Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [729,2,Mod(28,729)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(729, base_ring=CyclotomicField(54))
chi = DirichletCharacter(H, H._module([44]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("729.28");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 729 = 3^{6} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 729.g (of order \(27\), degree \(18\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.82109430735\) |
Analytic rank: | \(0\) |
Dimension: | \(144\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{27})\) |
Twist minimal: | no (minimal twist has level 81) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{27}]$ |
Embedding invariants
Embedding label | 541.2 | ||
Character | \(\chi\) | \(=\) | 729.541 |
Dual form | 729.2.g.d.190.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{8}{27}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.03395 | − | 1.38884i | −0.731113 | − | 0.982055i | −0.999823 | − | 0.0188339i | \(-0.994005\pi\) |
0.268710 | − | 0.963221i | \(-0.413403\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.286206 | + | 0.955993i | −0.143103 | + | 0.477997i | ||||
\(5\) | 1.15051 | − | 0.756701i | 0.514523 | − | 0.338407i | −0.265548 | − | 0.964098i | \(-0.585553\pi\) |
0.780071 | + | 0.625690i | \(0.215183\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.25654 | + | 2.39179i | −0.852890 | + | 0.904011i | −0.996325 | − | 0.0856487i | \(-0.972704\pi\) |
0.143435 | + | 0.989660i | \(0.454185\pi\) | |||||||
\(8\) | −1.63042 | + | 0.593424i | −0.576441 | + | 0.209807i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.24050 | − | 0.815476i | −0.708509 | − | 0.257876i | ||||
\(11\) | −0.183502 | + | 0.0921584i | −0.0553280 | + | 0.0277868i | −0.476248 | − | 0.879311i | \(-0.658004\pi\) |
0.420920 | + | 0.907098i | \(0.361707\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.08132 | + | 4.82504i | 0.577254 | + | 1.33823i | 0.917443 | + | 0.397868i | \(0.130250\pi\) |
−0.340189 | + | 0.940357i | \(0.610491\pi\) | |||||||
\(14\) | 5.65495 | + | 0.660968i | 1.51135 | + | 0.176651i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.17744 | + | 2.74754i | 1.04436 | + | 0.686886i | ||||
\(17\) | 3.88762 | − | 3.26210i | 0.942887 | − | 0.791176i | −0.0351981 | − | 0.999380i | \(-0.511206\pi\) |
0.978085 | + | 0.208204i | \(0.0667618\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.25026 | − | 1.88819i | −0.516245 | − | 0.433181i | 0.347075 | − | 0.937837i | \(-0.387175\pi\) |
−0.863320 | + | 0.504656i | \(0.831619\pi\) | |||||||
\(20\) | 0.394119 | + | 1.31645i | 0.0881278 | + | 0.294367i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.317725 | + | 0.159568i | 0.0677392 | + | 0.0340199i | ||||
\(23\) | 2.58175 | + | 2.73649i | 0.538332 | + | 0.570598i | 0.938252 | − | 0.345952i | \(-0.112444\pi\) |
−0.399921 | + | 0.916550i | \(0.630962\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.22933 | + | 2.84990i | −0.245865 | + | 0.569980i | ||||
\(26\) | 4.54921 | − | 7.87946i | 0.892173 | − | 1.54529i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.64070 | − | 2.84178i | −0.310063 | − | 0.537045i | ||||
\(29\) | 6.26558 | − | 0.732341i | 1.16349 | − | 0.135992i | 0.487648 | − | 0.873040i | \(-0.337855\pi\) |
0.675840 | + | 0.737048i | \(0.263781\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.94436 | − | 1.17183i | 0.888033 | − | 0.210468i | 0.238811 | − | 0.971066i | \(-0.423242\pi\) |
0.649223 | + | 0.760598i | \(0.275094\pi\) | |||||||
\(32\) | −0.301604 | − | 5.17835i | −0.0533166 | − | 0.915411i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.55013 | − | 2.02642i | −1.46634 | − | 0.347528i | ||||
\(35\) | −0.786294 | + | 4.45930i | −0.132908 | + | 0.753759i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.44468 | + | 8.19321i | 0.237505 | + | 1.34696i | 0.837274 | + | 0.546783i | \(0.184148\pi\) |
−0.599770 | + | 0.800173i | \(0.704741\pi\) | |||||||
\(38\) | −0.295733 | + | 5.07754i | −0.0479742 | + | 0.823685i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.42677 | + | 1.91648i | −0.225592 | + | 0.303022i | ||||
\(41\) | −1.64966 | + | 2.21588i | −0.257634 | + | 0.346062i | −0.912055 | − | 0.410068i | \(-0.865505\pi\) |
0.654421 | + | 0.756130i | \(0.272912\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.0922521 | − | 1.58391i | 0.0140683 | − | 0.241544i | −0.983942 | − | 0.178490i | \(-0.942879\pi\) |
0.998010 | − | 0.0630541i | \(-0.0200841\pi\) | |||||||
\(44\) | −0.0355834 | − | 0.201803i | −0.00536439 | − | 0.0304230i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.13114 | − | 6.41502i | 0.166778 | − | 0.945843i | ||||
\(47\) | −2.02520 | − | 0.479981i | −0.295406 | − | 0.0700125i | 0.0802406 | − | 0.996776i | \(-0.474431\pi\) |
−0.375646 | + | 0.926763i | \(0.622579\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.221683 | − | 3.80615i | −0.0316690 | − | 0.543736i | ||||
\(50\) | 5.22910 | − | 1.23932i | 0.739507 | − | 0.175266i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.20839 | + | 0.608774i | −0.722274 | + | 0.0844217i | ||||
\(53\) | 4.51663 | + | 7.82303i | 0.620407 | + | 1.07458i | 0.989410 | + | 0.145148i | \(0.0463659\pi\) |
−0.369003 | + | 0.929428i | \(0.620301\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.141385 | + | 0.244885i | −0.0190643 | + | 0.0330203i | ||||
\(56\) | 2.25976 | − | 5.23870i | 0.301973 | − | 0.700051i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.49539 | − | 7.94465i | −0.984193 | − | 1.04318i | ||||
\(59\) | −13.2668 | − | 6.66285i | −1.72719 | − | 0.867429i | −0.978976 | − | 0.203976i | \(-0.934614\pi\) |
−0.748218 | − | 0.663453i | \(-0.769090\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.432126 | + | 1.44340i | 0.0553281 | + | 0.184809i | 0.981187 | − | 0.193062i | \(-0.0618417\pi\) |
−0.925859 | + | 0.377870i | \(0.876657\pi\) | |||||||
\(62\) | −6.73971 | − | 5.65528i | −0.855943 | − | 0.718222i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.780406 | − | 0.654838i | 0.0975508 | − | 0.0818548i | ||||
\(65\) | 6.04569 | + | 3.97631i | 0.749875 | + | 0.493201i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.3182 | + | 1.55668i | 1.62708 | + | 0.190178i | 0.880140 | − | 0.474715i | \(-0.157449\pi\) |
0.746938 | + | 0.664893i | \(0.231523\pi\) | |||||||
\(68\) | 2.00589 | + | 4.65018i | 0.243250 | + | 0.563917i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.00622 | − | 3.51865i | 0.837403 | − | 0.420560i | ||||
\(71\) | 4.39214 | + | 1.59861i | 0.521252 | + | 0.189720i | 0.589228 | − | 0.807967i | \(-0.299432\pi\) |
−0.0679763 | + | 0.997687i | \(0.521654\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.3008 | − | 5.56905i | 1.79083 | − | 0.651808i | 0.791662 | − | 0.610960i | \(-0.209216\pi\) |
0.999165 | − | 0.0408483i | \(-0.0130060\pi\) | |||||||
\(74\) | 9.88529 | − | 10.4778i | 1.14914 | − | 1.21802i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.44914 | − | 1.61082i | 0.280935 | − | 0.184774i | ||||
\(77\) | 0.193656 | − | 0.646857i | 0.0220692 | − | 0.0737162i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.887948 | − | 1.19272i | −0.0999020 | − | 0.134192i | 0.749361 | − | 0.662162i | \(-0.230361\pi\) |
−0.849263 | + | 0.527970i | \(0.822953\pi\) | |||||||
\(80\) | 6.88524 | 0.769794 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.78316 | 0.528211 | ||||||||
\(83\) | −8.51037 | − | 11.4314i | −0.934134 | − | 1.25476i | −0.966863 | − | 0.255296i | \(-0.917827\pi\) |
0.0327287 | − | 0.999464i | \(-0.489580\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.00431 | − | 6.69485i | 0.217397 | − | 0.726158i | ||||
\(86\) | −2.29517 | + | 1.50956i | −0.247495 | + | 0.162780i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.244497 | − | 0.259152i | 0.0260635 | − | 0.0276257i | ||||
\(89\) | −4.83016 | + | 1.75803i | −0.511996 | + | 0.186351i | −0.585082 | − | 0.810974i | \(-0.698938\pi\) |
0.0730859 | + | 0.997326i | \(0.476715\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −16.2370 | − | 5.90980i | −1.70210 | − | 0.619515i | ||||
\(92\) | −3.35498 | + | 1.68493i | −0.349781 | + | 0.175667i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.42734 | + | 3.30895i | 0.147219 | + | 0.341292i | ||||
\(95\) | −4.01774 | − | 0.469606i | −0.412211 | − | 0.0481806i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.50005 | + | 0.986599i | 0.152307 | + | 0.100174i | 0.623375 | − | 0.781923i | \(-0.285761\pi\) |
−0.471068 | + | 0.882097i | \(0.656131\pi\) | |||||||
\(98\) | −5.05691 | + | 4.24325i | −0.510825 | + | 0.428633i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.37264 | − | 1.99088i | −0.237264 | − | 0.199088i | ||||
\(101\) | 3.29109 | + | 10.9930i | 0.327475 | + | 1.09384i | 0.950262 | + | 0.311452i | \(0.100815\pi\) |
−0.622787 | + | 0.782392i | \(0.714000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.446992 | + | 0.224488i | 0.0440434 | + | 0.0221194i | 0.470685 | − | 0.882302i | \(-0.344007\pi\) |
−0.426641 | + | 0.904421i | \(0.640303\pi\) | |||||||
\(104\) | −6.25672 | − | 6.63174i | −0.613522 | − | 0.650295i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.19494 | − | 14.3615i | 0.601706 | − | 1.39491i | ||||
\(107\) | −2.72183 | + | 4.71434i | −0.263129 | + | 0.455752i | −0.967072 | − | 0.254504i | \(-0.918088\pi\) |
0.703943 | + | 0.710257i | \(0.251421\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.38980 | − | 14.5316i | −0.803597 | − | 1.39187i | −0.917234 | − | 0.398348i | \(-0.869584\pi\) |
0.113637 | − | 0.993522i | \(-0.463750\pi\) | |||||||
\(110\) | 0.486290 | − | 0.0568392i | 0.0463660 | − | 0.00541940i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −15.9981 | + | 3.79161i | −1.51168 | + | 0.358274i | ||||
\(113\) | 0.513560 | + | 8.81749i | 0.0483117 | + | 0.829480i | 0.932236 | + | 0.361850i | \(0.117855\pi\) |
−0.883925 | + | 0.467629i | \(0.845108\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.04103 | + | 1.19475i | 0.470078 | + | 0.111411i | ||||
\(116\) | −1.09313 | + | 6.19945i | −0.101495 | + | 0.575604i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.46363 | + | 25.3145i | 0.410910 | + | 2.33039i | ||||
\(119\) | −0.970301 | + | 16.6594i | −0.0889474 | + | 1.52717i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.54356 | + | 8.78953i | −0.594870 | + | 0.799048i | ||||
\(122\) | 1.55785 | − | 2.09256i | 0.141041 | − | 0.189451i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.294837 | + | 5.06216i | −0.0264772 | + | 0.454596i | ||||
\(125\) | 1.93778 | + | 10.9897i | 0.173321 | + | 0.982950i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.21170 | + | 6.87190i | −0.107521 | + | 0.609783i | 0.882662 | + | 0.470008i | \(0.155749\pi\) |
−0.990183 | + | 0.139775i | \(0.955362\pi\) | |||||||
\(128\) | −11.8110 | − | 2.79925i | −1.04395 | − | 0.247421i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.728495 | − | 12.5078i | −0.0638932 | − | 1.09700i | ||||
\(131\) | 5.48768 | − | 1.30061i | 0.479461 | − | 0.113634i | 0.0162234 | − | 0.999868i | \(-0.494836\pi\) |
0.463238 | + | 0.886234i | \(0.346688\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.59395 | − | 1.12137i | 0.831901 | − | 0.0972352i | ||||
\(134\) | −11.6084 | − | 20.1063i | −1.00281 | − | 1.73692i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.40265 | + | 7.62561i | −0.377524 | + | 0.653891i | ||||
\(137\) | −0.441416 | + | 1.02332i | −0.0377127 | + | 0.0874280i | −0.936031 | − | 0.351917i | \(-0.885530\pi\) |
0.898319 | + | 0.439345i | \(0.144789\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.26512 | + | 3.46082i | 0.276944 | + | 0.293543i | 0.850884 | − | 0.525354i | \(-0.176067\pi\) |
−0.573940 | + | 0.818897i | \(0.694586\pi\) | |||||||
\(140\) | −4.03802 | − | 2.02797i | −0.341275 | − | 0.171395i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.32105 | − | 7.75285i | −0.194778 | − | 0.650605i | ||||
\(143\) | −0.826595 | − | 0.693595i | −0.0691233 | − | 0.0580014i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.65443 | − | 5.58373i | 0.552621 | − | 0.463704i | ||||
\(146\) | −23.5548 | − | 15.4922i | −1.94941 | − | 1.28215i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.24613 | − | 0.963835i | −0.677828 | − | 0.0792267i | ||||
\(149\) | 3.04091 | + | 7.04963i | 0.249121 | + | 0.577528i | 0.996189 | − | 0.0872197i | \(-0.0277982\pi\) |
−0.747068 | + | 0.664748i | \(0.768539\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.76017 | − | 1.38621i | 0.224620 | − | 0.112808i | −0.332931 | − | 0.942951i | \(-0.608038\pi\) |
0.557551 | + | 0.830143i | \(0.311741\pi\) | |||||||
\(152\) | 4.78937 | + | 1.74319i | 0.388469 | + | 0.141391i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.09861 | + | 0.399861i | −0.0885285 | + | 0.0322217i | ||||
\(155\) | 4.80180 | − | 5.08961i | 0.385690 | − | 0.408807i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.12220 | + | 3.36893i | −0.408796 | + | 0.268870i | −0.737209 | − | 0.675665i | \(-0.763857\pi\) |
0.328413 | + | 0.944534i | \(0.393486\pi\) | |||||||
\(158\) | −0.738400 | + | 2.46643i | −0.0587440 | + | 0.196219i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.26546 | − | 5.72951i | −0.337214 | − | 0.452958i | ||||
\(161\) | −12.3709 | −0.974965 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.171894 | −0.0134638 | −0.00673188 | − | 0.999977i | \(-0.502143\pi\) | ||||
−0.00673188 | + | 0.999977i | \(0.502143\pi\) | |||||||
\(164\) | −1.64622 | − | 2.21126i | −0.128548 | − | 0.172670i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.07705 | + | 23.6390i | −0.549286 | + | 1.83474i | ||||
\(167\) | 0.245915 | − | 0.161741i | 0.0190295 | − | 0.0125159i | −0.539959 | − | 0.841692i | \(-0.681560\pi\) |
0.558988 | + | 0.829176i | \(0.311190\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.0280 | + | 10.6290i | −0.771383 | + | 0.817618i | ||||
\(170\) | −11.3704 | + | 4.13849i | −0.872069 | + | 0.317407i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.48780 | + | 0.541516i | 0.113444 | + | 0.0412902i | ||||
\(173\) | −2.40115 | + | 1.20590i | −0.182556 | + | 0.0916831i | −0.537730 | − | 0.843117i | \(-0.680718\pi\) |
0.355174 | + | 0.934800i | \(0.384422\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.04233 | − | 9.37119i | −0.305572 | − | 0.708395i | ||||
\(176\) | −1.01978 | − | 0.119195i | −0.0768687 | − | 0.00898466i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.43576 | + | 4.89058i | 0.557334 | + | 0.366564i | ||||
\(179\) | −1.83356 | + | 1.53854i | −0.137047 | + | 0.114996i | −0.708734 | − | 0.705476i | \(-0.750733\pi\) |
0.571687 | + | 0.820471i | \(0.306289\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.8278 | + | 10.7638i | 0.953481 | + | 0.800065i | 0.979880 | − | 0.199586i | \(-0.0639598\pi\) |
−0.0263995 | + | 0.999651i | \(0.508404\pi\) | |||||||
\(182\) | 8.58055 | + | 28.6610i | 0.636032 | + | 2.12450i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.83323 | − | 2.92956i | −0.430032 | − | 0.215970i | ||||
\(185\) | 7.86193 | + | 8.33316i | 0.578021 | + | 0.612666i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.412758 | + | 0.956881i | −0.0301839 | + | 0.0699741i | ||||
\(188\) | 1.03848 | − | 1.79870i | 0.0757391 | − | 0.131184i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.50193 | + | 6.06553i | 0.254057 | + | 0.440040i | ||||
\(191\) | −14.0948 | + | 1.64745i | −1.01987 | + | 0.119205i | −0.609558 | − | 0.792742i | \(-0.708653\pi\) |
−0.410308 | + | 0.911947i | \(0.634579\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.06333 | + | 0.963026i | −0.292485 | + | 0.0693202i | −0.374239 | − | 0.927332i | \(-0.622096\pi\) |
0.0817540 | + | 0.996653i | \(0.473948\pi\) | |||||||
\(194\) | −0.180754 | − | 3.10342i | −0.0129774 | − | 0.222813i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.70211 | + | 0.877415i | 0.264436 | + | 0.0626725i | ||||
\(197\) | 3.59768 | − | 20.4035i | 0.256324 | − | 1.45369i | −0.536326 | − | 0.844011i | \(-0.680188\pi\) |
0.792650 | − | 0.609677i | \(-0.208701\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.499478 | + | 2.83268i | 0.0354071 | + | 0.200803i | 0.997380 | − | 0.0723417i | \(-0.0230472\pi\) |
−0.961973 | + | 0.273145i | \(0.911936\pi\) | |||||||
\(200\) | 0.313119 | − | 5.37604i | 0.0221408 | − | 0.380144i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 11.8646 | − | 15.9370i | 0.834793 | − | 1.12132i | ||||
\(203\) | −12.3869 | + | 16.6385i | −0.869389 | + | 1.16779i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.221190 | + | 3.79769i | −0.0154486 | + | 0.265242i | ||||
\(206\) | −0.150390 | − | 0.852907i | −0.0104782 | − | 0.0594248i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.56243 | + | 25.8748i | −0.316347 | + | 1.79409i | ||||
\(209\) | 0.586941 | + | 0.139107i | 0.0405995 | + | 0.00962227i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.617143 | + | 10.5959i | 0.0424859 | + | 0.729454i | 0.950540 | + | 0.310602i | \(0.100531\pi\) |
−0.908054 | + | 0.418852i | \(0.862432\pi\) | |||||||
\(212\) | −8.77146 | + | 2.07887i | −0.602426 | + | 0.142778i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.36167 | − | 1.09422i | 0.639951 | − | 0.0747995i | ||||
\(215\) | −1.09241 | − | 1.89211i | −0.0745016 | − | 0.129041i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.35434 | + | 14.4701i | −0.567130 | + | 0.982298i | ||||
\(218\) | −11.5073 | + | 26.6770i | −0.779374 | + | 1.80679i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.193644 | − | 0.205250i | −0.0130555 | − | 0.0138380i | ||||
\(221\) | 23.8312 | + | 11.9685i | 1.60306 | + | 0.805086i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.79008 | + | 22.6805i | 0.454698 | + | 1.51880i | 0.811351 | + | 0.584559i | \(0.198733\pi\) |
−0.356653 | + | 0.934237i | \(0.616082\pi\) | |||||||
\(224\) | 13.0661 | + | 10.9638i | 0.873015 | + | 0.732547i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.7150 | − | 9.83009i | 0.779273 | − | 0.653888i | ||||
\(227\) | −0.383501 | − | 0.252232i | −0.0254538 | − | 0.0167412i | 0.536718 | − | 0.843761i | \(-0.319664\pi\) |
−0.562172 | + | 0.827020i | \(0.690034\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.8851 | − | 1.85670i | −1.04971 | − | 0.122694i | −0.426297 | − | 0.904583i | \(-0.640182\pi\) |
−0.623417 | + | 0.781889i | \(0.714256\pi\) | |||||||
\(230\) | −3.55287 | − | 8.23647i | −0.234269 | − | 0.543097i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.78093 | + | 4.91217i | −0.642150 | + | 0.322500i | ||||
\(233\) | −7.46875 | − | 2.71840i | −0.489294 | − | 0.178089i | 0.0855784 | − | 0.996331i | \(-0.472726\pi\) |
−0.574873 | + | 0.818243i | \(0.694948\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.69321 | + | 0.980249i | −0.175686 | + | 0.0639444i | ||||
\(236\) | 10.1667 | − | 10.7761i | 0.661795 | − | 0.701461i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 24.1404 | − | 15.8774i | 1.56479 | − | 1.02918i | ||||
\(239\) | 6.08524 | − | 20.3261i | 0.393621 | − | 1.31479i | −0.500023 | − | 0.866012i | \(-0.666675\pi\) |
0.893645 | − | 0.448775i | \(-0.148140\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.7905 | − | 14.4942i | −0.695079 | − | 0.933653i | 0.304745 | − | 0.952434i | \(-0.401429\pi\) |
−0.999824 | + | 0.0187813i | \(0.994021\pi\) | |||||||
\(242\) | 18.9729 | 1.21963 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.50356 | −0.0962556 | ||||||||
\(245\) | −3.13517 | − | 4.21127i | −0.200299 | − | 0.269048i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.42709 | − | 14.7875i | 0.281689 | − | 0.940907i | ||||
\(248\) | −7.36599 | + | 4.84469i | −0.467741 | + | 0.307638i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 13.2593 | − | 14.0541i | 0.838594 | − | 0.888857i | ||||
\(251\) | 7.58786 | − | 2.76176i | 0.478942 | − | 0.174321i | −0.0912569 | − | 0.995827i | \(-0.529088\pi\) |
0.570199 | + | 0.821507i | \(0.306866\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.725947 | − | 0.264223i | −0.0456399 | − | 0.0166116i | ||||
\(254\) | 10.7968 | − | 5.42235i | 0.677450 | − | 0.340228i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.51724 | + | 17.4269i | 0.469828 | + | 1.08918i | ||||
\(257\) | −16.4217 | − | 1.91942i | −1.02436 | − | 0.119730i | −0.412711 | − | 0.910862i | \(-0.635418\pi\) |
−0.611646 | + | 0.791132i | \(0.709492\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −22.8564 | − | 15.0329i | −1.42023 | − | 0.934099i | ||||
\(260\) | −5.53164 | + | 4.64160i | −0.343058 | + | 0.287860i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.48032 | − | 6.27673i | −0.462135 | − | 0.387778i | ||||
\(263\) | 0.00481531 | + | 0.0160843i | 0.000296925 | + | 0.000991797i | 0.958138 | − | 0.286307i | \(-0.0924278\pi\) |
−0.957841 | + | 0.287299i | \(0.907243\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.1161 | + | 5.58273i | 0.682858 | + | 0.342944i | ||||
\(266\) | −11.4771 | − | 12.1650i | −0.703704 | − | 0.745882i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.29992 | + | 12.2866i | −0.323744 | + | 0.750523i | ||||
\(269\) | −3.16338 | + | 5.47913i | −0.192874 | + | 0.334068i | −0.946202 | − | 0.323578i | \(-0.895114\pi\) |
0.753327 | + | 0.657646i | \(0.228448\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.98751 | − | 17.2989i | −0.606698 | − | 1.05083i | −0.991781 | − | 0.127950i | \(-0.959160\pi\) |
0.385082 | − | 0.922882i | \(-0.374173\pi\) | |||||||
\(272\) | 25.2031 | − | 2.94582i | 1.52816 | − | 0.178616i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.87762 | − | 0.445005i | 0.113431 | − | 0.0268837i | ||||
\(275\) | −0.0370577 | − | 0.636256i | −0.00223466 | − | 0.0383677i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.08715 | + | 1.44268i | 0.365741 | + | 0.0866822i | 0.409377 | − | 0.912365i | \(-0.365746\pi\) |
−0.0436360 | + | 0.999047i | \(0.513894\pi\) | |||||||
\(278\) | 1.43055 | − | 8.11303i | 0.0857985 | − | 0.486587i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.36427 | − | 7.73713i | −0.0815304 | − | 0.462382i | ||||
\(281\) | 0.338495 | − | 5.81173i | 0.0201929 | − | 0.346699i | −0.973046 | − | 0.230611i | \(-0.925928\pi\) |
0.993239 | − | 0.116088i | \(-0.0370354\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.13375 | + | 6.89582i | −0.305170 | + | 0.409914i | −0.928081 | − | 0.372379i | \(-0.878542\pi\) |
0.622911 | + | 0.782292i | \(0.285950\pi\) | |||||||
\(284\) | −2.78532 | + | 3.74133i | −0.165278 | + | 0.222007i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.108632 | + | 1.86515i | −0.00642357 | + | 0.110288i | ||||
\(287\) | −1.57739 | − | 8.94585i | −0.0931106 | − | 0.528057i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.52028 | − | 8.62194i | 0.0894282 | − | 0.507173i | ||||
\(290\) | −14.6352 | − | 3.46862i | −0.859411 | − | 0.203684i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.944788 | + | 16.2214i | 0.0552896 | + | 0.949285i | ||||
\(293\) | 6.26236 | − | 1.48421i | 0.365851 | − | 0.0867083i | −0.0435786 | − | 0.999050i | \(-0.513876\pi\) |
0.409430 | + | 0.912342i | \(0.365728\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.3054 | + | 2.37336i | −1.18222 | + | 0.138182i | ||||
\(296\) | −7.21749 | − | 12.5011i | −0.419508 | − | 0.726610i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.64663 | − | 11.5123i | 0.385029 | − | 0.666889i | ||||
\(299\) | −7.83024 | + | 18.1525i | −0.452835 | + | 1.04979i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.58020 | + | 3.79479i | 0.206359 | + | 0.218728i | ||||
\(302\) | −4.77910 | − | 2.40015i | −0.275006 | − | 0.138113i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.21243 | − | 14.0705i | −0.241599 | − | 0.806998i | ||||
\(305\) | 1.58939 | + | 1.33366i | 0.0910082 | + | 0.0763649i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.8060 | − | 15.7801i | 1.07332 | − | 0.900619i | 0.0779670 | − | 0.996956i | \(-0.475157\pi\) |
0.995349 | + | 0.0963370i | \(0.0307127\pi\) | |||||||
\(308\) | 0.562966 | + | 0.370269i | 0.0320780 | + | 0.0210980i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −12.0334 | − | 1.40651i | −0.683454 | − | 0.0798843i | ||||
\(311\) | −5.14380 | − | 11.9247i | −0.291678 | − | 0.676186i | 0.707867 | − | 0.706346i | \(-0.249658\pi\) |
−0.999545 | + | 0.0301598i | \(0.990398\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.67199 | − | 2.34636i | 0.264076 | − | 0.132624i | −0.311835 | − | 0.950136i | \(-0.600944\pi\) |
0.575911 | + | 0.817512i | \(0.304647\pi\) | |||||||
\(314\) | 9.97498 | + | 3.63060i | 0.562921 | + | 0.204886i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.39437 | − | 0.507509i | 0.0784394 | − | 0.0285496i | ||||
\(317\) | 20.9694 | − | 22.2263i | 1.17776 | − | 1.24835i | 0.215412 | − | 0.976523i | \(-0.430891\pi\) |
0.962346 | − | 0.271827i | \(-0.0876280\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.08226 | + | 0.711811i | −0.0605947 | + | 0.0398538i | ||||
\(320\) | 0.402347 | − | 1.34393i | 0.0224919 | − | 0.0751280i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 12.7909 | + | 17.1812i | 0.712809 | + | 0.957469i | ||||
\(323\) | −14.9076 | −0.829483 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.3095 | −0.904688 | ||||||||
\(326\) | 0.177730 | + | 0.238732i | 0.00984353 | + | 0.0132222i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.37468 | − | 4.59176i | 0.0759042 | − | 0.253538i | ||||
\(329\) | 5.71795 | − | 3.76075i | 0.315241 | − | 0.207337i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.18477 | + | 2.31572i | −0.120086 | + | 0.127283i | −0.784627 | − | 0.619968i | \(-0.787146\pi\) |
0.664541 | + | 0.747252i | \(0.268627\pi\) | |||||||
\(332\) | 13.3641 | − | 4.86412i | 0.733449 | − | 0.266953i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.478896 | − | 0.174304i | −0.0262040 | − | 0.00953748i | ||||
\(335\) | 16.5006 | − | 8.28694i | 0.901527 | − | 0.452764i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.9802 | − | 30.0915i | −0.707076 | − | 1.63919i | −0.767528 | − | 0.641016i | \(-0.778513\pi\) |
0.0604518 | − | 0.998171i | \(-0.480746\pi\) | |||||||
\(338\) | 25.1304 | + | 2.93732i | 1.36691 | + | 0.159769i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.82659 | + | 3.83221i | 0.315991 | + | 0.207831i | ||||
\(341\) | −0.799307 | + | 0.670699i | −0.0432849 | + | 0.0363204i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.02888 | − | 6.73703i | −0.433519 | − | 0.363765i | ||||
\(344\) | 0.789520 | + | 2.63718i | 0.0425681 | + | 0.142187i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.15747 | + | 2.08796i | 0.223507 | + | 0.112249i | ||||
\(347\) | 15.3768 | + | 16.2984i | 0.825468 | + | 0.874944i | 0.993845 | − | 0.110778i | \(-0.0353343\pi\) |
−0.168378 | + | 0.985723i | \(0.553853\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.74057 | − | 20.2629i | 0.467872 | − | 1.08465i | −0.507013 | − | 0.861939i | \(-0.669250\pi\) |
0.974885 | − | 0.222711i | \(-0.0714905\pi\) | |||||||
\(350\) | −8.83546 | + | 15.3035i | −0.472275 | + | 0.818005i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.532573 | + | 0.922444i | 0.0283863 | + | 0.0491664i | ||||
\(353\) | 10.8430 | − | 1.26736i | 0.577114 | − | 0.0674550i | 0.177472 | − | 0.984126i | \(-0.443208\pi\) |
0.399643 | + | 0.916671i | \(0.369134\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.26287 | − | 1.48433i | 0.332399 | − | 0.0787799i | ||||
\(356\) | −0.298250 | − | 5.12076i | −0.0158072 | − | 0.271400i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.03259 | + | 0.955741i | 0.213129 | + | 0.0505125i | ||||
\(359\) | −4.30460 | + | 24.4126i | −0.227188 | + | 1.28845i | 0.631269 | + | 0.775564i | \(0.282534\pi\) |
−0.858457 | + | 0.512885i | \(0.828577\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.80092 | − | 10.2135i | −0.0947851 | − | 0.537553i | ||||
\(362\) | 1.68585 | − | 28.9449i | 0.0886061 | − | 1.52131i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 10.2969 | − | 13.8311i | 0.539702 | − | 0.724946i | ||||
\(365\) | 13.3896 | − | 17.9854i | 0.700845 | − | 0.941399i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.747077 | − | 12.8268i | 0.0389971 | − | 0.669555i | −0.921003 | − | 0.389555i | \(-0.872629\pi\) |
0.960000 | − | 0.279999i | \(-0.0903343\pi\) | |||||||
\(368\) | 3.26645 | + | 18.5250i | 0.170276 | + | 0.965681i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.44455 | − | 19.5350i | 0.179074 | − | 1.01558i | ||||
\(371\) | −28.9030 | − | 6.85013i | −1.50057 | − | 0.355641i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.129702 | − | 2.22690i | −0.00671572 | − | 0.115304i | 0.993284 | − | 0.115700i | \(-0.0369111\pi\) |
−1.00000 | 0.000395600i | \(0.999874\pi\) | ||||||||
\(374\) | 1.75572 | − | 0.416114i | 0.0907862 | − | 0.0215167i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.58676 | − | 0.419232i | 0.184973 | − | 0.0216202i | ||||
\(377\) | 16.5742 | + | 28.7074i | 0.853617 | + | 1.47851i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.67947 | − | 6.37302i | 0.189001 | − | 0.327360i | −0.755916 | − | 0.654668i | \(-0.772808\pi\) |
0.944918 | + | 0.327308i | \(0.106142\pi\) | |||||||
\(380\) | 1.59884 | − | 3.70653i | 0.0820188 | − | 0.190141i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 16.8614 | + | 17.8720i | 0.862703 | + | 0.914412i | ||||
\(383\) | 12.9185 | + | 6.48791i | 0.660104 | + | 0.331517i | 0.747119 | − | 0.664690i | \(-0.231437\pi\) |
−0.0870152 | + | 0.996207i | \(0.527733\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.266675 | − | 0.890755i | −0.0135910 | − | 0.0453971i | ||||
\(386\) | 5.53876 | + | 4.64757i | 0.281916 | + | 0.236555i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.37251 | + | 1.15167i | −0.0696784 | + | 0.0584671i | ||||
\(389\) | 7.10510 | + | 4.67310i | 0.360243 | + | 0.236935i | 0.716708 | − | 0.697373i | \(-0.245648\pi\) |
−0.356466 | + | 0.934308i | \(0.616018\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.9636 | + | 2.21653i | 0.959030 | + | 0.112094i | ||||
\(392\) | 2.62010 | + | 6.07408i | 0.132335 | + | 0.306787i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −32.0569 | + | 16.0996i | −1.61500 | + | 0.811085i | ||||
\(395\) | −1.92413 | − | 0.700325i | −0.0968133 | − | 0.0352372i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.16106 | + | 1.87847i | −0.259026 | + | 0.0942779i | −0.468269 | − | 0.883586i | \(-0.655122\pi\) |
0.209243 | + | 0.977864i | \(0.432900\pi\) | |||||||
\(398\) | 3.41769 | − | 3.62254i | 0.171313 | − | 0.181582i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12.9656 | + | 8.52764i | −0.648282 | + | 0.426382i | ||||
\(401\) | −2.69850 | + | 9.01361i | −0.134757 | + | 0.450118i | −0.998556 | − | 0.0537173i | \(-0.982893\pi\) |
0.863800 | + | 0.503835i | \(0.168078\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.9449 | + | 21.4178i | 0.794274 | + | 1.06690i | ||||
\(404\) | −11.4512 | −0.569716 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 35.9155 | 1.78246 | ||||||||
\(407\) | −1.02018 | − | 1.37033i | −0.0505682 | − | 0.0679249i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.42300 | − | 14.7739i | 0.218703 | − | 0.730520i | −0.776272 | − | 0.630398i | \(-0.782892\pi\) |
0.994975 | − | 0.100122i | \(-0.0319233\pi\) | |||||||
\(410\) | 5.50306 | − | 3.61942i | 0.271777 | − | 0.178750i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.342540 | + | 0.363071i | −0.0168757 | + | 0.0178872i | ||||
\(413\) | 45.8732 | − | 16.6965i | 2.25727 | − | 0.821580i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.4414 | − | 6.71212i | −0.905253 | − | 0.329485i | ||||
\(416\) | 24.3580 | − | 12.2331i | 1.19425 | − | 0.599775i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.413670 | − | 0.958994i | −0.0202332 | − | 0.0469059i | ||||
\(419\) | −24.5377 | − | 2.86805i | −1.19875 | − | 0.140113i | −0.506801 | − | 0.862063i | \(-0.669172\pi\) |
−0.691945 | + | 0.721950i | \(0.743246\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.155228 | + | 0.102095i | 0.00756535 | + | 0.00497581i | 0.553286 | − | 0.832991i | \(-0.313374\pi\) |
−0.545721 | + | 0.837967i | \(0.683744\pi\) | |||||||
\(422\) | 14.0779 | − | 11.8128i | 0.685302 | − | 0.575037i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −12.0064 | − | 10.0746i | −0.583082 | − | 0.489264i | ||||
\(425\) | 4.51751 | + | 15.0895i | 0.219131 | + | 0.731949i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.42742 | − | 2.22354i | −0.214258 | − | 0.107604i | ||||
\(428\) | −3.72788 | − | 3.95132i | −0.180194 | − | 0.190994i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.49833 | + | 3.47352i | −0.0722559 | + | 0.167508i | ||||
\(431\) | 7.27612 | − | 12.6026i | 0.350478 | − | 0.607046i | −0.635855 | − | 0.771808i | \(-0.719352\pi\) |
0.986333 | + | 0.164762i | \(0.0526857\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.3096 | + | 29.9811i | 0.831846 | + | 1.44080i | 0.896573 | + | 0.442897i | \(0.146049\pi\) |
−0.0647264 | + | 0.997903i | \(0.520617\pi\) | |||||||
\(434\) | 28.7346 | − | 3.35860i | 1.37931 | − | 0.161218i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 16.2933 | − | 3.86158i | 0.780307 | − | 0.184936i | ||||
\(437\) | −0.642579 | − | 11.0327i | −0.0307387 | − | 0.527763i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.91282 | − | 0.453346i | −0.0912937 | − | 0.0216370i | 0.184715 | − | 0.982792i | \(-0.440864\pi\) |
−0.276009 | + | 0.961155i | \(0.589012\pi\) | |||||||
\(440\) | 0.0851954 | − | 0.483167i | 0.00406153 | − | 0.0230341i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.01800 | − | 45.4724i | −0.381378 | − | 2.16290i | ||||
\(443\) | −1.84950 | + | 31.7547i | −0.0878725 | + | 1.50871i | 0.609949 | + | 0.792441i | \(0.291190\pi\) |
−0.697821 | + | 0.716272i | \(0.745847\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.22683 | + | 5.67762i | −0.200371 | + | 0.269145i | ||||
\(446\) | 24.4788 | − | 32.8808i | 1.15911 | − | 1.55695i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.194779 | + | 3.34423i | −0.00920246 | + | 0.158000i | ||||
\(449\) | −5.17251 | − | 29.3348i | −0.244106 | − | 1.38439i | −0.822560 | − | 0.568679i | \(-0.807455\pi\) |
0.578454 | − | 0.815715i | \(-0.303656\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.0985049 | − | 0.558649i | 0.00463841 | − | 0.0263057i | ||||
\(452\) | −8.57645 | − | 2.03266i | −0.403402 | − | 0.0956081i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.0462111 | + | 0.793415i | 0.00216880 | + | 0.0372368i | ||||
\(455\) | −23.1528 | + | 5.48732i | −1.08542 | + | 0.257249i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.6602 | + | 1.47977i | −0.592220 | + | 0.0692206i | −0.406924 | − | 0.913462i | \(-0.633399\pi\) |
−0.185296 | + | 0.982683i | \(0.559325\pi\) | |||||||
\(458\) | 13.8457 | + | 23.9815i | 0.646968 | + | 1.12058i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.58494 | + | 4.47725i | −0.120523 | + | 0.208753i | ||||
\(461\) | 8.18619 | − | 18.9777i | 0.381269 | − | 0.883880i | −0.614232 | − | 0.789126i | \(-0.710534\pi\) |
0.995501 | − | 0.0947547i | \(-0.0302067\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.4261 | + | 12.1109i | 0.531014 | + | 0.562842i | 0.936234 | − | 0.351377i | \(-0.114286\pi\) |
−0.405220 | + | 0.914219i | \(0.632805\pi\) | |||||||
\(464\) | 28.1862 | + | 14.1556i | 1.30851 | + | 0.657159i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.94690 | + | 13.1836i | 0.182837 | + | 0.610717i | ||||
\(467\) | −22.4416 | − | 18.8308i | −1.03848 | − | 0.871384i | −0.0466403 | − | 0.998912i | \(-0.514851\pi\) |
−0.991835 | + | 0.127527i | \(0.959296\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −33.7762 | + | 28.3416i | −1.55964 | + | 1.30870i | ||||
\(470\) | 4.14605 | + | 2.72690i | 0.191243 | + | 0.125783i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 25.5844 | + | 2.99039i | 1.17762 | + | 0.137644i | ||||
\(473\) | 0.129042 | + | 0.299153i | 0.00593335 | + | 0.0137551i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.14746 | − | 4.09181i | 0.373831 | − | 0.187745i | ||||
\(476\) | −15.6486 | − | 5.69562i | −0.717252 | − | 0.261059i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −34.5215 | + | 12.5648i | −1.57897 | + | 0.574700i | ||||
\(479\) | −15.3457 | + | 16.2655i | −0.701162 | + | 0.743189i | −0.975873 | − | 0.218338i | \(-0.929936\pi\) |
0.274711 | + | 0.961527i | \(0.411418\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −36.5257 | + | 24.0233i | −1.66543 | + | 1.09537i | ||||
\(482\) | −8.97318 | + | 29.9725i | −0.408717 | + | 1.36521i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.52993 | − | 8.77122i | −0.296815 | − | 0.398692i | ||||
\(485\) | 2.47238 | 0.112265 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.73936 | 0.169447 | 0.0847233 | − | 0.996405i | \(-0.472999\pi\) | ||||
0.0847233 | + | 0.996405i | \(0.472999\pi\) | |||||||
\(488\) | −1.56110 | − | 2.09692i | −0.0706676 | − | 0.0949230i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.60715 | + | 8.70847i | −0.117779 | + | 0.393409i | ||||
\(491\) | 1.00818 | − | 0.663088i | 0.0454984 | − | 0.0299248i | −0.526556 | − | 0.850140i | \(-0.676517\pi\) |
0.572054 | + | 0.820216i | \(0.306147\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 21.9692 | − | 23.2860i | 0.989444 | − | 1.04875i | ||||
\(494\) | −25.1148 | + | 9.14105i | −1.12997 | + | 0.411275i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 23.8744 | + | 8.68957i | 1.07199 | + | 0.390173i | ||||
\(497\) | −13.7346 | + | 6.89776i | −0.616079 | + | 0.309407i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.32207 | + | 3.06491i | 0.0591842 | + | 0.137204i | 0.945242 | − | 0.326371i | \(-0.105826\pi\) |
−0.886058 | + | 0.463575i | \(0.846566\pi\) | |||||||
\(500\) | −11.0607 | − | 1.29281i | −0.494649 | − | 0.0578162i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −11.6811 | − | 7.68278i | −0.521353 | − | 0.342899i | ||||
\(503\) | 18.7108 | − | 15.7002i | 0.834274 | − | 0.700039i | −0.121994 | − | 0.992531i | \(-0.538929\pi\) |
0.956268 | + | 0.292492i | \(0.0944844\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.1048 | + | 10.1572i | 0.538658 | + | 0.451988i | ||||
\(506\) | 0.383630 | + | 1.28142i | 0.0170545 | + | 0.0569658i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.22270 | − | 3.12516i | −0.276087 | − | 0.138656i | ||||
\(509\) | −21.2317 | − | 22.5042i | −0.941076 | − | 0.997483i | 0.0589233 | − | 0.998263i | \(-0.481233\pi\) |
−1.00000 | 0.000779780i | \(0.999752\pi\) | ||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −21.2069 | + | 49.1631i | −0.938138 | + | 2.17485i | ||||
\(512\) | 4.29252 | − | 7.43487i | 0.189705 | − | 0.328578i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 14.3134 | + | 24.7916i | 0.631339 | + | 1.09351i | ||||
\(515\) | 0.684138 | − | 0.0799642i | 0.0301467 | − | 0.00352364i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.415863 | − | 0.0985614i | 0.0182896 | − | 0.00433473i | ||||
\(518\) | 2.75416 | + | 47.2871i | 0.121011 | + | 2.07767i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −12.2167 | − | 2.89540i | −0.535736 | − | 0.126972i | ||||
\(521\) | 2.47495 | − | 14.0361i | 0.108430 | − | 0.614934i | −0.881365 | − | 0.472435i | \(-0.843375\pi\) |
0.989795 | − | 0.142499i | \(-0.0455138\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.234960 | + | 1.33253i | 0.0102741 | + | 0.0582673i | 0.989514 | − | 0.144439i | \(-0.0461376\pi\) |
−0.979240 | + | 0.202706i | \(0.935026\pi\) | |||||||
\(524\) | −0.327236 | + | 5.61843i | −0.0142954 | + | 0.245442i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.0173596 | − | 0.0233180i | 0.000756914 | − | 0.00101671i | ||||
\(527\) | 15.3992 | − | 20.6847i | 0.670798 | − | 0.901038i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.514360 | − | 8.83122i | 0.0223635 | − | 0.383966i | ||||
\(530\) | −3.74002 | − | 21.2107i | −0.162456 | − | 0.921335i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.67382 | + | 9.49269i | −0.0725692 | + | 0.411560i | ||||
\(533\) | −14.1252 | − | 3.34773i | −0.611829 | − | 0.145006i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.435864 | + | 7.48350i | 0.0188440 | + | 0.323540i | ||||
\(536\) | −22.6380 | + | 5.36531i | −0.977814 | + | 0.231746i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10.8804 | − | 1.27173i | 0.469086 | − | 0.0548283i | ||||
\(539\) | 0.391448 | + | 0.678008i | 0.0168609 | + | 0.0292039i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.5060 | − | 21.6611i | 0.537676 | − | 0.931283i | −0.461352 | − | 0.887217i | \(-0.652636\pi\) |
0.999029 | − | 0.0440659i | \(-0.0140312\pi\) | |||||||
\(542\) | −13.6987 | + | 31.7572i | −0.588410 | + | 1.36409i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −18.0648 | − | 19.1476i | −0.774524 | − | 0.820947i | ||||
\(545\) | −20.6486 | − | 10.3701i | −0.884488 | − | 0.444207i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.14494 | − | 27.2060i | −0.348253 | − | 1.16325i | −0.935348 | − | 0.353728i | \(-0.884914\pi\) |
0.587096 | − | 0.809517i | \(-0.300271\pi\) | |||||||
\(548\) | −0.851950 | − | 0.714871i | −0.0363935 | − | 0.0305378i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.845339 | + | 0.709324i | −0.0360454 | + | 0.0302457i | ||||
\(551\) | −15.4820 | − | 10.1827i | −0.659554 | − | 0.433796i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.85642 | + | 0.567635i | 0.206516 | + | 0.0241383i | ||||
\(554\) | −4.29016 | − | 9.94570i | −0.182271 | − | 0.422552i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.24302 | + | 2.13093i | −0.179944 | + | 0.0903714i | ||||
\(557\) | −34.6621 | − | 12.6160i | −1.46868 | − | 0.534556i | −0.520938 | − | 0.853594i | \(-0.674418\pi\) |
−0.947742 | + | 0.319039i | \(0.896640\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.83442 | − | 2.85150i | 0.331361 | − | 0.120605i | ||||
\(560\) | −15.5368 | + | 16.4680i | −0.656550 | + | 0.695902i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.42152 | + | 5.53892i | −0.355240 | + | 0.233645i | ||||
\(563\) | −6.35470 | + | 21.2262i | −0.267819 | + | 0.894576i | 0.713249 | + | 0.700911i | \(0.247223\pi\) |
−0.981068 | + | 0.193666i | \(0.937962\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.26306 | + | 9.75598i | 0.305559 | + | 0.410437i | ||||
\(566\) | 14.8852 | 0.625671 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.10969 | −0.340275 | ||||||||
\(569\) | 3.82370 | + | 5.13612i | 0.160298 | + | 0.215317i | 0.875014 | − | 0.484097i | \(-0.160852\pi\) |
−0.714717 | + | 0.699414i | \(0.753444\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.58425 | − | 5.29175i | 0.0662986 | − | 0.221453i | −0.918420 | − | 0.395607i | \(-0.870534\pi\) |
0.984718 | + | 0.174155i | \(0.0557193\pi\) | |||||||
\(572\) | 0.899649 | − | 0.591708i | 0.0376162 | − | 0.0247406i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −10.7934 | + | 11.4403i | −0.450506 | + | 0.477509i | ||||
\(575\) | −10.9725 | + | 3.99368i | −0.457586 | + | 0.166548i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.7599 | + | 13.3795i | 1.53033 | + | 0.556996i | 0.963703 | − | 0.266977i | \(-0.0860246\pi\) |
0.566630 | + | 0.823972i | \(0.308247\pi\) | |||||||
\(578\) | −13.5463 | + | 6.80323i | −0.563454 | + | 0.282977i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.43348 | + | 7.95969i | 0.142567 | + | 0.330508i | ||||
\(581\) | 46.5455 | + | 5.44038i | 1.93103 | + | 0.225705i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.54977 | − | 1.01930i | −0.0641849 | − | 0.0422151i | ||||
\(584\) | −21.6420 | + | 18.1598i | −0.895551 | + | 0.751457i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.53628 | − | 7.16279i | −0.352631 | − | 0.295892i | ||||
\(587\) | −3.98891 | − | 13.3239i | −0.164640 | − | 0.549935i | −1.00000 | 0.000232108i | \(-0.999926\pi\) | |
0.835360 | − | 0.549703i | \(-0.185259\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.3387 | − | 6.69897i | −0.549613 | − | 0.276026i | ||||
\(590\) | 24.2909 | + | 25.7469i | 1.00004 | + | 1.05998i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −16.4761 | + | 38.1959i | −0.677164 | + | 1.56984i | ||||
\(593\) | 8.67989 | − | 15.0340i | 0.356441 | − | 0.617373i | −0.630923 | − | 0.775846i | \(-0.717324\pi\) |
0.987363 | + | 0.158472i | \(0.0506569\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.4899 | + | 19.9010i | 0.471039 | + | 0.815863i | ||||
\(596\) | −7.60973 | + | 0.889450i | −0.311707 | + | 0.0364333i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 33.3070 | − | 7.89390i | 1.36202 | − | 0.322806i | ||||
\(599\) | −2.41727 | − | 41.5029i | −0.0987669 | − | 1.69576i | −0.576372 | − | 0.817187i | \(-0.695532\pi\) |
0.477606 | − | 0.878574i | \(-0.341505\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.98563 | − | 2.12963i | −0.366532 | − | 0.0868696i | 0.0432228 | − | 0.999065i | \(-0.486237\pi\) |
−0.409754 | + | 0.912196i | \(0.634386\pi\) | |||||||
\(602\) | 1.56859 | − | 8.89594i | 0.0639311 | − | 0.362571i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.535232 | + | 3.03545i | 0.0217783 | + | 0.123511i | ||||
\(605\) | −0.877375 | + | 15.0640i | −0.0356704 | + | 0.612437i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.05551 | + | 10.8204i | −0.326963 | + | 0.439187i | −0.934961 | − | 0.354751i | \(-0.884566\pi\) |
0.607998 | + | 0.793939i | \(0.291973\pi\) | |||||||
\(608\) | −9.09903 | + | 12.2221i | −0.369014 | + | 0.495672i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.208880 | − | 3.58633i | 0.00845731 | − | 0.145206i | ||||
\(611\) | −1.89916 | − | 10.7707i | −0.0768317 | − | 0.435734i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.675007 | + | 3.82815i | −0.0272633 | + | 0.154618i | −0.995400 | − | 0.0958034i | \(-0.969458\pi\) |
0.968137 | + | 0.250421i | \(0.0805691\pi\) | |||||||
\(614\) | −41.3605 | − | 9.80261i | −1.66917 | − | 0.395601i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.0681197 | + | 1.16957i | 0.00274462 | + | 0.0471233i | ||||
\(617\) | 23.3671 | − | 5.53810i | 0.940723 | − | 0.222956i | 0.268480 | − | 0.963285i | \(-0.413479\pi\) |
0.672244 | + | 0.740330i | \(0.265331\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.1098 | − | 1.18167i | 0.406348 | − | 0.0474953i | 0.0895361 | − | 0.995984i | \(-0.471462\pi\) |
0.316812 | + | 0.948488i | \(0.397387\pi\) | |||||||
\(620\) | 3.49133 | + | 6.04716i | 0.140215 | + | 0.242860i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −11.2430 | + | 19.4734i | −0.450802 | + | 0.780812i | ||||
\(623\) | 6.69458 | − | 15.5198i | 0.268213 | − | 0.621787i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.104193 | − | 0.110438i | −0.00416772 | − | 0.00441753i | ||||
\(626\) | −8.08931 | − | 4.06260i | −0.323314 | − | 0.162374i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.75467 | − | 5.86100i | −0.0700189 | − | 0.233879i | ||||
\(629\) | 32.3435 | + | 27.1394i | 1.28962 | + | 1.08212i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.7162 | + | 31.6476i | −1.50146 | + | 1.25987i | −0.622836 | + | 0.782352i | \(0.714020\pi\) |
−0.878621 | + | 0.477520i | \(0.841536\pi\) | |||||||
\(632\) | 2.15552 | + | 1.41771i | 0.0857419 | + | 0.0563934i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −52.5499 | − | 6.14220i | −2.08702 | − | 0.243938i | ||||
\(635\) | 3.80590 | + | 8.82307i | 0.151033 | + | 0.350133i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.9035 | − | 8.99145i | 0.709361 | − | 0.356254i | ||||
\(638\) | 2.10759 | + | 0.767099i | 0.0834402 | + | 0.0303698i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −15.7068 | + | 5.71682i | −0.620867 | + | 0.225977i | ||||
\(641\) | 23.3866 | − | 24.7883i | 0.923714 | − | 0.979080i | −0.0761236 | − | 0.997098i | \(-0.524254\pi\) |
0.999838 | + | 0.0180187i | \(0.00573585\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.6064 | − | 10.9222i | 0.654891 | − | 0.430728i | −0.178102 | − | 0.984012i | \(-0.556996\pi\) |
0.832993 | + | 0.553284i | \(0.186625\pi\) | |||||||
\(644\) | 3.54063 | − | 11.8265i | 0.139520 | − | 0.466030i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 15.4138 | + | 20.7043i | 0.606446 | + | 0.814598i | ||||
\(647\) | −37.1636 | −1.46105 | −0.730525 | − | 0.682886i | \(-0.760725\pi\) | ||||
−0.730525 | + | 0.682886i | \(0.760725\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.04853 | 0.119665 | ||||||||
\(650\) | 16.8632 | + | 22.6512i | 0.661429 | + | 0.888453i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.0491970 | − | 0.164329i | 0.00192670 | − | 0.00643563i | ||||
\(653\) | 4.60149 | − | 3.02645i | 0.180070 | − | 0.118434i | −0.456274 | − | 0.889839i | \(-0.650816\pi\) |
0.636344 | + | 0.771405i | \(0.280446\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.32946 | − | 5.64889i | 0.208239 | − | 0.220721i | ||||
\(656\) | −12.9796 | + | 4.72418i | −0.506767 | + | 0.184448i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −11.1351 | − | 4.05286i | −0.434093 | − | 0.157997i | ||||
\(659\) | 34.0326 | − | 17.0918i | 1.32572 | − | 0.665802i | 0.361866 | − | 0.932230i | \(-0.382140\pi\) |
0.963855 | + | 0.266428i | \(0.0858435\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.1606 | − | 25.8732i | −0.434097 | − | 1.00635i | −0.985121 | − | 0.171861i | \(-0.945022\pi\) |
0.551024 | − | 0.834490i | \(-0.314237\pi\) | |||||||
\(662\) | 5.47509 | + | 0.639947i | 0.212796 | + | 0.0248722i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 20.6592 | + | 13.5877i | 0.801731 | + | 0.527307i | ||||
\(665\) | 10.1894 | − | 8.54990i | 0.395127 | − | 0.331551i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.1802 | + | 15.2550i | 0.703939 | + | 0.590675i | ||||
\(668\) | 0.0842410 | + | 0.281385i | 0.00325938 | + | 0.0108871i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −28.5700 | − | 14.3484i | −1.10376 | − | 0.554327i | ||||
\(671\) | −0.212318 | − | 0.225044i | −0.00819644 | − | 0.00868772i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.84070 | − | 22.8133i | 0.379331 | − | 0.879388i | −0.616430 | − | 0.787410i | \(-0.711422\pi\) |
0.995761 | − | 0.0919783i | \(-0.0293190\pi\) | |||||||
\(674\) | −28.3712 | + | 49.1404i | −1.09282 | + | 1.89282i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.29123 | − | 12.6288i | −0.280432 | − | 0.485722i | ||||
\(677\) | −35.0463 | + | 4.09633i | −1.34694 | + | 0.157435i | −0.758800 | − | 0.651324i | \(-0.774214\pi\) |
−0.588141 | + | 0.808759i | \(0.700140\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.74466 | + | 1.36151i | −0.220460 | + | 0.0522499i | ||||
\(680\) | 0.705025 | + | 12.1048i | 0.0270365 | + | 0.464199i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.75793 | + | 0.416638i | 0.0673148 | + | 0.0159539i | ||||
\(683\) | −6.86569 | + | 38.9372i | −0.262708 | + | 1.48989i | 0.512774 | + | 0.858523i | \(0.328618\pi\) |
−0.775483 | + | 0.631369i | \(0.782493\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.266493 | + | 1.51136i | 0.0101822 | + | 0.0577460i | ||||
\(686\) | −1.05517 | + | 18.1165i | −0.0402865 | + | 0.691693i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.73723 | − | 6.36321i | 0.180605 | − | 0.242595i | ||||
\(689\) | −28.3459 | + | 38.0752i | −1.07989 | + | 1.45055i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.987935 | − | 16.9622i | 0.0375828 | − | 0.645272i | −0.925944 | − | 0.377661i | \(-0.876729\pi\) |
0.963527 | − | 0.267612i | \(-0.0862344\pi\) | |||||||
\(692\) | −0.465612 | − | 2.64062i | −0.0176999 | − | 0.100381i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.73702 | − | 38.2075i | 0.255734 | − | 1.45034i | ||||
\(695\) | 6.37536 | + | 1.51099i | 0.241831 | + | 0.0573150i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.815166 | + | 13.9959i | 0.0308766 | + | 0.530131i | ||||
\(698\) | −37.1792 | + | 8.81163i | −1.40725 | + | 0.333525i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 10.1157 | − | 1.18236i | 0.382339 | − | 0.0446890i | ||||
\(701\) | 16.3741 | + | 28.3608i | 0.618442 | + | 1.07117i | 0.989770 | + | 0.142672i | \(0.0455693\pi\) |
−0.371328 | + | 0.928502i | \(0.621097\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.2194 | − | 21.1647i | 0.460865 | − | 0.798241i | ||||
\(704\) | −0.0828575 | + | 0.192085i | −0.00312281 | + | 0.00723949i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.9713 | − | 13.7487i | −0.488180 | − | 0.517441i | ||||
\(707\) | −33.7194 | − | 16.9345i | −1.26815 | − | 0.636887i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.41268 | − | 31.4405i | −0.353500 | − | 1.18077i | −0.931195 | − | 0.364521i | \(-0.881233\pi\) |
0.577695 | − | 0.816253i | \(-0.303952\pi\) | |||||||
\(710\) | −8.53698 | − | 7.16337i | −0.320387 | − | 0.268837i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.83193 | − | 5.73267i | 0.256037 | − | 0.214841i | ||||
\(713\) | 15.9718 | + | 10.5048i | 0.598149 | + | 0.393409i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.47585 | − | 0.172502i | −0.0551936 | − | 0.00645121i | ||||
\(716\) | −0.946059 | − | 2.19321i | −0.0353559 | − | 0.0819641i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 38.3559 | − | 19.2630i | 1.43143 | − | 0.718890i | ||||
\(719\) | −15.8250 | − | 5.75983i | −0.590173 | − | 0.214806i | 0.0296323 | − | 0.999561i | \(-0.490566\pi\) |
−0.619806 | + | 0.784755i | \(0.712789\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.54558 | + | 0.562545i | −0.0575604 | + | 0.0209503i | ||||
\(722\) | −12.3228 | + | 13.0614i | −0.458608 | + | 0.486096i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −13.9615 | + | 9.18261i | −0.518874 | + | 0.341269i | ||||
\(725\) | −5.61534 | + | 18.7565i | −0.208548 | + | 0.696600i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.01783 | − | 6.74011i | −0.186101 | − | 0.249977i | 0.699275 | − | 0.714853i | \(-0.253506\pi\) |
−0.885376 | + | 0.464876i | \(0.846099\pi\) | |||||||
\(728\) | 29.9802 | 1.11114 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −38.8230 | −1.43690 | ||||||||
\(731\) | −4.80823 | − | 6.45857i | −0.177839 | − | 0.238879i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.54104 | + | 11.8279i | −0.130791 | + | 0.436874i | −0.998149 | − | 0.0608113i | \(-0.980631\pi\) |
0.867358 | + | 0.497685i | \(0.165816\pi\) | |||||||
\(734\) | −18.5868 | + | 12.2247i | −0.686051 | + | 0.451223i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13.3918 | − | 14.1945i | 0.493630 | − | 0.523217i | ||||
\(737\) | −2.58738 | + | 0.941730i | −0.0953075 | + | 0.0346891i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.3973 | + | 13.6115i | 1.37568 | + | 0.500707i | 0.920866 | − | 0.389879i | \(-0.127483\pi\) |
0.454815 | + | 0.890586i | \(0.349705\pi\) | |||||||
\(740\) | −10.2166 | + | 5.13096i | −0.375569 | + | 0.188618i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 20.3705 | + | 47.2242i | 0.747826 | + | 1.73365i | ||||
\(743\) | −19.7041 | − | 2.30308i | −0.722873 | − | 0.0844917i | −0.253303 | − | 0.967387i | \(-0.581517\pi\) |
−0.469570 | + | 0.882895i | \(0.655591\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.83306 | + | 5.80960i | 0.323618 | + | 0.212847i | ||||
\(746\) | −2.95869 | + | 2.48263i | −0.108325 | + | 0.0908957i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.796638 | − | 0.668459i | −0.0291280 | − | 0.0244413i | ||||
\(749\) | −5.13381 | − | 17.1481i | −0.187585 | − | 0.626578i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.2956 | + | 17.2239i | 1.25146 | + | 0.628509i | 0.946146 | − | 0.323742i | \(-0.104941\pi\) |
0.305318 | + | 0.952250i | \(0.401237\pi\) | |||||||
\(752\) | −7.14137 | − | 7.56941i | −0.260419 | − | 0.276028i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 22.7330 | − | 52.7009i | 0.827885 | − | 1.91925i | ||||
\(755\) | 2.12665 | − | 3.68347i | 0.0773969 | − | 0.134055i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.07444 | + | 12.2533i | 0.257125 | + | 0.445353i | 0.965470 | − | 0.260513i | \(-0.0838915\pi\) |
−0.708346 | + | 0.705866i | \(0.750558\pi\) | |||||||
\(758\) | −12.6555 | + | 1.47921i | −0.459667 | + | 0.0537274i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.82928 | − | 1.61857i | 0.247724 | − | 0.0587117i | ||||
\(761\) | −0.551159 | − | 9.46303i | −0.0199795 | − | 0.343034i | −0.993454 | − | 0.114237i | \(-0.963558\pi\) |
0.973474 | − | 0.228797i | \(-0.0734794\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 53.6883 | + | 12.7244i | 1.94365 | + | 0.460653i | ||||
\(764\) | 2.45907 | − | 13.9461i | 0.0889660 | − | 0.504551i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.34643 | − | 24.6498i | −0.157043 | − | 0.890634i | ||||
\(767\) | 4.53602 | − | 77.8805i | 0.163786 | − | 2.81210i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.47719 | + | 10.0436i | −0.269634 | + | 0.362182i | −0.916231 | − | 0.400650i | \(-0.868784\pi\) |
0.646597 | + | 0.762832i | \(0.276192\pi\) | |||||||
\(770\) | −0.961384 | + | 1.29136i | −0.0346459 | + | 0.0465375i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.242300 | − | 4.16014i | 0.00872059 | − | 0.149727i | ||||
\(773\) | 6.23462 | + | 35.3583i | 0.224244 | + | 1.27175i | 0.864125 | + | 0.503277i | \(0.167872\pi\) |
−0.639882 | + | 0.768474i | \(0.721017\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.73862 | + | 15.5315i | −0.0983742 | + | 0.557908i | ||||
\(776\) | −3.03119 | − | 0.718404i | −0.108813 | − | 0.0257892i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.856152 | − | 14.6996i | −0.0306945 | − | 0.527005i | ||||
\(779\) | 7.89617 | − | 1.87143i | 0.282910 | − | 0.0670508i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.953294 | + | 0.111424i | −0.0341115 | + | 0.00398707i | ||||
\(782\) | −16.5290 | − | 28.6291i | −0.591076 | − | 1.02377i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 9.53150 | − | 16.5091i | 0.340411 | − | 0.589609i | ||||
\(785\) | −3.34387 | + | 7.75195i | −0.119348 | + | 0.276679i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27.4162 | − | 29.0594i | −0.977281 | − | 1.03586i | −0.999348 | − | 0.0361007i | \(-0.988506\pi\) |
0.0220673 | − | 0.999756i | \(-0.492975\pi\) | |||||||
\(788\) | 18.4759 | + | 9.27895i | 0.658177 | + | 0.330549i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.01681 | + | 3.39639i | 0.0361766 | + | 0.120838i | ||||
\(791\) | −22.2484 | − | 18.6687i | −0.791063 | − | 0.663781i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.06508 | + | 5.08921i | −0.215377 | + | 0.180723i | ||||
\(794\) | 7.94517 | + | 5.22562i | 0.281964 | + | 0.185450i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.85098 | − | 0.333231i | −0.101050 | − | 0.0118111i | ||||
\(797\) | −13.5008 | − | 31.2984i | −0.478224 | − | 1.10865i | −0.971127 | − | 0.238563i | \(-0.923324\pi\) |
0.492903 | − | 0.870084i | \(-0.335936\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.43896 | + | 4.74043i | −0.333927 | + | 0.167704i | ||||
\(800\) | 15.1285 | + | 5.50634i | 0.534875 | + | 0.194678i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 15.3085 | − | 5.57185i | 0.540563 | − | 0.196749i | ||||
\(803\) | −2.29451 | + | 2.43203i | −0.0809713 | + | 0.0858246i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.2328 | + | 9.36109i | −0.501642 | + | 0.329935i | ||||
\(806\) | 13.2595 | − | 44.2898i | 0.467046 | − | 1.56004i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11.8894 | − | 15.9702i | −0.418266 | − | 0.561829i | ||||
\(809\) | 7.57622 | 0.266366 | 0.133183 | − | 0.991091i | \(-0.457480\pi\) | ||||
0.133183 | + | 0.991091i | \(0.457480\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.5558 | 0.721810 | 0.360905 | − | 0.932602i | \(-0.382468\pi\) | ||||
0.360905 | + | 0.932602i | \(0.382468\pi\) | |||||||
\(812\) | −12.3611 | − | 16.6038i | −0.433789 | − | 0.582680i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.848358 | + | 2.83371i | −0.0297349 | + | 0.0993216i | ||||
\(815\) | −0.197765 | + | 0.130072i | −0.00692742 | + | 0.00455623i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.19831 | + | 3.39001i | −0.111895 | + | 0.118602i | ||||
\(818\) | −25.0916 | + | 9.13260i | −0.877308 | + | 0.319314i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.56726 | − | 1.29838i | −0.124574 | − | 0.0453412i | ||||
\(821\) | −27.2335 | + | 13.6772i | −0.950455 | + | 0.477337i | −0.855304 | − | 0.518126i | \(-0.826630\pi\) |
−0.0951512 | + | 0.995463i | \(0.530333\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.83984 | − | 20.4930i | −0.308137 | − | 0.714343i | 0.691833 | − | 0.722058i | \(-0.256803\pi\) |
−0.999970 | + | 0.00771507i | \(0.997544\pi\) | |||||||
\(824\) | −0.862001 | − | 0.100753i | −0.0300292 | − | 0.00350991i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −70.6192 | − | 46.4470i | −2.45716 | − | 1.61610i | ||||
\(827\) | −27.2509 | + | 22.8662i | −0.947606 | + | 0.795136i | −0.978893 | − | 0.204374i | \(-0.934484\pi\) |
0.0312864 | + | 0.999510i | \(0.490040\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.4520 | − | 11.2875i | −0.467206 | − | 0.392032i | 0.378568 | − | 0.925573i | \(-0.376416\pi\) |
−0.845774 | + | 0.533541i | \(0.820861\pi\) | |||||||
\(830\) | 9.74546 | + | 32.5521i | 0.338270 | + | 1.12990i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.78390 | + | 2.40256i | 0.165852 | + | 0.0832939i | ||||
\(833\) | −13.2779 | − | 14.0737i | −0.460052 | − | 0.487626i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.160538 | − | 0.372169i | 0.00555565 | − | 0.0128794i | ||||
\(836\) | −0.300972 | + | 0.521298i | −0.0104093 | + | 0.0180295i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 21.3875 | + | 37.0443i | 0.738820 | + | 1.27967i | ||||
\(839\) | 38.0724 | − | 4.45002i | 1.31440 | − | 0.153632i | 0.570157 | − | 0.821536i | \(-0.306882\pi\) |
0.744247 | + | 0.667904i | \(0.232808\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.5028 | − | 2.48921i | 0.362166 | − | 0.0858350i | ||||
\(842\) | −0.0187047 | − | 0.321147i | −0.000644606 | − | 0.0110675i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.3063 | − | 2.44263i | −0.354757 | − | 0.0840789i | ||||
\(845\) | −3.49427 | + | 19.8170i | −0.120206 | + | 0.681725i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.25691 | − | 35.4847i | −0.214990 | − | 1.21927i | ||||
\(848\) | −2.62619 | + | 45.0899i | −0.0901836 | + | 1.54839i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 16.2860 | − | 21.8759i | 0.558605 | − | 0.750337i | ||||
\(851\) | −18.6908 | + | 25.1062i | −0.640714 | + | 0.860628i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.488107 | + | 8.38047i | −0.0167125 | + | 0.286942i | 0.979589 | + | 0.201012i | \(0.0644231\pi\) |
−0.996301 | + | 0.0859296i | \(0.972614\pi\) | |||||||
\(854\) | 1.48961 | + | 8.44799i | 0.0509733 | + | 0.289084i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.64011 | − | 9.30155i | 0.0560580 | − | 0.317920i | ||||
\(857\) | 46.8244 | + | 11.0976i | 1.59949 | + | 0.379087i | 0.931112 | − | 0.364733i | \(-0.118840\pi\) |
0.668380 | + | 0.743820i | \(0.266988\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.97006 | − | 50.9939i | −0.101337 | − | 1.73989i | −0.540377 | − | 0.841423i | \(-0.681718\pi\) |
0.439040 | − | 0.898467i | \(-0.355319\pi\) | |||||||
\(860\) | 2.12149 | − | 0.502804i | 0.0723424 | − | 0.0171455i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −25.0261 | + | 2.92513i | −0.852392 | + | 0.0996303i | ||||
\(863\) | −18.3885 | − | 31.8499i | −0.625953 | − | 1.08418i | −0.988356 | − | 0.152161i | \(-0.951377\pi\) |
0.362403 | − | 0.932022i | \(-0.381957\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.85003 | + | 3.20435i | −0.0629031 | + | 0.108951i | ||||
\(866\) | 23.7416 | − | 55.0391i | 0.806771 | − | 1.87031i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −11.4423 | − | 12.1281i | −0.388377 | − | 0.411656i | ||||
\(869\) | 0.272860 | + | 0.137035i | 0.00925614 | + | 0.00464861i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.2084 | + | 67.5008i | 0.684736 | + | 2.28718i | ||||
\(872\) | 22.3023 | + | 18.7138i | 0.755250 | + | 0.633730i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −14.6581 | + | 12.2996i | −0.495819 | + | 0.416042i | ||||
\(875\) | −30.6577 | − | 20.1639i | −1.03642 | − | 0.681665i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.03239 | + | 0.471319i | 0.136164 | + | 0.0159153i | 0.183902 | − | 0.982945i | \(-0.441127\pi\) |
−0.0477378 | + | 0.998860i | \(0.515201\pi\) | |||||||
\(878\) | 1.34813 | + | 3.12532i | 0.0454973 | + | 0.105475i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.26346 | + | 0.634533i | −0.0425912 | + | 0.0213901i | ||||
\(881\) | 38.2223 | + | 13.9118i | 1.28774 | + | 0.468700i | 0.892986 | − | 0.450085i | \(-0.148606\pi\) |
0.394758 | + | 0.918785i | \(0.370829\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.6043 | + | 8.95523i | −0.828000 | + | 0.301367i | −0.721038 | − | 0.692896i | \(-0.756335\pi\) |
−0.106962 | + | 0.994263i | \(0.534112\pi\) | |||||||
\(884\) | −18.2624 | + | 19.3570i | −0.614231 | + | 0.651046i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 46.0144 | − | 30.2641i | 1.54588 | − | 1.01674i | ||||
\(887\) | −6.23488 | + | 20.8260i | −0.209347 | + | 0.699267i | 0.787235 | + | 0.616654i | \(0.211512\pi\) |
−0.996582 | + | 0.0826140i | \(0.973673\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.7019 | − | 18.4048i | −0.459546 | − | 0.617278i | ||||
\(890\) | 12.2556 | 0.410809 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −23.6257 | −0.791048 | ||||||||
\(893\) | 3.65093 | + | 4.90405i | 0.122174 | + | 0.164108i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.945312 | + | 3.15756i | −0.0315983 | + | 0.105546i | ||||
\(896\) | 33.3471 | − | 21.9327i | 1.11405 | − | 0.732721i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −35.3931 | + | 37.5145i | −1.18108 | + | 1.25187i | ||||
\(899\) | 30.1211 | − | 10.9632i | 1.00459 | − | 0.365642i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 43.0785 | + | 15.6793i | 1.43515 | + | 0.522353i | ||||
\(902\) | −0.877720 | + | 0.440808i | −0.0292249 | + | 0.0146773i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.06983 | − | 14.0715i | −0.201880 | − | 0.468010i | ||||
\(905\) | 22.9034 | + | 2.67703i | 0.761336 | + | 0.0889874i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 44.0406 | + | 28.9659i | 1.46234 | + | 0.961798i | 0.997059 | + | 0.0766368i | \(0.0244182\pi\) |
0.465284 | + | 0.885161i | \(0.345952\pi\) | |||||||
\(908\) | 0.350892 | − | 0.294434i | 0.0116448 | − | 0.00977113i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 31.5598 | + | 26.4818i | 1.04620 | + | 0.877864i | ||||
\(911\) | −12.3476 | − | 41.2438i | −0.409094 | − | 1.36647i | −0.876063 | − | 0.482196i | \(-0.839839\pi\) |
0.466969 | − | 0.884273i | \(-0.345346\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.61517 | + | 1.31339i | 0.0865496 | + | 0.0434668i | ||||
\(914\) | 15.1452 | + | 16.0530i | 0.500958 | + | 0.530985i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.32139 | − | 14.6546i | 0.208864 | − | 0.484202i | ||||
\(917\) | −9.27238 | + | 16.0602i | −0.306201 | + | 0.530356i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.2136 | − | 43.6712i | −0.831719 | − | 1.44058i | −0.896674 | − | 0.442691i | \(-0.854024\pi\) |
0.0649552 | − | 0.997888i | \(-0.479310\pi\) | |||||||
\(920\) | −8.92799 | + | 1.04353i | −0.294347 | + | 0.0344042i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −34.8210 | + | 8.25274i | −1.14677 | + | 0.271789i | ||||
\(923\) | 1.42810 | + | 24.5195i | 0.0470064 | + | 0.807069i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.1258 | − | 5.95493i | −0.826131 | − | 0.195797i | ||||
\(926\) | 5.00610 | − | 28.3910i | 0.164511 | − | 0.932987i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.68204 | − | 32.2245i | −0.186522 | − | 1.05782i | ||||
\(929\) | 0.923930 | − | 15.8633i | 0.0303132 | − | 0.520457i | −0.948638 | − | 0.316363i | \(-0.897538\pi\) |
0.978951 | − | 0.204094i | \(-0.0654248\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.68791 | + | 8.98342i | −0.219187 | + | 0.294420i | ||||
\(932\) | 4.73638 | − | 6.36206i | 0.155145 | − | 0.208396i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.94932 | + | 50.6378i | −0.0965046 | + | 1.65692i | ||||
\(935\) | 0.249191 | + | 1.41323i | 0.00814943 | + | 0.0462177i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.98093 | − | 22.5770i | 0.130051 | − | 0.737557i | −0.848128 | − | 0.529792i | \(-0.822270\pi\) |
0.978179 | − | 0.207765i | \(-0.0666189\pi\) | |||||||
\(938\) | 74.2848 | + | 17.6058i | 2.42549 | + | 0.574851i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.166299 | − | 2.85525i | −0.00542408 | − | 0.0931278i | ||||
\(941\) | 13.7585 | − | 3.26083i | 0.448516 | − | 0.106300i | −0.000149695 | − | 1.00000i | \(-0.500048\pi\) |
0.448665 | + | 0.893700i | \(0.351900\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.3227 | + | 1.20656i | −0.336155 | + | 0.0392908i | ||||
\(944\) | −37.1148 | − | 64.2848i | −1.20799 | − | 2.09229i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.282051 | − | 0.488527i | 0.00917027 | − | 0.0158834i | ||||
\(947\) | −22.6121 | + | 52.4208i | −0.734796 | + | 1.70345i | −0.0243417 | + | 0.999704i | \(0.507749\pi\) |
−0.710454 | + | 0.703744i | \(0.751510\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 58.7168 | + | 62.2362i | 1.90603 | + | 2.02027i | ||||
\(950\) | −14.1069 | − | 7.08476i | −0.457689 | − | 0.229860i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8.30411 | − | 27.7377i | −0.269138 | − | 0.898983i | ||||
\(953\) | −13.5816 | − | 11.3963i | −0.439951 | − | 0.369163i | 0.395740 | − | 0.918363i | \(-0.370488\pi\) |
−0.835691 | + | 0.549200i | \(0.814933\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.9696 | + | 12.5610i | −0.484405 | + | 0.406464i | ||||
\(956\) | 17.6900 | + | 11.6349i | 0.572136 | + | 0.376299i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 38.4567 | + | 4.49495i | 1.24248 | + | 0.145225i | ||||
\(959\) | −1.45149 | − | 3.36493i | −0.0468710 | − | 0.108659i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.62911 | + | 2.32483i | −0.149326 | + | 0.0749945i | ||||
\(962\) | 71.1302 | + | 25.8893i | 2.29333 | + | 0.834704i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 16.9447 | − | 6.16735i | 0.545751 | − | 0.198637i | ||||
\(965\) | −3.94617 | + | 4.18270i | −0.127032 | + | 0.134646i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.4795 | − | 12.1541i | 0.594260 | − | 0.390851i | −0.216455 | − | 0.976293i | \(-0.569449\pi\) |
0.810714 | + | 0.585442i | \(0.199079\pi\) | |||||||
\(968\) | 5.45284 | − | 18.2137i | 0.175261 | − | 0.585412i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.55632 | − | 3.43373i | −0.0820785 | − | 0.110251i | ||||
\(971\) | −5.09901 | −0.163635 | −0.0818176 | − | 0.996647i | \(-0.526072\pi\) | ||||
−0.0818176 | + | 0.996647i | \(0.526072\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.6454 | −0.501569 | ||||||||
\(974\) | −3.86631 | − | 5.19336i | −0.123885 | − | 0.166406i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.16063 | + | 7.21701i | −0.0691601 | + | 0.231011i | ||||
\(977\) | −19.4106 | + | 12.7666i | −0.621001 | + | 0.408439i | −0.820652 | − | 0.571429i | \(-0.806389\pi\) |
0.199651 | + | 0.979867i | \(0.436019\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.724328 | − | 0.767743i | 0.0231496 | − | 0.0245372i | ||||
\(980\) | 4.92325 | − | 1.79191i | 0.157267 | − | 0.0572406i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.96332 | − | 0.714592i | −0.0626522 | − | 0.0228035i | ||||
\(983\) | −15.0614 | + | 7.56411i | −0.480384 | + | 0.241258i | −0.672476 | − | 0.740119i | \(-0.734769\pi\) |
0.192092 | + | 0.981377i | \(0.438473\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.3002 | − | 26.1967i | −0.360053 | − | 0.834698i | ||||
\(986\) | −55.0555 | − | 6.43507i | −1.75333 | − | 0.204934i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 12.8697 | + | 8.46454i | 0.409440 | + | 0.269293i | ||||
\(989\) | 4.57252 | − | 3.83680i | 0.145398 | − | 0.122003i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.316451 | − | 0.265534i | −0.0100524 | − | 0.00843496i | 0.637748 | − | 0.770245i | \(-0.279866\pi\) |
−0.647800 | + | 0.761810i | \(0.724311\pi\) | |||||||
\(992\) | −7.55941 | − | 25.2502i | −0.240012 | − | 0.801694i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 23.7807 | + | 11.9431i | 0.754278 | + | 0.378813i | ||||
\(995\) | 2.71815 | + | 2.88107i | 0.0861710 | + | 0.0913360i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.31383 | − | 5.36406i | 0.0732797 | − | 0.169882i | −0.877639 | − | 0.479322i | \(-0.840883\pi\) |
0.950919 | + | 0.309441i | \(0.100142\pi\) | |||||||
\(998\) | 2.88970 | − | 5.00511i | 0.0914719 | − | 0.158434i | ||||
\(999\) | 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 | 729.2.g.d.541.2 | 144 | ||
3.2 | odd | 2 | 729.2.g.a.541.7 | 144 | |||
9.2 | odd | 6 | 243.2.g.a.181.7 | 144 | |||
9.4 | even | 3 | 729.2.g.c.298.7 | 144 | |||
9.5 | odd | 6 | 729.2.g.b.298.2 | 144 | |||
9.7 | even | 3 | 81.2.g.a.34.2 | yes | 144 | ||
81.4 | even | 27 | 81.2.g.a.31.2 | ✓ | 144 | ||
81.23 | odd | 54 | 729.2.g.a.190.7 | 144 | |||
81.25 | even | 27 | 6561.2.a.c.1.17 | 72 | |||
81.31 | even | 27 | 729.2.g.c.433.7 | 144 | |||
81.50 | odd | 54 | 729.2.g.b.433.2 | 144 | |||
81.56 | odd | 54 | 6561.2.a.d.1.56 | 72 | |||
81.58 | even | 27 | inner | 729.2.g.d.190.2 | 144 | ||
81.77 | odd | 54 | 243.2.g.a.145.7 | 144 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
81.2.g.a.31.2 | ✓ | 144 | 81.4 | even | 27 | ||
81.2.g.a.34.2 | yes | 144 | 9.7 | even | 3 | ||
243.2.g.a.145.7 | 144 | 81.77 | odd | 54 | |||
243.2.g.a.181.7 | 144 | 9.2 | odd | 6 | |||
729.2.g.a.190.7 | 144 | 81.23 | odd | 54 | |||
729.2.g.a.541.7 | 144 | 3.2 | odd | 2 | |||
729.2.g.b.298.2 | 144 | 9.5 | odd | 6 | |||
729.2.g.b.433.2 | 144 | 81.50 | odd | 54 | |||
729.2.g.c.298.7 | 144 | 9.4 | even | 3 | |||
729.2.g.c.433.7 | 144 | 81.31 | even | 27 | |||
729.2.g.d.190.2 | 144 | 81.58 | even | 27 | inner | ||
729.2.g.d.541.2 | 144 | 1.1 | even | 1 | trivial | ||
6561.2.a.c.1.17 | 72 | 81.25 | even | 27 | |||
6561.2.a.d.1.56 | 72 | 81.56 | odd | 54 |