Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1890,2,Mod(719,1890)]
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, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1890.719");
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.bi (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: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 899.8 | ||
Character | \(\chi\) | \(=\) | 1890.899 |
Dual form | 1890.2.bi.b.719.8 |
$q$-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 \(\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(1081\) | \(1541\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.47412 | + | 1.68136i | −0.659248 | + | 0.751926i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.31170 | + | 2.29771i | 0.495775 | + | 0.868451i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.47412 | + | 1.68136i | −0.466159 | + | 0.531692i | ||||
\(11\) | −3.56894 | + | 2.06053i | −1.07608 | + | 0.621273i | −0.929835 | − | 0.367976i | \(-0.880051\pi\) |
−0.146241 | + | 0.989249i | \(0.546718\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.18566 | + | 2.05363i | 0.328844 | + | 0.569575i | 0.982283 | − | 0.187405i | \(-0.0600076\pi\) |
−0.653439 | + | 0.756979i | \(0.726674\pi\) | |||||||
\(14\) | 1.31170 | + | 2.29771i | 0.350566 | + | 0.614088i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.28111 | − | 1.31700i | −0.553250 | − | 0.319419i | 0.197182 | − | 0.980367i | \(-0.436821\pi\) |
−0.750432 | + | 0.660948i | \(0.770154\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.956982 | − | 0.552514i | 0.219547 | − | 0.126755i | −0.386194 | − | 0.922418i | \(-0.626210\pi\) |
0.605740 | + | 0.795662i | \(0.292877\pi\) | |||||||
\(20\) | −1.47412 | + | 1.68136i | −0.329624 | + | 0.375963i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.56894 | + | 2.06053i | −0.760901 | + | 0.439306i | ||||
\(23\) | −0.296239 | + | 0.513101i | −0.0617701 | + | 0.106989i | −0.895257 | − | 0.445551i | \(-0.853008\pi\) |
0.833487 | + | 0.552540i | \(0.186341\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.653922 | − | 4.95705i | −0.130784 | − | 0.991411i | ||||
\(26\) | 1.18566 | + | 2.05363i | 0.232528 | + | 0.402750i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.31170 | + | 2.29771i | 0.247887 | + | 0.434226i | ||||
\(29\) | −2.36953 | − | 1.36805i | −0.440010 | − | 0.254040i | 0.263592 | − | 0.964634i | \(-0.415093\pi\) |
−0.703602 | + | 0.710594i | \(0.748426\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.69755i | 0.484495i | 0.970215 | + | 0.242247i | \(0.0778845\pi\) | ||||
−0.970215 | + | 0.242247i | \(0.922115\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.28111 | − | 1.31700i | −0.391207 | − | 0.225863i | ||||
\(35\) | −5.79687 | − | 1.18167i | −0.979849 | − | 0.199739i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.05512 | + | 3.49593i | −0.995456 | + | 0.574727i | −0.906901 | − | 0.421345i | \(-0.861558\pi\) |
−0.0885553 | + | 0.996071i | \(0.528225\pi\) | |||||||
\(38\) | 0.956982 | − | 0.552514i | 0.155243 | − | 0.0896295i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.47412 | + | 1.68136i | −0.233079 | + | 0.265846i | ||||
\(41\) | −0.257087 | − | 0.445287i | −0.0401502 | − | 0.0695422i | 0.845252 | − | 0.534368i | \(-0.179450\pi\) |
−0.885402 | + | 0.464826i | \(0.846117\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.4023 | − | 6.00577i | −1.58634 | − | 0.915872i | −0.993904 | − | 0.110251i | \(-0.964834\pi\) |
−0.592432 | − | 0.805620i | \(-0.701832\pi\) | |||||||
\(44\) | −3.56894 | + | 2.06053i | −0.538038 | + | 0.310636i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.296239 | + | 0.513101i | −0.0436781 | + | 0.0756527i | ||||
\(47\) | 4.12973i | 0.602384i | 0.953564 | + | 0.301192i | \(0.0973844\pi\) | ||||
−0.953564 | + | 0.301192i | \(0.902616\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.55890 | + | 6.02779i | −0.508414 | + | 0.861113i | ||||
\(50\) | −0.653922 | − | 4.95705i | −0.0924786 | − | 0.701033i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.18566 | + | 2.05363i | 0.164422 | + | 0.284787i | ||||
\(53\) | −4.54406 | + | 7.87055i | −0.624175 | + | 1.08110i | 0.364525 | + | 0.931194i | \(0.381232\pi\) |
−0.988700 | + | 0.149909i | \(0.952102\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.79657 | − | 9.03814i | 0.242250 | − | 1.21870i | ||||
\(56\) | 1.31170 | + | 2.29771i | 0.175283 | + | 0.307044i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.36953 | − | 1.36805i | −0.311134 | − | 0.179633i | ||||
\(59\) | 6.93948 | 0.903443 | 0.451722 | − | 0.892159i | \(-0.350810\pi\) | ||||
0.451722 | + | 0.892159i | \(0.350810\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 4.29324i | − | 0.549693i | −0.961488 | − | 0.274847i | \(-0.911373\pi\) | ||
0.961488 | − | 0.274847i | \(-0.0886271\pi\) | |||||||
\(62\) | 2.69755i | 0.342589i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.20070 | − | 1.03378i | −0.645068 | − | 0.128225i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.5150i | 1.65112i | 0.564315 | + | 0.825560i | \(0.309141\pi\) | ||||
−0.564315 | + | 0.825560i | \(0.690859\pi\) | |||||||
\(68\) | −2.28111 | − | 1.31700i | −0.276625 | − | 0.159709i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.79687 | − | 1.18167i | −0.692858 | − | 0.141237i | ||||
\(71\) | − | 1.60164i | − | 0.190079i | −0.995473 | − | 0.0950396i | \(-0.969702\pi\) | ||
0.995473 | − | 0.0950396i | \(-0.0302978\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.29147 | − | 5.70100i | 0.385238 | − | 0.667252i | −0.606564 | − | 0.795035i | \(-0.707453\pi\) |
0.991802 | + | 0.127783i | \(0.0407860\pi\) | |||||||
\(74\) | −6.05512 | + | 3.49593i | −0.703894 | + | 0.406393i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.956982 | − | 0.552514i | 0.109773 | − | 0.0633777i | ||||
\(77\) | −9.41586 | − | 5.49759i | −1.07304 | − | 0.626508i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.4434 | 1.51251 | 0.756253 | − | 0.654280i | \(-0.227028\pi\) | ||||
0.756253 | + | 0.654280i | \(0.227028\pi\) | |||||||
\(80\) | −1.47412 | + | 1.68136i | −0.164812 | + | 0.187981i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.257087 | − | 0.445287i | −0.0283905 | − | 0.0491738i | ||||
\(83\) | 3.80374 | + | 2.19609i | 0.417515 | + | 0.241052i | 0.694013 | − | 0.719962i | \(-0.255841\pi\) |
−0.276499 | + | 0.961014i | \(0.589174\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.57698 | − | 1.89394i | 0.604908 | − | 0.205426i | ||||
\(86\) | −10.4023 | − | 6.00577i | −1.12171 | − | 0.647619i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.56894 | + | 2.06053i | −0.380450 | + | 0.219653i | ||||
\(89\) | 7.82648 | + | 13.5559i | 0.829605 | + | 1.43692i | 0.898349 | + | 0.439283i | \(0.144768\pi\) |
−0.0687438 | + | 0.997634i | \(0.521899\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.16341 | + | 5.41805i | −0.331615 | + | 0.567966i | ||||
\(92\) | −0.296239 | + | 0.513101i | −0.0308851 | + | 0.0534945i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.12973i | 0.425949i | ||||||||
\(95\) | −0.481736 | + | 2.42350i | −0.0494251 | + | 0.248646i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.92406 | − | 11.9928i | 0.703032 | − | 1.21769i | −0.264365 | − | 0.964423i | \(-0.585162\pi\) |
0.967397 | − | 0.253265i | \(-0.0815044\pi\) | |||||||
\(98\) | −3.55890 | + | 6.02779i | −0.359503 | + | 0.608899i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.653922 | − | 4.95705i | −0.0653922 | − | 0.495705i | ||||
\(101\) | −1.35453 | − | 2.34612i | −0.134781 | − | 0.233448i | 0.790733 | − | 0.612162i | \(-0.209700\pi\) |
−0.925514 | + | 0.378714i | \(0.876366\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.07239 | + | 15.7138i | −0.893929 | + | 1.54833i | −0.0588041 | + | 0.998270i | \(0.518729\pi\) |
−0.835125 | + | 0.550061i | \(0.814605\pi\) | |||||||
\(104\) | 1.18566 | + | 2.05363i | 0.116264 | + | 0.201375i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.54406 | + | 7.87055i | −0.441358 | + | 0.764455i | ||||
\(107\) | −4.33862 | − | 7.51471i | −0.419430 | − | 0.726475i | 0.576452 | − | 0.817131i | \(-0.304437\pi\) |
−0.995882 | + | 0.0906565i | \(0.971103\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.55567 | + | 13.0868i | −0.723702 | + | 1.25349i | 0.235804 | + | 0.971801i | \(0.424228\pi\) |
−0.959506 | + | 0.281688i | \(0.909106\pi\) | |||||||
\(110\) | 1.79657 | − | 9.03814i | 0.171297 | − | 0.861753i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.31170 | + | 2.29771i | 0.123944 | + | 0.217113i | ||||
\(113\) | 0.503287 | + | 0.871718i | 0.0473452 | + | 0.0820044i | 0.888727 | − | 0.458437i | \(-0.151591\pi\) |
−0.841382 | + | 0.540441i | \(0.818257\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.426013 | − | 1.25446i | −0.0397260 | − | 0.116979i | ||||
\(116\) | −2.36953 | − | 1.36805i | −0.220005 | − | 0.127020i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.93948 | 0.638831 | ||||||||
\(119\) | 0.0339510 | − | 6.96882i | 0.00311228 | − | 0.638830i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.99156 | − | 5.18154i | 0.271960 | − | 0.471049i | ||||
\(122\) | − | 4.29324i | − | 0.388692i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.69755i | 0.242247i | ||||||||
\(125\) | 9.29854 | + | 6.20783i | 0.831687 | + | 0.555245i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.12538i | 0.277333i | 0.990339 | + | 0.138666i | \(0.0442816\pi\) | ||||
−0.990339 | + | 0.138666i | \(0.955718\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.20070 | − | 1.03378i | −0.456132 | − | 0.0906685i | ||||
\(131\) | 10.7870 | − | 18.6837i | 0.942469 | − | 1.63240i | 0.181727 | − | 0.983349i | \(-0.441831\pi\) |
0.760742 | − | 0.649055i | \(-0.224835\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.52478 | + | 1.47413i | 0.218926 | + | 0.127823i | ||||
\(134\) | 13.5150i | 1.16752i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.28111 | − | 1.31700i | −0.195603 | − | 0.112932i | ||||
\(137\) | −1.88397 | − | 3.26314i | −0.160959 | − | 0.278789i | 0.774254 | − | 0.632875i | \(-0.218125\pi\) |
−0.935213 | + | 0.354086i | \(0.884792\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.20651 | − | 3.00598i | 0.441610 | − | 0.254964i | −0.262670 | − | 0.964886i | \(-0.584603\pi\) |
0.704280 | + | 0.709922i | \(0.251270\pi\) | |||||||
\(140\) | −5.79687 | − | 1.18167i | −0.489925 | − | 0.0998693i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 1.60164i | − | 0.134406i | ||||||
\(143\) | −8.46313 | − | 4.88619i | −0.707723 | − | 0.408604i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.79315 | − | 1.96735i | 0.481095 | − | 0.163379i | ||||
\(146\) | 3.29147 | − | 5.70100i | 0.272404 | − | 0.471818i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.05512 | + | 3.49593i | −0.497728 | + | 0.287363i | ||||
\(149\) | 9.69236 | + | 5.59589i | 0.794029 | + | 0.458433i | 0.841379 | − | 0.540445i | \(-0.181744\pi\) |
−0.0473497 | + | 0.998878i | \(0.515078\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.27469 | + | 16.0642i | 0.754763 | + | 1.30729i | 0.945492 | + | 0.325645i | \(0.105582\pi\) |
−0.190729 | + | 0.981643i | \(0.561085\pi\) | |||||||
\(152\) | 0.956982 | − | 0.552514i | 0.0776215 | − | 0.0448148i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −9.41586 | − | 5.49759i | −0.758752 | − | 0.443008i | ||||
\(155\) | −4.53555 | − | 3.97652i | −0.364304 | − | 0.319402i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.6703 | −0.931389 | −0.465695 | − | 0.884945i | \(-0.654196\pi\) | ||||
−0.465695 | + | 0.884945i | \(0.654196\pi\) | |||||||
\(158\) | 13.4434 | 1.06950 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.47412 | + | 1.68136i | −0.116540 | + | 0.132923i | ||||
\(161\) | −1.56753 | − | 0.00763677i | −0.123539 | − | 0.000601862i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.7728 | + | 6.21967i | −0.843789 | + | 0.487162i | −0.858550 | − | 0.512729i | \(-0.828634\pi\) |
0.0147613 | + | 0.999891i | \(0.495301\pi\) | |||||||
\(164\) | −0.257087 | − | 0.445287i | −0.0200751 | − | 0.0347711i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.80374 | + | 2.19609i | 0.295227 | + | 0.170450i | ||||
\(167\) | −11.4205 | + | 6.59363i | −0.883745 | + | 0.510230i | −0.871891 | − | 0.489699i | \(-0.837107\pi\) |
−0.0118537 | + | 0.999930i | \(0.503773\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.68840 | − | 6.38850i | 0.283723 | − | 0.491423i | ||||
\(170\) | 5.57698 | − | 1.89394i | 0.427735 | − | 0.145258i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.4023 | − | 6.00577i | −0.793168 | − | 0.457936i | ||||
\(173\) | 14.8129i | 1.12620i | 0.826387 | + | 0.563102i | \(0.190392\pi\) | ||||
−0.826387 | + | 0.563102i | \(0.809608\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.5321 | − | 8.00467i | 0.796152 | − | 0.605097i | ||||
\(176\) | −3.56894 | + | 2.06053i | −0.269019 | + | 0.155318i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.82648 | + | 13.5559i | 0.586619 | + | 1.01605i | ||||
\(179\) | −20.6373 | − | 11.9149i | −1.54250 | − | 0.890564i | −0.998680 | − | 0.0513644i | \(-0.983643\pi\) |
−0.543823 | − | 0.839200i | \(-0.683024\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.6911i | 0.868992i | 0.900674 | + | 0.434496i | \(0.143074\pi\) | ||||
−0.900674 | + | 0.434496i | \(0.856926\pi\) | |||||||
\(182\) | −3.16341 | + | 5.41805i | −0.234487 | + | 0.401612i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.296239 | + | 0.513101i | −0.0218390 | + | 0.0378263i | ||||
\(185\) | 3.04810 | − | 15.3342i | 0.224100 | − | 1.12740i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.8549 | 0.793785 | ||||||||
\(188\) | 4.12973i | 0.301192i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.481736 | + | 2.42350i | −0.0349488 | + | 0.175819i | ||||
\(191\) | − | 26.0254i | − | 1.88313i | −0.336825 | − | 0.941567i | \(-0.609353\pi\) | ||
0.336825 | − | 0.941567i | \(-0.390647\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.0736i | 1.30096i | 0.759522 | + | 0.650482i | \(0.225433\pi\) | ||||
−0.759522 | + | 0.650482i | \(0.774567\pi\) | |||||||
\(194\) | 6.92406 | − | 11.9928i | 0.497119 | − | 0.861035i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.55890 | + | 6.02779i | −0.254207 | + | 0.430556i | ||||
\(197\) | 19.0964 | 1.36056 | 0.680281 | − | 0.732951i | \(-0.261858\pi\) | ||||
0.680281 | + | 0.732951i | \(0.261858\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.6198 | + | 12.4822i | 1.53259 | + | 0.884840i | 0.999241 | + | 0.0389429i | \(0.0123991\pi\) |
0.533346 | + | 0.845897i | \(0.320934\pi\) | |||||||
\(200\) | −0.653922 | − | 4.95705i | −0.0462393 | − | 0.350517i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.35453 | − | 2.34612i | −0.0953046 | − | 0.165072i | ||||
\(203\) | 0.0352670 | − | 7.23893i | 0.00247526 | − | 0.508074i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.12766 | + | 0.224154i | 0.0787595 | + | 0.0156556i | ||||
\(206\) | −9.07239 | + | 15.7138i | −0.632103 | + | 1.09483i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.18566 | + | 2.05363i | 0.0822110 | + | 0.142394i | ||||
\(209\) | −2.27694 | + | 3.94378i | −0.157499 | + | 0.272797i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.61689 | − | 11.4608i | −0.455525 | − | 0.788993i | 0.543193 | − | 0.839608i | \(-0.317215\pi\) |
−0.998718 | + | 0.0506149i | \(0.983882\pi\) | |||||||
\(212\) | −4.54406 | + | 7.87055i | −0.312088 | + | 0.540552i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.33862 | − | 7.51471i | −0.296582 | − | 0.513695i | ||||
\(215\) | 25.4321 | − | 8.63673i | 1.73446 | − | 0.589020i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.19818 | + | 3.53837i | −0.420760 | + | 0.240200i | ||||
\(218\) | −7.55567 | + | 13.0868i | −0.511735 | + | 0.886351i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.79657 | − | 9.03814i | 0.121125 | − | 0.609351i | ||||
\(221\) | − | 6.24607i | − | 0.420156i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.44383 | + | 4.23284i | −0.163651 | + | 0.283452i | −0.936175 | − | 0.351533i | \(-0.885660\pi\) |
0.772524 | + | 0.634985i | \(0.218994\pi\) | |||||||
\(224\) | 1.31170 | + | 2.29771i | 0.0876415 | + | 0.153522i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.503287 | + | 0.871718i | 0.0334781 | + | 0.0579858i | ||||
\(227\) | 10.3873 | − | 5.99711i | 0.689429 | − | 0.398042i | −0.113969 | − | 0.993484i | \(-0.536356\pi\) |
0.803398 | + | 0.595442i | \(0.203023\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.16676 | + | 5.29243i | 0.605757 | + | 0.349734i | 0.771303 | − | 0.636468i | \(-0.219605\pi\) |
−0.165546 | + | 0.986202i | \(0.552939\pi\) | |||||||
\(230\) | −0.426013 | − | 1.25446i | −0.0280905 | − | 0.0827165i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.36953 | − | 1.36805i | −0.155567 | − | 0.0898166i | ||||
\(233\) | 0.259858 | + | 0.450088i | 0.0170239 | + | 0.0294862i | 0.874412 | − | 0.485184i | \(-0.161248\pi\) |
−0.857388 | + | 0.514671i | \(0.827914\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.94356 | − | 6.08774i | −0.452948 | − | 0.397120i | ||||
\(236\) | 6.93948 | 0.451722 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.0339510 | − | 6.96882i | 0.00220072 | − | 0.451721i | ||||
\(239\) | 2.39886 | − | 1.38498i | 0.155169 | − | 0.0895869i | −0.420405 | − | 0.907337i | \(-0.638112\pi\) |
0.575574 | + | 0.817750i | \(0.304779\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.4943 | − | 10.1004i | 1.12691 | − | 0.650621i | 0.183753 | − | 0.982972i | \(-0.441175\pi\) |
0.943156 | + | 0.332351i | \(0.107842\pi\) | |||||||
\(242\) | 2.99156 | − | 5.18154i | 0.192305 | − | 0.333082i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 4.29324i | − | 0.274847i | ||||||
\(245\) | −4.88861 | − | 14.8695i | −0.312322 | − | 0.949976i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.26932 | + | 1.31019i | 0.144393 | + | 0.0833655i | ||||
\(248\) | 2.69755i | 0.171295i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.29854 | + | 6.20783i | 0.588091 | + | 0.392618i | ||||
\(251\) | 20.9869 | 1.32468 | 0.662340 | − | 0.749203i | \(-0.269563\pi\) | ||||
0.662340 | + | 0.749203i | \(0.269563\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.44164i | − | 0.153504i | ||||||
\(254\) | 3.12538i | 0.196104i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −8.21246 | − | 4.74146i | −0.512279 | − | 0.295764i | 0.221491 | − | 0.975162i | \(-0.428908\pi\) |
−0.733770 | + | 0.679398i | \(0.762241\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.9751 | − | 9.32729i | −0.992644 | − | 0.579570i | ||||
\(260\) | −5.20070 | − | 1.03378i | −0.322534 | − | 0.0641123i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.7870 | − | 18.6837i | 0.666426 | − | 1.15428i | ||||
\(263\) | 5.83660 | + | 10.1093i | 0.359900 | + | 0.623365i | 0.987944 | − | 0.154813i | \(-0.0494774\pi\) |
−0.628044 | + | 0.778178i | \(0.716144\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.53469 | − | 19.2424i | −0.401423 | − | 1.18205i | ||||
\(266\) | 2.52478 | + | 1.47413i | 0.154804 | + | 0.0903848i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 13.5150i | 0.825560i | ||||||||
\(269\) | −8.14330 | + | 14.1046i | −0.496506 | + | 0.859973i | −0.999992 | − | 0.00403039i | \(-0.998717\pi\) |
0.503486 | + | 0.864003i | \(0.332050\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.8041 | − | 12.5886i | 1.32450 | − | 0.764703i | 0.340060 | − | 0.940404i | \(-0.389553\pi\) |
0.984444 | + | 0.175701i | \(0.0562192\pi\) | |||||||
\(272\) | −2.28111 | − | 1.31700i | −0.138312 | − | 0.0798547i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.88397 | − | 3.26314i | −0.113815 | − | 0.197133i | ||||
\(275\) | 12.5480 | + | 16.3440i | 0.756671 | + | 0.985581i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.9632 | − | 10.3710i | 1.07930 | − | 0.623136i | 0.148594 | − | 0.988898i | \(-0.452525\pi\) |
0.930708 | + | 0.365763i | \(0.119192\pi\) | |||||||
\(278\) | 5.20651 | − | 3.00598i | 0.312265 | − | 0.180287i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.79687 | − | 1.18167i | −0.346429 | − | 0.0706183i | ||||
\(281\) | −1.17815 | − | 0.680206i | −0.0702827 | − | 0.0405777i | 0.464447 | − | 0.885601i | \(-0.346253\pi\) |
−0.534730 | + | 0.845023i | \(0.679587\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.9351 | 0.887802 | 0.443901 | − | 0.896076i | \(-0.353594\pi\) | ||||
0.443901 | + | 0.896076i | \(0.353594\pi\) | |||||||
\(284\) | − | 1.60164i | − | 0.0950396i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.46313 | − | 4.88619i | −0.500435 | − | 0.288927i | ||||
\(287\) | 0.685919 | − | 1.17479i | 0.0404885 | − | 0.0693458i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.03103 | − | 8.71400i | −0.295943 | − | 0.512589i | ||||
\(290\) | 5.79315 | − | 1.96735i | 0.340185 | − | 0.115527i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.29147 | − | 5.70100i | 0.192619 | − | 0.333626i | ||||
\(293\) | 9.63607 | − | 5.56339i | 0.562945 | − | 0.325016i | −0.191382 | − | 0.981516i | \(-0.561297\pi\) |
0.754327 | + | 0.656499i | \(0.227963\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.2296 | + | 11.6677i | −0.595593 | + | 0.679322i | ||||
\(296\) | −6.05512 | + | 3.49593i | −0.351947 | + | 0.203197i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.69236 | + | 5.59589i | 0.561464 | + | 0.324161i | ||||
\(299\) | −1.40496 | −0.0812510 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.154823 | − | 31.7792i | 0.00892386 | − | 1.83172i | ||||
\(302\) | 9.27469 | + | 16.0642i | 0.533698 | + | 0.924392i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.956982 | − | 0.552514i | 0.0548867 | − | 0.0316888i | ||||
\(305\) | 7.21847 | + | 6.32877i | 0.413329 | + | 0.362384i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.1337 | 0.806651 | 0.403325 | − | 0.915057i | \(-0.367854\pi\) | ||||
0.403325 | + | 0.915057i | \(0.367854\pi\) | |||||||
\(308\) | −9.41586 | − | 5.49759i | −0.536518 | − | 0.313254i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.53555 | − | 3.97652i | −0.257602 | − | 0.225851i | ||||
\(311\) | 5.87504 | 0.333143 | 0.166572 | − | 0.986029i | \(-0.446730\pi\) | ||||
0.166572 | + | 0.986029i | \(0.446730\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.0369 | −1.07603 | −0.538014 | − | 0.842936i | \(-0.680825\pi\) | ||||
−0.538014 | + | 0.842936i | \(0.680825\pi\) | |||||||
\(314\) | −11.6703 | −0.658592 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.4434 | 0.756253 | ||||||||
\(317\) | −15.4166 | −0.865882 | −0.432941 | − | 0.901422i | \(-0.642524\pi\) | ||||
−0.432941 | + | 0.901422i | \(0.642524\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.2756 | 0.631312 | ||||||||
\(320\) | −1.47412 | + | 1.68136i | −0.0824060 | + | 0.0939907i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.56753 | − | 0.00763677i | −0.0873551 | − | 0.000425581i | ||||
\(323\) | −2.91064 | −0.161952 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.40463 | − | 7.22032i | 0.521675 | − | 0.400511i | ||||
\(326\) | −10.7728 | + | 6.21967i | −0.596649 | + | 0.344475i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.257087 | − | 0.445287i | −0.0141952 | − | 0.0245869i | ||||
\(329\) | −9.48891 | + | 5.41696i | −0.523141 | + | 0.298647i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.9300 | −1.70007 | −0.850033 | − | 0.526730i | \(-0.823418\pi\) | ||||
−0.850033 | + | 0.526730i | \(0.823418\pi\) | |||||||
\(332\) | 3.80374 | + | 2.19609i | 0.208757 | + | 0.120526i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −11.4205 | + | 6.59363i | −0.624902 | + | 0.360787i | ||||
\(335\) | −22.7235 | − | 19.9228i | −1.24152 | − | 1.08850i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.3417 | − | 12.3216i | 1.16256 | − | 0.671202i | 0.210640 | − | 0.977564i | \(-0.432445\pi\) |
0.951915 | + | 0.306362i | \(0.0991119\pi\) | |||||||
\(338\) | 3.68840 | − | 6.38850i | 0.200623 | − | 0.347489i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.57698 | − | 1.89394i | 0.302454 | − | 0.102713i | ||||
\(341\) | −5.55839 | − | 9.62741i | −0.301003 | − | 0.521353i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.5183 | − | 0.270672i | −0.999893 | − | 0.0146149i | ||||
\(344\) | −10.4023 | − | 6.00577i | −0.560854 | − | 0.323809i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.8129i | 0.796347i | ||||||||
\(347\) | 0.546144 | 0.0293186 | 0.0146593 | − | 0.999893i | \(-0.495334\pi\) | ||||
0.0146593 | + | 0.999893i | \(0.495334\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.63017 | − | 3.25058i | −0.301376 | − | 0.174000i | 0.341685 | − | 0.939815i | \(-0.389003\pi\) |
−0.643061 | + | 0.765815i | \(0.722336\pi\) | |||||||
\(350\) | 10.5321 | − | 8.00467i | 0.562965 | − | 0.427868i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.56894 | + | 2.06053i | −0.190225 | + | 0.109827i | ||||
\(353\) | −5.67627 | + | 3.27719i | −0.302117 | + | 0.174427i | −0.643394 | − | 0.765536i | \(-0.722474\pi\) |
0.341276 | + | 0.939963i | \(0.389141\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.69292 | + | 2.36101i | 0.142925 | + | 0.125309i | ||||
\(356\) | 7.82648 | + | 13.5559i | 0.414802 | + | 0.718459i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −20.6373 | − | 11.9149i | −1.09071 | − | 0.629724i | ||||
\(359\) | 3.55244 | − | 2.05100i | 0.187490 | − | 0.108248i | −0.403317 | − | 0.915060i | \(-0.632143\pi\) |
0.590807 | + | 0.806813i | \(0.298809\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.88946 | + | 15.3970i | −0.467866 | + | 0.810368i | ||||
\(362\) | 11.6911i | 0.614470i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.16341 | + | 5.41805i | −0.165807 | + | 0.283983i | ||||
\(365\) | 4.73338 | + | 13.9381i | 0.247756 | + | 0.729555i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.0785 | − | 17.4565i | −0.526096 | − | 0.911224i | −0.999538 | − | 0.0303995i | \(-0.990322\pi\) |
0.473442 | − | 0.880825i | \(-0.343011\pi\) | |||||||
\(368\) | −0.296239 | + | 0.513101i | −0.0154425 | + | 0.0267473i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.04810 | − | 15.3342i | 0.158463 | − | 0.797190i | ||||
\(371\) | −24.0446 | − | 0.117142i | −1.24834 | − | 0.00608170i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.94553 | + | 2.85530i | 0.256070 | + | 0.147842i | 0.622540 | − | 0.782588i | \(-0.286101\pi\) |
−0.366471 | + | 0.930430i | \(0.619434\pi\) | |||||||
\(374\) | 10.8549 | 0.561291 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.12973i | 0.212975i | ||||||||
\(377\) | − | 6.48817i | − | 0.334158i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.42424 | 0.278624 | 0.139312 | − | 0.990249i | \(-0.455511\pi\) | ||||
0.139312 | + | 0.990249i | \(0.455511\pi\) | |||||||
\(380\) | −0.481736 | + | 2.42350i | −0.0247125 | + | 0.124323i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 26.0254i | − | 1.33158i | ||||||
\(383\) | 28.8586 | + | 16.6615i | 1.47460 | + | 0.851363i | 0.999590 | − | 0.0286163i | \(-0.00911009\pi\) |
0.475013 | + | 0.879979i | \(0.342443\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 23.1235 | − | 7.72730i | 1.17848 | − | 0.393820i | ||||
\(386\) | 18.0736i | 0.919920i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.92406 | − | 11.9928i | 0.351516 | − | 0.608844i | ||||
\(389\) | −25.3567 | + | 14.6397i | −1.28564 | + | 0.742263i | −0.977873 | − | 0.209200i | \(-0.932914\pi\) |
−0.307764 | + | 0.951463i | \(0.599581\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.35151 | − | 0.780293i | 0.0683486 | − | 0.0394611i | ||||
\(392\) | −3.55890 | + | 6.02779i | −0.179752 | + | 0.304449i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 19.0964 | 0.962063 | ||||||||
\(395\) | −19.8173 | + | 22.6032i | −0.997116 | + | 1.13729i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.42713 | − | 9.40006i | −0.272380 | − | 0.471775i | 0.697091 | − | 0.716983i | \(-0.254477\pi\) |
−0.969471 | + | 0.245207i | \(0.921144\pi\) | |||||||
\(398\) | 21.6198 | + | 12.4822i | 1.08370 | + | 0.625676i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.653922 | − | 4.95705i | −0.0326961 | − | 0.247853i | ||||
\(401\) | 15.8321 | + | 9.14066i | 0.790616 | + | 0.456463i | 0.840180 | − | 0.542308i | \(-0.182450\pi\) |
−0.0495631 | + | 0.998771i | \(0.515783\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.53978 | + | 3.19839i | −0.275956 | + | 0.159323i | ||||
\(404\) | −1.35453 | − | 2.34612i | −0.0673905 | − | 0.116724i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.0352670 | − | 7.23893i | 0.00175027 | − | 0.359262i | ||||
\(407\) | 14.4069 | − | 24.9535i | 0.714124 | − | 1.23690i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.67827i | 0.478560i | 0.970951 | + | 0.239280i | \(0.0769113\pi\) | ||||
−0.970951 | + | 0.239280i | \(0.923089\pi\) | |||||||
\(410\) | 1.12766 | + | 0.224154i | 0.0556914 | + | 0.0110702i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.07239 | + | 15.7138i | −0.446964 | + | 0.774165i | ||||
\(413\) | 9.10250 | + | 15.9449i | 0.447905 | + | 0.784596i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.29959 | + | 3.15814i | −0.456499 | + | 0.155027i | ||||
\(416\) | 1.18566 | + | 2.05363i | 0.0581320 | + | 0.100688i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.27694 | + | 3.94378i | −0.111369 | + | 0.192896i | ||||
\(419\) | −5.02659 | − | 8.70630i | −0.245565 | − | 0.425331i | 0.716725 | − | 0.697355i | \(-0.245640\pi\) |
−0.962290 | + | 0.272025i | \(0.912307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.61761 | + | 11.4620i | −0.322522 | + | 0.558625i | −0.981008 | − | 0.193968i | \(-0.937864\pi\) |
0.658485 | + | 0.752594i | \(0.271197\pi\) | |||||||
\(422\) | −6.61689 | − | 11.4608i | −0.322105 | − | 0.557902i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.54406 | + | 7.87055i | −0.220679 | + | 0.382228i | ||||
\(425\) | −5.03676 | + | 12.1688i | −0.244319 | + | 0.590273i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.86461 | − | 5.63143i | 0.477382 | − | 0.272524i | ||||
\(428\) | −4.33862 | − | 7.51471i | −0.209715 | − | 0.363237i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 25.4321 | − | 8.63673i | 1.22645 | − | 0.416500i | ||||
\(431\) | −4.44716 | − | 2.56757i | −0.214212 | − | 0.123675i | 0.389055 | − | 0.921214i | \(-0.372801\pi\) |
−0.603267 | + | 0.797539i | \(0.706135\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.97362 | −0.383188 | −0.191594 | − | 0.981474i | \(-0.561366\pi\) | ||||
−0.191594 | + | 0.981474i | \(0.561366\pi\) | |||||||
\(434\) | −6.19818 | + | 3.53837i | −0.297522 | + | 0.169847i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.55567 | + | 13.0868i | −0.361851 | + | 0.626745i | ||||
\(437\) | 0.654705i | 0.0313188i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 25.8078i | − | 1.23174i | −0.787849 | − | 0.615869i | \(-0.788805\pi\) | ||
0.787849 | − | 0.615869i | \(-0.211195\pi\) | |||||||
\(440\) | 1.79657 | − | 9.03814i | 0.0856483 | − | 0.430876i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 6.24607i | − | 0.297095i | ||||||
\(443\) | 31.2880 | 1.48654 | 0.743269 | − | 0.668992i | \(-0.233274\pi\) | ||||
0.743269 | + | 0.668992i | \(0.233274\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −34.3294 | − | 6.82390i | −1.62737 | − | 0.323484i | ||||
\(446\) | −2.44383 | + | 4.23284i | −0.115719 | + | 0.200431i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.31170 | + | 2.29771i | 0.0619719 | + | 0.108556i | ||||
\(449\) | 6.93666i | 0.327361i | 0.986513 | + | 0.163681i | \(0.0523366\pi\) | ||||
−0.986513 | + | 0.163681i | \(0.947663\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.83506 | + | 1.05947i | 0.0864094 | + | 0.0498885i | ||||
\(452\) | 0.503287 | + | 0.871718i | 0.0236726 | + | 0.0410022i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 10.3873 | − | 5.99711i | 0.487500 | − | 0.281458i | ||||
\(455\) | −4.44642 | − | 13.3057i | −0.208452 | − | 0.623780i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.4150i | 1.28242i | 0.767366 | + | 0.641209i | \(0.221567\pi\) | ||||
−0.767366 | + | 0.641209i | \(0.778433\pi\) | |||||||
\(458\) | 9.16676 | + | 5.29243i | 0.428335 | + | 0.247299i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.426013 | − | 1.25446i | −0.0198630 | − | 0.0584894i | ||||
\(461\) | 9.16139 | − | 15.8680i | 0.426689 | − | 0.739046i | −0.569888 | − | 0.821722i | \(-0.693013\pi\) |
0.996576 | + | 0.0826762i | \(0.0263467\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.6964 | − | 9.63966i | 0.775947 | − | 0.447993i | −0.0590450 | − | 0.998255i | \(-0.518806\pi\) |
0.834992 | + | 0.550262i | \(0.185472\pi\) | |||||||
\(464\) | −2.36953 | − | 1.36805i | −0.110002 | − | 0.0635099i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.259858 | + | 0.450088i | 0.0120377 | + | 0.0208499i | ||||
\(467\) | 11.2146 | − | 6.47476i | 0.518951 | − | 0.299616i | −0.217555 | − | 0.976048i | \(-0.569808\pi\) |
0.736505 | + | 0.676432i | \(0.236475\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −31.0535 | + | 17.7276i | −1.43392 | + | 0.818584i | ||||
\(470\) | −6.94356 | − | 6.08774i | −0.320282 | − | 0.280806i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.93948 | 0.319415 | ||||||||
\(473\) | 49.5003 | 2.27602 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.36463 | − | 4.38251i | −0.154380 | − | 0.201083i | ||||
\(476\) | 0.0339510 | − | 6.96882i | 0.00155614 | − | 0.319415i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.39886 | − | 1.38498i | 0.109721 | − | 0.0633475i | ||||
\(479\) | 13.5378 | + | 23.4482i | 0.618560 | + | 1.07138i | 0.989749 | + | 0.142820i | \(0.0456169\pi\) |
−0.371189 | + | 0.928557i | \(0.621050\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.3587 | − | 8.28999i | −0.654700 | − | 0.377991i | ||||
\(482\) | 17.4943 | − | 10.1004i | 0.796845 | − | 0.460059i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.99156 | − | 5.18154i | 0.135980 | − | 0.235524i | ||||
\(485\) | 9.95731 | + | 29.3207i | 0.452138 | + | 1.33139i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.98800 | − | 1.72512i | −0.135399 | − | 0.0781727i | 0.430770 | − | 0.902462i | \(-0.358242\pi\) |
−0.566169 | + | 0.824289i | \(0.691575\pi\) | |||||||
\(488\) | − | 4.29324i | − | 0.194346i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.88861 | − | 14.8695i | −0.220845 | − | 0.671735i | ||||
\(491\) | 36.9916 | − | 21.3571i | 1.66941 | − | 0.963833i | 0.701449 | − | 0.712719i | \(-0.252537\pi\) |
0.967958 | − | 0.251113i | \(-0.0807967\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.60343 | + | 6.24132i | 0.162290 | + | 0.281095i | ||||
\(494\) | 2.26932 | + | 1.31019i | 0.102101 | + | 0.0589483i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.69755i | 0.121124i | ||||||||
\(497\) | 3.68009 | − | 2.10086i | 0.165075 | − | 0.0942365i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.0193 | + | 31.2103i | −0.806654 | + | 1.39717i | 0.108514 | + | 0.994095i | \(0.465391\pi\) |
−0.915169 | + | 0.403071i | \(0.867943\pi\) | |||||||
\(500\) | 9.29854 | + | 6.20783i | 0.415843 | + | 0.277623i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 20.9869 | 0.936691 | ||||||||
\(503\) | − | 4.41774i | − | 0.196977i | −0.995138 | − | 0.0984887i | \(-0.968599\pi\) | ||
0.995138 | − | 0.0984887i | \(-0.0314008\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.94141 | + | 1.18102i | 0.264389 | + | 0.0525545i | ||||
\(506\) | − | 2.44164i | − | 0.108544i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.12538i | 0.138666i | ||||||||
\(509\) | −12.1022 | + | 20.9617i | −0.536422 | + | 0.929110i | 0.462671 | + | 0.886530i | \(0.346891\pi\) |
−0.999093 | + | 0.0425803i | \(0.986442\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.4166 | + | 0.0848512i | 0.770467 | + | 0.00375360i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −8.21246 | − | 4.74146i | −0.362236 | − | 0.209137i | ||||
\(515\) | −13.0467 | − | 38.4180i | −0.574908 | − | 1.69290i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.50944 | − | 14.7388i | −0.374245 | − | 0.648211i | ||||
\(518\) | −15.9751 | − | 9.32729i | −0.701905 | − | 0.409818i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.20070 | − | 1.03378i | −0.228066 | − | 0.0453342i | ||||
\(521\) | −7.58138 | + | 13.1313i | −0.332146 | + | 0.575294i | −0.982932 | − | 0.183967i | \(-0.941106\pi\) |
0.650786 | + | 0.759261i | \(0.274439\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.294517 | − | 0.510118i | −0.0128783 | − | 0.0223059i | 0.859514 | − | 0.511111i | \(-0.170766\pi\) |
−0.872393 | + | 0.488806i | \(0.837433\pi\) | |||||||
\(524\) | 10.7870 | − | 18.6837i | 0.471234 | − | 0.816202i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.83660 | + | 10.1093i | 0.254488 | + | 0.440786i | ||||
\(527\) | 3.55267 | − | 6.15341i | 0.154757 | − | 0.268047i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.3245 | + | 19.6146i | 0.492369 | + | 0.852808i | ||||
\(530\) | −6.53469 | − | 19.2424i | −0.283849 | − | 0.835834i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.52478 | + | 1.47413i | 0.109463 | + | 0.0639117i | ||||
\(533\) | 0.609637 | − | 1.05592i | 0.0264063 | − | 0.0457371i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.0306 | + | 3.78284i | 0.822763 | + | 0.163546i | ||||
\(536\) | 13.5150i | 0.583759i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.14330 | + | 14.1046i | −0.351082 | + | 0.608093i | ||||
\(539\) | 0.281074 | − | 28.8460i | 0.0121067 | − | 1.24249i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.2555 | − | 36.8156i | −0.913846 | − | 1.58283i | −0.808582 | − | 0.588384i | \(-0.799764\pi\) |
−0.105264 | − | 0.994444i | \(-0.533569\pi\) | |||||||
\(542\) | 21.8041 | − | 12.5886i | 0.936566 | − | 0.540726i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.28111 | − | 1.31700i | −0.0978017 | − | 0.0564658i | ||||
\(545\) | −10.8656 | − | 31.9954i | −0.465431 | − | 1.37053i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.46589 | + | 4.31044i | 0.319219 | + | 0.184301i | 0.651044 | − | 0.759040i | \(-0.274331\pi\) |
−0.331826 | + | 0.943341i | \(0.607665\pi\) | |||||||
\(548\) | −1.88397 | − | 3.26314i | −0.0804793 | − | 0.139394i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 12.5480 | + | 16.3440i | 0.535047 | + | 0.696911i | ||||
\(551\) | −3.02346 | −0.128804 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.6337 | + | 30.8891i | 0.749862 | + | 1.31354i | ||||
\(554\) | 17.9632 | − | 10.3710i | 0.763182 | − | 0.440623i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.20651 | − | 3.00598i | 0.220805 | − | 0.127482i | ||||
\(557\) | −3.09319 | + | 5.35757i | −0.131063 | + | 0.227007i | −0.924087 | − | 0.382183i | \(-0.875172\pi\) |
0.793024 | + | 0.609191i | \(0.208506\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 28.4833i | − | 1.20472i | ||||||
\(560\) | −5.79687 | − | 1.18167i | −0.244962 | − | 0.0499346i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.17815 | − | 0.680206i | −0.0496974 | − | 0.0286928i | ||||
\(563\) | 32.6001i | 1.37393i | 0.726690 | + | 0.686966i | \(0.241058\pi\) | ||||
−0.726690 | + | 0.686966i | \(0.758942\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.20758 | − | 0.438815i | −0.0928734 | − | 0.0184611i | ||||
\(566\) | 14.9351 | 0.627771 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 1.60164i | − | 0.0672032i | ||||||
\(569\) | − | 6.56784i | − | 0.275338i | −0.990478 | − | 0.137669i | \(-0.956039\pi\) | ||
0.990478 | − | 0.137669i | \(-0.0439611\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.9871 | −0.752737 | −0.376369 | − | 0.926470i | \(-0.622827\pi\) | ||||
−0.376369 | + | 0.926470i | \(0.622827\pi\) | |||||||
\(572\) | −8.46313 | − | 4.88619i | −0.353861 | − | 0.204302i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.685919 | − | 1.17479i | 0.0286297 | − | 0.0490349i | ||||
\(575\) | 2.73719 | + | 1.13295i | 0.114149 | + | 0.0472471i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.8915 | + | 20.5968i | −0.495051 | + | 0.857454i | −0.999984 | − | 0.00570479i | \(-0.998184\pi\) |
0.504932 | + | 0.863159i | \(0.331517\pi\) | |||||||
\(578\) | −5.03103 | − | 8.71400i | −0.209263 | − | 0.362455i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.79315 | − | 1.96735i | 0.240547 | − | 0.0816897i | ||||
\(581\) | −0.0566132 | + | 11.6205i | −0.00234871 | + | 0.482098i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 37.4527i | − | 1.55113i | ||||||
\(584\) | 3.29147 | − | 5.70100i | 0.136202 | − | 0.235909i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.63607 | − | 5.56339i | 0.398062 | − | 0.229821i | ||||
\(587\) | −14.2796 | − | 8.24435i | −0.589384 | − | 0.340281i | 0.175470 | − | 0.984485i | \(-0.443855\pi\) |
−0.764854 | + | 0.644204i | \(0.777189\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.49043 | + | 2.58151i | 0.0614123 | + | 0.106369i | ||||
\(590\) | −10.2296 | + | 11.6677i | −0.421148 | + | 0.480353i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.05512 | + | 3.49593i | −0.248864 | + | 0.143682i | ||||
\(593\) | 8.69178 | − | 5.01820i | 0.356928 | − | 0.206073i | −0.310804 | − | 0.950474i | \(-0.600598\pi\) |
0.667733 | + | 0.744401i | \(0.267265\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.6670 | + | 10.3300i | 0.478301 | + | 0.423488i | ||||
\(596\) | 9.69236 | + | 5.59589i | 0.397015 | + | 0.229217i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.40496 | −0.0574531 | ||||||||
\(599\) | − | 35.1519i | − | 1.43627i | −0.695905 | − | 0.718134i | \(-0.744997\pi\) | ||
0.695905 | − | 0.718134i | \(-0.255003\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.5093 | − | 18.7692i | −1.32608 | − | 0.765613i | −0.341390 | − | 0.939922i | \(-0.610898\pi\) |
−0.984691 | + | 0.174309i | \(0.944231\pi\) | |||||||
\(602\) | 0.154823 | − | 31.7792i | 0.00631013 | − | 1.29522i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 9.27469 | + | 16.0642i | 0.377382 | + | 0.653644i | ||||
\(605\) | 4.30208 | + | 12.6681i | 0.174905 | + | 0.515032i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.0927 | − | 20.9451i | 0.490827 | − | 0.850136i | −0.509118 | − | 0.860697i | \(-0.670028\pi\) |
0.999944 | + | 0.0105604i | \(0.00336154\pi\) | |||||||
\(608\) | 0.956982 | − | 0.552514i | 0.0388107 | − | 0.0224074i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.21847 | + | 6.32877i | 0.292267 | + | 0.256244i | ||||
\(611\) | −8.48095 | + | 4.89648i | −0.343102 | + | 0.198090i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.6618 | + | 13.6611i | 0.955690 | + | 0.551768i | 0.894844 | − | 0.446379i | \(-0.147287\pi\) |
0.0608460 | + | 0.998147i | \(0.480620\pi\) | |||||||
\(614\) | 14.1337 | 0.570388 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.41586 | − | 5.49759i | −0.379376 | − | 0.221504i | ||||
\(617\) | −7.76658 | − | 13.4521i | −0.312671 | − | 0.541562i | 0.666269 | − | 0.745712i | \(-0.267890\pi\) |
−0.978940 | + | 0.204150i | \(0.934557\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.4101 | − | 10.6291i | 0.739963 | − | 0.427218i | −0.0820931 | − | 0.996625i | \(-0.526160\pi\) |
0.822056 | + | 0.569407i | \(0.192827\pi\) | |||||||
\(620\) | −4.53555 | − | 3.97652i | −0.182152 | − | 0.159701i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.87504 | 0.235568 | ||||||||
\(623\) | −20.8814 | + | 35.7641i | −0.836595 | + | 1.43286i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.1448 | + | 6.48305i | −0.965791 | + | 0.259322i | ||||
\(626\) | −19.0369 | −0.760866 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.6703 | −0.465695 | ||||||||
\(629\) | 18.4165 | 0.734314 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.0357 | 0.877226 | 0.438613 | − | 0.898676i | \(-0.355470\pi\) | ||||
0.438613 | + | 0.898676i | \(0.355470\pi\) | |||||||
\(632\) | 13.4434 | 0.534751 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −15.4166 | −0.612271 | ||||||||
\(635\) | −5.25488 | − | 4.60720i | −0.208534 | − | 0.182831i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.5985 | − | 0.161735i | −0.657657 | − | 0.00640816i | ||||
\(638\) | 11.2756 | 0.446405 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.47412 | + | 1.68136i | −0.0582698 | + | 0.0664615i | ||||
\(641\) | −22.2308 | + | 12.8350i | −0.878065 | + | 0.506951i | −0.870020 | − | 0.493016i | \(-0.835894\pi\) |
−0.00804523 | + | 0.999968i | \(0.502561\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.505064 | − | 0.874797i | −0.0199178 | − | 0.0344986i | 0.855895 | − | 0.517150i | \(-0.173007\pi\) |
−0.875813 | + | 0.482651i | \(0.839674\pi\) | |||||||
\(644\) | −1.56753 | − | 0.00763677i | −0.0617694 | − | 0.000300931i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.91064 | −0.114517 | ||||||||
\(647\) | 12.5056 | + | 7.22013i | 0.491647 | + | 0.283852i | 0.725257 | − | 0.688478i | \(-0.241721\pi\) |
−0.233611 | + | 0.972330i | \(0.575054\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.7666 | + | 14.2990i | −0.972174 | + | 0.561285i | ||||
\(650\) | 9.40463 | − | 7.22032i | 0.368880 | − | 0.283204i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.7728 | + | 6.21967i | −0.421895 | + | 0.243581i | ||||
\(653\) | −22.1117 | + | 38.2986i | −0.865299 | + | 1.49874i | 0.00145120 | + | 0.999999i | \(0.499538\pi\) |
−0.866750 | + | 0.498743i | \(0.833795\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.5126 | + | 45.6790i | 0.606126 | + | 1.78483i | ||||
\(656\) | −0.257087 | − | 0.445287i | −0.0100376 | − | 0.0173855i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −9.48891 | + | 5.41696i | −0.369916 | + | 0.211175i | ||||
\(659\) | 24.1702 | + | 13.9547i | 0.941539 | + | 0.543598i | 0.890442 | − | 0.455096i | \(-0.150395\pi\) |
0.0510965 | + | 0.998694i | \(0.483728\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 0.0428492i | − | 0.00166664i | −1.00000 | 0.000833320i | \(-0.999735\pi\) | |||
1.00000 | 0.000833320i | \(-0.000265254\pi\) | ||||||||
\(662\) | −30.9300 | −1.20213 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.80374 | + | 2.19609i | 0.147614 | + | 0.0852248i | ||||
\(665\) | −6.20038 | + | 2.07201i | −0.240441 | + | 0.0803492i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.40389 | − | 0.810538i | 0.0543589 | − | 0.0313841i | ||||
\(668\) | −11.4205 | + | 6.59363i | −0.441873 | + | 0.255115i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −22.7235 | − | 19.9228i | −0.877887 | − | 0.769684i | ||||
\(671\) | 8.84635 | + | 15.3223i | 0.341510 | + | 0.591512i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.4536 | + | 10.0769i | 0.672788 | + | 0.388434i | 0.797132 | − | 0.603805i | \(-0.206349\pi\) |
−0.124344 | + | 0.992239i | \(0.539683\pi\) | |||||||
\(674\) | 21.3417 | − | 12.3216i | 0.822051 | − | 0.474611i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.68840 | − | 6.38850i | 0.141862 | − | 0.245711i | ||||
\(677\) | 28.0616i | 1.07850i | 0.842147 | + | 0.539248i | \(0.181291\pi\) | ||||
−0.842147 | + | 0.539248i | \(0.818709\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 36.6383 | + | 0.178496i | 1.40605 | + | 0.00685005i | ||||
\(680\) | 5.57698 | − | 1.89394i | 0.213867 | − | 0.0726292i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.55839 | − | 9.62741i | −0.212842 | − | 0.368652i | ||||
\(683\) | −14.7248 | + | 25.5040i | −0.563428 | + | 0.975885i | 0.433767 | + | 0.901025i | \(0.357184\pi\) |
−0.997194 | + | 0.0748598i | \(0.976149\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.26371 | + | 1.64263i | 0.315740 | + | 0.0627618i | ||||
\(686\) | −18.5183 | − | 0.270672i | −0.707031 | − | 0.0103343i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −10.4023 | − | 6.00577i | −0.396584 | − | 0.228968i | ||||
\(689\) | −21.5509 | −0.821025 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 6.96725i | − | 0.265047i | −0.991180 | − | 0.132523i | \(-0.957692\pi\) | ||
0.991180 | − | 0.132523i | \(-0.0423080\pi\) | |||||||
\(692\) | 14.8129i | 0.563102i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.546144 | 0.0207313 | ||||||||
\(695\) | −2.62091 | + | 13.1852i | −0.0994168 | + | 0.500142i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.35433i | 0.0512989i | ||||||||
\(698\) | −5.63017 | − | 3.25058i | −0.213105 | − | 0.123036i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 10.5321 | − | 8.00467i | 0.398076 | − | 0.302548i | ||||
\(701\) | − | 17.0338i | − | 0.643357i | −0.946849 | − | 0.321678i | \(-0.895753\pi\) | ||
0.946849 | − | 0.321678i | \(-0.104247\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.86309 | + | 6.69107i | −0.145699 | + | 0.252359i | ||||
\(704\) | −3.56894 | + | 2.06053i | −0.134510 | + | 0.0776591i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.67627 | + | 3.27719i | −0.213629 | + | 0.123339i | ||||
\(707\) | 3.61396 | − | 6.18972i | 0.135917 | − | 0.232788i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.02107 | −0.0383470 | −0.0191735 | − | 0.999816i | \(-0.506103\pi\) | ||||
−0.0191735 | + | 0.999816i | \(0.506103\pi\) | |||||||
\(710\) | 2.69292 | + | 2.36101i | 0.101064 | + | 0.0886071i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.82648 | + | 13.5559i | 0.293310 | + | 0.508027i | ||||
\(713\) | −1.38412 | − | 0.799121i | −0.0518356 | − | 0.0299273i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.6911 | − | 7.02670i | 0.773804 | − | 0.262784i | ||||
\(716\) | −20.6373 | − | 11.9149i | −0.771251 | − | 0.445282i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.55244 | − | 2.05100i | 0.132576 | − | 0.0765426i | ||||
\(719\) | 20.6417 | + | 35.7524i | 0.769804 | + | 1.33334i | 0.937669 | + | 0.347530i | \(0.112980\pi\) |
−0.167865 | + | 0.985810i | \(0.553687\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −48.0060 | − | 0.233878i | −1.78784 | − | 0.00871006i | ||||
\(722\) | −8.88946 | + | 15.3970i | −0.330831 | + | 0.573017i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11.6911i | 0.434496i | ||||||||
\(725\) | −5.23199 | + | 12.6405i | −0.194311 | + | 0.469455i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.79834 | − | 13.5071i | 0.289224 | − | 0.500951i | −0.684400 | − | 0.729106i | \(-0.739936\pi\) |
0.973625 | + | 0.228155i | \(0.0732693\pi\) | |||||||
\(728\) | −3.16341 | + | 5.41805i | −0.117244 | + | 0.200806i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.73338 | + | 13.9381i | 0.175190 | + | 0.515873i | ||||
\(731\) | 15.8192 | + | 27.3996i | 0.585093 | + | 1.01341i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.3150 | + | 38.6507i | −0.824222 | + | 1.42759i | 0.0782904 | + | 0.996931i | \(0.475054\pi\) |
−0.902512 | + | 0.430664i | \(0.858279\pi\) | |||||||
\(734\) | −10.0785 | − | 17.4565i | −0.372006 | − | 0.644333i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.296239 | + | 0.513101i | −0.0109195 | + | 0.0189132i | ||||
\(737\) | −27.8480 | − | 48.2342i | −1.02580 | − | 1.77673i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.6785 | + | 25.4239i | −0.539957 | + | 0.935233i | 0.458949 | + | 0.888463i | \(0.348226\pi\) |
−0.998906 | + | 0.0467704i | \(0.985107\pi\) | |||||||
\(740\) | 3.04810 | − | 15.3342i | 0.112050 | − | 0.563698i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −24.0446 | − | 0.117142i | −0.882706 | − | 0.00430041i | ||||
\(743\) | −20.1964 | − | 34.9813i | −0.740936 | − | 1.28334i | −0.952070 | − | 0.305881i | \(-0.901049\pi\) |
0.211134 | − | 0.977457i | \(-0.432284\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.6964 | + | 8.04729i | −0.868170 | + | 0.294830i | ||||
\(746\) | 4.94553 | + | 2.85530i | 0.181069 | + | 0.104540i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 10.8549 | 0.396893 | ||||||||
\(749\) | 11.5756 | − | 19.8259i | 0.422965 | − | 0.724423i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.9318 | − | 18.9344i | 0.398905 | − | 0.690924i | −0.594686 | − | 0.803958i | \(-0.702724\pi\) |
0.993591 | + | 0.113034i | \(0.0360568\pi\) | |||||||
\(752\) | 4.12973i | 0.150596i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 6.48817i | − | 0.236285i | ||||||
\(755\) | −40.6817 | − | 8.08659i | −1.48056 | − | 0.294301i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 14.0506i | − | 0.510679i | −0.966851 | − | 0.255339i | \(-0.917813\pi\) | ||
0.966851 | − | 0.255339i | \(-0.0821872\pi\) | |||||||
\(758\) | 5.42424 | 0.197017 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.481736 | + | 2.42350i | −0.0174744 | + | 0.0879096i | ||||
\(761\) | −19.5919 | + | 33.9341i | −0.710204 | + | 1.23011i | 0.254576 | + | 0.967053i | \(0.418064\pi\) |
−0.964780 | + | 0.263057i | \(0.915269\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −39.9804 | − | 0.194778i | −1.44739 | − | 0.00705145i | ||||
\(764\) | − | 26.0254i | − | 0.941567i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 28.8586 | + | 16.6615i | 1.04270 | + | 0.602004i | ||||
\(767\) | 8.22789 | + | 14.2511i | 0.297092 | + | 0.514578i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.4424 | − | 9.49301i | 0.592927 | − | 0.342327i | −0.173327 | − | 0.984864i | \(-0.555452\pi\) |
0.766254 | + | 0.642538i | \(0.222118\pi\) | |||||||
\(770\) | 23.1235 | − | 7.72730i | 0.833315 | − | 0.278473i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 18.0736i | 0.650482i | ||||||||
\(773\) | −28.9315 | − | 16.7036i | −1.04060 | − | 0.600788i | −0.120593 | − | 0.992702i | \(-0.538480\pi\) |
−0.920002 | + | 0.391914i | \(0.871813\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.3719 | − | 1.76399i | 0.480333 | − | 0.0633644i | ||||
\(776\) | 6.92406 | − | 11.9928i | 0.248559 | − | 0.430518i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −25.3567 | + | 14.6397i | −0.909082 | + | 0.524859i | ||||
\(779\) | −0.492055 | − | 0.284088i | −0.0176297 | − | 0.0101785i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.30022 | + | 5.71615i | 0.118091 | + | 0.204540i | ||||
\(782\) | 1.35151 | − | 0.780293i | 0.0483298 | − | 0.0279032i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.55890 | + | 6.02779i | −0.127104 | + | 0.215278i | ||||
\(785\) | 17.2034 | − | 19.6219i | 0.614017 | − | 0.700336i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.872685 | −0.0311079 | −0.0155539 | − | 0.999879i | \(-0.504951\pi\) | ||||
−0.0155539 | + | 0.999879i | \(0.504951\pi\) | |||||||
\(788\) | 19.0964 | 0.680281 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −19.8173 | + | 22.6032i | −0.705067 | + | 0.804187i | ||||
\(791\) | −1.34279 | + | 2.29984i | −0.0477442 | + | 0.0817727i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.81673 | − | 5.09034i | 0.313091 | − | 0.180763i | ||||
\(794\) | −5.42713 | − | 9.40006i | −0.192601 | − | 0.333596i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 21.6198 | + | 12.4822i | 0.766294 | + | 0.442420i | ||||
\(797\) | −24.9244 | + | 14.3901i | −0.882867 | + | 0.509724i | −0.871603 | − | 0.490213i | \(-0.836919\pi\) |
−0.0112647 | + | 0.999937i | \(0.503586\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.43885 | − | 9.42037i | 0.192413 | − | 0.333269i | ||||
\(800\) | −0.653922 | − | 4.95705i | −0.0231196 | − | 0.175258i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 15.8321 | + | 9.14066i | 0.559050 | + | 0.322768i | ||||
\(803\) | 27.1287i | 0.957352i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.32358 | − | 2.62432i | 0.0818953 | − | 0.0924952i | ||||
\(806\) | −5.53978 | + | 3.19839i | −0.195130 | + | 0.112659i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.35453 | − | 2.34612i | −0.0476523 | − | 0.0825362i | ||||
\(809\) | −3.58630 | − | 2.07055i | −0.126088 | − | 0.0727967i | 0.435630 | − | 0.900126i | \(-0.356526\pi\) |
−0.561717 | + | 0.827329i | \(0.689859\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 17.4383i | − | 0.612342i | −0.951977 | − | 0.306171i | \(-0.900952\pi\) | ||
0.951977 | − | 0.306171i | \(-0.0990479\pi\) | |||||||
\(812\) | 0.0352670 | − | 7.23893i | 0.00123763 | − | 0.254037i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 14.4069 | − | 24.9535i | 0.504962 | − | 0.874620i | ||||
\(815\) | 5.42292 | − | 27.2814i | 0.189957 | − | 0.955627i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.2731 | −0.464366 | ||||||||
\(818\) | 9.67827i | 0.338393i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.12766 | + | 0.224154i | 0.0393797 | + | 0.00782779i | ||||
\(821\) | 30.7953i | 1.07476i | 0.843339 | + | 0.537381i | \(0.180586\pi\) | ||||
−0.843339 | + | 0.537381i | \(0.819414\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 35.0046i | − | 1.22018i | −0.792331 | − | 0.610092i | \(-0.791133\pi\) | ||
0.792331 | − | 0.610092i | \(-0.208867\pi\) | |||||||
\(824\) | −9.07239 | + | 15.7138i | −0.316052 | + | 0.547417i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.10250 | + | 15.9449i | 0.316716 | + | 0.554793i | ||||
\(827\) | −34.7736 | −1.20919 | −0.604597 | − | 0.796531i | \(-0.706666\pi\) | ||||
−0.604597 | + | 0.796531i | \(0.706666\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.21777 | − | 4.16718i | −0.250683 | − | 0.144732i | 0.369394 | − | 0.929273i | \(-0.379565\pi\) |
−0.620077 | + | 0.784541i | \(0.712899\pi\) | |||||||
\(830\) | −9.29959 | + | 3.15814i | −0.322793 | + | 0.109620i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.18566 | + | 2.05363i | 0.0411055 | + | 0.0711968i | ||||
\(833\) | 16.0568 | − | 9.06297i | 0.556336 | − | 0.314013i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.74898 | − | 28.9218i | 0.198952 | − | 1.00088i | ||||
\(836\) | −2.27694 | + | 3.94378i | −0.0787496 | + | 0.136398i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5.02659 | − | 8.70630i | −0.173641 | − | 0.300754i | ||||
\(839\) | 15.4855 | − | 26.8216i | 0.534618 | − | 0.925985i | −0.464564 | − | 0.885540i | \(-0.653789\pi\) |
0.999182 | − | 0.0404455i | \(-0.0128777\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.7569 | − | 18.6315i | −0.370928 | − | 0.642465i | ||||
\(842\) | −6.61761 | + | 11.4620i | −0.228058 | + | 0.395008i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.61689 | − | 11.4608i | −0.227763 | − | 0.394497i | ||||
\(845\) | 5.30419 | + | 15.6190i | 0.182470 | + | 0.537308i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.8297 | + | 0.0771197i | 0.543914 | + | 0.00264987i | ||||
\(848\) | −4.54406 | + | 7.87055i | −0.156044 | + | 0.270276i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5.03676 | + | 12.1688i | −0.172760 | + | 0.417386i | ||||
\(851\) | − | 4.14252i | − | 0.142004i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.6526 | + | 21.9150i | −0.433217 | + | 0.750355i | −0.997148 | − | 0.0754673i | \(-0.975955\pi\) |
0.563931 | + | 0.825822i | \(0.309288\pi\) | |||||||
\(854\) | 9.86461 | − | 5.63143i | 0.337560 | − | 0.192704i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.33862 | − | 7.51471i | −0.148291 | − | 0.256848i | ||||
\(857\) | 12.9904 | − | 7.50003i | 0.443745 | − | 0.256196i | −0.261440 | − | 0.965220i | \(-0.584197\pi\) |
0.705185 | + | 0.709023i | \(0.250864\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.5617 | + | 17.6448i | 1.04275 | + | 0.602032i | 0.920611 | − | 0.390480i | \(-0.127691\pi\) |
0.122140 | + | 0.992513i | \(0.461024\pi\) | |||||||
\(860\) | 25.4321 | − | 8.63673i | 0.867228 | − | 0.294510i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.44716 | − | 2.56757i | −0.151471 | − | 0.0874517i | ||||
\(863\) | 8.04268 | + | 13.9303i | 0.273776 | + | 0.474194i | 0.969826 | − | 0.243800i | \(-0.0783940\pi\) |
−0.696050 | + | 0.717994i | \(0.745061\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24.9058 | − | 21.8360i | −0.846822 | − | 0.742448i | ||||
\(866\) | −7.97362 | −0.270955 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.19818 | + | 3.53837i | −0.210380 | + | 0.120100i | ||||
\(869\) | −47.9789 | + | 27.7006i | −1.62757 | + | 0.939679i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −27.7548 | + | 16.0242i | −0.940436 | + | 0.542961i | ||||
\(872\) | −7.55567 | + | 13.0868i | −0.255867 | + | 0.443175i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.654705i | 0.0221457i | ||||||||
\(875\) | −2.06690 | + | 29.5081i | −0.0698740 | + | 0.997556i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.0991 | + | 13.9136i | 0.813767 | + | 0.469829i | 0.848262 | − | 0.529576i | \(-0.177649\pi\) |
−0.0344952 | + | 0.999405i | \(0.510982\pi\) | |||||||
\(878\) | − | 25.8078i | − | 0.870970i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.79657 | − | 9.03814i | 0.0605625 | − | 0.304676i | ||||
\(881\) | 36.4477 | 1.22795 | 0.613977 | − | 0.789324i | \(-0.289569\pi\) | ||||
0.613977 | + | 0.789324i | \(0.289569\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.9433i | 0.940367i | 0.882569 | + | 0.470184i | \(0.155812\pi\) | ||||
−0.882569 | + | 0.470184i | \(0.844188\pi\) | |||||||
\(884\) | − | 6.24607i | − | 0.210078i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 31.2880 | 1.05114 | ||||||||
\(887\) | −46.0356 | − | 26.5787i | −1.54572 | − | 0.892424i | −0.998461 | − | 0.0554632i | \(-0.982336\pi\) |
−0.547263 | − | 0.836961i | \(-0.684330\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.18120 | + | 4.09955i | −0.240850 | + | 0.137495i | ||||
\(890\) | −34.3294 | − | 6.82390i | −1.15072 | − | 0.228738i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.44383 | + | 4.23284i | −0.0818255 | + | 0.141726i | ||||
\(893\) | 2.28173 | + | 3.95208i | 0.0763553 | + | 0.132251i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 50.4552 | − | 17.1345i | 1.68653 | − | 0.572745i | ||||
\(896\) | 1.31170 | + | 2.29771i | 0.0438207 | + | 0.0767610i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.93666i | 0.231479i | ||||||||
\(899\) | 3.69038 | − | 6.39192i | 0.123081 | − | 0.213182i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.7310 | − | 11.9690i | 0.690650 | − | 0.398747i | ||||
\(902\) | 1.83506 | + | 1.05947i | 0.0611006 | + | 0.0352765i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.503287 | + | 0.871718i | 0.0167391 | + | 0.0289929i | ||||
\(905\) | −19.6569 | − | 17.2341i | −0.653417 | − | 0.572881i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.9054 | + | 8.02828i | −0.461721 | + | 0.266575i | −0.712768 | − | 0.701400i | \(-0.752559\pi\) |
0.251047 | + | 0.967975i | \(0.419225\pi\) | |||||||
\(908\) | 10.3873 | − | 5.99711i | 0.344714 | − | 0.199021i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.44642 | − | 13.3057i | −0.147398 | − | 0.441079i | ||||
\(911\) | 36.7577 | + | 21.2220i | 1.21784 | + | 0.703118i | 0.964455 | − | 0.264249i | \(-0.0851240\pi\) |
0.253381 | + | 0.967367i | \(0.418457\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.1004 | −0.599037 | ||||||||
\(914\) | 27.4150i | 0.906806i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.16676 | + | 5.29243i | 0.302878 | + | 0.174867i | ||||
\(917\) | 57.0790 | + | 0.278080i | 1.88492 | + | 0.00918302i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.3435 | − | 19.6475i | −0.374188 | − | 0.648112i | 0.616017 | − | 0.787732i | \(-0.288745\pi\) |
−0.990205 | + | 0.139621i | \(0.955412\pi\) | |||||||
\(920\) | −0.426013 | − | 1.25446i | −0.0140452 | − | 0.0413583i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9.16139 | − | 15.8680i | 0.301714 | − | 0.522585i | ||||
\(923\) | 3.28917 | − | 1.89900i | 0.108264 | − | 0.0625064i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.2891 | + | 27.7295i | 0.699980 | + | 0.911740i | ||||
\(926\) | 16.6964 | − | 9.63966i | 0.548677 | − | 0.316779i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.36953 | − | 1.36805i | −0.0777835 | − | 0.0449083i | ||||
\(929\) | 5.64081 | 0.185069 | 0.0925345 | − | 0.995709i | \(-0.470503\pi\) | ||||
0.0925345 | + | 0.995709i | \(0.470503\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.0753675 | + | 7.73482i | −0.00247007 | + | 0.253499i | ||||
\(932\) | 0.259858 | + | 0.450088i | 0.00851194 | + | 0.0147431i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11.2146 | − | 6.47476i | 0.366953 | − | 0.211861i | ||||
\(935\) | −16.0014 | + | 18.2509i | −0.523301 | + | 0.596868i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.6125 | −1.09807 | −0.549036 | − | 0.835799i | \(-0.685005\pi\) | ||||
−0.549036 | + | 0.835799i | \(0.685005\pi\) | |||||||
\(938\) | −31.0535 | + | 17.7276i | −1.01393 | + | 0.578826i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.94356 | − | 6.08774i | −0.226474 | − | 0.198560i | ||||
\(941\) | −0.233263 | −0.00760416 | −0.00380208 | − | 0.999993i | \(-0.501210\pi\) | ||||
−0.00380208 | + | 0.999993i | \(0.501210\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.304637 | 0.00992033 | ||||||||
\(944\) | 6.93948 | 0.225861 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 49.5003 | 1.60939 | ||||||||
\(947\) | −2.62504 | −0.0853024 | −0.0426512 | − | 0.999090i | \(-0.513580\pi\) | ||||
−0.0426512 | + | 0.999090i | \(0.513580\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.6103 | 0.506733 | ||||||||
\(950\) | −3.36463 | − | 4.38251i | −0.109163 | − | 0.142187i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.0339510 | − | 6.96882i | 0.00110036 | − | 0.225861i | ||||
\(953\) | −15.1772 | −0.491637 | −0.245818 | − | 0.969316i | \(-0.579057\pi\) | ||||
−0.245818 | + | 0.969316i | \(0.579057\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 43.7581 | + | 38.3647i | 1.41598 | + | 1.24145i | ||||
\(956\) | 2.39886 | − | 1.38498i | 0.0775846 | − | 0.0447935i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 13.5378 | + | 23.4482i | 0.437388 | + | 0.757578i | ||||
\(959\) | 5.02653 | − | 8.60906i | 0.162315 | − | 0.278001i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.7232 | 0.765265 | ||||||||
\(962\) | −14.3587 | − | 8.28999i | −0.462942 | − | 0.267280i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 17.4943 | − | 10.1004i | 0.563454 | − | 0.325310i | ||||
\(965\) | −30.3881 | − | 26.6427i | −0.978228 | − | 0.857658i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.1551 | + | 6.44040i | −0.358724 | + | 0.207109i | −0.668521 | − | 0.743693i | \(-0.733072\pi\) |
0.309797 | + | 0.950803i | \(0.399739\pi\) | |||||||
\(968\) | 2.99156 | − | 5.18154i | 0.0961525 | − | 0.166541i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 9.95731 | + | 29.3207i | 0.319710 | + | 0.941432i | ||||
\(971\) | −14.3294 | − | 24.8192i | −0.459851 | − | 0.796486i | 0.539101 | − | 0.842241i | \(-0.318764\pi\) |
−0.998953 | + | 0.0457549i | \(0.985431\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.7362 | + | 8.02008i | 0.440363 | + | 0.257112i | ||||
\(974\) | −2.98800 | − | 1.72512i | −0.0957416 | − | 0.0552765i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 4.29324i | − | 0.137423i | ||||||
\(977\) | 14.1607 | 0.453042 | 0.226521 | − | 0.974006i | \(-0.427265\pi\) | ||||
0.226521 | + | 0.974006i | \(0.427265\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −55.8645 | − | 32.2534i | −1.78544 | − | 1.03082i | ||||
\(980\) | −4.88861 | − | 14.8695i | −0.156161 | − | 0.474988i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 36.9916 | − | 21.3571i | 1.18045 | − | 0.681533i | ||||
\(983\) | 34.2530 | − | 19.7760i | 1.09250 | − | 0.630755i | 0.158259 | − | 0.987398i | \(-0.449412\pi\) |
0.934241 | + | 0.356643i | \(0.116079\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −28.1505 | + | 32.1079i | −0.896948 | + | 1.02304i | ||||
\(986\) | 3.60343 | + | 6.24132i | 0.114757 | + | 0.198764i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.26932 | + | 1.31019i | 0.0721966 | + | 0.0416827i | ||||
\(989\) | 6.16314 | − | 3.55829i | 0.195976 | − | 0.113147i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.3535 | − | 17.9329i | 0.328891 | − | 0.569656i | −0.653401 | − | 0.757012i | \(-0.726658\pi\) |
0.982292 | + | 0.187356i | \(0.0599917\pi\) | |||||||
\(992\) | 2.69755i | 0.0856474i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.68009 | − | 2.10086i | 0.116725 | − | 0.0666353i | ||||
\(995\) | −52.8573 | + | 17.9503i | −1.67569 | + | 0.569063i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.8760 | − | 43.0865i | −0.787831 | − | 1.36456i | −0.927293 | − | 0.374336i | \(-0.877871\pi\) |
0.139462 | − | 0.990227i | \(-0.455463\pi\) | |||||||
\(998\) | −18.0193 | + | 31.2103i | −0.570391 | + | 0.987946i | ||||
\(999\) | 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.bi.b.899.8 | 48 | ||
3.2 | odd | 2 | 630.2.bi.a.479.16 | yes | 48 | ||
5.4 | even | 2 | 1890.2.bi.a.899.9 | 48 | |||
7.5 | odd | 6 | 1890.2.r.a.89.3 | 48 | |||
9.4 | even | 3 | 630.2.r.a.59.16 | ✓ | 48 | ||
9.5 | odd | 6 | 1890.2.r.b.1529.3 | 48 | |||
15.14 | odd | 2 | 630.2.bi.b.479.9 | yes | 48 | ||
21.5 | even | 6 | 630.2.r.b.299.9 | yes | 48 | ||
35.19 | odd | 6 | 1890.2.r.b.89.3 | 48 | |||
45.4 | even | 6 | 630.2.r.b.59.9 | yes | 48 | ||
45.14 | odd | 6 | 1890.2.r.a.1529.3 | 48 | |||
63.5 | even | 6 | 1890.2.bi.a.719.9 | 48 | |||
63.40 | odd | 6 | 630.2.bi.b.509.9 | yes | 48 | ||
105.89 | even | 6 | 630.2.r.a.299.16 | yes | 48 | ||
315.194 | even | 6 | inner | 1890.2.bi.b.719.8 | 48 | ||
315.229 | odd | 6 | 630.2.bi.a.509.16 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.r.a.59.16 | ✓ | 48 | 9.4 | even | 3 | ||
630.2.r.a.299.16 | yes | 48 | 105.89 | even | 6 | ||
630.2.r.b.59.9 | yes | 48 | 45.4 | even | 6 | ||
630.2.r.b.299.9 | yes | 48 | 21.5 | even | 6 | ||
630.2.bi.a.479.16 | yes | 48 | 3.2 | odd | 2 | ||
630.2.bi.a.509.16 | yes | 48 | 315.229 | odd | 6 | ||
630.2.bi.b.479.9 | yes | 48 | 15.14 | odd | 2 | ||
630.2.bi.b.509.9 | yes | 48 | 63.40 | odd | 6 | ||
1890.2.r.a.89.3 | 48 | 7.5 | odd | 6 | |||
1890.2.r.a.1529.3 | 48 | 45.14 | odd | 6 | |||
1890.2.r.b.89.3 | 48 | 35.19 | odd | 6 | |||
1890.2.r.b.1529.3 | 48 | 9.5 | odd | 6 | |||
1890.2.bi.a.719.9 | 48 | 63.5 | even | 6 | |||
1890.2.bi.a.899.9 | 48 | 5.4 | even | 2 | |||
1890.2.bi.b.719.8 | 48 | 315.194 | even | 6 | inner | ||
1890.2.bi.b.899.8 | 48 | 1.1 | even | 1 | trivial |