Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,3,Mod(557,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.557");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.s (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.0327593166\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 18) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 863.1 | ||
Root | \(-1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.863 |
Dual form | 882.3.s.d.557.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22474 | − | 0.707107i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | + | 1.73205i | 0.250000 | + | 0.433013i | ||||
\(5\) | −3.67423 | − | 2.12132i | −0.734847 | − | 0.424264i | 0.0853458 | − | 0.996351i | \(-0.472801\pi\) |
−0.820193 | + | 0.572087i | \(0.806134\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.00000 | + | 5.19615i | 0.300000 | + | 0.519615i | ||||
\(11\) | 14.6969 | − | 8.48528i | 1.33609 | − | 0.771389i | 0.349861 | − | 0.936802i | \(-0.386229\pi\) |
0.986224 | + | 0.165412i | \(0.0528955\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −8.00000 | −0.615385 | −0.307692 | − | 0.951486i | \(-0.599557\pi\) | ||||
−0.307692 | + | 0.951486i | \(0.599557\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.125000 | + | 0.216506i | ||||
\(17\) | 11.0227 | − | 6.36396i | 0.648394 | − | 0.374351i | −0.139446 | − | 0.990230i | \(-0.544532\pi\) |
0.787841 | + | 0.615879i | \(0.211199\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.00000 | + | 13.8564i | −0.421053 | + | 0.729285i | −0.996043 | − | 0.0888758i | \(-0.971673\pi\) |
0.574990 | + | 0.818160i | \(0.305006\pi\) | |||||||
\(20\) | − | 8.48528i | − | 0.424264i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −24.0000 | −1.09091 | ||||||||
\(23\) | 14.6969 | + | 8.48528i | 0.638997 | + | 0.368925i | 0.784228 | − | 0.620473i | \(-0.213059\pi\) |
−0.145231 | + | 0.989398i | \(0.546392\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.50000 | − | 6.06218i | −0.140000 | − | 0.242487i | ||||
\(26\) | 9.79796 | + | 5.65685i | 0.376845 | + | 0.217571i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.24264i | 0.146298i | 0.997321 | + | 0.0731490i | \(0.0233049\pi\) | ||||
−0.997321 | + | 0.0731490i | \(0.976695\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 22.0000 | + | 38.1051i | 0.709677 | + | 1.22920i | 0.964977 | + | 0.262335i | \(0.0844926\pi\) |
−0.255299 | + | 0.966862i | \(0.582174\pi\) | |||||||
\(32\) | 4.89898 | − | 2.82843i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −18.0000 | −0.529412 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 17.0000 | − | 29.4449i | 0.459459 | − | 0.795807i | −0.539473 | − | 0.842003i | \(-0.681376\pi\) |
0.998932 | + | 0.0461958i | \(0.0147098\pi\) | |||||||
\(38\) | 19.5959 | − | 11.3137i | 0.515682 | − | 0.297729i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.00000 | + | 10.3923i | −0.150000 | + | 0.259808i | ||||
\(41\) | − | 46.6690i | − | 1.13827i | −0.822244 | − | 0.569135i | \(-0.807278\pi\) | ||
0.822244 | − | 0.569135i | \(-0.192722\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −40.0000 | −0.930233 | −0.465116 | − | 0.885250i | \(-0.653987\pi\) | ||||
−0.465116 | + | 0.885250i | \(0.653987\pi\) | |||||||
\(44\) | 29.3939 | + | 16.9706i | 0.668043 | + | 0.385695i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −12.0000 | − | 20.7846i | −0.260870 | − | 0.451839i | ||||
\(47\) | −73.4847 | − | 42.4264i | −1.56350 | − | 0.902690i | −0.996898 | − | 0.0787005i | \(-0.974923\pi\) |
−0.566606 | − | 0.823989i | \(-0.691744\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 9.89949i | 0.197990i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −8.00000 | − | 13.8564i | −0.153846 | − | 0.266469i | ||||
\(53\) | 33.0681 | − | 19.0919i | 0.623927 | − | 0.360224i | −0.154470 | − | 0.987998i | \(-0.549367\pi\) |
0.778396 | + | 0.627773i | \(0.216034\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −72.0000 | −1.30909 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.00000 | − | 5.19615i | 0.0517241 | − | 0.0895888i | ||||
\(59\) | −29.3939 | + | 16.9706i | −0.498201 | + | 0.287637i | −0.727970 | − | 0.685609i | \(-0.759536\pi\) |
0.229769 | + | 0.973245i | \(0.426203\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 25.0000 | − | 43.3013i | 0.409836 | − | 0.709857i | −0.585035 | − | 0.811008i | \(-0.698919\pi\) |
0.994871 | + | 0.101151i | \(0.0322526\pi\) | |||||||
\(62\) | − | 62.2254i | − | 1.00364i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 29.3939 | + | 16.9706i | 0.452213 | + | 0.261086i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | − | 6.92820i | −0.0597015 | − | 0.103406i | 0.834630 | − | 0.550811i | \(-0.185682\pi\) |
−0.894331 | + | 0.447405i | \(0.852348\pi\) | |||||||
\(68\) | 22.0454 | + | 12.7279i | 0.324197 | + | 0.187175i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 50.9117i | − | 0.717066i | −0.933517 | − | 0.358533i | \(-0.883277\pi\) | ||
0.933517 | − | 0.358533i | \(-0.116723\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.00000 | − | 13.8564i | −0.109589 | − | 0.189814i | 0.806015 | − | 0.591895i | \(-0.201620\pi\) |
−0.915604 | + | 0.402082i | \(0.868287\pi\) | |||||||
\(74\) | −41.6413 | + | 24.0416i | −0.562721 | + | 0.324887i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −32.0000 | −0.421053 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 38.0000 | − | 65.8179i | 0.481013 | − | 0.833138i | −0.518750 | − | 0.854926i | \(-0.673602\pi\) |
0.999763 | + | 0.0217876i | \(0.00693577\pi\) | |||||||
\(80\) | 14.6969 | − | 8.48528i | 0.183712 | − | 0.106066i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −33.0000 | + | 57.1577i | −0.402439 | + | 0.697045i | ||||
\(83\) | − | 118.794i | − | 1.43125i | −0.698484 | − | 0.715626i | \(-0.746141\pi\) | ||
0.698484 | − | 0.715626i | \(-0.253859\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −54.0000 | −0.635294 | ||||||||
\(86\) | 48.9898 | + | 28.2843i | 0.569649 | + | 0.328887i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −24.0000 | − | 41.5692i | −0.272727 | − | 0.472377i | ||||
\(89\) | 11.0227 | + | 6.36396i | 0.123851 | + | 0.0715052i | 0.560645 | − | 0.828056i | \(-0.310553\pi\) |
−0.436795 | + | 0.899561i | \(0.643886\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 33.9411i | 0.368925i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 60.0000 | + | 103.923i | 0.638298 | + | 1.10556i | ||||
\(95\) | 58.7878 | − | 33.9411i | 0.618818 | − | 0.357275i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −176.000 | −1.81443 | −0.907216 | − | 0.420664i | \(-0.861797\pi\) | ||||
−0.907216 | + | 0.420664i | \(0.861797\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.00000 | − | 12.1244i | 0.0700000 | − | 0.121244i | ||||
\(101\) | −25.7196 | + | 14.8492i | −0.254650 | + | 0.147022i | −0.621892 | − | 0.783103i | \(-0.713636\pi\) |
0.367242 | + | 0.930126i | \(0.380302\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.0000 | + | 24.2487i | −0.135922 | + | 0.235424i | −0.925949 | − | 0.377648i | \(-0.876733\pi\) |
0.790027 | + | 0.613072i | \(0.210066\pi\) | |||||||
\(104\) | 22.6274i | 0.217571i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −54.0000 | −0.509434 | ||||||||
\(107\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −28.0000 | − | 48.4974i | −0.256881 | − | 0.444930i | 0.708524 | − | 0.705687i | \(-0.249361\pi\) |
−0.965405 | + | 0.260756i | \(0.916028\pi\) | |||||||
\(110\) | 88.1816 | + | 50.9117i | 0.801651 | + | 0.462834i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 156.978i | − | 1.38918i | −0.719404 | − | 0.694592i | \(-0.755585\pi\) | ||
0.719404 | − | 0.694592i | \(-0.244415\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −36.0000 | − | 62.3538i | −0.313043 | − | 0.542207i | ||||
\(116\) | −7.34847 | + | 4.24264i | −0.0633489 | + | 0.0365745i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 48.0000 | 0.406780 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 83.5000 | − | 144.626i | 0.690083 | − | 1.19526i | ||||
\(122\) | −61.2372 | + | 35.3553i | −0.501945 | + | 0.289798i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −44.0000 | + | 76.2102i | −0.354839 | + | 0.614599i | ||||
\(125\) | 135.765i | 1.08612i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 92.0000 | 0.724409 | 0.362205 | − | 0.932099i | \(-0.382024\pi\) | ||||
0.362205 | + | 0.932099i | \(0.382024\pi\) | |||||||
\(128\) | 9.79796 | + | 5.65685i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −24.0000 | − | 41.5692i | −0.184615 | − | 0.319763i | ||||
\(131\) | −146.969 | − | 84.8528i | −1.12190 | − | 0.647731i | −0.180017 | − | 0.983663i | \(-0.557615\pi\) |
−0.941886 | + | 0.335932i | \(0.890949\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 11.3137i | 0.0844307i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −18.0000 | − | 31.1769i | −0.132353 | − | 0.229242i | ||||
\(137\) | 135.947 | − | 78.4889i | 0.992312 | − | 0.572911i | 0.0863471 | − | 0.996265i | \(-0.472481\pi\) |
0.905964 | + | 0.423354i | \(0.139147\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −152.000 | −1.09353 | −0.546763 | − | 0.837288i | \(-0.684140\pi\) | ||||
−0.546763 | + | 0.837288i | \(0.684140\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −36.0000 | + | 62.3538i | −0.253521 | + | 0.439111i | ||||
\(143\) | −117.576 | + | 67.8823i | −0.822206 | + | 0.474701i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.00000 | − | 15.5885i | 0.0620690 | − | 0.107507i | ||||
\(146\) | 22.6274i | 0.154982i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 68.0000 | 0.459459 | ||||||||
\(149\) | −238.825 | − | 137.886i | −1.60285 | − | 0.925408i | −0.990913 | − | 0.134505i | \(-0.957056\pi\) |
−0.611941 | − | 0.790903i | \(-0.709611\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 74.0000 | + | 128.172i | 0.490066 | + | 0.848820i | 0.999935 | − | 0.0114328i | \(-0.00363925\pi\) |
−0.509868 | + | 0.860252i | \(0.670306\pi\) | |||||||
\(152\) | 39.1918 | + | 22.6274i | 0.257841 | + | 0.148865i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 186.676i | − | 1.20436i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −41.0000 | − | 71.0141i | −0.261146 | − | 0.452319i | 0.705400 | − | 0.708809i | \(-0.250767\pi\) |
−0.966547 | + | 0.256490i | \(0.917434\pi\) | |||||||
\(158\) | −93.0806 | + | 53.7401i | −0.589118 | + | 0.340127i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −24.0000 | −0.150000 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −28.0000 | + | 48.4974i | −0.171779 | + | 0.297530i | −0.939042 | − | 0.343803i | \(-0.888285\pi\) |
0.767263 | + | 0.641333i | \(0.221618\pi\) | |||||||
\(164\) | 80.8332 | − | 46.6690i | 0.492885 | − | 0.284567i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −84.0000 | + | 145.492i | −0.506024 | + | 0.876459i | ||||
\(167\) | − | 33.9411i | − | 0.203240i | −0.994823 | − | 0.101620i | \(-0.967597\pi\) | ||
0.994823 | − | 0.101620i | \(-0.0324026\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −105.000 | −0.621302 | ||||||||
\(170\) | 66.1362 | + | 38.1838i | 0.389037 | + | 0.224610i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −40.0000 | − | 69.2820i | −0.232558 | − | 0.402803i | ||||
\(173\) | −150.644 | − | 86.9741i | −0.870772 | − | 0.502741i | −0.00316754 | − | 0.999995i | \(-0.501008\pi\) |
−0.867605 | + | 0.497254i | \(0.834342\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 67.8823i | 0.385695i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −9.00000 | − | 15.5885i | −0.0505618 | − | 0.0875756i | ||||
\(179\) | −176.363 | + | 101.823i | −0.985270 | + | 0.568846i | −0.903857 | − | 0.427835i | \(-0.859277\pi\) |
−0.0814127 | + | 0.996680i | \(0.525943\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 232.000 | 1.28177 | 0.640884 | − | 0.767638i | \(-0.278568\pi\) | ||||
0.640884 | + | 0.767638i | \(0.278568\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 24.0000 | − | 41.5692i | 0.130435 | − | 0.225920i | ||||
\(185\) | −124.924 | + | 72.1249i | −0.675265 | + | 0.389864i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 108.000 | − | 187.061i | 0.577540 | − | 1.00033i | ||||
\(188\) | − | 169.706i | − | 0.902690i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −96.0000 | −0.505263 | ||||||||
\(191\) | 29.3939 | + | 16.9706i | 0.153895 | + | 0.0888511i | 0.574970 | − | 0.818175i | \(-0.305014\pi\) |
−0.421075 | + | 0.907026i | \(0.638347\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −103.000 | − | 178.401i | −0.533679 | − | 0.924359i | −0.999226 | − | 0.0393357i | \(-0.987476\pi\) |
0.465547 | − | 0.885023i | \(-0.345858\pi\) | |||||||
\(194\) | 215.555 | + | 124.451i | 1.11111 | + | 0.641499i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 165.463i | 0.839914i | 0.907544 | + | 0.419957i | \(0.137955\pi\) | ||||
−0.907544 | + | 0.419957i | \(0.862045\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.0000 | + | 17.3205i | 0.0502513 | + | 0.0870377i | 0.890057 | − | 0.455849i | \(-0.150664\pi\) |
−0.839806 | + | 0.542887i | \(0.817331\pi\) | |||||||
\(200\) | −17.1464 | + | 9.89949i | −0.0857321 | + | 0.0494975i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 42.0000 | 0.207921 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −99.0000 | + | 171.473i | −0.482927 | + | 0.836454i | ||||
\(206\) | 34.2929 | − | 19.7990i | 0.166470 | − | 0.0961116i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 16.0000 | − | 27.7128i | 0.0769231 | − | 0.133235i | ||||
\(209\) | 271.529i | 1.29918i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 296.000 | 1.40284 | 0.701422 | − | 0.712746i | \(-0.252549\pi\) | ||||
0.701422 | + | 0.712746i | \(0.252549\pi\) | |||||||
\(212\) | 66.1362 | + | 38.1838i | 0.311963 | + | 0.180112i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 146.969 | + | 84.8528i | 0.683579 | + | 0.394664i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 79.1960i | 0.363284i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −72.0000 | − | 124.708i | −0.327273 | − | 0.566853i | ||||
\(221\) | −88.1816 | + | 50.9117i | −0.399012 | + | 0.230370i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 436.000 | 1.95516 | 0.977578 | − | 0.210571i | \(-0.0675325\pi\) | ||||
0.977578 | + | 0.210571i | \(0.0675325\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −111.000 | + | 192.258i | −0.491150 | + | 0.850698i | ||||
\(227\) | −14.6969 | + | 8.48528i | −0.0647442 | + | 0.0373801i | −0.532023 | − | 0.846730i | \(-0.678568\pi\) |
0.467278 | + | 0.884110i | \(0.345235\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.00000 | − | 6.92820i | 0.0174672 | − | 0.0302542i | −0.857160 | − | 0.515051i | \(-0.827773\pi\) |
0.874627 | + | 0.484797i | \(0.161106\pi\) | |||||||
\(230\) | 101.823i | 0.442710i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12.0000 | 0.0517241 | ||||||||
\(233\) | 11.0227 | + | 6.36396i | 0.0473077 | + | 0.0273131i | 0.523467 | − | 0.852046i | \(-0.324638\pi\) |
−0.476160 | + | 0.879359i | \(0.657972\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 180.000 | + | 311.769i | 0.765957 | + | 1.32668i | ||||
\(236\) | −58.7878 | − | 33.9411i | −0.249101 | − | 0.143818i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 135.765i | 0.568052i | 0.958817 | + | 0.284026i | \(0.0916703\pi\) | ||||
−0.958817 | + | 0.284026i | \(0.908330\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.0000 | + | 27.7128i | 0.0663900 | + | 0.114991i | 0.897310 | − | 0.441401i | \(-0.145519\pi\) |
−0.830920 | + | 0.556392i | \(0.812185\pi\) | |||||||
\(242\) | −204.532 | + | 118.087i | −0.845175 | + | 0.487962i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 100.000 | 0.409836 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 64.0000 | − | 110.851i | 0.259109 | − | 0.448790i | ||||
\(248\) | 107.778 | − | 62.2254i | 0.434587 | − | 0.250909i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 96.0000 | − | 166.277i | 0.384000 | − | 0.665108i | ||||
\(251\) | − | 50.9117i | − | 0.202835i | −0.994844 | − | 0.101418i | \(-0.967662\pi\) | ||
0.994844 | − | 0.101418i | \(-0.0323379\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 288.000 | 1.13834 | ||||||||
\(254\) | −112.677 | − | 65.0538i | −0.443608 | − | 0.256117i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −157.992 | − | 91.2168i | −0.614755 | − | 0.354929i | 0.160069 | − | 0.987106i | \(-0.448828\pi\) |
−0.774824 | + | 0.632177i | \(0.782162\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 67.8823i | 0.261086i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 120.000 | + | 207.846i | 0.458015 | + | 0.793306i | ||||
\(263\) | 323.333 | − | 186.676i | 1.22940 | − | 0.709795i | 0.262497 | − | 0.964933i | \(-0.415454\pi\) |
0.966905 | + | 0.255137i | \(0.0821207\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −162.000 | −0.611321 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.00000 | − | 13.8564i | 0.0298507 | − | 0.0517030i | ||||
\(269\) | 297.613 | − | 171.827i | 1.10637 | − | 0.638762i | 0.168482 | − | 0.985705i | \(-0.446114\pi\) |
0.937886 | + | 0.346943i | \(0.112780\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 190.000 | − | 329.090i | 0.701107 | − | 1.21435i | −0.266971 | − | 0.963705i | \(-0.586023\pi\) |
0.968078 | − | 0.250648i | \(-0.0806438\pi\) | |||||||
\(272\) | 50.9117i | 0.187175i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −222.000 | −0.810219 | ||||||||
\(275\) | −102.879 | − | 59.3970i | −0.374104 | − | 0.215989i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 164.000 | + | 284.056i | 0.592058 | + | 1.02547i | 0.993955 | + | 0.109789i | \(0.0350176\pi\) |
−0.401897 | + | 0.915685i | \(0.631649\pi\) | |||||||
\(278\) | 186.161 | + | 107.480i | 0.669645 | + | 0.386620i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 284.257i | 1.01159i | 0.862654 | + | 0.505795i | \(0.168801\pi\) | ||||
−0.862654 | + | 0.505795i | \(0.831199\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −104.000 | − | 180.133i | −0.367491 | − | 0.636513i | 0.621681 | − | 0.783270i | \(-0.286450\pi\) |
−0.989173 | + | 0.146757i | \(0.953117\pi\) | |||||||
\(284\) | 88.1816 | − | 50.9117i | 0.310499 | − | 0.179267i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 192.000 | 0.671329 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −63.5000 | + | 109.985i | −0.219723 | + | 0.380572i | ||||
\(290\) | −22.0454 | + | 12.7279i | −0.0760186 | + | 0.0438894i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 16.0000 | − | 27.7128i | 0.0547945 | − | 0.0949069i | ||||
\(293\) | 436.992i | 1.49144i | 0.666259 | + | 0.745720i | \(0.267894\pi\) | ||||
−0.666259 | + | 0.745720i | \(0.732106\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 144.000 | 0.488136 | ||||||||
\(296\) | −83.2827 | − | 48.0833i | −0.281360 | − | 0.162443i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 195.000 | + | 337.750i | 0.654362 | + | 1.13339i | ||||
\(299\) | −117.576 | − | 67.8823i | −0.393229 | − | 0.227031i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 209.304i | − | 0.693058i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −32.0000 | − | 55.4256i | −0.105263 | − | 0.182321i | ||||
\(305\) | −183.712 | + | 106.066i | −0.602334 | + | 0.347757i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 520.000 | 1.69381 | 0.846906 | − | 0.531743i | \(-0.178463\pi\) | ||||
0.846906 | + | 0.531743i | \(0.178463\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −132.000 | + | 228.631i | −0.425806 | + | 0.737518i | ||||
\(311\) | 323.333 | − | 186.676i | 1.03965 | − | 0.600245i | 0.119919 | − | 0.992784i | \(-0.461736\pi\) |
0.919736 | + | 0.392539i | \(0.128403\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −47.0000 | + | 81.4064i | −0.150160 | + | 0.260084i | −0.931286 | − | 0.364289i | \(-0.881312\pi\) |
0.781126 | + | 0.624373i | \(0.214645\pi\) | |||||||
\(314\) | 115.966i | 0.369317i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 152.000 | 0.481013 | ||||||||
\(317\) | −290.265 | − | 167.584i | −0.915661 | − | 0.528657i | −0.0334128 | − | 0.999442i | \(-0.510638\pi\) |
−0.882248 | + | 0.470785i | \(0.843971\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 36.0000 | + | 62.3538i | 0.112853 | + | 0.195467i | ||||
\(320\) | 29.3939 | + | 16.9706i | 0.0918559 | + | 0.0530330i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 203.647i | 0.630485i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 28.0000 | + | 48.4974i | 0.0861538 | + | 0.149223i | ||||
\(326\) | 68.5857 | − | 39.5980i | 0.210386 | − | 0.121466i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −132.000 | −0.402439 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −268.000 | + | 464.190i | −0.809668 | + | 1.40239i | 0.103427 | + | 0.994637i | \(0.467019\pi\) |
−0.913094 | + | 0.407748i | \(0.866314\pi\) | |||||||
\(332\) | 205.757 | − | 118.794i | 0.619750 | − | 0.357813i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −24.0000 | + | 41.5692i | −0.0718563 | + | 0.124459i | ||||
\(335\) | 33.9411i | 0.101317i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −208.000 | −0.617211 | −0.308605 | − | 0.951190i | \(-0.599862\pi\) | ||||
−0.308605 | + | 0.951190i | \(0.599862\pi\) | |||||||
\(338\) | 128.598 | + | 74.2462i | 0.380468 | + | 0.219663i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −54.0000 | − | 93.5307i | −0.158824 | − | 0.275090i | ||||
\(341\) | 646.665 | + | 373.352i | 1.89638 | + | 1.09488i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 113.137i | 0.328887i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 123.000 | + | 213.042i | 0.355491 | + | 0.615729i | ||||
\(347\) | 249.848 | − | 144.250i | 0.720023 | − | 0.415705i | −0.0947382 | − | 0.995502i | \(-0.530201\pi\) |
0.814761 | + | 0.579797i | \(0.196868\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 238.000 | 0.681948 | 0.340974 | − | 0.940073i | \(-0.389243\pi\) | ||||
0.340974 | + | 0.940073i | \(0.389243\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 48.0000 | − | 83.1384i | 0.136364 | − | 0.236189i | ||||
\(353\) | 194.734 | − | 112.430i | 0.551656 | − | 0.318499i | −0.198134 | − | 0.980175i | \(-0.563488\pi\) |
0.749789 | + | 0.661676i | \(0.230155\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −108.000 | + | 187.061i | −0.304225 | + | 0.526934i | ||||
\(356\) | 25.4558i | 0.0715052i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 288.000 | 0.804469 | ||||||||
\(359\) | 484.999 | + | 280.014i | 1.35097 | + | 0.779984i | 0.988386 | − | 0.151966i | \(-0.0485605\pi\) |
0.362586 | + | 0.931950i | \(0.381894\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 52.5000 | + | 90.9327i | 0.145429 | + | 0.251891i | ||||
\(362\) | −284.141 | − | 164.049i | −0.784919 | − | 0.453173i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 67.8823i | 0.185979i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 142.000 | + | 245.951i | 0.386921 | + | 0.670167i | 0.992034 | − | 0.125973i | \(-0.0402053\pi\) |
−0.605113 | + | 0.796140i | \(0.706872\pi\) | |||||||
\(368\) | −58.7878 | + | 33.9411i | −0.159749 | + | 0.0922313i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 204.000 | 0.551351 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 95.0000 | − | 164.545i | 0.254692 | − | 0.441139i | −0.710120 | − | 0.704081i | \(-0.751359\pi\) |
0.964812 | + | 0.262942i | \(0.0846927\pi\) | |||||||
\(374\) | −264.545 | + | 152.735i | −0.707339 | + | 0.408383i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −120.000 | + | 207.846i | −0.319149 | + | 0.552782i | ||||
\(377\) | − | 33.9411i | − | 0.0900295i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −160.000 | −0.422164 | −0.211082 | − | 0.977468i | \(-0.567699\pi\) | ||||
−0.211082 | + | 0.977468i | \(0.567699\pi\) | |||||||
\(380\) | 117.576 | + | 67.8823i | 0.309409 | + | 0.178638i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −24.0000 | − | 41.5692i | −0.0628272 | − | 0.108820i | ||||
\(383\) | −235.151 | − | 135.765i | −0.613971 | − | 0.354477i | 0.160547 | − | 0.987028i | \(-0.448674\pi\) |
−0.774518 | + | 0.632552i | \(0.782008\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 291.328i | 0.754736i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −176.000 | − | 304.841i | −0.453608 | − | 0.785673i | ||||
\(389\) | −349.052 | + | 201.525i | −0.897307 | + | 0.518060i | −0.876325 | − | 0.481720i | \(-0.840012\pi\) |
−0.0209813 | + | 0.999780i | \(0.506679\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 216.000 | 0.552430 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 117.000 | − | 202.650i | 0.296954 | − | 0.514340i | ||||
\(395\) | −279.242 | + | 161.220i | −0.706941 | + | 0.408153i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 73.0000 | − | 126.440i | 0.183879 | − | 0.318488i | −0.759319 | − | 0.650718i | \(-0.774468\pi\) |
0.943198 | + | 0.332230i | \(0.107801\pi\) | |||||||
\(398\) | − | 28.2843i | − | 0.0710660i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 28.0000 | 0.0700000 | ||||||||
\(401\) | −282.916 | − | 163.342i | −0.705526 | − | 0.407336i | 0.103876 | − | 0.994590i | \(-0.466875\pi\) |
−0.809402 | + | 0.587254i | \(0.800209\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −176.000 | − | 304.841i | −0.436725 | − | 0.756429i | ||||
\(404\) | −51.4393 | − | 29.6985i | −0.127325 | − | 0.0735111i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 576.999i | − | 1.41769i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 184.000 | + | 318.697i | 0.449878 | + | 0.779211i | 0.998378 | − | 0.0569395i | \(-0.0181342\pi\) |
−0.548500 | + | 0.836151i | \(0.684801\pi\) | |||||||
\(410\) | 242.499 | − | 140.007i | 0.591462 | − | 0.341481i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −56.0000 | −0.135922 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −252.000 | + | 436.477i | −0.607229 | + | 1.05175i | ||||
\(416\) | −39.1918 | + | 22.6274i | −0.0942111 | + | 0.0543928i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 192.000 | − | 332.554i | 0.459330 | − | 0.795583i | ||||
\(419\) | − | 390.323i | − | 0.931558i | −0.884901 | − | 0.465779i | \(-0.845774\pi\) | ||
0.884901 | − | 0.465779i | \(-0.154226\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −40.0000 | −0.0950119 | −0.0475059 | − | 0.998871i | \(-0.515127\pi\) | ||||
−0.0475059 | + | 0.998871i | \(0.515127\pi\) | |||||||
\(422\) | −362.524 | − | 209.304i | −0.859063 | − | 0.495980i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −54.0000 | − | 93.5307i | −0.127358 | − | 0.220591i | ||||
\(425\) | −77.1589 | − | 44.5477i | −0.181550 | − | 0.104818i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −120.000 | − | 207.846i | −0.279070 | − | 0.483363i | ||||
\(431\) | −132.272 | + | 76.3675i | −0.306897 | + | 0.177187i | −0.645537 | − | 0.763729i | \(-0.723366\pi\) |
0.338640 | + | 0.940916i | \(0.390033\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −542.000 | −1.25173 | −0.625866 | − | 0.779931i | \(-0.715254\pi\) | ||||
−0.625866 | + | 0.779931i | \(0.715254\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 56.0000 | − | 96.9948i | 0.128440 | − | 0.222465i | ||||
\(437\) | −235.151 | + | 135.765i | −0.538103 | + | 0.310674i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.00000 | + | 3.46410i | −0.00455581 | + | 0.00789089i | −0.868294 | − | 0.496049i | \(-0.834783\pi\) |
0.863739 | + | 0.503940i | \(0.168117\pi\) | |||||||
\(440\) | 203.647i | 0.462834i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 144.000 | 0.325792 | ||||||||
\(443\) | −279.242 | − | 161.220i | −0.630343 | − | 0.363929i | 0.150542 | − | 0.988604i | \(-0.451898\pi\) |
−0.780885 | + | 0.624675i | \(0.785231\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −27.0000 | − | 46.7654i | −0.0606742 | − | 0.105091i | ||||
\(446\) | −533.989 | − | 308.299i | −1.19728 | − | 0.691252i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 216.375i | 0.481904i | 0.970537 | + | 0.240952i | \(0.0774596\pi\) | ||||
−0.970537 | + | 0.240952i | \(0.922540\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −396.000 | − | 685.892i | −0.878049 | − | 1.52083i | ||||
\(452\) | 271.893 | − | 156.978i | 0.601534 | − | 0.347296i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 24.0000 | 0.0528634 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 200.000 | − | 346.410i | 0.437637 | − | 0.758009i | −0.559870 | − | 0.828580i | \(-0.689149\pi\) |
0.997507 | + | 0.0705714i | \(0.0224823\pi\) | |||||||
\(458\) | −9.79796 | + | 5.65685i | −0.0213929 | + | 0.0123512i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 72.0000 | − | 124.708i | 0.156522 | − | 0.271104i | ||||
\(461\) | 301.227i | 0.653422i | 0.945124 | + | 0.326711i | \(0.105940\pi\) | ||||
−0.945124 | + | 0.326711i | \(0.894060\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −604.000 | −1.30454 | −0.652268 | − | 0.757989i | \(-0.726182\pi\) | ||||
−0.652268 | + | 0.757989i | \(0.726182\pi\) | |||||||
\(464\) | −14.6969 | − | 8.48528i | −0.0316744 | − | 0.0182872i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.00000 | − | 15.5885i | −0.0193133 | − | 0.0334516i | ||||
\(467\) | 308.636 | + | 178.191i | 0.660890 | + | 0.381565i | 0.792616 | − | 0.609721i | \(-0.208719\pi\) |
−0.131726 | + | 0.991286i | \(0.542052\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 509.117i | − | 1.08323i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 48.0000 | + | 83.1384i | 0.101695 | + | 0.176141i | ||||
\(473\) | −587.878 | + | 339.411i | −1.24287 | + | 0.717571i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 112.000 | 0.235789 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 96.0000 | − | 166.277i | 0.200837 | − | 0.347860i | ||||
\(479\) | −455.605 | + | 263.044i | −0.951159 | + | 0.549152i | −0.893441 | − | 0.449181i | \(-0.851716\pi\) |
−0.0577181 | + | 0.998333i | \(0.518382\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −136.000 | + | 235.559i | −0.282744 | + | 0.489727i | ||||
\(482\) | − | 45.2548i | − | 0.0938897i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 334.000 | 0.690083 | ||||||||
\(485\) | 646.665 | + | 373.352i | 1.33333 | + | 0.769799i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −298.000 | − | 516.151i | −0.611910 | − | 1.05986i | −0.990918 | − | 0.134465i | \(-0.957068\pi\) |
0.379009 | − | 0.925393i | \(-0.376265\pi\) | |||||||
\(488\) | −122.474 | − | 70.7107i | −0.250972 | − | 0.144899i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 271.529i | − | 0.553012i | −0.961012 | − | 0.276506i | \(-0.910823\pi\) | ||
0.961012 | − | 0.276506i | \(-0.0891766\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.0000 | + | 46.7654i | 0.0547667 | + | 0.0948588i | ||||
\(494\) | −156.767 | + | 90.5097i | −0.317343 | + | 0.183218i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −176.000 | −0.354839 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −112.000 | + | 193.990i | −0.224449 | + | 0.388757i | −0.956154 | − | 0.292864i | \(-0.905392\pi\) |
0.731705 | + | 0.681621i | \(0.238725\pi\) | |||||||
\(500\) | −235.151 | + | 135.765i | −0.470302 | + | 0.271529i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −36.0000 | + | 62.3538i | −0.0717131 | + | 0.124211i | ||||
\(503\) | − | 865.499i | − | 1.72067i | −0.509726 | − | 0.860337i | \(-0.670253\pi\) | ||
0.509726 | − | 0.860337i | \(-0.329747\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 126.000 | 0.249505 | ||||||||
\(506\) | −352.727 | − | 203.647i | −0.697088 | − | 0.402464i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 92.0000 | + | 159.349i | 0.181102 | + | 0.313678i | ||||
\(509\) | 415.189 | + | 239.709i | 0.815695 | + | 0.470941i | 0.848929 | − | 0.528506i | \(-0.177248\pi\) |
−0.0332350 | + | 0.999448i | \(0.510581\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 129.000 | + | 223.435i | 0.250973 | + | 0.434698i | ||||
\(515\) | 102.879 | − | 59.3970i | 0.199764 | − | 0.115334i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1440.00 | −2.78530 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 48.0000 | − | 83.1384i | 0.0923077 | − | 0.159882i | ||||
\(521\) | 451.931 | − | 260.922i | 0.867430 | − | 0.500811i | 0.000936430 | − | 1.00000i | \(-0.499702\pi\) |
0.866493 | + | 0.499189i | \(0.166369\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −368.000 | + | 637.395i | −0.703633 | + | 1.21873i | 0.263550 | + | 0.964646i | \(0.415107\pi\) |
−0.967183 | + | 0.254082i | \(0.918227\pi\) | |||||||
\(524\) | − | 339.411i | − | 0.647731i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −528.000 | −1.00380 | ||||||||
\(527\) | 484.999 | + | 280.014i | 0.920302 | + | 0.531336i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −120.500 | − | 208.712i | −0.227788 | − | 0.394541i | ||||
\(530\) | 198.409 | + | 114.551i | 0.374356 | + | 0.216135i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 373.352i | 0.700474i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −19.5959 | + | 11.3137i | −0.0365595 | + | 0.0211077i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −486.000 | −0.903346 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 404.000 | − | 699.749i | 0.746765 | − | 1.29344i | −0.202600 | − | 0.979262i | \(-0.564939\pi\) |
0.949365 | − | 0.314174i | \(-0.101727\pi\) | |||||||
\(542\) | −465.403 | + | 268.701i | −0.858677 | + | 0.495758i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 36.0000 | − | 62.3538i | 0.0661765 | − | 0.114621i | ||||
\(545\) | 237.588i | 0.435941i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 536.000 | 0.979890 | 0.489945 | − | 0.871753i | \(-0.337017\pi\) | ||||
0.489945 | + | 0.871753i | \(0.337017\pi\) | |||||||
\(548\) | 271.893 | + | 156.978i | 0.496156 | + | 0.286456i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 84.0000 | + | 145.492i | 0.152727 | + | 0.264531i | ||||
\(551\) | −58.7878 | − | 33.9411i | −0.106693 | − | 0.0615991i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 463.862i | − | 0.837296i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −152.000 | − | 263.272i | −0.273381 | − | 0.473510i | ||||
\(557\) | −143.295 | + | 82.7315i | −0.257262 | + | 0.148531i | −0.623085 | − | 0.782154i | \(-0.714121\pi\) |
0.365823 | + | 0.930685i | \(0.380788\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 320.000 | 0.572451 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 201.000 | − | 348.142i | 0.357651 | − | 0.619470i | ||||
\(563\) | 279.242 | − | 161.220i | 0.495989 | − | 0.286359i | −0.231067 | − | 0.972938i | \(-0.574222\pi\) |
0.727056 | + | 0.686579i | \(0.240888\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −333.000 | + | 576.773i | −0.589381 | + | 1.02084i | ||||
\(566\) | 294.156i | 0.519711i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −144.000 | −0.253521 | ||||||||
\(569\) | −135.947 | − | 78.4889i | −0.238922 | − | 0.137942i | 0.375759 | − | 0.926717i | \(-0.377382\pi\) |
−0.614681 | + | 0.788776i | \(0.710715\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −184.000 | − | 318.697i | −0.322242 | − | 0.558139i | 0.658709 | − | 0.752398i | \(-0.271103\pi\) |
−0.980950 | + | 0.194259i | \(0.937770\pi\) | |||||||
\(572\) | −235.151 | − | 135.765i | −0.411103 | − | 0.237351i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 118.794i | − | 0.206598i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −71.0000 | − | 122.976i | −0.123050 | − | 0.213129i | 0.797919 | − | 0.602765i | \(-0.205934\pi\) |
−0.920969 | + | 0.389636i | \(0.872601\pi\) | |||||||
\(578\) | 155.543 | − | 89.8026i | 0.269105 | − | 0.155368i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 36.0000 | 0.0620690 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 324.000 | − | 561.184i | 0.555746 | − | 0.962581i | ||||
\(584\) | −39.1918 | + | 22.6274i | −0.0671093 | + | 0.0387456i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 309.000 | − | 535.204i | 0.527304 | − | 0.913317i | ||||
\(587\) | − | 373.352i | − | 0.636035i | −0.948085 | − | 0.318017i | \(-0.896983\pi\) | ||
0.948085 | − | 0.318017i | \(-0.103017\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −704.000 | −1.19525 | ||||||||
\(590\) | −176.363 | − | 101.823i | −0.298921 | − | 0.172582i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 68.0000 | + | 117.779i | 0.114865 | + | 0.198952i | ||||
\(593\) | 958.975 | + | 553.665i | 1.61716 | + | 0.933667i | 0.987650 | + | 0.156674i | \(0.0500770\pi\) |
0.629508 | + | 0.776994i | \(0.283256\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 551.543i | − | 0.925408i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 96.0000 | + | 166.277i | 0.160535 | + | 0.278055i | ||||
\(599\) | 690.756 | − | 398.808i | 1.15318 | − | 0.665790i | 0.203521 | − | 0.979070i | \(-0.434761\pi\) |
0.949661 | + | 0.313280i | \(0.101428\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −158.000 | −0.262895 | −0.131448 | − | 0.991323i | \(-0.541963\pi\) | ||||
−0.131448 | + | 0.991323i | \(0.541963\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −148.000 | + | 256.344i | −0.245033 | + | 0.424410i | ||||
\(605\) | −613.597 | + | 354.260i | −1.01421 | + | 0.585555i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 166.000 | − | 287.520i | 0.273476 | − | 0.473675i | −0.696273 | − | 0.717777i | \(-0.745160\pi\) |
0.969750 | + | 0.244102i | \(0.0784932\pi\) | |||||||
\(608\) | 90.5097i | 0.148865i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 300.000 | 0.491803 | ||||||||
\(611\) | 587.878 | + | 339.411i | 0.962156 | + | 0.555501i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −289.000 | − | 500.563i | −0.471452 | − | 0.816579i | 0.528015 | − | 0.849235i | \(-0.322937\pi\) |
−0.999467 | + | 0.0326566i | \(0.989603\pi\) | |||||||
\(614\) | −636.867 | − | 367.696i | −1.03724 | − | 0.598853i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 55.1543i | − | 0.0893911i | −0.999001 | − | 0.0446956i | \(-0.985768\pi\) | ||
0.999001 | − | 0.0446956i | \(-0.0142318\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 448.000 | + | 775.959i | 0.723748 | + | 1.25357i | 0.959487 | + | 0.281752i | \(0.0909155\pi\) |
−0.235739 | + | 0.971816i | \(0.575751\pi\) | |||||||
\(620\) | 323.333 | − | 186.676i | 0.521504 | − | 0.301091i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −528.000 | −0.848875 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 200.500 | − | 347.276i | 0.320800 | − | 0.555642i | ||||
\(626\) | 115.126 | − | 66.4680i | 0.183907 | − | 0.106179i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 82.0000 | − | 142.028i | 0.130573 | − | 0.226160i | ||||
\(629\) | − | 432.749i | − | 0.687996i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.0000 | 0.0316957 | 0.0158479 | − | 0.999874i | \(-0.494955\pi\) | ||||
0.0158479 | + | 0.999874i | \(0.494955\pi\) | |||||||
\(632\) | −186.161 | − | 107.480i | −0.294559 | − | 0.170064i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 237.000 | + | 410.496i | 0.373817 | + | 0.647470i | ||||
\(635\) | −338.030 | − | 195.161i | −0.532330 | − | 0.307341i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 101.823i | − | 0.159598i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −24.0000 | − | 41.5692i | −0.0375000 | − | 0.0649519i | ||||
\(641\) | 224.128 | − | 129.401i | 0.349654 | − | 0.201873i | −0.314879 | − | 0.949132i | \(-0.601964\pi\) |
0.664533 | + | 0.747259i | \(0.268631\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −728.000 | −1.13219 | −0.566096 | − | 0.824339i | \(-0.691547\pi\) | ||||
−0.566096 | + | 0.824339i | \(0.691547\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 144.000 | − | 249.415i | 0.222910 | − | 0.386092i | ||||
\(647\) | 396.817 | − | 229.103i | 0.613319 | − | 0.354100i | −0.160944 | − | 0.986963i | \(-0.551454\pi\) |
0.774263 | + | 0.632864i | \(0.218121\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −288.000 | + | 498.831i | −0.443760 | + | 0.768614i | ||||
\(650\) | − | 79.1960i | − | 0.121840i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −112.000 | −0.171779 | ||||||||
\(653\) | −260.871 | − | 150.614i | −0.399496 | − | 0.230649i | 0.286771 | − | 0.957999i | \(-0.407418\pi\) |
−0.686266 | + | 0.727350i | \(0.740752\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 360.000 | + | 623.538i | 0.549618 | + | 0.951967i | ||||
\(656\) | 161.666 | + | 93.3381i | 0.246443 | + | 0.142284i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1052.17i | − | 1.59662i | −0.602244 | − | 0.798312i | \(-0.705727\pi\) | ||
0.602244 | − | 0.798312i | \(-0.294273\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.0000 | + | 53.6936i | 0.0468986 | + | 0.0812308i | 0.888522 | − | 0.458834i | \(-0.151733\pi\) |
−0.841623 | + | 0.540065i | \(0.818400\pi\) | |||||||
\(662\) | 656.463 | − | 379.009i | 0.991636 | − | 0.572522i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −336.000 | −0.506024 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −36.0000 | + | 62.3538i | −0.0539730 | + | 0.0934840i | ||||
\(668\) | 58.7878 | − | 33.9411i | 0.0880056 | − | 0.0508101i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 24.0000 | − | 41.5692i | 0.0358209 | − | 0.0620436i | ||||
\(671\) | − | 848.528i | − | 1.26457i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −670.000 | −0.995542 | −0.497771 | − | 0.867308i | \(-0.665848\pi\) | ||||
−0.497771 | + | 0.867308i | \(0.665848\pi\) | |||||||
\(674\) | 254.747 | + | 147.078i | 0.377963 | + | 0.218217i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −105.000 | − | 181.865i | −0.155325 | − | 0.269032i | ||||
\(677\) | −1120.64 | − | 647.003i | −1.65531 | − | 0.955691i | −0.974839 | − | 0.222912i | \(-0.928444\pi\) |
−0.680466 | − | 0.732779i | \(-0.738223\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 152.735i | 0.224610i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −528.000 | − | 914.523i | −0.774194 | − | 1.34094i | ||||
\(683\) | −484.999 | + | 280.014i | −0.710101 | + | 0.409977i | −0.811098 | − | 0.584910i | \(-0.801130\pi\) |
0.100997 | + | 0.994887i | \(0.467797\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −666.000 | −0.972263 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 80.0000 | − | 138.564i | 0.116279 | − | 0.201401i | ||||
\(689\) | −264.545 | + | 152.735i | −0.383955 | + | 0.221676i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.0000 | + | 34.6410i | −0.0289436 | + | 0.0501317i | −0.880134 | − | 0.474725i | \(-0.842548\pi\) |
0.851191 | + | 0.524856i | \(0.175881\pi\) | |||||||
\(692\) | − | 347.897i | − | 0.502741i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −408.000 | −0.587896 | ||||||||
\(695\) | 558.484 | + | 322.441i | 0.803574 | + | 0.463943i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −297.000 | − | 514.419i | −0.426112 | − | 0.738047i | ||||
\(698\) | −291.489 | − | 168.291i | −0.417606 | − | 0.241105i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 954.594i | 1.36176i | 0.732395 | + | 0.680880i | \(0.238403\pi\) | ||||
−0.732395 | + | 0.680880i | \(0.761597\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 272.000 | + | 471.118i | 0.386913 | + | 0.670153i | ||||
\(704\) | −117.576 | + | 67.8823i | −0.167011 | + | 0.0964237i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −318.000 | −0.450425 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −484.000 | + | 838.313i | −0.682652 | + | 1.18239i | 0.291517 | + | 0.956566i | \(0.405840\pi\) |
−0.974169 | + | 0.225822i | \(0.927493\pi\) | |||||||
\(710\) | 264.545 | − | 152.735i | 0.372598 | − | 0.215120i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 18.0000 | − | 31.1769i | 0.0252809 | − | 0.0437878i | ||||
\(713\) | 746.705i | 1.04727i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 576.000 | 0.805594 | ||||||||
\(716\) | −352.727 | − | 203.647i | −0.492635 | − | 0.284423i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −396.000 | − | 685.892i | −0.551532 | − | 0.955282i | ||||
\(719\) | 1014.09 | + | 585.484i | 1.41042 | + | 0.814304i | 0.995427 | − | 0.0955230i | \(-0.0304523\pi\) |
0.414988 | + | 0.909827i | \(0.363786\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 148.492i | − | 0.205668i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 232.000 | + | 401.836i | 0.320442 | + | 0.555022i | ||||
\(725\) | 25.7196 | − | 14.8492i | 0.0354754 | − | 0.0204817i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 508.000 | 0.698762 | 0.349381 | − | 0.936981i | \(-0.386392\pi\) | ||||
0.349381 | + | 0.936981i | \(0.386392\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 48.0000 | − | 83.1384i | 0.0657534 | − | 0.113888i | ||||
\(731\) | −440.908 | + | 254.558i | −0.603158 | + | 0.348233i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −572.000 | + | 990.733i | −0.780355 | + | 1.35161i | 0.151380 | + | 0.988476i | \(0.451628\pi\) |
−0.931735 | + | 0.363138i | \(0.881705\pi\) | |||||||
\(734\) | − | 401.637i | − | 0.547189i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 96.0000 | 0.130435 | ||||||||
\(737\) | −117.576 | − | 67.8823i | −0.159533 | − | 0.0921062i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 152.000 | + | 263.272i | 0.205683 | + | 0.356254i | 0.950350 | − | 0.311182i | \(-0.100725\pi\) |
−0.744667 | + | 0.667436i | \(0.767392\pi\) | |||||||
\(740\) | −249.848 | − | 144.250i | −0.337632 | − | 0.194932i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 848.528i | 1.14203i | 0.820940 | + | 0.571015i | \(0.193450\pi\) | ||||
−0.820940 | + | 0.571015i | \(0.806550\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 585.000 | + | 1013.25i | 0.785235 | + | 1.36007i | ||||
\(746\) | −232.702 | + | 134.350i | −0.311932 | + | 0.180094i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 432.000 | 0.577540 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −94.0000 | + | 162.813i | −0.125166 | + | 0.216795i | −0.921798 | − | 0.387671i | \(-0.873280\pi\) |
0.796632 | + | 0.604465i | \(0.206613\pi\) | |||||||
\(752\) | 293.939 | − | 169.706i | 0.390876 | − | 0.225672i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −24.0000 | + | 41.5692i | −0.0318302 | + | 0.0551316i | ||||
\(755\) | − | 627.911i | − | 0.831670i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1240.00 | −1.63804 | −0.819022 | − | 0.573761i | \(-0.805484\pi\) | ||||
−0.819022 | + | 0.573761i | \(0.805484\pi\) | |||||||
\(758\) | 195.959 | + | 113.137i | 0.258521 | + | 0.149257i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −96.0000 | − | 166.277i | −0.126316 | − | 0.218785i | ||||
\(761\) | −135.947 | − | 78.4889i | −0.178642 | − | 0.103139i | 0.408012 | − | 0.912976i | \(-0.366222\pi\) |
−0.586655 | + | 0.809837i | \(0.699555\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 67.8823i | 0.0888511i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 192.000 | + | 332.554i | 0.250653 | + | 0.434143i | ||||
\(767\) | 235.151 | − | 135.765i | 0.306585 | − | 0.177007i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 910.000 | 1.18336 | 0.591678 | − | 0.806175i | \(-0.298466\pi\) | ||||
0.591678 | + | 0.806175i | \(0.298466\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 206.000 | − | 356.802i | 0.266839 | − | 0.462179i | ||||
\(773\) | 1201.47 | − | 693.672i | 1.55430 | − | 0.897376i | 0.556517 | − | 0.830836i | \(-0.312137\pi\) |
0.997784 | − | 0.0665401i | \(-0.0211960\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 154.000 | − | 266.736i | 0.198710 | − | 0.344175i | ||||
\(776\) | 497.803i | 0.641499i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 570.000 | 0.732648 | ||||||||
\(779\) | 646.665 | + | 373.352i | 0.830122 | + | 0.479271i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −432.000 | − | 748.246i | −0.553137 | − | 0.958061i | ||||
\(782\) | −264.545 | − | 152.735i | −0.338293 | − | 0.195313i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 347.897i | 0.443180i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −680.000 | − | 1177.79i | −0.864041 | − | 1.49656i | −0.867997 | − | 0.496570i | \(-0.834593\pi\) |
0.00395593 | − | 0.999992i | \(-0.498741\pi\) | |||||||
\(788\) | −286.590 | + | 165.463i | −0.363693 | + | 0.209978i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 456.000 | 0.577215 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −200.000 | + | 346.410i | −0.252207 | + | 0.436835i | ||||
\(794\) | −178.813 | + | 103.238i | −0.225205 | + | 0.130022i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −20.0000 | + | 34.6410i | −0.0251256 | + | 0.0435189i | ||||
\(797\) | 106.066i | 0.133082i | 0.997784 | + | 0.0665408i | \(0.0211963\pi\) | ||||
−0.997784 | + | 0.0665408i | \(0.978804\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1080.00 | −1.35169 | ||||||||
\(800\) | −34.2929 | − | 19.7990i | −0.0428661 | − | 0.0247487i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 231.000 | + | 400.104i | 0.288030 | + | 0.498882i | ||||
\(803\) | −235.151 | − | 135.765i | −0.292841 | − | 0.169072i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 497.803i | 0.617622i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 42.0000 | + | 72.7461i | 0.0519802 | + | 0.0900323i | ||||
\(809\) | −958.975 | + | 553.665i | −1.18538 | + | 0.684381i | −0.957254 | − | 0.289249i | \(-0.906594\pi\) |
−0.228130 | + | 0.973631i | \(0.573261\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 160.000 | 0.197287 | 0.0986436 | − | 0.995123i | \(-0.468550\pi\) | ||||
0.0986436 | + | 0.995123i | \(0.468550\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −408.000 | + | 706.677i | −0.501229 | + | 0.868153i | ||||
\(815\) | 205.757 | − | 118.794i | 0.252463 | − | 0.145759i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 320.000 | − | 554.256i | 0.391677 | − | 0.678404i | ||||
\(818\) | − | 520.431i | − | 0.636223i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −396.000 | −0.482927 | ||||||||
\(821\) | −378.446 | − | 218.496i | −0.460958 | − | 0.266134i | 0.251489 | − | 0.967860i | \(-0.419080\pi\) |
−0.712447 | + | 0.701726i | \(0.752413\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −166.000 | − | 287.520i | −0.201701 | − | 0.349357i | 0.747376 | − | 0.664402i | \(-0.231314\pi\) |
−0.949077 | + | 0.315045i | \(0.897980\pi\) | |||||||
\(824\) | 68.5857 | + | 39.5980i | 0.0832351 | + | 0.0480558i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 101.823i | 0.123124i | 0.998103 | + | 0.0615619i | \(0.0196082\pi\) | ||||
−0.998103 | + | 0.0615619i | \(0.980392\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 316.000 | + | 547.328i | 0.381182 | + | 0.660227i | 0.991232 | − | 0.132137i | \(-0.0421837\pi\) |
−0.610049 | + | 0.792363i | \(0.708850\pi\) | |||||||
\(830\) | 617.271 | − | 356.382i | 0.743701 | − | 0.429376i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 64.0000 | 0.0769231 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −72.0000 | + | 124.708i | −0.0862275 | + | 0.149350i | ||||
\(836\) | −470.302 | + | 271.529i | −0.562562 | + | 0.324795i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −276.000 | + | 478.046i | −0.329356 | + | 0.570461i | ||||
\(839\) | − | 729.734i | − | 0.869767i | −0.900487 | − | 0.434883i | \(-0.856790\pi\) | ||
0.900487 | − | 0.434883i | \(-0.143210\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 823.000 | 0.978597 | ||||||||
\(842\) | 48.9898 | + | 28.2843i | 0.0581827 | + | 0.0335918i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 296.000 | + | 512.687i | 0.350711 | + | 0.607449i | ||||
\(845\) | 385.795 | + | 222.739i | 0.456562 | + | 0.263596i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 152.735i | 0.180112i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 63.0000 | + | 109.119i | 0.0741176 | + | 0.128376i | ||||
\(851\) | 499.696 | − | 288.500i | 0.587187 | − | 0.339012i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −446.000 | −0.522860 | −0.261430 | − | 0.965222i | \(-0.584194\pi\) | ||||
−0.261430 | + | 0.965222i | \(0.584194\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 371.098 | − | 214.253i | 0.433019 | − | 0.250004i | −0.267613 | − | 0.963527i | \(-0.586235\pi\) |
0.700632 | + | 0.713523i | \(0.252901\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 364.000 | − | 630.466i | 0.423749 | − | 0.733954i | −0.572554 | − | 0.819867i | \(-0.694047\pi\) |
0.996303 | + | 0.0859129i | \(0.0273807\pi\) | |||||||
\(860\) | 339.411i | 0.394664i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 216.000 | 0.250580 | ||||||||
\(863\) | 793.635 | + | 458.205i | 0.919623 | + | 0.530945i | 0.883515 | − | 0.468403i | \(-0.155171\pi\) |
0.0361083 | + | 0.999348i | \(0.488504\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 369.000 | + | 639.127i | 0.426590 | + | 0.738875i | ||||
\(866\) | 663.812 | + | 383.252i | 0.766526 | + | 0.442554i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1289.76i | − | 1.48419i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.0000 | + | 55.4256i | 0.0367394 | + | 0.0636345i | ||||
\(872\) | −137.171 | + | 79.1960i | −0.157307 | + | 0.0908211i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 384.000 | 0.439359 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 455.000 | − | 788.083i | 0.518814 | − | 0.898612i | −0.480947 | − | 0.876750i | \(-0.659707\pi\) |
0.999761 | − | 0.0218627i | \(-0.00695967\pi\) | |||||||
\(878\) | 4.89898 | − | 2.82843i | 0.00557970 | − | 0.00322144i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 144.000 | − | 249.415i | 0.163636 | − | 0.283426i | ||||
\(881\) | 929.138i | 1.05464i | 0.849667 | + | 0.527320i | \(0.176803\pi\) | ||||
−0.849667 | + | 0.527320i | \(0.823197\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1064.00 | 1.20498 | 0.602492 | − | 0.798125i | \(-0.294175\pi\) | ||||
0.602492 | + | 0.798125i | \(0.294175\pi\) | |||||||
\(884\) | −176.363 | − | 101.823i | −0.199506 | − | 0.115185i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 228.000 | + | 394.908i | 0.257336 | + | 0.445720i | ||||
\(887\) | −1205.15 | − | 695.793i | −1.35868 | − | 0.784434i | −0.369234 | − | 0.929337i | \(-0.620380\pi\) |
−0.989446 | + | 0.144902i | \(0.953713\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 76.3675i | 0.0858062i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 436.000 | + | 755.174i | 0.488789 | + | 0.846608i | ||||
\(893\) | 1175.76 | − | 678.823i | 1.31664 | − | 0.760160i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 864.000 | 0.965363 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 153.000 | − | 265.004i | 0.170379 | − | 0.295104i | ||||
\(899\) | −161.666 | + | 93.3381i | −0.179829 | + | 0.103824i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 243.000 | − | 420.888i | 0.269700 | − | 0.467135i | ||||
\(902\) | 1120.06i | 1.24175i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −444.000 | −0.491150 | ||||||||
\(905\) | −852.422 | − | 492.146i | −0.941903 | − | 0.543808i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 884.000 | + | 1531.13i | 0.974642 | + | 1.68813i | 0.681112 | + | 0.732179i | \(0.261496\pi\) |
0.293529 | + | 0.955950i | \(0.405170\pi\) | |||||||
\(908\) | −29.3939 | − | 16.9706i | −0.0323721 | − | 0.0186900i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 237.588i | − | 0.260799i | −0.991462 | − | 0.130399i | \(-0.958374\pi\) | ||
0.991462 | − | 0.130399i | \(-0.0416260\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1008.00 | − | 1745.91i | −1.10405 | − | 1.91228i | ||||
\(914\) | −489.898 | + | 282.843i | −0.535993 | + | 0.309456i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 16.0000 | 0.0174672 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −190.000 | + | 329.090i | −0.206746 | + | 0.358095i | −0.950688 | − | 0.310150i | \(-0.899621\pi\) |
0.743941 | + | 0.668245i | \(0.232954\pi\) | |||||||
\(920\) | −176.363 | + | 101.823i | −0.191699 | + | 0.110678i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 213.000 | − | 368.927i | 0.231020 | − | 0.400138i | ||||
\(923\) | 407.294i | 0.441271i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −238.000 | −0.257297 | ||||||||
\(926\) | 739.746 | + | 427.092i | 0.798862 | + | 0.461223i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 12.0000 | + | 20.7846i | 0.0129310 | + | 0.0223972i | ||||
\(929\) | 576.855 | + | 333.047i | 0.620942 | + | 0.358501i | 0.777236 | − | 0.629210i | \(-0.216621\pi\) |
−0.156294 | + | 0.987711i | \(0.549955\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 25.4558i | 0.0273131i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −252.000 | − | 436.477i | −0.269807 | − | 0.467320i | ||||
\(935\) | −793.635 | + | 458.205i | −0.848807 | + | 0.490059i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 178.000 | 0.189968 | 0.0949840 | − | 0.995479i | \(-0.469720\pi\) | ||||
0.0949840 | + | 0.995479i | \(0.469720\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −360.000 | + | 623.538i | −0.382979 | + | 0.663339i | ||||
\(941\) | 378.446 | − | 218.496i | 0.402174 | − | 0.232196i | −0.285247 | − | 0.958454i | \(-0.592076\pi\) |
0.687422 | + | 0.726258i | \(0.258742\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 396.000 | − | 685.892i | 0.419936 | − | 0.727351i | ||||
\(944\) | − | 135.765i | − | 0.143818i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 960.000 | 1.01480 | ||||||||
\(947\) | −1557.88 | − | 899.440i | −1.64506 | − | 0.949778i | −0.978994 | − | 0.203889i | \(-0.934642\pi\) |
−0.666070 | − | 0.745889i | \(-0.732025\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 64.0000 | + | 110.851i | 0.0674394 | + | 0.116808i | ||||
\(950\) | −137.171 | − | 79.1960i | −0.144391 | − | 0.0833642i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1310.98i | 1.37563i | 0.725886 | + | 0.687815i | \(0.241430\pi\) | ||||
−0.725886 | + | 0.687815i | \(0.758570\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −72.0000 | − | 124.708i | −0.0753927 | − | 0.130584i | ||||
\(956\) | −235.151 | + | 135.765i | −0.245974 | + | 0.142013i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 744.000 | 0.776618 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −487.500 | + | 844.375i | −0.507284 | + | 0.878642i | ||||
\(962\) | 333.131 | − | 192.333i | 0.346290 | − | 0.199930i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −32.0000 | + | 55.4256i | −0.0331950 | + | 0.0574955i | ||||
\(965\) | 873.984i | 0.905683i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1700.00 | 1.75801 | 0.879007 | − | 0.476808i | \(-0.158206\pi\) | ||||
0.879007 | + | 0.476808i | \(0.158206\pi\) | |||||||
\(968\) | −409.065 | − | 236.174i | −0.422588 | − | 0.243981i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −528.000 | − | 914.523i | −0.544330 | − | 0.942807i | ||||
\(971\) | 396.817 | + | 229.103i | 0.408669 | + | 0.235945i | 0.690218 | − | 0.723602i | \(-0.257515\pi\) |
−0.281549 | + | 0.959547i | \(0.590848\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 842.871i | 0.865371i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 100.000 | + | 173.205i | 0.102459 | + | 0.177464i | ||||
\(977\) | 657.688 | − | 379.716i | 0.673171 | − | 0.388655i | −0.124106 | − | 0.992269i | \(-0.539606\pi\) |
0.797277 | + | 0.603614i | \(0.206273\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 216.000 | 0.220633 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −192.000 | + | 332.554i | −0.195519 | + | 0.338649i | ||||
\(983\) | 911.210 | − | 526.087i | 0.926969 | − | 0.535186i | 0.0411171 | − | 0.999154i | \(-0.486908\pi\) |
0.885852 | + | 0.463969i | \(0.153575\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 351.000 | − | 607.950i | 0.356345 | − | 0.617208i | ||||
\(986\) | − | 76.3675i | − | 0.0774519i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 256.000 | 0.259109 | ||||||||
\(989\) | −587.878 | − | 339.411i | −0.594416 | − | 0.343186i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 386.000 | + | 668.572i | 0.389506 | + | 0.674643i | 0.992383 | − | 0.123190i | \(-0.0393126\pi\) |
−0.602878 | + | 0.797834i | \(0.705979\pi\) | |||||||
\(992\) | 215.555 | + | 124.451i | 0.217293 | + | 0.125454i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 84.8528i | − | 0.0852792i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 97.0000 | + | 168.009i | 0.0972919 | + | 0.168514i | 0.910563 | − | 0.413371i | \(-0.135649\pi\) |
−0.813271 | + | 0.581885i | \(0.802315\pi\) | |||||||
\(998\) | 274.343 | − | 158.392i | 0.274893 | − | 0.158709i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))