Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1890,2,Mod(1151,1890)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1890, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 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("1890.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1890.t (of order \(6\), degree \(2\), not 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: | \(15.0917259820\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1601.2 | ||
Character | \(\chi\) | \(=\) | 1890.1601 |
Dual form | 1890.2.t.b.1151.2 |
$q$-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 \(\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(1081\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.36047 | + | 1.19507i | −0.892173 | + | 0.451693i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.866025 | + | 0.500000i | −0.273861 | + | 0.158114i | ||||
\(11\) | 3.17454i | 0.957161i | 0.878044 | + | 0.478581i | \(0.158849\pi\) | ||||
−0.878044 | + | 0.478581i | \(0.841151\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.82400 | + | 1.05309i | −0.505887 | + | 0.292074i | −0.731141 | − | 0.682226i | \(-0.761012\pi\) |
0.225254 | + | 0.974300i | \(0.427679\pi\) | |||||||
\(14\) | 1.44669 | − | 2.21519i | 0.386645 | − | 0.592035i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0.0900212 | + | 0.155921i | 0.0218333 | + | 0.0378165i | 0.876736 | − | 0.480973i | \(-0.159716\pi\) |
−0.854902 | + | 0.518789i | \(0.826383\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.17571 | − | 2.98820i | −1.18739 | − | 0.685540i | −0.229678 | − | 0.973267i | \(-0.573767\pi\) |
−0.957713 | + | 0.287727i | \(0.907101\pi\) | |||||||
\(20\) | 0.500000 | − | 0.866025i | 0.111803 | − | 0.193649i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.58727 | − | 2.74924i | −0.338408 | − | 0.586139i | ||||
\(23\) | − | 0.789076i | − | 0.164534i | −0.996610 | − | 0.0822669i | \(-0.973784\pi\) | ||
0.996610 | − | 0.0822669i | \(-0.0262160\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.05309 | − | 1.82400i | 0.206528 | − | 0.357716i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.145275 | + | 2.64176i | −0.0274544 | + | 0.499246i | ||||
\(29\) | 6.84694 | + | 3.95308i | 1.27144 | + | 0.734069i | 0.975260 | − | 0.221062i | \(-0.0709522\pi\) |
0.296185 | + | 0.955131i | \(0.404286\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.40319 | − | 4.85159i | −1.50926 | − | 0.871370i | −0.999942 | − | 0.0107910i | \(-0.996565\pi\) |
−0.509316 | − | 0.860579i | \(-0.670102\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.155921 | − | 0.0900212i | −0.0267403 | − | 0.0154385i | ||||
\(35\) | −2.36047 | + | 1.19507i | −0.398992 | + | 0.202003i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.27097 | − | 7.39754i | 0.702143 | − | 1.21615i | −0.265569 | − | 0.964092i | \(-0.585560\pi\) |
0.967713 | − | 0.252056i | \(-0.0811068\pi\) | |||||||
\(38\) | 5.97640 | 0.969500 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000i | 0.158114i | ||||||||
\(41\) | −5.85731 | − | 10.1452i | −0.914758 | − | 1.58441i | −0.807256 | − | 0.590202i | \(-0.799048\pi\) |
−0.107502 | − | 0.994205i | \(-0.534285\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.84922 | + | 3.20294i | −0.282003 | + | 0.488443i | −0.971878 | − | 0.235485i | \(-0.924332\pi\) |
0.689875 | + | 0.723929i | \(0.257665\pi\) | |||||||
\(44\) | 2.74924 | + | 1.58727i | 0.414463 | + | 0.239290i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.394538 | + | 0.683360i | 0.0581715 | + | 0.100756i | ||||
\(47\) | 1.04181 | + | 1.80446i | 0.151963 | + | 0.263207i | 0.931949 | − | 0.362589i | \(-0.118107\pi\) |
−0.779986 | + | 0.625797i | \(0.784774\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.14362 | − | 5.64184i | 0.591946 | − | 0.805977i | ||||
\(50\) | −0.866025 | + | 0.500000i | −0.122474 | + | 0.0707107i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.10618i | 0.292074i | ||||||||
\(53\) | −0.613086 | + | 0.353965i | −0.0842138 | + | 0.0486209i | −0.541516 | − | 0.840691i | \(-0.682149\pi\) |
0.457302 | + | 0.889312i | \(0.348816\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.17454i | 0.428055i | ||||||||
\(56\) | −1.19507 | − | 2.36047i | −0.159698 | − | 0.315431i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.90616 | −1.03813 | ||||||||
\(59\) | 5.88665 | − | 10.1960i | 0.766377 | − | 1.32740i | −0.173138 | − | 0.984898i | \(-0.555391\pi\) |
0.939515 | − | 0.342506i | \(-0.111276\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.50805 | − | 1.44802i | 0.321122 | − | 0.185400i | −0.330770 | − | 0.943711i | \(-0.607309\pi\) |
0.651893 | + | 0.758311i | \(0.273975\pi\) | |||||||
\(62\) | 9.70317 | 1.23230 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −1.82400 | + | 1.05309i | −0.226240 | + | 0.130620i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.97848 | + | 8.62299i | −0.608219 | + | 1.05347i | 0.383315 | + | 0.923618i | \(0.374782\pi\) |
−0.991534 | + | 0.129848i | \(0.958551\pi\) | |||||||
\(68\) | 0.180042 | 0.0218333 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.44669 | − | 2.21519i | 0.172913 | − | 0.264766i | ||||
\(71\) | − | 10.1885i | − | 1.20915i | −0.796549 | − | 0.604574i | \(-0.793344\pi\) | ||
0.796549 | − | 0.604574i | \(-0.206656\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.09156 | + | 2.93961i | −0.595921 | + | 0.344055i | −0.767435 | − | 0.641126i | \(-0.778467\pi\) |
0.171514 | + | 0.985182i | \(0.445134\pi\) | |||||||
\(74\) | 8.54194i | 0.992981i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.17571 | + | 2.98820i | −0.593695 | + | 0.342770i | ||||
\(77\) | −3.79380 | − | 7.49341i | −0.432343 | − | 0.853953i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.50268 | − | 9.53091i | −0.619099 | − | 1.07231i | −0.989650 | − | 0.143499i | \(-0.954164\pi\) |
0.370551 | − | 0.928812i | \(-0.379169\pi\) | |||||||
\(80\) | −0.500000 | − | 0.866025i | −0.0559017 | − | 0.0968246i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 10.1452 | + | 5.85731i | 1.12034 | + | 0.646831i | ||||
\(83\) | −4.41475 | + | 7.64657i | −0.484582 | + | 0.839320i | −0.999843 | − | 0.0177130i | \(-0.994361\pi\) |
0.515261 | + | 0.857033i | \(0.327695\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.0900212 | + | 0.155921i | 0.00976417 | + | 0.0169120i | ||||
\(86\) | − | 3.69843i | − | 0.398812i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.17454 | −0.338408 | ||||||||
\(89\) | −2.91136 | + | 5.04262i | −0.308603 | + | 0.534516i | −0.978057 | − | 0.208337i | \(-0.933195\pi\) |
0.669454 | + | 0.742854i | \(0.266528\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.04699 | − | 4.66559i | 0.319411 | − | 0.489087i | ||||
\(92\) | −0.683360 | − | 0.394538i | −0.0712452 | − | 0.0411335i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.80446 | − | 1.04181i | −0.186116 | − | 0.107454i | ||||
\(95\) | −5.17571 | − | 2.98820i | −0.531017 | − | 0.306583i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.79334 | − | 2.19008i | −0.385155 | − | 0.222369i | 0.294904 | − | 0.955527i | \(-0.404712\pi\) |
−0.680059 | + | 0.733158i | \(0.738046\pi\) | |||||||
\(98\) | −0.767563 | + | 6.95779i | −0.0775355 | + | 0.702843i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.500000 | − | 0.866025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | −16.9191 | −1.68352 | −0.841759 | − | 0.539854i | \(-0.818479\pi\) | ||||
−0.841759 | + | 0.539854i | \(0.818479\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.31108i | 0.523316i | 0.965161 | + | 0.261658i | \(0.0842693\pi\) | ||||
−0.965161 | + | 0.261658i | \(0.915731\pi\) | |||||||
\(104\) | −1.05309 | − | 1.82400i | −0.103264 | − | 0.178858i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.353965 | − | 0.613086i | 0.0343801 | − | 0.0595482i | ||||
\(107\) | −7.07344 | − | 4.08385i | −0.683816 | − | 0.394801i | 0.117476 | − | 0.993076i | \(-0.462520\pi\) |
−0.801291 | + | 0.598275i | \(0.795853\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.606828 | − | 1.05106i | −0.0581235 | − | 0.100673i | 0.835500 | − | 0.549491i | \(-0.185178\pi\) |
−0.893623 | + | 0.448818i | \(0.851845\pi\) | |||||||
\(110\) | −1.58727 | − | 2.74924i | −0.151340 | − | 0.262129i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.21519 | + | 1.44669i | 0.209316 | + | 0.136700i | ||||
\(113\) | 1.23720 | − | 0.714296i | 0.116386 | − | 0.0671953i | −0.440677 | − | 0.897666i | \(-0.645262\pi\) |
0.557063 | + | 0.830470i | \(0.311928\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 0.789076i | − | 0.0735818i | ||||||
\(116\) | 6.84694 | − | 3.95308i | 0.635722 | − | 0.367034i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.7733i | 1.08382i | ||||||||
\(119\) | −0.398829 | − | 0.260466i | −0.0365606 | − | 0.0238769i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.922270 | 0.0838427 | ||||||||
\(122\) | −1.44802 | + | 2.50805i | −0.131098 | + | 0.227068i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8.40319 | + | 4.85159i | −0.754629 | + | 0.435685i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.1021 | −1.34010 | −0.670048 | − | 0.742318i | \(-0.733726\pi\) | ||||
−0.670048 | + | 0.742318i | \(0.733726\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.05309 | − | 1.82400i | 0.0923620 | − | 0.159976i | ||||
\(131\) | 8.38038 | 0.732197 | 0.366099 | − | 0.930576i | \(-0.380693\pi\) | ||||
0.366099 | + | 0.930576i | \(0.380693\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15.7882 | + | 0.868221i | 1.36901 | + | 0.0752843i | ||||
\(134\) | − | 9.95697i | − | 0.860151i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.155921 | + | 0.0900212i | −0.0133701 | + | 0.00771925i | ||||
\(137\) | − | 8.76324i | − | 0.748694i | −0.927289 | − | 0.374347i | \(-0.877867\pi\) | ||
0.927289 | − | 0.374347i | \(-0.122133\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.76711 | − | 1.59759i | 0.234704 | − | 0.135506i | −0.378036 | − | 0.925791i | \(-0.623401\pi\) |
0.612740 | + | 0.790285i | \(0.290067\pi\) | |||||||
\(140\) | −0.145275 | + | 2.64176i | −0.0122780 | + | 0.223269i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.09423 | + | 8.82346i | 0.427498 | + | 0.740448i | ||||
\(143\) | −3.34308 | − | 5.79038i | −0.279562 | − | 0.484216i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.84694 | + | 3.95308i | 0.568607 | + | 0.328286i | ||||
\(146\) | 2.93961 | − | 5.09156i | 0.243284 | − | 0.421380i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.27097 | − | 7.39754i | −0.351072 | − | 0.608074i | ||||
\(149\) | 6.20523i | 0.508353i | 0.967158 | + | 0.254176i | \(0.0818044\pi\) | ||||
−0.967158 | + | 0.254176i | \(0.918196\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.6607 | 0.867559 | 0.433779 | − | 0.901019i | \(-0.357180\pi\) | ||||
0.433779 | + | 0.901019i | \(0.357180\pi\) | |||||||
\(152\) | 2.98820 | − | 5.17571i | 0.242375 | − | 0.419806i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.03223 | + | 4.59259i | 0.566673 | + | 0.370081i | ||||
\(155\) | −8.40319 | − | 4.85159i | −0.674961 | − | 0.389689i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.80928 | − | 2.19929i | −0.304014 | − | 0.175523i | 0.340231 | − | 0.940342i | \(-0.389495\pi\) |
−0.644245 | + | 0.764819i | \(0.722828\pi\) | |||||||
\(158\) | 9.53091 | + | 5.50268i | 0.758239 | + | 0.437769i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.866025 | + | 0.500000i | 0.0684653 | + | 0.0395285i | ||||
\(161\) | 0.943000 | + | 1.86259i | 0.0743188 | + | 0.146793i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.94559 | − | 17.2263i | 0.778999 | − | 1.34927i | −0.153520 | − | 0.988146i | \(-0.549061\pi\) |
0.932519 | − | 0.361120i | \(-0.117606\pi\) | |||||||
\(164\) | −11.7146 | −0.914758 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 8.82950i | − | 0.685302i | ||||||
\(167\) | −7.13831 | − | 12.3639i | −0.552379 | − | 0.956749i | −0.998102 | − | 0.0615778i | \(-0.980387\pi\) |
0.445723 | − | 0.895171i | \(-0.352947\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.28201 | + | 7.41666i | −0.329385 | + | 0.570512i | ||||
\(170\) | −0.155921 | − | 0.0900212i | −0.0119586 | − | 0.00690431i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.84922 | + | 3.20294i | 0.141001 | + | 0.244222i | ||||
\(173\) | 6.61430 | + | 11.4563i | 0.502876 | + | 0.871007i | 0.999994 | + | 0.00332403i | \(0.00105807\pi\) |
−0.497119 | + | 0.867683i | \(0.665609\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.36047 | + | 1.19507i | −0.178435 | + | 0.0903387i | ||||
\(176\) | 2.74924 | − | 1.58727i | 0.207231 | − | 0.119645i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 5.82271i | − | 0.436431i | ||||||
\(179\) | −3.52462 | + | 2.03494i | −0.263442 | + | 0.152098i | −0.625904 | − | 0.779900i | \(-0.715270\pi\) |
0.362462 | + | 0.931999i | \(0.381936\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 21.7339i | − | 1.61547i | −0.589546 | − | 0.807735i | \(-0.700693\pi\) | ||
0.589546 | − | 0.807735i | \(-0.299307\pi\) | |||||||
\(182\) | −0.305975 | + | 5.56401i | −0.0226803 | + | 0.412432i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.789076 | 0.0581715 | ||||||||
\(185\) | 4.27097 | − | 7.39754i | 0.314008 | − | 0.543878i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.494979 | + | 0.285776i | −0.0361964 | + | 0.0208980i | ||||
\(188\) | 2.08361 | 0.151963 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.97640 | 0.433574 | ||||||||
\(191\) | −6.73693 | + | 3.88957i | −0.487467 | + | 0.281439i | −0.723523 | − | 0.690300i | \(-0.757478\pi\) |
0.236056 | + | 0.971739i | \(0.424145\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.14681 | + | 7.18249i | −0.298494 | + | 0.517007i | −0.975792 | − | 0.218702i | \(-0.929818\pi\) |
0.677298 | + | 0.735709i | \(0.263151\pi\) | |||||||
\(194\) | 4.38017 | 0.314478 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.81417 | − | 6.40940i | −0.201012 | − | 0.457815i | ||||
\(197\) | 13.3008i | 0.947643i | 0.880621 | + | 0.473822i | \(0.157126\pi\) | ||||
−0.880621 | + | 0.473822i | \(0.842874\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.1833 | + | 9.34343i | −1.14720 | + | 0.662338i | −0.948204 | − | 0.317661i | \(-0.897102\pi\) |
−0.198999 | + | 0.980000i | \(0.563769\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 14.6524 | − | 8.45957i | 1.03094 | − | 0.595213i | ||||
\(203\) | −20.8862 | − | 1.14857i | −1.46592 | − | 0.0806136i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.85731 | − | 10.1452i | −0.409092 | − | 0.708568i | ||||
\(206\) | −2.65554 | − | 4.59953i | −0.185020 | − | 0.320464i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.82400 | + | 1.05309i | 0.126472 | + | 0.0730185i | ||||
\(209\) | 9.48617 | − | 16.4305i | 0.656172 | − | 1.13652i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.1577 | − | 21.0578i | −0.836971 | − | 1.44968i | −0.892416 | − | 0.451214i | \(-0.850991\pi\) |
0.0554450 | − | 0.998462i | \(-0.482342\pi\) | |||||||
\(212\) | 0.707930i | 0.0486209i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.16771 | 0.558333 | ||||||||
\(215\) | −1.84922 | + | 3.20294i | −0.126116 | + | 0.218439i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 25.6334 | + | 1.40963i | 1.74011 | + | 0.0956917i | ||||
\(218\) | 1.05106 | + | 0.606828i | 0.0711865 | + | 0.0410996i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.74924 | + | 1.58727i | 0.185353 | + | 0.107014i | ||||
\(221\) | −0.328398 | − | 0.189601i | −0.0220904 | − | 0.0127539i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.5348 | − | 8.39165i | −0.973320 | − | 0.561946i | −0.0730731 | − | 0.997327i | \(-0.523281\pi\) |
−0.900247 | + | 0.435380i | \(0.856614\pi\) | |||||||
\(224\) | −2.64176 | − | 0.145275i | −0.176510 | − | 0.00970659i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.714296 | + | 1.23720i | −0.0475143 | + | 0.0822971i | ||||
\(227\) | −16.7913 | −1.11448 | −0.557240 | − | 0.830351i | \(-0.688140\pi\) | ||||
−0.557240 | + | 0.830351i | \(0.688140\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 6.63136i | − | 0.438213i | −0.975701 | − | 0.219106i | \(-0.929686\pi\) | ||
0.975701 | − | 0.219106i | \(-0.0703142\pi\) | |||||||
\(230\) | 0.394538 | + | 0.683360i | 0.0260151 | + | 0.0450594i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.95308 | + | 6.84694i | −0.259533 | + | 0.449524i | ||||
\(233\) | −6.79700 | − | 3.92425i | −0.445286 | − | 0.257086i | 0.260551 | − | 0.965460i | \(-0.416096\pi\) |
−0.705837 | + | 0.708374i | \(0.749429\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.04181 | + | 1.80446i | 0.0679599 | + | 0.117710i | ||||
\(236\) | −5.88665 | − | 10.1960i | −0.383189 | − | 0.663702i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.475629 | + | 0.0261556i | 0.0308304 | + | 0.00169542i | ||||
\(239\) | 14.3341 | − | 8.27578i | 0.927195 | − | 0.535316i | 0.0412714 | − | 0.999148i | \(-0.486859\pi\) |
0.885923 | + | 0.463832i | \(0.153526\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 19.2604i | − | 1.24067i | −0.784336 | − | 0.620336i | \(-0.786996\pi\) | ||
0.784336 | − | 0.620336i | \(-0.213004\pi\) | |||||||
\(242\) | −0.798709 | + | 0.461135i | −0.0513430 | + | 0.0296429i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 2.89604i | − | 0.185400i | ||||||
\(245\) | 4.14362 | − | 5.64184i | 0.264726 | − | 0.360444i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.5874 | 0.800914 | ||||||||
\(248\) | 4.85159 | − | 8.40319i | 0.308076 | − | 0.533603i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.866025 | + | 0.500000i | −0.0547723 | + | 0.0316228i | ||||
\(251\) | 22.0186 | 1.38980 | 0.694901 | − | 0.719105i | \(-0.255448\pi\) | ||||
0.694901 | + | 0.719105i | \(0.255448\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.50496 | 0.157485 | ||||||||
\(254\) | 13.0788 | − | 7.55105i | 0.820637 | − | 0.473795i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 20.8442 | 1.30022 | 0.650112 | − | 0.759839i | \(-0.274722\pi\) | ||||
0.650112 | + | 0.759839i | \(0.274722\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.24093 | + | 22.5658i | −0.0771076 | + | 1.40217i | ||||
\(260\) | 2.10618i | 0.130620i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.25762 | + | 4.19019i | −0.448377 | + | 0.258871i | ||||
\(263\) | 22.5371i | 1.38969i | 0.719157 | + | 0.694847i | \(0.244528\pi\) | ||||
−0.719157 | + | 0.694847i | \(0.755472\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.613086 | + | 0.353965i | −0.0376616 | + | 0.0217439i | ||||
\(266\) | −14.1071 | + | 7.14221i | −0.864962 | + | 0.437917i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.97848 | + | 8.62299i | 0.304109 | + | 0.526733i | ||||
\(269\) | 11.8691 | + | 20.5578i | 0.723670 | + | 1.25343i | 0.959519 | + | 0.281643i | \(0.0908794\pi\) |
−0.235849 | + | 0.971790i | \(0.575787\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.2170 | − | 5.89877i | −0.620636 | − | 0.358325i | 0.156480 | − | 0.987681i | \(-0.449985\pi\) |
−0.777117 | + | 0.629356i | \(0.783319\pi\) | |||||||
\(272\) | 0.0900212 | − | 0.155921i | 0.00545834 | − | 0.00945412i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.38162 | + | 7.58919i | 0.264703 | + | 0.458480i | ||||
\(275\) | 3.17454i | 0.191432i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.3064 | −1.09993 | −0.549963 | − | 0.835189i | \(-0.685358\pi\) | ||||
−0.549963 | + | 0.835189i | \(0.685358\pi\) | |||||||
\(278\) | −1.59759 | + | 2.76711i | −0.0958173 | + | 0.165960i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.19507 | − | 2.36047i | −0.0714190 | − | 0.141065i | ||||
\(281\) | −18.8875 | − | 10.9047i | −1.12674 | − | 0.650521i | −0.183624 | − | 0.982997i | \(-0.558783\pi\) |
−0.943112 | + | 0.332475i | \(0.892116\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.31465 | + | 0.759014i | 0.0781479 | + | 0.0451187i | 0.538565 | − | 0.842584i | \(-0.318967\pi\) |
−0.460417 | + | 0.887703i | \(0.652300\pi\) | |||||||
\(284\) | −8.82346 | − | 5.09423i | −0.523576 | − | 0.302287i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.79038 | + | 3.34308i | 0.342392 | + | 0.197680i | ||||
\(287\) | 25.9501 | + | 16.9474i | 1.53179 | + | 1.00038i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.48379 | − | 14.6944i | 0.499047 | − | 0.864374i | ||||
\(290\) | −7.90616 | −0.464266 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.87922i | 0.344055i | ||||||||
\(293\) | −2.79327 | − | 4.83808i | −0.163184 | − | 0.282643i | 0.772825 | − | 0.634620i | \(-0.218843\pi\) |
−0.936009 | + | 0.351976i | \(0.885510\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.88665 | − | 10.1960i | 0.342734 | − | 0.593633i | ||||
\(296\) | 7.39754 | + | 4.27097i | 0.429973 | + | 0.248245i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.10262 | − | 5.37389i | −0.179730 | − | 0.311301i | ||||
\(299\) | 0.830967 | + | 1.43928i | 0.0480561 | + | 0.0832356i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.537290 | − | 9.77038i | 0.0309689 | − | 0.563155i | ||||
\(302\) | −9.23247 | + | 5.33037i | −0.531269 | + | 0.306728i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.97640i | 0.342770i | ||||||||
\(305\) | 2.50805 | − | 1.44802i | 0.143610 | − | 0.0829134i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.8941i | 1.30663i | 0.757085 | + | 0.653316i | \(0.226623\pi\) | ||||
−0.757085 | + | 0.653316i | \(0.773377\pi\) | |||||||
\(308\) | −8.38638 | − | 0.461181i | −0.477859 | − | 0.0262783i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9.70317 | 0.551103 | ||||||||
\(311\) | −10.8658 | + | 18.8202i | −0.616146 | + | 1.06720i | 0.374037 | + | 0.927414i | \(0.377973\pi\) |
−0.990182 | + | 0.139782i | \(0.955360\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.71267 | + | 1.56616i | −0.153329 | + | 0.0885247i | −0.574702 | − | 0.818363i | \(-0.694882\pi\) |
0.421372 | + | 0.906888i | \(0.361549\pi\) | |||||||
\(314\) | 4.39858 | 0.248226 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.0054 | −0.619099 | ||||||||
\(317\) | 24.8434 | − | 14.3433i | 1.39534 | − | 0.805602i | 0.401444 | − | 0.915884i | \(-0.368509\pi\) |
0.993900 | + | 0.110281i | \(0.0351752\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.5492 | + | 21.7359i | −0.702622 | + | 1.21698i | ||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.74796 | − | 1.14155i | −0.0974098 | − | 0.0636161i | ||||
\(323\) | − | 1.07601i | − | 0.0598705i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.82400 | + | 1.05309i | −0.101177 | + | 0.0584148i | ||||
\(326\) | 19.8912i | 1.10167i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 10.1452 | − | 5.85731i | 0.560172 | − | 0.323416i | ||||
\(329\) | −4.61560 | − | 3.01434i | −0.254466 | − | 0.166186i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.85472 | + | 4.94451i | 0.156909 | + | 0.271775i | 0.933753 | − | 0.357919i | \(-0.116514\pi\) |
−0.776843 | + | 0.629694i | \(0.783180\pi\) | |||||||
\(332\) | 4.41475 | + | 7.64657i | 0.242291 | + | 0.419660i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.3639 | + | 7.13831i | 0.676523 | + | 0.390591i | ||||
\(335\) | −4.97848 | + | 8.62299i | −0.272004 | + | 0.471124i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.41618 | + | 9.38110i | 0.295038 | + | 0.511021i | 0.974994 | − | 0.222232i | \(-0.0713343\pi\) |
−0.679956 | + | 0.733253i | \(0.738001\pi\) | |||||||
\(338\) | − | 8.56402i | − | 0.465821i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.180042 | 0.00976417 | ||||||||
\(341\) | 15.4016 | − | 26.6763i | 0.834042 | − | 1.44460i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.03851 | + | 18.2693i | −0.164064 | + | 0.986450i | ||||
\(344\) | −3.20294 | − | 1.84922i | −0.172691 | − | 0.0997031i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11.4563 | − | 6.61430i | −0.615895 | − | 0.355587i | ||||
\(347\) | −16.7740 | − | 9.68446i | −0.900474 | − | 0.519889i | −0.0231203 | − | 0.999733i | \(-0.507360\pi\) |
−0.877354 | + | 0.479844i | \(0.840693\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.1942 | + | 9.92710i | 0.920387 | + | 0.531385i | 0.883758 | − | 0.467944i | \(-0.155005\pi\) |
0.0366282 | + | 0.999329i | \(0.488338\pi\) | |||||||
\(350\) | 1.44669 | − | 2.21519i | 0.0773289 | − | 0.118407i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.58727 | + | 2.74924i | −0.0846019 | + | 0.146535i | ||||
\(353\) | −11.4940 | −0.611763 | −0.305881 | − | 0.952070i | \(-0.598951\pi\) | ||||
−0.305881 | + | 0.952070i | \(0.598951\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 10.1885i | − | 0.540747i | ||||||
\(356\) | 2.91136 | + | 5.04262i | 0.154302 | + | 0.267258i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.03494 | − | 3.52462i | 0.107550 | − | 0.186282i | ||||
\(359\) | 19.1794 | + | 11.0732i | 1.01225 | + | 0.584422i | 0.911849 | − | 0.410525i | \(-0.134654\pi\) |
0.100400 | + | 0.994947i | \(0.467988\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.35868 | + | 14.4777i | 0.439930 | + | 0.761982i | ||||
\(362\) | 10.8670 | + | 18.8221i | 0.571155 | + | 0.989269i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.51702 | − | 4.97156i | −0.131928 | − | 0.260581i | ||||
\(365\) | −5.09156 | + | 2.93961i | −0.266504 | + | 0.153866i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.1428i | 1.05144i | 0.850656 | + | 0.525722i | \(0.176205\pi\) | ||||
−0.850656 | + | 0.525722i | \(0.823795\pi\) | |||||||
\(368\) | −0.683360 | + | 0.394538i | −0.0356226 | + | 0.0205667i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.54194i | 0.444074i | ||||||||
\(371\) | 1.02416 | − | 1.56820i | 0.0531716 | − | 0.0814171i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.2910 | 1.41308 | 0.706538 | − | 0.707675i | \(-0.250256\pi\) | ||||
0.706538 | + | 0.707675i | \(0.250256\pi\) | |||||||
\(374\) | 0.285776 | − | 0.494979i | 0.0147771 | − | 0.0255948i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.80446 | + | 1.04181i | −0.0930579 | + | 0.0537270i | ||||
\(377\) | −16.6518 | −0.857610 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.6022 | −1.00690 | −0.503448 | − | 0.864026i | \(-0.667935\pi\) | ||||
−0.503448 | + | 0.864026i | \(0.667935\pi\) | |||||||
\(380\) | −5.17571 | + | 2.98820i | −0.265509 | + | 0.153291i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.88957 | − | 6.73693i | 0.199008 | − | 0.344691i | ||||
\(383\) | 3.97158 | 0.202938 | 0.101469 | − | 0.994839i | \(-0.467646\pi\) | ||||
0.101469 | + | 0.994839i | \(0.467646\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.79380 | − | 7.49341i | −0.193350 | − | 0.381900i | ||||
\(386\) | − | 8.29363i | − | 0.422134i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.79334 | + | 2.19008i | −0.192577 | + | 0.111185i | ||||
\(389\) | 18.8926i | 0.957891i | 0.877845 | + | 0.478945i | \(0.158981\pi\) | ||||
−0.877845 | + | 0.478945i | \(0.841019\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.123034 | − | 0.0710336i | 0.00622209 | − | 0.00359232i | ||||
\(392\) | 5.64184 | + | 4.14362i | 0.284956 | + | 0.209285i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.65040 | − | 11.5188i | −0.335042 | − | 0.580311i | ||||
\(395\) | −5.50268 | − | 9.53091i | −0.276870 | − | 0.479552i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.5990 | − | 17.6664i | −1.53572 | − | 0.886649i | −0.999082 | − | 0.0428377i | \(-0.986360\pi\) |
−0.536640 | − | 0.843812i | \(-0.680307\pi\) | |||||||
\(398\) | 9.34343 | − | 16.1833i | 0.468344 | − | 0.811195i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.500000 | − | 0.866025i | −0.0250000 | − | 0.0433013i | ||||
\(401\) | 0.623333i | 0.0311278i | 0.999879 | + | 0.0155639i | \(0.00495434\pi\) | ||||
−0.999879 | + | 0.0155639i | \(0.995046\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.4366 | 1.01802 | ||||||||
\(404\) | −8.45957 | + | 14.6524i | −0.420879 | + | 0.728984i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 18.6623 | − | 9.44841i | 0.926192 | − | 0.468916i | ||||
\(407\) | 23.4838 | + | 13.5584i | 1.16405 | + | 0.672064i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.20408 | + | 0.695174i | 0.0595377 | + | 0.0343741i | 0.529473 | − | 0.848327i | \(-0.322390\pi\) |
−0.469936 | + | 0.882701i | \(0.655723\pi\) | |||||||
\(410\) | 10.1452 | + | 5.85731i | 0.501033 | + | 0.289272i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.59953 | + | 2.65554i | 0.226603 | + | 0.130829i | ||||
\(413\) | −1.71037 | + | 31.1023i | −0.0841616 | + | 1.53044i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.41475 | + | 7.64657i | −0.216711 | + | 0.375355i | ||||
\(416\) | −2.10618 | −0.103264 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 18.9723i | 0.927968i | ||||||||
\(419\) | 13.7784 | + | 23.8650i | 0.673121 | + | 1.16588i | 0.977014 | + | 0.213174i | \(0.0683800\pi\) |
−0.303893 | + | 0.952706i | \(0.598287\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.1806 | + | 29.7576i | −0.837331 | + | 1.45030i | 0.0547882 | + | 0.998498i | \(0.482552\pi\) |
−0.892119 | + | 0.451801i | \(0.850782\pi\) | |||||||
\(422\) | 21.0578 | + | 12.1577i | 1.02508 | + | 0.591828i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.353965 | − | 0.613086i | −0.0171901 | − | 0.0297741i | ||||
\(425\) | 0.0900212 | + | 0.155921i | 0.00436667 | + | 0.00756329i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.18968 | + | 6.41529i | −0.202753 | + | 0.310458i | ||||
\(428\) | −7.07344 | + | 4.08385i | −0.341908 | + | 0.197401i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 3.69843i | − | 0.178354i | ||||||
\(431\) | −24.3620 | + | 14.0654i | −1.17348 | + | 0.677508i | −0.954497 | − | 0.298221i | \(-0.903607\pi\) |
−0.218981 | + | 0.975729i | \(0.570273\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 11.9782i | − | 0.575635i | −0.957685 | − | 0.287817i | \(-0.907070\pi\) | ||
0.957685 | − | 0.287817i | \(-0.0929296\pi\) | |||||||
\(434\) | −22.9040 | + | 11.5960i | −1.09943 | + | 0.556623i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.21366 | −0.0581235 | ||||||||
\(437\) | −2.35792 | + | 4.08403i | −0.112795 | + | 0.195366i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.40402 | − | 5.42941i | 0.448829 | − | 0.259132i | −0.258506 | − | 0.966010i | \(-0.583230\pi\) |
0.707336 | + | 0.706878i | \(0.249897\pi\) | |||||||
\(440\) | −3.17454 | −0.151340 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.379201 | 0.0180368 | ||||||||
\(443\) | −1.83321 | + | 1.05840i | −0.0870983 | + | 0.0502862i | −0.542917 | − | 0.839787i | \(-0.682680\pi\) |
0.455818 | + | 0.890073i | \(0.349347\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.91136 | + | 5.04262i | −0.138011 | + | 0.239043i | ||||
\(446\) | 16.7833 | 0.794712 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.36047 | − | 1.19507i | 0.111522 | − | 0.0564617i | ||||
\(449\) | 12.2537i | 0.578290i | 0.957285 | + | 0.289145i | \(0.0933710\pi\) | ||||
−0.957285 | + | 0.289145i | \(0.906629\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 32.2062 | − | 18.5943i | 1.51653 | − | 0.875571i | ||||
\(452\) | − | 1.42859i | − | 0.0671953i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14.5417 | − | 8.39567i | 0.682477 | − | 0.394028i | ||||
\(455\) | 3.04699 | − | 4.66559i | 0.142845 | − | 0.218726i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.5567 | + | 28.6771i | 0.774490 | + | 1.34146i | 0.935080 | + | 0.354435i | \(0.115327\pi\) |
−0.160590 | + | 0.987021i | \(0.551340\pi\) | |||||||
\(458\) | 3.31568 | + | 5.74293i | 0.154932 | + | 0.268349i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.683360 | − | 0.394538i | −0.0318618 | − | 0.0183954i | ||||
\(461\) | −14.1222 | + | 24.4604i | −0.657737 | + | 1.13923i | 0.323463 | + | 0.946241i | \(0.395153\pi\) |
−0.981200 | + | 0.192994i | \(0.938180\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.1122 | + | 34.8353i | 0.934692 | + | 1.61893i | 0.775181 | + | 0.631739i | \(0.217658\pi\) |
0.159511 | + | 0.987196i | \(0.449008\pi\) | |||||||
\(464\) | − | 7.90616i | − | 0.367034i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.84850 | 0.363575 | ||||||||
\(467\) | 0.824539 | − | 1.42814i | 0.0381551 | − | 0.0660866i | −0.846317 | − | 0.532679i | \(-0.821185\pi\) |
0.884472 | + | 0.466593i | \(0.154519\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.44650 | − | 26.3039i | 0.0667930 | − | 1.21460i | ||||
\(470\) | −1.80446 | − | 1.04181i | −0.0832335 | − | 0.0480549i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 10.1960 | + | 5.88665i | 0.469308 | + | 0.270955i | ||||
\(473\) | −10.1679 | − | 5.87042i | −0.467519 | − | 0.269922i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.17571 | − | 2.98820i | −0.237478 | − | 0.137108i | ||||
\(476\) | −0.424984 | + | 0.215163i | −0.0194791 | + | 0.00986198i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.27578 | + | 14.3341i | −0.378526 | + | 0.655626i | ||||
\(479\) | −28.2535 | −1.29093 | −0.645467 | − | 0.763788i | \(-0.723337\pi\) | ||||
−0.645467 | + | 0.763788i | \(0.723337\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.9908i | 0.820312i | ||||||||
\(482\) | 9.63020 | + | 16.6800i | 0.438644 | + | 0.759753i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.461135 | − | 0.798709i | 0.0209607 | − | 0.0363050i | ||||
\(485\) | −3.79334 | − | 2.19008i | −0.172246 | − | 0.0994465i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.70797 | − | 6.42239i | −0.168024 | − | 0.291026i | 0.769701 | − | 0.638405i | \(-0.220405\pi\) |
−0.937725 | + | 0.347378i | \(0.887072\pi\) | |||||||
\(488\) | 1.44802 | + | 2.50805i | 0.0655488 | + | 0.113534i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.767563 | + | 6.95779i | −0.0346749 | + | 0.314321i | ||||
\(491\) | −20.6718 | + | 11.9348i | −0.932904 | + | 0.538612i | −0.887729 | − | 0.460367i | \(-0.847718\pi\) |
−0.0451748 | + | 0.998979i | \(0.514384\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.42344i | 0.0641087i | ||||||||
\(494\) | −10.9010 | + | 6.29368i | −0.490458 | + | 0.283166i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.70317i | 0.435685i | ||||||||
\(497\) | 12.1759 | + | 24.0495i | 0.546164 | + | 1.07877i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.96588 | −0.356602 | −0.178301 | − | 0.983976i | \(-0.557060\pi\) | ||||
−0.178301 | + | 0.983976i | \(0.557060\pi\) | |||||||
\(500\) | 0.500000 | − | 0.866025i | 0.0223607 | − | 0.0387298i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −19.0687 | + | 11.0093i | −0.851076 | + | 0.491369i | ||||
\(503\) | 39.3978 | 1.75666 | 0.878332 | − | 0.478052i | \(-0.158657\pi\) | ||||
0.878332 | + | 0.478052i | \(0.158657\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.9191 | −0.752892 | ||||||||
\(506\) | −2.16936 | + | 1.25248i | −0.0964397 | + | 0.0556795i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.55105 | + | 13.0788i | −0.335024 | + | 0.580278i | ||||
\(509\) | −2.27010 | −0.100620 | −0.0503102 | − | 0.998734i | \(-0.516021\pi\) | ||||
−0.0503102 | + | 0.998734i | \(0.516021\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.50542 | − | 13.0236i | 0.376258 | − | 0.576131i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −18.0516 | + | 10.4221i | −0.796221 | + | 0.459698i | ||||
\(515\) | 5.31108i | 0.234034i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.72834 | + | 3.30726i | −0.251932 | + | 0.145453i | ||||
\(518\) | −10.2082 | − | 20.1630i | −0.448523 | − | 0.885911i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.05309 | − | 1.82400i | −0.0461810 | − | 0.0799878i | ||||
\(521\) | −9.24087 | − | 16.0057i | −0.404850 | − | 0.701221i | 0.589454 | − | 0.807802i | \(-0.299343\pi\) |
−0.994304 | + | 0.106581i | \(0.966010\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.9554 | − | 17.8721i | −1.35359 | − | 0.781493i | −0.364836 | − | 0.931072i | \(-0.618875\pi\) |
−0.988750 | + | 0.149578i | \(0.952208\pi\) | |||||||
\(524\) | 4.19019 | − | 7.25762i | 0.183049 | − | 0.317051i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.2685 | − | 19.5177i | −0.491331 | − | 0.851011i | ||||
\(527\) | − | 1.74698i | − | 0.0760997i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.3774 | 0.972929 | ||||||||
\(530\) | 0.353965 | − | 0.613086i | 0.0153753 | − | 0.0266307i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.64601 | − | 13.2389i | 0.374852 | − | 0.573978i | ||||
\(533\) | 21.3675 | + | 12.3365i | 0.925529 | + | 0.534354i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.07344 | − | 4.08385i | −0.305812 | − | 0.176560i | ||||
\(536\) | −8.62299 | − | 4.97848i | −0.372456 | − | 0.215038i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −20.5578 | − | 11.8691i | −0.886311 | − | 0.511712i | ||||
\(539\) | 17.9103 | + | 13.1541i | 0.771450 | + | 0.566588i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.94967 | − | 10.3051i | 0.255796 | − | 0.443052i | −0.709315 | − | 0.704891i | \(-0.750996\pi\) |
0.965111 | + | 0.261839i | \(0.0843291\pi\) | |||||||
\(542\) | 11.7975 | 0.506748 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.180042i | 0.00771925i | ||||||||
\(545\) | −0.606828 | − | 1.05106i | −0.0259936 | − | 0.0450223i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.70794 | − | 13.3505i | 0.329568 | − | 0.570828i | −0.652858 | − | 0.757480i | \(-0.726430\pi\) |
0.982426 | + | 0.186652i | \(0.0597637\pi\) | |||||||
\(548\) | −7.58919 | − | 4.38162i | −0.324194 | − | 0.187174i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.58727 | − | 2.74924i | −0.0676815 | − | 0.117228i | ||||
\(551\) | −23.6252 | − | 40.9200i | −1.00647 | − | 1.74325i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.3790 | + | 15.9213i | 1.03670 | + | 0.677045i | ||||
\(554\) | 15.8538 | − | 9.15321i | 0.673564 | − | 0.388883i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 3.19519i | − | 0.135506i | ||||||
\(557\) | −14.4583 | + | 8.34752i | −0.612619 | + | 0.353696i | −0.773990 | − | 0.633198i | \(-0.781742\pi\) |
0.161371 | + | 0.986894i | \(0.448408\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 7.78956i | − | 0.329463i | ||||||
\(560\) | 2.21519 | + | 1.44669i | 0.0936090 | + | 0.0611339i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 21.8094 | 0.919976 | ||||||||
\(563\) | −14.7212 | + | 25.4979i | −0.620427 | + | 1.07461i | 0.368980 | + | 0.929437i | \(0.379707\pi\) |
−0.989406 | + | 0.145173i | \(0.953626\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.23720 | − | 0.714296i | 0.0520493 | − | 0.0300507i | ||||
\(566\) | −1.51803 | −0.0638075 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.1885 | 0.427498 | ||||||||
\(569\) | −4.93176 | + | 2.84736i | −0.206750 | + | 0.119367i | −0.599800 | − | 0.800150i | \(-0.704753\pi\) |
0.393050 | + | 0.919517i | \(0.371420\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.78017 | − | 3.08334i | 0.0744976 | − | 0.129034i | −0.826370 | − | 0.563127i | \(-0.809598\pi\) |
0.900868 | + | 0.434094i | \(0.142931\pi\) | |||||||
\(572\) | −6.68615 | −0.279562 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −30.9472 | − | 1.70184i | −1.29171 | − | 0.0710334i | ||||
\(575\) | − | 0.789076i | − | 0.0329068i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.31447 | + | 3.06831i | −0.221244 | + | 0.127735i | −0.606526 | − | 0.795064i | \(-0.707437\pi\) |
0.385282 | + | 0.922799i | \(0.374104\pi\) | |||||||
\(578\) | 16.9676i | 0.705758i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.84694 | − | 3.95308i | 0.284304 | − | 0.164143i | ||||
\(581\) | 1.28270 | − | 23.3254i | 0.0532155 | − | 0.967701i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.12368 | − | 1.94627i | −0.0465380 | − | 0.0806062i | ||||
\(584\) | −2.93961 | − | 5.09156i | −0.121642 | − | 0.210690i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.83808 | + | 2.79327i | 0.199859 | + | 0.115389i | ||||
\(587\) | 1.76206 | − | 3.05198i | 0.0727279 | − | 0.125969i | −0.827368 | − | 0.561660i | \(-0.810163\pi\) |
0.900096 | + | 0.435692i | \(0.143496\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.9950 | + | 50.2208i | 1.19472 | + | 2.06931i | ||||
\(590\) | 11.7733i | 0.484699i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8.54194 | −0.351072 | ||||||||
\(593\) | 20.0316 | − | 34.6957i | 0.822598 | − | 1.42478i | −0.0811430 | − | 0.996702i | \(-0.525857\pi\) |
0.903741 | − | 0.428079i | \(-0.140810\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.398829 | − | 0.260466i | −0.0163504 | − | 0.0106781i | ||||
\(596\) | 5.37389 | + | 3.10262i | 0.220123 | + | 0.127088i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.43928 | − | 0.830967i | −0.0588564 | − | 0.0339808i | ||||
\(599\) | −1.57658 | − | 0.910237i | −0.0644172 | − | 0.0371913i | 0.467446 | − | 0.884022i | \(-0.345174\pi\) |
−0.531863 | + | 0.846831i | \(0.678508\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.9038 | − | 9.18204i | −0.648728 | − | 0.374543i | 0.139241 | − | 0.990259i | \(-0.455534\pi\) |
−0.787969 | + | 0.615715i | \(0.788867\pi\) | |||||||
\(602\) | 4.41988 | + | 8.73004i | 0.180141 | + | 0.355810i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.33037 | − | 9.23247i | 0.216890 | − | 0.375664i | ||||
\(605\) | 0.922270 | 0.0374956 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.9070i | 1.17330i | 0.809842 | + | 0.586649i | \(0.199553\pi\) | ||||
−0.809842 | + | 0.586649i | \(0.800447\pi\) | |||||||
\(608\) | −2.98820 | − | 5.17571i | −0.121188 | − | 0.209903i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.44802 | + | 2.50805i | −0.0586287 | + | 0.101548i | ||||
\(611\) | −3.80051 | − | 2.19423i | −0.153752 | − | 0.0887689i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.0655 | + | 34.7545i | 0.810439 | + | 1.40372i | 0.912557 | + | 0.408949i | \(0.134104\pi\) |
−0.102119 | + | 0.994772i | \(0.532562\pi\) | |||||||
\(614\) | −11.4470 | − | 19.8268i | −0.461964 | − | 0.800146i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.49341 | − | 3.79380i | 0.301918 | − | 0.152856i | ||||
\(617\) | 4.18249 | − | 2.41476i | 0.168381 | − | 0.0972146i | −0.413441 | − | 0.910531i | \(-0.635673\pi\) |
0.581822 | + | 0.813316i | \(0.302340\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.9309i | 0.720705i | 0.932816 | + | 0.360352i | \(0.117344\pi\) | ||||
−0.932816 | + | 0.360352i | \(0.882656\pi\) | |||||||
\(620\) | −8.40319 | + | 4.85159i | −0.337480 | + | 0.194844i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 21.7317i | − | 0.871362i | ||||||
\(623\) | 0.845893 | − | 15.3822i | 0.0338900 | − | 0.616275i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 1.56616 | − | 2.71267i | 0.0625964 | − | 0.108420i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.80928 | + | 2.19929i | −0.152007 | + | 0.0877613i | ||||
\(629\) | 1.53791 | 0.0613206 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.6119 | 0.621502 | 0.310751 | − | 0.950491i | \(-0.399420\pi\) | ||||
0.310751 | + | 0.950491i | \(0.399420\pi\) | |||||||
\(632\) | 9.53091 | − | 5.50268i | 0.379119 | − | 0.218885i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −14.3433 | + | 24.8434i | −0.569647 | + | 0.986657i | ||||
\(635\) | −15.1021 | −0.599309 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.61662 | + | 14.6543i | −0.0640529 | + | 0.580626i | ||||
\(638\) | − | 25.0985i | − | 0.993658i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.866025 | − | 0.500000i | 0.0342327 | − | 0.0197642i | ||||
\(641\) | − | 15.3319i | − | 0.605572i | −0.953059 | − | 0.302786i | \(-0.902083\pi\) | ||
0.953059 | − | 0.302786i | \(-0.0979168\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.2575 | − | 15.1598i | 1.03550 | − | 0.597844i | 0.116941 | − | 0.993139i | \(-0.462691\pi\) |
0.918554 | + | 0.395295i | \(0.129358\pi\) | |||||||
\(644\) | 2.08455 | + | 0.114633i | 0.0821428 | + | 0.00451717i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.538003 | + | 0.931848i | 0.0211674 | + | 0.0366631i | ||||
\(647\) | −14.5503 | − | 25.2018i | −0.572030 | − | 0.990785i | −0.996357 | − | 0.0852761i | \(-0.972823\pi\) |
0.424327 | − | 0.905509i | \(-0.360511\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 32.3676 | + | 18.6874i | 1.27054 | + | 0.733546i | ||||
\(650\) | 1.05309 | − | 1.82400i | 0.0413055 | − | 0.0715433i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.94559 | − | 17.2263i | −0.389500 | − | 0.674633i | ||||
\(653\) | 3.29591i | 0.128979i | 0.997918 | + | 0.0644895i | \(0.0205419\pi\) | ||||
−0.997918 | + | 0.0644895i | \(0.979458\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.38038 | 0.327449 | ||||||||
\(656\) | −5.85731 | + | 10.1452i | −0.228689 | + | 0.396102i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.50440 | + | 0.302696i | 0.214584 | + | 0.0118003i | ||||
\(659\) | −5.58702 | − | 3.22567i | −0.217639 | − | 0.125654i | 0.387217 | − | 0.921988i | \(-0.373436\pi\) |
−0.604857 | + | 0.796334i | \(0.706770\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32.5957 | − | 18.8191i | −1.26783 | − | 0.731979i | −0.293249 | − | 0.956036i | \(-0.594737\pi\) |
−0.974576 | + | 0.224057i | \(0.928070\pi\) | |||||||
\(662\) | −4.94451 | − | 2.85472i | −0.192174 | − | 0.110952i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.64657 | − | 4.41475i | −0.296744 | − | 0.171325i | ||||
\(665\) | 15.7882 | + | 0.868221i | 0.612241 | + | 0.0336682i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.11928 | − | 5.40276i | 0.120779 | − | 0.209196i | ||||
\(668\) | −14.2766 | −0.552379 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 9.95697i | − | 0.384671i | ||||||
\(671\) | 4.59681 | + | 7.96190i | 0.177458 | + | 0.307366i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.8051 | − | 42.9637i | 0.956166 | − | 1.65613i | 0.224490 | − | 0.974476i | \(-0.427928\pi\) |
0.731676 | − | 0.681652i | \(-0.238738\pi\) | |||||||
\(674\) | −9.38110 | − | 5.41618i | −0.361347 | − | 0.208624i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.28201 | + | 7.41666i | 0.164693 | + | 0.285256i | ||||
\(677\) | −3.63663 | − | 6.29882i | −0.139767 | − | 0.242083i | 0.787641 | − | 0.616134i | \(-0.211302\pi\) |
−0.927408 | + | 0.374050i | \(0.877969\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.5713 | + | 0.636328i | 0.444068 | + | 0.0244200i | ||||
\(680\) | −0.155921 | + | 0.0900212i | −0.00597931 | + | 0.00345215i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 30.8031i | 1.17951i | ||||||||
\(683\) | 14.4216 | − | 8.32633i | 0.551828 | − | 0.318598i | −0.198031 | − | 0.980196i | \(-0.563455\pi\) |
0.749859 | + | 0.661598i | \(0.230121\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 8.76324i | − | 0.334826i | ||||||
\(686\) | −6.50323 | − | 17.3409i | −0.248294 | − | 0.662080i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.69843 | 0.141001 | ||||||||
\(689\) | 0.745513 | − | 1.29127i | 0.0284018 | − | 0.0491934i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.8682 | − | 19.5538i | 1.28841 | − | 0.743863i | 0.310038 | − | 0.950724i | \(-0.399658\pi\) |
0.978370 | + | 0.206862i | \(0.0663250\pi\) | |||||||
\(692\) | 13.2286 | 0.502876 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 19.3689 | 0.735234 | ||||||||
\(695\) | 2.76711 | − | 1.59759i | 0.104963 | − | 0.0606002i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.05456 | − | 1.82656i | 0.0399444 | − | 0.0691858i | ||||
\(698\) | −19.8542 | −0.751492 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.145275 | + | 2.64176i | −0.00549087 | + | 0.0998491i | ||||
\(701\) | − | 38.2997i | − | 1.44656i | −0.690555 | − | 0.723280i | \(-0.742634\pi\) | ||
0.690555 | − | 0.723280i | \(-0.257366\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −44.2107 | + | 25.5250i | −1.66744 | + | 0.962695i | ||||
\(704\) | − | 3.17454i | − | 0.119645i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.95408 | − | 5.74699i | 0.374627 | − | 0.216291i | ||||
\(707\) | 39.9371 | − | 20.2195i | 1.50199 | − | 0.760434i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.58548 | + | 7.94229i | 0.172211 | + | 0.298279i | 0.939193 | − | 0.343390i | \(-0.111575\pi\) |
−0.766981 | + | 0.641670i | \(0.778242\pi\) | |||||||
\(710\) | 5.09423 | + | 8.82346i | 0.191183 | + | 0.331139i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.04262 | − | 2.91136i | −0.188980 | − | 0.109108i | ||||
\(713\) | −3.82827 | + | 6.63076i | −0.143370 | + | 0.248324i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.34308 | − | 5.79038i | −0.125024 | − | 0.216548i | ||||
\(716\) | 4.06988i | 0.152098i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −22.1465 | −0.826498 | ||||||||
\(719\) | −16.5618 | + | 28.6858i | −0.617650 | + | 1.06980i | 0.372263 | + | 0.928127i | \(0.378582\pi\) |
−0.989913 | + | 0.141674i | \(0.954752\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.34710 | − | 12.5366i | −0.236378 | − | 0.466889i | ||||
\(722\) | −14.4777 | − | 8.35868i | −0.538802 | − | 0.311078i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −18.8221 | − | 10.8670i | −0.699519 | − | 0.403867i | ||||
\(725\) | 6.84694 | + | 3.95308i | 0.254289 | + | 0.146814i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.5870 | − | 12.4633i | −0.800617 | − | 0.462236i | 0.0430699 | − | 0.999072i | \(-0.486286\pi\) |
−0.843687 | + | 0.536836i | \(0.819620\pi\) | |||||||
\(728\) | 4.66559 | + | 3.04699i | 0.172918 | + | 0.112929i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.93961 | − | 5.09156i | 0.108800 | − | 0.188447i | ||||
\(731\) | −0.665875 | −0.0246283 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 14.7249i | − | 0.543878i | −0.962314 | − | 0.271939i | \(-0.912335\pi\) | ||
0.962314 | − | 0.271939i | \(-0.0876649\pi\) | |||||||
\(734\) | −10.0714 | − | 17.4441i | −0.371742 | − | 0.643875i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.394538 | − | 0.683360i | 0.0145429 | − | 0.0251890i | ||||
\(737\) | −27.3740 | − | 15.8044i | −1.00834 | − | 0.582163i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.3365 | + | 23.0995i | 0.490590 | + | 0.849727i | 0.999941 | − | 0.0108315i | \(-0.00344786\pi\) |
−0.509351 | + | 0.860559i | \(0.670115\pi\) | |||||||
\(740\) | −4.27097 | − | 7.39754i | −0.157004 | − | 0.271939i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.102845 | + | 1.87018i | −0.00377554 | + | 0.0686566i | ||||
\(743\) | −4.24232 | + | 2.44930i | −0.155636 | + | 0.0898562i | −0.575795 | − | 0.817594i | \(-0.695307\pi\) |
0.420160 | + | 0.907450i | \(0.361974\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.20523i | 0.227342i | ||||||||
\(746\) | −23.6347 | + | 13.6455i | −0.865329 | + | 0.499598i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.571552i | 0.0208980i | ||||||||
\(749\) | 21.5771 | + | 1.18656i | 0.788411 | + | 0.0433561i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.9206 | −0.580949 | −0.290475 | − | 0.956883i | \(-0.593813\pi\) | ||||
−0.290475 | + | 0.956883i | \(0.593813\pi\) | |||||||
\(752\) | 1.04181 | − | 1.80446i | 0.0379907 | − | 0.0658019i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 14.4209 | − | 8.32589i | 0.525177 | − | 0.303211i | ||||
\(755\) | 10.6607 | 0.387984 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.4236 | −0.996729 | −0.498365 | − | 0.866968i | \(-0.666066\pi\) | ||||
−0.498365 | + | 0.866968i | \(0.666066\pi\) | |||||||
\(758\) | 16.9760 | − | 9.80108i | 0.616595 | − | 0.355991i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.98820 | − | 5.17571i | 0.108393 | − | 0.187743i | ||||
\(761\) | 1.54724 | 0.0560874 | 0.0280437 | − | 0.999607i | \(-0.491072\pi\) | ||||
0.0280437 | + | 0.999607i | \(0.491072\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.68848 | + | 1.75578i | 0.0973296 | + | 0.0635637i | ||||
\(764\) | 7.77914i | 0.281439i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.43949 | + | 1.98579i | −0.124274 | + | 0.0717495i | ||||
\(767\) | 24.7967i | 0.895356i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.38768 | − | 1.37853i | 0.0861019 | − | 0.0497110i | −0.456331 | − | 0.889810i | \(-0.650837\pi\) |
0.542433 | + | 0.840099i | \(0.317503\pi\) | |||||||
\(770\) | 7.03223 | + | 4.59259i | 0.253424 | + | 0.165505i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.14681 | + | 7.18249i | 0.149247 | + | 0.258503i | ||||
\(773\) | −0.745114 | − | 1.29057i | −0.0267999 | − | 0.0464187i | 0.852314 | − | 0.523030i | \(-0.175198\pi\) |
−0.879114 | + | 0.476611i | \(0.841865\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.40319 | − | 4.85159i | −0.301852 | − | 0.174274i | ||||
\(776\) | 2.19008 | − | 3.79334i | 0.0786194 | − | 0.136173i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.44628 | − | 16.3614i | −0.338666 | − | 0.586586i | ||||
\(779\) | 70.0112i | 2.50841i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.3437 | 1.15735 | ||||||||
\(782\) | −0.0710336 | + | 0.123034i | −0.00254016 | + | 0.00439968i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.95779 | − | 0.767563i | −0.248493 | − | 0.0274130i | ||||
\(785\) | −3.80928 | − | 2.19929i | −0.135959 | − | 0.0784961i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.4311 | − | 11.2185i | −0.692643 | − | 0.399898i | 0.111958 | − | 0.993713i | \(-0.464288\pi\) |
−0.804602 | + | 0.593815i | \(0.797621\pi\) | |||||||
\(788\) | 11.5188 | + | 6.65040i | 0.410341 | + | 0.236911i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 9.53091 | + | 5.50268i | 0.339095 | + | 0.195776i | ||||
\(791\) | −2.06673 | + | 3.16461i | −0.0734845 | + | 0.112520i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.04979 | + | 5.28239i | −0.108301 | + | 0.187583i | ||||
\(794\) | 35.3327 | 1.25391 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.6869i | 0.662338i | ||||||||
\(797\) | 16.4080 | + | 28.4195i | 0.581202 | + | 1.00667i | 0.995337 | + | 0.0964565i | \(0.0307509\pi\) |
−0.414135 | + | 0.910216i | \(0.635916\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.187569 | + | 0.324879i | −0.00663572 | + | 0.0114934i | ||||
\(800\) | 0.866025 | + | 0.500000i | 0.0306186 | + | 0.0176777i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −0.311666 | − | 0.539822i | −0.0110053 | − | 0.0190618i | ||||
\(803\) | −9.33192 | − | 16.1634i | −0.329316 | − | 0.570393i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.943000 | + | 1.86259i | 0.0332364 | + | 0.0656477i | ||||
\(806\) | −17.6986 | + | 10.2183i | −0.623407 | + | 0.359924i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 16.9191i | − | 0.595213i | ||||||
\(809\) | 9.17296 | − | 5.29601i | 0.322504 | − | 0.186198i | −0.330004 | − | 0.943980i | \(-0.607050\pi\) |
0.652508 | + | 0.757782i | \(0.273717\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.0365i | 0.808921i | 0.914555 | + | 0.404461i | \(0.132541\pi\) | ||||
−0.914555 | + | 0.404461i | \(0.867459\pi\) | |||||||
\(812\) | −11.4378 | + | 17.5137i | −0.401387 | + | 0.614610i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −27.1168 | −0.950442 | ||||||||
\(815\) | 9.94559 | − | 17.2263i | 0.348379 | − | 0.603410i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.1420 | − | 11.0517i | 0.669695 | − | 0.386649i | ||||
\(818\) | −1.39035 | −0.0486124 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.7146 | −0.409092 | ||||||||
\(821\) | 2.33352 | − | 1.34726i | 0.0814404 | − | 0.0470196i | −0.458727 | − | 0.888577i | \(-0.651694\pi\) |
0.540167 | + | 0.841558i | \(0.318361\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.04054 | − | 1.80226i | 0.0362708 | − | 0.0628229i | −0.847320 | − | 0.531082i | \(-0.821785\pi\) |
0.883591 | + | 0.468260i | \(0.155119\pi\) | |||||||
\(824\) | −5.31108 | −0.185020 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −14.0699 | − | 27.7905i | −0.489555 | − | 0.966956i | ||||
\(827\) | 37.0830i | 1.28950i | 0.764393 | + | 0.644751i | \(0.223039\pi\) | ||||
−0.764393 | + | 0.644751i | \(0.776961\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.9461 | + | 8.05176i | −0.484367 | + | 0.279649i | −0.722234 | − | 0.691648i | \(-0.756885\pi\) |
0.237868 | + | 0.971298i | \(0.423551\pi\) | |||||||
\(830\) | − | 8.82950i | − | 0.306476i | ||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.82400 | − | 1.05309i | 0.0632359 | − | 0.0365093i | ||||
\(833\) | 1.25270 | + | 0.138194i | 0.0434034 | + | 0.00478813i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.13831 | − | 12.3639i | −0.247031 | − | 0.427871i | ||||
\(836\) | −9.48617 | − | 16.4305i | −0.328086 | − | 0.568262i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −23.8650 | − | 13.7784i | −0.824402 | − | 0.475968i | ||||
\(839\) | 9.48006 | − | 16.4199i | 0.327288 | − | 0.566879i | −0.654685 | − | 0.755902i | \(-0.727199\pi\) |
0.981973 | + | 0.189023i | \(0.0605319\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.7537 | + | 29.0183i | 0.577714 | + | 1.00063i | ||||
\(842\) | − | 34.3612i | − | 1.18416i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −24.3154 | −0.836971 | ||||||||
\(845\) | −4.28201 | + | 7.41666i | −0.147306 | + | 0.255141i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.17699 | + | 1.10218i | −0.0748022 | + | 0.0378712i | ||||
\(848\) | 0.613086 | + | 0.353965i | 0.0210535 | + | 0.0121552i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.155921 | − | 0.0900212i | −0.00534806 | − | 0.00308770i | ||||
\(851\) | −5.83722 | − | 3.37012i | −0.200097 | − | 0.115526i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.4322 | − | 11.2192i | −0.665347 | − | 0.384138i | 0.128964 | − | 0.991649i | \(-0.458835\pi\) |
−0.794311 | + | 0.607511i | \(0.792168\pi\) | |||||||
\(854\) | 0.420722 | − | 7.65065i | 0.0143968 | − | 0.261800i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.08385 | − | 7.07344i | 0.139583 | − | 0.241765i | ||||
\(857\) | 35.1457 | 1.20055 | 0.600277 | − | 0.799792i | \(-0.295057\pi\) | ||||
0.600277 | + | 0.799792i | \(0.295057\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 32.5488i | − | 1.11055i | −0.831667 | − | 0.555275i | \(-0.812613\pi\) | ||
0.831667 | − | 0.555275i | \(-0.187387\pi\) | |||||||
\(860\) | 1.84922 | + | 3.20294i | 0.0630578 | + | 0.109219i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14.0654 | − | 24.3620i | 0.479070 | − | 0.829774i | ||||
\(863\) | −10.9055 | − | 6.29628i | −0.371227 | − | 0.214328i | 0.302768 | − | 0.953064i | \(-0.402089\pi\) |
−0.673994 | + | 0.738737i | \(0.735423\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.61430 | + | 11.4563i | 0.224893 | + | 0.389526i | ||||
\(866\) | 5.98909 | + | 10.3734i | 0.203518 | + | 0.352503i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 14.0375 | − | 21.4944i | 0.476464 | − | 0.729568i | ||||
\(869\) | 30.2563 | − | 17.4685i | 1.02637 | − | 0.592578i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 20.9711i | − | 0.710580i | ||||||
\(872\) | 1.05106 | − | 0.606828i | 0.0355933 | − | 0.0205498i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 4.71584i | − | 0.159516i | ||||||
\(875\) | −2.36047 | + | 1.19507i | −0.0797984 | + | 0.0404007i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27.2268 | −0.919383 | −0.459691 | − | 0.888079i | \(-0.652040\pi\) | ||||
−0.459691 | + | 0.888079i | \(0.652040\pi\) | |||||||
\(878\) | −5.42941 | + | 9.40402i | −0.183234 | + | 0.317370i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.74924 | − | 1.58727i | 0.0926767 | − | 0.0535069i | ||||
\(881\) | 8.99478 | 0.303042 | 0.151521 | − | 0.988454i | \(-0.451583\pi\) | ||||
0.151521 | + | 0.988454i | \(0.451583\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.9491 | −0.536730 | −0.268365 | − | 0.963317i | \(-0.586483\pi\) | ||||
−0.268365 | + | 0.963317i | \(0.586483\pi\) | |||||||
\(884\) | −0.328398 | + | 0.189601i | −0.0110452 | + | 0.00637696i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.05840 | − | 1.83321i | 0.0355577 | − | 0.0615878i | ||||
\(887\) | 28.7064 | 0.963867 | 0.481934 | − | 0.876208i | \(-0.339935\pi\) | ||||
0.481934 | + | 0.876208i | \(0.339935\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 35.6480 | − | 18.0480i | 1.19560 | − | 0.605312i | ||||
\(890\) | − | 5.82271i | − | 0.195178i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −14.5348 | + | 8.39165i | −0.486660 | + | 0.280973i | ||||
\(893\) | − | 12.4525i | − | 0.416707i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.52462 | + | 2.03494i | −0.117815 | + | 0.0680205i | ||||
\(896\) | −1.44669 | + | 2.21519i | −0.0483306 | + | 0.0740044i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.12687 | − | 10.6121i | −0.204456 | − | 0.354129i | ||||
\(899\) | −38.3574 | − | 66.4370i | −1.27929 | − | 2.21580i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.110381 | − | 0.0637287i | −0.00367734 | − | 0.00212311i | ||||
\(902\) | −18.5943 | + | 32.2062i | −0.619122 | + | 1.07235i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.714296 | + | 1.23720i | 0.0237571 | + | 0.0411485i | ||||
\(905\) | − | 21.7339i | − | 0.722460i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.9291 | −0.694938 | −0.347469 | − | 0.937692i | \(-0.612959\pi\) | ||||
−0.347469 | + | 0.937692i | \(0.612959\pi\) | |||||||
\(908\) | −8.39567 | + | 14.5417i | −0.278620 | + | 0.482584i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.305975 | + | 5.56401i | −0.0101430 | + | 0.184445i | ||||
\(911\) | 48.9296 | + | 28.2495i | 1.62111 | + | 0.935949i | 0.986623 | + | 0.163017i | \(0.0521224\pi\) |
0.634488 | + | 0.772933i | \(0.281211\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.2744 | − | 14.0148i | −0.803364 | − | 0.463823i | ||||
\(914\) | −28.6771 | − | 16.5567i | −0.948553 | − | 0.547647i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.74293 | − | 3.31568i | −0.189752 | − | 0.109553i | ||||
\(917\) | −19.7816 | + | 10.0151i | −0.653247 | + | 0.330729i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.93346 | + | 13.7412i | −0.261701 | + | 0.453279i | −0.966694 | − | 0.255935i | \(-0.917617\pi\) |
0.704993 | + | 0.709214i | \(0.250950\pi\) | |||||||
\(920\) | 0.789076 | 0.0260151 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 28.2444i | − | 0.930181i | ||||||
\(923\) | 10.7293 | + | 18.5838i | 0.353161 | + | 0.611692i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.27097 | − | 7.39754i | 0.140429 | − | 0.243230i | ||||
\(926\) | −34.8353 | − | 20.1122i | −1.14476 | − | 0.660927i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.95308 | + | 6.84694i | 0.129766 | + | 0.224762i | ||||
\(929\) | −24.0288 | − | 41.6191i | −0.788359 | − | 1.36548i | −0.926972 | − | 0.375131i | \(-0.877598\pi\) |
0.138613 | − | 0.990347i | \(-0.455736\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −38.3052 | + | 16.8186i | −1.25540 | + | 0.551207i | ||||
\(932\) | −6.79700 | + | 3.92425i | −0.222643 | + | 0.128543i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.64908i | 0.0539595i | ||||||||
\(935\) | −0.494979 | + | 0.285776i | −0.0161875 | + | 0.00934588i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 8.04349i | − | 0.262769i | −0.991331 | − | 0.131385i | \(-0.958058\pi\) | ||
0.991331 | − | 0.131385i | \(-0.0419423\pi\) | |||||||
\(938\) | 11.8993 | + | 23.5031i | 0.388524 | + | 0.767404i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.08361 | 0.0679599 | ||||||||
\(941\) | 16.6440 | − | 28.8283i | 0.542579 | − | 0.939775i | −0.456175 | − | 0.889890i | \(-0.650781\pi\) |
0.998755 | − | 0.0498854i | \(-0.0158856\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.00530 | + | 4.62186i | −0.260689 | + | 0.150509i | ||||
\(944\) | −11.7733 | −0.383189 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11.7408 | 0.381728 | ||||||||
\(947\) | 27.0229 | − | 15.6017i | 0.878128 | − | 0.506987i | 0.00808714 | − | 0.999967i | \(-0.497426\pi\) |
0.870041 | + | 0.492980i | \(0.164092\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.19134 | − | 10.7237i | 0.200979 | − | 0.348107i | ||||
\(950\) | 5.97640 | 0.193900 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.260466 | − | 0.398829i | 0.00844174 | − | 0.0129261i | ||||
\(953\) | − | 10.1723i | − | 0.329512i | −0.986334 | − | 0.164756i | \(-0.947316\pi\) | ||
0.986334 | − | 0.164756i | \(-0.0526837\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.73693 | + | 3.88957i | −0.218002 | + | 0.125863i | ||||
\(956\) | − | 16.5516i | − | 0.535316i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 24.4682 | − | 14.1267i | 0.790533 | − | 0.456414i | ||||
\(959\) | 10.4727 | + | 20.6853i | 0.338180 | + | 0.667965i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.5758 | + | 54.6908i | 1.01857 | + | 1.76422i | ||||
\(962\) | −8.99542 | − | 15.5805i | −0.290024 | − | 0.502336i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −16.6800 | − | 9.63020i | −0.537227 | − | 0.310168i | ||||
\(965\) | −4.14681 | + | 7.18249i | −0.133491 | + | 0.231213i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.3617 | − | 45.6599i | −0.847737 | − | 1.46832i | −0.883223 | − | 0.468953i | \(-0.844631\pi\) |
0.0354867 | − | 0.999370i | \(-0.488702\pi\) | |||||||
\(968\) | 0.922270i | 0.0296429i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.38017 | 0.140639 | ||||||||
\(971\) | −4.76329 | + | 8.25026i | −0.152861 | + | 0.264763i | −0.932278 | − | 0.361742i | \(-0.882182\pi\) |
0.779417 | + | 0.626506i | \(0.215515\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.62245 | + | 7.07796i | −0.148189 | + | 0.226909i | ||||
\(974\) | 6.42239 | + | 3.70797i | 0.205787 | + | 0.118811i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.50805 | − | 1.44802i | −0.0802806 | − | 0.0463500i | ||||
\(977\) | −26.6154 | − | 15.3664i | −0.851503 | − | 0.491616i | 0.00965461 | − | 0.999953i | \(-0.496927\pi\) |
−0.861158 | + | 0.508338i | \(0.830260\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.0080 | − | 9.24223i | −0.511618 | − | 0.295383i | ||||
\(980\) | −2.81417 | − | 6.40940i | −0.0898953 | − | 0.204741i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 11.9348 | − | 20.6718i | 0.380856 | − | 0.659662i | ||||
\(983\) | −10.3495 | −0.330097 | −0.165049 | − | 0.986285i | \(-0.552778\pi\) | ||||
−0.165049 | + | 0.986285i | \(0.552778\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.3008i | 0.423799i | ||||||||
\(986\) | −0.711722 | − | 1.23274i | −0.0226659 | − | 0.0392584i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.29368 | − | 10.9010i | 0.200229 | − | 0.346806i | ||||
\(989\) | 2.52736 | + | 1.45917i | 0.0803655 | + | 0.0463990i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.948097 | − | 1.64215i | −0.0301173 | − | 0.0521647i | 0.850574 | − | 0.525856i | \(-0.176255\pi\) |
−0.880691 | + | 0.473691i | \(0.842921\pi\) | |||||||
\(992\) | −4.85159 | − | 8.40319i | −0.154038 | − | 0.266802i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −22.5694 | − | 14.7396i | −0.715858 | − | 0.467510i | ||||
\(995\) | −16.1833 | + | 9.34343i | −0.513045 | + | 0.296207i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.6657i | 0.907852i | 0.891039 | + | 0.453926i | \(0.149977\pi\) | ||||
−0.891039 | + | 0.453926i | \(0.850023\pi\) | |||||||
\(998\) | 6.89865 | − | 3.98294i | 0.218373 | − | 0.126078i | ||||
\(999\) | 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 | 1890.2.t.b.1601.2 | 28 | ||
3.2 | odd | 2 | 630.2.t.b.551.11 | yes | 28 | ||
7.3 | odd | 6 | 1890.2.bk.b.521.4 | 28 | |||
9.4 | even | 3 | 630.2.bk.b.131.1 | yes | 28 | ||
9.5 | odd | 6 | 1890.2.bk.b.341.4 | 28 | |||
21.17 | even | 6 | 630.2.bk.b.101.8 | yes | 28 | ||
63.31 | odd | 6 | 630.2.t.b.311.11 | ✓ | 28 | ||
63.59 | even | 6 | inner | 1890.2.t.b.1151.2 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.t.b.311.11 | ✓ | 28 | 63.31 | odd | 6 | ||
630.2.t.b.551.11 | yes | 28 | 3.2 | odd | 2 | ||
630.2.bk.b.101.8 | yes | 28 | 21.17 | even | 6 | ||
630.2.bk.b.131.1 | yes | 28 | 9.4 | even | 3 | ||
1890.2.t.b.1151.2 | 28 | 63.59 | even | 6 | inner | ||
1890.2.t.b.1601.2 | 28 | 1.1 | even | 1 | trivial | ||
1890.2.bk.b.341.4 | 28 | 9.5 | odd | 6 | |||
1890.2.bk.b.521.4 | 28 | 7.3 | odd | 6 |