Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [440,2,Mod(89,440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(440, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("440.89");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 440 = 2^{3} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 440.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: | \(3.51341768894\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.47985531136.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 19x^{6} + 91x^{4} + 45x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 89.1 | ||
Root | \(-3.36007i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 440.89 |
Dual form | 440.2.b.d.89.8 |
$q$-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 \(\left(\mathbb{Z}/440\mathbb{Z}\right)^\times\).
\(n\) | \(111\) | \(177\) | \(221\) | \(321\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | − | 3.36007i | − | 1.93994i | −0.243227 | − | 0.969969i | \(-0.578206\pi\) | ||
0.243227 | − | 0.969969i | \(-0.421794\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.256321 | − | 2.22133i | −0.114630 | − | 0.993408i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.08258i | 0.409178i | 0.978848 | + | 0.204589i | \(0.0655858\pi\) | ||||
−0.978848 | + | 0.204589i | \(0.934414\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.29009 | −2.76336 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.00000i | − | 1.10940i | −0.832050 | − | 0.554700i | \(-0.812833\pi\) | ||
0.832050 | − | 0.554700i | \(-0.187167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.46382 | + | 0.861256i | −1.92715 | + | 0.222375i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 0.107866i | − | 0.0261614i | −0.999914 | − | 0.0130807i | \(-0.995836\pi\) | ||
0.999914 | − | 0.0130807i | \(-0.00416384\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.61228 | 1.51696 | 0.758480 | − | 0.651696i | \(-0.225942\pi\) | ||||
0.758480 | + | 0.651696i | \(0.225942\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.63756 | 0.793781 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.97235i | 1.24532i | 0.782492 | + | 0.622661i | \(0.213948\pi\) | ||||
−0.782492 | + | 0.622661i | \(0.786052\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.86860 | + | 1.13874i | −0.973720 | + | 0.227749i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 17.7751i | 3.42082i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.80273 | −1.44893 | −0.724465 | − | 0.689311i | \(-0.757913\pi\) | ||||
−0.724465 | + | 0.689311i | \(0.757913\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.12492 | 0.202042 | 0.101021 | − | 0.994884i | \(-0.467789\pi\) | ||||
0.101021 | + | 0.994884i | \(0.467789\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 3.36007i | − | 0.584914i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.40477 | − | 0.277489i | 0.406481 | − | 0.0469041i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 7.05494i | − | 1.15982i | −0.814679 | − | 0.579912i | \(-0.803087\pi\) | ||
0.814679 | − | 0.579912i | \(-0.196913\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −13.4403 | −2.15217 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.19045 | 0.810612 | 0.405306 | − | 0.914181i | \(-0.367165\pi\) | ||||
0.405306 | + | 0.914181i | \(0.367165\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 5.52969i | − | 0.843271i | −0.906766 | − | 0.421635i | \(-0.861456\pi\) | ||
0.906766 | − | 0.421635i | \(-0.138544\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.12492 | + | 18.4150i | 0.316764 | + | 2.74515i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 7.69486i | − | 1.12241i | −0.827676 | − | 0.561206i | \(-0.810338\pi\) | ||
0.827676 | − | 0.561206i | \(-0.189662\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.82801 | 0.832573 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.362439 | −0.0507516 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.77745i | 0.656233i | 0.944637 | + | 0.328116i | \(0.106414\pi\) | ||||
−0.944637 | + | 0.328116i | \(0.893586\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.256321 | − | 2.22133i | −0.0345623 | − | 0.299524i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 22.2177i | − | 2.94281i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.677809 | 0.0882433 | 0.0441216 | − | 0.999026i | \(-0.485951\pi\) | ||||
0.0441216 | + | 0.999026i | \(0.485951\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.197271 | 0.0252579 | 0.0126290 | − | 0.999920i | \(-0.495980\pi\) | ||||
0.0126290 | + | 0.999920i | \(0.495980\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 8.97472i | − | 1.13071i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.88531 | + | 1.02528i | −1.10209 | + | 0.127171i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.41737i | − | 0.173160i | −0.996245 | − | 0.0865799i | \(-0.972406\pi\) | ||
0.996245 | − | 0.0865799i | \(-0.0275938\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 20.0675 | 2.41585 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.15020 | −0.729895 | −0.364947 | − | 0.931028i | \(-0.618913\pi\) | ||||
−0.364947 | + | 0.931028i | \(0.618913\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.16517i | − | 0.721578i | −0.932647 | − | 0.360789i | \(-0.882507\pi\) | ||
0.932647 | − | 0.360789i | \(-0.117493\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.82626 | + | 16.3588i | 0.441819 | + | 1.88896i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.08258i | 0.123372i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.35562 | 1.05259 | 0.526295 | − | 0.850302i | \(-0.323581\pi\) | ||||
0.526295 | + | 0.850302i | \(0.323581\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 34.8553 | 3.87281 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 13.7454i | − | 1.50876i | −0.656440 | − | 0.754378i | \(-0.727938\pi\) | ||
0.656440 | − | 0.754378i | \(-0.272062\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.239607 | + | 0.0276484i | −0.0259890 | + | 0.00299889i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 26.2177i | 2.81084i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.29009 | 0.136749 | 0.0683745 | − | 0.997660i | \(-0.478219\pi\) | ||||
0.0683745 | + | 0.997660i | \(0.478219\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.33034 | 0.453943 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 3.77981i | − | 0.391948i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.69486 | − | 14.6880i | −0.173889 | − | 1.50696i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.60782i | − | 0.670923i | −0.942054 | − | 0.335461i | \(-0.891108\pi\) | ||
0.942054 | − | 0.335461i | \(-0.108892\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.29009 | −0.833185 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.4403 | −1.53637 | −0.768183 | − | 0.640230i | \(-0.778839\pi\) | ||||
−0.768183 | + | 0.640230i | \(0.778839\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.74543i | 0.566114i | 0.959103 | + | 0.283057i | \(0.0913485\pi\) | ||||
−0.959103 | + | 0.283057i | \(0.908651\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.932382 | − | 8.08022i | −0.0909911 | − | 0.788549i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.30514i | 0.416193i | 0.978108 | + | 0.208097i | \(0.0667269\pi\) | ||||
−0.978108 | + | 0.208097i | \(0.933273\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.33034 | 0.223206 | 0.111603 | − | 0.993753i | \(-0.464402\pi\) | ||||
0.111603 | + | 0.993753i | \(0.464402\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −23.7051 | −2.24999 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 10.9471i | − | 1.02981i | −0.857246 | − | 0.514907i | \(-0.827827\pi\) | ||
0.857246 | − | 0.514907i | \(-0.172173\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.2666 | − | 1.53084i | 1.23711 | − | 0.142751i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 33.1604i | 3.06568i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.116774 | 0.0107047 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 17.4403i | − | 1.57254i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.77745 | + | 10.5229i | 0.337865 | + | 0.941195i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.5802i | 1.11631i | 0.829737 | + | 0.558155i | \(0.188491\pi\) | ||||
−0.829737 | + | 0.558155i | \(0.811509\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −18.5802 | −1.63589 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.2430 | 1.33179 | 0.665894 | − | 0.746046i | \(-0.268050\pi\) | ||||
0.665894 | + | 0.746046i | \(0.268050\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.15835i | 0.620707i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 39.4843 | − | 4.55612i | 3.39827 | − | 0.392128i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.6078i | 1.24803i | 0.781412 | + | 0.624015i | \(0.214500\pi\) | ||||
−0.781412 | + | 0.624015i | \(0.785500\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.4150 | 1.73158 | 0.865789 | − | 0.500409i | \(-0.166817\pi\) | ||||
0.865789 | + | 0.500409i | \(0.166817\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −25.8553 | −2.17741 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 4.00000i | − | 0.334497i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.00000 | + | 17.3324i | 0.166091 | + | 1.43938i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 19.5825i | − | 1.61514i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.8874 | 1.30155 | 0.650773 | − | 0.759272i | \(-0.274445\pi\) | ||||
0.650773 | + | 0.759272i | \(0.274445\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.58018 | 0.535487 | 0.267744 | − | 0.963490i | \(-0.413722\pi\) | ||||
0.267744 | + | 0.963490i | \(0.413722\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.894222i | 0.0722935i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.288340 | − | 2.49882i | −0.0231600 | − | 0.200710i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.38535i | 0.509607i | 0.966993 | + | 0.254803i | \(0.0820108\pi\) | ||||
−0.966993 | + | 0.254803i | \(0.917989\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 16.0526 | 1.27305 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.46557 | −0.509559 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.3071i | 1.43393i | 0.697111 | + | 0.716963i | \(0.254468\pi\) | ||||
−0.697111 | + | 0.716963i | \(0.745532\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.46382 | + | 0.861256i | −0.581058 | + | 0.0670487i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.197271i | 0.0152653i | 0.999971 | + | 0.00763263i | \(0.00242956\pi\) | ||||
−0.999971 | + | 0.00763263i | \(0.997570\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.00000 | −0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −54.8164 | −4.19191 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 14.7201i | − | 1.11915i | −0.828779 | − | 0.559576i | \(-0.810964\pi\) | ||
0.828779 | − | 0.559576i | \(-0.189036\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.23279 | − | 5.27067i | −0.0931899 | − | 0.398425i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 2.27749i | − | 0.171187i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.8518 | −0.885845 | −0.442923 | − | 0.896560i | \(-0.646058\pi\) | ||||
−0.442923 | + | 0.896560i | \(0.646058\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.7625 | −0.799969 | −0.399984 | − | 0.916522i | \(-0.630984\pi\) | ||||
−0.399984 | + | 0.916522i | \(0.630984\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 0.662843i | − | 0.0489988i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −15.6713 | + | 1.80833i | −1.15218 | + | 0.132951i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 0.107866i | − | 0.00788797i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −19.2430 | −1.39972 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.70309 | 0.123231 | 0.0616157 | − | 0.998100i | \(-0.480375\pi\) | ||||
0.0616157 | + | 0.998100i | \(0.480375\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 10.8280i | − | 0.779417i | −0.920938 | − | 0.389709i | \(-0.872576\pi\) | ||
0.920938 | − | 0.389709i | \(-0.127424\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.44502 | + | 29.8553i | 0.246703 | + | 2.13798i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 6.72015i | − | 0.478791i | −0.970922 | − | 0.239395i | \(-0.923051\pi\) | ||
0.970922 | − | 0.239395i | \(-0.0769492\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.8280 | 0.767577 | 0.383789 | − | 0.923421i | \(-0.374619\pi\) | ||||
0.383789 | + | 0.923421i | \(0.374619\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.76248 | −0.335920 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 8.44711i | − | 0.592871i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.33042 | − | 11.5297i | −0.0929205 | − | 0.805269i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 49.5113i | − | 3.44127i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.61228 | 0.457381 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.447111 | 0.0307804 | 0.0153902 | − | 0.999882i | \(-0.495101\pi\) | ||||
0.0153902 | + | 0.999882i | \(0.495101\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 20.6651i | 1.41595i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.2833 | + | 1.41737i | −0.837712 | + | 0.0966641i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.21782i | 0.0826710i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −20.7154 | −1.39982 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.431465 | −0.0290235 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.8577i | 1.19584i | 0.801555 | + | 0.597922i | \(0.204007\pi\) | ||||
−0.801555 | + | 0.597922i | \(0.795993\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 40.3611 | − | 9.44029i | 2.69074 | − | 0.629353i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.31396i | 0.0872107i | 0.999049 | + | 0.0436054i | \(0.0138844\pi\) | ||||
−0.999049 | + | 0.0436054i | \(0.986116\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.84298 | −0.320033 | −0.160016 | − | 0.987114i | \(-0.551155\pi\) | ||||
−0.160016 | + | 0.987114i | \(0.551155\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.63756 | 0.239334 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.3829i | 1.33533i | 0.744462 | + | 0.667664i | \(0.232706\pi\) | ||||
−0.744462 | + | 0.667664i | \(0.767294\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.0928 | + | 1.97235i | −1.11501 | + | 0.128662i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 31.4356i | − | 2.04196i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.35562 | 0.605165 | 0.302582 | − | 0.953123i | \(-0.402151\pi\) | ||||
0.302582 | + | 0.953123i | \(0.402151\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.3004 | 1.43650 | 0.718248 | − | 0.695788i | \(-0.244944\pi\) | ||||
0.718248 | + | 0.695788i | \(0.244944\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 63.7911i | − | 4.09220i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.49384 | − | 12.9459i | −0.0954379 | − | 0.827085i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 26.4491i | − | 1.68292i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −46.1856 | −2.92690 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.9276 | −0.689747 | −0.344874 | − | 0.938649i | \(-0.612078\pi\) | ||||
−0.344874 | + | 0.938649i | \(0.612078\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.97235i | 0.375479i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.0929005 | + | 0.805096i | 0.00581766 | + | 0.0504170i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.4403i | 1.33741i | 0.743528 | + | 0.668704i | \(0.233151\pi\) | ||||
−0.743528 | + | 0.668704i | \(0.766849\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.63756 | 0.474575 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 64.6853 | 4.00392 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.52287i | 0.402218i | 0.979569 | + | 0.201109i | \(0.0644545\pi\) | ||||
−0.979569 | + | 0.201109i | \(0.935546\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.6123 | − | 1.22456i | 0.651907 | − | 0.0752240i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 4.33479i | − | 0.265285i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.60546 | −0.341771 | −0.170885 | − | 0.985291i | \(-0.554663\pi\) | ||||
−0.170885 | + | 0.985291i | \(0.554663\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.9446 | −1.75826 | −0.879130 | − | 0.476582i | \(-0.841876\pi\) | ||||
−0.879130 | + | 0.476582i | \(0.841876\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 14.5502i | − | 0.880621i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.86860 | + | 1.13874i | −0.293588 | + | 0.0686689i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.3850i | 1.52524i | 0.646849 | + | 0.762618i | \(0.276086\pi\) | ||||
−0.646849 | + | 0.762618i | \(0.723914\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.32569 | −0.558314 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.1604 | −1.62025 | −0.810125 | − | 0.586257i | \(-0.800601\pi\) | ||||
−0.810125 | + | 0.586257i | \(0.800601\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.0205i | 1.30898i | 0.756070 | + | 0.654490i | \(0.227117\pi\) | ||||
−0.756070 | + | 0.654490i | \(0.772883\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −49.3529 | + | 5.69486i | −2.92341 | + | 0.337335i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.61910i | 0.331685i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.9884 | 0.999316 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −22.2028 | −1.30155 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 1.44029i | − | 0.0841427i | −0.999115 | − | 0.0420713i | \(-0.986604\pi\) | ||
0.999115 | − | 0.0420713i | \(-0.0133957\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.173736 | − | 1.50564i | −0.0101153 | − | 0.0876616i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 17.7751i | 1.03141i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 23.8894 | 1.38156 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.98636 | 0.345048 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 51.8805i | 2.98046i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.0505645 | − | 0.438203i | −0.00289532 | − | 0.0250914i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.80955i | − | 0.160349i | −0.996781 | − | 0.0801747i | \(-0.974452\pi\) | ||
0.996781 | − | 0.0801747i | \(-0.0255478\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 19.3051 | 1.09823 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.5529 | −0.655104 | −0.327552 | − | 0.944833i | \(-0.606224\pi\) | ||||
−0.327552 | + | 0.944833i | \(0.606224\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 26.1580i | − | 1.47854i | −0.673411 | − | 0.739268i | \(-0.735171\pi\) | ||
0.673411 | − | 0.739268i | \(-0.264829\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −19.9358 | + | 2.30040i | −1.12325 | + | 0.129613i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 29.3805i | 1.65018i | 0.565005 | + | 0.825088i | \(0.308874\pi\) | ||||
−0.565005 | + | 0.825088i | \(0.691126\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.80273 | −0.436869 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.4656 | 0.807390 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 0.713242i | − | 0.0396859i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.55498 | + | 19.4744i | 0.252665 | + | 1.08025i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 7.83010i | − | 0.433005i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.33034 | 0.459266 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.2833 | 0.675149 | 0.337575 | − | 0.941299i | \(-0.390393\pi\) | ||||
0.337575 | + | 0.941299i | \(0.390393\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 58.4860i | 3.20502i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.14845 | + | 0.363302i | −0.172018 | + | 0.0198493i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 21.3324i | − | 1.16205i | −0.813885 | − | 0.581026i | \(-0.802652\pi\) | ||
0.813885 | − | 0.581026i | \(-0.197348\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −36.7829 | −1.99778 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.12492 | 0.0609178 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.8874i | 0.749849i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.14372 | − | 44.5766i | −0.276929 | − | 2.39992i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.4150i | 0.559107i | 0.960130 | + | 0.279553i | \(0.0901864\pi\) | ||||
−0.960130 | + | 0.279553i | \(0.909814\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.4909 | 0.722149 | 0.361074 | − | 0.932537i | \(-0.382410\pi\) | ||||
0.361074 | + | 0.932537i | \(0.382410\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 71.1003 | 3.79505 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.7177i | 0.676895i | 0.940985 | + | 0.338447i | \(0.109902\pi\) | ||||
−0.940985 | + | 0.338447i | \(0.890098\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.57642 | + | 13.6616i | 0.0836679 | + | 0.725083i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 0.392370i | − | 0.0207664i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.8212 | 1.04612 | 0.523061 | − | 0.852295i | \(-0.324790\pi\) | ||||
0.523061 | + | 0.852295i | \(0.324790\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 24.7222 | 1.30117 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 3.36007i | − | 0.176358i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.6949 | + | 1.58026i | −0.716822 | + | 0.0827146i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.3027i | 0.537796i | 0.963169 | + | 0.268898i | \(0.0866594\pi\) | ||||
−0.963169 | + | 0.268898i | \(0.913341\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −43.0293 | −2.24002 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.17199 | −0.268516 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 23.3344i | − | 1.20821i | −0.796904 | − | 0.604105i | \(-0.793531\pi\) | ||
0.796904 | − | 0.604105i | \(-0.206469\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 35.3576 | − | 12.6925i | 1.82586 | − | 0.655438i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 31.2109i | 1.60744i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.2074 | 1.08935 | 0.544676 | − | 0.838647i | \(-0.316653\pi\) | ||||
0.544676 | + | 0.838647i | \(0.316653\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 42.2703 | 2.16557 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.972434i | 0.0496891i | 0.999691 | + | 0.0248445i | \(0.00790908\pi\) | ||||
−0.999691 | + | 0.0248445i | \(0.992091\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.40477 | − | 0.277489i | 0.122559 | − | 0.0141421i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 45.8417i | 2.33026i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.76248 | −0.140063 | −0.0700317 | − | 0.997545i | \(-0.522310\pi\) | ||||
−0.0700317 | + | 0.997545i | \(0.522310\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.644216 | 0.0325794 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 51.2177i | − | 2.58359i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.39804 | − | 20.7819i | −0.120658 | − | 1.04565i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 11.2751i | − | 0.565882i | −0.959137 | − | 0.282941i | \(-0.908690\pi\) | ||
0.959137 | − | 0.282941i | \(-0.0913101\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 24.0526 | 1.20413 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.4471 | −0.521704 | −0.260852 | − | 0.965379i | \(-0.584003\pi\) | ||||
−0.260852 | + | 0.965379i | \(0.584003\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 4.49968i | − | 0.224145i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.93413 | − | 77.4251i | −0.443940 | − | 3.84728i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 7.05494i | − | 0.349700i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.27512 | 0.0630507 | 0.0315254 | − | 0.999503i | \(-0.489963\pi\) | ||||
0.0315254 | + | 0.999503i | \(0.489963\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 49.0834 | 2.42110 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.733786i | 0.0361072i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −30.5331 | + | 3.52324i | −1.49881 | + | 0.172949i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 68.5959i | − | 3.35916i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.7795 | −0.917436 | −0.458718 | − | 0.888582i | \(-0.651691\pi\) | ||||
−0.458718 | + | 0.888582i | \(0.651691\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.27512 | −0.0621457 | −0.0310728 | − | 0.999517i | \(-0.509892\pi\) | ||||
−0.0310728 | + | 0.999517i | \(0.509892\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 63.7911i | 3.10163i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.122832 | + | 0.525158i | 0.00595824 | + | 0.0254739i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.213562i | 0.0103350i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −13.4403 | −0.648903 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.63556 | 0.0787820 | 0.0393910 | − | 0.999224i | \(-0.487458\pi\) | ||||
0.0393910 | + | 0.999224i | \(0.487458\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.4932i | 1.27318i | 0.771201 | + | 0.636591i | \(0.219656\pi\) | ||||
−0.771201 | + | 0.636591i | \(0.780344\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 58.2382 | − | 6.72015i | 2.79231 | − | 0.322206i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 39.4909i | 1.88910i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −31.9358 | −1.52421 | −0.762106 | − | 0.647452i | \(-0.775835\pi\) | ||||
−0.762106 | + | 0.647452i | \(0.775835\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −48.3147 | −2.30070 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.02765i | 0.0963365i | 0.998839 | + | 0.0481682i | \(0.0153384\pi\) | ||||
−0.998839 | + | 0.0481682i | \(0.984662\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.330676 | − | 2.86571i | −0.0156756 | − | 0.135848i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 53.3828i | − | 2.52492i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.0675 | 0.475116 | 0.237558 | − | 0.971373i | \(-0.423653\pi\) | ||||
0.237558 | + | 0.971373i | \(0.423653\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.19045 | 0.244409 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 22.1099i | − | 1.03881i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.10995 | − | 9.61910i | −0.0520355 | − | 0.450950i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 6.04839i | − | 0.282932i | −0.989943 | − | 0.141466i | \(-0.954818\pi\) | ||
0.989943 | − | 0.141466i | \(-0.0451816\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.91733 | 0.0894934 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.8397 | 1.48292 | 0.741460 | − | 0.670997i | \(-0.234134\pi\) | ||||
0.741460 | + | 0.670997i | \(0.234134\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 30.2474i | − | 1.40572i | −0.711330 | − | 0.702858i | \(-0.751907\pi\) | ||
0.711330 | − | 0.702858i | \(-0.248093\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.39621 | + | 0.968844i | −0.389365 | + | 0.0449291i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 31.3417i | − | 1.45032i | −0.688580 | − | 0.725160i | \(-0.741766\pi\) | ||
0.688580 | − | 0.725160i | \(-0.258234\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.53443 | 0.0708533 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 21.4553 | 0.988606 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 5.52969i | − | 0.254256i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −32.1925 | + | 7.52969i | −1.47709 | + | 0.345486i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 39.6055i | − | 1.81341i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.59663 | −0.301408 | −0.150704 | − | 0.988579i | \(-0.548154\pi\) | ||||
−0.150704 | + | 0.988579i | \(0.548154\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −28.2197 | −1.28671 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 21.7248i | 0.988512i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.6781 | + | 1.69372i | −0.666500 | + | 0.0769079i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 1.13343i | − | 0.0513605i | −0.999670 | − | 0.0256802i | \(-0.991825\pi\) | ||
0.999670 | − | 0.0256802i | \(-0.00817517\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 61.5133 | 2.78173 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 43.5569 | 1.96570 | 0.982848 | − | 0.184419i | \(-0.0590404\pi\) | ||||
0.982848 | + | 0.184419i | \(0.0590404\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.841652i | 0.0379061i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.12492 | + | 18.4150i | 0.0955081 | + | 0.827693i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 6.65811i | − | 0.298657i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 34.5502 | 1.54668 | 0.773341 | − | 0.633991i | \(-0.218584\pi\) | ||||
0.773341 | + | 0.633991i | \(0.218584\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.662843 | 0.0296137 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 5.92424i | − | 0.264149i | −0.991240 | − | 0.132074i | \(-0.957836\pi\) | ||
0.991240 | − | 0.132074i | \(-0.0421638\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.95766 | + | 34.2980i | 0.176114 | + | 1.52624i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.0802i | 0.447678i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 42.3679 | 1.87793 | 0.938963 | − | 0.344018i | \(-0.111788\pi\) | ||||
0.938963 | + | 0.344018i | \(0.111788\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.67431 | 0.295254 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 117.534i | 5.18924i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.7625 | − | 1.47267i | 0.562382 | − | 0.0648936i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 7.69486i | − | 0.338420i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −49.4608 | −2.17109 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.2116 | 0.929297 | 0.464648 | − | 0.885495i | \(-0.346181\pi\) | ||||
0.464648 | + | 0.885495i | \(0.346181\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.19045i | 0.226963i | 0.993540 | + | 0.113481i | \(0.0362002\pi\) | ||||
−0.993540 | + | 0.113481i | \(0.963800\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −17.7098 | + | 4.14225i | −0.772920 | + | 0.180783i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 0.121341i | − | 0.00528570i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.6690 | −0.550825 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.61910 | −0.243848 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 20.7618i | − | 0.899293i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.56312 | − | 1.10350i | 0.413450 | − | 0.0477083i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 39.8229i | 1.71849i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.82801 | 0.251030 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.0185 | −1.03263 | −0.516317 | − | 0.856397i | \(-0.672697\pi\) | ||||
−0.516317 | + | 0.856397i | \(0.672697\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 36.1627i | 1.55189i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.597313 | − | 5.17644i | −0.0255861 | − | 0.221734i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 12.8601i | − | 0.549859i | −0.961464 | − | 0.274929i | \(-0.911346\pi\) | ||
0.961464 | − | 0.274929i | \(-0.0886545\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.63539 | −0.0697968 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −51.5938 | −2.19797 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.1282i | 0.430697i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.07610 | + | 52.6568i | 0.257916 | + | 2.23516i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 31.3344i | − | 1.32768i | −0.747874 | − | 0.663841i | \(-0.768925\pi\) | ||
0.747874 | − | 0.663841i | \(-0.231075\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22.1188 | −0.935525 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.362439 | −0.0153022 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.6901i | 0.745550i | 0.927922 | + | 0.372775i | \(0.121594\pi\) | ||||
−0.927922 | + | 0.372775i | \(0.878406\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −24.3170 | + | 2.80596i | −1.02303 | + | 0.118048i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 37.7338i | 1.58467i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26.3004 | −1.10257 | −0.551285 | − | 0.834317i | \(-0.685862\pi\) | ||||
−0.551285 | + | 0.834317i | \(0.685862\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.9884 | −1.50607 | −0.753033 | − | 0.657983i | \(-0.771410\pi\) | ||||
−0.753033 | + | 0.657983i | \(0.771410\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 5.72251i | − | 0.239061i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.80098 | − | 29.0770i | −0.283621 | − | 1.21259i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 32.6031i | − | 1.35728i | −0.734469 | − | 0.678642i | \(-0.762569\pi\) | ||
0.734469 | − | 0.678642i | \(-0.237431\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −36.3829 | −1.51202 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.8806 | 0.617351 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.77745i | 0.197862i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 73.6600 | − | 8.49968i | 3.04547 | − | 0.351419i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.6287i | 0.727612i | 0.931475 | + | 0.363806i | \(0.118523\pi\) | ||||
−0.931475 | + | 0.363806i | \(0.881477\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.43829 | 0.306489 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −22.5802 | −0.928824 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 13.2246i | − | 0.543068i | −0.962429 | − | 0.271534i | \(-0.912469\pi\) | ||
0.962429 | − | 0.271534i | \(-0.0875309\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.0299317 | − | 0.259394i | −0.00122708 | − | 0.0106341i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 36.3829i | − | 1.48905i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37.2771 | −1.52310 | −0.761551 | − | 0.648105i | \(-0.775562\pi\) | ||||
−0.761551 | + | 0.648105i | \(0.775562\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.0594 | 0.695867 | 0.347934 | − | 0.937519i | \(-0.386883\pi\) | ||||
0.347934 | + | 0.937519i | \(0.386883\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.7502i | 0.478503i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.256321 | − | 2.22133i | −0.0104209 | − | 0.0903098i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.92624i | 0.321716i | 0.986978 | + | 0.160858i | \(0.0514262\pi\) | ||||
−0.986978 | + | 0.160858i | \(0.948574\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −28.3829 | −1.15013 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −30.7795 | −1.24520 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 9.93596i | − | 0.401310i | −0.979662 | − | 0.200655i | \(-0.935693\pi\) | ||
0.979662 | − | 0.200655i | \(-0.0643070\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −38.7406 | + | 4.47031i | −1.56217 | + | 0.180260i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.1010i | 1.53389i | 0.641715 | + | 0.766944i | \(0.278223\pi\) | ||||
−0.641715 | + | 0.766944i | \(0.721777\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.70309 | −0.229227 | −0.114613 | − | 0.993410i | \(-0.536563\pi\) | ||||
−0.114613 | + | 0.993410i | \(0.536563\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −106.159 | −4.26002 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.39663i | 0.0559548i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.4065 | − | 11.0882i | 0.896261 | − | 0.443527i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 22.2177i | − | 0.887291i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.760990 | −0.0303427 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.3242 | 0.689665 | 0.344833 | − | 0.938664i | \(-0.387936\pi\) | ||||
0.344833 | + | 0.938664i | \(0.387936\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 1.50232i | − | 0.0597120i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 27.9447 | − | 3.22456i | 1.10895 | − | 0.127963i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 23.3120i | − | 0.923657i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 50.9857 | 2.01696 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.3523 | −0.882863 | −0.441431 | − | 0.897295i | \(-0.645529\pi\) | ||||
−0.441431 | + | 0.897295i | \(0.645529\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.2911i | 0.997385i | 0.866779 | + | 0.498693i | \(0.166186\pi\) | ||||
−0.866779 | + | 0.498693i | \(0.833814\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.76248 | + | 41.2727i | 0.187523 | + | 1.62511i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.4262i | 0.881665i | 0.897589 | + | 0.440832i | \(0.145317\pi\) | ||||
−0.897589 | + | 0.440832i | \(0.854683\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.677809 | 0.0266063 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.09197 | 0.160377 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 11.8391i | − | 0.463301i | −0.972799 | − | 0.231650i | \(-0.925587\pi\) | ||
0.972799 | − | 0.231650i | \(-0.0744125\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.90710 | − | 33.8598i | −0.152663 | − | 1.32301i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 51.1098i | 1.99398i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.7522 | 0.613617 | 0.306809 | − | 0.951771i | \(-0.400739\pi\) | ||||
0.306809 | + | 0.951771i | \(0.400739\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.15702 | −0.278376 | −0.139188 | − | 0.990266i | \(-0.544449\pi\) | ||||
−0.139188 | + | 0.990266i | \(0.544449\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.44976i | 0.0563038i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.9010 | − | 1.83483i | 0.616616 | − | 0.0711517i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 46.6006i | − | 1.80438i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 60.0033 | 2.31986 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.197271 | 0.00761555 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.4976i | 0.443200i | 0.975138 | + | 0.221600i | \(0.0711279\pi\) | ||||
−0.975138 | + | 0.221600i | \(0.928872\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −20.2413 | − | 86.5398i | −0.779087 | − | 3.33092i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 21.9953i | − | 0.845347i | −0.906282 | − | 0.422673i | \(-0.861092\pi\) | ||
0.906282 | − | 0.422673i | \(-0.138908\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.15353 | 0.274527 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.41501 | 0.169183 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 0.468300i | − | 0.0179190i | −0.999960 | − | 0.00895950i | \(-0.997148\pi\) | ||
0.999960 | − | 0.00895950i | \(-0.00285194\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 32.4488 | − | 3.74429i | 1.23980 | − | 0.143062i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.2728i | 0.620844i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19.1098 | 0.728025 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.9140 | −1.40428 | −0.702138 | − | 0.712041i | \(-0.747771\pi\) | ||||
−0.702138 | + | 0.712041i | \(0.747771\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 8.97472i | − | 0.340921i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.23279 | − | 45.3484i | −0.198491 | − | 1.72016i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 0.559875i | − | 0.0212068i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 68.4880 | 2.59046 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.6628 | 0.704886 | 0.352443 | − | 0.935833i | \(-0.385351\pi\) | ||||
0.352443 | + | 0.935833i | \(0.385351\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 46.6492i | − | 1.75941i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.62724 | + | 57.4331i | 0.249596 | + | 2.16306i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 16.7154i | − | 0.628648i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.66135 | −0.250172 | −0.125086 | − | 0.992146i | \(-0.539921\pi\) | ||||
−0.125086 | + | 0.992146i | \(0.539921\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −77.5589 | −2.90869 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.71842i | 0.251607i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.88531 | + | 1.02528i | −0.332292 | + | 0.0383434i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 31.4356i | − | 1.17398i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.11128 | 0.116031 | 0.0580156 | − | 0.998316i | \(-0.481523\pi\) | ||||
0.0580156 | + | 0.998316i | \(0.481523\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.21991 | −0.231641 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 74.9310i | − | 2.78671i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 37.9884 | − | 8.88531i | 1.41085 | − | 0.329992i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.9540i | 1.25928i | 0.776886 | + | 0.629642i | \(0.216798\pi\) | ||||
−0.776886 | + | 0.629642i | \(0.783202\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −109.777 | −4.06581 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.596468 | −0.0220612 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 21.0457i | − | 0.777342i | −0.921377 | − | 0.388671i | \(-0.872934\pi\) | ||
0.921377 | − | 0.388671i | \(-0.127066\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −43.4993 | + | 5.01941i | −1.60449 | + | 0.185144i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.41737i | − | 0.0522097i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.0253 | 0.626285 | 0.313143 | − | 0.949706i | \(-0.398618\pi\) | ||||
0.313143 | + | 0.949706i | \(0.398618\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −88.8710 | −3.26476 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 23.7563i | − | 0.871536i | −0.900059 | − | 0.435768i | \(-0.856477\pi\) | ||
0.900059 | − | 0.435768i | \(-0.143523\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.07227 | − | 35.2911i | −0.149196 | − | 1.29297i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 113.951i | 4.16924i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.66067 | −0.170297 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −44.8654 | −1.63716 | −0.818582 | − | 0.574390i | \(-0.805239\pi\) | ||||
−0.818582 | + | 0.574390i | \(0.805239\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 36.7177i | 1.33807i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.68663 | − | 14.6167i | −0.0613829 | − | 0.531957i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.3761i | 1.50384i | 0.659255 | + | 0.751920i | \(0.270872\pi\) | ||||
−0.659255 | + | 0.751920i | \(0.729128\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 20.0675 | 0.728405 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.3002 | 0.590883 | 0.295442 | − | 0.955361i | \(-0.404533\pi\) | ||||
0.295442 | + | 0.955361i | \(0.404533\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.52279i | 0.0913310i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.98636 | − | 0.229207i | 0.0718170 | − | 0.00828701i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 2.71124i | − | 0.0978971i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.1262 | −1.48305 | −0.741525 | − | 0.670925i | \(-0.765897\pi\) | ||||
−0.741525 | + | 0.670925i | \(0.765897\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 72.0409 | 2.59449 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 9.77280i | − | 0.351503i | −0.984435 | − | 0.175752i | \(-0.943764\pi\) | ||
0.984435 | − | 0.175752i | \(-0.0562355\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.47679 | + | 1.28100i | −0.196732 | + | 0.0460147i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 25.6628i | − | 0.920646i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 34.3207 | 1.22967 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.15020 | −0.220072 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 138.694i | − | 4.95652i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.1840 | − | 1.63670i | 0.506248 | − | 0.0584162i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.25466i | 0.187308i | 0.995605 | + | 0.0936541i | \(0.0298548\pi\) | ||||
−0.995605 | + | 0.0936541i | \(0.970145\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.9173 | 0.780278 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.8511 | 0.421377 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 0.789082i | − | 0.0280211i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.11460 | − | 35.6580i | −0.145930 | − | 1.26466i | ||||
\(796\) | 0 |