Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(49,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.u (of order \(9\), degree \(6\), 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: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{9})\) |
Twist minimal: | no (minimal twist has level 216) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Character | \(\chi\) | \(=\) | 432.49 |
Dual form | 432.2.u.f.97.2 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{7}{9}\right)\) |
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 | 0 | ||||||||
\(3\) | −1.10062 | − | 1.33740i | −0.635442 | − | 0.772148i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.74067 | − | 1.36149i | 1.67288 | − | 0.608879i | 0.680573 | − | 0.732680i | \(-0.261731\pi\) |
0.992307 | + | 0.123801i | \(0.0395085\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.452652 | + | 2.56712i | 0.171086 | + | 0.970278i | 0.942565 | + | 0.334023i | \(0.108406\pi\) |
−0.771479 | + | 0.636255i | \(0.780483\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.577279 | + | 2.94393i | −0.192426 | + | 0.981311i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.99402 | + | 1.81767i | 1.50575 | + | 0.548050i | 0.957543 | − | 0.288291i | \(-0.0930869\pi\) |
0.548211 | + | 0.836340i | \(0.315309\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.0404003 | − | 0.0338999i | −0.0112050 | − | 0.00940214i | 0.637168 | − | 0.770725i | \(-0.280106\pi\) |
−0.648373 | + | 0.761323i | \(0.724550\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.93792 | − | 3.50429i | −1.53316 | − | 0.904805i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.69081 | + | 2.92857i | −0.410082 | + | 0.710284i | −0.994898 | − | 0.100882i | \(-0.967833\pi\) |
0.584816 | + | 0.811166i | \(0.301167\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.23206 | − | 2.13399i | −0.282653 | − | 0.489570i | 0.689384 | − | 0.724396i | \(-0.257881\pi\) |
−0.972037 | + | 0.234826i | \(0.924548\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.93506 | − | 3.43079i | 0.640484 | − | 0.748660i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.964125 | − | 5.46782i | 0.201034 | − | 1.14012i | −0.702526 | − | 0.711658i | \(-0.747945\pi\) |
0.903560 | − | 0.428462i | \(-0.140944\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.30876 | − | 6.97187i | 1.66175 | − | 1.39437i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.57258 | − | 2.46810i | 0.879994 | − | 0.474985i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.29991 | + | 5.28625i | −1.16986 | + | 0.981632i | −0.999993 | − | 0.00383417i | \(-0.998780\pi\) |
−0.169871 | + | 0.985466i | \(0.554335\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.115728 | − | 0.656323i | 0.0207853 | − | 0.117879i | −0.972650 | − | 0.232276i | \(-0.925383\pi\) |
0.993435 | + | 0.114397i | \(0.0364937\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.06555 | − | 8.67957i | −0.533644 | − | 1.51092i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.18834 | + | 8.98646i | 0.876989 | + | 1.51899i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.67730 | − | 4.63722i | 0.440145 | − | 0.762353i | −0.557555 | − | 0.830140i | \(-0.688260\pi\) |
0.997700 | + | 0.0677866i | \(0.0215937\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.000872395 | 0.0913423i | −0.000139695 | 0.0146265i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.31122 | − | 4.45664i | −0.829473 | − | 0.696010i | 0.125697 | − | 0.992069i | \(-0.459883\pi\) |
−0.955170 | + | 0.296058i | \(0.904328\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.0524095 | + | 0.0190755i | 0.00799237 | + | 0.00290898i | 0.346013 | − | 0.938230i | \(-0.387535\pi\) |
−0.338021 | + | 0.941139i | \(0.609757\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.84874 | + | 11.7983i | 0.275593 | + | 1.75878i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.0794772 | + | 0.450737i | 0.0115929 | + | 0.0657468i | 0.990055 | − | 0.140678i | \(-0.0449282\pi\) |
−0.978462 | + | 0.206425i | \(0.933817\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.192660 | − | 0.0701224i | 0.0275228 | − | 0.0100175i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.77762 | − | 0.961949i | 0.809028 | − | 0.134700i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.38667 | 0.190474 | 0.0952370 | − | 0.995455i | \(-0.469639\pi\) | ||||
0.0952370 | + | 0.995455i | \(0.469639\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 21.1558 | 2.85264 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.49797 | + | 3.99646i | −0.198411 | + | 0.529344i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.99339 | + | 1.45348i | −0.519895 | + | 0.189226i | −0.588621 | − | 0.808409i | \(-0.700329\pi\) |
0.0687257 | + | 0.997636i | \(0.478107\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.457339 | + | 2.59370i | 0.0585563 | + | 0.332089i | 0.999987 | − | 0.00511752i | \(-0.00162896\pi\) |
−0.941431 | + | 0.337207i | \(0.890518\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.81873 | − | 0.149364i | −0.985067 | − | 0.0188181i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.197279 | − | 0.0718037i | −0.0244694 | − | 0.00890615i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.16941 | − | 6.01585i | −0.875882 | − | 0.734953i | 0.0894458 | − | 0.995992i | \(-0.471490\pi\) |
−0.965328 | + | 0.261039i | \(0.915935\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.37380 | + | 4.72856i | −1.00809 | + | 0.569252i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.18697 | + | 12.4482i | −0.852937 | + | 1.47733i | 0.0256094 | + | 0.999672i | \(0.491847\pi\) |
−0.878546 | + | 0.477658i | \(0.841486\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.15357 | − | 12.3903i | −0.837262 | − | 1.45018i | −0.892176 | − | 0.451689i | \(-0.850822\pi\) |
0.0549141 | − | 0.998491i | \(-0.482512\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −18.4690 | − | 3.43876i | −2.13261 | − | 0.397074i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.40563 | + | 13.6430i | −0.274147 | + | 1.55476i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.93415 | + | 4.97935i | −0.667644 | + | 0.560220i | −0.912367 | − | 0.409373i | \(-0.865747\pi\) |
0.244723 | + | 0.969593i | \(0.421303\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.33350 | − | 3.39894i | −0.925944 | − | 0.377660i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.83808 | + | 1.54234i | −0.201756 | + | 0.169293i | −0.738068 | − | 0.674727i | \(-0.764262\pi\) |
0.536312 | + | 0.844020i | \(0.319817\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.33755 | + | 13.2569i | −0.253542 | + | 1.43791i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 14.0036 | + | 2.60735i | 1.50135 | + | 0.279538i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.04047 | + | 3.53420i | 0.216290 | + | 0.374625i | 0.953671 | − | 0.300852i | \(-0.0972711\pi\) |
−0.737381 | + | 0.675477i | \(0.763938\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0687377 | − | 0.119057i | 0.00720567 | − | 0.0124806i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.00514 | + | 0.567588i | −0.104228 | + | 0.0588561i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.51413 | − | 6.30511i | −0.770934 | − | 0.646890i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.8711 | − | 4.32074i | −1.20533 | − | 0.438705i | −0.340250 | − | 0.940335i | \(-0.610512\pi\) |
−0.865082 | + | 0.501630i | \(0.832734\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.23406 | + | 13.6528i | −0.827554 | + | 1.37215i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.52514 | + | 8.64948i | 0.151757 | + | 0.860655i | 0.961691 | + | 0.274135i | \(0.0883915\pi\) |
−0.809934 | + | 0.586520i | \(0.800497\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.59095 | + | 2.39891i | −0.649426 | + | 0.236372i | −0.645664 | − | 0.763621i | \(-0.723419\pi\) |
−0.00376127 | + | 0.999993i | \(0.501197\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.30812 | − | 16.8295i | 0.615609 | − | 1.64240i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.10320 | 0.880040 | 0.440020 | − | 0.897988i | \(-0.354971\pi\) | ||||
0.440020 | + | 0.897988i | \(0.354971\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.5496 | 1.39360 | 0.696801 | − | 0.717264i | \(-0.254606\pi\) | ||||
0.696801 | + | 0.717264i | \(0.254606\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.14850 | + | 1.52319i | −0.868337 | + | 0.144574i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.0868 | − | 5.12716i | 1.32517 | − | 0.482323i | 0.420059 | − | 0.907497i | \(-0.362009\pi\) |
0.905112 | + | 0.425174i | \(0.139787\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.83793 | − | 21.7660i | −0.357889 | − | 2.02969i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.123121 | − | 0.0993662i | 0.0113826 | − | 0.00918641i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.28334 | − | 3.01489i | −0.759332 | − | 0.276374i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.2098 | + | 11.0843i | 1.20089 | + | 1.00767i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.114689 | + | 12.0083i | −0.0103412 | + | 1.08275i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.6363 | − | 20.1547i | 1.04079 | − | 1.80269i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00053 | + | 1.73296i | 0.0887824 | + | 0.153776i | 0.906997 | − | 0.421138i | \(-0.138369\pi\) |
−0.818214 | + | 0.574913i | \(0.805036\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.0321713 | − | 0.0910872i | −0.00283252 | − | 0.00801978i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.156341 | + | 0.886652i | −0.0136595 | + | 0.0774671i | −0.990876 | − | 0.134780i | \(-0.956967\pi\) |
0.977216 | + | 0.212247i | \(0.0680783\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.92049 | − | 4.12878i | 0.426661 | − | 0.358011i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 13.7442 | − | 15.4579i | 1.18292 | − | 1.33040i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.5185 | + | 8.82610i | −0.898659 | + | 0.754065i | −0.969928 | − | 0.243393i | \(-0.921740\pi\) |
0.0712687 | + | 0.997457i | \(0.477295\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.00441448 | + | 0.0250358i | −0.000374432 | + | 0.00212351i | −0.984994 | − | 0.172586i | \(-0.944788\pi\) |
0.984620 | + | 0.174710i | \(0.0558987\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.515342 | − | 0.602383i | 0.0433996 | − | 0.0507298i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.140141 | − | 0.242731i | −0.0117192 | − | 0.0202982i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.3687 | + | 28.3514i | −1.35935 | + | 2.35446i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.305827 | − | 0.180485i | −0.0252241 | − | 0.0148862i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.35550 | + | 7.85019i | 0.766432 | + | 0.643113i | 0.939793 | − | 0.341746i | \(-0.111018\pi\) |
−0.173360 | + | 0.984858i | \(0.555463\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.76321 | − | 1.00573i | −0.224867 | − | 0.0818448i | 0.227130 | − | 0.973864i | \(-0.427066\pi\) |
−0.451996 | + | 0.892020i | \(0.649288\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.64546 | − | 6.66825i | −0.618099 | − | 0.539096i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.460682 | − | 2.61265i | −0.0370028 | − | 0.209853i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.3273 | + | 4.12280i | −0.904016 | + | 0.329035i | −0.751861 | − | 0.659322i | \(-0.770844\pi\) |
−0.152155 | + | 0.988357i | \(0.548621\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.52620 | − | 1.85453i | −0.121035 | − | 0.147074i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 14.4729 | 1.14063 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.3746 | 0.812605 | 0.406302 | − | 0.913739i | \(-0.366818\pi\) | ||||
0.406302 | + | 0.913739i | \(0.366818\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −23.2844 | − | 28.2937i | −1.81269 | − | 2.20266i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.57455 | − | 1.66500i | 0.353989 | − | 0.128842i | −0.158904 | − | 0.987294i | \(-0.550796\pi\) |
0.512893 | + | 0.858453i | \(0.328574\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.25694 | − | 12.7998i | −0.173611 | − | 0.984597i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.99355 | − | 2.39519i | 0.534810 | − | 0.183165i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.4101 | − | 5.24484i | −1.09558 | − | 0.398758i | −0.269894 | − | 0.962890i | \(-0.586989\pi\) |
−0.825685 | + | 0.564132i | \(0.809211\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 21.6586 | + | 18.1737i | 1.63723 | + | 1.37380i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.33908 | + | 3.74104i | 0.476474 | + | 0.281194i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.10111 | − | 14.0315i | 0.605505 | − | 1.04877i | −0.386466 | − | 0.922304i | \(-0.626304\pi\) |
0.991971 | − | 0.126462i | \(-0.0403623\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.93187 | + | 8.54226i | 0.366583 | + | 0.634941i | 0.989029 | − | 0.147722i | \(-0.0471941\pi\) |
−0.622446 | + | 0.782663i | \(0.713861\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.96546 | − | 3.46632i | 0.219213 | − | 0.256238i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.70136 | − | 20.9914i | 0.272129 | − | 1.54332i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.7672 | + | 11.5520i | −1.00675 | + | 0.844767i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.40567 | + | 10.6212i | 0.611423 | + | 0.772576i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.4067 | + | 8.73226i | −0.753003 | + | 0.631844i | −0.936295 | − | 0.351214i | \(-0.885769\pi\) |
0.183293 | + | 0.983058i | \(0.441324\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.599757 | + | 3.40139i | −0.0431715 | + | 0.244838i | −0.998755 | − | 0.0498825i | \(-0.984115\pi\) |
0.955584 | + | 0.294720i | \(0.0952264\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.121099 | + | 0.342869i | 0.00867205 | + | 0.0245534i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.413665 | − | 0.716488i | −0.0294724 | − | 0.0510477i | 0.850913 | − | 0.525307i | \(-0.176049\pi\) |
−0.880385 | + | 0.474259i | \(0.842716\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.28337 | + | 2.22286i | −0.0909755 | + | 0.157574i | −0.907922 | − | 0.419139i | \(-0.862332\pi\) |
0.816946 | + | 0.576714i | \(0.195665\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.154814 | + | 16.2095i | −0.0109198 | + | 1.14333i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.4221 | − | 13.7798i | −1.15260 | − | 0.967150i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −25.9352 | − | 9.43965i | −1.81139 | − | 0.659294i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15.5403 | + | 5.99478i | 1.08013 | + | 0.416666i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.27403 | − | 12.8966i | −0.157298 | − | 0.892080i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.6574 | − | 6.06281i | 1.14674 | − | 0.417381i | 0.302400 | − | 0.953181i | \(-0.402212\pi\) |
0.844345 | + | 0.535801i | \(0.179990\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 24.5583 | − | 4.08886i | 1.68271 | − | 0.280164i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.222018 | 0.0151415 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.73724 | 0.117932 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.69750 | + | 23.2042i | −0.587722 | + | 1.56800i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.167588 | − | 0.0609970i | 0.0112732 | − | 0.00410310i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.62276 | − | 20.5457i | −0.242598 | − | 1.37584i | −0.826005 | − | 0.563663i | \(-0.809392\pi\) |
0.583407 | − | 0.812180i | \(-0.301719\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 15.7283 | + | 28.4851i | 1.04855 | + | 1.89901i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.39434 | + | 1.23544i | 0.225290 | + | 0.0819989i | 0.452199 | − | 0.891917i | \(-0.350640\pi\) |
−0.226909 | + | 0.973916i | \(0.572862\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.11755 | − | 2.61593i | −0.206013 | − | 0.172866i | 0.533943 | − | 0.845520i | \(-0.320710\pi\) |
−0.739957 | + | 0.672655i | \(0.765154\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 20.8938 | − | 11.7984i | 1.37471 | − | 0.776281i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.2458 | + | 21.2104i | −0.802252 | + | 1.38954i | 0.115879 | + | 0.993263i | \(0.463031\pi\) |
−0.918131 | + | 0.396277i | \(0.870302\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.910974 | + | 1.57785i | 0.0594254 | + | 0.102928i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.1906 | + | 2.45598i | 0.856823 | + | 0.159533i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.92957 | + | 22.2857i | −0.254183 | + | 1.44154i | 0.543978 | + | 0.839100i | \(0.316918\pi\) |
−0.798161 | + | 0.602444i | \(0.794194\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.75006 | − | 7.34218i | 0.563641 | − | 0.472951i | −0.315888 | − | 0.948797i | \(-0.602302\pi\) |
0.879529 | + | 0.475845i | \(0.157858\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.62626 | + | 14.8862i | 0.296774 | + | 0.954948i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.625206 | − | 0.524610i | 0.0399429 | − | 0.0335161i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.0225664 | + | 0.127980i | −0.00143586 | + | 0.00814319i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.08575 | + | 0.760731i | 0.258924 | + | 0.0482094i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.27111 | − | 2.20163i | −0.0802317 | − | 0.138965i | 0.823118 | − | 0.567871i | \(-0.192233\pi\) |
−0.903349 | + | 0.428905i | \(0.858899\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.7536 | − | 25.5540i | 0.927550 | − | 1.60656i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 20.3025 | − | 11.4645i | 1.27139 | − | 0.717937i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.7955 | − | 11.5758i | −0.860539 | − | 0.722078i | 0.101545 | − | 0.994831i | \(-0.467621\pi\) |
−0.962084 | + | 0.272753i | \(0.912066\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.1162 | + | 4.77389i | 0.814998 | + | 0.296635i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.9256 | − | 21.5982i | −0.738174 | − | 1.33689i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.130638 | − | 0.740886i | −0.00805550 | − | 0.0456850i | 0.980515 | − | 0.196444i | \(-0.0629394\pi\) |
−0.988571 | + | 0.150759i | \(0.951828\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.18709 | − | 1.88795i | 0.318640 | − | 0.115976i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.48086 | − | 6.61874i | 0.151826 | − | 0.405060i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.748703 | 0.0456493 | 0.0228246 | − | 0.999739i | \(-0.492734\pi\) | ||||
0.0228246 | + | 0.999739i | \(0.492734\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.7361 | −1.74559 | −0.872795 | − | 0.488086i | \(-0.837695\pi\) | ||||
−0.872795 | + | 0.488086i | \(0.837695\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.234881 | + | 0.0391067i | −0.0142156 | + | 0.00236684i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 54.1667 | − | 19.7151i | 3.26638 | − | 1.18886i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.02567 | + | 11.4881i | 0.121711 | + | 0.690255i | 0.983207 | + | 0.182492i | \(0.0584163\pi\) |
−0.861497 | + | 0.507763i | \(0.830473\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.86537 | + | 0.719576i | 0.111677 | + | 0.0430799i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.59722 | − | 2.76516i | −0.453212 | − | 0.164956i | 0.105320 | − | 0.994438i | \(-0.466413\pi\) |
−0.558533 | + | 0.829483i | \(0.688635\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.9217 | − | 20.9118i | −1.48144 | − | 1.24308i | −0.904628 | − | 0.426201i | \(-0.859852\pi\) |
−0.576813 | − | 0.816876i | \(-0.695704\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.162258 | + | 16.9889i | −0.00961136 | + | 1.00634i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.03658 | − | 15.6518i | 0.533412 | − | 0.923897i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.78230 | + | 4.81909i | 0.163665 | + | 0.283476i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.28704 | + | 20.6320i | 0.427174 | + | 1.20947i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.929693 | − | 5.27255i | 0.0543132 | − | 0.308026i | −0.945534 | − | 0.325524i | \(-0.894459\pi\) |
0.999847 | + | 0.0174987i | \(0.00557030\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.9591 | + | 10.8740i | −0.754506 | + | 0.633106i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 27.3218 | − | 4.01425i | 1.58537 | − | 0.232930i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.224310 | + | 0.188218i | −0.0129722 | + | 0.0108849i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.0252457 | + | 0.143176i | −0.00145514 | + | 0.00825251i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.88922 | − | 11.5595i | 0.568121 | − | 0.664076i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.24206 | + | 9.07952i | 0.300160 | + | 0.519892i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.29583 | − | 5.70854i | 0.188103 | − | 0.325804i | −0.756515 | − | 0.653977i | \(-0.773100\pi\) |
0.944618 | + | 0.328173i | \(0.106433\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.4624 | + | 6.17445i | 0.595186 | + | 0.351252i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.3382 | − | 17.0658i | −1.15327 | − | 0.967712i | −0.153483 | − | 0.988151i | \(-0.549049\pi\) |
−0.999791 | + | 0.0204396i | \(0.993493\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.9416 | + | 6.53022i | 1.01412 | + | 0.369110i | 0.795014 | − | 0.606591i | \(-0.207463\pi\) |
0.219107 | + | 0.975701i | \(0.429686\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −29.4507 | + | 10.0864i | −1.65936 | + | 0.568306i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.36707 | − | 7.75306i | −0.0767825 | − | 0.435455i | −0.998829 | − | 0.0483765i | \(-0.984595\pi\) |
0.922047 | − | 0.387079i | \(-0.126516\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −41.0706 | + | 14.9485i | −2.29951 | + | 0.836953i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.0192 | − | 12.1746i | −0.559214 | − | 0.679521i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.33271 | 0.463645 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.572022 | −0.0317301 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.0136 | − | 19.4587i | −0.885554 | − | 1.07607i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.12112 | + | 0.408054i | −0.0618093 | + | 0.0224967i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.21881 | − | 6.91220i | −0.0669917 | − | 0.379929i | −0.999808 | − | 0.0195775i | \(-0.993768\pi\) |
0.932817 | − | 0.360351i | \(-0.117343\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.1061 | + | 10.5588i | 0.663411 | + | 0.578616i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −35.0090 | − | 12.7422i | −1.91274 | − | 0.696182i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.0600 | − | 22.7060i | −1.47405 | − | 1.23688i | −0.912269 | − | 0.409592i | \(-0.865671\pi\) |
−0.561783 | − | 0.827284i | \(-0.689885\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −22.3612 | − | 13.1966i | −1.21449 | − | 0.716740i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.77093 | − | 3.06734i | 0.0959011 | − | 0.166106i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.39073 | + | 16.2652i | 0.507052 | + | 0.878240i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −24.8857 | + | 29.0889i | −1.33980 | + | 1.56609i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.838421 | − | 4.75492i | 0.0450088 | − | 0.255258i | −0.953998 | − | 0.299813i | \(-0.903076\pi\) |
0.999007 | + | 0.0445550i | \(0.0141870\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.1473 | + | 11.8710i | −0.757288 | + | 0.635440i | −0.937419 | − | 0.348203i | \(-0.886792\pi\) |
0.180131 | + | 0.983643i | \(0.442348\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.268402 | − | 0.0552982i | −0.0143262 | − | 0.00295160i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.8590 | − | 12.4682i | 0.790867 | − | 0.663616i | −0.155093 | − | 0.987900i | \(-0.549568\pi\) |
0.945960 | + | 0.324284i | \(0.105123\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.93597 | + | 56.3497i | −0.527347 | + | 2.99073i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.08468 | + | 14.3964i | 0.269110 | + | 0.761937i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.99948 | + | 17.3196i | 0.527752 | + | 0.914094i | 0.999477 | + | 0.0323477i | \(0.0102984\pi\) |
−0.471724 | + | 0.881746i | \(0.656368\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.46407 | − | 11.1961i | 0.340214 | − | 0.589268i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.285249 | − | 29.8664i | 0.0149717 | − | 1.56758i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −43.6285 | − | 36.6087i | −2.28362 | − | 1.91619i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.6495 | + | 12.6114i | 1.80869 | + | 0.658309i | 0.997270 | + | 0.0738470i | \(0.0235277\pi\) |
0.811421 | + | 0.584462i | \(0.198695\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 16.1861 | − | 13.0632i | 0.842615 | − | 0.680041i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.627679 | + | 3.55975i | 0.0325875 | + | 0.184813i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.12357 | + | 2.95674i | −0.420623 | + | 0.153094i | −0.543655 | − | 0.839309i | \(-0.682960\pi\) |
0.123033 | + | 0.992403i | \(0.460738\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −39.7621 | + | 6.62022i | −2.05331 | + | 0.341867i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.433722 | 0.0223378 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.55752 | −0.285471 | −0.142735 | − | 0.989761i | \(-0.545590\pi\) | ||||
−0.142735 | + | 0.989761i | \(0.545590\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.21647 | − | 3.24544i | 0.0623215 | − | 0.166269i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.70080 | − | 2.43889i | 0.342395 | − | 0.124622i | −0.165099 | − | 0.986277i | \(-0.552794\pi\) |
0.507494 | + | 0.861656i | \(0.330572\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.57619 | + | 54.3093i | 0.488048 | + | 2.76786i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.0864118 | + | 0.143278i | −0.00439256 | + | 0.00728324i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 28.6659 | + | 10.4335i | 1.45342 | + | 0.529002i | 0.943544 | − | 0.331246i | \(-0.107469\pi\) |
0.509876 | + | 0.860248i | \(0.329691\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.3828 | + | 12.0686i | 0.727368 | + | 0.610334i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.35788 | − | 0.766775i | 0.0684960 | − | 0.0386787i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.4184 | + | 26.7054i | −0.775783 | + | 1.34370i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.04665 | + | 5.27696i | 0.152907 | + | 0.264843i | 0.932295 | − | 0.361699i | \(-0.117803\pi\) |
−0.779388 | + | 0.626542i | \(0.784470\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10.9374 | − | 2.03645i | −0.547556 | − | 0.101950i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.45733 | + | 13.9362i | −0.122713 | + | 0.695941i | 0.859927 | + | 0.510418i | \(0.170509\pi\) |
−0.982640 | + | 0.185523i | \(0.940602\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.0269247 | + | 0.0225925i | −0.00134122 | + | 0.00112541i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −35.8005 | − | 1.36832i | −1.77894 | − | 0.0679926i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.7994 | − | 18.2919i | 1.08056 | − | 0.906695i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.50869 | − | 14.2275i | 0.124047 | − | 0.703503i | −0.857823 | − | 0.513945i | \(-0.828184\pi\) |
0.981870 | − | 0.189558i | \(-0.0607054\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 23.3809 | + | 4.35333i | 1.15330 | + | 0.214734i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.53885 | − | 9.59358i | −0.272549 | − | 0.472069i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.77579 | + | 8.27192i | −0.234435 | + | 0.406053i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.0383415 | − | 0.0216509i | 0.00187759 | − | 0.00106025i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.6121 | + | 14.7783i | 0.860405 | + | 0.721966i | 0.962055 | − | 0.272855i | \(-0.0879678\pi\) |
−0.101650 | + | 0.994820i | \(0.532412\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.3391 | − | 10.6785i | −1.42990 | − | 0.520441i | −0.492996 | − | 0.870031i | \(-0.664098\pi\) |
−0.936902 | + | 0.349591i | \(0.886321\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.37282 | − | 0.0262256i | −0.0667489 | − | 0.00127513i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.36910 | + | 36.1210i | 0.308947 | + | 1.75212i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.45131 | + | 2.34809i | −0.312201 | + | 0.113632i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.170387 | + | 0.454579i | −0.00822638 | + | 0.0219473i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.9923 | −0.577649 | −0.288825 | − | 0.957382i | \(-0.593264\pi\) | ||||
−0.288825 | + | 0.957382i | \(0.593264\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.69798 | −0.321885 | −0.160942 | − | 0.986964i | \(-0.551453\pi\) | ||||
−0.160942 | + | 0.986964i | \(0.551453\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 55.9329 | − | 9.31259i | 2.68178 | − | 0.446505i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.8561 | + | 4.67924i | −0.614991 | + | 0.223838i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.65291 | + | 9.37410i | 0.0788889 | + | 0.447401i | 0.998509 | + | 0.0545918i | \(0.0173858\pi\) |
−0.919620 | + | 0.392810i | \(0.871503\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.0952174 | + | 0.607658i | 0.00453416 | + | 0.0289361i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.1355 | + | 5.14490i | 0.671598 | + | 0.244442i | 0.655236 | − | 0.755424i | \(-0.272569\pi\) |
0.0163624 | + | 0.999866i | \(0.494791\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.4445 | + | 10.4422i | 0.589928 | + | 0.495008i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.202020 | − | 21.1521i | 0.00955523 | − | 1.00046i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.1437 | + | 19.3014i | −0.525902 | + | 0.910889i | 0.473642 | + | 0.880717i | \(0.342939\pi\) |
−0.999545 | + | 0.0301722i | \(0.990394\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.4236 | − | 31.9106i | −0.867534 | − | 1.50261i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.69618 | + | 4.80243i | 0.0796935 | + | 0.225638i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.0950297 | − | 0.538940i | 0.00445506 | − | 0.0252659i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.9820 | + | 12.5714i | −0.700830 | + | 0.588066i | −0.922010 | − | 0.387167i | \(-0.873454\pi\) |
0.221179 | + | 0.975233i | \(0.429009\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.503382 | + | 17.5642i | −0.0234959 | + | 0.819828i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.9993 | − | 26.0115i | 1.44378 | − | 1.21148i | 0.506814 | − | 0.862055i | \(-0.330823\pi\) |
0.936966 | − | 0.349420i | \(-0.113621\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.40694 | − | 13.6505i | 0.111860 | − | 0.634390i | −0.876397 | − | 0.481590i | \(-0.840060\pi\) |
0.988257 | − | 0.152801i | \(-0.0488293\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.98713 | + | 3.49165i | −0.138525 | + | 0.161921i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.8137 | − | 27.3901i | −0.731769 | − | 1.26746i | −0.956126 | − | 0.292955i | \(-0.905361\pi\) |
0.224357 | − | 0.974507i | \(-0.427972\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.1981 | − | 21.1278i | 0.563257 | − | 0.975590i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.9809 | + | 10.6115i | 0.828514 | + | 0.488952i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.227061 | + | 0.190527i | 0.0104403 | + | 0.00876043i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −25.1147 | − | 9.14102i | −1.15234 | − | 0.419419i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.800496 | + | 4.08227i | −0.0366522 | + | 0.186914i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.33650 | + | 35.9361i | 0.289522 | + | 1.64196i | 0.688669 | + | 0.725076i | \(0.258195\pi\) |
−0.399147 | + | 0.916887i | \(0.630694\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.265365 | + | 0.0965849i | −0.0120996 | + | 0.00440389i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −15.9292 | − | 19.3561i | −0.724803 | − | 0.880734i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −50.2887 | −2.28349 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.637186 | −0.0288737 | −0.0144368 | − | 0.999896i | \(-0.504596\pi\) | ||||
−0.0144368 | + | 0.999896i | \(0.504596\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11.4185 | − | 13.8751i | −0.516364 | − | 0.627452i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.6019 | + | 6.04262i | −0.749235 | + | 0.272699i | −0.688284 | − | 0.725441i | \(-0.741636\pi\) |
−0.0609515 | + | 0.998141i | \(0.519413\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.82921 | − | 27.3878i | −0.217497 | − | 1.23349i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −12.2128 | + | 62.2812i | −0.548923 | + | 2.79933i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −35.2092 | − | 12.8151i | −1.57935 | − | 0.574835i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.39153 | + | 6.20223i | 0.330891 | + | 0.277650i | 0.793063 | − | 0.609140i | \(-0.208485\pi\) |
−0.462172 | + | 0.886790i | \(0.652930\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.26160 | − | 4.28547i | −0.324424 | − | 0.191461i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.0802 | − | 20.9235i | 0.538628 | − | 0.932931i | −0.460351 | − | 0.887737i | \(-0.652276\pi\) |
0.998978 | − | 0.0451934i | \(-0.0143904\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.4813 | + | 30.2784i | 0.777906 | + | 1.34737i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14.6344 | + | 17.1061i | −0.649935 | + | 0.759708i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.31124 | + | 18.7790i | −0.146768 | + | 0.832362i | 0.819163 | + | 0.573561i | \(0.194439\pi\) |
−0.965931 | + | 0.258801i | \(0.916673\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.5694 | − | 23.9725i | 1.26383 | − | 1.06048i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.9006 | − | 6.71699i | −0.481272 | − | 0.296562i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −21.3885 | + | 17.9471i | −0.942490 | + | 0.790843i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.422383 | + | 2.39546i | −0.0185764 | + | 0.105352i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.84555 | + | 25.0446i | 0.388277 | + | 1.09934i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.4319 | + | 24.9968i | 0.632273 | + | 1.09513i | 0.987086 | + | 0.160191i | \(0.0512111\pi\) |
−0.354813 | + | 0.934937i | \(0.615456\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.76804 | − | 13.4546i | 0.339673 | − | 0.588330i | −0.644698 | − | 0.764437i | \(-0.723017\pi\) |
0.984371 | + | 0.176107i | \(0.0563504\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.467690 | − | 48.9685i | 0.0204117 | − | 2.13716i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.72642 | + | 1.44864i | 0.0752040 | + | 0.0631036i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.35461 | − | 2.67686i | −0.319766 | − | 0.116385i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.97364 | − | 12.5953i | −0.0856485 | − | 0.546591i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.0634953 | + | 0.360100i | 0.00275028 | + | 0.0155976i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 34.0521 | − | 12.3940i | 1.47220 | − | 0.535837i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −27.6820 | + | 4.60894i | −1.19457 | + | 0.198890i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.08961 | 0.0469327 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.78149 | −0.291559 | −0.145779 | − | 0.989317i | \(-0.546569\pi\) | ||||
−0.145779 | + | 0.989317i | \(0.546569\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.99631 | − | 15.9977i | 0.257326 | − | 0.686525i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 54.4255 | − | 19.8092i | 2.33133 | − | 0.848535i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.14447 | − | 6.49059i | −0.0489339 | − | 0.277518i | 0.950516 | − | 0.310675i | \(-0.100555\pi\) |
−0.999450 | + | 0.0331570i | \(0.989444\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.89969 | − | 0.150911i | −0.337151 | − | 0.00644073i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.0426 | + | 6.93095i | 0.811243 | + | 0.295268i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.4687 | − | 12.9797i | −0.657794 | − | 0.551955i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −32.1477 | + | 18.1534i | −1.36460 | + | 0.770567i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.421123 | − | 0.729407i | 0.0178436 | − | 0.0309060i | −0.856966 | − | 0.515373i | \(-0.827653\pi\) |
0.874809 | + | 0.484467i | \(0.160987\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.00147070 | − | 0.00254733i | −6.22041e−5 | − | 0.000107741i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 30.6020 | + | 5.69784i | 1.29202 | + | 0.240563i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.13172 | + | 40.4460i | −0.300566 | + | 1.70460i | 0.343108 | + | 0.939296i | \(0.388520\pi\) |
−0.643674 | + | 0.765300i | \(0.722591\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 45.7134 | − | 38.3581i | 1.92318 | − | 1.61374i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.95330 | − | 22.9316i | 0.208019 | − | 0.963036i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.5383 | + | 11.3600i | −0.567555 | + | 0.476235i | −0.880834 | − | 0.473426i | \(-0.843017\pi\) |
0.313278 | + | 0.949661i | \(0.398573\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.49724 | − | 42.5189i | 0.313750 | − | 1.77936i | −0.265397 | − | 0.964139i | \(-0.585503\pi\) |
0.579147 | − | 0.815223i | \(-0.303386\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23.1323 | + | 4.30704i | 0.966367 | + | 0.179929i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −30.1103 | − | 52.1526i | −1.25569 | − | 2.17491i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.83839 | − | 15.3085i | 0.367947 | − | 0.637303i | −0.621297 | − | 0.783575i | \(-0.713394\pi\) |
0.989244 | + | 0.146272i | \(0.0467275\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.20913 | − | 2.94152i | 0.216484 | − | 0.122245i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.79137 | − | 4.02043i | −0.198779 | − | 0.166796i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.92507 | + | 2.52052i | 0.286807 | + | 0.104389i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.325270 | − | 0.539326i | 0.0134483 | − | 0.0222984i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.91945 | − | 16.5570i | −0.120499 | − | 0.683381i | −0.983880 | − | 0.178830i | \(-0.942769\pi\) |
0.863381 | − | 0.504552i | \(-0.168342\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.54317 | + | 0.561667i | −0.0635851 | + | 0.0231431i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.502945 | + | 1.34182i | −0.0206884 | + | 0.0551949i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 30.6747 | 1.25966 | 0.629829 | − | 0.776734i | \(-0.283125\pi\) | ||||
0.629829 | + | 0.776734i | \(0.283125\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −35.0900 | −1.43855 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.38535 | − | 0.730142i | 0.179480 | − | 0.0298827i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.8656 | + | 3.95476i | −0.443957 | + | 0.161587i | −0.554319 | − | 0.832304i | \(-0.687021\pi\) |
0.110362 | + | 0.993891i | \(0.464799\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.36971 | + | 30.4531i | 0.219035 | + | 1.24221i | 0.873766 | + | 0.486347i | \(0.161671\pi\) |
−0.654731 | + | 0.755862i | \(0.727218\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 21.8490 | − | 17.6334i | 0.889760 | − | 0.718089i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 64.5049 | + | 23.4779i | 2.62250 | + | 0.954511i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.3480 | + | 10.3612i | 0.501190 | + | 0.420549i | 0.858016 | − | 0.513622i | \(-0.171697\pi\) |
−0.356826 | + | 0.934171i | \(0.616141\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.354614 | + | 37.1292i | −0.0143697 | + | 1.50455i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.0120690 | − | 0.0209042i | 0.000488261 | − | 0.000845694i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.76761 | + | 13.4539i | 0.313731 | + | 0.543398i | 0.979167 | − | 0.203057i | \(-0.0650877\pi\) |
−0.665436 | + | 0.746455i | \(0.731754\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 15.9202 | + | 45.0752i | 0.641964 | + | 1.81761i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.72338 | + | 32.4589i | −0.230415 | + | 1.30675i | 0.621644 | + | 0.783300i | \(0.286465\pi\) |
−0.852059 | + | 0.523446i | \(0.824646\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.0195 | − | 15.9593i | 0.764460 | − | 0.641458i | −0.174824 | − | 0.984600i | \(-0.555936\pi\) |
0.939284 | + | 0.343142i | \(0.111491\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.08657 | − | 27.3816i | −0.364631 | − | 1.09879i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.14908 | + | 6.83789i | −0.326486 | + | 0.273954i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.66999 | − | 37.8274i | 0.266799 | − | 1.51309i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −14.7451 | + | 17.2356i | −0.588864 | + | 0.688322i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.05362 | + | 15.6813i | 0.360991 | + | 0.625256i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.5573 | − | 33.8742i | 0.778563 | − | 1.34851i | −0.154207 | − | 0.988039i | \(-0.549282\pi\) |
0.932770 | − | 0.360472i | \(-0.117384\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −26.4419 | − | 15.6048i | −1.05097 | − | 0.620235i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.10206 | + | 5.12024i | 0.242153 | + | 0.203191i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.0101607 | − | 0.00369818i | −0.000402580 | − | 0.000146527i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −32.4978 | − | 28.3441i | −1.28559 | − | 1.12127i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.31018 | − | 47.1293i | −0.328232 | − | 1.86150i | −0.485913 | − | 0.874007i | \(-0.661513\pi\) |
0.157681 | − | 0.987490i | \(-0.449598\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 41.2546 | − | 15.0155i | 1.62692 | − | 0.592152i | 0.642241 | − | 0.766503i | \(-0.278005\pi\) |
0.984684 | + | 0.174351i | \(0.0557828\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.244357 | − | 0.296927i | −0.00962154 | − | 0.0116915i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15.9642 | −0.627618 | −0.313809 | − | 0.949486i | \(-0.601605\pi\) | ||||
−0.313809 | + | 0.949486i | \(0.601605\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22.5850 | −0.886539 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.91204 | − | 2.32339i | −0.0749388 | − | 0.0910608i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.8697 | − | 5.04816i | 0.542763 | − | 0.197550i | −0.0560649 | − | 0.998427i | \(-0.517855\pi\) |
0.598828 | + | 0.800877i | \(0.295633\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.622352 | + | 3.52953i | 0.0243173 | + | 0.137910i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 40.6059 | − | 13.9069i | 1.58419 | − | 0.542562i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.91286 | − | 3.60799i | −0.386150 | − | 0.140547i | 0.141648 | − | 0.989917i | \(-0.454760\pi\) |
−0.527798 | + | 0.849370i | \(0.676982\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.1093 | + | 21.0692i | 0.976640 | + | 0.819499i | 0.983579 | − | 0.180477i | \(-0.0577643\pi\) |
−0.00693878 | + | 0.999976i | \(0.502209\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.266028 | − | 0.156998i | −0.0103317 | − | 0.00609728i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.7847 | − | 22.1437i | 0.495767 | − | 0.858694i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22.8304 | + | 39.5434i | 0.883996 | + | 1.53113i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −23.4906 | + | 27.4581i | −0.908198 | + | 1.06159i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.43054 | + | 13.7843i | −0.0938300 | + | 0.532136i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.6106 | − | 13.0988i | 0.601743 | − | 0.504922i | −0.290262 | − | 0.956947i | \(-0.593743\pi\) |
0.892005 | + | 0.452025i | \(0.149298\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 20.7852 | − | 52.3863i | 0.800024 | − | 2.01635i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.95863 | − | 7.51718i | 0.344308 | − | 0.288909i | −0.454192 | − | 0.890904i | \(-0.650072\pi\) |
0.798500 | + | 0.601995i | \(0.205627\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.71835 | − | 32.4304i | 0.219450 | − | 1.24456i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.08360 | − | 5.89934i | −0.0798436 | − | 0.226063i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.7585 | + | 39.4189i | 0.870830 | + | 1.50832i | 0.861140 | + | 0.508368i | \(0.169751\pi\) |
0.00968953 | + | 0.999953i | \(0.496916\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −27.3297 | + | 47.3365i | −1.04422 | + | 1.80863i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.0673196 | + | 7.04855i | −0.00256840 | + | 0.268919i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.0560220 | − | 0.0470080i | −0.00213427 | − | 0.00179086i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.68876 | − | 1.70657i | −0.178369 | − | 0.0649210i | 0.251292 | − | 0.967911i | \(-0.419145\pi\) |
−0.429661 | + | 0.902990i | \(0.641367\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −38.7754 | − | 14.9578i | −1.47295 | − | 0.568201i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.0175729 | + | 0.0996610i | 0.000666579 | + | 0.00378036i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.0319 | − | 8.01895i | 0.834517 | − | 0.303739i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 41.8448 | − | 6.96698i | 1.58272 | − | 0.263516i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.9484 | 0.980059 | 0.490029 | − | 0.871706i | \(-0.336986\pi\) | ||||
0.490029 | + | 0.871706i | \(0.336986\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.1943 | −0.497634 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.10759 | − | 2.95495i | 0.0417141 | − | 0.111290i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −21.5139 | + | 7.83040i | −0.809112 | + | 0.294493i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.73503 | − | 9.83985i | −0.0651605 | − | 0.369543i | −0.999899 | − | 0.0142073i | \(-0.995478\pi\) |
0.934739 | − | 0.355336i | \(-0.115634\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.2332 | − | 20.3442i | −0.421278 | − | 0.762968i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.47708 | − | 1.26556i | −0.130218 | − | 0.0473954i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.854700 | − | 0.717178i | −0.0319640 | − | 0.0268209i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 34.1299 | − | 19.2727i | 1.27460 | − | 0.719751i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.41746 | + | 9.38332i | −0.202037 | + | 0.349939i | −0.949185 | − | 0.314719i | \(-0.898090\pi\) |
0.747147 | + | 0.664658i | \(0.231423\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.14168 | − | 15.8339i | −0.340454 | − | 0.589684i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −19.4499 | − | 3.62141i | −0.723350 | − | 0.134682i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −15.4893 | + | 87.8443i | −0.575259 | + | 3.26246i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.4070 | + | 11.2498i | −0.497237 | + | 0.417232i | −0.856612 | − | 0.515962i | \(-0.827435\pi\) |
0.359374 | + | 0.933194i | \(0.382990\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14.8170 | − | 22.5711i | 0.548778 | − | 0.835968i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.144479 | + | 0.121232i | −0.00534373 | + | 0.00448392i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.10784 | + | 23.2967i | −0.151727 | + | 0.860484i | 0.809991 | + | 0.586442i | \(0.199472\pi\) |
−0.961718 | + | 0.274042i | \(0.911639\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.38973 | − | 0.258755i | −0.0512609 | − | 0.00954433i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −24.8693 | − | 43.0749i | −0.916073 | − | 1.58668i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.39583 | − | 2.41766i | 0.0513466 | − | 0.0889349i | −0.839210 | − | 0.543808i | \(-0.816982\pi\) |
0.890556 | + | 0.454873i | \(0.150315\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.195998 | − | 0.110677i | 0.00720016 | − | 0.00406583i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.2480 | + | 23.7029i | 1.03632 | + | 0.869576i | 0.991589 | − | 0.129423i | \(-0.0413127\pi\) |
0.0447304 | + | 0.998999i | \(0.485757\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 45.6839 | + | 16.6276i | 1.67373 | + | 0.609187i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.47945 | − | 6.30156i | −0.127306 | − | 0.230562i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.12058 | + | 23.3690i | 0.150563 | + | 0.853884i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.4717 | + | 4.17535i | −0.418608 | + | 0.152361i | −0.542732 | − | 0.839906i | \(-0.682610\pi\) |
0.124124 | + | 0.992267i | \(0.460388\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.54545 | + | 4.12313i | −0.0563193 | + | 0.150255i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.7055 | −0.426009 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.4136 | 0.632907 | 0.316453 | − | 0.948608i | \(-0.397508\pi\) | ||||
0.316453 | + | 0.948608i | \(0.397508\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −50.4139 | + | 8.39370i | −1.82991 | + | 0.304672i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.1950 | − | 6.98639i | 0.695816 | − | 0.253256i | 0.0301929 | − | 0.999544i | \(-0.490388\pi\) |
0.665624 | + | 0.746288i | \(0.268166\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.58592 | + | 37.3506i | 0.238426 | + | 1.35218i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −37.6780 | − | 14.5345i | −1.36225 | − | 0.525496i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.210607 | + | 0.0766547i | 0.00760458 | + | 0.00276784i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.7022 | − | 10.6584i | −0.458052 | − | 0.384351i | 0.384362 | − | 0.923183i | \(-0.374422\pi\) |
−0.842414 | + | 0.538831i | \(0.818866\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.297896 | + | 31.1906i | −0.0107285 | + | 1.12330i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.24355 | + | 16.0103i | −0.332467 | + | 0.575850i | −0.982995 | − | 0.183632i | \(-0.941214\pi\) |
0.650528 | + | 0.759482i | \(0.274548\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.61425 | − | 6.26007i | −0.129828 | − | 0.224868i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.05128 | − | 22.7958i | −0.288838 | − | 0.817794i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.96668 | + | 16.8249i | −0.106292 | + | 0.602814i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −58.5187 | + | 49.1030i | −2.09396 | + | 1.75704i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −15.7599 | + | 39.7206i | −0.563212 | + | 1.41950i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −36.7585 | + | 30.8441i | −1.31197 | + | 1.10087i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.19112 | + | 35.1116i | −0.220690 | + | 1.25159i | 0.650066 | + | 0.759877i | \(0.274741\pi\) |
−0.870756 | + | 0.491715i | \(0.836370\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.847078 | + | 0.990148i | −0.0301568 | + | 0.0352502i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19.5384 | + | 33.8415i | 0.694706 | + | 1.20327i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.0694495 | − | 0.120290i | 0.00246622 | − | 0.00427163i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.23394 | − | 4.85930i | −0.292028 | − | 0.172342i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.2168 | + | 11.9293i | 0.503586 | + | 0.422559i | 0.858866 | − | 0.512201i | \(-0.171170\pi\) |
−0.355279 | + | 0.934760i | \(0.615614\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.45440 | − | 0.529358i | −0.0514529 | − | 0.0187273i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.5824 | + | 3.96680i | −0.409243 | + | 0.140160i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.2034 | − | 74.8805i | −0.465940 | − | 2.64247i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 54.1386 | − | 19.7048i | 1.90813 | − | 0.694504i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.824037 | − | 1.00132i | −0.0290075 | − | 0.0352480i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.0764 | −0.389426 | −0.194713 | − | 0.980860i | \(-0.562378\pi\) | ||||
−0.194713 | + | 0.980860i | \(0.562378\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.205736 | 0.00722437 | 0.00361219 | − | 0.999993i | \(-0.498850\pi\) | ||||
0.00361219 | + | 0.999993i | \(0.498850\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 31.6274 | + | 38.4316i | 1.10922 | + | 1.34786i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 38.8082 | − | 14.1250i | 1.35939 | − | 0.494778i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.0238646 | − | 0.135343i | −0.000834918 | − | 0.00473506i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.310816 | + | 0.271088i | 0.0108608 | + | 0.00947260i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.5004 | − | 4.54976i | −0.436266 | − | 0.158788i | 0.114545 | − | 0.993418i | \(-0.463459\pi\) |
−0.550810 | + | 0.834630i | \(0.685681\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −38.6476 | − | 32.4292i | −1.34717 | − | 1.13041i | −0.979721 | − | 0.200366i | \(-0.935787\pi\) |
−0.367449 | − | 0.930044i | \(-0.619769\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −85.9838 | − | 50.7438i | −2.99357 | − | 1.76667i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.1769 | − | 34.9473i | 0.701618 | − | 1.21524i | −0.266280 | − | 0.963896i | \(-0.585795\pi\) |
0.967898 | − | 0.251342i | \(-0.0808720\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.3346 | − | 38.6847i | −0.775713 | − | 1.34357i | −0.934393 | − | 0.356244i | \(-0.884057\pi\) |
0.158680 | − | 0.987330i | \(-0.449276\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.1347 | − | 15.3532i | 0.455639 | − | 0.532596i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.120393 | + | 0.682782i | −0.00417137 | + | 0.0236570i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.8450 | − | 12.4564i | 0.513733 | − | 0.431073i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.09070 | − | 3.28672i | −0.0376999 | − | 0.113606i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 41.5143 | − | 34.8347i | 1.43323 | − | 1.20263i | 0.489463 | − | 0.872024i | \(-0.337193\pi\) |
0.943770 | − | 0.330602i | \(-0.107252\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.70860 | − | 38.0464i | 0.231331 | − | 1.31194i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.66351 | + | 13.2039i | 0.160620 | + | 0.454767i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −25.8693 | − | 44.8069i | −0.889931 | − | 1.54141i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22.4754 | + | 38.9285i | −0.772262 | + | 1.33760i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.538153 | + | 56.3462i | −0.0184694 | + | 1.93380i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22.7742 | − | 19.1098i | −0.780690 | − | 0.655077i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.2184 | + | 8.08683i | 0.760743 | + | 0.276888i | 0.693119 | − | 0.720823i | \(-0.256236\pi\) |
0.0676240 | + | 0.997711i | \(0.478458\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 22.8996 | − | 18.4813i | 0.783149 | − | 0.632047i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.20838 | − | 29.5382i | −0.177915 | − | 1.00901i | −0.934725 | − | 0.355371i | \(-0.884354\pi\) |
0.756810 | − | 0.653635i | \(-0.226757\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.0283 | − | 4.74190i | 0.444519 | − | 0.161792i | −0.110056 | − | 0.993925i | \(-0.535103\pi\) |
0.554575 | + | 0.832134i | \(0.312881\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −30.8786 | + | 5.14115i | −1.05234 | + | 0.175210i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31.8027 | 1.08258 | 0.541288 | − | 0.840837i | \(-0.317937\pi\) | ||||
0.541288 | + | 0.840837i | \(0.317937\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −61.0443 | −2.07557 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.38280 | − | 9.02502i | 0.114886 | − | 0.306506i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −38.6861 | + | 14.0806i | −1.31234 | + | 0.477651i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.0857098 | + | 0.486084i | 0.00290417 | + | 0.0164703i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 19.5729 | − | 32.4536i | 0.662444 | − | 1.09839i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 57.0067 | + | 20.7487i | 1.92718 | + | 0.701435i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.2529 | + | 16.1551i | 0.650123 | + | 0.545518i | 0.907108 | − | 0.420897i | \(-0.138285\pi\) |
−0.256985 | + | 0.966415i | \(0.582729\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.07475 | + | 4.55969i | −0.272354 | + | 0.153795i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.6586 | − | 23.6574i | 0.460170 | − | 0.797038i | −0.538799 | − | 0.842434i | \(-0.681122\pi\) |
0.998969 | + | 0.0453966i | \(0.0144552\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.7742 | + | 29.0538i | 0.564498 | + | 0.977739i | 0.997096 | + | 0.0761523i | \(0.0242635\pi\) |
−0.432598 | + | 0.901587i | \(0.642403\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 28.8058 | + | 5.36340i | 0.968297 | + | 0.180289i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.41514 | + | 8.02565i | −0.0475157 | + | 0.269475i | −0.999305 | − | 0.0372778i | \(-0.988131\pi\) |
0.951789 | + | 0.306753i | \(0.0992425\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.99583 | + | 3.35290i | −0.134016 | + | 0.112453i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −35.4395 | − | 32.1220i | −1.18727 | − | 1.07613i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.863946 | − | 0.724937i | 0.0289109 | − | 0.0242591i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.1998 | − | 63.5170i | 0.374367 | − | 2.12314i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.498602 | + | 0.0928354i | 0.0166478 | + | 0.00309968i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.74042 | + | 4.74654i | 0.0913980 | + | 0.158306i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.34460 | + | 4.06097i | −0.0781100 | + | 0.135291i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.219269 | − | 0.123818i | 0.00729682 | − | 0.00412041i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 30.0788 | + | 25.2391i | 0.999852 | + | 0.838976i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 53.9060 | + | 19.6202i | 1.78992 | + | 0.651478i | 0.999229 | + | 0.0392630i | \(0.0125010\pi\) |
0.790692 | + | 0.612215i | \(0.209721\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −26.3439 | − | 0.503259i | −0.873773 | − | 0.0166920i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.88969 | + | 33.4021i | 0.195134 | + | 1.10666i | 0.912228 | + | 0.409684i | \(0.134361\pi\) |
−0.717093 | + | 0.696977i | \(0.754528\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.9829 | + | 4.36142i | −0.396576 | + | 0.144342i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.37344 | − | 17.0038i | 0.210700 | − | 0.562129i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.34691 | −0.0775017 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.2454 | 0.700822 | 0.350411 | − | 0.936596i | \(-0.386042\pi\) | ||||
0.350411 | + | 0.936596i | \(0.386042\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.2621 | + | 1.87508i | −0.371097 | + | 0.0617861i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.712349 | − | 0.259274i | 0.0234472 | − | 0.00853410i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.0851 | − | 57.1953i | −0.331595 | − | 1.88057i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.25742 | − | 20.7882i | −0.106988 | − | 0.682773i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.5796 | − | 3.85065i | −0.347104 | − | 0.126336i | 0.162584 | − | 0.986695i | \(-0.448017\pi\) |
−0.509688 | + | 0.860359i | \(0.670239\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.387008 | − | 0.324738i | −0.0126837 | − | 0.0106429i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.439178 | + | 45.9832i | −0.0143781 | + | 1.50542i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −35.7704 | + | 61.9562i | −1.16982 | + | 2.02619i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.61998 | − | 8.00203i | −0.150928 | − | 0.261415i | 0.780641 | − | 0.624980i | \(-0.214893\pi\) |
−0.931569 | + | 0.363565i | \(0.881560\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.0134 | − | 31.1824i | −0.359408 | − | 1.01760i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.71426 | − | 38.0785i | 0.218879 | − | 1.24132i | −0.655169 | − | 0.755483i | \(-0.727402\pi\) |
0.874048 | − | 0.485840i | \(-0.161486\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −29.4888 | + | 24.7440i | −0.960287 | + | 0.805777i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 45.9035 | + | 28.2860i | 1.49324 | + | 0.920144i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.5183 | + | 23.9297i | −0.926720 | + | 0.777610i | −0.975226 | − | 0.221213i | \(-0.928999\pi\) |
0.0485057 | + | 0.998823i | \(0.484554\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.131025 | + | 0.743079i | −0.00425325 | + | 0.0241214i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.86432 | + | 10.3615i | −0.287445 | + | 0.335994i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.34521 | + | 10.9902i | 0.205542 | + | 0.356008i | 0.950305 | − | 0.311320i | \(-0.100771\pi\) |
−0.744764 | + | 0.667328i | \(0.767438\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −27.0392 | + | 46.8332i | −0.874967 | + | 1.51549i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 65.1951 | + | 38.4752i | 2.10746 | + | 1.24373i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −27.4189 | − | 23.0071i | −0.885401 | − | 0.742940i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.7131 | + | 10.4507i | 0.926229 | + | 0.337120i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.25509 | + | 26.7992i | −0.169343 | + | 0.863593i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.38748 | + | 13.5401i | 0.0768557 | + | 0.435870i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.3212 | + | 11.7639i | −1.03938 | + | 0.378303i | −0.804645 | − | 0.593757i | \(-0.797644\pi\) |
−0.234734 | + | 0.972060i | \(0.575422\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.17114 | − | 11.1442i | −0.294619 | − | 0.358002i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −44.5140 | −1.42852 | −0.714261 | − | 0.699880i | \(-0.753237\pi\) | ||||
−0.714261 | + | 0.699880i | \(0.753237\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.0662680 | −0.00212445 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.629578 | + | 0.765023i | 0.0201626 | + | 0.0245003i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.8596 | + | 7.59228i | −0.667359 | + | 0.242899i | −0.653410 | − | 0.757004i | \(-0.726662\pi\) |
−0.0139485 | + | 0.999903i | \(0.504440\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.76613 | + | 21.3588i | 0.120366 | + | 0.682630i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.39920 | + | 42.8332i | −0.268166 | + | 1.36756i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.3730 | − | 7.77915i | −0.681694 | − | 0.248116i | −0.0221192 | − | 0.999755i | \(-0.507041\pi\) |
−0.659575 | + | 0.751639i | \(0.729264\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.52288 | − | 2.11695i | −0.0803856 | − | 0.0674516i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.77966 | + | 1.05027i | 0.0566471 | + | 0.0334306i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.154831 | − | 0.268174i | 0.00492333 | − | 0.00852745i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.7002 | − | 34.1217i | −0.625798 | − | 1.08391i | −0.988386 | − | 0.151964i | \(-0.951440\pi\) |
0.362589 | − | 0.931949i | \(-0.381893\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.90294 | + | 9.23773i | −0.250792 | + | 0.293150i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.77425 | + | 10.0623i | −0.0562476 | + | 0.318996i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.3941 | − | 13.7563i | 0.519205 | − | 0.435665i | −0.345149 | − | 0.938548i | \(-0.612172\pi\) |
0.864355 | + | 0.502883i | \(0.167727\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.797074 | − | 27.8119i | 0.0252183 | − | 0.879929i |
(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 | 432.2.u.f.49.2 | 30 | ||
4.3 | odd | 2 | 216.2.q.b.49.4 | ✓ | 30 | ||
12.11 | even | 2 | 648.2.q.b.361.1 | 30 | |||
27.16 | even | 9 | inner | 432.2.u.f.97.2 | 30 | ||
108.11 | even | 18 | 648.2.q.b.289.1 | 30 | |||
108.23 | even | 18 | 5832.2.a.l.1.15 | 15 | |||
108.31 | odd | 18 | 5832.2.a.k.1.1 | 15 | |||
108.43 | odd | 18 | 216.2.q.b.97.4 | yes | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.2.q.b.49.4 | ✓ | 30 | 4.3 | odd | 2 | ||
216.2.q.b.97.4 | yes | 30 | 108.43 | odd | 18 | ||
432.2.u.f.49.2 | 30 | 1.1 | even | 1 | trivial | ||
432.2.u.f.97.2 | 30 | 27.16 | even | 9 | inner | ||
648.2.q.b.289.1 | 30 | 108.11 | even | 18 | |||
648.2.q.b.361.1 | 30 | 12.11 | even | 2 | |||
5832.2.a.k.1.1 | 15 | 108.31 | odd | 18 | |||
5832.2.a.l.1.15 | 15 | 108.23 | even | 18 |