Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(299,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 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("525.299");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.q (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: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 299.7 | ||
Character | \(\chi\) | \(=\) | 525.299 |
Dual form | 525.2.q.g.374.7 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.450666 | + | 0.780577i | −0.318669 | + | 0.551951i | −0.980211 | − | 0.197957i | \(-0.936569\pi\) |
0.661541 | + | 0.749909i | \(0.269903\pi\) | |||||||
\(3\) | 0.248842 | − | 1.71408i | 0.143669 | − | 0.989626i | ||||
\(4\) | 0.593800 | + | 1.02849i | 0.296900 | + | 0.514245i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.22583 | + | 0.966719i | 0.500443 | + | 0.394662i | ||||
\(7\) | −2.64365 | − | 0.105498i | −0.999205 | − | 0.0398746i | ||||
\(8\) | −2.87309 | −1.01579 | ||||||||
\(9\) | −2.87616 | − | 0.853070i | −0.958719 | − | 0.284357i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.46176 | − | 3.15335i | 1.64678 | − | 0.950770i | 0.668442 | − | 0.743765i | \(-0.266962\pi\) |
0.978340 | − | 0.207005i | \(-0.0663717\pi\) | |||||||
\(12\) | 1.91068 | − | 0.761890i | 0.551566 | − | 0.219939i | ||||
\(13\) | 3.77183 | 1.04612 | 0.523059 | − | 0.852297i | \(-0.324791\pi\) | ||||
0.523059 | + | 0.852297i | \(0.324791\pi\) | |||||||
\(14\) | 1.27375 | − | 2.01603i | 0.340425 | − | 0.538806i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.107205 | − | 0.185685i | 0.0268013 | − | 0.0464212i | ||||
\(17\) | 3.27294 | − | 1.88963i | 0.793804 | − | 0.458303i | −0.0474963 | − | 0.998871i | \(-0.515124\pi\) |
0.841300 | + | 0.540569i | \(0.181791\pi\) | |||||||
\(18\) | 1.96207 | − | 1.86061i | 0.462465 | − | 0.438550i | ||||
\(19\) | 4.57893 | + | 2.64365i | 1.05048 | + | 0.606494i | 0.922783 | − | 0.385319i | \(-0.125909\pi\) |
0.127695 | + | 0.991813i | \(0.459242\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.838682 | + | 4.50518i | −0.183015 | + | 0.983110i | ||||
\(22\) | 5.68443i | 1.21192i | ||||||||
\(23\) | 3.38933 | − | 5.87050i | 0.706725 | − | 1.22408i | −0.259340 | − | 0.965786i | \(-0.583505\pi\) |
0.966065 | − | 0.258298i | \(-0.0831615\pi\) | |||||||
\(24\) | −0.714944 | + | 4.92471i | −0.145937 | + | 1.00525i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.69984 | + | 2.94420i | −0.333365 | + | 0.577406i | ||||
\(27\) | −2.17794 | + | 4.71769i | −0.419144 | + | 0.907920i | ||||
\(28\) | −1.46129 | − | 2.78161i | −0.276158 | − | 0.525675i | ||||
\(29\) | − | 3.06327i | − | 0.568834i | −0.958701 | − | 0.284417i | \(-0.908200\pi\) | ||
0.958701 | − | 0.284417i | \(-0.0918000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.349819 | − | 0.201968i | 0.0628294 | − | 0.0362746i | −0.468256 | − | 0.883593i | \(-0.655118\pi\) |
0.531086 | + | 0.847318i | \(0.321784\pi\) | |||||||
\(32\) | −2.77646 | − | 4.80897i | −0.490813 | − | 0.850114i | ||||
\(33\) | −4.04598 | − | 10.1466i | −0.704315 | − | 1.76629i | ||||
\(34\) | 3.40637i | 0.584188i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.830485 | − | 3.46465i | −0.138414 | − | 0.577442i | ||||
\(37\) | 1.15705 | + | 0.668021i | 0.190217 | + | 0.109822i | 0.592084 | − | 0.805876i | \(-0.298305\pi\) |
−0.401867 | + | 0.915698i | \(0.631639\pi\) | |||||||
\(38\) | −4.12714 | + | 2.38281i | −0.669511 | + | 0.386542i | ||||
\(39\) | 0.938588 | − | 6.46523i | 0.150294 | − | 1.03526i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.53749 | −1.02098 | −0.510492 | − | 0.859882i | \(-0.670537\pi\) | ||||
−0.510492 | + | 0.859882i | \(0.670537\pi\) | |||||||
\(42\) | −3.13867 | − | 2.68499i | −0.484308 | − | 0.414303i | ||||
\(43\) | 4.84564i | 0.738954i | 0.929240 | + | 0.369477i | \(0.120463\pi\) | ||||
−0.929240 | + | 0.369477i | \(0.879537\pi\) | |||||||
\(44\) | 6.48638 | + | 3.74491i | 0.977858 | + | 0.564567i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.05492 | + | 5.29127i | 0.450423 | + | 0.780156i | ||||
\(47\) | 1.68073 | + | 0.970371i | 0.245160 | + | 0.141543i | 0.617546 | − | 0.786535i | \(-0.288127\pi\) |
−0.372386 | + | 0.928078i | \(0.621460\pi\) | |||||||
\(48\) | −0.291602 | − | 0.229964i | −0.0420891 | − | 0.0331925i | ||||
\(49\) | 6.97774 | + | 0.557800i | 0.996820 | + | 0.0796858i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.42454 | − | 6.08030i | −0.339503 | − | 0.851412i | ||||
\(52\) | 2.23971 | + | 3.87929i | 0.310592 | + | 0.537961i | ||||
\(53\) | 0.720381 | + | 1.24774i | 0.0989519 | + | 0.171390i | 0.911251 | − | 0.411851i | \(-0.135118\pi\) |
−0.812299 | + | 0.583241i | \(0.801784\pi\) | |||||||
\(54\) | −2.70100 | − | 3.82615i | −0.367559 | − | 0.520673i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 7.59543 | + | 0.303106i | 1.01498 | + | 0.0405042i | ||||
\(57\) | 5.67086 | − | 7.19082i | 0.751123 | − | 0.952447i | ||||
\(58\) | 2.39112 | + | 1.38051i | 0.313969 | + | 0.181270i | ||||
\(59\) | 1.60223 | + | 2.77514i | 0.208592 | + | 0.361293i | 0.951271 | − | 0.308355i | \(-0.0997785\pi\) |
−0.742679 | + | 0.669648i | \(0.766445\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.3644 | − | 6.56124i | −1.45506 | − | 0.840080i | −0.456300 | − | 0.889826i | \(-0.650825\pi\) |
−0.998762 | + | 0.0497461i | \(0.984159\pi\) | |||||||
\(62\) | 0.364081i | 0.0462384i | ||||||||
\(63\) | 7.51354 | + | 2.55864i | 0.946618 | + | 0.322359i | ||||
\(64\) | 5.43385 | 0.679231 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 9.74358 | + | 1.41452i | 1.19935 | + | 0.174116i | ||||
\(67\) | −2.68611 | + | 1.55082i | −0.328160 | + | 0.189463i | −0.655024 | − | 0.755608i | \(-0.727341\pi\) |
0.326864 | + | 0.945071i | \(0.394008\pi\) | |||||||
\(68\) | 3.88694 | + | 2.24412i | 0.471360 | + | 0.272140i | ||||
\(69\) | −9.21911 | − | 7.27042i | −1.10985 | − | 0.875256i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.21562i | − | 0.262946i | −0.991320 | − | 0.131473i | \(-0.958029\pi\) | ||
0.991320 | − | 0.131473i | \(-0.0419707\pi\) | |||||||
\(72\) | 8.26345 | + | 2.45094i | 0.973857 | + | 0.288847i | ||||
\(73\) | 1.25932 | + | 2.18121i | 0.147393 | + | 0.255292i | 0.930263 | − | 0.366893i | \(-0.119579\pi\) |
−0.782870 | + | 0.622185i | \(0.786245\pi\) | |||||||
\(74\) | −1.04288 | + | 0.602109i | −0.121233 | + | 0.0699938i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.27919i | 0.720272i | ||||||||
\(77\) | −14.7716 | + | 7.76013i | −1.68338 | + | 0.884349i | ||||
\(78\) | 4.62362 | + | 3.64630i | 0.523522 | + | 0.412862i | ||||
\(79\) | 3.05960 | − | 5.29938i | 0.344232 | − | 0.596227i | −0.640982 | − | 0.767556i | \(-0.721473\pi\) |
0.985214 | + | 0.171329i | \(0.0548061\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.54454 | + | 4.90712i | 0.838283 | + | 0.545236i | ||||
\(82\) | 2.94623 | − | 5.10301i | 0.325356 | − | 0.563534i | ||||
\(83\) | 8.53654i | 0.937007i | 0.883462 | + | 0.468503i | \(0.155207\pi\) | ||||
−0.883462 | + | 0.468503i | \(0.844793\pi\) | |||||||
\(84\) | −5.13154 | + | 1.81259i | −0.559897 | + | 0.197770i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.78240 | − | 2.18377i | −0.407867 | − | 0.235482i | ||||
\(87\) | −5.25069 | − | 0.762268i | −0.562933 | − | 0.0817237i | ||||
\(88\) | −15.6921 | + | 9.05984i | −1.67278 | + | 0.965782i | ||||
\(89\) | 0.590783 | − | 1.02327i | 0.0626229 | − | 0.108466i | −0.833014 | − | 0.553252i | \(-0.813387\pi\) |
0.895637 | + | 0.444786i | \(0.146720\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.97138 | − | 0.397921i | −1.04529 | − | 0.0417135i | ||||
\(92\) | 8.05034 | 0.839306 | ||||||||
\(93\) | −0.259141 | − | 0.649878i | −0.0268716 | − | 0.0673892i | ||||
\(94\) | −1.51490 | + | 0.874627i | −0.156250 | + | 0.0902109i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −8.93387 | + | 3.56241i | −0.911809 | + | 0.363587i | ||||
\(97\) | −9.10556 | −0.924530 | −0.462265 | − | 0.886742i | \(-0.652963\pi\) | ||||
−0.462265 | + | 0.886742i | \(0.652963\pi\) | |||||||
\(98\) | −3.58004 | + | 5.19528i | −0.361639 | + | 0.524803i | ||||
\(99\) | −18.3989 | + | 4.41026i | −1.84916 | + | 0.443247i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.15241 | + | 1.99604i | 0.114669 | + | 0.198613i | 0.917647 | − | 0.397395i | \(-0.130086\pi\) |
−0.802978 | + | 0.596008i | \(0.796753\pi\) | |||||||
\(102\) | 5.83880 | + | 0.847647i | 0.578128 | + | 0.0839296i | ||||
\(103\) | −3.89335 | + | 6.74347i | −0.383623 | + | 0.664454i | −0.991577 | − | 0.129518i | \(-0.958657\pi\) |
0.607954 | + | 0.793972i | \(0.291990\pi\) | |||||||
\(104\) | −10.8368 | −1.06264 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.29861 | −0.126132 | ||||||||
\(107\) | 2.72952 | − | 4.72768i | 0.263873 | − | 0.457042i | −0.703395 | − | 0.710800i | \(-0.748333\pi\) |
0.967268 | + | 0.253758i | \(0.0816666\pi\) | |||||||
\(108\) | −6.14536 | + | 0.561371i | −0.591337 | + | 0.0540179i | ||||
\(109\) | −3.29331 | − | 5.70418i | −0.315442 | − | 0.546362i | 0.664089 | − | 0.747653i | \(-0.268819\pi\) |
−0.979531 | + | 0.201292i | \(0.935486\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.43296 | − | 1.81704i | 0.136011 | − | 0.172466i | ||||
\(112\) | −0.303002 | + | 0.479575i | −0.0286310 | + | 0.0453156i | ||||
\(113\) | −0.214344 | −0.0201638 | −0.0100819 | − | 0.999949i | \(-0.503209\pi\) | ||||
−0.0100819 | + | 0.999949i | \(0.503209\pi\) | |||||||
\(114\) | 3.05732 | + | 7.66720i | 0.286344 | + | 0.718099i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.15054 | − | 1.81897i | 0.292520 | − | 0.168887i | ||||
\(117\) | −10.8484 | − | 3.21763i | −1.00293 | − | 0.297470i | ||||
\(118\) | −2.88828 | −0.265888 | ||||||||
\(119\) | −8.85184 | + | 4.65023i | −0.811447 | + | 0.426286i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.3872 | − | 24.9193i | 1.30793 | − | 2.26539i | ||||
\(122\) | 10.2431 | − | 5.91386i | 0.927367 | − | 0.535415i | ||||
\(123\) | −1.62680 | + | 11.2058i | −0.146683 | + | 1.01039i | ||||
\(124\) | 0.415445 | + | 0.239857i | 0.0373081 | + | 0.0215398i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −5.38332 | + | 4.71181i | −0.479584 | + | 0.419761i | ||||
\(127\) | 1.05320i | 0.0934560i | 0.998908 | + | 0.0467280i | \(0.0148794\pi\) | ||||
−0.998908 | + | 0.0467280i | \(0.985121\pi\) | |||||||
\(128\) | 3.10407 | − | 5.37640i | 0.274363 | − | 0.475211i | ||||
\(129\) | 8.30583 | + | 1.20580i | 0.731288 | + | 0.106165i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.22860 | + | 9.05621i | −0.456825 | + | 0.791245i | −0.998791 | − | 0.0491560i | \(-0.984347\pi\) |
0.541966 | + | 0.840401i | \(0.317680\pi\) | |||||||
\(132\) | 8.03317 | − | 10.1863i | 0.699197 | − | 0.886603i | ||||
\(133\) | −11.8262 | − | 7.47194i | −1.02546 | − | 0.647899i | ||||
\(134\) | − | 2.79562i | − | 0.241505i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.40343 | + | 5.42907i | −0.806338 | + | 0.465539i | ||||
\(137\) | 3.64697 | + | 6.31673i | 0.311581 | + | 0.539675i | 0.978705 | − | 0.205272i | \(-0.0658080\pi\) |
−0.667124 | + | 0.744947i | \(0.732475\pi\) | |||||||
\(138\) | 9.82987 | − | 3.91969i | 0.836774 | − | 0.333666i | ||||
\(139\) | 10.8548i | 0.920693i | 0.887739 | + | 0.460347i | \(0.152275\pi\) | ||||
−0.887739 | + | 0.460347i | \(0.847725\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.08153 | − | 2.63944i | 0.175297 | − | 0.222281i | ||||
\(142\) | 1.72946 | + | 0.998507i | 0.145133 | + | 0.0837928i | ||||
\(143\) | 20.6008 | − | 11.8939i | 1.72273 | − | 0.994617i | ||||
\(144\) | −0.466740 | + | 0.442605i | −0.0388950 | + | 0.0368837i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.27014 | −0.187878 | ||||||||
\(147\) | 2.69247 | − | 11.8216i | 0.222071 | − | 0.975031i | ||||
\(148\) | 1.58668i | 0.130425i | ||||||||
\(149\) | −2.54658 | − | 1.47027i | −0.208624 | − | 0.120449i | 0.392048 | − | 0.919945i | \(-0.371767\pi\) |
−0.600672 | + | 0.799496i | \(0.705100\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.49298 | − | 4.31797i | −0.202876 | − | 0.351391i | 0.746578 | − | 0.665298i | \(-0.231695\pi\) |
−0.949454 | + | 0.313907i | \(0.898362\pi\) | |||||||
\(152\) | −13.1557 | − | 7.59543i | −1.06707 | − | 0.616071i | ||||
\(153\) | −11.0255 | + | 2.64283i | −0.891356 | + | 0.213660i | ||||
\(154\) | 0.599698 | − | 15.0276i | 0.0483250 | − | 1.21096i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 7.20676 | − | 2.87372i | 0.577002 | − | 0.230082i | ||||
\(157\) | 3.54960 | + | 6.14808i | 0.283289 | + | 0.490671i | 0.972193 | − | 0.234182i | \(-0.0752412\pi\) |
−0.688904 | + | 0.724853i | \(0.741908\pi\) | |||||||
\(158\) | 2.75772 | + | 4.77650i | 0.219392 | + | 0.379998i | ||||
\(159\) | 2.31798 | − | 0.924303i | 0.183828 | − | 0.0733020i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.57953 | + | 15.1620i | −0.754973 | + | 1.19493i | ||||
\(162\) | −7.23046 | + | 3.67762i | −0.568079 | + | 0.288941i | ||||
\(163\) | 15.3156 | + | 8.84246i | 1.19961 | + | 0.692595i | 0.960468 | − | 0.278390i | \(-0.0898008\pi\) |
0.239141 | + | 0.970985i | \(0.423134\pi\) | |||||||
\(164\) | −3.88196 | − | 6.72375i | −0.303130 | − | 0.525036i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.66343 | − | 3.84713i | −0.517182 | − | 0.298595i | ||||
\(167\) | 10.9235i | 0.845287i | 0.906296 | + | 0.422643i | \(0.138898\pi\) | ||||
−0.906296 | + | 0.422643i | \(0.861102\pi\) | |||||||
\(168\) | 2.40961 | − | 12.9438i | 0.185905 | − | 0.998633i | ||||
\(169\) | 1.22669 | 0.0943611 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.9145 | − | 11.5097i | −0.834653 | − | 0.880168i | ||||
\(172\) | −4.98370 | + | 2.87734i | −0.380004 | + | 0.219395i | ||||
\(173\) | −20.0145 | − | 11.5554i | −1.52167 | − | 0.878539i | −0.999672 | − | 0.0255936i | \(-0.991852\pi\) |
−0.522001 | − | 0.852945i | \(-0.674814\pi\) | |||||||
\(174\) | 2.96132 | − | 3.75504i | 0.224497 | − | 0.284669i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 1.35222i | − | 0.101927i | ||||||
\(177\) | 5.15552 | − | 2.05578i | 0.387513 | − | 0.154522i | ||||
\(178\) | 0.532492 | + | 0.922304i | 0.0399120 | + | 0.0691296i | ||||
\(179\) | −15.2776 | + | 8.82051i | −1.14190 | + | 0.659276i | −0.946900 | − | 0.321527i | \(-0.895804\pi\) |
−0.194999 | + | 0.980803i | \(0.562470\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.8545i | 1.10413i | 0.833802 | + | 0.552064i | \(0.186160\pi\) | ||||
−0.833802 | + | 0.552064i | \(0.813840\pi\) | |||||||
\(182\) | 4.80438 | − | 7.60411i | 0.356124 | − | 0.563654i | ||||
\(183\) | −14.0744 | + | 17.8468i | −1.04041 | + | 1.31927i | ||||
\(184\) | −9.73785 | + | 16.8665i | −0.717884 | + | 1.24341i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.624066 | + | 0.0905986i | 0.0457587 | + | 0.00664301i | ||||
\(187\) | 11.9173 | − | 20.6414i | 0.871481 | − | 1.50945i | ||||
\(188\) | 2.30482i | 0.168097i | ||||||||
\(189\) | 6.25541 | − | 12.2421i | 0.455014 | − | 0.890484i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.1877 | − | 9.34599i | −1.17130 | − | 0.676252i | −0.217316 | − | 0.976101i | \(-0.569730\pi\) |
−0.953987 | + | 0.299850i | \(0.903064\pi\) | |||||||
\(192\) | 1.35217 | − | 9.31407i | 0.0975843 | − | 0.672185i | ||||
\(193\) | 2.24781 | − | 1.29778i | 0.161801 | − | 0.0934160i | −0.416913 | − | 0.908946i | \(-0.636888\pi\) |
0.578714 | + | 0.815530i | \(0.303555\pi\) | |||||||
\(194\) | 4.10357 | − | 7.10759i | 0.294619 | − | 0.510295i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.56969 | + | 7.50776i | 0.254978 | + | 0.536269i | ||||
\(197\) | −7.83600 | −0.558292 | −0.279146 | − | 0.960249i | \(-0.590051\pi\) | ||||
−0.279146 | + | 0.960249i | \(0.590051\pi\) | |||||||
\(198\) | 4.84921 | − | 16.3493i | 0.344619 | − | 1.16189i | ||||
\(199\) | −3.06915 | + | 1.77198i | −0.217566 | + | 0.125612i | −0.604823 | − | 0.796360i | \(-0.706756\pi\) |
0.387256 | + | 0.921972i | \(0.373423\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.98983 | + | 4.99012i | 0.140351 | + | 0.351976i | ||||
\(202\) | −2.07741 | −0.146166 | ||||||||
\(203\) | −0.323169 | + | 8.09819i | −0.0226820 | + | 0.568382i | ||||
\(204\) | 4.81384 | − | 6.10410i | 0.337036 | − | 0.427372i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.50920 | − | 6.07811i | −0.244498 | − | 0.423482i | ||||
\(207\) | −14.7562 | + | 13.9931i | −1.02563 | + | 0.972590i | ||||
\(208\) | 0.404359 | − | 0.700371i | 0.0280373 | − | 0.0485620i | ||||
\(209\) | 33.3453 | 2.30655 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.9742 | 1.65045 | 0.825225 | − | 0.564804i | \(-0.191048\pi\) | ||||
0.825225 | + | 0.564804i | \(0.191048\pi\) | |||||||
\(212\) | −0.855523 | + | 1.48181i | −0.0587576 | + | 0.101771i | ||||
\(213\) | −3.79776 | − | 0.551339i | −0.260218 | − | 0.0377771i | ||||
\(214\) | 2.46021 | + | 4.26121i | 0.168177 | + | 0.291290i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 6.25741 | − | 13.5543i | 0.425763 | − | 0.922256i | ||||
\(217\) | −0.946107 | + | 0.497028i | −0.0642259 | + | 0.0337404i | ||||
\(218\) | 5.93674 | 0.402087 | ||||||||
\(219\) | 4.05215 | − | 1.61581i | 0.273819 | − | 0.109186i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.3450 | − | 7.12736i | 0.830412 | − | 0.479438i | ||||
\(222\) | 0.772552 | + | 1.93742i | 0.0518503 | + | 0.130031i | ||||
\(223\) | 16.9380 | 1.13425 | 0.567125 | − | 0.823632i | \(-0.308056\pi\) | ||||
0.567125 | + | 0.823632i | \(0.308056\pi\) | |||||||
\(224\) | 6.83264 | + | 13.0061i | 0.456525 | + | 0.869009i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.0965976 | − | 0.167312i | 0.00642557 | − | 0.0111294i | ||||
\(227\) | −18.9635 | + | 10.9486i | −1.25865 | + | 0.726685i | −0.972813 | − | 0.231592i | \(-0.925606\pi\) |
−0.285842 | + | 0.958277i | \(0.592273\pi\) | |||||||
\(228\) | 10.7630 | + | 1.56252i | 0.712800 | + | 0.103481i | ||||
\(229\) | 0.218276 | + | 0.126022i | 0.0144241 | + | 0.00832775i | 0.507195 | − | 0.861831i | \(-0.330682\pi\) |
−0.492771 | + | 0.870159i | \(0.664016\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.62570 | + | 27.2508i | 0.633325 | + | 1.79297i | ||||
\(232\) | 8.80103i | 0.577816i | ||||||||
\(233\) | −7.47118 | + | 12.9405i | −0.489453 | + | 0.847758i | −0.999926 | − | 0.0121359i | \(-0.996137\pi\) |
0.510473 | + | 0.859894i | \(0.329470\pi\) | |||||||
\(234\) | 7.40061 | − | 7.01791i | 0.483793 | − | 0.458775i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.90281 | + | 3.29576i | −0.123862 | + | 0.214535i | ||||
\(237\) | −8.32221 | − | 6.56311i | −0.540586 | − | 0.426320i | ||||
\(238\) | 0.359366 | − | 9.00525i | 0.0232943 | − | 0.583723i | ||||
\(239\) | 19.5021i | 1.26149i | 0.775991 | + | 0.630744i | \(0.217250\pi\) | ||||
−0.775991 | + | 0.630744i | \(0.782750\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.54154 | − | 4.93146i | 0.550209 | − | 0.317663i | −0.198997 | − | 0.980000i | \(-0.563768\pi\) |
0.749206 | + | 0.662337i | \(0.230435\pi\) | |||||||
\(242\) | 12.9676 | + | 22.4606i | 0.833592 | + | 1.44382i | ||||
\(243\) | 10.2886 | − | 11.7109i | 0.660015 | − | 0.751253i | ||||
\(244\) | − | 15.5842i | − | 0.997678i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.01384 | − | 6.31992i | −0.510944 | − | 0.402943i | ||||
\(247\) | 17.2709 | + | 9.97138i | 1.09892 | + | 0.634464i | ||||
\(248\) | −1.00506 | + | 0.580273i | −0.0638215 | + | 0.0368474i | ||||
\(249\) | 14.6323 | + | 2.12425i | 0.927286 | + | 0.134619i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.5460 | 1.67557 | 0.837784 | − | 0.546002i | \(-0.183851\pi\) | ||||
0.837784 | + | 0.546002i | \(0.183851\pi\) | |||||||
\(252\) | 1.83000 | + | 9.24693i | 0.115279 | + | 0.582502i | ||||
\(253\) | − | 42.7510i | − | 2.68773i | ||||||
\(254\) | −0.822100 | − | 0.474640i | −0.0515832 | − | 0.0297815i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.23165 | + | 14.2576i | 0.514478 | + | 0.891102i | ||||
\(257\) | 13.2758 | + | 7.66481i | 0.828124 | + | 0.478117i | 0.853210 | − | 0.521568i | \(-0.174653\pi\) |
−0.0250861 | + | 0.999685i | \(0.507986\pi\) | |||||||
\(258\) | −4.68438 | + | 5.93993i | −0.291637 | + | 0.369804i | ||||
\(259\) | −2.98835 | − | 1.88808i | −0.185687 | − | 0.117319i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.61318 | + | 8.81043i | −0.161752 | + | 0.545352i | ||||
\(262\) | −4.71271 | − | 8.16266i | −0.291152 | − | 0.504291i | ||||
\(263\) | −10.9949 | − | 19.0437i | −0.677972 | − | 1.17428i | −0.975591 | − | 0.219598i | \(-0.929526\pi\) |
0.297618 | − | 0.954685i | \(-0.403808\pi\) | |||||||
\(264\) | 11.6245 | + | 29.1520i | 0.715436 | + | 1.79418i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 11.1621 | − | 5.86389i | 0.684391 | − | 0.359538i | ||||
\(267\) | −1.60695 | − | 1.26728i | −0.0983438 | − | 0.0775564i | ||||
\(268\) | −3.19002 | − | 1.84176i | −0.194861 | − | 0.112503i | ||||
\(269\) | −14.9395 | − | 25.8760i | −0.910878 | − | 1.57769i | −0.812826 | − | 0.582506i | \(-0.802072\pi\) |
−0.0980517 | − | 0.995181i | \(-0.531261\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.7412 | − | 6.20142i | −0.652480 | − | 0.376710i | 0.136926 | − | 0.990581i | \(-0.456278\pi\) |
−0.789406 | + | 0.613872i | \(0.789611\pi\) | |||||||
\(272\) | − | 0.810312i | − | 0.0491324i | ||||||
\(273\) | −3.16336 | + | 16.9928i | −0.191456 | + | 1.02845i | ||||
\(274\) | −6.57426 | −0.397166 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.00326 | − | 13.7989i | 0.120582 | − | 0.830599i | ||||
\(277\) | −6.98725 | + | 4.03409i | −0.419823 | + | 0.242385i | −0.695002 | − | 0.719008i | \(-0.744596\pi\) |
0.275178 | + | 0.961393i | \(0.411263\pi\) | |||||||
\(278\) | −8.47302 | − | 4.89190i | −0.508178 | − | 0.293397i | ||||
\(279\) | −1.17843 | + | 0.282472i | −0.0705507 | + | 0.0169112i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 17.6732i | − | 1.05430i | −0.849773 | − | 0.527149i | \(-0.823261\pi\) | ||
0.849773 | − | 0.527149i | \(-0.176739\pi\) | |||||||
\(282\) | 1.12221 | + | 2.81430i | 0.0668268 | + | 0.167589i | ||||
\(283\) | 11.8369 | + | 20.5021i | 0.703629 | + | 1.21872i | 0.967184 | + | 0.254077i | \(0.0817715\pi\) |
−0.263555 | + | 0.964644i | \(0.584895\pi\) | |||||||
\(284\) | 2.27875 | − | 1.31564i | 0.135219 | − | 0.0780686i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 21.4407i | 1.26781i | ||||||||
\(287\) | 17.2828 | + | 0.689694i | 1.02017 | + | 0.0407113i | ||||
\(288\) | 3.88315 | + | 16.1999i | 0.228817 | + | 0.954586i | ||||
\(289\) | −1.35859 | + | 2.35315i | −0.0799172 | + | 0.138421i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.26584 | + | 15.6077i | −0.132826 | + | 0.914938i | ||||
\(292\) | −1.49557 | + | 2.59041i | −0.0875217 | + | 0.151592i | ||||
\(293\) | − | 2.70804i | − | 0.158205i | −0.996866 | − | 0.0791026i | \(-0.974795\pi\) | ||
0.996866 | − | 0.0791026i | \(-0.0252055\pi\) | |||||||
\(294\) | 8.01428 | + | 7.42928i | 0.467402 | + | 0.433285i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.32430 | − | 1.91928i | −0.193221 | − | 0.111556i | ||||
\(297\) | 2.98114 | + | 32.6347i | 0.172983 | + | 1.89365i | ||||
\(298\) | 2.29532 | − | 1.32520i | 0.132964 | − | 0.0767670i | ||||
\(299\) | 12.7840 | − | 22.1425i | 0.739317 | − | 1.28053i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.511207 | − | 12.8102i | 0.0294655 | − | 0.738366i | ||||
\(302\) | 4.49401 | 0.258601 | ||||||||
\(303\) | 3.70814 | − | 1.47863i | 0.213027 | − | 0.0849452i | ||||
\(304\) | 0.981769 | − | 0.566825i | 0.0563083 | − | 0.0325096i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.90587 | − | 9.79726i | 0.166118 | − | 0.560072i | ||||
\(307\) | 5.49592 | 0.313669 | 0.156834 | − | 0.987625i | \(-0.449871\pi\) | ||||
0.156834 | + | 0.987625i | \(0.449871\pi\) | |||||||
\(308\) | −16.7526 | − | 10.5845i | −0.954569 | − | 0.603109i | ||||
\(309\) | 10.5900 | + | 8.35157i | 0.602446 | + | 0.475104i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.9235 | + | 18.9201i | 0.619416 | + | 1.07286i | 0.989593 | + | 0.143898i | \(0.0459637\pi\) |
−0.370177 | + | 0.928961i | \(0.620703\pi\) | |||||||
\(312\) | −2.69664 | + | 18.5752i | −0.152667 | + | 1.05161i | ||||
\(313\) | 12.2955 | − | 21.2964i | 0.694983 | − | 1.20375i | −0.275203 | − | 0.961386i | \(-0.588745\pi\) |
0.970186 | − | 0.242360i | \(-0.0779214\pi\) | |||||||
\(314\) | −6.39874 | −0.361102 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.26715 | 0.408809 | ||||||||
\(317\) | 11.9775 | − | 20.7457i | 0.672726 | − | 1.16520i | −0.304402 | − | 0.952544i | \(-0.598457\pi\) |
0.977128 | − | 0.212652i | \(-0.0682101\pi\) | |||||||
\(318\) | −0.323147 | + | 2.22592i | −0.0181212 | + | 0.124823i | ||||
\(319\) | −9.65954 | − | 16.7308i | −0.540830 | − | 0.936746i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.42441 | − | 5.85507i | −0.414390 | − | 0.326798i | ||||
\(322\) | −7.51791 | − | 14.3105i | −0.418956 | − | 0.797496i | ||||
\(323\) | 19.9821 | 1.11183 | ||||||||
\(324\) | −0.566985 | + | 10.6733i | −0.0314992 | + | 0.592963i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −13.8044 | + | 7.97000i | −0.764557 | + | 0.441417i | ||||
\(327\) | −10.5969 | + | 4.22557i | −0.586013 | + | 0.233674i | ||||
\(328\) | 18.7828 | 1.03711 | ||||||||
\(329\) | −4.34089 | − | 2.74263i | −0.239321 | − | 0.151206i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.5511 | + | 23.4712i | −0.744837 | + | 1.29009i | 0.205434 | + | 0.978671i | \(0.434139\pi\) |
−0.950271 | + | 0.311424i | \(0.899194\pi\) | |||||||
\(332\) | −8.77975 | + | 5.06899i | −0.481852 | + | 0.278197i | ||||
\(333\) | −2.75798 | − | 2.90837i | −0.151136 | − | 0.159378i | ||||
\(334\) | −8.52664 | − | 4.92286i | −0.466557 | − | 0.269367i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.746631 | + | 0.638708i | 0.0407321 | + | 0.0348444i | ||||
\(337\) | − | 3.19846i | − | 0.174231i | −0.996198 | − | 0.0871155i | \(-0.972235\pi\) | ||
0.996198 | − | 0.0871155i | \(-0.0277649\pi\) | |||||||
\(338\) | −0.552830 | + | 0.957529i | −0.0300700 | + | 0.0520827i | ||||
\(339\) | −0.0533377 | + | 0.367403i | −0.00289690 | + | 0.0199546i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.27375 | − | 2.20620i | 0.0689776 | − | 0.119473i | ||||
\(342\) | 13.9030 | − | 3.33258i | 0.751788 | − | 0.180205i | ||||
\(343\) | −18.3878 | − | 2.21077i | −0.992850 | − | 0.119370i | ||||
\(344\) | − | 13.9220i | − | 0.750622i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.0397 | − | 10.4152i | 0.969821 | − | 0.559926i | ||||
\(347\) | −16.3140 | − | 28.2567i | −0.875783 | − | 1.51690i | −0.855927 | − | 0.517097i | \(-0.827012\pi\) |
−0.0198563 | − | 0.999803i | \(-0.506321\pi\) | |||||||
\(348\) | −2.33387 | − | 5.85292i | −0.125109 | − | 0.313750i | ||||
\(349\) | 32.4849i | 1.73888i | 0.494041 | + | 0.869439i | \(0.335519\pi\) | ||||
−0.494041 | + | 0.869439i | \(0.664481\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.21481 | + | 17.7943i | −0.438474 | + | 0.949790i | ||||
\(352\) | −30.3287 | − | 17.5103i | −1.61653 | − | 0.933301i | ||||
\(353\) | −5.77784 | + | 3.33584i | −0.307523 | + | 0.177549i | −0.645818 | − | 0.763492i | \(-0.723483\pi\) |
0.338294 | + | 0.941040i | \(0.390150\pi\) | |||||||
\(354\) | −0.718725 | + | 4.95075i | −0.0381998 | + | 0.263130i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.40323 | 0.0743709 | ||||||||
\(357\) | 5.76817 | + | 16.3300i | 0.305284 | + | 0.864273i | ||||
\(358\) | − | 15.9004i | − | 0.840364i | ||||||
\(359\) | 14.0322 | + | 8.10148i | 0.740590 | + | 0.427580i | 0.822284 | − | 0.569078i | \(-0.192700\pi\) |
−0.0816940 | + | 0.996657i | \(0.526033\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.47774 | + | 7.75567i | 0.235671 | + | 0.408193i | ||||
\(362\) | −11.5951 | − | 6.69443i | −0.609425 | − | 0.351852i | ||||
\(363\) | −39.1337 | − | 30.8618i | −2.05398 | − | 1.61982i | ||||
\(364\) | −5.51175 | − | 10.4918i | −0.288894 | − | 0.549918i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −7.58793 | − | 19.0291i | −0.396627 | − | 0.994669i | ||||
\(367\) | −8.60716 | − | 14.9080i | −0.449290 | − | 0.778193i | 0.549050 | − | 0.835789i | \(-0.314990\pi\) |
−0.998340 | + | 0.0575965i | \(0.981656\pi\) | |||||||
\(368\) | −0.726708 | − | 1.25869i | −0.0378823 | − | 0.0656140i | ||||
\(369\) | 18.8028 | + | 5.57693i | 0.978836 | + | 0.290324i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.77280 | − | 3.37457i | −0.0920391 | − | 0.175199i | ||||
\(372\) | 0.514515 | − | 0.652421i | 0.0266764 | − | 0.0338264i | ||||
\(373\) | 10.6793 | + | 6.16568i | 0.552952 | + | 0.319247i | 0.750312 | − | 0.661084i | \(-0.229903\pi\) |
−0.197360 | + | 0.980331i | \(0.563237\pi\) | |||||||
\(374\) | 10.7415 | + | 18.6048i | 0.555428 | + | 0.962030i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.82889 | − | 2.78796i | −0.249031 | − | 0.143778i | ||||
\(377\) | − | 11.5541i | − | 0.595067i | ||||||
\(378\) | 6.73683 | + | 10.3999i | 0.346505 | + | 0.534916i | ||||
\(379\) | 3.57576 | 0.183675 | 0.0918373 | − | 0.995774i | \(-0.470726\pi\) | ||||
0.0918373 | + | 0.995774i | \(0.470726\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.80526 | + | 0.262079i | 0.0924864 | + | 0.0134267i | ||||
\(382\) | 14.5905 | − | 8.42384i | 0.746516 | − | 0.431001i | ||||
\(383\) | 20.0319 | + | 11.5654i | 1.02358 | + | 0.590965i | 0.915139 | − | 0.403138i | \(-0.132081\pi\) |
0.108442 | + | 0.994103i | \(0.465414\pi\) | |||||||
\(384\) | −8.44317 | − | 6.65850i | −0.430864 | − | 0.339790i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.33946i | 0.119075i | ||||||||
\(387\) | 4.13367 | − | 13.9368i | 0.210126 | − | 0.708449i | ||||
\(388\) | −5.40688 | − | 9.36499i | −0.274493 | − | 0.475435i | ||||
\(389\) | −14.7169 | + | 8.49679i | −0.746175 | + | 0.430804i | −0.824310 | − | 0.566138i | \(-0.808437\pi\) |
0.0781352 | + | 0.996943i | \(0.475103\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 25.6184i | − | 1.29558i | ||||||
\(392\) | −20.0477 | − | 1.60261i | −1.01256 | − | 0.0809440i | ||||
\(393\) | 14.2220 | + | 11.2158i | 0.717405 | + | 0.565763i | ||||
\(394\) | 3.53142 | − | 6.11660i | 0.177910 | − | 0.308150i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −15.4612 | − | 16.3043i | −0.776952 | − | 0.819321i | ||||
\(397\) | 10.8448 | − | 18.7837i | 0.544283 | − | 0.942726i | −0.454368 | − | 0.890814i | \(-0.650135\pi\) |
0.998652 | − | 0.0519125i | \(-0.0165317\pi\) | |||||||
\(398\) | − | 3.19428i | − | 0.160115i | ||||||
\(399\) | −15.7504 | + | 18.4117i | −0.788504 | + | 0.921739i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.425230 | − | 0.245507i | −0.0212350 | − | 0.0122600i | 0.489345 | − | 0.872090i | \(-0.337236\pi\) |
−0.510580 | + | 0.859830i | \(0.670569\pi\) | |||||||
\(402\) | −4.79192 | − | 0.695666i | −0.238999 | − | 0.0346967i | ||||
\(403\) | 1.31946 | − | 0.761790i | 0.0657270 | − | 0.0379475i | ||||
\(404\) | −1.36860 | + | 2.37049i | −0.0680906 | + | 0.117936i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.17562 | − | 3.90184i | −0.306491 | − | 0.193645i | ||||
\(407\) | 8.42601 | 0.417662 | ||||||||
\(408\) | 6.96592 | + | 17.4692i | 0.344864 | + | 0.864856i | ||||
\(409\) | −24.2867 | + | 14.0219i | −1.20090 | + | 0.693339i | −0.960755 | − | 0.277399i | \(-0.910528\pi\) |
−0.240143 | + | 0.970738i | \(0.577194\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.7349 | − | 4.67933i | 0.578840 | − | 0.230815i | ||||
\(412\) | −9.24747 | −0.455590 | ||||||||
\(413\) | −3.94295 | − | 7.50553i | −0.194020 | − | 0.369323i | ||||
\(414\) | −4.27260 | − | 17.8246i | −0.209987 | − | 0.876031i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −10.4723 | − | 18.1386i | −0.513448 | − | 0.889319i | ||||
\(417\) | 18.6060 | + | 2.70113i | 0.911142 | + | 0.132275i | ||||
\(418\) | −15.0276 | + | 26.0286i | −0.735025 | + | 1.27310i | ||||
\(419\) | 3.44153 | 0.168130 | 0.0840649 | − | 0.996460i | \(-0.473210\pi\) | ||||
0.0840649 | + | 0.996460i | \(0.473210\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.7964 | 0.916078 | 0.458039 | − | 0.888932i | \(-0.348552\pi\) | ||||
0.458039 | + | 0.888932i | \(0.348552\pi\) | |||||||
\(422\) | −10.8044 | + | 18.7137i | −0.525948 | + | 0.910968i | ||||
\(423\) | −4.00625 | − | 4.22472i | −0.194791 | − | 0.205413i | ||||
\(424\) | −2.06972 | − | 3.58485i | −0.100514 | − | 0.174096i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.14188 | − | 2.71597i | 0.103775 | − | 0.131589i | ||||
\(427\) | 29.3512 | + | 18.5445i | 1.42041 | + | 0.897432i | ||||
\(428\) | 6.48316 | 0.313375 | ||||||||
\(429\) | −15.2608 | − | 38.2712i | −0.736796 | − | 1.84775i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.95390 | + | 3.43749i | −0.286789 | + | 0.165578i | −0.636493 | − | 0.771282i | \(-0.719616\pi\) |
0.349704 | + | 0.936860i | \(0.386282\pi\) | |||||||
\(432\) | 0.642516 | + | 0.910170i | 0.0309131 | + | 0.0437906i | ||||
\(433\) | −15.2776 | −0.734193 | −0.367096 | − | 0.930183i | \(-0.619648\pi\) | ||||
−0.367096 | + | 0.930183i | \(0.619648\pi\) | |||||||
\(434\) | 0.0384100 | − | 0.962503i | 0.00184374 | − | 0.0462016i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.91113 | − | 6.77428i | 0.187309 | − | 0.324429i | ||||
\(437\) | 31.0391 | − | 17.9204i | 1.48480 | − | 0.857249i | ||||
\(438\) | −0.564905 | + | 3.89121i | −0.0269922 | + | 0.185929i | ||||
\(439\) | −33.3367 | − | 19.2469i | −1.59107 | − | 0.918606i | −0.993124 | − | 0.117071i | \(-0.962650\pi\) |
−0.597948 | − | 0.801535i | \(-0.704017\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.5932 | − | 7.55682i | −0.933011 | − | 0.359849i | ||||
\(442\) | 12.8483i | 0.611129i | ||||||||
\(443\) | −1.92829 | + | 3.33990i | −0.0916158 | + | 0.158683i | −0.908191 | − | 0.418556i | \(-0.862536\pi\) |
0.816575 | + | 0.577239i | \(0.195870\pi\) | |||||||
\(444\) | 2.71970 | + | 0.394833i | 0.129071 | + | 0.0187379i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.63337 | + | 13.2214i | −0.361450 | + | 0.626050i | ||||
\(447\) | −3.15386 | + | 3.99919i | −0.149172 | + | 0.189155i | ||||
\(448\) | −14.3652 | − | 0.573262i | −0.678691 | − | 0.0270841i | ||||
\(449\) | 2.52159i | 0.119001i | 0.998228 | + | 0.0595005i | \(0.0189508\pi\) | ||||
−0.998228 | + | 0.0595005i | \(0.981049\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −35.7062 | + | 20.6150i | −1.68134 | + | 0.970721i | ||||
\(452\) | −0.127277 | − | 0.220451i | −0.00598662 | − | 0.0103691i | ||||
\(453\) | −8.02171 | + | 3.19868i | −0.376893 | + | 0.150287i | ||||
\(454\) | − | 19.7367i | − | 0.926288i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −16.2929 | + | 20.6598i | −0.762984 | + | 0.967486i | ||||
\(457\) | 8.05795 | + | 4.65226i | 0.376935 | + | 0.217623i | 0.676484 | − | 0.736457i | \(-0.263503\pi\) |
−0.299549 | + | 0.954081i | \(0.596836\pi\) | |||||||
\(458\) | −0.196739 | + | 0.113588i | −0.00919303 | + | 0.00530760i | ||||
\(459\) | 1.78643 | + | 19.5562i | 0.0833836 | + | 0.912805i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.3898 | 0.530477 | 0.265238 | − | 0.964183i | \(-0.414549\pi\) | ||||
0.265238 | + | 0.964183i | \(0.414549\pi\) | |||||||
\(462\) | −25.6094 | − | 4.76743i | −1.19146 | − | 0.221801i | ||||
\(463\) | 0.322319i | 0.0149795i | 0.999972 | + | 0.00748973i | \(0.00238408\pi\) | ||||
−0.999972 | + | 0.00748973i | \(0.997616\pi\) | |||||||
\(464\) | −0.568801 | − | 0.328398i | −0.0264059 | − | 0.0152455i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.73402 | − | 11.6637i | −0.311947 | − | 0.540309i | ||||
\(467\) | −20.1915 | − | 11.6576i | −0.934353 | − | 0.539449i | −0.0461675 | − | 0.998934i | \(-0.514701\pi\) |
−0.888186 | + | 0.459485i | \(0.848034\pi\) | |||||||
\(468\) | −3.13245 | − | 13.0681i | −0.144798 | − | 0.604072i | ||||
\(469\) | 7.26473 | − | 3.81645i | 0.335454 | − | 0.176227i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.4216 | − | 4.55440i | 0.526280 | − | 0.209856i | ||||
\(472\) | −4.60334 | − | 7.97323i | −0.211886 | − | 0.366997i | ||||
\(473\) | 15.2800 | + | 26.4657i | 0.702575 | + | 1.21690i | ||||
\(474\) | 8.87355 | − | 3.53836i | 0.407576 | − | 0.162522i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −10.0389 | − | 6.34274i | −0.460134 | − | 0.290719i | ||||
\(477\) | −1.00752 | − | 4.20322i | −0.0461312 | − | 0.192452i | ||||
\(478\) | −15.2229 | − | 8.78895i | −0.696280 | − | 0.401997i | ||||
\(479\) | −0.316556 | − | 0.548292i | −0.0144638 | − | 0.0250521i | 0.858703 | − | 0.512474i | \(-0.171271\pi\) |
−0.873167 | + | 0.487422i | \(0.837937\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.36418 | + | 2.51966i | 0.198990 | + | 0.114887i | ||||
\(482\) | 8.88978i | 0.404918i | ||||||||
\(483\) | 23.6051 | + | 20.1930i | 1.07407 | + | 0.918815i | ||||
\(484\) | 34.1724 | 1.55329 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 4.50451 | + | 13.3087i | 0.204329 | + | 0.603697i | ||||
\(487\) | 18.7500 | − | 10.8253i | 0.849642 | − | 0.490541i | −0.0108880 | − | 0.999941i | \(-0.503466\pi\) |
0.860530 | + | 0.509400i | \(0.170132\pi\) | |||||||
\(488\) | 32.6509 | + | 18.8510i | 1.47804 | + | 0.853345i | ||||
\(489\) | 18.9679 | − | 24.0518i | 0.857756 | − | 1.08766i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.1608i | 1.63191i | 0.578112 | + | 0.815957i | \(0.303789\pi\) | ||||
−0.578112 | + | 0.815957i | \(0.696211\pi\) | |||||||
\(492\) | −12.4910 | + | 4.98085i | −0.563140 | + | 0.224554i | ||||
\(493\) | −5.78844 | − | 10.0259i | −0.260698 | − | 0.451543i | ||||
\(494\) | −15.5669 | + | 8.98754i | −0.700387 | + | 0.404368i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 0.0866082i | − | 0.00388882i | ||||||
\(497\) | −0.233744 | + | 5.85732i | −0.0104849 | + | 0.262737i | ||||
\(498\) | −8.25244 | + | 10.4643i | −0.369801 | + | 0.468918i | ||||
\(499\) | −4.50676 | + | 7.80593i | −0.201750 | + | 0.349442i | −0.949092 | − | 0.314998i | \(-0.897996\pi\) |
0.747342 | + | 0.664439i | \(0.231330\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.7238 | + | 2.71822i | 0.836518 | + | 0.121441i | ||||
\(502\) | −11.9634 | + | 20.7212i | −0.533952 | + | 0.924832i | ||||
\(503\) | 18.9044i | 0.842907i | 0.906850 | + | 0.421453i | \(0.138480\pi\) | ||||
−0.906850 | + | 0.421453i | \(0.861520\pi\) | |||||||
\(504\) | −21.5871 | − | 7.35121i | −0.961565 | − | 0.327449i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 33.3704 | + | 19.2664i | 1.48350 | + | 0.856497i | ||||
\(507\) | 0.305252 | − | 2.10265i | 0.0135567 | − | 0.0933822i | ||||
\(508\) | −1.08320 | + | 0.625387i | −0.0480593 | + | 0.0277471i | ||||
\(509\) | −19.6636 | + | 34.0584i | −0.871574 | + | 1.50961i | −0.0112055 | + | 0.999937i | \(0.503567\pi\) |
−0.860368 | + | 0.509673i | \(0.829766\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.09909 | − | 5.89921i | −0.137096 | − | 0.260966i | ||||
\(512\) | −2.42264 | −0.107067 | ||||||||
\(513\) | −22.4445 | + | 15.8443i | −0.990950 | + | 0.699542i | ||||
\(514\) | −11.9659 | + | 6.90854i | −0.527795 | + | 0.304723i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.69185 | + | 9.25848i | 0.162525 | + | 0.407582i | ||||
\(517\) | 12.2397 | 0.538300 | ||||||||
\(518\) | 2.82054 | − | 1.48174i | 0.123927 | − | 0.0651040i | ||||
\(519\) | −24.7873 | + | 31.4310i | −1.08804 | + | 1.37967i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.61869 | − | 14.9280i | −0.377592 | − | 0.654008i | 0.613120 | − | 0.789990i | \(-0.289914\pi\) |
−0.990711 | + | 0.135982i | \(0.956581\pi\) | |||||||
\(522\) | −5.69955 | − | 6.01035i | −0.249462 | − | 0.263066i | ||||
\(523\) | −18.8880 | + | 32.7149i | −0.825914 | + | 1.43052i | 0.0753051 | + | 0.997161i | \(0.476007\pi\) |
−0.901219 | + | 0.433364i | \(0.857326\pi\) | |||||||
\(524\) | −12.4190 | −0.542525 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 19.8201 | 0.864196 | ||||||||
\(527\) | 0.763291 | − | 1.32206i | 0.0332495 | − | 0.0575898i | ||||
\(528\) | −2.31781 | − | 0.336488i | −0.100870 | − | 0.0146438i | ||||
\(529\) | −11.4752 | − | 19.8756i | −0.498920 | − | 0.864156i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.24087 | − | 9.34855i | −0.0972455 | − | 0.405693i | ||||
\(532\) | 0.662443 | − | 16.6000i | 0.0287206 | − | 0.719699i | ||||
\(533\) | −24.6583 | −1.06807 | ||||||||
\(534\) | 1.71341 | − | 0.683228i | 0.0741465 | − | 0.0295662i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 7.71742 | − | 4.45565i | 0.333342 | − | 0.192455i | ||||
\(537\) | 11.3174 | + | 28.3819i | 0.488381 | + | 1.22477i | ||||
\(538\) | 26.9309 | 1.16108 | ||||||||
\(539\) | 39.8697 | − | 18.9567i | 1.71731 | − | 0.816521i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.89533 | + | 17.1392i | −0.425433 | + | 0.736872i | −0.996461 | − | 0.0840587i | \(-0.973212\pi\) |
0.571027 | + | 0.820931i | \(0.306545\pi\) | |||||||
\(542\) | 9.68138 | − | 5.58955i | 0.415851 | − | 0.240092i | ||||
\(543\) | 25.4619 | + | 3.69642i | 1.09267 | + | 0.158629i | ||||
\(544\) | −18.1744 | − | 10.4930i | −0.779219 | − | 0.449882i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −11.8385 | − | 10.1273i | −0.506642 | − | 0.433409i | ||||
\(547\) | − | 8.91454i | − | 0.381158i | −0.981672 | − | 0.190579i | \(-0.938963\pi\) | ||
0.981672 | − | 0.190579i | \(-0.0610365\pi\) | |||||||
\(548\) | −4.33113 | + | 7.50174i | −0.185017 | + | 0.320459i | ||||
\(549\) | 27.0886 | + | 28.5658i | 1.15611 | + | 1.21916i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.09819 | − | 14.0265i | 0.344995 | − | 0.597548i | ||||
\(552\) | 26.4873 | + | 20.8886i | 1.12737 | + | 0.889076i | ||||
\(553\) | −8.64757 | + | 13.6869i | −0.367732 | + | 0.582026i | ||||
\(554\) | − | 7.27212i | − | 0.308963i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.1641 | + | 6.44558i | −0.473462 | + | 0.273354i | ||||
\(557\) | −10.4847 | − | 18.1599i | −0.444249 | − | 0.769462i | 0.553751 | − | 0.832683i | \(-0.313196\pi\) |
−0.998000 | + | 0.0632208i | \(0.979863\pi\) | |||||||
\(558\) | 0.310587 | − | 1.04716i | 0.0131482 | − | 0.0443296i | ||||
\(559\) | 18.2769i | 0.773032i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −32.4155 | − | 25.5637i | −1.36859 | − | 1.07930i | ||||
\(562\) | 13.7953 | + | 7.96474i | 0.581921 | + | 0.335972i | ||||
\(563\) | −15.6638 | + | 9.04347i | −0.660148 | + | 0.381137i | −0.792333 | − | 0.610088i | \(-0.791134\pi\) |
0.132185 | + | 0.991225i | \(0.457801\pi\) | |||||||
\(564\) | 3.95066 | + | 0.573536i | 0.166353 | + | 0.0241502i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −21.3379 | −0.896900 | ||||||||
\(567\) | −19.4274 | − | 13.7686i | −0.815875 | − | 0.578228i | ||||
\(568\) | 6.36568i | 0.267098i | ||||||||
\(569\) | −22.0888 | − | 12.7530i | −0.926010 | − | 0.534632i | −0.0404626 | − | 0.999181i | \(-0.512883\pi\) |
−0.885547 | + | 0.464549i | \(0.846216\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.8853 | − | 34.4424i | −0.832175 | − | 1.44137i | −0.896310 | − | 0.443428i | \(-0.853762\pi\) |
0.0641352 | − | 0.997941i | \(-0.479571\pi\) | |||||||
\(572\) | 24.4655 | + | 14.1252i | 1.02295 | + | 0.590603i | ||||
\(573\) | −20.0480 | + | 25.4214i | −0.837516 | + | 1.06199i | ||||
\(574\) | −8.32714 | + | 13.1797i | −0.347568 | + | 0.550112i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −15.6286 | − | 4.63545i | −0.651192 | − | 0.193144i | ||||
\(577\) | −0.997811 | − | 1.72826i | −0.0415394 | − | 0.0719484i | 0.844508 | − | 0.535543i | \(-0.179893\pi\) |
−0.886048 | + | 0.463594i | \(0.846560\pi\) | |||||||
\(578\) | −1.22454 | − | 2.12097i | −0.0509343 | − | 0.0882208i | ||||
\(579\) | −1.66515 | − | 4.17588i | −0.0692011 | − | 0.173544i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.900590 | − | 22.5676i | 0.0373628 | − | 0.936262i | ||||
\(582\) | −11.1619 | − | 8.80252i | −0.462674 | − | 0.364876i | ||||
\(583\) | 7.86909 | + | 4.54322i | 0.325904 | + | 0.188161i | ||||
\(584\) | −3.61815 | − | 6.26682i | −0.149720 | − | 0.259323i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.11383 | + | 1.22042i | 0.0873216 | + | 0.0504152i | ||||
\(587\) | 27.4257i | 1.13198i | 0.824413 | + | 0.565989i | \(0.191506\pi\) | ||||
−0.824413 | + | 0.565989i | \(0.808494\pi\) | |||||||
\(588\) | 13.7572 | − | 4.25049i | 0.567338 | − | 0.175287i | ||||
\(589\) | 2.13573 | 0.0880013 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.94992 | + | 13.4315i | −0.0802090 | + | 0.552500i | ||||
\(592\) | 0.248083 | − | 0.143231i | 0.0101961 | − | 0.00588674i | ||||
\(593\) | 1.05094 | + | 0.606763i | 0.0431571 | + | 0.0249168i | 0.521423 | − | 0.853298i | \(-0.325401\pi\) |
−0.478266 | + | 0.878215i | \(0.658735\pi\) | |||||||
\(594\) | −26.8174 | − | 12.3803i | −1.10033 | − | 0.507971i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 3.49218i | − | 0.143045i | ||||||
\(597\) | 2.27358 | + | 5.70172i | 0.0930514 | + | 0.233356i | ||||
\(598\) | 11.5226 | + | 19.9578i | 0.471195 | + | 0.816134i | ||||
\(599\) | 32.9617 | − | 19.0304i | 1.34678 | − | 0.777563i | 0.358986 | − | 0.933343i | \(-0.383122\pi\) |
0.987792 | + | 0.155780i | \(0.0497891\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.32414i | 0.339549i | 0.985483 | + | 0.169774i | \(0.0543039\pi\) | ||||
−0.985483 | + | 0.169774i | \(0.945696\pi\) | |||||||
\(602\) | 9.76894 | + | 6.17215i | 0.398152 | + | 0.251558i | ||||
\(603\) | 9.04862 | − | 2.16898i | 0.368488 | − | 0.0883275i | ||||
\(604\) | 2.96066 | − | 5.12802i | 0.120468 | − | 0.208656i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.516947 | + | 3.56086i | −0.0209995 | + | 0.144650i | ||||
\(607\) | −15.1263 | + | 26.1996i | −0.613959 | + | 1.06341i | 0.376607 | + | 0.926373i | \(0.377091\pi\) |
−0.990566 | + | 0.137036i | \(0.956242\pi\) | |||||||
\(608\) | − | 29.3599i | − | 1.19070i | ||||||
\(609\) | 13.8006 | + | 2.56911i | 0.559227 | + | 0.104105i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.33943 | + | 3.66007i | 0.256466 | + | 0.148071i | ||||
\(612\) | −9.26504 | − | 9.77028i | −0.374517 | − | 0.394940i | ||||
\(613\) | 2.45694 | − | 1.41851i | 0.0992349 | − | 0.0572933i | −0.449561 | − | 0.893249i | \(-0.648420\pi\) |
0.548796 | + | 0.835956i | \(0.315086\pi\) | |||||||
\(614\) | −2.47683 | + | 4.28999i | −0.0999566 | + | 0.173130i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 42.4402 | − | 22.2955i | 1.70996 | − | 0.898313i | ||||
\(617\) | −23.3983 | −0.941979 | −0.470990 | − | 0.882139i | \(-0.656103\pi\) | ||||
−0.470990 | + | 0.882139i | \(0.656103\pi\) | |||||||
\(618\) | −11.2916 | + | 4.50257i | −0.454216 | + | 0.181120i | ||||
\(619\) | 34.7980 | − | 20.0907i | 1.39865 | − | 0.807511i | 0.404400 | − | 0.914582i | \(-0.367481\pi\) |
0.994251 | + | 0.107071i | \(0.0341472\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 20.3134 | + | 28.7754i | 0.815150 | + | 1.15472i | ||||
\(622\) | −19.6914 | −0.789555 | ||||||||
\(623\) | −1.66978 | + | 2.64283i | −0.0668981 | + | 0.105883i | ||||
\(624\) | −1.09987 | − | 0.867386i | −0.0440301 | − | 0.0347232i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 11.0823 | + | 19.1952i | 0.442939 | + | 0.767194i | ||||
\(627\) | 8.29771 | − | 57.1567i | 0.331378 | − | 2.28262i | ||||
\(628\) | −4.21550 | + | 7.30146i | −0.168217 | + | 0.291360i | ||||
\(629\) | 5.04925 | 0.201327 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.9329 | −0.912945 | −0.456473 | − | 0.889737i | \(-0.650887\pi\) | ||||
−0.456473 | + | 0.889737i | \(0.650887\pi\) | |||||||
\(632\) | −8.79049 | + | 15.2256i | −0.349667 | + | 0.605641i | ||||
\(633\) | 5.96577 | − | 41.0937i | 0.237118 | − | 1.63333i | ||||
\(634\) | 10.7958 | + | 18.6988i | 0.428754 | + | 0.742624i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.32705 | + | 1.83517i | 0.0922737 | + | 0.0727694i | ||||
\(637\) | 26.3188 | + | 2.10393i | 1.04279 | + | 0.0833607i | ||||
\(638\) | 17.4129 | 0.689384 | ||||||||
\(639\) | −1.89008 | + | 6.37248i | −0.0747704 | + | 0.252091i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.70493 | + | 0.984339i | −0.0673405 | + | 0.0388791i | −0.533292 | − | 0.845931i | \(-0.679045\pi\) |
0.465952 | + | 0.884810i | \(0.345712\pi\) | |||||||
\(642\) | 7.91627 | − | 3.15664i | 0.312430 | − | 0.124583i | ||||
\(643\) | 18.9036 | 0.745483 | 0.372742 | − | 0.927935i | \(-0.378418\pi\) | ||||
0.372742 | + | 0.927935i | \(0.378418\pi\) | |||||||
\(644\) | −21.2823 | − | 0.849297i | −0.838638 | − | 0.0334670i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.00525 | + | 15.5975i | −0.354307 | + | 0.613677i | ||||
\(647\) | −5.77380 | + | 3.33350i | −0.226991 | + | 0.131054i | −0.609183 | − | 0.793029i | \(-0.708503\pi\) |
0.382192 | + | 0.924083i | \(0.375169\pi\) | |||||||
\(648\) | −21.6761 | − | 14.0986i | −0.851519 | − | 0.553845i | ||||
\(649\) | 17.5020 | + | 10.1048i | 0.687012 | + | 0.396647i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.616516 | + | 1.74539i | 0.0241632 | + | 0.0684071i | ||||
\(652\) | 21.0026i | 0.822525i | ||||||||
\(653\) | 16.9206 | − | 29.3074i | 0.662156 | − | 1.14689i | −0.317892 | − | 0.948127i | \(-0.602975\pi\) |
0.980048 | − | 0.198761i | \(-0.0636917\pi\) | |||||||
\(654\) | 1.47731 | − | 10.1761i | 0.0577673 | − | 0.397915i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.700852 | + | 1.21391i | −0.0273637 | + | 0.0473953i | ||||
\(657\) | −1.76129 | − | 7.34780i | −0.0687143 | − | 0.286665i | ||||
\(658\) | 4.09713 | − | 2.15239i | 0.159723 | − | 0.0839088i | ||||
\(659\) | 22.0797i | 0.860101i | 0.902805 | + | 0.430051i | \(0.141504\pi\) | ||||
−0.902805 | + | 0.430051i | \(0.858496\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.1770 | − | 15.6907i | 1.05706 | − | 0.610296i | 0.132445 | − | 0.991190i | \(-0.457717\pi\) |
0.924619 | + | 0.380894i | \(0.124384\pi\) | |||||||
\(662\) | −12.2141 | − | 21.1554i | −0.474713 | − | 0.822227i | ||||
\(663\) | −9.14495 | − | 22.9339i | −0.355160 | − | 0.890677i | ||||
\(664\) | − | 24.5262i | − | 0.951802i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.51314 | − | 0.842108i | 0.136131 | − | 0.0326310i | ||||
\(667\) | −17.9829 | − | 10.3824i | −0.696301 | − | 0.402009i | ||||
\(668\) | −11.2347 | + | 6.48638i | −0.434685 | + | 0.250965i | ||||
\(669\) | 4.21487 | − | 29.0330i | 0.162956 | − | 1.12248i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −82.7594 | −3.19489 | ||||||||
\(672\) | 23.9938 | − | 8.47525i | 0.925582 | − | 0.326940i | ||||
\(673\) | − | 40.5686i | − | 1.56380i | −0.623401 | − | 0.781902i | \(-0.714249\pi\) | ||
0.623401 | − | 0.781902i | \(-0.285751\pi\) | |||||||
\(674\) | 2.49664 | + | 1.44144i | 0.0961671 | + | 0.0555221i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.728410 | + | 1.26164i | 0.0280158 | + | 0.0485248i | ||||
\(677\) | 34.4733 | + | 19.9031i | 1.32491 | + | 0.764940i | 0.984508 | − | 0.175338i | \(-0.0561019\pi\) |
0.340407 | + | 0.940278i | \(0.389435\pi\) | |||||||
\(678\) | −0.262749 | − | 0.207210i | −0.0100908 | − | 0.00795786i | ||||
\(679\) | 24.0719 | + | 0.960621i | 0.923794 | + | 0.0368653i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.0479 | + | 35.2295i | 0.538317 | + | 1.35000i | ||||
\(682\) | 1.14808 | + | 1.98852i | 0.0439621 | + | 0.0761445i | ||||
\(683\) | −11.4962 | − | 19.9121i | −0.439892 | − | 0.761915i | 0.557789 | − | 0.829983i | \(-0.311650\pi\) |
−0.997681 | + | 0.0680680i | \(0.978317\pi\) | |||||||
\(684\) | 5.35658 | − | 18.0599i | 0.204814 | − | 0.690538i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 10.0125 | − | 13.3568i | 0.382277 | − | 0.509965i | ||||
\(687\) | 0.270328 | − | 0.342784i | 0.0103137 | − | 0.0130780i | ||||
\(688\) | 0.899762 | + | 0.519478i | 0.0343031 | + | 0.0198049i | ||||
\(689\) | 2.71715 | + | 4.70625i | 0.103515 | + | 0.179294i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.7325 | + | 11.9699i | 0.788702 | + | 0.455358i | 0.839506 | − | 0.543351i | \(-0.182845\pi\) |
−0.0508031 | + | 0.998709i | \(0.516178\pi\) | |||||||
\(692\) | − | 27.4463i | − | 1.04335i | ||||||
\(693\) | 49.1054 | − | 9.71811i | 1.86536 | − | 0.369161i | ||||
\(694\) | 29.4087 | 1.11634 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 15.0857 | + | 2.19006i | 0.571822 | + | 0.0830141i | ||||
\(697\) | −21.3968 | + | 12.3534i | −0.810461 | + | 0.467920i | ||||
\(698\) | −25.3570 | − | 14.6399i | −0.959776 | − | 0.554127i | ||||
\(699\) | 20.3219 | + | 16.0263i | 0.768644 | + | 0.606172i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.70996i | 0.291201i | 0.989343 | + | 0.145601i | \(0.0465115\pi\) | ||||
−0.989343 | + | 0.145601i | \(0.953489\pi\) | |||||||
\(702\) | −10.1877 | − | 14.4316i | −0.384510 | − | 0.544685i | ||||
\(703\) | 3.53202 | + | 6.11765i | 0.133213 | + | 0.230731i | ||||
\(704\) | 29.6784 | − | 17.1348i | 1.11855 | − | 0.645793i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 6.01340i | − | 0.226317i | ||||||
\(707\) | −2.83599 | − | 5.39839i | −0.106658 | − | 0.203027i | ||||
\(708\) | 5.17570 | + | 4.08169i | 0.194515 | + | 0.153399i | ||||
\(709\) | −1.62353 | + | 2.81203i | −0.0609729 | + | 0.105608i | −0.894901 | − | 0.446266i | \(-0.852754\pi\) |
0.833928 | + | 0.551874i | \(0.186087\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.3206 | + | 12.6318i | −0.499562 | + | 0.473729i | ||||
\(712\) | −1.69737 | + | 2.93993i | −0.0636117 | + | 0.110179i | ||||
\(713\) | − | 2.73815i | − | 0.102545i | ||||||
\(714\) | −15.3463 | − | 2.85686i | −0.574321 | − | 0.106915i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −18.1436 | − | 10.4752i | −0.678060 | − | 0.391478i | ||||
\(717\) | 33.4282 | + | 4.85294i | 1.24840 | + | 0.181236i | ||||
\(718\) | −12.6477 | + | 7.30213i | −0.472006 | + | 0.272513i | ||||
\(719\) | −17.8697 | + | 30.9513i | −0.666429 | + | 1.15429i | 0.312467 | + | 0.949929i | \(0.398845\pi\) |
−0.978896 | + | 0.204360i | \(0.934489\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.0041 | − | 17.4166i | 0.409813 | − | 0.648629i | ||||
\(722\) | −8.07187 | −0.300404 | ||||||||
\(723\) | −6.32744 | − | 15.8681i | −0.235320 | − | 0.590139i | ||||
\(724\) | −15.2777 | + | 8.82061i | −0.567793 | + | 0.327815i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 41.7262 | − | 16.6385i | 1.54861 | − | 0.617512i | ||||
\(727\) | −33.2693 | −1.23389 | −0.616945 | − | 0.787006i | \(-0.711630\pi\) | ||||
−0.616945 | + | 0.787006i | \(0.711630\pi\) | |||||||
\(728\) | 28.6487 | + | 1.14326i | 1.06179 | + | 0.0423722i | ||||
\(729\) | −17.5132 | − | 20.5497i | −0.648636 | − | 0.761099i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.15648 | + | 15.8595i | 0.338665 | + | 0.586584i | ||||
\(732\) | −26.7127 | − | 3.87800i | −0.987328 | − | 0.143335i | ||||
\(733\) | −8.40163 | + | 14.5521i | −0.310321 | + | 0.537492i | −0.978432 | − | 0.206570i | \(-0.933770\pi\) |
0.668111 | + | 0.744062i | \(0.267103\pi\) | |||||||
\(734\) | 15.5158 | 0.572700 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −37.6414 | −1.38748 | ||||||||
\(737\) | −9.78057 | + | 16.9404i | −0.360272 | + | 0.624009i | ||||
\(738\) | −12.8270 | + | 12.1637i | −0.472170 | + | 0.447753i | ||||
\(739\) | 18.4120 | + | 31.8906i | 0.677297 | + | 1.17311i | 0.975792 | + | 0.218702i | \(0.0701823\pi\) |
−0.298494 | + | 0.954411i | \(0.596484\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 21.3895 | − | 27.1225i | 0.785763 | − | 0.996371i | ||||
\(742\) | 3.43305 | + | 0.137001i | 0.126031 | + | 0.00502945i | ||||
\(743\) | −45.3970 | −1.66545 | −0.832727 | − | 0.553684i | \(-0.813221\pi\) | ||||
−0.832727 | + | 0.553684i | \(0.813221\pi\) | |||||||
\(744\) | 0.744534 | + | 1.86716i | 0.0272959 | + | 0.0684532i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −9.62558 | + | 5.55733i | −0.352417 | + | 0.203468i | ||||
\(747\) | 7.28226 | − | 24.5524i | 0.266444 | − | 0.898326i | ||||
\(748\) | 28.3060 | 1.03497 | ||||||||
\(749\) | −7.71466 | + | 12.2103i | −0.281888 | + | 0.446156i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.49215 | + | 16.4409i | −0.346374 | + | 0.599937i | −0.985602 | − | 0.169080i | \(-0.945920\pi\) |
0.639229 | + | 0.769017i | \(0.279254\pi\) | |||||||
\(752\) | 0.360366 | − | 0.208057i | 0.0131412 | − | 0.00758707i | ||||
\(753\) | 6.60575 | − | 45.5020i | 0.240727 | − | 1.65819i | ||||
\(754\) | 9.01888 | + | 5.20705i | 0.328448 | + | 0.189630i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 16.3054 | − | 0.835742i | 0.593021 | − | 0.0303956i | ||||
\(757\) | − | 24.7352i | − | 0.899017i | −0.893276 | − | 0.449508i | \(-0.851599\pi\) | ||
0.893276 | − | 0.449508i | \(-0.148401\pi\) | |||||||
\(758\) | −1.61148 | + | 2.79116i | −0.0585315 | + | 0.101379i | ||||
\(759\) | −73.2787 | − | 10.6382i | −2.65985 | − | 0.386143i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.8401 | − | 41.2923i | 0.864204 | − | 1.49685i | −0.00363106 | − | 0.999993i | \(-0.501156\pi\) |
0.867835 | − | 0.496852i | \(-0.165511\pi\) | |||||||
\(762\) | −1.01814 | + | 1.29104i | −0.0368835 | + | 0.0467693i | ||||
\(763\) | 8.10457 | + | 15.4273i | 0.293405 | + | 0.558505i | ||||
\(764\) | − | 22.1986i | − | 0.803116i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.0554 | + | 10.4243i | −0.652368 | + | 0.376645i | ||||
\(767\) | 6.04333 | + | 10.4674i | 0.218212 | + | 0.377954i | ||||
\(768\) | 26.4871 | − | 10.5618i | 0.955772 | − | 0.381117i | ||||
\(769\) | 48.8811i | 1.76270i | 0.472467 | + | 0.881349i | \(0.343364\pi\) | ||||
−0.472467 | + | 0.881349i | \(0.656636\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.4417 | − | 20.8485i | 0.592133 | − | 0.750842i | ||||
\(772\) | 2.66950 | + | 1.54124i | 0.0960775 | + | 0.0554704i | ||||
\(773\) | −9.55974 | + | 5.51932i | −0.343840 | + | 0.198516i | −0.661969 | − | 0.749531i | \(-0.730279\pi\) |
0.318129 | + | 0.948047i | \(0.396946\pi\) | |||||||
\(774\) | 9.01586 | + | 9.50751i | 0.324068 | + | 0.341740i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 26.1611 | 0.939128 | ||||||||
\(777\) | −3.97995 | + | 4.65244i | −0.142780 | + | 0.166905i | ||||
\(778\) | − | 15.3169i | − | 0.549136i | ||||||
\(779\) | −29.9347 | − | 17.2828i | −1.07252 | − | 0.619221i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.98662 | − | 12.1012i | −0.250001 | − | 0.433015i | ||||
\(782\) | 19.9971 | + | 11.5453i | 0.715095 | + | 0.412860i | ||||
\(783\) | 14.4515 | + | 6.67161i | 0.516456 | + | 0.238424i | ||||
\(784\) | 0.851624 | − | 1.23586i | 0.0304152 | − | 0.0441379i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −15.1642 | + | 6.04677i | −0.540889 | + | 0.215681i | ||||
\(787\) | 8.48325 | + | 14.6934i | 0.302395 | + | 0.523764i | 0.976678 | − | 0.214709i | \(-0.0688804\pi\) |
−0.674283 | + | 0.738473i | \(0.735547\pi\) | |||||||
\(788\) | −4.65301 | − | 8.05925i | −0.165757 | − | 0.287099i | ||||
\(789\) | −35.3784 | + | 14.1072i | −1.25950 | + | 0.502231i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.566649 | + | 0.0226129i | 0.0201477 | + | 0.000804022i | ||||
\(792\) | 52.8616 | − | 12.6711i | 1.87836 | − | 0.450246i | ||||
\(793\) | −42.8645 | − | 24.7479i | −1.52216 | − | 0.878822i | ||||
\(794\) | 9.77475 | + | 16.9304i | 0.346893 | + | 0.600836i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.64492 | − | 2.10440i | −0.129191 | − | 0.0745884i | ||||
\(797\) | 11.9116i | 0.421930i | 0.977494 | + | 0.210965i | \(0.0676605\pi\) | ||||
−0.977494 | + | 0.210965i | \(0.932339\pi\) | |||||||
\(798\) | −7.27360 | − | 20.5919i | −0.257483 | − | 0.728946i | ||||
\(799\) | 7.33457 | 0.259478 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.57210 | + | 2.43909i | −0.0908808 | + | 0.0861812i | ||||
\(802\) | 0.383274 | − | 0.221283i | 0.0135339 | − | 0.00781378i | ||||
\(803\) | 13.7562 | + | 7.94217i | 0.485447 | + | 0.280273i | ||||
\(804\) | −3.95073 | + | 5.00965i | −0.139332 | + | 0.176677i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.37325i | 0.0483708i | ||||||||
\(807\) | −48.0712 | + | 19.1685i | −1.69218 | + | 0.674764i | ||||
\(808\) | −3.31098 | − | 5.73479i | −0.116480 | − | 0.201749i | ||||
\(809\) | 8.58544 | − | 4.95680i | 0.301848 | − | 0.174272i | −0.341425 | − | 0.939909i | \(-0.610909\pi\) |
0.643273 | + | 0.765637i | \(0.277576\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.3504i | 1.41689i | 0.705765 | + | 0.708446i | \(0.250604\pi\) | ||||
−0.705765 | + | 0.708446i | \(0.749396\pi\) | |||||||
\(812\) | −8.52082 | + | 4.47633i | −0.299022 | + | 0.157088i | ||||
\(813\) | −13.3026 | + | 16.8681i | −0.466543 | + | 0.591590i | ||||
\(814\) | −3.79732 | + | 6.57715i | −0.133096 | + | 0.230529i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.38894 | − | 0.201639i | −0.0486227 | − | 0.00705879i | ||||
\(817\) | −12.8102 | + | 22.1879i | −0.448171 | + | 0.776255i | ||||
\(818\) | − | 25.2768i | − | 0.883783i | ||||||
\(819\) | 28.3398 | + | 9.65077i | 0.990273 | + | 0.337225i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.2757 | + | 12.2835i | 0.742527 | + | 0.428698i | 0.822987 | − | 0.568060i | \(-0.192306\pi\) |
−0.0804605 | + | 0.996758i | \(0.525639\pi\) | |||||||
\(822\) | −1.63595 | + | 11.2688i | −0.0570603 | + | 0.393045i | ||||
\(823\) | 28.9152 | − | 16.6942i | 1.00792 | − | 0.581924i | 0.0973396 | − | 0.995251i | \(-0.468967\pi\) |
0.910583 | + | 0.413327i | \(0.135633\pi\) | |||||||
\(824\) | 11.1859 | − | 19.3746i | 0.389680 | − | 0.674946i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.63560 | + | 0.304709i | 0.265677 | + | 0.0106022i | ||||
\(827\) | 35.0677 | 1.21942 | 0.609712 | − | 0.792623i | \(-0.291285\pi\) | ||||
0.609712 | + | 0.792623i | \(0.291285\pi\) | |||||||
\(828\) | −23.1540 | − | 6.86750i | −0.804658 | − | 0.238662i | ||||
\(829\) | 20.7299 | − | 11.9684i | 0.719979 | − | 0.415680i | −0.0947660 | − | 0.995500i | \(-0.530210\pi\) |
0.814745 | + | 0.579820i | \(0.196877\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.17605 | + | 12.9806i | 0.179555 | + | 0.450291i | ||||
\(832\) | 20.4956 | 0.710555 | ||||||||
\(833\) | 23.8917 | − | 11.3597i | 0.827800 | − | 0.393590i | ||||
\(834\) | −10.4936 | + | 13.3061i | −0.363362 | + | 0.460754i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 19.8004 | + | 34.2954i | 0.684813 | + | 1.18613i | ||||
\(837\) | 0.190938 | + | 2.09021i | 0.00659980 | + | 0.0722484i | ||||
\(838\) | −1.55098 | + | 2.68638i | −0.0535778 | + | 0.0927994i | ||||
\(839\) | −44.6267 | −1.54068 | −0.770342 | − | 0.637631i | \(-0.779914\pi\) | ||||
−0.770342 | + | 0.637631i | \(0.779914\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.6164 | 0.676428 | ||||||||
\(842\) | −8.47088 | + | 14.6720i | −0.291926 | + | 0.505631i | ||||
\(843\) | −30.2934 | − | 4.39784i | −1.04336 | − | 0.151470i | ||||
\(844\) | 14.2358 | + | 24.6572i | 0.490018 | + | 0.848736i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.10320 | − | 1.22325i | 0.175452 | − | 0.0420562i | ||||
\(847\) | −40.6636 | + | 64.3601i | −1.39722 | + | 2.21144i | ||||
\(848\) | 0.308914 | 0.0106081 | ||||||||
\(849\) | 38.0877 | − | 15.1876i | 1.30717 | − | 0.521237i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.84323 | − | 4.52829i | 0.268863 | − | 0.155228i | ||||
\(852\) | −1.68806 | − | 4.23335i | −0.0578320 | − | 0.145032i | ||||
\(853\) | 1.24909 | 0.0427680 | 0.0213840 | − | 0.999771i | \(-0.493193\pi\) | ||||
0.0213840 | + | 0.999771i | \(0.493193\pi\) | |||||||
\(854\) | −27.7030 | + | 14.5535i | −0.947979 | + | 0.498011i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.84216 | + | 13.5830i | −0.268040 | + | 0.464258i | ||||
\(857\) | −7.97918 | + | 4.60678i | −0.272564 | + | 0.157365i | −0.630052 | − | 0.776553i | \(-0.716966\pi\) |
0.357488 | + | 0.933918i | \(0.383633\pi\) | |||||||
\(858\) | 36.7511 | + | 5.33534i | 1.25466 | + | 0.182145i | ||||
\(859\) | −0.860775 | − | 0.496969i | −0.0293693 | − | 0.0169564i | 0.485243 | − | 0.874379i | \(-0.338731\pi\) |
−0.514613 | + | 0.857423i | \(0.672064\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.48287 | − | 29.4525i | 0.186856 | − | 1.00374i | ||||
\(862\) | − | 6.19664i | − | 0.211058i | ||||||
\(863\) | −2.04843 | + | 3.54799i | −0.0697295 | + | 0.120775i | −0.898782 | − | 0.438395i | \(-0.855547\pi\) |
0.829053 | + | 0.559170i | \(0.188880\pi\) | |||||||
\(864\) | 28.7342 | − | 2.62483i | 0.977557 | − | 0.0892986i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6.88508 | − | 11.9253i | 0.233965 | − | 0.405239i | ||||
\(867\) | 3.69542 | + | 2.91430i | 0.125503 | + | 0.0989749i | ||||
\(868\) | −1.07299 | − | 0.677927i | −0.0364195 | − | 0.0230104i | ||||
\(869\) | − | 38.5919i | − | 1.30914i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.1315 | + | 5.84944i | −0.343294 | + | 0.198201i | ||||
\(872\) | 9.46197 | + | 16.3886i | 0.320423 | + | 0.554989i | ||||
\(873\) | 26.1890 | + | 7.76768i | 0.886364 | + | 0.262896i | ||||
\(874\) | 32.3045i | 1.09272i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.06801 | + | 3.20813i | 0.137445 | + | 0.108393i | ||||
\(877\) | −8.72731 | − | 5.03871i | −0.294700 | − | 0.170145i | 0.345359 | − | 0.938471i | \(-0.387757\pi\) |
−0.640060 | + | 0.768325i | \(0.721090\pi\) | |||||||
\(878\) | 30.0474 | − | 17.3479i | 1.01405 | − | 0.585463i | ||||
\(879\) | −4.64180 | − | 0.673872i | −0.156564 | − | 0.0227291i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.3645 | 1.02301 | 0.511503 | − | 0.859281i | \(-0.329089\pi\) | ||||
0.511503 | + | 0.859281i | \(0.329089\pi\) | |||||||
\(882\) | 14.7287 | − | 11.8884i | 0.495941 | − | 0.400304i | ||||
\(883\) | − | 16.1748i | − | 0.544326i | −0.962251 | − | 0.272163i | \(-0.912261\pi\) | ||
0.962251 | − | 0.272163i | \(-0.0877390\pi\) | |||||||
\(884\) | 14.6609 | + | 8.46445i | 0.493098 | + | 0.284690i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.73803 | − | 3.01036i | −0.0583903 | − | 0.101135i | ||||
\(887\) | −3.97469 | − | 2.29479i | −0.133457 | − | 0.0770514i | 0.431785 | − | 0.901977i | \(-0.357884\pi\) |
−0.565242 | + | 0.824925i | \(0.691217\pi\) | |||||||
\(888\) | −4.11703 | + | 5.22052i | −0.138159 | + | 0.175189i | ||||
\(889\) | 0.111110 | − | 2.78428i | 0.00372652 | − | 0.0933816i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 56.6803 | + | 3.01095i | 1.89886 | + | 0.100871i | ||||
\(892\) | 10.0577 | + | 17.4205i | 0.336758 | + | 0.583283i | ||||
\(893\) | 5.13064 | + | 8.88652i | 0.171690 | + | 0.297376i | ||||
\(894\) | −1.70034 | − | 4.26413i | −0.0568678 | − | 0.142614i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −8.77326 | + | 13.8858i | −0.293094 | + | 0.463893i | ||||
\(897\) | −34.7729 | − | 27.4228i | −1.16103 | − | 0.915620i | ||||
\(898\) | −1.96829 | − | 1.13639i | −0.0656827 | − | 0.0379220i | ||||
\(899\) | −0.618683 | − | 1.07159i | −0.0206342 | − | 0.0357395i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.71552 | + | 2.72251i | 0.157097 | + | 0.0906998i | ||||
\(902\) | − | 37.1619i | − | 1.23736i | ||||||
\(903\) | −21.8305 | − | 4.06395i | −0.726473 | − | 0.135240i | ||||
\(904\) | 0.615829 | 0.0204822 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.11830 | − | 7.70310i | 0.0371529 | − | 0.255918i | ||||
\(907\) | 27.1205 | − | 15.6580i | 0.900521 | − | 0.519916i | 0.0231520 | − | 0.999732i | \(-0.492630\pi\) |
0.877369 | + | 0.479816i | \(0.159297\pi\) | |||||||
\(908\) | −22.5211 | − | 13.0026i | −0.747389 | − | 0.431505i | ||||
\(909\) | −1.61176 | − | 6.72400i | −0.0534586 | − | 0.223021i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 2.78118i | − | 0.0921447i | −0.998938 | − | 0.0460724i | \(-0.985330\pi\) | ||
0.998938 | − | 0.0460724i | \(-0.0146705\pi\) | |||||||
\(912\) | −0.727279 | − | 1.82388i | −0.0240826 | − | 0.0603948i | ||||
\(913\) | 26.9187 | + | 46.6245i | 0.890878 | + | 1.54305i | ||||
\(914\) | −7.26289 | + | 4.19323i | −0.240235 | + | 0.138700i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.299327i | 0.00989003i | ||||||||
\(917\) | 14.7780 | − | 23.3898i | 0.488012 | − | 0.772400i | ||||
\(918\) | −16.0702 | − | 7.41887i | −0.530396 | − | 0.244859i | ||||
\(919\) | 29.0225 | − | 50.2685i | 0.957365 | − | 1.65821i | 0.228506 | − | 0.973543i | \(-0.426616\pi\) |
0.728860 | − | 0.684663i | \(-0.240051\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.36761 | − | 9.42046i | 0.0450644 | − | 0.310415i | ||||
\(922\) | −5.13301 | + | 8.89063i | −0.169047 | + | 0.292797i | ||||
\(923\) | − | 8.35695i | − | 0.275072i | ||||||
\(924\) | −22.3115 | + | 26.0815i | −0.733994 | + | 0.858018i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −0.251595 | − | 0.145259i | −0.00826793 | − | 0.00477349i | ||||
\(927\) | 16.9505 | − | 16.0740i | 0.556728 | − | 0.527939i | ||||
\(928\) | −14.7312 | + | 8.50504i | −0.483574 | + | 0.279191i | ||||
\(929\) | 20.7329 | − | 35.9104i | 0.680224 | − | 1.17818i | −0.294689 | − | 0.955593i | \(-0.595216\pi\) |
0.974912 | − | 0.222589i | \(-0.0714508\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30.4760 | + | 21.0008i | 0.998809 | + | 0.688274i | ||||
\(932\) | −17.7455 | −0.581274 | ||||||||
\(933\) | 35.1488 | − | 14.0157i | 1.15072 | − | 0.458853i | ||||
\(934\) | 18.1993 | − | 10.5074i | 0.595499 | − | 0.343812i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 31.1683 | + | 9.24454i | 1.01877 | + | 0.302167i | ||||
\(937\) | −15.3201 | −0.500486 | −0.250243 | − | 0.968183i | \(-0.580511\pi\) | ||||
−0.250243 | + | 0.968183i | \(0.580511\pi\) | |||||||
\(938\) | −0.294933 | + | 7.39063i | −0.00962990 | + | 0.241312i | ||||
\(939\) | −33.4442 | − | 26.3749i | −1.09141 | − | 0.860714i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.5592 | − | 44.2698i | −0.833206 | − | 1.44316i | −0.895483 | − | 0.445096i | \(-0.853170\pi\) |
0.0622769 | − | 0.998059i | \(-0.480164\pi\) | |||||||
\(942\) | −1.59227 | + | 10.9680i | −0.0518790 | + | 0.357356i | ||||
\(943\) | −22.1577 | + | 38.3783i | −0.721555 | + | 1.24977i | ||||
\(944\) | 0.687068 | 0.0223622 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −27.5447 | −0.895556 | ||||||||
\(947\) | 4.01829 | − | 6.95988i | 0.130577 | − | 0.226166i | −0.793322 | − | 0.608802i | \(-0.791650\pi\) |
0.923899 | + | 0.382636i | \(0.124984\pi\) | |||||||
\(948\) | 1.80837 | − | 12.4565i | 0.0587331 | − | 0.404568i | ||||
\(949\) | 4.74996 | + | 8.22716i | 0.154190 | + | 0.267065i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −32.5794 | − | 25.6929i | −1.05646 | − | 0.833149i | ||||
\(952\) | 25.4321 | − | 13.3605i | 0.824260 | − | 0.433017i | ||||
\(953\) | −43.7448 | −1.41703 | −0.708516 | − | 0.705695i | \(-0.750635\pi\) | ||||
−0.708516 | + | 0.705695i | \(0.750635\pi\) | |||||||
\(954\) | 3.73499 | + | 1.10780i | 0.120925 | + | 0.0358664i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −20.0578 | + | 11.5804i | −0.648714 | + | 0.374535i | ||||
\(957\) | −31.0817 | + | 12.3939i | −1.00473 | + | 0.400639i | ||||
\(958\) | 0.570645 | 0.0184367 | ||||||||
\(959\) | −8.97489 | − | 17.0840i | −0.289814 | − | 0.551670i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.4184 | + | 26.7055i | −0.497368 | + | 0.861467i | ||||
\(962\) | −3.93358 | + | 2.27105i | −0.126824 | + | 0.0732217i | ||||
\(963\) | −11.8836 | + | 11.2691i | −0.382943 | + | 0.363140i | ||||
\(964\) | 10.1439 | + | 5.85660i | 0.326714 | + | 0.188628i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −26.4002 | + | 9.32525i | −0.849413 | + | 0.300035i | ||||
\(967\) | 28.3067i | 0.910281i | 0.890420 | + | 0.455140i | \(0.150411\pi\) | ||||
−0.890420 | + | 0.455140i | \(0.849589\pi\) | |||||||
\(968\) | −41.3357 | + | 71.5954i | −1.32858 | + | 2.30116i | ||||
\(969\) | 4.97237 | − | 34.2509i | 0.159735 | − | 1.10030i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.4304 | − | 28.4583i | 0.527277 | − | 0.913270i | −0.472218 | − | 0.881482i | \(-0.656546\pi\) |
0.999495 | − | 0.0317882i | \(-0.0101202\pi\) | |||||||
\(972\) | 18.1539 | + | 3.62783i | 0.582287 | + | 0.116363i | ||||
\(973\) | 1.14516 | − | 28.6963i | 0.0367123 | − | 0.919961i | ||||
\(974\) | 19.5144i | 0.625282i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.43664 | + | 1.40680i | −0.0779950 | + | 0.0450304i | ||||
\(977\) | 25.5291 | + | 44.2178i | 0.816750 | + | 1.41465i | 0.908065 | + | 0.418830i | \(0.137560\pi\) |
−0.0913150 | + | 0.995822i | \(0.529107\pi\) | |||||||
\(978\) | 10.2261 | + | 25.6452i | 0.326995 | + | 0.820044i | ||||
\(979\) | − | 7.45178i | − | 0.238160i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.60601 | + | 19.2155i | 0.147059 | + | 0.613505i | ||||
\(982\) | −28.2263 | − | 16.2965i | −0.900737 | − | 0.520041i | ||||
\(983\) | 26.1076 | − | 15.0732i | 0.832704 | − | 0.480762i | −0.0220736 | − | 0.999756i | \(-0.507027\pi\) |
0.854778 | + | 0.518994i | \(0.173693\pi\) | |||||||
\(984\) | 4.67394 | − | 32.1952i | 0.149000 | − | 1.02635i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 10.4346 | 0.332306 | ||||||||
\(987\) | −5.78129 | + | 6.75816i | −0.184021 | + | 0.215115i | ||||
\(988\) | 23.6840i | 0.753489i | ||||||||
\(989\) | 28.4463 | + | 16.4235i | 0.904541 | + | 0.522237i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.9382 | − | 44.9263i | −0.823955 | − | 1.42713i | −0.902715 | − | 0.430238i | \(-0.858430\pi\) |
0.0787606 | − | 0.996894i | \(-0.474904\pi\) | |||||||
\(992\) | −1.94252 | − | 1.12151i | −0.0616751 | − | 0.0356081i | ||||
\(993\) | 36.8595 | + | 29.0683i | 1.16970 | + | 0.922456i | ||||
\(994\) | −4.46675 | − | 2.82215i | −0.141677 | − | 0.0895133i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.50390 | + | 16.3106i | 0.206084 | + | 0.516821i | ||||
\(997\) | −25.3390 | − | 43.8884i | −0.802494 | − | 1.38996i | −0.917970 | − | 0.396649i | \(-0.870173\pi\) |
0.115477 | − | 0.993310i | \(-0.463160\pi\) | |||||||
\(998\) | −4.06209 | − | 7.03574i | −0.128583 | − | 0.222713i | ||||
\(999\) | −5.67149 | + | 4.00368i | −0.179438 | + | 0.126671i |
(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 | 525.2.q.g.299.7 | 40 | ||
3.2 | odd | 2 | inner | 525.2.q.g.299.13 | 40 | ||
5.2 | odd | 4 | 525.2.t.h.26.4 | ✓ | 20 | ||
5.3 | odd | 4 | 525.2.t.i.26.7 | yes | 20 | ||
5.4 | even | 2 | inner | 525.2.q.g.299.14 | 40 | ||
7.3 | odd | 6 | inner | 525.2.q.g.374.8 | 40 | ||
15.2 | even | 4 | 525.2.t.h.26.7 | yes | 20 | ||
15.8 | even | 4 | 525.2.t.i.26.4 | yes | 20 | ||
15.14 | odd | 2 | inner | 525.2.q.g.299.8 | 40 | ||
21.17 | even | 6 | inner | 525.2.q.g.374.14 | 40 | ||
35.3 | even | 12 | 525.2.t.i.101.4 | yes | 20 | ||
35.17 | even | 12 | 525.2.t.h.101.7 | yes | 20 | ||
35.24 | odd | 6 | inner | 525.2.q.g.374.13 | 40 | ||
105.17 | odd | 12 | 525.2.t.h.101.4 | yes | 20 | ||
105.38 | odd | 12 | 525.2.t.i.101.7 | yes | 20 | ||
105.59 | even | 6 | inner | 525.2.q.g.374.7 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.q.g.299.7 | 40 | 1.1 | even | 1 | trivial | ||
525.2.q.g.299.8 | 40 | 15.14 | odd | 2 | inner | ||
525.2.q.g.299.13 | 40 | 3.2 | odd | 2 | inner | ||
525.2.q.g.299.14 | 40 | 5.4 | even | 2 | inner | ||
525.2.q.g.374.7 | 40 | 105.59 | even | 6 | inner | ||
525.2.q.g.374.8 | 40 | 7.3 | odd | 6 | inner | ||
525.2.q.g.374.13 | 40 | 35.24 | odd | 6 | inner | ||
525.2.q.g.374.14 | 40 | 21.17 | even | 6 | inner | ||
525.2.t.h.26.4 | ✓ | 20 | 5.2 | odd | 4 | ||
525.2.t.h.26.7 | yes | 20 | 15.2 | even | 4 | ||
525.2.t.h.101.4 | yes | 20 | 105.17 | odd | 12 | ||
525.2.t.h.101.7 | yes | 20 | 35.17 | even | 12 | ||
525.2.t.i.26.4 | yes | 20 | 15.8 | even | 4 | ||
525.2.t.i.26.7 | yes | 20 | 5.3 | odd | 4 | ||
525.2.t.i.101.4 | yes | 20 | 35.3 | even | 12 | ||
525.2.t.i.101.7 | yes | 20 | 105.38 | odd | 12 |