Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [28,3,Mod(15,28)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(28, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("28.15");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 28 = 2^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 28.c (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: | \(0.762944740209\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.1539727.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 3x^{3} - 8x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 15.4 | ||
Root | \(1.35935 - 0.390070i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 28.15 |
Dual form | 28.3.c.a.15.3 |
$q$-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 \(\left(\mathbb{Z}/28\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(17\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.163664 | + | 1.99329i | −0.0818318 | + | 0.996646i | ||||
\(3\) | 1.56028i | 0.520093i | 0.965596 | + | 0.260046i | \(0.0837379\pi\) | ||||
−0.965596 | + | 0.260046i | \(0.916262\pi\) | |||||||
\(4\) | −3.94643 | − | 0.652459i | −0.986607 | − | 0.163115i | ||||
\(5\) | 3.43742 | 0.687484 | 0.343742 | − | 0.939064i | \(-0.388305\pi\) | ||||
0.343742 | + | 0.939064i | \(0.388305\pi\) | |||||||
\(6\) | −3.11009 | − | 0.255361i | −0.518349 | − | 0.0425602i | ||||
\(7\) | − | 2.64575i | − | 0.377964i | ||||||
\(8\) | 1.94643 | − | 7.75960i | 0.243304 | − | 0.969950i | ||||
\(9\) | 6.56553 | 0.729503 | ||||||||
\(10\) | −0.562581 | + | 6.85178i | −0.0562581 | + | 0.685178i | ||||
\(11\) | − | 8.48389i | − | 0.771263i | −0.922653 | − | 0.385631i | \(-0.873984\pi\) | ||
0.922653 | − | 0.385631i | \(-0.126016\pi\) | |||||||
\(12\) | 1.01802 | − | 6.15753i | 0.0848348 | − | 0.513127i | ||||
\(13\) | −18.5685 | −1.42834 | −0.714172 | − | 0.699970i | \(-0.753197\pi\) | ||||
−0.714172 | + | 0.699970i | \(0.753197\pi\) | |||||||
\(14\) | 5.27376 | + | 0.433013i | 0.376697 | + | 0.0309295i | ||||
\(15\) | 5.36333i | 0.357556i | ||||||||
\(16\) | 15.1486 | + | 5.14977i | 0.946787 | + | 0.321860i | ||||
\(17\) | −8.87484 | −0.522049 | −0.261025 | − | 0.965332i | \(-0.584060\pi\) | ||||
−0.261025 | + | 0.965332i | \(0.584060\pi\) | |||||||
\(18\) | −1.07454 | + | 13.0870i | −0.0596966 | + | 0.727057i | ||||
\(19\) | 30.3324i | 1.59644i | 0.602365 | + | 0.798221i | \(0.294225\pi\) | ||||
−0.602365 | + | 0.798221i | \(0.705775\pi\) | |||||||
\(20\) | −13.5655 | − | 2.24278i | −0.678276 | − | 0.112139i | ||||
\(21\) | 4.12811 | 0.196577 | ||||||||
\(22\) | 16.9109 | + | 1.38850i | 0.768676 | + | 0.0631138i | ||||
\(23\) | − | 26.5293i | − | 1.15345i | −0.816938 | − | 0.576725i | \(-0.804330\pi\) | ||
0.816938 | − | 0.576725i | \(-0.195670\pi\) | |||||||
\(24\) | 12.1071 | + | 3.03697i | 0.504464 | + | 0.126540i | ||||
\(25\) | −13.1841 | −0.527366 | ||||||||
\(26\) | 3.03899 | − | 37.0124i | 0.116884 | − | 1.42355i | ||||
\(27\) | 24.2866i | 0.899503i | ||||||||
\(28\) | −1.72624 | + | 10.4413i | −0.0616516 | + | 0.372902i | ||||
\(29\) | 18.6245 | 0.642225 | 0.321112 | − | 0.947041i | \(-0.395943\pi\) | ||||
0.321112 | + | 0.947041i | \(0.395943\pi\) | |||||||
\(30\) | −10.6907 | − | 0.877783i | −0.356356 | − | 0.0292594i | ||||
\(31\) | − | 41.2544i | − | 1.33079i | −0.746493 | − | 0.665393i | \(-0.768264\pi\) | ||
0.746493 | − | 0.665393i | \(-0.231736\pi\) | |||||||
\(32\) | −12.7443 | + | 29.3527i | −0.398258 | + | 0.917273i | ||||
\(33\) | 13.2372 | 0.401128 | ||||||||
\(34\) | 1.45249 | − | 17.6901i | 0.0427203 | − | 0.520298i | ||||
\(35\) | − | 9.09456i | − | 0.259844i | ||||||
\(36\) | −25.9104 | − | 4.28374i | −0.719733 | − | 0.118993i | ||||
\(37\) | −3.49346 | −0.0944178 | −0.0472089 | − | 0.998885i | \(-0.515033\pi\) | ||||
−0.0472089 | + | 0.998885i | \(0.515033\pi\) | |||||||
\(38\) | −60.4613 | − | 4.96431i | −1.59109 | − | 0.130640i | ||||
\(39\) | − | 28.9720i | − | 0.742872i | ||||||
\(40\) | 6.69069 | − | 26.6730i | 0.167267 | − | 0.666825i | ||||
\(41\) | 37.7556 | 0.920868 | 0.460434 | − | 0.887694i | \(-0.347694\pi\) | ||||
0.460434 | + | 0.887694i | \(0.347694\pi\) | |||||||
\(42\) | −0.675622 | + | 8.22853i | −0.0160862 | + | 0.195917i | ||||
\(43\) | 50.8159i | 1.18177i | 0.806757 | + | 0.590883i | \(0.201220\pi\) | ||||
−0.806757 | + | 0.590883i | \(0.798780\pi\) | |||||||
\(44\) | −5.53539 | + | 33.4811i | −0.125804 | + | 0.760933i | ||||
\(45\) | 22.5685 | 0.501522 | ||||||||
\(46\) | 52.8807 | + | 4.34189i | 1.14958 | + | 0.0943889i | ||||
\(47\) | 51.9810i | 1.10598i | 0.833188 | + | 0.552990i | \(0.186513\pi\) | ||||
−0.833188 | + | 0.552990i | \(0.813487\pi\) | |||||||
\(48\) | −8.03507 | + | 23.6360i | −0.167397 | + | 0.492417i | ||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 2.15777 | − | 26.2799i | 0.0431553 | − | 0.525597i | ||||
\(51\) | − | 13.8472i | − | 0.271514i | ||||||
\(52\) | 73.2792 | + | 12.1152i | 1.40921 | + | 0.232984i | ||||
\(53\) | 15.3814 | 0.290215 | 0.145107 | − | 0.989416i | \(-0.453647\pi\) | ||||
0.145107 | + | 0.989416i | \(0.453647\pi\) | |||||||
\(54\) | −48.4102 | − | 3.97483i | −0.896486 | − | 0.0736079i | ||||
\(55\) | − | 29.1627i | − | 0.530231i | ||||||
\(56\) | −20.5300 | − | 5.14977i | −0.366607 | − | 0.0919601i | ||||
\(57\) | −47.3270 | −0.830298 | ||||||||
\(58\) | −3.04816 | + | 37.1241i | −0.0525544 | + | 0.640071i | ||||
\(59\) | 38.3291i | 0.649645i | 0.945775 | + | 0.324823i | \(0.105305\pi\) | ||||
−0.945775 | + | 0.324823i | \(0.894695\pi\) | |||||||
\(60\) | 3.49936 | − | 21.1660i | 0.0583226 | − | 0.352767i | ||||
\(61\) | −72.5744 | −1.18974 | −0.594872 | − | 0.803820i | \(-0.702797\pi\) | ||||
−0.594872 | + | 0.803820i | \(0.702797\pi\) | |||||||
\(62\) | 82.2320 | + | 6.75184i | 1.32632 | + | 0.108901i | ||||
\(63\) | − | 17.3708i | − | 0.275726i | ||||||
\(64\) | −56.4228 | − | 30.2070i | −0.881607 | − | 0.471985i | ||||
\(65\) | −63.8276 | −0.981964 | ||||||||
\(66\) | −2.16645 | + | 26.3857i | −0.0328251 | + | 0.399783i | ||||
\(67\) | − | 32.0834i | − | 0.478856i | −0.970914 | − | 0.239428i | \(-0.923040\pi\) | ||
0.970914 | − | 0.239428i | \(-0.0769599\pi\) | |||||||
\(68\) | 35.0239 | + | 5.79047i | 0.515058 | + | 0.0851539i | ||||
\(69\) | 41.3932 | 0.599901 | ||||||||
\(70\) | 18.1281 | + | 1.48845i | 0.258973 | + | 0.0212635i | ||||
\(71\) | − | 50.6160i | − | 0.712902i | −0.934314 | − | 0.356451i | \(-0.883987\pi\) | ||
0.934314 | − | 0.356451i | \(-0.116013\pi\) | |||||||
\(72\) | 12.7793 | − | 50.9459i | 0.177491 | − | 0.707582i | ||||
\(73\) | −5.48756 | −0.0751720 | −0.0375860 | − | 0.999293i | \(-0.511967\pi\) | ||||
−0.0375860 | + | 0.999293i | \(0.511967\pi\) | |||||||
\(74\) | 0.571752 | − | 6.96348i | 0.00772638 | − | 0.0941011i | ||||
\(75\) | − | 20.5709i | − | 0.274279i | ||||||
\(76\) | 19.7906 | − | 119.705i | 0.260403 | − | 1.57506i | ||||
\(77\) | −22.4463 | −0.291510 | ||||||||
\(78\) | 57.7497 | + | 4.74166i | 0.740380 | + | 0.0607906i | ||||
\(79\) | 39.8894i | 0.504929i | 0.967606 | + | 0.252464i | \(0.0812410\pi\) | ||||
−0.967606 | + | 0.252464i | \(0.918759\pi\) | |||||||
\(80\) | 52.0721 | + | 17.7019i | 0.650901 | + | 0.221274i | ||||
\(81\) | 21.1959 | 0.261678 | ||||||||
\(82\) | −6.17922 | + | 75.2579i | −0.0753563 | + | 0.917779i | ||||
\(83\) | 4.28106i | 0.0515791i | 0.999667 | + | 0.0257895i | \(0.00820997\pi\) | ||||
−0.999667 | + | 0.0257895i | \(0.991790\pi\) | |||||||
\(84\) | −16.2913 | − | 2.69342i | −0.193944 | − | 0.0320646i | ||||
\(85\) | −30.5065 | −0.358901 | ||||||||
\(86\) | −101.291 | − | 8.31672i | −1.17780 | − | 0.0967060i | ||||
\(87\) | 29.0594i | 0.334017i | ||||||||
\(88\) | −65.8316 | − | 16.5133i | −0.748087 | − | 0.187651i | ||||
\(89\) | 123.906 | 1.39220 | 0.696099 | − | 0.717946i | \(-0.254917\pi\) | ||||
0.696099 | + | 0.717946i | \(0.254917\pi\) | |||||||
\(90\) | −3.69364 | + | 44.9856i | −0.0410404 | + | 0.499840i | ||||
\(91\) | 49.1276i | 0.539863i | ||||||||
\(92\) | −17.3093 | + | 104.696i | −0.188145 | + | 1.13800i | ||||
\(93\) | 64.3683 | 0.692132 | ||||||||
\(94\) | −103.613 | − | 8.50740i | −1.10227 | − | 0.0905043i | ||||
\(95\) | 104.265i | 1.09753i | ||||||||
\(96\) | −45.7985 | − | 19.8846i | −0.477067 | − | 0.207131i | ||||
\(97\) | −32.0177 | −0.330079 | −0.165040 | − | 0.986287i | \(-0.552775\pi\) | ||||
−0.165040 | + | 0.986287i | \(0.552775\pi\) | |||||||
\(98\) | 1.14565 | − | 13.9530i | 0.0116903 | − | 0.142378i | ||||
\(99\) | − | 55.7012i | − | 0.562639i | ||||||
\(100\) | 52.0303 | + | 8.60212i | 0.520303 | + | 0.0860212i | ||||
\(101\) | −0.718521 | −0.00711407 | −0.00355703 | − | 0.999994i | \(-0.501132\pi\) | ||||
−0.00355703 | + | 0.999994i | \(0.501132\pi\) | |||||||
\(102\) | 27.6016 | + | 2.26629i | 0.270604 | + | 0.0222185i | ||||
\(103\) | − | 116.453i | − | 1.13062i | −0.824880 | − | 0.565308i | \(-0.808757\pi\) | ||
0.824880 | − | 0.565308i | \(-0.191243\pi\) | |||||||
\(104\) | −36.1422 | + | 144.084i | −0.347521 | + | 1.38542i | ||||
\(105\) | 14.1900 | 0.135143 | ||||||||
\(106\) | −2.51737 | + | 30.6596i | −0.0237488 | + | 0.289241i | ||||
\(107\) | 37.9431i | 0.354608i | 0.984156 | + | 0.177304i | \(0.0567377\pi\) | ||||
−0.984156 | + | 0.177304i | \(0.943262\pi\) | |||||||
\(108\) | 15.8460 | − | 95.8452i | 0.146722 | − | 0.887456i | ||||
\(109\) | 88.2300 | 0.809450 | 0.404725 | − | 0.914438i | \(-0.367367\pi\) | ||||
0.404725 | + | 0.914438i | \(0.367367\pi\) | |||||||
\(110\) | 58.1298 | + | 4.77287i | 0.528452 | + | 0.0433898i | ||||
\(111\) | − | 5.45077i | − | 0.0491060i | ||||||
\(112\) | 13.6250 | − | 40.0794i | 0.121652 | − | 0.357852i | ||||
\(113\) | 125.115 | 1.10721 | 0.553605 | − | 0.832780i | \(-0.313252\pi\) | ||||
0.553605 | + | 0.832780i | \(0.313252\pi\) | |||||||
\(114\) | 7.74571 | − | 94.3366i | 0.0679448 | − | 0.827514i | ||||
\(115\) | − | 91.1925i | − | 0.792978i | ||||||
\(116\) | −73.5003 | − | 12.1517i | −0.633623 | − | 0.104756i | ||||
\(117\) | −121.912 | −1.04198 | ||||||||
\(118\) | −76.4011 | − | 6.27308i | −0.647467 | − | 0.0531617i | ||||
\(119\) | 23.4806i | 0.197316i | ||||||||
\(120\) | 41.6173 | + | 10.4393i | 0.346811 | + | 0.0869945i | ||||
\(121\) | 49.0236 | 0.405154 | ||||||||
\(122\) | 11.8778 | − | 144.662i | 0.0973589 | − | 1.18575i | ||||
\(123\) | 58.9092i | 0.478937i | ||||||||
\(124\) | −26.9168 | + | 162.807i | −0.217071 | + | 1.31296i | ||||
\(125\) | −131.255 | −1.05004 | ||||||||
\(126\) | 34.6250 | + | 2.84296i | 0.274802 | + | 0.0225632i | ||||
\(127\) | 51.8936i | 0.408611i | 0.978907 | + | 0.204305i | \(0.0654936\pi\) | ||||
−0.978907 | + | 0.204305i | \(0.934506\pi\) | |||||||
\(128\) | 69.4458 | − | 107.523i | 0.542545 | − | 0.840027i | ||||
\(129\) | −79.2870 | −0.614628 | ||||||||
\(130\) | 10.4463 | − | 127.227i | 0.0803559 | − | 0.978670i | ||||
\(131\) | − | 242.670i | − | 1.85245i | −0.376976 | − | 0.926223i | \(-0.623036\pi\) | ||
0.376976 | − | 0.926223i | \(-0.376964\pi\) | |||||||
\(132\) | −52.2398 | − | 8.63675i | −0.395756 | − | 0.0654300i | ||||
\(133\) | 80.2520 | 0.603398 | ||||||||
\(134\) | 63.9515 | + | 5.25088i | 0.477250 | + | 0.0391857i | ||||
\(135\) | 83.4831i | 0.618393i | ||||||||
\(136\) | −17.2742 | + | 68.8652i | −0.127016 | + | 0.506362i | ||||
\(137\) | −270.560 | −1.97489 | −0.987444 | − | 0.157970i | \(-0.949505\pi\) | ||||
−0.987444 | + | 0.157970i | \(0.949505\pi\) | |||||||
\(138\) | −6.77456 | + | 82.5087i | −0.0490910 | + | 0.597889i | ||||
\(139\) | − | 15.6948i | − | 0.112912i | −0.998405 | − | 0.0564562i | \(-0.982020\pi\) | ||
0.998405 | − | 0.0564562i | \(-0.0179801\pi\) | |||||||
\(140\) | −5.93383 | + | 35.8910i | −0.0423845 | + | 0.256364i | ||||
\(141\) | −81.1049 | −0.575212 | ||||||||
\(142\) | 100.893 | + | 8.28400i | 0.710511 | + | 0.0583381i | ||||
\(143\) | 157.533i | 1.10163i | ||||||||
\(144\) | 99.4585 | + | 33.8109i | 0.690684 | + | 0.234798i | ||||
\(145\) | 64.0203 | 0.441519 | ||||||||
\(146\) | 0.898114 | − | 10.9383i | 0.00615147 | − | 0.0749199i | ||||
\(147\) | − | 10.9220i | − | 0.0742990i | ||||||
\(148\) | 13.7867 | + | 2.27934i | 0.0931532 | + | 0.0154009i | ||||
\(149\) | 24.4627 | 0.164179 | 0.0820895 | − | 0.996625i | \(-0.473841\pi\) | ||||
0.0820895 | + | 0.996625i | \(0.473841\pi\) | |||||||
\(150\) | 41.0039 | + | 3.36672i | 0.273359 | + | 0.0224448i | ||||
\(151\) | 189.391i | 1.25425i | 0.778920 | + | 0.627124i | \(0.215768\pi\) | ||||
−0.778920 | + | 0.627124i | \(0.784232\pi\) | |||||||
\(152\) | 235.367 | + | 59.0398i | 1.54847 | + | 0.388420i | ||||
\(153\) | −58.2680 | −0.380837 | ||||||||
\(154\) | 3.67364 | − | 44.7420i | 0.0238548 | − | 0.290532i | ||||
\(155\) | − | 141.809i | − | 0.914894i | ||||||
\(156\) | −18.9030 | + | 114.336i | −0.121173 | + | 0.732923i | ||||
\(157\) | 101.743 | 0.648047 | 0.324024 | − | 0.946049i | \(-0.394964\pi\) | ||||
0.324024 | + | 0.946049i | \(0.394964\pi\) | |||||||
\(158\) | −79.5112 | − | 6.52844i | −0.503235 | − | 0.0413192i | ||||
\(159\) | 23.9992i | 0.150939i | ||||||||
\(160\) | −43.8074 | + | 100.898i | −0.273796 | + | 0.630611i | ||||
\(161\) | −70.1900 | −0.435963 | ||||||||
\(162\) | −3.46901 | + | 42.2497i | −0.0214136 | + | 0.260801i | ||||
\(163\) | − | 68.5832i | − | 0.420756i | −0.977620 | − | 0.210378i | \(-0.932531\pi\) | ||
0.977620 | − | 0.210378i | \(-0.0674695\pi\) | |||||||
\(164\) | −149.000 | − | 24.6340i | −0.908535 | − | 0.150207i | ||||
\(165\) | 45.5019 | 0.275769 | ||||||||
\(166\) | −8.53341 | − | 0.700654i | −0.0514061 | − | 0.00422081i | ||||
\(167\) | − | 55.7795i | − | 0.334009i | −0.985956 | − | 0.167004i | \(-0.946591\pi\) | ||
0.985956 | − | 0.167004i | \(-0.0534094\pi\) | |||||||
\(168\) | 8.03507 | − | 32.0325i | 0.0478278 | − | 0.190670i | ||||
\(169\) | 175.788 | 1.04017 | ||||||||
\(170\) | 4.99281 | − | 60.8085i | 0.0293695 | − | 0.357697i | ||||
\(171\) | 199.148i | 1.16461i | ||||||||
\(172\) | 33.1553 | − | 200.541i | 0.192763 | − | 1.16594i | ||||
\(173\) | 19.2284 | 0.111147 | 0.0555734 | − | 0.998455i | \(-0.482301\pi\) | ||||
0.0555734 | + | 0.998455i | \(0.482301\pi\) | |||||||
\(174\) | −57.9240 | − | 4.75597i | −0.332896 | − | 0.0273332i | ||||
\(175\) | 34.8820i | 0.199326i | ||||||||
\(176\) | 43.6901 | − | 128.519i | 0.248239 | − | 0.730222i | ||||
\(177\) | −59.8041 | −0.337876 | ||||||||
\(178\) | −20.2788 | + | 246.980i | −0.113926 | + | 1.38753i | ||||
\(179\) | − | 195.745i | − | 1.09355i | −0.837280 | − | 0.546774i | \(-0.815856\pi\) | ||
0.837280 | − | 0.546774i | \(-0.184144\pi\) | |||||||
\(180\) | −89.0649 | − | 14.7250i | −0.494805 | − | 0.0818056i | ||||
\(181\) | 82.5482 | 0.456067 | 0.228034 | − | 0.973653i | \(-0.426770\pi\) | ||||
0.228034 | + | 0.973653i | \(0.426770\pi\) | |||||||
\(182\) | −97.9256 | − | 8.04040i | −0.538053 | − | 0.0441780i | ||||
\(183\) | − | 113.236i | − | 0.618777i | ||||||
\(184\) | −205.857 | − | 51.6375i | −1.11879 | − | 0.280638i | ||||
\(185\) | −12.0085 | −0.0649107 | ||||||||
\(186\) | −10.5348 | + | 128.305i | −0.0566384 | + | 0.689811i | ||||
\(187\) | 75.2932i | 0.402637i | ||||||||
\(188\) | 33.9155 | − | 205.139i | 0.180402 | − | 1.09117i | ||||
\(189\) | 64.2562 | 0.339980 | ||||||||
\(190\) | −207.831 | − | 17.0644i | −1.09385 | − | 0.0898127i | ||||
\(191\) | 159.670i | 0.835968i | 0.908454 | + | 0.417984i | \(0.137263\pi\) | ||||
−0.908454 | + | 0.417984i | \(0.862737\pi\) | |||||||
\(192\) | 47.1314 | − | 88.0354i | 0.245476 | − | 0.458517i | ||||
\(193\) | 106.455 | 0.551583 | 0.275791 | − | 0.961218i | \(-0.411060\pi\) | ||||
0.275791 | + | 0.961218i | \(0.411060\pi\) | |||||||
\(194\) | 5.24013 | − | 63.8206i | 0.0270110 | − | 0.328972i | ||||
\(195\) | − | 99.5889i | − | 0.510712i | ||||||
\(196\) | 27.6250 | + | 4.56721i | 0.140944 | + | 0.0233021i | ||||
\(197\) | −177.868 | −0.902881 | −0.451441 | − | 0.892301i | \(-0.649090\pi\) | ||||
−0.451441 | + | 0.892301i | \(0.649090\pi\) | |||||||
\(198\) | 111.029 | + | 9.11627i | 0.560752 | + | 0.0460418i | ||||
\(199\) | − | 267.633i | − | 1.34489i | −0.740148 | − | 0.672444i | \(-0.765244\pi\) | ||
0.740148 | − | 0.672444i | \(-0.234756\pi\) | |||||||
\(200\) | −25.6620 | + | 102.304i | −0.128310 | + | 0.511519i | ||||
\(201\) | 50.0590 | 0.249050 | ||||||||
\(202\) | 0.117596 | − | 1.43222i | 0.000582157 | − | 0.00709021i | ||||
\(203\) | − | 49.2758i | − | 0.242738i | ||||||
\(204\) | −9.03475 | + | 54.6471i | −0.0442880 | + | 0.267878i | ||||
\(205\) | 129.782 | 0.633082 | ||||||||
\(206\) | 232.126 | + | 19.0592i | 1.12682 | + | 0.0925204i | ||||
\(207\) | − | 174.179i | − | 0.841445i | ||||||
\(208\) | −281.286 | − | 95.6233i | −1.35234 | − | 0.459727i | ||||
\(209\) | 257.337 | 1.23128 | ||||||||
\(210\) | −2.32239 | + | 28.2849i | −0.0110590 | + | 0.134690i | ||||
\(211\) | 162.784i | 0.771487i | 0.922606 | + | 0.385744i | \(0.126055\pi\) | ||||
−0.922606 | + | 0.385744i | \(0.873945\pi\) | |||||||
\(212\) | −60.7015 | − | 10.0357i | −0.286328 | − | 0.0473383i | ||||
\(213\) | 78.9751 | 0.370775 | ||||||||
\(214\) | −75.6317 | − | 6.20991i | −0.353419 | − | 0.0290183i | ||||
\(215\) | 174.676i | 0.812445i | ||||||||
\(216\) | 188.454 | + | 47.2721i | 0.872473 | + | 0.218852i | ||||
\(217\) | −109.149 | −0.502990 | ||||||||
\(218\) | −14.4401 | + | 175.868i | −0.0662388 | + | 0.806735i | ||||
\(219\) | − | 8.56212i | − | 0.0390965i | ||||||
\(220\) | −19.0275 | + | 115.088i | −0.0864885 | + | 0.523129i | ||||
\(221\) | 164.792 | 0.745666 | ||||||||
\(222\) | 10.8650 | + | 0.892093i | 0.0489413 | + | 0.00401844i | ||||
\(223\) | 317.727i | 1.42479i | 0.701780 | + | 0.712393i | \(0.252389\pi\) | ||||
−0.701780 | + | 0.712393i | \(0.747611\pi\) | |||||||
\(224\) | 77.6601 | + | 33.7181i | 0.346697 | + | 0.150527i | ||||
\(225\) | −86.5609 | −0.384715 | ||||||||
\(226\) | −20.4767 | + | 249.390i | −0.0906050 | + | 1.10350i | ||||
\(227\) | − | 116.168i | − | 0.511754i | −0.966709 | − | 0.255877i | \(-0.917636\pi\) | ||
0.966709 | − | 0.255877i | \(-0.0823642\pi\) | |||||||
\(228\) | 186.773 | + | 30.8789i | 0.819178 | + | 0.135434i | ||||
\(229\) | −357.643 | −1.56176 | −0.780880 | − | 0.624681i | \(-0.785229\pi\) | ||||
−0.780880 | + | 0.624681i | \(0.785229\pi\) | |||||||
\(230\) | 181.773 | + | 14.9249i | 0.790319 | + | 0.0648908i | ||||
\(231\) | − | 35.0224i | − | 0.151612i | ||||||
\(232\) | 36.2513 | − | 144.519i | 0.156256 | − | 0.622926i | ||||
\(233\) | −402.307 | −1.72664 | −0.863319 | − | 0.504658i | \(-0.831618\pi\) | ||||
−0.863319 | + | 0.504658i | \(0.831618\pi\) | |||||||
\(234\) | 19.9525 | − | 243.006i | 0.0852673 | − | 1.03849i | ||||
\(235\) | 178.681i | 0.760343i | ||||||||
\(236\) | 25.0082 | − | 151.263i | 0.105967 | − | 0.640945i | ||||
\(237\) | −62.2385 | −0.262610 | ||||||||
\(238\) | −46.8037 | − | 3.84292i | −0.196654 | − | 0.0161467i | ||||
\(239\) | 241.476i | 1.01036i | 0.863014 | + | 0.505179i | \(0.168574\pi\) | ||||
−0.863014 | + | 0.505179i | \(0.831426\pi\) | |||||||
\(240\) | −27.6199 | + | 81.2470i | −0.115083 | + | 0.338529i | ||||
\(241\) | −116.678 | −0.484143 | −0.242071 | − | 0.970258i | \(-0.577827\pi\) | ||||
−0.242071 | + | 0.970258i | \(0.577827\pi\) | |||||||
\(242\) | −8.02338 | + | 97.7183i | −0.0331545 | + | 0.403795i | ||||
\(243\) | 251.651i | 1.03560i | ||||||||
\(244\) | 286.410 | + | 47.3518i | 1.17381 | + | 0.194065i | ||||
\(245\) | −24.0619 | −0.0982120 | ||||||||
\(246\) | −117.423 | − | 9.64130i | −0.477331 | − | 0.0391923i | ||||
\(247\) | − | 563.226i | − | 2.28027i | ||||||
\(248\) | −320.117 | − | 80.2986i | −1.29080 | − | 0.323785i | ||||
\(249\) | −6.67965 | −0.0268259 | ||||||||
\(250\) | 21.4817 | − | 261.629i | 0.0859266 | − | 1.04652i | ||||
\(251\) | − | 7.21755i | − | 0.0287552i | −0.999897 | − | 0.0143776i | \(-0.995423\pi\) | ||
0.999897 | − | 0.0143776i | \(-0.00457669\pi\) | |||||||
\(252\) | −11.3337 | + | 68.5525i | −0.0449750 | + | 0.272034i | ||||
\(253\) | −225.072 | −0.889613 | ||||||||
\(254\) | −103.439 | − | 8.49309i | −0.407240 | − | 0.0334374i | ||||
\(255\) | − | 47.5987i | − | 0.186662i | ||||||
\(256\) | 202.960 | + | 156.023i | 0.792812 | + | 0.609466i | ||||
\(257\) | 380.233 | 1.47951 | 0.739754 | − | 0.672878i | \(-0.234942\pi\) | ||||
0.739754 | + | 0.672878i | \(0.234942\pi\) | |||||||
\(258\) | 12.9764 | − | 158.042i | 0.0502961 | − | 0.612567i | ||||
\(259\) | 9.24282i | 0.0356866i | ||||||||
\(260\) | 251.891 | + | 41.6449i | 0.968812 | + | 0.160173i | ||||
\(261\) | 122.280 | 0.468505 | ||||||||
\(262\) | 483.713 | + | 39.7163i | 1.84623 | + | 0.151589i | ||||
\(263\) | − | 313.354i | − | 1.19146i | −0.803184 | − | 0.595731i | \(-0.796863\pi\) | ||
0.803184 | − | 0.595731i | \(-0.203137\pi\) | |||||||
\(264\) | 25.7653 | − | 102.716i | 0.0975960 | − | 0.389075i | ||||
\(265\) | 52.8723 | 0.199518 | ||||||||
\(266\) | −13.1343 | + | 159.966i | −0.0493772 | + | 0.601375i | ||||
\(267\) | 193.327i | 0.724072i | ||||||||
\(268\) | −20.9331 | + | 126.615i | −0.0781085 | + | 0.472443i | ||||
\(269\) | −170.127 | −0.632442 | −0.316221 | − | 0.948686i | \(-0.602414\pi\) | ||||
−0.316221 | + | 0.948686i | \(0.602414\pi\) | |||||||
\(270\) | −166.406 | − | 13.6632i | −0.616319 | − | 0.0506043i | ||||
\(271\) | − | 50.3103i | − | 0.185647i | −0.995683 | − | 0.0928234i | \(-0.970411\pi\) | ||
0.995683 | − | 0.0928234i | \(-0.0295892\pi\) | |||||||
\(272\) | −134.441 | − | 45.7033i | −0.494270 | − | 0.168027i | ||||
\(273\) | −76.6527 | −0.280779 | ||||||||
\(274\) | 44.2808 | − | 539.304i | 0.161609 | − | 1.96826i | ||||
\(275\) | 111.853i | 0.406738i | ||||||||
\(276\) | −163.355 | − | 27.0074i | −0.591867 | − | 0.0978527i | ||||
\(277\) | 58.9777 | 0.212916 | 0.106458 | − | 0.994317i | \(-0.466049\pi\) | ||||
0.106458 | + | 0.994317i | \(0.466049\pi\) | |||||||
\(278\) | 31.2844 | + | 2.56867i | 0.112534 | + | 0.00923983i | ||||
\(279\) | − | 270.857i | − | 0.970812i | ||||||
\(280\) | −70.5701 | − | 17.7019i | −0.252036 | − | 0.0632211i | ||||
\(281\) | 325.523 | 1.15844 | 0.579222 | − | 0.815170i | \(-0.303356\pi\) | ||||
0.579222 | + | 0.815170i | \(0.303356\pi\) | |||||||
\(282\) | 13.2739 | − | 161.666i | 0.0470706 | − | 0.573283i | ||||
\(283\) | − | 282.815i | − | 0.999348i | −0.866214 | − | 0.499674i | \(-0.833453\pi\) | ||
0.866214 | − | 0.499674i | \(-0.166547\pi\) | |||||||
\(284\) | −33.0249 | + | 199.753i | −0.116285 | + | 0.703354i | ||||
\(285\) | −162.683 | −0.570817 | ||||||||
\(286\) | −314.009 | − | 25.7824i | −1.09793 | − | 0.0901483i | ||||
\(287\) | − | 99.8919i | − | 0.348055i | ||||||
\(288\) | −83.6728 | + | 192.716i | −0.290531 | + | 0.669154i | ||||
\(289\) | −210.237 | −0.727464 | ||||||||
\(290\) | −10.4778 | + | 127.611i | −0.0361303 | + | 0.440038i | ||||
\(291\) | − | 49.9565i | − | 0.171672i | ||||||
\(292\) | 21.6563 | + | 3.58041i | 0.0741653 | + | 0.0122617i | ||||
\(293\) | 47.5056 | 0.162135 | 0.0810676 | − | 0.996709i | \(-0.474167\pi\) | ||||
0.0810676 | + | 0.996709i | \(0.474167\pi\) | |||||||
\(294\) | 21.7706 | + | 1.78753i | 0.0740498 | + | 0.00608002i | ||||
\(295\) | 131.753i | 0.446621i | ||||||||
\(296\) | −6.79976 | + | 27.1078i | −0.0229722 | + | 0.0915805i | ||||
\(297\) | 206.045 | 0.693753 | ||||||||
\(298\) | −4.00365 | + | 48.7613i | −0.0134351 | + | 0.163628i | ||||
\(299\) | 492.610i | 1.64752i | ||||||||
\(300\) | −13.4217 | + | 81.1818i | −0.0447390 | + | 0.270606i | ||||
\(301\) | 134.446 | 0.446665 | ||||||||
\(302\) | −377.512 | − | 30.9965i | −1.25004 | − | 0.102637i | ||||
\(303\) | − | 1.12109i | − | 0.00369998i | ||||||
\(304\) | −156.205 | + | 459.493i | −0.513831 | + | 1.51149i | ||||
\(305\) | −249.469 | −0.817930 | ||||||||
\(306\) | 9.53636 | − | 116.145i | 0.0311646 | − | 0.379559i | ||||
\(307\) | 349.978i | 1.13999i | 0.821647 | + | 0.569997i | \(0.193055\pi\) | ||||
−0.821647 | + | 0.569997i | \(0.806945\pi\) | |||||||
\(308\) | 88.5826 | + | 14.6453i | 0.287606 | + | 0.0475496i | ||||
\(309\) | 181.700 | 0.588026 | ||||||||
\(310\) | 282.666 | + | 23.2089i | 0.911825 | + | 0.0748674i | ||||
\(311\) | 344.941i | 1.10914i | 0.832138 | + | 0.554568i | \(0.187116\pi\) | ||||
−0.832138 | + | 0.554568i | \(0.812884\pi\) | |||||||
\(312\) | −224.811 | − | 56.3919i | −0.720549 | − | 0.180743i | ||||
\(313\) | 281.520 | 0.899424 | 0.449712 | − | 0.893174i | \(-0.351527\pi\) | ||||
0.449712 | + | 0.893174i | \(0.351527\pi\) | |||||||
\(314\) | −16.6517 | + | 202.804i | −0.0530309 | + | 0.645874i | ||||
\(315\) | − | 59.7106i | − | 0.189557i | ||||||
\(316\) | 26.0262 | − | 157.420i | 0.0823613 | − | 0.498166i | ||||
\(317\) | 525.202 | 1.65679 | 0.828394 | − | 0.560146i | \(-0.189255\pi\) | ||||
0.828394 | + | 0.560146i | \(0.189255\pi\) | |||||||
\(318\) | −47.8375 | − | 3.92780i | −0.150432 | − | 0.0123516i | ||||
\(319\) | − | 158.008i | − | 0.495324i | ||||||
\(320\) | −193.949 | − | 103.834i | −0.606090 | − | 0.324482i | ||||
\(321\) | −59.2018 | −0.184429 | ||||||||
\(322\) | 11.4876 | − | 139.909i | 0.0356757 | − | 0.434501i | ||||
\(323\) | − | 269.195i | − | 0.833421i | ||||||
\(324\) | −83.6483 | − | 13.8295i | −0.258174 | − | 0.0426836i | ||||
\(325\) | 244.810 | 0.753260 | ||||||||
\(326\) | 136.706 | + | 11.2246i | 0.419345 | + | 0.0344312i | ||||
\(327\) | 137.663i | 0.420989i | ||||||||
\(328\) | 73.4885 | − | 292.968i | 0.224050 | − | 0.893196i | ||||
\(329\) | 137.529 | 0.418021 | ||||||||
\(330\) | −7.44701 | + | 90.6987i | −0.0225667 | + | 0.274844i | ||||
\(331\) | − | 177.187i | − | 0.535309i | −0.963515 | − | 0.267655i | \(-0.913751\pi\) | ||
0.963515 | − | 0.267655i | \(-0.0862486\pi\) | |||||||
\(332\) | 2.79322 | − | 16.8949i | 0.00841331 | − | 0.0508883i | ||||
\(333\) | −22.9364 | −0.0688781 | ||||||||
\(334\) | 111.185 | + | 9.12907i | 0.332889 | + | 0.0273326i | ||||
\(335\) | − | 110.284i | − | 0.329206i | ||||||
\(336\) | 62.5351 | + | 21.2588i | 0.186116 | + | 0.0632702i | ||||
\(337\) | −111.377 | −0.330495 | −0.165247 | − | 0.986252i | \(-0.552842\pi\) | ||||
−0.165247 | + | 0.986252i | \(0.552842\pi\) | |||||||
\(338\) | −28.7702 | + | 350.398i | −0.0851188 | + | 1.03668i | ||||
\(339\) | 195.214i | 0.575852i | ||||||||
\(340\) | 120.392 | + | 19.9043i | 0.354094 | + | 0.0585420i | ||||
\(341\) | −349.997 | −1.02639 | ||||||||
\(342\) | −396.961 | − | 32.5933i | −1.16070 | − | 0.0953021i | ||||
\(343\) | 18.5203i | 0.0539949i | ||||||||
\(344\) | 394.311 | + | 98.9095i | 1.14625 | + | 0.287528i | ||||
\(345\) | 142.286 | 0.412422 | ||||||||
\(346\) | −3.14699 | + | 38.3278i | −0.00909534 | + | 0.110774i | ||||
\(347\) | 52.1533i | 0.150298i | 0.997172 | + | 0.0751488i | \(0.0239432\pi\) | ||||
−0.997172 | + | 0.0751488i | \(0.976057\pi\) | |||||||
\(348\) | 18.9601 | − | 114.681i | 0.0544830 | − | 0.329543i | ||||
\(349\) | −419.921 | −1.20321 | −0.601606 | − | 0.798793i | \(-0.705472\pi\) | ||||
−0.601606 | + | 0.798793i | \(0.705472\pi\) | |||||||
\(350\) | −69.5300 | − | 5.70891i | −0.198657 | − | 0.0163112i | ||||
\(351\) | − | 450.965i | − | 1.28480i | ||||||
\(352\) | 249.026 | + | 108.121i | 0.707459 | + | 0.307162i | ||||
\(353\) | −198.456 | −0.562198 | −0.281099 | − | 0.959679i | \(-0.590699\pi\) | ||||
−0.281099 | + | 0.959679i | \(0.590699\pi\) | |||||||
\(354\) | 9.78775 | − | 119.207i | 0.0276490 | − | 0.336743i | ||||
\(355\) | − | 173.989i | − | 0.490108i | ||||||
\(356\) | −488.985 | − | 80.8433i | −1.37355 | − | 0.227088i | ||||
\(357\) | −36.6363 | −0.102623 | ||||||||
\(358\) | 390.177 | + | 32.0363i | 1.08988 | + | 0.0894870i | ||||
\(359\) | 234.090i | 0.652063i | 0.945359 | + | 0.326031i | \(0.105711\pi\) | ||||
−0.945359 | + | 0.326031i | \(0.894289\pi\) | |||||||
\(360\) | 43.9279 | − | 175.122i | 0.122022 | − | 0.486451i | ||||
\(361\) | −559.054 | −1.54863 | ||||||||
\(362\) | −13.5101 | + | 164.543i | −0.0373208 | + | 0.454538i | ||||
\(363\) | 76.4905i | 0.210718i | ||||||||
\(364\) | 32.0537 | − | 193.878i | 0.0880597 | − | 0.532633i | ||||
\(365\) | −18.8630 | −0.0516796 | ||||||||
\(366\) | 225.713 | + | 18.5327i | 0.616702 | + | 0.0506357i | ||||
\(367\) | − | 369.480i | − | 1.00676i | −0.864066 | − | 0.503379i | \(-0.832090\pi\) | ||
0.864066 | − | 0.503379i | \(-0.167910\pi\) | |||||||
\(368\) | 136.620 | − | 401.882i | 0.371250 | − | 1.09207i | ||||
\(369\) | 247.885 | 0.671776 | ||||||||
\(370\) | 1.96535 | − | 23.9364i | 0.00531176 | − | 0.0646930i | ||||
\(371\) | − | 40.6953i | − | 0.109691i | ||||||
\(372\) | −254.025 | − | 41.9977i | −0.682863 | − | 0.112897i | ||||
\(373\) | −280.481 | −0.751960 | −0.375980 | − | 0.926628i | \(-0.622694\pi\) | ||||
−0.375980 | + | 0.926628i | \(0.622694\pi\) | |||||||
\(374\) | −150.081 | − | 12.3228i | −0.401287 | − | 0.0329485i | ||||
\(375\) | − | 204.794i | − | 0.546118i | ||||||
\(376\) | 403.352 | + | 101.177i | 1.07274 | + | 0.269089i | ||||
\(377\) | −345.829 | −0.917318 | ||||||||
\(378\) | −10.5164 | + | 128.081i | −0.0278212 | + | 0.338840i | ||||
\(379\) | 259.908i | 0.685772i | 0.939377 | + | 0.342886i | \(0.111404\pi\) | ||||
−0.939377 | + | 0.342886i | \(0.888596\pi\) | |||||||
\(380\) | 68.0288 | − | 411.475i | 0.179023 | − | 1.08283i | ||||
\(381\) | −80.9685 | −0.212516 | ||||||||
\(382\) | −318.269 | − | 26.1322i | −0.833164 | − | 0.0684088i | ||||
\(383\) | − | 412.996i | − | 1.07832i | −0.842203 | − | 0.539160i | \(-0.818742\pi\) | ||
0.842203 | − | 0.539160i | \(-0.181258\pi\) | |||||||
\(384\) | 167.767 | + | 108.355i | 0.436892 | + | 0.282174i | ||||
\(385\) | −77.1572 | −0.200408 | ||||||||
\(386\) | −17.4229 | + | 212.197i | −0.0451370 | + | 0.549733i | ||||
\(387\) | 333.633i | 0.862102i | ||||||||
\(388\) | 126.356 | + | 20.8902i | 0.325659 | + | 0.0538408i | ||||
\(389\) | 348.842 | 0.896766 | 0.448383 | − | 0.893842i | \(-0.352000\pi\) | ||||
0.448383 | + | 0.893842i | \(0.352000\pi\) | |||||||
\(390\) | 198.510 | + | 16.2991i | 0.509000 | + | 0.0417925i | ||||
\(391\) | 235.444i | 0.602158i | ||||||||
\(392\) | −13.6250 | + | 54.3172i | −0.0347577 | + | 0.138564i | ||||
\(393\) | 378.634 | 0.963444 | ||||||||
\(394\) | 29.1105 | − | 354.542i | 0.0738844 | − | 0.899853i | ||||
\(395\) | 137.116i | 0.347130i | ||||||||
\(396\) | −36.3428 | + | 219.821i | −0.0917747 | + | 0.555103i | ||||
\(397\) | 33.6988 | 0.0848836 | 0.0424418 | − | 0.999099i | \(-0.486486\pi\) | ||||
0.0424418 | + | 0.999099i | \(0.486486\pi\) | |||||||
\(398\) | 533.470 | + | 43.8018i | 1.34038 | + | 0.110055i | ||||
\(399\) | 125.215i | 0.313823i | ||||||||
\(400\) | −199.721 | − | 67.8953i | −0.499303 | − | 0.169738i | ||||
\(401\) | 140.120 | 0.349426 | 0.174713 | − | 0.984619i | \(-0.444100\pi\) | ||||
0.174713 | + | 0.984619i | \(0.444100\pi\) | |||||||
\(402\) | −8.19284 | + | 99.7822i | −0.0203802 | + | 0.248214i | ||||
\(403\) | 766.031i | 1.90082i | ||||||||
\(404\) | 2.83559 | + | 0.468805i | 0.00701879 | + | 0.00116041i | ||||
\(405\) | 72.8593 | 0.179900 | ||||||||
\(406\) | 98.2211 | + | 8.06466i | 0.241924 | + | 0.0198637i | ||||
\(407\) | 29.6381i | 0.0728209i | ||||||||
\(408\) | −107.449 | − | 26.9526i | −0.263355 | − | 0.0660604i | ||||
\(409\) | −707.963 | −1.73096 | −0.865480 | − | 0.500943i | \(-0.832987\pi\) | ||||
−0.865480 | + | 0.500943i | \(0.832987\pi\) | |||||||
\(410\) | −21.2406 | + | 258.693i | −0.0518062 | + | 0.630958i | ||||
\(411\) | − | 422.148i | − | 1.02713i | ||||||
\(412\) | −75.9811 | + | 459.575i | −0.184420 | + | 1.11547i | ||||
\(413\) | 101.409 | 0.245543 | ||||||||
\(414\) | 347.190 | + | 28.5068i | 0.838623 | + | 0.0688570i | ||||
\(415\) | 14.7158i | 0.0354598i | ||||||||
\(416\) | 236.642 | − | 545.036i | 0.568850 | − | 1.31018i | ||||
\(417\) | 24.4883 | 0.0587250 | ||||||||
\(418\) | −42.1167 | + | 512.947i | −0.100758 | + | 1.22715i | ||||
\(419\) | − | 596.341i | − | 1.42325i | −0.702560 | − | 0.711625i | \(-0.747960\pi\) | ||
0.702560 | − | 0.711625i | \(-0.252040\pi\) | |||||||
\(420\) | −56.0000 | − | 9.25842i | −0.133333 | − | 0.0220439i | ||||
\(421\) | −162.813 | −0.386728 | −0.193364 | − | 0.981127i | \(-0.561940\pi\) | ||||
−0.193364 | + | 0.981127i | \(0.561940\pi\) | |||||||
\(422\) | −324.476 | − | 26.6418i | −0.768900 | − | 0.0631322i | ||||
\(423\) | 341.283i | 0.806815i | ||||||||
\(424\) | 29.9388 | − | 119.353i | 0.0706103 | − | 0.281494i | ||||
\(425\) | 117.007 | 0.275311 | ||||||||
\(426\) | −12.9254 | + | 157.420i | −0.0303412 | + | 0.369532i | ||||
\(427\) | 192.014i | 0.449681i | ||||||||
\(428\) | 24.7563 | − | 149.740i | 0.0578419 | − | 0.349859i | ||||
\(429\) | −245.795 | −0.572950 | ||||||||
\(430\) | −348.180 | − | 28.5880i | −0.809720 | − | 0.0664838i | ||||
\(431\) | 386.832i | 0.897522i | 0.893652 | + | 0.448761i | \(0.148135\pi\) | ||||
−0.893652 | + | 0.448761i | \(0.851865\pi\) | |||||||
\(432\) | −125.070 | + | 367.907i | −0.289514 | + | 0.851637i | ||||
\(433\) | 574.844 | 1.32758 | 0.663792 | − | 0.747918i | \(-0.268946\pi\) | ||||
0.663792 | + | 0.747918i | \(0.268946\pi\) | |||||||
\(434\) | 17.8637 | − | 217.565i | 0.0411606 | − | 0.501303i | ||||
\(435\) | 99.8895i | 0.229631i | ||||||||
\(436\) | −348.194 | − | 57.5665i | −0.798609 | − | 0.132033i | ||||
\(437\) | 804.699 | 1.84142 | ||||||||
\(438\) | 17.0668 | + | 1.40131i | 0.0389653 | + | 0.00319933i | ||||
\(439\) | − | 295.206i | − | 0.672450i | −0.941782 | − | 0.336225i | \(-0.890850\pi\) | ||
0.941782 | − | 0.336225i | \(-0.109150\pi\) | |||||||
\(440\) | −226.291 | − | 56.7631i | −0.514297 | − | 0.129007i | ||||
\(441\) | −45.9587 | −0.104215 | ||||||||
\(442\) | −26.9705 | + | 328.479i | −0.0610192 | + | 0.743165i | ||||
\(443\) | − | 426.510i | − | 0.962776i | −0.876508 | − | 0.481388i | \(-0.840133\pi\) | ||
0.876508 | − | 0.481388i | \(-0.159867\pi\) | |||||||
\(444\) | −3.55640 | + | 21.5111i | −0.00800992 | + | 0.0484483i | ||||
\(445\) | 425.916 | 0.957114 | ||||||||
\(446\) | −633.324 | − | 52.0004i | −1.42001 | − | 0.116593i | ||||
\(447\) | 38.1686i | 0.0853884i | ||||||||
\(448\) | −79.9203 | + | 149.281i | −0.178393 | + | 0.333216i | ||||
\(449\) | −458.779 | −1.02178 | −0.510889 | − | 0.859646i | \(-0.670684\pi\) | ||||
−0.510889 | + | 0.859646i | \(0.670684\pi\) | |||||||
\(450\) | 14.1669 | − | 172.541i | 0.0314819 | − | 0.383425i | ||||
\(451\) | − | 320.314i | − | 0.710231i | ||||||
\(452\) | −493.756 | − | 81.6322i | −1.09238 | − | 0.180602i | ||||
\(453\) | −295.503 | −0.652325 | ||||||||
\(454\) | 231.557 | + | 19.0125i | 0.510038 | + | 0.0418778i | ||||
\(455\) | 168.872i | 0.371147i | ||||||||
\(456\) | −92.1186 | + | 367.239i | −0.202015 | + | 0.805348i | ||||
\(457\) | 384.429 | 0.841202 | 0.420601 | − | 0.907246i | \(-0.361819\pi\) | ||||
0.420601 | + | 0.907246i | \(0.361819\pi\) | |||||||
\(458\) | 58.5332 | − | 712.887i | 0.127802 | − | 1.55652i | ||||
\(459\) | − | 215.539i | − | 0.469585i | ||||||
\(460\) | −59.4994 | + | 359.885i | −0.129346 | + | 0.782358i | ||||
\(461\) | −48.0796 | −0.104294 | −0.0521471 | − | 0.998639i | \(-0.516606\pi\) | ||||
−0.0521471 | + | 0.998639i | \(0.516606\pi\) | |||||||
\(462\) | 69.8100 | + | 5.73190i | 0.151104 | + | 0.0124067i | ||||
\(463\) | 62.2803i | 0.134515i | 0.997736 | + | 0.0672573i | \(0.0214249\pi\) | ||||
−0.997736 | + | 0.0672573i | \(0.978575\pi\) | |||||||
\(464\) | 282.135 | + | 95.9119i | 0.608050 | + | 0.206707i | ||||
\(465\) | 221.261 | 0.475830 | ||||||||
\(466\) | 65.8430 | − | 801.915i | 0.141294 | − | 1.72085i | ||||
\(467\) | − | 358.971i | − | 0.768674i | −0.923193 | − | 0.384337i | \(-0.874430\pi\) | ||
0.923193 | − | 0.384337i | \(-0.125570\pi\) | |||||||
\(468\) | 481.117 | + | 79.5425i | 1.02803 | + | 0.169963i | ||||
\(469\) | −84.8846 | −0.180991 | ||||||||
\(470\) | −356.163 | − | 29.2435i | −0.757793 | − | 0.0622202i | ||||
\(471\) | 158.748i | 0.337045i | ||||||||
\(472\) | 297.418 | + | 74.6048i | 0.630124 | + | 0.158061i | ||||
\(473\) | 431.117 | 0.911452 | ||||||||
\(474\) | 10.1862 | − | 124.060i | 0.0214898 | − | 0.261729i | ||||
\(475\) | − | 399.907i | − | 0.841909i | ||||||
\(476\) | 15.3201 | − | 92.6646i | 0.0321852 | − | 0.194673i | ||||
\(477\) | 100.987 | 0.211713 | ||||||||
\(478\) | −481.332 | − | 39.5208i | −1.00697 | − | 0.0826795i | ||||
\(479\) | 196.744i | 0.410740i | 0.978684 | + | 0.205370i | \(0.0658398\pi\) | ||||
−0.978684 | + | 0.205370i | \(0.934160\pi\) | |||||||
\(480\) | −157.429 | − | 68.3517i | −0.327976 | − | 0.142399i | ||||
\(481\) | 64.8682 | 0.134861 | ||||||||
\(482\) | 19.0960 | − | 232.574i | 0.0396183 | − | 0.482519i | ||||
\(483\) | − | 109.516i | − | 0.226741i | ||||||
\(484\) | −193.468 | − | 31.9859i | −0.399727 | − | 0.0660865i | ||||
\(485\) | −110.058 | −0.226924 | ||||||||
\(486\) | −501.613 | − | 41.1861i | −1.03213 | − | 0.0847450i | ||||
\(487\) | 490.201i | 1.00657i | 0.864120 | + | 0.503287i | \(0.167876\pi\) | ||||
−0.864120 | + | 0.503287i | \(0.832124\pi\) | |||||||
\(488\) | −141.261 | + | 563.148i | −0.289469 | + | 1.15399i | ||||
\(489\) | 107.009 | 0.218832 | ||||||||
\(490\) | 3.93806 | − | 47.9625i | 0.00803687 | − | 0.0978826i | ||||
\(491\) | − | 852.129i | − | 1.73550i | −0.497004 | − | 0.867748i | \(-0.665567\pi\) | ||
0.497004 | − | 0.867748i | \(-0.334433\pi\) | |||||||
\(492\) | 38.4359 | − | 232.481i | 0.0781217 | − | 0.472522i | ||||
\(493\) | −165.290 | −0.335273 | ||||||||
\(494\) | 1122.67 | + | 92.1797i | 2.27262 | + | 0.186599i | ||||
\(495\) | − | 191.469i | − | 0.386805i | ||||||
\(496\) | 212.450 | − | 624.945i | 0.428327 | − | 1.25997i | ||||
\(497\) | −133.917 | −0.269452 | ||||||||
\(498\) | 1.09322 | − | 13.3145i | 0.00219521 | − | 0.0267359i | ||||
\(499\) | 851.935i | 1.70729i | 0.520859 | + | 0.853643i | \(0.325612\pi\) | ||||
−0.520859 | + | 0.853643i | \(0.674388\pi\) | |||||||
\(500\) | 517.988 | + | 85.6385i | 1.03598 | + | 0.171277i | ||||
\(501\) | 87.0315 | 0.173716 | ||||||||
\(502\) | 14.3867 | + | 1.18125i | 0.0286587 | + | 0.00235309i | ||||
\(503\) | 483.294i | 0.960823i | 0.877043 | + | 0.480411i | \(0.159513\pi\) | ||||
−0.877043 | + | 0.480411i | \(0.840487\pi\) | |||||||
\(504\) | −134.790 | − | 33.8109i | −0.267441 | − | 0.0670852i | ||||
\(505\) | −2.46986 | −0.00489081 | ||||||||
\(506\) | 36.8361 | − | 448.634i | 0.0727986 | − | 0.886629i | ||||
\(507\) | 274.279i | 0.540984i | ||||||||
\(508\) | 33.8584 | − | 204.794i | 0.0666505 | − | 0.403138i | ||||
\(509\) | −653.399 | −1.28369 | −0.641846 | − | 0.766833i | \(-0.721831\pi\) | ||||
−0.641846 | + | 0.766833i | \(0.721831\pi\) | |||||||
\(510\) | 94.8782 | + | 7.79018i | 0.186036 | + | 0.0152749i | ||||
\(511\) | 14.5187i | 0.0284124i | ||||||||
\(512\) | −344.217 | + | 379.023i | −0.672300 | + | 0.740279i | ||||
\(513\) | −736.670 | −1.43600 | ||||||||
\(514\) | −62.2304 | + | 757.916i | −0.121071 | + | 1.47455i | ||||
\(515\) | − | 400.299i | − | 0.777280i | ||||||
\(516\) | 312.900 | + | 51.7315i | 0.606396 | + | 0.100255i | ||||
\(517\) | 441.001 | 0.853001 | ||||||||
\(518\) | −18.4236 | − | 1.51271i | −0.0355669 | − | 0.00292030i | ||||
\(519\) | 30.0016i | 0.0578066i | ||||||||
\(520\) | −124.236 | + | 495.277i | −0.238915 | + | 0.952456i | ||||
\(521\) | −70.1290 | −0.134605 | −0.0673023 | − | 0.997733i | \(-0.521439\pi\) | ||||
−0.0673023 | + | 0.997733i | \(0.521439\pi\) | |||||||
\(522\) | −20.0128 | + | 243.739i | −0.0383386 | + | 0.466934i | ||||
\(523\) | − | 288.438i | − | 0.551507i | −0.961228 | − | 0.275753i | \(-0.911073\pi\) | ||
0.961228 | − | 0.275753i | \(-0.0889273\pi\) | |||||||
\(524\) | −158.332 | + | 957.681i | −0.302161 | + | 1.82764i | ||||
\(525\) | −54.4256 | −0.103668 | ||||||||
\(526\) | 624.607 | + | 51.2847i | 1.18747 | + | 0.0974995i | ||||
\(527\) | 366.126i | 0.694736i | ||||||||
\(528\) | 200.526 | + | 68.1687i | 0.379783 | + | 0.129107i | ||||
\(529\) | −174.806 | −0.330446 | ||||||||
\(530\) | −8.65327 | + | 105.390i | −0.0163269 | + | 0.198849i | ||||
\(531\) | 251.651i | 0.473918i | ||||||||
\(532\) | −316.709 | − | 52.3611i | −0.595317 | − | 0.0984232i | ||||
\(533\) | −701.064 | −1.31532 | ||||||||
\(534\) | −385.358 | − | 31.6407i | −0.721644 | − | 0.0592522i | ||||
\(535\) | 130.426i | 0.243788i | ||||||||
\(536\) | −248.954 | − | 62.4480i | −0.464467 | − | 0.116507i | ||||
\(537\) | 305.417 | 0.568746 | ||||||||
\(538\) | 27.8436 | − | 339.112i | 0.0517539 | − | 0.630321i | ||||
\(539\) | 59.3872i | 0.110180i | ||||||||
\(540\) | 54.4693 | − | 329.460i | 0.100869 | − | 0.610111i | ||||
\(541\) | −9.90711 | −0.0183126 | −0.00915630 | − | 0.999958i | \(-0.502915\pi\) | ||||
−0.00915630 | + | 0.999958i | \(0.502915\pi\) | |||||||
\(542\) | 100.283 | + | 8.23397i | 0.185024 | + | 0.0151918i | ||||
\(543\) | 128.798i | 0.237197i | ||||||||
\(544\) | 113.103 | − | 260.501i | 0.207910 | − | 0.478862i | ||||
\(545\) | 303.284 | 0.556484 | ||||||||
\(546\) | 12.5453 | − | 152.791i | 0.0229767 | − | 0.279838i | ||||
\(547\) | − | 265.156i | − | 0.484746i | −0.970183 | − | 0.242373i | \(-0.922074\pi\) | ||
0.970183 | − | 0.242373i | \(-0.0779257\pi\) | |||||||
\(548\) | 1067.74 | + | 176.529i | 1.94844 | + | 0.322133i | ||||
\(549\) | −476.489 | −0.867922 | ||||||||
\(550\) | −222.955 | − | 18.3063i | −0.405374 | − | 0.0332841i | ||||
\(551\) | 564.926i | 1.02527i | ||||||||
\(552\) | 80.5689 | − | 321.195i | 0.145958 | − | 0.581874i | ||||
\(553\) | 105.537 | 0.190845 | ||||||||
\(554\) | −9.65251 | + | 117.560i | −0.0174233 | + | 0.212202i | ||||
\(555\) | − | 18.7366i | − | 0.0337596i | ||||||
\(556\) | −10.2402 | + | 61.9385i | −0.0184177 | + | 0.111400i | ||||
\(557\) | −718.935 | −1.29073 | −0.645363 | − | 0.763876i | \(-0.723294\pi\) | ||||
−0.645363 | + | 0.763876i | \(0.723294\pi\) | |||||||
\(558\) | 539.896 | + | 44.3294i | 0.967556 | + | 0.0794434i | ||||
\(559\) | − | 943.574i | − | 1.68797i | ||||||
\(560\) | 46.8348 | − | 137.770i | 0.0836336 | − | 0.246017i | ||||
\(561\) | −117.478 | −0.209409 | ||||||||
\(562\) | −53.2763 | + | 648.862i | −0.0947976 | + | 1.15456i | ||||
\(563\) | 283.534i | 0.503613i | 0.967778 | + | 0.251807i | \(0.0810247\pi\) | ||||
−0.967778 | + | 0.251807i | \(0.918975\pi\) | |||||||
\(564\) | 320.075 | + | 52.9176i | 0.567508 | + | 0.0938256i | ||||
\(565\) | 430.072 | 0.761189 | ||||||||
\(566\) | 563.734 | + | 46.2866i | 0.995996 | + | 0.0817785i | ||||
\(567\) | − | 56.0792i | − | 0.0989051i | ||||||
\(568\) | −392.760 | − | 98.5205i | −0.691479 | − | 0.173452i | ||||
\(569\) | 31.4542 | 0.0552798 | 0.0276399 | − | 0.999618i | \(-0.491201\pi\) | ||||
0.0276399 | + | 0.999618i | \(0.491201\pi\) | |||||||
\(570\) | 26.6253 | − | 324.274i | 0.0467110 | − | 0.568902i | ||||
\(571\) | − | 580.635i | − | 1.01687i | −0.861099 | − | 0.508437i | \(-0.830224\pi\) | ||
0.861099 | − | 0.508437i | \(-0.169776\pi\) | |||||||
\(572\) | 102.784 | − | 621.693i | 0.179692 | − | 1.08688i | ||||
\(573\) | −249.130 | −0.434781 | ||||||||
\(574\) | 199.114 | + | 16.3487i | 0.346888 | + | 0.0284820i | ||||
\(575\) | 349.767i | 0.608290i | ||||||||
\(576\) | −370.446 | − | 198.325i | −0.643135 | − | 0.344314i | ||||
\(577\) | 909.096 | 1.57556 | 0.787778 | − | 0.615959i | \(-0.211231\pi\) | ||||
0.787778 | + | 0.615959i | \(0.211231\pi\) | |||||||
\(578\) | 34.4082 | − | 419.064i | 0.0595297 | − | 0.725025i | ||||
\(579\) | 166.100i | 0.286874i | ||||||||
\(580\) | −252.651 | − | 41.7706i | −0.435606 | − | 0.0720183i | ||||
\(581\) | 11.3266 | 0.0194951 | ||||||||
\(582\) | 99.5780 | + | 8.17607i | 0.171096 | + | 0.0140482i | ||||
\(583\) | − | 130.494i | − | 0.223832i | ||||||
\(584\) | −10.6811 | + | 42.5813i | −0.0182896 | + | 0.0729131i | ||||
\(585\) | −419.062 | −0.716346 | ||||||||
\(586\) | −7.77495 | + | 94.6926i | −0.0132678 | + | 0.161591i | ||||
\(587\) | 30.9295i | 0.0526908i | 0.999653 | + | 0.0263454i | \(0.00838696\pi\) | ||||
−0.999653 | + | 0.0263454i | \(0.991613\pi\) | |||||||
\(588\) | −7.12613 | + | 43.1027i | −0.0121193 | + | 0.0733039i | ||||
\(589\) | 1251.34 | 2.12452 | ||||||||
\(590\) | −262.622 | − | 21.5632i | −0.445123 | − | 0.0365478i | ||||
\(591\) | − | 277.523i | − | 0.469582i | ||||||
\(592\) | −52.9210 | − | 17.9905i | −0.0893935 | − | 0.0303893i | ||||
\(593\) | −879.391 | −1.48295 | −0.741476 | − | 0.670979i | \(-0.765874\pi\) | ||||
−0.741476 | + | 0.670979i | \(0.765874\pi\) | |||||||
\(594\) | −33.7220 | + | 410.707i | −0.0567711 | + | 0.691426i | ||||
\(595\) | 80.7127i | 0.135652i | ||||||||
\(596\) | −96.5402 | − | 15.9609i | −0.161980 | − | 0.0267800i | ||||
\(597\) | 417.582 | 0.699467 | ||||||||
\(598\) | −981.915 | − | 80.6223i | −1.64200 | − | 0.134820i | ||||
\(599\) | 252.069i | 0.420816i | 0.977614 | + | 0.210408i | \(0.0674793\pi\) | ||||
−0.977614 | + | 0.210408i | \(0.932521\pi\) | |||||||
\(600\) | −159.622 | − | 40.0399i | −0.266037 | − | 0.0667331i | ||||
\(601\) | −475.958 | −0.791943 | −0.395972 | − | 0.918263i | \(-0.629592\pi\) | ||||
−0.395972 | + | 0.918263i | \(0.629592\pi\) | |||||||
\(602\) | −22.0040 | + | 267.991i | −0.0365514 | + | 0.445167i | ||||
\(603\) | − | 210.644i | − | 0.349327i | ||||||
\(604\) | 123.570 | − | 747.420i | 0.204586 | − | 1.23745i | ||||
\(605\) | 168.515 | 0.278537 | ||||||||
\(606\) | 2.23467 | + | 0.183482i | 0.00368757 | + | 0.000302776i | ||||
\(607\) | 150.523i | 0.247979i | 0.992284 | + | 0.123989i | \(0.0395689\pi\) | ||||
−0.992284 | + | 0.123989i | \(0.960431\pi\) | |||||||
\(608\) | −890.339 | − | 386.564i | −1.46437 | − | 0.635796i | ||||
\(609\) | 76.8841 | 0.126246 | ||||||||
\(610\) | 40.8289 | − | 497.264i | 0.0669327 | − | 0.815187i | ||||
\(611\) | − | 965.208i | − | 1.57972i | ||||||
\(612\) | 229.951 | + | 38.0175i | 0.375736 | + | 0.0621201i | ||||
\(613\) | 184.999 | 0.301794 | 0.150897 | − | 0.988550i | \(-0.451784\pi\) | ||||
0.150897 | + | 0.988550i | \(0.451784\pi\) | |||||||
\(614\) | −697.608 | − | 57.2787i | −1.13617 | − | 0.0932877i | ||||
\(615\) | 202.496i | 0.329261i | ||||||||
\(616\) | −43.6901 | + | 174.174i | −0.0709254 | + | 0.282750i | ||||
\(617\) | −40.0241 | −0.0648689 | −0.0324345 | − | 0.999474i | \(-0.510326\pi\) | ||||
−0.0324345 | + | 0.999474i | \(0.510326\pi\) | |||||||
\(618\) | −29.7377 | + | 362.181i | −0.0481192 | + | 0.586053i | ||||
\(619\) | − | 389.507i | − | 0.629253i | −0.949216 | − | 0.314626i | \(-0.898121\pi\) | ||
0.949216 | − | 0.314626i | \(-0.101879\pi\) | |||||||
\(620\) | −92.5242 | + | 559.637i | −0.149233 | + | 0.902641i | ||||
\(621\) | 644.307 | 1.03753 | ||||||||
\(622\) | −687.569 | − | 56.4544i | −1.10542 | − | 0.0907626i | ||||
\(623\) | − | 327.823i | − | 0.526201i | ||||||
\(624\) | 149.199 | − | 438.885i | 0.239101 | − | 0.703342i | ||||
\(625\) | −121.575 | −0.194519 | ||||||||
\(626\) | −46.0745 | + | 561.151i | −0.0736015 | + | 0.896407i | ||||
\(627\) | 401.517i | 0.640378i | ||||||||
\(628\) | −401.523 | − | 66.3834i | −0.639368 | − | 0.105706i | ||||
\(629\) | 31.0039 | 0.0492907 | ||||||||
\(630\) | 119.021 | + | 9.77245i | 0.188922 | + | 0.0155118i | ||||
\(631\) | 615.708i | 0.975765i | 0.872909 | + | 0.487883i | \(0.162231\pi\) | ||||
−0.872909 | + | 0.487883i | \(0.837769\pi\) | |||||||
\(632\) | 309.526 | + | 77.6418i | 0.489756 | + | 0.122851i | ||||
\(633\) | −253.988 | −0.401245 | ||||||||
\(634\) | −85.9565 | + | 1046.88i | −0.135578 | + | 1.65123i | ||||
\(635\) | 178.380i | 0.280913i | ||||||||
\(636\) | 15.6585 | − | 94.7113i | 0.0246203 | − | 0.148917i | ||||
\(637\) | 129.979 | 0.204049 | ||||||||
\(638\) | 314.957 | + | 25.8602i | 0.493663 | + | 0.0405333i | ||||
\(639\) | − | 332.321i | − | 0.520064i | ||||||
\(640\) | 238.714 | − | 369.603i | 0.372991 | − | 0.577505i | ||||
\(641\) | 975.771 | 1.52226 | 0.761132 | − | 0.648597i | \(-0.224644\pi\) | ||||
0.761132 | + | 0.648597i | \(0.224644\pi\) | |||||||
\(642\) | 9.68919 | − | 118.007i | 0.0150922 | − | 0.183811i | ||||
\(643\) | 888.565i | 1.38190i | 0.722900 | + | 0.690952i | \(0.242809\pi\) | ||||
−0.722900 | + | 0.690952i | \(0.757191\pi\) | |||||||
\(644\) | 277.000 | + | 45.7961i | 0.430124 | + | 0.0711120i | ||||
\(645\) | −272.543 | −0.422547 | ||||||||
\(646\) | 536.585 | + | 44.0575i | 0.830626 | + | 0.0682004i | ||||
\(647\) | − | 263.161i | − | 0.406740i | −0.979102 | − | 0.203370i | \(-0.934811\pi\) | ||
0.979102 | − | 0.203370i | \(-0.0651894\pi\) | |||||||
\(648\) | 41.2564 | − | 164.472i | 0.0636673 | − | 0.253815i | ||||
\(649\) | 325.180 | 0.501047 | ||||||||
\(650\) | −40.0664 | + | 487.977i | −0.0616407 | + | 0.750734i | ||||
\(651\) | − | 170.303i | − | 0.261601i | ||||||
\(652\) | −44.7478 | + | 270.659i | −0.0686315 | + | 0.415121i | ||||
\(653\) | 923.879 | 1.41482 | 0.707411 | − | 0.706803i | \(-0.249863\pi\) | ||||
0.707411 | + | 0.706803i | \(0.249863\pi\) | |||||||
\(654\) | −274.404 | − | 22.5305i | −0.419577 | − | 0.0344503i | ||||
\(655\) | − | 834.160i | − | 1.27353i | ||||||
\(656\) | 571.944 | + | 194.432i | 0.871866 | + | 0.296391i | ||||
\(657\) | −36.0287 | −0.0548383 | ||||||||
\(658\) | −22.5085 | + | 274.135i | −0.0342074 | + | 0.416619i | ||||
\(659\) | 1297.45i | 1.96882i | 0.175881 | + | 0.984411i | \(0.443723\pi\) | ||||
−0.175881 | + | 0.984411i | \(0.556277\pi\) | |||||||
\(660\) | −179.570 | − | 29.6881i | −0.272076 | − | 0.0449820i | ||||
\(661\) | −597.632 | −0.904133 | −0.452067 | − | 0.891984i | \(-0.649313\pi\) | ||||
−0.452067 | + | 0.891984i | \(0.649313\pi\) | |||||||
\(662\) | 353.186 | + | 28.9991i | 0.533514 | + | 0.0438053i | ||||
\(663\) | 257.122i | 0.387816i | ||||||||
\(664\) | 33.2193 | + | 8.33278i | 0.0500291 | + | 0.0125494i | ||||
\(665\) | 275.860 | 0.414827 | ||||||||
\(666\) | 3.75385 | − | 45.7189i | 0.00563642 | − | 0.0686471i | ||||
\(667\) | − | 494.096i | − | 0.740774i | ||||||
\(668\) | −36.3938 | + | 220.130i | −0.0544818 | + | 0.329535i | ||||
\(669\) | −495.743 | −0.741022 | ||||||||
\(670\) | 219.828 | + | 18.0495i | 0.328102 | + | 0.0269395i | ||||
\(671\) | 615.713i | 0.917605i | ||||||||
\(672\) | −52.6097 | + | 121.171i | −0.0782883 | + | 0.180315i | ||||
\(673\) | 478.696 | 0.711287 | 0.355643 | − | 0.934622i | \(-0.384262\pi\) | ||||
0.355643 | + | 0.934622i | \(0.384262\pi\) | |||||||
\(674\) | 18.2283 | − | 222.006i | 0.0270450 | − | 0.329386i | ||||
\(675\) | − | 320.198i | − | 0.474367i | ||||||
\(676\) | −693.736 | − | 114.695i | −1.02624 | − | 0.169667i | ||||
\(677\) | 208.658 | 0.308210 | 0.154105 | − | 0.988054i | \(-0.450751\pi\) | ||||
0.154105 | + | 0.988054i | \(0.450751\pi\) | |||||||
\(678\) | −389.118 | − | 31.9494i | −0.573920 | − | 0.0471230i | ||||
\(679\) | 84.7109i | 0.124758i | ||||||||
\(680\) | −59.3788 | + | 236.719i | −0.0873218 | + | 0.348116i | ||||
\(681\) | 181.255 | 0.266160 | ||||||||
\(682\) | 57.2819 | − | 697.647i | 0.0839910 | − | 1.02294i | ||||
\(683\) | 12.4224i | 0.0181880i | 0.999959 | + | 0.00909400i | \(0.00289475\pi\) | ||||
−0.999959 | + | 0.00909400i | \(0.997105\pi\) | |||||||
\(684\) | 129.936 | − | 785.924i | 0.189965 | − | 1.14901i | ||||
\(685\) | −930.027 | −1.35770 | ||||||||
\(686\) | −36.9163 | − | 3.03109i | −0.0538138 | − | 0.00441850i | ||||
\(687\) | − | 558.023i | − | 0.812261i | ||||||
\(688\) | −261.690 | + | 769.790i | −0.380363 | + | 1.11888i | ||||
\(689\) | −285.609 | −0.414527 | ||||||||
\(690\) | −23.2870 | + | 283.617i | −0.0337493 | + | 0.411039i | ||||
\(691\) | 914.850i | 1.32395i | 0.749526 | + | 0.661975i | \(0.230282\pi\) | ||||
−0.749526 | + | 0.661975i | \(0.769718\pi\) | |||||||
\(692\) | −75.8834 | − | 12.5457i | −0.109658 | − | 0.0181297i | ||||
\(693\) | −147.372 | −0.212657 | ||||||||
\(694\) | −103.957 | − | 8.53560i | −0.149794 | − | 0.0122991i | ||||
\(695\) | − | 53.9497i | − | 0.0776255i | ||||||
\(696\) | 225.490 | + | 56.5621i | 0.323979 | + | 0.0812674i | ||||
\(697\) | −335.075 | −0.480738 | ||||||||
\(698\) | 68.7258 | − | 837.026i | 0.0984611 | − | 1.19918i | ||||
\(699\) | − | 627.711i | − | 0.898012i | ||||||
\(700\) | 22.7591 | − | 137.659i | 0.0325129 | − | 0.196656i | ||||
\(701\) | 338.736 | 0.483218 | 0.241609 | − | 0.970374i | \(-0.422325\pi\) | ||||
0.241609 | + | 0.970374i | \(0.422325\pi\) | |||||||
\(702\) | 898.904 | + | 73.8065i | 1.28049 | + | 0.105137i | ||||
\(703\) | − | 105.965i | − | 0.150732i | ||||||
\(704\) | −256.273 | + | 478.685i | −0.364024 | + | 0.679951i | ||||
\(705\) | −278.792 | −0.395449 | ||||||||
\(706\) | 32.4800 | − | 395.581i | 0.0460057 | − | 0.560313i | ||||
\(707\) | 1.90103i | 0.00268886i | ||||||||
\(708\) | 236.012 | + | 39.0197i | 0.333351 | + | 0.0551126i | ||||
\(709\) | −665.756 | −0.939006 | −0.469503 | − | 0.882931i | \(-0.655567\pi\) | ||||
−0.469503 | + | 0.882931i | \(0.655567\pi\) | |||||||
\(710\) | 346.810 | + | 28.4756i | 0.488465 | + | 0.0401065i | ||||
\(711\) | 261.895i | 0.368347i | ||||||||
\(712\) | 241.173 | − | 961.458i | 0.338727 | − | 1.35036i | ||||
\(713\) | −1094.45 | −1.53499 | ||||||||
\(714\) | 5.99603 | − | 73.0269i | 0.00839780 | − | 0.102279i | ||||
\(715\) | 541.507i | 0.757352i | ||||||||
\(716\) | −127.716 | + | 772.494i | −0.178374 | + | 1.07890i | ||||
\(717\) | −376.769 | −0.525480 | ||||||||
\(718\) | −466.611 | − | 38.3121i | −0.649876 | − | 0.0533595i | ||||
\(719\) | 517.776i | 0.720134i | 0.932926 | + | 0.360067i | \(0.117246\pi\) | ||||
−0.932926 | + | 0.360067i | \(0.882754\pi\) | |||||||
\(720\) | 341.881 | + | 116.222i | 0.474834 | + | 0.161420i | ||||
\(721\) | −308.107 | −0.427333 | ||||||||
\(722\) | 91.4969 | − | 1114.36i | 0.126727 | − | 1.54343i | ||||
\(723\) | − | 182.051i | − | 0.251799i | ||||||
\(724\) | −325.771 | − | 53.8593i | −0.449959 | − | 0.0743913i | ||||
\(725\) | −245.548 | −0.338687 | ||||||||
\(726\) | −152.468 | − | 12.5187i | −0.210011 | − | 0.0172434i | ||||
\(727\) | − | 428.891i | − | 0.589946i | −0.955506 | − | 0.294973i | \(-0.904689\pi\) | ||
0.955506 | − | 0.294973i | \(-0.0953106\pi\) | |||||||
\(728\) | 381.210 | + | 95.6233i | 0.523641 | + | 0.131351i | ||||
\(729\) | −201.882 | −0.276930 | ||||||||
\(730\) | 3.08719 | − | 37.5996i | 0.00422903 | − | 0.0515062i | ||||
\(731\) | − | 450.983i | − | 0.616940i | ||||||
\(732\) | −73.8820 | + | 446.879i | −0.100932 | + | 0.610490i | ||||
\(733\) | 758.896 | 1.03533 | 0.517665 | − | 0.855584i | \(-0.326802\pi\) | ||||
0.517665 | + | 0.855584i | \(0.326802\pi\) | |||||||
\(734\) | 736.482 | + | 60.4705i | 1.00338 | + | 0.0823849i | ||||
\(735\) | − | 37.5433i | − | 0.0510794i | ||||||
\(736\) | 778.709 | + | 338.097i | 1.05803 | + | 0.459371i | ||||
\(737\) | −272.192 | −0.369324 | ||||||||
\(738\) | −40.5698 | + | 494.108i | −0.0549727 | + | 0.669523i | ||||
\(739\) | − | 1100.00i | − | 1.48849i | −0.667906 | − | 0.744246i | \(-0.732809\pi\) | ||
0.667906 | − | 0.744246i | \(-0.267191\pi\) | |||||||
\(740\) | 47.3906 | + | 7.83504i | 0.0640413 | + | 0.0105879i | ||||
\(741\) | 878.790 | 1.18595 | ||||||||
\(742\) | 81.1176 | + | 6.66034i | 0.109323 | + | 0.00897620i | ||||
\(743\) | − | 1056.59i | − | 1.42205i | −0.703165 | − | 0.711027i | \(-0.748231\pi\) | ||
0.703165 | − | 0.711027i | \(-0.251769\pi\) | |||||||
\(744\) | 125.288 | − | 499.472i | 0.168398 | − | 0.671334i | ||||
\(745\) | 84.0885 | 0.112870 | ||||||||
\(746\) | 45.9046 | − | 559.081i | 0.0615343 | − | 0.749438i | ||||
\(747\) | 28.1074i | 0.0376271i | ||||||||
\(748\) | 49.1257 | − | 297.139i | 0.0656761 | − | 0.397245i | ||||
\(749\) | 100.388 | 0.134029 | ||||||||
\(750\) | 408.215 | + | 33.5174i | 0.544287 | + | 0.0446898i | ||||
\(751\) | − | 42.1730i | − | 0.0561557i | −0.999606 | − | 0.0280779i | \(-0.991061\pi\) | ||
0.999606 | − | 0.0280779i | \(-0.00893864\pi\) | |||||||
\(752\) | −267.690 | + | 787.439i | −0.355971 | + | 1.04713i | ||||
\(753\) | 11.2614 | 0.0149554 | ||||||||
\(754\) | 56.5996 | − | 689.338i | 0.0750658 | − | 0.914242i | ||||
\(755\) | 651.018i | 0.862275i | ||||||||
\(756\) | −253.583 | − | 41.9245i | −0.335427 | − | 0.0554558i | ||||
\(757\) | −931.250 | −1.23018 | −0.615092 | − | 0.788455i | \(-0.710881\pi\) | ||||
−0.615092 | + | 0.788455i | \(0.710881\pi\) | |||||||
\(758\) | −518.072 | − | 42.5374i | −0.683472 | − | 0.0561180i | ||||
\(759\) | − | 351.175i | − | 0.462681i | ||||||
\(760\) | 809.056 | + | 202.945i | 1.06455 | + | 0.267032i | ||||
\(761\) | −423.281 | −0.556217 | −0.278108 | − | 0.960550i | \(-0.589707\pi\) | ||||
−0.278108 | + | 0.960550i | \(0.589707\pi\) | |||||||
\(762\) | 13.2516 | − | 161.394i | 0.0173905 | − | 0.211803i | ||||
\(763\) | − | 233.435i | − | 0.305943i | ||||||
\(764\) | 104.178 | − | 630.126i | 0.136359 | − | 0.824772i | ||||
\(765\) | −200.292 | −0.261819 | ||||||||
\(766\) | 823.223 | + | 67.5925i | 1.07470 | + | 0.0882409i | ||||
\(767\) | − | 711.713i | − | 0.927917i | ||||||
\(768\) | −243.440 | + | 316.674i | −0.316979 | + | 0.412336i | ||||
\(769\) | 600.534 | 0.780928 | 0.390464 | − | 0.920618i | \(-0.372315\pi\) | ||||
0.390464 | + | 0.920618i | \(0.372315\pi\) | |||||||
\(770\) | 12.6278 | − | 153.797i | 0.0163998 | − | 0.199736i | ||||
\(771\) | 593.270i | 0.769481i | ||||||||
\(772\) | −420.119 | − | 69.4578i | −0.544196 | − | 0.0899713i | ||||
\(773\) | 120.049 | 0.155303 | 0.0776516 | − | 0.996981i | \(-0.475258\pi\) | ||||
0.0776516 | + | 0.996981i | \(0.475258\pi\) | |||||||
\(774\) | −665.029 | − | 54.6037i | −0.859210 | − | 0.0705474i | ||||
\(775\) | 543.903i | 0.701811i | ||||||||
\(776\) | −62.3201 | + | 248.445i | −0.0803095 | + | 0.320160i | ||||
\(777\) | −14.4214 | −0.0185603 | ||||||||
\(778\) | −57.0928 | + | 695.344i | −0.0733840 | + | 0.893758i | ||||
\(779\) | 1145.22i | 1.47011i | ||||||||
\(780\) | −64.9777 | + | 393.021i | −0.0833047 | + | 0.503873i | ||||
\(781\) | −429.421 | −0.549835 | ||||||||
\(782\) | −469.308 | − | 38.5336i | −0.600138 | − | 0.0492757i | ||||
\(783\) | 452.326i | 0.577683i | ||||||||
\(784\) | −106.040 | − | 36.0484i | −0.135255 | − | 0.0459800i | ||||
\(785\) | 349.735 | 0.445522 | ||||||||
\(786\) | −61.9685 | + | 754.727i | −0.0788404 | + | 0.960213i | ||||
\(787\) | 1277.61i | 1.62339i | 0.584081 | + | 0.811696i | \(0.301455\pi\) | ||||
−0.584081 | + | 0.811696i | \(0.698545\pi\) | |||||||
\(788\) | 701.942 | + | 116.051i | 0.890789 | + | 0.147273i | ||||
\(789\) | 488.920 | 0.619671 | ||||||||
\(790\) | −273.313 | − | 22.4410i | −0.345966 | − | 0.0284063i | ||||
\(791\) | − | 331.022i | − | 0.418486i | ||||||
\(792\) | −432.219 | − | 108.418i | −0.545732 | − | 0.136892i | ||||
\(793\) | 1347.60 | 1.69936 | ||||||||
\(794\) | −5.51527 | + | 67.1715i | −0.00694618 | + | 0.0845989i | ||||
\(795\) | 82.4955i | 0.103768i | ||||||||
\(796\) | −174.619 | + | 1056.19i | −0.219371 | + | 1.32688i | ||||
\(797\) | 84.2194 | 0.105670 | 0.0528352 | − | 0.998603i | \(-0.483174\pi\) | ||||
0.0528352 | + | 0.998603i | \(0.483174\pi\) | |||||||
\(798\) | −249.591 | − | 20.4932i | −0.312771 | − | 0.0256807i | ||||
\(799\) | − | 461.323i | − | 0.577376i | ||||||
\(800\) | 168.022 | − | 386.991i | 0.210028 | − | 0.483739i | ||||
\(801\) | 813.506 | 1.01561 | ||||||||
\(802\) | −22.9326 | + | 279.300i | −0.0285942 | + | 0.348254i | ||||
\(803\) | 46.5559i | 0.0579774i | ||||||||
\(804\) | −197.554 | − | 32.6614i | −0.245714 | − | 0.0406237i | ||||
\(805\) | −241.273 | −0.299718 | ||||||||
\(806\) | −1526.92 | − | 125.371i | −1.89445 | − | 0.155548i | ||||
\(807\) | − | 265.445i | − | 0.328928i | ||||||
\(808\) | −1.39855 | + | 5.57544i | −0.00173088 | + | 0.00690029i | ||||
\(809\) | 1224.02 | 1.51300 | 0.756501 | − | 0.653993i | \(-0.226907\pi\) | ||||
0.756501 | + | 0.653993i | \(0.226907\pi\) | |||||||
\(810\) | −11.9244 | + | 145.230i | −0.0147215 | + | 0.179296i | ||||
\(811\) | 346.748i | 0.427556i | 0.976882 | + | 0.213778i | \(0.0685769\pi\) | ||||
−0.976882 | + | 0.213778i | \(0.931423\pi\) | |||||||
\(812\) | −32.1505 | + | 194.464i | −0.0395942 | + | 0.239487i | ||||
\(813\) | 78.4981 | 0.0965536 | ||||||||
\(814\) | −59.0774 | − | 4.85068i | −0.0725767 | − | 0.00595907i | ||||
\(815\) | − | 235.749i | − | 0.289263i | ||||||
\(816\) | 71.3100 | − | 209.766i | 0.0873897 | − | 0.257066i | ||||
\(817\) | −1541.37 | −1.88662 | ||||||||
\(818\) | 115.868 | − | 1411.18i | 0.141648 | − | 1.72515i | ||||
\(819\) | 322.549i | 0.393832i | ||||||||
\(820\) | −512.174 | − | 84.6773i | −0.624603 | − | 0.103265i | ||||
\(821\) | −1288.46 | −1.56938 | −0.784690 | − | 0.619888i | \(-0.787178\pi\) | ||||
−0.784690 | + | 0.619888i | \(0.787178\pi\) | |||||||
\(822\) | 841.465 | + | 69.0904i | 1.02368 | + | 0.0840515i | ||||
\(823\) | 496.071i | 0.602759i | 0.953504 | + | 0.301379i | \(0.0974471\pi\) | ||||
−0.953504 | + | 0.301379i | \(0.902553\pi\) | |||||||
\(824\) | −903.633 | − | 226.668i | −1.09664 | − | 0.275083i | ||||
\(825\) | −174.522 | −0.211541 | ||||||||
\(826\) | −16.5970 | + | 202.138i | −0.0200932 | + | 0.244719i | ||||
\(827\) | 2.15878i | 0.00261037i | 0.999999 | + | 0.00130519i | \(0.000415453\pi\) | ||||
−0.999999 | + | 0.00130519i | \(0.999585\pi\) | |||||||
\(828\) | −113.645 | + | 687.386i | −0.137252 | + | 0.830176i | ||||
\(829\) | 501.082 | 0.604442 | 0.302221 | − | 0.953238i | \(-0.402272\pi\) | ||||
0.302221 | + | 0.953238i | \(0.402272\pi\) | |||||||
\(830\) | −29.3329 | − | 2.40844i | −0.0353408 | − | 0.00290174i | ||||
\(831\) | 92.0217i | 0.110736i | ||||||||
\(832\) | 1047.69 | + | 560.898i | 1.25924 | + | 0.674157i | ||||
\(833\) | 62.1239 | 0.0745785 | ||||||||
\(834\) | −4.00785 | + | 48.8124i | −0.00480557 | + | 0.0585280i | ||||
\(835\) | − | 191.737i | − | 0.229626i | ||||||
\(836\) | −1015.56 | − | 167.902i | −1.21479 | − | 0.200839i | ||||
\(837\) | 1001.93 | 1.19704 | ||||||||
\(838\) | 1188.68 | + | 97.5994i | 1.41848 | + | 0.116467i | ||||
\(839\) | − | 1576.56i | − | 1.87909i | −0.342424 | − | 0.939546i | \(-0.611248\pi\) | ||
0.342424 | − | 0.939546i | \(-0.388752\pi\) | |||||||
\(840\) | 27.6199 | − | 110.109i | 0.0328808 | − | 0.131082i | ||||
\(841\) | −494.127 | −0.587547 | ||||||||
\(842\) | 26.6465 | − | 324.533i | 0.0316467 | − | 0.385431i | ||||
\(843\) | 507.907i | 0.602499i | ||||||||
\(844\) | 106.210 | − | 642.415i | 0.125841 | − | 0.761155i | ||||
\(845\) | 604.258 | 0.715099 | ||||||||
\(846\) | −680.277 | − | 55.8556i | −0.804109 | − | 0.0660232i | ||||
\(847\) | − | 129.704i | − | 0.153134i | ||||||
\(848\) | 233.006 | + | 79.2105i | 0.274772 | + | 0.0934086i | ||||
\(849\) | 441.271 | 0.519754 | ||||||||
\(850\) | −19.1498 | + | 233.230i | −0.0225292 | + | 0.274388i | ||||
\(851\) | 92.6791i | 0.108906i | ||||||||
\(852\) | −311.670 | − | 51.5280i | −0.365809 | − | 0.0604789i | ||||
\(853\) | 1502.12 | 1.76098 | 0.880490 | − | 0.474065i | \(-0.157214\pi\) | ||||
0.880490 | + | 0.474065i | \(0.157214\pi\) | |||||||
\(854\) | −382.740 | − | 31.4257i | −0.448173 | − | 0.0367982i | ||||
\(855\) | 684.556i | 0.800650i | ||||||||
\(856\) | 294.423 | + | 73.8535i | 0.343953 | + | 0.0862775i | ||||
\(857\) | −112.940 | −0.131786 | −0.0658929 | − | 0.997827i | \(-0.520990\pi\) | ||||
−0.0658929 | + | 0.997827i | \(0.520990\pi\) | |||||||
\(858\) | 40.2278 | − | 489.942i | 0.0468855 | − | 0.571028i | ||||
\(859\) | − | 7.56729i | − | 0.00880941i | −0.999990 | − | 0.00440471i | \(-0.998598\pi\) | ||
0.999990 | − | 0.00440471i | \(-0.00140207\pi\) | |||||||
\(860\) | 113.969 | − | 689.345i | 0.132522 | − | 0.801564i | ||||
\(861\) | 155.859 | 0.181021 | ||||||||
\(862\) | −771.069 | − | 63.3104i | −0.894512 | − | 0.0734459i | ||||
\(863\) | − | 1013.78i | − | 1.17472i | −0.809327 | − | 0.587358i | \(-0.800168\pi\) | ||
0.809327 | − | 0.587358i | \(-0.199832\pi\) | |||||||
\(864\) | −712.878 | − | 309.514i | −0.825090 | − | 0.358234i | ||||
\(865\) | 66.0960 | 0.0764116 | ||||||||
\(866\) | −94.0810 | + | 1145.83i | −0.108639 | + | 1.32313i | ||||
\(867\) | − | 328.029i | − | 0.378349i | ||||||
\(868\) | 430.748 | + | 71.2151i | 0.496253 | + | 0.0820450i | ||||
\(869\) | 338.417 | 0.389433 | ||||||||
\(870\) | −199.109 | − | 16.3483i | −0.228861 | − | 0.0187911i | ||||
\(871\) | 595.739i | 0.683972i | ||||||||
\(872\) | 171.733 | − | 684.630i | 0.196942 | − | 0.785126i | ||||
\(873\) | −210.213 | −0.240794 | ||||||||
\(874\) | −131.700 | + | 1604.00i | −0.150686 | + | 1.83524i | ||||
\(875\) | 347.268i | 0.396878i | ||||||||
\(876\) | −5.58643 | + | 33.7898i | −0.00637721 | + | 0.0385728i | ||||
\(877\) | −1231.12 | −1.40378 | −0.701890 | − | 0.712285i | \(-0.747660\pi\) | ||||
−0.701890 | + | 0.712285i | \(0.747660\pi\) | |||||||
\(878\) | 588.431 | + | 48.3144i | 0.670195 | + | 0.0550278i | ||||
\(879\) | 74.1220i | 0.0843254i | ||||||||
\(880\) | 150.181 | − | 441.774i | 0.170660 | − | 0.502016i | ||||
\(881\) | 1270.31 | 1.44189 | 0.720945 | − | 0.692992i | \(-0.243708\pi\) | ||||
0.720945 | + | 0.692992i | \(0.243708\pi\) | |||||||
\(882\) | 7.52177 | − | 91.6091i | 0.00852808 | − | 0.103865i | ||||
\(883\) | − | 1407.95i | − | 1.59451i | −0.603646 | − | 0.797253i | \(-0.706286\pi\) | ||
0.603646 | − | 0.797253i | \(-0.293714\pi\) | |||||||
\(884\) | −650.341 | − | 107.520i | −0.735680 | − | 0.121629i | ||||
\(885\) | −205.572 | −0.232284 | ||||||||
\(886\) | 850.159 | + | 69.8042i | 0.959547 | + | 0.0787857i | ||||
\(887\) | − | 1721.23i | − | 1.94051i | −0.242093 | − | 0.970253i | \(-0.577834\pi\) | ||
0.242093 | − | 0.970253i | \(-0.422166\pi\) | |||||||
\(888\) | −42.2958 | − | 10.6095i | −0.0476304 | − | 0.0119477i | ||||
\(889\) | 137.298 | 0.154440 | ||||||||
\(890\) | −69.7069 | + | 848.974i | −0.0783224 | + | 0.953904i | ||||
\(891\) | − | 179.824i | − | 0.201823i | ||||||
\(892\) | 207.304 | − | 1253.89i | 0.232404 | − | 1.40570i | ||||
\(893\) | −1576.71 | −1.76563 | ||||||||
\(894\) | −76.0812 | − | 6.24681i | −0.0851020 | − | 0.00698749i | ||||
\(895\) | − | 672.858i | − | 0.751796i | ||||||
\(896\) | −284.480 | − | 183.736i | −0.317500 | − | 0.205063i | ||||
\(897\) | −768.608 | −0.856865 | ||||||||
\(898\) | 75.0854 | − | 914.480i | 0.0836140 | − | 1.01835i | ||||
\(899\) | − | 768.342i | − | 0.854663i | ||||||
\(900\) | 341.606 | + | 56.4774i | 0.379563 | + | 0.0627527i | ||||
\(901\) | −136.507 | −0.151506 | ||||||||
\(902\) | 638.480 | + | 52.4238i | 0.707849 | + | 0.0581195i | ||||
\(903\) | 209.774i | 0.232308i | ||||||||
\(904\) | 243.527 | − | 970.840i | 0.269388 | − | 1.07394i | ||||
\(905\) | 283.753 | 0.313539 | ||||||||
\(906\) | 48.3632 | − | 589.025i | 0.0533810 | − | 0.650138i | ||||
\(907\) | 1181.35i | 1.30248i | 0.758871 | + | 0.651241i | \(0.225751\pi\) | ||||
−0.758871 | + | 0.651241i | \(0.774249\pi\) | |||||||
\(908\) | −75.7950 | + | 458.449i | −0.0834746 | + | 0.504900i | ||||
\(909\) | −4.71747 | −0.00518974 | ||||||||
\(910\) | −336.611 | − | 27.6382i | −0.369903 | − | 0.0303717i | ||||
\(911\) | 1286.03i | 1.41166i | 0.708379 | + | 0.705832i | \(0.249427\pi\) | ||||
−0.708379 | + | 0.705832i | \(0.750573\pi\) | |||||||
\(912\) | −716.938 | − | 243.723i | −0.786116 | − | 0.267240i | ||||
\(913\) | 36.3201 | 0.0397810 | ||||||||
\(914\) | −62.9171 | + | 766.280i | −0.0688371 | + | 0.838381i | ||||
\(915\) | − | 389.241i | − | 0.425400i | ||||||
\(916\) | 1411.41 | + | 233.347i | 1.54084 | + | 0.254746i | ||||
\(917\) | −642.046 | −0.700159 | ||||||||
\(918\) | 429.633 | + | 35.2760i | 0.468010 | + | 0.0384270i | ||||
\(919\) | 1618.74i | 1.76142i | 0.473659 | + | 0.880708i | \(0.342933\pi\) | ||||
−0.473659 | + | 0.880708i | \(0.657067\pi\) | |||||||
\(920\) | −707.617 | − | 177.500i | −0.769149 | − | 0.192934i | ||||
\(921\) | −546.063 | −0.592902 | ||||||||
\(922\) | 7.86889 | − | 95.8368i | 0.00853459 | − | 0.103944i | ||||
\(923\) | 939.863i | 1.01827i | ||||||||
\(924\) | −22.8507 | + | 138.214i | −0.0247302 | + | 0.149582i | ||||
\(925\) | 46.0583 | 0.0497927 | ||||||||
\(926\) | −124.143 | − | 10.1930i | −0.134064 | − | 0.0110076i | ||||
\(927\) | − | 764.579i | − | 0.824788i | ||||||
\(928\) | −237.356 | + | 546.681i | −0.255771 | + | 0.589096i | ||||
\(929\) | −551.019 | −0.593131 | −0.296566 | − | 0.955012i | \(-0.595841\pi\) | ||||
−0.296566 | + | 0.955012i | \(0.595841\pi\) | |||||||
\(930\) | −36.2124 | + | 441.038i | −0.0389380 | + | 0.474234i | ||||
\(931\) | − | 212.327i | − | 0.228063i | ||||||
\(932\) | 1587.67 | + | 262.489i | 1.70351 | + | 0.281640i | ||||
\(933\) | −538.205 | −0.576854 | ||||||||
\(934\) | 715.533 | + | 58.7504i | 0.766096 | + | 0.0629020i | ||||
\(935\) | 258.814i | 0.276807i | ||||||||
\(936\) | −237.293 | + | 945.988i | −0.253518 | + | 1.01067i | ||||
\(937\) | −1710.84 | −1.82587 | −0.912934 | − | 0.408108i | \(-0.866189\pi\) | ||||
−0.912934 | + | 0.408108i | \(0.866189\pi\) | |||||||
\(938\) | 13.8925 | − | 169.200i | 0.0148108 | − | 0.180384i | ||||
\(939\) | 439.249i | 0.467784i | ||||||||
\(940\) | 116.582 | − | 705.150i | 0.124023 | − | 0.750160i | ||||
\(941\) | 32.9788 | 0.0350466 | 0.0175233 | − | 0.999846i | \(-0.494422\pi\) | ||||
0.0175233 | + | 0.999846i | \(0.494422\pi\) | |||||||
\(942\) | −316.431 | − | 25.9813i | −0.335914 | − | 0.0275810i | ||||
\(943\) | − | 1001.63i | − | 1.06217i | ||||||
\(944\) | −197.386 | + | 580.632i | −0.209095 | + | 0.615076i | ||||
\(945\) | 220.876 | 0.233731 | ||||||||
\(946\) | −70.5581 | + | 859.342i | −0.0745858 | + | 0.908395i | ||||
\(947\) | 1186.26i | 1.25265i | 0.779560 | + | 0.626327i | \(0.215443\pi\) | ||||
−0.779560 | + | 0.626327i | \(0.784557\pi\) | |||||||
\(948\) | 245.620 | + | 40.6081i | 0.259093 | + | 0.0428355i | ||||
\(949\) | 101.896 | 0.107372 | ||||||||
\(950\) | 797.131 | + | 65.4502i | 0.839085 | + | 0.0688950i | ||||
\(951\) | 819.461i | 0.861684i | ||||||||
\(952\) | 182.200 | + | 45.7033i | 0.191387 | + | 0.0480077i | ||||
\(953\) | 572.985 | 0.601244 | 0.300622 | − | 0.953743i | \(-0.402806\pi\) | ||||
0.300622 | + | 0.953743i | \(0.402806\pi\) | |||||||
\(954\) | −16.5279 | + | 201.296i | −0.0173248 | + | 0.211003i | ||||
\(955\) | 548.852i | 0.574715i | ||||||||
\(956\) | 157.553 | − | 952.966i | 0.164804 | − | 0.996827i | ||||
\(957\) | 246.537 | 0.257615 | ||||||||
\(958\) | −392.169 | − | 32.1999i | −0.409362 | − | 0.0336116i | ||||
\(959\) | 715.833i | 0.746437i | ||||||||
\(960\) | 162.010 | − | 302.614i | 0.168761 | − | 0.315223i | ||||
\(961\) | −740.921 | −0.770990 | ||||||||
\(962\) | −10.6166 | + | 129.301i | −0.0110359 | + | 0.134409i | ||||
\(963\) | 249.117i | 0.258688i | ||||||||
\(964\) | 460.463 | + | 76.1278i | 0.477658 | + | 0.0789708i | ||||
\(965\) | 365.932 | 0.379204 | ||||||||
\(966\) | 218.298 | + | 17.9238i | 0.225981 | + | 0.0185547i | ||||
\(967\) | − | 717.087i | − | 0.741558i | −0.928721 | − | 0.370779i | \(-0.879091\pi\) | ||
0.928721 | − | 0.370779i | \(-0.120909\pi\) | |||||||
\(968\) | 95.4209 | − | 380.404i | 0.0985753 | − | 0.392979i | ||||
\(969\) | 420.020 | 0.433457 | ||||||||
\(970\) | 18.0125 | − | 219.378i | 0.0185696 | − | 0.226163i | ||||
\(971\) | − | 675.604i | − | 0.695782i | −0.937535 | − | 0.347891i | \(-0.886898\pi\) | ||
0.937535 | − | 0.347891i | \(-0.113102\pi\) | |||||||
\(972\) | 164.192 | − | 993.121i | 0.168922 | − | 1.02173i | ||||
\(973\) | −41.5246 | −0.0426769 | ||||||||
\(974\) | −977.114 | − | 80.2281i | −1.00320 | − | 0.0823697i | ||||
\(975\) | 381.971i | 0.391765i | ||||||||
\(976\) | −1099.40 | − | 373.741i | −1.12643 | − | 0.382931i | ||||
\(977\) | 582.678 | 0.596395 | 0.298197 | − | 0.954504i | \(-0.403615\pi\) | ||||
0.298197 | + | 0.954504i | \(0.403615\pi\) | |||||||
\(978\) | −17.5135 | + | 213.300i | −0.0179074 | + | 0.218098i | ||||
\(979\) | − | 1051.20i | − | 1.07375i | ||||||
\(980\) | 94.9587 | + | 15.6994i | 0.0968966 | + | 0.0160198i | ||||
\(981\) | 579.277 | 0.590496 | ||||||||
\(982\) | 1698.54 | + | 139.462i | 1.72968 | + | 0.142019i | ||||
\(983\) | − | 448.087i | − | 0.455837i | −0.973680 | − | 0.227918i | \(-0.926808\pi\) | ||
0.973680 | − | 0.227918i | \(-0.0731919\pi\) | |||||||
\(984\) | 457.112 | + | 114.663i | 0.464545 | + | 0.116527i | ||||
\(985\) | −611.406 | −0.620716 | ||||||||
\(986\) | 27.0519 | − | 329.470i | 0.0274360 | − | 0.334149i | ||||
\(987\) | 214.583i | 0.217410i | ||||||||
\(988\) | −367.482 | + | 2222.73i | −0.371946 | + | 2.24973i | ||||
\(989\) | 1348.11 | 1.36311 | ||||||||
\(990\) | 381.653 | + | 31.3364i | 0.385508 | + | 0.0316530i | ||||
\(991\) | 872.154i | 0.880075i | 0.897979 | + | 0.440037i | \(0.145035\pi\) | ||||
−0.897979 | + | 0.440037i | \(0.854965\pi\) | |||||||
\(992\) | 1210.93 | + | 525.756i | 1.22069 | + | 0.529996i | ||||
\(993\) | 276.462 | 0.278410 | ||||||||
\(994\) | 21.9174 | − | 266.937i | 0.0220497 | − | 0.268548i | ||||
\(995\) | − | 919.966i | − | 0.924589i | ||||||
\(996\) | 26.3608 | + | 4.35820i | 0.0264666 | + | 0.00437570i | ||||
\(997\) | −1176.24 | −1.17978 | −0.589888 | − | 0.807485i | \(-0.700828\pi\) | ||||
−0.589888 | + | 0.807485i | \(0.700828\pi\) | |||||||
\(998\) | −1698.16 | − | 139.431i | −1.70156 | − | 0.139710i | ||||
\(999\) | − | 84.8441i | − | 0.0849290i |
(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 | 28.3.c.a.15.4 | yes | 6 | |
3.2 | odd | 2 | 252.3.g.a.127.3 | 6 | |||
4.3 | odd | 2 | inner | 28.3.c.a.15.3 | ✓ | 6 | |
7.2 | even | 3 | 196.3.g.k.67.6 | 12 | |||
7.3 | odd | 6 | 196.3.g.j.79.2 | 12 | |||
7.4 | even | 3 | 196.3.g.k.79.2 | 12 | |||
7.5 | odd | 6 | 196.3.g.j.67.6 | 12 | |||
7.6 | odd | 2 | 196.3.c.g.99.4 | 6 | |||
8.3 | odd | 2 | 448.3.d.d.127.4 | 6 | |||
8.5 | even | 2 | 448.3.d.d.127.3 | 6 | |||
12.11 | even | 2 | 252.3.g.a.127.4 | 6 | |||
16.3 | odd | 4 | 1792.3.g.g.127.7 | 12 | |||
16.5 | even | 4 | 1792.3.g.g.127.8 | 12 | |||
16.11 | odd | 4 | 1792.3.g.g.127.6 | 12 | |||
16.13 | even | 4 | 1792.3.g.g.127.5 | 12 | |||
28.3 | even | 6 | 196.3.g.j.79.6 | 12 | |||
28.11 | odd | 6 | 196.3.g.k.79.6 | 12 | |||
28.19 | even | 6 | 196.3.g.j.67.2 | 12 | |||
28.23 | odd | 6 | 196.3.g.k.67.2 | 12 | |||
28.27 | even | 2 | 196.3.c.g.99.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.3.c.a.15.3 | ✓ | 6 | 4.3 | odd | 2 | inner | |
28.3.c.a.15.4 | yes | 6 | 1.1 | even | 1 | trivial | |
196.3.c.g.99.3 | 6 | 28.27 | even | 2 | |||
196.3.c.g.99.4 | 6 | 7.6 | odd | 2 | |||
196.3.g.j.67.2 | 12 | 28.19 | even | 6 | |||
196.3.g.j.67.6 | 12 | 7.5 | odd | 6 | |||
196.3.g.j.79.2 | 12 | 7.3 | odd | 6 | |||
196.3.g.j.79.6 | 12 | 28.3 | even | 6 | |||
196.3.g.k.67.2 | 12 | 28.23 | odd | 6 | |||
196.3.g.k.67.6 | 12 | 7.2 | even | 3 | |||
196.3.g.k.79.2 | 12 | 7.4 | even | 3 | |||
196.3.g.k.79.6 | 12 | 28.11 | odd | 6 | |||
252.3.g.a.127.3 | 6 | 3.2 | odd | 2 | |||
252.3.g.a.127.4 | 6 | 12.11 | even | 2 | |||
448.3.d.d.127.3 | 6 | 8.5 | even | 2 | |||
448.3.d.d.127.4 | 6 | 8.3 | odd | 2 | |||
1792.3.g.g.127.5 | 12 | 16.13 | even | 4 | |||
1792.3.g.g.127.6 | 12 | 16.11 | odd | 4 | |||
1792.3.g.g.127.7 | 12 | 16.3 | odd | 4 | |||
1792.3.g.g.127.8 | 12 | 16.5 | even | 4 |