Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [171,3,Mod(46,171)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(171, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("171.46");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 171 = 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 171.p (of order \(6\), 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: | \(4.65941252056\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.19163381760000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 14x^{6} + 177x^{4} - 266x^{2} + 361 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.3 | ||
Root | \(1.06868 - 0.617004i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 171.145 |
Dual form | 171.3.p.f.46.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/171\mathbb{Z}\right)^\times\).
\(n\) | \(20\) | \(154\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.06868 | − | 0.617004i | 0.534341 | − | 0.308502i | −0.208441 | − | 0.978035i | \(-0.566839\pi\) |
0.742782 | + | 0.669533i | \(0.233506\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.23861 | + | 2.14534i | −0.309653 | + | 0.536335i | ||||
\(5\) | −4.08850 | − | 7.08149i | −0.817700 | − | 1.41630i | −0.907373 | − | 0.420327i | \(-0.861915\pi\) |
0.0896726 | − | 0.995971i | \(-0.471418\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.4772 | −1.49675 | −0.748373 | − | 0.663278i | \(-0.769165\pi\) | ||||
−0.748373 | + | 0.663278i | \(0.769165\pi\) | |||||||
\(8\) | 7.99294i | 0.999118i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −8.73861 | − | 5.04524i | −0.873861 | − | 0.504524i | ||||
\(11\) | −3.90227 | −0.354752 | −0.177376 | − | 0.984143i | \(-0.556761\pi\) | ||||
−0.177376 | + | 0.984143i | \(0.556761\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.02277 | − | 1.16785i | −0.155598 | − | 0.0898346i | 0.420179 | − | 0.907441i | \(-0.361967\pi\) |
−0.575777 | + | 0.817607i | \(0.695300\pi\) | |||||||
\(14\) | −11.1968 | + | 6.46449i | −0.799773 | + | 0.461749i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.0227744 | − | 0.0394465i | −0.00142340 | − | 0.00246540i | ||||
\(17\) | 2.13736 | + | 3.70202i | 0.125727 | + | 0.217766i | 0.922017 | − | 0.387149i | \(-0.126540\pi\) |
−0.796290 | + | 0.604915i | \(0.793207\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −17.4772 | − | 7.45296i | −0.919854 | − | 0.392261i | ||||
\(20\) | 20.2563 | 1.01281 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.17029 | + | 2.40772i | −0.189559 | + | 0.109442i | ||||
\(23\) | 20.0701 | − | 34.7623i | 0.872611 | − | 1.51141i | 0.0133248 | − | 0.999911i | \(-0.495758\pi\) |
0.859286 | − | 0.511495i | \(-0.170908\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −20.9317 | + | 36.2547i | −0.837267 | + | 1.45019i | ||||
\(26\) | −2.88227 | −0.110857 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 12.9772 | − | 22.4772i | 0.463472 | − | 0.802758i | ||||
\(29\) | 10.6868 | + | 6.17004i | 0.368511 | + | 0.212760i | 0.672808 | − | 0.739817i | \(-0.265088\pi\) |
−0.304297 | + | 0.952577i | \(0.598421\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 22.2148i | − | 0.716608i | −0.933605 | − | 0.358304i | \(-0.883355\pi\) | ||
0.933605 | − | 0.358304i | \(-0.116645\pi\) | |||||||
\(32\) | −27.7370 | − | 16.0140i | −0.866783 | − | 0.500437i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.56832 | + | 2.63752i | 0.134362 | + | 0.0775742i | ||||
\(35\) | 42.8361 | + | 74.1944i | 1.22389 | + | 2.11984i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 62.2749i | 1.68311i | 0.540174 | + | 0.841553i | \(0.318358\pi\) | ||||
−0.540174 | + | 0.841553i | \(0.681642\pi\) | |||||||
\(38\) | −23.2761 | + | 2.81867i | −0.612529 | + | 0.0741756i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 56.6020 | − | 32.6792i | 1.41505 | − | 0.816979i | ||||
\(41\) | −44.7873 | + | 25.8579i | −1.09237 | + | 0.630682i | −0.934207 | − | 0.356731i | \(-0.883891\pi\) |
−0.158166 | + | 0.987413i | \(0.550558\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.67029 | + | 11.5533i | 0.155123 | + | 0.268681i | 0.933104 | − | 0.359607i | \(-0.117089\pi\) |
−0.777981 | + | 0.628288i | \(0.783756\pi\) | |||||||
\(44\) | 4.83341 | − | 8.37171i | 0.109850 | − | 0.190266i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 49.5332i | − | 1.07681i | ||||||
\(47\) | 24.1586 | − | 41.8438i | 0.514012 | − | 0.890294i | −0.485856 | − | 0.874039i | \(-0.661492\pi\) |
0.999868 | − | 0.0162556i | \(-0.00517456\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 60.7723 | 1.24025 | ||||||||
\(50\) | 51.6597i | 1.03319i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.01087 | − | 2.89303i | 0.0963629 | − | 0.0556351i | ||||
\(53\) | −67.7396 | − | 39.1095i | −1.27811 | − | 0.737915i | −0.301606 | − | 0.953433i | \(-0.597523\pi\) |
−0.976500 | + | 0.215518i | \(0.930856\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.9545 | + | 27.6339i | 0.290081 | + | 0.502435i | ||||
\(56\) | − | 83.7439i | − | 1.49543i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 15.2277 | 0.262547 | ||||||||
\(59\) | 82.7011 | − | 47.7475i | 1.40171 | − | 0.809280i | 0.407146 | − | 0.913363i | \(-0.366524\pi\) |
0.994569 | + | 0.104083i | \(0.0331908\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 18.8861 | − | 32.7117i | 0.309609 | − | 0.536258i | −0.668668 | − | 0.743561i | \(-0.733135\pi\) |
0.978277 | + | 0.207303i | \(0.0664686\pi\) | |||||||
\(62\) | −13.7066 | − | 23.7406i | −0.221075 | − | 0.382913i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −39.3406 | −0.614697 | ||||||||
\(65\) | 19.0990i | 0.293831i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −52.6247 | − | 30.3829i | −0.785444 | − | 0.453476i | 0.0529122 | − | 0.998599i | \(-0.483150\pi\) |
−0.838356 | + | 0.545123i | \(0.816483\pi\) | |||||||
\(68\) | −10.5895 | −0.155727 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 91.5564 | + | 52.8601i | 1.30795 | + | 0.755145i | ||||
\(71\) | −78.8877 | + | 45.5459i | −1.11110 | + | 0.641491i | −0.939113 | − | 0.343609i | \(-0.888350\pi\) |
−0.171982 | + | 0.985100i | \(0.555017\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 41.7950 | + | 72.3911i | 0.572535 | + | 0.991659i | 0.996305 | + | 0.0858893i | \(0.0273731\pi\) |
−0.423770 | + | 0.905770i | \(0.639294\pi\) | |||||||
\(74\) | 38.4239 | + | 66.5521i | 0.519241 | + | 0.899353i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 37.6366 | − | 28.2633i | 0.495219 | − | 0.371885i | ||||
\(77\) | 40.8850 | 0.530974 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.466357 | − | 0.269251i | 0.00590325 | − | 0.00340825i | −0.497045 | − | 0.867724i | \(-0.665582\pi\) |
0.502949 | + | 0.864316i | \(0.332248\pi\) | |||||||
\(80\) | −0.186227 | + | 0.322554i | −0.00232783 | + | 0.00403192i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −31.9089 | + | 55.2678i | −0.389133 | + | 0.673998i | ||||
\(83\) | −54.0816 | −0.651586 | −0.325793 | − | 0.945441i | \(-0.605631\pi\) | ||||
−0.325793 | + | 0.945441i | \(0.605631\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.4772 | − | 30.2714i | 0.205614 | − | 0.356135i | ||||
\(86\) | 14.2568 | + | 8.23119i | 0.165777 | + | 0.0957115i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 31.1907i | − | 0.354439i | ||||||
\(89\) | −81.6811 | − | 47.1586i | −0.917766 | − | 0.529872i | −0.0348441 | − | 0.999393i | \(-0.511093\pi\) |
−0.882922 | + | 0.469521i | \(0.844427\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 21.1931 | + | 12.2358i | 0.232891 | + | 0.134460i | ||||
\(92\) | 49.7180 | + | 86.1142i | 0.540414 | + | 0.936024i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 59.6237i | − | 0.634294i | ||||||
\(95\) | 18.6776 | + | 154.236i | 0.196606 | + | 1.62354i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −126.909 | + | 73.2709i | −1.30834 | + | 0.755370i | −0.981819 | − | 0.189820i | \(-0.939209\pi\) |
−0.326520 | + | 0.945190i | \(0.605876\pi\) | |||||||
\(98\) | 64.9462 | − | 37.4967i | 0.662716 | − | 0.382619i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −51.8525 | − | 89.8111i | −0.518525 | − | 0.898111i | ||||
\(101\) | 59.3764 | − | 102.843i | 0.587885 | − | 1.01825i | −0.406624 | − | 0.913596i | \(-0.633294\pi\) |
0.994509 | − | 0.104651i | \(-0.0333725\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 26.1248i | − | 0.253639i | −0.991926 | − | 0.126819i | \(-0.959523\pi\) | ||
0.991926 | − | 0.126819i | \(-0.0404769\pi\) | |||||||
\(104\) | 9.33456 | − | 16.1679i | 0.0897553 | − | 0.155461i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −96.5228 | −0.910592 | ||||||||
\(107\) | − | 120.708i | − | 1.12811i | −0.825737 | − | 0.564056i | \(-0.809240\pi\) | ||
0.825737 | − | 0.564056i | \(-0.190760\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −91.9545 | + | 53.0899i | −0.843619 | + | 0.487064i | −0.858493 | − | 0.512826i | \(-0.828599\pi\) |
0.0148739 | + | 0.999889i | \(0.495265\pi\) | |||||||
\(110\) | 34.1005 | + | 19.6879i | 0.310004 | + | 0.178981i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.238613 | + | 0.413289i | 0.00213047 | + | 0.00369008i | ||||
\(113\) | 101.609i | 0.899194i | 0.893232 | + | 0.449597i | \(0.148432\pi\) | ||||
−0.893232 | + | 0.449597i | \(0.851568\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −328.226 | −2.85414 | ||||||||
\(116\) | −26.4737 | + | 15.2846i | −0.228221 | + | 0.131764i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 58.9208 | − | 102.054i | 0.499329 | − | 0.864863i | ||||
\(119\) | −22.3936 | − | 38.7869i | −0.188182 | − | 0.325941i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −105.772 | −0.874151 | ||||||||
\(122\) | − | 46.6112i | − | 0.382059i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 47.6584 | + | 27.5156i | 0.384342 | + | 0.221900i | ||||
\(125\) | 137.892 | 1.10313 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 95.7267 | + | 55.2678i | 0.753754 | + | 0.435180i | 0.827049 | − | 0.562130i | \(-0.190018\pi\) |
−0.0732950 | + | 0.997310i | \(0.523351\pi\) | |||||||
\(128\) | 68.9056 | − | 39.7827i | 0.538325 | − | 0.310802i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 11.7842 | + | 20.4108i | 0.0906474 | + | 0.157006i | ||||
\(131\) | −28.1582 | − | 48.7714i | −0.214948 | − | 0.372301i | 0.738309 | − | 0.674463i | \(-0.235625\pi\) |
−0.953256 | + | 0.302162i | \(0.902292\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 183.113 | + | 78.0863i | 1.37679 | + | 0.587115i | ||||
\(134\) | −74.9855 | −0.559593 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −29.5901 | + | 17.0838i | −0.217574 | + | 0.125616i | ||||
\(137\) | −69.9658 | + | 121.184i | −0.510700 | + | 0.884558i | 0.489224 | + | 0.872158i | \(0.337280\pi\) |
−0.999923 | + | 0.0123992i | \(0.996053\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 85.1475 | − | 147.480i | 0.612572 | − | 1.06101i | −0.378233 | − | 0.925710i | \(-0.623468\pi\) |
0.990805 | − | 0.135296i | \(-0.0431984\pi\) | |||||||
\(140\) | −212.230 | −1.51593 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −56.2039 | + | 97.3481i | −0.395802 | + | 0.685550i | ||||
\(143\) | 7.89342 | + | 4.55727i | 0.0551987 | + | 0.0318690i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 100.905i | − | 0.695895i | ||||||
\(146\) | 89.3312 | + | 51.5754i | 0.611857 | + | 0.353256i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −133.601 | − | 77.1345i | −0.902709 | − | 0.521179i | ||||
\(149\) | −59.4652 | − | 102.997i | −0.399096 | − | 0.691254i | 0.594519 | − | 0.804082i | \(-0.297343\pi\) |
−0.993615 | + | 0.112828i | \(0.964009\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 150.898i | 0.999322i | 0.866221 | + | 0.499661i | \(0.166542\pi\) | ||||
−0.866221 | + | 0.499661i | \(0.833458\pi\) | |||||||
\(152\) | 59.5711 | − | 139.694i | 0.391915 | − | 0.919043i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 43.6931 | − | 25.2262i | 0.283721 | − | 0.163807i | ||||
\(155\) | −157.314 | + | 90.8254i | −1.01493 | + | 0.585970i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.11387 | + | 8.85749i | 0.0325724 | + | 0.0564171i | 0.881852 | − | 0.471526i | \(-0.156297\pi\) |
−0.849280 | + | 0.527943i | \(0.822963\pi\) | |||||||
\(158\) | 0.332258 | − | 0.575488i | 0.00210290 | − | 0.00364233i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 261.893i | 1.63683i | ||||||||
\(161\) | −210.278 | + | 364.213i | −1.30608 | + | 2.26219i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −42.8851 | −0.263099 | −0.131549 | − | 0.991310i | \(-0.541995\pi\) | ||||
−0.131549 | + | 0.991310i | \(0.541995\pi\) | |||||||
\(164\) | − | 128.112i | − | 0.781170i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −57.7961 | + | 33.3686i | −0.348169 | + | 0.201016i | ||||
\(167\) | −1.48133 | − | 0.855246i | −0.00887024 | − | 0.00512123i | 0.495558 | − | 0.868575i | \(-0.334963\pi\) |
−0.504429 | + | 0.863453i | \(0.668297\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −81.7723 | − | 141.634i | −0.483860 | − | 0.838069i | ||||
\(170\) | − | 43.1341i | − | 0.253730i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −33.0476 | −0.192137 | ||||||||
\(173\) | 176.089 | − | 101.665i | 1.01786 | − | 0.587660i | 0.104374 | − | 0.994538i | \(-0.466716\pi\) |
0.913482 | + | 0.406879i | \(0.133383\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 219.306 | − | 379.849i | 1.25318 | − | 2.17057i | ||||
\(176\) | 0.0888721 | + | 0.153931i | 0.000504955 | + | 0.000874607i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −116.388 | −0.653866 | ||||||||
\(179\) | − | 34.9725i | − | 0.195377i | −0.995217 | − | 0.0976885i | \(-0.968855\pi\) | ||
0.995217 | − | 0.0976885i | \(-0.0311449\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 100.295 | + | 57.9054i | 0.554116 | + | 0.319919i | 0.750781 | − | 0.660552i | \(-0.229678\pi\) |
−0.196664 | + | 0.980471i | \(0.563011\pi\) | |||||||
\(182\) | 30.1982 | 0.165924 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 277.854 | + | 160.419i | 1.51007 | + | 0.871841i | ||||
\(185\) | 440.999 | − | 254.611i | 2.38378 | − | 1.37628i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.34058 | − | 14.4463i | −0.0446020 | − | 0.0772530i | ||||
\(188\) | 59.8462 | + | 103.657i | 0.318331 | + | 0.551365i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 115.125 | + | 153.305i | 0.605920 | + | 0.806870i | ||||
\(191\) | −175.247 | −0.917523 | −0.458761 | − | 0.888559i | \(-0.651707\pi\) | ||||
−0.458761 | + | 0.888559i | \(0.651707\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 290.884 | − | 167.942i | 1.50717 | − | 0.870166i | 0.507206 | − | 0.861825i | \(-0.330678\pi\) |
0.999965 | − | 0.00834091i | \(-0.00265502\pi\) | |||||||
\(194\) | −90.4168 | + | 156.607i | −0.466066 | + | 0.807250i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −75.2733 | + | 130.377i | −0.384047 | + | 0.665190i | ||||
\(197\) | 243.998 | 1.23857 | 0.619284 | − | 0.785167i | \(-0.287423\pi\) | ||||
0.619284 | + | 0.785167i | \(0.287423\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 169.738 | − | 293.994i | 0.852953 | − | 1.47736i | −0.0255788 | − | 0.999673i | \(-0.508143\pi\) |
0.878531 | − | 0.477685i | \(-0.158524\pi\) | |||||||
\(200\) | −289.782 | − | 167.306i | −1.44891 | − | 0.836529i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 146.542i | − | 0.725454i | ||||||
\(203\) | −111.968 | − | 64.6449i | −0.551568 | − | 0.318448i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 366.226 | + | 211.440i | 1.78647 | + | 1.03142i | ||||
\(206\) | −16.1191 | − | 27.9191i | −0.0782481 | − | 0.135530i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.106388i | 0.000511483i | ||||||||
\(209\) | 68.2009 | + | 29.0835i | 0.326320 | + | 0.139155i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −85.0782 | + | 49.1199i | −0.403214 | + | 0.232796i | −0.687870 | − | 0.725834i | \(-0.741454\pi\) |
0.284656 | + | 0.958630i | \(0.408121\pi\) | |||||||
\(212\) | 167.806 | − | 96.8830i | 0.791539 | − | 0.456995i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −74.4772 | − | 128.998i | −0.348024 | − | 0.602796i | ||||
\(215\) | 54.5430 | − | 94.4712i | 0.253688 | − | 0.439401i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 232.750i | 1.07258i | ||||||||
\(218\) | −65.5134 | + | 113.472i | −0.300520 | + | 0.520516i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −79.0455 | −0.359298 | ||||||||
\(221\) | − | 9.98447i | − | 0.0451786i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 57.3535 | − | 33.1131i | 0.257191 | − | 0.148489i | −0.365862 | − | 0.930669i | \(-0.619226\pi\) |
0.623052 | + | 0.782180i | \(0.285892\pi\) | |||||||
\(224\) | 290.607 | + | 167.782i | 1.29735 | + | 0.749028i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 62.6931 | + | 108.588i | 0.277403 | + | 0.480476i | ||||
\(227\) | 375.221i | 1.65296i | 0.562968 | + | 0.826479i | \(0.309659\pi\) | ||||
−0.562968 | + | 0.826479i | \(0.690341\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 40.4534 | 0.176652 | 0.0883262 | − | 0.996092i | \(-0.471848\pi\) | ||||
0.0883262 | + | 0.996092i | \(0.471848\pi\) | |||||||
\(230\) | −350.769 | + | 202.516i | −1.52508 | + | 0.880506i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −49.3168 | + | 85.4191i | −0.212572 | + | 0.368186i | ||||
\(233\) | 134.459 | + | 232.890i | 0.577078 | + | 0.999529i | 0.995812 | + | 0.0914198i | \(0.0291405\pi\) |
−0.418734 | + | 0.908109i | \(0.637526\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −395.089 | −1.68123 | ||||||||
\(236\) | 236.563i | 1.00238i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −47.8634 | − | 27.6339i | −0.201107 | − | 0.116109i | ||||
\(239\) | 58.1786 | 0.243425 | 0.121713 | − | 0.992565i | \(-0.461161\pi\) | ||||
0.121713 | + | 0.992565i | \(0.461161\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 125.159 | + | 72.2608i | 0.519334 | + | 0.299837i | 0.736662 | − | 0.676261i | \(-0.236401\pi\) |
−0.217328 | + | 0.976099i | \(0.569734\pi\) | |||||||
\(242\) | −113.037 | + | 65.2619i | −0.467095 | + | 0.269677i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 46.7852 | + | 81.0343i | 0.191743 | + | 0.332108i | ||||
\(245\) | −248.467 | − | 430.358i | −1.01415 | − | 1.75656i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.6486 | + | 35.4864i | 0.107889 | + | 0.143670i | ||||
\(248\) | 177.562 | 0.715976 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 147.362 | − | 85.0797i | 0.589449 | − | 0.340319i | ||||
\(251\) | 46.8273 | − | 81.1072i | 0.186563 | − | 0.323136i | −0.757539 | − | 0.652790i | \(-0.773599\pi\) |
0.944102 | + | 0.329653i | \(0.106932\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −78.3188 | + | 135.652i | −0.309561 | + | 0.536175i | ||||
\(254\) | 136.402 | 0.537015 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 127.773 | − | 221.310i | 0.499114 | − | 0.864492i | ||||
\(257\) | −358.565 | − | 207.018i | −1.39519 | − | 0.805516i | −0.401310 | − | 0.915942i | \(-0.631445\pi\) |
−0.993884 | + | 0.110427i | \(0.964778\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 652.469i | − | 2.51918i | ||||||
\(260\) | −40.9739 | − | 23.6563i | −0.157592 | − | 0.0909857i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −60.1843 | − | 34.7474i | −0.229711 | − | 0.132624i | ||||
\(263\) | −85.7696 | − | 148.557i | −0.326120 | − | 0.564857i | 0.655618 | − | 0.755093i | \(-0.272408\pi\) |
−0.981738 | + | 0.190236i | \(0.939075\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 639.597i | 2.41357i | ||||||||
\(266\) | 243.869 | − | 29.5319i | 0.916800 | − | 0.111022i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 130.363 | − | 75.2653i | 0.486430 | − | 0.280841i | ||||
\(269\) | −5.85341 | + | 3.37947i | −0.0217599 | + | 0.0125631i | −0.510840 | − | 0.859676i | \(-0.670666\pi\) |
0.489081 | + | 0.872239i | \(0.337332\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −123.499 | − | 213.906i | −0.455716 | − | 0.789323i | 0.543013 | − | 0.839724i | \(-0.317283\pi\) |
−0.998729 | + | 0.0504013i | \(0.983950\pi\) | |||||||
\(272\) | 0.0973545 | − | 0.168623i | 0.000357921 | − | 0.000619937i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 172.677i | 0.630207i | ||||||||
\(275\) | 81.6811 | − | 141.476i | 0.297022 | − | 0.514458i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 67.6356 | 0.244172 | 0.122086 | − | 0.992520i | \(-0.461042\pi\) | ||||
0.122086 | + | 0.992520i | \(0.461042\pi\) | |||||||
\(278\) | − | 210.145i | − | 0.755918i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −593.032 | + | 342.387i | −2.11797 | + | 1.22281i | ||||
\(281\) | −22.1270 | − | 12.7750i | −0.0787439 | − | 0.0454628i | 0.460111 | − | 0.887861i | \(-0.347810\pi\) |
−0.538855 | + | 0.842399i | \(0.681143\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.477226 | + | 0.826579i | 0.00168631 | + | 0.00292077i | 0.866867 | − | 0.498539i | \(-0.166130\pi\) |
−0.865181 | + | 0.501460i | \(0.832797\pi\) | |||||||
\(284\) | − | 225.655i | − | 0.794559i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.2474 | 0.0393266 | ||||||||
\(287\) | 469.246 | − | 270.920i | 1.63501 | − | 0.943971i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 135.363 | − | 234.456i | 0.468385 | − | 0.811267i | ||||
\(290\) | −62.2586 | − | 107.835i | −0.214685 | − | 0.371845i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −207.071 | −0.709149 | ||||||||
\(293\) | 297.002i | 1.01366i | 0.862046 | + | 0.506830i | \(0.169183\pi\) | ||||
−0.862046 | + | 0.506830i | \(0.830817\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −676.247 | − | 390.432i | −2.29236 | − | 1.32350i | ||||
\(296\) | −497.760 | −1.68162 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −127.099 | − | 73.3806i | −0.426506 | − | 0.246243i | ||||
\(299\) | −81.1944 | + | 46.8776i | −0.271553 | + | 0.156781i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −69.8861 | − | 121.046i | −0.232180 | − | 0.402147i | ||||
\(302\) | 93.1044 | + | 161.262i | 0.308293 | + | 0.533979i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.104041 | + | 0.859152i | 0.000342240 | + | 0.00282616i | ||||
\(305\) | −308.864 | −1.01267 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 47.8634 | − | 27.6339i | 0.155907 | − | 0.0900128i | −0.420017 | − | 0.907516i | \(-0.637976\pi\) |
0.575924 | + | 0.817503i | \(0.304643\pi\) | |||||||
\(308\) | −50.6407 | + | 87.7123i | −0.164418 | + | 0.284780i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −112.079 | + | 194.127i | −0.361546 | + | 0.626216i | ||||
\(311\) | −110.770 | −0.356175 | −0.178088 | − | 0.984015i | \(-0.556991\pi\) | ||||
−0.178088 | + | 0.984015i | \(0.556991\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −105.727 | + | 183.124i | −0.337785 | + | 0.585061i | −0.984016 | − | 0.178081i | \(-0.943011\pi\) |
0.646231 | + | 0.763142i | \(0.276344\pi\) | |||||||
\(314\) | 10.9302 | + | 6.31056i | 0.0348096 | + | 0.0200973i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.33399i | 0.00422150i | ||||||||
\(317\) | 143.470 | + | 82.8324i | 0.452587 | + | 0.261301i | 0.708922 | − | 0.705287i | \(-0.249182\pi\) |
−0.256335 | + | 0.966588i | \(0.582515\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −41.7029 | − | 24.0772i | −0.130730 | − | 0.0754770i | ||||
\(320\) | 160.844 | + | 278.590i | 0.502637 | + | 0.870594i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 518.970i | 1.61171i | ||||||||
\(323\) | −9.76417 | − | 80.6308i | −0.0302296 | − | 0.249631i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 84.6801 | − | 48.8901i | 0.260554 | − | 0.150431i | ||||
\(326\) | −45.8305 | + | 26.4603i | −0.140584 | + | 0.0811664i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −206.681 | − | 357.982i | −0.630125 | − | 1.09141i | ||||
\(329\) | −253.115 | + | 438.407i | −0.769345 | + | 1.33255i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 358.233i | − | 1.08227i | −0.840934 | − | 0.541137i | \(-0.817994\pi\) | ||
0.840934 | − | 0.541137i | \(-0.182006\pi\) | |||||||
\(332\) | 66.9862 | − | 116.024i | 0.201766 | − | 0.349468i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.11076 | −0.00631964 | ||||||||
\(335\) | 496.882i | 1.48323i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −550.179 | + | 317.646i | −1.63258 | + | 0.942570i | −0.649285 | + | 0.760545i | \(0.724932\pi\) |
−0.983294 | + | 0.182025i | \(0.941735\pi\) | |||||||
\(338\) | −174.777 | − | 100.908i | −0.517092 | − | 0.298543i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 43.2950 | + | 74.9892i | 0.127338 | + | 0.220556i | ||||
\(341\) | 86.6884i | 0.254218i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −123.341 | −0.359594 | ||||||||
\(344\) | −92.3447 | + | 53.3153i | −0.268444 | + | 0.154986i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 125.455 | − | 217.295i | 0.362588 | − | 0.628021i | ||||
\(347\) | −74.7992 | − | 129.556i | −0.215560 | − | 0.373360i | 0.737886 | − | 0.674926i | \(-0.235824\pi\) |
−0.953446 | + | 0.301565i | \(0.902491\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 211.863 | 0.607058 | 0.303529 | − | 0.952822i | \(-0.401835\pi\) | ||||
0.303529 | + | 0.952822i | \(0.401835\pi\) | |||||||
\(350\) | − | 541.250i | − | 1.54643i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 108.238 | + | 62.4910i | 0.307493 | + | 0.177531i | ||||
\(353\) | 154.974 | 0.439019 | 0.219509 | − | 0.975610i | \(-0.429554\pi\) | ||||
0.219509 | + | 0.975610i | \(0.429554\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 645.065 | + | 372.429i | 1.81709 | + | 1.04909i | ||||
\(356\) | 202.343 | − | 116.823i | 0.568378 | − | 0.328153i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −21.5782 | − | 37.3745i | −0.0602742 | − | 0.104398i | ||||
\(359\) | 124.695 | + | 215.978i | 0.347340 | + | 0.601610i | 0.985776 | − | 0.168064i | \(-0.0537517\pi\) |
−0.638436 | + | 0.769675i | \(0.720418\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 249.907 | + | 260.514i | 0.692263 | + | 0.721646i | ||||
\(362\) | 142.911 | 0.394783 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −52.5000 | + | 30.3109i | −0.144231 | + | 0.0832717i | ||||
\(365\) | 341.758 | − | 591.942i | 0.936323 | − | 1.62176i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −326.714 | + | 565.885i | −0.890228 | + | 1.54192i | −0.0506268 | + | 0.998718i | \(0.516122\pi\) |
−0.839601 | + | 0.543203i | \(0.817211\pi\) | |||||||
\(368\) | −1.82834 | −0.00496830 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 314.192 | − | 544.197i | 0.849168 | − | 1.47080i | ||||
\(371\) | 709.723 | + | 409.759i | 1.91300 | + | 1.10447i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 324.494i | − | 0.869956i | −0.900441 | − | 0.434978i | \(-0.856756\pi\) | ||
0.900441 | − | 0.434978i | \(-0.143244\pi\) | |||||||
\(374\) | −17.8269 | − | 10.2923i | −0.0476654 | − | 0.0275196i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 334.455 | + | 193.098i | 0.889509 | + | 0.513558i | ||||
\(377\) | −14.4113 | − | 24.9612i | −0.0382264 | − | 0.0662100i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 21.4534i | − | 0.0566053i | −0.999599 | − | 0.0283026i | \(-0.990990\pi\) | ||
0.999599 | − | 0.0283026i | \(-0.00901021\pi\) | |||||||
\(380\) | −354.024 | − | 150.969i | −0.931641 | − | 0.397287i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −187.283 | + | 108.128i | −0.490270 | + | 0.283057i | ||||
\(383\) | −185.197 | + | 106.924i | −0.483544 | + | 0.279174i | −0.721892 | − | 0.692006i | \(-0.756727\pi\) |
0.238348 | + | 0.971180i | \(0.423394\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −167.158 | − | 289.527i | −0.434178 | − | 0.752018i | ||||
\(386\) | 207.242 | − | 358.953i | 0.536896 | − | 0.929930i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 363.017i | − | 0.935611i | ||||||
\(389\) | 188.727 | − | 326.885i | 0.485160 | − | 0.840321i | −0.514695 | − | 0.857373i | \(-0.672095\pi\) |
0.999855 | + | 0.0170523i | \(0.00542818\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 171.588 | 0.438844 | ||||||||
\(392\) | 485.749i | 1.23916i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 260.756 | − | 150.548i | 0.661818 | − | 0.382101i | ||||
\(395\) | −3.81340 | − | 2.20167i | −0.00965418 | − | 0.00557385i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 132.294 | + | 229.140i | 0.333234 | + | 0.577179i | 0.983144 | − | 0.182833i | \(-0.0585267\pi\) |
−0.649910 | + | 0.760011i | \(0.725193\pi\) | |||||||
\(398\) | − | 418.915i | − | 1.05255i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.90683 | 0.00476707 | ||||||||
\(401\) | −424.726 | + | 245.216i | −1.05917 | + | 0.611510i | −0.925202 | − | 0.379476i | \(-0.876104\pi\) |
−0.133965 | + | 0.990986i | \(0.542771\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −25.9436 | + | 44.9356i | −0.0643761 | + | 0.111503i | ||||
\(404\) | 147.089 | + | 254.765i | 0.364081 | + | 0.630607i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −159.545 | −0.392967 | ||||||||
\(407\) | − | 243.014i | − | 0.597086i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −364.046 | − | 210.182i | −0.890087 | − | 0.513892i | −0.0161160 | − | 0.999870i | \(-0.505130\pi\) |
−0.873971 | + | 0.485978i | \(0.838463\pi\) | |||||||
\(410\) | 521.838 | 1.27278 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 56.0466 | + | 32.3585i | 0.136035 | + | 0.0785401i | ||||
\(413\) | −866.479 | + | 500.262i | −2.09801 | + | 1.21129i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 221.113 | + | 382.979i | 0.532802 | + | 0.922840i | ||||
\(416\) | 37.4039 | + | 64.7854i | 0.0899131 | + | 0.155734i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 90.8297 | − | 10.9992i | 0.217296 | − | 0.0263140i | ||||
\(419\) | 646.178 | 1.54219 | 0.771095 | − | 0.636720i | \(-0.219709\pi\) | ||||
0.771095 | + | 0.636720i | \(0.219709\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 468.113 | − | 270.265i | 1.11191 | − | 0.641960i | 0.172584 | − | 0.984995i | \(-0.444788\pi\) |
0.939323 | + | 0.343035i | \(0.111455\pi\) | |||||||
\(422\) | −60.6143 | + | 104.987i | −0.143636 | + | 0.248785i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 312.600 | − | 541.439i | 0.737264 | − | 1.27698i | ||||
\(425\) | −178.954 | −0.421069 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −197.874 | + | 342.728i | −0.463406 | + | 0.802642i | ||||
\(428\) | 258.960 | + | 149.510i | 0.605046 | + | 0.349323i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 134.613i | − | 0.313053i | ||||||
\(431\) | −198.483 | − | 114.594i | −0.460517 | − | 0.265880i | 0.251745 | − | 0.967794i | \(-0.418996\pi\) |
−0.712262 | + | 0.701914i | \(0.752329\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 238.975 | + | 137.972i | 0.551906 | + | 0.318643i | 0.749890 | − | 0.661562i | \(-0.230106\pi\) |
−0.197985 | + | 0.980205i | \(0.563440\pi\) | |||||||
\(434\) | 143.608 | + | 248.736i | 0.330893 | + | 0.573123i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 263.031i | − | 0.603283i | ||||||
\(437\) | −609.851 | + | 457.968i | −1.39554 | + | 1.04798i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.6486 | − | 6.14794i | 0.0242564 | − | 0.0140044i | −0.487823 | − | 0.872943i | \(-0.662209\pi\) |
0.512079 | + | 0.858938i | \(0.328875\pi\) | |||||||
\(440\) | −220.876 | + | 127.523i | −0.501992 | + | 0.289825i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.16046 | − | 10.6702i | −0.0139377 | − | 0.0241408i | ||||
\(443\) | 31.4933 | − | 54.5480i | 0.0710910 | − | 0.123133i | −0.828289 | − | 0.560301i | \(-0.810685\pi\) |
0.899380 | + | 0.437168i | \(0.144019\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 771.232i | 1.73311i | ||||||||
\(446\) | 40.8618 | − | 70.7747i | 0.0916183 | − | 0.158688i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 412.180 | 0.920045 | ||||||||
\(449\) | − | 679.936i | − | 1.51433i | −0.653222 | − | 0.757167i | \(-0.726583\pi\) | ||
0.653222 | − | 0.757167i | \(-0.273417\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 174.772 | − | 100.905i | 0.387522 | − | 0.223736i | ||||
\(452\) | −217.986 | − | 125.854i | −0.482269 | − | 0.278438i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 231.513 | + | 400.992i | 0.509940 | + | 0.883243i | ||||
\(455\) | − | 200.105i | − | 0.439790i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −434.089 | −0.949867 | −0.474933 | − | 0.880022i | \(-0.657528\pi\) | ||||
−0.474933 | + | 0.880022i | \(0.657528\pi\) | |||||||
\(458\) | 43.2318 | − | 24.9599i | 0.0943926 | − | 0.0544976i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 406.545 | − | 704.156i | 0.883792 | − | 1.53077i | ||||
\(461\) | −265.088 | − | 459.146i | −0.575028 | − | 0.995978i | −0.996039 | − | 0.0889223i | \(-0.971658\pi\) |
0.421010 | − | 0.907056i | \(-0.361676\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −450.022 | −0.971969 | −0.485985 | − | 0.873967i | \(-0.661539\pi\) | ||||
−0.485985 | + | 0.873967i | \(0.661539\pi\) | |||||||
\(464\) | − | 0.562076i | − | 0.00121137i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 287.388 | + | 165.924i | 0.616713 | + | 0.356059i | ||||
\(467\) | −733.340 | −1.57032 | −0.785161 | − | 0.619292i | \(-0.787420\pi\) | ||||
−0.785161 | + | 0.619292i | \(0.787420\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 551.361 | + | 318.329i | 1.17561 | + | 0.678739i | ||||
\(470\) | −422.224 | + | 243.771i | −0.898350 | + | 0.518663i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 381.643 | + | 661.026i | 0.808566 | + | 1.40048i | ||||
\(473\) | −26.0293 | − | 45.0841i | −0.0550302 | − | 0.0953152i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 636.033 | − | 477.629i | 1.33902 | − | 1.00554i | ||||
\(476\) | 110.948 | 0.233084 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 62.1744 | − | 35.8964i | 0.130072 | − | 0.0750971i | ||||
\(479\) | −131.657 | + | 228.037i | −0.274859 | + | 0.476069i | −0.970099 | − | 0.242708i | \(-0.921964\pi\) |
0.695241 | + | 0.718777i | \(0.255298\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 72.7277 | − | 125.968i | 0.151201 | − | 0.261888i | ||||
\(482\) | 178.341 | 0.370002 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 131.011 | − | 226.917i | 0.270684 | − | 0.468838i | ||||
\(485\) | 1037.73 | + | 599.136i | 2.13966 | + | 1.23533i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 307.749i | 0.631929i | 0.948771 | + | 0.315964i | \(0.102328\pi\) | ||||
−0.948771 | + | 0.315964i | \(0.897672\pi\) | |||||||
\(488\) | 261.463 | + | 150.956i | 0.535785 | + | 0.309336i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −531.065 | − | 306.611i | −1.08381 | − | 0.625736i | ||||
\(491\) | −296.882 | − | 514.214i | −0.604647 | − | 1.04728i | −0.992107 | − | 0.125393i | \(-0.959981\pi\) |
0.387460 | − | 0.921887i | \(-0.373353\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 52.7505i | 0.106999i | ||||||||
\(494\) | 50.3741 | + | 21.4814i | 0.101972 | + | 0.0434847i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.876297 | + | 0.505930i | −0.00176673 | + | 0.00102002i | ||||
\(497\) | 826.525 | − | 477.194i | 1.66303 | − | 0.960149i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 327.577 | + | 567.380i | 0.656467 | + | 1.13703i | 0.981524 | + | 0.191340i | \(0.0612833\pi\) |
−0.325057 | + | 0.945695i | \(0.605383\pi\) | |||||||
\(500\) | −170.794 | + | 295.825i | −0.341589 | + | 0.591649i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 115.570i | − | 0.230220i | ||||||
\(503\) | 383.121 | − | 663.586i | 0.761673 | − | 1.31926i | −0.180315 | − | 0.983609i | \(-0.557712\pi\) |
0.941988 | − | 0.335647i | \(-0.108955\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −971.041 | −1.92285 | ||||||||
\(506\) | 193.292i | 0.382000i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −237.137 | + | 136.911i | −0.466804 | + | 0.269510i | ||||
\(509\) | −757.837 | − | 437.537i | −1.48887 | − | 0.859602i | −0.488955 | − | 0.872309i | \(-0.662622\pi\) |
−0.999919 | + | 0.0127070i | \(0.995955\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −437.896 | − | 758.458i | −0.856939 | − | 1.48426i | ||||
\(512\) | 2.91512i | 0.00569359i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −510.922 | −0.994012 | ||||||||
\(515\) | −185.003 | + | 106.811i | −0.359228 | + | 0.207401i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −94.2733 | + | 163.286i | −0.182347 | + | 0.315834i | ||||
\(518\) | −402.576 | − | 697.281i | −0.777173 | − | 1.34610i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −152.657 | −0.293572 | ||||||||
\(521\) | 445.728i | 0.855525i | 0.903891 | + | 0.427762i | \(0.140698\pi\) | ||||
−0.903891 | + | 0.427762i | \(0.859302\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 764.415 | + | 441.335i | 1.46160 | + | 0.843853i | 0.999085 | − | 0.0427611i | \(-0.0136154\pi\) |
0.462510 | + | 0.886614i | \(0.346949\pi\) | |||||||
\(524\) | 139.508 | 0.266237 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −183.321 | − | 105.840i | −0.348519 | − | 0.201217i | ||||
\(527\) | 82.2398 | − | 47.4812i | 0.156053 | − | 0.0900971i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −541.114 | − | 937.237i | −1.02290 | − | 1.77171i | ||||
\(530\) | 394.633 | + | 683.525i | 0.744591 | + | 1.28967i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −394.328 | + | 296.121i | −0.741217 | + | 0.556618i | ||||
\(533\) | 120.793 | 0.226628 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −854.792 | + | 493.514i | −1.59774 | + | 0.922457i | ||||
\(536\) | 242.849 | − | 420.627i | 0.453076 | − | 0.784751i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.17029 | + | 7.22315i | −0.00775147 | + | 0.0134259i | ||||
\(539\) | −237.150 | −0.439981 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −72.3654 | + | 125.341i | −0.133762 | + | 0.231683i | −0.925124 | − | 0.379665i | \(-0.876039\pi\) |
0.791362 | + | 0.611348i | \(0.209373\pi\) | |||||||
\(542\) | −263.962 | − | 152.399i | −0.487015 | − | 0.281178i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 136.911i | − | 0.251674i | ||||||
\(545\) | 751.912 | + | 434.116i | 1.37965 | + | 0.796544i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −91.2148 | − | 52.6629i | −0.166755 | − | 0.0962758i | 0.414300 | − | 0.910140i | \(-0.364026\pi\) |
−0.581055 | + | 0.813865i | \(0.697360\pi\) | |||||||
\(548\) | −173.321 | − | 300.201i | −0.316279 | − | 0.547812i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | − | 201.590i | − | 0.366528i | ||||||
\(551\) | −140.791 | − | 187.484i | −0.255519 | − | 0.340261i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.88613 | + | 2.82101i | −0.00883567 | + | 0.00510128i | ||||
\(554\) | 72.2809 | − | 41.7314i | 0.130471 | − | 0.0753275i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 210.930 | + | 365.341i | 0.379370 | + | 0.657088i | ||||
\(557\) | −298.372 | + | 516.795i | −0.535676 | + | 0.927819i | 0.463454 | + | 0.886121i | \(0.346610\pi\) |
−0.999130 | + | 0.0416975i | \(0.986723\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 31.1596i | − | 0.0557416i | ||||||
\(560\) | 1.95114 | − | 3.37947i | 0.00348417 | − | 0.00603477i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −31.5290 | −0.0561014 | ||||||||
\(563\) | 709.552i | 1.26031i | 0.776471 | + | 0.630153i | \(0.217008\pi\) | ||||
−0.776471 | + | 0.630153i | \(0.782992\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 719.542 | − | 415.428i | 1.27353 | − | 0.735271i | ||||
\(566\) | 1.02000 | + | 0.588900i | 0.00180213 | + | 0.00104046i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −364.046 | − | 630.545i | −0.640925 | − | 1.11012i | ||||
\(569\) | − | 275.069i | − | 0.483425i | −0.970348 | − | 0.241712i | \(-0.922291\pi\) | ||
0.970348 | − | 0.241712i | \(-0.0777090\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −924.109 | −1.61840 | −0.809202 | − | 0.587531i | \(-0.800100\pi\) | ||||
−0.809202 | + | 0.587531i | \(0.800100\pi\) | |||||||
\(572\) | −19.5538 | + | 11.2894i | −0.0341849 | + | 0.0197367i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 334.317 | − | 579.054i | 0.582433 | − | 1.00880i | ||||
\(575\) | 840.200 | + | 1455.27i | 1.46122 | + | 2.53090i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −443.905 | −0.769332 | −0.384666 | − | 0.923056i | \(-0.625683\pi\) | ||||
−0.384666 | + | 0.923056i | \(0.625683\pi\) | |||||||
\(578\) | − | 334.079i | − | 0.577991i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 216.475 | + | 124.982i | 0.373233 | + | 0.215486i | ||||
\(581\) | 566.626 | 0.975259 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 264.339 | + | 152.616i | 0.453411 | + | 0.261777i | ||||
\(584\) | −578.618 | + | 334.065i | −0.990785 | + | 0.572030i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 183.252 | + | 317.401i | 0.312716 | + | 0.541640i | ||||
\(587\) | −255.163 | − | 441.955i | −0.434690 | − | 0.752905i | 0.562580 | − | 0.826743i | \(-0.309809\pi\) |
−0.997270 | + | 0.0738374i | \(0.976475\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −165.566 | + | 388.254i | −0.281097 | + | 0.659174i | ||||
\(590\) | −963.591 | −1.63321 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.45653 | − | 1.41828i | 0.00414954 | − | 0.00239574i | ||||
\(593\) | 57.1501 | − | 98.9869i | 0.0963746 | − | 0.166926i | −0.813807 | − | 0.581135i | \(-0.802609\pi\) |
0.910181 | + | 0.414210i | \(0.135942\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −183.113 | + | 317.161i | −0.307753 | + | 0.533043i | ||||
\(596\) | 294.618 | 0.494325 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −57.8473 | + | 100.194i | −0.0967346 | + | 0.167549i | ||||
\(599\) | −530.087 | − | 306.046i | −0.884954 | − | 0.510928i | −0.0126651 | − | 0.999920i | \(-0.504032\pi\) |
−0.872288 | + | 0.488992i | \(0.837365\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 46.8204i | − | 0.0779041i | −0.999241 | − | 0.0389520i | \(-0.987598\pi\) | ||
0.999241 | − | 0.0389520i | \(-0.0124020\pi\) | |||||||
\(602\) | −149.372 | − | 86.2400i | −0.248126 | − | 0.143256i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −323.727 | − | 186.904i | −0.535971 | − | 0.309443i | ||||
\(605\) | 432.450 | + | 749.025i | 0.714793 | + | 1.23806i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 177.626i | − | 0.292629i | −0.989238 | − | 0.146315i | \(-0.953259\pi\) | ||
0.989238 | − | 0.146315i | \(-0.0467412\pi\) | |||||||
\(608\) | 365.415 | + | 486.603i | 0.601012 | + | 0.800334i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −330.077 | + | 190.570i | −0.541110 | + | 0.312410i | ||||
\(611\) | −97.7346 | + | 56.4271i | −0.159958 | + | 0.0923520i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −194.067 | − | 336.134i | −0.316586 | − | 0.548343i | 0.663187 | − | 0.748454i | \(-0.269203\pi\) |
−0.979773 | + | 0.200110i | \(0.935870\pi\) | |||||||
\(614\) | 34.1005 | − | 59.0637i | 0.0555382 | − | 0.0961950i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 326.792i | 0.530506i | ||||||||
\(617\) | 113.174 | − | 196.024i | 0.183427 | − | 0.317705i | −0.759618 | − | 0.650369i | \(-0.774614\pi\) |
0.943045 | + | 0.332664i | \(0.107948\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −168.929 | −0.272906 | −0.136453 | − | 0.990647i | \(-0.543570\pi\) | ||||
−0.136453 | + | 0.990647i | \(0.543570\pi\) | |||||||
\(620\) | − | 449.990i | − | 0.725790i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −118.378 | + | 68.3458i | −0.190319 | + | 0.109881i | ||||
\(623\) | 855.792 | + | 494.092i | 1.37366 | + | 0.793084i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −40.4783 | − | 70.1104i | −0.0647652 | − | 0.112177i | ||||
\(626\) | 260.935i | 0.416829i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −25.3364 | −0.0403446 | ||||||||
\(629\) | −230.543 | + | 133.104i | −0.366523 | + | 0.211612i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −355.351 | + | 615.487i | −0.563156 | + | 0.975415i | 0.434063 | + | 0.900883i | \(0.357080\pi\) |
−0.997219 | + | 0.0745321i | \(0.976254\pi\) | |||||||
\(632\) | 2.15211 | + | 3.72757i | 0.00340524 | + | 0.00589805i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 204.432 | 0.322447 | ||||||||
\(635\) | − | 903.850i | − | 1.42339i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −122.929 | − | 70.9728i | −0.192980 | − | 0.111417i | ||||
\(638\) | −59.4228 | −0.0931392 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −563.442 | − | 325.303i | −0.880377 | − | 0.508286i | ||||
\(641\) | 901.332 | − | 520.385i | 1.40613 | − | 0.811832i | 0.411122 | − | 0.911580i | \(-0.365137\pi\) |
0.995013 | + | 0.0997480i | \(0.0318037\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.89596 | + | 13.6762i | 0.0122799 | + | 0.0212694i | 0.872100 | − | 0.489328i | \(-0.162758\pi\) |
−0.859820 | + | 0.510597i | \(0.829424\pi\) | |||||||
\(644\) | −520.907 | − | 902.238i | −0.808862 | − | 1.40099i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −60.1843 | − | 80.1441i | −0.0931645 | − | 0.124062i | ||||
\(647\) | −214.998 | −0.332299 | −0.166150 | − | 0.986101i | \(-0.553133\pi\) | ||||
−0.166150 | + | 0.986101i | \(0.553133\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −322.723 | + | 186.324i | −0.497261 | + | 0.287094i | ||||
\(650\) | 60.3307 | − | 104.496i | 0.0928165 | − | 0.160763i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 53.1180 | − | 92.0031i | 0.0814694 | − | 0.141109i | ||||
\(653\) | 371.833 | 0.569423 | 0.284712 | − | 0.958613i | \(-0.408102\pi\) | ||||
0.284712 | + | 0.958613i | \(0.408102\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −230.249 | + | 398.804i | −0.351526 | + | 0.608861i | ||||
\(656\) | 2.04001 | + | 1.17780i | 0.00310977 | + | 0.00179543i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 624.691i | 0.949378i | ||||||||
\(659\) | −113.255 | − | 65.3877i | −0.171859 | − | 0.0992226i | 0.411603 | − | 0.911363i | \(-0.364969\pi\) |
−0.583462 | + | 0.812140i | \(0.698302\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −194.222 | − | 112.134i | −0.293830 | − | 0.169643i | 0.345838 | − | 0.938294i | \(-0.387595\pi\) |
−0.639668 | + | 0.768652i | \(0.720928\pi\) | |||||||
\(662\) | −221.031 | − | 382.837i | −0.333884 | − | 0.578303i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 432.272i | − | 0.651011i | ||||||
\(665\) | −195.689 | − | 1615.97i | −0.294270 | − | 2.43003i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 428.970 | − | 247.666i | 0.643133 | − | 0.371313i | ||||
\(668\) | 3.66959 | − | 2.11864i | 0.00549339 | − | 0.00317161i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 306.578 | + | 531.009i | 0.457579 | + | 0.792551i | ||||
\(671\) | −73.6989 | + | 127.650i | −0.109834 | + | 0.190239i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 101.375i | 0.150631i | 0.997160 | + | 0.0753154i | \(0.0239964\pi\) | ||||
−0.997160 | + | 0.0753154i | \(0.976004\pi\) | |||||||
\(674\) | −391.978 | + | 678.925i | −0.581569 | + | 1.00731i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 405.137 | 0.599315 | ||||||||
\(677\) | 60.9135i | 0.0899756i | 0.998988 | + | 0.0449878i | \(0.0143249\pi\) | ||||
−0.998988 | + | 0.0449878i | \(0.985675\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1329.65 | − | 767.676i | 1.95825 | − | 1.13060i | ||||
\(680\) | 241.958 | + | 139.694i | 0.355821 | + | 0.205433i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 53.4871 | + | 92.6423i | 0.0784268 | + | 0.135839i | ||||
\(683\) | 118.773i | 0.173898i | 0.996213 | + | 0.0869492i | \(0.0277118\pi\) | ||||
−0.996213 | + | 0.0869492i | \(0.972288\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1144.22 | 1.67040 | ||||||||
\(686\) | −131.812 | + | 76.1016i | −0.192146 | + | 0.110935i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.303824 | − | 0.526239i | 0.000441605 | − | 0.000764882i | ||||
\(689\) | 91.3480 | + | 158.219i | 0.132580 | + | 0.229636i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −55.9089 | −0.0809101 | −0.0404551 | − | 0.999181i | \(-0.512881\pi\) | ||||
−0.0404551 | + | 0.999181i | \(0.512881\pi\) | |||||||
\(692\) | 503.695i | 0.727883i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −159.873 | − | 92.3028i | −0.230365 | − | 0.133001i | ||||
\(695\) | −1392.50 | −2.00360 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −191.453 | − | 110.536i | −0.274682 | − | 0.158588i | ||||
\(698\) | 226.415 | − | 130.720i | 0.324376 | − | 0.187279i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 543.270 | + | 940.972i | 0.776100 | + | 1.34425i | ||||
\(701\) | −16.5402 | − | 28.6485i | −0.0235952 | − | 0.0408681i | 0.853987 | − | 0.520295i | \(-0.174178\pi\) |
−0.877582 | + | 0.479427i | \(0.840845\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 464.132 | − | 1088.39i | 0.660217 | − | 1.54821i | ||||
\(704\) | 153.518 | 0.218065 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 165.617 | − | 95.6193i | 0.234586 | − | 0.135438i | ||||
\(707\) | −622.100 | + | 1077.51i | −0.879915 | + | 1.52406i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 371.042 | − | 642.664i | 0.523332 | − | 0.906438i | −0.476299 | − | 0.879283i | \(-0.658022\pi\) |
0.999631 | − | 0.0271545i | \(-0.00864459\pi\) | |||||||
\(710\) | 919.159 | 1.29459 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 376.936 | − | 652.873i | 0.529405 | − | 0.916956i | ||||
\(713\) | −772.240 | − | 445.853i | −1.08309 | − | 0.625320i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 74.5296i | − | 0.104237i | ||||||
\(716\) | 75.0279 | + | 43.3174i | 0.104788 | + | 0.0604991i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 266.519 | + | 153.875i | 0.371196 | + | 0.214310i | ||||
\(719\) | −672.563 | − | 1164.91i | −0.935414 | − | 1.62018i | −0.773894 | − | 0.633315i | \(-0.781694\pi\) |
−0.161520 | − | 0.986869i | \(-0.551640\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 273.715i | 0.379633i | ||||||||
\(722\) | 427.809 | + | 124.213i | 0.592533 | + | 0.172040i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −248.453 | + | 143.445i | −0.343168 | + | 0.198128i | ||||
\(725\) | −447.386 | + | 258.298i | −0.617084 | + | 0.356274i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 107.104 | + | 185.510i | 0.147323 | + | 0.255171i | 0.930237 | − | 0.366958i | \(-0.119601\pi\) |
−0.782914 | + | 0.622130i | \(0.786268\pi\) | |||||||
\(728\) | −97.8002 | + | 169.395i | −0.134341 | + | 0.232685i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | − | 843.464i | − | 1.15543i | ||||||
\(731\) | −28.5137 | + | 49.3871i | −0.0390064 | + | 0.0675610i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 503.818 | 0.687337 | 0.343668 | − | 0.939091i | \(-0.388330\pi\) | ||||
0.343668 | + | 0.939091i | \(0.388330\pi\) | |||||||
\(734\) | 806.334i | 1.09855i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1113.37 | + | 642.803i | −1.51273 | + | 0.873374i | ||||
\(737\) | 205.356 | + | 118.562i | 0.278638 | + | 0.160872i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 708.464 | + | 1227.10i | 0.958680 | + | 1.66048i | 0.725713 | + | 0.687997i | \(0.241510\pi\) |
0.232966 | + | 0.972485i | \(0.425157\pi\) | |||||||
\(740\) | 1261.46i | 1.70467i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1011.29 | 1.36293 | ||||||||
\(743\) | −539.026 | + | 311.207i | −0.725472 | + | 0.418852i | −0.816764 | − | 0.576973i | \(-0.804234\pi\) |
0.0912911 | + | 0.995824i | \(0.470901\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −486.247 | + | 842.205i | −0.652681 | + | 1.13048i | ||||
\(746\) | −200.214 | − | 346.780i | −0.268383 | − | 0.464853i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 41.3230 | 0.0552446 | ||||||||
\(749\) | 1264.68i | 1.68850i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −484.987 | − | 280.007i | −0.645788 | − | 0.372846i | 0.141052 | − | 0.990002i | \(-0.454951\pi\) |
−0.786841 | + | 0.617156i | \(0.788285\pi\) | |||||||
\(752\) | −2.20079 | −0.00292658 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −30.8023 | − | 17.7837i | −0.0408518 | − | 0.0235858i | ||||
\(755\) | 1068.58 | − | 616.945i | 1.41534 | − | 0.817146i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −686.860 | − | 1189.68i | −0.907345 | − | 1.57157i | −0.817738 | − | 0.575591i | \(-0.804772\pi\) |
−0.0896071 | − | 0.995977i | \(-0.528561\pi\) | |||||||
\(758\) | −13.2368 | − | 22.9269i | −0.0174628 | − | 0.0302465i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1232.80 | + | 149.289i | −1.62211 | + | 0.196433i | ||||
\(761\) | 1196.22 | 1.57191 | 0.785953 | − | 0.618286i | \(-0.212173\pi\) | ||||
0.785953 | + | 0.618286i | \(0.212173\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 963.428 | − | 556.235i | 1.26268 | − | 0.729011i | ||||
\(764\) | 217.063 | − | 375.964i | 0.284114 | − | 0.492100i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −131.945 | + | 228.535i | −0.172251 | + | 0.298348i | ||||
\(767\) | −223.048 | −0.290805 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 73.0921 | − | 126.599i | 0.0950483 | − | 0.164628i | −0.814580 | − | 0.580051i | \(-0.803033\pi\) |
0.909629 | + | 0.415422i | \(0.136366\pi\) | |||||||
\(770\) | −357.278 | − | 206.275i | −0.463998 | − | 0.267889i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 832.060i | 1.07780i | ||||||||
\(773\) | −486.540 | − | 280.904i | −0.629418 | − | 0.363395i | 0.151109 | − | 0.988517i | \(-0.451716\pi\) |
−0.780527 | + | 0.625123i | \(0.785049\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 805.393 | + | 464.994i | 1.03922 | + | 0.599992i | ||||
\(776\) | −585.650 | − | 1014.38i | −0.754704 | − | 1.30719i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 465.781i | − | 0.598691i | ||||||
\(779\) | 975.476 | − | 118.127i | 1.25222 | − | 0.151640i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 307.842 | − | 177.732i | 0.394163 | − | 0.227570i | ||||
\(782\) | 183.373 | − | 105.870i | 0.234492 | − | 0.135384i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.38405 | − | 2.39725i | −0.00176537 | − | 0.00305772i | ||||
\(785\) | 41.8161 | − | 72.4277i | 0.0532690 | − | 0.0922646i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1067.08i | − | 1.35589i | −0.735114 | − | 0.677944i | \(-0.762871\pi\) | ||
0.735114 | − | 0.677944i | \(-0.237129\pi\) | |||||||
\(788\) | −302.219 | + | 523.459i | −0.383527 | + | 0.664288i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.43375 | −0.00687817 | ||||||||
\(791\) | − | 1064.58i | − | 1.34587i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −76.4048 | + | 44.1123i | −0.0963490 | + | 0.0556271i | ||||
\(794\) | 282.760 | + | 163.252i | 0.356121 | + | 0.205607i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 420.478 | + | 728.290i | 0.528239 | + | 0.914937i | ||||
\(797\) | − | 396.451i | − | 0.497429i | −0.968577 | − | 0.248715i | \(-0.919992\pi\) | ||
0.968577 | − | 0.248715i | \(-0.0800081\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 206.542 | 0.258501 | ||||||||
\(800\) | 1161.17 | − | 670.399i | 1.45146 | − | 0.837999i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −302.598 | + | 524.115i | −0.377304 | + | 0.653510i | ||||
\(803\) | −163.096 | − | 282.490i | −0.203108 | − | 0.351793i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3438.89 | 4.27192 | ||||||||
\(806\) | 64.0291i | 0.0794406i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 822.018 | + | 474.592i | 1.01735 | + | 0.587366i | ||||
\(809\) | 227.128 | 0.280751 | 0.140376 | − | 0.990098i | \(-0.455169\pi\) | ||||
0.140376 | + | 0.990098i | \(0.455169\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −692.720 | − | 399.942i | −0.854156 | − | 0.493147i | 0.00789497 | − | 0.999969i | \(-0.497487\pi\) |
−0.862051 | + | 0.506822i | \(0.830820\pi\) | |||||||
\(812\) | 277.370 | − | 160.140i | 0.341589 | − | 0.197217i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −149.940 | − | 259.705i | −0.184202 | − | 0.319047i | ||||
\(815\) | 175.336 | + | 303.690i | 0.215136 | + | 0.372626i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −30.4720 | − | 251.633i | −0.0372975 | − | 0.307996i | ||||
\(818\) | −518.732 | −0.634146 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −907.224 | + | 523.786i | −1.10637 | + | 0.638763i | ||||
\(821\) | 73.4787 | − | 127.269i | 0.0894990 | − | 0.155017i | −0.817800 | − | 0.575502i | \(-0.804807\pi\) |
0.907299 | + | 0.420485i | \(0.138140\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −307.863 | + | 533.235i | −0.374075 | + | 0.647916i | −0.990188 | − | 0.139741i | \(-0.955373\pi\) |
0.616114 | + | 0.787657i | \(0.288706\pi\) | |||||||
\(824\) | 208.814 | 0.253415 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −617.327 | + | 1069.24i | −0.747369 | + | 1.29448i | ||||
\(827\) | −410.031 | − | 236.731i | −0.495805 | − | 0.286253i | 0.231174 | − | 0.972912i | \(-0.425743\pi\) |
−0.726980 | + | 0.686659i | \(0.759077\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 264.846i | − | 0.319476i | −0.987159 | − | 0.159738i | \(-0.948935\pi\) | ||
0.987159 | − | 0.159738i | \(-0.0510650\pi\) | |||||||
\(830\) | 472.599 | + | 272.855i | 0.569396 | + | 0.328741i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 79.5771 | + | 45.9439i | 0.0956456 | + | 0.0552210i | ||||
\(833\) | 129.892 | + | 224.980i | 0.155933 | + | 0.270084i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.9867i | 0.0167505i | ||||||||
\(836\) | −146.869 | + | 110.291i | −0.175680 | + | 0.131927i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 690.558 | − | 398.694i | 0.824055 | − | 0.475769i | ||||
\(839\) | 264.910 | − | 152.946i | 0.315745 | − | 0.182296i | −0.333749 | − | 0.942662i | \(-0.608314\pi\) |
0.649495 | + | 0.760366i | \(0.274981\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −344.361 | − | 596.451i | −0.409466 | − | 0.709217i | ||||
\(842\) | 333.509 | − | 577.655i | 0.396092 | − | 0.686051i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 243.362i | − | 0.288344i | ||||||
\(845\) | −668.652 | + | 1158.14i | −0.791304 | + | 1.37058i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1108.20 | 1.30838 | ||||||||
\(848\) | 3.56278i | 0.00420140i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −191.245 | + | 110.416i | −0.224995 | + | 0.129901i | ||||
\(851\) | 2164.82 | + | 1249.86i | 2.54386 | + | 1.46870i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −578.769 | − | 1002.46i | −0.678510 | − | 1.17521i | −0.975430 | − | 0.220311i | \(-0.929293\pi\) |
0.296919 | − | 0.954903i | \(-0.404041\pi\) | |||||||
\(854\) | 488.357i | 0.571846i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 964.812 | 1.12712 | ||||||||
\(857\) | −787.565 | + | 454.701i | −0.918979 | + | 0.530573i | −0.883309 | − | 0.468791i | \(-0.844690\pi\) |
−0.0356701 | + | 0.999364i | \(0.511357\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −556.807 | + | 964.418i | −0.648204 | + | 1.12272i | 0.335348 | + | 0.942094i | \(0.391146\pi\) |
−0.983552 | + | 0.180627i | \(0.942187\pi\) | |||||||
\(860\) | 135.115 | + | 234.026i | 0.157111 | + | 0.272124i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −282.820 | −0.328097 | ||||||||
\(863\) | 511.832i | 0.593085i | 0.955020 | + | 0.296542i | \(0.0958336\pi\) | ||||
−0.955020 | + | 0.296542i | \(0.904166\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1439.88 | − | 831.316i | −1.66460 | − | 0.961059i | ||||
\(866\) | 340.518 | 0.393208 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −499.328 | − | 288.287i | −0.575262 | − | 0.332128i | ||||
\(869\) | −1.81985 | + | 1.05069i | −0.00209419 | + | 0.00120908i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 70.9653 | + | 122.916i | 0.0814757 | + | 0.141120i | ||||
\(872\) | −424.345 | − | 734.987i | −0.486634 | − | 0.842875i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −369.169 | + | 865.703i | −0.422390 | + | 0.990506i | ||||
\(875\) | −1444.72 | −1.65111 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −270.775 | + | 156.332i | −0.308752 | + | 0.178258i | −0.646368 | − | 0.763026i | \(-0.723713\pi\) |
0.337616 | + | 0.941284i | \(0.390379\pi\) | |||||||
\(878\) | 7.58661 | − | 13.1404i | 0.00864079 | − | 0.0149663i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.726707 | − | 1.25869i | 0.000825803 | − | 0.00143033i | ||||
\(881\) | −858.585 | −0.974557 | −0.487279 | − | 0.873246i | \(-0.662010\pi\) | ||||
−0.487279 | + | 0.873246i | \(0.662010\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −544.512 | + | 943.122i | −0.616661 | + | 1.06809i | 0.373429 | + | 0.927659i | \(0.378182\pi\) |
−0.990091 | + | 0.140430i | \(0.955151\pi\) | |||||||
\(884\) | 21.4201 | + | 12.3669i | 0.0242309 | + | 0.0139897i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 77.7259i | − | 0.0877268i | ||||||
\(887\) | 241.738 | + | 139.567i | 0.272534 | + | 0.157348i | 0.630039 | − | 0.776564i | \(-0.283039\pi\) |
−0.357505 | + | 0.933911i | \(0.616372\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1002.95 | − | 579.054i | −1.12818 | − | 0.651354i | ||||
\(890\) | 475.853 | + | 824.202i | 0.534667 | + | 0.926070i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 164.057i | 0.183921i | ||||||||
\(893\) | −734.085 | + | 551.262i | −0.822043 | + | 0.617314i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −247.657 | + | 142.985i | −0.276712 | + | 0.159760i | ||||
\(896\) | −721.940 | + | 416.812i | −0.805737 | + | 0.465192i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −419.523 | − | 726.635i | −0.467175 | − | 0.809170i | ||||
\(899\) | 137.066 | − | 237.406i | 0.152465 | − | 0.264078i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 334.365i | − | 0.371104i | ||||||
\(902\) | 124.517 | − | 215.670i | 0.138046 | − | 0.239102i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −812.154 | −0.898401 | ||||||||
\(905\) | − | 946.984i | − | 1.04639i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 224.436 | − | 129.578i | 0.247449 | − | 0.142864i | −0.371147 | − | 0.928574i | \(-0.621035\pi\) |
0.618595 | + | 0.785710i | \(0.287702\pi\) | |||||||
\(908\) | −804.977 | − | 464.754i | −0.886539 | − | 0.511844i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −123.465 | − | 213.848i | −0.135676 | − | 0.234998i | ||||
\(911\) | 922.079i | 1.01216i | 0.862486 | + | 0.506081i | \(0.168906\pi\) | ||||
−0.862486 | + | 0.506081i | \(0.831094\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 211.041 | 0.231152 | ||||||||
\(914\) | −463.903 | + | 267.835i | −0.507553 | + | 0.293036i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −50.1061 | + | 86.7863i | −0.0547010 | + | 0.0947449i | ||||
\(917\) | 295.020 | + | 510.989i | 0.321723 | + | 0.557240i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 434.655 | 0.472965 | 0.236483 | − | 0.971636i | \(-0.424005\pi\) | ||||
0.236483 | + | 0.971636i | \(0.424005\pi\) | |||||||
\(920\) | − | 2623.49i | − | 2.85162i | ||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −566.590 | − | 327.121i | −0.614522 | − | 0.354795i | ||||
\(923\) | 212.763 | 0.230512 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2257.76 | − | 1303.52i | −2.44082 | − | 1.40921i | ||||
\(926\) | −480.930 | + | 277.665i | −0.519363 | + | 0.299854i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −197.614 | − | 342.277i | −0.212946 | − | 0.368833i | ||||
\(929\) | 223.539 | + | 387.180i | 0.240623 | + | 0.416771i | 0.960892 | − | 0.276924i | \(-0.0893150\pi\) |
−0.720269 | + | 0.693695i | \(0.755982\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1062.13 | − | 452.933i | −1.14085 | − | 0.486502i | ||||
\(932\) | −666.172 | −0.714776 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −783.707 | + | 452.473i | −0.839087 | + | 0.484447i | ||||
\(935\) | −68.2009 | + | 118.127i | −0.0729422 | + | 0.126340i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 296.047 | − | 512.768i | 0.315952 | − | 0.547244i | −0.663688 | − | 0.748010i | \(-0.731010\pi\) |
0.979639 | + | 0.200766i | \(0.0643430\pi\) | |||||||
\(938\) | 785.640 | 0.837569 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 489.362 | − | 847.600i | 0.520598 | − | 0.901703i | ||||
\(941\) | −534.341 | − | 308.502i | −0.567844 | − | 0.327845i | 0.188444 | − | 0.982084i | \(-0.439656\pi\) |
−0.756288 | + | 0.654239i | \(0.772989\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2075.88i | 2.20136i | ||||||||
\(944\) | −3.76694 | − | 2.17485i | −0.00399040 | − | 0.00230386i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −55.6341 | − | 32.1203i | −0.0588098 | − | 0.0339539i | ||||
\(947\) | 469.361 | + | 812.957i | 0.495629 | + | 0.858455i | 0.999987 | − | 0.00503973i | \(-0.00160420\pi\) |
−0.504358 | + | 0.863495i | \(0.668271\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 195.241i | − | 0.205734i | ||||||
\(950\) | 385.018 | − | 902.868i | 0.405282 | − | 0.950387i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 310.022 | − | 178.991i | 0.325653 | − | 0.188016i | ||||
\(953\) | 1138.99 | − | 657.596i | 1.19516 | − | 0.690028i | 0.235690 | − | 0.971828i | \(-0.424265\pi\) |
0.959473 | + | 0.281801i | \(0.0909317\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 716.497 | + | 1241.01i | 0.750259 | + | 1.29949i | ||||
\(956\) | −72.0608 | + | 124.813i | −0.0753774 | + | 0.130557i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 324.932i | 0.339178i | ||||||||
\(959\) | 733.048 | − | 1269.68i | 0.764388 | − | 1.32396i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 467.501 | 0.486474 | ||||||||
\(962\) | − | 179.493i | − | 0.186583i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −310.048 | + | 179.006i | −0.321627 | + | 0.185691i | ||||
\(965\) | −2378.56 | − | 1373.26i | −2.46483 | − | 1.42307i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 105.759 | + | 183.181i | 0.109368 | + | 0.189432i | 0.915515 | − | 0.402285i | \(-0.131784\pi\) |
−0.806146 | + | 0.591717i | \(0.798450\pi\) | |||||||
\(968\) | − | 845.432i | − | 0.873380i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1478.68 | 1.52441 | ||||||||
\(971\) | 840.225 | − | 485.104i | 0.865319 | − | 0.499592i | −0.000470648 | − | 1.00000i | \(-0.500150\pi\) |
0.865790 | + | 0.500408i | \(0.166816\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −892.110 | + | 1545.18i | −0.916865 | + | 1.58806i | ||||
\(974\) | 189.882 | + | 328.886i | 0.194951 | + | 0.337665i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.72048 | −0.00176279 | ||||||||
\(977\) | 957.081i | 0.979612i | 0.871831 | + | 0.489806i | \(0.162932\pi\) | ||||
−0.871831 | + | 0.489806i | \(0.837068\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 318.742 | + | 184.026i | 0.325579 | + | 0.187973i | ||||
\(980\) | 1231.02 | 1.25614 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −634.545 | − | 366.354i | −0.646176 | − | 0.373070i | ||||
\(983\) | 408.211 | − | 235.681i | 0.415271 | − | 0.239757i | −0.277781 | − | 0.960644i | \(-0.589599\pi\) |
0.693052 | + | 0.720888i | \(0.256266\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −997.586 | − | 1727.87i | −1.01278 | − | 1.75418i | ||||
\(986\) | 32.5472 | + | 56.3735i | 0.0330094 | + | 0.0571739i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −109.138 | + | 13.2163i | −0.110463 | + | 0.0133768i | ||||
\(989\) | 535.492 | 0.541448 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 584.759 | − | 337.611i | 0.590070 | − | 0.340677i | −0.175055 | − | 0.984559i | \(-0.556010\pi\) |
0.765125 | + | 0.643882i | \(0.222677\pi\) | |||||||
\(992\) | −355.748 | + | 616.174i | −0.358617 | + | 0.621143i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 588.861 | − | 1019.94i | 0.592416 | − | 1.02609i | ||||
\(995\) | −2775.89 | −2.78984 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −352.522 | + | 610.586i | −0.353582 | + | 0.612423i | −0.986874 | − | 0.161490i | \(-0.948370\pi\) |
0.633292 | + | 0.773913i | \(0.281703\pi\) | |||||||
\(998\) | 700.151 | + | 404.233i | 0.701555 | + | 0.405043i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 171.3.p.f.145.3 | yes | 8 | |
3.2 | odd | 2 | inner | 171.3.p.f.145.2 | yes | 8 | |
19.8 | odd | 6 | inner | 171.3.p.f.46.3 | yes | 8 | |
57.8 | even | 6 | inner | 171.3.p.f.46.2 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
171.3.p.f.46.2 | ✓ | 8 | 57.8 | even | 6 | inner | |
171.3.p.f.46.3 | yes | 8 | 19.8 | odd | 6 | inner | |
171.3.p.f.145.2 | yes | 8 | 3.2 | odd | 2 | inner | |
171.3.p.f.145.3 | yes | 8 | 1.1 | even | 1 | trivial |