Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,2,Mod(139,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.139");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.u (of order \(4\), 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: | \(2.68297350792\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(32\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 139.5 | ||
Character | \(\chi\) | \(=\) | 336.139 |
Dual form | 336.2.u.a.307.5 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.20526 | + | 0.739825i | −0.852250 | + | 0.523135i | ||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | 0.905318 | − | 1.78337i | 0.452659 | − | 0.891684i | ||||
\(5\) | −1.32544 | + | 1.32544i | −0.592756 | + | 0.592756i | −0.938375 | − | 0.345619i | \(-0.887669\pi\) |
0.345619 | + | 0.938375i | \(0.387669\pi\) | |||||||
\(6\) | 0.329115 | − | 1.37538i | 0.134360 | − | 0.561499i | ||||
\(7\) | 2.64192 | + | 0.142388i | 0.998551 | + | 0.0538175i | ||||
\(8\) | 0.228233 | + | 2.81920i | 0.0806925 | + | 0.996739i | ||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0.616912 | − | 2.57810i | 0.195085 | − | 0.815268i | ||||
\(11\) | −1.18514 | + | 1.18514i | −0.357332 | + | 0.357332i | −0.862829 | − | 0.505497i | \(-0.831309\pi\) |
0.505497 | + | 0.862829i | \(0.331309\pi\) | |||||||
\(12\) | 0.620874 | + | 1.90119i | 0.179231 | + | 0.548826i | ||||
\(13\) | 2.02086 | + | 2.02086i | 0.560487 | + | 0.560487i | 0.929446 | − | 0.368959i | \(-0.120286\pi\) |
−0.368959 | + | 0.929446i | \(0.620286\pi\) | |||||||
\(14\) | −3.28955 | + | 1.78294i | −0.879168 | + | 0.476511i | ||||
\(15\) | − | 1.87446i | − | 0.483983i | ||||||
\(16\) | −2.36080 | − | 3.22903i | −0.590199 | − | 0.807257i | ||||
\(17\) | 0.276387i | 0.0670337i | 0.999438 | + | 0.0335169i | \(0.0106707\pi\) | ||||
−0.999438 | + | 0.0335169i | \(0.989329\pi\) | |||||||
\(18\) | 0.739825 | + | 1.20526i | 0.174378 | + | 0.284083i | ||||
\(19\) | −4.58131 | + | 4.58131i | −1.05102 | + | 1.05102i | −0.0523978 | + | 0.998626i | \(0.516686\pi\) |
−0.998626 | + | 0.0523978i | \(0.983314\pi\) | |||||||
\(20\) | 1.16380 | + | 3.56370i | 0.260235 | + | 0.796868i | ||||
\(21\) | −1.96880 | + | 1.76743i | −0.429628 | + | 0.385686i | ||||
\(22\) | 0.551607 | − | 2.30519i | 0.117603 | − | 0.491469i | ||||
\(23\) | −1.81753 | −0.378981 | −0.189491 | − | 0.981883i | \(-0.560684\pi\) | ||||
−0.189491 | + | 0.981883i | \(0.560684\pi\) | |||||||
\(24\) | −2.15486 | − | 1.83209i | −0.439860 | − | 0.373974i | ||||
\(25\) | 1.48640i | 0.297280i | ||||||||
\(26\) | −3.93076 | − | 0.940587i | −0.770885 | − | 0.184464i | ||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 2.64571 | − | 4.58260i | 0.499991 | − | 0.866030i | ||||
\(29\) | −2.64137 | + | 2.64137i | −0.490490 | + | 0.490490i | −0.908461 | − | 0.417970i | \(-0.862742\pi\) |
0.417970 | + | 0.908461i | \(0.362742\pi\) | |||||||
\(30\) | 1.38677 | + | 2.25922i | 0.253189 | + | 0.412475i | ||||
\(31\) | −7.11326 | −1.27758 | −0.638790 | − | 0.769382i | \(-0.720565\pi\) | ||||
−0.638790 | + | 0.769382i | \(0.720565\pi\) | |||||||
\(32\) | 5.23430 | + | 2.14525i | 0.925302 | + | 0.379231i | ||||
\(33\) | − | 1.67603i | − | 0.291760i | ||||||
\(34\) | −0.204478 | − | 0.333119i | −0.0350677 | − | 0.0571295i | ||||
\(35\) | −3.69044 | + | 3.31298i | −0.623798 | + | 0.559997i | ||||
\(36\) | −1.78337 | − | 0.905318i | −0.297228 | − | 0.150886i | ||||
\(37\) | −0.786692 | − | 0.786692i | −0.129331 | − | 0.129331i | 0.639478 | − | 0.768809i | \(-0.279150\pi\) |
−0.768809 | + | 0.639478i | \(0.779150\pi\) | |||||||
\(38\) | 2.13232 | − | 8.91105i | 0.345907 | − | 1.44556i | ||||
\(39\) | −2.85793 | −0.457636 | ||||||||
\(40\) | −4.03920 | − | 3.43419i | −0.638654 | − | 0.542992i | ||||
\(41\) | 7.33055 | 1.14484 | 0.572420 | − | 0.819961i | \(-0.306005\pi\) | ||||
0.572420 | + | 0.819961i | \(0.306005\pi\) | |||||||
\(42\) | 1.06533 | − | 3.58679i | 0.164384 | − | 0.553454i | ||||
\(43\) | −1.69851 | + | 1.69851i | −0.259020 | + | 0.259020i | −0.824656 | − | 0.565635i | \(-0.808631\pi\) |
0.565635 | + | 0.824656i | \(0.308631\pi\) | |||||||
\(44\) | 1.04061 | + | 3.18646i | 0.156877 | + | 0.480376i | ||||
\(45\) | 1.32544 | + | 1.32544i | 0.197585 | + | 0.197585i | ||||
\(46\) | 2.19060 | − | 1.34465i | 0.322987 | − | 0.198258i | ||||
\(47\) | −11.5721 | −1.68796 | −0.843982 | − | 0.536372i | \(-0.819795\pi\) | ||||
−0.843982 | + | 0.536372i | \(0.819795\pi\) | |||||||
\(48\) | 3.95261 | + | 0.613933i | 0.570509 | + | 0.0886136i | ||||
\(49\) | 6.95945 | + | 0.752353i | 0.994207 | + | 0.107479i | ||||
\(50\) | −1.09968 | − | 1.79150i | −0.155518 | − | 0.253357i | ||||
\(51\) | −0.195435 | − | 0.195435i | −0.0273664 | − | 0.0273664i | ||||
\(52\) | 5.43347 | − | 1.77442i | 0.753487 | − | 0.246067i | ||||
\(53\) | 3.85262 | + | 3.85262i | 0.529198 | + | 0.529198i | 0.920333 | − | 0.391135i | \(-0.127917\pi\) |
−0.391135 | + | 0.920333i | \(0.627917\pi\) | |||||||
\(54\) | −1.37538 | − | 0.329115i | −0.187166 | − | 0.0447868i | ||||
\(55\) | − | 3.14166i | − | 0.423621i | ||||||
\(56\) | 0.201552 | + | 7.48060i | 0.0269336 | + | 0.999637i | ||||
\(57\) | − | 6.47895i | − | 0.858158i | ||||||
\(58\) | 1.22939 | − | 5.13770i | 0.161427 | − | 0.674613i | ||||
\(59\) | 4.25247 | + | 4.25247i | 0.553625 | + | 0.553625i | 0.927485 | − | 0.373860i | \(-0.121966\pi\) |
−0.373860 | + | 0.927485i | \(0.621966\pi\) | |||||||
\(60\) | −3.34285 | − | 1.69698i | −0.431560 | − | 0.219080i | ||||
\(61\) | 1.14204 | + | 1.14204i | 0.146223 | + | 0.146223i | 0.776428 | − | 0.630206i | \(-0.217029\pi\) |
−0.630206 | + | 0.776428i | \(0.717029\pi\) | |||||||
\(62\) | 8.57335 | − | 5.26257i | 1.08882 | − | 0.668347i | ||||
\(63\) | 0.142388 | − | 2.64192i | 0.0179392 | − | 0.332850i | ||||
\(64\) | −7.89582 | + | 1.28687i | −0.986977 | + | 0.160859i | ||||
\(65\) | −5.35708 | −0.664464 | ||||||||
\(66\) | 1.23997 | + | 2.02006i | 0.152630 | + | 0.248653i | ||||
\(67\) | −3.05161 | − | 3.05161i | −0.372813 | − | 0.372813i | 0.495688 | − | 0.868501i | \(-0.334916\pi\) |
−0.868501 | + | 0.495688i | \(0.834916\pi\) | |||||||
\(68\) | 0.492900 | + | 0.250218i | 0.0597729 | + | 0.0303434i | ||||
\(69\) | 1.28519 | − | 1.28519i | 0.154718 | − | 0.154718i | ||||
\(70\) | 1.99692 | − | 6.72330i | 0.238678 | − | 0.803588i | ||||
\(71\) | 8.36612 | 0.992876 | 0.496438 | − | 0.868072i | \(-0.334641\pi\) | ||||
0.496438 | + | 0.868072i | \(0.334641\pi\) | |||||||
\(72\) | 2.81920 | − | 0.228233i | 0.332246 | − | 0.0268975i | ||||
\(73\) | 16.9603 | 1.98505 | 0.992527 | − | 0.122024i | \(-0.0389386\pi\) | ||||
0.992527 | + | 0.122024i | \(0.0389386\pi\) | |||||||
\(74\) | 1.53018 | + | 0.366156i | 0.177880 | + | 0.0425648i | ||||
\(75\) | −1.05104 | − | 1.05104i | −0.121364 | − | 0.121364i | ||||
\(76\) | 4.02261 | + | 12.3177i | 0.461425 | + | 1.41294i | ||||
\(77\) | −3.29978 | + | 2.96228i | −0.376045 | + | 0.337583i | ||||
\(78\) | 3.44456 | − | 2.11437i | 0.390020 | − | 0.239405i | ||||
\(79\) | 13.8414i | 1.55728i | 0.627470 | + | 0.778641i | \(0.284091\pi\) | ||||
−0.627470 | + | 0.778641i | \(0.715909\pi\) | |||||||
\(80\) | 7.40900 | + | 1.15079i | 0.828351 | + | 0.128663i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −8.83525 | + | 5.42333i | −0.975690 | + | 0.598906i | ||||
\(83\) | 9.90941 | − | 9.90941i | 1.08770 | − | 1.08770i | 0.0919340 | − | 0.995765i | \(-0.470695\pi\) |
0.995765 | − | 0.0919340i | \(-0.0293049\pi\) | |||||||
\(84\) | 1.36959 | + | 5.11119i | 0.149435 | + | 0.557676i | ||||
\(85\) | −0.366336 | − | 0.366336i | −0.0397347 | − | 0.0397347i | ||||
\(86\) | 0.790551 | − | 3.30375i | 0.0852474 | − | 0.356253i | ||||
\(87\) | − | 3.73546i | − | 0.400484i | ||||||
\(88\) | −3.61163 | − | 3.07065i | −0.385001 | − | 0.327333i | ||||
\(89\) | 7.94992 | 0.842690 | 0.421345 | − | 0.906901i | \(-0.361558\pi\) | ||||
0.421345 | + | 0.906901i | \(0.361558\pi\) | |||||||
\(90\) | −2.57810 | − | 0.616912i | −0.271756 | − | 0.0650282i | ||||
\(91\) | 5.05121 | + | 5.62670i | 0.529511 | + | 0.589839i | ||||
\(92\) | −1.64544 | + | 3.24132i | −0.171549 | + | 0.337931i | ||||
\(93\) | 5.02983 | − | 5.02983i | 0.521569 | − | 0.521569i | ||||
\(94\) | 13.9474 | − | 8.56132i | 1.43857 | − | 0.883033i | ||||
\(95\) | − | 12.1445i | − | 1.24600i | ||||||
\(96\) | −5.21813 | + | 2.18428i | −0.532573 | + | 0.222933i | ||||
\(97\) | − | 13.1657i | − | 1.33678i | −0.743812 | − | 0.668388i | \(-0.766984\pi\) | ||
0.743812 | − | 0.668388i | \(-0.233016\pi\) | |||||||
\(98\) | −8.94458 | + | 4.24199i | −0.903539 | + | 0.428506i | ||||
\(99\) | 1.18514 | + | 1.18514i | 0.119111 | + | 0.119111i | ||||
\(100\) | 2.65080 | + | 1.34566i | 0.265080 | + | 0.134566i | ||||
\(101\) | −1.20635 | + | 1.20635i | −0.120036 | + | 0.120036i | −0.764573 | − | 0.644537i | \(-0.777050\pi\) |
0.644537 | + | 0.764573i | \(0.277050\pi\) | |||||||
\(102\) | 0.380139 | + | 0.0909630i | 0.0376393 | + | 0.00900668i | ||||
\(103\) | − | 11.4220i | − | 1.12544i | −0.826647 | − | 0.562722i | \(-0.809754\pi\) | ||
0.826647 | − | 0.562722i | \(-0.190246\pi\) | |||||||
\(104\) | −5.23600 | + | 6.15846i | −0.513432 | + | 0.603886i | ||||
\(105\) | 0.266900 | − | 4.95217i | 0.0260468 | − | 0.483282i | ||||
\(106\) | −7.49369 | − | 1.79316i | −0.727852 | − | 0.174167i | ||||
\(107\) | 9.18783 | − | 9.18783i | 0.888221 | − | 0.888221i | −0.106131 | − | 0.994352i | \(-0.533846\pi\) |
0.994352 | + | 0.106131i | \(0.0338464\pi\) | |||||||
\(108\) | 1.90119 | − | 0.620874i | 0.182942 | − | 0.0597437i | ||||
\(109\) | 0.541341 | − | 0.541341i | 0.0518511 | − | 0.0518511i | −0.680706 | − | 0.732557i | \(-0.738327\pi\) |
0.732557 | + | 0.680706i | \(0.238327\pi\) | |||||||
\(110\) | 2.32428 | + | 3.78653i | 0.221611 | + | 0.361031i | ||||
\(111\) | 1.11255 | 0.105599 | ||||||||
\(112\) | −5.77726 | − | 8.86698i | −0.545900 | − | 0.837851i | ||||
\(113\) | −11.9427 | −1.12347 | −0.561735 | − | 0.827317i | \(-0.689866\pi\) | ||||
−0.561735 | + | 0.827317i | \(0.689866\pi\) | |||||||
\(114\) | 4.79329 | + | 7.80884i | 0.448932 | + | 0.731365i | ||||
\(115\) | 2.40903 | − | 2.40903i | 0.224644 | − | 0.224644i | ||||
\(116\) | 2.31925 | + | 7.10182i | 0.215337 | + | 0.659387i | ||||
\(117\) | 2.02086 | − | 2.02086i | 0.186829 | − | 0.186829i | ||||
\(118\) | −8.27144 | − | 1.97926i | −0.761447 | − | 0.182206i | ||||
\(119\) | −0.0393541 | + | 0.730192i | −0.00360759 | + | 0.0669366i | ||||
\(120\) | 5.28448 | − | 0.427813i | 0.482405 | − | 0.0390538i | ||||
\(121\) | 8.19091i | 0.744628i | ||||||||
\(122\) | −2.22136 | − | 0.531547i | −0.201113 | − | 0.0481240i | ||||
\(123\) | −5.18348 | + | 5.18348i | −0.467379 | + | 0.467379i | ||||
\(124\) | −6.43976 | + | 12.6856i | −0.578308 | + | 1.13920i | ||||
\(125\) | −8.59736 | − | 8.59736i | −0.768971 | − | 0.768971i | ||||
\(126\) | 1.78294 | + | 3.28955i | 0.158837 | + | 0.293056i | ||||
\(127\) | 18.8618i | 1.67371i | 0.547422 | + | 0.836857i | \(0.315609\pi\) | ||||
−0.547422 | + | 0.836857i | \(0.684391\pi\) | |||||||
\(128\) | 8.56448 | − | 7.39254i | 0.757000 | − | 0.653414i | ||||
\(129\) | − | 2.40206i | − | 0.211489i | ||||||
\(130\) | 6.45669 | − | 3.96330i | 0.566289 | − | 0.347605i | ||||
\(131\) | −8.80983 | + | 8.80983i | −0.769718 | + | 0.769718i | −0.978057 | − | 0.208339i | \(-0.933194\pi\) |
0.208339 | + | 0.978057i | \(0.433194\pi\) | |||||||
\(132\) | −2.98899 | − | 1.51735i | −0.260158 | − | 0.132068i | ||||
\(133\) | −12.7558 | + | 11.4511i | −1.10606 | + | 0.992937i | ||||
\(134\) | 5.93565 | + | 1.42033i | 0.512762 | + | 0.122698i | ||||
\(135\) | −1.87446 | −0.161328 | ||||||||
\(136\) | −0.779192 | + | 0.0630806i | −0.0668151 | + | 0.00540912i | ||||
\(137\) | 4.34380i | 0.371116i | 0.982633 | + | 0.185558i | \(0.0594092\pi\) | ||||
−0.982633 | + | 0.185558i | \(0.940591\pi\) | |||||||
\(138\) | −0.598176 | + | 2.49980i | −0.0509201 | + | 0.212797i | ||||
\(139\) | 1.64886 | + | 1.64886i | 0.139854 | + | 0.139854i | 0.773568 | − | 0.633714i | \(-0.218470\pi\) |
−0.633714 | + | 0.773568i | \(0.718470\pi\) | |||||||
\(140\) | 2.56725 | + | 9.58071i | 0.216972 | + | 0.809718i | ||||
\(141\) | 8.18271 | − | 8.18271i | 0.689108 | − | 0.689108i | ||||
\(142\) | −10.0834 | + | 6.18946i | −0.846178 | + | 0.519408i | ||||
\(143\) | −4.79000 | −0.400560 | ||||||||
\(144\) | −3.22903 | + | 2.36080i | −0.269086 | + | 0.196733i | ||||
\(145\) | − | 7.00197i | − | 0.581482i | ||||||
\(146\) | −20.4416 | + | 12.5477i | −1.69176 | + | 1.03845i | ||||
\(147\) | −5.45307 | + | 4.38908i | −0.449762 | + | 0.362005i | ||||
\(148\) | −2.11517 | + | 0.690754i | −0.173866 | + | 0.0567796i | ||||
\(149\) | −10.1553 | − | 10.1553i | −0.831955 | − | 0.831955i | 0.155829 | − | 0.987784i | \(-0.450195\pi\) |
−0.987784 | + | 0.155829i | \(0.950195\pi\) | |||||||
\(150\) | 2.04437 | + | 0.489196i | 0.166922 | + | 0.0399427i | ||||
\(151\) | −8.92611 | −0.726397 | −0.363198 | − | 0.931712i | \(-0.618315\pi\) | ||||
−0.363198 | + | 0.931712i | \(0.618315\pi\) | |||||||
\(152\) | −13.9612 | − | 11.8700i | −1.13241 | − | 0.962787i | ||||
\(153\) | 0.276387 | 0.0223446 | ||||||||
\(154\) | 1.78553 | − | 6.01159i | 0.143882 | − | 0.484427i | ||||
\(155\) | 9.42822 | − | 9.42822i | 0.757293 | − | 0.757293i | ||||
\(156\) | −2.58734 | + | 5.09675i | −0.207153 | + | 0.408066i | ||||
\(157\) | −5.83300 | − | 5.83300i | −0.465524 | − | 0.465524i | 0.434937 | − | 0.900461i | \(-0.356771\pi\) |
−0.900461 | + | 0.434937i | \(0.856771\pi\) | |||||||
\(158\) | −10.2402 | − | 16.6826i | −0.814669 | − | 1.32719i | ||||
\(159\) | −5.44843 | −0.432089 | ||||||||
\(160\) | −9.78118 | + | 4.09435i | −0.773270 | + | 0.323687i | ||||
\(161\) | −4.80176 | − | 0.258794i | −0.378432 | − | 0.0203958i | ||||
\(162\) | 1.20526 | − | 0.739825i | 0.0946944 | − | 0.0581261i | ||||
\(163\) | 12.4751 | + | 12.4751i | 0.977129 | + | 0.977129i | 0.999744 | − | 0.0226151i | \(-0.00719923\pi\) |
−0.0226151 | + | 0.999744i | \(0.507199\pi\) | |||||||
\(164\) | 6.63648 | − | 13.0731i | 0.518222 | − | 1.02084i | ||||
\(165\) | 2.22149 | + | 2.22149i | 0.172943 | + | 0.172943i | ||||
\(166\) | −4.61222 | + | 19.2747i | −0.357978 | + | 1.49600i | ||||
\(167\) | − | 21.3378i | − | 1.65117i | −0.564280 | − | 0.825584i | \(-0.690846\pi\) | ||
0.564280 | − | 0.825584i | \(-0.309154\pi\) | |||||||
\(168\) | −5.43210 | − | 5.14706i | −0.419096 | − | 0.397105i | ||||
\(169\) | − | 4.83221i | − | 0.371709i | ||||||
\(170\) | 0.712555 | + | 0.170507i | 0.0546505 | + | 0.0130773i | ||||
\(171\) | 4.58131 | + | 4.58131i | 0.350341 | + | 0.350341i | ||||
\(172\) | 1.49138 | + | 4.56676i | 0.113716 | + | 0.348212i | ||||
\(173\) | 10.7377 | + | 10.7377i | 0.816371 | + | 0.816371i | 0.985580 | − | 0.169209i | \(-0.0541213\pi\) |
−0.169209 | + | 0.985580i | \(0.554121\pi\) | |||||||
\(174\) | 2.76359 | + | 4.50221i | 0.209507 | + | 0.341312i | ||||
\(175\) | −0.211645 | + | 3.92695i | −0.0159989 | + | 0.296849i | ||||
\(176\) | 6.62470 | + | 1.02897i | 0.499356 | + | 0.0775618i | ||||
\(177\) | −6.01391 | −0.452033 | ||||||||
\(178\) | −9.58174 | + | 5.88155i | −0.718182 | + | 0.440841i | ||||
\(179\) | 2.41822 | + | 2.41822i | 0.180746 | + | 0.180746i | 0.791681 | − | 0.610935i | \(-0.209206\pi\) |
−0.610935 | + | 0.791681i | \(0.709206\pi\) | |||||||
\(180\) | 3.56370 | − | 1.16380i | 0.265623 | − | 0.0867448i | ||||
\(181\) | −0.318290 | + | 0.318290i | −0.0236583 | + | 0.0236583i | −0.718837 | − | 0.695179i | \(-0.755325\pi\) |
0.695179 | + | 0.718837i | \(0.255325\pi\) | |||||||
\(182\) | −10.2508 | − | 3.04465i | −0.759841 | − | 0.225684i | ||||
\(183\) | −1.61508 | −0.119390 | ||||||||
\(184\) | −0.414820 | − | 5.12399i | −0.0305809 | − | 0.377745i | ||||
\(185\) | 2.08543 | 0.153324 | ||||||||
\(186\) | −2.34108 | + | 9.78347i | −0.171656 | + | 0.717359i | ||||
\(187\) | −0.327556 | − | 0.327556i | −0.0239533 | − | 0.0239533i | ||||
\(188\) | −10.4764 | + | 20.6373i | −0.764072 | + | 1.50513i | ||||
\(189\) | 1.76743 | + | 1.96880i | 0.128562 | + | 0.143209i | ||||
\(190\) | 8.98482 | + | 14.6374i | 0.651828 | + | 1.06191i | ||||
\(191\) | − | 24.4401i | − | 1.76842i | −0.467088 | − | 0.884211i | \(-0.654697\pi\) | ||
0.467088 | − | 0.884211i | \(-0.345303\pi\) | |||||||
\(192\) | 4.67323 | − | 6.49314i | 0.337262 | − | 0.468602i | ||||
\(193\) | 22.3910 | 1.61174 | 0.805871 | − | 0.592091i | \(-0.201698\pi\) | ||||
0.805871 | + | 0.592091i | \(0.201698\pi\) | |||||||
\(194\) | 9.74033 | + | 15.8682i | 0.699315 | + | 1.13927i | ||||
\(195\) | 3.78803 | − | 3.78803i | 0.271266 | − | 0.271266i | ||||
\(196\) | 7.64224 | − | 11.7301i | 0.545874 | − | 0.837867i | ||||
\(197\) | 13.4527 | + | 13.4527i | 0.958463 | + | 0.958463i | 0.999171 | − | 0.0407083i | \(-0.0129614\pi\) |
−0.0407083 | + | 0.999171i | \(0.512961\pi\) | |||||||
\(198\) | −2.30519 | − | 0.551607i | −0.163823 | − | 0.0392010i | ||||
\(199\) | 5.64437i | 0.400119i | 0.979784 | + | 0.200059i | \(0.0641135\pi\) | ||||
−0.979784 | + | 0.200059i | \(0.935886\pi\) | |||||||
\(200\) | −4.19046 | + | 0.339245i | −0.296311 | + | 0.0239883i | ||||
\(201\) | 4.31563 | 0.304401 | ||||||||
\(202\) | 0.561482 | − | 2.34646i | 0.0395057 | − | 0.165096i | ||||
\(203\) | −7.35438 | + | 6.60218i | −0.516176 | + | 0.463382i | ||||
\(204\) | −0.525464 | + | 0.171602i | −0.0367898 | + | 0.0120145i | ||||
\(205\) | −9.71623 | + | 9.71623i | −0.678611 | + | 0.678611i | ||||
\(206\) | 8.45028 | + | 13.7665i | 0.588759 | + | 0.959159i | ||||
\(207\) | 1.81753i | 0.126327i | ||||||||
\(208\) | 1.75458 | − | 11.2963i | 0.121658 | − | 0.783256i | ||||
\(209\) | − | 10.8589i | − | 0.751129i | ||||||
\(210\) | 3.34205 | + | 6.16612i | 0.230624 | + | 0.425503i | ||||
\(211\) | −13.9095 | − | 13.9095i | −0.957568 | − | 0.957568i | 0.0415678 | − | 0.999136i | \(-0.486765\pi\) |
−0.999136 | + | 0.0415678i | \(0.986765\pi\) | |||||||
\(212\) | 10.3585 | − | 3.38279i | 0.711424 | − | 0.232331i | ||||
\(213\) | −5.91574 | + | 5.91574i | −0.405340 | + | 0.405340i | ||||
\(214\) | −4.27637 | + | 17.8711i | −0.292326 | + | 1.22165i | ||||
\(215\) | − | 4.50256i | − | 0.307072i | ||||||
\(216\) | −1.83209 | + | 2.15486i | −0.124658 | + | 0.146620i | ||||
\(217\) | −18.7926 | − | 1.01284i | −1.27573 | − | 0.0687561i | ||||
\(218\) | −0.251961 | + | 1.05296i | −0.0170649 | + | 0.0713152i | ||||
\(219\) | −11.9928 | + | 11.9928i | −0.810395 | + | 0.810395i | ||||
\(220\) | −5.60273 | − | 2.84420i | −0.377736 | − | 0.191756i | ||||
\(221\) | −0.558541 | + | 0.558541i | −0.0375715 | + | 0.0375715i | ||||
\(222\) | −1.34092 | + | 0.823092i | −0.0899963 | + | 0.0552423i | ||||
\(223\) | 15.4893 | 1.03724 | 0.518622 | − | 0.855004i | \(-0.326445\pi\) | ||||
0.518622 | + | 0.855004i | \(0.326445\pi\) | |||||||
\(224\) | 13.5231 | + | 6.41288i | 0.903552 | + | 0.428479i | ||||
\(225\) | 1.48640 | 0.0990933 | ||||||||
\(226\) | 14.3940 | − | 8.83548i | 0.957478 | − | 0.587727i | ||||
\(227\) | 4.24437 | − | 4.24437i | 0.281709 | − | 0.281709i | −0.552081 | − | 0.833790i | \(-0.686166\pi\) |
0.833790 | + | 0.552081i | \(0.186166\pi\) | |||||||
\(228\) | −11.5543 | − | 5.86551i | −0.765205 | − | 0.388453i | ||||
\(229\) | 2.39096 | − | 2.39096i | 0.157999 | − | 0.157999i | −0.623680 | − | 0.781679i | \(-0.714363\pi\) |
0.781679 | + | 0.623680i | \(0.214363\pi\) | |||||||
\(230\) | −1.12126 | + | 4.68578i | −0.0739334 | + | 0.308971i | ||||
\(231\) | 0.238647 | − | 4.42795i | 0.0157018 | − | 0.291337i | ||||
\(232\) | −8.04941 | − | 6.84371i | −0.528470 | − | 0.449312i | ||||
\(233\) | 2.92061i | 0.191336i | 0.995413 | + | 0.0956678i | \(0.0304987\pi\) | ||||
−0.995413 | + | 0.0956678i | \(0.969501\pi\) | |||||||
\(234\) | −0.940587 | + | 3.93076i | −0.0614881 | + | 0.256962i | ||||
\(235\) | 15.3382 | − | 15.3382i | 1.00055 | − | 1.00055i | ||||
\(236\) | 11.4336 | − | 3.73388i | 0.744262 | − | 0.243055i | ||||
\(237\) | −9.78736 | − | 9.78736i | −0.635758 | − | 0.635758i | ||||
\(238\) | −0.492782 | − | 0.909189i | −0.0319423 | − | 0.0589339i | ||||
\(239\) | − | 7.83859i | − | 0.507036i | −0.967331 | − | 0.253518i | \(-0.918412\pi\) | ||
0.967331 | − | 0.253518i | \(-0.0815877\pi\) | |||||||
\(240\) | −6.05269 | + | 4.42522i | −0.390699 | + | 0.285647i | ||||
\(241\) | 18.3656i | 1.18303i | 0.806293 | + | 0.591516i | \(0.201470\pi\) | ||||
−0.806293 | + | 0.591516i | \(0.798530\pi\) | |||||||
\(242\) | −6.05984 | − | 9.87220i | −0.389541 | − | 0.634609i | ||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 3.07058 | − | 1.00276i | 0.196574 | − | 0.0641954i | ||||
\(245\) | −10.2216 | + | 8.22716i | −0.653031 | + | 0.525614i | ||||
\(246\) | 2.41259 | − | 10.0823i | 0.153821 | − | 0.642826i | ||||
\(247\) | −18.5164 | −1.17817 | ||||||||
\(248\) | −1.62348 | − | 20.0537i | −0.103091 | − | 1.27341i | ||||
\(249\) | 14.0140i | 0.888103i | ||||||||
\(250\) | 16.7226 | + | 4.00154i | 1.05763 | + | 0.253079i | ||||
\(251\) | 16.2774 | + | 16.2774i | 1.02742 | + | 1.02742i | 0.999613 | + | 0.0278042i | \(0.00885149\pi\) |
0.0278042 | + | 0.999613i | \(0.491149\pi\) | |||||||
\(252\) | −4.58260 | − | 2.64571i | −0.288677 | − | 0.166664i | ||||
\(253\) | 2.15402 | − | 2.15402i | 0.135422 | − | 0.135422i | ||||
\(254\) | −13.9544 | − | 22.7334i | −0.875578 | − | 1.42642i | ||||
\(255\) | 0.518077 | 0.0324432 | ||||||||
\(256\) | −4.85327 | + | 15.2462i | −0.303329 | + | 0.952886i | ||||
\(257\) | − | 13.6309i | − | 0.850274i | −0.905129 | − | 0.425137i | \(-0.860226\pi\) | ||
0.905129 | − | 0.425137i | \(-0.139774\pi\) | |||||||
\(258\) | 1.77710 | + | 2.89511i | 0.110637 | + | 0.180242i | ||||
\(259\) | −1.96636 | − | 2.19039i | −0.122184 | − | 0.136104i | ||||
\(260\) | −4.84986 | + | 9.55365i | −0.300776 | + | 0.592492i | ||||
\(261\) | 2.64137 | + | 2.64137i | 0.163497 | + | 0.163497i | ||||
\(262\) | 4.10043 | − | 17.1359i | 0.253325 | − | 1.05866i | ||||
\(263\) | 5.88266 | 0.362740 | 0.181370 | − | 0.983415i | \(-0.441947\pi\) | ||||
0.181370 | + | 0.983415i | \(0.441947\pi\) | |||||||
\(264\) | 4.72508 | − | 0.382526i | 0.290809 | − | 0.0235429i | ||||
\(265\) | −10.2129 | −0.627371 | ||||||||
\(266\) | 6.90222 | − | 23.2386i | 0.423203 | − | 1.42485i | ||||
\(267\) | −5.62144 | + | 5.62144i | −0.344027 | + | 0.344027i | ||||
\(268\) | −8.20481 | + | 2.67946i | −0.501189 | + | 0.163674i | ||||
\(269\) | −7.28207 | − | 7.28207i | −0.443995 | − | 0.443995i | 0.449357 | − | 0.893352i | \(-0.351653\pi\) |
−0.893352 | + | 0.449357i | \(0.851653\pi\) | |||||||
\(270\) | 2.25922 | − | 1.38677i | 0.137492 | − | 0.0843963i | ||||
\(271\) | 7.65390 | 0.464941 | 0.232471 | − | 0.972603i | \(-0.425319\pi\) | ||||
0.232471 | + | 0.972603i | \(0.425319\pi\) | |||||||
\(272\) | 0.892462 | − | 0.652494i | 0.0541135 | − | 0.0395633i | ||||
\(273\) | −7.55042 | − | 0.406935i | −0.456972 | − | 0.0246288i | ||||
\(274\) | −3.21365 | − | 5.23542i | −0.194144 | − | 0.316283i | ||||
\(275\) | −1.76159 | − | 1.76159i | −0.106228 | − | 0.106228i | ||||
\(276\) | −1.12846 | − | 3.45547i | −0.0679252 | − | 0.207995i | ||||
\(277\) | −20.9351 | − | 20.9351i | −1.25787 | − | 1.25787i | −0.952109 | − | 0.305758i | \(-0.901090\pi\) |
−0.305758 | − | 0.952109i | \(-0.598910\pi\) | |||||||
\(278\) | −3.20717 | − | 0.767440i | −0.192353 | − | 0.0460280i | ||||
\(279\) | 7.11326i | 0.425860i | ||||||||
\(280\) | −10.1823 | − | 9.64797i | −0.608506 | − | 0.576576i | ||||
\(281\) | 13.2903i | 0.792835i | 0.918070 | + | 0.396417i | \(0.129747\pi\) | ||||
−0.918070 | + | 0.396417i | \(0.870253\pi\) | |||||||
\(282\) | −3.80854 | + | 15.9161i | −0.226796 | + | 0.947789i | ||||
\(283\) | 7.97242 | + | 7.97242i | 0.473911 | + | 0.473911i | 0.903178 | − | 0.429267i | \(-0.141228\pi\) |
−0.429267 | + | 0.903178i | \(0.641228\pi\) | |||||||
\(284\) | 7.57400 | − | 14.9199i | 0.449434 | − | 0.885331i | ||||
\(285\) | 8.58748 | + | 8.58748i | 0.508678 | + | 0.508678i | ||||
\(286\) | 5.77321 | − | 3.54376i | 0.341377 | − | 0.209547i | ||||
\(287\) | 19.3667 | + | 1.04378i | 1.14318 | + | 0.0616124i | ||||
\(288\) | 2.14525 | − | 5.23430i | 0.126410 | − | 0.308434i | ||||
\(289\) | 16.9236 | 0.995506 | ||||||||
\(290\) | 5.18024 | + | 8.43922i | 0.304194 | + | 0.495568i | ||||
\(291\) | 9.30957 | + | 9.30957i | 0.545737 | + | 0.545737i | ||||
\(292\) | 15.3545 | − | 30.2465i | 0.898553 | − | 1.77004i | ||||
\(293\) | −11.7572 | + | 11.7572i | −0.686863 | + | 0.686863i | −0.961537 | − | 0.274674i | \(-0.911430\pi\) |
0.274674 | + | 0.961537i | \(0.411430\pi\) | |||||||
\(294\) | 3.32523 | − | 9.32431i | 0.193931 | − | 0.543805i | ||||
\(295\) | −11.2728 | −0.656329 | ||||||||
\(296\) | 2.03829 | − | 2.39739i | 0.118473 | − | 0.139346i | ||||
\(297\) | −1.67603 | −0.0972534 | ||||||||
\(298\) | 19.7530 | + | 4.72667i | 1.14426 | + | 0.273808i | ||||
\(299\) | −3.67298 | − | 3.67298i | −0.212414 | − | 0.212414i | ||||
\(300\) | −2.82593 | + | 0.922868i | −0.163155 | + | 0.0532818i | ||||
\(301\) | −4.72917 | + | 4.24548i | −0.272585 | + | 0.244705i | ||||
\(302\) | 10.7583 | − | 6.60376i | 0.619071 | − | 0.380004i | ||||
\(303\) | − | 1.70604i | − | 0.0980093i | ||||||
\(304\) | 25.6087 | + | 3.97764i | 1.46876 | + | 0.228133i | ||||
\(305\) | −3.02741 | −0.173349 | ||||||||
\(306\) | −0.333119 | + | 0.204478i | −0.0190432 | + | 0.0116892i | ||||
\(307\) | 20.0939 | − | 20.0939i | 1.14682 | − | 1.14682i | 0.159645 | − | 0.987174i | \(-0.448965\pi\) |
0.987174 | − | 0.159645i | \(-0.0510350\pi\) | |||||||
\(308\) | 2.29549 | + | 8.56653i | 0.130797 | + | 0.488123i | ||||
\(309\) | 8.07657 | + | 8.07657i | 0.459460 | + | 0.459460i | ||||
\(310\) | −4.38825 | + | 18.3387i | −0.249236 | + | 1.04157i | ||||
\(311\) | 26.0652i | 1.47802i | 0.673693 | + | 0.739012i | \(0.264707\pi\) | ||||
−0.673693 | + | 0.739012i | \(0.735293\pi\) | |||||||
\(312\) | −0.652274 | − | 8.05710i | −0.0369278 | − | 0.456143i | ||||
\(313\) | 13.5651 | 0.766743 | 0.383372 | − | 0.923594i | \(-0.374763\pi\) | ||||
0.383372 | + | 0.923594i | \(0.374763\pi\) | |||||||
\(314\) | 11.3457 | + | 2.71490i | 0.640275 | + | 0.153211i | ||||
\(315\) | 3.31298 | + | 3.69044i | 0.186666 | + | 0.207933i | ||||
\(316\) | 24.6843 | + | 12.5309i | 1.38860 | + | 0.704918i | ||||
\(317\) | 21.5304 | − | 21.5304i | 1.20927 | − | 1.20927i | 0.238004 | − | 0.971264i | \(-0.423507\pi\) |
0.971264 | − | 0.238004i | \(-0.0764931\pi\) | |||||||
\(318\) | 6.56679 | − | 4.03089i | 0.368247 | − | 0.226041i | ||||
\(319\) | − | 6.26077i | − | 0.350536i | ||||||
\(320\) | 8.75979 | − | 12.1711i | 0.489687 | − | 0.680387i | ||||
\(321\) | 12.9935i | 0.725229i | ||||||||
\(322\) | 5.97885 | − | 3.24055i | 0.333188 | − | 0.180589i | ||||
\(323\) | −1.26621 | − | 1.26621i | −0.0704541 | − | 0.0704541i | ||||
\(324\) | −0.905318 | + | 1.78337i | −0.0502955 | + | 0.0990760i | ||||
\(325\) | −3.00381 | + | 3.00381i | −0.166622 | + | 0.166622i | ||||
\(326\) | −24.2653 | − | 5.80641i | −1.34393 | − | 0.321587i | ||||
\(327\) | 0.765572i | 0.0423362i | ||||||||
\(328\) | 1.67307 | + | 20.6663i | 0.0923800 | + | 1.14111i | ||||
\(329\) | −30.5725 | − | 1.64772i | −1.68552 | − | 0.0908420i | ||||
\(330\) | −4.32099 | − | 1.03397i | −0.237863 | − | 0.0569180i | ||||
\(331\) | 5.85042 | − | 5.85042i | 0.321568 | − | 0.321568i | −0.527800 | − | 0.849369i | \(-0.676983\pi\) |
0.849369 | + | 0.527800i | \(0.176983\pi\) | |||||||
\(332\) | −8.70095 | − | 26.6433i | −0.477527 | − | 1.46224i | ||||
\(333\) | −0.786692 | + | 0.786692i | −0.0431104 | + | 0.0431104i | ||||
\(334\) | 15.7862 | + | 25.7176i | 0.863784 | + | 1.40721i | ||||
\(335\) | 8.08947 | 0.441975 | ||||||||
\(336\) | 10.3550 | + | 2.18476i | 0.564914 | + | 0.119189i | ||||
\(337\) | 11.1243 | 0.605980 | 0.302990 | − | 0.952994i | \(-0.402015\pi\) | ||||
0.302990 | + | 0.952994i | \(0.402015\pi\) | |||||||
\(338\) | 3.57499 | + | 5.82409i | 0.194454 | + | 0.316789i | ||||
\(339\) | 8.44474 | − | 8.44474i | 0.458655 | − | 0.458655i | ||||
\(340\) | −0.984961 | + | 0.321661i | −0.0534170 | + | 0.0174445i | ||||
\(341\) | 8.43018 | − | 8.43018i | 0.456520 | − | 0.456520i | ||||
\(342\) | −8.91105 | − | 2.13232i | −0.481854 | − | 0.115302i | ||||
\(343\) | 18.2792 | + | 2.97859i | 0.986982 | + | 0.160829i | ||||
\(344\) | −5.17610 | − | 4.40079i | −0.279077 | − | 0.237275i | ||||
\(345\) | 3.40689i | 0.183421i | ||||||||
\(346\) | −20.8857 | − | 4.99773i | −1.12282 | − | 0.268680i | ||||
\(347\) | −16.7722 | + | 16.7722i | −0.900379 | + | 0.900379i | −0.995469 | − | 0.0950894i | \(-0.969686\pi\) |
0.0950894 | + | 0.995469i | \(0.469686\pi\) | |||||||
\(348\) | −6.66170 | − | 3.38178i | −0.357105 | − | 0.181283i | ||||
\(349\) | −11.9769 | − | 11.9769i | −0.641110 | − | 0.641110i | 0.309718 | − | 0.950828i | \(-0.399765\pi\) |
−0.950828 | + | 0.309718i | \(0.899765\pi\) | |||||||
\(350\) | −2.65016 | − | 4.88958i | −0.141657 | − | 0.261359i | ||||
\(351\) | 2.85793i | 0.152545i | ||||||||
\(352\) | −8.74577 | + | 3.66094i | −0.466151 | + | 0.195129i | ||||
\(353\) | 34.7417i | 1.84912i | 0.381041 | + | 0.924558i | \(0.375566\pi\) | ||||
−0.381041 | + | 0.924558i | \(0.624434\pi\) | |||||||
\(354\) | 7.24834 | − | 4.44924i | 0.385245 | − | 0.236474i | ||||
\(355\) | −11.0888 | + | 11.0888i | −0.588533 | + | 0.588533i | ||||
\(356\) | 7.19721 | − | 14.1776i | 0.381451 | − | 0.751413i | ||||
\(357\) | −0.488496 | − | 0.544151i | −0.0258540 | − | 0.0287995i | ||||
\(358\) | −4.70364 | − | 1.12553i | −0.248595 | − | 0.0594861i | ||||
\(359\) | 22.2884 | 1.17634 | 0.588168 | − | 0.808739i | \(-0.299850\pi\) | ||||
0.588168 | + | 0.808739i | \(0.299850\pi\) | |||||||
\(360\) | −3.43419 | + | 4.03920i | −0.180997 | + | 0.212885i | ||||
\(361\) | − | 22.9768i | − | 1.20930i | ||||||
\(362\) | 0.148144 | − | 0.619102i | 0.00778629 | − | 0.0325393i | ||||
\(363\) | −5.79185 | − | 5.79185i | −0.303993 | − | 0.303993i | ||||
\(364\) | 14.6074 | − | 3.91421i | 0.765637 | − | 0.205160i | ||||
\(365\) | −22.4799 | + | 22.4799i | −1.17665 | + | 1.17665i | ||||
\(366\) | 1.94660 | − | 1.19488i | 0.101750 | − | 0.0624573i | ||||
\(367\) | −35.3887 | −1.84728 | −0.923639 | − | 0.383264i | \(-0.874800\pi\) | ||||
−0.923639 | + | 0.383264i | \(0.874800\pi\) | |||||||
\(368\) | 4.29082 | + | 5.86886i | 0.223675 | + | 0.305935i | ||||
\(369\) | − | 7.33055i | − | 0.381613i | ||||||
\(370\) | −2.51349 | + | 1.54285i | −0.130670 | + | 0.0802091i | ||||
\(371\) | 9.62974 | + | 10.7269i | 0.499951 | + | 0.556912i | ||||
\(372\) | −4.41644 | − | 13.5236i | −0.228982 | − | 0.701168i | ||||
\(373\) | 6.16397 | + | 6.16397i | 0.319158 | + | 0.319158i | 0.848444 | − | 0.529285i | \(-0.177540\pi\) |
−0.529285 | + | 0.848444i | \(0.677540\pi\) | |||||||
\(374\) | 0.637126 | + | 0.152457i | 0.0329450 | + | 0.00788337i | ||||
\(375\) | 12.1585 | 0.627862 | ||||||||
\(376\) | −2.64113 | − | 32.6241i | −0.136206 | − | 1.68246i | ||||
\(377\) | −10.6757 | −0.549827 | ||||||||
\(378\) | −3.58679 | − | 1.06533i | −0.184485 | − | 0.0547947i | ||||
\(379\) | 7.14409 | − | 7.14409i | 0.366967 | − | 0.366967i | −0.499403 | − | 0.866370i | \(-0.666447\pi\) |
0.866370 | + | 0.499403i | \(0.166447\pi\) | |||||||
\(380\) | −21.6582 | − | 10.9947i | −1.11104 | − | 0.564014i | ||||
\(381\) | −13.3373 | − | 13.3373i | −0.683291 | − | 0.683291i | ||||
\(382\) | 18.0814 | + | 29.4567i | 0.925123 | + | 1.50714i | ||||
\(383\) | 15.8856 | 0.811718 | 0.405859 | − | 0.913936i | \(-0.366972\pi\) | ||||
0.405859 | + | 0.913936i | \(0.366972\pi\) | |||||||
\(384\) | −0.828688 | + | 11.2833i | −0.0422888 | + | 0.575799i | ||||
\(385\) | 0.447334 | − | 8.30001i | 0.0227982 | − | 0.423007i | ||||
\(386\) | −26.9871 | + | 16.5654i | −1.37361 | + | 0.843159i | ||||
\(387\) | 1.69851 | + | 1.69851i | 0.0863401 | + | 0.0863401i | ||||
\(388\) | −23.4793 | − | 11.9192i | −1.19198 | − | 0.605104i | ||||
\(389\) | 3.30347 | + | 3.30347i | 0.167493 | + | 0.167493i | 0.785876 | − | 0.618384i | \(-0.212212\pi\) |
−0.618384 | + | 0.785876i | \(0.712212\pi\) | |||||||
\(390\) | −1.76309 | + | 7.36805i | −0.0892777 | + | 0.373096i | ||||
\(391\) | − | 0.502342i | − | 0.0254045i | ||||||
\(392\) | −0.532661 | + | 19.7918i | −0.0269034 | + | 0.999638i | ||||
\(393\) | − | 12.4590i | − | 0.628472i | ||||||
\(394\) | −26.1666 | − | 6.26139i | −1.31826 | − | 0.315444i | ||||
\(395\) | −18.3460 | − | 18.3460i | −0.923088 | − | 0.923088i | ||||
\(396\) | 3.18646 | − | 1.04061i | 0.160125 | − | 0.0522925i | ||||
\(397\) | 11.0837 | + | 11.0837i | 0.556274 | + | 0.556274i | 0.928244 | − | 0.371971i | \(-0.121318\pi\) |
−0.371971 | + | 0.928244i | \(0.621318\pi\) | |||||||
\(398\) | −4.17585 | − | 6.80295i | −0.209316 | − | 0.341001i | ||||
\(399\) | 0.922522 | − | 17.1168i | 0.0461839 | − | 0.856914i | ||||
\(400\) | 4.79963 | − | 3.50909i | 0.239981 | − | 0.175454i | ||||
\(401\) | −12.6471 | −0.631566 | −0.315783 | − | 0.948831i | \(-0.602267\pi\) | ||||
−0.315783 | + | 0.948831i | \(0.602267\pi\) | |||||||
\(402\) | −5.20146 | + | 3.19281i | −0.259425 | + | 0.159243i | ||||
\(403\) | −14.3749 | − | 14.3749i | −0.716066 | − | 0.716066i | ||||
\(404\) | 1.05924 | + | 3.24350i | 0.0526989 | + | 0.161370i | ||||
\(405\) | 1.32544 | − | 1.32544i | 0.0658618 | − | 0.0658618i | ||||
\(406\) | 3.97950 | − | 13.3983i | 0.197499 | − | 0.664948i | ||||
\(407\) | 1.86467 | 0.0924284 | ||||||||
\(408\) | 0.506367 | − | 0.595576i | 0.0250689 | − | 0.0294854i | ||||
\(409\) | −6.39999 | −0.316459 | −0.158230 | − | 0.987402i | \(-0.550579\pi\) | ||||
−0.158230 | + | 0.987402i | \(0.550579\pi\) | |||||||
\(410\) | 4.52231 | − | 18.8989i | 0.223341 | − | 0.933352i | ||||
\(411\) | −3.07153 | − | 3.07153i | −0.151507 | − | 0.151507i | ||||
\(412\) | −20.3696 | − | 10.3405i | −1.00354 | − | 0.509442i | ||||
\(413\) | 10.6292 | + | 11.8402i | 0.523028 | + | 0.582617i | ||||
\(414\) | −1.34465 | − | 2.19060i | −0.0660861 | − | 0.107662i | ||||
\(415\) | 26.2687i | 1.28948i | ||||||||
\(416\) | 6.24254 | + | 14.9131i | 0.306066 | + | 0.731174i | ||||
\(417\) | −2.33183 | −0.114190 | ||||||||
\(418\) | 8.03372 | + | 13.0879i | 0.392942 | + | 0.640149i | ||||
\(419\) | −3.92319 | + | 3.92319i | −0.191660 | + | 0.191660i | −0.796413 | − | 0.604753i | \(-0.793272\pi\) |
0.604753 | + | 0.796413i | \(0.293272\pi\) | |||||||
\(420\) | −8.58990 | − | 4.95927i | −0.419144 | − | 0.241988i | ||||
\(421\) | −19.9120 | − | 19.9120i | −0.970449 | − | 0.970449i | 0.0291264 | − | 0.999576i | \(-0.490727\pi\) |
−0.999576 | + | 0.0291264i | \(0.990727\pi\) | |||||||
\(422\) | 27.0552 | + | 6.47400i | 1.31702 | + | 0.315149i | ||||
\(423\) | 11.5721i | 0.562655i | ||||||||
\(424\) | −9.98203 | + | 11.7406i | −0.484770 | + | 0.570175i | ||||
\(425\) | −0.410822 | −0.0199278 | ||||||||
\(426\) | 2.75341 | − | 11.5066i | 0.133403 | − | 0.557498i | ||||
\(427\) | 2.85455 | + | 3.17978i | 0.138142 | + | 0.153880i | ||||
\(428\) | −8.06736 | − | 24.7032i | −0.389951 | − | 1.19407i | ||||
\(429\) | 3.38704 | − | 3.38704i | 0.163528 | − | 0.163528i | ||||
\(430\) | 3.33110 | + | 5.42677i | 0.160640 | + | 0.261702i | ||||
\(431\) | 23.6983i | 1.14151i | 0.821122 | + | 0.570753i | \(0.193349\pi\) | ||||
−0.821122 | + | 0.570753i | \(0.806651\pi\) | |||||||
\(432\) | 0.613933 | − | 3.95261i | 0.0295379 | − | 0.190170i | ||||
\(433\) | 25.8198i | 1.24082i | 0.784278 | + | 0.620410i | \(0.213034\pi\) | ||||
−0.784278 | + | 0.620410i | \(0.786966\pi\) | |||||||
\(434\) | 23.3994 | − | 12.6825i | 1.12321 | − | 0.608781i | ||||
\(435\) | 4.95114 | + | 4.95114i | 0.237389 | + | 0.237389i | ||||
\(436\) | −0.475324 | − | 1.45550i | −0.0227639 | − | 0.0697056i | ||||
\(437\) | 8.32666 | − | 8.32666i | 0.398318 | − | 0.398318i | ||||
\(438\) | 5.58188 | − | 23.3270i | 0.266713 | − | 1.11461i | ||||
\(439\) | 13.7981i | 0.658548i | 0.944234 | + | 0.329274i | \(0.106804\pi\) | ||||
−0.944234 | + | 0.329274i | \(0.893196\pi\) | |||||||
\(440\) | 8.85698 | − | 0.717030i | 0.422240 | − | 0.0341831i | ||||
\(441\) | 0.752353 | − | 6.95945i | 0.0358263 | − | 0.331402i | ||||
\(442\) | 0.259966 | − | 1.08641i | 0.0123653 | − | 0.0516753i | ||||
\(443\) | 9.61155 | − | 9.61155i | 0.456658 | − | 0.456658i | −0.440898 | − | 0.897557i | \(-0.645340\pi\) |
0.897557 | + | 0.440898i | \(0.145340\pi\) | |||||||
\(444\) | 1.00721 | − | 1.98408i | 0.0478001 | − | 0.0941605i | ||||
\(445\) | −10.5372 | + | 10.5372i | −0.499510 | + | 0.499510i | ||||
\(446\) | −18.6687 | + | 11.4594i | −0.883990 | + | 0.542619i | ||||
\(447\) | 14.3618 | 0.679288 | ||||||||
\(448\) | −21.0433 | + | 2.27554i | −0.994204 | + | 0.107509i | ||||
\(449\) | −27.2681 | −1.28686 | −0.643430 | − | 0.765505i | \(-0.722489\pi\) | ||||
−0.643430 | + | 0.765505i | \(0.722489\pi\) | |||||||
\(450\) | −1.79150 | + | 1.09968i | −0.0844523 | + | 0.0518392i | ||||
\(451\) | −8.68770 | + | 8.68770i | −0.409088 | + | 0.409088i | ||||
\(452\) | −10.8119 | + | 21.2981i | −0.508549 | + | 1.00178i | ||||
\(453\) | 6.31171 | − | 6.31171i | 0.296550 | − | 0.296550i | ||||
\(454\) | −1.97549 | + | 8.25567i | −0.0927144 | + | 0.387458i | ||||
\(455\) | −14.1530 | − | 0.762782i | −0.663501 | − | 0.0357598i | ||||
\(456\) | 18.2655 | − | 1.47871i | 0.855359 | − | 0.0692469i | ||||
\(457\) | − | 15.7041i | − | 0.734607i | −0.930101 | − | 0.367303i | \(-0.880281\pi\) | ||
0.930101 | − | 0.367303i | \(-0.119719\pi\) | |||||||
\(458\) | −1.11284 | + | 4.65062i | −0.0519997 | + | 0.217309i | ||||
\(459\) | −0.195435 | + | 0.195435i | −0.00912214 | + | 0.00912214i | ||||
\(460\) | −2.11525 | − | 6.47713i | −0.0986240 | − | 0.301998i | ||||
\(461\) | −8.60225 | − | 8.60225i | −0.400647 | − | 0.400647i | 0.477814 | − | 0.878461i | \(-0.341429\pi\) |
−0.878461 | + | 0.477814i | \(0.841429\pi\) | |||||||
\(462\) | 2.98827 | + | 5.51340i | 0.139027 | + | 0.256506i | ||||
\(463\) | 1.85673i | 0.0862897i | 0.999069 | + | 0.0431449i | \(0.0137377\pi\) | ||||
−0.999069 | + | 0.0431449i | \(0.986262\pi\) | |||||||
\(464\) | 14.7648 | + | 2.29332i | 0.685439 | + | 0.106465i | ||||
\(465\) | 13.3335i | 0.618327i | ||||||||
\(466\) | −2.16074 | − | 3.52011i | −0.100094 | − | 0.163066i | ||||
\(467\) | −12.0605 | + | 12.0605i | −0.558093 | + | 0.558093i | −0.928764 | − | 0.370671i | \(-0.879128\pi\) |
0.370671 | + | 0.928764i | \(0.379128\pi\) | |||||||
\(468\) | −1.77442 | − | 5.43347i | −0.0820225 | − | 0.251162i | ||||
\(469\) | −7.62758 | − | 8.49661i | −0.352209 | − | 0.392337i | ||||
\(470\) | −7.13896 | + | 29.8341i | −0.329296 | + | 1.37614i | ||||
\(471\) | 8.24911 | 0.380099 | ||||||||
\(472\) | −11.0180 | + | 12.9591i | −0.507146 | + | 0.596493i | ||||
\(473\) | − | 4.02593i | − | 0.185112i | ||||||
\(474\) | 19.0373 | + | 4.55541i | 0.874411 | + | 0.209237i | ||||
\(475\) | −6.80966 | − | 6.80966i | −0.312448 | − | 0.312448i | ||||
\(476\) | 1.26657 | + | 0.731239i | 0.0580533 | + | 0.0335163i | ||||
\(477\) | 3.85262 | − | 3.85262i | 0.176399 | − | 0.176399i | ||||
\(478\) | 5.79918 | + | 9.44756i | 0.265248 | + | 0.432121i | ||||
\(479\) | −14.9496 | −0.683063 | −0.341531 | − | 0.939870i | \(-0.610946\pi\) | ||||
−0.341531 | + | 0.939870i | \(0.610946\pi\) | |||||||
\(480\) | 4.02119 | − | 9.81148i | 0.183541 | − | 0.447831i | ||||
\(481\) | − | 3.17959i | − | 0.144977i | ||||||
\(482\) | −13.5873 | − | 22.1354i | −0.618886 | − | 1.00824i | ||||
\(483\) | 3.57835 | − | 3.21236i | 0.162821 | − | 0.146168i | ||||
\(484\) | 14.6074 | + | 7.41538i | 0.663973 | + | 0.337063i | ||||
\(485\) | 17.4504 | + | 17.4504i | 0.792383 | + | 0.792383i | ||||
\(486\) | −0.329115 | + | 1.37538i | −0.0149289 | + | 0.0623887i | ||||
\(487\) | 2.67317 | 0.121133 | 0.0605664 | − | 0.998164i | \(-0.480709\pi\) | ||||
0.0605664 | + | 0.998164i | \(0.480709\pi\) | |||||||
\(488\) | −2.95898 | + | 3.48028i | −0.133947 | + | 0.157545i | ||||
\(489\) | −17.6425 | −0.797823 | ||||||||
\(490\) | 6.23301 | − | 17.4781i | 0.281579 | − | 0.789578i | ||||
\(491\) | −7.71425 | + | 7.71425i | −0.348139 | + | 0.348139i | −0.859416 | − | 0.511277i | \(-0.829173\pi\) |
0.511277 | + | 0.859416i | \(0.329173\pi\) | |||||||
\(492\) | 4.55135 | + | 13.9368i | 0.205191 | + | 0.628318i | ||||
\(493\) | −0.730041 | − | 0.730041i | −0.0328794 | − | 0.0328794i | ||||
\(494\) | 22.3171 | − | 13.6989i | 1.00410 | − | 0.616342i | ||||
\(495\) | −3.14166 | −0.141207 | ||||||||
\(496\) | 16.7930 | + | 22.9689i | 0.754026 | + | 1.03134i | ||||
\(497\) | 22.1026 | + | 1.19123i | 0.991437 | + | 0.0534341i | ||||
\(498\) | −10.3679 | − | 16.8906i | −0.464598 | − | 0.756885i | ||||
\(499\) | −10.9644 | − | 10.9644i | −0.490835 | − | 0.490835i | 0.417734 | − | 0.908569i | \(-0.362824\pi\) |
−0.908569 | + | 0.417734i | \(0.862824\pi\) | |||||||
\(500\) | −23.1156 | + | 7.54890i | −1.03376 | + | 0.337597i | ||||
\(501\) | 15.0881 | + | 15.0881i | 0.674086 | + | 0.674086i | ||||
\(502\) | −31.6609 | − | 7.57610i | −1.41309 | − | 0.338138i | ||||
\(503\) | 16.3842i | 0.730533i | 0.930903 | + | 0.365267i | \(0.119022\pi\) | ||||
−0.930903 | + | 0.365267i | \(0.880978\pi\) | |||||||
\(504\) | 7.48060 | − | 0.201552i | 0.333212 | − | 0.00897785i | ||||
\(505\) | − | 3.19790i | − | 0.142305i | ||||||
\(506\) | −1.00256 | + | 4.18976i | −0.0445694 | + | 0.186257i | ||||
\(507\) | 3.41689 | + | 3.41689i | 0.151749 | + | 0.151749i | ||||
\(508\) | 33.6375 | + | 17.0759i | 1.49242 | + | 0.757622i | ||||
\(509\) | 18.7512 | + | 18.7512i | 0.831133 | + | 0.831133i | 0.987672 | − | 0.156539i | \(-0.0500337\pi\) |
−0.156539 | + | 0.987672i | \(0.550034\pi\) | |||||||
\(510\) | −0.624419 | + | 0.383286i | −0.0276497 | + | 0.0169722i | ||||
\(511\) | 44.8077 | + | 2.41494i | 1.98218 | + | 0.106831i | ||||
\(512\) | −5.43003 | − | 21.9662i | −0.239976 | − | 0.970779i | ||||
\(513\) | −6.47895 | −0.286053 | ||||||||
\(514\) | 10.0845 | + | 16.4288i | 0.444808 | + | 0.724645i | ||||
\(515\) | 15.1392 | + | 15.1392i | 0.667113 | + | 0.667113i | ||||
\(516\) | −4.28375 | − | 2.17463i | −0.188581 | − | 0.0957325i | ||||
\(517\) | 13.7145 | − | 13.7145i | 0.603163 | − | 0.603163i | ||||
\(518\) | 3.99048 | + | 1.18523i | 0.175332 | + | 0.0520762i | ||||
\(519\) | −15.1854 | −0.666564 | ||||||||
\(520\) | −1.22266 | − | 15.1027i | −0.0536173 | − | 0.662297i | ||||
\(521\) | −4.36154 | −0.191083 | −0.0955413 | − | 0.995425i | \(-0.530458\pi\) | ||||
−0.0955413 | + | 0.995425i | \(0.530458\pi\) | |||||||
\(522\) | −5.13770 | − | 1.22939i | −0.224871 | − | 0.0538092i | ||||
\(523\) | −28.7720 | − | 28.7720i | −1.25811 | − | 1.25811i | −0.951994 | − | 0.306118i | \(-0.900970\pi\) |
−0.306118 | − | 0.951994i | \(-0.599030\pi\) | |||||||
\(524\) | 7.73546 | + | 23.6869i | 0.337925 | + | 1.03477i | ||||
\(525\) | −2.62711 | − | 2.92643i | −0.114657 | − | 0.127720i | ||||
\(526\) | −7.09015 | + | 4.35214i | −0.309145 | + | 0.189762i | ||||
\(527\) | − | 1.96601i | − | 0.0856409i | ||||||
\(528\) | −5.41197 | + | 3.95678i | −0.235526 | + | 0.172197i | ||||
\(529\) | −19.6966 | −0.856373 | ||||||||
\(530\) | 12.3092 | − | 7.55573i | 0.534677 | − | 0.328200i | ||||
\(531\) | 4.25247 | − | 4.25247i | 0.184542 | − | 0.184542i | ||||
\(532\) | 8.87352 | + | 33.1151i | 0.384716 | + | 1.43572i | ||||
\(533\) | 14.8141 | + | 14.8141i | 0.641668 | + | 0.641668i | ||||
\(534\) | 2.61643 | − | 10.9342i | 0.113224 | − | 0.473169i | ||||
\(535\) | 24.3559i | 1.05300i | ||||||||
\(536\) | 7.90663 | − | 9.29958i | 0.341514 | − | 0.401681i | ||||
\(537\) | −3.41987 | −0.147578 | ||||||||
\(538\) | 14.1643 | + | 3.38935i | 0.610665 | + | 0.146125i | ||||
\(539\) | −9.13953 | + | 7.35625i | −0.393668 | + | 0.316856i | ||||
\(540\) | −1.69698 | + | 3.34285i | −0.0730265 | + | 0.143853i | ||||
\(541\) | −11.4795 | + | 11.4795i | −0.493541 | + | 0.493541i | −0.909420 | − | 0.415879i | \(-0.863474\pi\) |
0.415879 | + | 0.909420i | \(0.363474\pi\) | |||||||
\(542\) | −9.22496 | + | 5.66254i | −0.396246 | + | 0.243227i | ||||
\(543\) | − | 0.450130i | − | 0.0193169i | ||||||
\(544\) | −0.592921 | + | 1.44669i | −0.0254213 | + | 0.0620265i | ||||
\(545\) | 1.43503i | 0.0614701i | ||||||||
\(546\) | 9.40131 | − | 5.09553i | 0.402339 | − | 0.218068i | ||||
\(547\) | −27.5701 | − | 27.5701i | −1.17881 | − | 1.17881i | −0.980047 | − | 0.198764i | \(-0.936307\pi\) |
−0.198764 | − | 0.980047i | \(-0.563693\pi\) | |||||||
\(548\) | 7.74659 | + | 3.93252i | 0.330918 | + | 0.167989i | ||||
\(549\) | 1.14204 | − | 1.14204i | 0.0487409 | − | 0.0487409i | ||||
\(550\) | 3.42644 | + | 0.819909i | 0.146104 | + | 0.0349610i | ||||
\(551\) | − | 24.2019i | − | 1.03103i | ||||||
\(552\) | 3.91653 | + | 3.32988i | 0.166699 | + | 0.141729i | ||||
\(553\) | −1.97085 | + | 36.5679i | −0.0838090 | + | 1.55502i | ||||
\(554\) | 40.7206 | + | 9.74399i | 1.73005 | + | 0.413982i | ||||
\(555\) | −1.47462 | + | 1.47462i | −0.0625942 | + | 0.0625942i | ||||
\(556\) | 4.43325 | − | 1.44778i | 0.188012 | − | 0.0613994i | ||||
\(557\) | 7.84102 | − | 7.84102i | 0.332235 | − | 0.332235i | −0.521200 | − | 0.853435i | \(-0.674515\pi\) |
0.853435 | + | 0.521200i | \(0.174515\pi\) | |||||||
\(558\) | −5.26257 | − | 8.57335i | −0.222782 | − | 0.362939i | ||||
\(559\) | −6.86492 | −0.290355 | ||||||||
\(560\) | 19.4101 | + | 4.09525i | 0.820227 | + | 0.173056i | ||||
\(561\) | 0.463235 | 0.0195578 | ||||||||
\(562\) | −9.83252 | − | 16.0183i | −0.414760 | − | 0.675693i | ||||
\(563\) | 20.5300 | − | 20.5300i | 0.865238 | − | 0.865238i | −0.126703 | − | 0.991941i | \(-0.540439\pi\) |
0.991941 | + | 0.126703i | \(0.0404395\pi\) | |||||||
\(564\) | −7.18482 | − | 22.0007i | −0.302535 | − | 0.926398i | ||||
\(565\) | 15.8293 | − | 15.8293i | 0.665944 | − | 0.665944i | ||||
\(566\) | −15.5071 | − | 3.71067i | −0.651810 | − | 0.155971i | ||||
\(567\) | −2.64192 | − | 0.142388i | −0.110950 | − | 0.00597972i | ||||
\(568\) | 1.90942 | + | 23.5858i | 0.0801176 | + | 0.989638i | ||||
\(569\) | − | 8.26625i | − | 0.346539i | −0.984874 | − | 0.173270i | \(-0.944567\pi\) | ||
0.984874 | − | 0.173270i | \(-0.0554332\pi\) | |||||||
\(570\) | −16.7034 | − | 3.99694i | −0.699628 | − | 0.167413i | ||||
\(571\) | 11.1033 | − | 11.1033i | 0.464659 | − | 0.464659i | −0.435520 | − | 0.900179i | \(-0.643435\pi\) |
0.900179 | + | 0.435520i | \(0.143435\pi\) | |||||||
\(572\) | −4.33647 | + | 8.54232i | −0.181317 | + | 0.357172i | ||||
\(573\) | 17.2817 | + | 17.2817i | 0.721955 | + | 0.721955i | ||||
\(574\) | −24.1142 | + | 13.0699i | −1.00651 | + | 0.545529i | ||||
\(575\) | − | 2.70158i | − | 0.112664i | ||||||
\(576\) | 1.28687 | + | 7.89582i | 0.0536196 | + | 0.328992i | ||||
\(577\) | − | 1.00276i | − | 0.0417454i | −0.999782 | − | 0.0208727i | \(-0.993356\pi\) | ||
0.999782 | − | 0.0208727i | \(-0.00664447\pi\) | |||||||
\(578\) | −20.3974 | + | 12.5205i | −0.848420 | + | 0.520784i | ||||
\(579\) | −15.8328 | + | 15.8328i | −0.657991 | + | 0.657991i | ||||
\(580\) | −12.4871 | − | 6.33902i | −0.518498 | − | 0.263213i | ||||
\(581\) | 27.5908 | − | 24.7689i | 1.14466 | − | 1.02759i | ||||
\(582\) | −18.1079 | − | 4.33303i | −0.750598 | − | 0.179610i | ||||
\(583\) | −9.13176 | −0.378199 | ||||||||
\(584\) | 3.87090 | + | 47.8146i | 0.160179 | + | 1.97858i | ||||
\(585\) | 5.35708i | 0.221488i | ||||||||
\(586\) | 5.47225 | − | 22.8688i | 0.226057 | − | 0.944701i | ||||
\(587\) | −2.42198 | − | 2.42198i | −0.0999658 | − | 0.0999658i | 0.655355 | − | 0.755321i | \(-0.272519\pi\) |
−0.755321 | + | 0.655355i | \(0.772519\pi\) | |||||||
\(588\) | 2.89058 | + | 13.6983i | 0.119206 | + | 0.564910i | ||||
\(589\) | 32.5880 | − | 32.5880i | 1.34277 | − | 1.34277i | ||||
\(590\) | 13.5867 | − | 8.33992i | 0.559357 | − | 0.343349i | ||||
\(591\) | −19.0249 | −0.782582 | ||||||||
\(592\) | −0.683031 | + | 4.39747i | −0.0280724 | + | 0.180735i | ||||
\(593\) | − | 22.2544i | − | 0.913881i | −0.889497 | − | 0.456940i | \(-0.848945\pi\) | ||
0.889497 | − | 0.456940i | \(-0.151055\pi\) | |||||||
\(594\) | 2.02006 | − | 1.23997i | 0.0828842 | − | 0.0508767i | ||||
\(595\) | −0.915666 | − | 1.01999i | −0.0375387 | − | 0.0418155i | ||||
\(596\) | −27.3044 | + | 8.91686i | −1.11843 | + | 0.365249i | ||||
\(597\) | −3.99117 | − | 3.99117i | −0.163348 | − | 0.163348i | ||||
\(598\) | 7.14427 | + | 1.70955i | 0.292151 | + | 0.0699085i | ||||
\(599\) | −6.97729 | −0.285085 | −0.142542 | − | 0.989789i | \(-0.545528\pi\) | ||||
−0.142542 | + | 0.989789i | \(0.545528\pi\) | |||||||
\(600\) | 2.72322 | − | 3.20299i | 0.111175 | − | 0.130761i | ||||
\(601\) | −9.75706 | −0.397999 | −0.198999 | − | 0.980000i | \(-0.563769\pi\) | ||||
−0.198999 | + | 0.980000i | \(0.563769\pi\) | |||||||
\(602\) | 2.55898 | − | 8.61567i | 0.104296 | − | 0.351149i | ||||
\(603\) | −3.05161 | + | 3.05161i | −0.124271 | + | 0.124271i | ||||
\(604\) | −8.08097 | + | 15.9185i | −0.328810 | + | 0.647716i | ||||
\(605\) | −10.8566 | − | 10.8566i | −0.441383 | − | 0.441383i | ||||
\(606\) | 1.26217 | + | 2.05622i | 0.0512721 | + | 0.0835284i | ||||
\(607\) | −0.646351 | −0.0262346 | −0.0131173 | − | 0.999914i | \(-0.504175\pi\) | ||||
−0.0131173 | + | 0.999914i | \(0.504175\pi\) | |||||||
\(608\) | −33.8080 | + | 14.1519i | −1.37110 | + | 0.573934i | ||||
\(609\) | 0.531884 | − | 9.86878i | 0.0215530 | − | 0.399903i | ||||
\(610\) | 3.64882 | − | 2.23975i | 0.147737 | − | 0.0906849i | ||||
\(611\) | −23.3856 | − | 23.3856i | −0.946082 | − | 0.946082i | ||||
\(612\) | 0.250218 | − | 0.492900i | 0.0101145 | − | 0.0199243i | ||||
\(613\) | −22.8864 | − | 22.8864i | −0.924372 | − | 0.924372i | 0.0729627 | − | 0.997335i | \(-0.476755\pi\) |
−0.997335 | + | 0.0729627i | \(0.976755\pi\) | |||||||
\(614\) | −9.35247 | + | 39.0844i | −0.377435 | + | 1.57732i | ||||
\(615\) | − | 13.7408i | − | 0.554084i | ||||||
\(616\) | −9.10439 | − | 8.62666i | −0.366826 | − | 0.347578i | ||||
\(617\) | 28.2900i | 1.13891i | 0.822022 | + | 0.569456i | \(0.192846\pi\) | ||||
−0.822022 | + | 0.569456i | \(0.807154\pi\) | |||||||
\(618\) | −15.7096 | − | 3.75915i | −0.631935 | − | 0.151215i | ||||
\(619\) | −27.0007 | − | 27.0007i | −1.08525 | − | 1.08525i | −0.996010 | − | 0.0892388i | \(-0.971557\pi\) |
−0.0892388 | − | 0.996010i | \(-0.528443\pi\) | |||||||
\(620\) | −8.27844 | − | 25.3495i | −0.332470 | − | 1.01806i | ||||
\(621\) | −1.28519 | − | 1.28519i | −0.0515728 | − | 0.0515728i | ||||
\(622\) | −19.2837 | − | 31.4155i | −0.773206 | − | 1.25964i | ||||
\(623\) | 21.0030 | + | 1.13197i | 0.841468 | + | 0.0453514i | ||||
\(624\) | 6.74700 | + | 9.22835i | 0.270096 | + | 0.369430i | ||||
\(625\) | 15.3586 | 0.614345 | ||||||||
\(626\) | −16.3495 | + | 10.0358i | −0.653457 | + | 0.401110i | ||||
\(627\) | 7.67843 | + | 7.67843i | 0.306647 | + | 0.306647i | ||||
\(628\) | −15.6831 | + | 5.12166i | −0.625824 | + | 0.204376i | ||||
\(629\) | 0.217431 | − | 0.217431i | 0.00866956 | − | 0.00866956i | ||||
\(630\) | −6.72330 | − | 1.99692i | −0.267863 | − | 0.0795592i | ||||
\(631\) | 31.2622 | 1.24453 | 0.622265 | − | 0.782807i | \(-0.286213\pi\) | ||||
0.622265 | + | 0.782807i | \(0.286213\pi\) | |||||||
\(632\) | −39.0218 | + | 3.15907i | −1.55220 | + | 0.125661i | ||||
\(633\) | 19.6710 | 0.781851 | ||||||||
\(634\) | −10.0211 | + | 41.8785i | −0.397988 | + | 1.66321i | ||||
\(635\) | −25.0002 | − | 25.0002i | −0.992104 | − | 0.992104i | ||||
\(636\) | −4.93256 | + | 9.71655i | −0.195589 | + | 0.385286i | ||||
\(637\) | 12.5437 | + | 15.5845i | 0.497000 | + | 0.617481i | ||||
\(638\) | 4.63187 | + | 7.54587i | 0.183377 | + | 0.298744i | ||||
\(639\) | − | 8.36612i | − | 0.330959i | ||||||
\(640\) | −1.55334 | + | 21.1501i | −0.0614012 | + | 0.836032i | ||||
\(641\) | 13.0504 | 0.515458 | 0.257729 | − | 0.966217i | \(-0.417026\pi\) | ||||
0.257729 | + | 0.966217i | \(0.417026\pi\) | |||||||
\(642\) | −9.61295 | − | 15.6606i | −0.379393 | − | 0.618076i | ||||
\(643\) | 0.786696 | − | 0.786696i | 0.0310242 | − | 0.0310242i | −0.691424 | − | 0.722449i | \(-0.743017\pi\) |
0.722449 | + | 0.691424i | \(0.243017\pi\) | |||||||
\(644\) | −4.80865 | + | 8.32902i | −0.189487 | + | 0.328209i | ||||
\(645\) | 3.18379 | + | 3.18379i | 0.125362 | + | 0.125362i | ||||
\(646\) | 2.46290 | + | 0.589345i | 0.0969015 | + | 0.0231875i | ||||
\(647\) | 22.9721i | 0.903125i | 0.892239 | + | 0.451563i | \(0.149133\pi\) | ||||
−0.892239 | + | 0.451563i | \(0.850867\pi\) | |||||||
\(648\) | −0.228233 | − | 2.81920i | −0.00896583 | − | 0.110749i | ||||
\(649\) | −10.0795 | −0.395656 | ||||||||
\(650\) | 1.39809 | − | 5.84268i | 0.0548376 | − | 0.229169i | ||||
\(651\) | 14.0046 | − | 12.5722i | 0.548883 | − | 0.492744i | ||||
\(652\) | 33.5418 | − | 10.9538i | 1.31360 | − | 0.428984i | ||||
\(653\) | −11.7129 | + | 11.7129i | −0.458362 | + | 0.458362i | −0.898118 | − | 0.439756i | \(-0.855065\pi\) |
0.439756 | + | 0.898118i | \(0.355065\pi\) | |||||||
\(654\) | −0.566389 | − | 0.922715i | −0.0221476 | − | 0.0360810i | ||||
\(655\) | − | 23.3539i | − | 0.912511i | ||||||
\(656\) | −17.3060 | − | 23.6706i | −0.675684 | − | 0.924181i | ||||
\(657\) | − | 16.9603i | − | 0.661685i | ||||||
\(658\) | 38.0670 | − | 20.6324i | 1.48400 | − | 0.804333i | ||||
\(659\) | 28.8441 | + | 28.8441i | 1.12361 | + | 1.12361i | 0.991195 | + | 0.132413i | \(0.0422725\pi\) |
0.132413 | + | 0.991195i | \(0.457728\pi\) | |||||||
\(660\) | 5.97289 | − | 1.95058i | 0.232494 | − | 0.0759261i | ||||
\(661\) | 20.5775 | − | 20.5775i | 0.800371 | − | 0.800371i | −0.182782 | − | 0.983153i | \(-0.558510\pi\) |
0.983153 | + | 0.182782i | \(0.0585103\pi\) | |||||||
\(662\) | −2.72301 | + | 11.3796i | −0.105833 | + | 0.442280i | ||||
\(663\) | − | 0.789896i | − | 0.0306770i | ||||||
\(664\) | 30.1983 | + | 25.6750i | 1.17192 | + | 0.996383i | ||||
\(665\) | 1.72923 | − | 32.0848i | 0.0670567 | − | 1.24420i | ||||
\(666\) | 0.366156 | − | 1.53018i | 0.0141883 | − | 0.0592934i | ||||
\(667\) | 4.80077 | − | 4.80077i | 0.185887 | − | 0.185887i | ||||
\(668\) | −38.0531 | − | 19.3175i | −1.47232 | − | 0.747416i | ||||
\(669\) | −10.9526 | + | 10.9526i | −0.423453 | + | 0.423453i | ||||
\(670\) | −9.74994 | + | 5.98479i | −0.376673 | + | 0.231213i | ||||
\(671\) | −2.70694 | −0.104500 | ||||||||
\(672\) | −14.0969 | + | 5.02770i | −0.543799 | + | 0.193948i | ||||
\(673\) | 19.3585 | 0.746215 | 0.373108 | − | 0.927788i | \(-0.378292\pi\) | ||||
0.373108 | + | 0.927788i | \(0.378292\pi\) | |||||||
\(674\) | −13.4077 | + | 8.23004i | −0.516446 | + | 0.317009i | ||||
\(675\) | −1.05104 | + | 1.05104i | −0.0404547 | + | 0.0404547i | ||||
\(676\) | −8.61761 | − | 4.37469i | −0.331447 | − | 0.168257i | ||||
\(677\) | 26.0458 | − | 26.0458i | 1.00102 | − | 1.00102i | 0.00102364 | − | 0.999999i | \(-0.499674\pi\) |
0.999999 | − | 0.00102364i | \(-0.000325836\pi\) | |||||||
\(678\) | −3.93050 | + | 16.4258i | −0.150950 | + | 0.630827i | ||||
\(679\) | 1.87464 | − | 34.7828i | 0.0719420 | − | 1.33484i | ||||
\(680\) | 0.949165 | − | 1.11638i | 0.0363988 | − | 0.0428114i | ||||
\(681\) | 6.00245i | 0.230014i | ||||||||
\(682\) | −3.92373 | + | 16.3974i | −0.150247 | + | 0.627890i | ||||
\(683\) | −21.8826 | + | 21.8826i | −0.837315 | + | 0.837315i | −0.988505 | − | 0.151189i | \(-0.951690\pi\) |
0.151189 | + | 0.988505i | \(0.451690\pi\) | |||||||
\(684\) | 12.3177 | − | 4.02261i | 0.470979 | − | 0.153808i | ||||
\(685\) | −5.75746 | − | 5.75746i | −0.219981 | − | 0.219981i | ||||
\(686\) | −24.2348 | + | 9.93339i | −0.925291 | + | 0.379259i | ||||
\(687\) | 3.38133i | 0.129006i | ||||||||
\(688\) | 9.49438 | + | 1.47470i | 0.361970 | + | 0.0562225i | ||||
\(689\) | 15.5713i | 0.593218i | ||||||||
\(690\) | −2.52050 | − | 4.10620i | −0.0959538 | − | 0.156320i | ||||
\(691\) | −12.1294 | + | 12.1294i | −0.461424 | + | 0.461424i | −0.899122 | − | 0.437698i | \(-0.855794\pi\) |
0.437698 | + | 0.899122i | \(0.355794\pi\) | |||||||
\(692\) | 28.8703 | − | 9.42821i | 1.09748 | − | 0.358407i | ||||
\(693\) | 2.96228 | + | 3.29978i | 0.112528 | + | 0.125348i | ||||
\(694\) | 7.80643 | − | 32.6234i | 0.296328 | − | 1.23837i | ||||
\(695\) | −4.37093 | −0.165799 | ||||||||
\(696\) | 10.5310 | − | 0.852555i | 0.399178 | − | 0.0323160i | ||||
\(697\) | 2.02607i | 0.0767429i | ||||||||
\(698\) | 23.2962 | + | 5.57452i | 0.881774 | + | 0.210999i | ||||
\(699\) | −2.06518 | − | 2.06518i | −0.0781125 | − | 0.0781125i | ||||
\(700\) | 6.81158 | + | 3.93258i | 0.257454 | + | 0.148637i | ||||
\(701\) | −1.76393 | + | 1.76393i | −0.0666225 | + | 0.0666225i | −0.739633 | − | 0.673010i | \(-0.765001\pi\) |
0.673010 | + | 0.739633i | \(0.265001\pi\) | |||||||
\(702\) | −2.11437 | − | 3.44456i | −0.0798018 | − | 0.130007i | ||||
\(703\) | 7.20815 | 0.271861 | ||||||||
\(704\) | 7.83250 | − | 10.8827i | 0.295199 | − | 0.410158i | ||||
\(705\) | 21.6914i | 0.816947i | ||||||||
\(706\) | −25.7028 | − | 41.8729i | −0.967338 | − | 1.57591i | ||||
\(707\) | −3.35885 | + | 3.01531i | −0.126322 | + | 0.113402i | ||||
\(708\) | −5.44450 | + | 10.7250i | −0.204617 | + | 0.403070i | ||||
\(709\) | 24.0457 | + | 24.0457i | 0.903055 | + | 0.903055i | 0.995699 | − | 0.0926439i | \(-0.0295318\pi\) |
−0.0926439 | + | 0.995699i | \(0.529532\pi\) | |||||||
\(710\) | 5.16116 | − | 21.5687i | 0.193695 | − | 0.809460i | ||||
\(711\) | 13.8414 | 0.519094 | ||||||||
\(712\) | 1.81443 | + | 22.4124i | 0.0679987 | + | 0.839942i | ||||
\(713\) | 12.9286 | 0.484178 | ||||||||
\(714\) | 0.991343 | + | 0.294444i | 0.0371001 | + | 0.0110193i | ||||
\(715\) | 6.34887 | − | 6.34887i | 0.237434 | − | 0.237434i | ||||
\(716\) | 6.50182 | − | 2.12331i | 0.242984 | − | 0.0793519i | ||||
\(717\) | 5.54272 | + | 5.54272i | 0.206997 | + | 0.206997i | ||||
\(718\) | −26.8633 | + | 16.4895i | −1.00253 | + | 0.615382i | ||||
\(719\) | −21.8470 | −0.814754 | −0.407377 | − | 0.913260i | \(-0.633556\pi\) | ||||
−0.407377 | + | 0.913260i | \(0.633556\pi\) | |||||||
\(720\) | 1.15079 | − | 7.40900i | 0.0428875 | − | 0.276117i | ||||
\(721\) | 1.62635 | − | 30.1760i | 0.0605685 | − | 1.12381i | ||||
\(722\) | 16.9988 | + | 27.6930i | 0.632629 | + | 1.03063i | ||||
\(723\) | −12.9864 | − | 12.9864i | −0.482971 | − | 0.482971i | ||||
\(724\) | 0.279474 | + | 0.855781i | 0.0103866 | + | 0.0318049i | ||||
\(725\) | −3.92613 | − | 3.92613i | −0.145813 | − | 0.145813i | ||||
\(726\) | 11.2656 | + | 2.69575i | 0.418107 | + | 0.100049i | ||||
\(727\) | 42.6131i | 1.58043i | 0.612829 | + | 0.790216i | \(0.290031\pi\) | ||||
−0.612829 | + | 0.790216i | \(0.709969\pi\) | |||||||
\(728\) | −14.7100 | + | 15.5246i | −0.545188 | + | 0.575379i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 10.4630 | − | 43.7254i | 0.387254 | − | 1.61835i | ||||
\(731\) | −0.469446 | − | 0.469446i | −0.0173631 | − | 0.0173631i | ||||
\(732\) | −1.46216 | + | 2.88029i | −0.0540432 | + | 0.106458i | ||||
\(733\) | 27.0115 | + | 27.0115i | 0.997693 | + | 0.997693i | 0.999997 | − | 0.00230393i | \(-0.000733364\pi\) |
−0.00230393 | + | 0.999997i | \(0.500733\pi\) | |||||||
\(734\) | 42.6528 | − | 26.1815i | 1.57434 | − | 0.966376i | ||||
\(735\) | 1.41026 | − | 13.0452i | 0.0520180 | − | 0.481180i | ||||
\(736\) | −9.51350 | − | 3.89906i | −0.350672 | − | 0.143721i | ||||
\(737\) | 7.23314 | 0.266436 | ||||||||
\(738\) | 5.42333 | + | 8.83525i | 0.199635 | + | 0.325230i | ||||
\(739\) | −1.43265 | − | 1.43265i | −0.0527008 | − | 0.0527008i | 0.680265 | − | 0.732966i | \(-0.261865\pi\) |
−0.732966 | + | 0.680265i | \(0.761865\pi\) | |||||||
\(740\) | 1.88798 | − | 3.71909i | 0.0694034 | − | 0.136716i | ||||
\(741\) | 13.0931 | − | 13.0931i | 0.480986 | − | 0.480986i | ||||
\(742\) | −19.5424 | − | 5.80438i | −0.717424 | − | 0.213086i | ||||
\(743\) | −21.5309 | −0.789892 | −0.394946 | − | 0.918704i | \(-0.629237\pi\) | ||||
−0.394946 | + | 0.918704i | \(0.629237\pi\) | |||||||
\(744\) | 15.3281 | + | 13.0322i | 0.561955 | + | 0.477782i | ||||
\(745\) | 26.9206 | 0.986293 | ||||||||
\(746\) | −11.9895 | − | 2.86895i | −0.438966 | − | 0.105040i | ||||
\(747\) | −9.90941 | − | 9.90941i | −0.362566 | − | 0.362566i | ||||
\(748\) | −0.880696 | + | 0.287610i | −0.0322014 | + | 0.0105161i | ||||
\(749\) | 25.5817 | − | 22.9652i | 0.934735 | − | 0.839132i | ||||
\(750\) | −14.6542 | + | 8.99516i | −0.535095 | + | 0.328457i | ||||
\(751\) | − | 4.47866i | − | 0.163429i | −0.996656 | − | 0.0817143i | \(-0.973960\pi\) | ||
0.996656 | − | 0.0817143i | \(-0.0260395\pi\) | |||||||
\(752\) | 27.3194 | + | 37.3666i | 0.996235 | + | 1.36262i | ||||
\(753\) | −23.0197 | −0.838883 | ||||||||
\(754\) | 12.8670 | − | 7.89815i | 0.468590 | − | 0.287634i | ||||
\(755\) | 11.8311 | − | 11.8311i | 0.430576 | − | 0.430576i | ||||
\(756\) | 5.11119 | − | 1.36959i | 0.185892 | − | 0.0498116i | ||||
\(757\) | −13.9860 | − | 13.9860i | −0.508329 | − | 0.508329i | 0.405684 | − | 0.914013i | \(-0.367033\pi\) |
−0.914013 | + | 0.405684i | \(0.867033\pi\) | |||||||
\(758\) | −3.32513 | + | 13.8959i | −0.120774 | + | 0.504721i | ||||
\(759\) | 3.04624i | 0.110572i | ||||||||
\(760\) | 34.2379 | − | 2.77178i | 1.24194 | − | 0.100543i | ||||
\(761\) | 26.8043 | 0.971653 | 0.485827 | − | 0.874055i | \(-0.338519\pi\) | ||||
0.485827 | + | 0.874055i | \(0.338519\pi\) | |||||||
\(762\) | 25.9422 | + | 6.20769i | 0.939788 | + | 0.224881i | ||||
\(763\) | 1.50726 | − | 1.35310i | 0.0545664 | − | 0.0489854i | ||||
\(764\) | −43.5856 | − | 22.1260i | −1.57687 | − | 0.800492i | ||||
\(765\) | −0.366336 | + | 0.366336i | −0.0132449 | + | 0.0132449i | ||||
\(766\) | −19.1464 | + | 11.7526i | −0.691787 | + | 0.424638i | ||||
\(767\) | 17.1873i | 0.620599i | ||||||||
\(768\) | −7.34889 | − | 14.2125i | −0.265180 | − | 0.512848i | ||||
\(769\) | 31.2390i | 1.12651i | 0.826285 | + | 0.563253i | \(0.190450\pi\) | ||||
−0.826285 | + | 0.563253i | \(0.809550\pi\) | |||||||
\(770\) | 5.60140 | + | 10.3346i | 0.201860 | + | 0.372435i | ||||
\(771\) | 9.63852 | + | 9.63852i | 0.347123 | + | 0.347123i | ||||
\(772\) | 20.2710 | − | 39.9314i | 0.729570 | − | 1.43716i | ||||
\(773\) | 21.9282 | − | 21.9282i | 0.788703 | − | 0.788703i | −0.192578 | − | 0.981282i | \(-0.561685\pi\) |
0.981282 | + | 0.192578i | \(0.0616850\pi\) | |||||||
\(774\) | −3.30375 | − | 0.790551i | −0.118751 | − | 0.0284158i | ||||
\(775\) | − | 10.5731i | − | 0.379799i | ||||||
\(776\) | 37.1169 | − | 3.00485i | 1.33242 | − | 0.107868i | ||||
\(777\) | 2.93926 | + | 0.158413i | 0.105446 | + | 0.00568305i | ||||
\(778\) | −6.42554 | − | 1.53756i | −0.230367 | − | 0.0551242i | ||||
\(779\) | −33.5835 | + | 33.5835i | −1.20325 | + | 1.20325i | ||||
\(780\) | −3.32608 | − | 10.1848i | −0.119093 | − | 0.364675i | ||||
\(781\) | −9.91499 | + | 9.91499i | −0.354786 | + | 0.354786i | ||||
\(782\) | 0.371645 | + | 0.605454i | 0.0132900 | + | 0.0216510i | ||||
\(783\) | −3.73546 | −0.133495 | ||||||||
\(784\) | −14.0005 | − | 24.2484i | −0.500017 | − | 0.866015i | ||||
\(785\) | 15.4626 | 0.551885 | ||||||||
\(786\) | 9.21746 | + | 15.0163i | 0.328776 | + | 0.535615i | ||||
\(787\) | 33.9965 | − | 33.9965i | 1.21184 | − | 1.21184i | 0.241424 | − | 0.970420i | \(-0.422385\pi\) |
0.970420 | − | 0.241424i | \(-0.0776145\pi\) | |||||||
\(788\) | 36.1700 | − | 11.8121i | 1.28850 | − | 0.420789i | ||||
\(789\) | −4.15967 | + | 4.15967i | −0.148088 | + | 0.148088i | ||||
\(790\) | 35.6846 | + | 8.53894i | 1.26960 | + | 0.303802i | ||||
\(791\) | −31.5515 | − | 1.70049i | −1.12184 | − | 0.0604624i | ||||
\(792\) | −3.07065 | + | 3.61163i | −0.109111 | + | 0.128334i | ||||
\(793\) | 4.61580i | 0.163912i | ||||||||
\(794\) | −21.5587 | − | 5.15877i | −0.765091 | − | 0.183078i | ||||
\(795\) | 7.22159 | − | 7.22159i | 0.256123 | − | 0.256123i | ||||
\(796\) | 10.0660 | + | 5.10995i | 0.356780 | + | 0.181117i | ||||
\(797\) | 4.75244 | + | 4.75244i | 0.168340 | + | 0.168340i | 0.786249 | − | 0.617909i | \(-0.212020\pi\) |
−0.617909 | + | 0.786249i | \(0.712020\pi\) | |||||||
\(798\) | 11.5516 | + | 21.3128i | 0.408922 | + | 0.754465i | ||||
\(799\) | − | 3.19838i | − | 0.113151i | ||||||
\(800\) | −3.18870 | + | 7.78026i | −0.112738 | + | 0.275074i | ||||
\(801\) | − | 7.94992i | − | 0.280897i | ||||||
\(802\) | 15.2431 | − | 9.35664i | 0.538252 | − | 0.330395i | ||||
\(803\) | −20.1003 | + | 20.1003i | −0.709323 | + | 0.709323i | ||||
\(804\) | 3.90701 | − | 7.69634i | 0.137790 | − | 0.271429i | ||||
\(805\) | 6.70748 | − | 6.02145i | 0.236408 | − | 0.212228i | ||||
\(806\) | 27.9605 | + | 6.69064i | 0.984867 | + | 0.235668i | ||||
\(807\) | 10.2984 | 0.362521 | ||||||||
\(808\) | −3.67628 | − | 3.12562i | −0.129331 | − | 0.109959i | ||||
\(809\) | − | 32.4123i | − | 1.13956i | −0.821798 | − | 0.569778i | \(-0.807029\pi\) | ||
0.821798 | − | 0.569778i | \(-0.192971\pi\) | |||||||
\(810\) | −0.616912 | + | 2.57810i | −0.0216761 | + | 0.0905853i | ||||
\(811\) | −0.225151 | − | 0.225151i | −0.00790612 | − | 0.00790612i | 0.703143 | − | 0.711049i | \(-0.251780\pi\) |
−0.711049 | + | 0.703143i | \(0.751780\pi\) | |||||||
\(812\) | 5.11606 | + | 19.0926i | 0.179539 | + | 0.670020i | ||||
\(813\) | −5.41212 | + | 5.41212i | −0.189811 | + | 0.189811i | ||||
\(814\) | −2.24742 | + | 1.37953i | −0.0787721 | + | 0.0483525i | ||||
\(815\) | −33.0702 | −1.15840 | ||||||||
\(816\) | −0.169683 | + | 1.09245i | −0.00594010 | + | 0.0382434i | ||||
\(817\) | − | 15.5628i | − | 0.544473i | ||||||
\(818\) | 7.71367 | − | 4.73487i | 0.269702 | − | 0.165551i | ||||
\(819\) | 5.62670 | − | 5.05121i | 0.196613 | − | 0.176504i | ||||
\(820\) | 8.53133 | + | 26.1239i | 0.297927 | + | 0.912286i | ||||
\(821\) | −37.0047 | − | 37.0047i | −1.29147 | − | 1.29147i | −0.933875 | − | 0.357599i | \(-0.883595\pi\) |
−0.357599 | − | 0.933875i | \(-0.616405\pi\) | |||||||
\(822\) | 5.97440 | + | 1.42961i | 0.208381 | + | 0.0498633i | ||||
\(823\) | −1.21299 | −0.0422821 | −0.0211411 | − | 0.999777i | \(-0.506730\pi\) | ||||
−0.0211411 | + | 0.999777i | \(0.506730\pi\) | |||||||
\(824\) | 32.2009 | − | 2.60688i | 1.12177 | − | 0.0908148i | ||||
\(825\) | 2.49126 | 0.0867345 | ||||||||
\(826\) | −21.5706 | − | 6.40680i | −0.750538 | − | 0.222921i | ||||
\(827\) | 22.1226 | − | 22.1226i | 0.769278 | − | 0.769278i | −0.208701 | − | 0.977979i | \(-0.566924\pi\) |
0.977979 | + | 0.208701i | \(0.0669236\pi\) | |||||||
\(828\) | 3.24132 | + | 1.64544i | 0.112644 | + | 0.0571831i | ||||
\(829\) | −27.0435 | − | 27.0435i | −0.939258 | − | 0.939258i | 0.0589998 | − | 0.998258i | \(-0.481209\pi\) |
−0.998258 | + | 0.0589998i | \(0.981209\pi\) | |||||||
\(830\) | −19.4343 | − | 31.6607i | −0.674573 | − | 1.09896i | ||||
\(831\) | 29.6067 | 1.02704 | ||||||||
\(832\) | −18.5570 | − | 13.3558i | −0.643347 | − | 0.463029i | ||||
\(833\) | −0.207941 | + | 1.92350i | −0.00720472 | + | 0.0666454i | ||||
\(834\) | 2.81047 | − | 1.72515i | 0.0973187 | − | 0.0597370i | ||||
\(835\) | 28.2820 | + | 28.2820i | 0.978740 | + | 0.978740i | ||||
\(836\) | −19.3655 | − | 9.83080i | −0.669769 | − | 0.340005i | ||||
\(837\) | −5.02983 | − | 5.02983i | −0.173856 | − | 0.173856i | ||||
\(838\) | 1.82600 | − | 7.63095i | 0.0630783 | − | 0.263607i | ||||
\(839\) | 18.8066i | 0.649277i | 0.945838 | + | 0.324639i | \(0.105243\pi\) | ||||
−0.945838 | + | 0.324639i | \(0.894757\pi\) | |||||||
\(840\) | 14.0221 | − | 0.377802i | 0.483808 | − | 0.0130354i | ||||
\(841\) | 15.0463i | 0.518839i | ||||||||
\(842\) | 38.7305 | + | 9.26778i | 1.33474 | + | 0.319389i | ||||
\(843\) | −9.39768 | − | 9.39768i | −0.323673 | − | 0.323673i | ||||
\(844\) | −37.3982 | + | 12.2132i | −1.28730 | + | 0.420396i | ||||
\(845\) | 6.40483 | + | 6.40483i | 0.220333 | + | 0.220333i | ||||
\(846\) | −8.56132 | − | 13.9474i | −0.294344 | − | 0.479522i | ||||
\(847\) | −1.16628 | + | 21.6397i | −0.0400740 | + | 0.743549i | ||||
\(848\) | 3.34497 | − | 21.5355i | 0.114867 | − | 0.739532i | ||||
\(849\) | −11.2747 | −0.386947 | ||||||||
\(850\) | 0.495148 | − | 0.303936i | 0.0169835 | − | 0.0104249i | ||||
\(851\) | 1.42984 | + | 1.42984i | 0.0490141 | + | 0.0490141i | ||||
\(852\) | 5.19431 | + | 15.9056i | 0.177954 | + | 0.544916i | ||||
\(853\) | −13.4226 | + | 13.4226i | −0.459581 | + | 0.459581i | −0.898518 | − | 0.438937i | \(-0.855355\pi\) |
0.438937 | + | 0.898518i | \(0.355355\pi\) | |||||||
\(854\) | −5.79297 | − | 1.72060i | −0.198231 | − | 0.0588777i | ||||
\(855\) | −12.1445 | −0.415334 | ||||||||
\(856\) | 27.9993 | + | 23.8054i | 0.956997 | + | 0.813652i | ||||
\(857\) | 14.2069 | 0.485297 | 0.242649 | − | 0.970114i | \(-0.421984\pi\) | ||||
0.242649 | + | 0.970114i | \(0.421984\pi\) | |||||||
\(858\) | −1.57646 | + | 6.58809i | −0.0538194 | + | 0.224914i | ||||
\(859\) | 12.7166 | + | 12.7166i | 0.433886 | + | 0.433886i | 0.889948 | − | 0.456062i | \(-0.150741\pi\) |
−0.456062 | + | 0.889948i | \(0.650741\pi\) | |||||||
\(860\) | −8.02971 | − | 4.07625i | −0.273811 | − | 0.138999i | ||||
\(861\) | −14.4324 | + | 12.9563i | −0.491855 | + | 0.441549i | ||||
\(862\) | −17.5326 | − | 28.5627i | −0.597162 | − | 0.972849i | ||||
\(863\) | 0.417666i | 0.0142175i | 0.999975 | + | 0.00710875i | \(0.00226281\pi\) | ||||
−0.999975 | + | 0.00710875i | \(0.997737\pi\) | |||||||
\(864\) | 2.18428 | + | 5.21813i | 0.0743109 | + | 0.177524i | ||||
\(865\) | −28.4644 | −0.967818 | ||||||||
\(866\) | −19.1021 | − | 31.1196i | −0.649116 | − | 1.05749i | ||||
\(867\) | −11.9668 | + | 11.9668i | −0.406414 | + | 0.406414i | ||||
\(868\) | −18.8196 | + | 32.5972i | −0.638778 | + | 1.10642i | ||||
\(869\) | −16.4040 | − | 16.4040i | −0.556466 | − | 0.556466i | ||||
\(870\) | −9.63041 | − | 2.30445i | −0.326501 | − | 0.0781282i | ||||
\(871\) | − | 12.3338i | − | 0.417914i | ||||||
\(872\) | 1.64970 | + | 1.40260i | 0.0558660 | + | 0.0474980i | ||||
\(873\) | −13.1657 | −0.445592 | ||||||||
\(874\) | −3.87555 | + | 16.1961i | −0.131092 | + | 0.547841i | ||||
\(875\) | −21.4893 | − | 23.9377i | −0.726472 | − | 0.809241i | ||||
\(876\) | 10.5302 | + | 32.2447i | 0.355783 | + | 1.08945i | ||||
\(877\) | −37.3450 | + | 37.3450i | −1.26105 | + | 1.26105i | −0.310468 | + | 0.950584i | \(0.600486\pi\) |
−0.950584 | + | 0.310468i | \(0.899514\pi\) | |||||||
\(878\) | −10.2082 | − | 16.6303i | −0.344509 | − | 0.561247i | ||||
\(879\) | − | 16.6272i | − | 0.560821i | ||||||
\(880\) | −10.1445 | + | 7.41682i | −0.341972 | + | 0.250021i | ||||
\(881\) | 40.8076i | 1.37484i | 0.726259 | + | 0.687421i | \(0.241257\pi\) | ||||
−0.726259 | + | 0.687421i | \(0.758743\pi\) | |||||||
\(882\) | 4.24199 | + | 8.94458i | 0.142835 | + | 0.301180i | ||||
\(883\) | 38.1593 | + | 38.1593i | 1.28416 | + | 1.28416i | 0.938277 | + | 0.345886i | \(0.112421\pi\) |
0.345886 | + | 0.938277i | \(0.387579\pi\) | |||||||
\(884\) | 0.490426 | + | 1.50174i | 0.0164948 | + | 0.0505090i | ||||
\(885\) | 7.97109 | − | 7.97109i | 0.267945 | − | 0.267945i | ||||
\(886\) | −4.47358 | + | 18.6953i | −0.150293 | + | 0.628081i | ||||
\(887\) | 34.0533i | 1.14340i | 0.820464 | + | 0.571698i | \(0.193715\pi\) | ||||
−0.820464 | + | 0.571698i | \(0.806285\pi\) | |||||||
\(888\) | 0.253920 | + | 3.13650i | 0.00852101 | + | 0.105254i | ||||
\(889\) | −2.68569 | + | 49.8313i | −0.0900750 | + | 1.67129i | ||||
\(890\) | 4.90440 | − | 20.4957i | 0.164396 | − | 0.687018i | ||||
\(891\) | 1.18514 | − | 1.18514i | 0.0397035 | − | 0.0397035i | ||||
\(892\) | 14.0228 | − | 27.6232i | 0.469518 | − | 0.924893i | ||||
\(893\) | 53.0153 | − | 53.0153i | 1.77409 | − | 1.77409i | ||||
\(894\) | −17.3097 | + | 10.6252i | −0.578923 | + | 0.355360i | ||||
\(895\) | −6.41042 | −0.214277 | ||||||||
\(896\) | 23.6793 | − | 18.3110i | 0.791068 | − | 0.611728i | ||||
\(897\) | 5.19438 | 0.173435 | ||||||||
\(898\) | 32.8652 | − | 20.1736i | 1.09673 | − | 0.673201i | ||||
\(899\) | 18.7888 | − | 18.7888i | 0.626640 | − | 0.626640i | ||||
\(900\) | 1.34566 | − | 2.65080i | 0.0448555 | − | 0.0883599i | ||||
\(901\) | −1.06482 | + | 1.06482i | −0.0354741 | + | 0.0354741i | ||||
\(902\) | 4.04359 | − | 16.8983i | 0.134637 | − | 0.562653i | ||||
\(903\) | 0.342023 | − | 6.34603i | 0.0113818 | − | 0.211183i | ||||
\(904\) | −2.72571 | − | 33.6688i | −0.0906557 | − | 1.11981i | ||||
\(905\) | − | 0.843750i | − | 0.0280472i | ||||||
\(906\) | −2.93771 | + | 12.2768i | −0.0975990 | + | 0.407871i | ||||
\(907\) | −1.29406 | + | 1.29406i | −0.0429685 | + | 0.0429685i | −0.728265 | − | 0.685296i | \(-0.759673\pi\) |
0.685296 | + | 0.728265i | \(0.259673\pi\) | |||||||
\(908\) | −3.72677 | − | 11.4118i | −0.123677 | − | 0.378713i | ||||
\(909\) | 1.20635 | + | 1.20635i | 0.0400121 | + | 0.0400121i | ||||
\(910\) | 17.6224 | − | 9.55136i | 0.584176 | − | 0.316625i | ||||
\(911\) | − | 21.1193i | − | 0.699715i | −0.936803 | − | 0.349857i | \(-0.886230\pi\) | ||
0.936803 | − | 0.349857i | \(-0.113770\pi\) | |||||||
\(912\) | −20.9207 | + | 15.2955i | −0.692754 | + | 0.506484i | ||||
\(913\) | 23.4880i | 0.777339i | ||||||||
\(914\) | 11.6183 | + | 18.9276i | 0.384299 | + | 0.626068i | ||||
\(915\) | 2.14070 | − | 2.14070i | 0.0707694 | − | 0.0707694i | ||||
\(916\) | −2.09938 | − | 6.42853i | −0.0693654 | − | 0.212405i | ||||
\(917\) | −24.5292 | + | 22.0204i | −0.810027 | + | 0.727178i | ||||
\(918\) | 0.0909630 | − | 0.380139i | 0.00300223 | − | 0.0125464i | ||||
\(919\) | 0.462843 | 0.0152678 | 0.00763389 | − | 0.999971i | \(-0.497570\pi\) | ||||
0.00763389 | + | 0.999971i | \(0.497570\pi\) | |||||||
\(920\) | 7.34138 | + | 6.24173i | 0.242038 | + | 0.205784i | ||||
\(921\) | 28.4171i | 0.936374i | ||||||||
\(922\) | 16.7321 | + | 4.00382i | 0.551044 | + | 0.131859i | ||||
\(923\) | 16.9068 | + | 16.9068i | 0.556494 | + | 0.556494i | ||||
\(924\) | −7.68060 | − | 4.43429i | −0.252673 | − | 0.145878i | ||||
\(925\) | 1.16934 | − | 1.16934i | 0.0384476 | − | 0.0384476i | ||||
\(926\) | −1.37366 | − | 2.23785i | −0.0451412 | − | 0.0735404i | ||||
\(927\) | −11.4220 | −0.375148 | ||||||||
\(928\) | −19.4921 | + | 8.15931i | −0.639861 | + | 0.267843i | ||||
\(929\) | 7.13095i | 0.233959i | 0.993134 | + | 0.116980i | \(0.0373212\pi\) | ||||
−0.993134 | + | 0.116980i | \(0.962679\pi\) | |||||||
\(930\) | −9.86447 | − | 16.0704i | −0.323469 | − | 0.526969i | ||||
\(931\) | −35.3301 | + | 28.4366i | −1.15790 | + | 0.931973i | ||||
\(932\) | 5.20852 | + | 2.64408i | 0.170611 | + | 0.0866098i | ||||
\(933\) | −18.4309 | − | 18.4309i | −0.603400 | − | 0.603400i | ||||
\(934\) | 5.61342 | − | 23.4587i | 0.183677 | − | 0.767593i | ||||
\(935\) | 0.868315 | 0.0283969 | ||||||||
\(936\) | 6.15846 | + | 5.23600i | 0.201295 | + | 0.171144i | ||||
\(937\) | −5.02900 | −0.164290 | −0.0821452 | − | 0.996620i | \(-0.526177\pi\) | ||||
−0.0821452 | + | 0.996620i | \(0.526177\pi\) | |||||||
\(938\) | 15.4792 | + | 4.59757i | 0.505415 | + | 0.150116i | ||||
\(939\) | −9.59195 | + | 9.59195i | −0.313022 | + | 0.313022i | ||||
\(940\) | −13.4677 | − | 41.2395i | −0.439266 | − | 1.34508i | ||||
\(941\) | −38.2671 | − | 38.2671i | −1.24747 | − | 1.24747i | −0.956833 | − | 0.290639i | \(-0.906132\pi\) |
−0.290639 | − | 0.956833i | \(-0.593868\pi\) | |||||||
\(942\) | −9.94235 | + | 6.10290i | −0.323939 | + | 0.198843i | ||||
\(943\) | −13.3235 | −0.433873 | ||||||||
\(944\) | 3.69214 | − | 23.7706i | 0.120169 | − | 0.773667i | ||||
\(945\) | −4.95217 | − | 0.266900i | −0.161094 | − | 0.00868226i | ||||
\(946\) | 2.97848 | + | 4.85230i | 0.0968388 | + | 0.157762i | ||||
\(947\) | −4.42949 | − | 4.42949i | −0.143939 | − | 0.143939i | 0.631465 | − | 0.775404i | \(-0.282454\pi\) |
−0.775404 | + | 0.631465i | \(0.782454\pi\) | |||||||
\(948\) | −26.3151 | + | 8.59378i | −0.854676 | + | 0.279113i | ||||
\(949\) | 34.2745 | + | 34.2745i | 1.11260 | + | 1.11260i | ||||
\(950\) | 13.2454 | + | 3.16947i | 0.429737 | + | 0.102831i | ||||
\(951\) | 30.4486i | 0.987363i | ||||||||
\(952\) | −2.06754 | + | 0.0557065i | −0.0670094 | + | 0.00180546i | ||||
\(953\) | − | 40.8007i | − | 1.32166i | −0.750534 | − | 0.660832i | \(-0.770204\pi\) | ||
0.750534 | − | 0.660832i | \(-0.229796\pi\) | |||||||
\(954\) | −1.79316 | + | 7.49369i | −0.0580556 | + | 0.242617i | ||||
\(955\) | 32.3939 | + | 32.3939i | 1.04824 | + | 1.04824i | ||||
\(956\) | −13.9791 | − | 7.09642i | −0.452116 | − | 0.229514i | ||||
\(957\) | 4.42703 | + | 4.42703i | 0.143106 | + | 0.143106i | ||||
\(958\) | 18.0181 | − | 11.0601i | 0.582140 | − | 0.357334i | ||||
\(959\) | −0.618504 | + | 11.4760i | −0.0199725 | + | 0.370578i | ||||
\(960\) | 2.41219 | + | 14.8004i | 0.0778530 | + | 0.477681i | ||||
\(961\) | 19.5985 | 0.632208 | ||||||||
\(962\) | 2.35234 | + | 3.83225i | 0.0758426 | + | 0.123557i | ||||
\(963\) | −9.18783 | − | 9.18783i | −0.296074 | − | 0.296074i | ||||
\(964\) | 32.7526 | + | 16.6267i | 1.05489 | + | 0.535510i | ||||
\(965\) | −29.6780 | + | 29.6780i | −0.955370 | + | 0.955370i | ||||
\(966\) | −1.93627 | + | 6.51910i | −0.0622985 | + | 0.209749i | ||||
\(967\) | −2.09367 | −0.0673278 | −0.0336639 | − | 0.999433i | \(-0.510718\pi\) | ||||
−0.0336639 | + | 0.999433i | \(0.510718\pi\) | |||||||
\(968\) | −23.0918 | + | 1.86943i | −0.742200 | + | 0.0600859i | ||||
\(969\) | 1.79070 | 0.0575255 | ||||||||
\(970\) | −33.9426 | − | 8.12209i | −1.08983 | − | 0.260785i | ||||
\(971\) | 12.1592 | + | 12.1592i | 0.390208 | + | 0.390208i | 0.874762 | − | 0.484554i | \(-0.161018\pi\) |
−0.484554 | + | 0.874762i | \(0.661018\pi\) | |||||||
\(972\) | −0.620874 | − | 1.90119i | −0.0199146 | − | 0.0609806i | ||||
\(973\) | 4.12136 | + | 4.59092i | 0.132125 | + | 0.147178i | ||||
\(974\) | −3.22187 | + | 1.97768i | −0.103235 | + | 0.0633689i | ||||
\(975\) | − | 4.24803i | − | 0.136046i | ||||||
\(976\) | 0.991553 | − | 6.38379i | 0.0317388 | − | 0.204340i | ||||
\(977\) | 45.8415 | 1.46660 | 0.733300 | − | 0.679906i | \(-0.237979\pi\) | ||||
0.733300 | + | 0.679906i | \(0.237979\pi\) | |||||||
\(978\) | 21.2639 | − | 13.0524i | 0.679944 | − | 0.417369i | ||||
\(979\) | −9.42173 | + | 9.42173i | −0.301120 | + | 0.301120i | ||||
\(980\) | 5.41828 | + | 25.6770i | 0.173081 | + | 0.820221i | ||||
\(981\) | −0.541341 | − | 0.541341i | −0.0172837 | − | 0.0172837i | ||||
\(982\) | 3.59051 | − | 15.0049i | 0.114578 | − | 0.478825i | ||||
\(983\) | − | 7.70439i | − | 0.245732i | −0.992423 | − | 0.122866i | \(-0.960791\pi\) | ||
0.992423 | − | 0.122866i | \(-0.0392085\pi\) | |||||||
\(984\) | −15.7963 | − | 13.4303i | −0.503569 | − | 0.428141i | ||||
\(985\) | −35.6615 | −1.13627 | ||||||||
\(986\) | 1.41999 | + | 0.339789i | 0.0452218 | + | 0.0108211i | ||||
\(987\) | 22.7832 | − | 20.4529i | 0.725196 | − | 0.651024i | ||||
\(988\) | −16.7632 | + | 33.0215i | −0.533310 | + | 1.05056i | ||||
\(989\) | 3.08709 | − | 3.08709i | 0.0981639 | − | 0.0981639i | ||||
\(990\) | 3.78653 | − | 2.32428i | 0.120344 | − | 0.0738704i | ||||
\(991\) | − | 6.61965i | − | 0.210280i | −0.994457 | − | 0.105140i | \(-0.966471\pi\) | ||
0.994457 | − | 0.105140i | \(-0.0335291\pi\) | |||||||
\(992\) | −37.2329 | − | 15.2597i | −1.18215 | − | 0.484497i | ||||
\(993\) | 8.27375i | 0.262559i | ||||||||
\(994\) | −27.5207 | + | 14.9163i | −0.872905 | + | 0.473116i | ||||
\(995\) | −7.48130 | − | 7.48130i | −0.237173 | − | 0.237173i | ||||
\(996\) | 24.9922 | + | 12.6872i | 0.791907 | + | 0.402008i | ||||
\(997\) | −20.8831 | + | 20.8831i | −0.661376 | + | 0.661376i | −0.955704 | − | 0.294329i | \(-0.904904\pi\) |
0.294329 | + | 0.955704i | \(0.404904\pi\) | |||||||
\(998\) | 21.3268 | + | 5.10326i | 0.675087 | + | 0.161541i | ||||
\(999\) | − | 1.11255i | − | 0.0351995i |
(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 | 336.2.u.a.139.5 | ✓ | 64 | |
4.3 | odd | 2 | 1344.2.u.a.1231.21 | 64 | |||
7.6 | odd | 2 | inner | 336.2.u.a.139.6 | yes | 64 | |
16.3 | odd | 4 | inner | 336.2.u.a.307.6 | yes | 64 | |
16.13 | even | 4 | 1344.2.u.a.559.12 | 64 | |||
28.27 | even | 2 | 1344.2.u.a.1231.12 | 64 | |||
112.13 | odd | 4 | 1344.2.u.a.559.21 | 64 | |||
112.83 | even | 4 | inner | 336.2.u.a.307.5 | yes | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.2.u.a.139.5 | ✓ | 64 | 1.1 | even | 1 | trivial | |
336.2.u.a.139.6 | yes | 64 | 7.6 | odd | 2 | inner | |
336.2.u.a.307.5 | yes | 64 | 112.83 | even | 4 | inner | |
336.2.u.a.307.6 | yes | 64 | 16.3 | odd | 4 | inner | |
1344.2.u.a.559.12 | 64 | 16.13 | even | 4 | |||
1344.2.u.a.559.21 | 64 | 112.13 | odd | 4 | |||
1344.2.u.a.1231.12 | 64 | 28.27 | even | 2 | |||
1344.2.u.a.1231.21 | 64 | 4.3 | odd | 2 |