Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(47,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.be (of order \(18\), degree \(6\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 239.1 | ||
Character | \(\chi\) | \(=\) | 432.239 |
Dual form | 432.2.be.c.47.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{11}{18}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.50778 | + | 0.852402i | −0.870519 | + | 0.492134i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.12767 | − | 0.375166i | −0.951524 | − | 0.167779i | −0.323722 | − | 0.946152i | \(-0.604934\pi\) |
−0.627802 | + | 0.778373i | \(0.716045\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.50142 | + | 2.98107i | 0.945447 | + | 1.12674i | 0.991798 | + | 0.127815i | \(0.0407964\pi\) |
−0.0463507 | + | 0.998925i | \(0.514759\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.54682 | − | 2.57047i | 0.515607 | − | 0.856825i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.0357619 | + | 0.202816i | 0.0107826 | + | 0.0611513i | 0.989724 | − | 0.142989i | \(-0.0456713\pi\) |
−0.978942 | + | 0.204140i | \(0.934560\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.01394 | + | 0.733014i | −0.558566 | + | 0.203302i | −0.605848 | − | 0.795580i | \(-0.707166\pi\) |
0.0472822 | + | 0.998882i | \(0.484944\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.52786 | − | 1.24796i | 0.910890 | − | 0.322223i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.87137 | − | 3.38984i | −1.42402 | − | 0.822156i | −0.427377 | − | 0.904074i | \(-0.640562\pi\) |
−0.996639 | + | 0.0819176i | \(0.973896\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.56062 | + | 3.78777i | −1.50511 | + | 0.868975i | −0.505127 | + | 0.863045i | \(0.668554\pi\) |
−0.999982 | + | 0.00592975i | \(0.998112\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.31267 | − | 2.36260i | −1.37754 | − | 0.515562i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.99143 | − | 3.34921i | −0.832271 | − | 0.698358i | 0.123540 | − | 0.992340i | \(-0.460575\pi\) |
−0.955811 | + | 0.293982i | \(0.905020\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.312223 | − | 0.113640i | −0.0624446 | − | 0.0227280i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.141195 | + | 5.19423i | −0.0271730 | + | 0.999631i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.709501 | + | 1.94934i | −0.131751 | + | 0.361983i | −0.987973 | − | 0.154625i | \(-0.950583\pi\) |
0.856222 | + | 0.516608i | \(0.172805\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.02516 | + | 1.22174i | −0.184125 | + | 0.219431i | −0.850209 | − | 0.526445i | \(-0.823525\pi\) |
0.666084 | + | 0.745876i | \(0.267969\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.226802 | − | 0.275319i | −0.0394811 | − | 0.0479269i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.20380 | − | 7.28120i | −0.710572 | − | 1.23075i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.90071 | − | 6.75622i | 0.641272 | − | 1.11072i | −0.343877 | − | 0.939015i | \(-0.611740\pi\) |
0.985149 | − | 0.171701i | \(-0.0549264\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.41176 | − | 2.82191i | 0.386191 | − | 0.451868i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.12650 | + | 11.3375i | 0.644452 | + | 1.77062i | 0.637269 | + | 0.770642i | \(0.280064\pi\) |
0.00718287 | + | 0.999974i | \(0.497714\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.15496 | + | 1.08528i | −0.938622 | + | 0.165504i | −0.621973 | − | 0.783038i | \(-0.713669\pi\) |
−0.316649 | + | 0.948543i | \(0.602558\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.25549 | + | 4.88881i | −0.634370 | + | 0.728781i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.44521 | − | 2.89087i | 0.502535 | − | 0.421677i | −0.355958 | − | 0.934502i | \(-0.615845\pi\) |
0.858493 | + | 0.512825i | \(0.171401\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.41417 | + | 8.02017i | −0.202025 | + | 1.14574i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.7423 | + | 0.106374i | 1.64424 | + | 0.0148953i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 6.89537i | − | 0.947152i | −0.880753 | − | 0.473576i | \(-0.842963\pi\) | ||
0.880753 | − | 0.473576i | \(-0.157037\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.444942i | − | 0.0599960i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.66329 | − | 11.3034i | 0.882574 | − | 1.49718i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.0937549 | − | 0.531710i | 0.0122058 | − | 0.0692228i | −0.978096 | − | 0.208152i | \(-0.933255\pi\) |
0.990302 | + | 0.138930i | \(0.0443661\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.695271 | − | 0.583402i | 0.0890203 | − | 0.0746969i | −0.597191 | − | 0.802099i | \(-0.703717\pi\) |
0.686212 | + | 0.727402i | \(0.259272\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 11.5320 | − | 1.81864i | 1.45290 | − | 0.229127i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.56001 | − | 0.804052i | 0.565599 | − | 0.0997304i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.77754 | + | 4.88376i | 0.217161 | + | 0.596646i | 0.999662 | − | 0.0260040i | \(-0.00827827\pi\) |
−0.782500 | + | 0.622650i | \(0.786056\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.87308 | + | 1.64758i | 1.06819 | + | 0.198345i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.04889 | + | 8.74494i | −0.599193 | + | 1.03783i | 0.393747 | + | 0.919219i | \(0.371179\pi\) |
−0.992940 | + | 0.118614i | \(0.962155\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.46358 | + | 2.53500i | 0.171299 | + | 0.296699i | 0.938874 | − | 0.344260i | \(-0.111870\pi\) |
−0.767575 | + | 0.640959i | \(0.778537\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.567631 | − | 0.0947951i | 0.0655444 | − | 0.0109460i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.515154 | + | 0.613936i | −0.0587072 | + | 0.0699645i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.25749 | + | 3.45493i | −0.141479 | + | 0.388710i | −0.990113 | − | 0.140270i | \(-0.955203\pi\) |
0.848634 | + | 0.528980i | \(0.177425\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.21468 | − | 7.95213i | −0.468298 | − | 0.883571i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.0574 | − | 3.66058i | −1.10394 | − | 0.401800i | −0.275171 | − | 0.961395i | \(-0.588735\pi\) |
−0.828766 | + | 0.559595i | \(0.810957\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.2206 | + | 9.41520i | 1.21704 | + | 1.02122i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.591846 | − | 3.54396i | −0.0634525 | − | 0.379953i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.79768 | + | 5.65669i | −1.03855 | + | 0.599608i | −0.919423 | − | 0.393270i | \(-0.871344\pi\) |
−0.119129 | + | 0.992879i | \(0.538010\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.22287 | − | 4.17013i | −0.757163 | − | 0.437148i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.504309 | − | 2.71597i | 0.0522944 | − | 0.281633i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 15.3799 | − | 5.59782i | 1.57794 | − | 0.574324i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.67663 | + | 9.50863i | 0.170236 | + | 0.965455i | 0.943500 | + | 0.331372i | \(0.107511\pi\) |
−0.773265 | + | 0.634084i | \(0.781378\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.576651 | + | 0.221795i | 0.0579556 | + | 0.0222912i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.78270 | + | 6.89155i | 0.575400 | + | 0.685735i | 0.972730 | − | 0.231941i | \(-0.0745076\pi\) |
−0.397330 | + | 0.917676i | \(0.630063\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.36511 | + | 0.946015i | 0.528640 | + | 0.0932136i | 0.431597 | − | 0.902067i | \(-0.357950\pi\) |
0.0970435 | + | 0.995280i | \(0.469061\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 12.5449 | + | 7.39514i | 1.22426 | + | 0.721692i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.67182 | −0.161621 | −0.0808106 | − | 0.996729i | \(-0.525751\pi\) | ||||
−0.0808106 | + | 0.996729i | \(0.525751\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.6614 | 1.50009 | 0.750043 | − | 0.661389i | \(-0.230033\pi\) | ||||
0.750043 | + | 0.661389i | \(0.230033\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.122405 | + | 13.5119i | −0.0116181 | + | 1.28249i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.6094 | − | 3.28135i | −1.75063 | − | 0.308683i | −0.795738 | − | 0.605641i | \(-0.792917\pi\) |
−0.954890 | + | 0.296958i | \(0.904028\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.23595 | + | 8.62347i | 0.674755 | + | 0.804142i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.23101 | + | 6.31062i | −0.113807 | + | 0.583417i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.58140 | − | 25.9824i | −0.419976 | − | 2.38180i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.2968 | − | 3.74772i | 0.936069 | − | 0.340701i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −15.8860 | − | 13.5770i | −1.43239 | − | 1.22420i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.97689 | + | 5.76016i | 0.892360 | + | 0.515205i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.2182 | − | 7.63155i | 1.17293 | − | 0.677191i | 0.218561 | − | 0.975823i | \(-0.429864\pi\) |
0.954368 | + | 0.298633i | \(0.0965305\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.35524 | − | 6.88287i | 0.735638 | − | 0.606003i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.54614 | + | 5.49286i | 0.571939 | + | 0.479914i | 0.882289 | − | 0.470709i | \(-0.156002\pi\) |
−0.310350 | + | 0.950622i | \(0.600446\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −27.7025 | − | 10.0829i | −2.40211 | − | 0.874297i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.24912 | − | 10.9987i | 0.193573 | − | 0.946614i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.62113 | − | 9.94898i | 0.309374 | − | 0.849999i | −0.683405 | − | 0.730040i | \(-0.739501\pi\) |
0.992779 | − | 0.119959i | \(-0.0382763\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.73633 | − | 4.45278i | 0.316911 | − | 0.377680i | −0.583948 | − | 0.811791i | \(-0.698493\pi\) |
0.900859 | + | 0.434111i | \(0.142937\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.73044 | + | 7.29551i | −0.229945 | + | 0.614393i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.220689 | − | 0.382245i | −0.0184550 | − | 0.0319649i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.24091 | − | 3.88137i | 0.186098 | − | 0.322331i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.70414 | − | 13.2981i | −0.387991 | − | 1.09681i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.99214 | + | 8.22085i | 0.245126 | + | 0.673478i | 0.999848 | + | 0.0174333i | \(0.00554947\pi\) |
−0.754722 | + | 0.656045i | \(0.772228\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.7992 | + | 3.84379i | −1.77400 | + | 0.312803i | −0.962445 | − | 0.271478i | \(-0.912487\pi\) |
−0.811551 | + | 0.584282i | \(0.801376\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −17.7955 | + | 9.84873i | −1.43868 | + | 0.796223i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.63957 | − | 2.21486i | 0.212015 | − | 0.177902i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.835627 | + | 4.73908i | −0.0666903 | + | 0.378220i | 0.933135 | + | 0.359526i | \(0.117062\pi\) |
−0.999825 | + | 0.0186933i | \(0.994049\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.87763 | + | 10.3967i | 0.466126 | + | 0.824514i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 20.2765i | − | 1.59801i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 0.859928i | − | 0.0673547i | −0.999433 | − | 0.0336774i | \(-0.989278\pi\) | ||
0.999433 | − | 0.0336774i | \(-0.0107219\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.379270 | + | 0.670877i | 0.0295261 | + | 0.0522277i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.13490 | + | 12.1076i | −0.165203 | + | 0.936915i | 0.783651 | + | 0.621201i | \(0.213355\pi\) |
−0.948854 | + | 0.315714i | \(0.897756\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.43994 | + | 5.40375i | −0.495380 | + | 0.415673i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.411729 | + | 22.7229i | −0.0314857 | + | 1.73766i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.9738 | − | 3.34560i | 1.44255 | − | 0.254361i | 0.603045 | − | 0.797707i | \(-0.293954\pi\) |
0.839509 | + | 0.543346i | \(0.182843\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.442231 | − | 1.21502i | −0.0334295 | − | 0.0918469i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.311869 | + | 0.881621i | 0.0234415 | + | 0.0662667i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.93879 | + | 12.0183i | −0.518629 | + | 0.898292i | 0.481136 | + | 0.876646i | \(0.340224\pi\) |
−0.999766 | + | 0.0216464i | \(0.993109\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.0771 | − | 20.9182i | −0.897687 | − | 1.55484i | −0.830443 | − | 0.557103i | \(-0.811913\pi\) |
−0.0672441 | − | 0.997737i | \(-0.521421\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.551026 | + | 1.47229i | −0.0407330 | + | 0.108835i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.8341 | + | 12.9116i | −0.796541 | + | 0.949281i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.477541 | − | 1.31203i | 0.0349213 | − | 0.0959454i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −15.8376 | + | 12.5720i | −1.15201 | + | 0.914481i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.84293 | + | 2.49062i | 0.495137 | + | 0.180215i | 0.577505 | − | 0.816387i | \(-0.304026\pi\) |
−0.0823686 | + | 0.996602i | \(0.526248\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.46660 | + | 6.26522i | 0.537458 | + | 0.450981i | 0.870667 | − | 0.491872i | \(-0.163687\pi\) |
−0.333210 | + | 0.942853i | \(0.608132\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.19013 | + | 5.09929i | −0.443284 | + | 0.365168i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.00953 | + | 2.89226i | −0.356914 | + | 0.206065i | −0.667726 | − | 0.744407i | \(-0.732732\pi\) |
0.310812 | + | 0.950471i | \(0.399399\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.57936 | − | 2.06654i | −0.253734 | − | 0.146493i | 0.367739 | − | 0.929929i | \(-0.380132\pi\) |
−0.621473 | + | 0.783436i | \(0.713465\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.84307 | − | 5.84847i | −0.482673 | − | 0.412519i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.58588 | + | 2.76104i | −0.532425 | + | 0.193787i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.52641 | − | 25.6706i | −0.316138 | − | 1.79291i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −14.7831 | + | 5.07924i | −1.02750 | + | 0.353032i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.00284 | − | 1.19514i | −0.0693680 | − | 0.0826695i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.16208 | + | 1.61552i | 0.630744 | + | 0.111217i | 0.479875 | − | 0.877337i | \(-0.340682\pi\) |
0.150868 | + | 0.988554i | \(0.451793\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.158435 | − | 17.4892i | 0.0108558 | − | 1.19834i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.5029 | 0.920890 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.20646 | −0.421322 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.36760 | − | 2.57467i | −0.295135 | − | 0.173980i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.3094 | + | 2.52313i | 0.962553 | + | 0.169724i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.613674 | − | 0.731349i | −0.0410947 | − | 0.0489747i | 0.745106 | − | 0.666946i | \(-0.232399\pi\) |
−0.786200 | + | 0.617972i | \(0.787955\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.775062 | + | 0.626781i | −0.0516708 | + | 0.0417854i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.84335 | + | 27.4680i | 0.321465 | + | 1.82312i | 0.533436 | + | 0.845840i | \(0.320900\pi\) |
−0.211972 | + | 0.977276i | \(0.567989\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.0424 | + | 4.01909i | −0.729700 | + | 0.265589i | −0.680038 | − | 0.733177i | \(-0.738037\pi\) |
−0.0496624 | + | 0.998766i | \(0.515815\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.253420 | − | 1.36480i | 0.0166738 | − | 0.0897973i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.8253 | − | 7.40471i | −0.840216 | − | 0.485099i | 0.0171219 | − | 0.999853i | \(-0.494550\pi\) |
−0.857337 | + | 0.514755i | \(0.827883\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.41483 | + | 4.85831i | −0.548923 | + | 0.316921i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.04896 | − | 6.28118i | −0.0681375 | − | 0.408006i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.1559 | + | 15.2346i | 1.17441 | + | 0.985446i | 1.00000 | 0.000772466i | \(0.000245884\pi\) | |
0.174409 | + | 0.984673i | \(0.444199\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.90441 | − | 2.87697i | −0.509168 | − | 0.185322i | 0.0746451 | − | 0.997210i | \(-0.476218\pi\) |
−0.583813 | + | 0.811888i | \(0.698440\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.1332 | + | 8.39749i | 0.842498 | + | 0.538700i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.01779 | − | 16.5338i | 0.384463 | − | 1.05630i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.4362 | − | 12.4374i | 0.664039 | − | 0.791371i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 18.2846 | − | 3.05355i | 1.15874 | − | 0.193511i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.92565 | − | 13.7276i | −0.500263 | − | 0.866481i | −1.00000 | 0.000303448i | \(-0.999903\pi\) | |
0.499737 | − | 0.866177i | \(-0.333430\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.536531 | − | 0.929300i | 0.0337314 | − | 0.0584246i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −24.9438 | − | 4.63162i | −1.56204 | − | 0.290044i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.10717 | − | 8.53688i | −0.193820 | − | 0.532516i | 0.804272 | − | 0.594261i | \(-0.202555\pi\) |
−0.998092 | + | 0.0617455i | \(0.980333\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 29.8981 | − | 5.27184i | 1.85778 | − | 0.327576i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.91325 | + | 4.83904i | 0.242224 | + | 0.299529i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.0506 | + | 11.7898i | −0.866396 | + | 0.726993i | −0.963336 | − | 0.268297i | \(-0.913539\pi\) |
0.0969397 | + | 0.995290i | \(0.469095\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.58691 | + | 14.6711i | −0.158913 | + | 0.901238i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.95101 | − | 16.8806i | 0.608992 | − | 1.03308i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 15.0367i | − | 0.916806i | −0.888745 | − | 0.458403i | \(-0.848422\pi\) | ||
0.888745 | − | 0.458403i | \(-0.151578\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 17.2892i | − | 1.05025i | −0.851027 | − | 0.525123i | \(-0.824019\pi\) | ||
0.851027 | − | 0.525123i | \(-0.175981\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 14.4452 | + | 0.130859i | 0.874261 | + | 0.00791996i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.0118823 | − | 0.0673878i | 0.000716528 | − | 0.00406363i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.22261 | + | 7.73869i | −0.554133 | + | 0.464973i | −0.876338 | − | 0.481697i | \(-0.840020\pi\) |
0.322205 | + | 0.946670i | \(0.395576\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.55471 | + | 4.52497i | 0.0930781 | + | 0.270903i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.09306 | − | 1.25070i | 0.423137 | − | 0.0746104i | 0.0419746 | − | 0.999119i | \(-0.486635\pi\) |
0.381162 | + | 0.924508i | \(0.375524\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.6550 | − | 29.2743i | −0.633373 | − | 1.74018i | −0.671604 | − | 0.740910i | \(-0.734395\pi\) |
0.0382310 | − | 0.999269i | \(-0.487828\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −18.4179 | + | 21.5502i | −1.09099 | + | 1.27652i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −23.4757 | + | 40.6612i | −1.38573 | + | 2.40015i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.4820 | + | 25.0835i | 0.851881 | + | 1.47550i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.6332 | − | 12.9078i | −0.623327 | − | 0.756668i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.3668 | + | 17.1217i | −0.839316 | + | 1.00026i | 0.160596 | + | 0.987020i | \(0.448658\pi\) |
−0.999912 | + | 0.0132378i | \(0.995786\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.398959 | + | 1.09613i | −0.0232283 | + | 0.0638193i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.05852 | + | 0.157119i | −0.0614217 | + | 0.00911698i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.4935 | + | 3.81933i | 0.606856 | + | 0.220877i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.6314 | − | 15.6336i | −1.07390 | − | 0.901107i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.5934 | − | 5.46179i | −0.838371 | − | 0.313771i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.69818 | + | 0.980446i | −0.0972376 | + | 0.0561402i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.17802 | − | 4.72158i | −0.466744 | − | 0.269475i | 0.248132 | − | 0.968726i | \(-0.420183\pi\) |
−0.714876 | + | 0.699252i | \(0.753517\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.89582 | + | 3.14685i | −0.506065 | + | 0.179018i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.0789 | + | 4.03239i | −0.628227 | + | 0.228656i | −0.636460 | − | 0.771310i | \(-0.719602\pi\) |
0.00823228 | + | 0.999966i | \(0.497380\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.74976 | − | 9.92336i | −0.0989020 | − | 0.560901i | −0.993482 | − | 0.113993i | \(-0.963636\pi\) |
0.894580 | − | 0.446909i | \(-0.147475\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −25.2187 | − | 0.456951i | −1.42091 | − | 0.0257463i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.34365 | + | 11.1353i | 0.524792 | + | 0.625422i | 0.961707 | − | 0.274080i | \(-0.0883734\pi\) |
−0.436915 | + | 0.899503i | \(0.643929\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.420730 | − | 0.0741861i | −0.0235564 | − | 0.00415362i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.52075 | − | 1.42506i | 0.140694 | − | 0.0795394i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 51.3597 | 2.85773 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.712098 | 0.0395001 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −23.6140 | + | 13.3498i | −1.30585 | + | 0.738244i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 17.2358 | + | 3.03914i | 0.950241 | + | 0.167553i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.36795 | + | 7.58902i | 0.350014 | + | 0.417130i | 0.912113 | − | 0.409940i | \(-0.134450\pi\) |
−0.562099 | + | 0.827070i | \(0.690006\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11.3330 | − | 20.4773i | −0.621045 | − | 1.12215i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.94981 | − | 11.0579i | −0.106529 | − | 0.604158i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.9688 | + | 5.81216i | −0.869874 | + | 0.316608i | −0.738116 | − | 0.674674i | \(-0.764284\pi\) |
−0.131758 | + | 0.991282i | \(0.542062\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 30.8560 | − | 10.9152i | 1.67587 | − | 0.592830i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.284450 | − | 0.164227i | −0.0154039 | − | 0.00889342i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.85511 | + | 2.22575i | −0.208156 | + | 0.120179i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −18.2609 | − | 6.83438i | −0.983134 | − | 0.367951i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.11669 | − | 3.45432i | −0.220996 | − | 0.185437i | 0.525568 | − | 0.850752i | \(-0.323853\pi\) |
−0.746563 | + | 0.665314i | \(0.768297\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.9030 | + | 6.15220i | 0.904799 | + | 0.329320i | 0.752174 | − | 0.658964i | \(-0.229005\pi\) |
0.152625 | + | 0.988284i | \(0.451227\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.52309 | − | 10.5644i | −0.188049 | − | 0.563884i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.47242 | + | 6.79292i | −0.131594 | + | 0.361551i | −0.987937 | − | 0.154856i | \(-0.950509\pi\) |
0.856343 | + | 0.516407i | \(0.172731\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.0232 | − | 16.7122i | 0.744274 | − | 0.886991i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 29.0552 | + | 35.2706i | 1.53776 | + | 1.86672i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.4680 | − | 18.1311i | −0.552481 | − | 0.956925i | −0.998095 | − | 0.0616998i | \(-0.980348\pi\) |
0.445614 | − | 0.895225i | \(-0.352985\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.1945 | − | 33.2458i | 1.01024 | − | 1.74978i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.3307 | + | 14.4277i | −0.647195 | + | 0.757259i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.16298 | − | 5.94273i | −0.113215 | − | 0.311057i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.0472 | − | 1.77160i | 0.524461 | − | 0.0924766i | 0.0948516 | − | 0.995491i | \(-0.469762\pi\) |
0.429609 | + | 0.903015i | \(0.358651\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 35.5257 | + | 6.92998i | 1.84939 | + | 0.360760i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 20.5556 | − | 17.2482i | 1.06719 | − | 0.895482i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.55154 | − | 14.4705i | 0.132114 | − | 0.749254i | −0.844712 | − | 0.535220i | \(-0.820229\pi\) |
0.976826 | − | 0.214034i | \(-0.0686603\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −19.9530 | − | 0.180755i | −1.03037 | − | 0.00933413i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 4.44593i | − | 0.228977i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1.47535i | − | 0.0757834i | −0.999282 | − | 0.0378917i | \(-0.987936\pi\) | ||
0.999282 | − | 0.0378917i | \(-0.0120642\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.4251 | + | 22.7740i | −0.687788 | + | 1.16675i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.50484 | − | 19.8770i | 0.179089 | − | 1.01567i | −0.754228 | − | 0.656613i | \(-0.771989\pi\) |
0.933317 | − | 0.359053i | \(-0.116900\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.32641 | − | 1.11299i | 0.0675999 | − | 0.0567231i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.73092 | + | 17.4999i | −0.342152 | + | 0.889570i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.1450 | − | 2.14149i | 0.615777 | − | 0.108578i | 0.142945 | − | 0.989731i | \(-0.454343\pi\) |
0.472832 | + | 0.881153i | \(0.343232\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.0819 | + | 33.1947i | 0.611008 | + | 1.67873i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.5523 | − | 2.70211i | −0.734066 | − | 0.136303i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.97170 | − | 6.87919i | 0.199838 | − | 0.346130i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.83157 | − | 15.2967i | −0.443244 | − | 0.767720i | 0.554684 | − | 0.832061i | \(-0.312839\pi\) |
−0.997928 | + | 0.0643404i | \(0.979506\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 50.3640 | − | 8.41085i | 2.52135 | − | 0.421069i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.13835 | − | 10.8907i | 0.456347 | − | 0.543853i | −0.487983 | − | 0.872853i | \(-0.662267\pi\) |
0.944330 | + | 0.329000i | \(0.106712\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.16906 | − | 3.21197i | 0.0582351 | − | 0.160000i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.98409 | + | 18.5007i | 0.297352 | + | 0.919309i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.50977 | + | 0.549510i | 0.0748363 | + | 0.0272382i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.7136 | + | 12.3461i | 0.727539 | + | 0.610477i | 0.929459 | − | 0.368925i | \(-0.120274\pi\) |
−0.201921 | + | 0.979402i | \(0.564718\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.02065 | + | 18.0876i | 0.148997 | + | 0.892194i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.81959 | − | 1.05054i | 0.0895361 | − | 0.0516937i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.0254 | + | 11.5617i | 0.983009 | + | 0.567541i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.83801 | + | 9.89868i | −0.0900079 | + | 0.484741i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.36997 | − | 1.95451i | 0.262340 | − | 0.0954840i | −0.207502 | − | 0.978235i | \(-0.566533\pi\) |
0.469842 | + | 0.882751i | \(0.344311\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.99357 | + | 28.3200i | 0.243372 | + | 1.38023i | 0.824244 | + | 0.566235i | \(0.191601\pi\) |
−0.580872 | + | 0.813995i | \(0.697288\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.10179 | − | 13.3275i | −0.102193 | − | 0.648005i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.44796 | + | 1.72561i | 0.0702361 | + | 0.0837042i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.47833 | + | 0.613323i | 0.168328 | + | 0.0296808i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.658578 | + | 0.388227i | 0.0317964 | + | 0.0187438i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.3077 | −0.689176 | −0.344588 | − | 0.938754i | \(-0.611981\pi\) | ||||
−0.344588 | + | 0.938754i | \(0.611981\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.66463 | 0.128054 | 0.0640269 | − | 0.997948i | \(-0.479606\pi\) | ||||
0.0640269 | + | 0.997948i | \(0.479606\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.0703202 | + | 7.76243i | −0.00337159 | + | 0.372180i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 38.8723 | + | 6.85423i | 1.85951 | + | 0.327882i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.2181 | − | 28.8620i | −1.15587 | − | 1.37751i | −0.913257 | − | 0.407383i | \(-0.866441\pi\) |
−0.242609 | − | 0.970124i | \(-0.578003\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.4282 | + | 16.0409i | 0.877533 | + | 0.763851i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.46327 | + | 19.6412i | 0.164545 | + | 0.933179i | 0.949533 | + | 0.313668i | \(0.101558\pi\) |
−0.784988 | + | 0.619511i | \(0.787331\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 22.9685 | − | 8.35983i | 1.08881 | − | 0.396294i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.5190 | − | 9.84475i | −0.544828 | − | 0.465641i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.0203 | + | 13.8682i | 1.13359 | + | 0.654479i | 0.944835 | − | 0.327546i | \(-0.106222\pi\) |
0.188755 | + | 0.982024i | \(0.439555\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.15185 | + | 1.24237i | −0.101327 | + | 0.0585009i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 29.5921 | − | 24.3773i | 1.39036 | − | 1.14535i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.8034 | + | 11.5824i | 0.647114 | + | 0.542993i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.0182308 | − | 0.00663549i | −0.000852803 | − | 0.000310395i | 0.341594 | − | 0.939848i | \(-0.389033\pi\) |
−0.342447 | + | 0.939537i | \(0.611256\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 18.4366 | − | 30.0186i | 0.860547 | − | 1.40115i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.58160 | + | 20.8303i | −0.353110 | + | 0.970163i | 0.628254 | + | 0.778008i | \(0.283770\pi\) |
−0.981365 | + | 0.192155i | \(0.938452\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.6835 | + | 31.8001i | −1.24009 | + | 1.47788i | −0.418068 | + | 0.908416i | \(0.637293\pi\) |
−0.822018 | + | 0.569461i | \(0.807152\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.09194 | + | 5.58950i | −0.0970116 | + | 0.259207i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.4135 | − | 19.7688i | −0.528154 | − | 0.914789i | −0.999461 | − | 0.0328204i | \(-0.989551\pi\) |
0.471307 | − | 0.881969i | \(-0.343782\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.1125 | + | 17.5153i | −0.466950 | + | 0.808782i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.77965 | − | 7.85779i | −0.128080 | − | 0.362068i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.440226 | − | 1.20951i | −0.0202416 | − | 0.0556134i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.47882 | − | 0.437082i | 0.113736 | − | 0.0200547i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −17.7244 | − | 10.6659i | −0.811543 | − | 0.488358i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.42704 | − | 2.03652i | 0.110894 | − | 0.0930512i | −0.585655 | − | 0.810561i | \(-0.699162\pi\) |
0.696549 | + | 0.717510i | \(0.254718\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.90338 | + | 16.4659i | −0.132383 | + | 0.750780i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 17.2837 | + | 30.5726i | 0.786438 | + | 1.39110i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 20.8603i | − | 0.947216i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 26.6585i | − | 1.20801i | −0.796980 | − | 0.604005i | \(-0.793571\pi\) | ||
0.796980 | − | 0.604005i | \(-0.206429\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.733004 | + | 1.29658i | 0.0331476 | + | 0.0586336i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.111406 | + | 0.631817i | −0.00502770 | + | 0.0285135i | −0.987218 | − | 0.159373i | \(-0.949053\pi\) |
0.982191 | + | 0.187887i | \(0.0601638\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.7737 | − | 9.04019i | 0.485222 | − | 0.407150i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.14371 | − | 0.688247i | −0.0514061 | − | 0.0309344i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −38.6987 | + | 6.82363i | −1.73587 | + | 0.306081i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.174102 | − | 0.478340i | −0.00779386 | − | 0.0214134i | 0.935735 | − | 0.352705i | \(-0.114738\pi\) |
−0.943529 | + | 0.331291i | \(0.892516\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.10159 | − | 20.0755i | −0.317276 | − | 0.896905i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.3187 | + | 29.9969i | −0.772203 | + | 1.33750i | 0.164150 | + | 0.986435i | \(0.447512\pi\) |
−0.936353 | + | 0.351060i | \(0.885821\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.71821 | − | 16.8324i | −0.432455 | − | 0.749034i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.10386 | − | 13.6371i | 0.226671 | − | 0.605645i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.71875 | + | 8.00710i | −0.297804 | + | 0.354908i | −0.894109 | − | 0.447849i | \(-0.852190\pi\) |
0.596306 | + | 0.802757i | \(0.296635\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.89599 | + | 10.7041i | −0.172348 | + | 0.473523i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −18.7483 | − | 34.6122i | −0.827756 | − | 1.52817i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.0603 | − | 4.02562i | −0.487375 | − | 0.177390i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.709522 | + | 0.595360i | 0.0312048 | + | 0.0261839i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −25.7566 | + | 21.2178i | −1.13059 | + | 0.931357i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.6891 | + | 10.7902i | −0.818785 | + | 0.472726i | −0.849997 | − | 0.526787i | \(-0.823397\pi\) |
0.0312124 | + | 0.999513i | \(0.490063\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.21284 | + | 1.27758i | 0.0967607 | + | 0.0558648i | 0.547600 | − | 0.836741i | \(-0.315542\pi\) |
−0.450839 | + | 0.892605i | \(0.648875\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.70247 | + | 1.45503i | 0.0743021 | + | 0.0635027i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.1606 | − | 3.69816i | 0.442603 | − | 0.161094i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.720415 | + | 4.08568i | 0.0313224 | + | 0.177638i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.22173 | − | 1.06346i | −0.0530184 | − | 0.0461501i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.6211 | − | 19.8082i | −0.719938 | − | 0.857988i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.55709 | + | 0.627211i | 0.153786 | + | 0.0271167i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.217740 | − | 24.0357i | 0.00939618 | − | 1.03722i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.67719 | −0.0722418 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.9264 | −0.512754 | −0.256377 | − | 0.966577i | \(-0.582529\pi\) | ||||
−0.256377 | + | 0.966577i | \(0.582529\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 36.0405 | + | 21.2456i | 1.54664 | + | 0.911735i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −33.3223 | − | 5.87561i | −1.42737 | − | 0.251684i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.7484 | − | 16.3847i | −0.587838 | − | 0.700558i | 0.387351 | − | 0.921932i | \(-0.373390\pi\) |
−0.975189 | + | 0.221374i | \(0.928946\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.424159 | − | 2.68960i | −0.0181027 | − | 0.114789i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.72889 | − | 15.4763i | −0.116255 | − | 0.659313i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.4449 | + | 4.89355i | −0.571736 | + | 0.208095i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.32964 | − | 28.7030i | 0.226231 | − | 1.21837i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.2042 | + | 13.3970i | 0.983196 | + | 0.567648i | 0.903233 | − | 0.429150i | \(-0.141187\pi\) |
0.0799622 | + | 0.996798i | \(0.474520\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.6002 | − | 6.69737i | 0.490635 | − | 0.283268i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.398351 | + | 2.38532i | 0.0168184 | + | 0.100708i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.0741 | − | 18.5223i | −0.930311 | − | 0.780624i | 0.0455620 | − | 0.998962i | \(-0.485492\pi\) |
−0.975873 | + | 0.218338i | \(0.929937\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 38.3637 | + | 13.9633i | 1.61397 | + | 0.587439i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 13.1632 | − | 32.4559i | 0.552803 | − | 1.36302i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.21939 | + | 25.3301i | −0.386497 | + | 1.06189i | 0.582070 | + | 0.813138i | \(0.302243\pi\) |
−0.968567 | + | 0.248753i | \(0.919979\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.01830 | + | 2.40531i | −0.0844631 | + | 0.100659i | −0.806621 | − | 0.591069i | \(-0.798706\pi\) |
0.722158 | + | 0.691728i | \(0.243150\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.4407 | + | 2.07761i | −0.519716 | + | 0.0867932i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.865612 | + | 1.49928i | 0.0360985 | + | 0.0625245i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.8980 | + | 34.4644i | −0.828366 | + | 1.43477i | 0.0709533 | + | 0.997480i | \(0.477396\pi\) |
−0.899319 | + | 0.437292i | \(0.855937\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.5985 | − | 3.08205i | −0.689811 | − | 0.128086i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.2452 | − | 39.1383i | −0.590990 | − | 1.62373i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.39849 | − | 0.246592i | 0.0579196 | − | 0.0102128i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.98672 | − | 12.9651i | 0.206176 | − | 0.536041i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.9410 | + | 10.8588i | −0.534132 | + | 0.448190i | −0.869525 | − | 0.493888i | \(-0.835575\pi\) |
0.335394 | + | 0.942078i | \(0.391131\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.09802 | − | 11.8985i | 0.0864474 | − | 0.490268i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.08793 | − | 8.63103i | 0.209289 | − | 0.355033i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.0610029i | 0.00250509i | 0.999999 | + | 0.00125254i | \(0.000398697\pi\) | ||||
−0.999999 | + | 0.00125254i | \(0.999601\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 57.0008i | 2.33680i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.15842 | + | 0.0648484i | 0.292975 | + | 0.00265407i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.17873 | − | 23.6987i | 0.170738 | − | 0.968304i | −0.772211 | − | 0.635366i | \(-0.780849\pi\) |
0.942949 | − | 0.332938i | \(-0.108040\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.4133 | + | 15.4506i | −0.751095 | + | 0.630244i | −0.935792 | − | 0.352552i | \(-0.885314\pi\) |
0.184697 | + | 0.982795i | \(0.440870\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.3031 | + | 2.98518i | 0.623191 | + | 0.121566i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −23.3142 | + | 4.11091i | −0.947855 | + | 0.167132i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.920929 | + | 2.53023i | 0.0373794 | + | 0.102699i | 0.956978 | − | 0.290160i | \(-0.0937084\pi\) |
−0.919599 | + | 0.392859i | \(0.871486\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.08436 | − | 10.6293i | 0.368117 | − | 0.430720i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.81939 | + | 8.34743i | −0.194972 | + | 0.337701i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.5649 | + | 23.4951i | 0.547880 | + | 0.948957i | 0.998420 | + | 0.0562001i | \(0.0178985\pi\) |
−0.450539 | + | 0.892757i | \(0.648768\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 28.7065 | + | 34.8473i | 1.15756 | + | 1.40518i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.5765 | − | 25.7138i | 0.868635 | − | 1.03520i | −0.130408 | − | 0.991460i | \(-0.541629\pi\) |
0.999043 | − | 0.0437387i | \(-0.0139269\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.2455 | + | 41.8867i | −0.612769 | + | 1.68357i | 0.111254 | + | 0.993792i | \(0.464513\pi\) |
−0.724022 | + | 0.689776i | \(0.757709\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 17.9601 | − | 20.2595i | 0.720715 | − | 0.812987i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −41.3711 | − | 15.0579i | −1.65750 | − | 0.603280i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.7939 | − | 14.9309i | −0.711756 | − | 0.597235i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.53081 | + | 0.947188i | 0.101071 | + | 0.0378270i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −45.8050 | + | 26.4455i | −1.82636 | + | 1.05445i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.8750 | − | 13.2069i | −0.910640 | − | 0.525758i | −0.0300027 | − | 0.999550i | \(-0.509552\pi\) |
−0.880637 | + | 0.473792i | \(0.842885\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −15.1915 | + | 5.37392i | −0.603808 | + | 0.213594i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −30.9872 | + | 11.2784i | −1.22969 | + | 0.447570i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.03084 | − | 17.1888i | −0.120086 | − | 0.681043i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.6689 | + | 26.5049i | 0.580293 | + | 1.04852i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.6135 | − | 13.8404i | −0.458704 | − | 0.546663i | 0.486269 | − | 0.873809i | \(-0.338357\pi\) |
−0.944974 | + | 0.327146i | \(0.893913\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −42.9848 | − | 7.57937i | −1.69515 | − | 0.298901i | −0.759156 | − | 0.650908i | \(-0.774388\pi\) |
−0.935997 | + | 0.352007i | \(0.885499\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −20.3594 | + | 11.5099i | −0.801652 | + | 0.453201i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 44.0779 | 1.73288 | 0.866441 | − | 0.499279i | \(-0.166402\pi\) | ||||
0.866441 | + | 0.499279i | \(0.166402\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.111192 | 0.00436468 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.35800 | − | 5.29040i | 0.366769 | − | 0.207347i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.7422 | − | 2.59945i | −0.576906 | − | 0.101724i | −0.122421 | − | 0.992478i | \(-0.539066\pi\) |
−0.454486 | + | 0.890754i | \(0.650177\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.8673 | − | 14.1429i | −0.463694 | − | 0.552609i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.78005 | + | 0.159091i | 0.342542 | + | 0.00620672i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.62215 | − | 14.8709i | −0.102144 | − | 0.579290i | −0.992323 | − | 0.123677i | \(-0.960531\pi\) |
0.890178 | − | 0.455613i | \(-0.150580\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.1294 | − | 6.59856i | 0.705152 | − | 0.256654i | 0.0355431 | − | 0.999368i | \(-0.488684\pi\) |
0.669609 | + | 0.742714i | \(0.266462\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −23.7262 | + | 8.39301i | −0.921448 | + | 0.325957i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 55.1591 | + | 31.8461i | 2.13898 | + | 1.23494i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.36067 | − | 5.40438i | 0.362446 | − | 0.209259i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.54869 | + | 0.579618i | 0.0598759 | + | 0.0224093i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.143187 | + | 0.120148i | 0.00552769 | + | 0.00463828i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.3140 | + | 3.75400i | 0.397576 | + | 0.144706i | 0.533068 | − | 0.846073i | \(-0.321039\pi\) |
−0.135491 | + | 0.990779i | \(0.543261\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.634356 | − | 1.60571i | 0.0244164 | − | 0.0618039i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.9926 | − | 30.2020i | 0.422481 | − | 1.16076i | −0.527802 | − | 0.849367i | \(-0.676984\pi\) |
0.950283 | − | 0.311388i | \(-0.100794\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.1520 | + | 28.7832i | −0.926868 | + | 1.10460i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −30.7165 | − | 37.2873i | −1.17706 | − | 1.42885i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.0306 | − | 27.7658i | −0.613394 | − | 1.06243i | −0.990664 | − | 0.136327i | \(-0.956470\pi\) |
0.377270 | − | 0.926103i | \(-0.376863\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.4371 | + | 19.8097i | −0.436989 | + | 0.756888i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.2236 | − | 15.4725i | 0.504513 | − | 0.590311i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.05440 | + | 13.8869i | 0.192557 | + | 0.529047i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.37408 | − | 0.771269i | 0.166398 | − | 0.0293405i | −0.0898284 | − | 0.995957i | \(-0.528632\pi\) |
0.256226 | + | 0.966617i | \(0.417521\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.781257 | + | 2.27384i | 0.0296775 | + | 0.0863761i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.62021 | + | 8.07232i | −0.364915 | + | 0.306200i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.2040 | − | 80.5547i | 0.538013 | − | 3.05123i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 25.6496 | + | 0.232361i | 0.970158 | + | 0.00878870i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.5938i | 1.04220i | 0.853495 | + | 0.521101i | \(0.174478\pi\) | ||||
−0.853495 | + | 0.521101i | \(0.825522\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 59.1000i | 2.22900i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.54652 | − | 14.4981i | 0.321880 | − | 0.546030i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.07928 | + | 34.4773i | −0.228635 | + | 1.29665i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.46960 | − | 6.26774i | 0.280527 | − | 0.235390i | −0.491657 | − | 0.870789i | \(-0.663609\pi\) |
0.772184 | + | 0.635399i | \(0.219164\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.93570 | + | 8.57652i | 0.260109 | + | 0.321644i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.18373 | − | 1.44301i | 0.306483 | − | 0.0540412i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.326149 | + | 0.896087i | 0.0121973 | + | 0.0335118i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −40.3612 | − | 7.49438i | −1.50732 | − | 0.279883i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.5609 | − | 28.6843i | 0.617616 | − | 1.06974i | −0.372304 | − | 0.928111i | \(-0.621432\pi\) |
0.989920 | − | 0.141631i | \(-0.0452347\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.6003 | + | 18.3602i | 0.394774 | + | 0.683769i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.3705 | − | 2.39989i | 0.534444 | − | 0.0892527i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.443045 | − | 0.528001i | 0.0164543 | − | 0.0196095i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.52972 | − | 9.69783i | 0.130910 | − | 0.359673i | −0.856869 | − | 0.515535i | \(-0.827593\pi\) |
0.987779 | + | 0.155862i | \(0.0498156\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.9601 | − | 1.46680i | −0.998523 | − | 0.0543260i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 39.8170 | + | 14.4922i | 1.47268 | + | 0.536013i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.0067 | − | 15.1094i | −0.665091 | − | 0.558078i | 0.246517 | − | 0.969138i | \(-0.420714\pi\) |
−0.911608 | + | 0.411061i | \(0.865158\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.01987 | + | 30.0589i | 0.185161 | + | 1.10874i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.926936 | + | 0.535166i | −0.0341441 | + | 0.0197131i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.0525 | + | 10.4226i | 0.664073 | + | 0.383403i | 0.793827 | − | 0.608143i | \(-0.208085\pi\) |
−0.129754 | + | 0.991546i | \(0.541419\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.13388 | + | 27.6487i | −0.188598 | + | 1.01570i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.7561 | − | 6.46269i | 0.651408 | − | 0.237093i | 0.00488550 | − | 0.999988i | \(-0.498445\pi\) |
0.646522 | + | 0.762895i | \(0.276223\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.28212 | − | 18.6138i | −0.120247 | − | 0.681957i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −24.9664 | + | 20.1899i | −0.913471 | + | 0.738710i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.18193 | − | 4.98383i | −0.152804 | − | 0.182105i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.970086 | + | 0.171052i | 0.0353989 | + | 0.00624179i | 0.191320 | − | 0.981528i | \(-0.438723\pi\) |
−0.155921 | + | 0.987770i | \(0.549834\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 23.6516 | + | 13.9425i | 0.861913 | + | 0.508091i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 47.8237 | 1.74048 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.04898 | 0.0381259 | 0.0190630 | − | 0.999818i | \(-0.493932\pi\) | ||||
0.0190630 | + | 0.999818i | \(0.493932\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.0168364 | + | 1.85852i | −0.000611124 | + | 0.0674601i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −45.5984 | − | 8.04023i | −1.65294 | − | 0.291458i | −0.732043 | − | 0.681259i | \(-0.761433\pi\) |
−0.920899 | + | 0.389801i | \(0.872544\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 39.1756 | + | 46.6877i | 1.41825 | + | 1.69021i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 41.5578 | − | 14.2786i | 1.50253 | − | 0.516245i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.200935 | + | 1.13956i | 0.00725532 | + | 0.0411470i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.85772 | − | 2.85997i | 0.283356 | − | 0.103133i | −0.196432 | − | 0.980517i | \(-0.562936\pi\) |
0.479789 | + | 0.877384i | \(0.340713\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.9618 | + | 10.2232i | 0.430793 | + | 0.368180i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.6959 | − | 10.7941i | −0.672445 | − | 0.388236i | 0.124557 | − | 0.992212i | \(-0.460249\pi\) |
−0.797003 | + | 0.603976i | \(0.793582\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.458918 | − | 0.264956i | 0.0164848 | − | 0.00951751i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −40.5861 | + | 33.4340i | −1.45602 | + | 1.19944i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −70.0162 | − | 58.7506i | −2.50859 | − | 2.10496i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.95417 | − | 0.711260i | −0.0699257 | − | 0.0254509i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.0251 | − | 3.96055i | −0.358269 | − | 0.141539i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.55588 | − | 9.76971i | 0.126915 | − | 0.348696i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.551585 | + | 0.657353i | −0.0196619 | + | 0.0234321i | −0.775786 | − | 0.630996i | \(-0.782646\pi\) |
0.756124 | + | 0.654428i | \(0.227091\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.1356 | − | 29.7533i | 0.396436 | − | 1.05924i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −36.7680 | − | 63.6841i | −1.30732 | − | 2.26435i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.972592 | + | 1.68458i | −0.0345378 | + | 0.0598212i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.60516 | − | 24.3259i | −0.305194 | − | 0.862751i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.33003 | + | 9.14917i | 0.117956 | + | 0.324080i | 0.984594 | − | 0.174857i | \(-0.0559462\pi\) |
−0.866638 | + | 0.498937i | \(0.833724\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30.0277 | + | 5.29469i | −1.06230 | + | 0.187313i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.614880 | + | 33.9346i | −0.0217257 | + | 1.19902i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.461798 | + | 0.387494i | −0.0162965 | + | 0.0136744i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.60706 | + | 43.1418i | −0.268114 | + | 1.52055i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.8173 | + | 22.6721i | 0.451192 | + | 0.798097i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.0689i | 0.354005i | 0.984210 | + | 0.177003i | \(0.0566401\pi\) | ||||
−0.984210 | + | 0.177003i | \(0.943360\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 18.3336i | − | 0.643779i | −0.946777 | − | 0.321889i | \(-0.895682\pi\) | ||
0.946777 | − | 0.321889i | \(-0.104318\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.7374 | + | 26.0684i | 0.516862 | + | 0.914259i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.322616 | + | 1.82964i | −0.0113007 | + | 0.0640896i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 36.2695 | − | 30.4337i | 1.26891 | − | 1.06474i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −21.8917 | + | 12.1158i | −0.764958 | + | 0.423359i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −40.0948 | + | 7.06979i | −1.39932 | + | 0.246737i | −0.821862 | − | 0.569686i | \(-0.807065\pi\) |
−0.577454 | + | 0.816423i | \(0.695954\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.35467 | + | 6.46940i | 0.0820786 | + | 0.225509i | 0.973943 | − | 0.226795i | \(-0.0728246\pi\) |
−0.891864 | + | 0.452304i | \(0.850602\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.0395255 | + | 0.111735i | 0.00137610 | + | 0.00389010i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.10736 | − | 15.7744i | 0.316694 | − | 0.548530i | −0.663102 | − | 0.748529i | \(-0.730761\pi\) |
0.979796 | + | 0.199999i | \(0.0640939\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.97068 | + | 12.0736i | 0.242102 | + | 0.419333i | 0.961313 | − | 0.275459i | \(-0.0888299\pi\) |
−0.719211 | + | 0.694792i | \(0.755497\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.30923 | − | 19.5296i | 0.253554 | − | 0.677475i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 35.4902 | − | 42.2956i | 1.22966 | − | 1.46546i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.08473 | − | 24.9601i | 0.314390 | − | 0.863780i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.20126 | − | 5.49744i | −0.214347 | − | 0.190019i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.4902 | + | 7.82180i | 0.741925 | + | 0.270039i | 0.685204 | − | 0.728352i | \(-0.259713\pi\) |
0.0567211 | + | 0.998390i | \(0.481935\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.9188 | + | 15.8747i | 0.652371 | + | 0.547404i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.62870 | + | 7.93192i | −0.331630 | + | 0.273190i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 15.7294 | − | 9.08136i | 0.541107 | − | 0.312408i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 36.9287 | + | 21.3208i | 1.26889 | + | 0.732592i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 41.0189 | + | 35.0570i | 1.40777 | + | 1.20315i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −38.1974 | + | 13.9027i | −1.30939 | + | 0.476579i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.14225 | + | 23.4919i | 0.141828 | + | 0.804346i | 0.969860 | + | 0.243664i | \(0.0783496\pi\) |
−0.828032 | + | 0.560681i | \(0.810539\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.40089 | − | 48.1925i | 0.321504 | − | 1.64815i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.33534 | + | 11.1254i | 0.318889 | + | 0.380037i | 0.901548 | − | 0.432680i | \(-0.142432\pi\) |
−0.582659 | + | 0.812717i | \(0.697987\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.2973 | − | 5.34222i | −1.03373 | − | 0.182274i | −0.369055 | − | 0.929408i | \(-0.620319\pi\) |
−0.664674 | + | 0.747133i | \(0.731430\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.736672 | − | 81.3190i | 0.0251057 | − | 2.77134i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.740209 | 0.0251970 | 0.0125985 | − | 0.999921i | \(-0.495990\pi\) | ||||
0.0125985 | + | 0.999921i | \(0.495990\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −41.6253 | −1.41530 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −43.2169 | − | 25.4761i | −1.46772 | − | 0.865212i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.745685 | − | 0.131484i | −0.0252956 | − | 0.00446030i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.15973 | − | 8.53263i | −0.242598 | − | 0.289117i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 27.0351 | + | 10.3984i | 0.915001 | + | 0.351934i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.78491 | + | 44.1504i | 0.263178 | + | 1.49256i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.300658 | + | 0.109431i | −0.0101525 | + | 0.00369521i | −0.347091 | − | 0.937831i | \(-0.612831\pi\) |
0.336939 | + | 0.941527i | \(0.390608\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.06746 | − | 38.0620i | 0.238379 | − | 1.28380i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.53702 | − | 1.46475i | −0.0854744 | − | 0.0493487i | 0.456654 | − | 0.889645i | \(-0.349048\pi\) |
−0.542128 | + | 0.840296i | \(0.682381\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.0872 | + | 27.1858i | −1.58461 | + | 0.914876i | −0.590438 | + | 0.807083i | \(0.701045\pi\) |
−0.994173 | + | 0.107793i | \(0.965622\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.332800 | − | 1.99280i | −0.0111870 | − | 0.0669873i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.16957 | + | 6.85508i | 0.274307 | + | 0.230171i | 0.769555 | − | 0.638581i | \(-0.220478\pi\) |
−0.495248 | + | 0.868752i | \(0.664923\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 55.8146 | + | 20.3148i | 1.87196 | + | 0.681338i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.46209 | − | 1.13919i | 0.0489820 | − | 0.0381642i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.6527 | + | 32.0156i | −0.389943 | + | 1.07136i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.2723 | − | 22.9679i | 0.644203 | − | 0.767731i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −19.0775 | + | 3.18597i | −0.636981 | + | 0.106377i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.65423 | − | 2.86522i | −0.0551718 | − | 0.0955603i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −23.3742 | + | 40.4852i | −0.778706 | + | 1.34876i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 41.4183 | + | 7.69066i | 1.37831 | + | 0.255929i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17.8484 | + | 49.0381i | 0.593301 | + | 1.63008i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.1993 | − | 4.26700i | 0.803526 | − | 0.141683i | 0.243222 | − | 0.969971i | \(-0.421796\pi\) |
0.560304 | + | 0.828287i | \(0.310684\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 26.6594 | − | 4.20428i | 0.884235 | − | 0.139447i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.38166 | + | 3.67665i | −0.145171 | + | 0.121813i | −0.712481 | − | 0.701691i | \(-0.752429\pi\) |
0.567310 | + | 0.823504i | \(0.307984\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.382753 | − | 2.17070i | 0.0126673 | − | 0.0718397i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.72476 | − | 2.92583i | 0.0570187 | − | 0.0967250i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 33.2545i | 1.09816i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 18.1413i | − | 0.598426i | −0.954186 | − | 0.299213i | \(-0.903276\pi\) | ||
0.954186 | − | 0.299213i | \(-0.0967242\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.3554 | + | 0.148164i | 0.538927 | + | 0.00488216i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.75800 | − | 21.3127i | 0.123696 | − | 0.701516i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.98567 | + | 1.66617i | −0.0652883 | + | 0.0547834i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.7306 | − | 12.3276i | 0.352439 | − | 0.404891i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.76282 | + | 1.01614i | −0.189072 | + | 0.0333385i | −0.267382 | − | 0.963591i | \(-0.586159\pi\) |
0.0783102 | + | 0.996929i | \(0.475048\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21.1008 | − | 57.9739i | −0.691550 | − | 1.90002i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.2674 | − | 15.5237i | 0.434354 | − | 0.508222i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.50828 | + | 2.61242i | −0.0493261 | + | 0.0854353i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.55013 | + | 11.3452i | 0.213983 | + | 0.370630i | 0.952958 | − | 0.303104i | \(-0.0980228\pi\) |
−0.738974 | + | 0.673734i | \(0.764690\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.0969 | + | 13.4708i | 0.362135 | + | 0.439602i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.91952 | − | 3.47934i | 0.0951735 | − | 0.113423i | −0.716356 | − | 0.697735i | \(-0.754191\pi\) |
0.811529 | + | 0.584312i | \(0.198636\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 21.5009 | − | 59.0732i | 0.700166 | − | 1.92369i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 38.4138 | − | 20.8075i | 1.24960 | − | 0.676867i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.58228 | + | 0.575904i | 0.0514173 | + | 0.0187144i | 0.367601 | − | 0.929984i | \(-0.380179\pi\) |
−0.316183 | + | 0.948698i | \(0.602402\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.80576 | − | 4.03251i | −0.156001 | − | 0.130901i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.5800 | − | 8.82512i | −0.764633 | − | 0.286174i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20.8678 | − | 12.0481i | 0.675975 | − | 0.390275i | −0.122362 | − | 0.992486i | \(-0.539047\pi\) |
0.798337 | + | 0.602211i | \(0.205713\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.6251 | − | 7.86646i | −0.440898 | − | 0.254553i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.697606 | − | 0.246775i | 0.0225504 | − | 0.00797709i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 38.7166 | − | 14.0917i | 1.25023 | − | 0.455045i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.94140 | + | 28.0241i | 0.159400 | + | 0.904002i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.58601 | + | 4.29738i | −0.0833331 | + | 0.138481i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13.5360 | − | 16.1316i | −0.435739 | − | 0.519293i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.2346 | + | 4.62588i | 0.843649 | + | 0.148758i | 0.578737 | − | 0.815514i | \(-0.303546\pi\) |
0.264912 | + | 0.964272i | \(0.414657\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −77.4394 | + | 43.7791i | −2.48771 | + | 1.40639i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.7928 | 0.506815 | 0.253408 | − | 0.967360i | \(-0.418449\pi\) | ||||
0.253408 | + | 0.967360i | \(0.418449\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.6202 | 0.725170 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.07369 | + | 0.606993i | −0.0343856 | + | 0.0194393i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.9884 | + | 3.17184i | 0.575501 | + | 0.101476i | 0.453821 | − | 0.891093i | \(-0.350061\pi\) |
0.121680 | + | 0.992569i | \(0.461172\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.49765 | − | 1.78483i | −0.0478651 | − | 0.0570435i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 24.2253 | − | 40.2572i | 0.773456 | − | 1.28531i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.63000 | + | 14.9154i | 0.0838838 | + | 0.475729i | 0.997592 | + | 0.0693576i | \(0.0220949\pi\) |
−0.913708 | + | 0.406371i | \(0.866794\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.7437 | − | 4.27436i | 0.374186 | − | 0.136193i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −28.5784 | + | 10.1095i | −0.909662 | + | 0.321788i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 28.2019 | + | 16.2824i | 0.896769 | + | 0.517750i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.4600 | − | 12.3899i | 0.681698 | − | 0.393578i | −0.118797 | − | 0.992919i | \(-0.537904\pi\) |
0.800494 | + | 0.599340i | \(0.204570\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −16.0704 | − | 6.01455i | −0.509978 | − | 0.190866i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.84040 | + | 5.73978i | 0.216855 | + | 0.181963i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.8546 | − | 5.40662i | −0.470448 | − | 0.171229i | 0.0959070 | − | 0.995390i | \(-0.469425\pi\) |
−0.566356 | + | 0.824161i | \(0.691647\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 34.5426 | + | 21.2151i | 1.09288 | + | 0.671217i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 432.2.be.c.239.1 | yes | 36 | |
4.3 | odd | 2 | 432.2.be.b.239.6 | yes | 36 | ||
27.20 | odd | 18 | 432.2.be.b.47.6 | ✓ | 36 | ||
108.47 | even | 18 | inner | 432.2.be.c.47.1 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
432.2.be.b.47.6 | ✓ | 36 | 27.20 | odd | 18 | ||
432.2.be.b.239.6 | yes | 36 | 4.3 | odd | 2 | ||
432.2.be.c.47.1 | yes | 36 | 108.47 | even | 18 | inner | |
432.2.be.c.239.1 | yes | 36 | 1.1 | even | 1 | trivial |