Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1380,2,Mod(91,1380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1380.91");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1380.p (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: | \(11.0193554789\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.16 | ||
Character | \(\chi\) | \(=\) | 1380.91 |
Dual form | 1380.2.p.a.91.15 |
$q$-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 \(\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(691\) | \(1201\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.952347 | + | 1.04548i | −0.673411 | + | 0.739268i | ||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −0.186069 | − | 1.99133i | −0.0930343 | − | 0.995663i | ||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | −1.04548 | − | 0.952347i | −0.426817 | − | 0.388794i | ||||
\(7\) | 3.49678 | 1.32166 | 0.660829 | − | 0.750537i | \(-0.270205\pi\) | ||||
0.660829 | + | 0.750537i | \(0.270205\pi\) | |||||||
\(8\) | 2.25910 | + | 1.70190i | 0.798712 | + | 0.601713i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −1.04548 | − | 0.952347i | −0.330611 | − | 0.301159i | ||||
\(11\) | 1.36625 | 0.411940 | 0.205970 | − | 0.978558i | \(-0.433965\pi\) | ||||
0.205970 | + | 0.978558i | \(0.433965\pi\) | |||||||
\(12\) | 1.99133 | − | 0.186069i | 0.574846 | − | 0.0537134i | ||||
\(13\) | 3.35306 | 0.929970 | 0.464985 | − | 0.885318i | \(-0.346060\pi\) | ||||
0.464985 | + | 0.885318i | \(0.346060\pi\) | |||||||
\(14\) | −3.33015 | + | 3.65582i | −0.890019 | + | 0.977059i | ||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | −3.93076 | + | 0.741046i | −0.982689 | + | 0.185262i | ||||
\(17\) | − | 0.0719348i | − | 0.0174468i | −0.999962 | − | 0.00872338i | \(-0.997223\pi\) | ||
0.999962 | − | 0.00872338i | \(-0.00277677\pi\) | |||||||
\(18\) | 0.952347 | − | 1.04548i | 0.224470 | − | 0.246423i | ||||
\(19\) | −5.04791 | −1.15807 | −0.579035 | − | 0.815303i | \(-0.696571\pi\) | ||||
−0.579035 | + | 0.815303i | \(0.696571\pi\) | |||||||
\(20\) | 1.99133 | − | 0.186069i | 0.445274 | − | 0.0416062i | ||||
\(21\) | 3.49678i | 0.763060i | ||||||||
\(22\) | −1.30115 | + | 1.42839i | −0.277405 | + | 0.304534i | ||||
\(23\) | 4.76200 | + | 0.568640i | 0.992946 | + | 0.118570i | ||||
\(24\) | −1.70190 | + | 2.25910i | −0.347399 | + | 0.461137i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −3.19327 | + | 3.50556i | −0.626253 | + | 0.687497i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −0.650640 | − | 6.96322i | −0.122959 | − | 1.31593i | ||||
\(29\) | 9.80417 | 1.82059 | 0.910294 | − | 0.413962i | \(-0.135855\pi\) | ||||
0.910294 | + | 0.413962i | \(0.135855\pi\) | |||||||
\(30\) | 0.952347 | − | 1.04548i | 0.173874 | − | 0.190878i | ||||
\(31\) | − | 8.07183i | − | 1.44974i | −0.688884 | − | 0.724872i | \(-0.741899\pi\) | ||
0.688884 | − | 0.724872i | \(-0.258101\pi\) | |||||||
\(32\) | 2.96870 | − | 4.81527i | 0.524796 | − | 0.851228i | ||||
\(33\) | 1.36625i | 0.237834i | ||||||||
\(34\) | 0.0752066 | + | 0.0685069i | 0.0128978 | + | 0.0117488i | ||||
\(35\) | 3.49678i | 0.591063i | ||||||||
\(36\) | 0.186069 | + | 1.99133i | 0.0310114 | + | 0.331888i | ||||
\(37\) | − | 3.32625i | − | 0.546833i | −0.961896 | − | 0.273416i | \(-0.911846\pi\) | ||
0.961896 | − | 0.273416i | \(-0.0881537\pi\) | |||||||
\(38\) | 4.80737 | − | 5.27750i | 0.779858 | − | 0.856124i | ||||
\(39\) | 3.35306i | 0.536919i | ||||||||
\(40\) | −1.70190 | + | 2.25910i | −0.269094 | + | 0.357195i | ||||
\(41\) | 1.37906 | 0.215373 | 0.107686 | − | 0.994185i | \(-0.465656\pi\) | ||||
0.107686 | + | 0.994185i | \(0.465656\pi\) | |||||||
\(42\) | −3.65582 | − | 3.33015i | −0.564105 | − | 0.513853i | ||||
\(43\) | 8.91103 | 1.35892 | 0.679459 | − | 0.733713i | \(-0.262214\pi\) | ||||
0.679459 | + | 0.733713i | \(0.262214\pi\) | |||||||
\(44\) | −0.254216 | − | 2.72065i | −0.0383246 | − | 0.410154i | ||||
\(45\) | − | 1.00000i | − | 0.149071i | ||||||
\(46\) | −5.12958 | + | 4.43705i | −0.756316 | + | 0.654207i | ||||
\(47\) | 12.6923i | 1.85137i | 0.378296 | + | 0.925684i | \(0.376510\pi\) | ||||
−0.378296 | + | 0.925684i | \(0.623490\pi\) | |||||||
\(48\) | −0.741046 | − | 3.93076i | −0.106961 | − | 0.567356i | ||||
\(49\) | 5.22746 | 0.746779 | ||||||||
\(50\) | 0.952347 | − | 1.04548i | 0.134682 | − | 0.147854i | ||||
\(51\) | 0.0719348 | 0.0100729 | ||||||||
\(52\) | −0.623898 | − | 6.67703i | −0.0865191 | − | 0.925937i | ||||
\(53\) | − | 10.9669i | − | 1.50642i | −0.657780 | − | 0.753210i | \(-0.728504\pi\) | ||
0.657780 | − | 0.753210i | \(-0.271496\pi\) | |||||||
\(54\) | 1.04548 | + | 0.952347i | 0.142272 | + | 0.129598i | ||||
\(55\) | 1.36625i | 0.184225i | ||||||||
\(56\) | 7.89957 | + | 5.95118i | 1.05562 | + | 0.795259i | ||||
\(57\) | − | 5.04791i | − | 0.668612i | ||||||
\(58\) | −9.33697 | + | 10.2501i | −1.22600 | + | 1.34590i | ||||
\(59\) | 4.71711i | 0.614116i | 0.951691 | + | 0.307058i | \(0.0993445\pi\) | ||||
−0.951691 | + | 0.307058i | \(0.900655\pi\) | |||||||
\(60\) | 0.186069 | + | 1.99133i | 0.0240213 | + | 0.257079i | ||||
\(61\) | − | 6.38461i | − | 0.817465i | −0.912654 | − | 0.408733i | \(-0.865971\pi\) | ||
0.912654 | − | 0.408733i | \(-0.134029\pi\) | |||||||
\(62\) | 8.43896 | + | 7.68719i | 1.07175 | + | 0.976274i | ||||
\(63\) | −3.49678 | −0.440553 | ||||||||
\(64\) | 2.20705 | + | 7.68953i | 0.275882 | + | 0.961192i | ||||
\(65\) | 3.35306i | 0.415895i | ||||||||
\(66\) | −1.42839 | − | 1.30115i | −0.175823 | − | 0.160160i | ||||
\(67\) | −15.2636 | −1.86475 | −0.932374 | − | 0.361496i | \(-0.882266\pi\) | ||||
−0.932374 | + | 0.361496i | \(0.882266\pi\) | |||||||
\(68\) | −0.143246 | + | 0.0133848i | −0.0173711 | + | 0.00162315i | ||||
\(69\) | −0.568640 | + | 4.76200i | −0.0684562 | + | 0.573277i | ||||
\(70\) | −3.65582 | − | 3.33015i | −0.436954 | − | 0.398029i | ||||
\(71\) | 15.7028i | 1.86358i | 0.362995 | + | 0.931791i | \(0.381754\pi\) | ||||
−0.362995 | + | 0.931791i | \(0.618246\pi\) | |||||||
\(72\) | −2.25910 | − | 1.70190i | −0.266237 | − | 0.200571i | ||||
\(73\) | 5.24792 | 0.614222 | 0.307111 | − | 0.951674i | \(-0.400638\pi\) | ||||
0.307111 | + | 0.951674i | \(0.400638\pi\) | |||||||
\(74\) | 3.47754 | + | 3.16775i | 0.404256 | + | 0.368243i | ||||
\(75\) | − | 1.00000i | − | 0.115470i | ||||||
\(76\) | 0.939258 | + | 10.0520i | 0.107740 | + | 1.15305i | ||||
\(77\) | 4.77748 | 0.544444 | ||||||||
\(78\) | −3.50556 | − | 3.19327i | −0.396927 | − | 0.361567i | ||||
\(79\) | 4.20591 | 0.473202 | 0.236601 | − | 0.971607i | \(-0.423967\pi\) | ||||
0.236601 | + | 0.971607i | \(0.423967\pi\) | |||||||
\(80\) | −0.741046 | − | 3.93076i | −0.0828515 | − | 0.439472i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.31334 | + | 1.44178i | −0.145034 | + | 0.159218i | ||||
\(83\) | −13.4916 | −1.48089 | −0.740447 | − | 0.672115i | \(-0.765386\pi\) | ||||
−0.740447 | + | 0.672115i | \(0.765386\pi\) | |||||||
\(84\) | 6.96322 | − | 0.650640i | 0.759750 | − | 0.0709907i | ||||
\(85\) | 0.0719348 | 0.00780242 | ||||||||
\(86\) | −8.48639 | + | 9.31632i | −0.915111 | + | 1.00461i | ||||
\(87\) | 9.80417i | 1.05112i | ||||||||
\(88\) | 3.08650 | + | 2.32523i | 0.329022 | + | 0.247870i | ||||
\(89\) | 11.5228i | 1.22141i | 0.791857 | + | 0.610706i | \(0.209114\pi\) | ||||
−0.791857 | + | 0.610706i | \(0.790886\pi\) | |||||||
\(90\) | 1.04548 | + | 0.952347i | 0.110204 | + | 0.100386i | ||||
\(91\) | 11.7249 | 1.22910 | ||||||||
\(92\) | 0.246289 | − | 9.58850i | 0.0256774 | − | 0.999670i | ||||
\(93\) | 8.07183 | 0.837010 | ||||||||
\(94\) | −13.2696 | − | 12.0875i | −1.36866 | − | 1.24673i | ||||
\(95\) | − | 5.04791i | − | 0.517905i | ||||||
\(96\) | 4.81527 | + | 2.96870i | 0.491457 | + | 0.302991i | ||||
\(97\) | − | 4.72490i | − | 0.479741i | −0.970805 | − | 0.239871i | \(-0.922895\pi\) | ||
0.970805 | − | 0.239871i | \(-0.0771050\pi\) | |||||||
\(98\) | −4.97835 | + | 5.46522i | −0.502890 | + | 0.552070i | ||||
\(99\) | −1.36625 | −0.137313 | ||||||||
\(100\) | 0.186069 | + | 1.99133i | 0.0186069 | + | 0.199133i | ||||
\(101\) | 10.7894 | 1.07358 | 0.536791 | − | 0.843715i | \(-0.319636\pi\) | ||||
0.536791 | + | 0.843715i | \(0.319636\pi\) | |||||||
\(102\) | −0.0685069 | + | 0.0752066i | −0.00678320 | + | 0.00744656i | ||||
\(103\) | 8.71856 | 0.859065 | 0.429533 | − | 0.903051i | \(-0.358678\pi\) | ||||
0.429533 | + | 0.903051i | \(0.358678\pi\) | |||||||
\(104\) | 7.57488 | + | 5.70657i | 0.742779 | + | 0.559576i | ||||
\(105\) | −3.49678 | −0.341251 | ||||||||
\(106\) | 11.4657 | + | 10.4443i | 1.11365 | + | 1.01444i | ||||
\(107\) | −15.4237 | −1.49106 | −0.745530 | − | 0.666472i | \(-0.767804\pi\) | ||||
−0.745530 | + | 0.666472i | \(0.767804\pi\) | |||||||
\(108\) | −1.99133 | + | 0.186069i | −0.191615 | + | 0.0179045i | ||||
\(109\) | 2.16171i | 0.207054i | 0.994627 | + | 0.103527i | \(0.0330129\pi\) | ||||
−0.994627 | + | 0.103527i | \(0.966987\pi\) | |||||||
\(110\) | −1.42839 | − | 1.30115i | −0.136192 | − | 0.124059i | ||||
\(111\) | 3.32625 | 0.315714 | ||||||||
\(112\) | −13.7450 | + | 2.59127i | −1.29878 | + | 0.244852i | ||||
\(113\) | − | 8.97756i | − | 0.844538i | −0.906471 | − | 0.422269i | \(-0.861234\pi\) | ||
0.906471 | − | 0.422269i | \(-0.138766\pi\) | |||||||
\(114\) | 5.27750 | + | 4.80737i | 0.494284 | + | 0.450251i | ||||
\(115\) | −0.568640 | + | 4.76200i | −0.0530260 | + | 0.444059i | ||||
\(116\) | −1.82425 | − | 19.5233i | −0.169377 | − | 1.81269i | ||||
\(117\) | −3.35306 | −0.309990 | ||||||||
\(118\) | −4.93166 | − | 4.49233i | −0.453996 | − | 0.413552i | ||||
\(119\) | − | 0.251540i | − | 0.0230586i | ||||||
\(120\) | −2.25910 | − | 1.70190i | −0.206227 | − | 0.155362i | ||||
\(121\) | −9.13336 | −0.830305 | ||||||||
\(122\) | 6.67500 | + | 6.08036i | 0.604326 | + | 0.550490i | ||||
\(123\) | 1.37906i | 0.124345i | ||||||||
\(124\) | −16.0737 | + | 1.50191i | −1.44346 | + | 0.134876i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 3.33015 | − | 3.65582i | 0.296673 | − | 0.325686i | ||||
\(127\) | 12.7171i | 1.12846i | 0.825618 | + | 0.564230i | \(0.190827\pi\) | ||||
−0.825618 | + | 0.564230i | \(0.809173\pi\) | |||||||
\(128\) | −10.1412 | − | 5.01567i | −0.896360 | − | 0.443327i | ||||
\(129\) | 8.91103i | 0.784572i | ||||||||
\(130\) | −3.50556 | − | 3.19327i | −0.307458 | − | 0.280069i | ||||
\(131\) | 21.4821i | 1.87690i | 0.345417 | + | 0.938449i | \(0.387738\pi\) | ||||
−0.345417 | + | 0.938449i | \(0.612262\pi\) | |||||||
\(132\) | 2.72065 | − | 0.254216i | 0.236802 | − | 0.0221267i | ||||
\(133\) | −17.6514 | −1.53057 | ||||||||
\(134\) | 14.5363 | − | 15.9578i | 1.25574 | − | 1.37855i | ||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0.122426 | − | 0.162508i | 0.0104979 | − | 0.0139349i | ||||
\(137\) | 8.83193i | 0.754562i | 0.926099 | + | 0.377281i | \(0.123141\pi\) | ||||
−0.926099 | + | 0.377281i | \(0.876859\pi\) | |||||||
\(138\) | −4.43705 | − | 5.12958i | −0.377707 | − | 0.436659i | ||||
\(139\) | − | 1.47914i | − | 0.125459i | −0.998031 | − | 0.0627295i | \(-0.980019\pi\) | ||
0.998031 | − | 0.0627295i | \(-0.0199805\pi\) | |||||||
\(140\) | 6.96322 | − | 0.650640i | 0.588500 | − | 0.0549892i | ||||
\(141\) | −12.6923 | −1.06889 | ||||||||
\(142\) | −16.4170 | − | 14.9545i | −1.37769 | − | 1.25496i | ||||
\(143\) | 4.58112 | 0.383092 | ||||||||
\(144\) | 3.93076 | − | 0.741046i | 0.327563 | − | 0.0617539i | ||||
\(145\) | 9.80417i | 0.814192i | ||||||||
\(146\) | −4.99784 | + | 5.48661i | −0.413624 | + | 0.454075i | ||||
\(147\) | 5.22746i | 0.431153i | ||||||||
\(148\) | −6.62366 | + | 0.618911i | −0.544461 | + | 0.0508742i | ||||
\(149\) | − | 12.9154i | − | 1.05807i | −0.848600 | − | 0.529034i | \(-0.822554\pi\) | ||
0.848600 | − | 0.529034i | \(-0.177446\pi\) | |||||||
\(150\) | 1.04548 | + | 0.952347i | 0.0853633 | + | 0.0777588i | ||||
\(151\) | − | 1.48821i | − | 0.121109i | −0.998165 | − | 0.0605546i | \(-0.980713\pi\) | ||
0.998165 | − | 0.0605546i | \(-0.0192869\pi\) | |||||||
\(152\) | −11.4037 | − | 8.59105i | −0.924965 | − | 0.696827i | ||||
\(153\) | 0.0719348i | 0.00581558i | ||||||||
\(154\) | −4.54982 | + | 4.99477i | −0.366635 | + | 0.402490i | ||||
\(155\) | 8.07183 | 0.648345 | ||||||||
\(156\) | 6.67703 | − | 0.623898i | 0.534590 | − | 0.0499518i | ||||
\(157\) | 0.789022i | 0.0629708i | 0.999504 | + | 0.0314854i | \(0.0100238\pi\) | ||||
−0.999504 | + | 0.0314854i | \(0.989976\pi\) | |||||||
\(158\) | −4.00549 | + | 4.39721i | −0.318659 | + | 0.349823i | ||||
\(159\) | 10.9669 | 0.869733 | ||||||||
\(160\) | 4.81527 | + | 2.96870i | 0.380681 | + | 0.234696i | ||||
\(161\) | 16.6517 | + | 1.98841i | 1.31233 | + | 0.156708i | ||||
\(162\) | −0.952347 | + | 1.04548i | −0.0748235 | + | 0.0821409i | ||||
\(163\) | 10.0679i | 0.788576i | 0.918987 | + | 0.394288i | \(0.129009\pi\) | ||||
−0.918987 | + | 0.394288i | \(0.870991\pi\) | |||||||
\(164\) | −0.256599 | − | 2.74615i | −0.0200370 | − | 0.214439i | ||||
\(165\) | −1.36625 | −0.106363 | ||||||||
\(166\) | 12.8487 | − | 14.1052i | 0.997251 | − | 1.09478i | ||||
\(167\) | − | 12.3125i | − | 0.952769i | −0.879237 | − | 0.476384i | \(-0.841947\pi\) | ||
0.879237 | − | 0.476384i | \(-0.158053\pi\) | |||||||
\(168\) | −5.95118 | + | 7.89957i | −0.459143 | + | 0.609465i | ||||
\(169\) | −1.75702 | −0.135155 | ||||||||
\(170\) | −0.0685069 | + | 0.0752066i | −0.00525424 | + | 0.00576808i | ||||
\(171\) | 5.04791 | 0.386023 | ||||||||
\(172\) | −1.65806 | − | 17.7448i | −0.126426 | − | 1.35303i | ||||
\(173\) | 3.04079 | 0.231187 | 0.115593 | − | 0.993297i | \(-0.463123\pi\) | ||||
0.115593 | + | 0.993297i | \(0.463123\pi\) | |||||||
\(174\) | −10.2501 | − | 9.33697i | −0.777057 | − | 0.707834i | ||||
\(175\) | −3.49678 | −0.264332 | ||||||||
\(176\) | −5.37040 | + | 1.01246i | −0.404809 | + | 0.0763167i | ||||
\(177\) | −4.71711 | −0.354560 | ||||||||
\(178\) | −12.0469 | − | 10.9737i | −0.902951 | − | 0.822513i | ||||
\(179\) | − | 9.66616i | − | 0.722483i | −0.932472 | − | 0.361242i | \(-0.882353\pi\) | ||
0.932472 | − | 0.361242i | \(-0.117647\pi\) | |||||||
\(180\) | −1.99133 | + | 0.186069i | −0.148425 | + | 0.0138687i | ||||
\(181\) | 26.0047i | 1.93291i | 0.256827 | + | 0.966457i | \(0.417323\pi\) | ||||
−0.256827 | + | 0.966457i | \(0.582677\pi\) | |||||||
\(182\) | −11.1662 | + | 12.2582i | −0.827692 | + | 0.908636i | ||||
\(183\) | 6.38461 | 0.471964 | ||||||||
\(184\) | 9.79006 | + | 9.38907i | 0.721733 | + | 0.692172i | ||||
\(185\) | 3.32625 | 0.244551 | ||||||||
\(186\) | −7.68719 | + | 8.43896i | −0.563652 | + | 0.618775i | ||||
\(187\) | − | 0.0982810i | − | 0.00718702i | ||||||
\(188\) | 25.2746 | − | 2.36165i | 1.84334 | − | 0.172241i | ||||
\(189\) | − | 3.49678i | − | 0.254353i | ||||||
\(190\) | 5.27750 | + | 4.80737i | 0.382870 | + | 0.348763i | ||||
\(191\) | 1.45243 | 0.105094 | 0.0525469 | − | 0.998618i | \(-0.483266\pi\) | ||||
0.0525469 | + | 0.998618i | \(0.483266\pi\) | |||||||
\(192\) | −7.68953 | + | 2.20705i | −0.554944 | + | 0.159280i | ||||
\(193\) | 12.6263 | 0.908861 | 0.454431 | − | 0.890782i | \(-0.349843\pi\) | ||||
0.454431 | + | 0.890782i | \(0.349843\pi\) | |||||||
\(194\) | 4.93981 | + | 4.49975i | 0.354657 | + | 0.323063i | ||||
\(195\) | −3.35306 | −0.240117 | ||||||||
\(196\) | −0.972665 | − | 10.4096i | −0.0694761 | − | 0.743541i | ||||
\(197\) | −23.9878 | −1.70906 | −0.854530 | − | 0.519401i | \(-0.826155\pi\) | ||||
−0.854530 | + | 0.519401i | \(0.826155\pi\) | |||||||
\(198\) | 1.30115 | − | 1.42839i | 0.0924684 | − | 0.101511i | ||||
\(199\) | −16.8297 | −1.19303 | −0.596513 | − | 0.802603i | \(-0.703448\pi\) | ||||
−0.596513 | + | 0.802603i | \(0.703448\pi\) | |||||||
\(200\) | −2.25910 | − | 1.70190i | −0.159742 | − | 0.120343i | ||||
\(201\) | − | 15.2636i | − | 1.07661i | ||||||
\(202\) | −10.2752 | + | 11.2801i | −0.722962 | + | 0.793665i | ||||
\(203\) | 34.2830 | 2.40619 | ||||||||
\(204\) | −0.0133848 | − | 0.143246i | −0.000937124 | − | 0.0100292i | ||||
\(205\) | 1.37906i | 0.0963176i | ||||||||
\(206\) | −8.30310 | + | 9.11510i | −0.578504 | + | 0.635079i | ||||
\(207\) | −4.76200 | − | 0.568640i | −0.330982 | − | 0.0395232i | ||||
\(208\) | −13.1800 | + | 2.48477i | −0.913872 | + | 0.172288i | ||||
\(209\) | −6.89672 | −0.477056 | ||||||||
\(210\) | 3.33015 | − | 3.65582i | 0.229802 | − | 0.252276i | ||||
\(211\) | − | 20.6790i | − | 1.42360i | −0.702382 | − | 0.711800i | \(-0.747880\pi\) | ||
0.702382 | − | 0.711800i | \(-0.252120\pi\) | |||||||
\(212\) | −21.8387 | + | 2.04060i | −1.49989 | + | 0.140149i | ||||
\(213\) | −15.7028 | −1.07594 | ||||||||
\(214\) | 14.6887 | − | 16.1252i | 1.00410 | − | 1.10229i | ||||
\(215\) | 8.91103i | 0.607727i | ||||||||
\(216\) | 1.70190 | − | 2.25910i | 0.115800 | − | 0.153712i | ||||
\(217\) | − | 28.2254i | − | 1.91607i | ||||||
\(218\) | −2.26003 | − | 2.05870i | −0.153069 | − | 0.139433i | ||||
\(219\) | 5.24792i | 0.354621i | ||||||||
\(220\) | 2.72065 | − | 0.254216i | 0.183426 | − | 0.0171393i | ||||
\(221\) | − | 0.241201i | − | 0.0162250i | ||||||
\(222\) | −3.16775 | + | 3.47754i | −0.212605 | + | 0.233397i | ||||
\(223\) | − | 10.0263i | − | 0.671409i | −0.941967 | − | 0.335704i | \(-0.891026\pi\) | ||
0.941967 | − | 0.335704i | \(-0.108974\pi\) | |||||||
\(224\) | 10.3809 | − | 16.8379i | 0.693601 | − | 1.12503i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 9.38588 | + | 8.54976i | 0.624340 | + | 0.568721i | ||||
\(227\) | −5.76617 | −0.382714 | −0.191357 | − | 0.981520i | \(-0.561289\pi\) | ||||
−0.191357 | + | 0.981520i | \(0.561289\pi\) | |||||||
\(228\) | −10.0520 | + | 0.939258i | −0.665712 | + | 0.0622039i | ||||
\(229\) | 2.46613i | 0.162966i | 0.996675 | + | 0.0814831i | \(0.0259657\pi\) | ||||
−0.996675 | + | 0.0814831i | \(0.974034\pi\) | |||||||
\(230\) | −4.43705 | − | 5.12958i | −0.292570 | − | 0.338235i | ||||
\(231\) | 4.77748i | 0.314335i | ||||||||
\(232\) | 22.1486 | + | 16.6857i | 1.45413 | + | 1.09547i | ||||
\(233\) | 17.1486 | 1.12344 | 0.561722 | − | 0.827326i | \(-0.310139\pi\) | ||||
0.561722 | + | 0.827326i | \(0.310139\pi\) | |||||||
\(234\) | 3.19327 | − | 3.50556i | 0.208751 | − | 0.229166i | ||||
\(235\) | −12.6923 | −0.827957 | ||||||||
\(236\) | 9.39331 | − | 0.877706i | 0.611452 | − | 0.0571338i | ||||
\(237\) | 4.20591i | 0.273203i | ||||||||
\(238\) | 0.262981 | + | 0.239554i | 0.0170465 | + | 0.0155279i | ||||
\(239\) | 7.88125i | 0.509796i | 0.966968 | + | 0.254898i | \(0.0820419\pi\) | ||||
−0.966968 | + | 0.254898i | \(0.917958\pi\) | |||||||
\(240\) | 3.93076 | − | 0.741046i | 0.253729 | − | 0.0478343i | ||||
\(241\) | 13.3123i | 0.857523i | 0.903418 | + | 0.428762i | \(0.141050\pi\) | ||||
−0.903418 | + | 0.428762i | \(0.858950\pi\) | |||||||
\(242\) | 8.69813 | − | 9.54877i | 0.559137 | − | 0.613818i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −12.7138 | + | 1.18797i | −0.813920 | + | 0.0760523i | ||||
\(245\) | 5.22746i | 0.333970i | ||||||||
\(246\) | −1.44178 | − | 1.31334i | −0.0919246 | − | 0.0837356i | ||||
\(247\) | −16.9259 | −1.07697 | ||||||||
\(248\) | 13.7375 | − | 18.2351i | 0.872330 | − | 1.15793i | ||||
\(249\) | − | 13.4916i | − | 0.854994i | ||||||
\(250\) | 1.04548 | + | 0.952347i | 0.0661221 | + | 0.0602317i | ||||
\(251\) | −16.9160 | −1.06773 | −0.533865 | − | 0.845570i | \(-0.679261\pi\) | ||||
−0.533865 | + | 0.845570i | \(0.679261\pi\) | |||||||
\(252\) | 0.650640 | + | 6.96322i | 0.0409865 | + | 0.438642i | ||||
\(253\) | 6.50609 | + | 0.776905i | 0.409034 | + | 0.0488436i | ||||
\(254\) | −13.2955 | − | 12.1111i | −0.834234 | − | 0.759918i | ||||
\(255\) | 0.0719348i | 0.00450473i | ||||||||
\(256\) | 14.9017 | − | 5.82575i | 0.931356 | − | 0.364109i | ||||
\(257\) | 19.6697 | 1.22696 | 0.613482 | − | 0.789709i | \(-0.289768\pi\) | ||||
0.613482 | + | 0.789709i | \(0.289768\pi\) | |||||||
\(258\) | −9.31632 | − | 8.48639i | −0.580009 | − | 0.528340i | ||||
\(259\) | − | 11.6312i | − | 0.722726i | ||||||
\(260\) | 6.67703 | − | 0.623898i | 0.414092 | − | 0.0386925i | ||||
\(261\) | −9.80417 | −0.606863 | ||||||||
\(262\) | −22.4592 | − | 20.4584i | −1.38753 | − | 1.26392i | ||||
\(263\) | 3.46611 | 0.213730 | 0.106865 | − | 0.994274i | \(-0.465919\pi\) | ||||
0.106865 | + | 0.994274i | \(0.465919\pi\) | |||||||
\(264\) | −2.32523 | + | 3.08650i | −0.143108 | + | 0.189961i | ||||
\(265\) | 10.9669 | 0.673692 | ||||||||
\(266\) | 16.8103 | − | 18.4543i | 1.03071 | − | 1.13150i | ||||
\(267\) | −11.5228 | −0.705183 | ||||||||
\(268\) | 2.84008 | + | 30.3948i | 0.173485 | + | 1.85666i | ||||
\(269\) | −0.230066 | −0.0140274 | −0.00701369 | − | 0.999975i | \(-0.502233\pi\) | ||||
−0.00701369 | + | 0.999975i | \(0.502233\pi\) | |||||||
\(270\) | −0.952347 | + | 1.04548i | −0.0579580 | + | 0.0636261i | ||||
\(271\) | − | 6.04603i | − | 0.367270i | −0.982994 | − | 0.183635i | \(-0.941214\pi\) | ||
0.982994 | − | 0.183635i | \(-0.0587865\pi\) | |||||||
\(272\) | 0.0533070 | + | 0.282758i | 0.00323221 | + | 0.0171447i | ||||
\(273\) | 11.7249i | 0.709623i | ||||||||
\(274\) | −9.23363 | − | 8.41106i | −0.557824 | − | 0.508131i | ||||
\(275\) | −1.36625 | −0.0823881 | ||||||||
\(276\) | 9.58850 | + | 0.246289i | 0.577160 | + | 0.0148248i | ||||
\(277\) | 14.3524 | 0.862355 | 0.431177 | − | 0.902267i | \(-0.358098\pi\) | ||||
0.431177 | + | 0.902267i | \(0.358098\pi\) | |||||||
\(278\) | 1.54642 | + | 1.40866i | 0.0927479 | + | 0.0844855i | ||||
\(279\) | 8.07183i | 0.483248i | ||||||||
\(280\) | −5.95118 | + | 7.89957i | −0.355651 | + | 0.472089i | ||||
\(281\) | − | 9.58403i | − | 0.571735i | −0.958269 | − | 0.285868i | \(-0.907718\pi\) | ||
0.958269 | − | 0.285868i | \(-0.0922818\pi\) | |||||||
\(282\) | 12.0875 | − | 13.2696i | 0.719802 | − | 0.790195i | ||||
\(283\) | 29.7360 | 1.76762 | 0.883812 | − | 0.467842i | \(-0.154969\pi\) | ||||
0.883812 | + | 0.467842i | \(0.154969\pi\) | |||||||
\(284\) | 31.2694 | − | 2.92180i | 1.85550 | − | 0.173377i | ||||
\(285\) | 5.04791 | 0.299012 | ||||||||
\(286\) | −4.36282 | + | 4.78948i | −0.257979 | + | 0.283208i | ||||
\(287\) | 4.82226 | 0.284649 | ||||||||
\(288\) | −2.96870 | + | 4.81527i | −0.174932 | + | 0.283743i | ||||
\(289\) | 16.9948 | 0.999696 | ||||||||
\(290\) | −10.2501 | − | 9.33697i | −0.601906 | − | 0.548286i | ||||
\(291\) | 4.72490 | 0.276979 | ||||||||
\(292\) | −0.976473 | − | 10.4503i | −0.0571437 | − | 0.611558i | ||||
\(293\) | − | 19.4305i | − | 1.13514i | −0.823324 | − | 0.567572i | \(-0.807883\pi\) | ||
0.823324 | − | 0.567572i | \(-0.192117\pi\) | |||||||
\(294\) | −5.46522 | − | 4.97835i | −0.318738 | − | 0.290344i | ||||
\(295\) | −4.71711 | −0.274641 | ||||||||
\(296\) | 5.66096 | − | 7.51434i | 0.329037 | − | 0.436762i | ||||
\(297\) | − | 1.36625i | − | 0.0792779i | ||||||
\(298\) | 13.5028 | + | 12.2999i | 0.782196 | + | 0.712516i | ||||
\(299\) | 15.9673 | + | 1.90668i | 0.923410 | + | 0.110266i | ||||
\(300\) | −1.99133 | + | 0.186069i | −0.114969 | + | 0.0107427i | ||||
\(301\) | 31.1599 | 1.79603 | ||||||||
\(302\) | 1.55590 | + | 1.41730i | 0.0895321 | + | 0.0815562i | ||||
\(303\) | 10.7894i | 0.619833i | ||||||||
\(304\) | 19.8421 | − | 3.74074i | 1.13802 | − | 0.214546i | ||||
\(305\) | 6.38461 | 0.365581 | ||||||||
\(306\) | −0.0752066 | − | 0.0685069i | −0.00429928 | − | 0.00391628i | ||||
\(307\) | − | 24.3915i | − | 1.39209i | −0.717996 | − | 0.696047i | \(-0.754941\pi\) | ||
0.717996 | − | 0.696047i | \(-0.245059\pi\) | |||||||
\(308\) | −0.888938 | − | 9.51351i | −0.0506520 | − | 0.542083i | ||||
\(309\) | 8.71856i | 0.495981i | ||||||||
\(310\) | −7.68719 | + | 8.43896i | −0.436603 | + | 0.479301i | ||||
\(311\) | − | 3.30836i | − | 0.187600i | −0.995591 | − | 0.0937999i | \(-0.970099\pi\) | ||
0.995591 | − | 0.0937999i | \(-0.0299014\pi\) | |||||||
\(312\) | −5.70657 | + | 7.57488i | −0.323071 | + | 0.428843i | ||||
\(313\) | 16.4380i | 0.929130i | 0.885539 | + | 0.464565i | \(0.153789\pi\) | ||||
−0.885539 | + | 0.464565i | \(0.846211\pi\) | |||||||
\(314\) | −0.824909 | − | 0.751424i | −0.0465523 | − | 0.0424053i | ||||
\(315\) | − | 3.49678i | − | 0.197021i | ||||||
\(316\) | −0.782588 | − | 8.37534i | −0.0440240 | − | 0.471149i | ||||
\(317\) | −21.1799 | −1.18958 | −0.594791 | − | 0.803880i | \(-0.702765\pi\) | ||||
−0.594791 | + | 0.803880i | \(0.702765\pi\) | |||||||
\(318\) | −10.4443 | + | 11.4657i | −0.585688 | + | 0.642965i | ||||
\(319\) | 13.3950 | 0.749974 | ||||||||
\(320\) | −7.68953 | + | 2.20705i | −0.429858 | + | 0.123378i | ||||
\(321\) | − | 15.4237i | − | 0.860864i | ||||||
\(322\) | −17.9370 | + | 15.5154i | −0.999591 | + | 0.864638i | ||||
\(323\) | 0.363121i | 0.0202046i | ||||||||
\(324\) | −0.186069 | − | 1.99133i | −0.0103371 | − | 0.110629i | ||||
\(325\) | −3.35306 | −0.185994 | ||||||||
\(326\) | −10.5258 | − | 9.58810i | −0.582969 | − | 0.531036i | ||||
\(327\) | −2.16171 | −0.119543 | ||||||||
\(328\) | 3.11543 | + | 2.34702i | 0.172021 | + | 0.129593i | ||||
\(329\) | 44.3823i | 2.44688i | ||||||||
\(330\) | 1.30115 | − | 1.42839i | 0.0716257 | − | 0.0786304i | ||||
\(331\) | 7.56275i | 0.415687i | 0.978162 | + | 0.207843i | \(0.0666444\pi\) | ||||
−0.978162 | + | 0.207843i | \(0.933356\pi\) | |||||||
\(332\) | 2.51036 | + | 26.8661i | 0.137774 | + | 1.47447i | ||||
\(333\) | 3.32625i | 0.182278i | ||||||||
\(334\) | 12.8725 | + | 11.7258i | 0.704351 | + | 0.641605i | ||||
\(335\) | − | 15.2636i | − | 0.833940i | ||||||
\(336\) | −2.59127 | − | 13.7450i | −0.141366 | − | 0.749850i | ||||
\(337\) | − | 16.3852i | − | 0.892556i | −0.894894 | − | 0.446278i | \(-0.852749\pi\) | ||
0.894894 | − | 0.446278i | \(-0.147251\pi\) | |||||||
\(338\) | 1.67329 | − | 1.83693i | 0.0910150 | − | 0.0999159i | ||||
\(339\) | 8.97756 | 0.487594 | ||||||||
\(340\) | −0.0133848 | − | 0.143246i | −0.000725893 | − | 0.00776859i | ||||
\(341\) | − | 11.0282i | − | 0.597208i | ||||||
\(342\) | −4.80737 | + | 5.27750i | −0.259953 | + | 0.285375i | ||||
\(343\) | −6.19819 | −0.334671 | ||||||||
\(344\) | 20.1309 | + | 15.1657i | 1.08538 | + | 0.817680i | ||||
\(345\) | −4.76200 | − | 0.568640i | −0.256377 | − | 0.0306145i | ||||
\(346\) | −2.89589 | + | 3.17909i | −0.155684 | + | 0.170909i | ||||
\(347\) | − | 10.3602i | − | 0.556166i | −0.960557 | − | 0.278083i | \(-0.910301\pi\) | ||
0.960557 | − | 0.278083i | \(-0.0896991\pi\) | |||||||
\(348\) | 19.5233 | − | 1.82425i | 1.04656 | − | 0.0977899i | ||||
\(349\) | 0.414108 | 0.0221667 | 0.0110833 | − | 0.999939i | \(-0.496472\pi\) | ||||
0.0110833 | + | 0.999939i | \(0.496472\pi\) | |||||||
\(350\) | 3.33015 | − | 3.65582i | 0.178004 | − | 0.195412i | ||||
\(351\) | − | 3.35306i | − | 0.178973i | ||||||
\(352\) | 4.05598 | − | 6.57887i | 0.216185 | − | 0.350655i | ||||
\(353\) | −33.5214 | −1.78416 | −0.892082 | − | 0.451874i | \(-0.850756\pi\) | ||||
−0.892082 | + | 0.451874i | \(0.850756\pi\) | |||||||
\(354\) | 4.49233 | − | 4.93166i | 0.238765 | − | 0.262115i | ||||
\(355\) | −15.7028 | −0.833419 | ||||||||
\(356\) | 22.9456 | − | 2.14403i | 1.21611 | − | 0.113633i | ||||
\(357\) | 0.251540 | 0.0133129 | ||||||||
\(358\) | 10.1058 | + | 9.20555i | 0.534109 | + | 0.486528i | ||||
\(359\) | −15.7877 | −0.833240 | −0.416620 | − | 0.909081i | \(-0.636786\pi\) | ||||
−0.416620 | + | 0.909081i | \(0.636786\pi\) | |||||||
\(360\) | 1.70190 | − | 2.25910i | 0.0896981 | − | 0.119065i | ||||
\(361\) | 6.48141 | 0.341127 | ||||||||
\(362\) | −27.1875 | − | 24.7655i | −1.42894 | − | 1.30165i | ||||
\(363\) | − | 9.13336i | − | 0.479377i | ||||||
\(364\) | −2.18163 | − | 23.3481i | −0.114349 | − | 1.22377i | ||||
\(365\) | 5.24792i | 0.274689i | ||||||||
\(366\) | −6.08036 | + | 6.67500i | −0.317826 | + | 0.348908i | ||||
\(367\) | −10.8732 | −0.567578 | −0.283789 | − | 0.958887i | \(-0.591592\pi\) | ||||
−0.283789 | + | 0.958887i | \(0.591592\pi\) | |||||||
\(368\) | −19.1397 | + | 1.29368i | −0.997723 | + | 0.0674376i | ||||
\(369\) | −1.37906 | −0.0717909 | ||||||||
\(370\) | −3.16775 | + | 3.47754i | −0.164683 | + | 0.180789i | ||||
\(371\) | − | 38.3488i | − | 1.99097i | ||||||
\(372\) | −1.50191 | − | 16.0737i | −0.0778706 | − | 0.833380i | ||||
\(373\) | − | 11.5032i | − | 0.595614i | −0.954626 | − | 0.297807i | \(-0.903745\pi\) | ||
0.954626 | − | 0.297807i | \(-0.0962551\pi\) | |||||||
\(374\) | 0.102751 | + | 0.0935977i | 0.00531313 | + | 0.00483982i | ||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | −21.6011 | + | 28.6733i | −1.11399 | + | 1.47871i | ||||
\(377\) | 32.8739 | 1.69309 | ||||||||
\(378\) | 3.65582 | + | 3.33015i | 0.188035 | + | 0.171284i | ||||
\(379\) | −22.3509 | −1.14809 | −0.574044 | − | 0.818825i | \(-0.694626\pi\) | ||||
−0.574044 | + | 0.818825i | \(0.694626\pi\) | |||||||
\(380\) | −10.0520 | + | 0.939258i | −0.515659 | + | 0.0481829i | ||||
\(381\) | −12.7171 | −0.651517 | ||||||||
\(382\) | −1.38321 | + | 1.51849i | −0.0707714 | + | 0.0776925i | ||||
\(383\) | 11.2864 | 0.576709 | 0.288354 | − | 0.957524i | \(-0.406892\pi\) | ||||
0.288354 | + | 0.957524i | \(0.406892\pi\) | |||||||
\(384\) | 5.01567 | − | 10.1412i | 0.255955 | − | 0.517514i | ||||
\(385\) | 4.77748i | 0.243483i | ||||||||
\(386\) | −12.0246 | + | 13.2006i | −0.612038 | + | 0.671892i | ||||
\(387\) | −8.91103 | −0.452973 | ||||||||
\(388\) | −9.40882 | + | 0.879156i | −0.477661 | + | 0.0446324i | ||||
\(389\) | − | 19.9787i | − | 1.01296i | −0.862252 | − | 0.506480i | \(-0.830946\pi\) | ||
0.862252 | − | 0.506480i | \(-0.169054\pi\) | |||||||
\(390\) | 3.19327 | − | 3.50556i | 0.161698 | − | 0.177511i | ||||
\(391\) | 0.0409050 | − | 0.342554i | 0.00206866 | − | 0.0173237i | ||||
\(392\) | 11.8093 | + | 8.89662i | 0.596462 | + | 0.449347i | ||||
\(393\) | −21.4821 | −1.08363 | ||||||||
\(394\) | 22.8447 | − | 25.0788i | 1.15090 | − | 1.26345i | ||||
\(395\) | 4.20591i | 0.211622i | ||||||||
\(396\) | 0.254216 | + | 2.72065i | 0.0127749 | + | 0.136718i | ||||
\(397\) | 17.1842 | 0.862452 | 0.431226 | − | 0.902244i | \(-0.358081\pi\) | ||||
0.431226 | + | 0.902244i | \(0.358081\pi\) | |||||||
\(398\) | 16.0277 | − | 17.5952i | 0.803397 | − | 0.881966i | ||||
\(399\) | − | 17.6514i | − | 0.883677i | ||||||
\(400\) | 3.93076 | − | 0.741046i | 0.196538 | − | 0.0370523i | ||||
\(401\) | − | 21.5671i | − | 1.07701i | −0.842622 | − | 0.538505i | \(-0.818989\pi\) | ||
0.842622 | − | 0.538505i | \(-0.181011\pi\) | |||||||
\(402\) | 15.9578 | + | 14.5363i | 0.795905 | + | 0.725003i | ||||
\(403\) | − | 27.0653i | − | 1.34822i | ||||||
\(404\) | −2.00756 | − | 21.4851i | −0.0998799 | − | 1.06893i | ||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | −32.6493 | + | 35.8423i | −1.62036 | + | 1.77882i | ||||
\(407\) | − | 4.54450i | − | 0.225262i | ||||||
\(408\) | 0.162508 | + | 0.122426i | 0.00804534 | + | 0.00606099i | ||||
\(409\) | 20.5077 | 1.01404 | 0.507021 | − | 0.861934i | \(-0.330747\pi\) | ||||
0.507021 | + | 0.861934i | \(0.330747\pi\) | |||||||
\(410\) | −1.44178 | − | 1.31334i | −0.0712045 | − | 0.0648613i | ||||
\(411\) | −8.83193 | −0.435647 | ||||||||
\(412\) | −1.62225 | − | 17.3615i | −0.0799225 | − | 0.855339i | ||||
\(413\) | 16.4947i | 0.811651i | ||||||||
\(414\) | 5.12958 | − | 4.43705i | 0.252105 | − | 0.218069i | ||||
\(415\) | − | 13.4916i | − | 0.662276i | ||||||
\(416\) | 9.95420 | − | 16.1459i | 0.488045 | − | 0.791617i | ||||
\(417\) | 1.47914 | 0.0724338 | ||||||||
\(418\) | 6.56807 | − | 7.21040i | 0.321255 | − | 0.352672i | ||||
\(419\) | −6.48385 | −0.316757 | −0.158378 | − | 0.987378i | \(-0.550627\pi\) | ||||
−0.158378 | + | 0.987378i | \(0.550627\pi\) | |||||||
\(420\) | 0.650640 | + | 6.96322i | 0.0317480 | + | 0.339771i | ||||
\(421\) | − | 16.5039i | − | 0.804351i | −0.915563 | − | 0.402175i | \(-0.868254\pi\) | ||
0.915563 | − | 0.402175i | \(-0.131746\pi\) | |||||||
\(422\) | 21.6195 | + | 19.6936i | 1.05242 | + | 0.958668i | ||||
\(423\) | − | 12.6923i | − | 0.617123i | ||||||
\(424\) | 18.6646 | − | 24.7753i | 0.906434 | − | 1.20320i | ||||
\(425\) | 0.0719348i | 0.00348935i | ||||||||
\(426\) | 14.9545 | − | 16.4170i | 0.724550 | − | 0.795408i | ||||
\(427\) | − | 22.3256i | − | 1.08041i | ||||||
\(428\) | 2.86986 | + | 30.7135i | 0.138720 | + | 1.48459i | ||||
\(429\) | 4.58112i | 0.221178i | ||||||||
\(430\) | −9.31632 | − | 8.48639i | −0.449273 | − | 0.409250i | ||||
\(431\) | 31.4733 | 1.51602 | 0.758009 | − | 0.652244i | \(-0.226172\pi\) | ||||
0.758009 | + | 0.652244i | \(0.226172\pi\) | |||||||
\(432\) | 0.741046 | + | 3.93076i | 0.0356536 | + | 0.189119i | ||||
\(433\) | − | 18.7432i | − | 0.900741i | −0.892842 | − | 0.450370i | \(-0.851292\pi\) | ||
0.892842 | − | 0.450370i | \(-0.148708\pi\) | |||||||
\(434\) | 29.5092 | + | 26.8804i | 1.41649 | + | 1.29030i | ||||
\(435\) | −9.80417 | −0.470074 | ||||||||
\(436\) | 4.30467 | − | 0.402227i | 0.206156 | − | 0.0192632i | ||||
\(437\) | −24.0382 | − | 2.87044i | −1.14990 | − | 0.137312i | ||||
\(438\) | −5.48661 | − | 4.99784i | −0.262160 | − | 0.238806i | ||||
\(439\) | − | 9.37553i | − | 0.447470i | −0.974650 | − | 0.223735i | \(-0.928175\pi\) | ||
0.974650 | − | 0.223735i | \(-0.0718250\pi\) | |||||||
\(440\) | −2.32523 | + | 3.08650i | −0.110851 | + | 0.147143i | ||||
\(441\) | −5.22746 | −0.248926 | ||||||||
\(442\) | 0.252172 | + | 0.229708i | 0.0119946 | + | 0.0109261i | ||||
\(443\) | − | 21.6166i | − | 1.02704i | −0.858079 | − | 0.513518i | \(-0.828342\pi\) | ||
0.858079 | − | 0.513518i | \(-0.171658\pi\) | |||||||
\(444\) | −0.618911 | − | 6.62366i | −0.0293722 | − | 0.314345i | ||||
\(445\) | −11.5228 | −0.546232 | ||||||||
\(446\) | 10.4823 | + | 9.54849i | 0.496351 | + | 0.452134i | ||||
\(447\) | 12.9154 | 0.610876 | ||||||||
\(448\) | 7.71758 | + | 26.8886i | 0.364621 | + | 1.27037i | ||||
\(449\) | −11.7632 | −0.555141 | −0.277571 | − | 0.960705i | \(-0.589529\pi\) | ||||
−0.277571 | + | 0.960705i | \(0.589529\pi\) | |||||||
\(450\) | −0.952347 | + | 1.04548i | −0.0448941 | + | 0.0492845i | ||||
\(451\) | 1.88414 | 0.0887207 | ||||||||
\(452\) | −17.8772 | + | 1.67044i | −0.840875 | + | 0.0785710i | ||||
\(453\) | 1.48821 | 0.0699224 | ||||||||
\(454\) | 5.49140 | − | 6.02843i | 0.257724 | − | 0.282928i | ||||
\(455\) | 11.7249i | 0.549671i | ||||||||
\(456\) | 8.59105 | − | 11.4037i | 0.402313 | − | 0.534029i | ||||
\(457\) | − | 35.4431i | − | 1.65796i | −0.559279 | − | 0.828980i | \(-0.688922\pi\) | ||
0.559279 | − | 0.828980i | \(-0.311078\pi\) | |||||||
\(458\) | −2.57829 | − | 2.34861i | −0.120476 | − | 0.109743i | ||||
\(459\) | −0.0719348 | −0.00335763 | ||||||||
\(460\) | 9.58850 | + | 0.246289i | 0.447066 | + | 0.0114833i | ||||
\(461\) | −14.2189 | −0.662240 | −0.331120 | − | 0.943589i | \(-0.607427\pi\) | ||||
−0.331120 | + | 0.943589i | \(0.607427\pi\) | |||||||
\(462\) | −4.99477 | − | 4.54982i | −0.232378 | − | 0.211677i | ||||
\(463\) | 1.35225i | 0.0628444i | 0.999506 | + | 0.0314222i | \(0.0100036\pi\) | ||||
−0.999506 | + | 0.0314222i | \(0.989996\pi\) | |||||||
\(464\) | −38.5378 | + | 7.26534i | −1.78907 | + | 0.337285i | ||||
\(465\) | 8.07183i | 0.374322i | ||||||||
\(466\) | −16.3314 | + | 17.9286i | −0.756539 | + | 0.830525i | ||||
\(467\) | −19.9740 | −0.924289 | −0.462144 | − | 0.886805i | \(-0.652920\pi\) | ||||
−0.462144 | + | 0.886805i | \(0.652920\pi\) | |||||||
\(468\) | 0.623898 | + | 6.67703i | 0.0288397 | + | 0.308646i | ||||
\(469\) | −53.3735 | −2.46456 | ||||||||
\(470\) | 12.0875 | − | 13.2696i | 0.557556 | − | 0.612082i | ||||
\(471\) | −0.789022 | −0.0363562 | ||||||||
\(472\) | −8.02807 | + | 10.6564i | −0.369522 | + | 0.490502i | ||||
\(473\) | 12.1747 | 0.559793 | ||||||||
\(474\) | −4.39721 | − | 4.00549i | −0.201970 | − | 0.183978i | ||||
\(475\) | 5.04791 | 0.231614 | ||||||||
\(476\) | −0.500898 | + | 0.0468037i | −0.0229586 | + | 0.00214524i | ||||
\(477\) | 10.9669i | 0.502140i | ||||||||
\(478\) | −8.23971 | − | 7.50569i | −0.376876 | − | 0.343302i | ||||
\(479\) | −27.9827 | −1.27856 | −0.639282 | − | 0.768972i | \(-0.720768\pi\) | ||||
−0.639282 | + | 0.768972i | \(0.720768\pi\) | |||||||
\(480\) | −2.96870 | + | 4.81527i | −0.135502 | + | 0.219786i | ||||
\(481\) | − | 11.1531i | − | 0.508538i | ||||||
\(482\) | −13.9178 | − | 12.6780i | −0.633939 | − | 0.577466i | ||||
\(483\) | −1.98841 | + | 16.6517i | −0.0904757 | + | 0.757677i | ||||
\(484\) | 1.69943 | + | 18.1875i | 0.0772468 | + | 0.826704i | ||||
\(485\) | 4.72490 | 0.214547 | ||||||||
\(486\) | −1.04548 | − | 0.952347i | −0.0474241 | − | 0.0431994i | ||||
\(487\) | 30.1729i | 1.36727i | 0.729826 | + | 0.683633i | \(0.239601\pi\) | ||||
−0.729826 | + | 0.683633i | \(0.760399\pi\) | |||||||
\(488\) | 10.8660 | − | 14.4235i | 0.491880 | − | 0.652919i | ||||
\(489\) | −10.0679 | −0.455284 | ||||||||
\(490\) | −5.46522 | − | 4.97835i | −0.246893 | − | 0.224899i | ||||
\(491\) | 7.08265i | 0.319635i | 0.987147 | + | 0.159818i | \(0.0510906\pi\) | ||||
−0.987147 | + | 0.159818i | \(0.948909\pi\) | |||||||
\(492\) | 2.74615 | − | 0.256599i | 0.123806 | − | 0.0115684i | ||||
\(493\) | − | 0.705261i | − | 0.0317633i | ||||||
\(494\) | 16.1194 | − | 17.6958i | 0.725245 | − | 0.796170i | ||||
\(495\) | − | 1.36625i | − | 0.0614084i | ||||||
\(496\) | 5.98160 | + | 31.7284i | 0.268582 | + | 1.42465i | ||||
\(497\) | 54.9093i | 2.46302i | ||||||||
\(498\) | 14.1052 | + | 12.8487i | 0.632070 | + | 0.575763i | ||||
\(499\) | 17.2498i | 0.772207i | 0.922455 | + | 0.386104i | \(0.126179\pi\) | ||||
−0.922455 | + | 0.386104i | \(0.873821\pi\) | |||||||
\(500\) | −1.99133 | + | 0.186069i | −0.0890548 | + | 0.00832124i | ||||
\(501\) | 12.3125 | 0.550081 | ||||||||
\(502\) | 16.1099 | − | 17.6854i | 0.719022 | − | 0.789339i | ||||
\(503\) | 34.6103 | 1.54320 | 0.771598 | − | 0.636111i | \(-0.219458\pi\) | ||||
0.771598 | + | 0.636111i | \(0.219458\pi\) | |||||||
\(504\) | −7.89957 | − | 5.95118i | −0.351875 | − | 0.265086i | ||||
\(505\) | 10.7894i | 0.480120i | ||||||||
\(506\) | −7.00830 | + | 6.06212i | −0.311557 | + | 0.269494i | ||||
\(507\) | − | 1.75702i | − | 0.0780318i | ||||||
\(508\) | 25.3239 | − | 2.36625i | 1.12357 | − | 0.104985i | ||||
\(509\) | −15.0316 | −0.666266 | −0.333133 | − | 0.942880i | \(-0.608106\pi\) | ||||
−0.333133 | + | 0.942880i | \(0.608106\pi\) | |||||||
\(510\) | −0.0752066 | − | 0.0685069i | −0.00333020 | − | 0.00303354i | ||||
\(511\) | 18.3508 | 0.811792 | ||||||||
\(512\) | −8.10088 | + | 21.1276i | −0.358012 | + | 0.933717i | ||||
\(513\) | 5.04791i | 0.222871i | ||||||||
\(514\) | −18.7324 | + | 20.5644i | −0.826251 | + | 0.907055i | ||||
\(515\) | 8.71856i | 0.384186i | ||||||||
\(516\) | 17.7448 | − | 1.65806i | 0.781169 | − | 0.0729921i | ||||
\(517\) | 17.3409i | 0.762653i | ||||||||
\(518\) | 12.1602 | + | 11.0769i | 0.534288 | + | 0.486692i | ||||
\(519\) | 3.04079i | 0.133476i | ||||||||
\(520\) | −5.70657 | + | 7.57488i | −0.250250 | + | 0.332181i | ||||
\(521\) | − | 2.09374i | − | 0.0917284i | −0.998948 | − | 0.0458642i | \(-0.985396\pi\) | ||
0.998948 | − | 0.0458642i | \(-0.0146041\pi\) | |||||||
\(522\) | 9.33697 | − | 10.2501i | 0.408668 | − | 0.448634i | ||||
\(523\) | −4.78053 | −0.209038 | −0.104519 | − | 0.994523i | \(-0.533330\pi\) | ||||
−0.104519 | + | 0.994523i | \(0.533330\pi\) | |||||||
\(524\) | 42.7778 | − | 3.99714i | 1.86876 | − | 0.174616i | ||||
\(525\) | − | 3.49678i | − | 0.152612i | ||||||
\(526\) | −3.30094 | + | 3.62376i | −0.143928 | + | 0.158003i | ||||
\(527\) | −0.580646 | −0.0252933 | ||||||||
\(528\) | −1.01246 | − | 5.37040i | −0.0440615 | − | 0.233717i | ||||
\(529\) | 22.3533 | + | 5.41573i | 0.971882 | + | 0.235466i | ||||
\(530\) | −10.4443 | + | 11.4657i | −0.453672 | + | 0.498039i | ||||
\(531\) | − | 4.71711i | − | 0.204705i | ||||||
\(532\) | 3.28438 | + | 35.1497i | 0.142396 | + | 1.52393i | ||||
\(533\) | 4.62406 | 0.200290 | ||||||||
\(534\) | 10.9737 | − | 12.0469i | 0.474878 | − | 0.521319i | ||||
\(535\) | − | 15.4237i | − | 0.666823i | ||||||
\(536\) | −34.4820 | − | 25.9772i | −1.48940 | − | 1.12204i | ||||
\(537\) | 9.66616 | 0.417126 | ||||||||
\(538\) | 0.219103 | − | 0.240530i | 0.00944620 | − | 0.0103700i | ||||
\(539\) | 7.14202 | 0.307629 | ||||||||
\(540\) | −0.186069 | − | 1.99133i | −0.00800712 | − | 0.0856930i | ||||
\(541\) | −32.7776 | −1.40922 | −0.704610 | − | 0.709594i | \(-0.748878\pi\) | ||||
−0.704610 | + | 0.709594i | \(0.748878\pi\) | |||||||
\(542\) | 6.32102 | + | 5.75792i | 0.271511 | + | 0.247324i | ||||
\(543\) | −26.0047 | −1.11597 | ||||||||
\(544\) | −0.346386 | − | 0.213553i | −0.0148512 | − | 0.00915599i | ||||
\(545\) | −2.16171 | −0.0925976 | ||||||||
\(546\) | −12.2582 | − | 11.1662i | −0.524601 | − | 0.477868i | ||||
\(547\) | − | 15.0838i | − | 0.644936i | −0.946580 | − | 0.322468i | \(-0.895487\pi\) | ||
0.946580 | − | 0.322468i | \(-0.104513\pi\) | |||||||
\(548\) | 17.5872 | − | 1.64334i | 0.751290 | − | 0.0702002i | ||||
\(549\) | 6.38461i | 0.272488i | ||||||||
\(550\) | 1.30115 | − | 1.42839i | 0.0554811 | − | 0.0609069i | ||||
\(551\) | −49.4906 | −2.10837 | ||||||||
\(552\) | −9.38907 | + | 9.79006i | −0.399626 | + | 0.416693i | ||||
\(553\) | 14.7071 | 0.625411 | ||||||||
\(554\) | −13.6685 | + | 15.0052i | −0.580720 | + | 0.637511i | ||||
\(555\) | 3.32625i | 0.141192i | ||||||||
\(556\) | −2.94545 | + | 0.275222i | −0.124915 | + | 0.0116720i | ||||
\(557\) | − | 18.7166i | − | 0.793048i | −0.918024 | − | 0.396524i | \(-0.870216\pi\) | ||
0.918024 | − | 0.396524i | \(-0.129784\pi\) | |||||||
\(558\) | −8.43896 | − | 7.68719i | −0.357250 | − | 0.325425i | ||||
\(559\) | 29.8792 | 1.26375 | ||||||||
\(560\) | −2.59127 | − | 13.7450i | −0.109501 | − | 0.580832i | ||||
\(561\) | 0.0982810 | 0.00414943 | ||||||||
\(562\) | 10.0199 | + | 9.12733i | 0.422666 | + | 0.385013i | ||||
\(563\) | −1.60093 | −0.0674712 | −0.0337356 | − | 0.999431i | \(-0.510740\pi\) | ||||
−0.0337356 | + | 0.999431i | \(0.510740\pi\) | |||||||
\(564\) | 2.36165 | + | 25.2746i | 0.0994433 | + | 1.06425i | ||||
\(565\) | 8.97756 | 0.377689 | ||||||||
\(566\) | −28.3190 | + | 31.0885i | −1.19034 | + | 1.30675i | ||||
\(567\) | 3.49678 | 0.146851 | ||||||||
\(568\) | −26.7247 | + | 35.4742i | −1.12134 | + | 1.48847i | ||||
\(569\) | 25.5371i | 1.07057i | 0.844672 | + | 0.535285i | \(0.179796\pi\) | ||||
−0.844672 | + | 0.535285i | \(0.820204\pi\) | |||||||
\(570\) | −4.80737 | + | 5.27750i | −0.201358 | + | 0.221050i | ||||
\(571\) | 14.4267 | 0.603738 | 0.301869 | − | 0.953349i | \(-0.402390\pi\) | ||||
0.301869 | + | 0.953349i | \(0.402390\pi\) | |||||||
\(572\) | −0.852402 | − | 9.12250i | −0.0356407 | − | 0.381431i | ||||
\(573\) | 1.45243i | 0.0606759i | ||||||||
\(574\) | −4.59247 | + | 5.04159i | −0.191686 | + | 0.210432i | ||||
\(575\) | −4.76200 | − | 0.568640i | −0.198589 | − | 0.0237139i | ||||
\(576\) | −2.20705 | − | 7.68953i | −0.0919606 | − | 0.320397i | ||||
\(577\) | 2.17614 | 0.0905938 | 0.0452969 | − | 0.998974i | \(-0.485577\pi\) | ||||
0.0452969 | + | 0.998974i | \(0.485577\pi\) | |||||||
\(578\) | −16.1850 | + | 17.7678i | −0.673206 | + | 0.739043i | ||||
\(579\) | 12.6263i | 0.524731i | ||||||||
\(580\) | 19.5233 | − | 1.82425i | 0.810660 | − | 0.0757477i | ||||
\(581\) | −47.1771 | −1.95723 | ||||||||
\(582\) | −4.49975 | + | 4.93981i | −0.186521 | + | 0.204762i | ||||
\(583\) | − | 14.9836i | − | 0.620555i | ||||||
\(584\) | 11.8556 | + | 8.93145i | 0.490587 | + | 0.369586i | ||||
\(585\) | − | 3.35306i | − | 0.138632i | ||||||
\(586\) | 20.3143 | + | 18.5046i | 0.839176 | + | 0.764419i | ||||
\(587\) | − | 30.9114i | − | 1.27585i | −0.770099 | − | 0.637925i | \(-0.779793\pi\) | ||
0.770099 | − | 0.637925i | \(-0.220207\pi\) | |||||||
\(588\) | 10.4096 | − | 0.972665i | 0.429283 | − | 0.0401120i | ||||
\(589\) | 40.7459i | 1.67891i | ||||||||
\(590\) | 4.49233 | − | 4.93166i | 0.184946 | − | 0.203033i | ||||
\(591\) | − | 23.9878i | − | 0.986727i | ||||||
\(592\) | 2.46491 | + | 13.0747i | 0.101307 | + | 0.537367i | ||||
\(593\) | −18.1730 | −0.746276 | −0.373138 | − | 0.927776i | \(-0.621718\pi\) | ||||
−0.373138 | + | 0.927776i | \(0.621718\pi\) | |||||||
\(594\) | 1.42839 | + | 1.30115i | 0.0586076 | + | 0.0533867i | ||||
\(595\) | 0.251540 | 0.0103121 | ||||||||
\(596\) | −25.7187 | + | 2.40315i | −1.05348 | + | 0.0984367i | ||||
\(597\) | − | 16.8297i | − | 0.688794i | ||||||
\(598\) | −17.1998 | + | 14.8777i | −0.703351 | + | 0.608393i | ||||
\(599\) | 13.0346i | 0.532581i | 0.963893 | + | 0.266291i | \(0.0857981\pi\) | ||||
−0.963893 | + | 0.266291i | \(0.914202\pi\) | |||||||
\(600\) | 1.70190 | − | 2.25910i | 0.0694799 | − | 0.0922273i | ||||
\(601\) | −28.6319 | −1.16792 | −0.583959 | − | 0.811783i | \(-0.698497\pi\) | ||||
−0.583959 | + | 0.811783i | \(0.698497\pi\) | |||||||
\(602\) | −29.6750 | + | 32.5771i | −1.20946 | + | 1.32774i | ||||
\(603\) | 15.2636 | 0.621582 | ||||||||
\(604\) | −2.96352 | + | 0.276910i | −0.120584 | + | 0.0112673i | ||||
\(605\) | − | 9.13336i | − | 0.371324i | ||||||
\(606\) | −11.2801 | − | 10.2752i | −0.458222 | − | 0.417402i | ||||
\(607\) | 8.85705i | 0.359496i | 0.983713 | + | 0.179748i | \(0.0575283\pi\) | ||||
−0.983713 | + | 0.179748i | \(0.942472\pi\) | |||||||
\(608\) | −14.9857 | + | 24.3071i | −0.607751 | + | 0.985782i | ||||
\(609\) | 34.2830i | 1.38922i | ||||||||
\(610\) | −6.08036 | + | 6.67500i | −0.246187 | + | 0.270263i | ||||
\(611\) | 42.5581i | 1.72172i | ||||||||
\(612\) | 0.143246 | − | 0.0133848i | 0.00579036 | − | 0.000541049i | ||||
\(613\) | 34.3412i | 1.38703i | 0.720443 | + | 0.693514i | \(0.243939\pi\) | ||||
−0.720443 | + | 0.693514i | \(0.756061\pi\) | |||||||
\(614\) | 25.5008 | + | 23.2291i | 1.02913 | + | 0.937452i | ||||
\(615\) | −1.37906 | −0.0556090 | ||||||||
\(616\) | 10.7928 | + | 8.13080i | 0.434854 | + | 0.327599i | ||||
\(617\) | − | 7.75901i | − | 0.312366i | −0.987728 | − | 0.156183i | \(-0.950081\pi\) | ||
0.987728 | − | 0.156183i | \(-0.0499190\pi\) | |||||||
\(618\) | −9.11510 | − | 8.30310i | −0.366663 | − | 0.334000i | ||||
\(619\) | −22.8208 | −0.917244 | −0.458622 | − | 0.888631i | \(-0.651657\pi\) | ||||
−0.458622 | + | 0.888631i | \(0.651657\pi\) | |||||||
\(620\) | −1.50191 | − | 16.0737i | −0.0603183 | − | 0.645533i | ||||
\(621\) | 0.568640 | − | 4.76200i | 0.0228187 | − | 0.191092i | ||||
\(622\) | 3.45883 | + | 3.15071i | 0.138686 | + | 0.126332i | ||||
\(623\) | 40.2926i | 1.61429i | ||||||||
\(624\) | −2.48477 | − | 13.1800i | −0.0994704 | − | 0.527624i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −17.1856 | − | 15.6547i | −0.686876 | − | 0.625687i | ||||
\(627\) | − | 6.89672i | − | 0.275428i | ||||||
\(628\) | 1.57120 | − | 0.146812i | 0.0626977 | − | 0.00585845i | ||||
\(629\) | −0.239273 | −0.00954046 | ||||||||
\(630\) | 3.65582 | + | 3.33015i | 0.145651 | + | 0.132676i | ||||
\(631\) | 42.6051 | 1.69608 | 0.848041 | − | 0.529931i | \(-0.177782\pi\) | ||||
0.848041 | + | 0.529931i | \(0.177782\pi\) | |||||||
\(632\) | 9.50157 | + | 7.15805i | 0.377952 | + | 0.284732i | ||||
\(633\) | 20.6790 | 0.821916 | ||||||||
\(634\) | 20.1706 | − | 22.1432i | 0.801078 | − | 0.879420i | ||||
\(635\) | −12.7171 | −0.504663 | ||||||||
\(636\) | −2.04060 | − | 21.8387i | −0.0809149 | − | 0.865960i | ||||
\(637\) | 17.5280 | 0.694483 | ||||||||
\(638\) | −12.7567 | + | 14.0042i | −0.505041 | + | 0.554431i | ||||
\(639\) | − | 15.7028i | − | 0.621194i | ||||||
\(640\) | 5.01567 | − | 10.1412i | 0.198262 | − | 0.400864i | ||||
\(641\) | 34.2171i | 1.35149i | 0.737134 | + | 0.675746i | \(0.236179\pi\) | ||||
−0.737134 | + | 0.675746i | \(0.763821\pi\) | |||||||
\(642\) | 16.1252 | + | 14.6887i | 0.636409 | + | 0.579716i | ||||
\(643\) | 10.3253 | 0.407189 | 0.203595 | − | 0.979055i | \(-0.434738\pi\) | ||||
0.203595 | + | 0.979055i | \(0.434738\pi\) | |||||||
\(644\) | 0.861217 | − | 33.5289i | 0.0339367 | − | 1.32122i | ||||
\(645\) | −8.91103 | −0.350871 | ||||||||
\(646\) | −0.379636 | − | 0.345817i | −0.0149366 | − | 0.0136060i | ||||
\(647\) | 4.42046i | 0.173786i | 0.996218 | + | 0.0868930i | \(0.0276938\pi\) | ||||
−0.996218 | + | 0.0868930i | \(0.972306\pi\) | |||||||
\(648\) | 2.25910 | + | 1.70190i | 0.0887458 | + | 0.0668570i | ||||
\(649\) | 6.44476i | 0.252979i | ||||||||
\(650\) | 3.19327 | − | 3.50556i | 0.125251 | − | 0.137499i | ||||
\(651\) | 28.2254 | 1.10624 | ||||||||
\(652\) | 20.0484 | − | 1.87331i | 0.785155 | − | 0.0733646i | ||||
\(653\) | −33.8914 | −1.32627 | −0.663137 | − | 0.748498i | \(-0.730775\pi\) | ||||
−0.663137 | + | 0.748498i | \(0.730775\pi\) | |||||||
\(654\) | 2.05870 | − | 2.26003i | 0.0805016 | − | 0.0883743i | ||||
\(655\) | −21.4821 | −0.839375 | ||||||||
\(656\) | −5.42074 | + | 1.02195i | −0.211644 | + | 0.0399003i | ||||
\(657\) | −5.24792 | −0.204741 | ||||||||
\(658\) | −46.4009 | − | 42.2674i | −1.80890 | − | 1.64775i | ||||
\(659\) | −35.4900 | −1.38250 | −0.691248 | − | 0.722618i | \(-0.742939\pi\) | ||||
−0.691248 | + | 0.722618i | \(0.742939\pi\) | |||||||
\(660\) | 0.254216 | + | 2.72065i | 0.00989536 | + | 0.105901i | ||||
\(661\) | − | 6.67221i | − | 0.259519i | −0.991546 | − | 0.129759i | \(-0.958579\pi\) | ||
0.991546 | − | 0.129759i | \(-0.0414205\pi\) | |||||||
\(662\) | −7.90673 | − | 7.20237i | −0.307304 | − | 0.279928i | ||||
\(663\) | 0.241201 | 0.00936749 | ||||||||
\(664\) | −30.4788 | − | 22.9614i | −1.18281 | − | 0.891074i | ||||
\(665\) | − | 17.6514i | − | 0.684493i | ||||||
\(666\) | −3.47754 | − | 3.16775i | −0.134752 | − | 0.122748i | ||||
\(667\) | 46.6874 | + | 5.57504i | 1.80775 | + | 0.215866i | ||||
\(668\) | −24.5182 | + | 2.29097i | −0.948637 | + | 0.0886402i | ||||
\(669\) | 10.0263 | 0.387638 | ||||||||
\(670\) | 15.9578 | + | 14.5363i | 0.616505 | + | 0.561585i | ||||
\(671\) | − | 8.72298i | − | 0.336747i | ||||||
\(672\) | 16.8379 | + | 10.3809i | 0.649538 | + | 0.400451i | ||||
\(673\) | 19.0840 | 0.735634 | 0.367817 | − | 0.929898i | \(-0.380105\pi\) | ||||
0.367817 | + | 0.929898i | \(0.380105\pi\) | |||||||
\(674\) | 17.1304 | + | 15.6044i | 0.659838 | + | 0.601058i | ||||
\(675\) | 1.00000i | 0.0384900i | ||||||||
\(676\) | 0.326926 | + | 3.49879i | 0.0125741 | + | 0.134569i | ||||
\(677\) | 31.0941i | 1.19505i | 0.801852 | + | 0.597523i | \(0.203848\pi\) | ||||
−0.801852 | + | 0.597523i | \(0.796152\pi\) | |||||||
\(678\) | −8.54976 | + | 9.38588i | −0.328351 | + | 0.360463i | ||||
\(679\) | − | 16.5219i | − | 0.634054i | ||||||
\(680\) | 0.162508 | + | 0.122426i | 0.00623189 | + | 0.00469482i | ||||
\(681\) | − | 5.76617i | − | 0.220960i | ||||||
\(682\) | 11.5297 | + | 10.5026i | 0.441497 | + | 0.402167i | ||||
\(683\) | − | 0.183753i | − | 0.00703110i | −0.999994 | − | 0.00351555i | \(-0.998881\pi\) | ||
0.999994 | − | 0.00351555i | \(-0.00111904\pi\) | |||||||
\(684\) | −0.939258 | − | 10.0520i | −0.0359134 | − | 0.384349i | ||||
\(685\) | −8.83193 | −0.337451 | ||||||||
\(686\) | 5.90283 | − | 6.48010i | 0.225371 | − | 0.247411i | ||||
\(687\) | −2.46613 | −0.0940886 | ||||||||
\(688\) | −35.0271 | + | 6.60348i | −1.33539 | + | 0.251755i | ||||
\(689\) | − | 36.7727i | − | 1.40093i | ||||||
\(690\) | 5.12958 | − | 4.43705i | 0.195280 | − | 0.168915i | ||||
\(691\) | 19.4942i | 0.741593i | 0.928714 | + | 0.370796i | \(0.120915\pi\) | ||||
−0.928714 | + | 0.370796i | \(0.879085\pi\) | |||||||
\(692\) | −0.565795 | − | 6.05520i | −0.0215083 | − | 0.230184i | ||||
\(693\) | −4.77748 | −0.181481 | ||||||||
\(694\) | 10.8314 | + | 9.86654i | 0.411156 | + | 0.374529i | ||||
\(695\) | 1.47914 | 0.0561070 | ||||||||
\(696\) | −16.6857 | + | 22.1486i | −0.632471 | + | 0.839540i | ||||
\(697\) | − | 0.0992022i | − | 0.00375755i | ||||||
\(698\) | −0.394374 | + | 0.432942i | −0.0149273 | + | 0.0163871i | ||||
\(699\) | 17.1486i | 0.648620i | ||||||||
\(700\) | 0.650640 | + | 6.96322i | 0.0245919 | + | 0.263185i | ||||
\(701\) | 8.26187i | 0.312047i | 0.987753 | + | 0.156023i | \(0.0498675\pi\) | ||||
−0.987753 | + | 0.156023i | \(0.950132\pi\) | |||||||
\(702\) | 3.50556 | + | 3.19327i | 0.132309 | + | 0.120522i | ||||
\(703\) | 16.7906i | 0.633271i | ||||||||
\(704\) | 3.01539 | + | 10.5058i | 0.113647 | + | 0.395954i | ||||
\(705\) | − | 12.6923i | − | 0.478021i | ||||||
\(706\) | 31.9240 | − | 35.0460i | 1.20148 | − | 1.31898i | ||||
\(707\) | 37.7280 | 1.41891 | ||||||||
\(708\) | 0.877706 | + | 9.39331i | 0.0329862 | + | 0.353022i | ||||
\(709\) | − | 18.7338i | − | 0.703564i | −0.936082 | − | 0.351782i | \(-0.885576\pi\) | ||
0.936082 | − | 0.351782i | \(-0.114424\pi\) | |||||||
\(710\) | 14.9545 | − | 16.4170i | 0.561234 | − | 0.616120i | ||||
\(711\) | −4.20591 | −0.157734 | ||||||||
\(712\) | −19.6106 | + | 26.0311i | −0.734940 | + | 0.975556i | ||||
\(713\) | 4.58997 | − | 38.4381i | 0.171896 | − | 1.43952i | ||||
\(714\) | −0.239554 | + | 0.262981i | −0.00896507 | + | 0.00984181i | ||||
\(715\) | 4.58112i | 0.171324i | ||||||||
\(716\) | −19.2485 | + | 1.79857i | −0.719350 | + | 0.0672157i | ||||
\(717\) | −7.88125 | −0.294331 | ||||||||
\(718\) | 15.0353 | − | 16.5057i | 0.561114 | − | 0.615988i | ||||
\(719\) | 15.0358i | 0.560741i | 0.959892 | + | 0.280370i | \(0.0904573\pi\) | ||||
−0.959892 | + | 0.280370i | \(0.909543\pi\) | |||||||
\(720\) | 0.741046 | + | 3.93076i | 0.0276172 | + | 0.146491i | ||||
\(721\) | 30.4869 | 1.13539 | ||||||||
\(722\) | −6.17256 | + | 6.77621i | −0.229719 | + | 0.252184i | ||||
\(723\) | −13.3123 | −0.495091 | ||||||||
\(724\) | 51.7838 | − | 4.83866i | 1.92453 | − | 0.179827i | ||||
\(725\) | −9.80417 | −0.364118 | ||||||||
\(726\) | 9.54877 | + | 8.69813i | 0.354388 | + | 0.322818i | ||||
\(727\) | −35.8931 | −1.33120 | −0.665601 | − | 0.746308i | \(-0.731825\pi\) | ||||
−0.665601 | + | 0.746308i | \(0.731825\pi\) | |||||||
\(728\) | 26.4877 | + | 19.9546i | 0.981699 | + | 0.739568i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −5.48661 | − | 4.99784i | −0.203068 | − | 0.184978i | ||||
\(731\) | − | 0.641013i | − | 0.0237087i | ||||||
\(732\) | −1.18797 | − | 12.7138i | −0.0439088 | − | 0.469917i | ||||
\(733\) | − | 31.3376i | − | 1.15748i | −0.815512 | − | 0.578740i | \(-0.803545\pi\) | ||
0.815512 | − | 0.578740i | \(-0.196455\pi\) | |||||||
\(734\) | 10.3551 | − | 11.3678i | 0.382213 | − | 0.419592i | ||||
\(735\) | −5.22746 | −0.192818 | ||||||||
\(736\) | 16.8751 | − | 21.2422i | 0.622024 | − | 0.782998i | ||||
\(737\) | −20.8539 | −0.768165 | ||||||||
\(738\) | 1.31334 | − | 1.44178i | 0.0483448 | − | 0.0530727i | ||||
\(739\) | − | 18.0131i | − | 0.662622i | −0.943522 | − | 0.331311i | \(-0.892509\pi\) | ||
0.943522 | − | 0.331311i | \(-0.107491\pi\) | |||||||
\(740\) | −0.618911 | − | 6.62366i | −0.0227516 | − | 0.243490i | ||||
\(741\) | − | 16.9259i | − | 0.621790i | ||||||
\(742\) | 40.0931 | + | 36.5214i | 1.47186 | + | 1.34074i | ||||
\(743\) | 5.74188 | 0.210649 | 0.105325 | − | 0.994438i | \(-0.466412\pi\) | ||||
0.105325 | + | 0.994438i | \(0.466412\pi\) | |||||||
\(744\) | 18.2351 | + | 13.7375i | 0.668530 | + | 0.503640i | ||||
\(745\) | 12.9154 | 0.473183 | ||||||||
\(746\) | 12.0264 | + | 10.9551i | 0.440318 | + | 0.401093i | ||||
\(747\) | 13.4916 | 0.493631 | ||||||||
\(748\) | −0.195710 | + | 0.0182870i | −0.00715585 | + | 0.000668639i | ||||
\(749\) | −53.9331 | −1.97067 | ||||||||
\(750\) | −0.952347 | + | 1.04548i | −0.0347748 | + | 0.0381756i | ||||
\(751\) | −47.7051 | −1.74078 | −0.870391 | − | 0.492361i | \(-0.836134\pi\) | ||||
−0.870391 | + | 0.492361i | \(0.836134\pi\) | |||||||
\(752\) | −9.40562 | − | 49.8905i | −0.342988 | − | 1.81932i | ||||
\(753\) | − | 16.9160i | − | 0.616454i | ||||||
\(754\) | −31.3074 | + | 34.3691i | −1.14015 | + | 1.25165i | ||||
\(755\) | 1.48821 | 0.0541616 | ||||||||
\(756\) | −6.96322 | + | 0.650640i | −0.253250 | + | 0.0236636i | ||||
\(757\) | − | 33.3125i | − | 1.21076i | −0.795935 | − | 0.605382i | \(-0.793020\pi\) | ||
0.795935 | − | 0.605382i | \(-0.206980\pi\) | |||||||
\(758\) | 21.2858 | − | 23.3675i | 0.773135 | − | 0.848744i | ||||
\(759\) | −0.776905 | + | 6.50609i | −0.0281999 | + | 0.236156i | ||||
\(760\) | 8.59105 | − | 11.4037i | 0.311630 | − | 0.413657i | ||||
\(761\) | −13.8151 | −0.500797 | −0.250399 | − | 0.968143i | \(-0.580562\pi\) | ||||
−0.250399 | + | 0.968143i | \(0.580562\pi\) | |||||||
\(762\) | 12.1111 | − | 13.2955i | 0.438739 | − | 0.481646i | ||||
\(763\) | 7.55903i | 0.273655i | ||||||||
\(764\) | −0.270251 | − | 2.89225i | −0.00977733 | − | 0.104638i | ||||
\(765\) | −0.0719348 | −0.00260081 | ||||||||
\(766\) | −10.7486 | + | 11.7997i | −0.388362 | + | 0.426342i | ||||
\(767\) | 15.8167i | 0.571109i | ||||||||
\(768\) | 5.82575 | + | 14.9017i | 0.210218 | + | 0.537719i | ||||
\(769\) | − | 32.1778i | − | 1.16036i | −0.814487 | − | 0.580181i | \(-0.802982\pi\) | ||
0.814487 | − | 0.580181i | \(-0.197018\pi\) | |||||||
\(770\) | −4.99477 | − | 4.54982i | −0.179999 | − | 0.163964i | ||||
\(771\) | 19.6697i | 0.708388i | ||||||||
\(772\) | −2.34936 | − | 25.1431i | −0.0845553 | − | 0.904919i | ||||
\(773\) | 9.57568i | 0.344413i | 0.985061 | + | 0.172207i | \(0.0550897\pi\) | ||||
−0.985061 | + | 0.172207i | \(0.944910\pi\) | |||||||
\(774\) | 8.48639 | − | 9.31632i | 0.305037 | − | 0.334868i | ||||
\(775\) | 8.07183i | 0.289949i | ||||||||
\(776\) | 8.04133 | − | 10.6740i | 0.288667 | − | 0.383175i | ||||
\(777\) | 11.6312 | 0.417266 | ||||||||
\(778\) | 20.8874 | + | 19.0267i | 0.748849 | + | 0.682139i | ||||
\(779\) | −6.96136 | −0.249417 | ||||||||
\(780\) | 0.623898 | + | 6.67703i | 0.0223391 | + | 0.239076i | ||||
\(781\) | 21.4540i | 0.767684i | ||||||||
\(782\) | 0.319178 | + | 0.368996i | 0.0114138 | + | 0.0131953i | ||||
\(783\) | − | 9.80417i | − | 0.350372i | ||||||
\(784\) | −20.5479 | + | 3.87379i | −0.733852 | + | 0.138350i | ||||
\(785\) | −0.789022 | −0.0281614 | ||||||||
\(786\) | 20.4584 | − | 22.4592i | 0.729727 | − | 0.801092i | ||||
\(787\) | 48.0736 | 1.71364 | 0.856819 | − | 0.515617i | \(-0.172437\pi\) | ||||
0.856819 | + | 0.515617i | \(0.172437\pi\) | |||||||
\(788\) | 4.46338 | + | 47.7675i | 0.159001 | + | 1.70165i | ||||
\(789\) | 3.46611i | 0.123397i | ||||||||
\(790\) | −4.39721 | − | 4.00549i | −0.156446 | − | 0.142509i | ||||
\(791\) | − | 31.3925i | − | 1.11619i | ||||||
\(792\) | −3.08650 | − | 2.32523i | −0.109674 | − | 0.0826233i | ||||
\(793\) | − | 21.4079i | − | 0.760218i | ||||||
\(794\) | −16.3654 | + | 17.9658i | −0.580785 | + | 0.637583i | ||||
\(795\) | 10.9669i | 0.388956i | ||||||||
\(796\) | 3.13148 | + | 33.5134i | 0.110992 | + | 1.18785i | ||||
\(797\) | 47.3644i | 1.67773i | 0.544338 | + | 0.838866i | \(0.316781\pi\) | ||||
−0.544338 | + | 0.838866i | \(0.683219\pi\) | |||||||
\(798\) | 18.4543 | + | 16.8103i | 0.653274 | + | 0.595078i | ||||
\(799\) | 0.913021 | 0.0323004 | ||||||||
\(800\) | −2.96870 | + | 4.81527i | −0.104959 | + | 0.170246i | ||||
\(801\) | − | 11.5228i | − | 0.407137i | ||||||
\(802\) | 22.5480 | + | 20.5394i | 0.796199 | + | 0.725271i | ||||
\(803\) | 7.16998 | 0.253023 | ||||||||
\(804\) | −30.3948 | + | 2.84008i | −1.07194 | + | 0.100162i | ||||
\(805\) | −1.98841 | + | 16.6517i | −0.0700822 | + | 0.586894i | ||||
\(806\) | 28.2963 | + | 25.7756i | 0.996695 | + | 0.907906i | ||||
\(807\) | − | 0.230066i | − | 0.00809871i | ||||||
\(808\) | 24.3742 | + | 18.3624i | 0.857483 | + | 0.645989i | ||||
\(809\) | 32.6507 | 1.14794 | 0.573970 | − | 0.818877i | \(-0.305403\pi\) | ||||
0.573970 | + | 0.818877i | \(0.305403\pi\) | |||||||
\(810\) | −1.04548 | − | 0.952347i | −0.0367345 | − | 0.0334621i | ||||
\(811\) | 32.8029i | 1.15187i | 0.817497 | + | 0.575934i | \(0.195361\pi\) | ||||
−0.817497 | + | 0.575934i | \(0.804639\pi\) | |||||||
\(812\) | −6.37899 | − | 68.2686i | −0.223859 | − | 2.39576i | ||||
\(813\) | 6.04603 | 0.212044 | ||||||||
\(814\) | 4.75120 | + | 4.32794i | 0.166529 | + | 0.151694i | ||||
\(815\) | −10.0679 | −0.352662 | ||||||||
\(816\) | −0.282758 | + | 0.0533070i | −0.00989852 | + | 0.00186612i | ||||
\(817\) | −44.9821 | −1.57372 | ||||||||
\(818\) | −19.5305 | + | 21.4405i | −0.682867 | + | 0.749648i | ||||
\(819\) | −11.7249 | −0.409701 | ||||||||
\(820\) | 2.74615 | − | 0.256599i | 0.0958998 | − | 0.00896084i | ||||
\(821\) | −12.6775 | −0.442446 | −0.221223 | − | 0.975223i | \(-0.571005\pi\) | ||||
−0.221223 | + | 0.975223i | \(0.571005\pi\) | |||||||
\(822\) | 8.41106 | − | 9.23363i | 0.293369 | − | 0.322060i | ||||
\(823\) | − | 34.7717i | − | 1.21207i | −0.795439 | − | 0.606033i | \(-0.792760\pi\) | ||
0.795439 | − | 0.606033i | \(-0.207240\pi\) | |||||||
\(824\) | 19.6961 | + | 14.8381i | 0.686146 | + | 0.516911i | ||||
\(825\) | − | 1.36625i | − | 0.0475668i | ||||||
\(826\) | −17.2449 | − | 15.7087i | −0.600027 | − | 0.546575i | ||||
\(827\) | 37.9777 | 1.32062 | 0.660308 | − | 0.750995i | \(-0.270426\pi\) | ||||
0.660308 | + | 0.750995i | \(0.270426\pi\) | |||||||
\(828\) | −0.246289 | + | 9.58850i | −0.00855913 | + | 0.333223i | ||||
\(829\) | 17.5863 | 0.610796 | 0.305398 | − | 0.952225i | \(-0.401210\pi\) | ||||
0.305398 | + | 0.952225i | \(0.401210\pi\) | |||||||
\(830\) | 14.1052 | + | 12.8487i | 0.489599 | + | 0.445984i | ||||
\(831\) | 14.3524i | 0.497881i | ||||||||
\(832\) | 7.40038 | + | 25.7834i | 0.256562 | + | 0.893880i | ||||
\(833\) | − | 0.376036i | − | 0.0130289i | ||||||
\(834\) | −1.40866 | + | 1.54642i | −0.0487778 | + | 0.0535480i | ||||
\(835\) | 12.3125 | 0.426091 | ||||||||
\(836\) | 1.28326 | + | 13.7336i | 0.0443825 | + | 0.474987i | ||||
\(837\) | −8.07183 | −0.279003 | ||||||||
\(838\) | 6.17488 | − | 6.77875i | 0.213308 | − | 0.234168i | ||||
\(839\) | −22.3742 | −0.772444 | −0.386222 | − | 0.922406i | \(-0.626220\pi\) | ||||
−0.386222 | + | 0.922406i | \(0.626220\pi\) | |||||||
\(840\) | −7.89957 | − | 5.95118i | −0.272561 | − | 0.205335i | ||||
\(841\) | 67.1217 | 2.31454 | ||||||||
\(842\) | 17.2545 | + | 15.7174i | 0.594631 | + | 0.541659i | ||||
\(843\) | 9.58403 | 0.330092 | ||||||||
\(844\) | −41.1786 | + | 3.84771i | −1.41743 | + | 0.132444i | ||||
\(845\) | − | 1.75702i | − | 0.0604432i | ||||||
\(846\) | 13.2696 | + | 12.0875i | 0.456219 | + | 0.415578i | ||||
\(847\) | −31.9373 | −1.09738 | ||||||||
\(848\) | 8.12699 | + | 43.1083i | 0.279082 | + | 1.48034i | ||||
\(849\) | 29.7360i | 1.02054i | ||||||||
\(850\) | −0.0752066 | − | 0.0685069i | −0.00257957 | − | 0.00234977i | ||||
\(851\) | 1.89144 | − | 15.8396i | 0.0648378 | − | 0.542975i | ||||
\(852\) | 2.92180 | + | 31.2694i | 0.100099 | + | 1.07127i | ||||
\(853\) | −42.0149 | −1.43856 | −0.719281 | − | 0.694719i | \(-0.755529\pi\) | ||||
−0.719281 | + | 0.694719i | \(0.755529\pi\) | |||||||
\(854\) | 23.3410 | + | 21.2617i | 0.798712 | + | 0.727560i | ||||
\(855\) | 5.04791i | 0.172635i | ||||||||
\(856\) | −34.8436 | − | 26.2496i | −1.19093 | − | 0.897191i | ||||
\(857\) | 6.03951 | 0.206306 | 0.103153 | − | 0.994666i | \(-0.467107\pi\) | ||||
0.103153 | + | 0.994666i | \(0.467107\pi\) | |||||||
\(858\) | −4.78948 | − | 4.36282i | −0.163510 | − | 0.148944i | ||||
\(859\) | 27.5246i | 0.939128i | 0.882899 | + | 0.469564i | \(0.155589\pi\) | ||||
−0.882899 | + | 0.469564i | \(0.844411\pi\) | |||||||
\(860\) | 17.7448 | − | 1.65806i | 0.605091 | − | 0.0565394i | ||||
\(861\) | 4.82226i | 0.164342i | ||||||||
\(862\) | −29.9736 | + | 32.9048i | −1.02090 | + | 1.12074i | ||||
\(863\) | − | 16.4378i | − | 0.559551i | −0.960066 | − | 0.279775i | \(-0.909740\pi\) | ||
0.960066 | − | 0.279775i | \(-0.0902600\pi\) | |||||||
\(864\) | −4.81527 | − | 2.96870i | −0.163819 | − | 0.100997i | ||||
\(865\) | 3.04079i | 0.103390i | ||||||||
\(866\) | 19.5957 | + | 17.8500i | 0.665889 | + | 0.606569i | ||||
\(867\) | 16.9948i | 0.577175i | ||||||||
\(868\) | −56.2060 | + | 5.25186i | −1.90776 | + | 0.178260i | ||||
\(869\) | 5.74633 | 0.194931 | ||||||||
\(870\) | 9.33697 | − | 10.2501i | 0.316553 | − | 0.347511i | ||||
\(871\) | −51.1798 | −1.73416 | ||||||||
\(872\) | −3.67902 | + | 4.88352i | −0.124587 | + | 0.165377i | ||||
\(873\) | 4.72490i | 0.159914i | ||||||||
\(874\) | 25.8937 | − | 22.3978i | 0.875867 | − | 0.757618i | ||||
\(875\) | − | 3.49678i | − | 0.118213i | ||||||
\(876\) | 10.4503 | − | 0.976473i | 0.353083 | − | 0.0329920i | ||||
\(877\) | −22.5117 | −0.760165 | −0.380083 | − | 0.924953i | \(-0.624104\pi\) | ||||
−0.380083 | + | 0.924953i | \(0.624104\pi\) | |||||||
\(878\) | 9.80196 | + | 8.92877i | 0.330800 | + | 0.301331i | ||||
\(879\) | 19.4305 | 0.655376 | ||||||||
\(880\) | −1.01246 | − | 5.37040i | −0.0341299 | − | 0.181036i | ||||
\(881\) | − | 16.5757i | − | 0.558448i | −0.960226 | − | 0.279224i | \(-0.909923\pi\) | ||
0.960226 | − | 0.279224i | \(-0.0900772\pi\) | |||||||
\(882\) | 4.97835 | − | 5.46522i | 0.167630 | − | 0.184023i | ||||
\(883\) | − | 23.5714i | − | 0.793239i | −0.917983 | − | 0.396620i | \(-0.870183\pi\) | ||
0.917983 | − | 0.396620i | \(-0.129817\pi\) | |||||||
\(884\) | −0.480311 | + | 0.0448800i | −0.0161546 | + | 0.00150948i | ||||
\(885\) | − | 4.71711i | − | 0.158564i | ||||||
\(886\) | 22.5998 | + | 20.5865i | 0.759255 | + | 0.691618i | ||||
\(887\) | 31.4813i | 1.05704i | 0.848921 | + | 0.528519i | \(0.177253\pi\) | ||||
−0.848921 | + | 0.528519i | \(0.822747\pi\) | |||||||
\(888\) | 7.51434 | + | 5.66096i | 0.252165 | + | 0.189969i | ||||
\(889\) | 44.4689i | 1.49144i | ||||||||
\(890\) | 10.9737 | − | 12.0469i | 0.367839 | − | 0.403812i | ||||
\(891\) | 1.36625 | 0.0457711 | ||||||||
\(892\) | −19.9656 | + | 1.86557i | −0.668497 | + | 0.0624640i | ||||
\(893\) | − | 64.0698i | − | 2.14402i | ||||||
\(894\) | −12.2999 | + | 13.5028i | −0.411371 | + | 0.451601i | ||||
\(895\) | 9.66616 | 0.323104 | ||||||||
\(896\) | −35.4614 | − | 17.5387i | −1.18468 | − | 0.585926i | ||||
\(897\) | −1.90668 | + | 15.9673i | −0.0636622 | + | 0.533131i | ||||
\(898\) | 11.2027 | − | 12.2983i | 0.373839 | − | 0.410398i | ||||
\(899\) | − | 79.1376i | − | 2.63939i | ||||||
\(900\) | −0.186069 | − | 1.99133i | −0.00620229 | − | 0.0663775i | ||||
\(901\) | −0.788903 | −0.0262822 | ||||||||
\(902\) | −1.79436 | + | 1.96984i | −0.0597455 | + | 0.0655883i | ||||
\(903\) | 31.1599i | 1.03694i | ||||||||
\(904\) | 15.2789 | − | 20.2812i | 0.508170 | − | 0.674542i | ||||
\(905\) | −26.0047 | −0.864426 | ||||||||
\(906\) | −1.41730 | + | 1.55590i | −0.0470865 | + | 0.0516914i | ||||
\(907\) | −3.62895 | −0.120497 | −0.0602486 | − | 0.998183i | \(-0.519189\pi\) | ||||
−0.0602486 | + | 0.998183i | \(0.519189\pi\) | |||||||
\(908\) | 1.07290 | + | 11.4823i | 0.0356056 | + | 0.381054i | ||||
\(909\) | −10.7894 | −0.357861 | ||||||||
\(910\) | −12.2582 | − | 11.1662i | −0.406354 | − | 0.370155i | ||||
\(911\) | 37.6483 | 1.24735 | 0.623673 | − | 0.781686i | \(-0.285640\pi\) | ||||
0.623673 | + | 0.781686i | \(0.285640\pi\) | |||||||
\(912\) | 3.74074 | + | 19.8421i | 0.123868 | + | 0.657038i | ||||
\(913\) | −18.4329 | −0.610040 | ||||||||
\(914\) | 37.0552 | + | 33.7542i | 1.22568 | + | 1.11649i | ||||
\(915\) | 6.38461i | 0.211069i | ||||||||
\(916\) | 4.91086 | − | 0.458868i | 0.162259 | − | 0.0151614i | ||||
\(917\) | 75.1181i | 2.48062i | ||||||||
\(918\) | 0.0685069 | − | 0.0752066i | 0.00226107 | − | 0.00248219i | ||||
\(919\) | 39.4637 | 1.30179 | 0.650893 | − | 0.759169i | \(-0.274395\pi\) | ||||
0.650893 | + | 0.759169i | \(0.274395\pi\) | |||||||
\(920\) | −9.38907 | + | 9.79006i | −0.309549 | + | 0.322769i | ||||
\(921\) | 24.3915 | 0.803726 | ||||||||
\(922\) | 13.5413 | − | 14.8656i | 0.445960 | − | 0.489573i | ||||
\(923\) | 52.6524i | 1.73308i | ||||||||
\(924\) | 9.51351 | − | 0.888938i | 0.312972 | − | 0.0292439i | ||||
\(925\) | 3.32625i | 0.109367i | ||||||||
\(926\) | −1.41375 | − | 1.28781i | −0.0464588 | − | 0.0423201i | ||||
\(927\) | −8.71856 | −0.286355 | ||||||||
\(928\) | 29.1056 | − | 47.2097i | 0.955438 | − | 1.54974i | ||||
\(929\) | −18.7511 | −0.615204 | −0.307602 | − | 0.951515i | \(-0.599527\pi\) | ||||
−0.307602 | + | 0.951515i | \(0.599527\pi\) | |||||||
\(930\) | −8.43896 | − | 7.68719i | −0.276724 | − | 0.252073i | ||||
\(931\) | −26.3877 | −0.864823 | ||||||||
\(932\) | −3.19082 | − | 34.1485i | −0.104519 | − | 1.11857i | ||||
\(933\) | 3.30836 | 0.108311 | ||||||||
\(934\) | 19.0222 | − | 20.8825i | 0.622426 | − | 0.683297i | ||||
\(935\) | 0.0982810 | 0.00321413 | ||||||||
\(936\) | −7.57488 | − | 5.70657i | −0.247593 | − | 0.186525i | ||||
\(937\) | − | 2.65735i | − | 0.0868117i | −0.999058 | − | 0.0434059i | \(-0.986179\pi\) | ||
0.999058 | − | 0.0434059i | \(-0.0138209\pi\) | |||||||
\(938\) | 50.8301 | − | 55.8010i | 1.65966 | − | 1.82197i | ||||
\(939\) | −16.4380 | −0.536434 | ||||||||
\(940\) | 2.36165 | + | 25.2746i | 0.0770284 | + | 0.824366i | ||||
\(941\) | − | 53.1284i | − | 1.73194i | −0.500100 | − | 0.865968i | \(-0.666704\pi\) | ||
0.500100 | − | 0.865968i | \(-0.333296\pi\) | |||||||
\(942\) | 0.751424 | − | 0.824909i | 0.0244827 | − | 0.0268770i | ||||
\(943\) | 6.56707 | + | 0.784187i | 0.213853 | + | 0.0255367i | ||||
\(944\) | −3.49560 | − | 18.5418i | −0.113772 | − | 0.603485i | ||||
\(945\) | 3.49678 | 0.113750 | ||||||||
\(946\) | −11.5945 | + | 12.7284i | −0.376971 | + | 0.413837i | ||||
\(947\) | − | 22.2269i | − | 0.722278i | −0.932512 | − | 0.361139i | \(-0.882388\pi\) | ||
0.932512 | − | 0.361139i | \(-0.117612\pi\) | |||||||
\(948\) | 8.37534 | − | 0.782588i | 0.272018 | − | 0.0254173i | ||||
\(949\) | 17.5966 | 0.571209 | ||||||||
\(950\) | −4.80737 | + | 5.27750i | −0.155972 | + | 0.171225i | ||||
\(951\) | − | 21.1799i | − | 0.686806i | ||||||
\(952\) | 0.428097 | − | 0.568254i | 0.0138747 | − | 0.0184172i | ||||
\(953\) | − | 26.2415i | − | 0.850046i | −0.905183 | − | 0.425023i | \(-0.860266\pi\) | ||
0.905183 | − | 0.425023i | \(-0.139734\pi\) | |||||||
\(954\) | −11.4657 | − | 10.4443i | −0.371216 | − | 0.338147i | ||||
\(955\) | 1.45243i | 0.0469994i | ||||||||
\(956\) | 15.6941 | − | 1.46645i | 0.507585 | − | 0.0474285i | ||||
\(957\) | 13.3950i | 0.432997i | ||||||||
\(958\) | 26.6493 | − | 29.2555i | 0.860999 | − | 0.945201i | ||||
\(959\) | 30.8833i | 0.997273i | ||||||||
\(960\) | −2.20705 | − | 7.68953i | −0.0712324 | − | 0.248179i | ||||
\(961\) | −34.1545 | −1.10176 | ||||||||
\(962\) | 11.6604 | + | 10.6216i | 0.375946 | + | 0.342456i | ||||
\(963\) | 15.4237 | 0.497020 | ||||||||
\(964\) | 26.5092 | − | 2.47701i | 0.853804 | − | 0.0797791i | ||||
\(965\) | 12.6263i | 0.406455i | ||||||||
\(966\) | −15.5154 | − | 17.9370i | −0.499199 | − | 0.577114i | ||||
\(967\) | − | 7.54606i | − | 0.242665i | −0.992612 | − | 0.121333i | \(-0.961283\pi\) | ||
0.992612 | − | 0.121333i | \(-0.0387167\pi\) | |||||||
\(968\) | −20.6332 | − | 15.5441i | −0.663175 | − | 0.499606i | ||||
\(969\) | −0.363121 | −0.0116651 | ||||||||
\(970\) | −4.49975 | + | 4.93981i | −0.144478 | + | 0.158608i | ||||
\(971\) | 11.9488 | 0.383456 | 0.191728 | − | 0.981448i | \(-0.438591\pi\) | ||||
0.191728 | + | 0.981448i | \(0.438591\pi\) | |||||||
\(972\) | 1.99133 | − | 0.186069i | 0.0638718 | − | 0.00596815i | ||||
\(973\) | − | 5.17223i | − | 0.165814i | ||||||
\(974\) | −31.5453 | − | 28.7351i | −1.01078 | − | 0.920732i | ||||
\(975\) | − | 3.35306i | − | 0.107384i | ||||||
\(976\) | 4.73129 | + | 25.0963i | 0.151445 | + | 0.803314i | ||||
\(977\) | − | 19.3143i | − | 0.617919i | −0.951075 | − | 0.308960i | \(-0.900019\pi\) | ||
0.951075 | − | 0.308960i | \(-0.0999808\pi\) | |||||||
\(978\) | 9.58810 | − | 10.5258i | 0.306594 | − | 0.336577i | ||||
\(979\) | 15.7430i | 0.503149i | ||||||||
\(980\) | 10.4096 | − | 0.972665i | 0.332521 | − | 0.0310707i | ||||
\(981\) | − | 2.16171i | − | 0.0690181i | ||||||
\(982\) | −7.40479 | − | 6.74514i | −0.236296 | − | 0.215246i | ||||
\(983\) | 5.59462 | 0.178441 | 0.0892204 | − | 0.996012i | \(-0.471562\pi\) | ||||
0.0892204 | + | 0.996012i | \(0.471562\pi\) | |||||||
\(984\) | −2.34702 | + | 3.11543i | −0.0748203 | + | 0.0993162i | ||||
\(985\) | − | 23.9878i | − | 0.764315i | ||||||
\(986\) | 0.737338 | + | 0.671653i | 0.0234816 | + | 0.0213898i | ||||
\(987\) | −44.3823 | −1.41270 | ||||||||
\(988\) | 3.14938 | + | 33.7050i | 0.100195 | + | 1.07230i | ||||
\(989\) | 42.4343 | + | 5.06717i | 1.34933 | + | 0.161126i | ||||
\(990\) | 1.42839 | + | 1.30115i | 0.0453973 | + | 0.0413531i | ||||
\(991\) | − | 46.6872i | − | 1.48307i | −0.670916 | − | 0.741533i | \(-0.734099\pi\) | ||
0.670916 | − | 0.741533i | \(-0.265901\pi\) | |||||||
\(992\) | −38.8681 | − | 23.9628i | −1.23406 | − | 0.760820i | ||||
\(993\) | −7.56275 | −0.239997 | ||||||||
\(994\) | −57.4067 | − | 52.2927i | −1.82083 | − | 1.65862i | ||||
\(995\) | − | 16.8297i | − | 0.533537i | ||||||
\(996\) | −26.8661 | + | 2.51036i | −0.851286 | + | 0.0795438i | ||||
\(997\) | −2.45370 | −0.0777095 | −0.0388547 | − | 0.999245i | \(-0.512371\pi\) | ||||
−0.0388547 | + | 0.999245i | \(0.512371\pi\) | |||||||
\(998\) | −18.0344 | − | 16.4278i | −0.570868 | − | 0.520013i | ||||
\(999\) | −3.32625 | −0.105238 |
(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 | 1380.2.p.a.91.16 | yes | 48 | |
4.3 | odd | 2 | 1380.2.p.b.91.15 | yes | 48 | ||
23.22 | odd | 2 | 1380.2.p.b.91.16 | yes | 48 | ||
92.91 | even | 2 | inner | 1380.2.p.a.91.15 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.2.p.a.91.15 | ✓ | 48 | 92.91 | even | 2 | inner | |
1380.2.p.a.91.16 | yes | 48 | 1.1 | even | 1 | trivial | |
1380.2.p.b.91.15 | yes | 48 | 4.3 | odd | 2 | ||
1380.2.p.b.91.16 | yes | 48 | 23.22 | odd | 2 |