Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(73,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.73");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.bz (of order \(12\), degree \(4\), 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: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 82.3 | ||
Character | \(\chi\) | \(=\) | 315.82 |
Dual form | 315.2.bz.d.73.3 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.49657 | + | 0.401003i | −1.05823 | + | 0.283552i | −0.745649 | − | 0.666338i | \(-0.767861\pi\) |
−0.312582 | + | 0.949891i | \(0.601194\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.346853 | − | 0.200256i | 0.173427 | − | 0.100128i | ||||
\(5\) | −1.61490 | − | 1.54664i | −0.722204 | − | 0.691680i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.44171 | − | 1.01885i | −0.922880 | − | 0.385088i | ||||
\(8\) | 1.75234 | − | 1.75234i | 0.619545 | − | 0.619545i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.03701 | + | 1.66707i | 0.960387 | + | 0.527175i | ||||
\(11\) | 2.59461 | + | 4.49400i | 0.782306 | + | 1.35499i | 0.930595 | + | 0.366049i | \(0.119290\pi\) |
−0.148290 | + | 0.988944i | \(0.547377\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.30901 | + | 3.30901i | 0.917755 | + | 0.917755i | 0.996866 | − | 0.0791106i | \(-0.0252080\pi\) |
−0.0791106 | + | 0.996866i | \(0.525208\pi\) | |||||||
\(14\) | 4.06274 | + | 0.545636i | 1.08581 | + | 0.145827i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.32031 | + | 4.01889i | −0.580077 | + | 1.00472i | ||||
\(17\) | −0.0194028 | − | 0.00519896i | −0.00470587 | − | 0.00126093i | 0.256465 | − | 0.966553i | \(-0.417442\pi\) |
−0.261171 | + | 0.965292i | \(0.584109\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.24048 | + | 2.14858i | −0.284586 | + | 0.492918i | −0.972509 | − | 0.232866i | \(-0.925190\pi\) |
0.687922 | + | 0.725784i | \(0.258523\pi\) | |||||||
\(20\) | −0.869856 | − | 0.213066i | −0.194506 | − | 0.0476429i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.68512 | − | 5.68512i | −1.21207 | − | 1.21207i | ||||
\(23\) | −0.601811 | − | 2.24599i | −0.125486 | − | 0.468321i | 0.874370 | − | 0.485259i | \(-0.161275\pi\) |
−0.999857 | + | 0.0169383i | \(0.994608\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.215788 | + | 4.99534i | 0.0431576 | + | 0.999068i | ||||
\(26\) | −6.27908 | − | 3.62523i | −1.23143 | − | 0.710966i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.05094 | + | 0.135576i | −0.198610 | + | 0.0256215i | ||||
\(29\) | 10.2081i | 1.89559i | 0.318874 | + | 0.947797i | \(0.396695\pi\) | ||||
−0.318874 | + | 0.947797i | \(0.603305\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.69268 | − | 3.28667i | 1.02244 | − | 0.590303i | 0.107627 | − | 0.994191i | \(-0.465675\pi\) |
0.914808 | + | 0.403888i | \(0.132342\pi\) | |||||||
\(32\) | 0.578101 | − | 2.15750i | 0.102195 | − | 0.381396i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.0311223 | 0.00533744 | ||||||||
\(35\) | 2.36732 | + | 5.42179i | 0.400150 | + | 0.916450i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.66573 | − | 0.714279i | 0.438243 | − | 0.117427i | −0.0329501 | − | 0.999457i | \(-0.510490\pi\) |
0.471193 | + | 0.882030i | \(0.343824\pi\) | |||||||
\(38\) | 0.994876 | − | 3.71293i | 0.161390 | − | 0.602316i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.54009 | + | 0.119604i | −0.875965 | + | 0.0189111i | ||||
\(41\) | 3.68910i | 0.576141i | 0.957609 | + | 0.288070i | \(0.0930137\pi\) | ||||
−0.957609 | + | 0.288070i | \(0.906986\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.79725 | + | 2.79725i | −0.426576 | + | 0.426576i | −0.887460 | − | 0.460884i | \(-0.847532\pi\) |
0.460884 | + | 0.887460i | \(0.347532\pi\) | |||||||
\(44\) | 1.79990 | + | 1.03917i | 0.271345 | + | 0.156661i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.80130 | + | 3.11994i | 0.265587 | + | 0.460010i | ||||
\(47\) | −0.303190 | − | 1.13152i | −0.0442248 | − | 0.165049i | 0.940282 | − | 0.340397i | \(-0.110562\pi\) |
−0.984506 | + | 0.175348i | \(0.943895\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.92390 | + | 4.97546i | 0.703415 | + | 0.710780i | ||||
\(50\) | −2.32609 | − | 7.38932i | −0.328959 | − | 1.04501i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.81039 | + | 0.485093i | 0.251056 | + | 0.0672702i | ||||
\(53\) | 4.60942 | + | 1.23509i | 0.633152 | + | 0.169653i | 0.561100 | − | 0.827748i | \(-0.310378\pi\) |
0.0720526 | + | 0.997401i | \(0.477045\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.76059 | − | 11.2703i | 0.372237 | − | 1.51969i | ||||
\(56\) | −6.06407 | + | 2.49334i | −0.810345 | + | 0.333187i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.09348 | − | 15.2771i | −0.537500 | − | 2.00598i | ||||
\(59\) | −0.222589 | − | 0.385535i | −0.0289786 | − | 0.0501924i | 0.851172 | − | 0.524886i | \(-0.175892\pi\) |
−0.880151 | + | 0.474694i | \(0.842559\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.18643 | + | 0.684984i | 0.151906 | + | 0.0877032i | 0.574027 | − | 0.818837i | \(-0.305381\pi\) |
−0.422120 | + | 0.906540i | \(0.638714\pi\) | |||||||
\(62\) | −7.20150 | + | 7.20150i | −0.914591 | + | 0.914591i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 5.82056i | − | 0.727570i | ||||||
\(65\) | −0.225854 | − | 10.4616i | −0.0280137 | − | 1.29760i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.52946 | + | 5.70802i | −0.186853 | + | 0.697346i | 0.807373 | + | 0.590041i | \(0.200889\pi\) |
−0.994226 | + | 0.107304i | \(0.965778\pi\) | |||||||
\(68\) | −0.00777104 | + | 0.00208224i | −0.000942377 | + | 0.000252509i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.71700 | − | 7.16476i | −0.683313 | − | 0.856352i | ||||
\(71\) | 2.14741 | 0.254850 | 0.127425 | − | 0.991848i | \(-0.459329\pi\) | ||||
0.127425 | + | 0.991848i | \(0.459329\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.91752 | − | 7.15629i | 0.224429 | − | 0.837580i | −0.758204 | − | 0.652018i | \(-0.773923\pi\) |
0.982632 | − | 0.185562i | \(-0.0594107\pi\) | |||||||
\(74\) | −3.70301 | + | 2.13793i | −0.430466 | + | 0.248529i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.993655i | 0.113980i | ||||||||
\(77\) | −1.75660 | − | 13.6166i | −0.200183 | − | 1.55175i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.47085 | + | 2.00389i | 0.390501 | + | 0.225456i | 0.682377 | − | 0.731000i | \(-0.260946\pi\) |
−0.291876 | + | 0.956456i | \(0.594280\pi\) | |||||||
\(80\) | 9.96285 | − | 2.90141i | 1.11388 | − | 0.324387i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.47934 | − | 5.52098i | −0.163366 | − | 0.609690i | ||||
\(83\) | −3.77525 | − | 3.77525i | −0.414387 | − | 0.414387i | 0.468876 | − | 0.883264i | \(-0.344659\pi\) |
−0.883264 | + | 0.468876i | \(0.844659\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.0232926 | + | 0.0384050i | 0.00252643 | + | 0.00416561i | ||||
\(86\) | 3.06456 | − | 5.30797i | 0.330460 | − | 0.572373i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 12.4217 | + | 3.32837i | 1.32415 | + | 0.354806i | ||||
\(89\) | 1.91942 | − | 3.32453i | 0.203458 | − | 0.352400i | −0.746182 | − | 0.665742i | \(-0.768115\pi\) |
0.949640 | + | 0.313342i | \(0.101449\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.70828 | − | 11.4510i | −0.493561 | − | 1.20039i | ||||
\(92\) | −0.658512 | − | 0.658512i | −0.0686546 | − | 0.0686546i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.907487 | + | 1.57181i | 0.0936001 | + | 0.162120i | ||||
\(95\) | 5.32634 | − | 1.55115i | 0.546471 | − | 0.159145i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.5936 | + | 10.5936i | −1.07561 | + | 1.07561i | −0.0787167 | + | 0.996897i | \(0.525082\pi\) |
−0.996897 | + | 0.0787167i | \(0.974918\pi\) | |||||||
\(98\) | −9.36412 | − | 5.47160i | −0.945919 | − | 0.552715i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.07519 | + | 1.68944i | 0.107519 | + | 0.168944i | ||||
\(101\) | 5.87655 | − | 3.39283i | 0.584738 | − | 0.337599i | −0.178276 | − | 0.983981i | \(-0.557052\pi\) |
0.763014 | + | 0.646382i | \(0.223719\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.09265 | + | 2.43637i | −0.895926 | + | 0.240063i | −0.677266 | − | 0.735739i | \(-0.736835\pi\) |
−0.218660 | + | 0.975801i | \(0.570169\pi\) | |||||||
\(104\) | 11.5970 | 1.13718 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.39357 | −0.718127 | ||||||||
\(107\) | −12.0162 | + | 3.21974i | −1.16165 | + | 0.311264i | −0.787625 | − | 0.616155i | \(-0.788690\pi\) |
−0.374026 | + | 0.927418i | \(0.622023\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.55937 | + | 4.36440i | −0.724056 | + | 0.418034i | −0.816244 | − | 0.577708i | \(-0.803947\pi\) |
0.0921875 | + | 0.995742i | \(0.470614\pi\) | |||||||
\(110\) | 0.388033 | + | 17.9737i | 0.0369974 | + | 1.71373i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 9.76015 | − | 7.44893i | 0.922247 | − | 0.703858i | ||||
\(113\) | 2.80125 | − | 2.80125i | 0.263519 | − | 0.263519i | −0.562963 | − | 0.826482i | \(-0.690339\pi\) |
0.826482 | + | 0.562963i | \(0.190339\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.50188 | + | 4.55783i | −0.233302 | + | 0.425020i | ||||
\(116\) | 2.04423 | + | 3.54071i | 0.189802 | + | 0.328746i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.487719 | + | 0.487719i | 0.0448982 | + | 0.0448982i | ||||
\(119\) | 0.0420790 | + | 0.0324628i | 0.00385738 | + | 0.00297586i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.96405 | + | 13.7941i | −0.724005 | + | 1.25401i | ||||
\(122\) | −2.05025 | − | 0.549362i | −0.185621 | − | 0.0497369i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.31635 | − | 2.27998i | 0.118212 | − | 0.204748i | ||||
\(125\) | 7.37754 | − | 8.40071i | 0.659867 | − | 0.751382i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.63342 | + | 2.63342i | 0.233679 | + | 0.233679i | 0.814226 | − | 0.580548i | \(-0.197162\pi\) |
−0.580548 | + | 0.814226i | \(0.697162\pi\) | |||||||
\(128\) | 3.49027 | + | 13.0259i | 0.308499 | + | 1.15133i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.53314 | + | 15.5659i | 0.397582 | + | 1.36522i | ||||
\(131\) | −2.60564 | − | 1.50437i | −0.227656 | − | 0.131437i | 0.381834 | − | 0.924231i | \(-0.375293\pi\) |
−0.609490 | + | 0.792794i | \(0.708626\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.21797 | − | 3.98235i | 0.452456 | − | 0.345313i | ||||
\(134\) | − | 9.15574i | − | 0.790936i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.0431106 | + | 0.0248899i | −0.00369670 | + | 0.00213429i | ||||
\(137\) | −2.73317 | + | 10.2003i | −0.233510 | + | 0.871472i | 0.745304 | + | 0.666724i | \(0.232304\pi\) |
−0.978815 | + | 0.204748i | \(0.934363\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.76721 | 0.149893 | 0.0749465 | − | 0.997188i | \(-0.476121\pi\) | ||||
0.0749465 | + | 0.997188i | \(0.476121\pi\) | |||||||
\(140\) | 1.90686 | + | 1.40649i | 0.161159 | + | 0.118870i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.21373 | + | 0.861117i | −0.269691 | + | 0.0722634i | ||||
\(143\) | −6.28511 | + | 23.4563i | −0.525587 | + | 1.96152i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.7883 | − | 16.4850i | 1.31114 | − | 1.36901i | ||||
\(146\) | 11.4788i | 0.949991i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.781577 | − | 0.781577i | 0.0642452 | − | 0.0642452i | ||||
\(149\) | 6.38521 | + | 3.68650i | 0.523097 | + | 0.302010i | 0.738201 | − | 0.674581i | \(-0.235676\pi\) |
−0.215104 | + | 0.976591i | \(0.569009\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.17823 | − | 14.1651i | −0.665535 | − | 1.15274i | −0.979140 | − | 0.203187i | \(-0.934870\pi\) |
0.313605 | − | 0.949554i | \(-0.398463\pi\) | |||||||
\(152\) | 1.59129 | + | 5.93879i | 0.129071 | + | 0.481699i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 8.08915 | + | 19.6737i | 0.651843 | + | 1.58535i | ||||
\(155\) | −14.2764 | − | 3.49691i | −1.14671 | − | 0.280878i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.1476 | + | 5.93444i | 1.76757 | + | 0.473620i | 0.988230 | − | 0.152977i | \(-0.0488861\pi\) |
0.779344 | + | 0.626597i | \(0.215553\pi\) | |||||||
\(158\) | −5.99791 | − | 1.60714i | −0.477168 | − | 0.127857i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.27046 | + | 2.59003i | −0.337610 | + | 0.204760i | ||||
\(161\) | −0.818870 | + | 6.09721i | −0.0645360 | + | 0.480527i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.95078 | + | 14.7445i | 0.309449 | + | 1.15488i | 0.929048 | + | 0.369960i | \(0.120628\pi\) |
−0.619599 | + | 0.784918i | \(0.712705\pi\) | |||||||
\(164\) | 0.738763 | + | 1.27958i | 0.0576877 | + | 0.0999180i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.16379 | + | 4.13602i | 0.556018 | + | 0.321017i | ||||
\(167\) | 8.60951 | − | 8.60951i | 0.666224 | − | 0.666224i | −0.290616 | − | 0.956840i | \(-0.593860\pi\) |
0.956840 | + | 0.290616i | \(0.0938603\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.89914i | 0.684550i | ||||||||
\(170\) | −0.0502594 | − | 0.0481352i | −0.00385472 | − | 0.00369180i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.410069 | + | 1.53040i | −0.0312675 | + | 0.116692i | ||||
\(173\) | −3.49279 | + | 0.935889i | −0.265552 | + | 0.0711543i | −0.389138 | − | 0.921179i | \(-0.627227\pi\) |
0.123586 | + | 0.992334i | \(0.460560\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.56260 | − | 12.4170i | 0.344900 | − | 0.938640i | ||||
\(176\) | −24.0812 | −1.81519 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.53939 | + | 5.74507i | −0.115382 | + | 0.430611i | ||||
\(179\) | −12.0294 | + | 6.94520i | −0.899122 | + | 0.519108i | −0.876915 | − | 0.480645i | \(-0.840403\pi\) |
−0.0222069 | + | 0.999753i | \(0.507069\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.4270i | 1.14668i | 0.819318 | + | 0.573339i | \(0.194352\pi\) | ||||
−0.819318 | + | 0.573339i | \(0.805648\pi\) | |||||||
\(182\) | 11.6381 | + | 15.2492i | 0.862677 | + | 1.13034i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.99031 | − | 2.88116i | −0.367890 | − | 0.212402i | ||||
\(185\) | −5.40961 | − | 2.96944i | −0.397722 | − | 0.218318i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.0269786 | − | 0.100686i | −0.00197287 | − | 0.00736285i | ||||
\(188\) | −0.331756 | − | 0.331756i | −0.0241958 | − | 0.0241958i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.34920 | + | 4.45728i | −0.533167 | + | 0.323365i | ||||
\(191\) | −0.0283971 | + | 0.0491852i | −0.00205474 | + | 0.00355891i | −0.867051 | − | 0.498219i | \(-0.833987\pi\) |
0.864996 | + | 0.501778i | \(0.167321\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.29559 | − | 0.615101i | −0.165240 | − | 0.0442760i | 0.175250 | − | 0.984524i | \(-0.443926\pi\) |
−0.340491 | + | 0.940248i | \(0.610593\pi\) | |||||||
\(194\) | 11.6059 | − | 20.1020i | 0.833256 | − | 1.44324i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.70423 | + | 0.739713i | 0.193160 | + | 0.0528367i | ||||
\(197\) | −0.251120 | − | 0.251120i | −0.0178916 | − | 0.0178916i | 0.698104 | − | 0.715996i | \(-0.254027\pi\) |
−0.715996 | + | 0.698104i | \(0.754027\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.5538 | − | 21.7439i | −0.889917 | − | 1.54138i | −0.839972 | − | 0.542629i | \(-0.817429\pi\) |
−0.0499447 | − | 0.998752i | \(-0.515905\pi\) | |||||||
\(200\) | 9.13166 | + | 8.37540i | 0.645706 | + | 0.592230i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.43410 | + | 7.43410i | −0.523062 | + | 0.523062i | ||||
\(203\) | 10.4005 | − | 24.9252i | 0.729970 | − | 1.74941i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.70572 | − | 5.95752i | 0.398505 | − | 0.416091i | ||||
\(206\) | 12.6308 | − | 7.29237i | 0.880026 | − | 0.508083i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −20.9765 | + | 5.62063i | −1.45446 | + | 0.389721i | ||||
\(209\) | −12.8743 | −0.890534 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.2060 | −1.04682 | −0.523411 | − | 0.852080i | \(-0.675341\pi\) | ||||
−0.523411 | + | 0.852080i | \(0.675341\pi\) | |||||||
\(212\) | 1.84612 | − | 0.494668i | 0.126792 | − | 0.0339739i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 16.6919 | − | 9.63709i | 1.14104 | − | 0.658778i | ||||
\(215\) | 8.84361 | − | 0.190923i | 0.603129 | − | 0.0130209i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.2485 | + | 2.22513i | −1.17090 | + | 0.151052i | ||||
\(218\) | 9.56295 | − | 9.56295i | 0.647685 | − | 0.647685i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.29942 | − | 4.46196i | −0.0876072 | − | 0.300825i | ||||
\(221\) | −0.0470007 | − | 0.0814075i | −0.00316161 | − | 0.00547606i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.59679 | − | 3.59679i | −0.240859 | − | 0.240859i | 0.576346 | − | 0.817205i | \(-0.304478\pi\) |
−0.817205 | + | 0.576346i | \(0.804478\pi\) | |||||||
\(224\) | −3.60972 | + | 4.67900i | −0.241185 | + | 0.312629i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.06894 | + | 5.31556i | −0.204143 | + | 0.353586i | ||||
\(227\) | 7.28798 | + | 1.95281i | 0.483720 | + | 0.129612i | 0.492434 | − | 0.870350i | \(-0.336107\pi\) |
−0.00871411 | + | 0.999962i | \(0.502774\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.8628 | − | 22.2790i | 0.849998 | − | 1.47224i | −0.0312109 | − | 0.999513i | \(-0.509936\pi\) |
0.881209 | − | 0.472727i | \(-0.156730\pi\) | |||||||
\(230\) | 1.91652 | − | 7.82435i | 0.126372 | − | 0.515922i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 17.8880 | + | 17.8880i | 1.17441 | + | 1.17441i | ||||
\(233\) | 6.94194 | + | 25.9077i | 0.454782 | + | 1.69727i | 0.688729 | + | 0.725019i | \(0.258169\pi\) |
−0.233947 | + | 0.972249i | \(0.575164\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.26044 | + | 2.29622i | −0.0822219 | + | 0.149789i | ||||
\(236\) | −0.154411 | − | 0.0891493i | −0.0100513 | − | 0.00580312i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.0759917 | − | 0.0317089i | −0.00492581 | − | 0.00205538i | ||||
\(239\) | 19.0811i | 1.23425i | 0.786863 | + | 0.617127i | \(0.211704\pi\) | ||||
−0.786863 | + | 0.617127i | \(0.788296\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.6084 | − | 6.12477i | 0.683348 | − | 0.394531i | −0.117767 | − | 0.993041i | \(-0.537574\pi\) |
0.801115 | + | 0.598510i | \(0.204240\pi\) | |||||||
\(242\) | 6.38722 | − | 23.8374i | 0.410586 | − | 1.53233i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.548688 | 0.0351261 | ||||||||
\(245\) | −0.256338 | − | 15.6504i | −0.0163769 | − | 0.999866i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.2145 | + | 3.00490i | −0.713559 | + | 0.191197i | ||||
\(248\) | 4.21614 | − | 15.7349i | 0.267725 | − | 0.999164i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7.67225 | + | 15.5306i | −0.485236 | + | 0.982243i | ||||
\(251\) | − | 24.6455i | − | 1.55561i | −0.628505 | − | 0.777806i | \(-0.716333\pi\) | ||
0.628505 | − | 0.777806i | \(-0.283667\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.53201 | − | 8.53201i | 0.536403 | − | 0.536403i | ||||
\(254\) | −4.99710 | − | 2.88508i | −0.313546 | − | 0.181026i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.62626 | − | 8.01293i | −0.289142 | − | 0.500808i | ||||
\(257\) | 2.19866 | + | 8.20551i | 0.137149 | + | 0.511846i | 0.999980 | + | 0.00635343i | \(0.00202237\pi\) |
−0.862831 | + | 0.505492i | \(0.831311\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.23667 | − | 0.971903i | −0.449665 | − | 0.0603911i | ||||
\(260\) | −2.17333 | − | 3.58340i | −0.134784 | − | 0.222233i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.50277 | + | 1.20651i | 0.278182 | + | 0.0745387i | ||||
\(263\) | −23.7671 | − | 6.36838i | −1.46554 | − | 0.392691i | −0.564143 | − | 0.825677i | \(-0.690793\pi\) |
−0.901401 | + | 0.432986i | \(0.857460\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.53349 | − | 9.12367i | −0.339920 | − | 0.560463i | ||||
\(266\) | −6.21210 | + | 8.05227i | −0.380888 | + | 0.493716i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.612566 | + | 2.28613i | 0.0374184 | + | 0.139647i | ||||
\(269\) | −9.96695 | − | 17.2633i | −0.607696 | − | 1.05256i | −0.991619 | − | 0.129195i | \(-0.958761\pi\) |
0.383923 | − | 0.923365i | \(-0.374573\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.4726 | + | 14.1293i | 1.48661 | + | 0.858293i | 0.999884 | − | 0.0152637i | \(-0.00485877\pi\) |
0.486723 | + | 0.873556i | \(0.338192\pi\) | |||||||
\(272\) | 0.0659145 | − | 0.0659145i | 0.00399665 | − | 0.00399665i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 16.3615i | − | 0.988432i | ||||||
\(275\) | −21.8892 | + | 13.9307i | −1.31997 | + | 0.840055i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.72993 | − | 28.8485i | 0.464447 | − | 1.73334i | −0.194270 | − | 0.980948i | \(-0.562234\pi\) |
0.658717 | − | 0.752391i | \(-0.271099\pi\) | |||||||
\(278\) | −2.64475 | + | 0.708658i | −0.158621 | + | 0.0425025i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 13.6492 | + | 5.35246i | 0.815693 | + | 0.319871i | ||||
\(281\) | 17.9592 | 1.07135 | 0.535677 | − | 0.844423i | \(-0.320056\pi\) | ||||
0.535677 | + | 0.844423i | \(0.320056\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.89965 | + | 22.0178i | −0.350698 | + | 1.30882i | 0.535116 | + | 0.844779i | \(0.320268\pi\) |
−0.885813 | + | 0.464042i | \(0.846399\pi\) | |||||||
\(284\) | 0.744834 | − | 0.430030i | 0.0441978 | − | 0.0255176i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 37.6243i | − | 2.22477i | ||||||
\(287\) | 3.75863 | − | 9.00771i | 0.221865 | − | 0.531709i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.7221 | − | 8.49980i | −0.866005 | − | 0.499988i | ||||
\(290\) | −17.0176 | + | 31.0020i | −0.999310 | + | 1.82050i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.767989 | − | 2.86617i | −0.0449432 | − | 0.167730i | ||||
\(293\) | 17.3271 | + | 17.3271i | 1.01226 | + | 1.01226i | 0.999924 | + | 0.0123342i | \(0.00392620\pi\) |
0.0123342 | + | 0.999924i | \(0.496074\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.236827 | + | 0.966865i | −0.0137886 | + | 0.0562930i | ||||
\(296\) | 3.41960 | − | 5.92292i | 0.198760 | − | 0.344262i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −11.0342 | − | 2.95660i | −0.639193 | − | 0.171271i | ||||
\(299\) | 5.44061 | − | 9.42341i | 0.314638 | − | 0.544970i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.68003 | − | 3.98010i | 0.557948 | − | 0.229409i | ||||
\(302\) | 17.9195 | + | 17.9195i | 1.03115 | + | 1.03115i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.75660 | − | 9.97073i | −0.330164 | − | 0.571860i | ||||
\(305\) | −0.856532 | − | 2.94116i | −0.0490449 | − | 0.168410i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.07730 | − | 7.07730i | 0.403923 | − | 0.403923i | −0.475690 | − | 0.879613i | \(-0.657802\pi\) |
0.879613 | + | 0.475690i | \(0.157802\pi\) | |||||||
\(308\) | −3.33608 | − | 4.37118i | −0.190091 | − | 0.249071i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 22.7678 | − | 0.491531i | 1.29313 | − | 0.0279171i | ||||
\(311\) | −4.32047 | + | 2.49442i | −0.244991 | + | 0.141446i | −0.617469 | − | 0.786596i | \(-0.711842\pi\) |
0.372477 | + | 0.928041i | \(0.378508\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.69853 | + | 1.52692i | −0.322100 | + | 0.0863064i | −0.416246 | − | 0.909252i | \(-0.636655\pi\) |
0.0941462 | + | 0.995558i | \(0.469988\pi\) | |||||||
\(314\) | −35.5251 | −2.00480 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.60516 | 0.0902975 | ||||||||
\(317\) | −0.852009 | + | 0.228295i | −0.0478536 | + | 0.0128223i | −0.282666 | − | 0.959218i | \(-0.591219\pi\) |
0.234813 | + | 0.972041i | \(0.424552\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −45.8752 | + | 26.4860i | −2.56852 | + | 1.48293i | ||||
\(320\) | −9.00234 | + | 9.39961i | −0.503246 | + | 0.525454i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.21951 | − | 9.45324i | −0.0679605 | − | 0.526808i | ||||
\(323\) | 0.0352392 | − | 0.0352392i | 0.00196076 | − | 0.00196076i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.8156 | + | 17.2437i | −0.877292 | + | 0.956508i | ||||
\(326\) | −11.8252 | − | 20.4818i | −0.654937 | − | 1.13438i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.46455 | + | 6.46455i | 0.356945 | + | 0.356945i | ||||
\(329\) | −0.412544 | + | 3.07175i | −0.0227443 | + | 0.169351i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.9792 | − | 20.7485i | 0.658435 | − | 1.14044i | −0.322585 | − | 0.946540i | \(-0.604552\pi\) |
0.981021 | − | 0.193903i | \(-0.0621147\pi\) | |||||||
\(332\) | −2.06547 | − | 0.553441i | −0.113357 | − | 0.0303740i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −9.43225 | + | 16.3371i | −0.516110 | + | 0.893928i | ||||
\(335\) | 11.2982 | − | 6.85234i | 0.617286 | − | 0.374383i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.18043 | − | 2.18043i | −0.118776 | − | 0.118776i | 0.645221 | − | 0.763996i | \(-0.276765\pi\) |
−0.763996 | + | 0.645221i | \(0.776765\pi\) | |||||||
\(338\) | −3.56859 | − | 13.3182i | −0.194106 | − | 0.724412i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.0157699 | + | 0.00865641i | 0.000855244 | + | 0.000469460i | ||||
\(341\) | 29.5406 | + | 17.0553i | 1.59971 | + | 0.923595i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.95352 | − | 17.1653i | −0.375455 | − | 0.926841i | ||||
\(344\) | 9.80345i | 0.528567i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.85189 | − | 2.80124i | 0.260839 | − | 0.150596i | ||||
\(347\) | 4.03656 | − | 15.0646i | 0.216694 | − | 0.808712i | −0.768870 | − | 0.639406i | \(-0.779180\pi\) |
0.985563 | − | 0.169307i | \(-0.0541529\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34.9635 | 1.87155 | 0.935776 | − | 0.352596i | \(-0.114701\pi\) | ||||
0.935776 | + | 0.352596i | \(0.114701\pi\) | |||||||
\(350\) | −1.84895 | + | 20.4125i | −0.0988305 | + | 1.09109i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 11.1958 | − | 2.99990i | 0.596737 | − | 0.159895i | ||||
\(353\) | 0.949422 | − | 3.54329i | 0.0505327 | − | 0.188590i | −0.936046 | − | 0.351878i | \(-0.885543\pi\) |
0.986579 | + | 0.163288i | \(0.0522098\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.46784 | − | 3.32127i | −0.184054 | − | 0.176275i | ||||
\(356\) | − | 1.53750i | − | 0.0814873i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 15.2178 | − | 15.2178i | 0.804285 | − | 0.804285i | ||||
\(359\) | 13.9528 | + | 8.05567i | 0.736402 | + | 0.425162i | 0.820760 | − | 0.571274i | \(-0.193550\pi\) |
−0.0843575 | + | 0.996436i | \(0.526884\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.42240 | + | 11.1239i | 0.338021 | + | 0.585470i | ||||
\(362\) | −6.18627 | − | 23.0875i | −0.325143 | − | 1.21345i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.92621 | − | 3.02897i | −0.205790 | − | 0.158761i | ||||
\(365\) | −14.1648 | + | 8.59095i | −0.741421 | + | 0.449671i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.5321 | − | 7.64516i | −1.48936 | − | 0.399074i | −0.579842 | − | 0.814729i | \(-0.696886\pi\) |
−0.909522 | + | 0.415655i | \(0.863552\pi\) | |||||||
\(368\) | 10.4228 | + | 2.79277i | 0.543324 | + | 0.145583i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 9.28659 | + | 2.27469i | 0.482787 | + | 0.118255i | ||||
\(371\) | −9.99650 | − | 7.71202i | −0.518992 | − | 0.400388i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.96300 | + | 7.32603i | 0.101640 | + | 0.379327i | 0.997942 | − | 0.0641169i | \(-0.0204231\pi\) |
−0.896302 | + | 0.443444i | \(0.853756\pi\) | |||||||
\(374\) | 0.0807505 | + | 0.139864i | 0.00417551 | + | 0.00723219i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.51410 | − | 1.45152i | −0.129655 | − | 0.0748562i | ||||
\(377\) | −33.7787 | + | 33.7787i | −1.73969 | + | 1.73969i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.5078i | 0.899317i | 0.893201 | + | 0.449658i | \(0.148454\pi\) | ||||
−0.893201 | + | 0.449658i | \(0.851546\pi\) | |||||||
\(380\) | 1.53683 | − | 1.60465i | 0.0788377 | − | 0.0823169i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.0227746 | − | 0.0849961i | 0.00116525 | − | 0.00434878i | ||||
\(383\) | −11.4817 | + | 3.07651i | −0.586687 | + | 0.157202i | −0.539939 | − | 0.841704i | \(-0.681553\pi\) |
−0.0467483 | + | 0.998907i | \(0.514886\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −18.2233 | + | 24.7062i | −0.928743 | + | 1.25914i | ||||
\(386\) | 3.68216 | 0.187417 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.55299 | + | 5.79583i | −0.0788410 | + | 0.294239i | ||||
\(389\) | 7.50204 | − | 4.33130i | 0.380368 | − | 0.219606i | −0.297610 | − | 0.954687i | \(-0.596190\pi\) |
0.677979 | + | 0.735082i | \(0.262856\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.0467072i | 0.00236209i | ||||||||
\(392\) | 17.3470 | + | 0.0903426i | 0.876157 | + | 0.00456299i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.476518 | + | 0.275118i | 0.0240066 | + | 0.0138602i | ||||
\(395\) | −2.50575 | − | 8.60424i | −0.126078 | − | 0.432926i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.677958 | − | 2.53017i | −0.0340257 | − | 0.126986i | 0.946824 | − | 0.321752i | \(-0.104272\pi\) |
−0.980850 | + | 0.194766i | \(0.937605\pi\) | |||||||
\(398\) | 27.5070 | + | 27.5070i | 1.37880 | + | 1.37880i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −20.5764 | − | 10.7235i | −1.02882 | − | 0.536175i | ||||
\(401\) | 4.98018 | − | 8.62592i | 0.248698 | − | 0.430758i | −0.714467 | − | 0.699669i | \(-0.753331\pi\) |
0.963165 | + | 0.268912i | \(0.0866639\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 29.7128 | + | 7.96152i | 1.48010 | + | 0.396591i | ||||
\(404\) | 1.35887 | − | 2.35362i | 0.0676061 | − | 0.117097i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.56990 | + | 41.4728i | −0.276430 | + | 2.05826i | ||||
\(407\) | 10.1265 | + | 10.1265i | 0.501952 | + | 0.501952i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.03282 | + | 6.98504i | 0.199410 | + | 0.345388i | 0.948337 | − | 0.317264i | \(-0.102764\pi\) |
−0.748927 | + | 0.662652i | \(0.769431\pi\) | |||||||
\(410\) | −6.15000 | + | 11.2038i | −0.303727 | + | 0.553318i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.66592 | + | 2.66592i | −0.131340 | + | 0.131340i | ||||
\(413\) | 0.150696 | + | 1.16815i | 0.00741527 | + | 0.0574808i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.257676 | + | 11.9356i | 0.0126488 | + | 0.585896i | ||||
\(416\) | 9.05215 | − | 5.22626i | 0.443818 | − | 0.256239i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 19.2672 | − | 5.16264i | 0.942391 | − | 0.252513i | ||||
\(419\) | −1.30845 | −0.0639222 | −0.0319611 | − | 0.999489i | \(-0.510175\pi\) | ||||
−0.0319611 | + | 0.999489i | \(0.510175\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.88085 | 0.140404 | 0.0702020 | − | 0.997533i | \(-0.477636\pi\) | ||||
0.0702020 | + | 0.997533i | \(0.477636\pi\) | |||||||
\(422\) | 22.7567 | − | 6.09764i | 1.10778 | − | 0.296829i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 10.2416 | − | 5.91297i | 0.497374 | − | 0.287159i | ||||
\(425\) | 0.0217837 | − | 0.0980454i | 0.00105666 | − | 0.00475590i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.19902 | − | 2.88132i | −0.106418 | − | 0.139437i | ||||
\(428\) | −3.52309 | + | 3.52309i | −0.170295 | + | 0.170295i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −13.1585 | + | 3.83205i | −0.634558 | + | 0.184798i | ||||
\(431\) | 10.4163 | + | 18.0415i | 0.501734 | + | 0.869028i | 0.999998 | + | 0.00200303i | \(0.000637585\pi\) |
−0.498264 | + | 0.867025i | \(0.666029\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.72121 | − | 5.72121i | −0.274944 | − | 0.274944i | 0.556143 | − | 0.831087i | \(-0.312281\pi\) |
−0.831087 | + | 0.556143i | \(0.812281\pi\) | |||||||
\(434\) | 24.9212 | − | 10.2468i | 1.19626 | − | 0.491860i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.74799 | + | 3.02761i | −0.0837137 | + | 0.144996i | ||||
\(437\) | 5.57222 | + | 1.49307i | 0.266555 | + | 0.0714233i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.31964 | + | 7.48184i | −0.206165 | + | 0.357089i | −0.950503 | − | 0.310714i | \(-0.899432\pi\) |
0.744338 | + | 0.667803i | \(0.232765\pi\) | |||||||
\(440\) | −14.9119 | − | 24.5869i | −0.710897 | − | 1.17213i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.102984 | + | 0.102984i | 0.00489846 | + | 0.00489846i | ||||
\(443\) | −8.05575 | − | 30.0644i | −0.382740 | − | 1.42841i | −0.841699 | − | 0.539948i | \(-0.818444\pi\) |
0.458959 | − | 0.888458i | \(-0.348223\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.24153 | + | 2.40012i | −0.390686 | + | 0.113777i | ||||
\(446\) | 6.82516 | + | 3.94051i | 0.323181 | + | 0.186589i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.93026 | + | 14.2121i | −0.280179 | + | 0.671460i | ||||
\(449\) | − | 40.3196i | − | 1.90280i | −0.307962 | − | 0.951399i | \(-0.599647\pi\) | ||
0.307962 | − | 0.951399i | \(-0.400353\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.5788 | + | 9.57179i | −0.780667 | + | 0.450718i | ||||
\(452\) | 0.410655 | − | 1.53259i | 0.0193156 | − | 0.0720868i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −11.6900 | −0.548640 | ||||||||
\(455\) | −10.1073 | + | 25.7743i | −0.473837 | + | 1.20832i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.9317 | − | 3.46505i | 0.604921 | − | 0.162088i | 0.0566576 | − | 0.998394i | \(-0.481956\pi\) |
0.548264 | + | 0.836305i | \(0.315289\pi\) | |||||||
\(458\) | −10.3161 | + | 38.5001i | −0.482038 | + | 1.79899i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.0449461 | + | 2.08191i | 0.00209562 | + | 0.0970697i | ||||
\(461\) | − | 2.07258i | − | 0.0965298i | −0.998835 | − | 0.0482649i | \(-0.984631\pi\) | ||
0.998835 | − | 0.0482649i | \(-0.0153692\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.9744 | − | 12.9744i | 0.602971 | − | 0.602971i | −0.338129 | − | 0.941100i | \(-0.609794\pi\) |
0.941100 | + | 0.338129i | \(0.109794\pi\) | |||||||
\(464\) | −41.0252 | − | 23.6859i | −1.90455 | − | 1.09959i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.7781 | − | 35.9888i | −0.962529 | − | 1.66715i | ||||
\(467\) | −6.66459 | − | 24.8726i | −0.308400 | − | 1.15097i | −0.929979 | − | 0.367614i | \(-0.880175\pi\) |
0.621578 | − | 0.783352i | \(-0.286492\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.55010 | − | 12.3791i | 0.440982 | − | 0.571611i | ||||
\(470\) | 0.965537 | − | 3.94188i | 0.0445369 | − | 0.181825i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.06564 | − | 0.285537i | −0.0490500 | − | 0.0131429i | ||||
\(473\) | −19.8286 | − | 5.31306i | −0.911721 | − | 0.244295i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.0006 | − | 5.73300i | −0.504741 | − | 0.263048i | ||||
\(476\) | 0.0210961 | + | 0.00283326i | 0.000966939 | + | 0.000129862i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.65159 | − | 28.5561i | −0.349976 | − | 1.30613i | ||||
\(479\) | −12.5000 | − | 21.6506i | −0.571138 | − | 0.989240i | −0.996449 | − | 0.0841932i | \(-0.973169\pi\) |
0.425311 | − | 0.905047i | \(-0.360165\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.1845 | + | 6.45737i | 0.509969 | + | 0.294431i | ||||
\(482\) | −13.4201 | + | 13.4201i | −0.611271 | + | 0.611271i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.37938i | 0.289972i | ||||||||
\(485\) | 33.4920 | − | 0.723054i | 1.52079 | − | 0.0328322i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.06031 | − | 26.3494i | 0.319933 | − | 1.19401i | −0.599375 | − | 0.800468i | \(-0.704584\pi\) |
0.919308 | − | 0.393538i | \(-0.128749\pi\) | |||||||
\(488\) | 3.27935 | − | 0.878698i | 0.148449 | − | 0.0397768i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.65948 | + | 23.3190i | 0.300845 | + | 1.05345i | ||||
\(491\) | 23.4800 | 1.05964 | 0.529820 | − | 0.848110i | \(-0.322260\pi\) | ||||
0.529820 | + | 0.848110i | \(0.322260\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.0530714 | − | 0.198065i | 0.00239022 | − | 0.00892041i | ||||
\(494\) | 15.5782 | − | 8.99407i | 0.700896 | − | 0.404662i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 30.5043i | 1.36968i | ||||||||
\(497\) | −5.24334 | − | 2.18788i | −0.235196 | − | 0.0981397i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.8192 | + | 14.3294i | 1.11106 | + | 0.641470i | 0.939104 | − | 0.343634i | \(-0.111658\pi\) |
0.171956 | + | 0.985105i | \(0.444991\pi\) | |||||||
\(500\) | 0.876631 | − | 4.39121i | 0.0392041 | − | 0.196381i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.88294 | + | 36.8836i | 0.441097 | + | 1.64620i | ||||
\(503\) | 7.43731 | + | 7.43731i | 0.331613 | + | 0.331613i | 0.853199 | − | 0.521586i | \(-0.174659\pi\) |
−0.521586 | + | 0.853199i | \(0.674659\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.7375 | − | 3.60986i | −0.655811 | − | 0.160637i | ||||
\(506\) | −9.34735 | + | 16.1901i | −0.415540 | + | 0.719737i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.44077 | + | 0.386053i | 0.0639238 | + | 0.0171283i | ||||
\(509\) | −5.08320 | + | 8.80437i | −0.225309 | + | 0.390247i | −0.956412 | − | 0.292020i | \(-0.905673\pi\) |
0.731103 | + | 0.682267i | \(0.239006\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.9732 | + | 15.5199i | −0.529663 | + | 0.686561i | ||||
\(512\) | −8.93446 | − | 8.93446i | −0.394851 | − | 0.394851i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.58087 | − | 11.3984i | −0.290270 | − | 0.502762i | ||||
\(515\) | 18.4519 | + | 10.1286i | 0.813088 | + | 0.446320i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.29840 | − | 4.29840i | 0.189043 | − | 0.189043i | ||||
\(518\) | 11.2199 | − | 1.44741i | 0.492974 | − | 0.0635957i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −18.7280 | − | 17.9365i | −0.821277 | − | 0.786566i | ||||
\(521\) | −23.4269 | + | 13.5255i | −1.02635 | + | 0.592565i | −0.915938 | − | 0.401321i | \(-0.868551\pi\) |
−0.110415 | + | 0.993886i | \(0.535218\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.57429 | − | 1.49363i | 0.243747 | − | 0.0653117i | −0.134877 | − | 0.990862i | \(-0.543064\pi\) |
0.378624 | + | 0.925551i | \(0.376397\pi\) | |||||||
\(524\) | −1.20503 | −0.0526421 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 38.1228 | 1.66223 | ||||||||
\(527\) | −0.127541 | + | 0.0341745i | −0.00555578 | + | 0.00148867i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.2363 | − | 8.79668i | 0.662448 | − | 0.382464i | ||||
\(530\) | 11.9399 | + | 11.4352i | 0.518634 | + | 0.496714i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.01238 | − | 2.42622i | 0.0438923 | − | 0.105190i | ||||
\(533\) | −12.2073 | + | 12.2073i | −0.528756 | + | 0.528756i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.3847 | + | 13.3853i | 1.05424 | + | 0.578695i | ||||
\(536\) | 7.32225 | + | 12.6825i | 0.316273 | + | 0.547801i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 21.8388 | + | 21.8388i | 0.941539 | + | 0.941539i | ||||
\(539\) | −9.58410 | + | 35.0374i | −0.412816 | + | 1.50917i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.0154 | − | 19.0793i | 0.473590 | − | 0.820283i | −0.525952 | − | 0.850514i | \(-0.676291\pi\) |
0.999543 | + | 0.0302312i | \(0.00962435\pi\) | |||||||
\(542\) | −42.2908 | − | 11.3318i | −1.81654 | − | 0.486742i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.0224335 | + | 0.0388560i | −0.000961830 | + | 0.00166594i | ||||
\(545\) | 18.9578 | + | 4.64358i | 0.812062 | + | 0.198909i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.7018 | + | 19.7018i | 0.842388 | + | 0.842388i | 0.989169 | − | 0.146781i | \(-0.0468913\pi\) |
−0.146781 | + | 0.989169i | \(0.546891\pi\) | |||||||
\(548\) | 1.09466 | + | 4.08535i | 0.0467618 | + | 0.174517i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 27.1723 | − | 29.6259i | 1.15863 | − | 1.26325i | ||||
\(551\) | −21.9329 | − | 12.6630i | −0.934372 | − | 0.539460i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.43314 | − | 8.42919i | −0.273565 | − | 0.358445i | ||||
\(554\) | 46.2734i | 1.96597i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.612963 | − | 0.353894i | 0.0259954 | − | 0.0150085i | ||||
\(557\) | 4.14131 | − | 15.4556i | 0.175473 | − | 0.654874i | −0.820998 | − | 0.570932i | \(-0.806582\pi\) |
0.996471 | − | 0.0839424i | \(-0.0267512\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.5123 | −0.782985 | ||||||||
\(560\) | −27.2825 | − | 3.06622i | −1.15290 | − | 0.129571i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −26.8771 | + | 7.20169i | −1.13374 | + | 0.303785i | ||||
\(563\) | −4.14791 | + | 15.4802i | −0.174813 | + | 0.652413i | 0.821770 | + | 0.569819i | \(0.192987\pi\) |
−0.996583 | + | 0.0825932i | \(0.973680\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.85625 | + | 0.191196i | −0.372585 | + | 0.00804369i | ||||
\(566\) | − | 35.3168i | − | 1.48448i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.76298 | − | 3.76298i | 0.157891 | − | 0.157891i | ||||
\(569\) | 22.2011 | + | 12.8178i | 0.930717 | + | 0.537350i | 0.887038 | − | 0.461696i | \(-0.152759\pi\) |
0.0436785 | + | 0.999046i | \(0.486092\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.33247 | + | 14.4323i | 0.348703 | + | 0.603971i | 0.986019 | − | 0.166631i | \(-0.0532888\pi\) |
−0.637316 | + | 0.770602i | \(0.719955\pi\) | |||||||
\(572\) | 2.51726 | + | 9.39453i | 0.105252 | + | 0.392805i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.01291 | + | 14.9879i | −0.0840171 | + | 0.625581i | ||||
\(575\) | 11.0896 | − | 3.49091i | 0.462469 | − | 0.145581i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.25450 | + | 1.13999i | 0.177117 | + | 0.0474584i | 0.346288 | − | 0.938128i | \(-0.387442\pi\) |
−0.169170 | + | 0.985587i | \(0.554109\pi\) | |||||||
\(578\) | 25.4410 | + | 6.81690i | 1.05821 | + | 0.283546i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.17499 | − | 8.87957i | 0.0903116 | − | 0.368704i | ||||
\(581\) | 5.37166 | + | 13.0645i | 0.222854 | + | 0.542005i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.40916 | + | 23.9193i | 0.265440 | + | 0.990637i | ||||
\(584\) | −9.18009 | − | 15.9004i | −0.379875 | − | 0.657963i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −32.8793 | − | 18.9829i | −1.35823 | − | 0.784175i | ||||
\(587\) | 25.1535 | − | 25.1535i | 1.03820 | − | 1.03820i | 0.0389571 | − | 0.999241i | \(-0.487596\pi\) |
0.999241 | − | 0.0389571i | \(-0.0124036\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.3082i | 0.671969i | ||||||||
\(590\) | −0.0332888 | − | 1.54194i | −0.00137048 | − | 0.0634808i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.31469 | + | 12.3706i | −0.136233 | + | 0.508429i | ||||
\(593\) | −41.1024 | + | 11.0134i | −1.68787 | + | 0.452265i | −0.969840 | − | 0.243742i | \(-0.921625\pi\) |
−0.718035 | + | 0.696007i | \(0.754958\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.0177449 | − | 0.117505i | −0.000727471 | − | 0.00481725i | ||||
\(596\) | 2.95297 | 0.120959 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.36340 | + | 16.2844i | −0.178433 | + | 0.665920i | ||||
\(599\) | −15.9783 | + | 9.22507i | −0.652855 | + | 0.376926i | −0.789549 | − | 0.613687i | \(-0.789686\pi\) |
0.136694 | + | 0.990613i | \(0.456352\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.13978i | 0.168865i | 0.996429 | + | 0.0844326i | \(0.0269078\pi\) | ||||
−0.996429 | + | 0.0844326i | \(0.973092\pi\) | |||||||
\(602\) | −12.8908 | + | 9.83821i | −0.525389 | + | 0.400976i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.67329 | − | 3.27548i | −0.230843 | − | 0.133277i | ||||
\(605\) | 34.1957 | − | 9.95857i | 1.39025 | − | 0.404874i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.39069 | − | 23.8504i | −0.259390 | − | 0.968058i | −0.965595 | − | 0.260050i | \(-0.916261\pi\) |
0.706205 | − | 0.708008i | \(-0.250406\pi\) | |||||||
\(608\) | 3.91844 | + | 3.91844i | 0.158914 | + | 0.158914i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.46127 | + | 4.05816i | 0.0996539 | + | 0.164310i | ||||
\(611\) | 2.74096 | − | 4.74748i | 0.110887 | − | 0.192062i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −46.8375 | − | 12.5501i | −1.89175 | − | 0.506893i | −0.998337 | − | 0.0576548i | \(-0.981638\pi\) |
−0.893412 | − | 0.449238i | \(-0.851696\pi\) | |||||||
\(614\) | −7.75362 | + | 13.4297i | −0.312910 | + | 0.541977i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −26.9390 | − | 20.7827i | −1.08540 | − | 0.837359i | ||||
\(617\) | 9.77318 | + | 9.77318i | 0.393453 | + | 0.393453i | 0.875916 | − | 0.482463i | \(-0.160258\pi\) |
−0.482463 | + | 0.875916i | \(0.660258\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.8899 | − | 24.0580i | −0.558281 | − | 0.966972i | −0.997640 | − | 0.0686600i | \(-0.978128\pi\) |
0.439359 | − | 0.898312i | \(-0.355206\pi\) | |||||||
\(620\) | −5.65209 | + | 1.64602i | −0.226993 | + | 0.0661056i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.46559 | − | 5.46559i | 0.219150 | − | 0.219150i | ||||
\(623\) | −8.07386 | + | 6.16195i | −0.323472 | + | 0.246873i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.9069 | + | 2.15587i | −0.996275 | + | 0.0862348i | ||||
\(626\) | 7.91592 | − | 4.57026i | 0.316384 | − | 0.182664i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.87038 | − | 2.37681i | 0.353967 | − | 0.0948451i | ||||
\(629\) | −0.0554360 | −0.00221038 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.9169 | 0.633641 | 0.316821 | − | 0.948486i | \(-0.397385\pi\) | ||||
0.316821 | + | 0.948486i | \(0.397385\pi\) | |||||||
\(632\) | 9.59360 | − | 2.57060i | 0.381613 | − | 0.102253i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.18354 | − | 0.683317i | 0.0470044 | − | 0.0271380i | ||||
\(635\) | −0.179742 | − | 8.32568i | −0.00713283 | − | 0.330394i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.170598 | + | 32.7571i | −0.00675932 | + | 1.29788i | ||||
\(638\) | 58.0342 | − | 58.0342i | 2.29760 | − | 2.29760i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 14.5099 | − | 26.4336i | 0.573555 | − | 1.04488i | ||||
\(641\) | −14.7911 | − | 25.6190i | −0.584214 | − | 1.01189i | −0.994973 | − | 0.100144i | \(-0.968070\pi\) |
0.410759 | − | 0.911744i | \(-0.365264\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.0451 | − | 23.0451i | −0.908809 | − | 0.908809i | 0.0873668 | − | 0.996176i | \(-0.472155\pi\) |
−0.996176 | + | 0.0873668i | \(0.972155\pi\) | |||||||
\(644\) | 0.936973 | + | 2.27882i | 0.0369219 | + | 0.0897980i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.0386067 | + | 0.0668688i | −0.00151896 | + | 0.00263092i | ||||
\(647\) | 26.5278 | + | 7.10809i | 1.04291 | + | 0.279448i | 0.739320 | − | 0.673354i | \(-0.235147\pi\) |
0.303593 | + | 0.952802i | \(0.401814\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.15506 | − | 2.00063i | 0.0453402 | − | 0.0785315i | ||||
\(650\) | 16.7543 | − | 32.1484i | 0.657158 | − | 1.26097i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.32301 | + | 4.32301i | 0.169302 | + | 0.169302i | ||||
\(653\) | −8.43850 | − | 31.4929i | −0.330224 | − | 1.23241i | −0.908955 | − | 0.416894i | \(-0.863119\pi\) |
0.578731 | − | 0.815518i | \(-0.303548\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.88112 | + | 6.45940i | 0.0735016 | + | 0.252390i | ||||
\(656\) | −14.8261 | − | 8.55984i | −0.578861 | − | 0.334206i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.614384 | − | 4.76250i | −0.0239512 | − | 0.185662i | ||||
\(659\) | − | 4.16401i | − | 0.162207i | −0.996706 | − | 0.0811034i | \(-0.974156\pi\) | ||
0.996706 | − | 0.0811034i | \(-0.0258444\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.2035 | + | 5.89099i | −0.396870 | + | 0.229133i | −0.685133 | − | 0.728418i | \(-0.740256\pi\) |
0.288262 | + | 0.957551i | \(0.406922\pi\) | |||||||
\(662\) | −9.60739 | + | 35.8553i | −0.373402 | + | 1.39355i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −13.2310 | −0.513463 | ||||||||
\(665\) | −14.5858 | − | 1.63926i | −0.565612 | − | 0.0635678i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22.9272 | − | 6.14334i | 0.887746 | − | 0.237871i | ||||
\(668\) | 1.26213 | − | 4.71034i | 0.0488333 | − | 0.182248i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −14.1607 | + | 14.7856i | −0.547074 | + | 0.571217i | ||||
\(671\) | 7.10908i | 0.274443i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.90660 | + | 7.90660i | −0.304777 | + | 0.304777i | −0.842879 | − | 0.538102i | \(-0.819141\pi\) |
0.538102 | + | 0.842879i | \(0.319141\pi\) | |||||||
\(674\) | 4.13752 | + | 2.38880i | 0.159371 | + | 0.0920130i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.78210 | + | 3.08669i | 0.0685425 | + | 0.118719i | ||||
\(677\) | 2.13283 | + | 7.95983i | 0.0819713 | + | 0.305921i | 0.994723 | − | 0.102593i | \(-0.0327139\pi\) |
−0.912752 | + | 0.408514i | \(0.866047\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 36.6596 | − | 15.0732i | 1.40687 | − | 0.578456i | ||||
\(680\) | 0.108115 | + | 0.0264821i | 0.00414602 | + | 0.00101554i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −51.0487 | − | 13.6785i | −1.95475 | − | 0.523775i | ||||
\(683\) | 20.9907 | + | 5.62443i | 0.803185 | + | 0.215213i | 0.636982 | − | 0.770879i | \(-0.280183\pi\) |
0.166203 | + | 0.986091i | \(0.446849\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.1900 | − | 12.2452i | 0.771422 | − | 0.467867i | ||||
\(686\) | 17.2897 | + | 22.9007i | 0.660126 | + | 0.874351i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.75135 | − | 17.7323i | −0.181144 | − | 0.676038i | ||||
\(689\) | 11.1657 | + | 19.3396i | 0.425379 | + | 0.736779i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.9666 | − | 14.4145i | −0.949775 | − | 0.548353i | −0.0567641 | − | 0.998388i | \(-0.518078\pi\) |
−0.893011 | + | 0.450035i | \(0.851412\pi\) | |||||||
\(692\) | −1.02407 | + | 1.02407i | −0.0389292 | + | 0.0389292i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24.1639i | 0.917249i | ||||||||
\(695\) | −2.85387 | − | 2.73325i | −0.108253 | − | 0.103678i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.0191795 | − | 0.0715788i | 0.000726475 | − | 0.00271124i | ||||
\(698\) | −52.3251 | + | 14.0205i | −1.98053 | + | 0.530683i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.904031 | − | 5.22057i | −0.0341692 | − | 0.197319i | ||||
\(701\) | −48.9967 | −1.85058 | −0.925290 | − | 0.379259i | \(-0.876179\pi\) | ||||
−0.925290 | + | 0.379259i | \(0.876179\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.77210 | + | 6.61358i | −0.0668361 | + | 0.249436i | ||||
\(704\) | 26.1576 | − | 15.1021i | 0.985853 | − | 0.569182i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.68349i | 0.213901i | ||||||||
\(707\) | −17.8056 | + | 2.29700i | −0.669649 | + | 0.0863876i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.3623 | + | 10.6015i | 0.689609 | + | 0.398146i | 0.803466 | − | 0.595351i | \(-0.202987\pi\) |
−0.113856 | + | 0.993497i | \(0.536320\pi\) | |||||||
\(710\) | 6.52169 | + | 3.57988i | 0.244755 | + | 0.134351i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.46223 | − | 9.18918i | −0.0922761 | − | 0.344379i | ||||
\(713\) | −10.8077 | − | 10.8077i | −0.404753 | − | 0.404753i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 46.4284 | − | 28.1588i | 1.73632 | − | 1.05308i | ||||
\(716\) | −2.78163 | + | 4.81793i | −0.103954 | + | 0.180054i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −24.1117 | − | 6.46070i | −0.899840 | − | 0.241111i | ||||
\(719\) | 7.96647 | − | 13.7983i | 0.297099 | − | 0.514591i | −0.678372 | − | 0.734719i | \(-0.737314\pi\) |
0.975471 | + | 0.220128i | \(0.0706475\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.6839 | + | 3.31511i | 0.919277 | + | 0.123461i | ||||
\(722\) | −14.0723 | − | 14.0723i | −0.523716 | − | 0.523716i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.08934 | + | 5.35089i | 0.114814 | + | 0.198864i | ||||
\(725\) | −50.9929 | + | 2.20278i | −1.89383 | + | 0.0818093i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.1000 | + | 20.1000i | −0.745467 | + | 0.745467i | −0.973624 | − | 0.228157i | \(-0.926730\pi\) |
0.228157 | + | 0.973624i | \(0.426730\pi\) | |||||||
\(728\) | −28.3166 | − | 11.8156i | −1.04948 | − | 0.437915i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 17.7536 | − | 18.5371i | 0.657090 | − | 0.686087i | ||||
\(731\) | 0.0688172 | − | 0.0397316i | 0.00254529 | − | 0.00146953i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.0293 | + | 3.75914i | −0.518184 | + | 0.138847i | −0.508427 | − | 0.861105i | \(-0.669773\pi\) |
−0.00975769 | + | 0.999952i | \(0.503106\pi\) | |||||||
\(734\) | 45.7659 | 1.68925 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.19363 | −0.191440 | ||||||||
\(737\) | −29.6202 | + | 7.93672i | −1.09108 | + | 0.292353i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.2873 | − | 6.51671i | 0.415209 | − | 0.239721i | −0.277816 | − | 0.960634i | \(-0.589611\pi\) |
0.693025 | + | 0.720913i | \(0.256277\pi\) | |||||||
\(740\) | −2.47099 | + | 0.0533458i | −0.0908353 | + | 0.00196103i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 18.0530 | + | 7.53292i | 0.662745 | + | 0.276542i | ||||
\(743\) | 18.6181 | − | 18.6181i | 0.683031 | − | 0.683031i | −0.277651 | − | 0.960682i | \(-0.589556\pi\) |
0.960682 | + | 0.277651i | \(0.0895558\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.60976 | − | 15.8290i | −0.168888 | − | 0.579929i | ||||
\(746\) | −5.87552 | − | 10.1767i | −0.215118 | − | 0.372596i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.0295205 | − | 0.0295205i | −0.00107937 | − | 0.00107937i | ||||
\(749\) | 32.6205 | + | 4.38102i | 1.19193 | + | 0.160079i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.7401 | − | 25.5305i | 0.537872 | − | 0.931622i | −0.461146 | − | 0.887324i | \(-0.652562\pi\) |
0.999018 | − | 0.0442977i | \(-0.0141050\pi\) | |||||||
\(752\) | 5.25095 | + | 1.40699i | 0.191482 | + | 0.0513075i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 37.0067 | − | 64.0974i | 1.34770 | − | 2.33429i | ||||
\(755\) | −8.70137 | + | 35.5240i | −0.316675 | + | 1.29285i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.70030 | + | 5.70030i | 0.207181 | + | 0.207181i | 0.803068 | − | 0.595887i | \(-0.203199\pi\) |
−0.595887 | + | 0.803068i | \(0.703199\pi\) | |||||||
\(758\) | −7.02070 | − | 26.2016i | −0.255003 | − | 0.951685i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.61541 | − | 12.0517i | 0.239966 | − | 0.437161i | ||||
\(761\) | 47.3925 | + | 27.3621i | 1.71798 | + | 0.991874i | 0.922601 | + | 0.385756i | \(0.126059\pi\) |
0.795375 | + | 0.606118i | \(0.207274\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22.9045 | − | 2.95477i | 0.829197 | − | 0.106970i | ||||
\(764\) | 0.0227467i | 0.000822947i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.9494 | − | 9.20839i | 0.576275 | − | 0.332713i | ||||
\(767\) | 0.539191 | − | 2.01229i | 0.0194691 | − | 0.0726595i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −42.0339 | −1.51578 | −0.757891 | − | 0.652381i | \(-0.773770\pi\) | ||||
−0.757891 | + | 0.652381i | \(0.773770\pi\) | |||||||
\(770\) | 17.3650 | − | 44.2820i | 0.625792 | − | 1.59581i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.919410 | + | 0.246355i | −0.0330903 | + | 0.00886651i | ||||
\(773\) | 7.39235 | − | 27.5886i | 0.265884 | − | 0.992294i | −0.695822 | − | 0.718214i | \(-0.744960\pi\) |
0.961707 | − | 0.274080i | \(-0.0883734\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.6464 | + | 27.7276i | 0.633879 | + | 0.996006i | ||||
\(776\) | 37.1270i | 1.33278i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.49042 | + | 9.49042i | −0.340248 | + | 0.340248i | ||||
\(779\) | −7.92632 | − | 4.57627i | −0.283990 | − | 0.163962i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.57169 | + | 9.65045i | 0.199371 | + | 0.345320i | ||||
\(782\) | −0.0187298 | − | 0.0699004i | −0.000669775 | − | 0.00249963i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −31.4208 | + | 8.24403i | −1.12217 | + | 0.294430i | ||||
\(785\) | −26.5877 | − | 43.8380i | −0.948955 | − | 1.56465i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.0514 | + | 4.30097i | 0.572172 | + | 0.153313i | 0.533293 | − | 0.845931i | \(-0.320954\pi\) |
0.0388795 | + | 0.999244i | \(0.487621\pi\) | |||||||
\(788\) | −0.137390 | − | 0.0368135i | −0.00489432 | − | 0.00131143i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7.20035 | + | 11.8720i | 0.256177 | + | 0.422387i | ||||
\(791\) | −9.69387 | + | 3.98579i | −0.344674 | + | 0.141718i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.65928 | + | 6.19252i | 0.0589228 | + | 0.219903i | ||||
\(794\) | 2.02922 | + | 3.51471i | 0.0720142 | + | 0.124732i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.70866 | − | 5.02795i | −0.308670 | − | 0.178211i | ||||
\(797\) | −18.2572 | + | 18.2572i | −0.646702 | + | 0.646702i | −0.952194 | − | 0.305492i | \(-0.901179\pi\) |
0.305492 | + | 0.952194i | \(0.401179\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.0235309i | 0.000832464i | ||||||||
\(800\) | 10.9022 | + | 2.42225i | 0.385451 | + | 0.0856394i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.99414 | + | 14.9063i | −0.141038 | + | 0.526361i | ||||
\(803\) | 37.1356 | − | 9.95046i | 1.31049 | − | 0.351144i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.7526 | − | 8.57986i | 0.378979 | − | 0.302400i | ||||
\(806\) | −47.6597 | −1.67874 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.35232 | − | 16.2431i | 0.153114 | − | 0.571430i | ||||
\(809\) | 23.6794 | − | 13.6713i | 0.832525 | − | 0.480658i | −0.0221916 | − | 0.999754i | \(-0.507064\pi\) |
0.854716 | + | 0.519095i | \(0.173731\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 23.3175i | − | 0.818788i | −0.912358 | − | 0.409394i | \(-0.865740\pi\) | ||
0.912358 | − | 0.409394i | \(-0.134260\pi\) | |||||||
\(812\) | −1.38398 | − | 10.7281i | −0.0485680 | − | 0.376484i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −19.2157 | − | 11.0942i | −0.673511 | − | 0.388852i | ||||
\(815\) | 16.4244 | − | 29.9213i | 0.575321 | − | 1.04810i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.54017 | − | 9.48005i | −0.0888693 | − | 0.331665i | ||||
\(818\) | −8.83640 | − | 8.83640i | −0.308958 | − | 0.308958i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.786020 | − | 3.20899i | 0.0274490 | − | 0.112063i | ||||
\(821\) | −3.20706 | + | 5.55480i | −0.111927 | + | 0.193864i | −0.916547 | − | 0.399926i | \(-0.869036\pi\) |
0.804620 | + | 0.593790i | \(0.202369\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.13547 | + | 1.64399i | 0.213869 | + | 0.0573061i | 0.364163 | − | 0.931335i | \(-0.381355\pi\) |
−0.150294 | + | 0.988641i | \(0.548022\pi\) | |||||||
\(824\) | −11.6641 | + | 20.2027i | −0.406337 | + | 0.703796i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.693958 | − | 1.68778i | −0.0241459 | − | 0.0587254i | ||||
\(827\) | 31.0388 | + | 31.0388i | 1.07932 | + | 1.07932i | 0.996570 | + | 0.0827533i | \(0.0263714\pi\) |
0.0827533 | + | 0.996570i | \(0.473629\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.4622 | + | 44.1019i | 0.884340 | + | 1.53172i | 0.846468 | + | 0.532439i | \(0.178724\pi\) |
0.0378716 | + | 0.999283i | \(0.487942\pi\) | |||||||
\(830\) | −5.17185 | − | 17.7591i | −0.179517 | − | 0.616427i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 19.2603 | − | 19.2603i | 0.667732 | − | 0.667732i | ||||
\(833\) | −0.0696702 | − | 0.122137i | −0.00241393 | − | 0.00423179i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −27.2193 | + | 0.587634i | −0.941963 | + | 0.0203359i | ||||
\(836\) | −4.46549 | + | 2.57815i | −0.154442 | + | 0.0891672i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.95819 | − | 0.524695i | 0.0676444 | − | 0.0181253i | ||||
\(839\) | −46.0999 | −1.59155 | −0.795773 | − | 0.605596i | \(-0.792935\pi\) | ||||
−0.795773 | + | 0.605596i | \(0.792935\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −75.2050 | −2.59328 | ||||||||
\(842\) | −4.31138 | + | 1.15523i | −0.148580 | + | 0.0398119i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.27423 | + | 3.04508i | −0.181547 | + | 0.104816i | ||||
\(845\) | 13.7638 | − | 14.3712i | 0.473489 | − | 0.494385i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 33.5000 | − | 25.5672i | 1.15107 | − | 0.878498i | ||||
\(848\) | −15.6590 | + | 15.6590i | −0.537731 | + | 0.537731i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.00671583 | + | 0.155467i | 0.000230351 | + | 0.00533246i | ||||
\(851\) | −3.20853 | − | 5.55733i | −0.109987 | − | 0.190503i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.59157 | + | 6.59157i | 0.225691 | + | 0.225691i | 0.810890 | − | 0.585199i | \(-0.198983\pi\) |
−0.585199 | + | 0.810890i | \(0.698983\pi\) | |||||||
\(854\) | 4.44639 | + | 3.43027i | 0.152152 | + | 0.117381i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15.4144 | + | 26.6985i | −0.526854 | + | 0.912538i | ||||
\(857\) | 10.5425 | + | 2.82487i | 0.360126 | + | 0.0964956i | 0.434345 | − | 0.900746i | \(-0.356980\pi\) |
−0.0742191 | + | 0.997242i | \(0.523646\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.71182 | + | 11.6252i | −0.229004 | + | 0.396647i | −0.957513 | − | 0.288389i | \(-0.906880\pi\) |
0.728509 | + | 0.685036i | \(0.240214\pi\) | |||||||
\(860\) | 3.02920 | − | 1.83721i | 0.103295 | − | 0.0626482i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −22.8233 | − | 22.8233i | −0.777365 | − | 0.777365i | ||||
\(863\) | 14.0677 | + | 52.5015i | 0.478871 | + | 1.78717i | 0.606200 | + | 0.795312i | \(0.292693\pi\) |
−0.127329 | + | 0.991861i | \(0.540640\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.08798 | + | 3.89073i | 0.240999 | + | 0.132289i | ||||
\(866\) | 10.8564 | + | 6.26794i | 0.368915 | + | 0.212993i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.53709 | + | 4.22590i | −0.187941 | + | 0.143436i | ||||
\(869\) | 20.7973i | 0.705501i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.9489 | + | 13.8269i | −0.811478 | + | 0.468507i | ||||
\(872\) | −5.59866 | + | 20.8945i | −0.189595 | + | 0.707577i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −8.93792 | −0.302330 | ||||||||
\(875\) | −26.5728 | + | 12.9955i | −0.898326 | + | 0.439329i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.7858 | + | 6.37339i | −0.803191 | + | 0.215214i | −0.636984 | − | 0.770877i | \(-0.719818\pi\) |
−0.166206 | + | 0.986091i | \(0.553152\pi\) | |||||||
\(878\) | 3.46438 | − | 12.9292i | 0.116917 | − | 0.436341i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 38.8887 | + | 37.2450i | 1.31094 | + | 1.25553i | ||||
\(881\) | − | 16.1540i | − | 0.544243i | −0.962263 | − | 0.272121i | \(-0.912275\pi\) | ||
0.962263 | − | 0.272121i | \(-0.0877253\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.4853 | + | 34.4853i | −1.16052 | + | 1.16052i | −0.176161 | + | 0.984361i | \(0.556368\pi\) |
−0.984361 | + | 0.176161i | \(0.943632\pi\) | |||||||
\(884\) | −0.0326046 | − | 0.0188243i | −0.00109661 | − | 0.000633130i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24.1119 | + | 41.7630i | 0.810055 | + | 1.40306i | ||||
\(887\) | −4.08925 | − | 15.2613i | −0.137304 | − | 0.512424i | −0.999978 | − | 0.00666382i | \(-0.997879\pi\) |
0.862674 | − | 0.505760i | \(-0.168788\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.74700 | − | 9.11311i | −0.125670 | − | 0.305644i | ||||
\(890\) | 11.3715 | − | 6.89682i | 0.381175 | − | 0.231182i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.96784 | − | 0.527280i | −0.0658880 | − | 0.0176546i | ||||
\(893\) | 2.80726 | + | 0.752204i | 0.0939415 | + | 0.0251715i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 30.1680 | + | 7.38946i | 1.00841 | + | 0.247003i | ||||
\(896\) | 4.74913 | − | 35.3614i | 0.158657 | − | 1.18134i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 16.1683 | + | 60.3408i | 0.539542 | + | 2.01360i | ||||
\(899\) | 33.5506 | + | 58.1113i | 1.11898 | + | 1.93812i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.0830144 | − | 0.0479284i | −0.00276561 | − | 0.00159673i | ||||
\(902\) | 20.9730 | − | 20.9730i | 0.698324 | − | 0.698324i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 9.81746i | − | 0.326524i | ||||||
\(905\) | 23.8600 | − | 24.9130i | 0.793134 | − | 0.828135i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.51643 | + | 35.5158i | −0.315988 | + | 1.17928i | 0.607078 | + | 0.794642i | \(0.292341\pi\) |
−0.923066 | + | 0.384641i | \(0.874325\pi\) | |||||||
\(908\) | 2.91892 | − | 0.782122i | 0.0968677 | − | 0.0259556i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4.79063 | − | 42.6259i | 0.158808 | − | 1.41304i | ||||
\(911\) | −30.1482 | −0.998856 | −0.499428 | − | 0.866355i | \(-0.666456\pi\) | ||||
−0.499428 | + | 0.866355i | \(0.666456\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.17067 | − | 26.7613i | 0.237314 | − | 0.885670i | ||||
\(914\) | −17.9637 | + | 10.3713i | −0.594186 | + | 0.343054i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 10.3034i | − | 0.340434i | ||||||
\(917\) | 4.82950 | + | 6.32798i | 0.159484 | + | 0.208968i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.03427 | − | 0.597138i | −0.0341175 | − | 0.0196978i | 0.482844 | − | 0.875706i | \(-0.339604\pi\) |
−0.516962 | + | 0.856009i | \(0.672937\pi\) | |||||||
\(920\) | 3.60272 | + | 12.3710i | 0.118778 | + | 0.407860i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.831113 | + | 3.10176i | 0.0273713 | + | 0.102151i | ||||
\(923\) | 7.10580 | + | 7.10580i | 0.233890 | + | 0.233890i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.14330 | + | 13.1621i | 0.136231 | + | 0.432767i | ||||
\(926\) | −14.2142 | + | 24.6198i | −0.467109 | + | 0.809056i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 22.0240 | + | 5.90131i | 0.722972 | + | 0.193720i | ||||
\(929\) | 6.23132 | − | 10.7930i | 0.204443 | − | 0.354105i | −0.745512 | − | 0.666492i | \(-0.767795\pi\) |
0.949955 | + | 0.312387i | \(0.101128\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.7982 | + | 4.40743i | −0.550538 | + | 0.144448i | ||||
\(932\) | 7.59599 | + | 7.59599i | 0.248815 | + | 0.248815i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 19.9480 | + | 34.5509i | 0.652718 | + | 1.13054i | ||||
\(935\) | −0.112157 | + | 0.204323i | −0.00366792 | + | 0.00668208i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.0770 | + | 34.0770i | −1.11325 | + | 1.11325i | −0.120539 | + | 0.992709i | \(0.538462\pi\) |
−0.992709 | + | 0.120539i | \(0.961538\pi\) | |||||||
\(938\) | −9.32830 | + | 22.3557i | −0.304580 | + | 0.729939i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.0226437 | + | 1.04886i | 0.000738555 | + | 0.0342100i | ||||
\(941\) | −40.3625 | + | 23.3033i | −1.31578 | + | 0.759666i | −0.983047 | − | 0.183354i | \(-0.941304\pi\) |
−0.332734 | + | 0.943021i | \(0.607971\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.28567 | − | 2.22014i | 0.269819 | − | 0.0722977i | ||||
\(944\) | 2.06590 | 0.0672392 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 31.8054 | 1.03408 | ||||||||
\(947\) | −11.3990 | + | 3.05436i | −0.370418 | + | 0.0992533i | −0.439226 | − | 0.898377i | \(-0.644747\pi\) |
0.0688075 | + | 0.997630i | \(0.478081\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30.0254 | − | 17.3352i | 0.974665 | − | 0.562723i | ||||
\(950\) | 18.7620 | + | 4.16854i | 0.608720 | + | 0.135245i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.130623 | − | 0.0168509i | 0.00423350 | − | 0.000546140i | ||||
\(953\) | 28.2281 | − | 28.2281i | 0.914399 | − | 0.914399i | −0.0822160 | − | 0.996615i | \(-0.526200\pi\) |
0.996615 | + | 0.0822160i | \(0.0261997\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.121930 | − | 0.0355089i | 0.00394557 | − | 0.00114904i | ||||
\(956\) | 3.82110 | + | 6.61834i | 0.123583 | + | 0.214052i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 27.3890 | + | 27.3890i | 0.884898 | + | 0.884898i | ||||
\(959\) | 17.0662 | − | 22.1216i | 0.551095 | − | 0.714342i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.10438 | − | 10.5731i | 0.196916 | − | 0.341068i | ||||
\(962\) | −19.3277 | − | 5.17885i | −0.623151 | − | 0.166973i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.45304 | − | 4.24879i | 0.0790072 | − | 0.136844i | ||||
\(965\) | 2.75580 | + | 4.54379i | 0.0887123 | + | 0.146270i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.3045 | − | 22.3045i | −0.717263 | − | 0.717263i | 0.250781 | − | 0.968044i | \(-0.419313\pi\) |
−0.968044 | + | 0.250781i | \(0.919313\pi\) | |||||||
\(968\) | 10.2163 | + | 38.1277i | 0.328364 | + | 1.22547i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −49.8330 | + | 14.5125i | −1.60004 | + | 0.465968i | ||||
\(971\) | 25.5151 | + | 14.7312i | 0.818819 | + | 0.472745i | 0.850009 | − | 0.526768i | \(-0.176596\pi\) |
−0.0311899 | + | 0.999513i | \(0.509930\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.31502 | − | 1.80052i | −0.138333 | − | 0.0577220i | ||||
\(974\) | 42.2648i | 1.35425i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.50575 | + | 3.17875i | −0.176235 | + | 0.101749i | ||||
\(977\) | 1.08082 | − | 4.03368i | 0.0345785 | − | 0.129049i | −0.946479 | − | 0.322765i | \(-0.895388\pi\) |
0.981058 | + | 0.193717i | \(0.0620542\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 19.9206 | 0.636666 | ||||||||
\(980\) | −3.22299 | − | 5.37705i | −0.102955 | − | 0.171763i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −35.1394 | + | 9.41557i | −1.12134 | + | 0.300463i | ||||
\(983\) | −0.763296 | + | 2.84866i | −0.0243454 | + | 0.0908581i | −0.977030 | − | 0.213104i | \(-0.931643\pi\) |
0.952684 | + | 0.303962i | \(0.0983095\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.0171400 | + | 0.793926i | 0.000546125 | + | 0.0252966i | ||||
\(986\) | 0.317700i | 0.0101176i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.28802 | + | 3.28802i | −0.104606 | + | 0.104606i | ||||
\(989\) | 7.96600 | + | 4.59917i | 0.253304 | + | 0.146245i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.7168 | + | 23.7582i | 0.435729 | + | 0.754706i | 0.997355 | − | 0.0726861i | \(-0.0231571\pi\) |
−0.561625 | + | 0.827392i | \(0.689824\pi\) | |||||||
\(992\) | −3.80005 | − | 14.1820i | −0.120652 | − | 0.450279i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.72435 | + | 1.17170i | 0.276720 | + | 0.0371641i | ||||
\(995\) | −13.3569 | + | 54.5304i | −0.423441 | + | 1.72873i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.6315 | + | 5.52820i | 0.653407 | + | 0.175080i | 0.570269 | − | 0.821458i | \(-0.306839\pi\) |
0.0831381 | + | 0.996538i | \(0.473506\pi\) | |||||||
\(998\) | −42.8897 | − | 11.4922i | −1.35765 | − | 0.363781i | ||||
\(999\) | 0 | 0 |
(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 | 315.2.bz.d.82.3 | 32 | ||
3.2 | odd | 2 | 105.2.u.a.82.6 | yes | 32 | ||
5.3 | odd | 4 | inner | 315.2.bz.d.208.6 | 32 | ||
7.3 | odd | 6 | inner | 315.2.bz.d.262.6 | 32 | ||
15.2 | even | 4 | 525.2.bc.e.418.6 | 32 | |||
15.8 | even | 4 | 105.2.u.a.103.3 | yes | 32 | ||
15.14 | odd | 2 | 525.2.bc.e.82.3 | 32 | |||
21.2 | odd | 6 | 735.2.m.c.97.6 | 32 | |||
21.5 | even | 6 | 735.2.m.c.97.5 | 32 | |||
21.11 | odd | 6 | 735.2.v.b.472.3 | 32 | |||
21.17 | even | 6 | 105.2.u.a.52.3 | ✓ | 32 | ||
21.20 | even | 2 | 735.2.v.b.607.6 | 32 | |||
35.3 | even | 12 | inner | 315.2.bz.d.73.3 | 32 | ||
105.17 | odd | 12 | 525.2.bc.e.493.3 | 32 | |||
105.23 | even | 12 | 735.2.m.c.538.5 | 32 | |||
105.38 | odd | 12 | 105.2.u.a.73.6 | yes | 32 | ||
105.53 | even | 12 | 735.2.v.b.178.6 | 32 | |||
105.59 | even | 6 | 525.2.bc.e.157.6 | 32 | |||
105.68 | odd | 12 | 735.2.m.c.538.6 | 32 | |||
105.83 | odd | 4 | 735.2.v.b.313.3 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.u.a.52.3 | ✓ | 32 | 21.17 | even | 6 | ||
105.2.u.a.73.6 | yes | 32 | 105.38 | odd | 12 | ||
105.2.u.a.82.6 | yes | 32 | 3.2 | odd | 2 | ||
105.2.u.a.103.3 | yes | 32 | 15.8 | even | 4 | ||
315.2.bz.d.73.3 | 32 | 35.3 | even | 12 | inner | ||
315.2.bz.d.82.3 | 32 | 1.1 | even | 1 | trivial | ||
315.2.bz.d.208.6 | 32 | 5.3 | odd | 4 | inner | ||
315.2.bz.d.262.6 | 32 | 7.3 | odd | 6 | inner | ||
525.2.bc.e.82.3 | 32 | 15.14 | odd | 2 | |||
525.2.bc.e.157.6 | 32 | 105.59 | even | 6 | |||
525.2.bc.e.418.6 | 32 | 15.2 | even | 4 | |||
525.2.bc.e.493.3 | 32 | 105.17 | odd | 12 | |||
735.2.m.c.97.5 | 32 | 21.5 | even | 6 | |||
735.2.m.c.97.6 | 32 | 21.2 | odd | 6 | |||
735.2.m.c.538.5 | 32 | 105.23 | even | 12 | |||
735.2.m.c.538.6 | 32 | 105.68 | odd | 12 | |||
735.2.v.b.178.6 | 32 | 105.53 | even | 12 | |||
735.2.v.b.313.3 | 32 | 105.83 | odd | 4 | |||
735.2.v.b.472.3 | 32 | 21.11 | odd | 6 | |||
735.2.v.b.607.6 | 32 | 21.20 | even | 2 |