Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,3,Mod(71,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.71");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.e (of order \(2\), degree \(1\), 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: | \(5.72208555157\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 34 x^{14} - 80 x^{13} + 97 x^{12} - 80 x^{11} + 498 x^{10} - 3288 x^{9} + \cdots + 43046721 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 71.9 | ||
Root | \(2.97371 - 0.396304i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.71 |
Dual form | 210.3.e.a.71.1 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421i | 0.707107i | ||||||||
\(3\) | −2.97371 | + | 0.396304i | −0.991236 | + | 0.132101i | ||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | − | 2.23607i | − | 0.447214i | ||||||
\(6\) | −0.560459 | − | 4.20546i | −0.0934098 | − | 0.700910i | ||||
\(7\) | −2.64575 | −0.377964 | ||||||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | 8.68589 | − | 2.35699i | 0.965098 | − | 0.261888i | ||||
\(10\) | 3.16228 | 0.316228 | ||||||||
\(11\) | − | 2.01787i | − | 0.183443i | −0.995785 | − | 0.0917215i | \(-0.970763\pi\) | ||
0.995785 | − | 0.0917215i | \(-0.0292369\pi\) | |||||||
\(12\) | 5.94742 | − | 0.792609i | 0.495618 | − | 0.0660507i | ||||
\(13\) | 11.6017 | 0.892435 | 0.446218 | − | 0.894925i | \(-0.352771\pi\) | ||||
0.446218 | + | 0.894925i | \(0.352771\pi\) | |||||||
\(14\) | − | 3.74166i | − | 0.267261i | ||||||
\(15\) | 0.886164 | + | 6.64941i | 0.0590776 | + | 0.443294i | ||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − | 17.3916i | − | 1.02303i | −0.859273 | − | 0.511517i | \(-0.829084\pi\) | ||
0.859273 | − | 0.511517i | \(-0.170916\pi\) | |||||||
\(18\) | 3.33328 | + | 12.2837i | 0.185182 | + | 0.682428i | ||||
\(19\) | 36.1315 | 1.90166 | 0.950829 | − | 0.309718i | \(-0.100234\pi\) | ||||
0.950829 | + | 0.309718i | \(0.100234\pi\) | |||||||
\(20\) | 4.47214i | 0.223607i | ||||||||
\(21\) | 7.86769 | − | 1.04852i | 0.374652 | − | 0.0499297i | ||||
\(22\) | 2.85370 | 0.129714 | ||||||||
\(23\) | 32.2831i | 1.40361i | 0.712368 | + | 0.701806i | \(0.247623\pi\) | ||||
−0.712368 | + | 0.701806i | \(0.752377\pi\) | |||||||
\(24\) | 1.12092 | + | 8.41092i | 0.0467049 | + | 0.350455i | ||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 16.4072i | 0.631047i | ||||||||
\(27\) | −24.8952 | + | 10.4512i | −0.922045 | + | 0.387083i | ||||
\(28\) | 5.29150 | 0.188982 | ||||||||
\(29\) | − | 46.1442i | − | 1.59118i | −0.605837 | − | 0.795589i | \(-0.707161\pi\) | ||
0.605837 | − | 0.795589i | \(-0.292839\pi\) | |||||||
\(30\) | −9.40369 | + | 1.25322i | −0.313456 | + | 0.0417742i | ||||
\(31\) | 34.0124 | 1.09717 | 0.548586 | − | 0.836094i | \(-0.315166\pi\) | ||||
0.548586 | + | 0.836094i | \(0.315166\pi\) | |||||||
\(32\) | 5.65685i | 0.176777i | ||||||||
\(33\) | 0.799692 | + | 6.00057i | 0.0242331 | + | 0.181835i | ||||
\(34\) | 24.5954 | 0.723394 | ||||||||
\(35\) | 5.91608i | 0.169031i | ||||||||
\(36\) | −17.3718 | + | 4.71398i | −0.482549 | + | 0.130944i | ||||
\(37\) | 31.4813 | 0.850845 | 0.425423 | − | 0.904995i | \(-0.360125\pi\) | ||||
0.425423 | + | 0.904995i | \(0.360125\pi\) | |||||||
\(38\) | 51.0976i | 1.34467i | ||||||||
\(39\) | −34.4999 | + | 4.59779i | −0.884614 | + | 0.117892i | ||||
\(40\) | −6.32456 | −0.158114 | ||||||||
\(41\) | − | 32.1651i | − | 0.784514i | −0.919856 | − | 0.392257i | \(-0.871694\pi\) | ||
0.919856 | − | 0.392257i | \(-0.128306\pi\) | |||||||
\(42\) | 1.48284 | + | 11.1266i | 0.0353056 | + | 0.264919i | ||||
\(43\) | −51.7542 | −1.20359 | −0.601793 | − | 0.798652i | \(-0.705547\pi\) | ||||
−0.601793 | + | 0.798652i | \(0.705547\pi\) | |||||||
\(44\) | 4.03575i | 0.0917215i | ||||||||
\(45\) | −5.27038 | − | 19.4222i | −0.117120 | − | 0.431605i | ||||
\(46\) | −45.6552 | −0.992503 | ||||||||
\(47\) | − | 92.3399i | − | 1.96468i | −0.187110 | − | 0.982339i | \(-0.559912\pi\) | ||
0.187110 | − | 0.982339i | \(-0.440088\pi\) | |||||||
\(48\) | −11.8948 | + | 1.58522i | −0.247809 | + | 0.0330254i | ||||
\(49\) | 7.00000 | 0.142857 | ||||||||
\(50\) | − | 7.07107i | − | 0.141421i | ||||||
\(51\) | 6.89236 | + | 51.7175i | 0.135144 | + | 1.01407i | ||||
\(52\) | −23.2033 | −0.446218 | ||||||||
\(53\) | 18.3315i | 0.345877i | 0.984933 | + | 0.172939i | \(0.0553262\pi\) | ||||
−0.984933 | + | 0.172939i | \(0.944674\pi\) | |||||||
\(54\) | −14.7803 | − | 35.2071i | −0.273709 | − | 0.651984i | ||||
\(55\) | −4.51210 | −0.0820382 | ||||||||
\(56\) | 7.48331i | 0.133631i | ||||||||
\(57\) | −107.445 | + | 14.3191i | −1.88499 | + | 0.251212i | ||||
\(58\) | 65.2577 | 1.12513 | ||||||||
\(59\) | − | 45.4634i | − | 0.770566i | −0.922798 | − | 0.385283i | \(-0.874104\pi\) | ||
0.922798 | − | 0.385283i | \(-0.125896\pi\) | |||||||
\(60\) | −1.77233 | − | 13.2988i | −0.0295388 | − | 0.221647i | ||||
\(61\) | 28.1445 | 0.461385 | 0.230693 | − | 0.973027i | \(-0.425901\pi\) | ||||
0.230693 | + | 0.973027i | \(0.425901\pi\) | |||||||
\(62\) | 48.1007i | 0.775818i | ||||||||
\(63\) | −22.9807 | + | 6.23600i | −0.364773 | + | 0.0989842i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | − | 25.9421i | − | 0.399109i | ||||||
\(66\) | −8.48608 | + | 1.13094i | −0.128577 | + | 0.0171354i | ||||
\(67\) | −33.7430 | −0.503626 | −0.251813 | − | 0.967776i | \(-0.581027\pi\) | ||||
−0.251813 | + | 0.967776i | \(0.581027\pi\) | |||||||
\(68\) | 34.7832i | 0.511517i | ||||||||
\(69\) | −12.7939 | − | 96.0005i | −0.185419 | − | 1.39131i | ||||
\(70\) | −8.36660 | −0.119523 | ||||||||
\(71\) | 25.2759i | 0.355999i | 0.984031 | + | 0.177999i | \(0.0569625\pi\) | ||||
−0.984031 | + | 0.177999i | \(0.943038\pi\) | |||||||
\(72\) | −6.66657 | − | 24.5674i | −0.0925912 | − | 0.341214i | ||||
\(73\) | 48.5331 | 0.664837 | 0.332418 | − | 0.943132i | \(-0.392135\pi\) | ||||
0.332418 | + | 0.943132i | \(0.392135\pi\) | |||||||
\(74\) | 44.5212i | 0.601638i | ||||||||
\(75\) | 14.8685 | − | 1.98152i | 0.198247 | − | 0.0264203i | ||||
\(76\) | −72.2630 | −0.950829 | ||||||||
\(77\) | 5.33879i | 0.0693349i | ||||||||
\(78\) | −6.50225 | − | 48.7903i | −0.0833622 | − | 0.625517i | ||||
\(79\) | 32.9331 | 0.416875 | 0.208437 | − | 0.978036i | \(-0.433162\pi\) | ||||
0.208437 | + | 0.978036i | \(0.433162\pi\) | |||||||
\(80\) | − | 8.94427i | − | 0.111803i | ||||||
\(81\) | 69.8892 | − | 40.9450i | 0.862830 | − | 0.505494i | ||||
\(82\) | 45.4883 | 0.554735 | ||||||||
\(83\) | 82.4176i | 0.992983i | 0.868041 | + | 0.496492i | \(0.165379\pi\) | ||||
−0.868041 | + | 0.496492i | \(0.834621\pi\) | |||||||
\(84\) | −15.7354 | + | 2.09705i | −0.187326 | + | 0.0249648i | ||||
\(85\) | −38.8888 | −0.457515 | ||||||||
\(86\) | − | 73.1915i | − | 0.851064i | ||||||
\(87\) | 18.2871 | + | 137.219i | 0.210197 | + | 1.57723i | ||||
\(88\) | −5.70741 | −0.0648569 | ||||||||
\(89\) | − | 48.8676i | − | 0.549075i | −0.961576 | − | 0.274537i | \(-0.911475\pi\) | ||
0.961576 | − | 0.274537i | \(-0.0885247\pi\) | |||||||
\(90\) | 27.4672 | − | 7.45345i | 0.305191 | − | 0.0828161i | ||||
\(91\) | −30.6951 | −0.337309 | ||||||||
\(92\) | − | 64.5661i | − | 0.701806i | ||||||
\(93\) | −101.143 | + | 13.4792i | −1.08756 | + | 0.144938i | ||||
\(94\) | 130.588 | 1.38924 | ||||||||
\(95\) | − | 80.7925i | − | 0.850447i | ||||||
\(96\) | −2.24184 | − | 16.8218i | −0.0233525 | − | 0.175227i | ||||
\(97\) | −14.5167 | −0.149657 | −0.0748283 | − | 0.997196i | \(-0.523841\pi\) | ||||
−0.0748283 | + | 0.997196i | \(0.523841\pi\) | |||||||
\(98\) | 9.89949i | 0.101015i | ||||||||
\(99\) | −4.75610 | − | 17.5270i | −0.0480414 | − | 0.177041i | ||||
\(100\) | 10.0000 | 0.100000 | ||||||||
\(101\) | 68.8829i | 0.682009i | 0.940062 | + | 0.341004i | \(0.110767\pi\) | ||||
−0.940062 | + | 0.341004i | \(0.889233\pi\) | |||||||
\(102\) | −73.1396 | + | 9.74727i | −0.717055 | + | 0.0955615i | ||||
\(103\) | −43.5237 | −0.422560 | −0.211280 | − | 0.977426i | \(-0.567763\pi\) | ||||
−0.211280 | + | 0.977426i | \(0.567763\pi\) | |||||||
\(104\) | − | 32.8144i | − | 0.315523i | ||||||
\(105\) | −2.34457 | − | 17.5927i | −0.0223292 | − | 0.167549i | ||||
\(106\) | −25.9247 | −0.244572 | ||||||||
\(107\) | 207.704i | 1.94116i | 0.240781 | + | 0.970579i | \(0.422596\pi\) | ||||
−0.240781 | + | 0.970579i | \(0.577404\pi\) | |||||||
\(108\) | 49.7904 | − | 20.9025i | 0.461022 | − | 0.193542i | ||||
\(109\) | −151.884 | −1.39343 | −0.696715 | − | 0.717348i | \(-0.745356\pi\) | ||||
−0.696715 | + | 0.717348i | \(0.745356\pi\) | |||||||
\(110\) | − | 6.38107i | − | 0.0580098i | ||||||
\(111\) | −93.6161 | + | 12.4762i | −0.843389 | + | 0.112398i | ||||
\(112\) | −10.5830 | −0.0944911 | ||||||||
\(113\) | − | 38.2266i | − | 0.338289i | −0.985591 | − | 0.169144i | \(-0.945900\pi\) | ||
0.985591 | − | 0.169144i | \(-0.0541004\pi\) | |||||||
\(114\) | −20.2502 | − | 151.949i | −0.177633 | − | 1.33289i | ||||
\(115\) | 72.1871 | 0.627714 | ||||||||
\(116\) | 92.2883i | 0.795589i | ||||||||
\(117\) | 100.771 | − | 27.3450i | 0.861288 | − | 0.233718i | ||||
\(118\) | 64.2949 | 0.544872 | ||||||||
\(119\) | 46.0138i | 0.386671i | ||||||||
\(120\) | 18.8074 | − | 2.50645i | 0.156728 | − | 0.0208871i | ||||
\(121\) | 116.928 | 0.966349 | ||||||||
\(122\) | 39.8023i | 0.326248i | ||||||||
\(123\) | 12.7472 | + | 95.6495i | 0.103635 | + | 0.777638i | ||||
\(124\) | −68.0247 | −0.548586 | ||||||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | −8.81904 | − | 32.4996i | −0.0699924 | − | 0.257933i | ||||
\(127\) | 101.520 | 0.799371 | 0.399685 | − | 0.916652i | \(-0.369119\pi\) | ||||
0.399685 | + | 0.916652i | \(0.369119\pi\) | |||||||
\(128\) | − | 11.3137i | − | 0.0883883i | ||||||
\(129\) | 153.902 | − | 20.5104i | 1.19304 | − | 0.158996i | ||||
\(130\) | 36.6877 | 0.282213 | ||||||||
\(131\) | 224.148i | 1.71105i | 0.517758 | + | 0.855527i | \(0.326767\pi\) | ||||
−0.517758 | + | 0.855527i | \(0.673233\pi\) | |||||||
\(132\) | −1.59938 | − | 12.0011i | −0.0121165 | − | 0.0909177i | ||||
\(133\) | −95.5949 | −0.718759 | ||||||||
\(134\) | − | 47.7198i | − | 0.356118i | ||||||
\(135\) | 23.3697 | + | 55.6674i | 0.173109 | + | 0.412351i | ||||
\(136\) | −49.1908 | −0.361697 | ||||||||
\(137\) | − | 122.440i | − | 0.893726i | −0.894602 | − | 0.446863i | \(-0.852541\pi\) | ||
0.894602 | − | 0.446863i | \(-0.147459\pi\) | |||||||
\(138\) | 135.765 | − | 18.0933i | 0.983805 | − | 0.131111i | ||||
\(139\) | 132.544 | 0.953551 | 0.476776 | − | 0.879025i | \(-0.341805\pi\) | ||||
0.476776 | + | 0.879025i | \(0.341805\pi\) | |||||||
\(140\) | − | 11.8322i | − | 0.0845154i | ||||||
\(141\) | 36.5947 | + | 274.592i | 0.259537 | + | 1.94746i | ||||
\(142\) | −35.7455 | −0.251729 | ||||||||
\(143\) | − | 23.4107i | − | 0.163711i | ||||||
\(144\) | 34.7435 | − | 9.42795i | 0.241275 | − | 0.0654719i | ||||
\(145\) | −103.181 | −0.711597 | ||||||||
\(146\) | 68.6361i | 0.470111i | ||||||||
\(147\) | −20.8160 | + | 2.77413i | −0.141605 | + | 0.0188716i | ||||
\(148\) | −62.9626 | −0.425423 | ||||||||
\(149\) | 11.7097i | 0.0785885i | 0.999228 | + | 0.0392943i | \(0.0125110\pi\) | ||||
−0.999228 | + | 0.0392943i | \(0.987489\pi\) | |||||||
\(150\) | 2.80230 | + | 21.0273i | 0.0186820 | + | 0.140182i | ||||
\(151\) | −73.1995 | −0.484765 | −0.242382 | − | 0.970181i | \(-0.577929\pi\) | ||||
−0.242382 | + | 0.970181i | \(0.577929\pi\) | |||||||
\(152\) | − | 102.195i | − | 0.672337i | ||||||
\(153\) | −40.9917 | − | 151.061i | −0.267920 | − | 0.987329i | ||||
\(154\) | −7.55019 | −0.0490272 | ||||||||
\(155\) | − | 76.0539i | − | 0.490671i | ||||||
\(156\) | 68.9999 | − | 9.19557i | 0.442307 | − | 0.0589460i | ||||
\(157\) | 290.488 | 1.85024 | 0.925120 | − | 0.379675i | \(-0.123964\pi\) | ||||
0.925120 | + | 0.379675i | \(0.123964\pi\) | |||||||
\(158\) | 46.5745i | 0.294775i | ||||||||
\(159\) | −7.26485 | − | 54.5125i | −0.0456909 | − | 0.342846i | ||||
\(160\) | 12.6491 | 0.0790569 | ||||||||
\(161\) | − | 85.4130i | − | 0.530515i | ||||||
\(162\) | 57.9050 | + | 98.8383i | 0.357439 | + | 0.610113i | ||||
\(163\) | 22.7666 | 0.139672 | 0.0698361 | − | 0.997558i | \(-0.477752\pi\) | ||||
0.0698361 | + | 0.997558i | \(0.477752\pi\) | |||||||
\(164\) | 64.3301i | 0.392257i | ||||||||
\(165\) | 13.4177 | − | 1.78817i | 0.0813192 | − | 0.0108374i | ||||
\(166\) | −116.556 | −0.702145 | ||||||||
\(167\) | − | 235.762i | − | 1.41175i | −0.708338 | − | 0.705874i | \(-0.750555\pi\) | ||
0.708338 | − | 0.705874i | \(-0.249445\pi\) | |||||||
\(168\) | −2.96567 | − | 22.2532i | −0.0176528 | − | 0.132460i | ||||
\(169\) | −34.4016 | −0.203560 | ||||||||
\(170\) | − | 54.9970i | − | 0.323512i | ||||||
\(171\) | 313.834 | − | 85.1615i | 1.83529 | − | 0.498020i | ||||
\(172\) | 103.508 | 0.601793 | ||||||||
\(173\) | 136.011i | 0.786189i | 0.919498 | + | 0.393095i | \(0.128596\pi\) | ||||
−0.919498 | + | 0.393095i | \(0.871404\pi\) | |||||||
\(174\) | −194.057 | + | 25.8619i | −1.11527 | + | 0.148632i | ||||
\(175\) | 13.2288 | 0.0755929 | ||||||||
\(176\) | − | 8.07149i | − | 0.0458607i | ||||||
\(177\) | 18.0173 | + | 135.195i | 0.101793 | + | 0.763813i | ||||
\(178\) | 69.1093 | 0.388254 | ||||||||
\(179\) | 12.3778i | 0.0691495i | 0.999402 | + | 0.0345748i | \(0.0110077\pi\) | ||||
−0.999402 | + | 0.0345748i | \(0.988992\pi\) | |||||||
\(180\) | 10.5408 | + | 38.8445i | 0.0585598 | + | 0.215803i | ||||
\(181\) | −55.8191 | −0.308393 | −0.154196 | − | 0.988040i | \(-0.549279\pi\) | ||||
−0.154196 | + | 0.988040i | \(0.549279\pi\) | |||||||
\(182\) | − | 43.4094i | − | 0.238513i | ||||||
\(183\) | −83.6935 | + | 11.1538i | −0.457342 | + | 0.0609496i | ||||
\(184\) | 91.3103 | 0.496252 | ||||||||
\(185\) | − | 70.3943i | − | 0.380510i | ||||||
\(186\) | −19.0625 | − | 143.038i | −0.102487 | − | 0.769019i | ||||
\(187\) | −35.0940 | −0.187668 | ||||||||
\(188\) | 184.680i | 0.982339i | ||||||||
\(189\) | 65.8665 | − | 27.6514i | 0.348500 | − | 0.146304i | ||||
\(190\) | 114.258 | 0.601357 | ||||||||
\(191\) | − | 198.559i | − | 1.03958i | −0.854295 | − | 0.519788i | \(-0.826011\pi\) | ||
0.854295 | − | 0.519788i | \(-0.173989\pi\) | |||||||
\(192\) | 23.7897 | − | 3.17044i | 0.123905 | − | 0.0165127i | ||||
\(193\) | 44.6577 | 0.231387 | 0.115694 | − | 0.993285i | \(-0.463091\pi\) | ||||
0.115694 | + | 0.993285i | \(0.463091\pi\) | |||||||
\(194\) | − | 20.5297i | − | 0.105823i | ||||||
\(195\) | 10.2810 | + | 77.1442i | 0.0527229 | + | 0.395611i | ||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | 0.952715i | 0.00483612i | 0.999997 | + | 0.00241806i | \(0.000769693\pi\) | ||||
−0.999997 | + | 0.00241806i | \(0.999230\pi\) | |||||||
\(198\) | 24.7869 | − | 6.72614i | 0.125187 | − | 0.0339704i | ||||
\(199\) | −131.143 | −0.659011 | −0.329505 | − | 0.944154i | \(-0.606882\pi\) | ||||
−0.329505 | + | 0.944154i | \(0.606882\pi\) | |||||||
\(200\) | 14.1421i | 0.0707107i | ||||||||
\(201\) | 100.342 | − | 13.3725i | 0.499213 | − | 0.0665298i | ||||
\(202\) | −97.4151 | −0.482253 | ||||||||
\(203\) | 122.086i | 0.601409i | ||||||||
\(204\) | −13.7847 | − | 103.435i | −0.0675722 | − | 0.507034i | ||||
\(205\) | −71.9233 | −0.350845 | ||||||||
\(206\) | − | 61.5518i | − | 0.298795i | ||||||
\(207\) | 76.0908 | + | 280.407i | 0.367588 | + | 1.35462i | ||||
\(208\) | 46.4066 | 0.223109 | ||||||||
\(209\) | − | 72.9087i | − | 0.348846i | ||||||
\(210\) | 24.8798 | − | 3.31572i | 0.118475 | − | 0.0157891i | ||||
\(211\) | −101.671 | −0.481855 | −0.240928 | − | 0.970543i | \(-0.577452\pi\) | ||||
−0.240928 | + | 0.970543i | \(0.577452\pi\) | |||||||
\(212\) | − | 36.6630i | − | 0.172939i | ||||||
\(213\) | −10.0170 | − | 75.1632i | −0.0470279 | − | 0.352879i | ||||
\(214\) | −293.738 | −1.37261 | ||||||||
\(215\) | 115.726i | 0.538260i | ||||||||
\(216\) | 29.5606 | + | 70.4143i | 0.136855 | + | 0.325992i | ||||
\(217\) | −89.9882 | −0.414692 | ||||||||
\(218\) | − | 214.796i | − | 0.985304i | ||||||
\(219\) | −144.323 | + | 19.2339i | −0.659010 | + | 0.0878259i | ||||
\(220\) | 9.02420 | 0.0410191 | ||||||||
\(221\) | − | 201.771i | − | 0.912992i | ||||||
\(222\) | −17.6440 | − | 132.393i | −0.0794773 | − | 0.596366i | ||||
\(223\) | −368.065 | −1.65051 | −0.825257 | − | 0.564757i | \(-0.808970\pi\) | ||||
−0.825257 | + | 0.564757i | \(0.808970\pi\) | |||||||
\(224\) | − | 14.9666i | − | 0.0668153i | ||||||
\(225\) | −43.4294 | + | 11.7849i | −0.193020 | + | 0.0523775i | ||||
\(226\) | 54.0606 | 0.239206 | ||||||||
\(227\) | − | 311.633i | − | 1.37283i | −0.727210 | − | 0.686415i | \(-0.759183\pi\) | ||
0.727210 | − | 0.686415i | \(-0.240817\pi\) | |||||||
\(228\) | 214.889 | − | 28.6381i | 0.942496 | − | 0.125606i | ||||
\(229\) | −121.083 | −0.528748 | −0.264374 | − | 0.964420i | \(-0.585165\pi\) | ||||
−0.264374 | + | 0.964420i | \(0.585165\pi\) | |||||||
\(230\) | 102.088i | 0.443861i | ||||||||
\(231\) | −2.11579 | − | 15.8760i | −0.00915925 | − | 0.0687273i | ||||
\(232\) | −130.515 | −0.562566 | ||||||||
\(233\) | 188.437i | 0.808744i | 0.914595 | + | 0.404372i | \(0.132510\pi\) | ||||
−0.914595 | + | 0.404372i | \(0.867490\pi\) | |||||||
\(234\) | 38.6716 | + | 142.511i | 0.165263 | + | 0.609022i | ||||
\(235\) | −206.478 | −0.878631 | ||||||||
\(236\) | 90.9268i | 0.385283i | ||||||||
\(237\) | −97.9335 | + | 13.0515i | −0.413221 | + | 0.0550698i | ||||
\(238\) | −65.0733 | −0.273417 | ||||||||
\(239\) | 242.788i | 1.01585i | 0.861402 | + | 0.507924i | \(0.169587\pi\) | ||||
−0.861402 | + | 0.507924i | \(0.830413\pi\) | |||||||
\(240\) | 3.54465 | + | 26.5977i | 0.0147694 | + | 0.110824i | ||||
\(241\) | −217.929 | −0.904272 | −0.452136 | − | 0.891949i | \(-0.649338\pi\) | ||||
−0.452136 | + | 0.891949i | \(0.649338\pi\) | |||||||
\(242\) | 165.361i | 0.683312i | ||||||||
\(243\) | −191.603 | + | 149.456i | −0.788492 | + | 0.615045i | ||||
\(244\) | −56.2890 | −0.230693 | ||||||||
\(245\) | − | 15.6525i | − | 0.0638877i | ||||||
\(246\) | −135.269 | + | 18.0272i | −0.549873 | + | 0.0732813i | ||||
\(247\) | 419.185 | 1.69711 | ||||||||
\(248\) | − | 96.2015i | − | 0.387909i | ||||||
\(249\) | −32.6625 | − | 245.086i | −0.131175 | − | 0.984281i | ||||
\(250\) | −15.8114 | −0.0632456 | ||||||||
\(251\) | − | 44.7224i | − | 0.178177i | −0.996024 | − | 0.0890885i | \(-0.971605\pi\) | ||
0.996024 | − | 0.0890885i | \(-0.0283954\pi\) | |||||||
\(252\) | 45.9614 | − | 12.4720i | 0.182386 | − | 0.0494921i | ||||
\(253\) | 65.1431 | 0.257483 | ||||||||
\(254\) | 143.571i | 0.565241i | ||||||||
\(255\) | 115.644 | − | 15.4118i | 0.453505 | − | 0.0604384i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − | 163.933i | − | 0.637872i | −0.947776 | − | 0.318936i | \(-0.896675\pi\) | ||
0.947776 | − | 0.318936i | \(-0.103325\pi\) | |||||||
\(258\) | 29.0061 | + | 217.650i | 0.112427 | + | 0.843606i | ||||
\(259\) | −83.2916 | −0.321589 | ||||||||
\(260\) | 51.8842i | 0.199555i | ||||||||
\(261\) | −108.761 | − | 400.803i | −0.416710 | − | 1.53564i | ||||
\(262\) | −316.993 | −1.20990 | ||||||||
\(263\) | − | 516.880i | − | 1.96532i | −0.185404 | − | 0.982662i | \(-0.559359\pi\) | ||
0.185404 | − | 0.982662i | \(-0.440641\pi\) | |||||||
\(264\) | 16.9722 | − | 2.26187i | 0.0642885 | − | 0.00856769i | ||||
\(265\) | 40.9905 | 0.154681 | ||||||||
\(266\) | − | 135.192i | − | 0.508239i | ||||||
\(267\) | 19.3665 | + | 145.318i | 0.0725336 | + | 0.544263i | ||||
\(268\) | 67.4859 | 0.251813 | ||||||||
\(269\) | 425.762i | 1.58276i | 0.611325 | + | 0.791380i | \(0.290637\pi\) | ||||
−0.611325 | + | 0.791380i | \(0.709363\pi\) | |||||||
\(270\) | −78.7256 | + | 33.0498i | −0.291576 | + | 0.122406i | ||||
\(271\) | −38.4253 | −0.141791 | −0.0708953 | − | 0.997484i | \(-0.522586\pi\) | ||||
−0.0708953 | + | 0.997484i | \(0.522586\pi\) | |||||||
\(272\) | − | 69.5663i | − | 0.255759i | ||||||
\(273\) | 91.2783 | − | 12.1646i | 0.334353 | − | 0.0445590i | ||||
\(274\) | 173.157 | 0.631960 | ||||||||
\(275\) | 10.0894i | 0.0366886i | ||||||||
\(276\) | 25.5878 | + | 192.001i | 0.0927096 | + | 0.695655i | ||||
\(277\) | −365.774 | −1.32048 | −0.660242 | − | 0.751053i | \(-0.729546\pi\) | ||||
−0.660242 | + | 0.751053i | \(0.729546\pi\) | |||||||
\(278\) | 187.445i | 0.674263i | ||||||||
\(279\) | 295.427 | − | 80.1667i | 1.05888 | − | 0.287336i | ||||
\(280\) | 16.7332 | 0.0597614 | ||||||||
\(281\) | 402.773i | 1.43336i | 0.697404 | + | 0.716678i | \(0.254338\pi\) | ||||
−0.697404 | + | 0.716678i | \(0.745662\pi\) | |||||||
\(282\) | −388.331 | + | 51.7527i | −1.37706 | + | 0.183520i | ||||
\(283\) | −390.233 | −1.37892 | −0.689458 | − | 0.724326i | \(-0.742151\pi\) | ||||
−0.689458 | + | 0.724326i | \(0.742151\pi\) | |||||||
\(284\) | − | 50.5518i | − | 0.177999i | ||||||
\(285\) | 32.0184 | + | 240.253i | 0.112345 | + | 0.842994i | ||||
\(286\) | 33.1077 | 0.115761 | ||||||||
\(287\) | 85.1008i | 0.296518i | ||||||||
\(288\) | 13.3331 | + | 49.1348i | 0.0462956 | + | 0.170607i | ||||
\(289\) | −13.4671 | −0.0465989 | ||||||||
\(290\) | − | 145.921i | − | 0.503175i | ||||||
\(291\) | 43.1684 | − | 5.75302i | 0.148345 | − | 0.0197698i | ||||
\(292\) | −97.0662 | −0.332418 | ||||||||
\(293\) | − | 22.6093i | − | 0.0771650i | −0.999255 | − | 0.0385825i | \(-0.987716\pi\) | ||
0.999255 | − | 0.0385825i | \(-0.0122842\pi\) | |||||||
\(294\) | −3.92321 | − | 29.4382i | −0.0133443 | − | 0.100130i | ||||
\(295\) | −101.659 | −0.344608 | ||||||||
\(296\) | − | 89.0425i | − | 0.300819i | ||||||
\(297\) | 21.0893 | + | 50.2354i | 0.0710077 | + | 0.169143i | ||||
\(298\) | −16.5600 | −0.0555705 | ||||||||
\(299\) | 374.537i | 1.25263i | ||||||||
\(300\) | −29.7371 | + | 3.96304i | −0.0991236 | + | 0.0132101i | ||||
\(301\) | 136.929 | 0.454913 | ||||||||
\(302\) | − | 103.520i | − | 0.342780i | ||||||
\(303\) | −27.2986 | − | 204.838i | −0.0900944 | − | 0.676032i | ||||
\(304\) | 144.526 | 0.475414 | ||||||||
\(305\) | − | 62.9330i | − | 0.206338i | ||||||
\(306\) | 213.633 | − | 57.9711i | 0.698147 | − | 0.189448i | ||||
\(307\) | 332.914 | 1.08441 | 0.542206 | − | 0.840246i | \(-0.317589\pi\) | ||||
0.542206 | + | 0.840246i | \(0.317589\pi\) | |||||||
\(308\) | − | 10.6776i | − | 0.0346675i | ||||||
\(309\) | 129.427 | − | 17.2486i | 0.418857 | − | 0.0558208i | ||||
\(310\) | 107.556 | 0.346956 | ||||||||
\(311\) | − | 145.028i | − | 0.466328i | −0.972437 | − | 0.233164i | \(-0.925092\pi\) | ||
0.972437 | − | 0.233164i | \(-0.0749080\pi\) | |||||||
\(312\) | 13.0045 | + | 97.5806i | 0.0416811 | + | 0.312758i | ||||
\(313\) | 345.934 | 1.10522 | 0.552611 | − | 0.833440i | \(-0.313632\pi\) | ||||
0.552611 | + | 0.833440i | \(0.313632\pi\) | |||||||
\(314\) | 410.812i | 1.30832i | ||||||||
\(315\) | 13.9441 | + | 51.3864i | 0.0442671 | + | 0.163131i | ||||
\(316\) | −65.8662 | −0.208437 | ||||||||
\(317\) | − | 155.393i | − | 0.490199i | −0.969498 | − | 0.245099i | \(-0.921179\pi\) | ||
0.969498 | − | 0.245099i | \(-0.0788206\pi\) | |||||||
\(318\) | 77.0924 | − | 10.2741i | 0.242429 | − | 0.0323083i | ||||
\(319\) | −93.1131 | −0.291890 | ||||||||
\(320\) | 17.8885i | 0.0559017i | ||||||||
\(321\) | −82.3140 | − | 617.651i | −0.256430 | − | 1.92415i | ||||
\(322\) | 120.792 | 0.375131 | ||||||||
\(323\) | − | 628.384i | − | 1.94546i | ||||||
\(324\) | −139.778 | + | 81.8901i | −0.431415 | + | 0.252747i | ||||
\(325\) | −58.0083 | −0.178487 | ||||||||
\(326\) | 32.1968i | 0.0987632i | ||||||||
\(327\) | 451.659 | − | 60.1923i | 1.38122 | − | 0.184074i | ||||
\(328\) | −90.9765 | −0.277367 | ||||||||
\(329\) | 244.308i | 0.742578i | ||||||||
\(330\) | 2.52885 | + | 18.9755i | 0.00766317 | + | 0.0575014i | ||||
\(331\) | 142.477 | 0.430443 | 0.215221 | − | 0.976565i | \(-0.430953\pi\) | ||||
0.215221 | + | 0.976565i | \(0.430953\pi\) | |||||||
\(332\) | − | 164.835i | − | 0.496492i | ||||||
\(333\) | 273.443 | − | 74.2010i | 0.821149 | − | 0.222826i | ||||
\(334\) | 333.418 | 0.998256 | ||||||||
\(335\) | 75.4516i | 0.225229i | ||||||||
\(336\) | 31.4708 | − | 4.19409i | 0.0936630 | − | 0.0124824i | ||||
\(337\) | −226.965 | −0.673487 | −0.336743 | − | 0.941596i | \(-0.609325\pi\) | ||||
−0.336743 | + | 0.941596i | \(0.609325\pi\) | |||||||
\(338\) | − | 48.6512i | − | 0.143938i | ||||||
\(339\) | 15.1494 | + | 113.675i | 0.0446884 | + | 0.335324i | ||||
\(340\) | 77.7775 | 0.228757 | ||||||||
\(341\) | − | 68.6326i | − | 0.201269i | ||||||
\(342\) | 120.437 | + | 443.828i | 0.352154 | + | 1.29774i | ||||
\(343\) | −18.5203 | −0.0539949 | ||||||||
\(344\) | 146.383i | 0.425532i | ||||||||
\(345\) | −214.664 | + | 28.6081i | −0.622213 | + | 0.0829220i | ||||
\(346\) | −192.348 | −0.555920 | ||||||||
\(347\) | 91.8895i | 0.264811i | 0.991196 | + | 0.132406i | \(0.0422701\pi\) | ||||
−0.991196 | + | 0.132406i | \(0.957730\pi\) | |||||||
\(348\) | −36.5743 | − | 274.439i | −0.105098 | − | 0.788617i | ||||
\(349\) | 442.343 | 1.26746 | 0.633729 | − | 0.773555i | \(-0.281524\pi\) | ||||
0.633729 | + | 0.773555i | \(0.281524\pi\) | |||||||
\(350\) | 18.7083i | 0.0534522i | ||||||||
\(351\) | −288.826 | + | 121.252i | −0.822865 | + | 0.345447i | ||||
\(352\) | 11.4148 | 0.0324284 | ||||||||
\(353\) | − | 88.1350i | − | 0.249674i | −0.992177 | − | 0.124837i | \(-0.960159\pi\) | ||
0.992177 | − | 0.124837i | \(-0.0398408\pi\) | |||||||
\(354\) | −191.194 | + | 25.4804i | −0.540097 | + | 0.0719784i | ||||
\(355\) | 56.5186 | 0.159207 | ||||||||
\(356\) | 97.7353i | 0.274537i | ||||||||
\(357\) | −18.2355 | − | 136.832i | −0.0510797 | − | 0.383282i | ||||
\(358\) | −17.5048 | −0.0488961 | ||||||||
\(359\) | − | 21.1772i | − | 0.0589894i | −0.999565 | − | 0.0294947i | \(-0.990610\pi\) | ||
0.999565 | − | 0.0294947i | \(-0.00938981\pi\) | |||||||
\(360\) | −54.9344 | + | 14.9069i | −0.152595 | + | 0.0414081i | ||||
\(361\) | 944.484 | 2.61630 | ||||||||
\(362\) | − | 78.9401i | − | 0.218067i | ||||||
\(363\) | −347.710 | + | 46.3392i | −0.957880 | + | 0.127656i | ||||
\(364\) | 61.3902 | 0.168654 | ||||||||
\(365\) | − | 108.523i | − | 0.297324i | ||||||
\(366\) | −15.7738 | − | 118.360i | −0.0430979 | − | 0.323389i | ||||
\(367\) | −306.468 | −0.835064 | −0.417532 | − | 0.908662i | \(-0.637105\pi\) | ||||
−0.417532 | + | 0.908662i | \(0.637105\pi\) | |||||||
\(368\) | 129.132i | 0.350903i | ||||||||
\(369\) | −75.8126 | − | 279.382i | −0.205454 | − | 0.757133i | ||||
\(370\) | 99.5525 | 0.269061 | ||||||||
\(371\) | − | 48.5006i | − | 0.130729i | ||||||
\(372\) | 202.286 | − | 26.9585i | 0.543779 | − | 0.0724691i | ||||
\(373\) | 536.875 | 1.43934 | 0.719671 | − | 0.694315i | \(-0.244292\pi\) | ||||
0.719671 | + | 0.694315i | \(0.244292\pi\) | |||||||
\(374\) | − | 49.6304i | − | 0.132702i | ||||||
\(375\) | −4.43082 | − | 33.2471i | −0.0118155 | − | 0.0886589i | ||||
\(376\) | −261.177 | −0.694619 | ||||||||
\(377\) | − | 535.349i | − | 1.42002i | ||||||
\(378\) | 39.1050 | + | 93.1493i | 0.103452 | + | 0.246427i | ||||
\(379\) | 457.399 | 1.20686 | 0.603429 | − | 0.797417i | \(-0.293801\pi\) | ||||
0.603429 | + | 0.797417i | \(0.293801\pi\) | |||||||
\(380\) | 161.585i | 0.425223i | ||||||||
\(381\) | −301.891 | + | 40.2329i | −0.792365 | + | 0.105598i | ||||
\(382\) | 280.805 | 0.735092 | ||||||||
\(383\) | 274.471i | 0.716633i | 0.933600 | + | 0.358317i | \(0.116649\pi\) | ||||
−0.933600 | + | 0.358317i | \(0.883351\pi\) | |||||||
\(384\) | 4.48367 | + | 33.6437i | 0.0116762 | + | 0.0876137i | ||||
\(385\) | 11.9379 | 0.0310075 | ||||||||
\(386\) | 63.1556i | 0.163615i | ||||||||
\(387\) | −449.531 | + | 121.984i | −1.16158 | + | 0.315204i | ||||
\(388\) | 29.0334 | 0.0748283 | ||||||||
\(389\) | 507.661i | 1.30504i | 0.757771 | + | 0.652521i | \(0.226288\pi\) | ||||
−0.757771 | + | 0.652521i | \(0.773712\pi\) | |||||||
\(390\) | −109.098 | + | 14.5395i | −0.279740 | + | 0.0372807i | ||||
\(391\) | 561.454 | 1.43594 | ||||||||
\(392\) | − | 19.7990i | − | 0.0505076i | ||||||
\(393\) | −88.8309 | − | 666.551i | −0.226033 | − | 1.69606i | ||||
\(394\) | −1.34734 | −0.00341965 | ||||||||
\(395\) | − | 73.6407i | − | 0.186432i | ||||||
\(396\) | 9.51220 | + | 35.0540i | 0.0240207 | + | 0.0885203i | ||||
\(397\) | −552.511 | −1.39171 | −0.695857 | − | 0.718180i | \(-0.744975\pi\) | ||||
−0.695857 | + | 0.718180i | \(0.744975\pi\) | |||||||
\(398\) | − | 185.464i | − | 0.465991i | ||||||
\(399\) | 284.271 | − | 37.8847i | 0.712460 | − | 0.0949491i | ||||
\(400\) | −20.0000 | −0.0500000 | ||||||||
\(401\) | 240.320i | 0.599302i | 0.954049 | + | 0.299651i | \(0.0968702\pi\) | ||||
−0.954049 | + | 0.299651i | \(0.903130\pi\) | |||||||
\(402\) | 18.9116 | + | 141.905i | 0.0470437 | + | 0.352997i | ||||
\(403\) | 394.600 | 0.979155 | ||||||||
\(404\) | − | 137.766i | − | 0.341004i | ||||||
\(405\) | −91.5559 | − | 156.277i | −0.226064 | − | 0.385869i | ||||
\(406\) | −172.656 | −0.425260 | ||||||||
\(407\) | − | 63.5252i | − | 0.156082i | ||||||
\(408\) | 146.279 | − | 19.4945i | 0.358527 | − | 0.0477807i | ||||
\(409\) | −441.083 | −1.07844 | −0.539222 | − | 0.842164i | \(-0.681281\pi\) | ||||
−0.539222 | + | 0.842164i | \(0.681281\pi\) | |||||||
\(410\) | − | 101.715i | − | 0.248085i | ||||||
\(411\) | 48.5237 | + | 364.102i | 0.118063 | + | 0.885894i | ||||
\(412\) | 87.0474 | 0.211280 | ||||||||
\(413\) | 120.285i | 0.291247i | ||||||||
\(414\) | −396.556 | + | 107.609i | −0.957864 | + | 0.259924i | ||||
\(415\) | 184.291 | 0.444076 | ||||||||
\(416\) | 65.6289i | 0.157762i | ||||||||
\(417\) | −394.146 | + | 52.5276i | −0.945195 | + | 0.125966i | ||||
\(418\) | 103.109 | 0.246671 | ||||||||
\(419\) | 412.950i | 0.985561i | 0.870154 | + | 0.492780i | \(0.164019\pi\) | ||||
−0.870154 | + | 0.492780i | \(0.835981\pi\) | |||||||
\(420\) | 4.68914 | + | 35.1854i | 0.0111646 | + | 0.0837747i | ||||
\(421\) | −147.333 | −0.349959 | −0.174980 | − | 0.984572i | \(-0.555986\pi\) | ||||
−0.174980 | + | 0.984572i | \(0.555986\pi\) | |||||||
\(422\) | − | 143.785i | − | 0.340723i | ||||||
\(423\) | −217.644 | − | 802.053i | −0.514525 | − | 1.89611i | ||||
\(424\) | 51.8493 | 0.122286 | ||||||||
\(425\) | 86.9579i | 0.204607i | ||||||||
\(426\) | 106.297 | − | 14.1661i | 0.249523 | − | 0.0332538i | ||||
\(427\) | −74.4633 | −0.174387 | ||||||||
\(428\) | − | 415.408i | − | 0.970579i | ||||||
\(429\) | 9.27775 | + | 69.6165i | 0.0216265 | + | 0.162276i | ||||
\(430\) | −163.661 | −0.380608 | ||||||||
\(431\) | − | 50.5951i | − | 0.117390i | −0.998276 | − | 0.0586950i | \(-0.981306\pi\) | ||
0.998276 | − | 0.0586950i | \(-0.0186939\pi\) | |||||||
\(432\) | −99.5808 | + | 41.8050i | −0.230511 | + | 0.0967708i | ||||
\(433\) | 653.464 | 1.50915 | 0.754577 | − | 0.656211i | \(-0.227842\pi\) | ||||
0.754577 | + | 0.656211i | \(0.227842\pi\) | |||||||
\(434\) | − | 127.263i | − | 0.293232i | ||||||
\(435\) | 306.832 | − | 40.8913i | 0.705360 | − | 0.0940029i | ||||
\(436\) | 303.768 | 0.696715 | ||||||||
\(437\) | 1166.44i | 2.66919i | ||||||||
\(438\) | −27.2008 | − | 204.104i | −0.0621023 | − | 0.465991i | ||||
\(439\) | −760.655 | −1.73270 | −0.866350 | − | 0.499438i | \(-0.833540\pi\) | ||||
−0.866350 | + | 0.499438i | \(0.833540\pi\) | |||||||
\(440\) | 12.7621i | 0.0290049i | ||||||||
\(441\) | 60.8012 | − | 16.4989i | 0.137871 | − | 0.0374125i | ||||
\(442\) | 285.347 | 0.645583 | ||||||||
\(443\) | 543.566i | 1.22701i | 0.789690 | + | 0.613506i | \(0.210241\pi\) | ||||
−0.789690 | + | 0.613506i | \(0.789759\pi\) | |||||||
\(444\) | 187.232 | − | 24.9523i | 0.421694 | − | 0.0561990i | ||||
\(445\) | −109.271 | −0.245554 | ||||||||
\(446\) | − | 520.522i | − | 1.16709i | ||||||
\(447\) | −4.64060 | − | 34.8212i | −0.0103817 | − | 0.0778998i | ||||
\(448\) | 21.1660 | 0.0472456 | ||||||||
\(449\) | 691.105i | 1.53921i | 0.638521 | + | 0.769604i | \(0.279546\pi\) | ||||
−0.638521 | + | 0.769604i | \(0.720454\pi\) | |||||||
\(450\) | −16.6664 | − | 61.4185i | −0.0370365 | − | 0.136486i | ||||
\(451\) | −64.9050 | −0.143914 | ||||||||
\(452\) | 76.4532i | 0.169144i | ||||||||
\(453\) | 217.674 | − | 29.0093i | 0.480516 | − | 0.0640381i | ||||
\(454\) | 440.715 | 0.970738 | ||||||||
\(455\) | 68.6363i | 0.150849i | ||||||||
\(456\) | 40.5004 | + | 303.899i | 0.0888167 | + | 0.666445i | ||||
\(457\) | 32.4937 | 0.0711022 | 0.0355511 | − | 0.999368i | \(-0.488681\pi\) | ||||
0.0355511 | + | 0.999368i | \(0.488681\pi\) | |||||||
\(458\) | − | 171.238i | − | 0.373882i | ||||||
\(459\) | 181.764 | + | 432.967i | 0.395999 | + | 0.943283i | ||||
\(460\) | −144.374 | −0.313857 | ||||||||
\(461\) | 18.9876i | 0.0411879i | 0.999788 | + | 0.0205940i | \(0.00655573\pi\) | ||||
−0.999788 | + | 0.0205940i | \(0.993444\pi\) | |||||||
\(462\) | 22.4521 | − | 2.99217i | 0.0485975 | − | 0.00647656i | ||||
\(463\) | 772.969 | 1.66948 | 0.834740 | − | 0.550645i | \(-0.185618\pi\) | ||||
0.834740 | + | 0.550645i | \(0.185618\pi\) | |||||||
\(464\) | − | 184.577i | − | 0.397795i | ||||||
\(465\) | 30.1405 | + | 226.162i | 0.0648183 | + | 0.486370i | ||||
\(466\) | −266.491 | −0.571868 | ||||||||
\(467\) | − | 335.729i | − | 0.718905i | −0.933163 | − | 0.359453i | \(-0.882963\pi\) | ||
0.933163 | − | 0.359453i | \(-0.117037\pi\) | |||||||
\(468\) | −201.541 | + | 54.6899i | −0.430644 | + | 0.116859i | ||||
\(469\) | 89.2755 | 0.190353 | ||||||||
\(470\) | − | 292.004i | − | 0.621286i | ||||||
\(471\) | −863.826 | + | 115.122i | −1.83402 | + | 0.244419i | ||||
\(472\) | −128.590 | −0.272436 | ||||||||
\(473\) | 104.433i | 0.220790i | ||||||||
\(474\) | −18.4577 | − | 138.499i | −0.0389402 | − | 0.292192i | ||||
\(475\) | −180.657 | −0.380331 | ||||||||
\(476\) | − | 92.0276i | − | 0.193335i | ||||||
\(477\) | 43.2071 | + | 159.225i | 0.0905809 | + | 0.333806i | ||||
\(478\) | −343.353 | −0.718313 | ||||||||
\(479\) | − | 937.543i | − | 1.95729i | −0.205551 | − | 0.978646i | \(-0.565899\pi\) | ||
0.205551 | − | 0.978646i | \(-0.434101\pi\) | |||||||
\(480\) | −37.6148 | + | 5.01290i | −0.0783641 | + | 0.0104435i | ||||
\(481\) | 365.235 | 0.759324 | ||||||||
\(482\) | − | 308.199i | − | 0.639417i | ||||||
\(483\) | 33.8495 | + | 253.993i | 0.0700819 | + | 0.525866i | ||||
\(484\) | −233.856 | −0.483174 | ||||||||
\(485\) | 32.4603i | 0.0669284i | ||||||||
\(486\) | −211.363 | − | 270.968i | −0.434903 | − | 0.557548i | ||||
\(487\) | 752.244 | 1.54465 | 0.772325 | − | 0.635228i | \(-0.219094\pi\) | ||||
0.772325 | + | 0.635228i | \(0.219094\pi\) | |||||||
\(488\) | − | 79.6046i | − | 0.163124i | ||||||
\(489\) | −67.7012 | + | 9.02249i | −0.138448 | + | 0.0184509i | ||||
\(490\) | 22.1359 | 0.0451754 | ||||||||
\(491\) | 854.568i | 1.74047i | 0.492641 | + | 0.870233i | \(0.336032\pi\) | ||||
−0.492641 | + | 0.870233i | \(0.663968\pi\) | |||||||
\(492\) | −25.4943 | − | 191.299i | −0.0518177 | − | 0.388819i | ||||
\(493\) | −802.520 | −1.62783 | ||||||||
\(494\) | 592.817i | 1.20003i | ||||||||
\(495\) | −39.1916 | + | 10.6350i | −0.0791749 | + | 0.0214848i | ||||
\(496\) | 136.049 | 0.274293 | ||||||||
\(497\) | − | 66.8738i | − | 0.134555i | ||||||
\(498\) | 346.604 | − | 46.1917i | 0.695992 | − | 0.0927544i | ||||
\(499\) | −364.673 | −0.730807 | −0.365404 | − | 0.930849i | \(-0.619069\pi\) | ||||
−0.365404 | + | 0.930849i | \(0.619069\pi\) | |||||||
\(500\) | − | 22.3607i | − | 0.0447214i | ||||||
\(501\) | 93.4334 | + | 701.087i | 0.186494 | + | 1.39937i | ||||
\(502\) | 63.2471 | 0.125990 | ||||||||
\(503\) | 251.341i | 0.499683i | 0.968287 | + | 0.249842i | \(0.0803785\pi\) | ||||
−0.968287 | + | 0.249842i | \(0.919621\pi\) | |||||||
\(504\) | 17.6381 | + | 64.9992i | 0.0349962 | + | 0.128967i | ||||
\(505\) | 154.027 | 0.305004 | ||||||||
\(506\) | 92.1263i | 0.182068i | ||||||||
\(507\) | 102.300 | − | 13.6335i | 0.201776 | − | 0.0268905i | ||||
\(508\) | −203.040 | −0.399685 | ||||||||
\(509\) | − | 377.854i | − | 0.742345i | −0.928564 | − | 0.371173i | \(-0.878956\pi\) | ||
0.928564 | − | 0.371173i | \(-0.121044\pi\) | |||||||
\(510\) | 21.7956 | + | 163.545i | 0.0427364 | + | 0.320677i | ||||
\(511\) | −128.406 | −0.251285 | ||||||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | −899.501 | + | 377.619i | −1.75341 | + | 0.736100i | ||||
\(514\) | 231.836 | 0.451043 | ||||||||
\(515\) | 97.3220i | 0.188975i | ||||||||
\(516\) | −307.804 | + | 41.0209i | −0.596519 | + | 0.0794978i | ||||
\(517\) | −186.330 | −0.360406 | ||||||||
\(518\) | − | 117.792i | − | 0.227398i | ||||||
\(519\) | −53.9017 | − | 404.456i | −0.103857 | − | 0.779299i | ||||
\(520\) | −73.3753 | −0.141106 | ||||||||
\(521\) | 959.258i | 1.84119i | 0.390524 | + | 0.920593i | \(0.372294\pi\) | ||||
−0.390524 | + | 0.920593i | \(0.627706\pi\) | |||||||
\(522\) | 566.821 | − | 153.812i | 1.08586 | − | 0.294658i | ||||
\(523\) | −372.766 | −0.712745 | −0.356372 | − | 0.934344i | \(-0.615987\pi\) | ||||
−0.356372 | + | 0.934344i | \(0.615987\pi\) | |||||||
\(524\) | − | 448.296i | − | 0.855527i | ||||||
\(525\) | −39.3385 | + | 5.24261i | −0.0749304 | + | 0.00998593i | ||||
\(526\) | 730.979 | 1.38969 | ||||||||
\(527\) | − | 591.529i | − | 1.12245i | ||||||
\(528\) | 3.19877 | + | 24.0023i | 0.00605827 | + | 0.0454588i | ||||
\(529\) | −513.197 | −0.970126 | ||||||||
\(530\) | 57.9693i | 0.109376i | ||||||||
\(531\) | −107.157 | − | 394.890i | −0.201802 | − | 0.743672i | ||||
\(532\) | 191.190 | 0.359379 | ||||||||
\(533\) | − | 373.168i | − | 0.700128i | ||||||
\(534\) | −205.511 | + | 27.3883i | −0.384852 | + | 0.0512890i | ||||
\(535\) | 464.440 | 0.868113 | ||||||||
\(536\) | 95.4395i | 0.178059i | ||||||||
\(537\) | −4.90536 | − | 36.8079i | −0.00913475 | − | 0.0685435i | ||||
\(538\) | −602.119 | −1.11918 | ||||||||
\(539\) | − | 14.1251i | − | 0.0262061i | ||||||
\(540\) | −46.7394 | − | 111.335i | −0.0865545 | − | 0.206175i | ||||
\(541\) | −425.367 | −0.786262 | −0.393131 | − | 0.919483i | \(-0.628608\pi\) | ||||
−0.393131 | + | 0.919483i | \(0.628608\pi\) | |||||||
\(542\) | − | 54.3415i | − | 0.100261i | ||||||
\(543\) | 165.990 | − | 22.1213i | 0.305690 | − | 0.0407391i | ||||
\(544\) | 98.3816 | 0.180849 | ||||||||
\(545\) | 339.623i | 0.623161i | ||||||||
\(546\) | 17.2033 | + | 129.087i | 0.0315080 | + | 0.236423i | ||||
\(547\) | −163.904 | −0.299641 | −0.149821 | − | 0.988713i | \(-0.547870\pi\) | ||||
−0.149821 | + | 0.988713i | \(0.547870\pi\) | |||||||
\(548\) | 244.881i | 0.446863i | ||||||||
\(549\) | 244.460 | − | 66.3362i | 0.445282 | − | 0.120831i | ||||
\(550\) | −14.2685 | −0.0259428 | ||||||||
\(551\) | − | 1667.26i | − | 3.02588i | ||||||
\(552\) | −271.530 | + | 36.1867i | −0.491903 | + | 0.0655556i | ||||
\(553\) | −87.1328 | −0.157564 | ||||||||
\(554\) | − | 517.283i | − | 0.933723i | ||||||
\(555\) | 27.8976 | + | 209.332i | 0.0502659 | + | 0.377175i | ||||
\(556\) | −265.087 | −0.476776 | ||||||||
\(557\) | − | 706.900i | − | 1.26912i | −0.772873 | − | 0.634560i | \(-0.781181\pi\) | ||
0.772873 | − | 0.634560i | \(-0.218819\pi\) | |||||||
\(558\) | 113.373 | + | 417.797i | 0.203177 | + | 0.748741i | ||||
\(559\) | −600.435 | −1.07412 | ||||||||
\(560\) | 23.6643i | 0.0422577i | ||||||||
\(561\) | 104.359 | − | 13.9079i | 0.186024 | − | 0.0247913i | ||||
\(562\) | −569.607 | −1.01354 | ||||||||
\(563\) | − | 456.163i | − | 0.810237i | −0.914264 | − | 0.405118i | \(-0.867230\pi\) | ||
0.914264 | − | 0.405118i | \(-0.132770\pi\) | |||||||
\(564\) | −73.1894 | − | 549.184i | −0.129768 | − | 0.973730i | ||||
\(565\) | −85.4773 | −0.151287 | ||||||||
\(566\) | − | 551.873i | − | 0.975040i | ||||||
\(567\) | −184.909 | + | 108.330i | −0.326119 | + | 0.191059i | ||||
\(568\) | 71.4911 | 0.125865 | ||||||||
\(569\) | 429.044i | 0.754032i | 0.926207 | + | 0.377016i | \(0.123050\pi\) | ||||
−0.926207 | + | 0.377016i | \(0.876950\pi\) | |||||||
\(570\) | −339.769 | + | 45.2809i | −0.596087 | + | 0.0794401i | ||||
\(571\) | −739.819 | −1.29566 | −0.647828 | − | 0.761787i | \(-0.724322\pi\) | ||||
−0.647828 | + | 0.761787i | \(0.724322\pi\) | |||||||
\(572\) | 46.8213i | 0.0818555i | ||||||||
\(573\) | 78.6899 | + | 590.457i | 0.137330 | + | 1.03047i | ||||
\(574\) | −120.351 | −0.209670 | ||||||||
\(575\) | − | 161.415i | − | 0.280722i | ||||||
\(576\) | −69.4871 | + | 18.8559i | −0.120637 | + | 0.0327359i | ||||
\(577\) | −826.999 | −1.43327 | −0.716637 | − | 0.697446i | \(-0.754320\pi\) | ||||
−0.716637 | + | 0.697446i | \(0.754320\pi\) | |||||||
\(578\) | − | 19.0453i | − | 0.0329504i | ||||||
\(579\) | −132.799 | + | 17.6981i | −0.229359 | + | 0.0305666i | ||||
\(580\) | 206.363 | 0.355798 | ||||||||
\(581\) | − | 218.057i | − | 0.375312i | ||||||
\(582\) | 8.13601 | + | 61.0493i | 0.0139794 | + | 0.104896i | ||||
\(583\) | 36.9906 | 0.0634488 | ||||||||
\(584\) | − | 137.272i | − | 0.235055i | ||||||
\(585\) | −61.1452 | − | 225.330i | −0.104522 | − | 0.385180i | ||||
\(586\) | 31.9744 | 0.0545639 | ||||||||
\(587\) | 419.920i | 0.715366i | 0.933843 | + | 0.357683i | \(0.116433\pi\) | ||||
−0.933843 | + | 0.357683i | \(0.883567\pi\) | |||||||
\(588\) | 41.6319 | − | 5.54826i | 0.0708026 | − | 0.00943582i | ||||
\(589\) | 1228.92 | 2.08645 | ||||||||
\(590\) | − | 143.768i | − | 0.243674i | ||||||
\(591\) | −0.377565 | − | 2.83310i | −0.000638858 | − | 0.00479374i | ||||
\(592\) | 125.925 | 0.212711 | ||||||||
\(593\) | 831.323i | 1.40189i | 0.713213 | + | 0.700947i | \(0.247239\pi\) | ||||
−0.713213 | + | 0.700947i | \(0.752761\pi\) | |||||||
\(594\) | −71.0435 | + | 29.8248i | −0.119602 | + | 0.0502100i | ||||
\(595\) | 102.890 | 0.172924 | ||||||||
\(596\) | − | 23.4194i | − | 0.0392943i | ||||||
\(597\) | 389.982 | − | 51.9726i | 0.653235 | − | 0.0870563i | ||||
\(598\) | −529.675 | −0.885745 | ||||||||
\(599\) | − | 902.352i | − | 1.50643i | −0.657774 | − | 0.753216i | \(-0.728502\pi\) | ||
0.657774 | − | 0.753216i | \(-0.271498\pi\) | |||||||
\(600\) | −5.60459 | − | 42.0546i | −0.00934098 | − | 0.0700910i | ||||
\(601\) | −149.891 | −0.249403 | −0.124702 | − | 0.992194i | \(-0.539797\pi\) | ||||
−0.124702 | + | 0.992194i | \(0.539797\pi\) | |||||||
\(602\) | 193.647i | 0.321672i | ||||||||
\(603\) | −293.088 | + | 79.5318i | −0.486049 | + | 0.131893i | ||||
\(604\) | 146.399 | 0.242382 | ||||||||
\(605\) | − | 261.459i | − | 0.432164i | ||||||
\(606\) | 289.684 | − | 38.6060i | 0.478027 | − | 0.0637063i | ||||
\(607\) | 14.9805 | 0.0246795 | 0.0123398 | − | 0.999924i | \(-0.496072\pi\) | ||||
0.0123398 | + | 0.999924i | \(0.496072\pi\) | |||||||
\(608\) | 204.391i | 0.336169i | ||||||||
\(609\) | −48.3832 | − | 363.048i | −0.0794470 | − | 0.596138i | ||||
\(610\) | 89.0007 | 0.145903 | ||||||||
\(611\) | − | 1071.30i | − | 1.75335i | ||||||
\(612\) | 81.9835 | + | 302.123i | 0.133960 | + | 0.493664i | ||||
\(613\) | 289.923 | 0.472958 | 0.236479 | − | 0.971637i | \(-0.424006\pi\) | ||||
0.236479 | + | 0.971637i | \(0.424006\pi\) | |||||||
\(614\) | 470.812i | 0.766795i | ||||||||
\(615\) | 213.879 | − | 28.5035i | 0.347770 | − | 0.0463472i | ||||
\(616\) | 15.1004 | 0.0245136 | ||||||||
\(617\) | 1118.36i | 1.81257i | 0.422662 | + | 0.906287i | \(0.361096\pi\) | ||||
−0.422662 | + | 0.906287i | \(0.638904\pi\) | |||||||
\(618\) | 24.3933 | + | 183.037i | 0.0394713 | + | 0.296177i | ||||
\(619\) | −963.589 | −1.55669 | −0.778343 | − | 0.627839i | \(-0.783940\pi\) | ||||
−0.778343 | + | 0.627839i | \(0.783940\pi\) | |||||||
\(620\) | 152.108i | 0.245335i | ||||||||
\(621\) | −337.398 | − | 803.694i | −0.543315 | − | 1.29419i | ||||
\(622\) | 205.101 | 0.329744 | ||||||||
\(623\) | 129.292i | 0.207531i | ||||||||
\(624\) | −138.000 | + | 18.3911i | −0.221153 | + | 0.0294730i | ||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 489.225i | 0.781509i | ||||||||
\(627\) | 28.8941 | + | 216.809i | 0.0460830 | + | 0.345788i | ||||
\(628\) | −580.975 | −0.925120 | ||||||||
\(629\) | − | 547.509i | − | 0.870444i | ||||||
\(630\) | −72.6713 | + | 19.7200i | −0.115351 | + | 0.0313015i | ||||
\(631\) | 408.113 | 0.646772 | 0.323386 | − | 0.946267i | \(-0.395179\pi\) | ||||
0.323386 | + | 0.946267i | \(0.395179\pi\) | |||||||
\(632\) | − | 93.1489i | − | 0.147388i | ||||||
\(633\) | 302.341 | − | 40.2928i | 0.477632 | − | 0.0636538i | ||||
\(634\) | 219.759 | 0.346623 | ||||||||
\(635\) | − | 227.006i | − | 0.357489i | ||||||
\(636\) | 14.5297 | + | 109.025i | 0.0228454 | + | 0.171423i | ||||
\(637\) | 81.2116 | 0.127491 | ||||||||
\(638\) | − | 131.682i | − | 0.206398i | ||||||
\(639\) | 59.5750 | + | 219.544i | 0.0932316 | + | 0.343574i | ||||
\(640\) | −25.2982 | −0.0395285 | ||||||||
\(641\) | 548.724i | 0.856044i | 0.903768 | + | 0.428022i | \(0.140789\pi\) | ||||
−0.903768 | + | 0.428022i | \(0.859211\pi\) | |||||||
\(642\) | 873.491 | − | 116.410i | 1.36058 | − | 0.181323i | ||||
\(643\) | −106.614 | −0.165807 | −0.0829033 | − | 0.996558i | \(-0.526419\pi\) | ||||
−0.0829033 | + | 0.996558i | \(0.526419\pi\) | |||||||
\(644\) | 170.826i | 0.265258i | ||||||||
\(645\) | −45.8627 | − | 344.135i | −0.0711050 | − | 0.533543i | ||||
\(646\) | 888.669 | 1.37565 | ||||||||
\(647\) | − | 316.788i | − | 0.489625i | −0.969570 | − | 0.244813i | \(-0.921274\pi\) | ||
0.969570 | − | 0.244813i | \(-0.0787265\pi\) | |||||||
\(648\) | −115.810 | − | 197.677i | −0.178719 | − | 0.305056i | ||||
\(649\) | −91.7393 | −0.141355 | ||||||||
\(650\) | − | 82.0361i | − | 0.126209i | ||||||
\(651\) | 267.599 | − | 35.6627i | 0.411058 | − | 0.0547815i | ||||
\(652\) | −45.5332 | −0.0698361 | ||||||||
\(653\) | 407.664i | 0.624293i | 0.950034 | + | 0.312147i | \(0.101048\pi\) | ||||
−0.950034 | + | 0.312147i | \(0.898952\pi\) | |||||||
\(654\) | 85.1247 | + | 638.742i | 0.130160 | + | 0.976669i | ||||
\(655\) | 501.210 | 0.765207 | ||||||||
\(656\) | − | 128.660i | − | 0.196128i | ||||||
\(657\) | 421.553 | − | 114.392i | 0.641633 | − | 0.174112i | ||||
\(658\) | −345.504 | −0.525082 | ||||||||
\(659\) | 442.719i | 0.671804i | 0.941897 | + | 0.335902i | \(0.109041\pi\) | ||||
−0.941897 | + | 0.335902i | \(0.890959\pi\) | |||||||
\(660\) | −26.8353 | + | 3.57633i | −0.0406596 | + | 0.00541868i | ||||
\(661\) | 300.069 | 0.453962 | 0.226981 | − | 0.973899i | \(-0.427114\pi\) | ||||
0.226981 | + | 0.973899i | \(0.427114\pi\) | |||||||
\(662\) | 201.492i | 0.304369i | ||||||||
\(663\) | 79.9628 | + | 600.009i | 0.120608 | + | 0.904990i | ||||
\(664\) | 233.112 | 0.351073 | ||||||||
\(665\) | 213.757i | 0.321439i | ||||||||
\(666\) | 104.936 | + | 386.706i | 0.157562 | + | 0.580640i | ||||
\(667\) | 1489.68 | 2.23340 | ||||||||
\(668\) | 471.524i | 0.705874i | ||||||||
\(669\) | 1094.52 | − | 145.866i | 1.63605 | − | 0.218035i | ||||
\(670\) | −106.705 | −0.159261 | ||||||||
\(671\) | − | 56.7920i | − | 0.0846378i | ||||||
\(672\) | 5.93134 | + | 44.5064i | 0.00882640 | + | 0.0662298i | ||||
\(673\) | 199.000 | 0.295691 | 0.147845 | − | 0.989011i | \(-0.452766\pi\) | ||||
0.147845 | + | 0.989011i | \(0.452766\pi\) | |||||||
\(674\) | − | 320.977i | − | 0.476227i | ||||||
\(675\) | 124.476 | − | 52.2562i | 0.184409 | − | 0.0774167i | ||||
\(676\) | 68.8031 | 0.101780 | ||||||||
\(677\) | 235.136i | 0.347321i | 0.984806 | + | 0.173660i | \(0.0555595\pi\) | ||||
−0.984806 | + | 0.173660i | \(0.944441\pi\) | |||||||
\(678\) | −160.760 | + | 21.4245i | −0.237110 | + | 0.0315995i | ||||
\(679\) | 38.4075 | 0.0565648 | ||||||||
\(680\) | 109.994i | 0.161756i | ||||||||
\(681\) | 123.501 | + | 926.704i | 0.181353 | + | 1.36080i | ||||
\(682\) | 97.0612 | 0.142318 | ||||||||
\(683\) | 698.860i | 1.02322i | 0.859218 | + | 0.511610i | \(0.170951\pi\) | ||||
−0.859218 | + | 0.511610i | \(0.829049\pi\) | |||||||
\(684\) | −627.668 | + | 170.323i | −0.917643 | + | 0.249010i | ||||
\(685\) | −273.785 | −0.399686 | ||||||||
\(686\) | − | 26.1916i | − | 0.0381802i | ||||||
\(687\) | 360.067 | − | 47.9859i | 0.524114 | − | 0.0698484i | ||||
\(688\) | −207.017 | −0.300897 | ||||||||
\(689\) | 212.676i | 0.308673i | ||||||||
\(690\) | −40.4579 | − | 303.580i | −0.0586347 | − | 0.439971i | ||||
\(691\) | 326.641 | 0.472708 | 0.236354 | − | 0.971667i | \(-0.424047\pi\) | ||||
0.236354 | + | 0.971667i | \(0.424047\pi\) | |||||||
\(692\) | − | 272.022i | − | 0.393095i | ||||||
\(693\) | 12.5835 | + | 46.3721i | 0.0181580 | + | 0.0669150i | ||||
\(694\) | −129.951 | −0.187250 | ||||||||
\(695\) | − | 296.377i | − | 0.426441i | ||||||
\(696\) | 388.115 | − | 51.7238i | 0.557636 | − | 0.0743159i | ||||
\(697\) | −559.401 | −0.802584 | ||||||||
\(698\) | 625.567i | 0.896228i | ||||||||
\(699\) | −74.6785 | − | 560.358i | −0.106836 | − | 0.801656i | ||||
\(700\) | −26.4575 | −0.0377964 | ||||||||
\(701\) | − | 482.417i | − | 0.688185i | −0.938936 | − | 0.344092i | \(-0.888187\pi\) | ||
0.938936 | − | 0.344092i | \(-0.111813\pi\) | |||||||
\(702\) | −171.476 | − | 408.461i | −0.244268 | − | 0.581853i | ||||
\(703\) | 1137.47 | 1.61802 | ||||||||
\(704\) | 16.1430i | 0.0229304i | ||||||||
\(705\) | 614.006 | − | 81.8282i | 0.870931 | − | 0.116068i | ||||
\(706\) | 124.642 | 0.176546 | ||||||||
\(707\) | − | 182.247i | − | 0.257775i | ||||||
\(708\) | −36.0347 | − | 270.390i | −0.0508964 | − | 0.381906i | ||||
\(709\) | −415.186 | −0.585594 | −0.292797 | − | 0.956175i | \(-0.594586\pi\) | ||||
−0.292797 | + | 0.956175i | \(0.594586\pi\) | |||||||
\(710\) | 79.9294i | 0.112577i | ||||||||
\(711\) | 286.053 | − | 77.6229i | 0.402325 | − | 0.109174i | ||||
\(712\) | −138.219 | −0.194127 | ||||||||
\(713\) | 1098.02i | 1.54000i | ||||||||
\(714\) | 193.509 | − | 25.7888i | 0.271021 | − | 0.0361188i | ||||
\(715\) | −52.3478 | −0.0732138 | ||||||||
\(716\) | − | 24.7555i | − | 0.0345748i | ||||||
\(717\) | −96.2178 | − | 721.979i | −0.134195 | − | 1.00694i | ||||
\(718\) | 29.9491 | 0.0417118 | ||||||||
\(719\) | − | 1341.45i | − | 1.86571i | −0.360249 | − | 0.932856i | \(-0.617308\pi\) | ||
0.360249 | − | 0.932856i | \(-0.382692\pi\) | |||||||
\(720\) | −21.0815 | − | 77.6889i | −0.0292799 | − | 0.107901i | ||||
\(721\) | 115.153 | 0.159713 | ||||||||
\(722\) | 1335.70i | 1.85000i | ||||||||
\(723\) | 648.059 | − | 86.3664i | 0.896347 | − | 0.119456i | ||||
\(724\) | 111.638 | 0.154196 | ||||||||
\(725\) | 230.721i | 0.318236i | ||||||||
\(726\) | −65.5335 | − | 491.737i | −0.0902665 | − | 0.677323i | ||||
\(727\) | 5.22241 | 0.00718351 | 0.00359175 | − | 0.999994i | \(-0.498857\pi\) | ||||
0.00359175 | + | 0.999994i | \(0.498857\pi\) | |||||||
\(728\) | 86.8188i | 0.119257i | ||||||||
\(729\) | 510.543 | − | 520.372i | 0.700333 | − | 0.713816i | ||||
\(730\) | 153.475 | 0.210240 | ||||||||
\(731\) | 900.088i | 1.23131i | ||||||||
\(732\) | 167.387 | − | 22.3076i | 0.228671 | − | 0.0304748i | ||||
\(733\) | −163.268 | −0.222739 | −0.111370 | − | 0.993779i | \(-0.535524\pi\) | ||||
−0.111370 | + | 0.993779i | \(0.535524\pi\) | |||||||
\(734\) | − | 433.412i | − | 0.590479i | ||||||
\(735\) | 6.20314 | + | 46.5459i | 0.00843965 | + | 0.0633278i | ||||
\(736\) | −182.621 | −0.248126 | ||||||||
\(737\) | 68.0890i | 0.0923867i | ||||||||
\(738\) | 395.106 | − | 107.215i | 0.535374 | − | 0.145278i | ||||
\(739\) | −995.463 | −1.34704 | −0.673520 | − | 0.739169i | \(-0.735219\pi\) | ||||
−0.673520 | + | 0.739169i | \(0.735219\pi\) | |||||||
\(740\) | 140.789i | 0.190255i | ||||||||
\(741\) | −1246.53 | + | 166.125i | −1.68223 | + | 0.224190i | ||||
\(742\) | 68.5902 | 0.0924396 | ||||||||
\(743\) | − | 1330.52i | − | 1.79074i | −0.445321 | − | 0.895371i | \(-0.646911\pi\) | ||
0.445321 | − | 0.895371i | \(-0.353089\pi\) | |||||||
\(744\) | 38.1251 | + | 286.075i | 0.0512434 | + | 0.384510i | ||||
\(745\) | 26.1837 | 0.0351459 | ||||||||
\(746\) | 759.256i | 1.01777i | ||||||||
\(747\) | 194.257 | + | 715.870i | 0.260050 | + | 0.958327i | ||||
\(748\) | 70.1880 | 0.0938342 | ||||||||
\(749\) | − | 549.533i | − | 0.733689i | ||||||
\(750\) | 47.0185 | − | 6.26612i | 0.0626913 | − | 0.00835483i | ||||
\(751\) | −1291.88 | −1.72021 | −0.860107 | − | 0.510113i | \(-0.829603\pi\) | ||||
−0.860107 | + | 0.510113i | \(0.829603\pi\) | |||||||
\(752\) | − | 369.359i | − | 0.491169i | ||||||
\(753\) | 17.7237 | + | 132.991i | 0.0235374 | + | 0.176615i | ||||
\(754\) | 757.098 | 1.00411 | ||||||||
\(755\) | 163.679i | 0.216793i | ||||||||
\(756\) | −131.733 | + | 55.3028i | −0.174250 | + | 0.0731519i | ||||
\(757\) | −608.247 | −0.803497 | −0.401748 | − | 0.915750i | \(-0.631597\pi\) | ||||
−0.401748 | + | 0.915750i | \(0.631597\pi\) | |||||||
\(758\) | 646.860i | 0.853378i | ||||||||
\(759\) | −193.717 | + | 25.8165i | −0.255226 | + | 0.0340138i | ||||
\(760\) | −228.516 | −0.300678 | ||||||||
\(761\) | 19.5785i | 0.0257273i | 0.999917 | + | 0.0128637i | \(0.00409475\pi\) | ||||
−0.999917 | + | 0.0128637i | \(0.995905\pi\) | |||||||
\(762\) | −56.8979 | − | 426.939i | −0.0746691 | − | 0.560287i | ||||
\(763\) | 401.847 | 0.526667 | ||||||||
\(764\) | 397.118i | 0.519788i | ||||||||
\(765\) | −337.783 | + | 91.6603i | −0.441547 | + | 0.119817i | ||||
\(766\) | −388.160 | −0.506736 | ||||||||
\(767\) | − | 527.451i | − | 0.687680i | ||||||
\(768\) | −47.5793 | + | 6.34087i | −0.0619523 | + | 0.00825634i | ||||
\(769\) | 1084.91 | 1.41081 | 0.705405 | − | 0.708804i | \(-0.250765\pi\) | ||||
0.705405 | + | 0.708804i | \(0.250765\pi\) | |||||||
\(770\) | 16.8827i | 0.0219256i | ||||||||
\(771\) | 64.9674 | + | 487.489i | 0.0842638 | + | 0.632282i | ||||
\(772\) | −89.3154 | −0.115694 | ||||||||
\(773\) | 564.003i | 0.729628i | 0.931080 | + | 0.364814i | \(0.118867\pi\) | ||||
−0.931080 | + | 0.364814i | \(0.881133\pi\) | |||||||
\(774\) | −172.512 | − | 635.733i | −0.222883 | − | 0.821361i | ||||
\(775\) | −170.062 | −0.219435 | ||||||||
\(776\) | 41.0594i | 0.0529116i | ||||||||
\(777\) | 247.685 | − | 33.0088i | 0.318771 | − | 0.0424824i | ||||
\(778\) | −717.941 | −0.922804 | ||||||||
\(779\) | − | 1162.17i | − | 1.49188i | ||||||
\(780\) | −20.5619 | − | 154.288i | −0.0263614 | − | 0.197806i | ||||
\(781\) | 51.0036 | 0.0653055 | ||||||||
\(782\) | 794.015i | 1.01536i | ||||||||
\(783\) | 482.264 | + | 1148.77i | 0.615918 | + | 1.46714i | ||||
\(784\) | 28.0000 | 0.0357143 | ||||||||
\(785\) | − | 649.550i | − | 0.827453i | ||||||
\(786\) | 942.645 | − | 125.626i | 1.19929 | − | 0.159829i | ||||
\(787\) | 1360.30 | 1.72846 | 0.864232 | − | 0.503094i | \(-0.167805\pi\) | ||||
0.864232 | + | 0.503094i | \(0.167805\pi\) | |||||||
\(788\) | − | 1.90543i | − | 0.00241806i | ||||||
\(789\) | 204.842 | + | 1537.05i | 0.259622 | + | 1.94810i | ||||
\(790\) | 104.144 | 0.131827 | ||||||||
\(791\) | 101.138i | 0.127861i | ||||||||
\(792\) | −49.5739 | + | 13.4523i | −0.0625933 | + | 0.0169852i | ||||
\(793\) | 326.523 | 0.411756 | ||||||||
\(794\) | − | 781.368i | − | 0.984091i | ||||||
\(795\) | −121.894 | + | 16.2447i | −0.153325 | + | 0.0204336i | ||||
\(796\) | 262.286 | 0.329505 | ||||||||
\(797\) | 81.4055i | 0.102140i | 0.998695 | + | 0.0510700i | \(0.0162631\pi\) | ||||
−0.998695 | + | 0.0510700i | \(0.983737\pi\) | |||||||
\(798\) | 53.5770 | + | 402.021i | 0.0671392 | + | 0.503785i | ||||
\(799\) | −1605.94 | −2.00993 | ||||||||
\(800\) | − | 28.2843i | − | 0.0353553i | ||||||
\(801\) | −115.180 | − | 424.459i | −0.143796 | − | 0.529911i | ||||
\(802\) | −339.864 | −0.423770 | ||||||||
\(803\) | − | 97.9336i | − | 0.121960i | ||||||
\(804\) | −200.683 | + | 26.7450i | −0.249606 | + | 0.0332649i | ||||
\(805\) | −190.989 | −0.237254 | ||||||||
\(806\) | 558.048i | 0.692367i | ||||||||
\(807\) | −168.731 | − | 1266.09i | −0.209085 | − | 1.56889i | ||||
\(808\) | 194.830 | 0.241127 | ||||||||
\(809\) | − | 907.697i | − | 1.12200i | −0.827816 | − | 0.560999i | \(-0.810417\pi\) | ||
0.827816 | − | 0.560999i | \(-0.189583\pi\) | |||||||
\(810\) | 221.009 | − | 129.480i | 0.272851 | − | 0.159851i | ||||
\(811\) | −451.340 | −0.556523 | −0.278261 | − | 0.960505i | \(-0.589758\pi\) | ||||
−0.278261 | + | 0.960505i | \(0.589758\pi\) | |||||||
\(812\) | − | 244.172i | − | 0.300704i | ||||||
\(813\) | 114.266 | − | 15.2281i | 0.140548 | − | 0.0187307i | ||||
\(814\) | 89.8382 | 0.110366 | ||||||||
\(815\) | − | 50.9076i | − | 0.0624633i | ||||||
\(816\) | 27.5694 | + | 206.870i | 0.0337861 | + | 0.253517i | ||||
\(817\) | −1869.96 | −2.28881 | ||||||||
\(818\) | − | 623.786i | − | 0.762574i | ||||||
\(819\) | −266.614 | + | 72.3480i | −0.325536 | + | 0.0883370i | ||||
\(820\) | 143.847 | 0.175423 | ||||||||
\(821\) | − | 248.662i | − | 0.302878i | −0.988467 | − | 0.151439i | \(-0.951609\pi\) | ||
0.988467 | − | 0.151439i | \(-0.0483906\pi\) | |||||||
\(822\) | −514.918 | + | 68.6229i | −0.626421 | + | 0.0834828i | ||||
\(823\) | −596.005 | −0.724186 | −0.362093 | − | 0.932142i | \(-0.617938\pi\) | ||||
−0.362093 | + | 0.932142i | \(0.617938\pi\) | |||||||
\(824\) | 123.104i | 0.149398i | ||||||||
\(825\) | −3.99846 | − | 30.0028i | −0.00484662 | − | 0.0363671i | ||||
\(826\) | −170.108 | −0.205942 | ||||||||
\(827\) | 758.271i | 0.916894i | 0.888722 | + | 0.458447i | \(0.151594\pi\) | ||||
−0.888722 | + | 0.458447i | \(0.848406\pi\) | |||||||
\(828\) | −152.182 | − | 560.814i | −0.183794 | − | 0.677312i | ||||
\(829\) | 509.182 | 0.614212 | 0.307106 | − | 0.951675i | \(-0.400639\pi\) | ||||
0.307106 | + | 0.951675i | \(0.400639\pi\) | |||||||
\(830\) | 260.627i | 0.314009i | ||||||||
\(831\) | 1087.71 | − | 144.958i | 1.30891 | − | 0.174438i | ||||
\(832\) | −92.8133 | −0.111554 | ||||||||
\(833\) | − | 121.741i | − | 0.146148i | ||||||
\(834\) | −74.2853 | − | 557.407i | −0.0890711 | − | 0.668353i | ||||
\(835\) | −527.179 | −0.631353 | ||||||||
\(836\) | 145.817i | 0.174423i | ||||||||
\(837\) | −846.745 | + | 355.472i | −1.01164 | + | 0.424697i | ||||
\(838\) | −584.000 | −0.696897 | ||||||||
\(839\) | 766.956i | 0.914131i | 0.889433 | + | 0.457065i | \(0.151099\pi\) | ||||
−0.889433 | + | 0.457065i | \(0.848901\pi\) | |||||||
\(840\) | −49.7597 | + | 6.63144i | −0.0592377 | + | 0.00789457i | ||||
\(841\) | −1288.28 | −1.53185 | ||||||||
\(842\) | − | 208.360i | − | 0.247459i | ||||||
\(843\) | −159.621 | − | 1197.73i | −0.189348 | − | 1.42079i | ||||
\(844\) | 203.343 | 0.240928 | ||||||||
\(845\) | 76.9242i | 0.0910346i | ||||||||
\(846\) | 1134.27 | − | 307.795i | 1.34075 | − | 0.363824i | ||||
\(847\) | −309.363 | −0.365245 | ||||||||
\(848\) | 73.3260i | 0.0864693i | ||||||||
\(849\) | 1160.44 | − | 154.651i | 1.36683 | − | 0.182157i | ||||
\(850\) | −122.977 | −0.144679 | ||||||||
\(851\) | 1016.31i | 1.19426i | ||||||||
\(852\) | 20.0339 | + | 150.326i | 0.0235140 | + | 0.176439i | ||||
\(853\) | 735.107 | 0.861790 | 0.430895 | − | 0.902402i | \(-0.358198\pi\) | ||||
0.430895 | + | 0.902402i | \(0.358198\pi\) | |||||||
\(854\) | − | 105.307i | − | 0.123310i | ||||||
\(855\) | −190.427 | − | 701.754i | −0.222721 | − | 0.820765i | ||||
\(856\) | 587.476 | 0.686303 | ||||||||
\(857\) | 514.911i | 0.600830i | 0.953809 | + | 0.300415i | \(0.0971252\pi\) | ||||
−0.953809 | + | 0.300415i | \(0.902875\pi\) | |||||||
\(858\) | −98.4526 | + | 13.1207i | −0.114747 | + | 0.0152922i | ||||
\(859\) | 1414.99 | 1.64726 | 0.823628 | − | 0.567131i | \(-0.191947\pi\) | ||||
0.823628 | + | 0.567131i | \(0.191947\pi\) | |||||||
\(860\) | − | 231.452i | − | 0.269130i | ||||||
\(861\) | −33.7258 | − | 253.065i | −0.0391705 | − | 0.293920i | ||||
\(862\) | 71.5523 | 0.0830073 | ||||||||
\(863\) | 249.645i | 0.289276i | 0.989485 | + | 0.144638i | \(0.0462017\pi\) | ||||
−0.989485 | + | 0.144638i | \(0.953798\pi\) | |||||||
\(864\) | −59.1212 | − | 140.829i | −0.0684273 | − | 0.162996i | ||||
\(865\) | 304.129 | 0.351595 | ||||||||
\(866\) | 924.138i | 1.06713i | ||||||||
\(867\) | 40.0472 | − | 5.33707i | 0.0461906 | − | 0.00615579i | ||||
\(868\) | 179.976 | 0.207346 | ||||||||
\(869\) | − | 66.4548i | − | 0.0764728i | ||||||
\(870\) | 57.8290 | + | 433.926i | 0.0664701 | + | 0.498765i | ||||
\(871\) | −391.474 | −0.449454 | ||||||||
\(872\) | 429.593i | 0.492652i | ||||||||
\(873\) | −126.090 | + | 34.2156i | −0.144433 | + | 0.0391932i | ||||
\(874\) | −1649.59 | −1.88740 | ||||||||
\(875\) | − | 29.5804i | − | 0.0338062i | ||||||
\(876\) | 288.646 | − | 38.4677i | 0.329505 | − | 0.0439130i | ||||
\(877\) | 767.333 | 0.874952 | 0.437476 | − | 0.899230i | \(-0.355872\pi\) | ||||
0.437476 | + | 0.899230i | \(0.355872\pi\) | |||||||
\(878\) | − | 1075.73i | − | 1.22520i | ||||||
\(879\) | 8.96018 | + | 67.2336i | 0.0101936 | + | 0.0764887i | ||||
\(880\) | −18.0484 | −0.0205095 | ||||||||
\(881\) | − | 1200.08i | − | 1.36217i | −0.732203 | − | 0.681087i | \(-0.761508\pi\) | ||
0.732203 | − | 0.681087i | \(-0.238492\pi\) | |||||||
\(882\) | 23.3330 | + | 85.9859i | 0.0264546 | + | 0.0974897i | ||||
\(883\) | −370.168 | −0.419217 | −0.209608 | − | 0.977785i | \(-0.567219\pi\) | ||||
−0.209608 | + | 0.977785i | \(0.567219\pi\) | |||||||
\(884\) | 403.542i | 0.456496i | ||||||||
\(885\) | 302.305 | − | 40.2880i | 0.341588 | − | 0.0455232i | ||||
\(886\) | −768.718 | −0.867628 | ||||||||
\(887\) | 797.714i | 0.899339i | 0.893195 | + | 0.449670i | \(0.148458\pi\) | ||||
−0.893195 | + | 0.449670i | \(0.851542\pi\) | |||||||
\(888\) | 35.2879 | + | 264.786i | 0.0397387 | + | 0.298183i | ||||
\(889\) | −268.597 | −0.302134 | ||||||||
\(890\) | − | 154.533i | − | 0.173633i | ||||||
\(891\) | −82.6219 | − | 141.028i | −0.0927294 | − | 0.158280i | ||||
\(892\) | 736.129 | 0.825257 | ||||||||
\(893\) | − | 3336.38i | − | 3.73614i | ||||||
\(894\) | 49.2446 | − | 6.56280i | 0.0550835 | − | 0.00734094i | ||||
\(895\) | 27.6775 | 0.0309246 | ||||||||
\(896\) | 29.9333i | 0.0334077i | ||||||||
\(897\) | −148.431 | − | 1113.76i | −0.165475 | − | 1.24165i | ||||
\(898\) | −977.369 | −1.08838 | ||||||||
\(899\) | − | 1569.47i | − | 1.74580i | ||||||
\(900\) | 86.8589 | − | 23.5699i | 0.0965098 | − | 0.0261888i | ||||
\(901\) | 318.814 | 0.353844 | ||||||||
\(902\) | − | 91.7895i | − | 0.101762i | ||||||
\(903\) | −407.186 | + | 54.2655i | −0.450926 | + | 0.0600947i | ||||
\(904\) | −108.121 | −0.119603 | ||||||||
\(905\) | 124.815i | 0.137917i | ||||||||
\(906\) | 41.0253 | + | 307.837i | 0.0452818 | + | 0.339776i | ||||
\(907\) | −60.6349 | −0.0668522 | −0.0334261 | − | 0.999441i | \(-0.510642\pi\) | ||||
−0.0334261 | + | 0.999441i | \(0.510642\pi\) | |||||||
\(908\) | 623.265i | 0.686415i | ||||||||
\(909\) | 162.356 | + | 598.309i | 0.178610 | + | 0.658206i | ||||
\(910\) | −97.0664 | −0.106666 | ||||||||
\(911\) | 1640.58i | 1.80085i | 0.435009 | + | 0.900426i | \(0.356745\pi\) | ||||
−0.435009 | + | 0.900426i | \(0.643255\pi\) | |||||||
\(912\) | −429.778 | + | 57.2763i | −0.471248 | + | 0.0628029i | ||||
\(913\) | 166.308 | 0.182156 | ||||||||
\(914\) | 45.9530i | 0.0502768i | ||||||||
\(915\) | 24.9406 | + | 187.144i | 0.0272575 | + | 0.204529i | ||||
\(916\) | 242.167 | 0.264374 | ||||||||
\(917\) | − | 593.040i | − | 0.646718i | ||||||
\(918\) | −612.308 | + | 257.053i | −0.667002 | + | 0.280014i | ||||
\(919\) | 904.955 | 0.984717 | 0.492358 | − | 0.870393i | \(-0.336135\pi\) | ||||
0.492358 | + | 0.870393i | \(0.336135\pi\) | |||||||
\(920\) | − | 204.176i | − | 0.221931i | ||||||
\(921\) | −989.990 | + | 131.935i | −1.07491 | + | 0.143252i | ||||
\(922\) | −26.8526 | −0.0291243 | ||||||||
\(923\) | 293.242i | 0.317706i | ||||||||
\(924\) | 4.23157 | + | 31.7520i | 0.00457962 | + | 0.0343636i | ||||
\(925\) | −157.406 | −0.170169 | ||||||||
\(926\) | 1093.14i | 1.18050i | ||||||||
\(927\) | −378.042 | + | 102.585i | −0.407812 | + | 0.110663i | ||||
\(928\) | 261.031 | 0.281283 | ||||||||
\(929\) | − | 320.892i | − | 0.345417i | −0.984973 | − | 0.172709i | \(-0.944748\pi\) | ||
0.984973 | − | 0.172709i | \(-0.0552519\pi\) | |||||||
\(930\) | −319.842 | + | 42.6251i | −0.343916 | + | 0.0458335i | ||||
\(931\) | 252.920 | 0.271665 | ||||||||
\(932\) | − | 376.875i | − | 0.404372i | ||||||
\(933\) | 57.4753 | + | 431.271i | 0.0616027 | + | 0.462242i | ||||
\(934\) | 474.792 | 0.508343 | ||||||||
\(935\) | 78.4726i | 0.0839279i | ||||||||
\(936\) | −77.3432 | − | 285.022i | −0.0826317 | − | 0.304511i | ||||
\(937\) | −862.831 | −0.920845 | −0.460422 | − | 0.887700i | \(-0.652302\pi\) | ||||
−0.460422 | + | 0.887700i | \(0.652302\pi\) | |||||||
\(938\) | 126.255i | 0.134600i | ||||||||
\(939\) | −1028.71 | + | 137.095i | −1.09554 | + | 0.146001i | ||||
\(940\) | 412.956 | 0.439315 | ||||||||
\(941\) | 1297.26i | 1.37859i | 0.724479 | + | 0.689297i | \(0.242080\pi\) | ||||
−0.724479 | + | 0.689297i | \(0.757920\pi\) | |||||||
\(942\) | −162.806 | − | 1221.63i | −0.172831 | − | 1.29685i | ||||
\(943\) | 1038.39 | 1.10115 | ||||||||
\(944\) | − | 181.854i | − | 0.192641i | ||||||
\(945\) | −61.8304 | − | 147.282i | −0.0654290 | − | 0.155854i | ||||
\(946\) | −147.691 | −0.156122 | ||||||||
\(947\) | 969.136i | 1.02337i | 0.859172 | + | 0.511687i | \(0.170979\pi\) | ||||
−0.859172 | + | 0.511687i | \(0.829021\pi\) | |||||||
\(948\) | 195.867 | − | 26.1031i | 0.206611 | − | 0.0275349i | ||||
\(949\) | 563.064 | 0.593324 | ||||||||
\(950\) | − | 255.488i | − | 0.268935i | ||||||
\(951\) | 61.5829 | + | 462.094i | 0.0647560 | + | 0.485903i | ||||
\(952\) | 130.147 | 0.136709 | ||||||||
\(953\) | − | 1341.41i | − | 1.40756i | −0.710416 | − | 0.703782i | \(-0.751493\pi\) | ||
0.710416 | − | 0.703782i | \(-0.248507\pi\) | |||||||
\(954\) | −225.179 | + | 61.1041i | −0.236036 | + | 0.0640504i | ||||
\(955\) | −443.992 | −0.464913 | ||||||||
\(956\) | − | 485.575i | − | 0.507924i | ||||||
\(957\) | 276.891 | − | 36.9011i | 0.289332 | − | 0.0385592i | ||||
\(958\) | 1325.89 | 1.38401 | ||||||||
\(959\) | 323.947i | 0.337797i | ||||||||
\(960\) | −7.08931 | − | 53.1953i | −0.00738470 | − | 0.0554118i | ||||
\(961\) | 195.840 | 0.203788 | ||||||||
\(962\) | 516.520i | 0.536923i | ||||||||
\(963\) | 489.556 | + | 1804.09i | 0.508365 | + | 1.87341i | ||||
\(964\) | 435.859 | 0.452136 | ||||||||
\(965\) | − | 99.8577i | − | 0.103479i | ||||||
\(966\) | −359.201 | + | 47.8705i | −0.371843 | + | 0.0495554i | ||||
\(967\) | −454.329 | −0.469834 | −0.234917 | − | 0.972015i | \(-0.575482\pi\) | ||||
−0.234917 | + | 0.972015i | \(0.575482\pi\) | |||||||
\(968\) | − | 330.723i | − | 0.341656i | ||||||
\(969\) | 249.031 | + | 1868.63i | 0.256998 | + | 1.92841i | ||||
\(970\) | −45.9058 | −0.0473255 | ||||||||
\(971\) | − | 1594.23i | − | 1.64185i | −0.571037 | − | 0.820924i | \(-0.693459\pi\) | ||
0.571037 | − | 0.820924i | \(-0.306541\pi\) | |||||||
\(972\) | 383.207 | − | 298.912i | 0.394246 | − | 0.307523i | ||||
\(973\) | −350.677 | −0.360408 | ||||||||
\(974\) | 1063.83i | 1.09223i | ||||||||
\(975\) | 172.500 | − | 22.9889i | 0.176923 | − | 0.0235784i | ||||
\(976\) | 112.578 | 0.115346 | ||||||||
\(977\) | 544.109i | 0.556918i | 0.960448 | + | 0.278459i | \(0.0898237\pi\) | ||||
−0.960448 | + | 0.278459i | \(0.910176\pi\) | |||||||
\(978\) | −12.7597 | − | 95.7439i | −0.0130468 | − | 0.0978977i | ||||
\(979\) | −98.6087 | −0.100724 | ||||||||
\(980\) | 31.3050i | 0.0319438i | ||||||||
\(981\) | −1319.25 | + | 357.989i | −1.34480 | + | 0.364922i | ||||
\(982\) | −1208.54 | −1.23069 | ||||||||
\(983\) | 605.161i | 0.615627i | 0.951447 | + | 0.307813i | \(0.0995973\pi\) | ||||
−0.951447 | + | 0.307813i | \(0.900403\pi\) | |||||||
\(984\) | 270.538 | − | 36.0544i | 0.274937 | − | 0.0366406i | ||||
\(985\) | 2.13034 | 0.00216278 | ||||||||
\(986\) | − | 1134.93i | − | 1.15105i | ||||||
\(987\) | −96.8205 | − | 726.502i | −0.0980957 | − | 0.736071i | ||||
\(988\) | −838.370 | −0.848553 | ||||||||
\(989\) | − | 1670.79i | − | 1.68937i | ||||||
\(990\) | −15.0401 | − | 55.4253i | −0.0151920 | − | 0.0559851i | ||||
\(991\) | −1002.42 | −1.01152 | −0.505761 | − | 0.862674i | \(-0.668788\pi\) | ||||
−0.505761 | + | 0.862674i | \(0.668788\pi\) | |||||||
\(992\) | 192.403i | 0.193955i | ||||||||
\(993\) | −423.684 | + | 56.4641i | −0.426670 | + | 0.0568621i | ||||
\(994\) | 94.5738 | 0.0951446 | ||||||||
\(995\) | 293.245i | 0.294719i | ||||||||
\(996\) | 65.3249 | + | 490.172i | 0.0655873 | + | 0.492141i | ||||
\(997\) | −9.04315 | −0.00907036 | −0.00453518 | − | 0.999990i | \(-0.501444\pi\) | ||||
−0.00453518 | + | 0.999990i | \(0.501444\pi\) | |||||||
\(998\) | − | 515.725i | − | 0.516759i | ||||||
\(999\) | −783.733 | + | 329.019i | −0.784517 | + | 0.329348i |
(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 | 210.3.e.a.71.9 | yes | 16 | |
3.2 | odd | 2 | inner | 210.3.e.a.71.1 | ✓ | 16 | |
4.3 | odd | 2 | 1680.3.l.c.1121.15 | 16 | |||
5.2 | odd | 4 | 1050.3.c.c.449.12 | 32 | |||
5.3 | odd | 4 | 1050.3.c.c.449.21 | 32 | |||
5.4 | even | 2 | 1050.3.e.d.701.8 | 16 | |||
12.11 | even | 2 | 1680.3.l.c.1121.16 | 16 | |||
15.2 | even | 4 | 1050.3.c.c.449.22 | 32 | |||
15.8 | even | 4 | 1050.3.c.c.449.11 | 32 | |||
15.14 | odd | 2 | 1050.3.e.d.701.16 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.e.a.71.1 | ✓ | 16 | 3.2 | odd | 2 | inner | |
210.3.e.a.71.9 | yes | 16 | 1.1 | even | 1 | trivial | |
1050.3.c.c.449.11 | 32 | 15.8 | even | 4 | |||
1050.3.c.c.449.12 | 32 | 5.2 | odd | 4 | |||
1050.3.c.c.449.21 | 32 | 5.3 | odd | 4 | |||
1050.3.c.c.449.22 | 32 | 15.2 | even | 4 | |||
1050.3.e.d.701.8 | 16 | 5.4 | even | 2 | |||
1050.3.e.d.701.16 | 16 | 15.14 | odd | 2 | |||
1680.3.l.c.1121.15 | 16 | 4.3 | odd | 2 | |||
1680.3.l.c.1121.16 | 16 | 12.11 | even | 2 |