Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [552,2,Mod(323,552)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(552, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("552.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 552 = 2^{3} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 552.j (of order \(2\), degree \(1\), 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: | \(4.40774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.1 | ||
Character | \(\chi\) | \(=\) | 552.323 |
Dual form | 552.2.j.d.323.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(185\) | \(277\) | \(415\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41381 | − | 0.0336448i | −0.999717 | − | 0.0237905i | ||||
\(3\) | 0.124259 | − | 1.72759i | 0.0717409 | − | 0.997423i | ||||
\(4\) | 1.99774 | + | 0.0951350i | 0.998868 | + | 0.0475675i | ||||
\(5\) | 1.31688 | 0.588927 | 0.294463 | − | 0.955663i | \(-0.404859\pi\) | ||||
0.294463 | + | 0.955663i | \(0.404859\pi\) | |||||||
\(6\) | −0.233803 | + | 2.43831i | −0.0954498 | + | 0.995434i | ||||
\(7\) | 2.00880i | 0.759257i | 0.925139 | + | 0.379628i | \(0.123948\pi\) | ||||
−0.925139 | + | 0.379628i | \(0.876052\pi\) | |||||||
\(8\) | −2.82122 | − | 0.201717i | −0.997454 | − | 0.0713176i | ||||
\(9\) | −2.96912 | − | 0.429336i | −0.989706 | − | 0.143112i | ||||
\(10\) | −1.86182 | − | 0.0443062i | −0.588760 | − | 0.0140109i | ||||
\(11\) | − | 2.03998i | − | 0.615077i | −0.951536 | − | 0.307538i | \(-0.900495\pi\) | ||
0.951536 | − | 0.307538i | \(-0.0995052\pi\) | |||||||
\(12\) | 0.412590 | − | 3.43944i | 0.119105 | − | 0.992882i | ||||
\(13\) | − | 2.24957i | − | 0.623919i | −0.950095 | − | 0.311959i | \(-0.899015\pi\) | ||
0.950095 | − | 0.311959i | \(-0.100985\pi\) | |||||||
\(14\) | 0.0675859 | − | 2.84007i | 0.0180631 | − | 0.759042i | ||||
\(15\) | 0.163634 | − | 2.27503i | 0.0422502 | − | 0.587409i | ||||
\(16\) | 3.98190 | + | 0.380109i | 0.995475 | + | 0.0950273i | ||||
\(17\) | − | 5.84585i | − | 1.41783i | −0.705295 | − | 0.708914i | \(-0.749185\pi\) | ||
0.705295 | − | 0.708914i | \(-0.250815\pi\) | |||||||
\(18\) | 4.18334 | + | 0.706897i | 0.986022 | + | 0.166617i | ||||
\(19\) | 5.65573 | 1.29751 | 0.648757 | − | 0.760996i | \(-0.275289\pi\) | ||||
0.648757 | + | 0.760996i | \(0.275289\pi\) | |||||||
\(20\) | 2.63078 | + | 0.125281i | 0.588260 | + | 0.0280138i | ||||
\(21\) | 3.47039 | + | 0.249612i | 0.757300 | + | 0.0544698i | ||||
\(22\) | −0.0686347 | + | 2.88415i | −0.0146330 | + | 0.614903i | ||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −0.699045 | + | 4.84885i | −0.142692 | + | 0.989767i | ||||
\(25\) | −3.26583 | −0.653165 | ||||||||
\(26\) | −0.0756864 | + | 3.18047i | −0.0148433 | + | 0.623742i | ||||
\(27\) | −1.11066 | + | 5.07607i | −0.213746 | + | 0.976889i | ||||
\(28\) | −0.191108 | + | 4.01306i | −0.0361159 | + | 0.758397i | ||||
\(29\) | 0.456913 | 0.0848466 | 0.0424233 | − | 0.999100i | \(-0.486492\pi\) | ||||
0.0424233 | + | 0.999100i | \(0.486492\pi\) | |||||||
\(30\) | −0.307891 | + | 3.21096i | −0.0562129 | + | 0.586238i | ||||
\(31\) | − | 4.61668i | − | 0.829181i | −0.910008 | − | 0.414590i | \(-0.863925\pi\) | ||
0.910008 | − | 0.414590i | \(-0.136075\pi\) | |||||||
\(32\) | −5.61687 | − | 0.671374i | −0.992932 | − | 0.118683i | ||||
\(33\) | −3.52424 | − | 0.253485i | −0.613492 | − | 0.0441262i | ||||
\(34\) | −0.196683 | + | 8.26495i | −0.0337308 | + | 1.41743i | ||||
\(35\) | 2.64536i | 0.447147i | ||||||||
\(36\) | −5.89067 | − | 1.14017i | −0.981779 | − | 0.190028i | ||||
\(37\) | − | 10.8770i | − | 1.78816i | −0.447904 | − | 0.894082i | \(-0.647829\pi\) | ||
0.447904 | − | 0.894082i | \(-0.352171\pi\) | |||||||
\(38\) | −7.99615 | − | 0.190286i | −1.29715 | − | 0.0308685i | ||||
\(39\) | −3.88633 | − | 0.279529i | −0.622311 | − | 0.0447605i | ||||
\(40\) | −3.71522 | − | 0.265637i | −0.587427 | − | 0.0420008i | ||||
\(41\) | − | 1.82621i | − | 0.285207i | −0.989780 | − | 0.142603i | \(-0.954453\pi\) | ||
0.989780 | − | 0.142603i | \(-0.0455473\pi\) | |||||||
\(42\) | −4.89808 | − | 0.469665i | −0.755790 | − | 0.0724709i | ||||
\(43\) | 7.89849 | 1.20451 | 0.602254 | − | 0.798304i | \(-0.294269\pi\) | ||||
0.602254 | + | 0.798304i | \(0.294269\pi\) | |||||||
\(44\) | 0.194073 | − | 4.07534i | 0.0292577 | − | 0.614380i | ||||
\(45\) | −3.90998 | − | 0.565385i | −0.582865 | − | 0.0842826i | ||||
\(46\) | −1.41381 | − | 0.0336448i | −0.208455 | − | 0.00496066i | ||||
\(47\) | 5.66287 | 0.826014 | 0.413007 | − | 0.910728i | \(-0.364479\pi\) | ||||
0.413007 | + | 0.910728i | \(0.364479\pi\) | |||||||
\(48\) | 1.15146 | − | 6.83185i | 0.166199 | − | 0.986092i | ||||
\(49\) | 2.96470 | 0.423529 | ||||||||
\(50\) | 4.61727 | + | 0.109878i | 0.652980 | + | 0.0155391i | ||||
\(51\) | −10.0992 | − | 0.726399i | −1.41417 | − | 0.101716i | ||||
\(52\) | 0.214013 | − | 4.49405i | 0.0296782 | − | 0.623212i | ||||
\(53\) | −10.1645 | −1.39620 | −0.698099 | − | 0.716002i | \(-0.745970\pi\) | ||||
−0.698099 | + | 0.716002i | \(0.745970\pi\) | |||||||
\(54\) | 1.74104 | − | 7.13924i | 0.236926 | − | 0.971528i | ||||
\(55\) | − | 2.68641i | − | 0.362235i | ||||||
\(56\) | 0.405209 | − | 5.66729i | 0.0541483 | − | 0.757323i | ||||
\(57\) | 0.702775 | − | 9.77077i | 0.0930848 | − | 1.29417i | ||||
\(58\) | −0.645990 | − | 0.0153728i | −0.0848226 | − | 0.00201854i | ||||
\(59\) | 9.04852i | 1.17802i | 0.808127 | + | 0.589008i | \(0.200481\pi\) | ||||
−0.808127 | + | 0.589008i | \(0.799519\pi\) | |||||||
\(60\) | 0.543332 | − | 4.52934i | 0.0701439 | − | 0.584735i | ||||
\(61\) | 3.19878i | 0.409561i | 0.978808 | + | 0.204781i | \(0.0656481\pi\) | ||||
−0.978808 | + | 0.204781i | \(0.934352\pi\) | |||||||
\(62\) | −0.155327 | + | 6.52713i | −0.0197266 | + | 0.828946i | ||||
\(63\) | 0.862453 | − | 5.96438i | 0.108659 | − | 0.751441i | ||||
\(64\) | 7.91862 | + | 1.13818i | 0.989828 | + | 0.142272i | ||||
\(65\) | − | 2.96242i | − | 0.367443i | ||||||
\(66\) | 4.97409 | + | 0.476954i | 0.612268 | + | 0.0587089i | ||||
\(67\) | 0.607466 | 0.0742138 | 0.0371069 | − | 0.999311i | \(-0.488186\pi\) | ||||
0.0371069 | + | 0.999311i | \(0.488186\pi\) | |||||||
\(68\) | 0.556145 | − | 11.6785i | 0.0674425 | − | 1.41622i | ||||
\(69\) | 0.124259 | − | 1.72759i | 0.0149590 | − | 0.207977i | ||||
\(70\) | 0.0890025 | − | 3.74004i | 0.0106378 | − | 0.447020i | ||||
\(71\) | −7.64044 | −0.906754 | −0.453377 | − | 0.891319i | \(-0.649781\pi\) | ||||
−0.453377 | + | 0.891319i | \(0.649781\pi\) | |||||||
\(72\) | 8.28995 | + | 1.81017i | 0.976980 | + | 0.213331i | ||||
\(73\) | −13.1992 | −1.54485 | −0.772423 | − | 0.635108i | \(-0.780955\pi\) | ||||
−0.772423 | + | 0.635108i | \(0.780955\pi\) | |||||||
\(74\) | −0.365954 | + | 15.3780i | −0.0425413 | + | 1.78766i | ||||
\(75\) | −0.405808 | + | 5.64200i | −0.0468586 | + | 0.651482i | ||||
\(76\) | 11.2987 | + | 0.538058i | 1.29605 | + | 0.0617195i | ||||
\(77\) | 4.09792 | 0.467001 | ||||||||
\(78\) | 5.48514 | + | 0.525957i | 0.621070 | + | 0.0595529i | ||||
\(79\) | − | 9.56833i | − | 1.07652i | −0.842779 | − | 0.538260i | \(-0.819082\pi\) | ||
0.842779 | − | 0.538260i | \(-0.180918\pi\) | |||||||
\(80\) | 5.24369 | + | 0.500558i | 0.586262 | + | 0.0559641i | ||||
\(81\) | 8.63134 | + | 2.54950i | 0.959038 | + | 0.283278i | ||||
\(82\) | −0.0614427 | + | 2.58193i | −0.00678521 | + | 0.285126i | ||||
\(83\) | − | 1.39264i | − | 0.152862i | −0.997075 | − | 0.0764312i | \(-0.975647\pi\) | ||
0.997075 | − | 0.0764312i | \(-0.0243526\pi\) | |||||||
\(84\) | 6.90917 | + | 0.828814i | 0.753852 | + | 0.0904310i | ||||
\(85\) | − | 7.69829i | − | 0.834997i | ||||||
\(86\) | −11.1670 | − | 0.265743i | −1.20417 | − | 0.0286558i | ||||
\(87\) | 0.0567755 | − | 0.789357i | 0.00608697 | − | 0.0846280i | ||||
\(88\) | −0.411497 | + | 5.75524i | −0.0438658 | + | 0.613511i | ||||
\(89\) | − | 5.14172i | − | 0.545022i | −0.962153 | − | 0.272511i | \(-0.912146\pi\) | ||
0.962153 | − | 0.272511i | \(-0.0878541\pi\) | |||||||
\(90\) | 5.50895 | + | 0.930899i | 0.580695 | + | 0.0981254i | ||||
\(91\) | 4.51895 | 0.473714 | ||||||||
\(92\) | 1.99774 | + | 0.0951350i | 0.208278 | + | 0.00991851i | ||||
\(93\) | −7.97573 | − | 0.573664i | −0.827044 | − | 0.0594862i | ||||
\(94\) | −8.00624 | − | 0.190526i | −0.825780 | − | 0.0196513i | ||||
\(95\) | 7.44792 | 0.764141 | ||||||||
\(96\) | −1.85780 | + | 9.62022i | −0.189611 | + | 0.981859i | ||||
\(97\) | 0.534995 | 0.0543205 | 0.0271602 | − | 0.999631i | \(-0.491354\pi\) | ||||
0.0271602 | + | 0.999631i | \(0.491354\pi\) | |||||||
\(98\) | −4.19154 | − | 0.0997469i | −0.423409 | − | 0.0100760i | ||||
\(99\) | −0.875837 | + | 6.05694i | −0.0880249 | + | 0.608745i | ||||
\(100\) | −6.52426 | − | 0.310694i | −0.652426 | − | 0.0310694i | ||||
\(101\) | 7.58160 | 0.754398 | 0.377199 | − | 0.926132i | \(-0.376887\pi\) | ||||
0.377199 | + | 0.926132i | \(0.376887\pi\) | |||||||
\(102\) | 14.2540 | + | 1.36678i | 1.41135 | + | 0.135331i | ||||
\(103\) | 12.5721i | 1.23877i | 0.785088 | + | 0.619384i | \(0.212617\pi\) | ||||
−0.785088 | + | 0.619384i | \(0.787383\pi\) | |||||||
\(104\) | −0.453776 | + | 6.34655i | −0.0444964 | + | 0.622330i | ||||
\(105\) | 4.57009 | + | 0.328709i | 0.445995 | + | 0.0320787i | ||||
\(106\) | 14.3707 | + | 0.341982i | 1.39580 | + | 0.0332162i | ||||
\(107\) | 12.4602i | 1.20458i | 0.798279 | + | 0.602288i | \(0.205744\pi\) | ||||
−0.798279 | + | 0.602288i | \(0.794256\pi\) | |||||||
\(108\) | −2.70171 | + | 10.0350i | −0.259972 | + | 0.965616i | ||||
\(109\) | 12.2589i | 1.17419i | 0.809517 | + | 0.587096i | \(0.199729\pi\) | ||||
−0.809517 | + | 0.587096i | \(0.800271\pi\) | |||||||
\(110\) | −0.0903837 | + | 3.79808i | −0.00861775 | + | 0.362133i | ||||
\(111\) | −18.7909 | − | 1.35156i | −1.78356 | − | 0.128284i | ||||
\(112\) | −0.763565 | + | 7.99886i | −0.0721501 | + | 0.755821i | ||||
\(113\) | 2.67442i | 0.251589i | 0.992056 | + | 0.125794i | \(0.0401479\pi\) | ||||
−0.992056 | + | 0.125794i | \(0.959852\pi\) | |||||||
\(114\) | −1.32233 | + | 13.7904i | −0.123847 | + | 1.29159i | ||||
\(115\) | 1.31688 | 0.122800 | ||||||||
\(116\) | 0.912792 | + | 0.0434684i | 0.0847506 | + | 0.00403594i | ||||
\(117\) | −0.965822 | + | 6.67924i | −0.0892903 | + | 0.617496i | ||||
\(118\) | 0.304436 | − | 12.7929i | 0.0280256 | − | 1.17768i | ||||
\(119\) | 11.7432 | 1.07650 | ||||||||
\(120\) | −0.920559 | + | 6.38536i | −0.0840352 | + | 0.582901i | ||||
\(121\) | 6.83849 | 0.621681 | ||||||||
\(122\) | 0.107622 | − | 4.52247i | 0.00974366 | − | 0.409445i | ||||
\(123\) | −3.15495 | − | 0.226923i | −0.284472 | − | 0.0204610i | ||||
\(124\) | 0.439208 | − | 9.22292i | 0.0394420 | − | 0.828242i | ||||
\(125\) | −10.8851 | −0.973593 | ||||||||
\(126\) | −1.42002 | + | 8.40350i | −0.126505 | + | 0.748644i | ||||
\(127\) | − | 15.1862i | − | 1.34755i | −0.738935 | − | 0.673777i | \(-0.764671\pi\) | ||
0.738935 | − | 0.673777i | \(-0.235329\pi\) | |||||||
\(128\) | −11.1572 | − | 1.87559i | −0.986163 | − | 0.165780i | ||||
\(129\) | 0.981457 | − | 13.6453i | 0.0864125 | − | 1.20140i | ||||
\(130\) | −0.0996700 | + | 4.18830i | −0.00874163 | + | 0.367339i | ||||
\(131\) | 14.0848i | 1.23060i | 0.788294 | + | 0.615299i | \(0.210965\pi\) | ||||
−0.788294 | + | 0.615299i | \(0.789035\pi\) | |||||||
\(132\) | −7.01639 | − | 0.841676i | −0.610698 | − | 0.0732585i | ||||
\(133\) | 11.3613i | 0.985146i | ||||||||
\(134\) | −0.858844 | − | 0.0204381i | −0.0741928 | − | 0.00176558i | ||||
\(135\) | −1.46260 | + | 6.68457i | −0.125881 | + | 0.575316i | ||||
\(136\) | −1.17921 | + | 16.4925i | −0.101116 | + | 1.41422i | ||||
\(137\) | 3.39029i | 0.289652i | 0.989457 | + | 0.144826i | \(0.0462622\pi\) | ||||
−0.989457 | + | 0.144826i | \(0.953738\pi\) | |||||||
\(138\) | −0.233803 | + | 2.43831i | −0.0199027 | + | 0.207562i | ||||
\(139\) | 7.73381 | 0.655973 | 0.327987 | − | 0.944682i | \(-0.393630\pi\) | ||||
0.327987 | + | 0.944682i | \(0.393630\pi\) | |||||||
\(140\) | −0.251666 | + | 5.28472i | −0.0212696 | + | 0.446641i | ||||
\(141\) | 0.703661 | − | 9.78310i | 0.0592590 | − | 0.823886i | ||||
\(142\) | 10.8022 | + | 0.257061i | 0.906497 | + | 0.0215721i | ||||
\(143\) | −4.58908 | −0.383758 | ||||||||
\(144\) | −11.6595 | − | 2.83816i | −0.971628 | − | 0.236514i | ||||
\(145\) | 0.601700 | 0.0499685 | ||||||||
\(146\) | 18.6612 | + | 0.444084i | 1.54441 | + | 0.0367526i | ||||
\(147\) | 0.368391 | − | 5.12179i | 0.0303844 | − | 0.422438i | ||||
\(148\) | 1.03478 | − | 21.7293i | 0.0850584 | − | 1.78614i | ||||
\(149\) | 18.4328 | 1.51007 | 0.755037 | − | 0.655682i | \(-0.227619\pi\) | ||||
0.755037 | + | 0.655682i | \(0.227619\pi\) | |||||||
\(150\) | 0.763560 | − | 7.96308i | 0.0623445 | − | 0.650183i | ||||
\(151\) | 12.3058i | 1.00143i | 0.865611 | + | 0.500716i | \(0.166930\pi\) | ||||
−0.865611 | + | 0.500716i | \(0.833070\pi\) | |||||||
\(152\) | −15.9561 | − | 1.14085i | −1.29421 | − | 0.0925355i | ||||
\(153\) | −2.50984 | + | 17.3570i | −0.202908 | + | 1.40323i | ||||
\(154\) | −5.79369 | − | 0.137874i | −0.466869 | − | 0.0111102i | ||||
\(155\) | − | 6.07962i | − | 0.488327i | ||||||
\(156\) | −7.73727 | − | 0.928151i | −0.619477 | − | 0.0743116i | ||||
\(157\) | − | 4.67084i | − | 0.372773i | −0.982476 | − | 0.186387i | \(-0.940322\pi\) | ||
0.982476 | − | 0.186387i | \(-0.0596777\pi\) | |||||||
\(158\) | −0.321925 | + | 13.5278i | −0.0256109 | + | 1.07622i | ||||
\(159\) | −1.26303 | + | 17.5600i | −0.100164 | + | 1.39260i | ||||
\(160\) | −7.39675 | − | 0.884119i | −0.584765 | − | 0.0698957i | ||||
\(161\) | 2.00880i | 0.158316i | ||||||||
\(162\) | −12.1173 | − | 3.89492i | −0.952027 | − | 0.306014i | ||||
\(163\) | −11.8718 | −0.929869 | −0.464935 | − | 0.885345i | \(-0.653922\pi\) | ||||
−0.464935 | + | 0.885345i | \(0.653922\pi\) | |||||||
\(164\) | 0.173737 | − | 3.64830i | 0.0135666 | − | 0.284884i | ||||
\(165\) | −4.64101 | − | 0.333810i | −0.361302 | − | 0.0259871i | ||||
\(166\) | −0.0468552 | + | 1.96894i | −0.00363667 | + | 0.152819i | ||||
\(167\) | 5.07003 | 0.392331 | 0.196165 | − | 0.980571i | \(-0.437151\pi\) | ||||
0.196165 | + | 0.980571i | \(0.437151\pi\) | |||||||
\(168\) | −9.74039 | − | 1.40425i | −0.751487 | − | 0.108340i | ||||
\(169\) | 7.93943 | 0.610725 | ||||||||
\(170\) | −0.259008 | + | 10.8839i | −0.0198650 | + | 0.834761i | ||||
\(171\) | −16.7925 | − | 2.42821i | −1.28416 | − | 0.185690i | ||||
\(172\) | 15.7791 | + | 0.751423i | 1.20314 | + | 0.0572954i | ||||
\(173\) | 23.4030 | 1.77930 | 0.889649 | − | 0.456645i | \(-0.150949\pi\) | ||||
0.889649 | + | 0.456645i | \(0.150949\pi\) | |||||||
\(174\) | −0.106828 | + | 1.11409i | −0.00809859 | + | 0.0844592i | ||||
\(175\) | − | 6.56040i | − | 0.495920i | ||||||
\(176\) | 0.775415 | − | 8.12299i | 0.0584491 | − | 0.612293i | ||||
\(177\) | 15.6321 | + | 1.12436i | 1.17498 | + | 0.0845120i | ||||
\(178\) | −0.172992 | + | 7.26944i | −0.0129663 | + | 0.544867i | ||||
\(179\) | 15.0656i | 1.12605i | 0.826438 | + | 0.563027i | \(0.190363\pi\) | ||||
−0.826438 | + | 0.563027i | \(0.809637\pi\) | |||||||
\(180\) | −7.75731 | − | 1.50146i | −0.578196 | − | 0.111913i | ||||
\(181\) | 11.7169i | 0.870911i | 0.900210 | + | 0.435455i | \(0.143413\pi\) | ||||
−0.900210 | + | 0.435455i | \(0.856587\pi\) | |||||||
\(182\) | −6.38895 | − | 0.152039i | −0.473580 | − | 0.0112699i | ||||
\(183\) | 5.52617 | + | 0.397476i | 0.408506 | + | 0.0293823i | ||||
\(184\) | −2.82122 | − | 0.201717i | −0.207983 | − | 0.0148707i | ||||
\(185\) | − | 14.3237i | − | 1.05310i | ||||||
\(186\) | 11.2569 | + | 1.07940i | 0.825395 | + | 0.0791451i | ||||
\(187\) | −11.9254 | −0.872073 | ||||||||
\(188\) | 11.3129 | + | 0.538737i | 0.825079 | + | 0.0392914i | ||||
\(189\) | −10.1968 | − | 2.23109i | −0.741710 | − | 0.162288i | ||||
\(190\) | −10.5300 | − | 0.250584i | −0.763925 | − | 0.0181793i | ||||
\(191\) | 15.7455 | 1.13931 | 0.569654 | − | 0.821885i | \(-0.307077\pi\) | ||||
0.569654 | + | 0.821885i | \(0.307077\pi\) | |||||||
\(192\) | 2.95026 | − | 13.5387i | 0.212916 | − | 0.977070i | ||||
\(193\) | −14.5266 | −1.04565 | −0.522824 | − | 0.852440i | \(-0.675122\pi\) | ||||
−0.522824 | + | 0.852440i | \(0.675122\pi\) | |||||||
\(194\) | −0.756383 | − | 0.0179998i | −0.0543051 | − | 0.00129231i | ||||
\(195\) | −5.11783 | − | 0.368107i | −0.366496 | − | 0.0263607i | ||||
\(196\) | 5.92270 | + | 0.282047i | 0.423050 | + | 0.0201462i | ||||
\(197\) | 17.5727 | 1.25200 | 0.626001 | − | 0.779822i | \(-0.284690\pi\) | ||||
0.626001 | + | 0.779822i | \(0.284690\pi\) | |||||||
\(198\) | 1.44205 | − | 8.53392i | 0.102482 | − | 0.606479i | ||||
\(199\) | 17.0863i | 1.21122i | 0.795763 | + | 0.605609i | \(0.207070\pi\) | ||||
−0.795763 | + | 0.605609i | \(0.792930\pi\) | |||||||
\(200\) | 9.21363 | + | 0.658771i | 0.651502 | + | 0.0465821i | ||||
\(201\) | 0.0754831 | − | 1.04945i | 0.00532416 | − | 0.0740226i | ||||
\(202\) | −10.7190 | − | 0.255082i | −0.754184 | − | 0.0179475i | ||||
\(203\) | 0.917849i | 0.0644204i | ||||||||
\(204\) | −20.1065 | − | 2.41194i | −1.40774 | − | 0.168870i | ||||
\(205\) | − | 2.40491i | − | 0.167966i | ||||||
\(206\) | 0.422987 | − | 17.7746i | 0.0294709 | − | 1.23842i | ||||
\(207\) | −2.96912 | − | 0.429336i | −0.206368 | − | 0.0298409i | ||||
\(208\) | 0.855082 | − | 8.95756i | 0.0592893 | − | 0.621095i | ||||
\(209\) | − | 11.5376i | − | 0.798071i | ||||||
\(210\) | −6.45019 | − | 0.618493i | −0.445105 | − | 0.0426801i | ||||
\(211\) | 2.15666 | 0.148471 | 0.0742354 | − | 0.997241i | \(-0.476348\pi\) | ||||
0.0742354 | + | 0.997241i | \(0.476348\pi\) | |||||||
\(212\) | −20.3059 | − | 0.966996i | −1.39462 | − | 0.0664136i | ||||
\(213\) | −0.949393 | + | 13.1995i | −0.0650513 | + | 0.904417i | ||||
\(214\) | 0.419222 | − | 17.6164i | 0.0286574 | − | 1.20423i | ||||
\(215\) | 10.4014 | 0.709367 | ||||||||
\(216\) | 4.15734 | − | 14.0967i | 0.282871 | − | 0.959158i | ||||
\(217\) | 9.27402 | 0.629561 | ||||||||
\(218\) | 0.412449 | − | 17.3318i | 0.0279346 | − | 1.17386i | ||||
\(219\) | −1.64011 | + | 22.8027i | −0.110829 | + | 1.54087i | ||||
\(220\) | 0.255571 | − | 5.36674i | 0.0172306 | − | 0.361825i | ||||
\(221\) | −13.1507 | −0.884609 | ||||||||
\(222\) | 26.5214 | + | 2.54307i | 1.78000 | + | 0.170680i | ||||
\(223\) | 20.3814i | 1.36484i | 0.730961 | + | 0.682419i | \(0.239072\pi\) | ||||
−0.730961 | + | 0.682419i | \(0.760928\pi\) | |||||||
\(224\) | 1.34866 | − | 11.2832i | 0.0901110 | − | 0.753890i | ||||
\(225\) | 9.69662 | + | 1.40214i | 0.646442 | + | 0.0934758i | ||||
\(226\) | 0.0899805 | − | 3.78114i | 0.00598542 | − | 0.251517i | ||||
\(227\) | − | 15.8343i | − | 1.05096i | −0.850806 | − | 0.525481i | \(-0.823886\pi\) | ||
0.850806 | − | 0.525481i | \(-0.176114\pi\) | |||||||
\(228\) | 2.33350 | − | 19.4526i | 0.154540 | − | 1.28828i | ||||
\(229\) | 11.7168i | 0.774269i | 0.922023 | + | 0.387135i | \(0.126535\pi\) | ||||
−0.922023 | + | 0.387135i | \(0.873465\pi\) | |||||||
\(230\) | −1.86182 | − | 0.0443062i | −0.122765 | − | 0.00292146i | ||||
\(231\) | 0.509203 | − | 7.07951i | 0.0335031 | − | 0.465798i | ||||
\(232\) | −1.28905 | − | 0.0921669i | −0.0846306 | − | 0.00605105i | ||||
\(233\) | − | 23.0711i | − | 1.51144i | −0.654897 | − | 0.755719i | \(-0.727288\pi\) | ||
0.654897 | − | 0.755719i | \(-0.272712\pi\) | |||||||
\(234\) | 1.59021 | − | 9.41071i | 0.103956 | − | 0.615197i | ||||
\(235\) | 7.45732 | 0.486462 | ||||||||
\(236\) | −0.860830 | + | 18.0765i | −0.0560353 | + | 1.17668i | ||||
\(237\) | −16.5301 | − | 1.18895i | −1.07375 | − | 0.0772306i | ||||
\(238\) | −16.6027 | − | 0.395097i | −1.07619 | − | 0.0256103i | ||||
\(239\) | −13.1778 | −0.852401 | −0.426201 | − | 0.904629i | \(-0.640148\pi\) | ||||
−0.426201 | + | 0.904629i | \(0.640148\pi\) | |||||||
\(240\) | 1.51633 | − | 8.99673i | 0.0978789 | − | 0.580736i | ||||
\(241\) | −5.44379 | −0.350666 | −0.175333 | − | 0.984509i | \(-0.556100\pi\) | ||||
−0.175333 | + | 0.984509i | \(0.556100\pi\) | |||||||
\(242\) | −9.66834 | − | 0.230080i | −0.621505 | − | 0.0147901i | ||||
\(243\) | 5.47701 | − | 14.5946i | 0.351350 | − | 0.936244i | ||||
\(244\) | −0.304316 | + | 6.39031i | −0.0194818 | + | 0.409098i | ||||
\(245\) | 3.90416 | 0.249428 | ||||||||
\(246\) | 4.45287 | + | 0.426975i | 0.283905 | + | 0.0272229i | ||||
\(247\) | − | 12.7230i | − | 0.809543i | ||||||
\(248\) | −0.931261 | + | 13.0247i | −0.0591352 | + | 0.827069i | ||||
\(249\) | −2.40591 | − | 0.173048i | −0.152469 | − | 0.0109665i | ||||
\(250\) | 15.3895 | + | 0.366227i | 0.973318 | + | 0.0231623i | ||||
\(251\) | − | 10.8606i | − | 0.685517i | −0.939424 | − | 0.342758i | \(-0.888639\pi\) | ||
0.939424 | − | 0.342758i | \(-0.111361\pi\) | |||||||
\(252\) | 2.29037 | − | 11.8332i | 0.144280 | − | 0.745422i | ||||
\(253\) | − | 2.03998i | − | 0.128252i | ||||||
\(254\) | −0.510935 | + | 21.4704i | −0.0320589 | + | 1.34717i | ||||
\(255\) | −13.2995 | − | 0.956581i | −0.832846 | − | 0.0599034i | ||||
\(256\) | 15.7110 | + | 3.02711i | 0.981940 | + | 0.189195i | ||||
\(257\) | 1.45048i | 0.0904784i | 0.998976 | + | 0.0452392i | \(0.0144050\pi\) | ||||
−0.998976 | + | 0.0452392i | \(0.985595\pi\) | |||||||
\(258\) | −1.84669 | + | 19.2589i | −0.114970 | + | 1.19901i | ||||
\(259\) | 21.8497 | 1.35768 | ||||||||
\(260\) | 0.281829 | − | 5.91813i | 0.0174783 | − | 0.367027i | ||||
\(261\) | −1.35663 | − | 0.196169i | −0.0839732 | − | 0.0121426i | ||||
\(262\) | 0.473882 | − | 19.9133i | 0.0292765 | − | 1.23025i | ||||
\(263\) | 5.61383 | 0.346164 | 0.173082 | − | 0.984907i | \(-0.444627\pi\) | ||||
0.173082 | + | 0.984907i | \(0.444627\pi\) | |||||||
\(264\) | 9.89155 | + | 1.42604i | 0.608783 | + | 0.0877665i | ||||
\(265\) | −13.3854 | −0.822258 | ||||||||
\(266\) | 0.382247 | − | 16.0627i | 0.0234371 | − | 0.984867i | ||||
\(267\) | −8.88278 | − | 0.638905i | −0.543617 | − | 0.0391003i | ||||
\(268\) | 1.21356 | + | 0.0577913i | 0.0741298 | + | 0.00353016i | ||||
\(269\) | −2.95147 | −0.179954 | −0.0899772 | − | 0.995944i | \(-0.528679\pi\) | ||||
−0.0899772 | + | 0.995944i | \(0.528679\pi\) | |||||||
\(270\) | 2.29275 | − | 9.40153i | 0.139532 | − | 0.572159i | ||||
\(271\) | − | 8.48737i | − | 0.515571i | −0.966202 | − | 0.257785i | \(-0.917007\pi\) | ||
0.966202 | − | 0.257785i | \(-0.0829928\pi\) | |||||||
\(272\) | 2.22206 | − | 23.2776i | 0.134732 | − | 1.41141i | ||||
\(273\) | 0.561519 | − | 7.80688i | 0.0339847 | − | 0.472494i | ||||
\(274\) | 0.114066 | − | 4.79323i | 0.00689095 | − | 0.289570i | ||||
\(275\) | 6.66221i | 0.401747i | ||||||||
\(276\) | 0.412590 | − | 3.43944i | 0.0248350 | − | 0.207030i | ||||
\(277\) | − | 31.0685i | − | 1.86673i | −0.358935 | − | 0.933363i | \(-0.616860\pi\) | ||
0.358935 | − | 0.933363i | \(-0.383140\pi\) | |||||||
\(278\) | −10.9342 | − | 0.260203i | −0.655788 | − | 0.0156059i | ||||
\(279\) | −1.98211 | + | 13.7075i | −0.118666 | + | 0.820646i | ||||
\(280\) | 0.533612 | − | 7.46314i | 0.0318894 | − | 0.446008i | ||||
\(281\) | 19.5511i | 1.16632i | 0.812357 | + | 0.583161i | \(0.198184\pi\) | ||||
−0.812357 | + | 0.583161i | \(0.801816\pi\) | |||||||
\(282\) | −1.32400 | + | 13.8078i | −0.0788428 | + | 0.822243i | ||||
\(283\) | −4.97196 | −0.295553 | −0.147776 | − | 0.989021i | \(-0.547212\pi\) | ||||
−0.147776 | + | 0.989021i | \(0.547212\pi\) | |||||||
\(284\) | −15.2636 | − | 0.726873i | −0.905727 | − | 0.0431320i | ||||
\(285\) | 0.925471 | − | 12.8669i | 0.0548202 | − | 0.762172i | ||||
\(286\) | 6.48810 | + | 0.154399i | 0.383649 | + | 0.00912978i | ||||
\(287\) | 3.66851 | 0.216545 | ||||||||
\(288\) | 16.3889 | + | 4.40492i | 0.965726 | + | 0.259562i | ||||
\(289\) | −17.1740 | −1.01024 | ||||||||
\(290\) | −0.850691 | − | 0.0202441i | −0.0499543 | − | 0.00118877i | ||||
\(291\) | 0.0664778 | − | 0.924250i | 0.00389700 | − | 0.0541805i | ||||
\(292\) | −26.3685 | − | 1.25570i | −1.54310 | − | 0.0734845i | ||||
\(293\) | −3.48481 | −0.203585 | −0.101792 | − | 0.994806i | \(-0.532458\pi\) | ||||
−0.101792 | + | 0.994806i | \(0.532458\pi\) | |||||||
\(294\) | −0.693157 | + | 7.22886i | −0.0404258 | + | 0.421595i | ||||
\(295\) | 11.9158i | 0.693766i | ||||||||
\(296\) | −2.19407 | + | 30.6864i | −0.127527 | + | 1.78361i | ||||
\(297\) | 10.3551 | + | 2.26571i | 0.600862 | + | 0.131470i | ||||
\(298\) | −26.0606 | − | 0.620169i | −1.50965 | − | 0.0359254i | ||||
\(299\) | − | 2.24957i | − | 0.130096i | ||||||
\(300\) | −1.34745 | + | 11.2326i | −0.0777950 | + | 0.648516i | ||||
\(301\) | 15.8665i | 0.914531i | ||||||||
\(302\) | 0.414027 | − | 17.3981i | 0.0238246 | − | 1.00115i | ||||
\(303\) | 0.942082 | − | 13.0979i | 0.0541212 | − | 0.752454i | ||||
\(304\) | 22.5206 | + | 2.14980i | 1.29164 | + | 0.123299i | ||||
\(305\) | 4.21241i | 0.241202i | ||||||||
\(306\) | 4.13242 | − | 24.4552i | 0.236234 | − | 1.39801i | ||||
\(307\) | 28.0776 | 1.60247 | 0.801237 | − | 0.598347i | \(-0.204175\pi\) | ||||
0.801237 | + | 0.598347i | \(0.204175\pi\) | |||||||
\(308\) | 8.18656 | + | 0.389855i | 0.466473 | + | 0.0222141i | ||||
\(309\) | 21.7194 | + | 1.56220i | 1.23558 | + | 0.0888703i | ||||
\(310\) | −0.204548 | + | 8.59545i | −0.0116175 | + | 0.488189i | ||||
\(311\) | −20.3473 | −1.15379 | −0.576894 | − | 0.816819i | \(-0.695736\pi\) | ||||
−0.576894 | + | 0.816819i | \(0.695736\pi\) | |||||||
\(312\) | 10.9078 | + | 1.57255i | 0.617534 | + | 0.0890282i | ||||
\(313\) | −20.8538 | −1.17873 | −0.589363 | − | 0.807868i | \(-0.700621\pi\) | ||||
−0.589363 | + | 0.807868i | \(0.700621\pi\) | |||||||
\(314\) | −0.157149 | + | 6.60369i | −0.00886845 | + | 0.372668i | ||||
\(315\) | 1.13575 | − | 7.85438i | 0.0639921 | − | 0.442544i | ||||
\(316\) | 0.910282 | − | 19.1150i | 0.0512074 | − | 1.07530i | ||||
\(317\) | −7.34290 | −0.412418 | −0.206209 | − | 0.978508i | \(-0.566113\pi\) | ||||
−0.206209 | + | 0.978508i | \(0.566113\pi\) | |||||||
\(318\) | 2.37649 | − | 24.7841i | 0.133267 | − | 1.38982i | ||||
\(319\) | − | 0.932093i | − | 0.0521872i | ||||||
\(320\) | 10.4279 | + | 1.49884i | 0.582936 | + | 0.0837878i | ||||
\(321\) | 21.5261 | + | 1.54829i | 1.20147 | + | 0.0864173i | ||||
\(322\) | 0.0675859 | − | 2.84007i | 0.00376641 | − | 0.158271i | ||||
\(323\) | − | 33.0626i | − | 1.83965i | ||||||
\(324\) | 17.0006 | + | 5.91437i | 0.944477 | + | 0.328576i | ||||
\(325\) | 7.34670i | 0.407522i | ||||||||
\(326\) | 16.7845 | + | 0.399424i | 0.929606 | + | 0.0221220i | ||||
\(327\) | 21.1784 | + | 1.52328i | 1.17117 | + | 0.0842376i | ||||
\(328\) | −0.368378 | + | 5.15216i | −0.0203403 | + | 0.284481i | ||||
\(329\) | 11.3756i | 0.627157i | ||||||||
\(330\) | 6.55029 | + | 0.628091i | 0.360581 | + | 0.0345753i | ||||
\(331\) | 19.9784 | 1.09811 | 0.549056 | − | 0.835786i | \(-0.314988\pi\) | ||||
0.549056 | + | 0.835786i | \(0.314988\pi\) | |||||||
\(332\) | 0.132489 | − | 2.78213i | 0.00727128 | − | 0.152689i | ||||
\(333\) | −4.66988 | + | 32.2950i | −0.255908 | + | 1.76976i | ||||
\(334\) | −7.16808 | − | 0.170580i | −0.392220 | − | 0.00933373i | ||||
\(335\) | 0.799960 | 0.0437065 | ||||||||
\(336\) | 13.7238 | + | 2.31305i | 0.748697 | + | 0.126187i | ||||
\(337\) | −29.8819 | −1.62777 | −0.813887 | − | 0.581024i | \(-0.802652\pi\) | ||||
−0.813887 | + | 0.581024i | \(0.802652\pi\) | |||||||
\(338\) | −11.2249 | − | 0.267121i | −0.610553 | − | 0.0145294i | ||||
\(339\) | 4.62030 | + | 0.332321i | 0.250940 | + | 0.0180492i | ||||
\(340\) | 0.732377 | − | 15.3792i | 0.0397187 | − | 0.834052i | ||||
\(341\) | −9.41794 | −0.510010 | ||||||||
\(342\) | 23.6598 | + | 3.99802i | 1.27938 | + | 0.216188i | ||||
\(343\) | 20.0171i | 1.08082i | ||||||||
\(344\) | −22.2834 | − | 1.59326i | −1.20144 | − | 0.0859026i | ||||
\(345\) | 0.163634 | − | 2.27503i | 0.00880977 | − | 0.122483i | ||||
\(346\) | −33.0875 | − | 0.787390i | −1.77879 | − | 0.0423303i | ||||
\(347\) | − | 20.6960i | − | 1.11102i | −0.831509 | − | 0.555511i | \(-0.812523\pi\) | ||
0.831509 | − | 0.555511i | \(-0.187477\pi\) | |||||||
\(348\) | 0.188518 | − | 1.57153i | 0.0101056 | − | 0.0842426i | ||||
\(349\) | 3.85538i | 0.206374i | 0.994662 | + | 0.103187i | \(0.0329040\pi\) | ||||
−0.994662 | + | 0.103187i | \(0.967096\pi\) | |||||||
\(350\) | −0.220724 | + | 9.27519i | −0.0117982 | + | 0.495780i | ||||
\(351\) | 11.4190 | + | 2.49850i | 0.609499 | + | 0.133360i | ||||
\(352\) | −1.36959 | + | 11.4583i | −0.0729993 | + | 0.610729i | ||||
\(353\) | 17.3265i | 0.922198i | 0.887349 | + | 0.461099i | \(0.152545\pi\) | ||||
−0.887349 | + | 0.461099i | \(0.847455\pi\) | |||||||
\(354\) | −22.0631 | − | 2.11557i | −1.17264 | − | 0.112441i | ||||
\(355\) | −10.0616 | −0.534012 | ||||||||
\(356\) | 0.489158 | − | 10.2718i | 0.0259253 | − | 0.544405i | ||||
\(357\) | 1.45919 | − | 20.2874i | 0.0772288 | − | 1.07372i | ||||
\(358\) | 0.506879 | − | 21.2999i | 0.0267894 | − | 1.12574i | ||||
\(359\) | −6.12585 | −0.323310 | −0.161655 | − | 0.986847i | \(-0.551683\pi\) | ||||
−0.161655 | + | 0.986847i | \(0.551683\pi\) | |||||||
\(360\) | 10.9169 | + | 2.38378i | 0.575370 | + | 0.125636i | ||||
\(361\) | 12.9873 | 0.683542 | ||||||||
\(362\) | 0.394213 | − | 16.5655i | 0.0207194 | − | 0.870664i | ||||
\(363\) | 0.849743 | − | 11.8141i | 0.0445999 | − | 0.620079i | ||||
\(364\) | 9.02767 | + | 0.429910i | 0.473178 | + | 0.0225334i | ||||
\(365\) | −17.3817 | −0.909802 | ||||||||
\(366\) | −7.79960 | − | 0.747884i | −0.407691 | − | 0.0390925i | ||||
\(367\) | − | 18.2451i | − | 0.952389i | −0.879340 | − | 0.476194i | \(-0.842016\pi\) | ||
0.879340 | − | 0.476194i | \(-0.157984\pi\) | |||||||
\(368\) | 3.98190 | + | 0.380109i | 0.207571 | + | 0.0198146i | ||||
\(369\) | −0.784060 | + | 5.42225i | −0.0408165 | + | 0.282271i | ||||
\(370\) | −0.481917 | + | 20.2510i | −0.0250537 | + | 1.05280i | ||||
\(371\) | − | 20.4184i | − | 1.06007i | ||||||
\(372\) | −15.8788 | − | 1.90480i | −0.823278 | − | 0.0987593i | ||||
\(373\) | 26.3578i | 1.36476i | 0.730999 | + | 0.682378i | \(0.239054\pi\) | ||||
−0.730999 | + | 0.682378i | \(0.760946\pi\) | |||||||
\(374\) | 16.8603 | + | 0.401228i | 0.871826 | + | 0.0207470i | ||||
\(375\) | −1.35257 | + | 18.8050i | −0.0698465 | + | 0.971085i | ||||
\(376\) | −15.9762 | − | 1.14229i | −0.823911 | − | 0.0589093i | ||||
\(377\) | − | 1.02786i | − | 0.0529374i | ||||||
\(378\) | 14.3413 | + | 3.49742i | 0.737639 | + | 0.179888i | ||||
\(379\) | −4.98877 | −0.256256 | −0.128128 | − | 0.991758i | \(-0.540897\pi\) | ||||
−0.128128 | + | 0.991758i | \(0.540897\pi\) | |||||||
\(380\) | 14.8790 | + | 0.708558i | 0.763276 | + | 0.0363483i | ||||
\(381\) | −26.2354 | − | 1.88701i | −1.34408 | − | 0.0966747i | ||||
\(382\) | −22.2613 | − | 0.529756i | −1.13899 | − | 0.0271047i | ||||
\(383\) | −6.02210 | −0.307715 | −0.153857 | − | 0.988093i | \(-0.549170\pi\) | ||||
−0.153857 | + | 0.988093i | \(0.549170\pi\) | |||||||
\(384\) | −4.62662 | + | 19.0419i | −0.236101 | + | 0.971728i | ||||
\(385\) | 5.39647 | 0.275030 | ||||||||
\(386\) | 20.5379 | + | 0.488745i | 1.04535 | + | 0.0248765i | ||||
\(387\) | −23.4516 | − | 3.39111i | −1.19211 | − | 0.172380i | ||||
\(388\) | 1.06878 | + | 0.0508967i | 0.0542590 | + | 0.00258389i | ||||
\(389\) | 11.5392 | 0.585061 | 0.292531 | − | 0.956256i | \(-0.405503\pi\) | ||||
0.292531 | + | 0.956256i | \(0.405503\pi\) | |||||||
\(390\) | 7.22328 | + | 0.692623i | 0.365765 | + | 0.0350723i | ||||
\(391\) | − | 5.84585i | − | 0.295638i | ||||||
\(392\) | −8.36410 | − | 0.598030i | −0.422451 | − | 0.0302051i | ||||
\(393\) | 24.3328 | + | 1.75017i | 1.22743 | + | 0.0882842i | ||||
\(394\) | −24.8445 | − | 0.591230i | −1.25165 | − | 0.0297857i | ||||
\(395\) | − | 12.6003i | − | 0.633992i | ||||||
\(396\) | −2.32592 | + | 12.0168i | −0.116882 | + | 0.603869i | ||||
\(397\) | 24.0649i | 1.20778i | 0.797066 | + | 0.603892i | \(0.206384\pi\) | ||||
−0.797066 | + | 0.603892i | \(0.793616\pi\) | |||||||
\(398\) | 0.574866 | − | 24.1569i | 0.0288154 | − | 1.21087i | ||||
\(399\) | 19.6276 | + | 1.41174i | 0.982608 | + | 0.0706753i | ||||
\(400\) | −13.0042 | − | 1.24137i | −0.650209 | − | 0.0620685i | ||||
\(401\) | 25.0724i | 1.25205i | 0.779801 | + | 0.626027i | \(0.215320\pi\) | ||||
−0.779801 | + | 0.626027i | \(0.784680\pi\) | |||||||
\(402\) | −0.142028 | + | 1.48119i | −0.00708369 | + | 0.0738749i | ||||
\(403\) | −10.3856 | −0.517341 | ||||||||
\(404\) | 15.1460 | + | 0.721276i | 0.753544 | + | 0.0358848i | ||||
\(405\) | 11.3664 | + | 3.35739i | 0.564803 | + | 0.166830i | ||||
\(406\) | 0.0308809 | − | 1.29767i | 0.00153259 | − | 0.0644021i | ||||
\(407\) | −22.1888 | −1.09986 | ||||||||
\(408\) | 28.3457 | + | 4.08652i | 1.40332 | + | 0.202313i | ||||
\(409\) | −26.2389 | −1.29743 | −0.648716 | − | 0.761031i | \(-0.724694\pi\) | ||||
−0.648716 | + | 0.761031i | \(0.724694\pi\) | |||||||
\(410\) | −0.0809127 | + | 3.40009i | −0.00399599 | + | 0.167918i | ||||
\(411\) | 5.85702 | + | 0.421273i | 0.288905 | + | 0.0207799i | ||||
\(412\) | −1.19605 | + | 25.1158i | −0.0589251 | + | 1.23737i | ||||
\(413\) | −18.1767 | −0.894417 | ||||||||
\(414\) | 4.18334 | + | 0.706897i | 0.205600 | + | 0.0347421i | ||||
\(415\) | − | 1.83395i | − | 0.0900248i | ||||||
\(416\) | −1.51030 | + | 12.6356i | −0.0740487 | + | 0.619509i | ||||
\(417\) | 0.960995 | − | 13.3608i | 0.0470601 | − | 0.654283i | ||||
\(418\) | −0.388179 | + | 16.3120i | −0.0189865 | + | 0.797845i | ||||
\(419\) | − | 5.67054i | − | 0.277024i | −0.990361 | − | 0.138512i | \(-0.955768\pi\) | ||
0.990361 | − | 0.138512i | \(-0.0442320\pi\) | |||||||
\(420\) | 9.09855 | + | 1.09145i | 0.443964 | + | 0.0532572i | ||||
\(421\) | − | 39.0265i | − | 1.90204i | −0.309133 | − | 0.951019i | \(-0.600039\pi\) | ||
0.309133 | − | 0.951019i | \(-0.399961\pi\) | |||||||
\(422\) | −3.04912 | − | 0.0725605i | −0.148429 | − | 0.00353219i | ||||
\(423\) | −16.8137 | − | 2.43127i | −0.817511 | − | 0.118213i | ||||
\(424\) | 28.6763 | + | 2.05034i | 1.39264 | + | 0.0995734i | ||||
\(425\) | 19.0915i | 0.926076i | ||||||||
\(426\) | 1.78636 | − | 18.6297i | 0.0865494 | − | 0.902614i | ||||
\(427\) | −6.42572 | −0.310962 | ||||||||
\(428\) | −1.18540 | + | 24.8922i | −0.0572986 | + | 1.20321i | ||||
\(429\) | −0.570234 | + | 7.92803i | −0.0275311 | + | 0.382769i | ||||
\(430\) | −14.7056 | − | 0.349952i | −0.709167 | − | 0.0168762i | ||||
\(431\) | −36.3903 | −1.75286 | −0.876431 | − | 0.481528i | \(-0.840082\pi\) | ||||
−0.876431 | + | 0.481528i | \(0.840082\pi\) | |||||||
\(432\) | −6.35198 | + | 19.7902i | −0.305610 | + | 0.952157i | ||||
\(433\) | 5.92766 | 0.284865 | 0.142433 | − | 0.989804i | \(-0.454508\pi\) | ||||
0.142433 | + | 0.989804i | \(0.454508\pi\) | |||||||
\(434\) | −13.1117 | − | 0.312023i | −0.629383 | − | 0.0149776i | ||||
\(435\) | 0.0747666 | − | 1.03949i | 0.00358478 | − | 0.0498397i | ||||
\(436\) | −1.16625 | + | 24.4901i | −0.0558534 | + | 1.17286i | ||||
\(437\) | 5.65573 | 0.270550 | ||||||||
\(438\) | 3.08601 | − | 32.1836i | 0.147455 | − | 1.53779i | ||||
\(439\) | − | 11.6261i | − | 0.554885i | −0.960742 | − | 0.277442i | \(-0.910513\pi\) | ||
0.960742 | − | 0.277442i | \(-0.0894867\pi\) | |||||||
\(440\) | −0.541893 | + | 7.57896i | −0.0258337 | + | 0.361313i | ||||
\(441\) | −8.80256 | − | 1.27286i | −0.419170 | − | 0.0606121i | ||||
\(442\) | 18.5926 | + | 0.442452i | 0.884359 | + | 0.0210453i | ||||
\(443\) | 21.8676i | 1.03896i | 0.854483 | + | 0.519480i | \(0.173874\pi\) | ||||
−0.854483 | + | 0.519480i | \(0.826126\pi\) | |||||||
\(444\) | −37.4107 | − | 4.48774i | −1.77543 | − | 0.212978i | ||||
\(445\) | − | 6.77104i | − | 0.320978i | ||||||
\(446\) | 0.685728 | − | 28.8155i | 0.0324701 | − | 1.36445i | ||||
\(447\) | 2.29044 | − | 31.8443i | 0.108334 | − | 1.50618i | ||||
\(448\) | −2.28637 | + | 15.9070i | −0.108021 | + | 0.751533i | ||||
\(449\) | 37.9704i | 1.79194i | 0.444119 | + | 0.895968i | \(0.353517\pi\) | ||||
−0.444119 | + | 0.895968i | \(0.646483\pi\) | |||||||
\(450\) | −13.6620 | − | 2.30860i | −0.644035 | − | 0.108829i | ||||
\(451\) | −3.72544 | −0.175424 | ||||||||
\(452\) | −0.254431 | + | 5.34279i | −0.0119674 | + | 0.251304i | ||||
\(453\) | 21.2594 | + | 1.52911i | 0.998853 | + | 0.0718437i | ||||
\(454\) | −0.532743 | + | 22.3868i | −0.0250029 | + | 1.05066i | ||||
\(455\) | 5.95092 | 0.278983 | ||||||||
\(456\) | −3.95361 | + | 27.4238i | −0.185145 | + | 1.28424i | ||||
\(457\) | −4.91821 | −0.230064 | −0.115032 | − | 0.993362i | \(-0.536697\pi\) | ||||
−0.115032 | + | 0.993362i | \(0.536697\pi\) | |||||||
\(458\) | 0.394210 | − | 16.5654i | 0.0184202 | − | 0.774050i | ||||
\(459\) | 29.6739 | + | 6.49273i | 1.38506 | + | 0.303055i | ||||
\(460\) | 2.63078 | + | 0.125281i | 0.122661 | + | 0.00584128i | ||||
\(461\) | 12.9620 | 0.603701 | 0.301851 | − | 0.953355i | \(-0.402396\pi\) | ||||
0.301851 | + | 0.953355i | \(0.402396\pi\) | |||||||
\(462\) | −0.958107 | + | 9.99198i | −0.0445752 | + | 0.464869i | ||||
\(463\) | 9.88660i | 0.459469i | 0.973253 | + | 0.229735i | \(0.0737858\pi\) | ||||
−0.973253 | + | 0.229735i | \(0.926214\pi\) | |||||||
\(464\) | 1.81938 | + | 0.173677i | 0.0844626 | + | 0.00806274i | ||||
\(465\) | −10.5031 | − | 0.755447i | −0.487069 | − | 0.0350330i | ||||
\(466\) | −0.776222 | + | 32.6182i | −0.0359578 | + | 1.51101i | ||||
\(467\) | 38.1940i | 1.76741i | 0.468048 | + | 0.883703i | \(0.344957\pi\) | ||||
−0.468048 | + | 0.883703i | \(0.655043\pi\) | |||||||
\(468\) | −2.56489 | + | 13.2515i | −0.118562 | + | 0.612550i | ||||
\(469\) | 1.22028i | 0.0563473i | ||||||||
\(470\) | −10.5433 | − | 0.250900i | −0.486324 | − | 0.0115732i | ||||
\(471\) | −8.06928 | − | 0.580393i | −0.371813 | − | 0.0267431i | ||||
\(472\) | 1.82524 | − | 25.5279i | 0.0840133 | − | 1.17502i | ||||
\(473\) | − | 16.1127i | − | 0.740865i | ||||||
\(474\) | 23.3305 | + | 2.23711i | 1.07161 | + | 0.102754i | ||||
\(475\) | −18.4706 | −0.847491 | ||||||||
\(476\) | 23.4598 | + | 1.11719i | 1.07528 | + | 0.0512062i | ||||
\(477\) | 30.1795 | + | 4.36398i | 1.38183 | + | 0.199813i | ||||
\(478\) | 18.6310 | + | 0.443365i | 0.852160 | + | 0.0202790i | ||||
\(479\) | 41.3560 | 1.88960 | 0.944802 | − | 0.327642i | \(-0.106254\pi\) | ||||
0.944802 | + | 0.327642i | \(0.106254\pi\) | |||||||
\(480\) | −2.44651 | + | 12.6687i | −0.111667 | + | 0.578243i | ||||
\(481\) | −24.4685 | −1.11567 | ||||||||
\(482\) | 7.69651 | + | 0.183155i | 0.350566 | + | 0.00834250i | ||||
\(483\) | 3.47039 | + | 0.249612i | 0.157908 | + | 0.0113577i | ||||
\(484\) | 13.6615 | + | 0.650579i | 0.620977 | + | 0.0295718i | ||||
\(485\) | 0.704524 | 0.0319908 | ||||||||
\(486\) | −8.23450 | + | 20.4498i | −0.373525 | + | 0.927620i | ||||
\(487\) | 6.12249i | 0.277436i | 0.990332 | + | 0.138718i | \(0.0442982\pi\) | ||||
−0.990332 | + | 0.138718i | \(0.955702\pi\) | |||||||
\(488\) | 0.645246 | − | 9.02447i | 0.0292089 | − | 0.408519i | ||||
\(489\) | −1.47517 | + | 20.5095i | −0.0667097 | + | 0.927473i | ||||
\(490\) | −5.51976 | − | 0.131355i | −0.249357 | − | 0.00593400i | ||||
\(491\) | − | 17.7014i | − | 0.798853i | −0.916765 | − | 0.399427i | \(-0.869209\pi\) | ||
0.916765 | − | 0.399427i | \(-0.130791\pi\) | |||||||
\(492\) | −6.28116 | − | 0.753479i | −0.283177 | − | 0.0339694i | ||||
\(493\) | − | 2.67105i | − | 0.120298i | ||||||
\(494\) | −0.428062 | + | 17.9879i | −0.0192594 | + | 0.809314i | ||||
\(495\) | −1.15337 | + | 7.97627i | −0.0518402 | + | 0.358507i | ||||
\(496\) | 1.75484 | − | 18.3832i | 0.0787948 | − | 0.825429i | ||||
\(497\) | − | 15.3482i | − | 0.688459i | ||||||
\(498\) | 3.39569 | + | 0.325605i | 0.152165 | + | 0.0145907i | ||||
\(499\) | 20.6853 | 0.926000 | 0.463000 | − | 0.886358i | \(-0.346773\pi\) | ||||
0.463000 | + | 0.886358i | \(0.346773\pi\) | |||||||
\(500\) | −21.7456 | − | 1.03555i | −0.972491 | − | 0.0463114i | ||||
\(501\) | 0.629996 | − | 8.75892i | 0.0281462 | − | 0.391320i | ||||
\(502\) | −0.365404 | + | 15.3549i | −0.0163088 | + | 0.685323i | ||||
\(503\) | 26.2288 | 1.16949 | 0.584743 | − | 0.811219i | \(-0.301195\pi\) | ||||
0.584743 | + | 0.811219i | \(0.301195\pi\) | |||||||
\(504\) | −3.63629 | + | 16.6529i | −0.161973 | + | 0.741779i | ||||
\(505\) | 9.98407 | 0.444285 | ||||||||
\(506\) | −0.0686347 | + | 2.88415i | −0.00305118 | + | 0.128216i | ||||
\(507\) | 0.986545 | − | 13.7161i | 0.0438140 | − | 0.609152i | ||||
\(508\) | 1.44473 | − | 30.3379i | 0.0640997 | − | 1.34603i | ||||
\(509\) | 12.1329 | 0.537782 | 0.268891 | − | 0.963171i | \(-0.413343\pi\) | ||||
0.268891 | + | 0.963171i | \(0.413343\pi\) | |||||||
\(510\) | 18.7708 | + | 1.79989i | 0.831185 | + | 0.0797003i | ||||
\(511\) | − | 26.5146i | − | 1.17294i | ||||||
\(512\) | −22.1106 | − | 4.80837i | −0.977161 | − | 0.212502i | ||||
\(513\) | −6.28157 | + | 28.7089i | −0.277338 | + | 1.26753i | ||||
\(514\) | 0.0488011 | − | 2.05071i | 0.00215252 | − | 0.0904528i | ||||
\(515\) | 16.5560i | 0.729544i | ||||||||
\(516\) | 3.25884 | − | 27.1664i | 0.143462 | − | 1.19593i | ||||
\(517\) | − | 11.5521i | − | 0.508062i | ||||||
\(518\) | −30.8914 | − | 0.735130i | −1.35729 | − | 0.0322997i | ||||
\(519\) | 2.90803 | − | 40.4308i | 0.127648 | − | 1.77471i | ||||
\(520\) | −0.597568 | + | 8.35764i | −0.0262051 | + | 0.366507i | ||||
\(521\) | 22.1658i | 0.971102i | 0.874208 | + | 0.485551i | \(0.161381\pi\) | ||||
−0.874208 | + | 0.485551i | \(0.838619\pi\) | |||||||
\(522\) | 1.91142 | + | 0.322990i | 0.0836606 | + | 0.0141369i | ||||
\(523\) | 24.0306 | 1.05078 | 0.525392 | − | 0.850860i | \(-0.323919\pi\) | ||||
0.525392 | + | 0.850860i | \(0.323919\pi\) | |||||||
\(524\) | −1.33996 | + | 28.1378i | −0.0585364 | + | 1.22920i | ||||
\(525\) | −11.3337 | − | 0.815189i | −0.494642 | − | 0.0355777i | ||||
\(526\) | −7.93691 | − | 0.188876i | −0.346066 | − | 0.00823540i | ||||
\(527\) | −26.9885 | −1.17564 | ||||||||
\(528\) | −13.9368 | − | 2.34895i | −0.606522 | − | 0.102225i | ||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 18.9244 | + | 0.450349i | 0.822025 | + | 0.0195619i | ||||
\(531\) | 3.88486 | − | 26.8661i | 0.168588 | − | 1.16589i | ||||
\(532\) | −1.08085 | + | 22.6968i | −0.0468609 | + | 0.984031i | ||||
\(533\) | −4.10820 | −0.177946 | ||||||||
\(534\) | 12.5371 | + | 1.20215i | 0.542533 | + | 0.0520222i | ||||
\(535\) | 16.4086i | 0.709407i | ||||||||
\(536\) | −1.71380 | − | 0.122536i | −0.0740248 | − | 0.00529275i | ||||
\(537\) | 26.0271 | + | 1.87203i | 1.12315 | + | 0.0807842i | ||||
\(538\) | 4.17283 | + | 0.0993017i | 0.179903 | + | 0.00428120i | ||||
\(539\) | − | 6.04793i | − | 0.260503i | ||||||
\(540\) | −3.55783 | + | 13.2149i | −0.153105 | + | 0.568677i | ||||
\(541\) | − | 41.0300i | − | 1.76402i | −0.471231 | − | 0.882010i | \(-0.656190\pi\) | ||
0.471231 | − | 0.882010i | \(-0.343810\pi\) | |||||||
\(542\) | −0.285556 | + | 11.9996i | −0.0122657 | + | 0.515425i | ||||
\(543\) | 20.2420 | + | 1.45593i | 0.868666 | + | 0.0624799i | ||||
\(544\) | −3.92475 | + | 32.8354i | −0.168272 | + | 1.40781i | ||||
\(545\) | 16.1435i | 0.691513i | ||||||||
\(546\) | −1.05654 | + | 11.0186i | −0.0452159 | + | 0.471552i | ||||
\(547\) | −20.2874 | −0.867425 | −0.433712 | − | 0.901051i | \(-0.642797\pi\) | ||||
−0.433712 | + | 0.901051i | \(0.642797\pi\) | |||||||
\(548\) | −0.322535 | + | 6.77290i | −0.0137780 | + | 0.289324i | ||||
\(549\) | 1.37335 | − | 9.49755i | 0.0586132 | − | 0.405346i | ||||
\(550\) | 0.224149 | − | 9.41913i | 0.00955774 | − | 0.401633i | ||||
\(551\) | 2.58418 | 0.110090 | ||||||||
\(552\) | −0.699045 | + | 4.84885i | −0.0297533 | + | 0.206381i | ||||
\(553\) | 19.2209 | 0.817356 | ||||||||
\(554\) | −1.04529 | + | 43.9251i | −0.0444103 | + | 1.86620i | ||||
\(555\) | −24.7454 | − | 1.77984i | −1.05038 | − | 0.0755502i | ||||
\(556\) | 15.4501 | + | 0.735756i | 0.655231 | + | 0.0312030i | ||||
\(557\) | −2.82028 | −0.119499 | −0.0597495 | − | 0.998213i | \(-0.519030\pi\) | ||||
−0.0597495 | + | 0.998213i | \(0.519030\pi\) | |||||||
\(558\) | 3.26352 | − | 19.3131i | 0.138156 | − | 0.817590i | ||||
\(559\) | − | 17.7682i | − | 0.751515i | ||||||
\(560\) | −1.00552 | + | 10.5335i | −0.0424911 | + | 0.445123i | ||||
\(561\) | −1.48184 | + | 20.6022i | −0.0625633 | + | 0.869826i | ||||
\(562\) | 0.657794 | − | 27.6416i | 0.0277474 | − | 1.16599i | ||||
\(563\) | − | 13.0757i | − | 0.551075i | −0.961290 | − | 0.275538i | \(-0.911144\pi\) | ||
0.961290 | − | 0.275538i | \(-0.0888558\pi\) | |||||||
\(564\) | 2.33644 | − | 19.4771i | 0.0983821 | − | 0.820134i | ||||
\(565\) | 3.52190i | 0.148167i | ||||||||
\(566\) | 7.02943 | + | 0.167281i | 0.295469 | + | 0.00703134i | ||||
\(567\) | −5.12145 | + | 17.3387i | −0.215081 | + | 0.728156i | ||||
\(568\) | 21.5554 | + | 1.54120i | 0.904445 | + | 0.0646675i | ||||
\(569\) | 0.331551i | 0.0138993i | 0.999976 | + | 0.00694966i | \(0.00221216\pi\) | ||||
−0.999976 | + | 0.00694966i | \(0.997788\pi\) | |||||||
\(570\) | −1.74135 | + | 18.1603i | −0.0729371 | + | 0.760652i | ||||
\(571\) | 28.3372 | 1.18587 | 0.592937 | − | 0.805249i | \(-0.297968\pi\) | ||||
0.592937 | + | 0.805249i | \(0.297968\pi\) | |||||||
\(572\) | −9.16776 | − | 0.436582i | −0.383323 | − | 0.0182544i | ||||
\(573\) | 1.95652 | − | 27.2018i | 0.0817350 | − | 1.13637i | ||||
\(574\) | −5.18659 | − | 0.123426i | −0.216484 | − | 0.00515171i | ||||
\(575\) | −3.26583 | −0.136194 | ||||||||
\(576\) | −23.0227 | − | 6.77913i | −0.959278 | − | 0.282464i | ||||
\(577\) | −12.4432 | −0.518018 | −0.259009 | − | 0.965875i | \(-0.583396\pi\) | ||||
−0.259009 | + | 0.965875i | \(0.583396\pi\) | |||||||
\(578\) | 24.2808 | + | 0.577816i | 1.00995 | + | 0.0240340i | ||||
\(579\) | −1.80506 | + | 25.0960i | −0.0750158 | + | 1.04295i | ||||
\(580\) | 1.20204 | + | 0.0572427i | 0.0499119 | + | 0.00237687i | ||||
\(581\) | 2.79755 | 0.116062 | ||||||||
\(582\) | −0.125083 | + | 1.30448i | −0.00518488 | + | 0.0540725i | ||||
\(583\) | 20.7353i | 0.858768i | ||||||||
\(584\) | 37.2378 | + | 2.66249i | 1.54091 | + | 0.110175i | ||||
\(585\) | −1.27187 | + | 8.79577i | −0.0525855 | + | 0.363660i | ||||
\(586\) | 4.92687 | + | 0.117246i | 0.203527 | + | 0.00484338i | ||||
\(587\) | 40.2414i | 1.66094i | 0.557062 | + | 0.830471i | \(0.311928\pi\) | ||||
−0.557062 | + | 0.830471i | \(0.688072\pi\) | |||||||
\(588\) | 1.22321 | − | 10.1969i | 0.0504443 | − | 0.420514i | ||||
\(589\) | − | 26.1107i | − | 1.07587i | ||||||
\(590\) | 0.400906 | − | 16.8467i | 0.0165050 | − | 0.693569i | ||||
\(591\) | 2.18356 | − | 30.3584i | 0.0898198 | − | 1.24878i | ||||
\(592\) | 4.13444 | − | 43.3110i | 0.169924 | − | 1.78007i | ||||
\(593\) | − | 44.8082i | − | 1.84005i | −0.391857 | − | 0.920026i | \(-0.628167\pi\) | ||
0.391857 | − | 0.920026i | \(-0.371833\pi\) | |||||||
\(594\) | −14.5639 | − | 3.55169i | −0.597564 | − | 0.145728i | ||||
\(595\) | 15.4644 | 0.633977 | ||||||||
\(596\) | 36.8239 | + | 1.75361i | 1.50837 | + | 0.0718305i | ||||
\(597\) | 29.5181 | + | 2.12313i | 1.20810 | + | 0.0868938i | ||||
\(598\) | −0.0756864 | + | 3.18047i | −0.00309505 | + | 0.130059i | ||||
\(599\) | −31.2851 | −1.27828 | −0.639138 | − | 0.769092i | \(-0.720709\pi\) | ||||
−0.639138 | + | 0.769092i | \(0.720709\pi\) | |||||||
\(600\) | 2.28296 | − | 15.8355i | 0.0932014 | − | 0.646481i | ||||
\(601\) | 16.9810 | 0.692670 | 0.346335 | − | 0.938111i | \(-0.387426\pi\) | ||||
0.346335 | + | 0.938111i | \(0.387426\pi\) | |||||||
\(602\) | 0.533826 | − | 22.4323i | 0.0217571 | − | 0.914272i | ||||
\(603\) | −1.80364 | − | 0.260807i | −0.0734499 | − | 0.0106209i | ||||
\(604\) | −1.17071 | + | 24.5838i | −0.0476356 | + | 1.00030i | ||||
\(605\) | 9.00547 | 0.366125 | ||||||||
\(606\) | −1.77260 | + | 18.4863i | −0.0720071 | + | 0.750953i | ||||
\(607\) | − | 25.5425i | − | 1.03674i | −0.855157 | − | 0.518368i | \(-0.826540\pi\) | ||
0.855157 | − | 0.518368i | \(-0.173460\pi\) | |||||||
\(608\) | −31.7675 | − | 3.79711i | −1.28834 | − | 0.153993i | ||||
\(609\) | 1.58566 | + | 0.114051i | 0.0642544 | + | 0.00462157i | ||||
\(610\) | 0.141726 | − | 5.95556i | 0.00573830 | − | 0.241133i | ||||
\(611\) | − | 12.7390i | − | 0.515366i | ||||||
\(612\) | −6.66525 | + | 34.4360i | −0.269427 | + | 1.39199i | ||||
\(613\) | 8.59550i | 0.347169i | 0.984819 | + | 0.173584i | \(0.0555350\pi\) | ||||
−0.984819 | + | 0.173584i | \(0.944465\pi\) | |||||||
\(614\) | −39.6965 | − | 0.944667i | −1.60202 | − | 0.0381236i | ||||
\(615\) | −4.15469 | − | 0.298831i | −0.167533 | − | 0.0120500i | ||||
\(616\) | −11.5612 | − | 0.826618i | −0.465812 | − | 0.0333054i | ||||
\(617\) | 24.6671i | 0.993060i | 0.868020 | + | 0.496530i | \(0.165393\pi\) | ||||
−0.868020 | + | 0.496530i | \(0.834607\pi\) | |||||||
\(618\) | −30.6547 | − | 2.93940i | −1.23311 | − | 0.118240i | ||||
\(619\) | −21.9073 | −0.880530 | −0.440265 | − | 0.897868i | \(-0.645116\pi\) | ||||
−0.440265 | + | 0.897868i | \(0.645116\pi\) | |||||||
\(620\) | 0.578385 | − | 12.1455i | 0.0232285 | − | 0.487774i | ||||
\(621\) | −1.11066 | + | 5.07607i | −0.0445691 | + | 0.203696i | ||||
\(622\) | 28.7673 | + | 0.684581i | 1.15346 | + | 0.0274492i | ||||
\(623\) | 10.3287 | 0.413811 | ||||||||
\(624\) | −15.3687 | − | 2.59029i | −0.615241 | − | 0.103694i | ||||
\(625\) | 1.99474 | 0.0797895 | ||||||||
\(626\) | 29.4834 | + | 0.701622i | 1.17839 | + | 0.0280424i | ||||
\(627\) | −19.9322 | − | 1.43365i | −0.796014 | − | 0.0572543i | ||||
\(628\) | 0.444360 | − | 9.33110i | 0.0177319 | − | 0.372351i | ||||
\(629\) | −63.5852 | −2.53531 | ||||||||
\(630\) | −1.86999 | + | 11.0664i | −0.0745023 | + | 0.440896i | ||||
\(631\) | − | 27.7857i | − | 1.10613i | −0.833138 | − | 0.553065i | \(-0.813458\pi\) | ||
0.833138 | − | 0.553065i | \(-0.186542\pi\) | |||||||
\(632\) | −1.93009 | + | 26.9944i | −0.0767748 | + | 1.07378i | ||||
\(633\) | 0.267985 | − | 3.72583i | 0.0106514 | − | 0.148088i | ||||
\(634\) | 10.3815 | + | 0.247051i | 0.412302 | + | 0.00981163i | ||||
\(635\) | − | 19.9984i | − | 0.793611i | ||||||
\(636\) | −4.19376 | + | 34.9601i | −0.166294 | + | 1.38626i | ||||
\(637\) | − | 6.66931i | − | 0.264248i | ||||||
\(638\) | −0.0313601 | + | 1.31781i | −0.00124156 | + | 0.0521724i | ||||
\(639\) | 22.6854 | + | 3.28032i | 0.897420 | + | 0.129767i | ||||
\(640\) | −14.6926 | − | 2.46993i | −0.580778 | − | 0.0976324i | ||||
\(641\) | − | 31.4114i | − | 1.24068i | −0.784334 | − | 0.620338i | \(-0.786995\pi\) | ||
0.784334 | − | 0.620338i | \(-0.213005\pi\) | |||||||
\(642\) | −30.3818 | − | 2.91324i | −1.19908 | − | 0.114976i | ||||
\(643\) | −18.4633 | −0.728122 | −0.364061 | − | 0.931375i | \(-0.618610\pi\) | ||||
−0.364061 | + | 0.931375i | \(0.618610\pi\) | |||||||
\(644\) | −0.191108 | + | 4.01306i | −0.00753069 | + | 0.158137i | ||||
\(645\) | 1.29246 | − | 17.9693i | 0.0508907 | − | 0.707540i | ||||
\(646\) | −1.11238 | + | 46.7443i | −0.0437662 | + | 1.83913i | ||||
\(647\) | 8.07781 | 0.317571 | 0.158786 | − | 0.987313i | \(-0.449242\pi\) | ||||
0.158786 | + | 0.987313i | \(0.449242\pi\) | |||||||
\(648\) | −23.8367 | − | 8.93380i | −0.936393 | − | 0.350953i | ||||
\(649\) | 18.4588 | 0.724571 | ||||||||
\(650\) | 0.247179 | − | 10.3869i | 0.00969514 | − | 0.407407i | ||||
\(651\) | 1.15238 | − | 16.0217i | 0.0451653 | − | 0.627939i | ||||
\(652\) | −23.7167 | − | 1.12942i | −0.928817 | − | 0.0442315i | ||||
\(653\) | 17.8146 | 0.697139 | 0.348569 | − | 0.937283i | \(-0.386668\pi\) | ||||
0.348569 | + | 0.937283i | \(0.386668\pi\) | |||||||
\(654\) | −29.8910 | − | 2.86618i | −1.16883 | − | 0.112076i | ||||
\(655\) | 18.5481i | 0.724732i | ||||||||
\(656\) | 0.694161 | − | 7.27180i | 0.0271024 | − | 0.283916i | ||||
\(657\) | 39.1899 | + | 5.66688i | 1.52894 | + | 0.221086i | ||||
\(658\) | 0.382730 | − | 16.0830i | 0.0149204 | − | 0.626979i | ||||
\(659\) | − | 16.9195i | − | 0.659089i | −0.944140 | − | 0.329545i | \(-0.893105\pi\) | ||
0.944140 | − | 0.329545i | \(-0.106895\pi\) | |||||||
\(660\) | −9.23975 | − | 1.10839i | −0.359657 | − | 0.0431439i | ||||
\(661\) | − | 0.802060i | − | 0.0311965i | −0.999878 | − | 0.0155983i | \(-0.995035\pi\) | ||
0.999878 | − | 0.0155983i | \(-0.00496528\pi\) | |||||||
\(662\) | −28.2457 | − | 0.672169i | −1.09780 | − | 0.0261246i | ||||
\(663\) | −1.63409 | + | 22.7189i | −0.0634627 | + | 0.882330i | ||||
\(664\) | −0.280919 | + | 3.92896i | −0.0109018 | + | 0.152473i | ||||
\(665\) | 14.9614i | 0.580179i | ||||||||
\(666\) | 7.68890 | − | 45.5020i | 0.297939 | − | 1.76317i | ||||
\(667\) | 0.456913 | 0.0176917 | ||||||||
\(668\) | 10.1286 | + | 0.482337i | 0.391887 | + | 0.0186622i | ||||
\(669\) | 35.2106 | + | 2.53257i | 1.36132 | + | 0.0979147i | ||||
\(670\) | −1.13099 | − | 0.0269145i | −0.0436941 | − | 0.00103980i | ||||
\(671\) | 6.52544 | 0.251912 | ||||||||
\(672\) | −19.3251 | − | 3.73196i | −0.745483 | − | 0.143964i | ||||
\(673\) | 45.4230 | 1.75093 | 0.875464 | − | 0.483284i | \(-0.160556\pi\) | ||||
0.875464 | + | 0.483284i | \(0.160556\pi\) | |||||||
\(674\) | 42.2475 | + | 1.00537i | 1.62731 | + | 0.0387255i | ||||
\(675\) | 3.62721 | − | 16.5775i | 0.139611 | − | 0.638070i | ||||
\(676\) | 15.8609 | + | 0.755318i | 0.610034 | + | 0.0290507i | ||||
\(677\) | −39.1422 | −1.50436 | −0.752179 | − | 0.658959i | \(-0.770997\pi\) | ||||
−0.752179 | + | 0.658959i | \(0.770997\pi\) | |||||||
\(678\) | −6.52107 | − | 0.625289i | −0.250440 | − | 0.0240141i | ||||
\(679\) | 1.07470i | 0.0412432i | ||||||||
\(680\) | −1.55287 | + | 21.7186i | −0.0595500 | + | 0.832871i | ||||
\(681\) | −27.3552 | − | 1.96756i | −1.04825 | − | 0.0753969i | ||||
\(682\) | 13.3152 | + | 0.316865i | 0.509865 | + | 0.0121334i | ||||
\(683\) | − | 21.7015i | − | 0.830386i | −0.909733 | − | 0.415193i | \(-0.863714\pi\) | ||
0.909733 | − | 0.415193i | \(-0.136286\pi\) | |||||||
\(684\) | −33.3161 | − | 6.44848i | −1.27387 | − | 0.246564i | ||||
\(685\) | 4.46460i | 0.170584i | ||||||||
\(686\) | 0.673473 | − | 28.3005i | 0.0257133 | − | 1.08052i | ||||
\(687\) | 20.2418 | + | 1.45592i | 0.772274 | + | 0.0555468i | ||||
\(688\) | 31.4510 | + | 3.00229i | 1.19906 | + | 0.114461i | ||||
\(689\) | 22.8657i | 0.871113i | ||||||||
\(690\) | −0.307891 | + | 3.21096i | −0.0117212 | + | 0.122239i | ||||
\(691\) | −36.7240 | −1.39705 | −0.698523 | − | 0.715588i | \(-0.746159\pi\) | ||||
−0.698523 | + | 0.715588i | \(0.746159\pi\) | |||||||
\(692\) | 46.7530 | + | 2.22644i | 1.77728 | + | 0.0846367i | ||||
\(693\) | −12.1672 | − | 1.75939i | −0.462194 | − | 0.0668335i | ||||
\(694\) | −0.696314 | + | 29.2603i | −0.0264317 | + | 1.11071i | ||||
\(695\) | 10.1845 | 0.386320 | ||||||||
\(696\) | −0.319403 | + | 2.21550i | −0.0121069 | + | 0.0839784i | ||||
\(697\) | −10.6758 | −0.404374 | ||||||||
\(698\) | 0.129714 | − | 5.45079i | 0.00490973 | − | 0.206315i | ||||
\(699\) | −39.8573 | − | 2.86679i | −1.50754 | − | 0.108432i | ||||
\(700\) | 0.624124 | − | 13.1060i | 0.0235897 | − | 0.495359i | ||||
\(701\) | −16.0748 | −0.607136 | −0.303568 | − | 0.952810i | \(-0.598178\pi\) | ||||
−0.303568 | + | 0.952810i | \(0.598178\pi\) | |||||||
\(702\) | −16.0602 | − | 3.91660i | −0.606154 | − | 0.147823i | ||||
\(703\) | − | 61.5172i | − | 2.32017i | ||||||
\(704\) | 2.32185 | − | 16.1538i | 0.0875082 | − | 0.608820i | ||||
\(705\) | 0.926638 | − | 12.8832i | 0.0348992 | − | 0.485208i | ||||
\(706\) | 0.582948 | − | 24.4965i | 0.0219395 | − | 0.921937i | ||||
\(707\) | 15.2300i | 0.572782i | ||||||||
\(708\) | 31.1219 | + | 3.73333i | 1.16963 | + | 0.140307i | ||||
\(709\) | 14.8490i | 0.557666i | 0.960340 | + | 0.278833i | \(0.0899475\pi\) | ||||
−0.960340 | + | 0.278833i | \(0.910052\pi\) | |||||||
\(710\) | 14.2252 | + | 0.338519i | 0.533861 | + | 0.0127044i | ||||
\(711\) | −4.10803 | + | 28.4095i | −0.154063 | + | 1.06544i | ||||
\(712\) | −1.03717 | + | 14.5060i | −0.0388696 | + | 0.543634i | ||||
\(713\) | − | 4.61668i | − | 0.172896i | ||||||
\(714\) | −2.74559 | + | 28.6335i | −0.102751 | + | 1.07158i | ||||
\(715\) | −6.04327 | −0.226005 | ||||||||
\(716\) | −1.43326 | + | 30.0971i | −0.0535636 | + | 1.12478i | ||||
\(717\) | −1.63746 | + | 22.7658i | −0.0611520 | + | 0.850205i | ||||
\(718\) | 8.66080 | + | 0.206103i | 0.323218 | + | 0.00769169i | ||||
\(719\) | −45.7333 | −1.70557 | −0.852783 | − | 0.522266i | \(-0.825087\pi\) | ||||
−0.852783 | + | 0.522266i | \(0.825087\pi\) | |||||||
\(720\) | −15.3542 | − | 3.73752i | −0.572218 | − | 0.139289i | ||||
\(721\) | −25.2549 | −0.940543 | ||||||||
\(722\) | −18.3616 | − | 0.436955i | −0.683349 | − | 0.0162618i | ||||
\(723\) | −0.676440 | + | 9.40463i | −0.0251571 | + | 0.349762i | ||||
\(724\) | −1.11469 | + | 23.4073i | −0.0414270 | + | 0.869925i | ||||
\(725\) | −1.49220 | −0.0554188 | ||||||||
\(726\) | −1.59886 | + | 16.6743i | −0.0593393 | + | 0.618842i | ||||
\(727\) | 22.2095i | 0.823706i | 0.911250 | + | 0.411853i | \(0.135118\pi\) | ||||
−0.911250 | + | 0.411853i | \(0.864882\pi\) | |||||||
\(728\) | −12.7490 | − | 0.911547i | −0.472508 | − | 0.0337842i | ||||
\(729\) | −24.5329 | − | 11.2755i | −0.908625 | − | 0.417612i | ||||
\(730\) | 24.5745 | + | 0.584805i | 0.909544 | + | 0.0216446i | ||||
\(731\) | − | 46.1734i | − | 1.70779i | ||||||
\(732\) | 11.0020 | + | 1.31978i | 0.406646 | + | 0.0487807i | ||||
\(733\) | − | 25.0905i | − | 0.926739i | −0.886165 | − | 0.463369i | \(-0.846640\pi\) | ||
0.886165 | − | 0.463369i | \(-0.153360\pi\) | |||||||
\(734\) | −0.613855 | + | 25.7952i | −0.0226578 | + | 0.952119i | ||||
\(735\) | 0.485127 | − | 6.74478i | 0.0178942 | − | 0.248785i | ||||
\(736\) | −5.61687 | − | 0.671374i | −0.207041 | − | 0.0247472i | ||||
\(737\) | − | 1.23922i | − | 0.0456472i | ||||||
\(738\) | 1.29095 | − | 7.63967i | 0.0475204 | − | 0.281220i | ||||
\(739\) | 43.4830 | 1.59955 | 0.799774 | − | 0.600302i | \(-0.204953\pi\) | ||||
0.799774 | + | 0.600302i | \(0.204953\pi\) | |||||||
\(740\) | 1.36268 | − | 28.6149i | 0.0500932 | − | 1.05191i | ||||
\(741\) | −21.9800 | − | 1.58094i | −0.807457 | − | 0.0580774i | ||||
\(742\) | −0.686974 | + | 28.8678i | −0.0252196 | + | 1.05977i | ||||
\(743\) | 32.9745 | 1.20972 | 0.604859 | − | 0.796333i | \(-0.293229\pi\) | ||||
0.604859 | + | 0.796333i | \(0.293229\pi\) | |||||||
\(744\) | 22.3856 | + | 3.22727i | 0.820696 | + | 0.118317i | ||||
\(745\) | 24.2738 | 0.889324 | ||||||||
\(746\) | 0.886804 | − | 37.2650i | 0.0324682 | − | 1.36437i | ||||
\(747\) | −0.597912 | + | 4.13492i | −0.0218765 | + | 0.151289i | ||||
\(748\) | −23.8238 | − | 1.13452i | −0.871086 | − | 0.0414823i | ||||
\(749\) | −25.0302 | −0.914582 | ||||||||
\(750\) | 2.54497 | − | 26.5412i | 0.0929293 | − | 0.969148i | ||||
\(751\) | 38.3311i | 1.39872i | 0.714769 | + | 0.699361i | \(0.246532\pi\) | ||||
−0.714769 | + | 0.699361i | \(0.753468\pi\) | |||||||
\(752\) | 22.5490 | + | 2.15251i | 0.822276 | + | 0.0784939i | ||||
\(753\) | −18.7627 | − | 1.34953i | −0.683751 | − | 0.0491796i | ||||
\(754\) | −0.0345821 | + | 1.45320i | −0.00125941 | + | 0.0529224i | ||||
\(755\) | 16.2053i | 0.589771i | ||||||||
\(756\) | −20.1583 | − | 5.42720i | −0.733151 | − | 0.197385i | ||||
\(757\) | − | 15.5710i | − | 0.565939i | −0.959129 | − | 0.282970i | \(-0.908680\pi\) | ||
0.959129 | − | 0.282970i | \(-0.0913196\pi\) | |||||||
\(758\) | 7.05320 | + | 0.167846i | 0.256184 | + | 0.00609646i | ||||
\(759\) | −3.52424 | − | 0.253485i | −0.127922 | − | 0.00920094i | ||||
\(760\) | −21.0123 | − | 1.50237i | −0.762195 | − | 0.0544967i | ||||
\(761\) | − | 42.7482i | − | 1.54962i | −0.632194 | − | 0.774810i | \(-0.717846\pi\) | ||
0.632194 | − | 0.774810i | \(-0.282154\pi\) | |||||||
\(762\) | 37.0285 | + | 3.55057i | 1.34140 | + | 0.128624i | ||||
\(763\) | −24.6258 | −0.891513 | ||||||||
\(764\) | 31.4554 | + | 1.49795i | 1.13802 | + | 0.0541940i | ||||
\(765\) | −3.30516 | + | 22.8572i | −0.119498 | + | 0.826402i | ||||
\(766\) | 8.51412 | + | 0.202612i | 0.307628 | + | 0.00732068i | ||||
\(767\) | 20.3553 | 0.734987 | ||||||||
\(768\) | 7.18184 | − | 26.7660i | 0.259152 | − | 0.965836i | ||||
\(769\) | −33.1519 | −1.19549 | −0.597743 | − | 0.801688i | \(-0.703936\pi\) | ||||
−0.597743 | + | 0.801688i | \(0.703936\pi\) | |||||||
\(770\) | −7.62960 | − | 0.181563i | −0.274952 | − | 0.00654308i | ||||
\(771\) | 2.50583 | + | 0.180235i | 0.0902453 | + | 0.00649100i | ||||
\(772\) | −29.0203 | − | 1.38199i | −1.04447 | − | 0.0497389i | ||||
\(773\) | −28.0896 | −1.01031 | −0.505156 | − | 0.863028i | \(-0.668565\pi\) | ||||
−0.505156 | + | 0.863028i | \(0.668565\pi\) | |||||||
\(774\) | 33.0420 | + | 5.58342i | 1.18767 | + | 0.200692i | ||||
\(775\) | 15.0773i | 0.541592i | ||||||||
\(776\) | −1.50934 | − | 0.107917i | −0.0541822 | − | 0.00387400i | ||||
\(777\) | 2.71502 | − | 37.7473i | 0.0974008 | − | 1.35418i | ||||
\(778\) | −16.3143 | − | 0.388235i | −0.584896 | − | 0.0139189i | ||||
\(779\) | − | 10.3286i | − | 0.370060i | ||||||
\(780\) | −10.1891 | − | 1.22226i | −0.364827 | − | 0.0437641i | ||||
\(781\) | 15.5863i | 0.557723i | ||||||||
\(782\) | −0.196683 | + | 8.26495i | −0.00703336 | + | 0.295554i | ||||
\(783\) | −0.507473 | + | 2.31932i | −0.0181356 | + | 0.0828857i | ||||
\(784\) | 11.8052 | + | 1.12691i | 0.421613 | + | 0.0402468i | ||||
\(785\) | − | 6.15093i | − | 0.219536i | ||||||
\(786\) | −34.3431 | − | 3.29308i | −1.22498 | − | 0.117460i | ||||
\(787\) | −14.8016 | −0.527621 | −0.263811 | − | 0.964574i | \(-0.584979\pi\) | ||||
−0.263811 | + | 0.964574i | \(0.584979\pi\) | |||||||
\(788\) | 35.1056 | + | 1.67178i | 1.25059 | + | 0.0595546i | ||||
\(789\) | 0.697569 | − | 9.69839i | 0.0248341 | − | 0.345272i | ||||
\(790\) | −0.423936 | + | 17.8145i | −0.0150830 | + | 0.633813i | ||||
\(791\) | −5.37240 | −0.191020 | ||||||||
\(792\) | 3.69272 | − | 16.9113i | 0.131215 | − | 0.600918i | ||||
\(793\) | 7.19587 | 0.255533 | ||||||||
\(794\) | 0.809660 | − | 34.0233i | 0.0287338 | − | 1.20744i | ||||
\(795\) | −1.66325 | + | 23.1244i | −0.0589895 | + | 0.820139i | ||||
\(796\) | −1.62551 | + | 34.1340i | −0.0576146 | + | 1.20985i | ||||
\(797\) | 28.4561 | 1.00797 | 0.503983 | − | 0.863714i | \(-0.331867\pi\) | ||||
0.503983 | + | 0.863714i | \(0.331867\pi\) | |||||||
\(798\) | −27.7022 | − | 2.65630i | −0.980648 | − | 0.0940320i | ||||
\(799\) | − | 33.1043i | − | 1.17115i | ||||||
\(800\) | 18.3437 | + | 2.19259i | 0.648549 | + | 0.0775197i | ||||
\(801\) | −2.20753 | + | 15.2664i | −0.0779992 | + | 0.539411i | ||||
\(802\) | 0.843556 | − | 35.4477i | 0.0297870 | − | 1.25170i | ||||
\(803\) | 26.9260i | 0.950199i | ||||||||
\(804\) | 0.250635 | − | 2.08934i | 0.00883920 | − | 0.0736855i | ||||
\(805\) | 2.64536i | 0.0932366i | ||||||||
\(806\) | 14.6832 | + | 0.349420i | 0.517195 | + | 0.0123078i | ||||
\(807\) | −0.366746 | + | 5.09892i | −0.0129101 | + | 0.179491i | ||||
\(808\) | −21.3894 | − | 1.52934i | −0.752477 | − | 0.0538018i | ||||
\(809\) | 47.7099i | 1.67739i | 0.544601 | + | 0.838696i | \(0.316681\pi\) | ||||
−0.544601 | + | 0.838696i | \(0.683319\pi\) | |||||||
\(810\) | −15.9571 | − | 5.12914i | −0.560674 | − | 0.180220i | ||||
\(811\) | 0.565059 | 0.0198419 | 0.00992094 | − | 0.999951i | \(-0.496842\pi\) | ||||
0.00992094 | + | 0.999951i | \(0.496842\pi\) | |||||||
\(812\) | −0.0873195 | + | 1.83362i | −0.00306431 | + | 0.0643474i | ||||
\(813\) | −14.6627 | − | 1.05463i | −0.514242 | − | 0.0369875i | ||||
\(814\) | 31.3708 | + | 0.746538i | 1.09955 | + | 0.0261661i | ||||
\(815\) | −15.6337 | −0.547625 | ||||||||
\(816\) | −39.9380 | − | 6.73126i | −1.39811 | − | 0.235641i | ||||
\(817\) | 44.6717 | 1.56287 | ||||||||
\(818\) | 37.0970 | + | 0.882804i | 1.29706 | + | 0.0308665i | ||||
\(819\) | −13.4173 | − | 1.94015i | −0.468838 | − | 0.0677943i | ||||
\(820\) | 0.228791 | − | 4.80437i | 0.00798972 | − | 0.167776i | ||||
\(821\) | 42.6322 | 1.48788 | 0.743938 | − | 0.668249i | \(-0.232956\pi\) | ||||
0.743938 | + | 0.668249i | \(0.232956\pi\) | |||||||
\(822\) | −8.26655 | − | 0.792660i | −0.288329 | − | 0.0276472i | ||||
\(823\) | 16.8841i | 0.588543i | 0.955722 | + | 0.294271i | \(0.0950770\pi\) | ||||
−0.955722 | + | 0.294271i | \(0.904923\pi\) | |||||||
\(824\) | 2.53600 | − | 35.4688i | 0.0883459 | − | 1.23561i | ||||
\(825\) | 11.5096 | + | 0.827839i | 0.400711 | + | 0.0288217i | ||||
\(826\) | 25.6985 | + | 0.611552i | 0.894164 | + | 0.0212786i | ||||
\(827\) | 13.4702i | 0.468405i | 0.972188 | + | 0.234202i | \(0.0752478\pi\) | ||||
−0.972188 | + | 0.234202i | \(0.924752\pi\) | |||||||
\(828\) | −5.89067 | − | 1.14017i | −0.204715 | − | 0.0396236i | ||||
\(829\) | − | 40.6857i | − | 1.41307i | −0.707677 | − | 0.706536i | \(-0.750257\pi\) | ||
0.707677 | − | 0.706536i | \(-0.249743\pi\) | |||||||
\(830\) | −0.0617028 | + | 2.59286i | −0.00214173 | + | 0.0899994i | ||||
\(831\) | −53.6736 | − | 3.86054i | −1.86192 | − | 0.133921i | ||||
\(832\) | 2.56041 | − | 17.8135i | 0.0887661 | − | 0.617572i | ||||
\(833\) | − | 17.3312i | − | 0.600491i | ||||||
\(834\) | −1.80819 | + | 18.8574i | −0.0626125 | + | 0.652978i | ||||
\(835\) | 6.67662 | 0.231054 | ||||||||
\(836\) | 1.09763 | − | 23.0490i | 0.0379622 | − | 0.797167i | ||||
\(837\) | 23.4346 | + | 5.12755i | 0.810018 | + | 0.177234i | ||||
\(838\) | −0.190784 | + | 8.01709i | −0.00659054 | + | 0.276946i | ||||
\(839\) | −34.8626 | −1.20359 | −0.601795 | − | 0.798650i | \(-0.705548\pi\) | ||||
−0.601795 | + | 0.798650i | \(0.705548\pi\) | |||||||
\(840\) | −12.8269 | − | 1.84922i | −0.442571 | − | 0.0638043i | ||||
\(841\) | −28.7912 | −0.992801 | ||||||||
\(842\) | −1.31304 | + | 55.1763i | −0.0452504 | + | 1.90150i | ||||
\(843\) | 33.7763 | + | 2.42940i | 1.16332 | + | 0.0836730i | ||||
\(844\) | 4.30844 | + | 0.205174i | 0.148303 | + | 0.00706238i | ||||
\(845\) | 10.4553 | 0.359673 | ||||||||
\(846\) | 23.6897 | + | 4.00306i | 0.814468 | + | 0.137628i | ||||
\(847\) | 13.7372i | 0.472015i | ||||||||
\(848\) | −40.4739 | − | 3.86361i | −1.38988 | − | 0.132677i | ||||
\(849\) | −0.617811 | + | 8.58950i | −0.0212032 | + | 0.294791i | ||||
\(850\) | 0.642331 | − | 26.9919i | 0.0220318 | − | 0.925813i | ||||
\(851\) | − | 10.8770i | − | 0.372858i | ||||||
\(852\) | −3.15237 | + | 26.2789i | −0.107999 | + | 0.900299i | ||||
\(853\) | 20.3449i | 0.696597i | 0.937384 | + | 0.348299i | \(0.113240\pi\) | ||||
−0.937384 | + | 0.348299i | \(0.886760\pi\) | |||||||
\(854\) | 9.08477 | + | 0.216192i | 0.310874 | + | 0.00739794i | ||||
\(855\) | −22.1138 | − | 3.19766i | −0.756275 | − | 0.109358i | ||||
\(856\) | 2.51343 | − | 35.1531i | 0.0859074 | − | 1.20151i | ||||
\(857\) | − | 11.5616i | − | 0.394938i | −0.980309 | − | 0.197469i | \(-0.936728\pi\) | ||
0.980309 | − | 0.197469i | \(-0.0632722\pi\) | |||||||
\(858\) | 1.07294 | − | 11.1896i | 0.0366296 | − | 0.382006i | ||||
\(859\) | −12.3481 | −0.421310 | −0.210655 | − | 0.977560i | \(-0.567560\pi\) | ||||
−0.210655 | + | 0.977560i | \(0.567560\pi\) | |||||||
\(860\) | 20.7792 | + | 0.989534i | 0.708564 | + | 0.0337428i | ||||
\(861\) | 0.455845 | − | 6.33767i | 0.0155351 | − | 0.215987i | ||||
\(862\) | 51.4491 | + | 1.22435i | 1.75236 | + | 0.0417014i | ||||
\(863\) | −19.4082 | −0.660662 | −0.330331 | − | 0.943865i | \(-0.607160\pi\) | ||||
−0.330331 | + | 0.943865i | \(0.607160\pi\) | |||||||
\(864\) | 9.64635 | − | 27.7659i | 0.328175 | − | 0.944617i | ||||
\(865\) | 30.8190 | 1.04788 | ||||||||
\(866\) | −8.38061 | − | 0.199435i | −0.284785 | − | 0.00677708i | ||||
\(867\) | −2.13402 | + | 29.6696i | −0.0724752 | + | 1.00763i | ||||
\(868\) | 18.5270 | + | 0.882283i | 0.628849 | + | 0.0299466i | ||||
\(869\) | −19.5192 | −0.662143 | ||||||||
\(870\) | −0.140679 | + | 1.46713i | −0.00476948 | + | 0.0497403i | ||||
\(871\) | − | 1.36654i | − | 0.0463034i | ||||||
\(872\) | 2.47283 | − | 34.5852i | 0.0837405 | − | 1.17120i | ||||
\(873\) | −1.58846 | − | 0.229693i | −0.0537613 | − | 0.00777392i | ||||
\(874\) | −7.99615 | − | 0.190286i | −0.270474 | − | 0.00643652i | ||||
\(875\) | − | 21.8661i | − | 0.739207i | ||||||
\(876\) | −5.44585 | + | 45.3978i | −0.183998 | + | 1.53385i | ||||
\(877\) | 42.3177i | 1.42897i | 0.699652 | + | 0.714484i | \(0.253338\pi\) | ||||
−0.699652 | + | 0.714484i | \(0.746662\pi\) | |||||||
\(878\) | −0.391159 | + | 16.4372i | −0.0132010 | + | 0.554728i | ||||
\(879\) | −0.433018 | + | 6.02031i | −0.0146053 | + | 0.203060i | ||||
\(880\) | 1.02113 | − | 10.6970i | 0.0344222 | − | 0.360596i | ||||
\(881\) | − | 5.20976i | − | 0.175521i | −0.996142 | − | 0.0877606i | \(-0.972029\pi\) | ||
0.996142 | − | 0.0877606i | \(-0.0279711\pi\) | |||||||
\(882\) | 12.4024 | + | 2.09574i | 0.417609 | + | 0.0705672i | ||||
\(883\) | 13.5991 | 0.457647 | 0.228824 | − | 0.973468i | \(-0.426512\pi\) | ||||
0.228824 | + | 0.973468i | \(0.426512\pi\) | |||||||
\(884\) | −26.2716 | − | 1.25109i | −0.883608 | − | 0.0420786i | ||||
\(885\) | 20.5856 | + | 1.48065i | 0.691978 | + | 0.0497714i | ||||
\(886\) | 0.735730 | − | 30.9167i | 0.0247173 | − | 1.03867i | ||||
\(887\) | 31.3869 | 1.05387 | 0.526935 | − | 0.849906i | \(-0.323341\pi\) | ||||
0.526935 | + | 0.849906i | \(0.323341\pi\) | |||||||
\(888\) | 52.7408 | + | 7.60350i | 1.76987 | + | 0.255157i | ||||
\(889\) | 30.5060 | 1.02314 | ||||||||
\(890\) | −0.227810 | + | 9.57298i | −0.00763622 | + | 0.320887i | ||||
\(891\) | 5.20093 | − | 17.6078i | 0.174238 | − | 0.589882i | ||||
\(892\) | −1.93898 | + | 40.7166i | −0.0649219 | + | 1.36329i | ||||
\(893\) | 32.0277 | 1.07176 | ||||||||
\(894\) | −4.30965 | + | 44.9448i | −0.144136 | + | 1.50318i | ||||
\(895\) | 19.8396i | 0.663164i | ||||||||
\(896\) | 3.76769 | − | 22.4126i | 0.125870 | − | 0.748751i | ||||
\(897\) | −3.88633 | − | 0.279529i | −0.129761 | − | 0.00933321i | ||||
\(898\) | 1.27751 | − | 53.6831i | 0.0426310 | − | 1.79143i | ||||
\(899\) | − | 2.10942i | − | 0.0703532i | ||||||
\(900\) | 19.2379 | + | 3.72359i | 0.641263 | + | 0.124120i | ||||
\(901\) | 59.4200i | 1.97957i | ||||||||
\(902\) | 5.26708 | + | 0.125342i | 0.175374 | + | 0.00417342i | ||||
\(903\) | 27.4108 | + | 1.97156i | 0.912175 | + | 0.0656093i | ||||
\(904\) | 0.539476 | − | 7.54515i | 0.0179427 | − | 0.250948i | ||||
\(905\) | 15.4298i | 0.512903i | ||||||||
\(906\) | −30.0053 | − | 2.87714i | −0.996861 | − | 0.0955865i | ||||
\(907\) | 5.42672 | 0.180191 | 0.0900956 | − | 0.995933i | \(-0.471283\pi\) | ||||
0.0900956 | + | 0.995933i | \(0.471283\pi\) | |||||||
\(908\) | 1.50640 | − | 31.6328i | 0.0499916 | − | 1.04977i | ||||
\(909\) | −22.5107 | − | 3.25506i | −0.746632 | − | 0.107963i | ||||
\(910\) | −8.41348 | − | 0.200217i | −0.278904 | − | 0.00663714i | ||||
\(911\) | 5.57731 | 0.184784 | 0.0923922 | − | 0.995723i | \(-0.470549\pi\) | ||||
0.0923922 | + | 0.995723i | \(0.470549\pi\) | |||||||
\(912\) | 6.51234 | − | 38.6391i | 0.215645 | − | 1.27947i | ||||
\(913\) | −2.84096 | −0.0940222 | ||||||||
\(914\) | 6.95343 | + | 0.165472i | 0.229999 | + | 0.00547334i | ||||
\(915\) | 7.27730 | + | 0.523429i | 0.240580 | + | 0.0173040i | ||||
\(916\) | −1.11468 | + | 23.4071i | −0.0368301 | + | 0.773393i | ||||
\(917\) | −28.2937 | −0.934340 | ||||||||
\(918\) | −41.7350 | − | 10.1779i | −1.37746 | − | 0.335920i | ||||
\(919\) | 31.7977i | 1.04891i | 0.851439 | + | 0.524454i | \(0.175731\pi\) | ||||
−0.851439 | + | 0.524454i | \(0.824269\pi\) | |||||||
\(920\) | −3.71522 | − | 0.265637i | −0.122487 | − | 0.00875778i | ||||
\(921\) | 3.48889 | − | 48.5066i | 0.114963 | − | 1.59835i | ||||
\(922\) | −18.3259 | − | 0.436105i | −0.603530 | − | 0.0143623i | ||||
\(923\) | 17.1877i | 0.565741i | ||||||||
\(924\) | 1.69076 | − | 14.0946i | 0.0556220 | − | 0.463677i | ||||
\(925\) | 35.5223i | 1.16797i | ||||||||
\(926\) | 0.332633 | − | 13.9778i | 0.0109310 | − | 0.459339i | ||||
\(927\) | 5.39767 | − | 37.3281i | 0.177283 | − | 1.22602i | ||||
\(928\) | −2.56642 | − | 0.306759i | −0.0842469 | − | 0.0100699i | ||||
\(929\) | − | 8.03771i | − | 0.263709i | −0.991269 | − | 0.131854i | \(-0.957907\pi\) | ||
0.991269 | − | 0.131854i | \(-0.0420931\pi\) | |||||||
\(930\) | 14.8240 | + | 1.42144i | 0.486097 | + | 0.0466107i | ||||
\(931\) | 16.7676 | 0.549535 | ||||||||
\(932\) | 2.19487 | − | 46.0899i | 0.0718953 | − | 1.50973i | ||||
\(933\) | −2.52833 | + | 35.1517i | −0.0827738 | + | 1.15082i | ||||
\(934\) | 1.28503 | − | 53.9991i | 0.0420474 | − | 1.76691i | ||||
\(935\) | −15.7044 | −0.513587 | ||||||||
\(936\) | 4.07212 | − | 18.6488i | 0.133101 | − | 0.609556i | ||||
\(937\) | −11.4972 | −0.375599 | −0.187799 | − | 0.982207i | \(-0.560135\pi\) | ||||
−0.187799 | + | 0.982207i | \(0.560135\pi\) | |||||||
\(938\) | 0.0410561 | − | 1.72525i | 0.00134053 | − | 0.0563314i | ||||
\(939\) | −2.59127 | + | 36.0267i | −0.0845628 | + | 1.17569i | ||||
\(940\) | 14.8978 | + | 0.709452i | 0.485911 | + | 0.0231398i | ||||
\(941\) | 36.9281 | 1.20382 | 0.601911 | − | 0.798563i | \(-0.294406\pi\) | ||||
0.601911 | + | 0.798563i | \(0.294406\pi\) | |||||||
\(942\) | 11.3889 | + | 1.09206i | 0.371071 | + | 0.0355811i | ||||
\(943\) | − | 1.82621i | − | 0.0594697i | ||||||
\(944\) | −3.43942 | + | 36.0303i | −0.111944 | + | 1.17269i | ||||
\(945\) | −13.4280 | − | 2.93808i | −0.436813 | − | 0.0955757i | ||||
\(946\) | −0.542110 | + | 22.7804i | −0.0176255 | + | 0.740655i | ||||
\(947\) | 18.6243i | 0.605210i | 0.953116 | + | 0.302605i | \(0.0978563\pi\) | ||||
−0.953116 | + | 0.302605i | \(0.902144\pi\) | |||||||
\(948\) | −32.9097 | − | 3.94780i | −1.06886 | − | 0.128219i | ||||
\(949\) | 29.6925i | 0.963858i | ||||||||
\(950\) | 26.1140 | + | 0.621441i | 0.847251 | + | 0.0201622i | ||||
\(951\) | −0.912421 | + | 12.6855i | −0.0295873 | + | 0.411356i | ||||
\(952\) | −33.1301 | − | 2.36879i | −1.07375 | − | 0.0767730i | ||||
\(953\) | − | 6.28063i | − | 0.203450i | −0.994813 | − | 0.101725i | \(-0.967564\pi\) | ||
0.994813 | − | 0.101725i | \(-0.0324361\pi\) | |||||||
\(954\) | −42.5214 | − | 7.18523i | −1.37668 | − | 0.232630i | ||||
\(955\) | 20.7350 | 0.670969 | ||||||||
\(956\) | −26.3258 | − | 1.25367i | −0.851436 | − | 0.0405466i | ||||
\(957\) | −1.61027 | − | 0.115821i | −0.0520527 | − | 0.00374395i | ||||
\(958\) | −58.4697 | − | 1.39142i | −1.88907 | − | 0.0449546i | ||||
\(959\) | −6.81042 | −0.219920 | ||||||||
\(960\) | 3.88514 | − | 17.8288i | 0.125392 | − | 0.575423i | ||||
\(961\) | 9.68623 | 0.312459 | ||||||||
\(962\) | 34.5939 | + | 0.823239i | 1.11535 | + | 0.0265423i | ||||
\(963\) | 5.34963 | − | 36.9959i | 0.172389 | − | 1.19218i | ||||
\(964\) | −10.8753 | − | 0.517895i | −0.350269 | − | 0.0166803i | ||||
\(965\) | −19.1298 | −0.615811 | ||||||||
\(966\) | −4.89808 | − | 0.469665i | −0.157593 | − | 0.0151112i | ||||
\(967\) | 57.5475i | 1.85060i | 0.379233 | + | 0.925301i | \(0.376188\pi\) | ||||
−0.379233 | + | 0.925301i | \(0.623812\pi\) | |||||||
\(968\) | −19.2929 | − | 1.37944i | −0.620098 | − | 0.0443368i | ||||
\(969\) | −57.1185 | − | 4.10832i | −1.83491 | − | 0.131978i | ||||
\(970\) | −0.996066 | − | 0.0237036i | −0.0319817 | − | 0.000761076i | ||||
\(971\) | − | 33.7961i | − | 1.08457i | −0.840195 | − | 0.542284i | \(-0.817560\pi\) | ||
0.840195 | − | 0.542284i | \(-0.182440\pi\) | |||||||
\(972\) | 12.3301 | − | 28.6351i | 0.395487 | − | 0.918471i | ||||
\(973\) | 15.5357i | 0.498052i | ||||||||
\(974\) | 0.205990 | − | 8.65606i | 0.00660034 | − | 0.277358i | ||||
\(975\) | 12.6921 | + | 0.912893i | 0.406472 | + | 0.0292360i | ||||
\(976\) | −1.21588 | + | 12.7372i | −0.0389195 | + | 0.407708i | ||||
\(977\) | − | 52.2944i | − | 1.67305i | −0.547932 | − | 0.836523i | \(-0.684585\pi\) | ||
0.547932 | − | 0.836523i | \(-0.315415\pi\) | |||||||
\(978\) | 2.77566 | − | 28.9470i | 0.0887558 | − | 0.925624i | ||||
\(979\) | −10.4890 | −0.335230 | ||||||||
\(980\) | 7.79948 | + | 0.371422i | 0.249145 | + | 0.0118647i | ||||
\(981\) | 5.26320 | − | 36.3982i | 0.168041 | − | 1.16211i | ||||
\(982\) | −0.595560 | + | 25.0265i | −0.0190051 | + | 0.798627i | ||||
\(983\) | 2.31390 | 0.0738018 | 0.0369009 | − | 0.999319i | \(-0.488251\pi\) | ||||
0.0369009 | + | 0.999319i | \(0.488251\pi\) | |||||||
\(984\) | 8.85504 | + | 1.27661i | 0.282288 | + | 0.0406967i | ||||
\(985\) | 23.1411 | 0.737338 | ||||||||
\(986\) | −0.0898669 | + | 3.77636i | −0.00286194 | + | 0.120264i | ||||
\(987\) | 19.6523 | + | 1.41352i | 0.625541 | + | 0.0449928i | ||||
\(988\) | 1.21040 | − | 25.4171i | 0.0385079 | − | 0.808627i | ||||
\(989\) | 7.89849 | 0.251157 | ||||||||
\(990\) | 1.89901 | − | 11.2381i | 0.0603546 | − | 0.357172i | ||||
\(991\) | − | 38.2038i | − | 1.21359i | −0.794860 | − | 0.606793i | \(-0.792456\pi\) | ||
0.794860 | − | 0.606793i | \(-0.207544\pi\) | |||||||
\(992\) | −3.09952 | + | 25.9313i | −0.0984098 | + | 0.823320i | ||||
\(993\) | 2.48249 | − | 34.5144i | 0.0787795 | − | 1.09528i | ||||
\(994\) | −0.516386 | + | 21.6994i | −0.0163788 | + | 0.688264i | ||||
\(995\) | 22.5007i | 0.713319i | ||||||||
\(996\) | −4.78992 | − | 0.574591i | −0.151774 | − | 0.0182066i | ||||
\(997\) | 6.82163i | 0.216043i | 0.994149 | + | 0.108022i | \(0.0344516\pi\) | ||||
−0.994149 | + | 0.108022i | \(0.965548\pi\) | |||||||
\(998\) | −29.2451 | − | 0.695952i | −0.925738 | − | 0.0220300i | ||||
\(999\) | 55.2122 | + | 12.0806i | 1.74684 | + | 0.382212i |
(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 | 552.2.j.d.323.1 | yes | 42 | |
3.2 | odd | 2 | 552.2.j.c.323.42 | yes | 42 | ||
4.3 | odd | 2 | 2208.2.j.d.47.22 | 42 | |||
8.3 | odd | 2 | 552.2.j.c.323.41 | ✓ | 42 | ||
8.5 | even | 2 | 2208.2.j.c.47.22 | 42 | |||
12.11 | even | 2 | 2208.2.j.c.47.21 | 42 | |||
24.5 | odd | 2 | 2208.2.j.d.47.21 | 42 | |||
24.11 | even | 2 | inner | 552.2.j.d.323.2 | yes | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
552.2.j.c.323.41 | ✓ | 42 | 8.3 | odd | 2 | ||
552.2.j.c.323.42 | yes | 42 | 3.2 | odd | 2 | ||
552.2.j.d.323.1 | yes | 42 | 1.1 | even | 1 | trivial | |
552.2.j.d.323.2 | yes | 42 | 24.11 | even | 2 | inner | |
2208.2.j.c.47.21 | 42 | 12.11 | even | 2 | |||
2208.2.j.c.47.22 | 42 | 8.5 | even | 2 | |||
2208.2.j.d.47.21 | 42 | 24.5 | odd | 2 | |||
2208.2.j.d.47.22 | 42 | 4.3 | odd | 2 |