Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(289,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.j (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.447703281.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 529.1 | ||
Root | \(1.26359 - 0.635098i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.529 |
Dual form | 546.2.j.d.289.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.97513 | − | 3.42102i | −0.883304 | − | 1.52993i | −0.847646 | − | 0.530563i | \(-0.821981\pi\) |
−0.0356582 | − | 0.999364i | \(-0.511353\pi\) | |||||||
\(6\) | 0.500000 | + | 0.866025i | 0.204124 | + | 0.353553i | ||||
\(7\) | −1.15207 | − | 2.38175i | −0.435441 | − | 0.900217i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −1.97513 | − | 3.42102i | −0.624590 | − | 1.08182i | ||||
\(11\) | −2.45689 | − | 4.25545i | −0.740779 | − | 1.28307i | −0.952141 | − | 0.305659i | \(-0.901123\pi\) |
0.211362 | − | 0.977408i | \(-0.432210\pi\) | |||||||
\(12\) | 0.500000 | + | 0.866025i | 0.144338 | + | 0.250000i | ||||
\(13\) | −3.39335 | + | 1.21869i | −0.941145 | + | 0.338004i | ||||
\(14\) | −1.15207 | − | 2.38175i | −0.307903 | − | 0.636550i | ||||
\(15\) | 1.97513 | − | 3.42102i | 0.509976 | − | 0.883304i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.140571 | 0.0340936 | 0.0170468 | − | 0.999855i | \(-0.494574\pi\) | ||||
0.0170468 | + | 0.999855i | \(0.494574\pi\) | |||||||
\(18\) | −0.500000 | + | 0.866025i | −0.117851 | + | 0.204124i | ||||
\(19\) | 0.388481 | − | 0.672870i | 0.0891238 | − | 0.154367i | −0.818017 | − | 0.575194i | \(-0.804927\pi\) |
0.907141 | + | 0.420827i | \(0.138260\pi\) | |||||||
\(20\) | −1.97513 | − | 3.42102i | −0.441652 | − | 0.764963i | ||||
\(21\) | 1.48662 | − | 2.18860i | 0.324408 | − | 0.477591i | ||||
\(22\) | −2.45689 | − | 4.25545i | −0.523810 | − | 0.907266i | ||||
\(23\) | 9.53690 | 1.98858 | 0.994291 | − | 0.106706i | \(-0.0340305\pi\) | ||||
0.994291 | + | 0.106706i | \(0.0340305\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | −5.30226 | + | 9.18378i | −1.06045 | + | 1.83676i | ||||
\(26\) | −3.39335 | + | 1.21869i | −0.665490 | + | 0.239005i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.15207 | − | 2.38175i | −0.217720 | − | 0.450109i | ||||
\(29\) | −0.629759 | + | 1.09077i | −0.116943 | + | 0.202552i | −0.918555 | − | 0.395293i | \(-0.870643\pi\) |
0.801612 | + | 0.597845i | \(0.203976\pi\) | |||||||
\(30\) | 1.97513 | − | 3.42102i | 0.360607 | − | 0.624590i | ||||
\(31\) | −1.67992 | + | 2.90971i | −0.301723 | + | 0.522600i | −0.976526 | − | 0.215398i | \(-0.930895\pi\) |
0.674803 | + | 0.737998i | \(0.264229\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 2.45689 | − | 4.25545i | 0.427689 | − | 0.740779i | ||||
\(34\) | 0.140571 | 0.0241078 | ||||||||
\(35\) | −5.87254 | + | 8.64551i | −0.992641 | + | 1.46136i | ||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | 11.1368 | 1.83088 | 0.915440 | − | 0.402454i | \(-0.131843\pi\) | ||||
0.915440 | + | 0.402454i | \(0.131843\pi\) | |||||||
\(38\) | 0.388481 | − | 0.672870i | 0.0630200 | − | 0.109154i | ||||
\(39\) | −2.75209 | − | 2.32938i | −0.440687 | − | 0.372999i | ||||
\(40\) | −1.97513 | − | 3.42102i | −0.312295 | − | 0.540911i | ||||
\(41\) | 4.65505 | − | 8.06279i | 0.726997 | − | 1.25920i | −0.231150 | − | 0.972918i | \(-0.574249\pi\) |
0.958147 | − | 0.286277i | \(-0.0924179\pi\) | |||||||
\(42\) | 1.48662 | − | 2.18860i | 0.229391 | − | 0.337708i | ||||
\(43\) | −0.541233 | − | 0.937443i | −0.0825372 | − | 0.142959i | 0.821802 | − | 0.569773i | \(-0.192969\pi\) |
−0.904339 | + | 0.426815i | \(0.859636\pi\) | |||||||
\(44\) | −2.45689 | − | 4.25545i | −0.370390 | − | 0.641534i | ||||
\(45\) | 3.95025 | 0.588869 | ||||||||
\(46\) | 9.53690 | 1.40614 | ||||||||
\(47\) | 3.33199 | + | 5.77118i | 0.486021 | + | 0.841813i | 0.999871 | − | 0.0160671i | \(-0.00511454\pi\) |
−0.513850 | + | 0.857880i | \(0.671781\pi\) | |||||||
\(48\) | 0.500000 | + | 0.866025i | 0.0721688 | + | 0.125000i | ||||
\(49\) | −4.34548 | + | 5.48788i | −0.620783 | + | 0.783983i | ||||
\(50\) | −5.30226 | + | 9.18378i | −0.749852 | + | 1.29878i | ||||
\(51\) | 0.0702857 | + | 0.121738i | 0.00984197 | + | 0.0170468i | ||||
\(52\) | −3.39335 | + | 1.21869i | −0.470572 | + | 0.169002i | ||||
\(53\) | 5.53204 | − | 9.58177i | 0.759884 | − | 1.31616i | −0.183026 | − | 0.983108i | \(-0.558589\pi\) |
0.942910 | − | 0.333049i | \(-0.108077\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −9.70533 | + | 16.8101i | −1.30867 | + | 2.26668i | ||||
\(56\) | −1.15207 | − | 2.38175i | −0.153952 | − | 0.318275i | ||||
\(57\) | 0.776963 | 0.102911 | ||||||||
\(58\) | −0.629759 | + | 1.09077i | −0.0826914 | + | 0.143226i | ||||
\(59\) | 0.431218 | 0.0561399 | 0.0280699 | − | 0.999606i | \(-0.491064\pi\) | ||||
0.0280699 | + | 0.999606i | \(0.491064\pi\) | |||||||
\(60\) | 1.97513 | − | 3.42102i | 0.254988 | − | 0.441652i | ||||
\(61\) | 4.14057 | − | 7.17168i | 0.530146 | − | 0.918240i | −0.469236 | − | 0.883073i | \(-0.655470\pi\) |
0.999381 | − | 0.0351665i | \(-0.0111962\pi\) | |||||||
\(62\) | −1.67992 | + | 2.90971i | −0.213351 | + | 0.369534i | ||||
\(63\) | 2.63869 | + | 0.193156i | 0.332444 | + | 0.0243353i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 10.8715 | + | 9.20163i | 1.34844 | + | 1.14132i | ||||
\(66\) | 2.45689 | − | 4.25545i | 0.302422 | − | 0.523810i | ||||
\(67\) | −4.09814 | − | 7.09819i | −0.500668 | − | 0.867182i | −1.00000 | 0.000771201i | \(-0.999755\pi\) | |
0.499332 | − | 0.866411i | \(-0.333579\pi\) | |||||||
\(68\) | 0.140571 | 0.0170468 | ||||||||
\(69\) | 4.76845 | + | 8.25920i | 0.574054 | + | 0.994291i | ||||
\(70\) | −5.87254 | + | 8.64551i | −0.701903 | + | 1.03334i | ||||
\(71\) | 1.93865 | + | 3.35783i | 0.230075 | + | 0.398502i | 0.957830 | − | 0.287336i | \(-0.0927695\pi\) |
−0.727755 | + | 0.685837i | \(0.759436\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | −0.0817820 | + | 0.141650i | −0.00957185 | + | 0.0165789i | −0.870772 | − | 0.491688i | \(-0.836380\pi\) |
0.861200 | + | 0.508267i | \(0.169714\pi\) | |||||||
\(74\) | 11.1368 | 1.29463 | ||||||||
\(75\) | −10.6045 | −1.22450 | ||||||||
\(76\) | 0.388481 | − | 0.672870i | 0.0445619 | − | 0.0771834i | ||||
\(77\) | −7.30493 | + | 10.7543i | −0.832474 | + | 1.22556i | ||||
\(78\) | −2.75209 | − | 2.32938i | −0.311613 | − | 0.263750i | ||||
\(79\) | 2.17517 | + | 3.76751i | 0.244726 | + | 0.423878i | 0.962055 | − | 0.272857i | \(-0.0879687\pi\) |
−0.717329 | + | 0.696735i | \(0.754635\pi\) | |||||||
\(80\) | −1.97513 | − | 3.42102i | −0.220826 | − | 0.382482i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 4.65505 | − | 8.06279i | 0.514064 | − | 0.890386i | ||||
\(83\) | −10.5220 | −1.15494 | −0.577472 | − | 0.816410i | \(-0.695961\pi\) | ||||
−0.577472 | + | 0.816410i | \(0.695961\pi\) | |||||||
\(84\) | 1.48662 | − | 2.18860i | 0.162204 | − | 0.238795i | ||||
\(85\) | −0.277647 | − | 0.480898i | −0.0301150 | − | 0.0521607i | ||||
\(86\) | −0.541233 | − | 0.937443i | −0.0583626 | − | 0.101087i | ||||
\(87\) | −1.25952 | −0.135035 | ||||||||
\(88\) | −2.45689 | − | 4.25545i | −0.261905 | − | 0.453633i | ||||
\(89\) | −1.07274 | −0.113710 | −0.0568550 | − | 0.998382i | \(-0.518107\pi\) | ||||
−0.0568550 | + | 0.998382i | \(0.518107\pi\) | |||||||
\(90\) | 3.95025 | 0.416393 | ||||||||
\(91\) | 6.81198 | + | 6.67809i | 0.714090 | + | 0.700054i | ||||
\(92\) | 9.53690 | 0.994291 | ||||||||
\(93\) | −3.35985 | −0.348400 | ||||||||
\(94\) | 3.33199 | + | 5.77118i | 0.343669 | + | 0.595252i | ||||
\(95\) | −3.06920 | −0.314893 | ||||||||
\(96\) | 0.500000 | + | 0.866025i | 0.0510310 | + | 0.0883883i | ||||
\(97\) | −6.54097 | − | 11.3293i | −0.664135 | − | 1.15032i | −0.979519 | − | 0.201351i | \(-0.935467\pi\) |
0.315384 | − | 0.948964i | \(-0.397867\pi\) | |||||||
\(98\) | −4.34548 | + | 5.48788i | −0.438960 | + | 0.554359i | ||||
\(99\) | 4.91377 | 0.493853 | ||||||||
\(100\) | −5.30226 | + | 9.18378i | −0.530226 | + | 0.918378i | ||||
\(101\) | −3.69262 | − | 6.39580i | −0.367429 | − | 0.636406i | 0.621734 | − | 0.783229i | \(-0.286429\pi\) |
−0.989163 | + | 0.146823i | \(0.953095\pi\) | |||||||
\(102\) | 0.0702857 | + | 0.121738i | 0.00695933 | + | 0.0120539i | ||||
\(103\) | −1.99107 | − | 3.44863i | −0.196186 | − | 0.339804i | 0.751103 | − | 0.660185i | \(-0.229522\pi\) |
−0.947289 | + | 0.320382i | \(0.896189\pi\) | |||||||
\(104\) | −3.39335 | + | 1.21869i | −0.332745 | + | 0.119502i | ||||
\(105\) | −10.4235 | − | 0.763015i | −1.01723 | − | 0.0744626i | ||||
\(106\) | 5.53204 | − | 9.58177i | 0.537319 | − | 0.930664i | ||||
\(107\) | −7.07358 | −0.683828 | −0.341914 | − | 0.939731i | \(-0.611075\pi\) | ||||
−0.341914 | + | 0.939731i | \(0.611075\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −7.42350 | + | 12.8579i | −0.711042 | + | 1.23156i | 0.253424 | + | 0.967355i | \(0.418443\pi\) |
−0.964466 | + | 0.264206i | \(0.914890\pi\) | |||||||
\(110\) | −9.70533 | + | 16.8101i | −0.925367 | + | 1.60278i | ||||
\(111\) | 5.56841 | + | 9.64476i | 0.528530 | + | 0.915440i | ||||
\(112\) | −1.15207 | − | 2.38175i | −0.108860 | − | 0.225054i | ||||
\(113\) | −0.785895 | − | 1.36121i | −0.0739308 | − | 0.128052i | 0.826690 | − | 0.562658i | \(-0.190221\pi\) |
−0.900621 | + | 0.434606i | \(0.856888\pi\) | |||||||
\(114\) | 0.776963 | 0.0727692 | ||||||||
\(115\) | −18.8366 | − | 32.6259i | −1.75652 | − | 3.04238i | ||||
\(116\) | −0.629759 | + | 1.09077i | −0.0584717 | + | 0.101276i | ||||
\(117\) | 0.641255 | − | 3.54807i | 0.0592841 | − | 0.328019i | ||||
\(118\) | 0.431218 | 0.0396969 | ||||||||
\(119\) | −0.161948 | − | 0.334806i | −0.0148457 | − | 0.0306916i | ||||
\(120\) | 1.97513 | − | 3.42102i | 0.180304 | − | 0.312295i | ||||
\(121\) | −6.57259 | + | 11.3841i | −0.597508 | + | 1.03491i | ||||
\(122\) | 4.14057 | − | 7.17168i | 0.374870 | − | 0.649293i | ||||
\(123\) | 9.31010 | 0.839464 | ||||||||
\(124\) | −1.67992 | + | 2.90971i | −0.150862 | + | 0.261300i | ||||
\(125\) | 22.1392 | 1.98019 | ||||||||
\(126\) | 2.63869 | + | 0.193156i | 0.235073 | + | 0.0172077i | ||||
\(127\) | −5.42757 | + | 9.40083i | −0.481619 | + | 0.834188i | −0.999777 | − | 0.0210962i | \(-0.993284\pi\) |
0.518159 | + | 0.855285i | \(0.326618\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0.541233 | − | 0.937443i | 0.0476529 | − | 0.0825372i | ||||
\(130\) | 10.8715 | + | 9.20163i | 0.953490 | + | 0.807037i | ||||
\(131\) | −0.961751 | − | 1.66580i | −0.0840285 | − | 0.145542i | 0.820948 | − | 0.571003i | \(-0.193445\pi\) |
−0.904977 | + | 0.425461i | \(0.860112\pi\) | |||||||
\(132\) | 2.45689 | − | 4.25545i | 0.213845 | − | 0.370390i | ||||
\(133\) | −2.05016 | − | 0.150075i | −0.177772 | − | 0.0130131i | ||||
\(134\) | −4.09814 | − | 7.09819i | −0.354026 | − | 0.613190i | ||||
\(135\) | 1.97513 | + | 3.42102i | 0.169992 | + | 0.294435i | ||||
\(136\) | 0.140571 | 0.0120539 | ||||||||
\(137\) | 15.8821 | 1.35690 | 0.678450 | − | 0.734646i | \(-0.262652\pi\) | ||||
0.678450 | + | 0.734646i | \(0.262652\pi\) | |||||||
\(138\) | 4.76845 | + | 8.25920i | 0.405917 | + | 0.703070i | ||||
\(139\) | 2.94351 | + | 5.09831i | 0.249665 | + | 0.432433i | 0.963433 | − | 0.267950i | \(-0.0863461\pi\) |
−0.713768 | + | 0.700383i | \(0.753013\pi\) | |||||||
\(140\) | −5.87254 | + | 8.64551i | −0.496320 | + | 0.730679i | ||||
\(141\) | −3.33199 | + | 5.77118i | −0.280604 | + | 0.486021i | ||||
\(142\) | 1.93865 | + | 3.35783i | 0.162688 | + | 0.281783i | ||||
\(143\) | 13.5231 | + | 11.4460i | 1.13086 | + | 0.957165i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 4.97542 | 0.413186 | ||||||||
\(146\) | −0.0817820 | + | 0.141650i | −0.00676832 | + | 0.0117231i | ||||
\(147\) | −6.92538 | − | 1.01936i | −0.571196 | − | 0.0840752i | ||||
\(148\) | 11.1368 | 0.915440 | ||||||||
\(149\) | 6.63504 | − | 11.4922i | 0.543564 | − | 0.941480i | −0.455132 | − | 0.890424i | \(-0.650408\pi\) |
0.998696 | − | 0.0510562i | \(-0.0162588\pi\) | |||||||
\(150\) | −10.6045 | −0.865855 | ||||||||
\(151\) | −8.06783 | + | 13.9739i | −0.656551 | + | 1.13718i | 0.324952 | + | 0.945731i | \(0.394652\pi\) |
−0.981503 | + | 0.191449i | \(0.938681\pi\) | |||||||
\(152\) | 0.388481 | − | 0.672870i | 0.0315100 | − | 0.0545769i | ||||
\(153\) | −0.0702857 | + | 0.121738i | −0.00568227 | + | 0.00984197i | ||||
\(154\) | −7.30493 | + | 10.7543i | −0.588648 | + | 0.866603i | ||||
\(155\) | 13.2723 | 1.06605 | ||||||||
\(156\) | −2.75209 | − | 2.32938i | −0.220344 | − | 0.186499i | ||||
\(157\) | −8.85322 | + | 15.3342i | −0.706564 | + | 1.22380i | 0.259561 | + | 0.965727i | \(0.416422\pi\) |
−0.966124 | + | 0.258077i | \(0.916911\pi\) | |||||||
\(158\) | 2.17517 | + | 3.76751i | 0.173047 | + | 0.299727i | ||||
\(159\) | 11.0641 | 0.877438 | ||||||||
\(160\) | −1.97513 | − | 3.42102i | −0.156148 | − | 0.270455i | ||||
\(161\) | −10.9872 | − | 22.7145i | −0.865909 | − | 1.79016i | ||||
\(162\) | −0.500000 | − | 0.866025i | −0.0392837 | − | 0.0680414i | ||||
\(163\) | −1.63571 | + | 2.83313i | −0.128119 | + | 0.221908i | −0.922948 | − | 0.384926i | \(-0.874227\pi\) |
0.794829 | + | 0.606833i | \(0.207560\pi\) | |||||||
\(164\) | 4.65505 | − | 8.06279i | 0.363498 | − | 0.629598i | ||||
\(165\) | −19.4107 | −1.51112 | ||||||||
\(166\) | −10.5220 | −0.816669 | ||||||||
\(167\) | −4.42914 | + | 7.67150i | −0.342737 | + | 0.593638i | −0.984940 | − | 0.172896i | \(-0.944687\pi\) |
0.642203 | + | 0.766535i | \(0.278021\pi\) | |||||||
\(168\) | 1.48662 | − | 2.18860i | 0.114695 | − | 0.168854i | ||||
\(169\) | 10.0296 | − | 8.27088i | 0.771506 | − | 0.636221i | ||||
\(170\) | −0.277647 | − | 0.480898i | −0.0212945 | − | 0.0368832i | ||||
\(171\) | 0.388481 | + | 0.672870i | 0.0297079 | + | 0.0514556i | ||||
\(172\) | −0.541233 | − | 0.937443i | −0.0412686 | − | 0.0714793i | ||||
\(173\) | 7.47486 | − | 12.9468i | 0.568303 | − | 0.984330i | −0.428431 | − | 0.903575i | \(-0.640933\pi\) |
0.996734 | − | 0.0807555i | \(-0.0257333\pi\) | |||||||
\(174\) | −1.25952 | −0.0954838 | ||||||||
\(175\) | 27.9820 | + | 2.04832i | 2.11524 | + | 0.154839i | ||||
\(176\) | −2.45689 | − | 4.25545i | −0.185195 | − | 0.320767i | ||||
\(177\) | 0.215609 | + | 0.373446i | 0.0162062 | + | 0.0280699i | ||||
\(178\) | −1.07274 | −0.0804051 | ||||||||
\(179\) | 11.6034 | + | 20.0977i | 0.867281 | + | 1.50217i | 0.864765 | + | 0.502177i | \(0.167468\pi\) |
0.00251612 | + | 0.999997i | \(0.499199\pi\) | |||||||
\(180\) | 3.95025 | 0.294435 | ||||||||
\(181\) | 19.4618 | 1.44658 | 0.723291 | − | 0.690543i | \(-0.242629\pi\) | ||||
0.723291 | + | 0.690543i | \(0.242629\pi\) | |||||||
\(182\) | 6.81198 | + | 6.67809i | 0.504938 | + | 0.495013i | ||||
\(183\) | 8.28114 | 0.612160 | ||||||||
\(184\) | 9.53690 | 0.703070 | ||||||||
\(185\) | −21.9966 | − | 38.0993i | −1.61722 | − | 2.80111i | ||||
\(186\) | −3.35985 | −0.246356 | ||||||||
\(187\) | −0.345368 | − | 0.598195i | −0.0252558 | − | 0.0437444i | ||||
\(188\) | 3.33199 | + | 5.77118i | 0.243010 | + | 0.420906i | ||||
\(189\) | 1.15207 | + | 2.38175i | 0.0838006 | + | 0.173247i | ||||
\(190\) | −3.06920 | −0.222663 | ||||||||
\(191\) | 7.29819 | − | 12.6408i | 0.528078 | − | 0.914658i | −0.471386 | − | 0.881927i | \(-0.656246\pi\) |
0.999464 | − | 0.0327313i | \(-0.0104206\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | 0.884301 | + | 1.53165i | 0.0636534 | + | 0.110251i | 0.896096 | − | 0.443861i | \(-0.146391\pi\) |
−0.832442 | + | 0.554111i | \(0.813058\pi\) | |||||||
\(194\) | −6.54097 | − | 11.3293i | −0.469614 | − | 0.813396i | ||||
\(195\) | −2.53312 | + | 14.0158i | −0.181401 | + | 1.00369i | ||||
\(196\) | −4.34548 | + | 5.48788i | −0.310391 | + | 0.391991i | ||||
\(197\) | 2.92757 | − | 5.07070i | 0.208581 | − | 0.361272i | −0.742687 | − | 0.669639i | \(-0.766449\pi\) |
0.951268 | + | 0.308366i | \(0.0997823\pi\) | |||||||
\(198\) | 4.91377 | 0.349207 | ||||||||
\(199\) | 13.9227 | 0.986958 | 0.493479 | − | 0.869758i | \(-0.335725\pi\) | ||||
0.493479 | + | 0.869758i | \(0.335725\pi\) | |||||||
\(200\) | −5.30226 | + | 9.18378i | −0.374926 | + | 0.649391i | ||||
\(201\) | 4.09814 | − | 7.09819i | 0.289061 | − | 0.500668i | ||||
\(202\) | −3.69262 | − | 6.39580i | −0.259812 | − | 0.450007i | ||||
\(203\) | 3.32348 | + | 0.243283i | 0.233262 | + | 0.0170751i | ||||
\(204\) | 0.0702857 | + | 0.121738i | 0.00492099 | + | 0.00852340i | ||||
\(205\) | −36.7773 | −2.56864 | ||||||||
\(206\) | −1.99107 | − | 3.44863i | −0.138724 | − | 0.240277i | ||||
\(207\) | −4.76845 | + | 8.25920i | −0.331430 | + | 0.574054i | ||||
\(208\) | −3.39335 | + | 1.21869i | −0.235286 | + | 0.0845010i | ||||
\(209\) | −3.81782 | −0.264084 | ||||||||
\(210\) | −10.4235 | − | 0.763015i | −0.719290 | − | 0.0526530i | ||||
\(211\) | 3.35399 | − | 5.80929i | 0.230898 | − | 0.399928i | −0.727174 | − | 0.686453i | \(-0.759167\pi\) |
0.958073 | + | 0.286525i | \(0.0925002\pi\) | |||||||
\(212\) | 5.53204 | − | 9.58177i | 0.379942 | − | 0.658079i | ||||
\(213\) | −1.93865 | + | 3.35783i | −0.132834 | + | 0.230075i | ||||
\(214\) | −7.07358 | −0.483540 | ||||||||
\(215\) | −2.13801 | + | 3.70314i | −0.145811 | + | 0.252552i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 8.86560 | + | 0.648974i | 0.601836 | + | 0.0440552i | ||||
\(218\) | −7.42350 | + | 12.8579i | −0.502783 | + | 0.870846i | ||||
\(219\) | −0.163564 | −0.0110526 | ||||||||
\(220\) | −9.70533 | + | 16.8101i | −0.654333 | + | 1.13334i | ||||
\(221\) | −0.477008 | + | 0.171313i | −0.0320870 | + | 0.0115238i | ||||
\(222\) | 5.56841 | + | 9.64476i | 0.373727 | + | 0.647314i | ||||
\(223\) | −1.02744 | + | 1.77957i | −0.0688023 | + | 0.119169i | −0.898374 | − | 0.439231i | \(-0.855251\pi\) |
0.829572 | + | 0.558400i | \(0.188584\pi\) | |||||||
\(224\) | −1.15207 | − | 2.38175i | −0.0769758 | − | 0.159137i | ||||
\(225\) | −5.30226 | − | 9.18378i | −0.353484 | − | 0.612252i | ||||
\(226\) | −0.785895 | − | 1.36121i | −0.0522770 | − | 0.0905463i | ||||
\(227\) | −25.8298 | −1.71438 | −0.857190 | − | 0.515000i | \(-0.827792\pi\) | ||||
−0.857190 | + | 0.515000i | \(0.827792\pi\) | |||||||
\(228\) | 0.776963 | 0.0514556 | ||||||||
\(229\) | 5.39496 | + | 9.34435i | 0.356509 | + | 0.617492i | 0.987375 | − | 0.158400i | \(-0.0506336\pi\) |
−0.630866 | + | 0.775892i | \(0.717300\pi\) | |||||||
\(230\) | −18.8366 | − | 32.6259i | −1.24205 | − | 2.15129i | ||||
\(231\) | −12.9659 | − | 0.949124i | −0.853096 | − | 0.0624478i | ||||
\(232\) | −0.629759 | + | 1.09077i | −0.0413457 | + | 0.0716129i | ||||
\(233\) | −1.92109 | − | 3.32742i | −0.125855 | − | 0.217987i | 0.796212 | − | 0.605018i | \(-0.206834\pi\) |
−0.922067 | + | 0.387031i | \(0.873501\pi\) | |||||||
\(234\) | 0.641255 | − | 3.54807i | 0.0419202 | − | 0.231945i | ||||
\(235\) | 13.1622 | − | 22.7976i | 0.858608 | − | 1.48715i | ||||
\(236\) | 0.431218 | 0.0280699 | ||||||||
\(237\) | −2.17517 | + | 3.76751i | −0.141293 | + | 0.244726i | ||||
\(238\) | −0.161948 | − | 0.334806i | −0.0104975 | − | 0.0217023i | ||||
\(239\) | 10.2560 | 0.663404 | 0.331702 | − | 0.943384i | \(-0.392377\pi\) | ||||
0.331702 | + | 0.943384i | \(0.392377\pi\) | |||||||
\(240\) | 1.97513 | − | 3.42102i | 0.127494 | − | 0.220826i | ||||
\(241\) | −0.632854 | −0.0407657 | −0.0203829 | − | 0.999792i | \(-0.506489\pi\) | ||||
−0.0203829 | + | 0.999792i | \(0.506489\pi\) | |||||||
\(242\) | −6.57259 | + | 11.3841i | −0.422502 | + | 0.731795i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 4.14057 | − | 7.17168i | 0.265073 | − | 0.459120i | ||||
\(245\) | 27.3570 | + | 4.02672i | 1.74778 | + | 0.257258i | ||||
\(246\) | 9.31010 | 0.593590 | ||||||||
\(247\) | −0.498231 | + | 2.75672i | −0.0317017 | + | 0.175406i | ||||
\(248\) | −1.67992 | + | 2.90971i | −0.106675 | + | 0.184767i | ||||
\(249\) | −5.26102 | − | 9.11236i | −0.333404 | − | 0.577472i | ||||
\(250\) | 22.1392 | 1.40021 | ||||||||
\(251\) | 7.53648 | + | 13.0536i | 0.475698 | + | 0.823934i | 0.999612 | − | 0.0278373i | \(-0.00886202\pi\) |
−0.523914 | + | 0.851771i | \(0.675529\pi\) | |||||||
\(252\) | 2.63869 | + | 0.193156i | 0.166222 | + | 0.0121677i | ||||
\(253\) | −23.4311 | − | 40.5838i | −1.47310 | − | 2.55148i | ||||
\(254\) | −5.42757 | + | 9.40083i | −0.340556 | + | 0.589860i | ||||
\(255\) | 0.277647 | − | 0.480898i | 0.0173869 | − | 0.0301150i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.1382 | 0.694780 | 0.347390 | − | 0.937721i | \(-0.387068\pi\) | ||||
0.347390 | + | 0.937721i | \(0.387068\pi\) | |||||||
\(258\) | 0.541233 | − | 0.937443i | 0.0336957 | − | 0.0583626i | ||||
\(259\) | −12.8304 | − | 26.5251i | −0.797240 | − | 1.64819i | ||||
\(260\) | 10.8715 | + | 9.20163i | 0.674219 | + | 0.570661i | ||||
\(261\) | −0.629759 | − | 1.09077i | −0.0389811 | − | 0.0675173i | ||||
\(262\) | −0.961751 | − | 1.66580i | −0.0594172 | − | 0.102914i | ||||
\(263\) | −8.58528 | − | 14.8701i | −0.529391 | − | 0.916932i | −0.999412 | − | 0.0342770i | \(-0.989087\pi\) |
0.470021 | − | 0.882655i | \(-0.344246\pi\) | |||||||
\(264\) | 2.45689 | − | 4.25545i | 0.151211 | − | 0.261905i | ||||
\(265\) | −43.7059 | −2.68483 | ||||||||
\(266\) | −2.05016 | − | 0.150075i | −0.125704 | − | 0.00920168i | ||||
\(267\) | −0.536369 | − | 0.929018i | −0.0328252 | − | 0.0568550i | ||||
\(268\) | −4.09814 | − | 7.09819i | −0.250334 | − | 0.433591i | ||||
\(269\) | 3.28711 | 0.200419 | 0.100209 | − | 0.994966i | \(-0.468049\pi\) | ||||
0.100209 | + | 0.994966i | \(0.468049\pi\) | |||||||
\(270\) | 1.97513 | + | 3.42102i | 0.120202 | + | 0.208197i | ||||
\(271\) | 14.7261 | 0.894545 | 0.447273 | − | 0.894398i | \(-0.352395\pi\) | ||||
0.447273 | + | 0.894398i | \(0.352395\pi\) | |||||||
\(272\) | 0.140571 | 0.00852340 | ||||||||
\(273\) | −2.37740 | + | 9.23840i | −0.143887 | + | 0.559133i | ||||
\(274\) | 15.8821 | 0.959474 | ||||||||
\(275\) | 52.1082 | 3.14224 | ||||||||
\(276\) | 4.76845 | + | 8.25920i | 0.287027 | + | 0.497145i | ||||
\(277\) | 18.5004 | 1.11158 | 0.555791 | − | 0.831322i | \(-0.312415\pi\) | ||||
0.555791 | + | 0.831322i | \(0.312415\pi\) | |||||||
\(278\) | 2.94351 | + | 5.09831i | 0.176540 | + | 0.305776i | ||||
\(279\) | −1.67992 | − | 2.90971i | −0.100574 | − | 0.174200i | ||||
\(280\) | −5.87254 | + | 8.64551i | −0.350951 | + | 0.516668i | ||||
\(281\) | −31.3463 | −1.86996 | −0.934981 | − | 0.354698i | \(-0.884584\pi\) | ||||
−0.934981 | + | 0.354698i | \(0.884584\pi\) | |||||||
\(282\) | −3.33199 | + | 5.77118i | −0.198417 | + | 0.343669i | ||||
\(283\) | 7.35985 | + | 12.7476i | 0.437498 | + | 0.757768i | 0.997496 | − | 0.0707258i | \(-0.0225315\pi\) |
−0.559998 | + | 0.828494i | \(0.689198\pi\) | |||||||
\(284\) | 1.93865 | + | 3.35783i | 0.115037 | + | 0.199251i | ||||
\(285\) | −1.53460 | − | 2.65801i | −0.0909019 | − | 0.157447i | ||||
\(286\) | 13.5231 | + | 11.4460i | 0.799640 | + | 0.676818i | ||||
\(287\) | −24.5665 | − | 1.79830i | −1.45011 | − | 0.106150i | ||||
\(288\) | −0.500000 | + | 0.866025i | −0.0294628 | + | 0.0510310i | ||||
\(289\) | −16.9802 | −0.998838 | ||||||||
\(290\) | 4.97542 | 0.292167 | ||||||||
\(291\) | 6.54097 | − | 11.3293i | 0.383438 | − | 0.664135i | ||||
\(292\) | −0.0817820 | + | 0.141650i | −0.00478593 | + | 0.00828947i | ||||
\(293\) | 8.39523 | + | 14.5410i | 0.490454 | + | 0.849492i | 0.999940 | − | 0.0109876i | \(-0.00349752\pi\) |
−0.509485 | + | 0.860479i | \(0.670164\pi\) | |||||||
\(294\) | −6.92538 | − | 1.01936i | −0.403896 | − | 0.0594501i | ||||
\(295\) | −0.851711 | − | 1.47521i | −0.0495886 | − | 0.0858899i | ||||
\(296\) | 11.1368 | 0.647314 | ||||||||
\(297\) | 2.45689 | + | 4.25545i | 0.142563 | + | 0.246926i | ||||
\(298\) | 6.63504 | − | 11.4922i | 0.384358 | − | 0.665727i | ||||
\(299\) | −32.3620 | + | 11.6225i | −1.87154 | + | 0.672149i | ||||
\(300\) | −10.6045 | −0.612252 | ||||||||
\(301\) | −1.60922 | + | 2.36908i | −0.0927538 | + | 0.136551i | ||||
\(302\) | −8.06783 | + | 13.9739i | −0.464252 | + | 0.804107i | ||||
\(303\) | 3.69262 | − | 6.39580i | 0.212135 | − | 0.367429i | ||||
\(304\) | 0.388481 | − | 0.672870i | 0.0222809 | − | 0.0385917i | ||||
\(305\) | −32.7126 | −1.87312 | ||||||||
\(306\) | −0.0702857 | + | 0.121738i | −0.00401797 | + | 0.00695933i | ||||
\(307\) | 5.69511 | 0.325037 | 0.162519 | − | 0.986705i | \(-0.448038\pi\) | ||||
0.162519 | + | 0.986705i | \(0.448038\pi\) | |||||||
\(308\) | −7.30493 | + | 10.7543i | −0.416237 | + | 0.612781i | ||||
\(309\) | 1.99107 | − | 3.44863i | 0.113268 | − | 0.196186i | ||||
\(310\) | 13.2723 | 0.753813 | ||||||||
\(311\) | 0.183797 | − | 0.318345i | 0.0104221 | − | 0.0180517i | −0.860767 | − | 0.508999i | \(-0.830016\pi\) |
0.871189 | + | 0.490947i | \(0.163349\pi\) | |||||||
\(312\) | −2.75209 | − | 2.32938i | −0.155806 | − | 0.131875i | ||||
\(313\) | −2.95742 | − | 5.12240i | −0.167163 | − | 0.289535i | 0.770258 | − | 0.637732i | \(-0.220127\pi\) |
−0.937421 | + | 0.348197i | \(0.886794\pi\) | |||||||
\(314\) | −8.85322 | + | 15.3342i | −0.499616 | + | 0.865360i | ||||
\(315\) | −4.55096 | − | 9.40852i | −0.256418 | − | 0.530110i | ||||
\(316\) | 2.17517 | + | 3.76751i | 0.122363 | + | 0.211939i | ||||
\(317\) | −4.28899 | − | 7.42875i | −0.240894 | − | 0.417240i | 0.720075 | − | 0.693896i | \(-0.244107\pi\) |
−0.960969 | + | 0.276656i | \(0.910774\pi\) | |||||||
\(318\) | 11.0641 | 0.620442 | ||||||||
\(319\) | 6.18899 | 0.346517 | ||||||||
\(320\) | −1.97513 | − | 3.42102i | −0.110413 | − | 0.191241i | ||||
\(321\) | −3.53679 | − | 6.12590i | −0.197404 | − | 0.341914i | ||||
\(322\) | −10.9872 | − | 22.7145i | −0.612290 | − | 1.26583i | ||||
\(323\) | 0.0546094 | − | 0.0945863i | 0.00303855 | − | 0.00526292i | ||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 6.80020 | − | 37.6255i | 0.377207 | − | 2.08709i | ||||
\(326\) | −1.63571 | + | 2.83313i | −0.0905935 | + | 0.156912i | ||||
\(327\) | −14.8470 | −0.821041 | ||||||||
\(328\) | 4.65505 | − | 8.06279i | 0.257032 | − | 0.445193i | ||||
\(329\) | 9.90683 | − | 14.5848i | 0.546181 | − | 0.804084i | ||||
\(330\) | −19.4107 | −1.06852 | ||||||||
\(331\) | 2.07489 | − | 3.59381i | 0.114046 | − | 0.197533i | −0.803352 | − | 0.595504i | \(-0.796952\pi\) |
0.917398 | + | 0.397971i | \(0.130286\pi\) | |||||||
\(332\) | −10.5220 | −0.577472 | ||||||||
\(333\) | −5.56841 | + | 9.64476i | −0.305147 | + | 0.528530i | ||||
\(334\) | −4.42914 | + | 7.67150i | −0.242352 | + | 0.419766i | ||||
\(335\) | −16.1887 | + | 28.0397i | −0.884483 | + | 1.53197i | ||||
\(336\) | 1.48662 | − | 2.18860i | 0.0811020 | − | 0.119398i | ||||
\(337\) | 18.5391 | 1.00989 | 0.504945 | − | 0.863152i | \(-0.331513\pi\) | ||||
0.504945 | + | 0.863152i | \(0.331513\pi\) | |||||||
\(338\) | 10.0296 | − | 8.27088i | 0.545537 | − | 0.449877i | ||||
\(339\) | 0.785895 | − | 1.36121i | 0.0426840 | − | 0.0739308i | ||||
\(340\) | −0.277647 | − | 0.480898i | −0.0150575 | − | 0.0260804i | ||||
\(341\) | 16.5095 | 0.894041 | ||||||||
\(342\) | 0.388481 | + | 0.672870i | 0.0210067 | + | 0.0363846i | ||||
\(343\) | 18.0770 | + | 4.02745i | 0.976069 | + | 0.217462i | ||||
\(344\) | −0.541233 | − | 0.937443i | −0.0291813 | − | 0.0505435i | ||||
\(345\) | 18.8366 | − | 32.6259i | 1.01413 | − | 1.75652i | ||||
\(346\) | 7.47486 | − | 12.9468i | 0.401851 | − | 0.696027i | ||||
\(347\) | −22.9868 | −1.23400 | −0.616999 | − | 0.786964i | \(-0.711652\pi\) | ||||
−0.616999 | + | 0.786964i | \(0.711652\pi\) | |||||||
\(348\) | −1.25952 | −0.0675173 | ||||||||
\(349\) | 7.29494 | − | 12.6352i | 0.390489 | − | 0.676347i | −0.602025 | − | 0.798477i | \(-0.705639\pi\) |
0.992514 | + | 0.122130i | \(0.0389726\pi\) | |||||||
\(350\) | 27.9820 | + | 2.04832i | 1.49570 | + | 0.109487i | ||||
\(351\) | 3.39335 | − | 1.21869i | 0.181123 | − | 0.0650489i | ||||
\(352\) | −2.45689 | − | 4.25545i | −0.130953 | − | 0.226816i | ||||
\(353\) | 9.86522 | + | 17.0871i | 0.525073 | + | 0.909453i | 0.999574 | + | 0.0291979i | \(0.00929529\pi\) |
−0.474501 | + | 0.880255i | \(0.657371\pi\) | |||||||
\(354\) | 0.215609 | + | 0.373446i | 0.0114595 | + | 0.0198484i | ||||
\(355\) | 7.65815 | − | 13.2643i | 0.406452 | − | 0.703996i | ||||
\(356\) | −1.07274 | −0.0568550 | ||||||||
\(357\) | 0.208977 | − | 0.307654i | 0.0110602 | − | 0.0162828i | ||||
\(358\) | 11.6034 | + | 20.0977i | 0.613260 | + | 1.06220i | ||||
\(359\) | 18.8344 | + | 32.6222i | 0.994044 | + | 1.72173i | 0.591401 | + | 0.806378i | \(0.298575\pi\) |
0.402644 | + | 0.915357i | \(0.368091\pi\) | |||||||
\(360\) | 3.95025 | 0.208197 | ||||||||
\(361\) | 9.19816 | + | 15.9317i | 0.484114 | + | 0.838510i | ||||
\(362\) | 19.4618 | 1.02289 | ||||||||
\(363\) | −13.1452 | −0.689943 | ||||||||
\(364\) | 6.81198 | + | 6.67809i | 0.357045 | + | 0.350027i | ||||
\(365\) | 0.646119 | 0.0338194 | ||||||||
\(366\) | 8.28114 | 0.432862 | ||||||||
\(367\) | −1.25141 | − | 2.16750i | −0.0653229 | − | 0.113143i | 0.831514 | − | 0.555503i | \(-0.187474\pi\) |
−0.896837 | + | 0.442361i | \(0.854141\pi\) | |||||||
\(368\) | 9.53690 | 0.497145 | ||||||||
\(369\) | 4.65505 | + | 8.06279i | 0.242332 | + | 0.419732i | ||||
\(370\) | −21.9966 | − | 38.0993i | −1.14355 | − | 1.98069i | ||||
\(371\) | −29.1947 | − | 2.13709i | −1.51571 | − | 0.110952i | ||||
\(372\) | −3.35985 | −0.174200 | ||||||||
\(373\) | 6.58371 | − | 11.4033i | 0.340891 | − | 0.590441i | −0.643707 | − | 0.765272i | \(-0.722605\pi\) |
0.984598 | + | 0.174831i | \(0.0559378\pi\) | |||||||
\(374\) | −0.345368 | − | 0.598195i | −0.0178586 | − | 0.0309319i | ||||
\(375\) | 11.0696 | + | 19.1731i | 0.571633 | + | 0.990097i | ||||
\(376\) | 3.33199 | + | 5.77118i | 0.171834 | + | 0.297626i | ||||
\(377\) | 0.807672 | − | 4.46886i | 0.0415972 | − | 0.230158i | ||||
\(378\) | 1.15207 | + | 2.38175i | 0.0592560 | + | 0.122504i | ||||
\(379\) | −5.93228 | + | 10.2750i | −0.304721 | + | 0.527792i | −0.977199 | − | 0.212325i | \(-0.931896\pi\) |
0.672478 | + | 0.740117i | \(0.265230\pi\) | |||||||
\(380\) | −3.06920 | −0.157447 | ||||||||
\(381\) | −10.8551 | −0.556126 | ||||||||
\(382\) | 7.29819 | − | 12.6408i | 0.373408 | − | 0.646761i | ||||
\(383\) | −8.21139 | + | 14.2225i | −0.419582 | + | 0.726738i | −0.995897 | − | 0.0904897i | \(-0.971157\pi\) |
0.576315 | + | 0.817228i | \(0.304490\pi\) | |||||||
\(384\) | 0.500000 | + | 0.866025i | 0.0255155 | + | 0.0441942i | ||||
\(385\) | 51.2187 | + | 3.74928i | 2.61035 | + | 0.191081i | ||||
\(386\) | 0.884301 | + | 1.53165i | 0.0450098 | + | 0.0779592i | ||||
\(387\) | 1.08247 | 0.0550248 | ||||||||
\(388\) | −6.54097 | − | 11.3293i | −0.332067 | − | 0.575158i | ||||
\(389\) | 9.03721 | − | 15.6529i | 0.458205 | − | 0.793634i | −0.540662 | − | 0.841240i | \(-0.681826\pi\) |
0.998866 | + | 0.0476065i | \(0.0151594\pi\) | |||||||
\(390\) | −2.53312 | + | 14.0158i | −0.128270 | + | 0.709716i | ||||
\(391\) | 1.34062 | 0.0677979 | ||||||||
\(392\) | −4.34548 | + | 5.48788i | −0.219480 | + | 0.277180i | ||||
\(393\) | 0.961751 | − | 1.66580i | 0.0485139 | − | 0.0840285i | ||||
\(394\) | 2.92757 | − | 5.07070i | 0.147489 | − | 0.255458i | ||||
\(395\) | 8.59248 | − | 14.8826i | 0.432335 | − | 0.748826i | ||||
\(396\) | 4.91377 | 0.246926 | ||||||||
\(397\) | 1.20491 | − | 2.08696i | 0.0604726 | − | 0.104742i | −0.834204 | − | 0.551456i | \(-0.814073\pi\) |
0.894677 | + | 0.446714i | \(0.147406\pi\) | |||||||
\(398\) | 13.9227 | 0.697884 | ||||||||
\(399\) | −0.895114 | − | 1.85053i | −0.0448117 | − | 0.0926425i | ||||
\(400\) | −5.30226 | + | 9.18378i | −0.265113 | + | 0.459189i | ||||
\(401\) | −24.9243 | −1.24466 | −0.622331 | − | 0.782754i | \(-0.713814\pi\) | ||||
−0.622331 | + | 0.782754i | \(0.713814\pi\) | |||||||
\(402\) | 4.09814 | − | 7.09819i | 0.204397 | − | 0.354026i | ||||
\(403\) | 2.15452 | − | 11.9210i | 0.107324 | − | 0.593826i | ||||
\(404\) | −3.69262 | − | 6.39580i | −0.183715 | − | 0.318203i | ||||
\(405\) | −1.97513 | + | 3.42102i | −0.0981449 | + | 0.169992i | ||||
\(406\) | 3.32348 | + | 0.243283i | 0.164941 | + | 0.0120739i | ||||
\(407\) | −27.3619 | − | 47.3922i | −1.35628 | − | 2.34914i | ||||
\(408\) | 0.0702857 | + | 0.121738i | 0.00347966 | + | 0.00602695i | ||||
\(409\) | 27.4769 | 1.35865 | 0.679323 | − | 0.733840i | \(-0.262274\pi\) | ||||
0.679323 | + | 0.733840i | \(0.262274\pi\) | |||||||
\(410\) | −36.7773 | −1.81630 | ||||||||
\(411\) | 7.94106 | + | 13.7543i | 0.391704 | + | 0.678450i | ||||
\(412\) | −1.99107 | − | 3.44863i | −0.0980929 | − | 0.169902i | ||||
\(413\) | −0.496793 | − | 1.02706i | −0.0244456 | − | 0.0505381i | ||||
\(414\) | −4.76845 | + | 8.25920i | −0.234357 | + | 0.405917i | ||||
\(415\) | 20.7824 | + | 35.9961i | 1.02017 | + | 1.76698i | ||||
\(416\) | −3.39335 | + | 1.21869i | −0.166372 | + | 0.0597512i | ||||
\(417\) | −2.94351 | + | 5.09831i | −0.144144 | + | 0.249665i | ||||
\(418\) | −3.81782 | −0.186736 | ||||||||
\(419\) | −5.16655 | + | 8.94872i | −0.252402 | + | 0.437174i | −0.964187 | − | 0.265224i | \(-0.914554\pi\) |
0.711784 | + | 0.702398i | \(0.247887\pi\) | |||||||
\(420\) | −10.4235 | − | 0.763015i | −0.508615 | − | 0.0372313i | ||||
\(421\) | −16.8702 | −0.822204 | −0.411102 | − | 0.911589i | \(-0.634856\pi\) | ||||
−0.411102 | + | 0.911589i | \(0.634856\pi\) | |||||||
\(422\) | 3.35399 | − | 5.80929i | 0.163270 | − | 0.282792i | ||||
\(423\) | −6.66398 | −0.324014 | ||||||||
\(424\) | 5.53204 | − | 9.58177i | 0.268659 | − | 0.465332i | ||||
\(425\) | −0.745346 | + | 1.29098i | −0.0361546 | + | 0.0626216i | ||||
\(426\) | −1.93865 | + | 3.35783i | −0.0939277 | + | 0.162688i | ||||
\(427\) | −21.8514 | − | 1.59955i | −1.05746 | − | 0.0774077i | ||||
\(428\) | −7.07358 | −0.341914 | ||||||||
\(429\) | −3.15098 | + | 17.4344i | −0.152131 | + | 0.841741i | ||||
\(430\) | −2.13801 | + | 3.70314i | −0.103104 | + | 0.178581i | ||||
\(431\) | −12.1718 | − | 21.0822i | −0.586294 | − | 1.01549i | −0.994713 | − | 0.102697i | \(-0.967253\pi\) |
0.408418 | − | 0.912795i | \(-0.366080\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 0.984059 | + | 1.70444i | 0.0472909 | + | 0.0819102i | 0.888702 | − | 0.458485i | \(-0.151608\pi\) |
−0.841411 | + | 0.540396i | \(0.818275\pi\) | |||||||
\(434\) | 8.86560 | + | 0.648974i | 0.425562 | + | 0.0311518i | ||||
\(435\) | 2.48771 | + | 4.30884i | 0.119276 | + | 0.206593i | ||||
\(436\) | −7.42350 | + | 12.8579i | −0.355521 | + | 0.615781i | ||||
\(437\) | 3.70491 | − | 6.41709i | 0.177230 | − | 0.306971i | ||||
\(438\) | −0.163564 | −0.00781539 | ||||||||
\(439\) | 20.2636 | 0.967128 | 0.483564 | − | 0.875309i | \(-0.339342\pi\) | ||||
0.483564 | + | 0.875309i | \(0.339342\pi\) | |||||||
\(440\) | −9.70533 | + | 16.8101i | −0.462683 | + | 0.801391i | ||||
\(441\) | −2.57990 | − | 6.50724i | −0.122852 | − | 0.309868i | ||||
\(442\) | −0.477008 | + | 0.171313i | −0.0226889 | + | 0.00814854i | ||||
\(443\) | −14.2707 | − | 24.7177i | −0.678024 | − | 1.17437i | −0.975575 | − | 0.219666i | \(-0.929503\pi\) |
0.297551 | − | 0.954706i | \(-0.403830\pi\) | |||||||
\(444\) | 5.56841 | + | 9.64476i | 0.264265 | + | 0.457720i | ||||
\(445\) | 2.11879 | + | 3.66986i | 0.100440 | + | 0.173968i | ||||
\(446\) | −1.02744 | + | 1.77957i | −0.0486505 | + | 0.0842652i | ||||
\(447\) | 13.2701 | 0.627653 | ||||||||
\(448\) | −1.15207 | − | 2.38175i | −0.0544301 | − | 0.112527i | ||||
\(449\) | 12.1517 | + | 21.0474i | 0.573475 | + | 0.993287i | 0.996206 | + | 0.0870320i | \(0.0277382\pi\) |
−0.422731 | + | 0.906255i | \(0.638928\pi\) | |||||||
\(450\) | −5.30226 | − | 9.18378i | −0.249951 | − | 0.432927i | ||||
\(451\) | −45.7477 | −2.15418 | ||||||||
\(452\) | −0.785895 | − | 1.36121i | −0.0369654 | − | 0.0640259i | ||||
\(453\) | −16.1357 | −0.758120 | ||||||||
\(454\) | −25.8298 | −1.21225 | ||||||||
\(455\) | 9.39135 | − | 36.4940i | 0.440273 | − | 1.71087i | ||||
\(456\) | 0.776963 | 0.0363846 | ||||||||
\(457\) | −6.25302 | −0.292504 | −0.146252 | − | 0.989247i | \(-0.546721\pi\) | ||||
−0.146252 | + | 0.989247i | \(0.546721\pi\) | |||||||
\(458\) | 5.39496 | + | 9.34435i | 0.252090 | + | 0.436633i | ||||
\(459\) | −0.140571 | −0.00656131 | ||||||||
\(460\) | −18.8366 | − | 32.6259i | −0.878261 | − | 1.52119i | ||||
\(461\) | 9.65625 | + | 16.7251i | 0.449736 | + | 0.778966i | 0.998369 | − | 0.0570976i | \(-0.0181846\pi\) |
−0.548632 | + | 0.836064i | \(0.684851\pi\) | |||||||
\(462\) | −12.9659 | − | 0.949124i | −0.603230 | − | 0.0441572i | ||||
\(463\) | 21.4480 | 0.996772 | 0.498386 | − | 0.866955i | \(-0.333926\pi\) | ||||
0.498386 | + | 0.866955i | \(0.333926\pi\) | |||||||
\(464\) | −0.629759 | + | 1.09077i | −0.0292358 | + | 0.0506379i | ||||
\(465\) | 6.63613 | + | 11.4941i | 0.307743 | + | 0.533027i | ||||
\(466\) | −1.92109 | − | 3.32742i | −0.0889928 | − | 0.154140i | ||||
\(467\) | 2.39255 | + | 4.14402i | 0.110714 | + | 0.191762i | 0.916058 | − | 0.401045i | \(-0.131353\pi\) |
−0.805344 | + | 0.592807i | \(0.798020\pi\) | |||||||
\(468\) | 0.641255 | − | 3.54807i | 0.0296420 | − | 0.164010i | ||||
\(469\) | −12.1848 | + | 17.9384i | −0.562641 | + | 0.828316i | ||||
\(470\) | 13.1622 | − | 22.7976i | 0.607128 | − | 1.05158i | ||||
\(471\) | −17.7064 | −0.815869 | ||||||||
\(472\) | 0.431218 | 0.0198484 | ||||||||
\(473\) | −2.65950 | + | 4.60638i | −0.122284 | + | 0.211802i | ||||
\(474\) | −2.17517 | + | 3.76751i | −0.0999090 | + | 0.173047i | ||||
\(475\) | 4.11966 | + | 7.13545i | 0.189023 | + | 0.327397i | ||||
\(476\) | −0.161948 | − | 0.334806i | −0.00742287 | − | 0.0153458i | ||||
\(477\) | 5.53204 | + | 9.58177i | 0.253295 | + | 0.438719i | ||||
\(478\) | 10.2560 | 0.469098 | ||||||||
\(479\) | 5.85660 | + | 10.1439i | 0.267595 | + | 0.463488i | 0.968240 | − | 0.250022i | \(-0.0804378\pi\) |
−0.700645 | + | 0.713510i | \(0.747104\pi\) | |||||||
\(480\) | 1.97513 | − | 3.42102i | 0.0901518 | − | 0.156148i | ||||
\(481\) | −37.7910 | + | 13.5723i | −1.72312 | + | 0.618845i | ||||
\(482\) | −0.632854 | −0.0288257 | ||||||||
\(483\) | 14.1778 | − | 20.8724i | 0.645111 | − | 0.949728i | ||||
\(484\) | −6.57259 | + | 11.3841i | −0.298754 | + | 0.517457i | ||||
\(485\) | −25.8385 | + | 44.7536i | −1.17327 | + | 2.03216i | ||||
\(486\) | 0.500000 | − | 0.866025i | 0.0226805 | − | 0.0392837i | ||||
\(487\) | −25.7570 | −1.16716 | −0.583581 | − | 0.812055i | \(-0.698349\pi\) | ||||
−0.583581 | + | 0.812055i | \(0.698349\pi\) | |||||||
\(488\) | 4.14057 | − | 7.17168i | 0.187435 | − | 0.324647i | ||||
\(489\) | −3.27142 | −0.147939 | ||||||||
\(490\) | 27.3570 | + | 4.02672i | 1.23586 | + | 0.181909i | ||||
\(491\) | 2.35012 | − | 4.07053i | 0.106059 | − | 0.183700i | −0.808111 | − | 0.589030i | \(-0.799510\pi\) |
0.914171 | + | 0.405330i | \(0.132843\pi\) | |||||||
\(492\) | 9.31010 | 0.419732 | ||||||||
\(493\) | −0.0885262 | + | 0.153332i | −0.00398702 | + | 0.00690572i | ||||
\(494\) | −0.498231 | + | 2.75672i | −0.0224165 | + | 0.124031i | ||||
\(495\) | −9.70533 | − | 16.8101i | −0.436222 | − | 0.755559i | ||||
\(496\) | −1.67992 | + | 2.90971i | −0.0754308 | + | 0.130650i | ||||
\(497\) | 5.76407 | − | 8.48583i | 0.258554 | − | 0.380641i | ||||
\(498\) | −5.26102 | − | 9.11236i | −0.235752 | − | 0.408335i | ||||
\(499\) | 16.3247 | + | 28.2752i | 0.730794 | + | 1.26577i | 0.956544 | + | 0.291587i | \(0.0941832\pi\) |
−0.225751 | + | 0.974185i | \(0.572483\pi\) | |||||||
\(500\) | 22.1392 | 0.990097 | ||||||||
\(501\) | −8.85828 | −0.395759 | ||||||||
\(502\) | 7.53648 | + | 13.0536i | 0.336370 | + | 0.582609i | ||||
\(503\) | 7.49164 | + | 12.9759i | 0.334036 | + | 0.578567i | 0.983299 | − | 0.181997i | \(-0.0582560\pi\) |
−0.649263 | + | 0.760564i | \(0.724923\pi\) | |||||||
\(504\) | 2.63869 | + | 0.193156i | 0.117537 | + | 0.00860384i | ||||
\(505\) | −14.5868 | + | 25.2650i | −0.649103 | + | 1.12428i | ||||
\(506\) | −23.4311 | − | 40.5838i | −1.04164 | − | 1.80417i | ||||
\(507\) | 12.1776 | + | 4.55044i | 0.540825 | + | 0.202092i | ||||
\(508\) | −5.42757 | + | 9.40083i | −0.240809 | + | 0.417094i | ||||
\(509\) | −0.420876 | −0.0186550 | −0.00932749 | − | 0.999956i | \(-0.502969\pi\) | ||||
−0.00932749 | + | 0.999956i | \(0.502969\pi\) | |||||||
\(510\) | 0.277647 | − | 0.480898i | 0.0122944 | − | 0.0212945i | ||||
\(511\) | 0.431595 | + | 0.0315933i | 0.0190926 | + | 0.00139761i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −0.388481 | + | 0.672870i | −0.0171519 | + | 0.0297079i | ||||
\(514\) | 11.1382 | 0.491284 | ||||||||
\(515\) | −7.86522 | + | 13.6230i | −0.346583 | + | 0.600300i | ||||
\(516\) | 0.541233 | − | 0.937443i | 0.0238264 | − | 0.0412686i | ||||
\(517\) | 16.3727 | − | 28.3583i | 0.720068 | − | 1.24720i | ||||
\(518\) | −12.8304 | − | 26.5251i | −0.563734 | − | 1.16545i | ||||
\(519\) | 14.9497 | 0.656220 | ||||||||
\(520\) | 10.8715 | + | 9.20163i | 0.476745 | + | 0.403518i | ||||
\(521\) | −15.5914 | + | 27.0050i | −0.683070 | + | 1.18311i | 0.290969 | + | 0.956732i | \(0.406022\pi\) |
−0.974039 | + | 0.226379i | \(0.927311\pi\) | |||||||
\(522\) | −0.629759 | − | 1.09077i | −0.0275638 | − | 0.0477419i | ||||
\(523\) | 14.3638 | 0.628087 | 0.314043 | − | 0.949409i | \(-0.398316\pi\) | ||||
0.314043 | + | 0.949409i | \(0.398316\pi\) | |||||||
\(524\) | −0.961751 | − | 1.66580i | −0.0420143 | − | 0.0727709i | ||||
\(525\) | 12.2171 | + | 25.2573i | 0.533199 | + | 1.10232i | ||||
\(526\) | −8.58528 | − | 14.8701i | −0.374336 | − | 0.648369i | ||||
\(527\) | −0.236149 | + | 0.409023i | −0.0102868 | + | 0.0178173i | ||||
\(528\) | 2.45689 | − | 4.25545i | 0.106922 | − | 0.185195i | ||||
\(529\) | 67.9525 | 2.95446 | ||||||||
\(530\) | −43.7059 | −1.89846 | ||||||||
\(531\) | −0.215609 | + | 0.373446i | −0.00935664 | + | 0.0162062i | ||||
\(532\) | −2.05016 | − | 0.150075i | −0.0888859 | − | 0.00650657i | ||||
\(533\) | −5.97015 | + | 33.0329i | −0.258596 | + | 1.43081i | ||||
\(534\) | −0.536369 | − | 0.929018i | −0.0232110 | − | 0.0402026i | ||||
\(535\) | 13.9712 | + | 24.1989i | 0.604028 | + | 1.04621i | ||||
\(536\) | −4.09814 | − | 7.09819i | −0.177013 | − | 0.306595i | ||||
\(537\) | −11.6034 | + | 20.0977i | −0.500725 | + | 0.867281i | ||||
\(538\) | 3.28711 | 0.141717 | ||||||||
\(539\) | 34.0298 | + | 5.00889i | 1.46577 | + | 0.215748i | ||||
\(540\) | 1.97513 | + | 3.42102i | 0.0849959 | + | 0.147217i | ||||
\(541\) | 4.68698 | + | 8.11808i | 0.201509 | + | 0.349024i | 0.949015 | − | 0.315232i | \(-0.102082\pi\) |
−0.747506 | + | 0.664255i | \(0.768749\pi\) | |||||||
\(542\) | 14.7261 | 0.632539 | ||||||||
\(543\) | 9.73088 | + | 16.8544i | 0.417592 | + | 0.723291i | ||||
\(544\) | 0.140571 | 0.00602695 | ||||||||
\(545\) | 58.6494 | 2.51227 | ||||||||
\(546\) | −2.37740 | + | 9.23840i | −0.101744 | + | 0.395367i | ||||
\(547\) | 17.7829 | 0.760343 | 0.380172 | − | 0.924916i | \(-0.375865\pi\) | ||||
0.380172 | + | 0.924916i | \(0.375865\pi\) | |||||||
\(548\) | 15.8821 | 0.678450 | ||||||||
\(549\) | 4.14057 | + | 7.17168i | 0.176715 | + | 0.306080i | ||||
\(550\) | 52.1082 | 2.22190 | ||||||||
\(551\) | 0.489299 | + | 0.847491i | 0.0208449 | + | 0.0361043i | ||||
\(552\) | 4.76845 | + | 8.25920i | 0.202959 | + | 0.351535i | ||||
\(553\) | 6.46732 | − | 9.52114i | 0.275019 | − | 0.404880i | ||||
\(554\) | 18.5004 | 0.786008 | ||||||||
\(555\) | 21.9966 | − | 38.0993i | 0.933704 | − | 1.61722i | ||||
\(556\) | 2.94351 | + | 5.09831i | 0.124833 | + | 0.216216i | ||||
\(557\) | −6.68207 | − | 11.5737i | −0.283128 | − | 0.490393i | 0.689025 | − | 0.724737i | \(-0.258039\pi\) |
−0.972154 | + | 0.234345i | \(0.924706\pi\) | |||||||
\(558\) | −1.67992 | − | 2.90971i | −0.0711169 | − | 0.123178i | ||||
\(559\) | 2.97904 | + | 2.52147i | 0.126000 | + | 0.106647i | ||||
\(560\) | −5.87254 | + | 8.64551i | −0.248160 | + | 0.365339i | ||||
\(561\) | 0.345368 | − | 0.598195i | 0.0145815 | − | 0.0252558i | ||||
\(562\) | −31.3463 | −1.32226 | ||||||||
\(563\) | −27.3883 | −1.15428 | −0.577139 | − | 0.816646i | \(-0.695831\pi\) | ||||
−0.577139 | + | 0.816646i | \(0.695831\pi\) | |||||||
\(564\) | −3.33199 | + | 5.77118i | −0.140302 | + | 0.243010i | ||||
\(565\) | −3.10449 | + | 5.37713i | −0.130607 | + | 0.226217i | ||||
\(566\) | 7.35985 | + | 12.7476i | 0.309357 | + | 0.535823i | ||||
\(567\) | −1.48662 | + | 2.18860i | −0.0624323 | + | 0.0919124i | ||||
\(568\) | 1.93865 | + | 3.35783i | 0.0813438 | + | 0.140892i | ||||
\(569\) | −10.9762 | −0.460145 | −0.230072 | − | 0.973173i | \(-0.573896\pi\) | ||||
−0.230072 | + | 0.973173i | \(0.573896\pi\) | |||||||
\(570\) | −1.53460 | − | 2.65801i | −0.0642773 | − | 0.111332i | ||||
\(571\) | −14.5552 | + | 25.2103i | −0.609115 | + | 1.05502i | 0.382271 | + | 0.924050i | \(0.375142\pi\) |
−0.991387 | + | 0.130969i | \(0.958191\pi\) | |||||||
\(572\) | 13.5231 | + | 11.4460i | 0.565431 | + | 0.478583i | ||||
\(573\) | 14.5964 | 0.609772 | ||||||||
\(574\) | −24.5665 | − | 1.79830i | −1.02539 | − | 0.0750596i | ||||
\(575\) | −50.5671 | + | 87.5847i | −2.10879 | + | 3.65254i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −10.0317 | + | 17.3753i | −0.417623 | + | 0.723345i | −0.995700 | − | 0.0926375i | \(-0.970470\pi\) |
0.578076 | + | 0.815983i | \(0.303804\pi\) | |||||||
\(578\) | −16.9802 | −0.706285 | ||||||||
\(579\) | −0.884301 | + | 1.53165i | −0.0367503 | + | 0.0636534i | ||||
\(580\) | 4.97542 | 0.206593 | ||||||||
\(581\) | 12.1221 | + | 25.0609i | 0.502910 | + | 1.03970i | ||||
\(582\) | 6.54097 | − | 11.3293i | 0.271132 | − | 0.469614i | ||||
\(583\) | −54.3663 | −2.25162 | ||||||||
\(584\) | −0.0817820 | + | 0.141650i | −0.00338416 | + | 0.00586154i | ||||
\(585\) | −13.4046 | + | 4.81414i | −0.554211 | + | 0.199040i | ||||
\(586\) | 8.39523 | + | 14.5410i | 0.346804 | + | 0.600681i | ||||
\(587\) | 16.0113 | − | 27.7323i | 0.660855 | − | 1.14463i | −0.319536 | − | 0.947574i | \(-0.603527\pi\) |
0.980391 | − | 0.197060i | \(-0.0631395\pi\) | |||||||
\(588\) | −6.92538 | − | 1.01936i | −0.285598 | − | 0.0420376i | ||||
\(589\) | 1.30524 | + | 2.26074i | 0.0537814 | + | 0.0931521i | ||||
\(590\) | −0.851711 | − | 1.47521i | −0.0350644 | − | 0.0607333i | ||||
\(591\) | 5.85514 | 0.240848 | ||||||||
\(592\) | 11.1368 | 0.457720 | ||||||||
\(593\) | 12.2192 | + | 21.1643i | 0.501784 | + | 0.869115i | 0.999998 | + | 0.00206106i | \(0.000656057\pi\) |
−0.498214 | + | 0.867054i | \(0.666011\pi\) | |||||||
\(594\) | 2.45689 | + | 4.25545i | 0.100807 | + | 0.174603i | ||||
\(595\) | −0.825512 | + | 1.21531i | −0.0338427 | + | 0.0498229i | ||||
\(596\) | 6.63504 | − | 11.4922i | 0.271782 | − | 0.470740i | ||||
\(597\) | 6.96137 | + | 12.0575i | 0.284910 | + | 0.493479i | ||||
\(598\) | −32.3620 | + | 11.6225i | −1.32338 | + | 0.475281i | ||||
\(599\) | −7.93636 | + | 13.7462i | −0.324271 | + | 0.561654i | −0.981365 | − | 0.192155i | \(-0.938452\pi\) |
0.657093 | + | 0.753809i | \(0.271786\pi\) | |||||||
\(600\) | −10.6045 | −0.432927 | ||||||||
\(601\) | −0.0246085 | + | 0.0426231i | −0.00100380 | + | 0.00173863i | −0.866527 | − | 0.499130i | \(-0.833653\pi\) |
0.865523 | + | 0.500869i | \(0.166986\pi\) | |||||||
\(602\) | −1.60922 | + | 2.36908i | −0.0655869 | + | 0.0965565i | ||||
\(603\) | 8.19628 | 0.333778 | ||||||||
\(604\) | −8.06783 | + | 13.9739i | −0.328275 | + | 0.568590i | ||||
\(605\) | 51.9268 | 2.11112 | ||||||||
\(606\) | 3.69262 | − | 6.39580i | 0.150002 | − | 0.259812i | ||||
\(607\) | −6.61325 | + | 11.4545i | −0.268423 | + | 0.464923i | −0.968455 | − | 0.249189i | \(-0.919836\pi\) |
0.700031 | + | 0.714112i | \(0.253169\pi\) | |||||||
\(608\) | 0.388481 | − | 0.672870i | 0.0157550 | − | 0.0272885i | ||||
\(609\) | 1.45105 | + | 2.99986i | 0.0587995 | + | 0.121560i | ||||
\(610\) | −32.7126 | −1.32450 | ||||||||
\(611\) | −18.3399 | − | 15.5229i | −0.741952 | − | 0.627991i | ||||
\(612\) | −0.0702857 | + | 0.121738i | −0.00284113 | + | 0.00492099i | ||||
\(613\) | 1.17548 | + | 2.03599i | 0.0474772 | + | 0.0822329i | 0.888787 | − | 0.458320i | \(-0.151549\pi\) |
−0.841310 | + | 0.540553i | \(0.818215\pi\) | |||||||
\(614\) | 5.69511 | 0.229836 | ||||||||
\(615\) | −18.3886 | − | 31.8501i | −0.741501 | − | 1.28432i | ||||
\(616\) | −7.30493 | + | 10.7543i | −0.294324 | + | 0.433302i | ||||
\(617\) | −16.1133 | − | 27.9090i | −0.648697 | − | 1.12358i | −0.983434 | − | 0.181264i | \(-0.941981\pi\) |
0.334738 | − | 0.942311i | \(-0.391352\pi\) | |||||||
\(618\) | 1.99107 | − | 3.44863i | 0.0800925 | − | 0.138724i | ||||
\(619\) | 9.49745 | − | 16.4501i | 0.381735 | − | 0.661184i | −0.609575 | − | 0.792728i | \(-0.708660\pi\) |
0.991310 | + | 0.131544i | \(0.0419934\pi\) | |||||||
\(620\) | 13.2723 | 0.533027 | ||||||||
\(621\) | −9.53690 | −0.382703 | ||||||||
\(622\) | 0.183797 | − | 0.318345i | 0.00736957 | − | 0.0127645i | ||||
\(623\) | 1.23587 | + | 2.55500i | 0.0495140 | + | 0.102364i | ||||
\(624\) | −2.75209 | − | 2.32938i | −0.110172 | − | 0.0932497i | ||||
\(625\) | −17.2165 | − | 29.8199i | −0.688662 | − | 1.19280i | ||||
\(626\) | −2.95742 | − | 5.12240i | −0.118202 | − | 0.204732i | ||||
\(627\) | −1.90891 | − | 3.30633i | −0.0762345 | − | 0.132042i | ||||
\(628\) | −8.85322 | + | 15.3342i | −0.353282 | + | 0.611902i | ||||
\(629\) | 1.56552 | 0.0624213 | ||||||||
\(630\) | −4.55096 | − | 9.40852i | −0.181315 | − | 0.374845i | ||||
\(631\) | −11.7271 | − | 20.3119i | −0.466849 | − | 0.808606i | 0.532434 | − | 0.846471i | \(-0.321277\pi\) |
−0.999283 | + | 0.0378658i | \(0.987944\pi\) | |||||||
\(632\) | 2.17517 | + | 3.76751i | 0.0865237 | + | 0.149863i | ||||
\(633\) | 6.70799 | 0.266618 | ||||||||
\(634\) | −4.28899 | − | 7.42875i | −0.170338 | − | 0.295033i | ||||
\(635\) | 42.8806 | 1.70166 | ||||||||
\(636\) | 11.0641 | 0.438719 | ||||||||
\(637\) | 8.05769 | − | 23.9181i | 0.319257 | − | 0.947668i | ||||
\(638\) | 6.18899 | 0.245024 | ||||||||
\(639\) | −3.87729 | −0.153383 | ||||||||
\(640\) | −1.97513 | − | 3.42102i | −0.0780738 | − | 0.135228i | ||||
\(641\) | 5.60442 | 0.221361 | 0.110681 | − | 0.993856i | \(-0.464697\pi\) | ||||
0.110681 | + | 0.993856i | \(0.464697\pi\) | |||||||
\(642\) | −3.53679 | − | 6.12590i | −0.139586 | − | 0.241770i | ||||
\(643\) | 11.5626 | + | 20.0270i | 0.455983 | + | 0.789786i | 0.998744 | − | 0.0501012i | \(-0.0159544\pi\) |
−0.542761 | + | 0.839887i | \(0.682621\pi\) | |||||||
\(644\) | −10.9872 | − | 22.7145i | −0.432955 | − | 0.895078i | ||||
\(645\) | −4.27601 | −0.168368 | ||||||||
\(646\) | 0.0546094 | − | 0.0945863i | 0.00214858 | − | 0.00372145i | ||||
\(647\) | −8.88782 | − | 15.3941i | −0.349416 | − | 0.605206i | 0.636730 | − | 0.771087i | \(-0.280287\pi\) |
−0.986146 | + | 0.165881i | \(0.946953\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | −1.05945 | − | 1.83503i | −0.0415872 | − | 0.0720312i | ||||
\(650\) | 6.80020 | − | 37.6255i | 0.266726 | − | 1.47579i | ||||
\(651\) | 3.87077 | + | 8.00232i | 0.151708 | + | 0.313636i | ||||
\(652\) | −1.63571 | + | 2.83313i | −0.0640593 | + | 0.110954i | ||||
\(653\) | 2.50502 | 0.0980290 | 0.0490145 | − | 0.998798i | \(-0.484392\pi\) | ||||
0.0490145 | + | 0.998798i | \(0.484392\pi\) | |||||||
\(654\) | −14.8470 | −0.580564 | ||||||||
\(655\) | −3.79916 | + | 6.58034i | −0.148445 | + | 0.257115i | ||||
\(656\) | 4.65505 | − | 8.06279i | 0.181749 | − | 0.314799i | ||||
\(657\) | −0.0817820 | − | 0.141650i | −0.00319062 | − | 0.00552631i | ||||
\(658\) | 9.90683 | − | 14.5848i | 0.386209 | − | 0.568573i | ||||
\(659\) | −15.8598 | − | 27.4700i | −0.617810 | − | 1.07008i | −0.989884 | − | 0.141876i | \(-0.954687\pi\) |
0.372074 | − | 0.928203i | \(-0.378647\pi\) | |||||||
\(660\) | −19.4107 | −0.755559 | ||||||||
\(661\) | −11.3573 | − | 19.6714i | −0.441747 | − | 0.765128i | 0.556072 | − | 0.831134i | \(-0.312308\pi\) |
−0.997819 | + | 0.0660056i | \(0.978974\pi\) | |||||||
\(662\) | 2.07489 | − | 3.59381i | 0.0806427 | − | 0.139677i | ||||
\(663\) | −0.386865 | − | 0.327444i | −0.0150246 | − | 0.0127169i | ||||
\(664\) | −10.5220 | −0.408335 | ||||||||
\(665\) | 3.53593 | + | 7.31007i | 0.137117 | + | 0.283473i | ||||
\(666\) | −5.56841 | + | 9.64476i | −0.215771 | + | 0.373727i | ||||
\(667\) | −6.00595 | + | 10.4026i | −0.232551 | + | 0.402791i | ||||
\(668\) | −4.42914 | + | 7.67150i | −0.171369 | + | 0.296819i | ||||
\(669\) | −2.05487 | −0.0794460 | ||||||||
\(670\) | −16.1887 | + | 28.0397i | −0.625424 | + | 1.08327i | ||||
\(671\) | −40.6917 | −1.57088 | ||||||||
\(672\) | 1.48662 | − | 2.18860i | 0.0573477 | − | 0.0844269i | ||||
\(673\) | −2.56027 | + | 4.43452i | −0.0986911 | + | 0.170938i | −0.911143 | − | 0.412090i | \(-0.864799\pi\) |
0.812452 | + | 0.583028i | \(0.198132\pi\) | |||||||
\(674\) | 18.5391 | 0.714100 | ||||||||
\(675\) | 5.30226 | − | 9.18378i | 0.204084 | − | 0.353484i | ||||
\(676\) | 10.0296 | − | 8.27088i | 0.385753 | − | 0.318111i | ||||
\(677\) | 1.02921 | + | 1.78264i | 0.0395556 | + | 0.0685123i | 0.885125 | − | 0.465353i | \(-0.154072\pi\) |
−0.845570 | + | 0.533865i | \(0.820739\pi\) | |||||||
\(678\) | 0.785895 | − | 1.36121i | 0.0301821 | − | 0.0522770i | ||||
\(679\) | −19.4479 | + | 28.6311i | −0.746342 | + | 1.09876i | ||||
\(680\) | −0.277647 | − | 0.480898i | −0.0106473 | − | 0.0184416i | ||||
\(681\) | −12.9149 | − | 22.3692i | −0.494899 | − | 0.857190i | ||||
\(682\) | 16.5095 | 0.632183 | ||||||||
\(683\) | −26.9289 | −1.03040 | −0.515202 | − | 0.857069i | \(-0.672283\pi\) | ||||
−0.515202 | + | 0.857069i | \(0.672283\pi\) | |||||||
\(684\) | 0.388481 | + | 0.672870i | 0.0148540 | + | 0.0257278i | ||||
\(685\) | −31.3692 | − | 54.3330i | −1.19856 | − | 2.07596i | ||||
\(686\) | 18.0770 | + | 4.02745i | 0.690185 | + | 0.153769i | ||||
\(687\) | −5.39496 | + | 9.34435i | −0.205831 | + | 0.356509i | ||||
\(688\) | −0.541233 | − | 0.937443i | −0.0206343 | − | 0.0357397i | ||||
\(689\) | −7.09489 | + | 39.2561i | −0.270294 | + | 1.49554i | ||||
\(690\) | 18.8366 | − | 32.6259i | 0.717097 | − | 1.24205i | ||||
\(691\) | 51.2761 | 1.95063 | 0.975316 | − | 0.220812i | \(-0.0708706\pi\) | ||||
0.975316 | + | 0.220812i | \(0.0708706\pi\) | |||||||
\(692\) | 7.47486 | − | 12.9468i | 0.284152 | − | 0.492165i | ||||
\(693\) | −5.66100 | − | 11.7034i | −0.215044 | − | 0.444575i | ||||
\(694\) | −22.9868 | −0.872568 | ||||||||
\(695\) | 11.6276 | − | 20.1396i | 0.441061 | − | 0.763939i | ||||
\(696\) | −1.25952 | −0.0477419 | ||||||||
\(697\) | 0.654367 | − | 1.13340i | 0.0247859 | − | 0.0429305i | ||||
\(698\) | 7.29494 | − | 12.6352i | 0.276118 | − | 0.478250i | ||||
\(699\) | 1.92109 | − | 3.32742i | 0.0726623 | − | 0.125855i | ||||
\(700\) | 27.9820 | + | 2.04832i | 1.05762 | + | 0.0774193i | ||||
\(701\) | −26.2809 | −0.992617 | −0.496308 | − | 0.868146i | \(-0.665311\pi\) | ||||
−0.496308 | + | 0.868146i | \(0.665311\pi\) | |||||||
\(702\) | 3.39335 | − | 1.21869i | 0.128074 | − | 0.0459965i | ||||
\(703\) | 4.32644 | − | 7.49362i | 0.163175 | − | 0.282627i | ||||
\(704\) | −2.45689 | − | 4.25545i | −0.0925974 | − | 0.160383i | ||||
\(705\) | 26.3244 | 0.991435 | ||||||||
\(706\) | 9.86522 | + | 17.0871i | 0.371283 | + | 0.643080i | ||||
\(707\) | −10.9791 | + | 16.1633i | −0.412910 | + | 0.607883i | ||||
\(708\) | 0.215609 | + | 0.373446i | 0.00810309 | + | 0.0140350i | ||||
\(709\) | −4.37966 | + | 7.58580i | −0.164482 | + | 0.284891i | −0.936471 | − | 0.350745i | \(-0.885928\pi\) |
0.771989 | + | 0.635635i | \(0.219262\pi\) | |||||||
\(710\) | 7.65815 | − | 13.2643i | 0.287405 | − | 0.497800i | ||||
\(711\) | −4.35034 | −0.163151 | ||||||||
\(712\) | −1.07274 | −0.0402026 | ||||||||
\(713\) | −16.0213 | + | 27.7496i | −0.600001 | + | 1.03923i | ||||
\(714\) | 0.208977 | − | 0.307654i | 0.00782076 | − | 0.0115137i | ||||
\(715\) | 12.4472 | − | 68.8703i | 0.465498 | − | 2.57560i | ||||
\(716\) | 11.6034 | + | 20.0977i | 0.433640 | + | 0.751087i | ||||
\(717\) | 5.12799 | + | 8.88194i | 0.191508 | + | 0.331702i | ||||
\(718\) | 18.8344 | + | 32.6222i | 0.702895 | + | 1.21745i | ||||
\(719\) | 1.13801 | − | 1.97109i | 0.0424405 | − | 0.0735091i | −0.844025 | − | 0.536304i | \(-0.819820\pi\) |
0.886465 | + | 0.462795i | \(0.153153\pi\) | |||||||
\(720\) | 3.95025 | 0.147217 | ||||||||
\(721\) | −5.91994 | + | 8.71528i | −0.220470 | + | 0.324574i | ||||
\(722\) | 9.19816 | + | 15.9317i | 0.342320 | + | 0.592916i | ||||
\(723\) | −0.316427 | − | 0.548068i | −0.0117681 | − | 0.0203829i | ||||
\(724\) | 19.4618 | 0.723291 | ||||||||
\(725\) | −6.67829 | − | 11.5671i | −0.248025 | − | 0.429592i | ||||
\(726\) | −13.1452 | −0.487863 | ||||||||
\(727\) | −39.8719 | −1.47877 | −0.739383 | − | 0.673285i | \(-0.764883\pi\) | ||||
−0.739383 | + | 0.673285i | \(0.764883\pi\) | |||||||
\(728\) | 6.81198 | + | 6.67809i | 0.252469 | + | 0.247506i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.646119 | 0.0239139 | ||||||||
\(731\) | −0.0760819 | − | 0.131778i | −0.00281399 | − | 0.00487398i | ||||
\(732\) | 8.28114 | 0.306080 | ||||||||
\(733\) | −12.8845 | − | 22.3167i | −0.475901 | − | 0.824284i | 0.523718 | − | 0.851892i | \(-0.324545\pi\) |
−0.999619 | + | 0.0276073i | \(0.991211\pi\) | |||||||
\(734\) | −1.25141 | − | 2.16750i | −0.0461903 | − | 0.0800039i | ||||
\(735\) | 10.1913 | + | 25.7052i | 0.375911 | + | 0.948152i | ||||
\(736\) | 9.53690 | 0.351535 | ||||||||
\(737\) | −20.1373 | + | 34.8789i | −0.741769 | + | 1.28478i | ||||
\(738\) | 4.65505 | + | 8.06279i | 0.171355 | + | 0.296795i | ||||
\(739\) | −6.40893 | − | 11.1006i | −0.235756 | − | 0.408342i | 0.723736 | − | 0.690077i | \(-0.242423\pi\) |
−0.959492 | + | 0.281735i | \(0.909090\pi\) | |||||||
\(740\) | −21.9966 | − | 38.0993i | −0.808612 | − | 1.40056i | ||||
\(741\) | −2.63650 | + | 0.946878i | −0.0968544 | + | 0.0347844i | ||||
\(742\) | −29.1947 | − | 2.13709i | −1.07177 | − | 0.0784551i | ||||
\(743\) | −10.1715 | + | 17.6176i | −0.373156 | + | 0.646326i | −0.990049 | − | 0.140721i | \(-0.955058\pi\) |
0.616893 | + | 0.787047i | \(0.288391\pi\) | |||||||
\(744\) | −3.35985 | −0.123178 | ||||||||
\(745\) | −52.4202 | −1.92053 | ||||||||
\(746\) | 6.58371 | − | 11.4033i | 0.241047 | − | 0.417505i | ||||
\(747\) | 5.26102 | − | 9.11236i | 0.192491 | − | 0.333404i | ||||
\(748\) | −0.345368 | − | 0.598195i | −0.0126279 | − | 0.0218722i | ||||
\(749\) | 8.14924 | + | 16.8475i | 0.297767 | + | 0.615594i | ||||
\(750\) | 11.0696 | + | 19.1731i | 0.404205 | + | 0.700104i | ||||
\(751\) | −30.4741 | −1.11202 | −0.556008 | − | 0.831177i | \(-0.687668\pi\) | ||||
−0.556008 | + | 0.831177i | \(0.687668\pi\) | |||||||
\(752\) | 3.33199 | + | 5.77118i | 0.121505 | + | 0.210453i | ||||
\(753\) | −7.53648 | + | 13.0536i | −0.274645 | + | 0.475698i | ||||
\(754\) | 0.807672 | − | 4.46886i | 0.0294137 | − | 0.162746i | ||||
\(755\) | 63.7400 | 2.31974 | ||||||||
\(756\) | 1.15207 | + | 2.38175i | 0.0419003 | + | 0.0866235i | ||||
\(757\) | 10.7264 | − | 18.5787i | 0.389859 | − | 0.675256i | −0.602571 | − | 0.798065i | \(-0.705857\pi\) |
0.992430 | + | 0.122809i | \(0.0391904\pi\) | |||||||
\(758\) | −5.93228 | + | 10.2750i | −0.215470 | + | 0.373205i | ||||
\(759\) | 23.4311 | − | 40.5838i | 0.850494 | − | 1.47310i | ||||
\(760\) | −3.06920 | −0.111332 | ||||||||
\(761\) | 25.0238 | − | 43.3425i | 0.907112 | − | 1.57116i | 0.0890544 | − | 0.996027i | \(-0.471615\pi\) |
0.818057 | − | 0.575137i | \(-0.195051\pi\) | |||||||
\(762\) | −10.8551 | −0.393240 | ||||||||
\(763\) | 39.1767 | + | 2.86779i | 1.41829 | + | 0.103821i | ||||
\(764\) | 7.29819 | − | 12.6408i | 0.264039 | − | 0.457329i | ||||
\(765\) | 0.555293 | 0.0200767 | ||||||||
\(766\) | −8.21139 | + | 14.2225i | −0.296690 | + | 0.513881i | ||||
\(767\) | −1.46327 | + | 0.525522i | −0.0528357 | + | 0.0189755i | ||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | 25.3820 | − | 43.9629i | 0.915298 | − | 1.58534i | 0.108833 | − | 0.994060i | \(-0.465289\pi\) |
0.806465 | − | 0.591282i | \(-0.201378\pi\) | |||||||
\(770\) | 51.2187 | + | 3.74928i | 1.84579 | + | 0.135115i | ||||
\(771\) | 5.56909 | + | 9.64595i | 0.200566 | + | 0.347390i | ||||
\(772\) | 0.884301 | + | 1.53165i | 0.0318267 | + | 0.0551255i | ||||
\(773\) | 14.2845 | 0.513778 | 0.256889 | − | 0.966441i | \(-0.417303\pi\) | ||||
0.256889 | + | 0.966441i | \(0.417303\pi\) | |||||||
\(774\) | 1.08247 | 0.0389084 | ||||||||
\(775\) | −17.8148 | − | 30.8561i | −0.639925 | − | 1.10838i | ||||
\(776\) | −6.54097 | − | 11.3293i | −0.234807 | − | 0.406698i | ||||
\(777\) | 16.5562 | − | 24.3740i | 0.593952 | − | 0.874411i | ||||
\(778\) | 9.03721 | − | 15.6529i | 0.324000 | − | 0.561184i | ||||
\(779\) | −3.61680 | − | 6.26448i | −0.129585 | − | 0.224448i | ||||
\(780\) | −2.53312 | + | 14.0158i | −0.0907003 | + | 0.501845i | ||||
\(781\) | 9.52607 | − | 16.4996i | 0.340870 | − | 0.590403i | ||||
\(782\) | 1.34062 | 0.0479403 | ||||||||
\(783\) | 0.629759 | − | 1.09077i | 0.0225058 | − | 0.0389811i | ||||
\(784\) | −4.34548 | + | 5.48788i | −0.155196 | + | 0.195996i | ||||
\(785\) | 69.9449 | 2.49644 | ||||||||
\(786\) | 0.961751 | − | 1.66580i | 0.0343045 | − | 0.0594172i | ||||
\(787\) | −6.53995 | −0.233124 | −0.116562 | − | 0.993183i | \(-0.537187\pi\) | ||||
−0.116562 | + | 0.993183i | \(0.537187\pi\) | |||||||
\(788\) | 2.92757 | − | 5.07070i | 0.104290 | − | 0.180636i | ||||
\(789\) | 8.58528 | − | 14.8701i | 0.305644 | − | 0.529391i | ||||
\(790\) | 8.59248 | − | 14.8826i | 0.305707 | − | 0.529500i | ||||
\(791\) | −2.33666 | + | 3.44001i | −0.0830821 | + | 0.122313i | ||||
\(792\) | 4.91377 | 0.174603 | ||||||||
\(793\) | −5.31033 | + | 29.3821i | −0.188575 | + | 1.04339i | ||||
\(794\) | 1.20491 | − | 2.08696i | 0.0427606 | − | 0.0740635i | ||||
\(795\) | −21.8530 | − | 37.8504i | −0.775044 | − | 1.34242i | ||||
\(796\) | 13.9227 | 0.493479 | ||||||||
\(797\) | −24.2958 | − | 42.0815i | −0.860601 | − | 1.49060i | −0.871350 | − | 0.490662i | \(-0.836755\pi\) |
0.0107495 | − | 0.999942i | \(-0.496578\pi\) | |||||||
\(798\) | −0.895114 | − | 1.85053i | −0.0316867 | − | 0.0655081i | ||||
\(799\) | 0.468383 | + | 0.811263i | 0.0165702 | + | 0.0287004i | ||||
\(800\) | −5.30226 | + | 9.18378i | −0.187463 | + | 0.324695i | ||||
\(801\) | 0.536369 | − | 0.929018i | 0.0189517 | − | 0.0328252i | ||||
\(802\) | −24.9243 | −0.880109 | ||||||||
\(803\) | 0.803716 | 0.0283625 | ||||||||
\(804\) | 4.09814 | − | 7.09819i | 0.144530 | − | 0.250334i | ||||
\(805\) | −56.0058 | + | 82.4514i | −1.97395 | + | 2.90603i | ||||
\(806\) | 2.15452 | − | 11.9210i | 0.0758897 | − | 0.419898i | ||||
\(807\) | 1.64355 | + | 2.84672i | 0.0578559 | + | 0.100209i | ||||
\(808\) | −3.69262 | − | 6.39580i | −0.129906 | − | 0.225003i | ||||
\(809\) | −20.8592 | − | 36.1291i | −0.733369 | − | 1.27023i | −0.955435 | − | 0.295201i | \(-0.904613\pi\) |
0.222066 | − | 0.975032i | \(-0.428720\pi\) | |||||||
\(810\) | −1.97513 | + | 3.42102i | −0.0693989 | + | 0.120202i | ||||
\(811\) | 2.40508 | 0.0844538 | 0.0422269 | − | 0.999108i | \(-0.486555\pi\) | ||||
0.0422269 | + | 0.999108i | \(0.486555\pi\) | |||||||
\(812\) | 3.32348 | + | 0.243283i | 0.116631 | + | 0.00853757i | ||||
\(813\) | 7.36304 | + | 12.7532i | 0.258233 | + | 0.447273i | ||||
\(814\) | −27.3619 | − | 47.3922i | −0.959034 | − | 1.66109i | ||||
\(815\) | 12.9229 | 0.452670 | ||||||||
\(816\) | 0.0702857 | + | 0.121738i | 0.00246049 | + | 0.00426170i | ||||
\(817\) | −0.841036 | −0.0294241 | ||||||||
\(818\) | 27.4769 | 0.960707 | ||||||||
\(819\) | −9.18939 | + | 2.56030i | −0.321103 | + | 0.0894643i | ||||
\(820\) | −36.7773 | −1.28432 | ||||||||
\(821\) | −0.453291 | −0.0158200 | −0.00790998 | − | 0.999969i | \(-0.502518\pi\) | ||||
−0.00790998 | + | 0.999969i | \(0.502518\pi\) | |||||||
\(822\) | 7.94106 | + | 13.7543i | 0.276976 | + | 0.479737i | ||||
\(823\) | −4.19063 | −0.146076 | −0.0730380 | − | 0.997329i | \(-0.523269\pi\) | ||||
−0.0730380 | + | 0.997329i | \(0.523269\pi\) | |||||||
\(824\) | −1.99107 | − | 3.44863i | −0.0693621 | − | 0.120139i | ||||
\(825\) | 26.0541 | + | 45.1270i | 0.907087 | + | 1.57112i | ||||
\(826\) | −0.496793 | − | 1.02706i | −0.0172856 | − | 0.0357358i | ||||
\(827\) | 1.35282 | 0.0470421 | 0.0235211 | − | 0.999723i | \(-0.492512\pi\) | ||||
0.0235211 | + | 0.999723i | \(0.492512\pi\) | |||||||
\(828\) | −4.76845 | + | 8.25920i | −0.165715 | + | 0.287027i | ||||
\(829\) | 24.1081 | + | 41.7564i | 0.837309 | + | 1.45026i | 0.892137 | + | 0.451765i | \(0.149206\pi\) |
−0.0548281 | + | 0.998496i | \(0.517461\pi\) | |||||||
\(830\) | 20.7824 | + | 35.9961i | 0.721367 | + | 1.24944i | ||||
\(831\) | 9.25021 | + | 16.0218i | 0.320886 | + | 0.555791i | ||||
\(832\) | −3.39335 | + | 1.21869i | −0.117643 | + | 0.0422505i | ||||
\(833\) | −0.610851 | + | 0.771439i | −0.0211647 | + | 0.0267288i | ||||
\(834\) | −2.94351 | + | 5.09831i | −0.101925 | + | 0.176540i | ||||
\(835\) | 34.9925 | 1.21096 | ||||||||
\(836\) | −3.81782 | −0.132042 | ||||||||
\(837\) | 1.67992 | − | 2.90971i | 0.0580667 | − | 0.100574i | ||||
\(838\) | −5.16655 | + | 8.94872i | −0.178475 | + | 0.309128i | ||||
\(839\) | 14.1093 | + | 24.4380i | 0.487107 | + | 0.843694i | 0.999890 | − | 0.0148244i | \(-0.00471891\pi\) |
−0.512783 | + | 0.858518i | \(0.671386\pi\) | |||||||
\(840\) | −10.4235 | − | 0.763015i | −0.359645 | − | 0.0263265i | ||||
\(841\) | 13.7068 | + | 23.7409i | 0.472649 | + | 0.818651i | ||||
\(842\) | −16.8702 | −0.581386 | ||||||||
\(843\) | −15.6731 | − | 27.1467i | −0.539812 | − | 0.934981i | ||||
\(844\) | 3.35399 | − | 5.80929i | 0.115449 | − | 0.199964i | ||||
\(845\) | −48.1046 | − | 17.9754i | −1.65485 | − | 0.618372i | ||||
\(846\) | −6.66398 | −0.229112 | ||||||||
\(847\) | 34.6860 | + | 2.53907i | 1.19183 | + | 0.0872434i | ||||
\(848\) | 5.53204 | − | 9.58177i | 0.189971 | − | 0.329039i | ||||
\(849\) | −7.35985 | + | 12.7476i | −0.252589 | + | 0.437498i | ||||
\(850\) | −0.745346 | + | 1.29098i | −0.0255652 | + | 0.0442801i | ||||
\(851\) | 106.211 | 3.64085 | ||||||||
\(852\) | −1.93865 | + | 3.35783i | −0.0664169 | + | 0.115037i | ||||
\(853\) | −3.29308 | −0.112753 | −0.0563764 | − | 0.998410i | \(-0.517955\pi\) | ||||
−0.0563764 | + | 0.998410i | \(0.517955\pi\) | |||||||
\(854\) | −21.8514 | − | 1.59955i | −0.747739 | − | 0.0547355i | ||||
\(855\) | 1.53460 | − | 2.65801i | 0.0524822 | − | 0.0909019i | ||||
\(856\) | −7.07358 | −0.241770 | ||||||||
\(857\) | 16.7918 | − | 29.0842i | 0.573596 | − | 0.993497i | −0.422597 | − | 0.906318i | \(-0.638881\pi\) |
0.996193 | − | 0.0871794i | \(-0.0277853\pi\) | |||||||
\(858\) | −3.15098 | + | 17.4344i | −0.107573 | + | 0.595201i | ||||
\(859\) | −13.6075 | − | 23.5688i | −0.464280 | − | 0.804157i | 0.534888 | − | 0.844923i | \(-0.320354\pi\) |
−0.999169 | + | 0.0407656i | \(0.987020\pi\) | |||||||
\(860\) | −2.13801 | + | 3.70314i | −0.0729054 | + | 0.126276i | ||||
\(861\) | −10.7259 | − | 22.1743i | −0.365537 | − | 0.755700i | ||||
\(862\) | −12.1718 | − | 21.0822i | −0.414573 | − | 0.718061i | ||||
\(863\) | −7.05959 | − | 12.2276i | −0.240311 | − | 0.416231i | 0.720492 | − | 0.693463i | \(-0.243916\pi\) |
−0.960803 | + | 0.277232i | \(0.910583\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −59.0552 | −2.00794 | ||||||||
\(866\) | 0.984059 | + | 1.70444i | 0.0334397 | + | 0.0579193i | ||||
\(867\) | −8.49012 | − | 14.7053i | −0.288340 | − | 0.499419i | ||||
\(868\) | 8.86560 | + | 0.648974i | 0.300918 | + | 0.0220276i | ||||
\(869\) | 10.6883 | − | 18.5127i | 0.362576 | − | 0.628000i | ||||
\(870\) | 2.48771 | + | 4.30884i | 0.0843412 | + | 0.146083i | ||||
\(871\) | 22.5569 | + | 19.0922i | 0.764312 | + | 0.646916i | ||||
\(872\) | −7.42350 | + | 12.8579i | −0.251391 | + | 0.435423i | ||||
\(873\) | 13.0819 | 0.442756 | ||||||||
\(874\) | 3.70491 | − | 6.41709i | 0.125320 | − | 0.217061i | ||||
\(875\) | −25.5059 | − | 52.7302i | −0.862257 | − | 1.78261i | ||||
\(876\) | −0.163564 | −0.00552631 | ||||||||
\(877\) | 4.00956 | − | 6.94476i | 0.135393 | − | 0.234508i | −0.790354 | − | 0.612650i | \(-0.790104\pi\) |
0.925748 | + | 0.378142i | \(0.123437\pi\) | |||||||
\(878\) | 20.2636 | 0.683863 | ||||||||
\(879\) | −8.39523 | + | 14.5410i | −0.283164 | + | 0.490454i | ||||
\(880\) | −9.70533 | + | 16.8101i | −0.327167 | + | 0.566669i | ||||
\(881\) | 13.1358 | − | 22.7519i | 0.442558 | − | 0.766532i | −0.555321 | − | 0.831636i | \(-0.687405\pi\) |
0.997878 | + | 0.0651039i | \(0.0207379\pi\) | |||||||
\(882\) | −2.57990 | − | 6.50724i | −0.0868698 | − | 0.219110i | ||||
\(883\) | −18.7341 | −0.630452 | −0.315226 | − | 0.949017i | \(-0.602080\pi\) | ||||
−0.315226 | + | 0.949017i | \(0.602080\pi\) | |||||||
\(884\) | −0.477008 | + | 0.171313i | −0.0160435 | + | 0.00576189i | ||||
\(885\) | 0.851711 | − | 1.47521i | 0.0286300 | − | 0.0495886i | ||||
\(886\) | −14.2707 | − | 24.7177i | −0.479435 | − | 0.830406i | ||||
\(887\) | −12.2377 | −0.410901 | −0.205450 | − | 0.978668i | \(-0.565866\pi\) | ||||
−0.205450 | + | 0.978668i | \(0.565866\pi\) | |||||||
\(888\) | 5.56841 | + | 9.64476i | 0.186863 | + | 0.323657i | ||||
\(889\) | 28.6434 | + | 2.09673i | 0.960667 | + | 0.0703222i | ||||
\(890\) | 2.11879 | + | 3.66986i | 0.0710221 | + | 0.123014i | ||||
\(891\) | −2.45689 | + | 4.25545i | −0.0823088 | + | 0.142563i | ||||
\(892\) | −1.02744 | + | 1.77957i | −0.0344011 | + | 0.0595845i | ||||
\(893\) | 5.17767 | 0.173264 | ||||||||
\(894\) | 13.2701 | 0.443818 | ||||||||
\(895\) | 45.8365 | − | 79.3911i | 1.53214 | − | 2.65375i | ||||
\(896\) | −1.15207 | − | 2.38175i | −0.0384879 | − | 0.0795687i | ||||
\(897\) | −26.2464 | − | 22.2150i | −0.876342 | − | 0.741739i | ||||
\(898\) | 12.1517 | + | 21.0474i | 0.405508 | + | 0.702360i | ||||
\(899\) | −2.11589 | − | 3.66484i | −0.0705690 | − | 0.122229i | ||||
\(900\) | −5.30226 | − | 9.18378i | −0.176742 | − | 0.306126i | ||||
\(901\) | 0.777647 | − | 1.34692i | 0.0259072 | − | 0.0448725i | ||||
\(902\) | −45.7477 | −1.52323 | ||||||||
\(903\) | −2.85629 | − | 0.209085i | −0.0950515 | − | 0.00695790i | ||||
\(904\) | −0.785895 | − | 1.36121i | −0.0261385 | − | 0.0452732i | ||||
\(905\) | −38.4395 | − | 66.5791i | −1.27777 | − | 2.21316i | ||||
\(906\) | −16.1357 | −0.536072 | ||||||||
\(907\) | 11.4450 | + | 19.8233i | 0.380024 | + | 0.658221i | 0.991065 | − | 0.133378i | \(-0.0425824\pi\) |
−0.611041 | + | 0.791599i | \(0.709249\pi\) | |||||||
\(908\) | −25.8298 | −0.857190 | ||||||||
\(909\) | 7.38523 | 0.244953 | ||||||||
\(910\) | 9.39135 | − | 36.4940i | 0.311320 | − | 1.20976i | ||||
\(911\) | 22.0074 | 0.729139 | 0.364570 | − | 0.931176i | \(-0.381216\pi\) | ||||
0.364570 | + | 0.931176i | \(0.381216\pi\) | |||||||
\(912\) | 0.776963 | 0.0257278 | ||||||||
\(913\) | 25.8515 | + | 44.7761i | 0.855559 | + | 1.48187i | ||||
\(914\) | −6.25302 | −0.206832 | ||||||||
\(915\) | −16.3563 | − | 28.3300i | −0.540723 | − | 0.936560i | ||||
\(916\) | 5.39496 | + | 9.34435i | 0.178255 | + | 0.308746i | ||||
\(917\) | −2.85952 | + | 4.20977i | −0.0944297 | + | 0.139019i | ||||
\(918\) | −0.140571 | −0.00463955 | ||||||||
\(919\) | −24.9601 | + | 43.2322i | −0.823358 | + | 1.42610i | 0.0798091 | + | 0.996810i | \(0.474569\pi\) |
−0.903167 | + | 0.429288i | \(0.858764\pi\) | |||||||
\(920\) | −18.8366 | − | 32.6259i | −0.621024 | − | 1.07565i | ||||
\(921\) | 2.84756 | + | 4.93211i | 0.0938302 | + | 0.162519i | ||||
\(922\) | 9.65625 | + | 16.7251i | 0.318012 | + | 0.550812i | ||||
\(923\) | −10.6707 | − | 9.03168i | −0.351229 | − | 0.297281i | ||||
\(924\) | −12.9659 | − | 0.949124i | −0.426548 | − | 0.0312239i | ||||
\(925\) | −59.0502 | + | 102.278i | −1.94156 | + | 3.36288i | ||||
\(926\) | 21.4480 | 0.704824 | ||||||||
\(927\) | 3.98214 | 0.130790 | ||||||||
\(928\) | −0.629759 | + | 1.09077i | −0.0206729 | + | 0.0358064i | ||||
\(929\) | −4.50148 | + | 7.79679i | −0.147689 | + | 0.255804i | −0.930373 | − | 0.366615i | \(-0.880517\pi\) |
0.782684 | + | 0.622419i | \(0.213850\pi\) | |||||||
\(930\) | 6.63613 | + | 11.4941i | 0.217607 | + | 0.376907i | ||||
\(931\) | 2.00449 | + | 5.05588i | 0.0656944 | + | 0.165700i | ||||
\(932\) | −1.92109 | − | 3.32742i | −0.0629274 | − | 0.108993i | ||||
\(933\) | 0.367593 | 0.0120345 | ||||||||
\(934\) | 2.39255 | + | 4.14402i | 0.0782866 | + | 0.135596i | ||||
\(935\) | −1.36429 | + | 2.36302i | −0.0446171 | + | 0.0772791i | ||||
\(936\) | 0.641255 | − | 3.54807i | 0.0209601 | − | 0.115972i | ||||
\(937\) | −42.4359 | −1.38632 | −0.693159 | − | 0.720784i | \(-0.743782\pi\) | ||||
−0.693159 | + | 0.720784i | \(0.743782\pi\) | |||||||
\(938\) | −12.1848 | + | 17.9384i | −0.397847 | + | 0.585708i | ||||
\(939\) | 2.95742 | − | 5.12240i | 0.0965117 | − | 0.167163i | ||||
\(940\) | 13.1622 | − | 22.7976i | 0.429304 | − | 0.743577i | ||||
\(941\) | −4.68568 | + | 8.11583i | −0.152749 | + | 0.264569i | −0.932237 | − | 0.361848i | \(-0.882146\pi\) |
0.779488 | + | 0.626417i | \(0.215479\pi\) | |||||||
\(942\) | −17.7064 | −0.576907 | ||||||||
\(943\) | 44.3948 | − | 76.8940i | 1.44569 | − | 2.50401i | ||||
\(944\) | 0.431218 | 0.0140350 | ||||||||
\(945\) | 5.87254 | − | 8.64551i | 0.191034 | − | 0.281238i | ||||
\(946\) | −2.65950 | + | 4.60638i | −0.0864677 | + | 0.149766i | ||||
\(947\) | −36.2822 | −1.17901 | −0.589507 | − | 0.807764i | \(-0.700678\pi\) | ||||
−0.589507 | + | 0.807764i | \(0.700678\pi\) | |||||||
\(948\) | −2.17517 | + | 3.76751i | −0.0706463 | + | 0.122363i | ||||
\(949\) | 0.104886 | − | 0.580336i | 0.00340475 | − | 0.0188385i | ||||
\(950\) | 4.11966 | + | 7.13545i | 0.133659 | + | 0.231505i | ||||
\(951\) | 4.28899 | − | 7.42875i | 0.139080 | − | 0.240894i | ||||
\(952\) | −0.161948 | − | 0.334806i | −0.00524876 | − | 0.0108511i | ||||
\(953\) | 9.41368 | + | 16.3050i | 0.304939 | + | 0.528170i | 0.977248 | − | 0.212101i | \(-0.0680306\pi\) |
−0.672309 | + | 0.740271i | \(0.734697\pi\) | |||||||
\(954\) | 5.53204 | + | 9.58177i | 0.179106 | + | 0.310221i | ||||
\(955\) | −57.6594 | −1.86581 | ||||||||
\(956\) | 10.2560 | 0.331702 | ||||||||
\(957\) | 3.09449 | + | 5.35982i | 0.100031 | + | 0.173258i | ||||
\(958\) | 5.85660 | + | 10.1439i | 0.189218 | + | 0.327735i | ||||
\(959\) | −18.2973 | − | 37.8273i | −0.590850 | − | 1.22151i | ||||
\(960\) | 1.97513 | − | 3.42102i | 0.0637470 | − | 0.110413i | ||||
\(961\) | 9.85571 | + | 17.0706i | 0.317926 | + | 0.550664i | ||||
\(962\) | −37.7910 | + | 13.5723i | −1.21843 | + | 0.437590i | ||||
\(963\) | 3.53679 | − | 6.12590i | 0.113971 | − | 0.197404i | ||||
\(964\) | −0.632854 | −0.0203829 | ||||||||
\(965\) | 3.49322 | − | 6.05043i | 0.112451 | − | 0.194770i | ||||
\(966\) | 14.1778 | − | 20.8724i | 0.456163 | − | 0.671559i | ||||
\(967\) | −9.63971 | −0.309992 | −0.154996 | − | 0.987915i | \(-0.549536\pi\) | ||||
−0.154996 | + | 0.987915i | \(0.549536\pi\) | |||||||
\(968\) | −6.57259 | + | 11.3841i | −0.211251 | + | 0.365897i | ||||
\(969\) | 0.109219 | 0.00350861 | ||||||||
\(970\) | −25.8385 | + | 44.7536i | −0.829624 | + | 1.43695i | ||||
\(971\) | −9.13666 | + | 15.8252i | −0.293209 | + | 0.507853i | −0.974567 | − | 0.224097i | \(-0.928057\pi\) |
0.681357 | + | 0.731951i | \(0.261390\pi\) | |||||||
\(972\) | 0.500000 | − | 0.866025i | 0.0160375 | − | 0.0277778i | ||||
\(973\) | 8.75178 | − | 12.8843i | 0.280569 | − | 0.413052i | ||||
\(974\) | −25.7570 | −0.825308 | ||||||||
\(975\) | 35.9848 | − | 12.9236i | 1.15243 | − | 0.413887i | ||||
\(976\) | 4.14057 | − | 7.17168i | 0.132536 | − | 0.229560i | ||||
\(977\) | −16.0432 | − | 27.7877i | −0.513268 | − | 0.889007i | −0.999882 | − | 0.0153892i | \(-0.995101\pi\) |
0.486613 | − | 0.873617i | \(-0.338232\pi\) | |||||||
\(978\) | −3.27142 | −0.104608 | ||||||||
\(979\) | 2.63560 | + | 4.56499i | 0.0842340 | + | 0.145898i | ||||
\(980\) | 27.3570 | + | 4.02672i | 0.873888 | + | 0.128629i | ||||
\(981\) | −7.42350 | − | 12.8579i | −0.237014 | − | 0.410521i | ||||
\(982\) | 2.35012 | − | 4.07053i | 0.0749954 | − | 0.129896i | ||||
\(983\) | −11.7559 | + | 20.3618i | −0.374955 | + | 0.649442i | −0.990320 | − | 0.138801i | \(-0.955675\pi\) |
0.615365 | + | 0.788242i | \(0.289009\pi\) | |||||||
\(984\) | 9.31010 | 0.296795 | ||||||||
\(985\) | −23.1293 | −0.736960 | ||||||||
\(986\) | −0.0885262 | + | 0.153332i | −0.00281925 | + | 0.00488308i | ||||
\(987\) | 17.5842 | + | 1.28719i | 0.559711 | + | 0.0409716i | ||||
\(988\) | −0.498231 | + | 2.75672i | −0.0158509 | + | 0.0877029i | ||||
\(989\) | −5.16168 | − | 8.94030i | −0.164132 | − | 0.284285i | ||||
\(990\) | −9.70533 | − | 16.8101i | −0.308456 | − | 0.534261i | ||||
\(991\) | −12.5930 | − | 21.8117i | −0.400029 | − | 0.692870i | 0.593700 | − | 0.804686i | \(-0.297667\pi\) |
−0.993729 | + | 0.111816i | \(0.964333\pi\) | |||||||
\(992\) | −1.67992 | + | 2.90971i | −0.0533376 | + | 0.0923835i | ||||
\(993\) | 4.14977 | 0.131689 | ||||||||
\(994\) | 5.76407 | − | 8.48583i | 0.182825 | − | 0.269154i | ||||
\(995\) | −27.4992 | − | 47.6300i | −0.871783 | − | 1.50997i | ||||
\(996\) | −5.26102 | − | 9.11236i | −0.166702 | − | 0.288736i | ||||
\(997\) | 14.9958 | 0.474921 | 0.237461 | − | 0.971397i | \(-0.423685\pi\) | ||||
0.237461 | + | 0.971397i | \(0.423685\pi\) | |||||||
\(998\) | 16.3247 | + | 28.2752i | 0.516749 | + | 0.895036i | ||||
\(999\) | −11.1368 | −0.352353 |
(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 | 546.2.j.d.529.1 | yes | 8 | |
3.2 | odd | 2 | 1638.2.m.g.1621.4 | 8 | |||
7.2 | even | 3 | 546.2.k.b.373.1 | yes | 8 | ||
13.3 | even | 3 | 546.2.k.b.445.1 | yes | 8 | ||
21.2 | odd | 6 | 1638.2.p.i.919.4 | 8 | |||
39.29 | odd | 6 | 1638.2.p.i.991.4 | 8 | |||
91.16 | even | 3 | inner | 546.2.j.d.289.1 | ✓ | 8 | |
273.107 | odd | 6 | 1638.2.m.g.289.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.j.d.289.1 | ✓ | 8 | 91.16 | even | 3 | inner | |
546.2.j.d.529.1 | yes | 8 | 1.1 | even | 1 | trivial | |
546.2.k.b.373.1 | yes | 8 | 7.2 | even | 3 | ||
546.2.k.b.445.1 | yes | 8 | 13.3 | even | 3 | ||
1638.2.m.g.289.4 | 8 | 273.107 | odd | 6 | |||
1638.2.m.g.1621.4 | 8 | 3.2 | odd | 2 | |||
1638.2.p.i.919.4 | 8 | 21.2 | odd | 6 | |||
1638.2.p.i.991.4 | 8 | 39.29 | odd | 6 |