Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(122,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.122");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.j (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Relative dimension: | \(48\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 122.18 | ||
Character | \(\chi\) | \(=\) | 429.122 |
Dual form | 429.2.j.a.320.18 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.680371 | − | 0.680371i | −0.481095 | − | 0.481095i | 0.424386 | − | 0.905481i | \(-0.360490\pi\) |
−0.905481 | + | 0.424386i | \(0.860490\pi\) | |||||||
\(3\) | −0.131936 | + | 1.72702i | −0.0761732 | + | 0.997095i | ||||
\(4\) | − | 1.07419i | − | 0.537095i | ||||||
\(5\) | −1.70906 | − | 1.70906i | −0.764316 | − | 0.764316i | 0.212783 | − | 0.977099i | \(-0.431747\pi\) |
−0.977099 | + | 0.212783i | \(0.931747\pi\) | |||||||
\(6\) | 1.26478 | − | 1.08525i | 0.516344 | − | 0.443051i | ||||
\(7\) | 2.81165 | + | 2.81165i | 1.06270 | + | 1.06270i | 0.997898 | + | 0.0648056i | \(0.0206427\pi\) |
0.0648056 | + | 0.997898i | \(0.479357\pi\) | |||||||
\(8\) | −2.09159 | + | 2.09159i | −0.739489 | + | 0.739489i | ||||
\(9\) | −2.96519 | − | 0.455712i | −0.988395 | − | 0.151904i | ||||
\(10\) | 2.32560i | 0.735418i | ||||||||
\(11\) | 0.707107 | − | 0.707107i | 0.213201 | − | 0.213201i | ||||
\(12\) | 1.85515 | + | 0.141724i | 0.535534 | + | 0.0409122i | ||||
\(13\) | 3.50480 | − | 0.846407i | 0.972056 | − | 0.234751i | ||||
\(14\) | − | 3.82593i | − | 1.02252i | ||||||
\(15\) | 3.17707 | − | 2.72610i | 0.820316 | − | 0.703875i | ||||
\(16\) | 0.697738 | 0.174434 | ||||||||
\(17\) | 5.81944 | 1.41142 | 0.705710 | − | 0.708500i | \(-0.250628\pi\) | ||||
0.705710 | + | 0.708500i | \(0.250628\pi\) | |||||||
\(18\) | 1.70737 | + | 2.32748i | 0.402432 | + | 0.548592i | ||||
\(19\) | 1.64641 | − | 1.64641i | 0.377713 | − | 0.377713i | −0.492563 | − | 0.870277i | \(-0.663940\pi\) |
0.870277 | + | 0.492563i | \(0.163940\pi\) | |||||||
\(20\) | −1.83586 | + | 1.83586i | −0.410510 | + | 0.410510i | ||||
\(21\) | −5.22673 | + | 4.48481i | −1.14057 | + | 0.978666i | ||||
\(22\) | −0.962190 | −0.205140 | ||||||||
\(23\) | 0.839365 | 0.175020 | 0.0875098 | − | 0.996164i | \(-0.472109\pi\) | ||||
0.0875098 | + | 0.996164i | \(0.472109\pi\) | |||||||
\(24\) | −3.33626 | − | 3.88817i | −0.681011 | − | 0.793670i | ||||
\(25\) | 0.841793i | 0.168359i | ||||||||
\(26\) | −2.96043 | − | 1.80869i | −0.580589 | − | 0.354714i | ||||
\(27\) | 1.17824 | − | 5.06081i | 0.226752 | − | 0.973953i | ||||
\(28\) | 3.02024 | − | 3.02024i | 0.570773 | − | 0.570773i | ||||
\(29\) | 0.447682i | 0.0831324i | 0.999136 | + | 0.0415662i | \(0.0132347\pi\) | ||||
−0.999136 | + | 0.0415662i | \(0.986765\pi\) | |||||||
\(30\) | −4.01635 | − | 0.306830i | −0.733281 | − | 0.0560192i | ||||
\(31\) | 2.48598 | − | 2.48598i | 0.446495 | − | 0.446495i | −0.447693 | − | 0.894188i | \(-0.647754\pi\) |
0.894188 | + | 0.447693i | \(0.147754\pi\) | |||||||
\(32\) | 3.70846 | + | 3.70846i | 0.655569 | + | 0.655569i | ||||
\(33\) | 1.12789 | + | 1.31448i | 0.196341 | + | 0.228821i | ||||
\(34\) | −3.95938 | − | 3.95938i | −0.679028 | − | 0.679028i | ||||
\(35\) | − | 9.61057i | − | 1.62448i | ||||||
\(36\) | −0.489521 | + | 3.18517i | −0.0815868 | + | 0.530862i | ||||
\(37\) | 5.15681 | + | 5.15681i | 0.847774 | + | 0.847774i | 0.989855 | − | 0.142081i | \(-0.0453795\pi\) |
−0.142081 | + | 0.989855i | \(0.545379\pi\) | |||||||
\(38\) | −2.24035 | −0.363432 | ||||||||
\(39\) | 0.999353 | + | 6.16452i | 0.160024 | + | 0.987113i | ||||
\(40\) | 7.14932 | 1.13041 | ||||||||
\(41\) | 5.85508 | + | 5.85508i | 0.914410 | + | 0.914410i | 0.996615 | − | 0.0822051i | \(-0.0261963\pi\) |
−0.0822051 | + | 0.996615i | \(0.526196\pi\) | |||||||
\(42\) | 6.60745 | + | 0.504778i | 1.01955 | + | 0.0778889i | ||||
\(43\) | − | 4.97364i | − | 0.758473i | −0.925300 | − | 0.379237i | \(-0.876187\pi\) | ||
0.925300 | − | 0.379237i | \(-0.123813\pi\) | |||||||
\(44\) | −0.759567 | − | 0.759567i | −0.114509 | − | 0.114509i | ||||
\(45\) | 4.28885 | + | 5.84653i | 0.639344 | + | 0.871549i | ||||
\(46\) | −0.571080 | − | 0.571080i | −0.0842011 | − | 0.0842011i | ||||
\(47\) | 2.83286 | − | 2.83286i | 0.413215 | − | 0.413215i | −0.469642 | − | 0.882857i | \(-0.655617\pi\) |
0.882857 | + | 0.469642i | \(0.155617\pi\) | |||||||
\(48\) | −0.0920567 | + | 1.20501i | −0.0132872 | + | 0.173928i | ||||
\(49\) | 8.81074i | 1.25868i | ||||||||
\(50\) | 0.572732 | − | 0.572732i | 0.0809966 | − | 0.0809966i | ||||
\(51\) | −0.767793 | + | 10.0503i | −0.107512 | + | 1.40732i | ||||
\(52\) | −0.909202 | − | 3.76482i | −0.126084 | − | 0.522086i | ||||
\(53\) | 1.33071i | 0.182787i | 0.995815 | + | 0.0913937i | \(0.0291322\pi\) | ||||
−0.995815 | + | 0.0913937i | \(0.970868\pi\) | |||||||
\(54\) | −4.24487 | + | 2.64159i | −0.577653 | + | 0.359475i | ||||
\(55\) | −2.41698 | −0.325906 | ||||||||
\(56\) | −11.7616 | −1.57172 | ||||||||
\(57\) | 2.62617 | + | 3.06061i | 0.347844 | + | 0.405388i | ||||
\(58\) | 0.304590 | − | 0.304590i | 0.0399946 | − | 0.0399946i | ||||
\(59\) | 9.10853 | − | 9.10853i | 1.18583 | − | 1.18583i | 0.207621 | − | 0.978209i | \(-0.433428\pi\) |
0.978209 | − | 0.207621i | \(-0.0665720\pi\) | |||||||
\(60\) | −2.92834 | − | 3.41278i | −0.378048 | − | 0.440587i | ||||
\(61\) | −13.8044 | −1.76747 | −0.883734 | − | 0.467990i | \(-0.844978\pi\) | ||||
−0.883734 | + | 0.467990i | \(0.844978\pi\) | |||||||
\(62\) | −3.38278 | −0.429613 | ||||||||
\(63\) | −7.05576 | − | 9.61836i | −0.888942 | − | 1.21180i | ||||
\(64\) | − | 6.44174i | − | 0.805217i | ||||||
\(65\) | −7.43648 | − | 4.54335i | −0.922382 | − | 0.563534i | ||||
\(66\) | 0.126947 | − | 1.66172i | 0.0156262 | − | 0.204544i | ||||
\(67\) | −10.4347 | + | 10.4347i | −1.27480 | + | 1.27480i | −0.331260 | + | 0.943540i | \(0.607474\pi\) |
−0.943540 | + | 0.331260i | \(0.892526\pi\) | |||||||
\(68\) | − | 6.25118i | − | 0.758067i | ||||||
\(69\) | −0.110742 | + | 1.44960i | −0.0133318 | + | 0.174511i | ||||
\(70\) | −6.53876 | + | 6.53876i | −0.781531 | + | 0.781531i | ||||
\(71\) | 0.802258 | + | 0.802258i | 0.0952105 | + | 0.0952105i | 0.753108 | − | 0.657897i | \(-0.228554\pi\) |
−0.657897 | + | 0.753108i | \(0.728554\pi\) | |||||||
\(72\) | 7.15512 | − | 5.24879i | 0.843239 | − | 0.618576i | ||||
\(73\) | 7.40166 | + | 7.40166i | 0.866299 | + | 0.866299i | 0.992061 | − | 0.125762i | \(-0.0401374\pi\) |
−0.125762 | + | 0.992061i | \(0.540137\pi\) | |||||||
\(74\) | − | 7.01709i | − | 0.815720i | ||||||
\(75\) | −1.45379 | − | 0.111063i | −0.167870 | − | 0.0128244i | ||||
\(76\) | −1.76856 | − | 1.76856i | −0.202868 | − | 0.202868i | ||||
\(77\) | 3.97627 | 0.453138 | ||||||||
\(78\) | 3.51423 | − | 4.87409i | 0.397908 | − | 0.551882i | ||||
\(79\) | −10.1499 | −1.14196 | −0.570978 | − | 0.820965i | \(-0.693436\pi\) | ||||
−0.570978 | + | 0.820965i | \(0.693436\pi\) | |||||||
\(80\) | −1.19248 | − | 1.19248i | −0.133323 | − | 0.133323i | ||||
\(81\) | 8.58465 | + | 2.70254i | 0.953850 | + | 0.300282i | ||||
\(82\) | − | 7.96726i | − | 0.879837i | ||||||
\(83\) | −7.43639 | − | 7.43639i | −0.816250 | − | 0.816250i | 0.169313 | − | 0.985562i | \(-0.445845\pi\) |
−0.985562 | + | 0.169313i | \(0.945845\pi\) | |||||||
\(84\) | 4.81754 | + | 5.61450i | 0.525637 | + | 0.612592i | ||||
\(85\) | −9.94579 | − | 9.94579i | −1.07877 | − | 1.07877i | ||||
\(86\) | −3.38392 | + | 3.38392i | −0.364898 | + | 0.364898i | ||||
\(87\) | −0.773154 | − | 0.0590653i | −0.0828909 | − | 0.00633246i | ||||
\(88\) | 2.95796i | 0.315319i | ||||||||
\(89\) | −9.42130 | + | 9.42130i | −0.998656 | + | 0.998656i | −0.999999 | − | 0.00134288i | \(-0.999573\pi\) |
0.00134288 | + | 0.999999i | \(0.499573\pi\) | |||||||
\(90\) | 1.05980 | − | 6.89582i | 0.111713 | − | 0.726883i | ||||
\(91\) | 12.2341 | + | 7.47446i | 1.28248 | + | 0.783536i | ||||
\(92\) | − | 0.901637i | − | 0.0940021i | ||||||
\(93\) | 3.96534 | + | 4.62132i | 0.411187 | + | 0.479209i | ||||
\(94\) | −3.85479 | −0.397591 | ||||||||
\(95\) | −5.62765 | −0.577385 | ||||||||
\(96\) | −6.89386 | + | 5.91530i | −0.703602 | + | 0.603728i | ||||
\(97\) | −6.07376 | + | 6.07376i | −0.616696 | + | 0.616696i | −0.944683 | − | 0.327986i | \(-0.893630\pi\) |
0.327986 | + | 0.944683i | \(0.393630\pi\) | |||||||
\(98\) | 5.99458 | − | 5.99458i | 0.605544 | − | 0.605544i | ||||
\(99\) | −2.41894 | + | 1.77447i | −0.243113 | + | 0.178341i | ||||
\(100\) | 0.904246 | 0.0904246 | ||||||||
\(101\) | −1.43632 | −0.142919 | −0.0714597 | − | 0.997443i | \(-0.522766\pi\) | ||||
−0.0714597 | + | 0.997443i | \(0.522766\pi\) | |||||||
\(102\) | 7.36030 | − | 6.31554i | 0.728779 | − | 0.625331i | ||||
\(103\) | − | 2.87211i | − | 0.282997i | −0.989938 | − | 0.141499i | \(-0.954808\pi\) | ||
0.989938 | − | 0.141499i | \(-0.0451921\pi\) | |||||||
\(104\) | −5.56026 | + | 9.10094i | −0.545228 | + | 0.892420i | ||||
\(105\) | 16.5976 | + | 1.26798i | 1.61976 | + | 0.123742i | ||||
\(106\) | 0.905379 | − | 0.905379i | 0.0879382 | − | 0.0879382i | ||||
\(107\) | − | 6.76615i | − | 0.654108i | −0.945006 | − | 0.327054i | \(-0.893944\pi\) | ||
0.945006 | − | 0.327054i | \(-0.106056\pi\) | |||||||
\(108\) | −5.43626 | − | 1.26565i | −0.523105 | − | 0.121787i | ||||
\(109\) | 8.32125 | − | 8.32125i | 0.797031 | − | 0.797031i | −0.185595 | − | 0.982626i | \(-0.559421\pi\) |
0.982626 | + | 0.185595i | \(0.0594213\pi\) | |||||||
\(110\) | 1.64444 | + | 1.64444i | 0.156792 | + | 0.156792i | ||||
\(111\) | −9.58627 | + | 8.22553i | −0.909888 | + | 0.780733i | ||||
\(112\) | 1.96179 | + | 1.96179i | 0.185372 | + | 0.185372i | ||||
\(113\) | − | 6.35372i | − | 0.597708i | −0.954299 | − | 0.298854i | \(-0.903396\pi\) | ||
0.954299 | − | 0.298854i | \(-0.0966044\pi\) | |||||||
\(114\) | 0.295582 | − | 3.86912i | 0.0276838 | − | 0.362376i | ||||
\(115\) | −1.43453 | − | 1.43453i | −0.133770 | − | 0.133770i | ||||
\(116\) | 0.480895 | 0.0446500 | ||||||||
\(117\) | −10.7781 | + | 0.912579i | −0.996435 | + | 0.0843680i | ||||
\(118\) | −12.3944 | −1.14099 | ||||||||
\(119\) | 16.3622 | + | 16.3622i | 1.49992 | + | 1.49992i | ||||
\(120\) | −0.943252 | + | 12.3470i | −0.0861067 | + | 1.12712i | ||||
\(121\) | − | 1.00000i | − | 0.0909091i | ||||||
\(122\) | 9.39210 | + | 9.39210i | 0.850320 | + | 0.850320i | ||||
\(123\) | −10.8843 | + | 9.33934i | −0.981407 | + | 0.842100i | ||||
\(124\) | −2.67041 | − | 2.67041i | −0.239810 | − | 0.239810i | ||||
\(125\) | −7.10664 | + | 7.10664i | −0.635637 | + | 0.635637i | ||||
\(126\) | −1.74352 | + | 11.3446i | −0.155325 | + | 1.01066i | ||||
\(127\) | − | 7.46419i | − | 0.662340i | −0.943571 | − | 0.331170i | \(-0.892557\pi\) | ||
0.943571 | − | 0.331170i | \(-0.107443\pi\) | |||||||
\(128\) | 3.03415 | − | 3.03415i | 0.268183 | − | 0.268183i | ||||
\(129\) | 8.58957 | + | 0.656202i | 0.756270 | + | 0.0577754i | ||||
\(130\) | 1.96840 | + | 8.15074i | 0.172640 | + | 0.714867i | ||||
\(131\) | 1.76387i | 0.154110i | 0.997027 | + | 0.0770550i | \(0.0245517\pi\) | ||||
−0.997027 | + | 0.0770550i | \(0.975448\pi\) | |||||||
\(132\) | 1.41200 | − | 1.21157i | 0.122899 | − | 0.105454i | ||||
\(133\) | 9.25828 | 0.802795 | ||||||||
\(134\) | 14.1989 | 1.22660 | ||||||||
\(135\) | −10.6629 | + | 6.63556i | −0.917718 | + | 0.571098i | ||||
\(136\) | −12.1719 | + | 12.1719i | −1.04373 | + | 1.04373i | ||||
\(137\) | −13.5834 | + | 13.5834i | −1.16051 | + | 1.16051i | −0.176148 | + | 0.984364i | \(0.556364\pi\) |
−0.984364 | + | 0.176148i | \(0.943636\pi\) | |||||||
\(138\) | 1.06161 | − | 0.910919i | 0.0903703 | − | 0.0775426i | ||||
\(139\) | −13.6260 | −1.15574 | −0.577870 | − | 0.816129i | \(-0.696116\pi\) | ||||
−0.577870 | + | 0.816129i | \(0.696116\pi\) | |||||||
\(140\) | −10.3236 | −0.872501 | ||||||||
\(141\) | 4.51864 | + | 5.26615i | 0.380538 | + | 0.443490i | ||||
\(142\) | − | 1.09167i | − | 0.0916106i | ||||||
\(143\) | 1.87976 | − | 3.07677i | 0.157194 | − | 0.257292i | ||||
\(144\) | −2.06892 | − | 0.317967i | −0.172410 | − | 0.0264973i | ||||
\(145\) | 0.765116 | − | 0.765116i | 0.0635394 | − | 0.0635394i | ||||
\(146\) | − | 10.0718i | − | 0.833545i | ||||||
\(147\) | −15.2163 | − | 1.16245i | −1.25502 | − | 0.0958775i | ||||
\(148\) | 5.53939 | − | 5.53939i | 0.455335 | − | 0.455335i | ||||
\(149\) | −4.01381 | − | 4.01381i | −0.328824 | − | 0.328824i | 0.523315 | − | 0.852139i | \(-0.324695\pi\) |
−0.852139 | + | 0.523315i | \(0.824695\pi\) | |||||||
\(150\) | 0.913555 | + | 1.06468i | 0.0745915 | + | 0.0869310i | ||||
\(151\) | 16.4170 | + | 16.4170i | 1.33599 | + | 1.33599i | 0.899904 | + | 0.436089i | \(0.143637\pi\) |
0.436089 | + | 0.899904i | \(0.356363\pi\) | |||||||
\(152\) | 6.88725i | 0.558630i | ||||||||
\(153\) | −17.2557 | − | 2.65198i | −1.39504 | − | 0.214400i | ||||
\(154\) | −2.70534 | − | 2.70534i | −0.218003 | − | 0.218003i | ||||
\(155\) | −8.49739 | −0.682527 | ||||||||
\(156\) | 6.62186 | − | 1.07349i | 0.530173 | − | 0.0859483i | ||||
\(157\) | 14.4641 | 1.15436 | 0.577182 | − | 0.816616i | \(-0.304152\pi\) | ||||
0.577182 | + | 0.816616i | \(0.304152\pi\) | |||||||
\(158\) | 6.90572 | + | 6.90572i | 0.549390 | + | 0.549390i | ||||
\(159\) | −2.29817 | − | 0.175569i | −0.182256 | − | 0.0139235i | ||||
\(160\) | − | 12.6760i | − | 1.00212i | ||||||
\(161\) | 2.36000 | + | 2.36000i | 0.185994 | + | 0.185994i | ||||
\(162\) | −4.00202 | − | 7.67948i | −0.314429 | − | 0.603357i | ||||
\(163\) | −2.49100 | − | 2.49100i | −0.195110 | − | 0.195110i | 0.602790 | − | 0.797900i | \(-0.294056\pi\) |
−0.797900 | + | 0.602790i | \(0.794056\pi\) | |||||||
\(164\) | 6.28947 | − | 6.28947i | 0.491125 | − | 0.491125i | ||||
\(165\) | 0.318886 | − | 4.17417i | 0.0248253 | − | 0.324959i | ||||
\(166\) | 10.1190i | 0.785388i | ||||||||
\(167\) | 5.44439 | − | 5.44439i | 0.421300 | − | 0.421300i | −0.464351 | − | 0.885651i | \(-0.653712\pi\) |
0.885651 | + | 0.464351i | \(0.153712\pi\) | |||||||
\(168\) | 1.55178 | − | 20.3126i | 0.119723 | − | 1.56715i | ||||
\(169\) | 11.5672 | − | 5.93297i | 0.889784 | − | 0.456382i | ||||
\(170\) | 13.5337i | 1.03798i | ||||||||
\(171\) | −5.63221 | + | 4.13163i | −0.430706 | + | 0.315954i | ||||
\(172\) | −5.34263 | −0.407372 | ||||||||
\(173\) | 4.69200 | 0.356726 | 0.178363 | − | 0.983965i | \(-0.442920\pi\) | ||||
0.178363 | + | 0.983965i | \(0.442920\pi\) | |||||||
\(174\) | 0.485846 | + | 0.566218i | 0.0368319 | + | 0.0429249i | ||||
\(175\) | −2.36683 | + | 2.36683i | −0.178915 | + | 0.178915i | ||||
\(176\) | 0.493375 | − | 0.493375i | 0.0371896 | − | 0.0371896i | ||||
\(177\) | 14.5289 | + | 16.9324i | 1.09206 | + | 1.27271i | ||||
\(178\) | 12.8200 | 0.960897 | ||||||||
\(179\) | 18.4698 | 1.38050 | 0.690250 | − | 0.723571i | \(-0.257501\pi\) | ||||
0.690250 | + | 0.723571i | \(0.257501\pi\) | |||||||
\(180\) | 6.28028 | − | 4.60704i | 0.468104 | − | 0.343388i | ||||
\(181\) | − | 13.9573i | − | 1.03744i | −0.854944 | − | 0.518720i | \(-0.826409\pi\) | ||
0.854944 | − | 0.518720i | \(-0.173591\pi\) | |||||||
\(182\) | −3.23830 | − | 13.4091i | −0.240038 | − | 0.993949i | ||||
\(183\) | 1.82129 | − | 23.8404i | 0.134634 | − | 1.76233i | ||||
\(184\) | −1.75561 | + | 1.75561i | −0.129425 | + | 0.129425i | ||||
\(185\) | − | 17.6266i | − | 1.29593i | ||||||
\(186\) | 0.446310 | − | 5.84212i | 0.0327250 | − | 0.428365i | ||||
\(187\) | 4.11496 | − | 4.11496i | 0.300916 | − | 0.300916i | ||||
\(188\) | −3.04303 | − | 3.04303i | −0.221936 | − | 0.221936i | ||||
\(189\) | 17.5420 | − | 10.9164i | 1.27599 | − | 0.794053i | ||||
\(190\) | 3.82889 | + | 3.82889i | 0.277777 | + | 0.277777i | ||||
\(191\) | − | 9.05696i | − | 0.655339i | −0.944792 | − | 0.327669i | \(-0.893737\pi\) | ||
0.944792 | − | 0.327669i | \(-0.106263\pi\) | |||||||
\(192\) | 11.1250 | + | 0.849896i | 0.802878 | + | 0.0613360i | ||||
\(193\) | −15.2790 | − | 15.2790i | −1.09980 | − | 1.09980i | −0.994433 | − | 0.105371i | \(-0.966397\pi\) |
−0.105371 | − | 0.994433i | \(-0.533603\pi\) | |||||||
\(194\) | 8.26482 | 0.593379 | ||||||||
\(195\) | 8.82760 | − | 12.2435i | 0.632157 | − | 0.876776i | ||||
\(196\) | 9.46441 | 0.676029 | ||||||||
\(197\) | 14.7409 | + | 14.7409i | 1.05024 | + | 1.05024i | 0.998669 | + | 0.0515755i | \(0.0164243\pi\) |
0.0515755 | + | 0.998669i | \(0.483576\pi\) | |||||||
\(198\) | 2.85307 | + | 0.438481i | 0.202759 | + | 0.0311615i | ||||
\(199\) | 8.62346i | 0.611301i | 0.952144 | + | 0.305651i | \(0.0988739\pi\) | ||||
−0.952144 | + | 0.305651i | \(0.901126\pi\) | |||||||
\(200\) | −1.76069 | − | 1.76069i | −0.124499 | − | 0.124499i | ||||
\(201\) | −16.6442 | − | 19.3976i | −1.17399 | − | 1.36820i | ||||
\(202\) | 0.977233 | + | 0.977233i | 0.0687579 | + | 0.0687579i | ||||
\(203\) | −1.25872 | + | 1.25872i | −0.0883451 | + | 0.0883451i | ||||
\(204\) | 10.7959 | + | 0.824755i | 0.755864 | + | 0.0577444i | ||||
\(205\) | − | 20.0134i | − | 1.39780i | ||||||
\(206\) | −1.95410 | + | 1.95410i | −0.136149 | + | 0.136149i | ||||
\(207\) | −2.48887 | − | 0.382508i | −0.172989 | − | 0.0265862i | ||||
\(208\) | 2.44543 | − | 0.590570i | 0.169560 | − | 0.0409487i | ||||
\(209\) | − | 2.32838i | − | 0.161058i | ||||||
\(210\) | −10.4299 | − | 12.1553i | −0.719729 | − | 0.838792i | ||||
\(211\) | −6.84506 | −0.471233 | −0.235617 | − | 0.971846i | \(-0.575711\pi\) | ||||
−0.235617 | + | 0.971846i | \(0.575711\pi\) | |||||||
\(212\) | 1.42944 | 0.0981742 | ||||||||
\(213\) | −1.49136 | + | 1.27967i | −0.102186 | + | 0.0876814i | ||||
\(214\) | −4.60349 | + | 4.60349i | −0.314688 | + | 0.314688i | ||||
\(215\) | −8.50027 | + | 8.50027i | −0.579713 | + | 0.579713i | ||||
\(216\) | 8.12075 | + | 13.0495i | 0.552547 | + | 0.887908i | ||||
\(217\) | 13.9794 | 0.948984 | ||||||||
\(218\) | −11.3231 | −0.766896 | ||||||||
\(219\) | −13.7594 | + | 11.8063i | −0.929771 | + | 0.797793i | ||||
\(220\) | 2.59629i | 0.175042i | ||||||||
\(221\) | 20.3959 | − | 4.92561i | 1.37198 | − | 0.331333i | ||||
\(222\) | 12.1186 | + | 0.925806i | 0.813350 | + | 0.0621360i | ||||
\(223\) | −8.92553 | + | 8.92553i | −0.597698 | + | 0.597698i | −0.939699 | − | 0.342001i | \(-0.888895\pi\) |
0.342001 | + | 0.939699i | \(0.388895\pi\) | |||||||
\(224\) | 20.8538i | 1.39335i | ||||||||
\(225\) | 0.383615 | − | 2.49607i | 0.0255743 | − | 0.166405i | ||||
\(226\) | −4.32289 | + | 4.32289i | −0.287555 | + | 0.287555i | ||||
\(227\) | −1.70381 | − | 1.70381i | −0.113086 | − | 0.113086i | 0.648300 | − | 0.761385i | \(-0.275480\pi\) |
−0.761385 | + | 0.648300i | \(0.775480\pi\) | |||||||
\(228\) | 3.28767 | − | 2.82100i | 0.217732 | − | 0.186825i | ||||
\(229\) | 4.35502 | + | 4.35502i | 0.287788 | + | 0.287788i | 0.836205 | − | 0.548417i | \(-0.184769\pi\) |
−0.548417 | + | 0.836205i | \(0.684769\pi\) | |||||||
\(230\) | 1.95202i | 0.128713i | ||||||||
\(231\) | −0.524613 | + | 6.86710i | −0.0345170 | + | 0.451822i | ||||
\(232\) | −0.936367 | − | 0.936367i | −0.0614755 | − | 0.0614755i | ||||
\(233\) | 1.44883 | 0.0949157 | 0.0474578 | − | 0.998873i | \(-0.484888\pi\) | ||||
0.0474578 | + | 0.998873i | \(0.484888\pi\) | |||||||
\(234\) | 7.95400 | + | 6.71221i | 0.519969 | + | 0.438791i | ||||
\(235\) | −9.68307 | −0.631654 | ||||||||
\(236\) | −9.78429 | − | 9.78429i | −0.636903 | − | 0.636903i | ||||
\(237\) | 1.33914 | − | 17.5291i | 0.0869865 | − | 1.13864i | ||||
\(238\) | − | 22.2648i | − | 1.44321i | ||||||
\(239\) | −8.31725 | − | 8.31725i | −0.537998 | − | 0.537998i | 0.384943 | − | 0.922941i | \(-0.374221\pi\) |
−0.922941 | + | 0.384943i | \(0.874221\pi\) | |||||||
\(240\) | 2.21676 | − | 1.90210i | 0.143091 | − | 0.122780i | ||||
\(241\) | 0.461259 | + | 0.461259i | 0.0297123 | + | 0.0297123i | 0.721807 | − | 0.692095i | \(-0.243312\pi\) |
−0.692095 | + | 0.721807i | \(0.743312\pi\) | |||||||
\(242\) | −0.680371 | + | 0.680371i | −0.0437359 | + | 0.0437359i | ||||
\(243\) | −5.79996 | + | 14.4693i | −0.372067 | + | 0.928206i | ||||
\(244\) | 14.8285i | 0.949298i | ||||||||
\(245\) | 15.0581 | − | 15.0581i | 0.962028 | − | 0.962028i | ||||
\(246\) | 13.7596 | + | 1.05117i | 0.877281 | + | 0.0670200i | ||||
\(247\) | 4.37681 | − | 7.16388i | 0.278490 | − | 0.455827i | ||||
\(248\) | 10.3993i | 0.660356i | ||||||||
\(249\) | 13.8239 | − | 11.8617i | 0.876054 | − | 0.751702i | ||||
\(250\) | 9.67031 | 0.611604 | ||||||||
\(251\) | −22.7631 | −1.43680 | −0.718398 | − | 0.695632i | \(-0.755124\pi\) | ||||
−0.718398 | + | 0.695632i | \(0.755124\pi\) | |||||||
\(252\) | −10.3319 | + | 7.57923i | −0.650851 | + | 0.477446i | ||||
\(253\) | 0.593520 | − | 0.593520i | 0.0373143 | − | 0.0373143i | ||||
\(254\) | −5.07842 | + | 5.07842i | −0.318648 | + | 0.318648i | ||||
\(255\) | 18.4888 | − | 15.8643i | 1.15781 | − | 0.993464i | ||||
\(256\) | −17.0122 | −1.06326 | ||||||||
\(257\) | −11.4934 | −0.716939 | −0.358469 | − | 0.933542i | \(-0.616701\pi\) | ||||
−0.358469 | + | 0.933542i | \(0.616701\pi\) | |||||||
\(258\) | −5.39764 | − | 6.29056i | −0.336042 | − | 0.391633i | ||||
\(259\) | 28.9983i | 1.80186i | ||||||||
\(260\) | −4.88042 | + | 7.98819i | −0.302671 | + | 0.495407i | ||||
\(261\) | 0.204014 | − | 1.32746i | 0.0126281 | − | 0.0821677i | ||||
\(262\) | 1.20009 | − | 1.20009i | 0.0741416 | − | 0.0741416i | ||||
\(263\) | 18.6484i | 1.14991i | 0.818186 | + | 0.574954i | \(0.194980\pi\) | ||||
−0.818186 | + | 0.574954i | \(0.805020\pi\) | |||||||
\(264\) | −5.10844 | − | 0.390261i | −0.314403 | − | 0.0240189i | ||||
\(265\) | 2.27427 | − | 2.27427i | 0.139707 | − | 0.139707i | ||||
\(266\) | −6.29907 | − | 6.29907i | −0.386221 | − | 0.386221i | ||||
\(267\) | −15.0278 | − | 17.5138i | −0.919684 | − | 1.07183i | ||||
\(268\) | 11.2088 | + | 11.2088i | 0.684688 | + | 0.684688i | ||||
\(269\) | 4.24668i | 0.258925i | 0.991584 | + | 0.129462i | \(0.0413251\pi\) | ||||
−0.991584 | + | 0.129462i | \(0.958675\pi\) | |||||||
\(270\) | 11.7694 | + | 2.74010i | 0.716262 | + | 0.166757i | ||||
\(271\) | −5.07172 | − | 5.07172i | −0.308085 | − | 0.308085i | 0.536081 | − | 0.844166i | \(-0.319904\pi\) |
−0.844166 | + | 0.536081i | \(0.819904\pi\) | |||||||
\(272\) | 4.06044 | 0.246200 | ||||||||
\(273\) | −14.5226 | + | 20.1423i | −0.878950 | + | 1.21907i | ||||
\(274\) | 18.4836 | 1.11663 | ||||||||
\(275\) | 0.595238 | + | 0.595238i | 0.0358942 | + | 0.0358942i | ||||
\(276\) | 1.55714 | + | 0.118958i | 0.0937290 | + | 0.00716045i | ||||
\(277\) | − | 32.4203i | − | 1.94795i | −0.226666 | − | 0.973973i | \(-0.572782\pi\) | ||
0.226666 | − | 0.973973i | \(-0.427218\pi\) | |||||||
\(278\) | 9.27072 | + | 9.27072i | 0.556021 | + | 0.556021i | ||||
\(279\) | −8.50428 | + | 6.23850i | −0.509138 | + | 0.373489i | ||||
\(280\) | 20.1014 | + | 20.1014i | 1.20129 | + | 1.20129i | ||||
\(281\) | 13.4081 | − | 13.4081i | 0.799862 | − | 0.799862i | −0.183212 | − | 0.983074i | \(-0.558649\pi\) |
0.983074 | + | 0.183212i | \(0.0586493\pi\) | |||||||
\(282\) | 0.508585 | − | 6.65730i | 0.0302858 | − | 0.396436i | ||||
\(283\) | − | 11.7358i | − | 0.697622i | −0.937193 | − | 0.348811i | \(-0.886586\pi\) | ||
0.937193 | − | 0.348811i | \(-0.113414\pi\) | |||||||
\(284\) | 0.861777 | − | 0.861777i | 0.0511371 | − | 0.0511371i | ||||
\(285\) | 0.742489 | − | 9.71906i | 0.0439813 | − | 0.575707i | ||||
\(286\) | −3.37228 | + | 0.814405i | −0.199407 | + | 0.0481568i | ||||
\(287\) | 32.9249i | 1.94349i | ||||||||
\(288\) | −9.30629 | − | 12.6863i | −0.548378 | − | 0.747545i | ||||
\(289\) | 16.8659 | 0.992109 | ||||||||
\(290\) | −1.04113 | −0.0611370 | ||||||||
\(291\) | −9.68814 | − | 11.2908i | −0.567929 | − | 0.661880i | ||||
\(292\) | 7.95079 | − | 7.95079i | 0.465285 | − | 0.465285i | ||||
\(293\) | −23.6422 | + | 23.6422i | −1.38119 | + | 1.38119i | −0.538683 | + | 0.842509i | \(0.681078\pi\) |
−0.842509 | + | 0.538683i | \(0.818922\pi\) | |||||||
\(294\) | 9.56185 | + | 11.1436i | 0.557658 | + | 0.649911i | ||||
\(295\) | −31.1341 | −1.81270 | ||||||||
\(296\) | −21.5719 | −1.25384 | ||||||||
\(297\) | −2.74539 | − | 4.41167i | −0.159304 | − | 0.255991i | ||||
\(298\) | 5.46176i | 0.316391i | ||||||||
\(299\) | 2.94180 | − | 0.710444i | 0.170129 | − | 0.0410861i | ||||
\(300\) | −0.119302 | + | 1.56165i | −0.00688793 | + | 0.0901619i | ||||
\(301\) | 13.9841 | − | 13.9841i | 0.806032 | − | 0.806032i | ||||
\(302\) | − | 22.3392i | − | 1.28548i | ||||||
\(303\) | 0.189503 | − | 2.48056i | 0.0108866 | − | 0.142504i | ||||
\(304\) | 1.14877 | − | 1.14877i | 0.0658862 | − | 0.0658862i | ||||
\(305\) | 23.5925 | + | 23.5925i | 1.35090 | + | 1.35090i | ||||
\(306\) | 9.93596 | + | 13.5446i | 0.568001 | + | 0.774295i | ||||
\(307\) | 1.93714 | + | 1.93714i | 0.110558 | + | 0.110558i | 0.760222 | − | 0.649664i | \(-0.225090\pi\) |
−0.649664 | + | 0.760222i | \(0.725090\pi\) | |||||||
\(308\) | − | 4.27127i | − | 0.243378i | ||||||
\(309\) | 4.96019 | + | 0.378935i | 0.282175 | + | 0.0215568i | ||||
\(310\) | 5.78138 | + | 5.78138i | 0.328360 | + | 0.328360i | ||||
\(311\) | 2.50035 | 0.141782 | 0.0708908 | − | 0.997484i | \(-0.477416\pi\) | ||||
0.0708908 | + | 0.997484i | \(0.477416\pi\) | |||||||
\(312\) | −14.9839 | − | 10.8034i | −0.848296 | − | 0.611623i | ||||
\(313\) | −0.146508 | −0.00828113 | −0.00414056 | − | 0.999991i | \(-0.501318\pi\) | ||||
−0.00414056 | + | 0.999991i | \(0.501318\pi\) | |||||||
\(314\) | −9.84099 | − | 9.84099i | −0.555359 | − | 0.555359i | ||||
\(315\) | −4.37965 | + | 28.4971i | −0.246765 | + | 1.60563i | ||||
\(316\) | 10.9029i | 0.613339i | ||||||||
\(317\) | 6.82979 | + | 6.82979i | 0.383599 | + | 0.383599i | 0.872397 | − | 0.488798i | \(-0.162564\pi\) |
−0.488798 | + | 0.872397i | \(0.662564\pi\) | |||||||
\(318\) | 1.44415 | + | 1.68306i | 0.0809842 | + | 0.0943812i | ||||
\(319\) | 0.316559 | + | 0.316559i | 0.0177239 | + | 0.0177239i | ||||
\(320\) | −11.0093 | + | 11.0093i | −0.615440 | + | 0.615440i | ||||
\(321\) | 11.6853 | + | 0.892698i | 0.652208 | + | 0.0498255i | ||||
\(322\) | − | 3.21135i | − | 0.178962i | ||||||
\(323\) | 9.58120 | − | 9.58120i | 0.533112 | − | 0.533112i | ||||
\(324\) | 2.90304 | − | 9.22155i | 0.161280 | − | 0.512308i | ||||
\(325\) | 0.712500 | + | 2.95031i | 0.0395224 | + | 0.163654i | ||||
\(326\) | 3.38961i | 0.187733i | ||||||||
\(327\) | 13.2731 | + | 15.4688i | 0.734003 | + | 0.855428i | ||||
\(328\) | −24.4929 | −1.35239 | ||||||||
\(329\) | 15.9300 | 0.878250 | ||||||||
\(330\) | −3.05695 | + | 2.62302i | −0.168279 | + | 0.144393i | ||||
\(331\) | 11.9272 | − | 11.9272i | 0.655577 | − | 0.655577i | −0.298753 | − | 0.954330i | \(-0.596571\pi\) |
0.954330 | + | 0.298753i | \(0.0965707\pi\) | |||||||
\(332\) | −7.98809 | + | 7.98809i | −0.438403 | + | 0.438403i | ||||
\(333\) | −12.9409 | − | 17.6409i | −0.709155 | − | 0.966716i | ||||
\(334\) | −7.40842 | −0.405371 | ||||||||
\(335\) | 35.6671 | 1.94870 | ||||||||
\(336\) | −3.64689 | + | 3.12922i | −0.198954 | + | 0.170713i | ||||
\(337\) | 17.9076i | 0.975489i | 0.872986 | + | 0.487744i | \(0.162180\pi\) | ||||
−0.872986 | + | 0.487744i | \(0.837820\pi\) | |||||||
\(338\) | −11.9066 | − | 3.83336i | −0.647634 | − | 0.208507i | ||||
\(339\) | 10.9730 | + | 0.838284i | 0.595971 | + | 0.0455294i | ||||
\(340\) | −10.6837 | + | 10.6837i | −0.579403 | + | 0.579403i | ||||
\(341\) | − | 3.51571i | − | 0.190386i | ||||||
\(342\) | 6.64304 | + | 1.02095i | 0.359215 | + | 0.0552067i | ||||
\(343\) | −5.09118 | + | 5.09118i | −0.274898 | + | 0.274898i | ||||
\(344\) | 10.4028 | + | 10.4028i | 0.560883 | + | 0.560883i | ||||
\(345\) | 2.66672 | − | 2.28819i | 0.143571 | − | 0.123192i | ||||
\(346\) | −3.19230 | − | 3.19230i | −0.171619 | − | 0.171619i | ||||
\(347\) | 22.8397i | 1.22610i | 0.790045 | + | 0.613049i | \(0.210057\pi\) | ||||
−0.790045 | + | 0.613049i | \(0.789943\pi\) | |||||||
\(348\) | −0.0634473 | + | 0.830514i | −0.00340113 | + | 0.0445202i | ||||
\(349\) | 18.4046 | + | 18.4046i | 0.985178 | + | 0.985178i | 0.999892 | − | 0.0147141i | \(-0.00468380\pi\) |
−0.0147141 | + | 0.999892i | \(0.504684\pi\) | |||||||
\(350\) | 3.22064 | 0.172151 | ||||||||
\(351\) | −0.154024 | − | 18.7344i | −0.00822119 | − | 0.999966i | ||||
\(352\) | 5.24455 | 0.279536 | ||||||||
\(353\) | −14.0280 | − | 14.0280i | −0.746637 | − | 0.746637i | 0.227209 | − | 0.973846i | \(-0.427040\pi\) |
−0.973846 | + | 0.227209i | \(0.927040\pi\) | |||||||
\(354\) | 1.63526 | − | 21.4053i | 0.0869132 | − | 1.13768i | ||||
\(355\) | − | 2.74222i | − | 0.145542i | ||||||
\(356\) | 10.1203 | + | 10.1203i | 0.536373 | + | 0.536373i | ||||
\(357\) | −30.4166 | + | 26.0991i | −1.60982 | + | 1.38131i | ||||
\(358\) | −12.5663 | − | 12.5663i | −0.664152 | − | 0.664152i | ||||
\(359\) | 1.62278 | − | 1.62278i | 0.0856470 | − | 0.0856470i | −0.662985 | − | 0.748632i | \(-0.730711\pi\) |
0.748632 | + | 0.662985i | \(0.230711\pi\) | |||||||
\(360\) | −21.1991 | − | 3.25803i | −1.11729 | − | 0.171713i | ||||
\(361\) | 13.5786i | 0.714665i | ||||||||
\(362\) | −9.49616 | + | 9.49616i | −0.499107 | + | 0.499107i | ||||
\(363\) | 1.72702 | + | 0.131936i | 0.0906450 | + | 0.00692484i | ||||
\(364\) | 8.02898 | − | 13.1417i | 0.420833 | − | 0.688812i | ||||
\(365\) | − | 25.2998i | − | 1.32425i | ||||||
\(366\) | −17.4595 | + | 14.9812i | −0.912622 | + | 0.783078i | ||||
\(367\) | 18.1285 | 0.946300 | 0.473150 | − | 0.880982i | \(-0.343117\pi\) | ||||
0.473150 | + | 0.880982i | \(0.343117\pi\) | |||||||
\(368\) | 0.585657 | 0.0305295 | ||||||||
\(369\) | −14.6932 | − | 20.0296i | −0.764896 | − | 1.04270i | ||||
\(370\) | −11.9926 | + | 11.9926i | −0.623468 | + | 0.623468i | ||||
\(371\) | −3.74150 | + | 3.74150i | −0.194249 | + | 0.194249i | ||||
\(372\) | 4.96418 | − | 4.25953i | 0.257381 | − | 0.220846i | ||||
\(373\) | −23.6499 | −1.22454 | −0.612272 | − | 0.790647i | \(-0.709744\pi\) | ||||
−0.612272 | + | 0.790647i | \(0.709744\pi\) | |||||||
\(374\) | −5.59941 | −0.289538 | ||||||||
\(375\) | −11.3357 | − | 13.2109i | −0.585372 | − | 0.682209i | ||||
\(376\) | 11.8504i | 0.611136i | ||||||||
\(377\) | 0.378921 | + | 1.56903i | 0.0195154 | + | 0.0808093i | ||||
\(378\) | −19.3623 | − | 4.50785i | −0.995889 | − | 0.231859i | ||||
\(379\) | 5.85006 | − | 5.85006i | 0.300497 | − | 0.300497i | −0.540711 | − | 0.841208i | \(-0.681845\pi\) |
0.841208 | + | 0.540711i | \(0.181845\pi\) | |||||||
\(380\) | 6.04516i | 0.310110i | ||||||||
\(381\) | 12.8908 | + | 0.984794i | 0.660415 | + | 0.0504525i | ||||
\(382\) | −6.16210 | + | 6.16210i | −0.315280 | + | 0.315280i | ||||
\(383\) | −8.71544 | − | 8.71544i | −0.445338 | − | 0.445338i | 0.448463 | − | 0.893801i | \(-0.351972\pi\) |
−0.893801 | + | 0.448463i | \(0.851972\pi\) | |||||||
\(384\) | 4.83972 | + | 5.64034i | 0.246976 | + | 0.287832i | ||||
\(385\) | −6.79570 | − | 6.79570i | −0.346341 | − | 0.346341i | ||||
\(386\) | 20.7907i | 1.05822i | ||||||||
\(387\) | −2.26655 | + | 14.7478i | −0.115215 | + | 0.749671i | ||||
\(388\) | 6.52436 | + | 6.52436i | 0.331224 | + | 0.331224i | ||||
\(389\) | −31.6941 | −1.60696 | −0.803478 | − | 0.595334i | \(-0.797020\pi\) | ||||
−0.803478 | + | 0.595334i | \(0.797020\pi\) | |||||||
\(390\) | −14.3362 | + | 2.32409i | −0.725941 | + | 0.117685i | ||||
\(391\) | 4.88463 | 0.247026 | ||||||||
\(392\) | −18.4285 | − | 18.4285i | −0.930778 | − | 0.930778i | ||||
\(393\) | −3.04624 | − | 0.232718i | −0.153662 | − | 0.0117391i | ||||
\(394\) | − | 20.0586i | − | 1.01054i | ||||||
\(395\) | 17.3469 | + | 17.3469i | 0.872816 | + | 0.872816i | ||||
\(396\) | 1.90611 | + | 2.59840i | 0.0957858 | + | 0.130574i | ||||
\(397\) | 11.6917 | + | 11.6917i | 0.586788 | + | 0.586788i | 0.936760 | − | 0.349972i | \(-0.113809\pi\) |
−0.349972 | + | 0.936760i | \(0.613809\pi\) | |||||||
\(398\) | 5.86716 | − | 5.86716i | 0.294094 | − | 0.294094i | ||||
\(399\) | −1.22150 | + | 15.9892i | −0.0611515 | + | 0.800462i | ||||
\(400\) | 0.587351i | 0.0293676i | ||||||||
\(401\) | −4.20239 | + | 4.20239i | −0.209857 | + | 0.209857i | −0.804207 | − | 0.594349i | \(-0.797410\pi\) |
0.594349 | + | 0.804207i | \(0.297410\pi\) | |||||||
\(402\) | −1.87335 | + | 24.5218i | −0.0934341 | + | 1.22304i | ||||
\(403\) | 6.60870 | − | 10.8170i | 0.329203 | − | 0.538833i | ||||
\(404\) | 1.54288i | 0.0767613i | ||||||||
\(405\) | −10.0529 | − | 19.2905i | −0.499533 | − | 0.958554i | ||||
\(406\) | 1.71280 | 0.0850048 | ||||||||
\(407\) | 7.29282 | 0.361492 | ||||||||
\(408\) | −19.4152 | − | 22.6270i | −0.961193 | − | 1.12020i | ||||
\(409\) | −19.5100 | + | 19.5100i | −0.964708 | + | 0.964708i | −0.999398 | − | 0.0346902i | \(-0.988956\pi\) |
0.0346902 | + | 0.999398i | \(0.488956\pi\) | |||||||
\(410\) | −13.6166 | + | 13.6166i | −0.672474 | + | 0.672474i | ||||
\(411\) | −21.6667 | − | 25.2510i | −1.06874 | − | 1.24554i | ||||
\(412\) | −3.08519 | −0.151996 | ||||||||
\(413\) | 51.2200 | 2.52037 | ||||||||
\(414\) | 1.43311 | + | 1.95361i | 0.0704335 | + | 0.0960145i | ||||
\(415\) | 25.4185i | 1.24775i | ||||||||
\(416\) | 16.1363 | + | 9.85853i | 0.791145 | + | 0.483354i | ||||
\(417\) | 1.79775 | − | 23.5323i | 0.0880364 | − | 1.15238i | ||||
\(418\) | −1.58416 | + | 1.58416i | −0.0774840 | + | 0.0774840i | ||||
\(419\) | − | 12.1343i | − | 0.592799i | −0.955064 | − | 0.296400i | \(-0.904214\pi\) | ||
0.955064 | − | 0.296400i | \(-0.0957861\pi\) | |||||||
\(420\) | 1.36205 | − | 17.8290i | 0.0664613 | − | 0.869966i | ||||
\(421\) | −20.0518 | + | 20.0518i | −0.977263 | + | 0.977263i | −0.999747 | − | 0.0224841i | \(-0.992842\pi\) |
0.0224841 | + | 0.999747i | \(0.492842\pi\) | |||||||
\(422\) | 4.65718 | + | 4.65718i | 0.226708 | + | 0.226708i | ||||
\(423\) | −9.69092 | + | 7.10899i | −0.471189 | + | 0.345651i | ||||
\(424\) | −2.78331 | − | 2.78331i | −0.135169 | − | 0.135169i | ||||
\(425\) | 4.89876i | 0.237625i | ||||||||
\(426\) | 1.88533 | + | 0.144030i | 0.0913445 | + | 0.00697828i | ||||
\(427\) | −38.8130 | − | 38.8130i | −1.87829 | − | 1.87829i | ||||
\(428\) | −7.26813 | −0.351318 | ||||||||
\(429\) | 5.06562 | + | 3.65232i | 0.244571 | + | 0.176336i | ||||
\(430\) | 11.5667 | 0.557795 | ||||||||
\(431\) | 1.23158 | + | 1.23158i | 0.0593231 | + | 0.0593231i | 0.736146 | − | 0.676823i | \(-0.236644\pi\) |
−0.676823 | + | 0.736146i | \(0.736644\pi\) | |||||||
\(432\) | 0.822100 | − | 3.53112i | 0.0395533 | − | 0.169891i | ||||
\(433\) | − | 31.1338i | − | 1.49620i | −0.663588 | − | 0.748098i | \(-0.730967\pi\) | ||
0.663588 | − | 0.748098i | \(-0.269033\pi\) | |||||||
\(434\) | −9.51119 | − | 9.51119i | −0.456552 | − | 0.456552i | ||||
\(435\) | 1.22042 | + | 1.42232i | 0.0585148 | + | 0.0681948i | ||||
\(436\) | −8.93860 | − | 8.93860i | −0.428081 | − | 0.428081i | ||||
\(437\) | 1.38194 | − | 1.38194i | 0.0661073 | − | 0.0661073i | ||||
\(438\) | 17.3941 | + | 1.32883i | 0.831123 | + | 0.0634938i | ||||
\(439\) | 15.2593i | 0.728286i | 0.931343 | + | 0.364143i | \(0.118638\pi\) | ||||
−0.931343 | + | 0.364143i | \(0.881362\pi\) | |||||||
\(440\) | 5.05533 | − | 5.05533i | 0.241004 | − | 0.241004i | ||||
\(441\) | 4.01516 | − | 26.1255i | 0.191198 | − | 1.24407i | ||||
\(442\) | −17.2281 | − | 10.5256i | −0.819455 | − | 0.500650i | ||||
\(443\) | − | 15.4602i | − | 0.734534i | −0.930115 | − | 0.367267i | \(-0.880293\pi\) | ||
0.930115 | − | 0.367267i | \(-0.119707\pi\) | |||||||
\(444\) | 8.83578 | + | 10.2975i | 0.419328 | + | 0.488696i | ||||
\(445\) | 32.2032 | 1.52658 | ||||||||
\(446\) | 12.1454 | 0.575099 | ||||||||
\(447\) | 7.46148 | − | 6.40235i | 0.352916 | − | 0.302821i | ||||
\(448\) | 18.1119 | − | 18.1119i | 0.855707 | − | 0.855707i | ||||
\(449\) | −0.400323 | + | 0.400323i | −0.0188924 | + | 0.0188924i | −0.716490 | − | 0.697597i | \(-0.754252\pi\) |
0.697597 | + | 0.716490i | \(0.254252\pi\) | |||||||
\(450\) | −1.95926 | + | 1.43726i | −0.0923603 | + | 0.0677529i | ||||
\(451\) | 8.28034 | 0.389906 | ||||||||
\(452\) | −6.82510 | −0.321026 | ||||||||
\(453\) | −30.5184 | + | 26.1864i | −1.43388 | + | 1.23034i | ||||
\(454\) | 2.31844i | 0.108810i | ||||||||
\(455\) | −8.13446 | − | 33.6831i | −0.381349 | − | 1.57909i | ||||
\(456\) | −11.8944 | − | 0.908675i | −0.557007 | − | 0.0425526i | ||||
\(457\) | 2.95148 | − | 2.95148i | 0.138065 | − | 0.138065i | −0.634697 | − | 0.772761i | \(-0.718875\pi\) |
0.772761 | + | 0.634697i | \(0.218875\pi\) | |||||||
\(458\) | − | 5.92607i | − | 0.276907i | ||||||
\(459\) | 6.85667 | − | 29.4510i | 0.320042 | − | 1.37466i | ||||
\(460\) | −1.54095 | + | 1.54095i | −0.0718474 | + | 0.0718474i | ||||
\(461\) | −10.4663 | − | 10.4663i | −0.487462 | − | 0.487462i | 0.420042 | − | 0.907505i | \(-0.362015\pi\) |
−0.907505 | + | 0.420042i | \(0.862015\pi\) | |||||||
\(462\) | 5.02911 | − | 4.31524i | 0.233975 | − | 0.200763i | ||||
\(463\) | −10.9144 | − | 10.9144i | −0.507235 | − | 0.507235i | 0.406442 | − | 0.913677i | \(-0.366769\pi\) |
−0.913677 | + | 0.406442i | \(0.866769\pi\) | |||||||
\(464\) | 0.312364i | 0.0145012i | ||||||||
\(465\) | 1.12111 | − | 14.6752i | 0.0519903 | − | 0.680544i | ||||
\(466\) | −0.985739 | − | 0.985739i | −0.0456635 | − | 0.0456635i | ||||
\(467\) | −24.0805 | −1.11431 | −0.557155 | − | 0.830408i | \(-0.688107\pi\) | ||||
−0.557155 | + | 0.830408i | \(0.688107\pi\) | |||||||
\(468\) | 0.980283 | + | 11.5777i | 0.0453136 | + | 0.535180i | ||||
\(469\) | −58.6773 | −2.70947 | ||||||||
\(470\) | 6.58808 | + | 6.58808i | 0.303886 | + | 0.303886i | ||||
\(471\) | −1.90834 | + | 24.9798i | −0.0879316 | + | 1.15101i | ||||
\(472\) | 38.1027i | 1.75382i | ||||||||
\(473\) | −3.51690 | − | 3.51690i | −0.161707 | − | 0.161707i | ||||
\(474\) | −12.8374 | + | 11.0152i | −0.589642 | + | 0.505945i | ||||
\(475\) | 1.38594 | + | 1.38594i | 0.0635913 | + | 0.0635913i | ||||
\(476\) | 17.5761 | − | 17.5761i | 0.805600 | − | 0.805600i | ||||
\(477\) | 0.606421 | − | 3.94581i | 0.0277661 | − | 0.180666i | ||||
\(478\) | 11.3176i | 0.517657i | ||||||||
\(479\) | 1.49406 | − | 1.49406i | 0.0682652 | − | 0.0682652i | −0.672150 | − | 0.740415i | \(-0.734629\pi\) |
0.740415 | + | 0.672150i | \(0.234629\pi\) | |||||||
\(480\) | 21.8917 | + | 1.67242i | 0.999213 | + | 0.0763351i | ||||
\(481\) | 22.4383 | + | 13.7088i | 1.02310 | + | 0.625067i | ||||
\(482\) | − | 0.627655i | − | 0.0285889i | ||||||
\(483\) | −4.38713 | + | 3.76439i | −0.199621 | + | 0.171286i | ||||
\(484\) | −1.07419 | −0.0488268 | ||||||||
\(485\) | 20.7609 | 0.942702 | ||||||||
\(486\) | 13.7906 | − | 5.89837i | 0.625555 | − | 0.267555i | ||||
\(487\) | 13.5688 | − | 13.5688i | 0.614860 | − | 0.614860i | −0.329348 | − | 0.944209i | \(-0.606829\pi\) |
0.944209 | + | 0.329348i | \(0.106829\pi\) | |||||||
\(488\) | 28.8731 | − | 28.8731i | 1.30702 | − | 1.30702i | ||||
\(489\) | 4.63065 | − | 3.97335i | 0.209405 | − | 0.179681i | ||||
\(490\) | −20.4902 | −0.925654 | ||||||||
\(491\) | −5.19051 | −0.234244 | −0.117122 | − | 0.993118i | \(-0.537367\pi\) | ||||
−0.117122 | + | 0.993118i | \(0.537367\pi\) | |||||||
\(492\) | 10.0322 | + | 11.6918i | 0.452288 | + | 0.527109i | ||||
\(493\) | 2.60526i | 0.117335i | ||||||||
\(494\) | −7.85196 | + | 1.89625i | −0.353276 | + | 0.0853161i | ||||
\(495\) | 7.16680 | + | 1.10145i | 0.322124 | + | 0.0495063i | ||||
\(496\) | 1.73456 | − | 1.73456i | 0.0778841 | − | 0.0778841i | ||||
\(497\) | 4.51134i | 0.202361i | ||||||||
\(498\) | −17.4757 | − | 1.33506i | −0.783106 | − | 0.0598255i | ||||
\(499\) | 1.21906 | − | 1.21906i | 0.0545728 | − | 0.0545728i | −0.679294 | − | 0.733866i | \(-0.737714\pi\) |
0.733866 | + | 0.679294i | \(0.237714\pi\) | |||||||
\(500\) | 7.63388 | + | 7.63388i | 0.341397 | + | 0.341397i | ||||
\(501\) | 8.68426 | + | 10.1209i | 0.387984 | + | 0.452168i | ||||
\(502\) | 15.4874 | + | 15.4874i | 0.691236 | + | 0.691236i | ||||
\(503\) | − | 4.14083i | − | 0.184630i | −0.995730 | − | 0.0923152i | \(-0.970573\pi\) | ||
0.995730 | − | 0.0923152i | \(-0.0294267\pi\) | |||||||
\(504\) | 34.8754 | + | 5.35991i | 1.55348 | + | 0.238750i | ||||
\(505\) | 2.45477 | + | 2.45477i | 0.109236 | + | 0.109236i | ||||
\(506\) | −0.807629 | −0.0359035 | ||||||||
\(507\) | 8.72022 | + | 20.7595i | 0.387279 | + | 0.921963i | ||||
\(508\) | −8.01795 | −0.355739 | ||||||||
\(509\) | −26.1591 | − | 26.1591i | −1.15948 | − | 1.15948i | −0.984587 | − | 0.174893i | \(-0.944042\pi\) |
−0.174893 | − | 0.984587i | \(-0.555958\pi\) | |||||||
\(510\) | −23.3729 | − | 1.78558i | −1.03497 | − | 0.0790666i | ||||
\(511\) | 41.6218i | 1.84124i | ||||||||
\(512\) | 5.50630 | + | 5.50630i | 0.243346 | + | 0.243346i | ||||
\(513\) | −6.39232 | − | 10.2720i | −0.282228 | − | 0.453522i | ||||
\(514\) | 7.81978 | + | 7.81978i | 0.344916 | + | 0.344916i | ||||
\(515\) | −4.90862 | + | 4.90862i | −0.216300 | + | 0.216300i | ||||
\(516\) | 0.704885 | − | 9.22683i | 0.0310308 | − | 0.406188i | ||||
\(517\) | − | 4.00627i | − | 0.176195i | ||||||
\(518\) | 19.7296 | − | 19.7296i | 0.866868 | − | 0.866868i | ||||
\(519\) | −0.619043 | + | 8.10316i | −0.0271730 | + | 0.355689i | ||||
\(520\) | 25.0569 | − | 6.05124i | 1.09882 | − | 0.265364i | ||||
\(521\) | 28.4750i | 1.24751i | 0.781620 | + | 0.623755i | \(0.214394\pi\) | ||||
−0.781620 | + | 0.623755i | \(0.785606\pi\) | |||||||
\(522\) | −1.04197 | + | 0.764360i | −0.0456058 | + | 0.0334551i | ||||
\(523\) | 0.443046 | 0.0193730 | 0.00968652 | − | 0.999953i | \(-0.496917\pi\) | ||||
0.00968652 | + | 0.999953i | \(0.496917\pi\) | |||||||
\(524\) | 1.89473 | 0.0827717 | ||||||||
\(525\) | −3.77529 | − | 4.39983i | −0.164767 | − | 0.192024i | ||||
\(526\) | 12.6878 | − | 12.6878i | 0.553215 | − | 0.553215i | ||||
\(527\) | 14.4670 | − | 14.4670i | 0.630192 | − | 0.630192i | ||||
\(528\) | 0.786974 | + | 0.917162i | 0.0342487 | + | 0.0399143i | ||||
\(529\) | −22.2955 | −0.969368 | ||||||||
\(530\) | −3.09470 | −0.134425 | ||||||||
\(531\) | −31.1594 | + | 22.8576i | −1.35220 | + | 0.991937i | ||||
\(532\) | − | 9.94515i | − | 0.431177i | ||||||
\(533\) | 25.4767 | + | 15.5651i | 1.10352 | + | 0.674199i | ||||
\(534\) | −1.69141 | + | 22.1403i | −0.0731947 | + | 0.958106i | ||||
\(535\) | −11.5638 | + | 11.5638i | −0.499946 | + | 0.499946i | ||||
\(536\) | − | 43.6502i | − | 1.88540i | ||||||
\(537\) | −2.43683 | + | 31.8977i | −0.105157 | + | 1.37649i | ||||
\(538\) | 2.88932 | − | 2.88932i | 0.124567 | − | 0.124567i | ||||
\(539\) | 6.23014 | + | 6.23014i | 0.268351 | + | 0.268351i | ||||
\(540\) | 7.12784 | + | 11.4540i | 0.306734 | + | 0.492901i | ||||
\(541\) | −15.0944 | − | 15.0944i | −0.648960 | − | 0.648960i | 0.303782 | − | 0.952742i | \(-0.401751\pi\) |
−0.952742 | + | 0.303782i | \(0.901751\pi\) | |||||||
\(542\) | 6.90131i | 0.296437i | ||||||||
\(543\) | 24.1045 | + | 1.84147i | 1.03443 | + | 0.0790251i | ||||
\(544\) | 21.5812 | + | 21.5812i | 0.925284 | + | 0.925284i | ||||
\(545\) | −28.4431 | −1.21837 | ||||||||
\(546\) | 23.5850 | − | 3.82345i | 1.00935 | − | 0.163629i | ||||
\(547\) | −19.0040 | −0.812553 | −0.406277 | − | 0.913750i | \(-0.633173\pi\) | ||||
−0.406277 | + | 0.913750i | \(0.633173\pi\) | |||||||
\(548\) | 14.5912 | + | 14.5912i | 0.623305 | + | 0.623305i | ||||
\(549\) | 40.9325 | + | 6.29081i | 1.74696 | + | 0.268485i | ||||
\(550\) | − | 0.809966i | − | 0.0345371i | ||||||
\(551\) | 0.737069 | + | 0.737069i | 0.0314002 | + | 0.0314002i | ||||
\(552\) | −2.80034 | − | 3.26359i | −0.119190 | − | 0.138908i | ||||
\(553\) | −28.5380 | − | 28.5380i | −1.21356 | − | 1.21356i | ||||
\(554\) | −22.0578 | + | 22.0578i | −0.937147 | + | 0.937147i | ||||
\(555\) | 30.4415 | + | 2.32558i | 1.29217 | + | 0.0987155i | ||||
\(556\) | 14.6369i | 0.620741i | ||||||||
\(557\) | 15.7586 | − | 15.7586i | 0.667715 | − | 0.667715i | −0.289471 | − | 0.957187i | \(-0.593480\pi\) |
0.957187 | + | 0.289471i | \(0.0934795\pi\) | |||||||
\(558\) | 10.0306 | + | 1.54157i | 0.424628 | + | 0.0652599i | ||||
\(559\) | −4.20973 | − | 17.4316i | −0.178052 | − | 0.737278i | ||||
\(560\) | − | 6.70566i | − | 0.283366i | ||||||
\(561\) | 6.56371 | + | 7.64953i | 0.277120 | + | 0.322963i | ||||
\(562\) | −18.2450 | −0.769620 | ||||||||
\(563\) | −5.81745 | −0.245176 | −0.122588 | − | 0.992458i | \(-0.539119\pi\) | ||||
−0.122588 | + | 0.992458i | \(0.539119\pi\) | |||||||
\(564\) | 5.65685 | − | 4.85388i | 0.238196 | − | 0.204385i | ||||
\(565\) | −10.8589 | + | 10.8589i | −0.456838 | + | 0.456838i | ||||
\(566\) | −7.98471 | + | 7.98471i | −0.335622 | + | 0.335622i | ||||
\(567\) | 16.5384 | + | 31.7356i | 0.694549 | + | 1.33277i | ||||
\(568\) | −3.35599 | −0.140814 | ||||||||
\(569\) | −31.5587 | −1.32301 | −0.661505 | − | 0.749940i | \(-0.730082\pi\) | ||||
−0.661505 | + | 0.749940i | \(0.730082\pi\) | |||||||
\(570\) | −7.11774 | + | 6.10740i | −0.298129 | + | 0.255811i | ||||
\(571\) | − | 41.1432i | − | 1.72179i | −0.508783 | − | 0.860895i | \(-0.669904\pi\) | ||
0.508783 | − | 0.860895i | \(-0.330096\pi\) | |||||||
\(572\) | −3.30503 | − | 2.01922i | −0.138190 | − | 0.0844280i | ||||
\(573\) | 15.6415 | + | 1.19494i | 0.653435 | + | 0.0499193i | ||||
\(574\) | 22.4011 | − | 22.4011i | 0.935006 | − | 0.935006i | ||||
\(575\) | 0.706572i | 0.0294661i | ||||||||
\(576\) | −2.93557 | + | 19.1009i | −0.122316 | + | 0.795873i | ||||
\(577\) | −27.0379 | + | 27.0379i | −1.12560 | + | 1.12560i | −0.134721 | + | 0.990884i | \(0.543014\pi\) |
−0.990884 | + | 0.134721i | \(0.956986\pi\) | |||||||
\(578\) | −11.4750 | − | 11.4750i | −0.477299 | − | 0.477299i | ||||
\(579\) | 28.4029 | − | 24.3712i | 1.18038 | − | 1.01283i | ||||
\(580\) | −0.821880 | − | 0.821880i | −0.0341267 | − | 0.0341267i | ||||
\(581\) | − | 41.8170i | − | 1.73486i | ||||||
\(582\) | −1.09043 | + | 14.2735i | −0.0451996 | + | 0.591655i | ||||
\(583\) | 0.940956 | + | 0.940956i | 0.0389704 | + | 0.0389704i | ||||
\(584\) | −30.9625 | −1.28124 | ||||||||
\(585\) | 19.9801 | + | 16.8608i | 0.826075 | + | 0.697107i | ||||
\(586\) | 32.1709 | 1.32897 | ||||||||
\(587\) | −18.7881 | − | 18.7881i | −0.775467 | − | 0.775467i | 0.203589 | − | 0.979056i | \(-0.434739\pi\) |
−0.979056 | + | 0.203589i | \(0.934739\pi\) | |||||||
\(588\) | −1.24870 | + | 16.3452i | −0.0514953 | + | 0.674065i | ||||
\(589\) | − | 8.18590i | − | 0.337294i | ||||||
\(590\) | 21.1828 | + | 21.1828i | 0.872081 | + | 0.872081i | ||||
\(591\) | −27.4026 | + | 23.5129i | −1.12719 | + | 0.967193i | ||||
\(592\) | 3.59810 | + | 3.59810i | 0.147881 | + | 0.147881i | ||||
\(593\) | −16.9522 | + | 16.9522i | −0.696145 | + | 0.696145i | −0.963577 | − | 0.267431i | \(-0.913825\pi\) |
0.267431 | + | 0.963577i | \(0.413825\pi\) | |||||||
\(594\) | −1.13369 | + | 4.86946i | −0.0465158 | + | 0.199796i | ||||
\(595\) | − | 55.9281i | − | 2.29283i | ||||||
\(596\) | −4.31159 | + | 4.31159i | −0.176610 | + | 0.176610i | ||||
\(597\) | −14.8929 | − | 1.13774i | −0.609525 | − | 0.0465648i | ||||
\(598\) | −2.48488 | − | 1.51815i | −0.101614 | − | 0.0620818i | ||||
\(599\) | 37.6173i | 1.53700i | 0.639848 | + | 0.768501i | \(0.278997\pi\) | ||||
−0.639848 | + | 0.768501i | \(0.721003\pi\) | |||||||
\(600\) | 3.27304 | − | 2.80844i | 0.133621 | − | 0.114654i | ||||
\(601\) | 18.6933 | 0.762516 | 0.381258 | − | 0.924469i | \(-0.375491\pi\) | ||||
0.381258 | + | 0.924469i | \(0.375491\pi\) | |||||||
\(602\) | −19.0288 | −0.775557 | ||||||||
\(603\) | 35.6960 | − | 26.1856i | 1.45365 | − | 1.06636i | ||||
\(604\) | 17.6349 | − | 17.6349i | 0.717555 | − | 0.717555i | ||||
\(605\) | −1.70906 | + | 1.70906i | −0.0694833 | + | 0.0694833i | ||||
\(606\) | −1.81663 | + | 1.55877i | −0.0737956 | + | 0.0633206i | ||||
\(607\) | 40.8474 | 1.65795 | 0.828973 | − | 0.559289i | \(-0.188926\pi\) | ||||
0.828973 | + | 0.559289i | \(0.188926\pi\) | |||||||
\(608\) | 12.2113 | 0.495235 | ||||||||
\(609\) | −2.00777 | − | 2.33991i | −0.0813589 | − | 0.0948179i | ||||
\(610\) | − | 32.1034i | − | 1.29983i | ||||||
\(611\) | 7.53084 | − | 12.3263i | 0.304665 | − | 0.498670i | ||||
\(612\) | −2.84873 | + | 18.5359i | −0.115153 | + | 0.749270i | ||||
\(613\) | 11.4619 | − | 11.4619i | 0.462943 | − | 0.462943i | −0.436676 | − | 0.899619i | \(-0.643844\pi\) |
0.899619 | + | 0.436676i | \(0.143844\pi\) | |||||||
\(614\) | − | 2.63595i | − | 0.106378i | ||||||
\(615\) | 34.5635 | + | 2.64049i | 1.39374 | + | 0.106475i | ||||
\(616\) | −8.31673 | + | 8.31673i | −0.335091 | + | 0.335091i | ||||
\(617\) | 7.74289 | + | 7.74289i | 0.311717 | + | 0.311717i | 0.845574 | − | 0.533858i | \(-0.179258\pi\) |
−0.533858 | + | 0.845574i | \(0.679258\pi\) | |||||||
\(618\) | −3.11695 | − | 3.63259i | −0.125382 | − | 0.146124i | ||||
\(619\) | 1.84445 | + | 1.84445i | 0.0741349 | + | 0.0741349i | 0.743202 | − | 0.669067i | \(-0.233306\pi\) |
−0.669067 | + | 0.743202i | \(0.733306\pi\) | |||||||
\(620\) | 9.12781i | 0.366582i | ||||||||
\(621\) | 0.988970 | − | 4.24786i | 0.0396860 | − | 0.170461i | ||||
\(622\) | −1.70116 | − | 1.70116i | −0.0682105 | − | 0.0682105i | ||||
\(623\) | −52.9788 | −2.12255 | ||||||||
\(624\) | 0.697286 | + | 4.30122i | 0.0279138 | + | 0.172187i | ||||
\(625\) | 28.5004 | 1.14001 | ||||||||
\(626\) | 0.0996799 | + | 0.0996799i | 0.00398401 | + | 0.00398401i | ||||
\(627\) | 4.02116 | + | 0.307197i | 0.160590 | + | 0.0122683i | ||||
\(628\) | − | 15.5372i | − | 0.620003i | ||||||
\(629\) | 30.0097 | + | 30.0097i | 1.19657 | + | 1.19657i | ||||
\(630\) | 22.3684 | − | 16.4088i | 0.891179 | − | 0.653744i | ||||
\(631\) | 10.4263 | + | 10.4263i | 0.415063 | + | 0.415063i | 0.883498 | − | 0.468435i | \(-0.155182\pi\) |
−0.468435 | + | 0.883498i | \(0.655182\pi\) | |||||||
\(632\) | 21.2295 | − | 21.2295i | 0.844464 | − | 0.844464i | ||||
\(633\) | 0.903109 | − | 11.8215i | 0.0358953 | − | 0.469864i | ||||
\(634\) | − | 9.29359i | − | 0.369096i | ||||||
\(635\) | −12.7568 | + | 12.7568i | −0.506237 | + | 0.506237i | ||||
\(636\) | −0.188594 | + | 2.46867i | −0.00747825 | + | 0.0978890i | ||||
\(637\) | 7.45748 | + | 30.8799i | 0.295476 | + | 1.22350i | ||||
\(638\) | − | 0.430755i | − | 0.0170538i | ||||||
\(639\) | −2.01325 | − | 2.74444i | −0.0796428 | − | 0.108568i | ||||
\(640\) | −10.3711 | −0.409954 | ||||||||
\(641\) | 12.0658 | 0.476572 | 0.238286 | − | 0.971195i | \(-0.423414\pi\) | ||||
0.238286 | + | 0.971195i | \(0.423414\pi\) | |||||||
\(642\) | −7.34295 | − | 8.55769i | −0.289803 | − | 0.337745i | ||||
\(643\) | −18.1964 | + | 18.1964i | −0.717595 | + | 0.717595i | −0.968112 | − | 0.250517i | \(-0.919399\pi\) |
0.250517 | + | 0.968112i | \(0.419399\pi\) | |||||||
\(644\) | 2.53509 | − | 2.53509i | 0.0998964 | − | 0.0998964i | ||||
\(645\) | −13.5586 | − | 15.8016i | −0.533870 | − | 0.622188i | ||||
\(646\) | −13.0376 | −0.512956 | ||||||||
\(647\) | −38.9982 | −1.53318 | −0.766588 | − | 0.642139i | \(-0.778047\pi\) | ||||
−0.766588 | + | 0.642139i | \(0.778047\pi\) | |||||||
\(648\) | −23.6082 | + | 12.3030i | −0.927417 | + | 0.483307i | ||||
\(649\) | − | 12.8814i | − | 0.505640i | ||||||
\(650\) | 1.52254 | − | 2.49207i | 0.0597191 | − | 0.0977472i | ||||
\(651\) | −1.84439 | + | 24.1427i | −0.0722872 | + | 0.946226i | ||||
\(652\) | −2.67580 | + | 2.67580i | −0.104793 | + | 0.104793i | ||||
\(653\) | 40.6601i | 1.59115i | 0.605853 | + | 0.795577i | \(0.292832\pi\) | ||||
−0.605853 | + | 0.795577i | \(0.707168\pi\) | |||||||
\(654\) | 1.49392 | − | 19.5552i | 0.0584169 | − | 0.764668i | ||||
\(655\) | 3.01456 | − | 3.01456i | 0.117789 | − | 0.117789i | ||||
\(656\) | 4.08531 | + | 4.08531i | 0.159505 | + | 0.159505i | ||||
\(657\) | −18.5743 | − | 25.3203i | −0.724652 | − | 0.987840i | ||||
\(658\) | −10.8383 | − | 10.8383i | −0.422522 | − | 0.422522i | ||||
\(659\) | − | 33.9929i | − | 1.32418i | −0.749426 | − | 0.662088i | \(-0.769670\pi\) | ||
0.749426 | − | 0.662088i | \(-0.230330\pi\) | |||||||
\(660\) | −4.48385 | − | 0.342545i | −0.174534 | − | 0.0133335i | ||||
\(661\) | 24.0884 | + | 24.0884i | 0.936932 | + | 0.936932i | 0.998126 | − | 0.0611940i | \(-0.0194908\pi\) |
−0.0611940 | + | 0.998126i | \(0.519491\pi\) | |||||||
\(662\) | −16.2298 | −0.630790 | ||||||||
\(663\) | 5.81567 | + | 35.8740i | 0.225862 | + | 1.39323i | ||||
\(664\) | 31.1078 | 1.20722 | ||||||||
\(665\) | −15.8230 | − | 15.8230i | −0.613589 | − | 0.613589i | ||||
\(666\) | −3.19777 | + | 20.8070i | −0.123911 | + | 0.806254i | ||||
\(667\) | 0.375768i | 0.0145498i | ||||||||
\(668\) | −5.84831 | − | 5.84831i | −0.226278 | − | 0.226278i | ||||
\(669\) | −14.2370 | − | 16.5922i | −0.550433 | − | 0.641490i | ||||
\(670\) | −24.2669 | − | 24.2669i | −0.937510 | − | 0.937510i | ||||
\(671\) | −9.76116 | + | 9.76116i | −0.376825 | + | 0.376825i | ||||
\(672\) | −36.0149 | − | 2.75136i | −1.38930 | − | 0.106136i | ||||
\(673\) | − | 8.09382i | − | 0.311994i | −0.987758 | − | 0.155997i | \(-0.950141\pi\) | ||
0.987758 | − | 0.155997i | \(-0.0498590\pi\) | |||||||
\(674\) | 12.1838 | − | 12.1838i | 0.469303 | − | 0.469303i | ||||
\(675\) | 4.26015 | + | 0.991832i | 0.163973 | + | 0.0381756i | ||||
\(676\) | −6.37313 | − | 12.4254i | −0.245121 | − | 0.477898i | ||||
\(677\) | 6.76042i | 0.259824i | 0.991526 | + | 0.129912i | \(0.0414695\pi\) | ||||
−0.991526 | + | 0.129912i | \(0.958530\pi\) | |||||||
\(678\) | −6.89537 | − | 8.03606i | −0.264815 | − | 0.308623i | ||||
\(679\) | −34.1545 | −1.31073 | ||||||||
\(680\) | 41.6050 | 1.59548 | ||||||||
\(681\) | 3.16730 | − | 2.71772i | 0.121371 | − | 0.104143i | ||||
\(682\) | −2.39199 | + | 2.39199i | −0.0915939 | + | 0.0915939i | ||||
\(683\) | 27.1344 | − | 27.1344i | 1.03827 | − | 1.03827i | 0.0390311 | − | 0.999238i | \(-0.487573\pi\) |
0.999238 | − | 0.0390311i | \(-0.0124271\pi\) | |||||||
\(684\) | 4.43816 | + | 6.05007i | 0.169697 | + | 0.231330i | ||||
\(685\) | 46.4299 | 1.77400 | ||||||||
\(686\) | 6.92778 | 0.264504 | ||||||||
\(687\) | −8.09579 | + | 6.94662i | −0.308874 | + | 0.265030i | ||||
\(688\) | − | 3.47030i | − | 0.132304i | ||||||
\(689\) | 1.12633 | + | 4.66388i | 0.0429096 | + | 0.177680i | ||||
\(690\) | −3.37118 | − | 0.257542i | −0.128339 | − | 0.00980445i | ||||
\(691\) | −33.4914 | + | 33.4914i | −1.27407 | + | 1.27407i | −0.330142 | + | 0.943931i | \(0.607097\pi\) |
−0.943931 | + | 0.330142i | \(0.892903\pi\) | |||||||
\(692\) | − | 5.04009i | − | 0.191596i | ||||||
\(693\) | −11.7904 | − | 1.81203i | −0.447880 | − | 0.0688334i | ||||
\(694\) | 15.5395 | − | 15.5395i | 0.589870 | − | 0.589870i | ||||
\(695\) | 23.2876 | + | 23.2876i | 0.883350 | + | 0.883350i | ||||
\(696\) | 1.74066 | − | 1.49358i | 0.0659797 | − | 0.0566141i | ||||
\(697\) | 34.0733 | + | 34.0733i | 1.29062 | + | 1.29062i | ||||
\(698\) | − | 25.0440i | − | 0.947929i | ||||||
\(699\) | −0.191152 | + | 2.50215i | −0.00723003 | + | 0.0946399i | ||||
\(700\) | 2.54242 | + | 2.54242i | 0.0960945 | + | 0.0960945i | ||||
\(701\) | 14.5002 | 0.547667 | 0.273833 | − | 0.961777i | \(-0.411708\pi\) | ||||
0.273833 | + | 0.961777i | \(0.411708\pi\) | |||||||
\(702\) | −12.6415 | + | 12.8511i | −0.477124 | + | 0.485034i | ||||
\(703\) | 16.9805 | 0.640431 | ||||||||
\(704\) | −4.55500 | − | 4.55500i | −0.171673 | − | 0.171673i | ||||
\(705\) | 1.27754 | − | 16.7228i | 0.0481151 | − | 0.629818i | ||||
\(706\) | 19.0885i | 0.718407i | ||||||||
\(707\) | −4.03844 | − | 4.03844i | −0.151881 | − | 0.151881i | ||||
\(708\) | 18.1886 | − | 15.6068i | 0.683568 | − | 0.586538i | ||||
\(709\) | 11.0696 | + | 11.0696i | 0.415726 | + | 0.415726i | 0.883728 | − | 0.468002i | \(-0.155026\pi\) |
−0.468002 | + | 0.883728i | \(0.655026\pi\) | |||||||
\(710\) | −1.86573 | + | 1.86573i | −0.0700195 | + | 0.0700195i | ||||
\(711\) | 30.0964 | + | 4.62544i | 1.12870 | + | 0.173468i | ||||
\(712\) | − | 39.4110i | − | 1.47699i | ||||||
\(713\) | 2.08664 | − | 2.08664i | 0.0781454 | − | 0.0781454i | ||||
\(714\) | 38.4517 | + | 2.93752i | 1.43902 | + | 0.109934i | ||||
\(715\) | −8.47102 | + | 2.04575i | −0.316798 | + | 0.0765067i | ||||
\(716\) | − | 19.8401i | − | 0.741459i | ||||||
\(717\) | 15.4614 | − | 13.2667i | 0.577416 | − | 0.495454i | ||||
\(718\) | −2.20818 | −0.0824087 | ||||||||
\(719\) | −44.7034 | −1.66715 | −0.833577 | − | 0.552403i | \(-0.813711\pi\) | ||||
−0.833577 | + | 0.552403i | \(0.813711\pi\) | |||||||
\(720\) | 2.99249 | + | 4.07934i | 0.111524 | + | 0.152028i | ||||
\(721\) | 8.07537 | − | 8.07537i | 0.300742 | − | 0.300742i | ||||
\(722\) | 9.23852 | − | 9.23852i | 0.343822 | − | 0.343822i | ||||
\(723\) | −0.857460 | + | 0.735747i | −0.0318893 | + | 0.0273627i | ||||
\(724\) | −14.9928 | −0.557203 | ||||||||
\(725\) | −0.376855 | −0.0139961 | ||||||||
\(726\) | −1.08525 | − | 1.26478i | −0.0402774 | − | 0.0469404i | ||||
\(727\) | 16.6524i | 0.617603i | 0.951126 | + | 0.308802i | \(0.0999279\pi\) | ||||
−0.951126 | + | 0.308802i | \(0.900072\pi\) | |||||||
\(728\) | −41.2221 | + | 9.95514i | −1.52779 | + | 0.368962i | ||||
\(729\) | −24.2235 | − | 11.9257i | −0.897167 | − | 0.441691i | ||||
\(730\) | −17.2133 | + | 17.2133i | −0.637092 | + | 0.637092i | ||||
\(731\) | − | 28.9438i | − | 1.07053i | ||||||
\(732\) | −25.6091 | − | 1.95641i | −0.946540 | − | 0.0723111i | ||||
\(733\) | 14.9699 | − | 14.9699i | 0.552926 | − | 0.552926i | −0.374358 | − | 0.927284i | \(-0.622137\pi\) |
0.927284 | + | 0.374358i | \(0.122137\pi\) | |||||||
\(734\) | −12.3341 | − | 12.3341i | −0.455261 | − | 0.455261i | ||||
\(735\) | 24.0189 | + | 27.9924i | 0.885952 | + | 1.03251i | ||||
\(736\) | 3.11275 | + | 3.11275i | 0.114738 | + | 0.114738i | ||||
\(737\) | 14.7569i | 0.543576i | ||||||||
\(738\) | −3.63077 | + | 23.6244i | −0.133651 | + | 0.869627i | ||||
\(739\) | −26.7056 | − | 26.7056i | −0.982382 | − | 0.982382i | 0.0174654 | − | 0.999847i | \(-0.494440\pi\) |
−0.999847 | + | 0.0174654i | \(0.994440\pi\) | |||||||
\(740\) | −18.9343 | −0.696040 | ||||||||
\(741\) | 11.7947 | + | 8.50400i | 0.433289 | + | 0.312402i | ||||
\(742\) | 5.09122 | 0.186904 | ||||||||
\(743\) | −5.55684 | − | 5.55684i | −0.203861 | − | 0.203861i | 0.597791 | − | 0.801652i | \(-0.296045\pi\) |
−0.801652 | + | 0.597791i | \(0.796045\pi\) | |||||||
\(744\) | −17.9598 | − | 1.37204i | −0.658438 | − | 0.0503015i | ||||
\(745\) | 13.7197i | 0.502651i | ||||||||
\(746\) | 16.0907 | + | 16.0907i | 0.589122 | + | 0.589122i | ||||
\(747\) | 18.6614 | + | 25.4391i | 0.682786 | + | 0.930769i | ||||
\(748\) | −4.42025 | − | 4.42025i | −0.161620 | − | 0.161620i | ||||
\(749\) | 19.0240 | − | 19.0240i | 0.695123 | − | 0.695123i | ||||
\(750\) | −1.27586 | + | 16.7008i | −0.0465878 | + | 0.609827i | ||||
\(751\) | 48.9900i | 1.78767i | 0.448395 | + | 0.893835i | \(0.351996\pi\) | ||||
−0.448395 | + | 0.893835i | \(0.648004\pi\) | |||||||
\(752\) | 1.97659 | − | 1.97659i | 0.0720789 | − | 0.0720789i | ||||
\(753\) | 3.00328 | − | 39.3124i | 0.109445 | − | 1.43262i | ||||
\(754\) | 0.809718 | − | 1.32533i | 0.0294882 | − | 0.0482657i | ||||
\(755\) | − | 56.1152i | − | 2.04224i | ||||||
\(756\) | −11.7263 | − | 18.8434i | −0.426482 | − | 0.685329i | ||||
\(757\) | 27.6161 | 1.00372 | 0.501862 | − | 0.864948i | \(-0.332648\pi\) | ||||
0.501862 | + | 0.864948i | \(0.332648\pi\) | |||||||
\(758\) | −7.96043 | −0.289136 | ||||||||
\(759\) | 0.946714 | + | 1.10333i | 0.0343635 | + | 0.0400483i | ||||
\(760\) | 11.7707 | − | 11.7707i | 0.426970 | − | 0.426970i | ||||
\(761\) | −10.9476 | + | 10.9476i | −0.396849 | + | 0.396849i | −0.877120 | − | 0.480271i | \(-0.840538\pi\) |
0.480271 | + | 0.877120i | \(0.340538\pi\) | |||||||
\(762\) | −8.10050 | − | 9.44055i | −0.293450 | − | 0.341995i | ||||
\(763\) | 46.7929 | 1.69402 | ||||||||
\(764\) | −9.72890 | −0.351979 | ||||||||
\(765\) | 24.9587 | + | 34.0235i | 0.902383 | + | 1.23012i | ||||
\(766\) | 11.8595i | 0.428500i | ||||||||
\(767\) | 24.2140 | − | 39.6331i | 0.874318 | − | 1.43107i | ||||
\(768\) | 2.24452 | − | 29.3803i | 0.0809920 | − | 1.06017i | ||||
\(769\) | −30.2179 | + | 30.2179i | −1.08969 | + | 1.08969i | −0.0941269 | + | 0.995560i | \(0.530006\pi\) |
−0.995560 | + | 0.0941269i | \(0.969994\pi\) | |||||||
\(770\) | 9.24720i | 0.333246i | ||||||||
\(771\) | 1.51639 | − | 19.8493i | 0.0546115 | − | 0.714856i | ||||
\(772\) | −16.4125 | + | 16.4125i | −0.590699 | + | 0.590699i | ||||
\(773\) | 1.22643 | + | 1.22643i | 0.0441117 | + | 0.0441117i | 0.728819 | − | 0.684707i | \(-0.240070\pi\) |
−0.684707 | + | 0.728819i | \(0.740070\pi\) | |||||||
\(774\) | 11.5761 | − | 8.49187i | 0.416093 | − | 0.305234i | ||||
\(775\) | 2.09268 | + | 2.09268i | 0.0751713 | + | 0.0751713i | ||||
\(776\) | − | 25.4076i | − | 0.912080i | ||||||
\(777\) | −50.0805 | − | 3.82591i | −1.79663 | − | 0.137254i | ||||
\(778\) | 21.5638 | + | 21.5638i | 0.773099 | + | 0.773099i | ||||
\(779\) | 19.2798 | 0.690770 | ||||||||
\(780\) | −13.1518 | − | 9.48251i | −0.470912 | − | 0.339528i | ||||
\(781\) | 1.13456 | 0.0405979 | ||||||||
\(782\) | −3.32336 | − | 3.32336i | −0.118843 | − | 0.118843i | ||||
\(783\) | 2.26563 | + | 0.527475i | 0.0809670 | + | 0.0188504i | ||||
\(784\) | 6.14759i | 0.219557i | ||||||||
\(785\) | −24.7201 | − | 24.7201i | −0.882299 | − | 0.882299i | ||||
\(786\) | 1.91424 | + | 2.23091i | 0.0682786 | + | 0.0795738i | ||||
\(787\) | −8.45316 | − | 8.45316i | −0.301323 | − | 0.301323i | 0.540209 | − | 0.841531i | \(-0.318345\pi\) |
−0.841531 | + | 0.540209i | \(0.818345\pi\) | |||||||
\(788\) | 15.8345 | − | 15.8345i | 0.564081 | − | 0.564081i | ||||
\(789\) | −32.2061 | − | 2.46039i | −1.14657 | − | 0.0875922i | ||||
\(790\) | − | 23.6046i | − | 0.839815i | ||||||
\(791\) | 17.8644 | − | 17.8644i | 0.635186 | − | 0.635186i | ||||
\(792\) | 1.34797 | − | 8.77089i | 0.0478982 | − | 0.311660i | ||||
\(793\) | −48.3815 | + | 11.6841i | −1.71808 | + | 0.414915i | ||||
\(794\) | − | 15.9094i | − | 0.564602i | ||||||
\(795\) | 3.62765 | + | 4.22777i | 0.128660 | + | 0.149944i | ||||
\(796\) | 9.26324 | 0.328327 | ||||||||
\(797\) | 31.6461 | 1.12096 | 0.560481 | − | 0.828168i | \(-0.310616\pi\) | ||||
0.560481 | + | 0.828168i | \(0.310616\pi\) | |||||||
\(798\) | 11.7097 | − | 10.0475i | 0.414518 | − | 0.355679i | ||||
\(799\) | 16.4856 | − | 16.4856i | 0.583220 | − | 0.583220i | ||||
\(800\) | −3.12176 | + | 3.12176i | −0.110371 | + | 0.110371i | ||||
\(801\) | 32.2293 | − | 23.6425i | 1.13877 | − | 0.835367i | ||||
\(802\) | 5.71838 | 0.201923 | ||||||||
\(803\) | 10.4675 | 0.369391 | ||||||||
\(804\) | −20.8367 | + | 17.8790i | −0.734854 | + | 0.630544i | ||||
\(805\) | − | 8.06678i | − | 0.284316i | ||||||
\(806\) | −11.8559 | + | 2.86321i | −0.417608 | + | 0.100852i | ||||
\(807\) | −7.33410 | − | 0.560290i | −0.258172 | − | 0.0197231i | ||||
\(808\) | 3.00420 | − | 3.00420i | 0.105687 | − | 0.105687i | ||||
\(809\) | 32.5336i | 1.14382i | 0.820317 | + | 0.571909i | \(0.193797\pi\) | ||||
−0.820317 | + | 0.571909i | \(0.806203\pi\) | |||||||
\(810\) | −6.28501 | + | 19.9644i | −0.220833 | + | 0.701479i | ||||
\(811\) | 7.10405 | − | 7.10405i | 0.249457 | − | 0.249457i | −0.571291 | − | 0.820748i | \(-0.693557\pi\) |
0.820748 | + | 0.571291i | \(0.193557\pi\) | |||||||
\(812\) | 1.35211 | + | 1.35211i | 0.0474497 | + | 0.0474497i | ||||
\(813\) | 9.42810 | − | 8.08982i | 0.330658 | − | 0.283722i | ||||
\(814\) | −4.96183 | − | 4.96183i | −0.173912 | − | 0.173912i | ||||
\(815\) | 8.51454i | 0.298251i | ||||||||
\(816\) | −0.535718 | + | 7.01246i | −0.0187539 | + | 0.245485i | ||||
\(817\) | −8.18867 | − | 8.18867i | −0.286485 | − | 0.286485i | ||||
\(818\) | 26.5481 | 0.928233 | ||||||||
\(819\) | −32.8701 | − | 27.7384i | −1.14857 | − | 0.969257i | ||||
\(820\) | −21.4982 | −0.750750 | ||||||||
\(821\) | 37.6418 | + | 37.6418i | 1.31371 | + | 1.31371i | 0.918662 | + | 0.395044i | \(0.129271\pi\) |
0.395044 | + | 0.918662i | \(0.370729\pi\) | |||||||
\(822\) | −2.43865 | + | 31.9215i | −0.0850576 | + | 1.11339i | ||||
\(823\) | 26.1139i | 0.910274i | 0.890422 | + | 0.455137i | \(0.150410\pi\) | ||||
−0.890422 | + | 0.455137i | \(0.849590\pi\) | |||||||
\(824\) | 6.00728 | + | 6.00728i | 0.209274 | + | 0.209274i | ||||
\(825\) | −1.10652 | + | 0.949454i | −0.0385241 | + | 0.0330557i | ||||
\(826\) | −34.8486 | − | 34.8486i | −1.21254 | − | 1.21254i | ||||
\(827\) | 5.04334 | − | 5.04334i | 0.175374 | − | 0.175374i | −0.613962 | − | 0.789336i | \(-0.710425\pi\) |
0.789336 | + | 0.613962i | \(0.210425\pi\) | |||||||
\(828\) | −0.410886 | + | 2.67352i | −0.0142793 | + | 0.0929113i | ||||
\(829\) | 29.9527i | 1.04030i | 0.854075 | + | 0.520150i | \(0.174124\pi\) | ||||
−0.854075 | + | 0.520150i | \(0.825876\pi\) | |||||||
\(830\) | 17.2940 | − | 17.2940i | 0.600284 | − | 0.600284i | ||||
\(831\) | 55.9904 | + | 4.27740i | 1.94229 | + | 0.148381i | ||||
\(832\) | −5.45233 | − | 22.5770i | −0.189026 | − | 0.782716i | ||||
\(833\) | 51.2736i | 1.77652i | ||||||||
\(834\) | −17.2338 | + | 14.7876i | −0.596759 | + | 0.512051i | ||||
\(835\) | −18.6096 | −0.644013 | ||||||||
\(836\) | −2.50112 | −0.0865031 | ||||||||
\(837\) | −9.65199 | − | 15.5101i | −0.333621 | − | 0.536109i | ||||
\(838\) | −8.25583 | + | 8.25583i | −0.285193 | + | 0.285193i | ||||
\(839\) | −17.9945 | + | 17.9945i | −0.621239 | + | 0.621239i | −0.945848 | − | 0.324609i | \(-0.894767\pi\) |
0.324609 | + | 0.945848i | \(0.394767\pi\) | |||||||
\(840\) | −37.3676 | + | 32.0634i | −1.28930 | + | 1.10629i | ||||
\(841\) | 28.7996 | 0.993089 | ||||||||
\(842\) | 27.2853 | 0.940313 | ||||||||
\(843\) | 21.3871 | + | 24.9251i | 0.736610 | + | 0.858466i | ||||
\(844\) | 7.35289i | 0.253097i | ||||||||
\(845\) | −29.9089 | − | 9.62924i | −1.02890 | − | 0.331256i | ||||
\(846\) | 11.4302 | + | 1.75667i | 0.392977 | + | 0.0603957i | ||||
\(847\) | 2.81165 | − | 2.81165i | 0.0966094 | − | 0.0966094i | ||||
\(848\) | 0.928489i | 0.0318844i | ||||||||
\(849\) | 20.2680 | + | 1.54837i | 0.695595 | + | 0.0531401i | ||||
\(850\) | 3.33298 | − | 3.33298i | 0.114320 | − | 0.114320i | ||||
\(851\) | 4.32844 | + | 4.32844i | 0.148377 | + | 0.148377i | ||||
\(852\) | 1.37461 | + | 1.60200i | 0.0470932 | + | 0.0548838i | ||||
\(853\) | −1.31174 | − | 1.31174i | −0.0449131 | − | 0.0449131i | 0.684294 | − | 0.729207i | \(-0.260111\pi\) |
−0.729207 | + | 0.684294i | \(0.760111\pi\) | |||||||
\(854\) | 52.8146i | 1.80728i | ||||||||
\(855\) | 16.6870 | + | 2.56459i | 0.570685 | + | 0.0877070i | ||||
\(856\) | 14.1520 | + | 14.1520i | 0.483706 | + | 0.483706i | ||||
\(857\) | −23.4162 | −0.799881 | −0.399941 | − | 0.916541i | \(-0.630969\pi\) | ||||
−0.399941 | + | 0.916541i | \(0.630969\pi\) | |||||||
\(858\) | −0.961568 | − | 5.93144i | −0.0328274 | − | 0.202496i | ||||
\(859\) | −37.7480 | −1.28794 | −0.643972 | − | 0.765049i | \(-0.722715\pi\) | ||||
−0.643972 | + | 0.765049i | \(0.722715\pi\) | |||||||
\(860\) | 9.13090 | + | 9.13090i | 0.311361 | + | 0.311361i | ||||
\(861\) | −56.8619 | − | 4.34397i | −1.93785 | − | 0.148042i | ||||
\(862\) | − | 1.67586i | − | 0.0570802i | ||||||
\(863\) | 14.4849 | + | 14.4849i | 0.493073 | + | 0.493073i | 0.909273 | − | 0.416200i | \(-0.136638\pi\) |
−0.416200 | + | 0.909273i | \(0.636638\pi\) | |||||||
\(864\) | 23.1372 | − | 14.3984i | 0.787145 | − | 0.489842i | ||||
\(865\) | −8.01892 | − | 8.01892i | −0.272651 | − | 0.272651i | ||||
\(866\) | −21.1826 | + | 21.1826i | −0.719813 | + | 0.719813i | ||||
\(867\) | −2.22521 | + | 29.1276i | −0.0755721 | + | 0.989226i | ||||
\(868\) | − | 15.0165i | − | 0.509694i | ||||||
\(869\) | −7.17709 | + | 7.17709i | −0.243466 | + | 0.243466i | ||||
\(870\) | 0.137362 | − | 1.79804i | 0.00465701 | − | 0.0609594i | ||||
\(871\) | −27.7394 | + | 45.4034i | −0.939915 | + | 1.53844i | ||||
\(872\) | 34.8093i | 1.17879i | ||||||||
\(873\) | 20.7777 | − | 15.2419i | 0.703218 | − | 0.515861i | ||||
\(874\) | −1.88047 | −0.0636078 | ||||||||
\(875\) | −39.9627 | −1.35099 | ||||||||
\(876\) | 12.6822 | + | 14.7802i | 0.428491 | + | 0.499375i | ||||
\(877\) | 29.9739 | − | 29.9739i | 1.01215 | − | 1.01215i | 0.0122215 | − | 0.999925i | \(-0.496110\pi\) |
0.999925 | − | 0.0122215i | \(-0.00389031\pi\) | |||||||
\(878\) | 10.3820 | − | 10.3820i | 0.350375 | − | 0.350375i | ||||
\(879\) | −37.7112 | − | 43.9498i | −1.27197 | − | 1.48239i | ||||
\(880\) | −1.68642 | −0.0568492 | ||||||||
\(881\) | 6.12371 | 0.206313 | 0.103157 | − | 0.994665i | \(-0.467106\pi\) | ||||
0.103157 | + | 0.994665i | \(0.467106\pi\) | |||||||
\(882\) | −20.5068 | + | 15.0432i | −0.690501 | + | 0.506532i | ||||
\(883\) | 23.1902i | 0.780412i | 0.920728 | + | 0.390206i | \(0.127596\pi\) | ||||
−0.920728 | + | 0.390206i | \(0.872404\pi\) | |||||||
\(884\) | −5.29104 | − | 21.9091i | −0.177957 | − | 0.736883i | ||||
\(885\) | 4.10771 | − | 53.7692i | 0.138079 | − | 1.80743i | ||||
\(886\) | −10.5186 | + | 10.5186i | −0.353381 | + | 0.353381i | ||||
\(887\) | − | 34.4025i | − | 1.15512i | −0.816347 | − | 0.577561i | \(-0.804005\pi\) | ||
0.816347 | − | 0.577561i | \(-0.195995\pi\) | |||||||
\(888\) | 2.84610 | − | 37.2550i | 0.0955089 | − | 1.25020i | ||||
\(889\) | 20.9867 | − | 20.9867i | 0.703871 | − | 0.703871i | ||||
\(890\) | −21.9101 | − | 21.9101i | −0.734430 | − | 0.734430i | ||||
\(891\) | 7.98125 | − | 4.15928i | 0.267382 | − | 0.139341i | ||||
\(892\) | 9.58772 | + | 9.58772i | 0.321020 | + | 0.321020i | ||||
\(893\) | − | 9.32812i | − | 0.312154i | ||||||
\(894\) | −9.43256 | − | 0.720602i | −0.315472 | − | 0.0241005i | ||||
\(895\) | −31.5661 | − | 31.5661i | −1.05514 | − | 1.05514i | ||||
\(896\) | 17.0619 | 0.569999 | ||||||||
\(897\) | 0.838821 | + | 5.17428i | 0.0280074 | + | 0.172764i | ||||
\(898\) | 0.544737 | 0.0181781 | ||||||||
\(899\) | 1.11293 | + | 1.11293i | 0.0371182 | + | 0.0371182i | ||||
\(900\) | −2.68126 | − | 0.412075i | −0.0893752 | − | 0.0137358i | ||||
\(901\) | 7.74400i | 0.257990i | ||||||||
\(902\) | −5.63370 | − | 5.63370i | −0.187582 | − | 0.187582i | ||||
\(903\) | 22.3059 | + | 25.9959i | 0.742292 | + | 0.865088i | ||||
\(904\) | 13.2894 | + | 13.2894i | 0.441999 | + | 0.441999i | ||||
\(905\) | −23.8539 | + | 23.8539i | −0.792932 | + | 0.792932i | ||||
\(906\) | 38.5803 | + | 2.94735i | 1.28174 | + | 0.0979191i | ||||
\(907\) | − | 33.8818i | − | 1.12503i | −0.826788 | − | 0.562514i | \(-0.809834\pi\) | ||
0.826788 | − | 0.562514i | \(-0.190166\pi\) | |||||||
\(908\) | −1.83021 | + | 1.83021i | −0.0607378 | + | 0.0607378i | ||||
\(909\) | 4.25896 | + | 0.654549i | 0.141261 | + | 0.0217100i | ||||
\(910\) | −17.3826 | + | 28.4515i | −0.576226 | + | 0.943157i | ||||
\(911\) | − | 23.1786i | − | 0.767942i | −0.923345 | − | 0.383971i | \(-0.874556\pi\) | ||
0.923345 | − | 0.383971i | \(-0.125444\pi\) | |||||||
\(912\) | 1.83238 | + | 2.13550i | 0.0606760 | + | 0.0707136i | ||||
\(913\) | −10.5166 | −0.348050 | ||||||||
\(914\) | −4.01621 | −0.132844 | ||||||||
\(915\) | −43.8574 | + | 37.6320i | −1.44988 | + | 1.24408i | ||||
\(916\) | 4.67812 | − | 4.67812i | 0.154569 | − | 0.154569i | ||||
\(917\) | −4.95938 | + | 4.95938i | −0.163773 | + | 0.163773i | ||||
\(918\) | −24.7027 | + | 15.3726i | −0.815312 | + | 0.507370i | ||||
\(919\) | −10.8639 | −0.358367 | −0.179183 | − | 0.983816i | \(-0.557346\pi\) | ||||
−0.179183 | + | 0.983816i | \(0.557346\pi\) | |||||||
\(920\) | 6.00089 | 0.197843 | ||||||||
\(921\) | −3.60105 | + | 3.08989i | −0.118659 | + | 0.101815i | ||||
\(922\) | 14.2419i | 0.469032i | ||||||||
\(923\) | 3.49079 | + | 2.13271i | 0.114901 | + | 0.0701991i | ||||
\(924\) | 7.37656 | + | 0.563534i | 0.242671 | + | 0.0185389i | ||||
\(925\) | −4.34097 | + | 4.34097i | −0.142730 | + | 0.142730i | ||||
\(926\) | 14.8517i | 0.488056i | ||||||||
\(927\) | −1.30885 | + | 8.51634i | −0.0429884 | + | 0.279713i | ||||
\(928\) | −1.66021 | + | 1.66021i | −0.0544990 | + | 0.0544990i | ||||
\(929\) | −31.1696 | − | 31.1696i | −1.02264 | − | 1.02264i | −0.999738 | − | 0.0229025i | \(-0.992709\pi\) |
−0.0229025 | − | 0.999738i | \(-0.507291\pi\) | |||||||
\(930\) | −10.7473 | + | 9.22178i | −0.352419 | + | 0.302394i | ||||
\(931\) | 14.5061 | + | 14.5061i | 0.475419 | + | 0.475419i | ||||
\(932\) | − | 1.55631i | − | 0.0509787i | ||||||
\(933\) | −0.329885 | + | 4.31814i | −0.0108000 | + | 0.141370i | ||||
\(934\) | 16.3837 | + | 16.3837i | 0.536090 | + | 0.536090i | ||||
\(935\) | −14.0655 | −0.459990 | ||||||||
\(936\) | 20.6346 | − | 24.4521i | 0.674463 | − | 0.799242i | ||||
\(937\) | 32.1756 | 1.05113 | 0.525565 | − | 0.850753i | \(-0.323854\pi\) | ||||
0.525565 | + | 0.850753i | \(0.323854\pi\) | |||||||
\(938\) | 39.9224 | + | 39.9224i | 1.30351 | + | 1.30351i | ||||
\(939\) | 0.0193297 | − | 0.253022i | 0.000630800 | − | 0.00825707i | ||||
\(940\) | 10.4015i | 0.339258i | ||||||||
\(941\) | −7.54952 | − | 7.54952i | −0.246107 | − | 0.246107i | 0.573264 | − | 0.819371i | \(-0.305677\pi\) |
−0.819371 | + | 0.573264i | \(0.805677\pi\) | |||||||
\(942\) | 18.2939 | − | 15.6972i | 0.596049 | − | 0.511442i | ||||
\(943\) | 4.91455 | + | 4.91455i | 0.160040 | + | 0.160040i | ||||
\(944\) | 6.35537 | − | 6.35537i | 0.206850 | − | 0.206850i | ||||
\(945\) | −48.6372 | − | 11.3235i | −1.58217 | − | 0.368354i | ||||
\(946\) | 4.78559i | 0.155593i | ||||||||
\(947\) | 36.5257 | − | 36.5257i | 1.18693 | − | 1.18693i | 0.209014 | − | 0.977913i | \(-0.432975\pi\) |
0.977913 | − | 0.209014i | \(-0.0670255\pi\) | |||||||
\(948\) | −18.8296 | − | 1.43849i | −0.611557 | − | 0.0467200i | ||||
\(949\) | 32.2061 | + | 19.6765i | 1.04546 | + | 0.638726i | ||||
\(950\) | − | 1.88591i | − | 0.0611870i | ||||||
\(951\) | −12.6963 | + | 10.8941i | −0.411705 | + | 0.353265i | ||||
\(952\) | −68.4461 | −2.21835 | ||||||||
\(953\) | 3.69885 | 0.119817 | 0.0599087 | − | 0.998204i | \(-0.480919\pi\) | ||||
0.0599087 | + | 0.998204i | \(0.480919\pi\) | |||||||
\(954\) | −3.09721 | + | 2.27203i | −0.100276 | + | 0.0735595i | ||||
\(955\) | −15.4789 | + | 15.4789i | −0.500886 | + | 0.500886i | ||||
\(956\) | −8.93430 | + | 8.93430i | −0.288956 | + | 0.288956i | ||||
\(957\) | −0.588468 | + | 0.504937i | −0.0190225 | + | 0.0163223i | ||||
\(958\) | −2.03303 | −0.0656841 | ||||||||
\(959\) | −76.3838 | −2.46656 | ||||||||
\(960\) | −17.5608 | − | 20.4659i | −0.566772 | − | 0.660532i | ||||
\(961\) | 18.6398i | 0.601284i | ||||||||
\(962\) | −5.93931 | − | 24.5935i | −0.191491 | − | 0.792925i | ||||
\(963\) | −3.08341 | + | 20.0629i | −0.0993616 | + | 0.646518i | ||||
\(964\) | 0.495480 | − | 0.495480i | 0.0159583 | − | 0.0159583i | ||||
\(965\) | 52.2254i | 1.68120i | ||||||||
\(966\) | 5.54606 | + | 0.423693i | 0.178442 | + | 0.0136321i | ||||
\(967\) | 15.1872 | − | 15.1872i | 0.488386 | − | 0.488386i | −0.419411 | − | 0.907797i | \(-0.637763\pi\) |
0.907797 | + | 0.419411i | \(0.137763\pi\) | |||||||
\(968\) | 2.09159 | + | 2.09159i | 0.0672263 | + | 0.0672263i | ||||
\(969\) | 15.2828 | + | 17.8110i | 0.490955 | + | 0.572172i | ||||
\(970\) | −14.1251 | − | 14.1251i | −0.453530 | − | 0.453530i | ||||
\(971\) | 31.7994i | 1.02049i | 0.860029 | + | 0.510246i | \(0.170446\pi\) | ||||
−0.860029 | + | 0.510246i | \(0.829554\pi\) | |||||||
\(972\) | 15.5428 | + | 6.23025i | 0.498534 | + | 0.199836i | ||||
\(973\) | −38.3114 | − | 38.3114i | −1.22821 | − | 1.22821i | ||||
\(974\) | −18.4636 | −0.591613 | ||||||||
\(975\) | −5.18925 | + | 0.841249i | −0.166189 | + | 0.0269415i | ||||
\(976\) | −9.63183 | −0.308307 | ||||||||
\(977\) | 8.96922 | + | 8.96922i | 0.286951 | + | 0.286951i | 0.835873 | − | 0.548922i | \(-0.184962\pi\) |
−0.548922 | + | 0.835873i | \(0.684962\pi\) | |||||||
\(978\) | −5.85391 | − | 0.447211i | −0.187188 | − | 0.0143002i | ||||
\(979\) | 13.3237i | 0.425828i | ||||||||
\(980\) | −16.1753 | − | 16.1753i | −0.516700 | − | 0.516700i | ||||
\(981\) | −28.4661 | + | 20.8820i | −0.908854 | + | 0.666710i | ||||
\(982\) | 3.53148 | + | 3.53148i | 0.112694 | + | 0.112694i | ||||
\(983\) | 18.4004 | − | 18.4004i | 0.586881 | − | 0.586881i | −0.349905 | − | 0.936785i | \(-0.613786\pi\) |
0.936785 | + | 0.349905i | \(0.113786\pi\) | |||||||
\(984\) | 3.23149 | − | 42.2996i | 0.103016 | − | 1.34846i | ||||
\(985\) | − | 50.3862i | − | 1.60544i | ||||||
\(986\) | 1.77254 | − | 1.77254i | 0.0564492 | − | 0.0564492i | ||||
\(987\) | −2.10174 | + | 27.5114i | −0.0668991 | + | 0.875698i | ||||
\(988\) | −7.69537 | − | 4.70152i | −0.244822 | − | 0.149575i | ||||
\(989\) | − | 4.17470i | − | 0.132748i | ||||||
\(990\) | −4.12669 | − | 5.62547i | −0.131155 | − | 0.178789i | ||||
\(991\) | 27.3003 | 0.867221 | 0.433611 | − | 0.901100i | \(-0.357239\pi\) | ||||
0.433611 | + | 0.901100i | \(0.357239\pi\) | |||||||
\(992\) | 18.4383 | 0.585417 | ||||||||
\(993\) | 19.0248 | + | 22.1721i | 0.603735 | + | 0.703610i | ||||
\(994\) | 3.06938 | − | 3.06938i | 0.0973550 | − | 0.0973550i | ||||
\(995\) | 14.7380 | − | 14.7380i | 0.467227 | − | 0.467227i | ||||
\(996\) | −12.7417 | − | 14.8495i | −0.403735 | − | 0.470524i | ||||
\(997\) | −25.6515 | −0.812391 | −0.406196 | − | 0.913786i | \(-0.633145\pi\) | ||||
−0.406196 | + | 0.913786i | \(0.633145\pi\) | |||||||
\(998\) | −1.65883 | −0.0525094 | ||||||||
\(999\) | 32.1735 | − | 20.0217i | 1.01793 | − | 0.633457i |
(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 | 429.2.j.a.122.18 | ✓ | 96 | |
3.2 | odd | 2 | inner | 429.2.j.a.122.31 | yes | 96 | |
13.8 | odd | 4 | inner | 429.2.j.a.320.31 | yes | 96 | |
39.8 | even | 4 | inner | 429.2.j.a.320.18 | yes | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.j.a.122.18 | ✓ | 96 | 1.1 | even | 1 | trivial | |
429.2.j.a.122.31 | yes | 96 | 3.2 | odd | 2 | inner | |
429.2.j.a.320.18 | yes | 96 | 39.8 | even | 4 | inner | |
429.2.j.a.320.31 | yes | 96 | 13.8 | odd | 4 | inner |