Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(55,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("756.55");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.b (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: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{12} - 4x^{10} - 4x^{8} - 16x^{6} - 16x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 55.6 | ||
Root | \(0.748450 + 1.19993i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 756.55 |
Dual form | 756.2.b.f.55.5 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.748450 | + | 1.19993i | −0.529234 | + | 0.848476i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.879646 | − | 1.79617i | −0.439823 | − | 0.898084i | ||||
\(5\) | 3.90968i | 1.74846i | 0.485510 | + | 0.874231i | \(0.338634\pi\) | ||||
−0.485510 | + | 0.874231i | \(0.661366\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.12924 | − | 2.39266i | 0.426812 | − | 0.904341i | ||||
\(8\) | 2.81364 | + | 0.288831i | 0.994772 | + | 0.102117i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.69133 | − | 2.92620i | −1.48353 | − | 0.925345i | ||||
\(11\) | − | 5.01901i | − | 1.51329i | −0.653826 | − | 0.756645i | \(-0.726837\pi\) | ||
0.653826 | − | 0.756645i | \(-0.273163\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.59667i | − | 1.55224i | −0.630586 | − | 0.776119i | \(-0.717186\pi\) | ||
0.630586 | − | 0.776119i | \(-0.282814\pi\) | |||||||
\(14\) | 2.02584 | + | 3.14579i | 0.541428 | + | 0.840747i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.45244 | + | 3.15999i | −0.613111 | + | 0.789997i | ||||
\(17\) | − | 2.41029i | − | 0.584582i | −0.956329 | − | 0.292291i | \(-0.905582\pi\) | ||
0.956329 | − | 0.292291i | \(-0.0944176\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.11590 | 0.714836 | 0.357418 | − | 0.933945i | \(-0.383657\pi\) | ||||
0.357418 | + | 0.933945i | \(0.383657\pi\) | |||||||
\(20\) | 7.02245 | − | 3.43914i | 1.57027 | − | 0.769014i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.02245 | + | 3.75648i | 1.28399 | + | 0.800884i | ||||
\(23\) | − | 3.45254i | − | 0.719905i | −0.932971 | − | 0.359953i | \(-0.882793\pi\) | ||
0.932971 | − | 0.359953i | \(-0.117207\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −10.2856 | −2.05712 | ||||||||
\(26\) | 6.71560 | + | 4.18883i | 1.31704 | + | 0.821497i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.29095 | + | 0.0763943i | −0.999896 | + | 0.0144372i | ||||
\(29\) | −4.76986 | −0.885741 | −0.442870 | − | 0.896586i | \(-0.646040\pi\) | ||||
−0.442870 | + | 0.896586i | \(0.646040\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.482412 | 0.0866437 | 0.0433219 | − | 0.999061i | \(-0.486206\pi\) | ||||
0.0433219 | + | 0.999061i | \(0.486206\pi\) | |||||||
\(32\) | −1.95622 | − | 5.30784i | −0.345814 | − | 0.938303i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.89217 | + | 1.80398i | 0.496004 | + | 0.309381i | ||||
\(35\) | 9.35454 | + | 4.41496i | 1.58121 | + | 0.746264i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.90489 | 0.970758 | 0.485379 | − | 0.874304i | \(-0.338682\pi\) | ||||
0.485379 | + | 0.874304i | \(0.338682\pi\) | |||||||
\(38\) | −2.33209 | + | 3.73885i | −0.378315 | + | 0.606521i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.12924 | + | 11.0004i | −0.178548 | + | 1.73932i | ||||
\(41\) | 1.51033i | 0.235873i | 0.993021 | + | 0.117937i | \(0.0376280\pi\) | ||||
−0.993021 | + | 0.117937i | \(0.962372\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.77561i | 0.270778i | 0.990793 | + | 0.135389i | \(0.0432284\pi\) | ||||
−0.990793 | + | 0.135389i | \(0.956772\pi\) | |||||||
\(44\) | −9.01499 | + | 4.41496i | −1.35906 | + | 0.665580i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.14280 | + | 2.58406i | 0.610822 | + | 0.380998i | ||||
\(47\) | 2.38630 | 0.348078 | 0.174039 | − | 0.984739i | \(-0.444318\pi\) | ||||
0.174039 | + | 0.984739i | \(0.444318\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.44965 | − | 5.40376i | −0.635664 | − | 0.771966i | ||||
\(50\) | 7.69825 | − | 12.3420i | 1.08870 | − | 1.74542i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −10.0526 | + | 4.92309i | −1.39404 | + | 0.682710i | ||||
\(53\) | 5.62728 | 0.772967 | 0.386483 | − | 0.922296i | \(-0.373690\pi\) | ||||
0.386483 | + | 0.922296i | \(0.373690\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 19.6227 | 2.64593 | ||||||||
\(56\) | 3.86834 | − | 6.40593i | 0.516929 | − | 0.856028i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.57000 | − | 5.72348i | 0.468764 | − | 0.751530i | ||||
\(59\) | 6.38071 | 0.830697 | 0.415349 | − | 0.909662i | \(-0.363660\pi\) | ||||
0.415349 | + | 0.909662i | \(0.363660\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 6.94384i | − | 0.889067i | −0.895762 | − | 0.444534i | \(-0.853369\pi\) | ||
0.895762 | − | 0.444534i | \(-0.146631\pi\) | |||||||
\(62\) | −0.361061 | + | 0.578859i | −0.0458548 | + | 0.0735151i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.83315 | + | 1.62533i | 0.979144 | + | 0.203167i | ||||
\(65\) | 21.8812 | 2.71403 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 3.92062i | − | 0.478980i | −0.970899 | − | 0.239490i | \(-0.923020\pi\) | ||
0.970899 | − | 0.239490i | \(-0.0769802\pi\) | |||||||
\(68\) | −4.32929 | + | 2.12021i | −0.525004 | + | 0.257113i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −12.2990 | + | 7.92038i | −1.47001 | + | 0.946667i | ||||
\(71\) | 8.25225i | 0.979362i | 0.871902 | + | 0.489681i | \(0.162887\pi\) | ||||
−0.871902 | + | 0.489681i | \(0.837113\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.59159i | 0.420364i | 0.977662 | + | 0.210182i | \(0.0674057\pi\) | ||||
−0.977662 | + | 0.210182i | \(0.932594\pi\) | |||||||
\(74\) | −4.41951 | + | 7.08543i | −0.513758 | + | 0.823665i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.74089 | − | 5.59667i | −0.314401 | − | 0.641983i | ||||
\(77\) | −12.0088 | − | 5.66766i | −1.36853 | − | 0.645889i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 9.32969i | − | 1.04967i | −0.851203 | − | 0.524836i | \(-0.824127\pi\) | ||
0.851203 | − | 0.524836i | \(-0.175873\pi\) | |||||||
\(80\) | −12.3545 | − | 9.58827i | −1.38128 | − | 1.07200i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.81228 | − | 1.13040i | −0.200133 | − | 0.124832i | ||||
\(83\) | −5.76701 | −0.633012 | −0.316506 | − | 0.948591i | \(-0.602510\pi\) | ||||
−0.316506 | + | 0.948591i | \(0.602510\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.42347 | 1.02212 | ||||||||
\(86\) | −2.13060 | − | 1.32895i | −0.229748 | − | 0.143305i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.44965 | − | 14.1217i | 0.154533 | − | 1.50538i | ||||
\(89\) | 17.6553i | 1.87146i | 0.352722 | + | 0.935728i | \(0.385256\pi\) | ||||
−0.352722 | + | 0.935728i | \(0.614744\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.3909 | − | 6.31997i | −1.40375 | − | 0.662513i | ||||
\(92\) | −6.20135 | + | 3.03702i | −0.646536 | + | 0.316631i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.78603 | + | 2.86339i | −0.184215 | + | 0.295336i | ||||
\(95\) | 12.1822i | 1.24986i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.5685i | 1.58074i | 0.612630 | + | 0.790370i | \(0.290112\pi\) | ||||
−0.612630 | + | 0.790370i | \(0.709888\pi\) | |||||||
\(98\) | 9.81445 | − | 1.29480i | 0.991409 | − | 0.130795i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.04769 | + | 18.4747i | 0.904769 | + | 1.84747i | ||||
\(101\) | − | 5.42001i | − | 0.539311i | −0.962957 | − | 0.269655i | \(-0.913090\pi\) | ||
0.962957 | − | 0.269655i | \(-0.0869098\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.89196 | 0.482019 | 0.241009 | − | 0.970523i | \(-0.422522\pi\) | ||||
0.241009 | + | 0.970523i | \(0.422522\pi\) | |||||||
\(104\) | 1.61649 | − | 15.7470i | 0.158510 | − | 1.54412i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.21174 | + | 6.75232i | −0.409080 | + | 0.655844i | ||||
\(107\) | − | 12.4743i | − | 1.20594i | −0.797766 | − | 0.602968i | \(-0.793985\pi\) | ||
0.797766 | − | 0.602968i | \(-0.206015\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.90489 | 0.565586 | 0.282793 | − | 0.959181i | \(-0.408739\pi\) | ||||
0.282793 | + | 0.959181i | \(0.408739\pi\) | |||||||
\(110\) | −14.6866 | + | 23.5458i | −1.40031 | + | 2.24501i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.79138 | + | 9.43624i | 0.452743 | + | 0.891641i | ||||
\(113\) | −15.3353 | −1.44262 | −0.721311 | − | 0.692611i | \(-0.756460\pi\) | ||||
−0.721311 | + | 0.692611i | \(0.756460\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.4983 | 1.25873 | ||||||||
\(116\) | 4.19579 | + | 8.56748i | 0.389569 | + | 0.795470i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.77564 | + | 7.65638i | −0.439633 | + | 0.704827i | ||||
\(119\) | −5.76701 | − | 2.72179i | −0.528661 | − | 0.249506i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14.1905 | −1.29004 | ||||||||
\(122\) | 8.33209 | + | 5.19711i | 0.754352 | + | 0.470524i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.424352 | − | 0.866493i | −0.0381079 | − | 0.0778134i | ||||
\(125\) | − | 20.6650i | − | 1.84833i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 0.910906i | − | 0.0808298i | −0.999183 | − | 0.0404149i | \(-0.987132\pi\) | ||
0.999183 | − | 0.0404149i | \(-0.0128680\pi\) | |||||||
\(128\) | −7.81300 | + | 8.18273i | −0.690578 | + | 0.723258i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −16.3770 | + | 26.2558i | −1.43636 | + | 2.30279i | ||||
\(131\) | −15.9421 | −1.39286 | −0.696432 | − | 0.717623i | \(-0.745230\pi\) | ||||
−0.696432 | + | 0.717623i | \(0.745230\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.51859 | − | 7.45528i | 0.305100 | − | 0.646455i | ||||
\(134\) | 4.70445 | + | 2.93439i | 0.406403 | + | 0.253492i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.696168 | − | 6.78170i | 0.0596959 | − | 0.581526i | ||||
\(137\) | −0.627922 | −0.0536470 | −0.0268235 | − | 0.999640i | \(-0.508539\pi\) | ||||
−0.0268235 | + | 0.999640i | \(0.508539\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.3643 | 1.47282 | 0.736409 | − | 0.676537i | \(-0.236520\pi\) | ||||
0.736409 | + | 0.676537i | \(0.236520\pi\) | |||||||
\(140\) | −0.298677 | − | 20.6859i | −0.0252428 | − | 1.74828i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.90209 | − | 6.17639i | −0.830965 | − | 0.518311i | ||||
\(143\) | −28.0898 | −2.34899 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 18.6486i | − | 1.54868i | ||||||
\(146\) | −4.30965 | − | 2.68813i | −0.356669 | − | 0.222471i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.19421 | − | 10.6062i | −0.426962 | − | 0.871822i | ||||
\(149\) | −0.726607 | −0.0595259 | −0.0297630 | − | 0.999557i | \(-0.509475\pi\) | ||||
−0.0297630 | + | 0.999557i | \(0.509475\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 6.27377i | − | 0.510552i | −0.966868 | − | 0.255276i | \(-0.917834\pi\) | ||
0.966868 | − | 0.255276i | \(-0.0821663\pi\) | |||||||
\(152\) | 8.76701 | + | 0.899968i | 0.711099 | + | 0.0729970i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 15.7887 | − | 10.1677i | 1.27229 | − | 0.819338i | ||||
\(155\) | 1.88608i | 0.151493i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.9958i | 1.59584i | 0.602765 | + | 0.797919i | \(0.294066\pi\) | ||||
−0.602765 | + | 0.797919i | \(0.705934\pi\) | |||||||
\(158\) | 11.1949 | + | 6.98280i | 0.890621 | + | 0.555522i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 20.7520 | − | 7.64819i | 1.64059 | − | 0.604643i | ||||
\(161\) | −8.26077 | − | 3.89874i | −0.651040 | − | 0.307264i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.0490i | 1.41371i | 0.707360 | + | 0.706854i | \(0.249886\pi\) | ||||
−0.707360 | + | 0.706854i | \(0.750114\pi\) | |||||||
\(164\) | 2.71280 | − | 1.32855i | 0.211834 | − | 0.103743i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.31632 | − | 6.91999i | 0.335011 | − | 0.537095i | ||||
\(167\) | 19.7035 | 1.52470 | 0.762350 | − | 0.647164i | \(-0.224045\pi\) | ||||
0.762350 | + | 0.647164i | \(0.224045\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −18.3228 | −1.40944 | ||||||||
\(170\) | −7.05300 | + | 11.3075i | −0.540940 | + | 0.867244i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.18929 | − | 1.56191i | 0.243181 | − | 0.119094i | ||||
\(173\) | − | 0.621296i | − | 0.0472363i | −0.999721 | − | 0.0236181i | \(-0.992481\pi\) | ||
0.999721 | − | 0.0236181i | \(-0.00751859\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.6149 | + | 24.6099i | −0.878002 | + | 1.86034i | ||||
\(176\) | 15.8600 | + | 12.3089i | 1.19549 | + | 0.927815i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −21.1850 | − | 13.2141i | −1.58789 | − | 0.990438i | ||||
\(179\) | − | 12.1294i | − | 0.906591i | −0.891360 | − | 0.453296i | \(-0.850248\pi\) | ||
0.891360 | − | 0.453296i | \(-0.149752\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 21.5510i | − | 1.60187i | −0.598750 | − | 0.800936i | \(-0.704336\pi\) | ||
0.598750 | − | 0.800936i | \(-0.295664\pi\) | |||||||
\(182\) | 17.6059 | − | 11.3380i | 1.30504 | − | 0.840426i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.997202 | − | 9.71422i | 0.0735147 | − | 0.716142i | ||||
\(185\) | 23.0862i | 1.69733i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.0973 | −0.884642 | ||||||||
\(188\) | −2.09910 | − | 4.28620i | −0.153093 | − | 0.312604i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −14.6177 | − | 9.11773i | −1.06048 | − | 0.661470i | ||||
\(191\) | − | 12.3487i | − | 0.893519i | −0.894654 | − | 0.446759i | \(-0.852578\pi\) | ||
0.894654 | − | 0.446759i | \(-0.147422\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.0526 | 1.29946 | 0.649728 | − | 0.760167i | \(-0.274883\pi\) | ||||
0.649728 | + | 0.760167i | \(0.274883\pi\) | |||||||
\(194\) | −18.6810 | − | 11.6522i | −1.34122 | − | 0.836581i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.79195 | + | 12.7457i | −0.413711 | + | 0.910408i | ||||
\(197\) | 6.84502 | 0.487687 | 0.243844 | − | 0.969815i | \(-0.421592\pi\) | ||||
0.243844 | + | 0.969815i | \(0.421592\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.4174 | −0.880246 | −0.440123 | − | 0.897937i | \(-0.645065\pi\) | ||||
−0.440123 | + | 0.897937i | \(0.645065\pi\) | |||||||
\(200\) | −28.9400 | − | 2.97080i | −2.04637 | − | 0.210067i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.50361 | + | 4.05660i | 0.457592 | + | 0.285421i | ||||
\(203\) | −5.38630 | + | 11.4127i | −0.378044 | + | 0.801011i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.90489 | −0.412415 | ||||||||
\(206\) | −3.66138 | + | 5.86999i | −0.255101 | + | 0.408982i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 17.6854 | + | 13.7255i | 1.22626 | + | 0.951695i | ||||
\(209\) | − | 15.6387i | − | 1.08175i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 20.0194i | − | 1.37819i | −0.724671 | − | 0.689095i | \(-0.758008\pi\) | ||
0.724671 | − | 0.689095i | \(-0.241992\pi\) | |||||||
\(212\) | −4.95002 | − | 10.1075i | −0.339969 | − | 0.694189i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 14.9682 | + | 9.33638i | 1.02321 | + | 0.638222i | ||||
\(215\) | −6.94206 | −0.473445 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.544757 | − | 1.15425i | 0.0369805 | − | 0.0783555i | ||||
\(218\) | −4.41951 | + | 7.08543i | −0.299327 | + | 0.479886i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −17.2611 | − | 35.2457i | −1.16374 | − | 2.37627i | ||||
\(221\) | −13.4896 | −0.907410 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.3982 | −1.76775 | −0.883876 | − | 0.467722i | \(-0.845075\pi\) | ||||
−0.883876 | + | 0.467722i | \(0.845075\pi\) | |||||||
\(224\) | −14.9089 | − | 1.31325i | −0.996143 | − | 0.0877449i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.4777 | − | 18.4012i | 0.763484 | − | 1.22403i | ||||
\(227\) | 2.00560 | 0.133116 | 0.0665580 | − | 0.997783i | \(-0.478798\pi\) | ||||
0.0665580 | + | 0.997783i | \(0.478798\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 14.3991i | − | 0.951520i | −0.879575 | − | 0.475760i | \(-0.842173\pi\) | ||
0.879575 | − | 0.475760i | \(-0.157827\pi\) | |||||||
\(230\) | −10.1028 | + | 16.1970i | −0.666161 | + | 1.06800i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −13.4207 | − | 1.37768i | −0.881111 | − | 0.0904494i | ||||
\(233\) | −12.6031 | −0.825658 | −0.412829 | − | 0.910809i | \(-0.635459\pi\) | ||||
−0.412829 | + | 0.910809i | \(0.635459\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.32969i | 0.608602i | ||||||||
\(236\) | −5.61277 | − | 11.4608i | −0.365360 | − | 0.746036i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.58227 | − | 4.88287i | 0.491485 | − | 0.316509i | ||||
\(239\) | 2.58274i | 0.167064i | 0.996505 | + | 0.0835319i | \(0.0266201\pi\) | ||||
−0.996505 | + | 0.0835319i | \(0.973380\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.63816i | 0.620848i | 0.950598 | + | 0.310424i | \(0.100471\pi\) | ||||
−0.950598 | + | 0.310424i | \(0.899529\pi\) | |||||||
\(242\) | 10.6209 | − | 17.0275i | 0.682735 | − | 1.09457i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −12.4723 | + | 6.10812i | −0.798457 | + | 0.391032i | ||||
\(245\) | 21.1270 | − | 17.3967i | 1.34975 | − | 1.11143i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 17.4387i | − | 1.10960i | ||||||
\(248\) | 1.35733 | + | 0.139336i | 0.0861908 | + | 0.00884782i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 24.7965 | + | 15.4667i | 1.56827 | + | 0.978201i | ||||
\(251\) | 12.9421 | 0.816896 | 0.408448 | − | 0.912782i | \(-0.366070\pi\) | ||||
0.408448 | + | 0.912782i | \(0.366070\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.3284 | −1.08942 | ||||||||
\(254\) | 1.09302 | + | 0.681767i | 0.0685822 | + | 0.0427779i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.97103 | − | 15.4994i | −0.248189 | − | 0.968712i | ||||
\(257\) | 19.7541i | 1.23223i | 0.787658 | + | 0.616113i | \(0.211294\pi\) | ||||
−0.787658 | + | 0.616113i | \(0.788706\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.66802 | − | 14.1284i | 0.414331 | − | 0.877896i | ||||
\(260\) | −19.2477 | − | 39.3023i | −1.19369 | − | 2.43743i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 11.9318 | − | 19.1293i | 0.737151 | − | 1.18181i | ||||
\(263\) | 4.77439i | 0.294401i | 0.989107 | + | 0.147201i | \(0.0470263\pi\) | ||||
−0.989107 | + | 0.147201i | \(0.952974\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 22.0009i | 1.35150i | ||||||||
\(266\) | 6.31230 | + | 9.80194i | 0.387032 | + | 0.600996i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.04209 | + | 3.44876i | −0.430164 | + | 0.210666i | ||||
\(269\) | 2.19366i | 0.133750i | 0.997761 | + | 0.0668750i | \(0.0213029\pi\) | ||||
−0.997761 | + | 0.0668750i | \(0.978697\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.5797 | −0.764163 | −0.382081 | − | 0.924129i | \(-0.624793\pi\) | ||||
−0.382081 | + | 0.924129i | \(0.624793\pi\) | |||||||
\(272\) | 7.61649 | + | 5.91111i | 0.461818 | + | 0.358414i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.469968 | − | 0.753460i | 0.0283918 | − | 0.0455182i | ||||
\(275\) | 51.6235i | 3.11302i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.7035 | 1.30404 | 0.652018 | − | 0.758204i | \(-0.273923\pi\) | ||||
0.652018 | + | 0.758204i | \(0.273923\pi\) | |||||||
\(278\) | −12.9963 | + | 20.8358i | −0.779465 | + | 1.24965i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 25.0451 | + | 15.1240i | 1.49673 | + | 0.903831i | ||||
\(281\) | 18.2595 | 1.08927 | 0.544635 | − | 0.838673i | \(-0.316668\pi\) | ||||
0.544635 | + | 0.838673i | \(0.316668\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.88324 | −0.290279 | −0.145139 | − | 0.989411i | \(-0.546363\pi\) | ||||
−0.145139 | + | 0.989411i | \(0.546363\pi\) | |||||||
\(284\) | 14.8224 | − | 7.25906i | 0.879550 | − | 0.430746i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 21.0238 | − | 33.7057i | 1.24316 | − | 1.99306i | ||||
\(287\) | 3.61370 | + | 1.70552i | 0.213310 | + | 0.100673i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.1905 | 0.658264 | ||||||||
\(290\) | 22.3770 | + | 13.9576i | 1.31402 | + | 0.819616i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.45111 | − | 3.15933i | 0.377522 | − | 0.184886i | ||||
\(293\) | − | 15.2450i | − | 0.890622i | −0.895376 | − | 0.445311i | \(-0.853093\pi\) | ||
0.895376 | − | 0.445311i | \(-0.146907\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.9465i | 1.45244i | ||||||||
\(296\) | 16.6142 | + | 1.70552i | 0.965683 | + | 0.0991311i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.543828 | − | 0.871874i | 0.0315031 | − | 0.0505063i | ||||
\(299\) | −19.3228 | −1.11746 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.24843 | + | 2.00508i | 0.244875 | + | 0.115571i | ||||
\(302\) | 7.52806 | + | 4.69560i | 0.433191 | + | 0.270201i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.64156 | + | 9.84619i | −0.438274 | + | 0.564718i | ||||
\(305\) | 27.1482 | 1.55450 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.30173 | 0.359659 | 0.179829 | − | 0.983698i | \(-0.442445\pi\) | ||||
0.179829 | + | 0.983698i | \(0.442445\pi\) | |||||||
\(308\) | 0.383424 | + | 26.5554i | 0.0218476 | + | 1.51313i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.26315 | − | 1.41163i | −0.128538 | − | 0.0801754i | ||||
\(311\) | 18.4761 | 1.04768 | 0.523841 | − | 0.851816i | \(-0.324498\pi\) | ||||
0.523841 | + | 0.851816i | \(0.324498\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.7951i | 1.06236i | 0.847258 | + | 0.531181i | \(0.178252\pi\) | ||||
−0.847258 | + | 0.531181i | \(0.821748\pi\) | |||||||
\(314\) | −23.9935 | − | 14.9658i | −1.35403 | − | 0.844571i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.7577 | + | 8.20682i | −0.942694 | + | 0.461670i | ||||
\(317\) | −2.06678 | −0.116082 | −0.0580410 | − | 0.998314i | \(-0.518485\pi\) | ||||
−0.0580410 | + | 0.998314i | \(0.518485\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23.9400i | 1.34038i | ||||||||
\(320\) | −6.35454 | + | 30.6251i | −0.355229 | + | 1.71200i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 10.8610 | − | 6.99430i | 0.605258 | − | 0.389777i | ||||
\(323\) | − | 7.51022i | − | 0.417880i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 57.5651i | 3.19314i | ||||||||
\(326\) | −21.6575 | − | 13.5088i | −1.19950 | − | 0.748182i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.436229 | + | 4.24951i | −0.0240867 | + | 0.234640i | ||||
\(329\) | 2.69470 | − | 5.70962i | 0.148564 | − | 0.314781i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.2531i | 1.71783i | 0.512121 | + | 0.858913i | \(0.328860\pi\) | ||||
−0.512121 | + | 0.858913i | \(0.671140\pi\) | |||||||
\(332\) | 5.07293 | + | 10.3585i | 0.278413 | + | 0.568498i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −14.7471 | + | 23.6427i | −0.806923 | + | 1.29367i | ||||
\(335\) | 15.3284 | 0.837478 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.4550 | 0.787417 | 0.393708 | − | 0.919235i | \(-0.371192\pi\) | ||||
0.393708 | + | 0.919235i | \(0.371192\pi\) | |||||||
\(338\) | 13.7137 | − | 21.9860i | 0.745925 | − | 1.19588i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8.28932 | − | 16.9262i | −0.449552 | − | 0.917949i | ||||
\(341\) | − | 2.42123i | − | 0.131117i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.9541 | + | 4.54436i | −0.969429 | + | 0.245373i | ||||
\(344\) | −0.512851 | + | 4.99592i | −0.0276511 | + | 0.269362i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.745510 | + | 0.465009i | 0.0400789 | + | 0.0249990i | ||||
\(347\) | − | 16.6510i | − | 0.893871i | −0.894566 | − | 0.446936i | \(-0.852515\pi\) | ||
0.894566 | − | 0.446936i | \(-0.147485\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.0294i | 0.911561i | 0.890092 | + | 0.455781i | \(0.150640\pi\) | ||||
−0.890092 | + | 0.455781i | \(0.849360\pi\) | |||||||
\(350\) | −20.8370 | − | 32.3563i | −1.11378 | − | 1.72952i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −26.6401 | + | 9.81829i | −1.41992 | + | 0.523317i | ||||
\(353\) | 26.9850i | 1.43627i | 0.695906 | + | 0.718133i | \(0.255003\pi\) | ||||
−0.695906 | + | 0.718133i | \(0.744997\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −32.2637 | −1.71238 | ||||||||
\(356\) | 31.7119 | − | 15.5304i | 1.68073 | − | 0.823110i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14.5543 | + | 9.07822i | 0.769221 | + | 0.479799i | ||||
\(359\) | − | 12.9242i | − | 0.682112i | −0.940043 | − | 0.341056i | \(-0.889215\pi\) | ||
0.940043 | − | 0.341056i | \(-0.110785\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.29119 | −0.489010 | ||||||||
\(362\) | 25.8596 | + | 16.1298i | 1.35915 | + | 0.847765i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.427554 | + | 29.6117i | 0.0224099 | + | 1.55208i | ||||
\(365\) | −14.0420 | −0.734991 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 33.8798 | 1.76851 | 0.884256 | − | 0.467003i | \(-0.154666\pi\) | ||||
0.884256 | + | 0.467003i | \(0.154666\pi\) | |||||||
\(368\) | 10.9100 | + | 8.46717i | 0.568723 | + | 0.441382i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −27.7018 | − | 17.2789i | −1.44015 | − | 0.898286i | ||||
\(371\) | 6.35454 | − | 13.4642i | 0.329911 | − | 0.699025i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.1849 | 0.734466 | 0.367233 | − | 0.930129i | \(-0.380305\pi\) | ||||
0.367233 | + | 0.930129i | \(0.380305\pi\) | |||||||
\(374\) | 9.05421 | − | 14.5159i | 0.468182 | − | 0.750597i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.71420 | + | 0.689239i | 0.346259 | + | 0.0355448i | ||||
\(377\) | 26.6954i | 1.37488i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 10.5772i | − | 0.543313i | −0.962394 | − | 0.271657i | \(-0.912429\pi\) | ||
0.962394 | − | 0.271657i | \(-0.0875715\pi\) | |||||||
\(380\) | 21.8812 | − | 10.7160i | 1.12248 | − | 0.549719i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 14.8175 | + | 9.24236i | 0.758129 | + | 0.472880i | ||||
\(383\) | 15.1477 | 0.774012 | 0.387006 | − | 0.922077i | \(-0.373509\pi\) | ||||
0.387006 | + | 0.922077i | \(0.373509\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 22.1587 | − | 46.9505i | 1.12931 | − | 2.39282i | ||||
\(386\) | −13.5115 | + | 21.6618i | −0.687716 | + | 1.10256i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 27.9636 | − | 13.6948i | 1.41964 | − | 0.695246i | ||||
\(389\) | −28.1976 | −1.42968 | −0.714838 | − | 0.699290i | \(-0.753500\pi\) | ||||
−0.714838 | + | 0.699290i | \(0.753500\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.32164 | −0.420844 | ||||||||
\(392\) | −10.9589 | − | 16.4894i | −0.553510 | − | 0.832843i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.12315 | + | 8.21352i | −0.258101 | + | 0.413791i | ||||
\(395\) | 36.4761 | 1.83531 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.98758i | 0.400885i | 0.979705 | + | 0.200443i | \(0.0642380\pi\) | ||||
−0.979705 | + | 0.200443i | \(0.935762\pi\) | |||||||
\(398\) | 9.29380 | − | 14.9000i | 0.465856 | − | 0.746868i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 25.2249 | − | 32.5024i | 1.26124 | − | 1.62512i | ||||
\(401\) | −11.8129 | −0.589908 | −0.294954 | − | 0.955512i | \(-0.595304\pi\) | ||||
−0.294954 | + | 0.955512i | \(0.595304\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 2.69990i | − | 0.134492i | ||||||
\(404\) | −9.73524 | + | 4.76769i | −0.484347 | + | 0.237201i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.66297 | − | 15.0050i | −0.479565 | − | 0.744684i | ||||
\(407\) | − | 29.6367i | − | 1.46904i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.79736i | 0.336108i | 0.985778 | + | 0.168054i | \(0.0537483\pi\) | ||||
−0.985778 | + | 0.168054i | \(0.946252\pi\) | |||||||
\(410\) | 4.41951 | − | 7.08543i | 0.218264 | − | 0.349925i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.30319 | − | 8.78678i | −0.212003 | − | 0.432894i | ||||
\(413\) | 7.20533 | − | 15.2669i | 0.354551 | − | 0.751233i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 22.5472i | − | 1.10680i | ||||||
\(416\) | −29.7063 | + | 10.9483i | −1.45647 | + | 0.536786i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 18.7653 | + | 11.7048i | 0.917841 | + | 0.572500i | ||||
\(419\) | −15.7091 | −0.767438 | −0.383719 | − | 0.923450i | \(-0.625357\pi\) | ||||
−0.383719 | + | 0.923450i | \(0.625357\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.0154 | 0.585597 | 0.292798 | − | 0.956174i | \(-0.405414\pi\) | ||||
0.292798 | + | 0.956174i | \(0.405414\pi\) | |||||||
\(422\) | 24.0218 | + | 14.9835i | 1.16936 | + | 0.729385i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 15.8332 | + | 1.62533i | 0.768926 | + | 0.0789332i | ||||
\(425\) | 24.7913i | 1.20255i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.6142 | − | 7.84124i | −0.804019 | − | 0.379464i | ||||
\(428\) | −22.4059 | + | 10.9730i | −1.08303 | + | 0.530398i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.19578 | − | 8.32996i | 0.250563 | − | 0.401706i | ||||
\(431\) | 10.0380i | 0.483515i | 0.970337 | + | 0.241757i | \(0.0777238\pi\) | ||||
−0.970337 | + | 0.241757i | \(0.922276\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.7389i | 1.23693i | 0.785811 | + | 0.618467i | \(0.212246\pi\) | ||||
−0.785811 | + | 0.618467i | \(0.787754\pi\) | |||||||
\(434\) | 0.977289 | + | 1.51757i | 0.0469114 | + | 0.0728455i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.19421 | − | 10.6062i | −0.248758 | − | 0.507944i | ||||
\(437\) | − | 10.7578i | − | 0.514614i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −28.6653 | −1.36812 | −0.684061 | − | 0.729425i | \(-0.739788\pi\) | ||||
−0.684061 | + | 0.729425i | \(0.739788\pi\) | |||||||
\(440\) | 55.2113 | + | 5.66766i | 2.63210 | + | 0.270195i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 10.0963 | − | 16.1866i | 0.480232 | − | 0.769916i | ||||
\(443\) | 3.16702i | 0.150470i | 0.997166 | + | 0.0752348i | \(0.0239706\pi\) | ||||
−0.997166 | + | 0.0752348i | \(0.976029\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −69.0265 | −3.27217 | ||||||||
\(446\) | 19.7577 | − | 31.6758i | 0.935554 | − | 1.49989i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 12.7344 | − | 16.9067i | 0.601642 | − | 0.798766i | ||||
\(449\) | 32.1416 | 1.51685 | 0.758427 | − | 0.651758i | \(-0.225968\pi\) | ||||
0.758427 | + | 0.651758i | \(0.225968\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.58034 | 0.356944 | ||||||||
\(452\) | 13.4896 | + | 27.5448i | 0.634499 | + | 1.29560i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.50109 | + | 2.40657i | −0.0704495 | + | 0.112946i | ||||
\(455\) | 24.7091 | − | 52.3543i | 1.15838 | − | 2.45441i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.4389 | 0.956092 | 0.478046 | − | 0.878335i | \(-0.341345\pi\) | ||||
0.478046 | + | 0.878335i | \(0.341345\pi\) | |||||||
\(458\) | 17.2779 | + | 10.7770i | 0.807342 | + | 0.503577i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −11.8738 | − | 24.2453i | −0.553617 | − | 1.13044i | ||||
\(461\) | − | 6.14287i | − | 0.286102i | −0.989715 | − | 0.143051i | \(-0.954309\pi\) | ||
0.989715 | − | 0.143051i | \(-0.0456913\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.13162i | 0.0990649i | 0.998773 | + | 0.0495324i | \(0.0157731\pi\) | ||||
−0.998773 | + | 0.0495324i | \(0.984227\pi\) | |||||||
\(464\) | 11.6978 | − | 15.0727i | 0.543058 | − | 0.699732i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.43280 | − | 15.1228i | 0.436966 | − | 0.700551i | ||||
\(467\) | 11.4817 | 0.531309 | 0.265654 | − | 0.964068i | \(-0.414412\pi\) | ||||
0.265654 | + | 0.964068i | \(0.414412\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.38071 | − | 4.42731i | −0.433161 | − | 0.204434i | ||||
\(470\) | −11.1949 | − | 6.98280i | −0.516384 | − | 0.322093i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 17.9530 | + | 1.84295i | 0.826355 | + | 0.0848285i | ||||
\(473\) | 8.91180 | 0.409765 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −32.0489 | −1.47050 | ||||||||
\(476\) | 0.184133 | + | 12.7527i | 0.00843971 | + | 0.584521i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.09910 | − | 1.93305i | −0.141750 | − | 0.0884159i | ||||
\(479\) | −14.3863 | −0.657327 | −0.328664 | − | 0.944447i | \(-0.606598\pi\) | ||||
−0.328664 | + | 0.944447i | \(0.606598\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 33.0477i | − | 1.50685i | ||||||
\(482\) | −11.5651 | − | 7.21368i | −0.526775 | − | 0.328574i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 12.4826 | + | 25.4885i | 0.567391 | + | 1.15857i | ||||
\(485\) | −60.8678 | −2.76386 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 20.3888i | − | 0.923904i | −0.886905 | − | 0.461952i | \(-0.847149\pi\) | ||
0.886905 | − | 0.461952i | \(-0.152851\pi\) | |||||||
\(488\) | 2.00560 | − | 19.5375i | 0.0907890 | − | 0.884419i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 5.06227 | + | 38.3714i | 0.228690 | + | 1.73344i | ||||
\(491\) | − | 19.9296i | − | 0.899409i | −0.893177 | − | 0.449705i | \(-0.851529\pi\) | ||
0.893177 | − | 0.449705i | \(-0.148471\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.4968i | 0.517788i | ||||||||
\(494\) | 20.9251 | + | 13.0520i | 0.941465 | + | 0.587235i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.18309 | + | 1.52442i | −0.0531222 | + | 0.0684483i | ||||
\(497\) | 19.7448 | + | 9.31875i | 0.885677 | + | 0.418003i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.62706i | 0.341434i | 0.985320 | + | 0.170717i | \(0.0546084\pi\) | ||||
−0.985320 | + | 0.170717i | \(0.945392\pi\) | |||||||
\(500\) | −37.1178 | + | 18.1779i | −1.65996 | + | 0.812940i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9.68648 | + | 15.5295i | −0.432329 | + | 0.693116i | ||||
\(503\) | −30.4761 | −1.35886 | −0.679431 | − | 0.733740i | \(-0.737773\pi\) | ||||
−0.679431 | + | 0.733740i | \(0.737773\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.1905 | 0.942964 | ||||||||
\(506\) | 12.9694 | − | 20.7928i | 0.576560 | − | 0.924351i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.63614 | + | 0.801275i | −0.0725920 | + | 0.0355508i | ||||
\(509\) | − | 6.22512i | − | 0.275923i | −0.990438 | − | 0.137962i | \(-0.955945\pi\) | ||
0.990438 | − | 0.137962i | \(-0.0440551\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.59346 | + | 4.05576i | 0.380152 | + | 0.179416i | ||||
\(512\) | 21.5702 | + | 6.83557i | 0.953279 | + | 0.302092i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −23.7035 | − | 14.7849i | −1.04551 | − | 0.652136i | ||||
\(515\) | 19.1260i | 0.842792i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 11.9769i | − | 0.526743i | ||||||
\(518\) | 11.9624 | + | 18.5755i | 0.525596 | + | 0.816162i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 61.5659 | + | 6.31997i | 2.69984 | + | 0.277149i | ||||
\(521\) | − | 4.99769i | − | 0.218953i | −0.993989 | − | 0.109476i | \(-0.965083\pi\) | ||
0.993989 | − | 0.109476i | \(-0.0349174\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.95318 | 0.216587 | 0.108294 | − | 0.994119i | \(-0.465461\pi\) | ||||
0.108294 | + | 0.994119i | \(0.465461\pi\) | |||||||
\(524\) | 14.0234 | + | 28.6346i | 0.612614 | + | 1.25091i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.72891 | − | 3.57339i | −0.249792 | − | 0.155807i | ||||
\(527\) | − | 1.16275i | − | 0.0506504i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0799 | 0.481736 | ||||||||
\(530\) | −26.3994 | − | 16.4665i | −1.14672 | − | 0.715261i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −16.4861 | + | 0.238037i | −0.714761 | + | 0.0103202i | ||||
\(533\) | 8.45280 | 0.366131 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 48.7705 | 2.10853 | ||||||||
\(536\) | 1.13240 | − | 11.0312i | 0.0489121 | − | 0.476476i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.63224 | − | 1.64185i | −0.113484 | − | 0.0707851i | ||||
\(539\) | −27.1215 | + | 22.3328i | −1.16821 | + | 0.961943i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −31.8044 | −1.36738 | −0.683690 | − | 0.729773i | \(-0.739626\pi\) | ||||
−0.683690 | + | 0.729773i | \(0.739626\pi\) | |||||||
\(542\) | 9.41527 | − | 15.0947i | 0.404421 | − | 0.648374i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −12.7935 | + | 4.71506i | −0.548515 | + | 0.202157i | ||||
\(545\) | 23.0862i | 0.988905i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40.9363i | 1.75031i | 0.483844 | + | 0.875154i | \(0.339240\pi\) | ||||
−0.483844 | + | 0.875154i | \(0.660760\pi\) | |||||||
\(548\) | 0.552349 | + | 1.12785i | 0.0235952 | + | 0.0481795i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −61.9445 | − | 38.6376i | −2.64132 | − | 1.64751i | ||||
\(551\) | −14.8624 | −0.633159 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −22.3228 | − | 10.5354i | −0.949261 | − | 0.448012i | ||||
\(554\) | −16.2440 | + | 26.0426i | −0.690140 | + | 1.10644i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15.2744 | − | 31.1891i | −0.647779 | − | 1.32271i | ||||
\(557\) | −13.9112 | −0.589435 | −0.294717 | − | 0.955584i | \(-0.595226\pi\) | ||||
−0.294717 | + | 0.955584i | \(0.595226\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.93750 | 0.420312 | ||||||||
\(560\) | −36.8927 | + | 18.7328i | −1.55900 | + | 0.791604i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13.6663 | + | 21.9100i | −0.576478 | + | 0.924219i | ||||
\(563\) | −37.5659 | −1.58321 | −0.791606 | − | 0.611032i | \(-0.790755\pi\) | ||||
−0.791606 | + | 0.611032i | \(0.790755\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 59.9561i | − | 2.52237i | ||||||
\(566\) | 3.65486 | − | 5.85953i | 0.153625 | − | 0.246294i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.38351 | + | 23.2189i | −0.100010 | + | 0.974242i | ||||
\(569\) | 4.83108 | 0.202529 | 0.101265 | − | 0.994860i | \(-0.467711\pi\) | ||||
0.101265 | + | 0.994860i | \(0.467711\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.4877i | 1.48511i | 0.669784 | + | 0.742556i | \(0.266387\pi\) | ||||
−0.669784 | + | 0.742556i | \(0.733613\pi\) | |||||||
\(572\) | 24.7091 | + | 50.4540i | 1.03314 | + | 2.10959i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.75116 | + | 3.05968i | −0.198310 | + | 0.127708i | ||||
\(575\) | 35.5115i | 1.48093i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.9331i | 0.455153i | 0.973760 | + | 0.227576i | \(0.0730801\pi\) | ||||
−0.973760 | + | 0.227576i | \(0.926920\pi\) | |||||||
\(578\) | −8.37552 | + | 13.4278i | −0.348376 | + | 0.558521i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −33.4961 | + | 16.4042i | −1.39085 | + | 0.681147i | ||||
\(581\) | −6.51232 | + | 13.7985i | −0.270177 | + | 0.572458i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 28.2434i | − | 1.16972i | ||||||
\(584\) | −1.03736 | + | 10.1055i | −0.0429264 | + | 0.418167i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18.2929 | + | 11.4101i | 0.755671 | + | 0.471347i | ||||
\(587\) | 12.1477 | 0.501390 | 0.250695 | − | 0.968066i | \(-0.419341\pi\) | ||||
0.250695 | + | 0.968066i | \(0.419341\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.50315 | 0.0619360 | ||||||||
\(590\) | −29.9340 | − | 18.6712i | −1.23236 | − | 0.768682i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −14.4814 | + | 18.6594i | −0.595182 | + | 0.766895i | ||||
\(593\) | − | 2.60504i | − | 0.106976i | −0.998568 | − | 0.0534882i | \(-0.982966\pi\) | ||
0.998568 | − | 0.0534882i | \(-0.0170339\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.6413 | − | 22.5472i | 0.436252 | − | 0.924344i | ||||
\(596\) | 0.639157 | + | 1.30511i | 0.0261809 | + | 0.0534593i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 14.4621 | − | 23.1859i | 0.591400 | − | 0.948142i | ||||
\(599\) | 34.5554i | 1.41190i | 0.708263 | + | 0.705948i | \(0.249479\pi\) | ||||
−0.708263 | + | 0.705948i | \(0.750521\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 12.3627i | − | 0.504286i | −0.967690 | − | 0.252143i | \(-0.918865\pi\) | ||
0.967690 | − | 0.252143i | \(-0.0811353\pi\) | |||||||
\(602\) | −5.58569 | + | 3.59710i | −0.227656 | + | 0.146607i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11.2687 | + | 5.51870i | −0.458519 | + | 0.224553i | ||||
\(605\) | − | 55.4803i | − | 2.25559i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.43840 | −0.139560 | −0.0697802 | − | 0.997562i | \(-0.522230\pi\) | ||||
−0.0697802 | + | 0.997562i | \(0.522230\pi\) | |||||||
\(608\) | −6.09538 | − | 16.5387i | −0.247200 | − | 0.670732i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −20.3190 | + | 32.5758i | −0.822694 | + | 1.31896i | ||||
\(611\) | − | 13.3554i | − | 0.540300i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.00000 | 0.0807792 | 0.0403896 | − | 0.999184i | \(-0.487140\pi\) | ||||
0.0403896 | + | 0.999184i | \(0.487140\pi\) | |||||||
\(614\) | −4.71653 | + | 7.56161i | −0.190344 | + | 0.305162i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −32.1514 | − | 19.4153i | −1.29542 | − | 0.782263i | ||||
\(617\) | 38.7921 | 1.56171 | 0.780856 | − | 0.624710i | \(-0.214783\pi\) | ||||
0.780856 | + | 0.624710i | \(0.214783\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 38.0592 | 1.52973 | 0.764865 | − | 0.644191i | \(-0.222806\pi\) | ||||
0.764865 | + | 0.644191i | \(0.222806\pi\) | |||||||
\(620\) | 3.38771 | − | 1.65908i | 0.136054 | − | 0.0666303i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −13.8284 | + | 22.1699i | −0.554469 | + | 0.888934i | ||||
\(623\) | 42.2431 | + | 19.9370i | 1.69243 | + | 0.798759i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 29.3655 | 1.17462 | ||||||||
\(626\) | −22.5527 | − | 14.0672i | −0.901389 | − | 0.562238i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 35.9158 | − | 17.5892i | 1.43320 | − | 0.701886i | ||||
\(629\) | − | 14.2325i | − | 0.567487i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 41.8076i | 1.66434i | 0.554524 | + | 0.832168i | \(0.312900\pi\) | ||||
−0.554524 | + | 0.832168i | \(0.687100\pi\) | |||||||
\(632\) | 2.69470 | − | 26.2504i | 0.107190 | − | 1.04418i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.54688 | − | 2.47999i | 0.0614345 | − | 0.0984928i | ||||
\(635\) | 3.56135 | 0.141328 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −30.2431 | + | 24.9032i | −1.19828 | + | 0.986702i | ||||
\(638\) | −28.7262 | − | 17.9179i | −1.13728 | − | 0.709376i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −31.9918 | − | 30.5463i | −1.26459 | − | 1.20745i | ||||
\(641\) | −29.5836 | −1.16848 | −0.584242 | − | 0.811580i | \(-0.698608\pi\) | ||||
−0.584242 | + | 0.811580i | \(0.698608\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −34.8510 | −1.37439 | −0.687194 | − | 0.726474i | \(-0.741158\pi\) | ||||
−0.687194 | + | 0.726474i | \(0.741158\pi\) | |||||||
\(644\) | 0.263755 | + | 18.2672i | 0.0103934 | + | 0.719830i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.01171 | + | 5.62102i | 0.354561 | + | 0.221156i | ||||
\(647\) | 22.8512 | 0.898373 | 0.449187 | − | 0.893438i | \(-0.351714\pi\) | ||||
0.449187 | + | 0.893438i | \(0.351714\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 32.0249i | − | 1.25709i | ||||||
\(650\) | −69.0739 | − | 43.0846i | −2.70930 | − | 1.68992i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 32.4191 | − | 15.8767i | 1.26963 | − | 0.621781i | ||||
\(653\) | 6.41751 | 0.251136 | 0.125568 | − | 0.992085i | \(-0.459925\pi\) | ||||
0.125568 | + | 0.992085i | \(0.459925\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 62.3284i | − | 2.43537i | ||||||
\(656\) | −4.77261 | − | 3.70399i | −0.186339 | − | 0.144617i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.83427 | + | 7.50680i | 0.188459 | + | 0.292646i | ||||
\(659\) | 3.31350i | 0.129076i | 0.997915 | + | 0.0645378i | \(0.0205573\pi\) | ||||
−0.997915 | + | 0.0645378i | \(0.979443\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.3760i | 1.02591i | 0.858416 | + | 0.512954i | \(0.171449\pi\) | ||||
−0.858416 | + | 0.512954i | \(0.828551\pi\) | |||||||
\(662\) | −37.5014 | − | 23.3914i | −1.45753 | − | 0.909132i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −16.2263 | − | 1.66569i | −0.629703 | − | 0.0646414i | ||||
\(665\) | 29.1478 | + | 13.7565i | 1.13030 | + | 0.533456i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.4682i | 0.637650i | ||||||||
\(668\) | −17.3321 | − | 35.3908i | −0.670599 | − | 1.36931i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −11.4725 | + | 18.3929i | −0.443222 | + | 0.710580i | ||||
\(671\) | −34.8512 | −1.34542 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.4389 | 0.787862 | 0.393931 | − | 0.919140i | \(-0.371115\pi\) | ||||
0.393931 | + | 0.919140i | \(0.371115\pi\) | |||||||
\(674\) | −10.8189 | + | 17.3450i | −0.416728 | + | 0.668104i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16.1176 | + | 32.9108i | 0.619906 | + | 1.26580i | ||||
\(677\) | 6.72464i | 0.258449i | 0.991615 | + | 0.129224i | \(0.0412488\pi\) | ||||
−0.991615 | + | 0.129224i | \(0.958751\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 37.2501 | + | 17.5805i | 1.42953 | + | 0.674678i | ||||
\(680\) | 26.5143 | + | 2.72179i | 1.01678 | + | 0.104376i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.90530 | + | 1.81217i | 0.111250 | + | 0.0693916i | ||||
\(683\) | − | 10.7935i | − | 0.413001i | −0.978446 | − | 0.206501i | \(-0.933792\pi\) | ||
0.978446 | − | 0.206501i | \(-0.0662075\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 2.45497i | − | 0.0937997i | ||||||
\(686\) | 7.98482 | − | 24.9448i | 0.304862 | − | 0.952397i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.61090 | − | 4.35458i | −0.213913 | − | 0.166017i | ||||
\(689\) | − | 31.4941i | − | 1.19983i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.9337 | 0.834398 | 0.417199 | − | 0.908815i | \(-0.363012\pi\) | ||||
0.417199 | + | 0.908815i | \(0.363012\pi\) | |||||||
\(692\) | −1.11595 | + | 0.546521i | −0.0424222 | + | 0.0207756i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 19.9799 | + | 12.4624i | 0.758428 | + | 0.473067i | ||||
\(695\) | 67.8887i | 2.57517i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.64033 | 0.137887 | ||||||||
\(698\) | −20.4340 | − | 12.7456i | −0.773438 | − | 0.482429i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 54.4206 | − | 0.785761i | 2.05691 | − | 0.0296990i | ||||
\(701\) | 18.3612 | 0.693493 | 0.346747 | − | 0.937959i | \(-0.387286\pi\) | ||||
0.346747 | + | 0.937959i | \(0.387286\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.3990 | 0.693932 | ||||||||
\(704\) | 8.15757 | − | 39.3147i | 0.307450 | − | 1.48173i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −32.3800 | − | 20.1969i | −1.21864 | − | 0.760120i | ||||
\(707\) | −12.9682 | − | 6.12047i | −0.487721 | − | 0.230184i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.9463 | −1.08710 | −0.543551 | − | 0.839376i | \(-0.682920\pi\) | ||||
−0.543551 | + | 0.839376i | \(0.682920\pi\) | |||||||
\(710\) | 24.1477 | − | 38.7140i | 0.906248 | − | 1.45291i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.09940 | + | 49.6756i | −0.191108 | + | 1.86167i | ||||
\(713\) | − | 1.66555i | − | 0.0623753i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 109.822i | − | 4.10711i | ||||||
\(716\) | −21.7864 | + | 10.6696i | −0.814196 | + | 0.398740i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 15.5081 | + | 9.67310i | 0.578756 | + | 0.360997i | ||||
\(719\) | −9.14772 | −0.341152 | −0.170576 | − | 0.985344i | \(-0.554563\pi\) | ||||
−0.170576 | + | 0.985344i | \(0.554563\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.52418 | − | 11.7048i | 0.205731 | − | 0.435909i | ||||
\(722\) | 6.95399 | − | 11.1487i | 0.258801 | − | 0.414913i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −38.7092 | + | 18.9572i | −1.43862 | + | 0.704540i | ||||
\(725\) | 49.0609 | 1.82208 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.7308 | 0.546334 | 0.273167 | − | 0.961967i | \(-0.411929\pi\) | ||||
0.273167 | + | 0.961967i | \(0.411929\pi\) | |||||||
\(728\) | −35.8519 | − | 21.6499i | −1.32876 | − | 0.802397i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 10.5097 | − | 16.8493i | 0.388982 | − | 0.623622i | ||||
\(731\) | 4.27974 | 0.158292 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.2453i | 0.895521i | 0.894154 | + | 0.447760i | \(0.147778\pi\) | ||||
−0.894154 | + | 0.447760i | \(0.852222\pi\) | |||||||
\(734\) | −25.3573 | + | 40.6533i | −0.935956 | + | 1.50054i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −18.3256 | + | 6.75394i | −0.675489 | + | 0.248953i | ||||
\(737\) | −19.6776 | −0.724835 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 31.2993i | − | 1.15136i | −0.817674 | − | 0.575682i | \(-0.804737\pi\) | ||
0.817674 | − | 0.575682i | \(-0.195263\pi\) | |||||||
\(740\) | 41.4668 | − | 20.3077i | 1.52435 | − | 0.746526i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11.4000 | + | 17.7022i | 0.418506 | + | 0.649869i | ||||
\(743\) | − | 35.0388i | − | 1.28545i | −0.766098 | − | 0.642724i | \(-0.777804\pi\) | ||
0.766098 | − | 0.642724i | \(-0.222196\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 2.84080i | − | 0.104079i | ||||||
\(746\) | −10.6167 | + | 17.0208i | −0.388704 | + | 0.623177i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 10.6413 | + | 21.7288i | 0.389086 | + | 0.794483i | ||||
\(749\) | −29.8467 | − | 14.0864i | −1.09058 | − | 0.514707i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 12.7356i | − | 0.464728i | −0.972629 | − | 0.232364i | \(-0.925354\pi\) | ||
0.972629 | − | 0.232364i | \(-0.0746460\pi\) | |||||||
\(752\) | −5.85228 | + | 7.54069i | −0.213411 | + | 0.274981i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −32.0325 | − | 19.9801i | −1.16655 | − | 0.727633i | ||||
\(755\) | 24.5284 | 0.892681 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.8565 | −0.467278 | −0.233639 | − | 0.972323i | \(-0.575063\pi\) | ||||
−0.233639 | + | 0.972323i | \(0.575063\pi\) | |||||||
\(758\) | 12.6918 | + | 7.91649i | 0.460988 | + | 0.287540i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.51859 | + | 34.2762i | −0.127633 | + | 1.24333i | ||||
\(761\) | − | 1.27182i | − | 0.0461034i | −0.999734 | − | 0.0230517i | \(-0.992662\pi\) | ||
0.999734 | − | 0.0230517i | \(-0.00733824\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.66802 | − | 14.1284i | 0.241399 | − | 0.511482i | ||||
\(764\) | −22.1803 | + | 10.8625i | −0.802455 | + | 0.392990i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −11.3373 | + | 18.1761i | −0.409634 | + | 0.656731i | ||||
\(767\) | − | 35.7108i | − | 1.28944i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 10.2961i | − | 0.371286i | −0.982617 | − | 0.185643i | \(-0.940563\pi\) | ||
0.982617 | − | 0.185643i | \(-0.0594368\pi\) | |||||||
\(770\) | 39.7525 | + | 61.7289i | 1.43258 | + | 2.22456i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −15.8799 | − | 32.4255i | −0.571531 | − | 1.16702i | ||||
\(773\) | 32.7274i | 1.17712i | 0.808453 | + | 0.588561i | \(0.200305\pi\) | ||||
−0.808453 | + | 0.588561i | \(0.799695\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.96190 | −0.178237 | ||||||||
\(776\) | −4.49666 | + | 43.8041i | −0.161421 | + | 1.57248i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 21.1045 | − | 33.8351i | 0.756633 | − | 1.21305i | ||||
\(779\) | 4.70602i | 0.168611i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 41.4181 | 1.48206 | ||||||||
\(782\) | 6.22833 | − | 9.98536i | 0.222725 | − | 0.357076i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 27.9883 | − | 0.808397i | 0.999583 | − | 0.0288713i | ||||
\(785\) | −78.1771 | −2.79026 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.89413 | 0.281395 | 0.140698 | − | 0.990053i | \(-0.455065\pi\) | ||||
0.140698 | + | 0.990053i | \(0.455065\pi\) | |||||||
\(788\) | −6.02120 | − | 12.2948i | −0.214496 | − | 0.437984i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −27.3005 | + | 43.7686i | −0.971309 | + | 1.55722i | ||||
\(791\) | −17.3172 | + | 36.6921i | −0.615728 | + | 1.30462i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −38.8624 | −1.38004 | ||||||||
\(794\) | −9.58451 | − | 5.97830i | −0.340142 | − | 0.212162i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10.9229 | + | 22.3037i | 0.387153 | + | 0.790535i | ||||
\(797\) | − | 37.8578i | − | 1.34099i | −0.741913 | − | 0.670496i | \(-0.766081\pi\) | ||
0.741913 | − | 0.670496i | \(-0.233919\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 5.75169i | − | 0.203480i | ||||||
\(800\) | 20.1209 | + | 54.5943i | 0.711381 | + | 1.93020i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8.84135 | − | 14.1746i | 0.312199 | − | 0.500522i | ||||
\(803\) | 18.0262 | 0.636132 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.2428 | − | 32.2970i | 0.537239 | − | 1.13832i | ||||
\(806\) | 3.23968 | + | 2.02074i | 0.114113 | + | 0.0711776i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.56547 | − | 15.2500i | 0.0550729 | − | 0.536491i | ||||
\(809\) | −20.6718 | −0.726783 | −0.363392 | − | 0.931636i | \(-0.618381\pi\) | ||||
−0.363392 | + | 0.931636i | \(0.618381\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.86591 | −0.135751 | −0.0678753 | − | 0.997694i | \(-0.521622\pi\) | ||||
−0.0678753 | + | 0.997694i | \(0.521622\pi\) | |||||||
\(812\) | 25.2371 | − | 0.364390i | 0.885649 | − | 0.0127876i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 35.5619 | + | 22.1816i | 1.24644 | + | 0.777464i | ||||
\(815\) | −70.5659 | −2.47181 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.53261i | 0.193562i | ||||||||
\(818\) | −8.15633 | − | 5.08748i | −0.285179 | − | 0.177880i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.19421 | + | 10.6062i | 0.181390 | + | 0.370384i | ||||
\(821\) | 29.6449 | 1.03461 | 0.517306 | − | 0.855800i | \(-0.326935\pi\) | ||||
0.517306 | + | 0.855800i | \(0.326935\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.7188i | 0.966216i | 0.875561 | + | 0.483108i | \(0.160492\pi\) | ||||
−0.875561 | + | 0.483108i | \(0.839508\pi\) | |||||||
\(824\) | 13.7642 | + | 1.41295i | 0.479499 | + | 0.0492224i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.9263 | + | 20.0724i | 0.449763 | + | 0.698406i | ||||
\(827\) | 42.1357i | 1.46520i | 0.680658 | + | 0.732601i | \(0.261694\pi\) | ||||
−0.680658 | + | 0.732601i | \(0.738306\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 41.5795i | − | 1.44412i | −0.691832 | − | 0.722058i | \(-0.743196\pi\) | ||
0.691832 | − | 0.722058i | \(-0.256804\pi\) | |||||||
\(830\) | 27.0549 | + | 16.8754i | 0.939091 | + | 0.585755i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 9.09647 | − | 43.8396i | 0.315363 | − | 1.51987i | ||||
\(833\) | −13.0246 | + | 10.7250i | −0.451277 | + | 0.371598i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 77.0343i | 2.66588i | ||||||||
\(836\) | −28.0898 | + | 13.7565i | −0.971505 | + | 0.475780i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 11.7574 | − | 18.8497i | 0.406154 | − | 0.651153i | ||||
\(839\) | −40.2704 | −1.39029 | −0.695145 | − | 0.718870i | \(-0.744660\pi\) | ||||
−0.695145 | + | 0.718870i | \(0.744660\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.24843 | −0.215463 | ||||||||
\(842\) | −8.99295 | + | 14.4176i | −0.309918 | + | 0.496865i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −35.9582 | + | 17.6100i | −1.23773 | + | 0.606160i | ||||
\(845\) | − | 71.6362i | − | 2.46436i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16.0244 | + | 33.9530i | −0.550606 | + | 1.16664i | ||||
\(848\) | −13.8006 | + | 17.7821i | −0.473915 | + | 0.610641i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −29.7477 | − | 18.5550i | −1.02034 | − | 0.636433i | ||||
\(851\) | − | 20.3869i | − | 0.698854i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.2555i | 0.967449i | 0.875220 | + | 0.483724i | \(0.160716\pi\) | ||||
−0.875220 | + | 0.483724i | \(0.839284\pi\) | |||||||
\(854\) | 21.8438 | − | 14.0671i | 0.747480 | − | 0.481366i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.60296 | − | 35.0982i | 0.123147 | − | 1.19963i | ||||
\(857\) | 51.6638i | 1.76480i | 0.470499 | + | 0.882400i | \(0.344074\pi\) | ||||
−0.470499 | + | 0.882400i | \(0.655926\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.9603 | 1.39755 | 0.698774 | − | 0.715343i | \(-0.253729\pi\) | ||||
0.698774 | + | 0.715343i | \(0.253729\pi\) | |||||||
\(860\) | 6.10656 | + | 12.4691i | 0.208232 | + | 0.425193i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12.0449 | − | 7.51296i | −0.410251 | − | 0.255892i | ||||
\(863\) | − | 51.1388i | − | 1.74078i | −0.492360 | − | 0.870392i | \(-0.663866\pi\) | ||
0.492360 | − | 0.870392i | \(-0.336134\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.42907 | 0.0825909 | ||||||||
\(866\) | −30.8848 | − | 19.2643i | −1.04951 | − | 0.654628i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.55242 | + | 0.0368535i | −0.0866347 | + | 0.00125089i | ||||
\(869\) | −46.8258 | −1.58846 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.9424 | −0.743491 | ||||||||
\(872\) | 16.6142 | + | 1.70552i | 0.562629 | + | 0.0577560i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 12.9085 | + | 8.05165i | 0.436638 | + | 0.272351i | ||||
\(875\) | −49.4443 | − | 23.3357i | −1.67152 | − | 0.788890i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.5244 | 0.524223 | 0.262112 | − | 0.965038i | \(-0.415581\pi\) | ||||
0.262112 | + | 0.965038i | \(0.415581\pi\) | |||||||
\(878\) | 21.4546 | − | 34.3963i | 0.724057 | − | 1.16082i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −48.1237 | + | 62.0076i | −1.62225 | + | 2.09027i | ||||
\(881\) | 23.2196i | 0.782287i | 0.920330 | + | 0.391144i | \(0.127920\pi\) | ||||
−0.920330 | + | 0.391144i | \(0.872080\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 5.98339i | − | 0.201357i | −0.994919 | − | 0.100678i | \(-0.967899\pi\) | ||
0.994919 | − | 0.100678i | \(-0.0321013\pi\) | |||||||
\(884\) | 11.8661 | + | 24.2296i | 0.399100 | + | 0.814931i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.80019 | − | 2.37035i | −0.127670 | − | 0.0796336i | ||||
\(887\) | 39.5090 | 1.32658 | 0.663291 | − | 0.748361i | \(-0.269159\pi\) | ||||
0.663291 | + | 0.748361i | \(0.269159\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.17949 | − | 1.02863i | −0.0730977 | − | 0.0344991i | ||||
\(890\) | 51.6629 | − | 82.8267i | 1.73174 | − | 2.77636i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 23.2210 | + | 47.4155i | 0.777498 | + | 1.58759i | ||||
\(893\) | 7.43547 | 0.248819 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 47.4219 | 1.58514 | ||||||||
\(896\) | 10.7558 | + | 27.9341i | 0.359324 | + | 0.933213i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −24.0563 | + | 38.5675i | −0.802770 | + | 1.28701i | ||||
\(899\) | −2.30104 | −0.0767439 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 13.5634i | − | 0.451862i | ||||||
\(902\) | −5.67350 | + | 9.09585i | −0.188907 | + | 0.302859i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −43.1480 | − | 4.42931i | −1.43508 | − | 0.147317i | ||||
\(905\) | 84.2574 | 2.80081 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.1580i | 0.669335i | 0.942336 | + | 0.334667i | \(0.108624\pi\) | ||||
−0.942336 | + | 0.334667i | \(0.891376\pi\) | |||||||
\(908\) | −1.76421 | − | 3.60239i | −0.0585475 | − | 0.119549i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 44.3278 | + | 68.8336i | 1.46945 | + | 2.28181i | ||||
\(911\) | 20.5534i | 0.680965i | 0.940251 | + | 0.340482i | \(0.110590\pi\) | ||||
−0.940251 | + | 0.340482i | \(0.889410\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28.9447i | 0.957930i | ||||||||
\(914\) | −15.2975 | + | 24.5252i | −0.505996 | + | 0.811221i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −25.8632 | + | 12.6661i | −0.854546 | + | 0.418501i | ||||
\(917\) | −18.0024 | + | 38.1439i | −0.594491 | + | 1.25962i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 54.4208i | − | 1.79518i | −0.440834 | − | 0.897588i | \(-0.645317\pi\) | ||
0.440834 | − | 0.897588i | \(-0.354683\pi\) | |||||||
\(920\) | 37.9795 | + | 3.89874i | 1.25215 | + | 0.128538i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7.37099 | + | 4.59763i | 0.242751 | + | 0.151415i | ||||
\(923\) | 46.1852 | 1.52020 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −60.7353 | −1.99696 | ||||||||
\(926\) | −2.55779 | − | 1.59541i | −0.0840542 | − | 0.0524285i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.33090 | + | 25.3177i | 0.306302 | + | 0.831093i | ||||
\(929\) | − | 26.0631i | − | 0.855103i | −0.903991 | − | 0.427552i | \(-0.859376\pi\) | ||
0.903991 | − | 0.427552i | \(-0.140624\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.8646 | − | 16.8376i | −0.454395 | − | 0.551829i | ||||
\(932\) | 11.0863 | + | 22.6373i | 0.363143 | + | 0.741510i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −8.59346 | + | 13.7772i | −0.281187 | + | 0.450803i | ||||
\(935\) | − | 47.2965i | − | 1.54676i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 0.657922i | − | 0.0214934i | −0.999942 | − | 0.0107467i | \(-0.996579\pi\) | ||
0.999942 | − | 0.0107467i | \(-0.00342084\pi\) | |||||||
\(938\) | 12.3334 | − | 7.94254i | 0.402701 | − | 0.259333i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 16.7577 | − | 8.20682i | 0.546576 | − | 0.267677i | ||||
\(941\) | − | 39.3462i | − | 1.28265i | −0.767269 | − | 0.641325i | \(-0.778385\pi\) | ||
0.767269 | − | 0.641325i | \(-0.221615\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.21447 | 0.169806 | ||||||||
\(944\) | −15.6483 | + | 20.1630i | −0.509310 | + | 0.656248i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.67003 | + | 10.6935i | −0.216861 | + | 0.347676i | ||||
\(947\) | − | 29.2121i | − | 0.949267i | −0.880184 | − | 0.474634i | \(-0.842581\pi\) | ||
0.880184 | − | 0.474634i | \(-0.157419\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.1010 | 0.652505 | ||||||||
\(950\) | 23.9870 | − | 38.4563i | 0.778239 | − | 1.24769i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −15.4402 | − | 9.32384i | −0.500419 | − | 0.302187i | ||||
\(953\) | −0.0993268 | −0.00321751 | −0.00160876 | − | 0.999999i | \(-0.500512\pi\) | ||||
−0.00160876 | + | 0.999999i | \(0.500512\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 48.2794 | 1.56228 | ||||||||
\(956\) | 4.63905 | − | 2.27190i | 0.150037 | − | 0.0734786i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.7674 | − | 17.2625i | 0.347880 | − | 0.557726i | ||||
\(959\) | −0.709073 | + | 1.50240i | −0.0228971 | + | 0.0485151i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7673 | −0.992493 | ||||||||
\(962\) | 39.6549 | + | 24.7346i | 1.27852 | + | 0.797475i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 17.3118 | − | 8.47817i | 0.557574 | − | 0.273063i | ||||
\(965\) | 70.5799i | 2.27205i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.9194i | 1.12293i | 0.827500 | + | 0.561466i | \(0.189762\pi\) | ||||
−0.827500 | + | 0.561466i | \(0.810238\pi\) | |||||||
\(968\) | −39.9269 | − | 4.09865i | −1.28330 | − | 0.131736i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 45.5565 | − | 73.0369i | 1.46273 | − | 2.34507i | ||||
\(971\) | −27.8736 | −0.894506 | −0.447253 | − | 0.894408i | \(-0.647598\pi\) | ||||
−0.447253 | + | 0.894408i | \(0.647598\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.6084 | − | 41.5468i | 0.628615 | − | 1.33193i | ||||
\(974\) | 24.4650 | + | 15.2600i | 0.783910 | + | 0.488961i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 21.9424 | + | 17.0294i | 0.702360 | + | 0.545097i | ||||
\(977\) | 6.42348 | 0.205505 | 0.102753 | − | 0.994707i | \(-0.467235\pi\) | ||||
0.102753 | + | 0.994707i | \(0.467235\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 88.6121 | 2.83205 | ||||||||
\(980\) | −49.8317 | − | 22.6447i | −1.59181 | − | 0.723358i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 23.9140 | + | 14.9163i | 0.763127 | + | 0.475998i | ||||
\(983\) | −16.8411 | −0.537147 | −0.268574 | − | 0.963259i | \(-0.586552\pi\) | ||||
−0.268574 | + | 0.963259i | \(0.586552\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26.7618i | 0.852703i | ||||||||
\(986\) | −13.7953 | − | 8.60475i | −0.439331 | − | 0.274031i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −31.3228 | + | 15.3398i | −0.996510 | + | 0.488026i | ||||
\(989\) | 6.13037 | 0.194934 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.6792i | 0.466299i | 0.972441 | + | 0.233149i | \(0.0749031\pi\) | ||||
−0.972441 | + | 0.233149i | \(0.925097\pi\) | |||||||
\(992\) | −0.943704 | − | 2.56057i | −0.0299626 | − | 0.0812981i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −25.9598 | + | 16.7177i | −0.823396 | + | 0.530254i | ||||
\(995\) | − | 48.5481i | − | 1.53908i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.0288i | 0.792671i | 0.918106 | + | 0.396336i | \(0.129718\pi\) | ||||
−0.918106 | + | 0.396336i | \(0.870282\pi\) | |||||||
\(998\) | −9.15191 | − | 5.70847i | −0.289699 | − | 0.180698i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 756.2.b.f.55.6 | yes | 16 | |
3.2 | odd | 2 | 756.2.b.e.55.11 | yes | 16 | ||
4.3 | odd | 2 | 756.2.b.e.55.5 | ✓ | 16 | ||
7.6 | odd | 2 | 756.2.b.e.55.6 | yes | 16 | ||
12.11 | even | 2 | inner | 756.2.b.f.55.12 | yes | 16 | |
21.20 | even | 2 | inner | 756.2.b.f.55.11 | yes | 16 | |
28.27 | even | 2 | inner | 756.2.b.f.55.5 | yes | 16 | |
84.83 | odd | 2 | 756.2.b.e.55.12 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.b.e.55.5 | ✓ | 16 | 4.3 | odd | 2 | ||
756.2.b.e.55.6 | yes | 16 | 7.6 | odd | 2 | ||
756.2.b.e.55.11 | yes | 16 | 3.2 | odd | 2 | ||
756.2.b.e.55.12 | yes | 16 | 84.83 | odd | 2 | ||
756.2.b.f.55.5 | yes | 16 | 28.27 | even | 2 | inner | |
756.2.b.f.55.6 | yes | 16 | 1.1 | even | 1 | trivial | |
756.2.b.f.55.11 | yes | 16 | 21.20 | even | 2 | inner | |
756.2.b.f.55.12 | yes | 16 | 12.11 | even | 2 | inner |