Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [425,2,Mod(49,425)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(425, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("425.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 425 = 5^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 425.n (of order \(8\), degree \(4\), 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: | \(3.39364208590\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 85) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 274.4 | ||
Character | \(\chi\) | \(=\) | 425.274 |
Dual form | 425.2.n.c.349.4 |
$q$-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 \(\left(\mathbb{Z}/425\mathbb{Z}\right)^\times\).
\(n\) | \(52\) | \(326\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{7}{8}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.09994 | − | 1.09994i | 0.777774 | − | 0.777774i | −0.201678 | − | 0.979452i | \(-0.564639\pi\) |
0.979452 | + | 0.201678i | \(0.0646394\pi\) | |||||||
\(3\) | −1.15110 | − | 2.77900i | −0.664588 | − | 1.60446i | −0.790533 | − | 0.612419i | \(-0.790196\pi\) |
0.125945 | − | 0.992037i | \(-0.459804\pi\) | |||||||
\(4\) | − | 0.419729i | − | 0.209865i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −4.32287 | − | 1.79059i | −1.76480 | − | 0.731006i | ||||
\(7\) | −3.19170 | − | 1.32205i | −1.20635 | − | 0.499687i | −0.313305 | − | 0.949653i | \(-0.601436\pi\) |
−0.893046 | + | 0.449966i | \(0.851436\pi\) | |||||||
\(8\) | 1.73820 | + | 1.73820i | 0.614547 | + | 0.614547i | ||||
\(9\) | −4.27649 | + | 4.27649i | −1.42550 | + | 1.42550i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.92026 | − | 1.62382i | −1.18200 | − | 0.489601i | −0.296860 | − | 0.954921i | \(-0.595939\pi\) |
−0.885143 | + | 0.465320i | \(0.845939\pi\) | |||||||
\(12\) | −1.16643 | + | 0.483150i | −0.336719 | + | 0.139473i | ||||
\(13\) | 0.127392 | 0.0353322 | 0.0176661 | − | 0.999844i | \(-0.494376\pi\) | ||||
0.0176661 | + | 0.999844i | \(0.494376\pi\) | |||||||
\(14\) | −4.96485 | + | 2.05651i | −1.32691 | + | 0.549625i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.66329 | 1.16582 | ||||||||
\(17\) | 0.193278 | − | 4.11857i | 0.0468767 | − | 0.998901i | ||||
\(18\) | 9.40776i | 2.21743i | ||||||||
\(19\) | −1.81966 | − | 1.81966i | −0.417458 | − | 0.417458i | 0.466869 | − | 0.884327i | \(-0.345382\pi\) |
−0.884327 | + | 0.466869i | \(0.845382\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 10.3916i | 2.26762i | ||||||||
\(22\) | −6.09815 | + | 2.52594i | −1.30013 | + | 0.538531i | ||||
\(23\) | 1.24457 | − | 3.00465i | 0.259510 | − | 0.626513i | −0.739396 | − | 0.673271i | \(-0.764889\pi\) |
0.998906 | + | 0.0467576i | \(0.0148888\pi\) | |||||||
\(24\) | 2.82962 | − | 6.83130i | 0.577593 | − | 1.39443i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.140123 | − | 0.140123i | 0.0274805 | − | 0.0274805i | ||||
\(27\) | 8.47004 | + | 3.50841i | 1.63006 | + | 0.675193i | ||||
\(28\) | −0.554901 | + | 1.33965i | −0.104866 | + | 0.253170i | ||||
\(29\) | 1.87644 | + | 4.53013i | 0.348446 | + | 0.841224i | 0.996804 | + | 0.0798877i | \(0.0254562\pi\) |
−0.648358 | + | 0.761336i | \(0.724544\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.95543 | − | 2.05261i | 0.890021 | − | 0.368659i | 0.109646 | − | 0.993971i | \(-0.465028\pi\) |
0.780375 | + | 0.625312i | \(0.215028\pi\) | |||||||
\(32\) | 1.65293 | − | 1.65293i | 0.292199 | − | 0.292199i | ||||
\(33\) | 12.7636i | 2.22185i | ||||||||
\(34\) | −4.31758 | − | 4.74277i | −0.740459 | − | 0.813378i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.79497 | + | 1.79497i | 0.299161 | + | 0.299161i | ||||
\(37\) | −0.677990 | − | 1.63681i | −0.111461 | − | 0.269090i | 0.858300 | − | 0.513149i | \(-0.171521\pi\) |
−0.969761 | + | 0.244059i | \(0.921521\pi\) | |||||||
\(38\) | −4.00302 | −0.649376 | ||||||||
\(39\) | −0.146641 | − | 0.354023i | −0.0234813 | − | 0.0566890i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.85069 | − | 9.29639i | 0.601377 | − | 1.45185i | −0.270787 | − | 0.962639i | \(-0.587284\pi\) |
0.872164 | − | 0.489214i | \(-0.162716\pi\) | |||||||
\(42\) | 11.4301 | + | 11.4301i | 1.76370 | + | 1.76370i | ||||
\(43\) | −1.79227 | − | 1.79227i | −0.273318 | − | 0.273318i | 0.557116 | − | 0.830434i | \(-0.311908\pi\) |
−0.830434 | + | 0.557116i | \(0.811908\pi\) | |||||||
\(44\) | −0.681566 | + | 1.64545i | −0.102750 | + | 0.248060i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.93598 | − | 4.67388i | −0.285445 | − | 0.689126i | ||||
\(47\) | −4.59479 | −0.670219 | −0.335109 | − | 0.942179i | \(-0.608773\pi\) | ||||
−0.335109 | + | 0.942179i | \(0.608773\pi\) | |||||||
\(48\) | −5.36791 | − | 12.9593i | −0.774791 | − | 1.87051i | ||||
\(49\) | 3.48941 | + | 3.48941i | 0.498487 | + | 0.498487i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.6680 | + | 4.20377i | −1.63385 | + | 0.588645i | ||||
\(52\) | − | 0.0534701i | − | 0.00741498i | ||||||
\(53\) | 1.15866 | − | 1.15866i | 0.159155 | − | 0.159155i | −0.623037 | − | 0.782192i | \(-0.714102\pi\) |
0.782192 | + | 0.623037i | \(0.214102\pi\) | |||||||
\(54\) | 13.1756 | − | 5.45749i | 1.79297 | − | 0.742671i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.24984 | − | 7.84580i | −0.434278 | − | 1.04844i | ||||
\(57\) | −2.96222 | + | 7.15144i | −0.392356 | + | 0.947231i | ||||
\(58\) | 7.04683 | + | 2.91889i | 0.925294 | + | 0.383269i | ||||
\(59\) | 4.34287 | − | 4.34287i | 0.565393 | − | 0.565393i | −0.365441 | − | 0.930834i | \(-0.619082\pi\) |
0.930834 | + | 0.365441i | \(0.119082\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.54679 | + | 3.73428i | −0.198046 | + | 0.478125i | −0.991437 | − | 0.130587i | \(-0.958314\pi\) |
0.793391 | + | 0.608713i | \(0.208314\pi\) | |||||||
\(62\) | 3.19293 | − | 7.70840i | 0.405502 | − | 0.978968i | ||||
\(63\) | 19.3030 | − | 7.99557i | 2.43195 | − | 1.00735i | ||||
\(64\) | 5.69034i | 0.711292i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 14.0392 | + | 14.0392i | 1.72810 | + | 1.72810i | ||||
\(67\) | − | 6.88856i | − | 0.841571i | −0.907160 | − | 0.420786i | \(-0.861754\pi\) | ||
0.907160 | − | 0.420786i | \(-0.138246\pi\) | |||||||
\(68\) | −1.72868 | − | 0.0811242i | −0.209634 | − | 0.00983776i | ||||
\(69\) | −9.78255 | −1.17768 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.66802 | + | 2.76198i | −0.791348 | + | 0.327787i | −0.741485 | − | 0.670969i | \(-0.765878\pi\) |
−0.0498626 | + | 0.998756i | \(0.515878\pi\) | |||||||
\(72\) | −14.8668 | −1.75207 | ||||||||
\(73\) | −13.5119 | + | 5.59682i | −1.58145 | + | 0.655058i | −0.988642 | − | 0.150287i | \(-0.951980\pi\) |
−0.592807 | + | 0.805345i | \(0.701980\pi\) | |||||||
\(74\) | −2.54614 | − | 1.05465i | −0.295983 | − | 0.122600i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.763763 | + | 0.763763i | −0.0876096 | + | 0.0876096i | ||||
\(77\) | 10.3655 | + | 10.3655i | 1.18126 | + | 1.18126i | ||||
\(78\) | −0.550699 | − | 0.228107i | −0.0623544 | − | 0.0258280i | ||||
\(79\) | 4.75854 | + | 1.97105i | 0.535378 | + | 0.221761i | 0.633957 | − | 0.773369i | \(-0.281430\pi\) |
−0.0985790 | + | 0.995129i | \(0.531430\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 9.43315i | − | 1.04813i | ||||||
\(82\) | −5.98994 | − | 14.4610i | −0.661478 | − | 1.59695i | ||||
\(83\) | 10.2150 | − | 10.2150i | 1.12124 | − | 1.12124i | 0.129685 | − | 0.991555i | \(-0.458603\pi\) |
0.991555 | − | 0.129685i | \(-0.0413967\pi\) | |||||||
\(84\) | 4.36164 | 0.475893 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.94276 | −0.425159 | ||||||||
\(87\) | 10.4293 | − | 10.4293i | 1.11813 | − | 1.11813i | ||||
\(88\) | −3.99166 | − | 9.63673i | −0.425513 | − | 1.02728i | ||||
\(89\) | 0.600876i | 0.0636927i | 0.999493 | + | 0.0318463i | \(0.0101387\pi\) | ||||
−0.999493 | + | 0.0318463i | \(0.989861\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.406598 | − | 0.168418i | −0.0426230 | − | 0.0176550i | ||||
\(92\) | −1.26114 | − | 0.522381i | −0.131483 | − | 0.0544620i | ||||
\(93\) | −11.4084 | − | 11.4084i | −1.18299 | − | 1.18299i | ||||
\(94\) | −5.05398 | + | 5.05398i | −0.521279 | + | 0.521279i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −6.49616 | − | 2.69080i | −0.663012 | − | 0.274628i | ||||
\(97\) | 7.09206 | − | 2.93763i | 0.720090 | − | 0.298271i | 0.00761730 | − | 0.999971i | \(-0.497575\pi\) |
0.712473 | + | 0.701700i | \(0.247575\pi\) | |||||||
\(98\) | 7.67628 | 0.775421 | ||||||||
\(99\) | 23.7092 | − | 9.82068i | 2.38287 | − | 0.987016i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.8485 | 1.67649 | 0.838243 | − | 0.545297i | \(-0.183583\pi\) | ||||
0.838243 | + | 0.545297i | \(0.183583\pi\) | |||||||
\(102\) | −8.21019 | + | 17.4580i | −0.812930 | + | 1.72860i | ||||
\(103\) | − | 4.32255i | − | 0.425914i | −0.977062 | − | 0.212957i | \(-0.931691\pi\) | ||
0.977062 | − | 0.212957i | \(-0.0683093\pi\) | |||||||
\(104\) | 0.221433 | + | 0.221433i | 0.0217133 | + | 0.0217133i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 2.54891i | − | 0.247572i | ||||||
\(107\) | −4.36120 | + | 1.80647i | −0.421613 | + | 0.174638i | −0.583395 | − | 0.812189i | \(-0.698276\pi\) |
0.161782 | + | 0.986827i | \(0.448276\pi\) | |||||||
\(108\) | 1.47258 | − | 3.55512i | 0.141699 | − | 0.342092i | ||||
\(109\) | 5.86580 | − | 14.1613i | 0.561842 | − | 1.35641i | −0.346450 | − | 0.938068i | \(-0.612613\pi\) |
0.908292 | − | 0.418338i | \(-0.137387\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.76827 | + | 3.76827i | −0.357668 | + | 0.357668i | ||||
\(112\) | −14.8838 | − | 6.16508i | −1.40639 | − | 0.582545i | ||||
\(113\) | −2.82099 | + | 6.81048i | −0.265377 | + | 0.640676i | −0.999255 | − | 0.0386052i | \(-0.987709\pi\) |
0.733878 | + | 0.679282i | \(0.237709\pi\) | |||||||
\(114\) | 4.60788 | + | 11.1244i | 0.431567 | + | 1.04190i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.90143 | − | 0.787596i | 0.176543 | − | 0.0731265i | ||||
\(117\) | −0.544791 | + | 0.544791i | −0.0503660 | + | 0.0503660i | ||||
\(118\) | − | 9.55378i | − | 0.879496i | ||||||
\(119\) | −6.06183 | + | 12.8897i | −0.555687 | + | 1.18160i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.95345 | + | 4.95345i | 0.450313 | + | 0.450313i | ||||
\(122\) | 2.40610 | + | 5.80885i | 0.217838 | + | 0.525909i | ||||
\(123\) | −30.2672 | −2.72910 | ||||||||
\(124\) | −0.861538 | − | 2.07994i | −0.0773684 | − | 0.186784i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 12.4375 | − | 30.0268i | 1.10802 | − | 2.67500i | ||||
\(127\) | −5.67103 | − | 5.67103i | −0.503223 | − | 0.503223i | 0.409215 | − | 0.912438i | \(-0.365803\pi\) |
−0.912438 | + | 0.409215i | \(0.865803\pi\) | |||||||
\(128\) | 9.56487 | + | 9.56487i | 0.845423 | + | 0.845423i | ||||
\(129\) | −2.91763 | + | 7.04378i | −0.256883 | + | 0.620170i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.43762 | + | 13.1276i | 0.475087 | + | 1.14696i | 0.961887 | + | 0.273448i | \(0.0881643\pi\) |
−0.486799 | + | 0.873514i | \(0.661836\pi\) | |||||||
\(132\) | 5.35725 | 0.466288 | ||||||||
\(133\) | 3.40213 | + | 8.21348i | 0.295002 | + | 0.712199i | ||||
\(134\) | −7.57699 | − | 7.57699i | −0.654552 | − | 0.654552i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.49486 | − | 6.82295i | 0.642679 | − | 0.585063i | ||||
\(137\) | 8.53083i | 0.728838i | 0.931235 | + | 0.364419i | \(0.118732\pi\) | ||||
−0.931235 | + | 0.364419i | \(0.881268\pi\) | |||||||
\(138\) | −10.7602 | + | 10.7602i | −0.915969 | + | 0.915969i | ||||
\(139\) | −6.31676 | + | 2.61649i | −0.535781 | + | 0.221928i | −0.634133 | − | 0.773224i | \(-0.718643\pi\) |
0.0983522 | + | 0.995152i | \(0.468643\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.28906 | + | 12.7689i | 0.445419 | + | 1.07534i | ||||
\(142\) | −4.29640 | + | 10.3724i | −0.360546 | + | 0.870434i | ||||
\(143\) | −0.499410 | − | 0.206862i | −0.0417627 | − | 0.0172987i | ||||
\(144\) | −19.9425 | + | 19.9425i | −1.66188 | + | 1.66188i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.70612 | + | 21.0184i | −0.720523 | + | 1.73950i | ||||
\(147\) | 5.68042 | − | 13.7137i | 0.468513 | − | 1.13109i | ||||
\(148\) | −0.687018 | + | 0.284572i | −0.0564725 | + | 0.0233917i | ||||
\(149\) | 7.04072i | 0.576798i | 0.957510 | + | 0.288399i | \(0.0931229\pi\) | ||||
−0.957510 | + | 0.288399i | \(0.906877\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.49500 | + | 4.49500i | 0.365798 | + | 0.365798i | 0.865942 | − | 0.500144i | \(-0.166720\pi\) |
−0.500144 | + | 0.865942i | \(0.666720\pi\) | |||||||
\(152\) | − | 6.32586i | − | 0.513095i | ||||||
\(153\) | 16.7865 | + | 18.4396i | 1.35711 | + | 1.49075i | ||||
\(154\) | 22.8029 | 1.83751 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.148594 | + | 0.0615495i | −0.0118970 | + | 0.00492790i | ||||
\(157\) | 16.7739 | 1.33870 | 0.669351 | − | 0.742947i | \(-0.266572\pi\) | ||||
0.669351 | + | 0.742947i | \(0.266572\pi\) | |||||||
\(158\) | 7.40214 | − | 3.06607i | 0.588882 | − | 0.243923i | ||||
\(159\) | −4.55366 | − | 1.88619i | −0.361129 | − | 0.149584i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.94458 | + | 7.94458i | −0.626121 | + | 0.626121i | ||||
\(162\) | −10.3759 | − | 10.3759i | −0.815206 | − | 0.815206i | ||||
\(163\) | 4.24468 | + | 1.75820i | 0.332469 | + | 0.137713i | 0.542672 | − | 0.839945i | \(-0.317413\pi\) |
−0.210203 | + | 0.977658i | \(0.567413\pi\) | |||||||
\(164\) | −3.90197 | − | 1.61625i | −0.304692 | − | 0.126208i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 22.4717i | − | 1.74414i | ||||||
\(167\) | 8.04650 | + | 19.4260i | 0.622657 | + | 1.50323i | 0.848572 | + | 0.529079i | \(0.177463\pi\) |
−0.225916 | + | 0.974147i | \(0.572537\pi\) | |||||||
\(168\) | −18.0626 | + | 18.0626i | −1.39356 | + | 1.39356i | ||||
\(169\) | −12.9838 | −0.998752 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 15.5635 | 1.19017 | ||||||||
\(172\) | −0.752266 | + | 0.752266i | −0.0573597 | + | 0.0573597i | ||||
\(173\) | 4.80360 | + | 11.5969i | 0.365211 | + | 0.881698i | 0.994520 | + | 0.104543i | \(0.0333379\pi\) |
−0.629309 | + | 0.777155i | \(0.716662\pi\) | |||||||
\(174\) | − | 22.9431i | − | 1.73931i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −18.2813 | − | 7.57236i | −1.37800 | − | 0.570788i | ||||
\(177\) | −17.0679 | − | 7.06976i | −1.28290 | − | 0.531396i | ||||
\(178\) | 0.660926 | + | 0.660926i | 0.0495385 | + | 0.0495385i | ||||
\(179\) | 8.59390 | − | 8.59390i | 0.642338 | − | 0.642338i | −0.308791 | − | 0.951130i | \(-0.599925\pi\) |
0.951130 | + | 0.308791i | \(0.0999245\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.1007 | − | 5.84068i | −1.04809 | − | 0.434135i | −0.208883 | − | 0.977941i | \(-0.566983\pi\) |
−0.839211 | + | 0.543806i | \(0.816983\pi\) | |||||||
\(182\) | −0.632482 | + | 0.261983i | −0.0468827 | + | 0.0194194i | ||||
\(183\) | 12.1581 | 0.898750 | ||||||||
\(184\) | 7.38600 | − | 3.05938i | 0.544503 | − | 0.225540i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −25.0970 | −1.84020 | ||||||||
\(187\) | −7.44554 | + | 15.8320i | −0.544472 | + | 1.15775i | ||||
\(188\) | 1.92857i | 0.140655i | ||||||||
\(189\) | −22.3956 | − | 22.3956i | −1.62904 | − | 1.62904i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.89972i | 0.643961i | 0.946746 | + | 0.321981i | \(0.104349\pi\) | ||||
−0.946746 | + | 0.321981i | \(0.895651\pi\) | |||||||
\(192\) | 15.8135 | − | 6.55015i | 1.14124 | − | 0.472716i | ||||
\(193\) | 7.03519 | − | 16.9844i | 0.506404 | − | 1.22257i | −0.439536 | − | 0.898225i | \(-0.644857\pi\) |
0.945940 | − | 0.324342i | \(-0.105143\pi\) | |||||||
\(194\) | 4.56962 | − | 11.0320i | 0.328080 | − | 0.792054i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.46461 | − | 1.46461i | 0.104615 | − | 0.104615i | ||||
\(197\) | 9.87591 | + | 4.09074i | 0.703629 | + | 0.291453i | 0.705666 | − | 0.708545i | \(-0.250648\pi\) |
−0.00203619 | + | 0.999998i | \(0.500648\pi\) | |||||||
\(198\) | 15.2765 | − | 36.8808i | 1.08566 | − | 2.62101i | ||||
\(199\) | −5.93889 | − | 14.3377i | −0.420996 | − | 1.01638i | −0.982054 | − | 0.188599i | \(-0.939605\pi\) |
0.561058 | − | 0.827777i | \(-0.310395\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19.1433 | + | 7.92942i | −1.35026 | + | 0.559298i | ||||
\(202\) | 18.5323 | − | 18.5323i | 1.30393 | − | 1.30393i | ||||
\(203\) | − | 16.9396i | − | 1.18892i | ||||||
\(204\) | 1.76444 | + | 4.89740i | 0.123536 | + | 0.342886i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.75454 | − | 4.75454i | −0.331264 | − | 0.331264i | ||||
\(207\) | 7.52699 | + | 18.1718i | 0.523162 | + | 1.26302i | ||||
\(208\) | 0.594066 | 0.0411910 | ||||||||
\(209\) | 4.17872 | + | 10.0883i | 0.289048 | + | 0.697824i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.34996 | − | 8.08752i | 0.230621 | − | 0.556768i | −0.765630 | − | 0.643281i | \(-0.777573\pi\) |
0.996251 | + | 0.0865134i | \(0.0275726\pi\) | |||||||
\(212\) | −0.486324 | − | 0.486324i | −0.0334009 | − | 0.0334009i | ||||
\(213\) | 15.3511 | + | 15.3511i | 1.05184 | + | 1.05184i | ||||
\(214\) | −2.81005 | + | 6.78406i | −0.192091 | + | 0.463748i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 8.62432 | + | 20.8209i | 0.586810 | + | 1.41669i | ||||
\(217\) | −18.5299 | −1.25789 | ||||||||
\(218\) | −9.12453 | − | 22.0286i | −0.617991 | − | 1.49196i | ||||
\(219\) | 31.1071 | + | 31.1071i | 2.10202 | + | 2.10202i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.0246220 | − | 0.524674i | 0.00165626 | − | 0.0352934i | ||||
\(222\) | 8.28973i | 0.556370i | ||||||||
\(223\) | −14.9621 | + | 14.9621i | −1.00193 | + | 1.00193i | −0.00193640 | + | 0.999998i | \(0.500616\pi\) |
−0.999998 | + | 0.00193640i | \(0.999384\pi\) | |||||||
\(224\) | −7.46089 | + | 3.09040i | −0.498502 | + | 0.206486i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.38819 | + | 10.5940i | 0.291898 | + | 0.704705i | ||||
\(227\) | 9.80944 | − | 23.6821i | 0.651075 | − | 1.57183i | −0.160145 | − | 0.987094i | \(-0.551196\pi\) |
0.811220 | − | 0.584741i | \(-0.198804\pi\) | |||||||
\(228\) | 3.00166 | + | 1.24333i | 0.198790 | + | 0.0823416i | ||||
\(229\) | 5.02072 | − | 5.02072i | 0.331779 | − | 0.331779i | −0.521483 | − | 0.853262i | \(-0.674621\pi\) |
0.853262 | + | 0.521483i | \(0.174621\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 16.8741 | − | 40.7376i | 1.11023 | − | 2.68033i | ||||
\(232\) | −4.61264 | + | 11.1359i | −0.302835 | + | 0.731108i | ||||
\(233\) | −21.9091 | + | 9.07503i | −1.43531 | + | 0.594525i | −0.958657 | − | 0.284566i | \(-0.908151\pi\) |
−0.476654 | + | 0.879091i | \(0.658151\pi\) | |||||||
\(234\) | 1.19847i | 0.0783467i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.82283 | − | 1.82283i | −0.118656 | − | 0.118656i | ||||
\(237\) | − | 15.4929i | − | 1.00637i | ||||||
\(238\) | 7.51028 | + | 20.8456i | 0.486819 | + | 1.35122i | ||||
\(239\) | −0.109315 | −0.00707103 | −0.00353551 | − | 0.999994i | \(-0.501125\pi\) | ||||
−0.00353551 | + | 0.999994i | \(0.501125\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.1558 | − | 6.69194i | 1.04069 | − | 0.431066i | 0.204127 | − | 0.978944i | \(-0.434564\pi\) |
0.836558 | + | 0.547878i | \(0.184564\pi\) | |||||||
\(242\) | 10.8970 | 0.700484 | ||||||||
\(243\) | −0.804604 | + | 0.333278i | −0.0516154 | + | 0.0213798i | ||||
\(244\) | 1.56739 | + | 0.649232i | 0.100342 | + | 0.0415628i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −33.2921 | + | 33.2921i | −2.12262 | + | 2.12262i | ||||
\(247\) | −0.231810 | − | 0.231810i | −0.0147497 | − | 0.0147497i | ||||
\(248\) | 12.1814 | + | 5.04569i | 0.773518 | + | 0.320401i | ||||
\(249\) | −40.1459 | − | 16.6290i | −2.54414 | − | 1.05382i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.28782i | 0.207525i | 0.994602 | + | 0.103763i | \(0.0330882\pi\) | ||||
−0.994602 | + | 0.103763i | \(0.966912\pi\) | |||||||
\(252\) | −3.35597 | − | 8.10204i | −0.211406 | − | 0.510380i | ||||
\(253\) | −9.75805 | + | 9.75805i | −0.613484 | + | 0.613484i | ||||
\(254\) | −12.4756 | −0.782787 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 9.66087 | 0.603804 | ||||||||
\(257\) | −15.1307 | + | 15.1307i | −0.943829 | + | 0.943829i | −0.998504 | − | 0.0546752i | \(-0.982588\pi\) |
0.0546752 | + | 0.998504i | \(0.482588\pi\) | |||||||
\(258\) | 4.53851 | + | 10.9569i | 0.282555 | + | 0.682149i | ||||
\(259\) | 6.12055i | 0.380313i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −27.3976 | − | 11.3485i | −1.69587 | − | 0.702453i | ||||
\(262\) | 20.4206 | + | 8.45848i | 1.26159 | + | 0.522567i | ||||
\(263\) | −7.16800 | − | 7.16800i | −0.441998 | − | 0.441998i | 0.450685 | − | 0.892683i | \(-0.351180\pi\) |
−0.892683 | + | 0.450685i | \(0.851180\pi\) | |||||||
\(264\) | −22.1857 | + | 22.1857i | −1.36543 | + | 1.36543i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 12.7765 | + | 5.29218i | 0.783375 | + | 0.324484i | ||||
\(267\) | 1.66983 | − | 0.691668i | 0.102192 | − | 0.0423294i | ||||
\(268\) | −2.89133 | −0.176616 | ||||||||
\(269\) | 13.9299 | − | 5.76996i | 0.849321 | − | 0.351800i | 0.0847993 | − | 0.996398i | \(-0.472975\pi\) |
0.764522 | + | 0.644598i | \(0.222975\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.80304 | −0.413255 | −0.206628 | − | 0.978420i | \(-0.566249\pi\) | ||||
−0.206628 | + | 0.978420i | \(0.566249\pi\) | |||||||
\(272\) | 0.901309 | − | 19.2061i | 0.0546499 | − | 1.16454i | ||||
\(273\) | 1.32380i | 0.0801201i | ||||||||
\(274\) | 9.38338 | + | 9.38338i | 0.566871 | + | 0.566871i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.10602i | 0.247153i | ||||||||
\(277\) | −16.0032 | + | 6.62876i | −0.961542 | + | 0.398284i | −0.807557 | − | 0.589790i | \(-0.799211\pi\) |
−0.153985 | + | 0.988073i | \(0.549211\pi\) | |||||||
\(278\) | −4.07007 | + | 9.82602i | −0.244107 | + | 0.589326i | ||||
\(279\) | −12.4139 | + | 29.9698i | −0.743200 | + | 1.79424i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.7436 | − | 12.7436i | 0.760218 | − | 0.760218i | −0.216143 | − | 0.976362i | \(-0.569348\pi\) |
0.976362 | + | 0.216143i | \(0.0693479\pi\) | |||||||
\(282\) | 19.8627 | + | 8.22738i | 1.18280 | + | 0.489934i | ||||
\(283\) | −7.23322 | + | 17.4625i | −0.429970 | + | 1.03804i | 0.549326 | + | 0.835608i | \(0.314885\pi\) |
−0.979296 | + | 0.202432i | \(0.935115\pi\) | |||||||
\(284\) | 1.15928 | + | 2.79876i | 0.0687909 | + | 0.166076i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.776856 | + | 0.321784i | −0.0459365 | + | 0.0190275i | ||||
\(287\) | −24.5805 | + | 24.5805i | −1.45094 | + | 1.45094i | ||||
\(288\) | 14.1374i | 0.833057i | ||||||||
\(289\) | −16.9253 | − | 1.59206i | −0.995605 | − | 0.0936504i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.3273 | − | 16.3273i | −0.957126 | − | 0.957126i | ||||
\(292\) | 2.34915 | + | 5.67134i | 0.137473 | + | 0.331890i | ||||
\(293\) | 7.53184 | 0.440015 | 0.220007 | − | 0.975498i | \(-0.429392\pi\) | ||||
0.220007 | + | 0.975498i | \(0.429392\pi\) | |||||||
\(294\) | −8.83616 | − | 21.3324i | −0.515335 | − | 1.24413i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.66663 | − | 4.02359i | 0.0968707 | − | 0.233866i | ||||
\(297\) | −27.5077 | − | 27.5077i | −1.59616 | − | 1.59616i | ||||
\(298\) | 7.74435 | + | 7.74435i | 0.448618 | + | 0.448618i | ||||
\(299\) | 0.158548 | − | 0.382769i | 0.00916907 | − | 0.0221361i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.35092 | + | 8.08984i | 0.193144 | + | 0.466290i | ||||
\(302\) | 9.88844 | 0.569016 | ||||||||
\(303\) | −19.3943 | − | 46.8219i | −1.11417 | − | 2.68985i | ||||
\(304\) | −8.48558 | − | 8.48558i | −0.486681 | − | 0.486681i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 38.7465 | + | 1.81831i | 2.21499 | + | 0.103946i | ||||
\(307\) | − | 7.77074i | − | 0.443499i | −0.975104 | − | 0.221750i | \(-0.928823\pi\) | ||
0.975104 | − | 0.221750i | \(-0.0711768\pi\) | |||||||
\(308\) | 4.35071 | − | 4.35071i | 0.247905 | − | 0.247905i | ||||
\(309\) | −12.0124 | + | 4.97569i | −0.683360 | + | 0.283057i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.30824 | + | 7.98679i | 0.187593 | + | 0.452889i | 0.989495 | − | 0.144566i | \(-0.0461786\pi\) |
−0.801902 | + | 0.597455i | \(0.796179\pi\) | |||||||
\(312\) | 0.360471 | − | 0.870254i | 0.0204076 | − | 0.0492684i | ||||
\(313\) | 11.3988 | + | 4.72153i | 0.644298 | + | 0.266877i | 0.680814 | − | 0.732456i | \(-0.261626\pi\) |
−0.0365165 | + | 0.999333i | \(0.511626\pi\) | |||||||
\(314\) | 18.4502 | − | 18.4502i | 1.04121 | − | 1.04121i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.827308 | − | 1.99730i | 0.0465397 | − | 0.112357i | ||||
\(317\) | 3.12750 | − | 7.55046i | 0.175658 | − | 0.424076i | −0.811389 | − | 0.584506i | \(-0.801288\pi\) |
0.987047 | + | 0.160430i | \(0.0512882\pi\) | |||||||
\(318\) | −7.08343 | + | 2.93405i | −0.397219 | + | 0.164534i | ||||
\(319\) | − | 20.8063i | − | 1.16493i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.0404 | + | 10.0404i | 0.560398 | + | 0.560398i | ||||
\(322\) | 17.4771i | 0.973960i | ||||||||
\(323\) | −7.84609 | + | 7.14269i | −0.436568 | + | 0.397430i | ||||
\(324\) | −3.95937 | −0.219965 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.60280 | − | 2.73497i | 0.365695 | − | 0.151476i | ||||
\(327\) | −46.1064 | −2.54969 | ||||||||
\(328\) | 22.8523 | − | 9.46572i | 1.26181 | − | 0.522657i | ||||
\(329\) | 14.6652 | + | 6.07452i | 0.808519 | + | 0.334899i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.5933 | − | 16.5933i | 0.912049 | − | 0.912049i | −0.0843846 | − | 0.996433i | \(-0.526892\pi\) |
0.996433 | + | 0.0843846i | \(0.0268924\pi\) | |||||||
\(332\) | −4.28753 | − | 4.28753i | −0.235309 | − | 0.235309i | ||||
\(333\) | 9.89923 | + | 4.10040i | 0.542475 | + | 0.224700i | ||||
\(334\) | 30.2180 | + | 12.5167i | 1.65346 | + | 0.684884i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 48.4588i | 2.64364i | ||||||||
\(337\) | −9.07655 | − | 21.9127i | −0.494431 | − | 1.19366i | −0.952443 | − | 0.304716i | \(-0.901438\pi\) |
0.458012 | − | 0.888946i | \(-0.348562\pi\) | |||||||
\(338\) | −14.2813 | + | 14.2813i | −0.776803 | + | 0.776803i | ||||
\(339\) | 22.1736 | 1.20430 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −22.7596 | −1.23250 | ||||||||
\(342\) | 17.1189 | − | 17.1189i | 0.925684 | − | 0.925684i | ||||
\(343\) | 2.73032 | + | 6.59159i | 0.147424 | + | 0.355912i | ||||
\(344\) | − | 6.23063i | − | 0.335933i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.0396 | + | 7.47223i | 0.969813 | + | 0.401710i | ||||
\(347\) | 6.48456 | + | 2.68599i | 0.348109 | + | 0.144192i | 0.549885 | − | 0.835240i | \(-0.314671\pi\) |
−0.201776 | + | 0.979432i | \(0.564671\pi\) | |||||||
\(348\) | −4.37746 | − | 4.37746i | −0.234657 | − | 0.234657i | ||||
\(349\) | 20.7773 | − | 20.7773i | 1.11219 | − | 1.11219i | 0.119331 | − | 0.992855i | \(-0.461925\pi\) |
0.992855 | − | 0.119331i | \(-0.0380750\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.07902 | + | 0.446943i | 0.0575936 | + | 0.0238561i | ||||
\(352\) | −9.16396 | + | 3.79583i | −0.488440 | + | 0.202319i | ||||
\(353\) | −9.09110 | −0.483870 | −0.241935 | − | 0.970292i | \(-0.577782\pi\) | ||||
−0.241935 | + | 0.970292i | \(0.577782\pi\) | |||||||
\(354\) | −26.5499 | + | 10.9973i | −1.41111 | + | 0.584502i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.252205 | 0.0133668 | ||||||||
\(357\) | 42.7984 | + | 2.00845i | 2.26513 | + | 0.106299i | ||||
\(358\) | − | 18.9055i | − | 0.999188i | ||||||
\(359\) | −3.70529 | − | 3.70529i | −0.195558 | − | 0.195558i | 0.602535 | − | 0.798093i | \(-0.294157\pi\) |
−0.798093 | + | 0.602535i | \(0.794157\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 12.3777i | − | 0.651458i | ||||||
\(362\) | −21.9342 | + | 9.08546i | −1.15284 | + | 0.477521i | ||||
\(363\) | 8.06372 | − | 19.4675i | 0.423235 | − | 1.02178i | ||||
\(364\) | −0.0706900 | + | 0.170661i | −0.00370516 | + | 0.00894506i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 13.3731 | − | 13.3731i | 0.699025 | − | 0.699025i | ||||
\(367\) | −16.8448 | − | 6.97736i | −0.879293 | − | 0.364215i | −0.103071 | − | 0.994674i | \(-0.532867\pi\) |
−0.776223 | + | 0.630459i | \(0.782867\pi\) | |||||||
\(368\) | 5.80377 | − | 14.0115i | 0.302543 | − | 0.730402i | ||||
\(369\) | 23.2885 | + | 56.2234i | 1.21235 | + | 2.92687i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.22991 | + | 2.16630i | −0.271524 | + | 0.112469i | ||||
\(372\) | −4.78843 | + | 4.78843i | −0.248268 | + | 0.248268i | ||||
\(373\) | − | 18.5489i | − | 0.960428i | −0.877151 | − | 0.480214i | \(-0.840559\pi\) | ||
0.877151 | − | 0.480214i | \(-0.159441\pi\) | |||||||
\(374\) | 9.22462 | + | 25.6039i | 0.476994 | + | 1.32395i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.98666 | − | 7.98666i | −0.411881 | − | 0.411881i | ||||
\(377\) | 0.239044 | + | 0.577102i | 0.0123114 | + | 0.0297223i | ||||
\(378\) | −49.2675 | −2.53405 | ||||||||
\(379\) | 7.67735 | + | 18.5348i | 0.394359 | + | 0.952067i | 0.988978 | + | 0.148060i | \(0.0473028\pi\) |
−0.594619 | + | 0.804007i | \(0.702697\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.23188 | + | 22.2877i | −0.472963 | + | 1.14183i | ||||
\(382\) | 9.78914 | + | 9.78914i | 0.500856 | + | 0.500856i | ||||
\(383\) | 7.72751 | + | 7.72751i | 0.394857 | + | 0.394857i | 0.876415 | − | 0.481557i | \(-0.159929\pi\) |
−0.481557 | + | 0.876415i | \(0.659929\pi\) | |||||||
\(384\) | 15.5707 | − | 37.5909i | 0.794587 | − | 1.91830i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10.9436 | − | 26.4201i | −0.557013 | − | 1.34475i | ||||
\(387\) | 15.3292 | 0.779228 | ||||||||
\(388\) | −1.23301 | − | 2.97674i | −0.0625965 | − | 0.151121i | ||||
\(389\) | −16.7947 | − | 16.7947i | −0.851526 | − | 0.851526i | 0.138795 | − | 0.990321i | \(-0.455677\pi\) |
−0.990321 | + | 0.138795i | \(0.955677\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.1343 | − | 5.70657i | −0.613659 | − | 0.288594i | ||||
\(392\) | 12.1306i | 0.612688i | ||||||||
\(393\) | 30.2223 | − | 30.2223i | 1.52451 | − | 1.52451i | ||||
\(394\) | 15.3624 | − | 6.36333i | 0.773949 | − | 0.320580i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −4.12203 | − | 9.95145i | −0.207140 | − | 0.500079i | ||||
\(397\) | 10.8631 | − | 26.2259i | 0.545205 | − | 1.31624i | −0.375804 | − | 0.926699i | \(-0.622633\pi\) |
0.921009 | − | 0.389542i | \(-0.127367\pi\) | |||||||
\(398\) | −22.3030 | − | 9.23822i | −1.11795 | − | 0.463070i | ||||
\(399\) | 18.9091 | − | 18.9091i | 0.946637 | − | 0.946637i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.33935 | + | 8.06191i | −0.166759 | + | 0.402592i | −0.985063 | − | 0.172193i | \(-0.944915\pi\) |
0.818304 | + | 0.574786i | \(0.194915\pi\) | |||||||
\(402\) | −12.3346 | + | 29.7783i | −0.615193 | + | 1.48521i | ||||
\(403\) | 0.631282 | − | 0.261486i | 0.0314464 | − | 0.0130255i | ||||
\(404\) | − | 7.07179i | − | 0.351835i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −18.6325 | − | 18.6325i | −0.924714 | − | 0.924714i | ||||
\(407\) | 7.51766i | 0.372637i | ||||||||
\(408\) | −27.5883 | − | 12.9743i | −1.36583 | − | 0.642325i | ||||
\(409\) | −10.5572 | −0.522020 | −0.261010 | − | 0.965336i | \(-0.584056\pi\) | ||||
−0.261010 | + | 0.965336i | \(0.584056\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 23.7072 | − | 9.81983i | 1.16939 | − | 0.484376i | ||||
\(412\) | −1.81430 | −0.0893841 | ||||||||
\(413\) | −19.6026 | + | 8.11967i | −0.964582 | + | 0.399543i | ||||
\(414\) | 28.2670 | + | 11.7086i | 1.38925 | + | 0.575446i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.210570 | − | 0.210570i | 0.0103240 | − | 0.0103240i | ||||
\(417\) | 14.5424 | + | 14.5424i | 0.712147 | + | 0.712147i | ||||
\(418\) | 15.6929 | + | 6.50020i | 0.767564 | + | 0.317935i | ||||
\(419\) | −13.2011 | − | 5.46806i | −0.644915 | − | 0.267132i | 0.0361604 | − | 0.999346i | \(-0.488487\pi\) |
−0.681075 | + | 0.732214i | \(0.738487\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 18.2694i | − | 0.890398i | −0.895432 | − | 0.445199i | \(-0.853133\pi\) | ||
0.895432 | − | 0.445199i | \(-0.146867\pi\) | |||||||
\(422\) | −5.21102 | − | 12.5805i | −0.253669 | − | 0.612410i | ||||
\(423\) | 19.6496 | − | 19.6496i | 0.955395 | − | 0.955395i | ||||
\(424\) | 4.02798 | 0.195616 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 33.7705 | 1.63619 | ||||||||
\(427\) | 9.87378 | − | 9.87378i | 0.477826 | − | 0.477826i | ||||
\(428\) | 0.758227 | + | 1.83052i | 0.0366503 | + | 0.0884816i | ||||
\(429\) | 1.62598i | 0.0785030i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.4407 | + | 8.05261i | 0.936427 | + | 0.387881i | 0.798113 | − | 0.602508i | \(-0.205832\pi\) |
0.138314 | + | 0.990388i | \(0.455832\pi\) | |||||||
\(432\) | 39.4982 | + | 16.3607i | 1.90036 | + | 0.787154i | ||||
\(433\) | −2.52902 | − | 2.52902i | −0.121537 | − | 0.121537i | 0.643722 | − | 0.765259i | \(-0.277389\pi\) |
−0.765259 | + | 0.643722i | \(0.777389\pi\) | |||||||
\(434\) | −20.3817 | + | 20.3817i | −0.978355 | + | 0.978355i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.94391 | − | 2.46205i | −0.284661 | − | 0.117911i | ||||
\(437\) | −7.73212 | + | 3.20275i | −0.369878 | + | 0.153208i | ||||
\(438\) | 68.4318 | 3.26980 | ||||||||
\(439\) | −3.03763 | + | 1.25823i | −0.144978 | + | 0.0600520i | −0.453993 | − | 0.891005i | \(-0.650001\pi\) |
0.309014 | + | 0.951057i | \(0.400001\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −29.8449 | −1.42119 | ||||||||
\(442\) | −0.550026 | − | 0.604191i | −0.0261621 | − | 0.0287384i | ||||
\(443\) | 24.9391i | 1.18489i | 0.805609 | + | 0.592447i | \(0.201838\pi\) | ||||
−0.805609 | + | 0.592447i | \(0.798162\pi\) | |||||||
\(444\) | 1.58165 | + | 1.58165i | 0.0750619 | + | 0.0750619i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 32.9147i | 1.55856i | ||||||||
\(447\) | 19.5662 | − | 8.10457i | 0.925447 | − | 0.383333i | ||||
\(448\) | 7.52289 | − | 18.1619i | 0.355423 | − | 0.858068i | ||||
\(449\) | −3.69533 | + | 8.92132i | −0.174394 | + | 0.421023i | −0.986773 | − | 0.162105i | \(-0.948172\pi\) |
0.812380 | + | 0.583128i | \(0.198172\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −30.1914 | + | 30.1914i | −1.42166 | + | 1.42166i | ||||
\(452\) | 2.85856 | + | 1.18405i | 0.134455 | + | 0.0556932i | ||||
\(453\) | 7.31741 | − | 17.6658i | 0.343802 | − | 0.830011i | ||||
\(454\) | −15.2590 | − | 36.8386i | −0.716143 | − | 1.72892i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −17.5796 | + | 7.28169i | −0.823239 | + | 0.340997i | ||||
\(457\) | −14.4798 | + | 14.4798i | −0.677338 | + | 0.677338i | −0.959397 | − | 0.282059i | \(-0.908982\pi\) |
0.282059 | + | 0.959397i | \(0.408982\pi\) | |||||||
\(458\) | − | 11.0450i | − | 0.516098i | ||||||
\(459\) | 16.0867 | − | 34.2064i | 0.750863 | − | 1.59662i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.3288 | − | 13.3288i | −0.620785 | − | 0.620785i | 0.324947 | − | 0.945732i | \(-0.394654\pi\) |
−0.945732 | + | 0.324947i | \(0.894654\pi\) | |||||||
\(462\) | −26.2484 | − | 63.3692i | −1.22119 | − | 2.94820i | ||||
\(463\) | 2.13430 | 0.0991892 | 0.0495946 | − | 0.998769i | \(-0.484207\pi\) | ||||
0.0495946 | + | 0.998769i | \(0.484207\pi\) | |||||||
\(464\) | 8.75038 | + | 21.1253i | 0.406226 | + | 0.980716i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.1166 | + | 34.0806i | −0.653941 | + | 1.57875i | ||||
\(467\) | 16.4498 | + | 16.4498i | 0.761208 | + | 0.761208i | 0.976541 | − | 0.215333i | \(-0.0690837\pi\) |
−0.215333 | + | 0.976541i | \(0.569084\pi\) | |||||||
\(468\) | 0.228665 | + | 0.228665i | 0.0105700 | + | 0.0105700i | ||||
\(469\) | −9.10700 | + | 21.9862i | −0.420522 | + | 1.01523i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.3084 | − | 46.6146i | −0.889684 | − | 2.14789i | ||||
\(472\) | 15.0976 | 0.694921 | ||||||||
\(473\) | 4.11582 | + | 9.93647i | 0.189246 | + | 0.456879i | ||||
\(474\) | −17.0412 | − | 17.0412i | −0.782728 | − | 0.782728i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5.41020 | + | 2.54433i | 0.247976 | + | 0.116619i | ||||
\(477\) | 9.91002i | 0.453749i | ||||||||
\(478\) | −0.120240 | + | 0.120240i | −0.00549966 | + | 0.00549966i | ||||
\(479\) | 28.8369 | − | 11.9446i | 1.31759 | − | 0.545763i | 0.390500 | − | 0.920603i | \(-0.372302\pi\) |
0.927090 | + | 0.374839i | \(0.122302\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.0863705 | − | 0.208517i | −0.00393816 | − | 0.00950755i | ||||
\(482\) | 10.4096 | − | 25.1311i | 0.474146 | − | 1.14469i | ||||
\(483\) | 31.2230 | + | 12.9330i | 1.42070 | + | 0.588471i | ||||
\(484\) | 2.07911 | − | 2.07911i | 0.0945048 | − | 0.0945048i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.518430 | + | 1.25160i | −0.0235164 | + | 0.0567737i | ||||
\(487\) | −5.60737 | + | 13.5374i | −0.254094 | + | 0.613438i | −0.998527 | − | 0.0542599i | \(-0.982720\pi\) |
0.744433 | + | 0.667698i | \(0.232720\pi\) | |||||||
\(488\) | −9.17956 | + | 3.80230i | −0.415539 | + | 0.172122i | ||||
\(489\) | − | 13.8198i | − | 0.624954i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.80148 | + | 9.80148i | 0.442334 | + | 0.442334i | 0.892796 | − | 0.450461i | \(-0.148741\pi\) |
−0.450461 | + | 0.892796i | \(0.648741\pi\) | |||||||
\(492\) | 12.7040i | 0.572742i | ||||||||
\(493\) | 19.0203 | − | 6.85268i | 0.856633 | − | 0.308629i | ||||
\(494\) | −0.509953 | −0.0229439 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 23.1086 | − | 9.57188i | 1.03761 | − | 0.429790i | ||||
\(497\) | 24.9338 | 1.11843 | ||||||||
\(498\) | −62.4489 | + | 25.8672i | −2.79840 | + | 1.15914i | ||||
\(499\) | −36.9847 | − | 15.3196i | −1.65566 | − | 0.685798i | −0.657929 | − | 0.753080i | \(-0.728567\pi\) |
−0.997734 | + | 0.0672815i | \(0.978567\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 44.7224 | − | 44.7224i | 1.99805 | − | 1.99805i | ||||
\(502\) | 3.61639 | + | 3.61639i | 0.161408 | + | 0.161408i | ||||
\(503\) | −36.2551 | − | 15.0174i | −1.61654 | − | 0.669591i | −0.622907 | − | 0.782296i | \(-0.714049\pi\) |
−0.993629 | + | 0.112704i | \(0.964049\pi\) | |||||||
\(504\) | 47.4504 | + | 19.6546i | 2.11361 | + | 0.875486i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 21.4665i | 0.954303i | ||||||||
\(507\) | 14.9456 | + | 36.0819i | 0.663758 | + | 1.60245i | ||||
\(508\) | −2.38030 | + | 2.38030i | −0.105609 | + | 0.105609i | ||||
\(509\) | 26.7005 | 1.18348 | 0.591740 | − | 0.806129i | \(-0.298441\pi\) | ||||
0.591740 | + | 0.806129i | \(0.298441\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 50.5253 | 2.23511 | ||||||||
\(512\) | −8.50339 | + | 8.50339i | −0.375800 | + | 0.375800i | ||||
\(513\) | −9.02847 | − | 21.7967i | −0.398617 | − | 0.962346i | ||||
\(514\) | 33.2857i | 1.46817i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.95648 | + | 1.22461i | 0.130152 | + | 0.0539106i | ||||
\(517\) | 18.0128 | + | 7.46113i | 0.792200 | + | 0.328140i | ||||
\(518\) | 6.73223 | + | 6.73223i | 0.295797 | + | 0.295797i | ||||
\(519\) | 26.6984 | − | 26.6984i | 1.17193 | − | 1.17193i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.28773 | + | 1.77604i | 0.187849 | + | 0.0778096i | 0.474625 | − | 0.880188i | \(-0.342584\pi\) |
−0.286776 | + | 0.957998i | \(0.592584\pi\) | |||||||
\(522\) | −42.6183 | + | 17.6531i | −1.86535 | + | 0.772655i | ||||
\(523\) | −9.21401 | −0.402900 | −0.201450 | − | 0.979499i | \(-0.564565\pi\) | ||||
−0.201450 | + | 0.979499i | \(0.564565\pi\) | |||||||
\(524\) | 5.51003 | − | 2.28233i | 0.240707 | − | 0.0997040i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.7687 | −0.687549 | ||||||||
\(527\) | −7.49603 | − | 20.8060i | −0.326532 | − | 0.906324i | ||||
\(528\) | 59.5202i | 2.59029i | ||||||||
\(529\) | 8.78447 | + | 8.78447i | 0.381934 | + | 0.381934i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 37.1445i | 1.61193i | ||||||||
\(532\) | 3.44743 | − | 1.42797i | 0.149465 | − | 0.0619105i | ||||
\(533\) | 0.490548 | − | 1.18429i | 0.0212480 | − | 0.0512972i | ||||
\(534\) | 1.07592 | − | 2.59751i | 0.0465597 | − | 0.112405i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 11.9737 | − | 11.9737i | 0.517185 | − | 0.517185i | ||||
\(537\) | −33.7749 | − | 13.9900i | −1.45749 | − | 0.603714i | ||||
\(538\) | 8.97544 | − | 21.6686i | 0.386959 | − | 0.934201i | ||||
\(539\) | −8.01321 | − | 19.3456i | −0.345153 | − | 0.833274i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.5380 | + | 12.2350i | −1.26994 | + | 0.526025i | −0.912945 | − | 0.408083i | \(-0.866197\pi\) |
−0.356991 | + | 0.934108i | \(0.616197\pi\) | |||||||
\(542\) | −7.48292 | + | 7.48292i | −0.321419 | + | 0.321419i | ||||
\(543\) | 45.9089i | 1.97014i | ||||||||
\(544\) | −6.48822 | − | 7.12717i | −0.278180 | − | 0.305575i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.45610 | + | 1.45610i | 0.0623153 | + | 0.0623153i | ||||
\(547\) | 3.21779 | + | 7.76844i | 0.137583 | + | 0.332155i | 0.977621 | − | 0.210372i | \(-0.0674676\pi\) |
−0.840038 | + | 0.542527i | \(0.817468\pi\) | |||||||
\(548\) | 3.58064 | 0.152957 | ||||||||
\(549\) | −9.35478 | − | 22.5844i | −0.399252 | − | 0.963881i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.82880 | − | 11.6578i | 0.205714 | − | 0.496637i | ||||
\(552\) | −17.0040 | − | 17.0040i | −0.723740 | − | 0.723740i | ||||
\(553\) | −12.5820 | − | 12.5820i | −0.535042 | − | 0.535042i | ||||
\(554\) | −10.3114 | + | 24.8938i | −0.438087 | + | 1.05764i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.09822 | + | 2.65133i | 0.0465747 | + | 0.112441i | ||||
\(557\) | 1.01642 | 0.0430670 | 0.0215335 | − | 0.999768i | \(-0.493145\pi\) | ||||
0.0215335 | + | 0.999768i | \(0.493145\pi\) | |||||||
\(558\) | 19.3104 | + | 46.6194i | 0.817475 | + | 1.97356i | ||||
\(559\) | −0.228320 | − | 0.228320i | −0.00965692 | − | 0.00965692i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 52.5677 | + | 2.46692i | 2.21941 | + | 0.104153i | ||||
\(562\) | − | 28.0343i | − | 1.18256i | ||||||
\(563\) | 7.34466 | − | 7.34466i | 0.309541 | − | 0.309541i | −0.535191 | − | 0.844731i | \(-0.679760\pi\) |
0.844731 | + | 0.535191i | \(0.179760\pi\) | |||||||
\(564\) | 5.35949 | − | 2.21997i | 0.225675 | − | 0.0934777i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 11.2516 | + | 27.1638i | 0.472941 | + | 1.14178i | ||||
\(567\) | −12.4711 | + | 30.1078i | −0.523735 | + | 1.26441i | ||||
\(568\) | −16.3912 | − | 6.78947i | −0.687761 | − | 0.284880i | ||||
\(569\) | 16.9517 | − | 16.9517i | 0.710651 | − | 0.710651i | −0.256020 | − | 0.966671i | \(-0.582411\pi\) |
0.966671 | + | 0.256020i | \(0.0824113\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.53513 | + | 10.9488i | −0.189789 | + | 0.458192i | −0.989919 | − | 0.141635i | \(-0.954764\pi\) |
0.800129 | + | 0.599827i | \(0.204764\pi\) | |||||||
\(572\) | −0.0868261 | + | 0.209617i | −0.00363038 | + | 0.00876452i | ||||
\(573\) | 24.7323 | − | 10.2445i | 1.03321 | − | 0.427969i | ||||
\(574\) | 54.0741i | 2.25701i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −24.3347 | − | 24.3347i | −1.01395 | − | 1.01395i | ||||
\(577\) | 22.5581i | 0.939107i | 0.882904 | + | 0.469553i | \(0.155585\pi\) | ||||
−0.882904 | + | 0.469553i | \(0.844415\pi\) | |||||||
\(578\) | −20.3679 | + | 16.8656i | −0.847195 | + | 0.701517i | ||||
\(579\) | −55.2980 | −2.29811 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −46.1079 | + | 19.0985i | −1.91288 | + | 0.792340i | ||||
\(582\) | −35.9181 | −1.48885 | ||||||||
\(583\) | −6.42372 | + | 2.66079i | −0.266043 | + | 0.110199i | ||||
\(584\) | −33.2148 | − | 13.7580i | −1.37444 | − | 0.569311i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.28456 | − | 8.28456i | 0.342232 | − | 0.342232i | ||||
\(587\) | −29.8211 | − | 29.8211i | −1.23085 | − | 1.23085i | −0.963638 | − | 0.267210i | \(-0.913898\pi\) |
−0.267210 | − | 0.963638i | \(-0.586102\pi\) | |||||||
\(588\) | −5.75605 | − | 2.38424i | −0.237376 | − | 0.0983242i | ||||
\(589\) | −12.7522 | − | 5.28214i | −0.525446 | − | 0.217647i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 32.1540i | − | 1.32264i | ||||||
\(592\) | −3.16166 | − | 7.63292i | −0.129943 | − | 0.313711i | ||||
\(593\) | −6.00168 | + | 6.00168i | −0.246460 | + | 0.246460i | −0.819516 | − | 0.573056i | \(-0.805758\pi\) |
0.573056 | + | 0.819516i | \(0.305758\pi\) | |||||||
\(594\) | −60.5136 | −2.48290 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.95519 | 0.121049 | ||||||||
\(597\) | −33.0083 | + | 33.0083i | −1.35094 | + | 1.35094i | ||||
\(598\) | −0.246629 | − | 0.595415i | −0.0100854 | − | 0.0243483i | ||||
\(599\) | 17.0226i | 0.695523i | 0.937583 | + | 0.347762i | \(0.113058\pi\) | ||||
−0.937583 | + | 0.347762i | \(0.886942\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.7530 | − | 7.76773i | −0.764949 | − | 0.316852i | −0.0341247 | − | 0.999418i | \(-0.510864\pi\) |
−0.730825 | + | 0.682565i | \(0.760864\pi\) | |||||||
\(602\) | 12.5841 | + | 5.21252i | 0.512891 | + | 0.212446i | ||||
\(603\) | 29.4589 | + | 29.4589i | 1.19966 | + | 1.19966i | ||||
\(604\) | 1.88668 | − | 1.88668i | 0.0767679 | − | 0.0767679i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −72.8337 | − | 30.1687i | −2.95867 | − | 1.22552i | ||||
\(607\) | 45.1162 | − | 18.6877i | 1.83121 | − | 0.758512i | 0.864500 | − | 0.502633i | \(-0.167635\pi\) |
0.966709 | − | 0.255879i | \(-0.0823648\pi\) | |||||||
\(608\) | −6.01552 | −0.243961 | ||||||||
\(609\) | −47.0750 | + | 19.4991i | −1.90758 | + | 0.790144i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.585340 | −0.0236803 | ||||||||
\(612\) | 7.73963 | − | 7.04578i | 0.312856 | − | 0.284809i | ||||
\(613\) | 21.5320i | 0.869669i | 0.900510 | + | 0.434834i | \(0.143193\pi\) | ||||
−0.900510 | + | 0.434834i | \(0.856807\pi\) | |||||||
\(614\) | −8.54733 | − | 8.54733i | −0.344942 | − | 0.344942i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 36.0347i | 1.45188i | ||||||||
\(617\) | 4.27386 | − | 1.77029i | 0.172059 | − | 0.0712692i | −0.294991 | − | 0.955500i | \(-0.595317\pi\) |
0.467050 | + | 0.884231i | \(0.345317\pi\) | |||||||
\(618\) | −7.73992 | + | 18.6858i | −0.311345 | + | 0.751654i | ||||
\(619\) | −17.8427 | + | 43.0760i | −0.717158 | + | 1.73137i | −0.0358698 | + | 0.999356i | \(0.511420\pi\) |
−0.681288 | + | 0.732016i | \(0.738580\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 21.0831 | − | 21.0831i | 0.846035 | − | 0.846035i | ||||
\(622\) | 12.4238 | + | 5.14612i | 0.498150 | + | 0.206341i | ||||
\(623\) | 0.794386 | − | 1.91782i | 0.0318264 | − | 0.0768357i | ||||
\(624\) | −0.683829 | − | 1.65091i | −0.0273751 | − | 0.0660892i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 17.7314 | − | 7.34457i | 0.708688 | − | 0.293548i | ||||
\(627\) | 23.2253 | − | 23.2253i | 0.927531 | − | 0.927531i | ||||
\(628\) | − | 7.04048i | − | 0.280946i | ||||||
\(629\) | −6.87237 | + | 2.47599i | −0.274019 | + | 0.0987243i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.5948 | + | 18.5948i | 0.740246 | + | 0.740246i | 0.972625 | − | 0.232380i | \(-0.0746511\pi\) |
−0.232380 | + | 0.972625i | \(0.574651\pi\) | |||||||
\(632\) | 4.84522 | + | 11.6974i | 0.192732 | + | 0.465297i | ||||
\(633\) | −26.3314 | −1.04658 | ||||||||
\(634\) | −4.86498 | − | 11.7451i | −0.193213 | − | 0.466457i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.791688 | + | 1.91130i | −0.0313925 | + | 0.0757881i | ||||
\(637\) | 0.444523 | + | 0.444523i | 0.0176127 | + | 0.0176127i | ||||
\(638\) | −22.8856 | − | 22.8856i | −0.906051 | − | 0.906051i | ||||
\(639\) | 16.7041 | − | 40.3273i | 0.660805 | − | 1.59532i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.51210 | + | 6.06476i | 0.0992222 | + | 0.239544i | 0.965694 | − | 0.259682i | \(-0.0836178\pi\) |
−0.866472 | + | 0.499226i | \(0.833618\pi\) | |||||||
\(642\) | 22.0875 | 0.871726 | ||||||||
\(643\) | 2.45187 | + | 5.91935i | 0.0966925 | + | 0.233436i | 0.964823 | − | 0.262899i | \(-0.0846786\pi\) |
−0.868131 | + | 0.496335i | \(0.834679\pi\) | |||||||
\(644\) | 3.33457 | + | 3.33457i | 0.131400 | + | 0.131400i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.773695 | + | 16.4867i | −0.0304406 | + | 0.648662i | ||||
\(647\) | − | 8.03230i | − | 0.315782i | −0.987457 | − | 0.157891i | \(-0.949530\pi\) | ||
0.987457 | − | 0.157891i | \(-0.0504695\pi\) | |||||||
\(648\) | 16.3967 | − | 16.3967i | 0.644123 | − | 0.644123i | ||||
\(649\) | −24.0772 | + | 9.97311i | −0.945114 | + | 0.391479i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 21.3298 | + | 51.4946i | 0.835979 | + | 2.01823i | ||||
\(652\) | 0.737969 | − | 1.78161i | 0.0289011 | − | 0.0697734i | ||||
\(653\) | 42.6883 | + | 17.6821i | 1.67052 | + | 0.691953i | 0.998806 | − | 0.0488551i | \(-0.0155573\pi\) |
0.671717 | + | 0.740808i | \(0.265557\pi\) | |||||||
\(654\) | −50.7142 | + | 50.7142i | −1.98308 | + | 1.98308i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 17.9569 | − | 43.3517i | 0.701098 | − | 1.69260i | ||||
\(657\) | 33.8488 | − | 81.7183i | 1.32057 | − | 3.18814i | ||||
\(658\) | 22.8124 | − | 9.44921i | 0.889321 | − | 0.368369i | ||||
\(659\) | 47.9496i | 1.86785i | 0.357465 | + | 0.933926i | \(0.383641\pi\) | ||||
−0.357465 | + | 0.933926i | \(0.616359\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.7821 | − | 26.7821i | −1.04170 | − | 1.04170i | −0.999092 | − | 0.0426129i | \(-0.986432\pi\) |
−0.0426129 | − | 0.999092i | \(-0.513568\pi\) | |||||||
\(662\) | − | 36.5032i | − | 1.41874i | ||||||
\(663\) | −1.48641 | + | 0.535527i | −0.0577274 | + | 0.0207981i | ||||
\(664\) | 35.5114 | 1.37811 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 15.3987 | − | 6.37836i | 0.596689 | − | 0.247157i | ||||
\(667\) | 15.9468 | 0.617463 | ||||||||
\(668\) | 8.15364 | − | 3.37735i | 0.315474 | − | 0.130674i | ||||
\(669\) | 58.8024 | + | 24.3568i | 2.27343 | + | 0.941687i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.1276 | − | 12.1276i | 0.468182 | − | 0.468182i | ||||
\(672\) | 17.1765 | + | 17.1765i | 0.662596 | + | 0.662596i | ||||
\(673\) | −3.75229 | − | 1.55425i | −0.144640 | − | 0.0599119i | 0.309189 | − | 0.951001i | \(-0.399942\pi\) |
−0.453829 | + | 0.891089i | \(0.649942\pi\) | |||||||
\(674\) | −34.0863 | − | 14.1190i | −1.31295 | − | 0.543844i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.44967i | 0.209603i | ||||||||
\(677\) | 1.33382 | + | 3.22013i | 0.0512629 | + | 0.123760i | 0.947436 | − | 0.319944i | \(-0.103664\pi\) |
−0.896173 | + | 0.443704i | \(0.853664\pi\) | |||||||
\(678\) | 24.3896 | − | 24.3896i | 0.936676 | − | 0.936676i | ||||
\(679\) | −26.5194 | −1.01772 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −77.1041 | −2.95464 | ||||||||
\(682\) | −25.0342 | + | 25.0342i | −0.958609 | + | 0.958609i | ||||
\(683\) | 5.38880 | + | 13.0097i | 0.206197 | + | 0.497803i | 0.992818 | − | 0.119632i | \(-0.0381716\pi\) |
−0.786621 | + | 0.617436i | \(0.788172\pi\) | |||||||
\(684\) | − | 6.53245i | − | 0.249775i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 10.2535 | + | 4.24715i | 0.391482 | + | 0.162157i | ||||
\(687\) | −19.7319 | − | 8.17324i | −0.752821 | − | 0.311829i | ||||
\(688\) | −8.35784 | − | 8.35784i | −0.318640 | − | 0.318640i | ||||
\(689\) | 0.147604 | − | 0.147604i | 0.00562328 | − | 0.00562328i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −41.2601 | − | 17.0905i | −1.56961 | − | 0.650153i | −0.582883 | − | 0.812556i | \(-0.698075\pi\) |
−0.986724 | + | 0.162403i | \(0.948075\pi\) | |||||||
\(692\) | 4.86756 | − | 2.01621i | 0.185037 | − | 0.0766448i | ||||
\(693\) | −88.6562 | −3.36777 | ||||||||
\(694\) | 10.0870 | − | 4.17819i | 0.382899 | − | 0.158602i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 36.2563 | 1.37429 | ||||||||
\(697\) | −37.5436 | − | 17.6561i | −1.42207 | − | 0.668774i | ||||
\(698\) | − | 45.7076i | − | 1.73006i | ||||||
\(699\) | 50.4390 | + | 50.4390i | 1.90778 | + | 1.90778i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.84833i | 0.0698103i | 0.999391 | + | 0.0349052i | \(0.0111129\pi\) | ||||
−0.999391 | + | 0.0349052i | \(0.988887\pi\) | |||||||
\(702\) | 1.67846 | − | 0.695241i | 0.0633494 | − | 0.0262402i | ||||
\(703\) | −1.74473 | + | 4.21215i | −0.0658037 | + | 0.158864i | ||||
\(704\) | 9.24011 | − | 22.3076i | 0.348250 | − | 0.840749i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.99965 | + | 9.99965i | −0.376342 | + | 0.376342i | ||||
\(707\) | −53.7753 | − | 22.2745i | −2.02243 | − | 0.837717i | ||||
\(708\) | −2.96738 | + | 7.16390i | −0.111521 | + | 0.269236i | ||||
\(709\) | −11.4834 | − | 27.7233i | −0.431267 | − | 1.04117i | −0.978879 | − | 0.204438i | \(-0.934463\pi\) |
0.547613 | − | 0.836732i | \(-0.315537\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −28.7791 | + | 11.9207i | −1.07930 | + | 0.447060i | ||||
\(712\) | −1.04444 | + | 1.04444i | −0.0391421 | + | 0.0391421i | ||||
\(713\) | − | 17.4439i | − | 0.653281i | ||||||
\(714\) | 49.2847 | − | 44.8664i | 1.84443 | − | 1.67908i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.60711 | − | 3.60711i | −0.134804 | − | 0.134804i | ||||
\(717\) | 0.125833 | + | 0.303788i | 0.00469932 | + | 0.0113452i | ||||
\(718\) | −8.15119 | −0.304200 | ||||||||
\(719\) | −14.6916 | − | 35.4687i | −0.547904 | − | 1.32276i | −0.919034 | − | 0.394177i | \(-0.871030\pi\) |
0.371130 | − | 0.928581i | \(-0.378970\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.71461 | + | 13.7963i | −0.212823 | + | 0.513801i | ||||
\(722\) | −13.6147 | − | 13.6147i | −0.506687 | − | 0.506687i | ||||
\(723\) | −37.1938 | − | 37.1938i | −1.38325 | − | 1.38325i | ||||
\(724\) | −2.45150 | + | 5.91846i | −0.0911094 | + | 0.219958i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −12.5435 | − | 30.2827i | −0.465533 | − | 1.12390i | ||||
\(727\) | 0.0992434 | 0.00368073 | 0.00184037 | − | 0.999998i | \(-0.499414\pi\) | ||||
0.00184037 | + | 0.999998i | \(0.499414\pi\) | |||||||
\(728\) | −0.414004 | − | 0.999493i | −0.0153440 | − | 0.0370437i | ||||
\(729\) | −18.1584 | − | 18.1584i | −0.672532 | − | 0.672532i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.72798 | + | 7.03517i | −0.285830 | + | 0.260205i | ||||
\(732\) | − | 5.10310i | − | 0.188616i | ||||||
\(733\) | 10.2168 | − | 10.2168i | 0.377365 | − | 0.377365i | −0.492786 | − | 0.870151i | \(-0.664021\pi\) |
0.870151 | + | 0.492786i | \(0.164021\pi\) | |||||||
\(734\) | −26.2030 | + | 10.8536i | −0.967169 | + | 0.400614i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.90929 | − | 7.02364i | −0.107238 | − | 0.258895i | ||||
\(737\) | −11.1858 | + | 27.0049i | −0.412035 | + | 0.994739i | ||||
\(738\) | 87.4582 | + | 36.2264i | 3.21938 | + | 1.33351i | ||||
\(739\) | 3.22478 | − | 3.22478i | 0.118625 | − | 0.118625i | −0.645302 | − | 0.763928i | \(-0.723268\pi\) |
0.763928 | + | 0.645302i | \(0.223268\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.377364 | + | 0.911036i | −0.0138628 | + | 0.0334677i | ||||
\(742\) | −3.36978 | + | 8.13538i | −0.123709 | + | 0.298659i | ||||
\(743\) | 30.7404 | − | 12.7331i | 1.12776 | − | 0.467131i | 0.260738 | − | 0.965410i | \(-0.416034\pi\) |
0.867017 | + | 0.498278i | \(0.166034\pi\) | |||||||
\(744\) | − | 39.6601i | − | 1.45401i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −20.4027 | − | 20.4027i | −0.746996 | − | 0.746996i | ||||
\(747\) | 87.3686i | 3.19665i | ||||||||
\(748\) | 6.64516 | + | 3.12511i | 0.242971 | + | 0.114265i | ||||
\(749\) | 16.3079 | 0.595877 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.4052 | + | 10.1090i | −0.890558 | + | 0.368881i | −0.780582 | − | 0.625053i | \(-0.785077\pi\) |
−0.109976 | + | 0.993934i | \(0.535077\pi\) | |||||||
\(752\) | −21.4268 | −0.781355 | ||||||||
\(753\) | 9.13684 | − | 3.78460i | 0.332965 | − | 0.137919i | ||||
\(754\) | 0.897710 | + | 0.371844i | 0.0326927 | + | 0.0135418i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −9.40007 | + | 9.40007i | −0.341877 | + | 0.341877i | ||||
\(757\) | 15.6840 | + | 15.6840i | 0.570043 | + | 0.570043i | 0.932140 | − | 0.362097i | \(-0.117939\pi\) |
−0.362097 | + | 0.932140i | \(0.617939\pi\) | |||||||
\(758\) | 28.8317 | + | 11.9425i | 1.04722 | + | 0.433771i | ||||
\(759\) | 38.3501 | + | 15.8851i | 1.39202 | + | 0.576594i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.1817i | 0.840337i | 0.907446 | + | 0.420168i | \(0.138029\pi\) | ||||
−0.907446 | + | 0.420168i | \(0.861971\pi\) | |||||||
\(762\) | 14.3606 | + | 34.6696i | 0.520231 | + | 1.25595i | ||||
\(763\) | −37.4438 | + | 37.4438i | −1.35556 | + | 1.35556i | ||||
\(764\) | 3.73547 | 0.135145 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 16.9996 | 0.614219 | ||||||||
\(767\) | 0.553247 | − | 0.553247i | 0.0199766 | − | 0.0199766i | ||||
\(768\) | −11.1206 | − | 26.8475i | −0.401281 | − | 0.968777i | ||||
\(769\) | − | 16.7701i | − | 0.604747i | −0.953190 | − | 0.302373i | \(-0.902221\pi\) | ||
0.953190 | − | 0.302373i | \(-0.0977789\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 59.4653 | + | 24.6313i | 2.14159 | + | 0.887076i | ||||
\(772\) | −7.12886 | − | 2.95287i | −0.256573 | − | 0.106276i | ||||
\(773\) | −9.68077 | − | 9.68077i | −0.348193 | − | 0.348193i | 0.511243 | − | 0.859436i | \(-0.329185\pi\) |
−0.859436 | + | 0.511243i | \(0.829185\pi\) | |||||||
\(774\) | 16.8612 | − | 16.8612i | 0.606063 | − | 0.606063i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 17.4336 | + | 7.22124i | 0.625830 | + | 0.259227i | ||||
\(777\) | 17.0090 | − | 7.04537i | 0.610195 | − | 0.252751i | ||||
\(778\) | −36.9463 | −1.32459 | ||||||||
\(779\) | −23.9232 | + | 9.90931i | −0.857137 | + | 0.355038i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 30.6253 | 1.09586 | ||||||||
\(782\) | −19.6239 | + | 7.07014i | −0.701749 | + | 0.252828i | ||||
\(783\) | 44.9537i | 1.60651i | ||||||||
\(784\) | 16.2721 | + | 16.2721i | 0.581147 | + | 0.581147i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | − | 66.4854i | − | 2.37145i | ||||||
\(787\) | 27.0058 | − | 11.1862i | 0.962651 | − | 0.398743i | 0.154680 | − | 0.987965i | \(-0.450565\pi\) |
0.807972 | + | 0.589221i | \(0.200565\pi\) | |||||||
\(788\) | 1.71700 | − | 4.14521i | 0.0611656 | − | 0.147667i | ||||
\(789\) | −11.6688 | + | 28.1710i | −0.415420 | + | 1.00291i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.0076 | − | 18.0076i | 0.640275 | − | 0.640275i | ||||
\(792\) | 58.2817 | + | 24.1411i | 2.07095 | + | 0.857816i | ||||
\(793\) | −0.197049 | + | 0.475718i | −0.00699740 | + | 0.0168932i | ||||
\(794\) | −16.8981 | − | 40.7957i | −0.599692 | − | 1.44778i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.01797 | + | 2.49272i | −0.213301 | + | 0.0883522i | ||||
\(797\) | −10.0043 | + | 10.0043i | −0.354369 | + | 0.354369i | −0.861732 | − | 0.507363i | \(-0.830620\pi\) |
0.507363 | + | 0.861732i | \(0.330620\pi\) | |||||||
\(798\) | − | 41.5976i | − | 1.47254i | ||||||
\(799\) | −0.888070 | + | 18.9240i | −0.0314176 | + | 0.669482i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.56964 | − | 2.56964i | −0.0907938 | − | 0.0907938i | ||||
\(802\) | 5.19452 | + | 12.5407i | 0.183425 | + | 0.442827i | ||||
\(803\) | 62.0584 | 2.18999 | ||||||||
\(804\) | 3.32821 | + | 8.03500i | 0.117377 | + | 0.283373i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.406753 | − | 0.981990i | 0.0143273 | − | 0.0345891i | ||||
\(807\) | −32.0694 | − | 32.0694i | −1.12890 | − | 1.12890i | ||||
\(808\) | 29.2860 | + | 29.2860i | 1.03028 | + | 1.03028i | ||||
\(809\) | −6.56799 | + | 15.8565i | −0.230918 | + | 0.557486i | −0.996286 | − | 0.0861076i | \(-0.972557\pi\) |
0.765368 | + | 0.643593i | \(0.222557\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.3259 | + | 41.8285i | 0.608396 | + | 1.46880i | 0.864744 | + | 0.502214i | \(0.167481\pi\) |
−0.256348 | + | 0.966585i | \(0.582519\pi\) | |||||||
\(812\) | −7.11003 | −0.249513 | ||||||||
\(813\) | 7.83097 | + | 18.9056i | 0.274644 | + | 0.663050i | ||||
\(814\) | 8.26897 | + | 8.26897i | 0.289827 | + | 0.289827i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −54.4112 | + | 19.6034i | −1.90477 | + | 0.686255i | ||||
\(817\) | 6.52262i | 0.228197i | ||||||||
\(818\) | −11.6123 | + | 11.6123i | −0.406013 | + | 0.406013i | ||||
\(819\) | 2.45905 | − | 1.01857i | 0.0859262 | − | 0.0355918i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.18115 | − | 22.1652i | −0.320424 | − | 0.773572i | −0.999229 | − | 0.0392539i | \(-0.987502\pi\) |
0.678805 | − | 0.734319i | \(-0.262498\pi\) | |||||||
\(822\) | 15.2752 | − | 36.8776i | 0.532784 | − | 1.28626i | ||||
\(823\) | −40.0669 | − | 16.5962i | −1.39664 | − | 0.578509i | −0.447766 | − | 0.894151i | \(-0.647780\pi\) |
−0.948878 | + | 0.315642i | \(0.897780\pi\) | |||||||
\(824\) | 7.51346 | − | 7.51346i | 0.261744 | − | 0.261744i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12.6305 | + | 30.4928i | −0.439473 | + | 1.06098i | ||||
\(827\) | 14.7306 | − | 35.5628i | 0.512233 | − | 1.23664i | −0.430347 | − | 0.902663i | \(-0.641609\pi\) |
0.942581 | − | 0.333978i | \(-0.108391\pi\) | |||||||
\(828\) | 7.62721 | − | 3.15929i | 0.265064 | − | 0.109793i | ||||
\(829\) | − | 54.4489i | − | 1.89109i | −0.325492 | − | 0.945545i | \(-0.605530\pi\) | ||
0.325492 | − | 0.945545i | \(-0.394470\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 36.8427 | + | 36.8427i | 1.27806 | + | 1.27806i | ||||
\(832\) | 0.724904i | 0.0251315i | ||||||||
\(833\) | 15.0458 | − | 13.6970i | 0.521307 | − | 0.474572i | ||||
\(834\) | 31.9916 | 1.10778 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.23437 | − | 1.75393i | 0.146449 | − | 0.0606610i | ||||
\(837\) | 49.1740 | 1.69970 | ||||||||
\(838\) | −20.5349 | + | 8.50583i | −0.709366 | + | 0.293829i | ||||
\(839\) | 10.9808 | + | 4.54840i | 0.379100 | + | 0.157028i | 0.564093 | − | 0.825712i | \(-0.309226\pi\) |
−0.184993 | + | 0.982740i | \(0.559226\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.50507 | − | 3.50507i | 0.120864 | − | 0.120864i | ||||
\(842\) | −20.0953 | − | 20.0953i | −0.692529 | − | 0.692529i | ||||
\(843\) | −50.0835 | − | 20.7453i | −1.72497 | − | 0.714505i | ||||
\(844\) | −3.39457 | − | 1.40608i | −0.116846 | − | 0.0483991i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 43.2266i | − | 1.48616i | ||||||
\(847\) | −9.26124 | − | 22.3586i | −0.318220 | − | 0.768251i | ||||
\(848\) | 5.40317 | − | 5.40317i | 0.185546 | − | 0.185546i | ||||
\(849\) | 56.8546 | 1.95124 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.76186 | −0.197514 | ||||||||
\(852\) | 6.44330 | − | 6.44330i | 0.220744 | − | 0.220744i | ||||
\(853\) | 13.1561 | + | 31.7617i | 0.450457 | + | 1.08750i | 0.972149 | + | 0.234365i | \(0.0753011\pi\) |
−0.521692 | + | 0.853134i | \(0.674699\pi\) | |||||||
\(854\) | − | 21.7211i | − | 0.743281i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.7206 | − | 4.44064i | −0.366424 | − | 0.151778i | ||||
\(857\) | 17.0386 | + | 7.05760i | 0.582026 | + | 0.241083i | 0.654216 | − | 0.756308i | \(-0.272999\pi\) |
−0.0721899 | + | 0.997391i | \(0.522999\pi\) | |||||||
\(858\) | 1.78848 | + | 1.78848i | 0.0610576 | + | 0.0610576i | ||||
\(859\) | −17.2644 | + | 17.2644i | −0.589054 | + | 0.589054i | −0.937375 | − | 0.348321i | \(-0.886752\pi\) |
0.348321 | + | 0.937375i | \(0.386752\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 96.6040 | + | 40.0147i | 3.29225 | + | 1.36370i | ||||
\(862\) | 30.2410 | − | 12.5262i | 1.03001 | − | 0.426645i | ||||
\(863\) | 22.5253 | 0.766770 | 0.383385 | − | 0.923589i | \(-0.374758\pi\) | ||||
0.383385 | + | 0.923589i | \(0.374758\pi\) | |||||||
\(864\) | 19.7995 | − | 8.20121i | 0.673592 | − | 0.279011i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −5.56353 | −0.189056 | ||||||||
\(867\) | 15.0584 | + | 48.8680i | 0.511409 | + | 1.65964i | ||||
\(868\) | 7.77753i | 0.263987i | ||||||||
\(869\) | −15.4541 | − | 15.4541i | −0.524243 | − | 0.524243i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 0.877548i | − | 0.0297346i | ||||||
\(872\) | 34.8111 | − | 14.4192i | 1.17885 | − | 0.488297i | ||||
\(873\) | −17.7664 | + | 42.8919i | −0.601302 | + | 1.45167i | ||||
\(874\) | −4.98203 | + | 12.0277i | −0.168520 | + | 0.406843i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 13.0566 | − | 13.0566i | 0.441140 | − | 0.441140i | ||||
\(877\) | 52.2583 | + | 21.6461i | 1.76464 | + | 0.730937i | 0.995806 | + | 0.0914856i | \(0.0291615\pi\) |
0.768832 | + | 0.639451i | \(0.220838\pi\) | |||||||
\(878\) | −1.95724 | + | 4.72519i | −0.0660535 | + | 0.159467i | ||||
\(879\) | −8.66990 | − | 20.9310i | −0.292428 | − | 0.705984i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.6744 | − | 12.7058i | 1.03345 | − | 0.428068i | 0.199492 | − | 0.979899i | \(-0.436071\pi\) |
0.833956 | + | 0.551831i | \(0.186071\pi\) | |||||||
\(882\) | −32.8275 | + | 32.8275i | −1.10536 | + | 1.10536i | ||||
\(883\) | 11.2453i | 0.378433i | 0.981935 | + | 0.189217i | \(0.0605949\pi\) | ||||
−0.981935 | + | 0.189217i | \(0.939405\pi\) | |||||||
\(884\) | −0.220221 | − | 0.0103346i | −0.00740682 | − | 0.000347590i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 27.4315 | + | 27.4315i | 0.921580 | + | 0.921580i | ||||
\(887\) | −0.387187 | − | 0.934751i | −0.0130005 | − | 0.0313859i | 0.917246 | − | 0.398321i | \(-0.130407\pi\) |
−0.930246 | + | 0.366935i | \(0.880407\pi\) | |||||||
\(888\) | −13.1000 | −0.439608 | ||||||||
\(889\) | 10.6029 | + | 25.5976i | 0.355609 | + | 0.858516i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.3178 | + | 36.9804i | −0.513165 | + | 1.23889i | ||||
\(892\) | 6.28002 | + | 6.28002i | 0.210271 | + | 0.210271i | ||||
\(893\) | 8.36094 | + | 8.36094i | 0.279788 | + | 0.279788i | ||||
\(894\) | 12.6070 | − | 30.4361i | 0.421642 | − | 1.01793i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −17.8830 | − | 43.1734i | −0.597430 | − | 1.44232i | ||||
\(897\) | −1.24622 | −0.0416100 | ||||||||
\(898\) | 5.74827 | + | 13.8775i | 0.191822 | + | 0.463100i | ||||
\(899\) | 18.5971 | + | 18.5971i | 0.620249 | + | 0.620249i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.54809 | − | 4.99598i | −0.151519 | − | 0.166440i | ||||
\(902\) | 66.4174i | 2.21146i | ||||||||
\(903\) | 18.6244 | − | 18.6244i | 0.619782 | − | 0.619782i | ||||
\(904\) | −16.7414 | + | 6.93453i | −0.556812 | + | 0.230639i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −11.3826 | − | 27.4800i | −0.378161 | − | 0.912961i | ||||
\(907\) | −7.01488 | + | 16.9354i | −0.232925 | + | 0.562331i | −0.996519 | − | 0.0833657i | \(-0.973433\pi\) |
0.763594 | + | 0.645697i | \(0.223433\pi\) | |||||||
\(908\) | −9.94006 | − | 4.11731i | −0.329872 | − | 0.136638i | ||||
\(909\) | −72.0523 | + | 72.0523i | −2.38983 | + | 2.38983i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.6365 | − | 25.6787i | 0.352402 | − | 0.850772i | −0.643921 | − | 0.765092i | \(-0.722694\pi\) |
0.996323 | − | 0.0856806i | \(-0.0273065\pi\) | |||||||
\(912\) | −13.8137 | + | 33.3492i | −0.457417 | + | 1.10430i | ||||
\(913\) | −56.6327 | + | 23.4580i | −1.87427 | + | 0.776348i | ||||
\(914\) | 31.8538i | 1.05363i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.10734 | − | 2.10734i | −0.0696286 | − | 0.0696286i | ||||
\(917\) | − | 49.0881i | − | 1.62103i | ||||||
\(918\) | −19.9305 | − | 55.3193i | −0.657806 | − | 1.82581i | ||||
\(919\) | 13.6372 | 0.449850 | 0.224925 | − | 0.974376i | \(-0.427786\pi\) | ||||
0.224925 | + | 0.974376i | \(0.427786\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.5949 | + | 8.94489i | −0.711575 | + | 0.294744i | ||||
\(922\) | −29.3218 | −0.965661 | ||||||||
\(923\) | −0.849453 | + | 0.351855i | −0.0279601 | + | 0.0115814i | ||||
\(924\) | −17.0987 | − | 7.08253i | −0.562507 | − | 0.232998i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.34760 | − | 2.34760i | 0.0771468 | − | 0.0771468i | ||||
\(927\) | 18.4854 | + | 18.4854i | 0.607139 | + | 0.607139i | ||||
\(928\) | 10.5896 | + | 4.38635i | 0.347620 | + | 0.143989i | ||||
\(929\) | 48.4225 | + | 20.0573i | 1.58869 | + | 0.658057i | 0.989760 | − | 0.142743i | \(-0.0455922\pi\) |
0.598931 | + | 0.800800i | \(0.295592\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 12.6991i | − | 0.416195i | ||||||
\(932\) | 3.80905 | + | 9.19587i | 0.124770 | + | 0.301221i | ||||
\(933\) | 18.3872 | − | 18.3872i | 0.601969 | − | 0.601969i | ||||
\(934\) | 36.1876 | 1.18409 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.89391 | −0.0619045 | ||||||||
\(937\) | −22.9966 | + | 22.9966i | −0.751266 | + | 0.751266i | −0.974715 | − | 0.223450i | \(-0.928268\pi\) |
0.223450 | + | 0.974715i | \(0.428268\pi\) | |||||||
\(938\) | 14.1664 | + | 34.2006i | 0.462548 | + | 1.11669i | ||||
\(939\) | − | 37.1122i | − | 1.21111i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.0374 | + | 6.64290i | 0.522804 | + | 0.216552i | 0.628448 | − | 0.777852i | \(-0.283690\pi\) |
−0.105644 | + | 0.994404i | \(0.533690\pi\) | |||||||
\(942\) | −72.5113 | − | 30.0351i | −2.36254 | − | 0.978598i | ||||
\(943\) | −23.1400 | − | 23.1400i | −0.753541 | − | 0.753541i | ||||
\(944\) | 20.2520 | − | 20.2520i | 0.659148 | − | 0.659148i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 15.4566 | + | 6.40235i | 0.502539 | + | 0.208158i | ||||
\(947\) | −13.1834 | + | 5.46073i | −0.428402 | + | 0.177450i | −0.586457 | − | 0.809980i | \(-0.699478\pi\) |
0.158055 | + | 0.987430i | \(0.449478\pi\) | |||||||
\(948\) | −6.50280 | −0.211201 | ||||||||
\(949\) | −1.72131 | + | 0.712990i | −0.0558761 | + | 0.0231446i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.5828 | −0.797152 | ||||||||
\(952\) | −32.9416 | + | 11.8683i | −1.06764 | + | 0.384653i | ||||
\(953\) | − | 30.1090i | − | 0.975326i | −0.873032 | − | 0.487663i | \(-0.837850\pi\) | ||
0.873032 | − | 0.487663i | \(-0.162150\pi\) | |||||||
\(954\) | 10.9004 | + | 10.9004i | 0.352914 | + | 0.352914i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.0458829i | 0.00148396i | ||||||||
\(957\) | −57.8207 | + | 23.9501i | −1.86908 | + | 0.774197i | ||||
\(958\) | 18.5804 | − | 44.8571i | 0.600306 | − | 1.44927i | ||||
\(959\) | 11.2781 | − | 27.2279i | 0.364190 | − | 0.879233i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.57724 | + | 1.57724i | −0.0508787 | + | 0.0508787i | ||||
\(962\) | −0.324358 | − | 0.134354i | −0.0104577 | − | 0.00433173i | ||||
\(963\) | 10.9253 | − | 26.3760i | 0.352063 | − | 0.849954i | ||||
\(964\) | −2.80880 | − | 6.78105i | −0.0904654 | − | 0.218403i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 48.5689 | − | 20.1179i | 1.56268 | − | 0.647282i | ||||
\(967\) | 12.3882 | − | 12.3882i | 0.398378 | − | 0.398378i | −0.479282 | − | 0.877661i | \(-0.659103\pi\) |
0.877661 | + | 0.479282i | \(0.159103\pi\) | |||||||
\(968\) | 17.2202i | 0.553477i | ||||||||
\(969\) | 28.8812 | + | 13.5823i | 0.927797 | + | 0.436328i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.22783 | − | 8.22783i | −0.264044 | − | 0.264044i | 0.562651 | − | 0.826695i | \(-0.309782\pi\) |
−0.826695 | + | 0.562651i | \(0.809782\pi\) | |||||||
\(972\) | 0.139886 | + | 0.337716i | 0.00448686 | + | 0.0108322i | ||||
\(973\) | 23.6203 | 0.757234 | ||||||||
\(974\) | 8.72253 | + | 21.0581i | 0.279488 | + | 0.674744i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.21312 | + | 17.4140i | −0.230886 | + | 0.557409i | ||||
\(977\) | 30.6475 | + | 30.6475i | 0.980501 | + | 0.980501i | 0.999813 | − | 0.0193125i | \(-0.00614775\pi\) |
−0.0193125 | + | 0.999813i | \(0.506148\pi\) | |||||||
\(978\) | −15.2010 | − | 15.2010i | −0.486073 | − | 0.486073i | ||||
\(979\) | 0.975716 | − | 2.35559i | 0.0311840 | − | 0.0752849i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 35.4756 | + | 85.6457i | 1.13265 | + | 2.73446i | ||||
\(982\) | 21.5620 | 0.688072 | ||||||||
\(983\) | −16.9881 | − | 41.0128i | −0.541835 | − | 1.30811i | −0.923427 | − | 0.383774i | \(-0.874624\pi\) |
0.381592 | − | 0.924331i | \(-0.375376\pi\) | |||||||
\(984\) | −52.6105 | − | 52.6105i | −1.67716 | − | 1.67716i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 13.3837 | − | 28.4587i | 0.426223 | − | 0.906310i | ||||
\(987\) | − | 47.7470i | − | 1.51980i | ||||||
\(988\) | −0.0972974 | + | 0.0972974i | −0.00309544 | + | 0.00309544i | ||||
\(989\) | −7.61573 | + | 3.15454i | −0.242166 | + | 0.100308i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.0859 | − | 53.3201i | −0.701583 | − | 1.69377i | −0.720033 | − | 0.693940i | \(-0.755873\pi\) |
0.0184501 | − | 0.999830i | \(-0.494127\pi\) | |||||||
\(992\) | 4.79815 | − | 11.5838i | 0.152341 | − | 0.367785i | ||||
\(993\) | −65.2132 | − | 27.0122i | −2.06948 | − | 0.857206i | ||||
\(994\) | 27.4256 | − | 27.4256i | 0.869889 | − | 0.869889i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.97967 | + | 16.8504i | −0.221159 | + | 0.533926i | ||||
\(997\) | −4.46444 | + | 10.7781i | −0.141390 | + | 0.341346i | −0.978673 | − | 0.205424i | \(-0.934143\pi\) |
0.837283 | + | 0.546770i | \(0.184143\pi\) | |||||||
\(998\) | −57.5315 | + | 23.8303i | −1.82113 | + | 0.754336i | ||||
\(999\) | − | 16.2425i | − | 0.513891i |
(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 | 425.2.n.c.274.4 | 24 | ||
5.2 | odd | 4 | 425.2.m.b.376.4 | 24 | |||
5.3 | odd | 4 | 85.2.l.a.36.3 | yes | 24 | ||
5.4 | even | 2 | 425.2.n.f.274.3 | 24 | |||
15.8 | even | 4 | 765.2.be.b.631.4 | 24 | |||
17.9 | even | 8 | 425.2.n.f.349.3 | 24 | |||
85.3 | even | 16 | 1445.2.a.q.1.4 | 12 | |||
85.9 | even | 8 | inner | 425.2.n.c.349.4 | 24 | ||
85.37 | even | 16 | 7225.2.a.bq.1.9 | 12 | |||
85.43 | odd | 8 | 85.2.l.a.26.3 | ✓ | 24 | ||
85.48 | even | 16 | 1445.2.a.p.1.4 | 12 | |||
85.63 | even | 16 | 1445.2.d.j.866.17 | 24 | |||
85.73 | even | 16 | 1445.2.d.j.866.18 | 24 | |||
85.77 | odd | 8 | 425.2.m.b.26.4 | 24 | |||
85.82 | even | 16 | 7225.2.a.bs.1.9 | 12 | |||
255.128 | even | 8 | 765.2.be.b.451.4 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
85.2.l.a.26.3 | ✓ | 24 | 85.43 | odd | 8 | ||
85.2.l.a.36.3 | yes | 24 | 5.3 | odd | 4 | ||
425.2.m.b.26.4 | 24 | 85.77 | odd | 8 | |||
425.2.m.b.376.4 | 24 | 5.2 | odd | 4 | |||
425.2.n.c.274.4 | 24 | 1.1 | even | 1 | trivial | ||
425.2.n.c.349.4 | 24 | 85.9 | even | 8 | inner | ||
425.2.n.f.274.3 | 24 | 5.4 | even | 2 | |||
425.2.n.f.349.3 | 24 | 17.9 | even | 8 | |||
765.2.be.b.451.4 | 24 | 255.128 | even | 8 | |||
765.2.be.b.631.4 | 24 | 15.8 | even | 4 | |||
1445.2.a.p.1.4 | 12 | 85.48 | even | 16 | |||
1445.2.a.q.1.4 | 12 | 85.3 | even | 16 | |||
1445.2.d.j.866.17 | 24 | 85.63 | even | 16 | |||
1445.2.d.j.866.18 | 24 | 85.73 | even | 16 | |||
7225.2.a.bq.1.9 | 12 | 85.37 | even | 16 | |||
7225.2.a.bs.1.9 | 12 | 85.82 | even | 16 |