.0723095 | + | 0.174570i | 0.955902 | − | 0.293686i | \(-0.0948822\pi\) |
−0.883592 | + | 0.468257i | \(0.844882\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.43150 | −1.33474 | −0.667369 | − | 0.744727i | \(-0.732580\pi\) | ||||
−0.667369 | + | 0.744727i | \(0.732580\pi\) | |||||||
\(32\) | −5.59976 | − | 0.801673i | −0.989907 | − | 0.141717i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.232478 | + | 8.17238i | −0.0398697 | + | 1.40155i | ||||
\(35\) | 1.17447 | + | 2.83541i | 0.198521 | + | 0.479272i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.67926 | − | 1.52400i | −0.604867 | − | 0.250544i | 0.0591650 | − | 0.998248i | \(-0.481156\pi\) |
−0.664032 | + | 0.747704i | \(0.731156\pi\) | |||||||
\(38\) | 1.49156 | − | 0.568695i | 0.241964 | − | 0.0922545i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.11232 | + | 2.13056i | 0.650215 | + | 0.336871i | ||||
\(41\) | −0.474313 | + | 0.474313i | −0.0740752 | + | 0.0740752i | −0.743174 | − | 0.669098i | \(-0.766680\pi\) |
0.669098 | + | 0.743174i | \(0.266680\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.409042 | + | 0.987514i | −0.0623783 | + | 0.150594i | −0.951995 | − | 0.306113i | \(-0.900971\pi\) |
0.889617 | + | 0.456708i | \(0.150971\pi\) | |||||||
\(44\) | −2.13264 | + | 4.41967i | −0.321507 | + | 0.666290i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.24042 | − | 5.89520i | 0.920099 | − | 0.869199i | ||||
\(47\) | − | 2.73234i | − | 0.398553i | −0.979943 | − | 0.199277i | \(-0.936141\pi\) | ||
0.979943 | − | 0.199277i | \(-0.0638592\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 3.48718i | − | 0.498169i | ||||||
\(50\) | 2.25182 | + | 2.38369i | 0.318456 | + | 0.337104i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −9.67683 | + | 3.37761i | −1.34193 | + | 0.468391i | ||||
\(53\) | 4.55362 | − | 10.9934i | 0.625488 | − | 1.51006i | −0.219686 | − | 0.975571i | \(-0.570503\pi\) |
0.845174 | − | 0.534491i | \(-0.179497\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.84100 | − | 2.84100i | 0.383080 | − | 0.383080i | ||||
\(56\) | 3.41544 | + | 4.05429i | 0.456408 | + | 0.541778i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.512665 | − | 1.34461i | −0.0673163 | − | 0.176556i | ||||
\(59\) | 8.68022 | + | 3.59546i | 1.13007 | + | 0.468089i | 0.867804 | − | 0.496907i | \(-0.165531\pi\) |
0.262264 | + | 0.964996i | \(0.415531\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.48345 | + | 3.58137i | 0.189937 | + | 0.458548i | 0.989947 | − | 0.141438i | \(-0.0451727\pi\) |
−0.800010 | + | 0.599986i | \(0.795173\pi\) | |||||||
\(62\) | 10.5055 | + | 0.298848i | 1.33420 | + | 0.0379537i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.88382 | + | 1.35847i | 0.985477 | + | 0.169808i | ||||
\(65\) | 8.39150 | 1.04084 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.11281 | + | 14.7576i | 0.746799 | + | 1.80293i | 0.575668 | + | 0.817683i | \(0.304742\pi\) |
0.171131 | + | 0.985248i | \(0.445258\pi\) | |||||||
\(68\) | 0.657282 | − | 11.5435i | 0.0797072 | − | 1.39985i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.54625 | − | 4.05549i | −0.184813 | − | 0.484724i | ||||
\(71\) | 10.5767 | + | 10.5767i | 1.25522 | + | 1.25522i | 0.953349 | + | 0.301869i | \(0.0976105\pi\) |
0.301869 | + | 0.953349i | \(0.402389\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.86117 | − | 6.86117i | 0.803040 | − | 0.803040i | −0.180530 | − | 0.983570i | \(-0.557781\pi\) |
0.983570 | + | 0.180530i | \(0.0577812\pi\) | |||||||
\(74\) | 5.13987 | + | 2.30235i | 0.597498 | + | 0.267642i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.13141 | + | 0.743950i | −0.244489 | + | 0.0853369i | ||||
\(77\) | 4.24870 | − | 1.75987i | 0.484184 | − | 0.200556i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 11.4744i | − | 1.29097i | −0.763771 | − | 0.645487i | \(-0.776655\pi\) | ||
0.763771 | − | 0.645487i | \(-0.223345\pi\) | |||||||
\(80\) | −5.72767 | − | 3.17722i | −0.640373 | − | 0.355224i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.689582 | − | 0.651435i | 0.0761516 | − | 0.0719389i | ||||
\(83\) | −15.2335 | + | 6.30991i | −1.67209 | + | 0.692603i | −0.998901 | − | 0.0468660i | \(-0.985077\pi\) |
−0.673191 | + | 0.739469i | \(0.735077\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.62261 | + | 8.74577i | −0.392928 | + | 0.948611i | ||||
\(86\) | 0.617950 | − | 1.37954i | 0.0666353 | − | 0.148760i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.19252 | − | 6.16206i | 0.340324 | − | 0.656878i | ||||
\(89\) | −6.07620 | − | 6.07620i | −0.644076 | − | 0.644076i | 0.307479 | − | 0.951555i | \(-0.400515\pi\) |
−0.951555 | + | 0.307479i | \(0.900515\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.87380 | + | 3.67565i | 0.930227 | + | 0.385313i | ||||
\(92\) | −9.05878 | + | 8.08275i | −0.944443 | + | 0.842685i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.109877 | + | 3.86255i | −0.0113330 | + | 0.398392i | ||||
\(95\) | 1.84830 | 0.189632 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.4135 | 1.56500 | 0.782501 | − | 0.622649i | \(-0.213944\pi\) | ||||
0.782501 | + | 0.622649i | \(0.213944\pi\) | |||||||
\(98\) | −0.140232 | + | 4.92962i | −0.0141656 | + | 0.497967i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.08741 | − | 3.46024i | −0.308741 | − | 0.346024i | ||||
\(101\) | −10.3874 | − | 4.30260i | −1.03358 | − | 0.428124i | −0.199579 | − | 0.979882i | \(-0.563957\pi\) |
−0.834005 | + | 0.551757i | \(0.813957\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.05089 | − | 8.05089i | −0.793278 | − | 0.793278i | 0.188748 | − | 0.982026i | \(-0.439557\pi\) |
−0.982026 | + | 0.188748i | \(0.939557\pi\) | |||||||
\(104\) | 13.8154 | − | 4.38560i | 1.35471 | − | 0.430043i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.87927 | + | 15.3576i | −0.668174 | + | 1.49167i | ||||
\(107\) | 1.76437 | − | 4.25957i | 0.170568 | − | 0.411788i | −0.815361 | − | 0.578953i | \(-0.803461\pi\) |
0.985929 | + | 0.167165i | \(0.0534613\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.20159 | + | 2.15457i | −0.498222 | + | 0.206370i | −0.617621 | − | 0.786476i | \(-0.711903\pi\) |
0.119399 | + | 0.992846i | \(0.461903\pi\) | |||||||
\(110\) | −4.13040 | + | 3.90191i | −0.393818 | + | 0.372032i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.66518 | − | 5.86867i | −0.440818 | − | 0.554537i | ||||
\(113\) | − | 4.12616i | − | 0.388156i | −0.980986 | − | 0.194078i | \(-0.937829\pi\) | ||
0.980986 | − | 0.194078i | \(-0.0621715\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.18324 | − | 3.80382i | 0.856342 | − | 0.354708i | ||||
\(116\) | 0.670653 | + | 1.92141i | 0.0622686 | + | 0.178399i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.1261 | − | 5.43176i | −1.11630 | − | 0.500034i | ||||
\(119\) | −7.66165 | + | 7.66165i | −0.702342 | + | 0.702342i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.52111 | + | 3.52111i | 0.320101 | + | 0.320101i | ||||
\(122\) | −1.95305 | − | 5.12243i | −0.176821 | − | 0.463763i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −14.8390 | − | 0.844928i | −1.33258 | − | 0.0758767i | ||||
\(125\) | 4.58613 | + | 11.0719i | 0.410196 | + | 0.990301i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.68466 | 0.681904 | 0.340952 | − | 0.940081i | \(-0.389251\pi\) | ||||
0.340952 | + | 0.940081i | \(0.389251\pi\) | |||||||
\(128\) | −11.0903 | − | 2.23742i | −0.980250 | − | 0.197762i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −11.8626 | − | 0.337453i | −1.04042 | − | 0.0295966i | ||||
\(131\) | −6.42051 | − | 15.5005i | −0.560963 | − | 1.35428i | −0.908997 | − | 0.416802i | \(-0.863151\pi\) |
0.348034 | − | 0.937482i | \(-0.386849\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.95453 | + | 0.809594i | 0.169480 | + | 0.0702007i | ||||
\(134\) | −8.04787 | − | 21.1078i | −0.695230 | − | 1.82344i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.39337 | + | 16.2919i | −0.119480 | + | 1.39702i | ||||
\(137\) | −16.1360 | + | 16.1360i | −1.37859 | + | 1.37859i | −0.531598 | + | 0.846997i | \(0.678408\pi\) |
−0.846997 | + | 0.531598i | \(0.821592\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.88036 | + | 6.95381i | −0.244309 | + | 0.589814i | −0.997702 | − | 0.0677564i | \(-0.978416\pi\) |
0.753393 | + | 0.657571i | \(0.228416\pi\) | |||||||
\(140\) | 2.02276 | + | 5.79519i | 0.170955 | + | 0.489783i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −14.5263 | − | 15.3769i | −1.21902 | − | 1.29040i | ||||
\(143\) | − | 12.5742i | − | 1.05150i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1.66620i | − | 0.138371i | ||||||
\(146\) | −9.97516 | + | 9.42333i | −0.825550 | + | 0.779880i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.17336 | − | 3.46139i | −0.589646 | − | 0.284524i | ||||
\(149\) | −1.57271 | + | 3.79687i | −0.128842 | + | 0.311051i | −0.975116 | − | 0.221696i | \(-0.928841\pi\) |
0.846274 | + | 0.532748i | \(0.178841\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.12337 | + | 4.12337i | −0.335555 | + | 0.335555i | −0.854692 | − | 0.519136i | \(-0.826254\pi\) |
0.519136 | + | 0.854692i | \(0.326254\pi\) | |||||||
\(152\) | 3.04296 | − | 0.965966i | 0.246817 | − | 0.0783502i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.07691 | + | 2.31697i | −0.489691 | + | 0.186707i | ||||
\(155\) | 11.2426 | + | 4.65682i | 0.903024 | + | 0.374045i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.772760 | + | 1.86561i | 0.0616730 | + | 0.148892i | 0.951712 | − | 0.306993i | \(-0.0993229\pi\) |
−0.890039 | + | 0.455885i | \(0.849323\pi\) | |||||||
\(158\) | −0.461428 | + | 16.2207i | −0.0367093 | + | 1.29045i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 7.96910 | + | 4.72178i | 0.630013 | + | 0.373290i | ||||
\(161\) | 11.3772 | 0.896649 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.46436 | − | 10.7779i | −0.349676 | − | 0.844192i | −0.996658 | − | 0.0816870i | \(-0.973969\pi\) |
0.646982 | − | 0.762505i | \(-0.276031\pi\) | |||||||
\(164\) | −1.00102 | + | 0.893165i | −0.0781665 | + | 0.0697444i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 21.7884 | − | 8.30736i | 1.69111 | − | 0.644777i | ||||
\(167\) | −9.15618 | − | 9.15618i | −0.708527 | − | 0.708527i | 0.257699 | − | 0.966225i | \(-0.417036\pi\) |
−0.966225 | + | 0.257699i | \(0.917036\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.37787 | − | 9.37787i | 0.721374 | − | 0.721374i | ||||
\(170\) | 5.47278 | − | 12.2177i | 0.419743 | − | 0.937055i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.929036 | + | 1.92533i | −0.0708383 | + | 0.146805i | ||||
\(173\) | 7.27037 | − | 3.01148i | 0.552756 | − | 0.228959i | −0.0887811 | − | 0.996051i | \(-0.528297\pi\) |
0.641537 | + | 0.767092i | \(0.278297\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.34581i | 0.328513i | ||||||||
\(176\) | −4.76088 | + | 8.58257i | −0.358865 | + | 0.646935i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.34522 | + | 8.83391i | 0.625501 | + | 0.662130i | ||||
\(179\) | −5.62849 | + | 2.33140i | −0.420693 | + | 0.174257i | −0.582979 | − | 0.812487i | \(-0.698113\pi\) |
0.162286 | + | 0.986744i | \(0.448113\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.09419 | + | 2.64161i | −0.0813306 | + | 0.196349i | −0.959314 | − | 0.282342i | \(-0.908889\pi\) |
0.877983 | + | 0.478691i | \(0.158889\pi\) | |||||||
\(182\) | −12.3966 | − | 5.55290i | −0.918894 | − | 0.411608i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 13.1309 | − | 11.0618i | 0.968023 | − | 0.815488i | ||||
\(185\) | 4.61109 | + | 4.61109i | 0.339014 | + | 0.339014i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.1050 | + | 5.42827i | 0.958333 | + | 0.396955i | ||||
\(188\) | 0.310655 | − | 5.45585i | 0.0226568 | − | 0.397909i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.61284 | − | 0.0743270i | −0.189555 | − | 0.00539225i | ||||
\(191\) | 4.24424 | 0.307102 | 0.153551 | − | 0.988141i | \(-0.450929\pi\) | ||||
0.153551 | + | 0.988141i | \(0.450929\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.04323 | −0.578964 | −0.289482 | − | 0.957183i | \(-0.593483\pi\) | ||||
−0.289482 | + | 0.957183i | \(0.593483\pi\) | |||||||
\(194\) | −21.7891 | − | 0.619832i | −1.56437 | − | 0.0445014i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.396476 | − | 6.96308i | 0.0283197 | − | 0.497363i | ||||
\(197\) | −20.4709 | − | 8.47934i | −1.45849 | − | 0.604128i | −0.494291 | − | 0.869296i | \(-0.664572\pi\) |
−0.964202 | + | 0.265169i | \(0.914572\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.58390 | + | 2.58390i | 0.183168 | + | 0.183168i | 0.792735 | − | 0.609567i | \(-0.208657\pi\) |
−0.609567 | + | 0.792735i | \(0.708657\pi\) | |||||||
\(200\) | 4.22535 | + | 5.01569i | 0.298777 | + | 0.354663i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 14.5110 | + | 6.50004i | 1.02099 | + | 0.457342i | ||||
\(203\) | 0.729831 | − | 1.76197i | 0.0512241 | − | 0.123666i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.01477 | − | 0.420332i | 0.0708748 | − | 0.0293573i | ||||
\(206\) | 11.0573 | + | 11.7048i | 0.770400 | + | 0.815514i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −19.7064 | + | 5.64409i | −1.36639 | + | 0.391348i | ||||
\(209\) | − | 2.76957i | − | 0.191575i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.04546 | + | 0.433043i | −0.0719723 | + | 0.0298119i | −0.418379 | − | 0.908272i | \(-0.637402\pi\) |
0.346407 | + | 0.938084i | \(0.387402\pi\) | |||||||
\(212\) | 10.3424 | − | 21.4335i | 0.710320 | − | 1.47206i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.66548 | + | 5.95055i | −0.182209 | + | 0.406771i | ||||
\(215\) | 1.23762 | − | 1.23762i | 0.0844048 | − | 0.0844048i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.84894 | + | 9.84894i | 0.668590 | + | 0.668590i | ||||
\(218\) | 7.43982 | − | 2.83661i | 0.503889 | − | 0.192120i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.99582 | − | 5.34980i | 0.404238 | − | 0.360683i | ||||
\(221\) | 11.3374 | + | 27.3710i | 0.762639 | + | 1.84117i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.40345 | −0.495772 | −0.247886 | − | 0.968789i | \(-0.579736\pi\) | ||||
−0.247886 | + | 0.968789i | \(0.579736\pi\) | |||||||
\(224\) | 6.35889 | + | 8.48379i | 0.424871 | + | 0.566847i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.165928 | + | 5.83290i | −0.0110373 | + | 0.387999i | ||||
\(227\) | −5.13477 | − | 12.3964i | −0.340806 | − | 0.822780i | −0.997635 | − | 0.0687393i | \(-0.978102\pi\) |
0.656828 | − | 0.754040i | \(-0.271898\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.6519 | − | 4.41217i | −0.703899 | − | 0.291564i | 0.00187845 | − | 0.999998i | \(-0.499402\pi\) |
−0.705777 | + | 0.708434i | \(0.749402\pi\) | |||||||
\(230\) | −13.1348 | + | 5.00795i | −0.866082 | + | 0.330215i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.870797 | − | 2.74316i | −0.0571706 | − | 0.180097i | ||||
\(233\) | −10.6029 | + | 10.6029i | −0.694620 | + | 0.694620i | −0.963245 | − | 0.268625i | \(-0.913431\pi\) |
0.268625 | + | 0.963245i | \(0.413431\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.71217 | + | 4.13355i | −0.111690 | + | 0.269643i | ||||
\(236\) | 16.9236 | + | 8.16620i | 1.10163 | + | 0.531574i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 11.1389 | − | 10.5227i | 0.722029 | − | 0.682087i | ||||
\(239\) | − | 27.7222i | − | 1.79320i | −0.442844 | − | 0.896598i | \(-0.646031\pi\) | ||
0.442844 | − | 0.896598i | \(-0.353969\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 19.1370i | − | 1.23273i | −0.787462 | − | 0.616363i | \(-0.788606\pi\) | ||
0.787462 | − | 0.616363i | \(-0.211394\pi\) | |||||||
\(242\) | −4.83599 | − | 5.11918i | −0.310869 | − | 0.329074i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.55492 | + | 7.31982i | 0.163562 | + | 0.468604i | ||||
\(245\) | −2.18518 | + | 5.27549i | −0.139606 | + | 0.337039i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.09026 | − | 4.09026i | 0.260257 | − | 0.260257i | ||||
\(248\) | 20.9430 | + | 1.79115i | 1.32988 | + | 0.113738i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.03790 | − | 15.8361i | −0.381871 | − | 1.00156i | ||||
\(251\) | 22.9873 | + | 9.52164i | 1.45094 | + | 0.601001i | 0.962424 | − | 0.271552i | \(-0.0875368\pi\) |
0.488520 | + | 0.872553i | \(0.337537\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.69980 | − | 13.7605i | −0.358343 | − | 0.865118i | ||||
\(254\) | −10.8634 | − | 0.309028i | −0.681628 | − | 0.0193902i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.5877 | + | 3.60889i | 0.974230 | + | 0.225556i | ||||
\(257\) | 11.2303 | 0.700525 | 0.350263 | − | 0.936651i | \(-0.386092\pi\) | ||||
0.350263 | + | 0.936651i | \(0.386092\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.85636 | + | 6.89587i | 0.177486 | + | 0.428488i | ||||
\(260\) | 16.7559 | + | 0.954075i | 1.03915 | + | 0.0591692i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.45297 | + | 22.1703i | 0.522227 | + | 1.36969i | ||||
\(263\) | 8.63436 | + | 8.63436i | 0.532417 | + | 0.532417i | 0.921291 | − | 0.388874i | \(-0.127136\pi\) |
−0.388874 | + | 0.921291i | \(0.627136\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.7777 | + | 13.7777i | −0.846355 | + | 0.846355i | ||||
\(266\) | −2.73045 | − | 1.22308i | −0.167415 | − | 0.0749915i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10.5280 | + | 30.1625i | 0.643099 | + | 1.84247i | ||||
\(269\) | −11.4515 | + | 4.74335i | −0.698208 | + | 0.289207i | −0.703415 | − | 0.710779i | \(-0.748342\pi\) |
0.00520737 | + | 0.999986i | \(0.498342\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 4.02905i | − | 0.244747i | −0.992484 | − | 0.122374i | \(-0.960949\pi\) | ||
0.992484 | − | 0.122374i | \(-0.0390506\pi\) | |||||||
\(272\) | 2.62488 | − | 22.9749i | 0.159157 | − | 1.39306i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 23.4595 | − | 22.1617i | 1.41724 | − | 1.33884i | ||||
\(275\) | 5.25619 | − | 2.17719i | 0.316960 | − | 0.131289i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.46812 | + | 10.7870i | −0.268464 | + | 0.648128i | −0.999411 | − | 0.0343049i | \(-0.989078\pi\) |
0.730948 | + | 0.682433i | \(0.239078\pi\) | |||||||
\(278\) | 4.35144 | − | 9.71436i | 0.260982 | − | 0.582629i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.62641 | − | 8.27366i | −0.156958 | − | 0.494446i | ||||
\(281\) | 4.45827 | + | 4.45827i | 0.265958 | + | 0.265958i | 0.827469 | − | 0.561511i | \(-0.189780\pi\) |
−0.561511 | + | 0.827469i | \(0.689780\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.9317 | − | 7.01336i | −1.00649 | − | 0.416901i | −0.182315 | − | 0.983240i | \(-0.558359\pi\) |
−0.824172 | + | 0.566339i | \(0.808359\pi\) | |||||||
\(284\) | 19.9166 | + | 22.3216i | 1.18183 | + | 1.32454i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.505653 | + | 17.7754i | −0.0298999 | + | 1.05108i | ||||
\(287\) | 1.25721 | 0.0742108 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4209 | −0.965937 | ||||||||
\(290\) | −0.0670041 | + | 2.35541i | −0.00393461 | + | 0.138315i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 14.4802 | − | 12.9201i | 0.847392 | − | 0.756090i | ||||
\(293\) | 16.9534 | + | 7.02234i | 0.990429 | + | 0.410249i | 0.818279 | − | 0.574821i | \(-0.194928\pi\) |
0.172150 | + | 0.985071i | \(0.444928\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.8786 | − | 10.8786i | −0.633377 | − | 0.633377i | ||||
\(296\) | 10.0014 | + | 5.18163i | 0.581317 | + | 0.301176i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.37594 | − | 5.30416i | 0.137634 | − | 0.307262i | ||||
\(299\) | 11.9046 | − | 28.7402i | 0.688459 | − | 1.66209i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.85085 | − | 0.766647i | 0.106681 | − | 0.0441888i | ||||
\(302\) | 5.99479 | − | 5.66316i | 0.344961 | − | 0.325878i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.34050 | + | 1.24316i | −0.248945 | + | 0.0713002i | ||||
\(305\) | − | 6.34757i | − | 0.363461i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.8443 | + | 11.1193i | −1.53209 | + | 0.634611i | −0.979968 | − | 0.199155i | \(-0.936180\pi\) |
−0.552118 | + | 0.833766i | \(0.686180\pi\) | |||||||
\(308\) | 8.68374 | − | 3.03099i | 0.494802 | − | 0.172707i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −15.7057 | − | 7.03518i | −0.892023 | − | 0.399572i | ||||
\(311\) | −11.6197 | + | 11.6197i | −0.658895 | + | 0.658895i | −0.955119 | − | 0.296224i | \(-0.904273\pi\) |
0.296224 | + | 0.955119i | \(0.404273\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.9034 | − | 12.9034i | −0.729344 | − | 0.729344i | 0.241145 | − | 0.970489i | \(-0.422477\pi\) |
−0.970489 | + | 0.241145i | \(0.922477\pi\) | |||||||
\(314\) | −1.01738 | − | 2.66838i | −0.0574143 | − | 0.150585i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.30459 | − | 22.9117i | 0.0733889 | − | 1.28889i | ||||
\(317\) | 6.08877 | + | 14.6996i | 0.341979 | + | 0.825612i | 0.997515 | + | 0.0704476i | \(0.0224428\pi\) |
−0.655536 | + | 0.755164i | \(0.727557\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.49670 | −0.139789 | ||||||||
\(320\) | −11.0756 | − | 6.99538i | −0.619143 | − | 0.391053i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −16.0833 | − | 0.457519i | −0.896286 | − | 0.0254965i | ||||
\(323\) | 2.49717 | + | 6.02871i | 0.138946 | + | 0.335446i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.9780 | + | 4.54726i | 0.608953 | + | 0.252236i | ||||
\(326\) | 5.87759 | + | 15.4156i | 0.325530 | + | 0.853794i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.45100 | − | 1.22236i | 0.0801181 | − | 0.0674936i | ||||
\(329\) | −3.62116 | + | 3.62116i | −0.199641 | + | 0.199641i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.88508 | − | 9.37942i | 0.213543 | − | 0.515539i | −0.780419 | − | 0.625256i | \(-0.784994\pi\) |
0.993963 | + | 0.109717i | \(0.0349944\pi\) | |||||||
\(332\) | −31.1351 | + | 10.8674i | −1.70876 | + | 0.596429i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.5754 | + | 13.3118i | 0.688093 | + | 0.728387i | ||||
\(335\) | − | 26.1562i | − | 1.42907i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.4416i | 1.44037i | 0.693784 | + | 0.720183i | \(0.255942\pi\) | ||||
−0.693784 | + | 0.720183i | \(0.744058\pi\) | |||||||
\(338\) | −13.6341 | + | 12.8798i | −0.741595 | + | 0.700570i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8.22787 | + | 17.0514i | −0.446219 | + | 0.924740i | ||||
\(341\) | 6.97797 | − | 16.8463i | 0.377878 | − | 0.912279i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.8986 | + | 13.8986i | −0.750455 | + | 0.750455i | ||||
\(344\) | 1.39075 | − | 2.68436i | 0.0749842 | − | 0.144731i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.3988 | + | 3.96479i | −0.559043 | + | 0.213149i | ||||
\(347\) | −21.7583 | − | 9.01258i | −1.16805 | − | 0.483820i | −0.287500 | − | 0.957781i | \(-0.592824\pi\) |
−0.880546 | + | 0.473960i | \(0.842824\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.65403 | + | 6.40740i | 0.142067 | + | 0.342980i | 0.978858 | − | 0.204543i | \(-0.0655708\pi\) |
−0.836791 | + | 0.547523i | \(0.815571\pi\) | |||||||
\(350\) | 0.174761 | − | 6.14343i | 0.00934137 | − | 0.328380i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.07531 | − | 11.9412i | 0.377115 | − | 0.636469i | ||||
\(353\) | 9.15953 | 0.487512 | 0.243756 | − | 0.969837i | \(-0.421620\pi\) | ||||
0.243756 | + | 0.969837i | \(0.421620\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.37295 | − | 22.6283i | −0.497465 | − | 1.20099i | ||||
\(356\) | −11.4419 | − | 12.8236i | −0.606420 | − | 0.679648i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.05042 | − | 3.06942i | 0.425478 | − | 0.162224i | ||||
\(359\) | 14.5008 | + | 14.5008i | 0.765322 | + | 0.765322i | 0.977279 | − | 0.211957i | \(-0.0679836\pi\) |
−0.211957 | + | 0.977279i | \(0.567984\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.5341 | + | 12.5341i | −0.659690 | + | 0.659690i | ||||
\(362\) | 1.65302 | − | 3.69029i | 0.0868810 | − | 0.193957i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 17.3010 | + | 8.34832i | 0.906819 | + | 0.437571i | ||||
\(365\) | −14.6792 | + | 6.08032i | −0.768344 | + | 0.318258i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.62846i | 0.293803i | 0.989151 | + | 0.146901i | \(0.0469300\pi\) | ||||
−0.989151 | + | 0.146901i | \(0.953070\pi\) | |||||||
\(368\) | −19.0072 | + | 15.1094i | −0.990821 | + | 0.787632i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.33300 | − | 6.70386i | −0.329237 | − | 0.348517i | ||||
\(371\) | −20.6044 | + | 8.53463i | −1.06973 | + | 0.443096i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.8400 | − | 28.5842i | 0.613050 | − | 1.48003i | −0.246584 | − | 0.969122i | \(-0.579308\pi\) |
0.859633 | − | 0.510911i | \(-0.170692\pi\) | |||||||
\(374\) | −18.3075 | − | 8.20063i | −0.946658 | − | 0.424045i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.658554 | + | 7.70012i | −0.0339623 | + | 0.397103i | ||||
\(377\) | −3.68728 | − | 3.68728i | −0.189904 | − | 0.189904i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.8544 | − | 10.2950i | −1.27668 | − | 0.528820i | −0.361694 | − | 0.932297i | \(-0.617802\pi\) |
−0.914990 | + | 0.403477i | \(0.867802\pi\) | |||||||
\(380\) | 3.69063 | + | 0.210143i | 0.189325 | + | 0.0107801i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5.99983 | − | 0.170676i | −0.306978 | − | 0.00873256i | ||||
\(383\) | −3.10697 | −0.158759 | −0.0793795 | − | 0.996844i | \(-0.525294\pi\) | ||||
−0.0793795 | + | 0.996844i | \(0.525294\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.53033 | −0.383781 | ||||||||
\(386\) | 11.3702 | + | 0.323447i | 0.578730 | + | 0.0164630i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 30.7771 | + | 1.75244i | 1.56247 | + | 0.0889667i | ||||
\(389\) | −8.30581 | − | 3.44038i | −0.421121 | − | 0.174434i | 0.162051 | − | 0.986782i | \(-0.448189\pi\) |
−0.583173 | + | 0.812348i | \(0.698189\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.8143 | + | 24.8143i | 1.25491 | + | 1.25491i | ||||
\(392\) | −0.840486 | + | 9.82736i | −0.0424510 | + | 0.496357i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 28.5976 | + | 12.8100i | 1.44072 | + | 0.645356i | ||||
\(395\) | −7.19025 | + | 17.3588i | −0.361781 | + | 0.873416i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.9030 | − | 6.58725i | 0.798150 | − | 0.330605i | 0.0539347 | − | 0.998544i | \(-0.482824\pi\) |
0.744215 | + | 0.667940i | \(0.232824\pi\) | |||||||
\(398\) | −3.54880 | − | 3.75662i | −0.177885 | − | 0.188302i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.77143 | − | 7.26030i | −0.288571 | − | 0.363015i | ||||
\(401\) | 17.8067i | 0.889227i | 0.895723 | + | 0.444613i | \(0.146659\pi\) | ||||
−0.895723 | + | 0.444613i | \(0.853341\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 35.1851 | − | 14.5741i | 1.75269 | − | 0.725990i | ||||
\(404\) | −20.2520 | − | 9.77228i | −1.00757 | − | 0.486189i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.10257 | + | 2.46144i | −0.0547198 | + | 0.122159i | ||||
\(407\) | 6.90945 | − | 6.90945i | 0.342489 | − | 0.342489i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.4187 | − | 15.4187i | −0.762408 | − | 0.762408i | 0.214349 | − | 0.976757i | \(-0.431237\pi\) |
−0.976757 | + | 0.214349i | \(0.931237\pi\) | |||||||
\(410\) | −1.45143 | + | 0.553392i | −0.0716809 | + | 0.0273301i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −15.1604 | − | 16.9911i | −0.746899 | − | 0.837091i | ||||
\(413\) | −6.73880 | − | 16.2689i | −0.331595 | − | 0.800541i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 26.9996 | 1.32536 | ||||||||
\(416\) | 28.0847 | − | 7.18626i | 1.37697 | − | 0.352335i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.111375 | + | 3.91518i | −0.00544751 | + | 0.191498i | ||||
\(419\) | −5.74289 | − | 13.8646i | −0.280559 | − | 0.677328i | 0.719290 | − | 0.694710i | \(-0.244467\pi\) |
−0.999849 | + | 0.0173813i | \(0.994467\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.87628 | + | 1.60561i | 0.188918 | + | 0.0782525i | 0.475137 | − | 0.879912i | \(-0.342398\pi\) |
−0.286219 | + | 0.958164i | \(0.592398\pi\) | |||||||
\(422\) | 1.49532 | − | 0.570126i | 0.0727909 | − | 0.0277533i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −15.4824 | + | 29.8835i | −0.751891 | + | 1.45127i | ||||
\(425\) | −9.47846 | + | 9.47846i | −0.459773 | + | 0.459773i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.78036 | − | 6.71239i | 0.134551 | − | 0.324835i | ||||
\(428\) | 4.00733 | − | 8.30476i | 0.193702 | − | 0.401426i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.79932 | + | 1.69978i | −0.0867707 | + | 0.0819706i | ||||
\(431\) | 16.2867i | 0.784503i | 0.919858 | + | 0.392252i | \(0.128304\pi\) | ||||
−0.919858 | + | 0.392252i | \(0.871696\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.2864i | 1.35936i | 0.733510 | + | 0.679678i | \(0.237881\pi\) | ||||
−0.733510 | + | 0.679678i | \(0.762119\pi\) | |||||||
\(434\) | −13.5268 | − | 14.3189i | −0.649308 | − | 0.687331i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.6313 | + | 3.71077i | −0.509148 | + | 0.177714i | ||||
\(437\) | 2.62209 | − | 6.33028i | 0.125431 | − | 0.302818i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.8438 | − | 13.8438i | 0.660730 | − | 0.660730i | −0.294822 | − | 0.955552i | \(-0.595260\pi\) |
0.955552 | + | 0.294822i | \(0.0952604\pi\) | |||||||
\(440\) | −8.69107 | + | 7.32158i | −0.414330 | + | 0.349043i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −14.9264 | − | 39.1487i | −0.709977 | − | 1.86212i | ||||
\(443\) | 5.95791 | + | 2.46785i | 0.283069 | + | 0.117251i | 0.519701 | − | 0.854348i | \(-0.326043\pi\) |
−0.236632 | + | 0.971599i | \(0.576043\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.38468 | + | 12.9998i | 0.255258 | + | 0.616248i | ||||
\(446\) | 10.4658 | + | 0.297720i | 0.495571 | + | 0.0140974i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8.64802 | − | 12.2488i | −0.408581 | − | 0.578700i | ||||
\(449\) | −27.7832 | −1.31117 | −0.655585 | − | 0.755121i | \(-0.727578\pi\) | ||||
−0.655585 | + | 0.755121i | \(0.727578\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.629843 | − | 1.52058i | −0.0296581 | − | 0.0716011i | ||||
\(452\) | 0.469125 | − | 8.23897i | 0.0220658 | − | 0.387528i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.76022 | + | 17.7306i | 0.317273 | + | 0.832138i | ||||
\(455\) | −11.1212 | − | 11.1212i | −0.521371 | − | 0.521371i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.61796 | − | 6.61796i | 0.309575 | − | 0.309575i | −0.535170 | − | 0.844745i | \(-0.679752\pi\) |
0.844745 | + | 0.535170i | \(0.179752\pi\) | |||||||
\(458\) | 14.8806 | + | 6.66558i | 0.695323 | + | 0.311462i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 18.7693 | − | 6.55125i | 0.875121 | − | 0.305454i | ||||
\(461\) | 25.1777 | − | 10.4289i | 1.17264 | − | 0.485724i | 0.290576 | − | 0.956852i | \(-0.406153\pi\) |
0.882065 | + | 0.471128i | \(0.156153\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 33.3492i | 1.54987i | 0.632040 | + | 0.774935i | \(0.282218\pi\) | ||||
−0.632040 | + | 0.774935i | \(0.717782\pi\) | |||||||
\(464\) | 1.12068 | + | 3.91286i | 0.0520263 | + | 0.181650i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15.4151 | − | 14.5623i | 0.714091 | − | 0.674588i | ||||
\(467\) | 7.09498 | − | 2.93884i | 0.328317 | − | 0.135993i | −0.212436 | − | 0.977175i | \(-0.568140\pi\) |
0.540752 | + | 0.841182i | \(0.318140\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.4569 | − | 27.6595i | 0.529033 | − | 1.27720i | ||||
\(470\) | 2.58663 | − | 5.77451i | 0.119312 | − | 0.266358i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −23.5955 | − | 12.2246i | −1.08607 | − | 0.562685i | ||||
\(473\) | −1.85449 | − | 1.85449i | −0.0852698 | − | 0.0852698i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.41801 | + | 1.00157i | 0.110946 | + | 0.0459553i | ||||
\(476\) | −16.1696 | + | 14.4274i | −0.741133 | + | 0.661280i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.11481 | + | 39.1892i | −0.0509902 | + | 1.79247i | ||||
\(479\) | 1.66547 | 0.0760971 | 0.0380485 | − | 0.999276i | \(-0.487886\pi\) | ||||
0.0380485 | + | 0.999276i | \(0.487886\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.4085 | 0.930549 | ||||||||
\(482\) | −0.769570 | + | 27.0529i | −0.0350530 | + | 1.23223i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.63050 | + | 7.43116i | 0.301386 | + | 0.337780i | ||||
\(485\) | −23.3179 | − | 9.65859i | −1.05881 | − | 0.438574i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.4292 | + | 15.4292i | 0.699165 | + | 0.699165i | 0.964230 | − | 0.265066i | \(-0.0853936\pi\) |
−0.265066 | + | 0.964230i | \(0.585394\pi\) | |||||||
\(488\) | −3.31739 | − | 10.4504i | −0.150171 | − | 0.473065i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.30121 | − | 7.36978i | 0.149133 | − | 0.332933i | ||||
\(491\) | −7.65362 | + | 18.4775i | −0.345403 | + | 0.833877i | 0.651747 | + | 0.758436i | \(0.274036\pi\) |
−0.997150 | + | 0.0754405i | \(0.975964\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.43474 | − | 2.25114i | 0.244769 | − | 0.101386i | ||||
\(494\) | −5.94665 | + | 5.61768i | −0.267553 | + | 0.252751i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −29.5339 | − | 3.37425i | −1.32611 | − | 0.151508i | ||||
\(497\) | − | 28.0344i | − | 1.25751i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.2740 | + | 11.2973i | −1.22095 | + | 0.505735i | −0.897712 | − | 0.440582i | \(-0.854772\pi\) |
−0.323240 | + | 0.946317i | \(0.604772\pi\) | |||||||
\(500\) | 7.89861 | + | 22.6294i | 0.353236 | + | 1.01202i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −32.1129 | − | 14.3846i | −1.43327 | − | 0.642016i | ||||
\(503\) | −22.9821 | + | 22.9821i | −1.02472 | + | 1.02472i | −0.0250340 | + | 0.999687i | \(0.507969\pi\) |
−0.999687 | + | 0.0250340i | \(0.992031\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.0181 | + | 13.0181i | 0.579300 | + | 0.579300i | ||||
\(506\) | 7.50412 | + | 19.6817i | 0.333599 | + | 0.874957i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 15.3445 | + | 0.873711i | 0.680801 | + | 0.0387646i | ||||
\(509\) | −6.17413 | − | 14.9057i | −0.273663 | − | 0.660682i | 0.725971 | − | 0.687725i | \(-0.241391\pi\) |
−0.999634 | + | 0.0270437i | \(0.991391\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.1862 | −0.804509 | ||||||||
\(512\) | −21.8903 | − | 5.72852i | −0.967423 | − | 0.253167i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −15.8756 | − | 0.451610i | −0.700242 | − | 0.0199197i | ||||
\(515\) | 7.13463 | + | 17.2245i | 0.314390 | + | 0.759004i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.19388 | + | 2.56559i | 0.272407 | + | 0.112835i | ||||
\(518\) | −3.76056 | − | 9.86315i | −0.165230 | − | 0.433362i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −23.6484 | − | 2.02253i | −1.03705 | − | 0.0886940i | ||||
\(521\) | 10.2507 | − | 10.2507i | 0.449093 | − | 0.449093i | −0.445960 | − | 0.895053i | \(-0.647138\pi\) |
0.895053 | + | 0.445960i | \(0.147138\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.70945 | − | 18.6123i | 0.337111 | − | 0.813857i | −0.660880 | − | 0.750492i | \(-0.729817\pi\) |
0.997990 | − | 0.0633655i | \(-0.0201834\pi\) | |||||||
\(524\) | −11.0579 | − | 31.6808i | −0.483068 | − | 1.38398i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.8587 | − | 12.5531i | −0.517063 | − | 0.547342i | ||||
\(527\) | 42.9622i | 1.87146i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 13.8481i | − | 0.602090i | ||||||
\(530\) | 20.0307 | − | 18.9226i | 0.870079 | − | 0.821946i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.81070 | + | 1.83879i | 0.165215 | + | 0.0797217i | ||||
\(533\) | 1.31549 | − | 3.17586i | 0.0569800 | − | 0.137562i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.33837 | + | 5.33837i | −0.230798 | + | 0.230798i | ||||
\(536\) | −13.6698 | − | 43.0624i | −0.590447 | − | 1.86001i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 16.3790 | − | 6.24489i | 0.706149 | − | 0.269236i | ||||
\(539\) | 7.90501 | + | 3.27436i | 0.340493 | + | 0.141037i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.8201 | − | 26.1221i | −0.465194 | − | 1.12308i | −0.966237 | − | 0.257655i | \(-0.917050\pi\) |
0.501043 | − | 0.865422i | \(-0.332950\pi\) | |||||||
\(542\) | −0.162023 | + | 5.69563i | −0.00695947 | + | 0.244648i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.63454 | + | 32.3727i | −0.198704 | + | 1.38797i | ||||
\(545\) | 9.21921 | 0.394908 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.17792 | + | 7.67217i | 0.135878 | + | 0.328038i | 0.977143 | − | 0.212585i | \(-0.0681883\pi\) |
−0.841265 | + | 0.540624i | \(0.818188\pi\) | |||||||
\(548\) | −34.0545 | + | 30.3853i | −1.45474 | + | 1.29800i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7.51793 | + | 2.86639i | −0.320565 | + | 0.122223i | ||||
\(551\) | −0.812156 | − | 0.812156i | −0.0345990 | − | 0.0345990i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.2070 | + | 15.2070i | −0.646668 | + | 0.646668i | ||||
\(554\) | 6.75011 | − | 15.0693i | 0.286785 | − | 0.640233i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.54202 | + | 13.5576i | −0.277444 | + | 0.574972i | ||||
\(557\) | 21.1381 | − | 8.75569i | 0.895650 | − | 0.370991i | 0.113104 | − | 0.993583i | \(-0.463921\pi\) |
0.782546 | + | 0.622593i | \(0.213921\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 5.47765i | − | 0.231680i | ||||||
\(560\) | 3.38010 | + | 11.8016i | 0.142835 | + | 0.498709i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.12311 | − | 6.48168i | −0.258288 | − | 0.273413i | ||||
\(563\) | 4.49306 | − | 1.86108i | 0.189360 | − | 0.0784354i | −0.285989 | − | 0.958233i | \(-0.592322\pi\) |
0.475348 | + | 0.879798i | \(0.342322\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.58558 | + | 6.24215i | −0.108776 | + | 0.262609i | ||||
\(566\) | 23.6534 | + | 10.5953i | 0.994226 | + | 0.445352i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −27.2573 | − | 32.3557i | −1.14369 | − | 1.35762i | ||||
\(569\) | −1.97117 | − | 1.97117i | −0.0826359 | − | 0.0826359i | 0.664581 | − | 0.747217i | \(-0.268610\pi\) |
−0.747217 | + | 0.664581i | \(0.768610\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.41522 | − | 1.82884i | −0.184771 | − | 0.0765347i | 0.288380 | − | 0.957516i | \(-0.406883\pi\) |
−0.473151 | + | 0.880981i | \(0.656883\pi\) | |||||||
\(572\) | 1.42962 | − | 25.1077i | 0.0597756 | − | 1.04980i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.77724 | − | 0.0505570i | −0.0741808 | − | 0.00211021i | ||||
\(575\) | 14.0751 | 0.586971 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.08446 | −0.211669 | −0.105834 | − | 0.994384i | \(-0.533751\pi\) | ||||
−0.105834 | + | 0.994384i | \(0.533751\pi\) | |||||||
\(578\) | 23.2133 | + | 0.660345i | 0.965546 | + | 0.0274667i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.189439 | − | 3.32702i | 0.00786605 | − | 0.138147i | ||||
\(581\) | 28.5514 | + | 11.8264i | 1.18451 | + | 0.490640i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.6450 | + | 20.6450i | 0.855029 | + | 0.855029i | ||||
\(584\) | −20.9894 | + | 17.6821i | −0.868549 | + | 0.731689i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −23.6837 | − | 10.6088i | −0.978363 | − | 0.438247i | ||||
\(587\) | −1.78191 | + | 4.30191i | −0.0735473 | + | 0.177559i | −0.956378 | − | 0.292133i | \(-0.905635\pi\) |
0.882830 | + | 0.469692i | \(0.155635\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.74983 | − | 3.21008i | 0.319326 | − | 0.132269i | ||||
\(590\) | 14.9410 | + | 15.8159i | 0.615111 | + | 0.651131i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −13.9300 | − | 7.72716i | −0.572518 | − | 0.317584i | ||||
\(593\) | − | 29.2644i | − | 1.20174i | −0.799345 | − | 0.600872i | \(-0.794820\pi\) | ||
0.799345 | − | 0.600872i | \(-0.205180\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.3918 | − | 6.78969i | 0.671997 | − | 0.278350i | ||||
\(596\) | −3.57203 | + | 7.40264i | −0.146316 | + | 0.303224i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −17.9845 | + | 40.1496i | −0.735442 | + | 1.64184i | ||||
\(599\) | 26.1363 | − | 26.1363i | 1.06790 | − | 1.06790i | 0.0703791 | − | 0.997520i | \(-0.477579\pi\) |
0.997520 | − | 0.0703791i | \(-0.0224209\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.06830 | + | 6.06830i | 0.247531 | + | 0.247531i | 0.819957 | − | 0.572426i | \(-0.193997\pi\) |
−0.572426 | + | 0.819957i | \(0.693997\pi\) | |||||||
\(602\) | −2.64727 | + | 1.00933i | −0.107895 | + | 0.0411374i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.70222 | + | 7.76461i | −0.354088 | + | 0.315937i | ||||
\(605\) | −3.12038 | − | 7.53326i | −0.126861 | − | 0.306271i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.7677 | 0.924111 | 0.462055 | − | 0.886851i | \(-0.347112\pi\) | ||||
0.462055 | + | 0.886851i | \(0.347112\pi\) | |||||||
\(608\) | 6.18591 | − | 1.58284i | 0.250872 | − | 0.0641926i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.255259 | + | 8.97319i | −0.0103351 | + | 0.363314i | ||||
\(611\) | 5.35847 | + | 12.9365i | 0.216781 | + | 0.523355i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.3883 | + | 10.1020i | 0.985034 | + | 0.408015i | 0.816288 | − | 0.577645i | \(-0.196028\pi\) |
0.168746 | + | 0.985660i | \(0.446028\pi\) | |||||||
\(614\) | 38.3954 | − | 14.6392i | 1.54951 | − | 0.590789i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.3976 | + | 3.93553i | −0.499513 | + | 0.158567i | ||||
\(617\) | 28.1146 | − | 28.1146i | 1.13185 | − | 1.13185i | 0.141980 | − | 0.989870i | \(-0.454653\pi\) |
0.989870 | − | 0.141980i | \(-0.0453467\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.80079 | − | 23.6612i | 0.393927 | − | 0.951024i | −0.595149 | − | 0.803616i | \(-0.702907\pi\) |
0.989076 | − | 0.147408i | \(-0.0470931\pi\) | |||||||
\(620\) | 21.9193 | + | 10.5768i | 0.880301 | + | 0.424775i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 16.8934 | − | 15.9589i | 0.677364 | − | 0.639892i | ||||
\(623\) | 16.1055i | 0.645254i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 8.03019i | − | 0.321208i | ||||||
\(626\) | 17.7219 | + | 18.7597i | 0.708310 | + | 0.749788i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.33091 | + | 3.81304i | 0.0531091 | + | 0.152157i | ||||
\(629\) | −8.81038 | + | 21.2701i | −0.351293 | + | 0.848096i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.2246 | − | 29.2246i | 1.16341 | − | 1.16341i | 0.179689 | − | 0.983723i | \(-0.442491\pi\) |
0.983723 | − | 0.179689i | \(-0.0575091\pi\) | |||||||
\(632\) | −2.76559 | + | 32.3365i | −0.110009 | + | 1.28628i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.01622 | − | 21.0248i | −0.318365 | − | 0.835002i | ||||
\(635\) | −11.6255 | − | 4.81546i | −0.461346 | − | 0.191096i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.83881 | + | 16.5104i | 0.270964 | + | 0.654164i | ||||
\(638\) | 3.52945 | + | 0.100402i | 0.139732 | + | 0.00397494i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 15.3756 | + | 10.3343i | 0.607773 | + | 0.408501i | ||||
\(641\) | 23.2229 | 0.917249 | 0.458624 | − | 0.888630i | \(-0.348342\pi\) | ||||
0.458624 | + | 0.888630i | \(0.348342\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.52528 | − | 6.09658i | −0.0995875 | − | 0.240425i | 0.866232 | − | 0.499643i | \(-0.166535\pi\) |
−0.965819 | + | 0.259217i | \(0.916535\pi\) | |||||||
\(644\) | 22.7176 | + | 1.29353i | 0.895199 | + | 0.0509724i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.28767 | − | 8.62286i | −0.129352 | − | 0.339262i | ||||
\(647\) | 2.80148 | + | 2.80148i | 0.110138 | + | 0.110138i | 0.760028 | − | 0.649890i | \(-0.225185\pi\) |
−0.649890 | + | 0.760028i | \(0.725185\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.3009 | + | 16.3009i | −0.639868 | + | 0.639868i | ||||
\(650\) | −15.3362 | − | 6.86966i | −0.601534 | − | 0.269450i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.68888 | − | 22.0286i | −0.301120 | − | 0.862705i | ||||
\(653\) | −13.9194 | + | 5.76560i | −0.544708 | + | 0.225625i | −0.638031 | − | 0.770011i | \(-0.720251\pi\) |
0.0933235 | + | 0.995636i | \(0.470251\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 27.4728i | 1.07345i | ||||||||
\(656\) | −2.10035 | + | 1.66963i | −0.0820049 | + | 0.0651881i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.26465 | − | 4.97341i | 0.205237 | − | 0.193884i | ||||
\(659\) | 3.09009 | − | 1.27996i | 0.120373 | − | 0.0498600i | −0.321684 | − | 0.946847i | \(-0.604249\pi\) |
0.442057 | + | 0.896987i | \(0.354249\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.40456 | − | 10.6336i | 0.171318 | − | 0.413598i | −0.814779 | − | 0.579772i | \(-0.803142\pi\) |
0.986096 | + | 0.166175i | \(0.0531415\pi\) | |||||||
\(662\) | −5.86929 | + | 13.1029i | −0.228117 | + | 0.509259i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 44.4509 | − | 14.1106i | 1.72503 | − | 0.547598i | ||||
\(665\) | −2.44955 | − | 2.44955i | −0.0949894 | − | 0.0949894i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.70660 | − | 2.36375i | −0.220960 | − | 0.0915248i | ||||
\(668\) | −17.2417 | − | 19.3238i | −0.667103 | − | 0.747659i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.05184 | + | 36.9755i | −0.0406360 | + | 1.42849i | ||||
\(671\) | −9.51145 | −0.367186 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32.6492 | −1.25853 | −0.629267 | − | 0.777190i | \(-0.716645\pi\) | ||||
−0.629267 | + | 0.777190i | \(0.716645\pi\) | |||||||
\(674\) | 1.06331 | − | 37.3790i | 0.0409573 | − | 1.43978i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 19.7916 | − | 17.6592i | 0.761216 | − | 0.679199i | ||||
\(677\) | −5.71034 | − | 2.36530i | −0.219466 | − | 0.0909059i | 0.270241 | − | 0.962793i | \(-0.412896\pi\) |
−0.489708 | + | 0.871887i | \(0.662896\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.4274 | − | 20.4274i | −0.783933 | − | 0.783933i | ||||
\(680\) | 12.3170 | − | 23.7737i | 0.472334 | − | 0.911678i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −10.5418 | + | 23.5340i | −0.403666 | + | 0.901165i | ||||
\(683\) | −5.03873 | + | 12.1646i | −0.192802 | + | 0.465465i | −0.990486 | − | 0.137610i | \(-0.956058\pi\) |
0.797685 | + | 0.603075i | \(0.206058\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 34.5224 | − | 14.2996i | 1.31903 | − | 0.546361i | ||||
\(686\) | 20.2066 | − | 19.0888i | 0.771491 | − | 0.728812i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.07397 | + | 3.73880i | −0.0790693 | + | 0.142540i | ||||
\(689\) | 60.9795i | 2.32313i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.3930 | + | 13.8318i | −1.27033 | + | 0.526187i | −0.913064 | − | 0.407816i | \(-0.866291\pi\) |
−0.357265 | + | 0.934003i | \(0.616291\pi\) | |||||||
\(692\) | 14.8596 | − | 5.18662i | 0.564878 | − | 0.197166i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 30.3960 | + | 13.6155i | 1.15382 | + | 0.516839i | ||||
\(695\) | 8.71497 | − | 8.71497i | 0.330577 | − | 0.330577i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.74204 | + | 2.74204i | 0.103862 | + | 0.103862i | ||||
\(698\) | −3.49419 | − | 9.16450i | −0.132257 | − | 0.346881i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.494099 | + | 8.67757i | −0.0186752 | + | 0.327981i | ||||
\(701\) | −10.9582 | − | 26.4553i | −0.413884 | − | 0.999204i | −0.984085 | − | 0.177699i | \(-0.943135\pi\) |
0.570201 | − | 0.821505i | \(-0.306865\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.49516 | 0.169538 | ||||||||
\(704\) | −10.4822 | + | 16.5961i | −0.395061 | + | 0.625488i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.9483 | − | 0.368338i | −0.487315 | − | 0.0138626i | ||||
\(707\) | 8.06415 | + | 19.4686i | 0.303284 | + | 0.732191i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.29870 | + | 3.02322i | 0.274109 | + | 0.113539i | 0.515503 | − | 0.856887i | \(-0.327605\pi\) |
−0.241395 | + | 0.970427i | \(0.577605\pi\) | |||||||
\(710\) | 12.3400 | + | 32.3652i | 0.463113 | + | 1.21465i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15.6591 | + | 18.5881i | 0.586849 | + | 0.696617i | ||||
\(713\) | 31.8984 | − | 31.8984i | 1.19461 | − | 1.19461i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.87938 | + | 19.0225i | −0.294672 | + | 0.711401i | ||||
\(716\) | −11.5038 | + | 4.01532i | −0.429919 | + | 0.150059i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −19.9158 | − | 21.0820i | −0.743251 | − | 0.786775i | ||||
\(719\) | 18.4601i | 0.688447i | 0.938888 | + | 0.344223i | \(0.111858\pi\) | ||||
−0.938888 | + | 0.344223i | \(0.888142\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21.3396i | 0.794729i | ||||||||
\(722\) | 18.2228 | − | 17.2147i | 0.678182 | − | 0.640665i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.48518 | + | 5.15027i | −0.0923611 | + | 0.191408i | ||||
\(725\) | 0.902895 | − | 2.17978i | 0.0335327 | − | 0.0809551i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.9545 | + | 30.9545i | −1.14804 | + | 1.14804i | −0.161099 | + | 0.986938i | \(0.551504\pi\) |
−0.986938 | + | 0.161099i | \(0.948496\pi\) | |||||||
\(728\) | −24.1217 | − | 12.4973i | −0.894009 | − | 0.463180i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 20.9956 | − | 8.00509i | 0.777083 | − | 0.296282i | ||||
\(731\) | 5.70890 | + | 2.36470i | 0.211151 | + | 0.0874618i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.44239 | + | 5.89645i | 0.0902118 | + | 0.217791i | 0.962545 | − | 0.271121i | \(-0.0873942\pi\) |
−0.872334 | + | 0.488911i | \(0.837394\pi\) | |||||||
\(734\) | 0.226341 | − | 7.95662i | 0.00835439 | − | 0.293684i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 27.4770 | − | 20.5949i | 1.01282 | − | 0.759140i | ||||
\(737\) | −39.1935 | −1.44371 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.8479 | − | 43.0886i | −0.656545 | − | 1.58504i | −0.803104 | − | 0.595839i | \(-0.796820\pi\) |
0.146559 | − | 0.989202i | \(-0.453180\pi\) | |||||||
\(740\) | 8.68301 | + | 9.73153i | 0.319194 | + | 0.357738i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 29.4705 | − | 11.2363i | 1.08190 | − | 0.412499i | ||||
\(743\) | −18.7851 | − | 18.7851i | −0.689157 | − | 0.689157i | 0.272889 | − | 0.962046i | \(-0.412021\pi\) |
−0.962046 | + | 0.272889i | \(0.912021\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.75848 | − | 4.75848i | 0.174337 | − | 0.174337i | ||||
\(746\) | −17.8869 | + | 39.9317i | −0.654887 | + | 1.46200i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 25.5505 | + | 12.3290i | 0.934217 | + | 0.450792i | ||||
\(749\) | −7.98350 | + | 3.30688i | −0.291711 | + | 0.120831i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 31.0990i | − | 1.13482i | −0.823436 | − | 0.567409i | \(-0.807946\pi\) | ||
0.823436 | − | 0.567409i | \(-0.192054\pi\) | |||||||
\(752\) | 1.24061 | − | 10.8587i | 0.0452404 | − | 0.395977i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.06421 | + | 5.36077i | 0.184428 | + | 0.195228i | ||||
\(755\) | 8.82178 | − | 3.65410i | 0.321058 | − | 0.132986i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.986433 | − | 2.38146i | 0.0358525 | − | 0.0865556i | −0.904939 | − | 0.425541i | \(-0.860084\pi\) |
0.940792 | + | 0.338986i | \(0.110084\pi\) | |||||||
\(758\) | 34.7212 | + | 15.5530i | 1.26113 | + | 0.564909i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.20877 | − | 0.445481i | −0.188942 | − | 0.0161593i | ||||
\(761\) | −28.0768 | − | 28.0768i | −1.01778 | − | 1.01778i | −0.999839 | − | 0.0179435i | \(-0.994288\pi\) |
−0.0179435 | − | 0.999839i | \(-0.505712\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.74908 | + | 4.03820i | 0.352941 | + | 0.146193i | ||||
\(764\) | 8.47475 | + | 0.482550i | 0.306606 | + | 0.0174581i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.39215 | + | 0.124943i | 0.158695 | + | 0.00451437i | ||||
\(767\) | −48.1484 | −1.73854 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.73480 | 0.0625585 | 0.0312793 | − | 0.999511i | \(-0.490042\pi\) | ||||
0.0312793 | + | 0.999511i | \(0.490042\pi\) | |||||||
\(770\) | 10.6452 | + | 0.302822i | 0.383626 | + | 0.0109129i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −16.0604 | − | 0.914478i | −0.578028 | − | 0.0329128i | ||||
\(773\) | 31.1210 | + | 12.8907i | 1.11934 | + | 0.463647i | 0.864146 | − | 0.503242i | \(-0.167860\pi\) |
0.255197 | + | 0.966889i | \(0.417860\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.1844 | + | 12.1844i | 0.437678 | + | 0.437678i | ||||
\(776\) | −43.4373 | − | 3.71498i | −1.55931 | − | 0.133360i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11.6031 | + | 5.19747i | 0.415991 | + | 0.186338i | ||||
\(779\) | 0.289747 | − | 0.699512i | 0.0103813 | − | 0.0250626i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −33.9072 | + | 14.0448i | −1.21329 | + | 0.502563i | ||||
\(782\) | −34.0806 | − | 36.0764i | −1.21872 | − | 1.29009i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.58334 | − | 13.8586i | 0.0565479 | − | 0.494949i | ||||
\(785\) | − | 3.30658i | − | 0.118017i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 45.0368 | − | 18.6548i | 1.60539 | − | 0.664974i | 0.613223 | − | 0.789910i | \(-0.289873\pi\) |
0.992165 | + | 0.124936i | \(0.0398726\pi\) | |||||||
\(788\) | −39.9116 | − | 19.2587i | −1.42179 | − | 0.686063i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 10.8625 | − | 24.2500i | 0.386470 | − | 0.862775i | ||||
\(791\) | −5.46838 | + | 5.46838i | −0.194433 | + | 0.194433i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.0471 | − | 14.0471i | −0.498826 | − | 0.498826i | ||||
\(794\) | −22.7461 | + | 8.67249i | −0.807228 | + | 0.307775i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.86566 | + | 5.45322i | 0.172459 | + | 0.193284i | ||||
\(797\) | −12.8982 | − | 31.1390i | −0.456877 | − | 1.10300i | −0.969655 | − | 0.244478i | \(-0.921384\pi\) |
0.512778 | − | 0.858521i | \(-0.328616\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.7959 | −0.558819 | ||||||||
\(800\) | 7.86677 | + | 10.4956i | 0.278132 | + | 0.371074i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.716074 | − | 25.1724i | 0.0252855 | − | 0.888867i | ||||
\(803\) | 9.11099 | + | 21.9959i | 0.321520 | + | 0.776218i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.2117 | − | 7.12932i | −0.606633 | − | 0.251276i | ||||
\(806\) | −50.3252 | + | 19.1877i | −1.77263 | + | 0.675857i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 28.2361 | + | 14.6289i | 0.993342 | + | 0.514643i | ||||
\(809\) | −1.33912 | + | 1.33912i | −0.0470811 | + | 0.0470811i | −0.730255 | − | 0.683174i | \(-0.760599\pi\) |
0.683174 | + | 0.730255i | \(0.260599\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.8815 | + | 47.9981i | −0.698132 | + | 1.68544i | 0.0295838 | + | 0.999562i | \(0.490582\pi\) |
−0.727716 | + | 0.685878i | \(0.759418\pi\) | |||||||
\(812\) | 1.65763 | − | 3.43526i | 0.0581713 | − | 0.120554i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −10.0453 | + | 9.48963i | −0.352089 | + | 0.332611i | ||||
\(815\) | 19.1026i | 0.669136i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1.20650i | − | 0.0422101i | ||||||
\(818\) | 21.1765 | + | 22.4166i | 0.740420 | + | 0.783779i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.07405 | − | 0.723930i | 0.0724290 | − | 0.0252807i | ||||
\(821\) | 0.106271 | − | 0.256562i | 0.00370889 | − | 0.00895406i | −0.922014 | − | 0.387156i | \(-0.873457\pi\) |
0.925723 | + | 0.378202i | \(0.123457\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.33537 | − | 1.33537i | 0.0465479 | − | 0.0465479i | −0.683450 | − | 0.729998i | \(-0.739521\pi\) |
0.729998 | + | 0.683450i | \(0.239521\pi\) | |||||||
\(824\) | 20.7481 | + | 24.6290i | 0.722794 | + | 0.857991i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.87202 | + | 23.2694i | 0.308697 | + | 0.809646i | ||||
\(827\) | −23.3468 | − | 9.67056i | −0.811848 | − | 0.336278i | −0.0621568 | − | 0.998066i | \(-0.519798\pi\) |
−0.749691 | + | 0.661788i | \(0.769798\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.2848 | − | 24.8297i | −0.357205 | − | 0.862370i | −0.995691 | − | 0.0927359i | \(-0.970439\pi\) |
0.638486 | − | 0.769634i | \(-0.279561\pi\) | |||||||
\(830\) | −38.1677 | − | 1.08575i | −1.32482 | − | 0.0376870i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −39.9907 | + | 9.02941i | −1.38643 | + | 0.313039i | ||||
\(833\) | −20.1597 | −0.698492 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.11414 | + | 19.5893i | 0.280801 | + | 0.677914i | ||||
\(836\) | 0.314887 | − | 5.53018i | 0.0108906 | − | 0.191265i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7.56084 | + | 19.8305i | 0.261185 | + | 0.685032i | ||||
\(839\) | 7.12216 | + | 7.12216i | 0.245884 | + | 0.245884i | 0.819279 | − | 0.573395i | \(-0.194374\pi\) |
−0.573395 | + | 0.819279i | \(0.694374\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.7740 | − | 19.7740i | 0.681861 | − | 0.681861i | ||||
\(842\) | −5.41510 | − | 2.42563i | −0.186617 | − | 0.0835928i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.13677 | + | 0.745821i | −0.0735506 | + | 0.0256722i | ||||
\(845\) | −20.0635 | + | 8.31059i | −0.690207 | + | 0.285893i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 9.33302i | − | 0.320687i | ||||||
\(848\) | 23.0883 | − | 41.6219i | 0.792855 | − | 1.42930i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 13.7803 | − | 13.0180i | 0.472661 | − | 0.446513i | ||||
\(851\) | 22.3341 | − | 9.25108i | 0.765603 | − | 0.317123i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.6705 | + | 25.7608i | −0.365349 | + | 0.882032i | 0.629149 | + | 0.777284i | \(0.283403\pi\) |
−0.994499 | + | 0.104747i | \(0.966597\pi\) | |||||||
\(854\) | −4.20037 | + | 9.37711i | −0.143734 | + | 0.320878i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.99889 | + | 11.5788i | −0.205038 | + | 0.395755i | ||||
\(857\) | 20.0048 | + | 20.0048i | 0.683349 | + | 0.683349i | 0.960753 | − | 0.277404i | \(-0.0894741\pi\) |
−0.277404 | + | 0.960753i | \(0.589474\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.53664 | − | 0.636496i | −0.0524294 | − | 0.0217170i | 0.356315 | − | 0.934366i | \(-0.384033\pi\) |
−0.408744 | + | 0.912649i | \(0.634033\pi\) | |||||||
\(860\) | 2.61194 | − | 2.33052i | 0.0890665 | − | 0.0794701i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.654948 | − | 23.0236i | 0.0223076 | − | 0.784186i | ||||
\(863\) | 3.22858 | 0.109902 | 0.0549510 | − | 0.998489i | \(-0.482500\pi\) | ||||
0.0549510 | + | 0.998489i | \(0.482500\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.8859 | −0.438133 | ||||||||
\(866\) | 1.13750 | − | 39.9868i | 0.0386538 | − | 1.35881i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 18.5463 | + | 20.7858i | 0.629501 | + | 0.705516i | ||||
\(869\) | 26.0111 | + | 10.7742i | 0.882366 | + | 0.365488i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −57.8832 | − | 57.8832i | −1.96130 | − | 1.96130i | ||||
\(872\) | 15.1781 | − | 4.81818i | 0.513995 | − | 0.163164i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.96125 | + | 8.84330i | −0.133991 | + | 0.299129i | ||||
\(875\) | 8.59556 | − | 20.7515i | 0.290583 | − | 0.701530i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.7751 | + | 9.84797i | −0.802828 | + | 0.332542i | −0.746089 | − | 0.665847i | \(-0.768070\pi\) |
−0.0567395 | + | 0.998389i | \(0.518070\pi\) | |||||||
\(878\) | −20.1269 | + | 19.0135i | −0.679251 | + | 0.641675i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 12.5805 | − | 10.0006i | 0.424088 | − | 0.337120i | ||||
\(881\) | 2.67200i | 0.0900220i | 0.998986 | + | 0.0450110i | \(0.0143323\pi\) | ||||
−0.998986 | + | 0.0450110i | \(0.985668\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.5907 | + | 16.3990i | −1.33233 | + | 0.551870i | −0.931320 | − | 0.364202i | \(-0.881342\pi\) |
−0.401013 | + | 0.916072i | \(0.631342\pi\) | |||||||
\(884\) | 19.5263 | + | 55.9425i | 0.656740 | + | 1.88155i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.32311 | − | 3.72824i | −0.279620 | − | 0.125253i | ||||
\(887\) | 33.5579 | − | 33.5579i | 1.12676 | − | 1.12676i | 0.136063 | − | 0.990700i | \(-0.456555\pi\) |
0.990700 | − | 0.136063i | \(-0.0434450\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.1845 | − | 10.1845i | −0.341576 | − | 0.341576i | ||||
\(890\) | −7.08924 | − | 18.5935i | −0.237632 | − | 0.623257i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −14.7830 | − | 0.841738i | −0.494970 | − | 0.0281835i | ||||
\(893\) | 1.18025 | + | 2.84938i | 0.0394956 | + | 0.0953508i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.97584 | 0.333456 | ||||||||
\(896\) | 11.7326 | + | 17.6631i | 0.391960 | + | 0.590084i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 39.2755 | + | 1.11726i | 1.31064 | + | 0.0372836i | ||||
\(899\) | −2.89382 | − | 6.98629i | −0.0965142 | − | 0.233006i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −63.5538 | − | 26.3249i | −2.11729 | − | 0.877008i | ||||
\(902\) | 0.829224 | + | 2.17488i | 0.0276102 | + | 0.0724155i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.994493 | + | 11.6281i | −0.0330763 | + | 0.386744i | ||||
\(905\) | 3.31064 | − | 3.31064i | 0.110049 | − | 0.110049i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.58909 | + | 15.9075i | −0.218787 | + | 0.528199i | −0.994721 | − | 0.102615i | \(-0.967279\pi\) |
0.775934 | + | 0.630814i | \(0.217279\pi\) | |||||||
\(908\) | −8.84351 | − | 25.3366i | −0.293482 | − | 0.840823i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 15.2742 | + | 16.1686i | 0.506335 | + | 0.535986i | ||||
\(911\) | − | 16.6033i | − | 0.550091i | −0.961431 | − | 0.275045i | \(-0.911307\pi\) | ||
0.961431 | − | 0.275045i | \(-0.0886929\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 40.4573i | − | 1.33894i | ||||||
\(914\) | −9.62155 | + | 9.08929i | −0.318253 | + | 0.300647i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −20.7677 | − | 10.0211i | −0.686186 | − | 0.331108i | ||||
\(917\) | −12.0337 | + | 29.0518i | −0.397386 | + | 0.959376i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29.2819 | + | 29.2819i | −0.965922 | + | 0.965922i | −0.999438 | − | 0.0335164i | \(-0.989329\pi\) |
0.0335164 | + | 0.999438i | \(0.489329\pi\) | |||||||
\(920\) | −26.7965 | + | 8.50634i | −0.883453 | + | 0.280446i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −36.0116 | + | 13.7303i | −1.18598 | + | 0.452183i | ||||
\(923\) | −70.8183 | − | 29.3339i | −2.33101 | − | 0.965537i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.53369 | + | 8.53108i | 0.116187 | + | 0.280500i | ||||
\(926\) | 1.34109 | − | 47.1439i | 0.0440711 | − | 1.54924i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.42689 | − | 5.57645i | −0.0468400 | − | 0.183056i | ||||
\(929\) | −48.4425 | −1.58935 | −0.794674 | − | 0.607036i | \(-0.792358\pi\) | ||||
−0.794674 | + | 0.607036i | \(0.792358\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.50631 | + | 3.63655i | 0.0493673 | + | 0.119183i | ||||
\(932\) | −22.3770 | + | 19.9660i | −0.732984 | + | 0.654009i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −10.1479 | + | 3.86915i | −0.332051 | + | 0.126602i | ||||
\(935\) | −16.4240 | − | 16.4240i | −0.537124 | − | 0.537124i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.17378 | − | 6.17378i | 0.201689 | − | 0.201689i | −0.599035 | − | 0.800723i | \(-0.704449\pi\) |
0.800723 | + | 0.599035i | \(0.204449\pi\) | |||||||
\(938\) | −17.3083 | + | 38.6399i | −0.565136 | + | 1.26164i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.88878 | + | 8.05907i | −0.126838 | + | 0.262858i | ||||
\(941\) | −28.8812 | + | 11.9630i | −0.941500 | + | 0.389982i | −0.800030 | − | 0.599960i | \(-0.795183\pi\) |
−0.141470 | + | 0.989942i | \(0.545183\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 4.07181i | − | 0.132596i | ||||||
\(944\) | 32.8639 | + | 18.2301i | 1.06963 | + | 0.593340i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.54702 | + | 2.69617i | 0.0828106 | + | 0.0876599i | ||||
\(947\) | 31.3266 | − | 12.9759i | 1.01798 | − | 0.421660i | 0.189618 | − | 0.981858i | \(-0.439275\pi\) |
0.828359 | + | 0.560198i | \(0.189275\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.0292 | + | 45.9405i | −0.617713 | + | 1.49129i | ||||
\(950\) | −3.37793 | − | 1.51310i | −0.109594 | − | 0.0490916i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 23.4382 | − | 19.7450i | 0.759637 | − | 0.639938i | ||||
\(953\) | 28.8836 | + | 28.8836i | 0.935631 | + | 0.935631i | 0.998050 | − | 0.0624188i | \(-0.0198814\pi\) |
−0.0624188 | + | 0.998050i | \(0.519881\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.42079 | − | 2.65958i | −0.207772 | − | 0.0860619i | ||||
\(956\) | 3.15188 | − | 55.3546i | 0.101939 | − | 1.79030i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.35437 | − | 0.0669745i | −0.0760663 | − | 0.00216385i | ||||
\(959\) | 42.7701 | 1.38112 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.2273 | 0.781525 | ||||||||
\(962\) | −28.8504 | − | 0.820702i | −0.930173 | − | 0.0264605i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.17579 | − | 38.2122i | 0.0700776 | − | 1.23073i | ||||
\(965\) | 12.1680 | + | 5.04015i | 0.391702 | + | 0.162248i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.5627 | + | 17.5627i | 0.564777 | + | 0.564777i | 0.930661 | − | 0.365884i | \(-0.119233\pi\) |
−0.365884 | + | 0.930661i | \(0.619233\pi\) | |||||||
\(968\) | −9.07431 | − | 10.7716i | −0.291659 | − | 0.346214i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 32.5747 | + | 14.5915i | 1.04591 | + | 0.468504i | ||||
\(971\) | −0.119416 | + | 0.288295i | −0.00383224 | + | 0.00925184i | −0.925784 | − | 0.378053i | \(-0.876594\pi\) |
0.921952 | + | 0.387305i | \(0.126594\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.0332 | − | 5.39852i | 0.417825 | − | 0.173069i | ||||
\(974\) | −21.1909 | − | 22.4319i | −0.679001 | − | 0.718763i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.26935 | + | 14.9065i | 0.136659 | + | 0.477144i | ||||
\(977\) | 46.5011i | 1.48770i | 0.668345 | + | 0.743851i | \(0.267003\pi\) | ||||
−0.668345 | + | 0.743851i | \(0.732997\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 19.4794 | − | 8.06862i | 0.622563 | − | 0.257874i | ||||
\(980\) | −4.96309 | + | 10.2855i | −0.158540 | + | 0.328558i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 11.5625 | − | 25.8127i | 0.368975 | − | 0.823718i | ||||
\(983\) | −12.1301 | + | 12.1301i | −0.386891 | + | 0.386891i | −0.873577 | − | 0.486686i | \(-0.838205\pi\) |
0.486686 | + | 0.873577i | \(0.338205\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.6555 | + | 25.6555i | 0.817452 | + | 0.817452i | ||||
\(986\) | −7.77331 | + | 2.96376i | −0.247553 | + | 0.0943854i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.63234 | − | 7.70225i | 0.274631 | − | 0.245041i | ||||
\(989\) | −2.48299 | − | 5.99447i | −0.0789545 | − | 0.190613i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.0269571 | −0.000856319 | −0.000428160 | − | 1.00000i | \(-0.500136\pi\) | ||||
−0.000428160 | 1.00000i | \(0.500136\pi\) | ||||||||
\(992\) | 41.6146 | + | 5.95764i | 1.32127 | + | 0.189155i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.12737 | + | 39.6306i | −0.0357579 | + | 1.25701i | ||||
\(995\) | −2.28983 | − | 5.52814i | −0.0725925 | − | 0.175254i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.81063 | + | 3.64948i | 0.279036 | + | 0.115580i | 0.517813 | − | 0.855494i | \(-0.326746\pi\) |
−0.238777 | + | 0.971074i | \(0.576746\pi\) | |||||||
\(998\) | 39.0100 | − | 14.8735i | 1.23484 | − | 0.470812i | ||||
\(999\) | 0 | 0 |
(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 | 288.2.v.c.37.1 | ✓ | 32 | |
3.2 | odd | 2 | inner | 288.2.v.c.37.8 | yes | 32 | |
4.3 | odd | 2 | 1152.2.v.d.1009.3 | 32 | |||
12.11 | even | 2 | 1152.2.v.d.1009.6 | 32 | |||
32.13 | even | 8 | inner | 288.2.v.c.109.1 | yes | 32 | |
32.19 | odd | 8 | 1152.2.v.d.145.3 | 32 | |||
96.77 | odd | 8 | inner | 288.2.v.c.109.8 | yes | 32 | |
96.83 | even | 8 | 1152.2.v.d.145.6 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.2.v.c.37.1 | ✓ | 32 | 1.1 | even | 1 | trivial | |
288.2.v.c.37.8 | yes | 32 | 3.2 | odd | 2 | inner | |
288.2.v.c.109.1 | yes | 32 | 32.13 | even | 8 | inner | |
288.2.v.c.109.8 | yes | 32 | 96.77 | odd | 8 | inner | |
1152.2.v.d.145.3 | 32 | 32.19 | odd | 8 | |||
1152.2.v.d.145.6 | 32 | 96.83 | even | 8 | |||
1152.2.v.d.1009.3 | 32 | 4.3 | odd | 2 | |||
1152.2.v.d.1009.6 | 32 | 12.11 | even | 2 |