Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [294,4,Mod(67,294)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(294, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("294.67");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 294 = 2 \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 294.e (of order \(3\), 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: | \(17.3465615417\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 79.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 294.79 |
Dual form | 294.4.e.j.67.1 |
$q$-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 \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(199\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.73205i | 0.353553 | − | 0.612372i | ||||
\(3\) | 1.50000 | + | 2.59808i | 0.288675 | + | 0.500000i | ||||
\(4\) | −2.00000 | − | 3.46410i | −0.250000 | − | 0.433013i | ||||
\(5\) | 4.00000 | − | 6.92820i | 0.357771 | − | 0.619677i | −0.629817 | − | 0.776743i | \(-0.716870\pi\) |
0.987588 | + | 0.157066i | \(0.0502036\pi\) | |||||||
\(6\) | 6.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | −4.50000 | + | 7.79423i | −0.166667 | + | 0.288675i | ||||
\(10\) | −8.00000 | − | 13.8564i | −0.252982 | − | 0.438178i | ||||
\(11\) | −20.0000 | − | 34.6410i | −0.548202 | − | 0.949514i | −0.998398 | − | 0.0565844i | \(-0.981979\pi\) |
0.450195 | − | 0.892930i | \(-0.351354\pi\) | |||||||
\(12\) | 6.00000 | − | 10.3923i | 0.144338 | − | 0.250000i | ||||
\(13\) | −4.00000 | −0.0853385 | −0.0426692 | − | 0.999089i | \(-0.513586\pi\) | ||||
−0.0426692 | + | 0.999089i | \(0.513586\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 24.0000 | 0.413118 | ||||||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | −42.0000 | − | 72.7461i | −0.599206 | − | 1.03785i | −0.992939 | − | 0.118630i | \(-0.962150\pi\) |
0.393733 | − | 0.919225i | \(-0.371183\pi\) | |||||||
\(18\) | 9.00000 | + | 15.5885i | 0.117851 | + | 0.204124i | ||||
\(19\) | 74.0000 | − | 128.172i | 0.893514 | − | 1.54761i | 0.0578808 | − | 0.998324i | \(-0.481566\pi\) |
0.835633 | − | 0.549288i | \(-0.185101\pi\) | |||||||
\(20\) | −32.0000 | −0.357771 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −80.0000 | −0.775275 | ||||||||
\(23\) | −42.0000 | + | 72.7461i | −0.380765 | + | 0.659505i | −0.991172 | − | 0.132583i | \(-0.957673\pi\) |
0.610406 | + | 0.792088i | \(0.291006\pi\) | |||||||
\(24\) | −12.0000 | − | 20.7846i | −0.102062 | − | 0.176777i | ||||
\(25\) | 30.5000 | + | 52.8275i | 0.244000 | + | 0.422620i | ||||
\(26\) | −4.00000 | + | 6.92820i | −0.0301717 | + | 0.0522589i | ||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 58.0000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 24.0000 | − | 41.5692i | 0.146059 | − | 0.252982i | ||||
\(31\) | −68.0000 | − | 117.779i | −0.393973 | − | 0.682381i | 0.598997 | − | 0.800752i | \(-0.295566\pi\) |
−0.992970 | + | 0.118370i | \(0.962233\pi\) | |||||||
\(32\) | 16.0000 | + | 27.7128i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 60.0000 | − | 103.923i | 0.316505 | − | 0.548202i | ||||
\(34\) | −168.000 | −0.847405 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | 111.000 | − | 192.258i | 0.493197 | − | 0.854242i | −0.506772 | − | 0.862080i | \(-0.669162\pi\) |
0.999969 | + | 0.00783774i | \(0.00249486\pi\) | |||||||
\(38\) | −148.000 | − | 256.344i | −0.631810 | − | 1.09433i | ||||
\(39\) | −6.00000 | − | 10.3923i | −0.0246351 | − | 0.0426692i | ||||
\(40\) | −32.0000 | + | 55.4256i | −0.126491 | + | 0.219089i | ||||
\(41\) | −420.000 | −1.59983 | −0.799914 | − | 0.600114i | \(-0.795122\pi\) | ||||
−0.799914 | + | 0.600114i | \(0.795122\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −164.000 | −0.581622 | −0.290811 | − | 0.956780i | \(-0.593925\pi\) | ||||
−0.290811 | + | 0.956780i | \(0.593925\pi\) | |||||||
\(44\) | −80.0000 | + | 138.564i | −0.274101 | + | 0.474757i | ||||
\(45\) | 36.0000 | + | 62.3538i | 0.119257 | + | 0.206559i | ||||
\(46\) | 84.0000 | + | 145.492i | 0.269242 | + | 0.466341i | ||||
\(47\) | 244.000 | − | 422.620i | 0.757257 | − | 1.31161i | −0.186988 | − | 0.982362i | \(-0.559873\pi\) |
0.944245 | − | 0.329245i | \(-0.106794\pi\) | |||||||
\(48\) | −48.0000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 122.000 | 0.345068 | ||||||||
\(51\) | 126.000 | − | 218.238i | 0.345952 | − | 0.599206i | ||||
\(52\) | 8.00000 | + | 13.8564i | 0.0213346 | + | 0.0369527i | ||||
\(53\) | −239.000 | − | 413.960i | −0.619418 | − | 1.07286i | −0.989592 | − | 0.143902i | \(-0.954035\pi\) |
0.370174 | − | 0.928963i | \(-0.379298\pi\) | |||||||
\(54\) | −27.0000 | + | 46.7654i | −0.0680414 | + | 0.117851i | ||||
\(55\) | −320.000 | −0.784523 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 444.000 | 1.03174 | ||||||||
\(58\) | 58.0000 | − | 100.459i | 0.131306 | − | 0.227429i | ||||
\(59\) | 274.000 | + | 474.582i | 0.604606 | + | 1.04721i | 0.992114 | + | 0.125342i | \(0.0400028\pi\) |
−0.387507 | + | 0.921867i | \(0.626664\pi\) | |||||||
\(60\) | −48.0000 | − | 83.1384i | −0.103280 | − | 0.178885i | ||||
\(61\) | 346.000 | − | 599.290i | 0.726242 | − | 1.25789i | −0.232219 | − | 0.972664i | \(-0.574599\pi\) |
0.958461 | − | 0.285224i | \(-0.0920681\pi\) | |||||||
\(62\) | −272.000 | −0.557162 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −16.0000 | + | 27.7128i | −0.0305316 | + | 0.0528823i | ||||
\(66\) | −120.000 | − | 207.846i | −0.223803 | − | 0.387638i | ||||
\(67\) | 454.000 | + | 786.351i | 0.827835 | + | 1.43385i | 0.899733 | + | 0.436440i | \(0.143761\pi\) |
−0.0718987 | + | 0.997412i | \(0.522906\pi\) | |||||||
\(68\) | −168.000 | + | 290.985i | −0.299603 | + | 0.518927i | ||||
\(69\) | −252.000 | −0.439670 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −524.000 | −0.875878 | −0.437939 | − | 0.899005i | \(-0.644291\pi\) | ||||
−0.437939 | + | 0.899005i | \(0.644291\pi\) | |||||||
\(72\) | 36.0000 | − | 62.3538i | 0.0589256 | − | 0.102062i | ||||
\(73\) | 220.000 | + | 381.051i | 0.352727 | + | 0.610941i | 0.986726 | − | 0.162393i | \(-0.0519212\pi\) |
−0.633999 | + | 0.773334i | \(0.718588\pi\) | |||||||
\(74\) | −222.000 | − | 384.515i | −0.348743 | − | 0.604040i | ||||
\(75\) | −91.5000 | + | 158.483i | −0.140873 | + | 0.244000i | ||||
\(76\) | −592.000 | −0.893514 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −24.0000 | −0.0348393 | ||||||||
\(79\) | −608.000 | + | 1053.09i | −0.865890 | + | 1.49977i | 0.000269874 | 1.00000i | \(0.499914\pi\) | |
−0.866160 | + | 0.499766i | \(0.833419\pi\) | |||||||
\(80\) | 64.0000 | + | 110.851i | 0.0894427 | + | 0.154919i | ||||
\(81\) | −40.5000 | − | 70.1481i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −420.000 | + | 727.461i | −0.565625 | + | 0.979691i | ||||
\(83\) | 684.000 | 0.904563 | 0.452282 | − | 0.891875i | \(-0.350610\pi\) | ||||
0.452282 | + | 0.891875i | \(0.350610\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −672.000 | −0.857513 | ||||||||
\(86\) | −164.000 | + | 284.056i | −0.205635 | + | 0.356170i | ||||
\(87\) | 87.0000 | + | 150.688i | 0.107211 | + | 0.185695i | ||||
\(88\) | 160.000 | + | 277.128i | 0.193819 | + | 0.335704i | ||||
\(89\) | 302.000 | − | 523.079i | 0.359685 | − | 0.622992i | −0.628223 | − | 0.778033i | \(-0.716218\pi\) |
0.987908 | + | 0.155041i | \(0.0495509\pi\) | |||||||
\(90\) | 144.000 | 0.168655 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 336.000 | 0.380765 | ||||||||
\(93\) | 204.000 | − | 353.338i | 0.227460 | − | 0.393973i | ||||
\(94\) | −488.000 | − | 845.241i | −0.535461 | − | 0.927446i | ||||
\(95\) | −592.000 | − | 1025.37i | −0.639347 | − | 1.10738i | ||||
\(96\) | −48.0000 | + | 83.1384i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | 832.000 | 0.870895 | 0.435447 | − | 0.900214i | \(-0.356590\pi\) | ||||
0.435447 | + | 0.900214i | \(0.356590\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 360.000 | 0.365468 | ||||||||
\(100\) | 122.000 | − | 211.310i | 0.122000 | − | 0.211310i | ||||
\(101\) | 232.000 | + | 401.836i | 0.228563 | + | 0.395883i | 0.957382 | − | 0.288823i | \(-0.0932640\pi\) |
−0.728819 | + | 0.684706i | \(0.759931\pi\) | |||||||
\(102\) | −252.000 | − | 436.477i | −0.244625 | − | 0.423702i | ||||
\(103\) | −316.000 | + | 547.328i | −0.302295 | + | 0.523591i | −0.976655 | − | 0.214812i | \(-0.931086\pi\) |
0.674360 | + | 0.738402i | \(0.264420\pi\) | |||||||
\(104\) | 32.0000 | 0.0301717 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −956.000 | −0.875990 | ||||||||
\(107\) | 80.0000 | − | 138.564i | 0.0722794 | − | 0.125192i | −0.827621 | − | 0.561288i | \(-0.810306\pi\) |
0.899900 | + | 0.436096i | \(0.143639\pi\) | |||||||
\(108\) | 54.0000 | + | 93.5307i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | 1099.00 | + | 1903.52i | 0.965735 | + | 1.67270i | 0.707627 | + | 0.706586i | \(0.249766\pi\) |
0.258108 | + | 0.966116i | \(0.416901\pi\) | |||||||
\(110\) | −320.000 | + | 554.256i | −0.277371 | + | 0.480421i | ||||
\(111\) | 666.000 | 0.569495 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 770.000 | 0.641022 | 0.320511 | − | 0.947245i | \(-0.396145\pi\) | ||||
0.320511 | + | 0.947245i | \(0.396145\pi\) | |||||||
\(114\) | 444.000 | − | 769.031i | 0.364776 | − | 0.631810i | ||||
\(115\) | 336.000 | + | 581.969i | 0.272454 | + | 0.471903i | ||||
\(116\) | −116.000 | − | 200.918i | −0.0928477 | − | 0.160817i | ||||
\(117\) | 18.0000 | − | 31.1769i | 0.0142231 | − | 0.0246351i | ||||
\(118\) | 1096.00 | 0.855042 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −192.000 | −0.146059 | ||||||||
\(121\) | −134.500 | + | 232.961i | −0.101052 | + | 0.175027i | ||||
\(122\) | −692.000 | − | 1198.58i | −0.513531 | − | 0.889461i | ||||
\(123\) | −630.000 | − | 1091.19i | −0.461831 | − | 0.799914i | ||||
\(124\) | −272.000 | + | 471.118i | −0.196986 | + | 0.341191i | ||||
\(125\) | 1488.00 | 1.06473 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −184.000 | −0.128562 | −0.0642809 | − | 0.997932i | \(-0.520475\pi\) | ||||
−0.0642809 | + | 0.997932i | \(0.520475\pi\) | |||||||
\(128\) | 64.0000 | − | 110.851i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −246.000 | − | 426.084i | −0.167900 | − | 0.290811i | ||||
\(130\) | 32.0000 | + | 55.4256i | 0.0215891 | + | 0.0373935i | ||||
\(131\) | −726.000 | + | 1257.47i | −0.484205 | + | 0.838668i | −0.999835 | − | 0.0181429i | \(-0.994225\pi\) |
0.515630 | + | 0.856811i | \(0.327558\pi\) | |||||||
\(132\) | −480.000 | −0.316505 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1816.00 | 1.17074 | ||||||||
\(135\) | −108.000 | + | 187.061i | −0.0688530 | + | 0.119257i | ||||
\(136\) | 336.000 | + | 581.969i | 0.211851 | + | 0.366937i | ||||
\(137\) | −323.000 | − | 559.452i | −0.201429 | − | 0.348885i | 0.747560 | − | 0.664194i | \(-0.231225\pi\) |
−0.948989 | + | 0.315309i | \(0.897892\pi\) | |||||||
\(138\) | −252.000 | + | 436.477i | −0.155447 | + | 0.269242i | ||||
\(139\) | 3012.00 | 1.83795 | 0.918973 | − | 0.394320i | \(-0.129020\pi\) | ||||
0.918973 | + | 0.394320i | \(0.129020\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1464.00 | 0.874405 | ||||||||
\(142\) | −524.000 | + | 907.595i | −0.309670 | + | 0.536364i | ||||
\(143\) | 80.0000 | + | 138.564i | 0.0467828 | + | 0.0810301i | ||||
\(144\) | −72.0000 | − | 124.708i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 232.000 | − | 401.836i | 0.132873 | − | 0.230142i | ||||
\(146\) | 880.000 | 0.498831 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −888.000 | −0.493197 | ||||||||
\(149\) | 1585.00 | − | 2745.30i | 0.871465 | − | 1.50942i | 0.0109833 | − | 0.999940i | \(-0.496504\pi\) |
0.860482 | − | 0.509482i | \(-0.170163\pi\) | |||||||
\(150\) | 183.000 | + | 316.965i | 0.0996126 | + | 0.172534i | ||||
\(151\) | 940.000 | + | 1628.13i | 0.506597 | + | 0.877451i | 0.999971 | + | 0.00763414i | \(0.00243005\pi\) |
−0.493374 | + | 0.869817i | \(0.664237\pi\) | |||||||
\(152\) | −592.000 | + | 1025.37i | −0.315905 | + | 0.547163i | ||||
\(153\) | 756.000 | 0.399470 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1088.00 | −0.563808 | ||||||||
\(156\) | −24.0000 | + | 41.5692i | −0.0123176 | + | 0.0213346i | ||||
\(157\) | 302.000 | + | 523.079i | 0.153517 | + | 0.265900i | 0.932518 | − | 0.361123i | \(-0.117607\pi\) |
−0.779001 | + | 0.627023i | \(0.784273\pi\) | |||||||
\(158\) | 1216.00 | + | 2106.17i | 0.612277 | + | 1.06049i | ||||
\(159\) | 717.000 | − | 1241.88i | 0.357621 | − | 0.619418i | ||||
\(160\) | 256.000 | 0.126491 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −162.000 | −0.0785674 | ||||||||
\(163\) | −558.000 | + | 966.484i | −0.268135 | + | 0.464423i | −0.968380 | − | 0.249479i | \(-0.919741\pi\) |
0.700246 | + | 0.713902i | \(0.253074\pi\) | |||||||
\(164\) | 840.000 | + | 1454.92i | 0.399957 | + | 0.692746i | ||||
\(165\) | −480.000 | − | 831.384i | −0.226472 | − | 0.392262i | ||||
\(166\) | 684.000 | − | 1184.72i | 0.319811 | − | 0.553930i | ||||
\(167\) | 1784.00 | 0.826647 | 0.413324 | − | 0.910584i | \(-0.364368\pi\) | ||||
0.413324 | + | 0.910584i | \(0.364368\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2181.00 | −0.992717 | ||||||||
\(170\) | −672.000 | + | 1163.94i | −0.303177 | + | 0.525118i | ||||
\(171\) | 666.000 | + | 1153.55i | 0.297838 | + | 0.515870i | ||||
\(172\) | 328.000 | + | 568.113i | 0.145406 | + | 0.251850i | ||||
\(173\) | −172.000 | + | 297.913i | −0.0755891 | + | 0.130924i | −0.901342 | − | 0.433107i | \(-0.857417\pi\) |
0.825753 | + | 0.564032i | \(0.190750\pi\) | |||||||
\(174\) | 348.000 | 0.151620 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 640.000 | 0.274101 | ||||||||
\(177\) | −822.000 | + | 1423.75i | −0.349070 | + | 0.604606i | ||||
\(178\) | −604.000 | − | 1046.16i | −0.254335 | − | 0.440522i | ||||
\(179\) | −696.000 | − | 1205.51i | −0.290623 | − | 0.503373i | 0.683334 | − | 0.730106i | \(-0.260529\pi\) |
−0.973957 | + | 0.226732i | \(0.927196\pi\) | |||||||
\(180\) | 144.000 | − | 249.415i | 0.0596285 | − | 0.103280i | ||||
\(181\) | −4052.00 | −1.66399 | −0.831997 | − | 0.554781i | \(-0.812802\pi\) | ||||
−0.831997 | + | 0.554781i | \(0.812802\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2076.00 | 0.838592 | ||||||||
\(184\) | 336.000 | − | 581.969i | 0.134621 | − | 0.233170i | ||||
\(185\) | −888.000 | − | 1538.06i | −0.352903 | − | 0.611246i | ||||
\(186\) | −408.000 | − | 706.677i | −0.160839 | − | 0.278581i | ||||
\(187\) | −1680.00 | + | 2909.85i | −0.656972 | + | 1.13791i | ||||
\(188\) | −1952.00 | −0.757257 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2368.00 | −0.904173 | ||||||||
\(191\) | 1554.00 | − | 2691.61i | 0.588709 | − | 1.01967i | −0.405692 | − | 0.914010i | \(-0.632970\pi\) |
0.994402 | − | 0.105665i | \(-0.0336971\pi\) | |||||||
\(192\) | 96.0000 | + | 166.277i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | −25.0000 | − | 43.3013i | −0.00932404 | − | 0.0161497i | 0.861326 | − | 0.508053i | \(-0.169635\pi\) |
−0.870650 | + | 0.491903i | \(0.836301\pi\) | |||||||
\(194\) | 832.000 | − | 1441.07i | 0.307908 | − | 0.533312i | ||||
\(195\) | −96.0000 | −0.0352549 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −162.000 | −0.0585889 | −0.0292945 | − | 0.999571i | \(-0.509326\pi\) | ||||
−0.0292945 | + | 0.999571i | \(0.509326\pi\) | |||||||
\(198\) | 360.000 | − | 623.538i | 0.129213 | − | 0.223803i | ||||
\(199\) | 772.000 | + | 1337.14i | 0.275003 | + | 0.476319i | 0.970136 | − | 0.242562i | \(-0.0779878\pi\) |
−0.695133 | + | 0.718881i | \(0.744654\pi\) | |||||||
\(200\) | −244.000 | − | 422.620i | −0.0862670 | − | 0.149419i | ||||
\(201\) | −1362.00 | + | 2359.05i | −0.477951 | + | 0.827835i | ||||
\(202\) | 928.000 | 0.323237 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1008.00 | −0.345952 | ||||||||
\(205\) | −1680.00 | + | 2909.85i | −0.572372 | + | 0.991378i | ||||
\(206\) | 632.000 | + | 1094.66i | 0.213755 | + | 0.370234i | ||||
\(207\) | −378.000 | − | 654.715i | −0.126922 | − | 0.219835i | ||||
\(208\) | 32.0000 | − | 55.4256i | 0.0106673 | − | 0.0184763i | ||||
\(209\) | −5920.00 | −1.95931 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1204.00 | −0.392828 | −0.196414 | − | 0.980521i | \(-0.562930\pi\) | ||||
−0.196414 | + | 0.980521i | \(0.562930\pi\) | |||||||
\(212\) | −956.000 | + | 1655.84i | −0.309709 | + | 0.536432i | ||||
\(213\) | −786.000 | − | 1361.39i | −0.252844 | − | 0.437939i | ||||
\(214\) | −160.000 | − | 277.128i | −0.0511092 | − | 0.0885238i | ||||
\(215\) | −656.000 | + | 1136.23i | −0.208088 | + | 0.360418i | ||||
\(216\) | 216.000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4396.00 | 1.36576 | ||||||||
\(219\) | −660.000 | + | 1143.15i | −0.203647 | + | 0.352727i | ||||
\(220\) | 640.000 | + | 1108.51i | 0.196131 | + | 0.339709i | ||||
\(221\) | 168.000 | + | 290.985i | 0.0511353 | + | 0.0885690i | ||||
\(222\) | 666.000 | − | 1153.55i | 0.201347 | − | 0.348743i | ||||
\(223\) | −2000.00 | −0.600583 | −0.300291 | − | 0.953848i | \(-0.597084\pi\) | ||||
−0.300291 | + | 0.953848i | \(0.597084\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −549.000 | −0.162667 | ||||||||
\(226\) | 770.000 | − | 1333.68i | 0.226636 | − | 0.392544i | ||||
\(227\) | 194.000 | + | 336.018i | 0.0567235 | + | 0.0982480i | 0.892993 | − | 0.450071i | \(-0.148601\pi\) |
−0.836269 | + | 0.548319i | \(0.815268\pi\) | |||||||
\(228\) | −888.000 | − | 1538.06i | −0.257935 | − | 0.446757i | ||||
\(229\) | 2090.00 | − | 3619.99i | 0.603105 | − | 1.04461i | −0.389243 | − | 0.921135i | \(-0.627263\pi\) |
0.992348 | − | 0.123474i | \(-0.0394034\pi\) | |||||||
\(230\) | 1344.00 | 0.385308 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −464.000 | −0.131306 | ||||||||
\(233\) | 661.000 | − | 1144.89i | 0.185852 | − | 0.321905i | −0.758011 | − | 0.652242i | \(-0.773829\pi\) |
0.943863 | + | 0.330336i | \(0.107162\pi\) | |||||||
\(234\) | −36.0000 | − | 62.3538i | −0.0100572 | − | 0.0174196i | ||||
\(235\) | −1952.00 | − | 3380.96i | −0.541849 | − | 0.938509i | ||||
\(236\) | 1096.00 | − | 1898.33i | 0.302303 | − | 0.523604i | ||||
\(237\) | −3648.00 | −0.999844 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2412.00 | 0.652800 | 0.326400 | − | 0.945232i | \(-0.394164\pi\) | ||||
0.326400 | + | 0.945232i | \(0.394164\pi\) | |||||||
\(240\) | −192.000 | + | 332.554i | −0.0516398 | + | 0.0894427i | ||||
\(241\) | −2168.00 | − | 3755.09i | −0.579474 | − | 1.00368i | −0.995540 | − | 0.0943434i | \(-0.969925\pi\) |
0.416066 | − | 0.909334i | \(-0.363409\pi\) | |||||||
\(242\) | 269.000 | + | 465.922i | 0.0714544 | + | 0.123763i | ||||
\(243\) | 121.500 | − | 210.444i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −2768.00 | −0.726242 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2520.00 | −0.653127 | ||||||||
\(247\) | −296.000 | + | 512.687i | −0.0762511 | + | 0.132071i | ||||
\(248\) | 544.000 | + | 942.236i | 0.139290 | + | 0.241258i | ||||
\(249\) | 1026.00 | + | 1777.08i | 0.261125 | + | 0.452282i | ||||
\(250\) | 1488.00 | − | 2577.29i | 0.376438 | − | 0.652009i | ||||
\(251\) | −764.000 | −0.192125 | −0.0960623 | − | 0.995375i | \(-0.530625\pi\) | ||||
−0.0960623 | + | 0.995375i | \(0.530625\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3360.00 | 0.834946 | ||||||||
\(254\) | −184.000 | + | 318.697i | −0.0454535 | + | 0.0787278i | ||||
\(255\) | −1008.00 | − | 1745.91i | −0.247543 | − | 0.428757i | ||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 2150.00 | − | 3723.91i | 0.521842 | − | 0.903856i | −0.477835 | − | 0.878449i | \(-0.658579\pi\) |
0.999677 | − | 0.0254070i | \(-0.00808817\pi\) | |||||||
\(258\) | −984.000 | −0.237446 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 128.000 | 0.0305316 | ||||||||
\(261\) | −261.000 | + | 452.065i | −0.0618984 | + | 0.107211i | ||||
\(262\) | 1452.00 | + | 2514.94i | 0.342385 | + | 0.593028i | ||||
\(263\) | 1930.00 | + | 3342.86i | 0.452505 | + | 0.783762i | 0.998541 | − | 0.0539998i | \(-0.0171970\pi\) |
−0.546036 | + | 0.837762i | \(0.683864\pi\) | |||||||
\(264\) | −480.000 | + | 831.384i | −0.111901 | + | 0.193819i | ||||
\(265\) | −3824.00 | −0.886439 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1812.00 | 0.415328 | ||||||||
\(268\) | 1816.00 | − | 3145.40i | 0.413917 | − | 0.716926i | ||||
\(269\) | −1400.00 | − | 2424.87i | −0.317322 | − | 0.549617i | 0.662607 | − | 0.748968i | \(-0.269450\pi\) |
−0.979928 | + | 0.199350i | \(0.936117\pi\) | |||||||
\(270\) | 216.000 | + | 374.123i | 0.0486864 | + | 0.0843274i | ||||
\(271\) | −2440.00 | + | 4226.20i | −0.546935 | + | 0.947320i | 0.451547 | + | 0.892247i | \(0.350872\pi\) |
−0.998482 | + | 0.0550723i | \(0.982461\pi\) | |||||||
\(272\) | 1344.00 | 0.299603 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1292.00 | −0.284863 | ||||||||
\(275\) | 1220.00 | − | 2113.10i | 0.267523 | − | 0.463363i | ||||
\(276\) | 504.000 | + | 872.954i | 0.109918 | + | 0.190383i | ||||
\(277\) | 3337.00 | + | 5779.85i | 0.723830 | + | 1.25371i | 0.959454 | + | 0.281866i | \(0.0909533\pi\) |
−0.235624 | + | 0.971844i | \(0.575713\pi\) | |||||||
\(278\) | 3012.00 | − | 5216.94i | 0.649812 | − | 1.12551i | ||||
\(279\) | 1224.00 | 0.262649 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9402.00 | −1.99600 | −0.998001 | − | 0.0632056i | \(-0.979868\pi\) | ||||
−0.998001 | + | 0.0632056i | \(0.979868\pi\) | |||||||
\(282\) | 1464.00 | − | 2535.72i | 0.309149 | − | 0.535461i | ||||
\(283\) | −4550.00 | − | 7880.83i | −0.955722 | − | 1.65536i | −0.732706 | − | 0.680545i | \(-0.761743\pi\) |
−0.223016 | − | 0.974815i | \(-0.571590\pi\) | |||||||
\(284\) | 1048.00 | + | 1815.19i | 0.218970 | + | 0.379266i | ||||
\(285\) | 1776.00 | − | 3076.12i | 0.369127 | − | 0.639347i | ||||
\(286\) | 320.000 | 0.0661608 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −288.000 | −0.0589256 | ||||||||
\(289\) | −1071.50 | + | 1855.89i | −0.218095 | + | 0.377751i | ||||
\(290\) | −464.000 | − | 803.672i | −0.0939552 | − | 0.162735i | ||||
\(291\) | 1248.00 | + | 2161.60i | 0.251406 | + | 0.435447i | ||||
\(292\) | 880.000 | − | 1524.20i | 0.176363 | − | 0.305470i | ||||
\(293\) | −5952.00 | −1.18676 | −0.593378 | − | 0.804924i | \(-0.702206\pi\) | ||||
−0.593378 | + | 0.804924i | \(0.702206\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4384.00 | 0.865242 | ||||||||
\(296\) | −888.000 | + | 1538.06i | −0.174371 | + | 0.302020i | ||||
\(297\) | 540.000 | + | 935.307i | 0.105502 | + | 0.182734i | ||||
\(298\) | −3170.00 | − | 5490.60i | −0.616219 | − | 1.06732i | ||||
\(299\) | 168.000 | − | 290.985i | 0.0324939 | − | 0.0562812i | ||||
\(300\) | 732.000 | 0.140873 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3760.00 | 0.716436 | ||||||||
\(303\) | −696.000 | + | 1205.51i | −0.131961 | + | 0.228563i | ||||
\(304\) | 1184.00 | + | 2050.75i | 0.223378 | + | 0.386903i | ||||
\(305\) | −2768.00 | − | 4794.32i | −0.519656 | − | 0.900071i | ||||
\(306\) | 756.000 | − | 1309.43i | 0.141234 | − | 0.244625i | ||||
\(307\) | 3004.00 | 0.558460 | 0.279230 | − | 0.960224i | \(-0.409921\pi\) | ||||
0.279230 | + | 0.960224i | \(0.409921\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1896.00 | −0.349060 | ||||||||
\(310\) | −1088.00 | + | 1884.47i | −0.199336 | + | 0.345261i | ||||
\(311\) | 344.000 | + | 595.825i | 0.0627217 | + | 0.108637i | 0.895681 | − | 0.444697i | \(-0.146689\pi\) |
−0.832959 | + | 0.553334i | \(0.813355\pi\) | |||||||
\(312\) | 48.0000 | + | 83.1384i | 0.00870982 | + | 0.0150859i | ||||
\(313\) | 2796.00 | − | 4842.81i | 0.504918 | − | 0.874543i | −0.495066 | − | 0.868855i | \(-0.664856\pi\) |
0.999984 | − | 0.00568790i | \(-0.00181052\pi\) | |||||||
\(314\) | 1208.00 | 0.217106 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4864.00 | 0.865890 | ||||||||
\(317\) | 1461.00 | − | 2530.53i | 0.258858 | − | 0.448355i | −0.707078 | − | 0.707135i | \(-0.749987\pi\) |
0.965936 | + | 0.258780i | \(0.0833205\pi\) | |||||||
\(318\) | −1434.00 | − | 2483.76i | −0.252876 | − | 0.437995i | ||||
\(319\) | −1160.00 | − | 2009.18i | −0.203597 | − | 0.352641i | ||||
\(320\) | 256.000 | − | 443.405i | 0.0447214 | − | 0.0774597i | ||||
\(321\) | 480.000 | 0.0834610 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12432.0 | −2.14159 | ||||||||
\(324\) | −162.000 | + | 280.592i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | −122.000 | − | 211.310i | −0.0208226 | − | 0.0360658i | ||||
\(326\) | 1116.00 | + | 1932.97i | 0.189600 | + | 0.328396i | ||||
\(327\) | −3297.00 | + | 5710.57i | −0.557567 | + | 0.965735i | ||||
\(328\) | 3360.00 | 0.565625 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1920.00 | −0.320280 | ||||||||
\(331\) | 3746.00 | − | 6488.26i | 0.622051 | − | 1.07742i | −0.367053 | − | 0.930200i | \(-0.619633\pi\) |
0.989103 | − | 0.147223i | \(-0.0470336\pi\) | |||||||
\(332\) | −1368.00 | − | 2369.45i | −0.226141 | − | 0.391687i | ||||
\(333\) | 999.000 | + | 1730.32i | 0.164399 | + | 0.284747i | ||||
\(334\) | 1784.00 | − | 3089.98i | 0.292264 | − | 0.506216i | ||||
\(335\) | 7264.00 | 1.18470 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10766.0 | 1.74024 | 0.870121 | − | 0.492839i | \(-0.164041\pi\) | ||||
0.870121 | + | 0.492839i | \(0.164041\pi\) | |||||||
\(338\) | −2181.00 | + | 3777.60i | −0.350979 | + | 0.607913i | ||||
\(339\) | 1155.00 | + | 2000.52i | 0.185047 | + | 0.320511i | ||||
\(340\) | 1344.00 | + | 2327.88i | 0.214378 | + | 0.371314i | ||||
\(341\) | −2720.00 | + | 4711.18i | −0.431954 | + | 0.748166i | ||||
\(342\) | 2664.00 | 0.421206 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1312.00 | 0.205635 | ||||||||
\(345\) | −1008.00 | + | 1745.91i | −0.157301 | + | 0.272454i | ||||
\(346\) | 344.000 | + | 595.825i | 0.0534496 | + | 0.0925774i | ||||
\(347\) | 1992.00 | + | 3450.25i | 0.308173 | + | 0.533772i | 0.977963 | − | 0.208779i | \(-0.0669490\pi\) |
−0.669789 | + | 0.742551i | \(0.733616\pi\) | |||||||
\(348\) | 348.000 | − | 602.754i | 0.0536056 | − | 0.0928477i | ||||
\(349\) | 180.000 | 0.0276080 | 0.0138040 | − | 0.999905i | \(-0.495606\pi\) | ||||
0.0138040 | + | 0.999905i | \(0.495606\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 108.000 | 0.0164234 | ||||||||
\(352\) | 640.000 | − | 1108.51i | 0.0969094 | − | 0.167852i | ||||
\(353\) | −5214.00 | − | 9030.91i | −0.786156 | − | 1.36166i | −0.928306 | − | 0.371818i | \(-0.878735\pi\) |
0.142149 | − | 0.989845i | \(-0.454599\pi\) | |||||||
\(354\) | 1644.00 | + | 2847.49i | 0.246829 | + | 0.427521i | ||||
\(355\) | −2096.00 | + | 3630.38i | −0.313364 | + | 0.542762i | ||||
\(356\) | −2416.00 | −0.359685 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2784.00 | −0.411003 | ||||||||
\(359\) | −4342.00 | + | 7520.56i | −0.638334 | + | 1.10563i | 0.347464 | + | 0.937693i | \(0.387043\pi\) |
−0.985798 | + | 0.167934i | \(0.946290\pi\) | |||||||
\(360\) | −288.000 | − | 498.831i | −0.0421637 | − | 0.0730297i | ||||
\(361\) | −7522.50 | − | 13029.4i | −1.09673 | − | 1.89960i | ||||
\(362\) | −4052.00 | + | 7018.27i | −0.588310 | + | 1.01898i | ||||
\(363\) | −807.000 | −0.116685 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3520.00 | 0.504781 | ||||||||
\(366\) | 2076.00 | − | 3595.74i | 0.296487 | − | 0.513531i | ||||
\(367\) | 2824.00 | + | 4891.31i | 0.401666 | + | 0.695707i | 0.993927 | − | 0.110040i | \(-0.0350978\pi\) |
−0.592261 | + | 0.805746i | \(0.701764\pi\) | |||||||
\(368\) | −672.000 | − | 1163.94i | −0.0951914 | − | 0.164876i | ||||
\(369\) | 1890.00 | − | 3273.58i | 0.266638 | − | 0.461831i | ||||
\(370\) | −3552.00 | −0.499080 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1632.00 | −0.227460 | ||||||||
\(373\) | 1273.00 | − | 2204.90i | 0.176712 | − | 0.306074i | −0.764041 | − | 0.645168i | \(-0.776787\pi\) |
0.940752 | + | 0.339095i | \(0.110121\pi\) | |||||||
\(374\) | 3360.00 | + | 5819.69i | 0.464549 | + | 0.804623i | ||||
\(375\) | 2232.00 | + | 3865.94i | 0.307360 | + | 0.532363i | ||||
\(376\) | −1952.00 | + | 3380.96i | −0.267731 | + | 0.463723i | ||||
\(377\) | −232.000 | −0.0316939 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8268.00 | 1.12058 | 0.560288 | − | 0.828298i | \(-0.310690\pi\) | ||||
0.560288 | + | 0.828298i | \(0.310690\pi\) | |||||||
\(380\) | −2368.00 | + | 4101.50i | −0.319673 | + | 0.553690i | ||||
\(381\) | −276.000 | − | 478.046i | −0.0371126 | − | 0.0642809i | ||||
\(382\) | −3108.00 | − | 5383.21i | −0.416280 | − | 0.721019i | ||||
\(383\) | −5436.00 | + | 9415.43i | −0.725239 | + | 1.25615i | 0.233636 | + | 0.972324i | \(0.424938\pi\) |
−0.958875 | + | 0.283827i | \(0.908396\pi\) | |||||||
\(384\) | 384.000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −100.000 | −0.0131862 | ||||||||
\(387\) | 738.000 | − | 1278.25i | 0.0969371 | − | 0.167900i | ||||
\(388\) | −1664.00 | − | 2882.13i | −0.217724 | − | 0.377109i | ||||
\(389\) | −5217.00 | − | 9036.11i | −0.679980 | − | 1.17776i | −0.974986 | − | 0.222265i | \(-0.928655\pi\) |
0.295006 | − | 0.955495i | \(-0.404678\pi\) | |||||||
\(390\) | −96.0000 | + | 166.277i | −0.0124645 | + | 0.0215891i | ||||
\(391\) | 7056.00 | 0.912627 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4356.00 | −0.559112 | ||||||||
\(394\) | −162.000 | + | 280.592i | −0.0207143 | + | 0.0358783i | ||||
\(395\) | 4864.00 | + | 8424.70i | 0.619581 | + | 1.07315i | ||||
\(396\) | −720.000 | − | 1247.08i | −0.0913671 | − | 0.158252i | ||||
\(397\) | −1522.00 | + | 2636.18i | −0.192411 | + | 0.333265i | −0.946049 | − | 0.324025i | \(-0.894964\pi\) |
0.753638 | + | 0.657290i | \(0.228297\pi\) | |||||||
\(398\) | 3088.00 | 0.388913 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −976.000 | −0.122000 | ||||||||
\(401\) | −4455.00 | + | 7716.29i | −0.554793 | + | 0.960930i | 0.443126 | + | 0.896459i | \(0.353869\pi\) |
−0.997920 | + | 0.0644709i | \(0.979464\pi\) | |||||||
\(402\) | 2724.00 | + | 4718.11i | 0.337962 | + | 0.585368i | ||||
\(403\) | 272.000 | + | 471.118i | 0.0336211 | + | 0.0582334i | ||||
\(404\) | 928.000 | − | 1607.34i | 0.114281 | − | 0.197941i | ||||
\(405\) | −648.000 | −0.0795046 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8880.00 | −1.08149 | ||||||||
\(408\) | −1008.00 | + | 1745.91i | −0.122312 | + | 0.211851i | ||||
\(409\) | 2808.00 | + | 4863.60i | 0.339478 | + | 0.587994i | 0.984335 | − | 0.176310i | \(-0.0564161\pi\) |
−0.644856 | + | 0.764304i | \(0.723083\pi\) | |||||||
\(410\) | 3360.00 | + | 5819.69i | 0.404728 | + | 0.701010i | ||||
\(411\) | 969.000 | − | 1678.36i | 0.116295 | − | 0.201429i | ||||
\(412\) | 2528.00 | 0.302295 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1512.00 | −0.179495 | ||||||||
\(415\) | 2736.00 | − | 4738.89i | 0.323626 | − | 0.560537i | ||||
\(416\) | −64.0000 | − | 110.851i | −0.00754293 | − | 0.0130647i | ||||
\(417\) | 4518.00 | + | 7825.41i | 0.530569 | + | 0.918973i | ||||
\(418\) | −5920.00 | + | 10253.7i | −0.692719 | + | 1.19983i | ||||
\(419\) | 8932.00 | 1.04142 | 0.520712 | − | 0.853732i | \(-0.325666\pi\) | ||||
0.520712 | + | 0.853732i | \(0.325666\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5538.00 | −0.641106 | −0.320553 | − | 0.947231i | \(-0.603869\pi\) | ||||
−0.320553 | + | 0.947231i | \(0.603869\pi\) | |||||||
\(422\) | −1204.00 | + | 2085.39i | −0.138886 | + | 0.240557i | ||||
\(423\) | 2196.00 | + | 3803.58i | 0.252419 | + | 0.437202i | ||||
\(424\) | 1912.00 | + | 3311.68i | 0.218997 | + | 0.379315i | ||||
\(425\) | 2562.00 | − | 4437.51i | 0.292412 | − | 0.506473i | ||||
\(426\) | −3144.00 | −0.357576 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −640.000 | −0.0722794 | ||||||||
\(429\) | −240.000 | + | 415.692i | −0.0270100 | + | 0.0467828i | ||||
\(430\) | 1312.00 | + | 2272.45i | 0.147140 | + | 0.254854i | ||||
\(431\) | 3350.00 | + | 5802.37i | 0.374394 | + | 0.648469i | 0.990236 | − | 0.139400i | \(-0.0445174\pi\) |
−0.615842 | + | 0.787870i | \(0.711184\pi\) | |||||||
\(432\) | 216.000 | − | 374.123i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | 5048.00 | 0.560257 | 0.280129 | − | 0.959962i | \(-0.409623\pi\) | ||||
0.280129 | + | 0.959962i | \(0.409623\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1392.00 | 0.153428 | ||||||||
\(436\) | 4396.00 | − | 7614.10i | 0.482867 | − | 0.836351i | ||||
\(437\) | 6216.00 | + | 10766.4i | 0.680438 | + | 1.17855i | ||||
\(438\) | 1320.00 | + | 2286.31i | 0.144000 | + | 0.249415i | ||||
\(439\) | −672.000 | + | 1163.94i | −0.0730588 | + | 0.126542i | −0.900240 | − | 0.435393i | \(-0.856609\pi\) |
0.827182 | + | 0.561935i | \(0.189943\pi\) | |||||||
\(440\) | 2560.00 | 0.277371 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 672.000 | 0.0723162 | ||||||||
\(443\) | 2196.00 | − | 3803.58i | 0.235519 | − | 0.407932i | −0.723904 | − | 0.689901i | \(-0.757654\pi\) |
0.959424 | + | 0.281969i | \(0.0909875\pi\) | |||||||
\(444\) | −1332.00 | − | 2307.09i | −0.142374 | − | 0.246598i | ||||
\(445\) | −2416.00 | − | 4184.63i | −0.257369 | − | 0.445777i | ||||
\(446\) | −2000.00 | + | 3464.10i | −0.212338 | + | 0.367780i | ||||
\(447\) | 9510.00 | 1.00628 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3666.00 | 0.385321 | 0.192661 | − | 0.981265i | \(-0.438288\pi\) | ||||
0.192661 | + | 0.981265i | \(0.438288\pi\) | |||||||
\(450\) | −549.000 | + | 950.896i | −0.0575114 | + | 0.0996126i | ||||
\(451\) | 8400.00 | + | 14549.2i | 0.877030 | + | 1.51906i | ||||
\(452\) | −1540.00 | − | 2667.36i | −0.160256 | − | 0.277571i | ||||
\(453\) | −2820.00 | + | 4884.38i | −0.292484 | + | 0.506597i | ||||
\(454\) | 776.000 | 0.0802191 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3552.00 | −0.364776 | ||||||||
\(457\) | −13.0000 | + | 22.5167i | −0.00133067 | + | 0.00230478i | −0.866690 | − | 0.498847i | \(-0.833757\pi\) |
0.865359 | + | 0.501152i | \(0.167090\pi\) | |||||||
\(458\) | −4180.00 | − | 7239.97i | −0.426460 | − | 0.738650i | ||||
\(459\) | 1134.00 | + | 1964.15i | 0.115317 | + | 0.199735i | ||||
\(460\) | 1344.00 | − | 2327.88i | 0.136227 | − | 0.235952i | ||||
\(461\) | −7656.00 | −0.773483 | −0.386741 | − | 0.922188i | \(-0.626399\pi\) | ||||
−0.386741 | + | 0.922188i | \(0.626399\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12608.0 | 1.26554 | 0.632768 | − | 0.774341i | \(-0.281919\pi\) | ||||
0.632768 | + | 0.774341i | \(0.281919\pi\) | |||||||
\(464\) | −464.000 | + | 803.672i | −0.0464238 | + | 0.0804084i | ||||
\(465\) | −1632.00 | − | 2826.71i | −0.162757 | − | 0.281904i | ||||
\(466\) | −1322.00 | − | 2289.77i | −0.131417 | − | 0.227621i | ||||
\(467\) | −1534.00 | + | 2656.97i | −0.152002 | + | 0.263276i | −0.931963 | − | 0.362552i | \(-0.881905\pi\) |
0.779961 | + | 0.625828i | \(0.215239\pi\) | |||||||
\(468\) | −144.000 | −0.0142231 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −7808.00 | −0.766290 | ||||||||
\(471\) | −906.000 | + | 1569.24i | −0.0886333 | + | 0.153517i | ||||
\(472\) | −2192.00 | − | 3796.66i | −0.213761 | − | 0.370244i | ||||
\(473\) | 3280.00 | + | 5681.13i | 0.318847 | + | 0.552259i | ||||
\(474\) | −3648.00 | + | 6318.52i | −0.353498 | + | 0.612277i | ||||
\(475\) | 9028.00 | 0.872070 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4302.00 | 0.412946 | ||||||||
\(478\) | 2412.00 | − | 4177.71i | 0.230800 | − | 0.399757i | ||||
\(479\) | 3228.00 | + | 5591.06i | 0.307915 | + | 0.533324i | 0.977906 | − | 0.209045i | \(-0.0670356\pi\) |
−0.669991 | + | 0.742369i | \(0.733702\pi\) | |||||||
\(480\) | 384.000 | + | 665.108i | 0.0365148 | + | 0.0632456i | ||||
\(481\) | −444.000 | + | 769.031i | −0.0420887 | + | 0.0728997i | ||||
\(482\) | −8672.00 | −0.819500 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1076.00 | 0.101052 | ||||||||
\(485\) | 3328.00 | − | 5764.27i | 0.311581 | − | 0.539674i | ||||
\(486\) | −243.000 | − | 420.888i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | −5948.00 | − | 10302.2i | −0.553449 | − | 0.958602i | −0.998022 | − | 0.0628592i | \(-0.979978\pi\) |
0.444574 | − | 0.895742i | \(-0.353355\pi\) | |||||||
\(488\) | −2768.00 | + | 4794.32i | −0.256765 | + | 0.444731i | ||||
\(489\) | −3348.00 | −0.309615 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −264.000 | −0.0242651 | −0.0121325 | − | 0.999926i | \(-0.503862\pi\) | ||||
−0.0121325 | + | 0.999926i | \(0.503862\pi\) | |||||||
\(492\) | −2520.00 | + | 4364.77i | −0.230915 | + | 0.399957i | ||||
\(493\) | −2436.00 | − | 4219.28i | −0.222539 | − | 0.385450i | ||||
\(494\) | 592.000 | + | 1025.37i | 0.0539177 | + | 0.0933882i | ||||
\(495\) | 1440.00 | − | 2494.15i | 0.130754 | − | 0.226472i | ||||
\(496\) | 2176.00 | 0.196986 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 4104.00 | 0.369286 | ||||||||
\(499\) | 1314.00 | − | 2275.91i | 0.117881 | − | 0.204176i | −0.801047 | − | 0.598602i | \(-0.795723\pi\) |
0.918928 | + | 0.394426i | \(0.129056\pi\) | |||||||
\(500\) | −2976.00 | − | 5154.58i | −0.266182 | − | 0.461040i | ||||
\(501\) | 2676.00 | + | 4634.97i | 0.238632 | + | 0.413324i | ||||
\(502\) | −764.000 | + | 1323.29i | −0.0679263 | + | 0.117652i | ||||
\(503\) | 13568.0 | 1.20272 | 0.601359 | − | 0.798979i | \(-0.294626\pi\) | ||||
0.601359 | + | 0.798979i | \(0.294626\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3712.00 | 0.327093 | ||||||||
\(506\) | 3360.00 | − | 5819.69i | 0.295198 | − | 0.511298i | ||||
\(507\) | −3271.50 | − | 5666.40i | −0.286573 | − | 0.496359i | ||||
\(508\) | 368.000 | + | 637.395i | 0.0321405 | + | 0.0556689i | ||||
\(509\) | 10328.0 | − | 17888.6i | 0.899372 | − | 1.55776i | 0.0710743 | − | 0.997471i | \(-0.477357\pi\) |
0.828298 | − | 0.560288i | \(-0.189309\pi\) | |||||||
\(510\) | −4032.00 | −0.350078 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | −1998.00 | + | 3460.64i | −0.171957 | + | 0.297838i | ||||
\(514\) | −4300.00 | − | 7447.82i | −0.368998 | − | 0.639123i | ||||
\(515\) | 2528.00 | + | 4378.62i | 0.216305 | + | 0.374651i | ||||
\(516\) | −984.000 | + | 1704.34i | −0.0839500 | + | 0.145406i | ||||
\(517\) | −19520.0 | −1.66052 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1032.00 | −0.0872828 | ||||||||
\(520\) | 128.000 | − | 221.703i | 0.0107946 | − | 0.0186967i | ||||
\(521\) | 1814.00 | + | 3141.94i | 0.152539 | + | 0.264205i | 0.932160 | − | 0.362046i | \(-0.117922\pi\) |
−0.779621 | + | 0.626251i | \(0.784588\pi\) | |||||||
\(522\) | 522.000 | + | 904.131i | 0.0437688 | + | 0.0758098i | ||||
\(523\) | 2426.00 | − | 4201.96i | 0.202833 | − | 0.351317i | −0.746607 | − | 0.665265i | \(-0.768319\pi\) |
0.949440 | + | 0.313948i | \(0.101652\pi\) | |||||||
\(524\) | 5808.00 | 0.484205 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7720.00 | 0.639939 | ||||||||
\(527\) | −5712.00 | + | 9893.47i | −0.472142 | + | 0.817773i | ||||
\(528\) | 960.000 | + | 1662.77i | 0.0791262 | + | 0.137051i | ||||
\(529\) | 2555.50 | + | 4426.26i | 0.210035 | + | 0.363792i | ||||
\(530\) | −3824.00 | + | 6623.36i | −0.313404 | + | 0.542831i | ||||
\(531\) | −4932.00 | −0.403071 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1680.00 | 0.136527 | ||||||||
\(534\) | 1812.00 | − | 3138.48i | 0.146841 | − | 0.254335i | ||||
\(535\) | −640.000 | − | 1108.51i | −0.0517189 | − | 0.0895798i | ||||
\(536\) | −3632.00 | − | 6290.81i | −0.292684 | − | 0.506943i | ||||
\(537\) | 2088.00 | − | 3616.52i | 0.167791 | − | 0.290623i | ||||
\(538\) | −5600.00 | −0.448760 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 864.000 | 0.0688530 | ||||||||
\(541\) | 3565.00 | − | 6174.76i | 0.283311 | − | 0.490709i | −0.688887 | − | 0.724869i | \(-0.741900\pi\) |
0.972198 | + | 0.234159i | \(0.0752338\pi\) | |||||||
\(542\) | 4880.00 | + | 8452.41i | 0.386742 | + | 0.669856i | ||||
\(543\) | −6078.00 | − | 10527.4i | −0.480353 | − | 0.831997i | ||||
\(544\) | 1344.00 | − | 2327.88i | 0.105926 | − | 0.183469i | ||||
\(545\) | 17584.0 | 1.38205 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12788.0 | −0.999589 | −0.499795 | − | 0.866144i | \(-0.666591\pi\) | ||||
−0.499795 | + | 0.866144i | \(0.666591\pi\) | |||||||
\(548\) | −1292.00 | + | 2237.81i | −0.100714 | + | 0.174443i | ||||
\(549\) | 3114.00 | + | 5393.61i | 0.242081 | + | 0.419296i | ||||
\(550\) | −2440.00 | − | 4226.20i | −0.189167 | − | 0.327647i | ||||
\(551\) | 4292.00 | − | 7433.96i | 0.331843 | − | 0.574768i | ||||
\(552\) | 2016.00 | 0.155447 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 13348.0 | 1.02365 | ||||||||
\(555\) | 2664.00 | − | 4614.18i | 0.203749 | − | 0.352903i | ||||
\(556\) | −6024.00 | − | 10433.9i | −0.459487 | − | 0.795854i | ||||
\(557\) | −1203.00 | − | 2083.66i | −0.0915130 | − | 0.158505i | 0.816635 | − | 0.577155i | \(-0.195837\pi\) |
−0.908148 | + | 0.418649i | \(0.862504\pi\) | |||||||
\(558\) | 1224.00 | − | 2120.03i | 0.0928603 | − | 0.160839i | ||||
\(559\) | 656.000 | 0.0496348 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10080.0 | −0.758606 | ||||||||
\(562\) | −9402.00 | + | 16284.7i | −0.705693 | + | 1.22230i | ||||
\(563\) | −12706.0 | − | 22007.4i | −0.951144 | − | 1.64743i | −0.742955 | − | 0.669341i | \(-0.766577\pi\) |
−0.208189 | − | 0.978089i | \(-0.566757\pi\) | |||||||
\(564\) | −2928.00 | − | 5071.44i | −0.218601 | − | 0.378628i | ||||
\(565\) | 3080.00 | − | 5334.72i | 0.229339 | − | 0.397227i | ||||
\(566\) | −18200.0 | −1.35160 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4192.00 | 0.309670 | ||||||||
\(569\) | 4845.00 | − | 8391.79i | 0.356965 | − | 0.618281i | −0.630487 | − | 0.776199i | \(-0.717145\pi\) |
0.987452 | + | 0.157918i | \(0.0504783\pi\) | |||||||
\(570\) | −3552.00 | − | 6152.24i | −0.261012 | − | 0.452086i | ||||
\(571\) | −2802.00 | − | 4853.21i | −0.205359 | − | 0.355692i | 0.744888 | − | 0.667190i | \(-0.232503\pi\) |
−0.950247 | + | 0.311497i | \(0.899170\pi\) | |||||||
\(572\) | 320.000 | − | 554.256i | 0.0233914 | − | 0.0405151i | ||||
\(573\) | 9324.00 | 0.679783 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5124.00 | −0.371627 | ||||||||
\(576\) | −288.000 | + | 498.831i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −10784.0 | − | 18678.4i | −0.778066 | − | 1.34765i | −0.933055 | − | 0.359733i | \(-0.882868\pi\) |
0.154990 | − | 0.987916i | \(-0.450466\pi\) | |||||||
\(578\) | 2143.00 | + | 3711.78i | 0.154216 | + | 0.267111i | ||||
\(579\) | 75.0000 | − | 129.904i | 0.00538324 | − | 0.00932404i | ||||
\(580\) | −1856.00 | −0.132873 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 4992.00 | 0.355541 | ||||||||
\(583\) | −9560.00 | + | 16558.4i | −0.679133 | + | 1.17629i | ||||
\(584\) | −1760.00 | − | 3048.41i | −0.124708 | − | 0.216000i | ||||
\(585\) | −144.000 | − | 249.415i | −0.0101772 | − | 0.0176274i | ||||
\(586\) | −5952.00 | + | 10309.2i | −0.419582 | + | 0.726737i | ||||
\(587\) | −20300.0 | −1.42738 | −0.713689 | − | 0.700463i | \(-0.752977\pi\) | ||||
−0.713689 | + | 0.700463i | \(0.752977\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20128.0 | −1.40808 | ||||||||
\(590\) | 4384.00 | − | 7593.31i | 0.305909 | − | 0.529850i | ||||
\(591\) | −243.000 | − | 420.888i | −0.0169132 | − | 0.0292945i | ||||
\(592\) | 1776.00 | + | 3076.12i | 0.123299 | + | 0.213561i | ||||
\(593\) | 6906.00 | − | 11961.5i | 0.478238 | − | 0.828333i | −0.521450 | − | 0.853282i | \(-0.674609\pi\) |
0.999689 | + | 0.0249483i | \(0.00794212\pi\) | |||||||
\(594\) | 2160.00 | 0.149202 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12680.0 | −0.871465 | ||||||||
\(597\) | −2316.00 | + | 4011.43i | −0.158773 | + | 0.275003i | ||||
\(598\) | −336.000 | − | 581.969i | −0.0229767 | − | 0.0397968i | ||||
\(599\) | 10998.0 | + | 19049.1i | 0.750194 | + | 1.29937i | 0.947728 | + | 0.319078i | \(0.103373\pi\) |
−0.197535 | + | 0.980296i | \(0.563294\pi\) | |||||||
\(600\) | 732.000 | − | 1267.86i | 0.0498063 | − | 0.0862670i | ||||
\(601\) | −8368.00 | −0.567950 | −0.283975 | − | 0.958832i | \(-0.591653\pi\) | ||||
−0.283975 | + | 0.958832i | \(0.591653\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8172.00 | −0.551890 | ||||||||
\(604\) | 3760.00 | − | 6512.51i | 0.253298 | − | 0.438726i | ||||
\(605\) | 1076.00 | + | 1863.69i | 0.0723068 | + | 0.125239i | ||||
\(606\) | 1392.00 | + | 2411.01i | 0.0933105 | + | 0.161618i | ||||
\(607\) | 10752.0 | − | 18623.0i | 0.718962 | − | 1.24528i | −0.242449 | − | 0.970164i | \(-0.577951\pi\) |
0.961411 | − | 0.275115i | \(-0.0887160\pi\) | |||||||
\(608\) | 4736.00 | 0.315905 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −11072.0 | −0.734905 | ||||||||
\(611\) | −976.000 | + | 1690.48i | −0.0646231 | + | 0.111931i | ||||
\(612\) | −1512.00 | − | 2618.86i | −0.0998676 | − | 0.172976i | ||||
\(613\) | 5135.00 | + | 8894.08i | 0.338337 | + | 0.586017i | 0.984120 | − | 0.177504i | \(-0.0568022\pi\) |
−0.645783 | + | 0.763521i | \(0.723469\pi\) | |||||||
\(614\) | 3004.00 | − | 5203.08i | 0.197446 | − | 0.341986i | ||||
\(615\) | −10080.0 | −0.660918 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28358.0 | 1.85032 | 0.925162 | − | 0.379572i | \(-0.123929\pi\) | ||||
0.925162 | + | 0.379572i | \(0.123929\pi\) | |||||||
\(618\) | −1896.00 | + | 3283.97i | −0.123411 | + | 0.213755i | ||||
\(619\) | 8146.00 | + | 14109.3i | 0.528942 | + | 0.916155i | 0.999430 | + | 0.0337488i | \(0.0107446\pi\) |
−0.470488 | + | 0.882406i | \(0.655922\pi\) | |||||||
\(620\) | 2176.00 | + | 3768.94i | 0.140952 | + | 0.244136i | ||||
\(621\) | 1134.00 | − | 1964.15i | 0.0732783 | − | 0.126922i | ||||
\(622\) | 1376.00 | 0.0887019 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 192.000 | 0.0123176 | ||||||||
\(625\) | 2139.50 | − | 3705.72i | 0.136928 | − | 0.237166i | ||||
\(626\) | −5592.00 | − | 9685.63i | −0.357031 | − | 0.618395i | ||||
\(627\) | −8880.00 | − | 15380.6i | −0.565603 | − | 0.979653i | ||||
\(628\) | 1208.00 | − | 2092.32i | 0.0767587 | − | 0.132950i | ||||
\(629\) | −18648.0 | −1.18211 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11256.0 | 0.710134 | 0.355067 | − | 0.934841i | \(-0.384458\pi\) | ||||
0.355067 | + | 0.934841i | \(0.384458\pi\) | |||||||
\(632\) | 4864.00 | − | 8424.70i | 0.306138 | − | 0.530247i | ||||
\(633\) | −1806.00 | − | 3128.08i | −0.113400 | − | 0.196414i | ||||
\(634\) | −2922.00 | − | 5061.05i | −0.183040 | − | 0.317035i | ||||
\(635\) | −736.000 | + | 1274.79i | −0.0459957 | + | 0.0796669i | ||||
\(636\) | −5736.00 | −0.357621 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4640.00 | −0.287930 | ||||||||
\(639\) | 2358.00 | − | 4084.18i | 0.145980 | − | 0.252844i | ||||
\(640\) | −512.000 | − | 886.810i | −0.0316228 | − | 0.0547723i | ||||
\(641\) | −7759.00 | − | 13439.0i | −0.478100 | − | 0.828093i | 0.521585 | − | 0.853199i | \(-0.325341\pi\) |
−0.999685 | + | 0.0251060i | \(0.992008\pi\) | |||||||
\(642\) | 480.000 | − | 831.384i | 0.0295079 | − | 0.0511092i | ||||
\(643\) | 10452.0 | 0.641037 | 0.320518 | − | 0.947242i | \(-0.396143\pi\) | ||||
0.320518 | + | 0.947242i | \(0.396143\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3936.00 | −0.240279 | ||||||||
\(646\) | −12432.0 | + | 21532.9i | −0.757168 | + | 1.31145i | ||||
\(647\) | 36.0000 | + | 62.3538i | 0.00218749 | + | 0.00378884i | 0.867117 | − | 0.498104i | \(-0.165970\pi\) |
−0.864930 | + | 0.501893i | \(0.832637\pi\) | |||||||
\(648\) | 324.000 | + | 561.184i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | 10960.0 | − | 18983.3i | 0.662893 | − | 1.14816i | ||||
\(650\) | −488.000 | −0.0294476 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4464.00 | 0.268135 | ||||||||
\(653\) | −5981.00 | + | 10359.4i | −0.358430 | + | 0.620819i | −0.987699 | − | 0.156369i | \(-0.950021\pi\) |
0.629269 | + | 0.777188i | \(0.283354\pi\) | |||||||
\(654\) | 6594.00 | + | 11421.1i | 0.394260 | + | 0.682878i | ||||
\(655\) | 5808.00 | + | 10059.8i | 0.346469 | + | 0.600102i | ||||
\(656\) | 3360.00 | − | 5819.69i | 0.199979 | − | 0.346373i | ||||
\(657\) | −3960.00 | −0.235151 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6016.00 | −0.355615 | −0.177807 | − | 0.984065i | \(-0.556900\pi\) | ||||
−0.177807 | + | 0.984065i | \(0.556900\pi\) | |||||||
\(660\) | −1920.00 | + | 3325.54i | −0.113236 | + | 0.196131i | ||||
\(661\) | 13034.0 | + | 22575.6i | 0.766965 | + | 1.32842i | 0.939201 | + | 0.343367i | \(0.111567\pi\) |
−0.172236 | + | 0.985056i | \(0.555099\pi\) | |||||||
\(662\) | −7492.00 | − | 12976.5i | −0.439856 | − | 0.761853i | ||||
\(663\) | −504.000 | + | 872.954i | −0.0295230 | + | 0.0511353i | ||||
\(664\) | −5472.00 | −0.319811 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3996.00 | 0.232495 | ||||||||
\(667\) | −2436.00 | + | 4219.28i | −0.141413 | + | 0.244934i | ||||
\(668\) | −3568.00 | − | 6179.96i | −0.206662 | − | 0.357949i | ||||
\(669\) | −3000.00 | − | 5196.15i | −0.173373 | − | 0.300291i | ||||
\(670\) | 7264.00 | − | 12581.6i | 0.418855 | − | 0.725478i | ||||
\(671\) | −27680.0 | −1.59251 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20530.0 | −1.17589 | −0.587945 | − | 0.808901i | \(-0.700063\pi\) | ||||
−0.587945 | + | 0.808901i | \(0.700063\pi\) | |||||||
\(674\) | 10766.0 | − | 18647.3i | 0.615268 | − | 1.06568i | ||||
\(675\) | −823.500 | − | 1426.34i | −0.0469578 | − | 0.0813333i | ||||
\(676\) | 4362.00 | + | 7555.21i | 0.248179 | + | 0.429859i | ||||
\(677\) | −5028.00 | + | 8708.75i | −0.285438 | + | 0.494394i | −0.972715 | − | 0.232002i | \(-0.925473\pi\) |
0.687277 | + | 0.726395i | \(0.258806\pi\) | |||||||
\(678\) | 4620.00 | 0.261696 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 5376.00 | 0.303177 | ||||||||
\(681\) | −582.000 | + | 1008.05i | −0.0327493 | + | 0.0567235i | ||||
\(682\) | 5440.00 | + | 9422.36i | 0.305437 | + | 0.529033i | ||||
\(683\) | −3076.00 | − | 5327.79i | −0.172328 | − | 0.298480i | 0.766905 | − | 0.641760i | \(-0.221795\pi\) |
−0.939233 | + | 0.343280i | \(0.888462\pi\) | |||||||
\(684\) | 2664.00 | − | 4614.18i | 0.148919 | − | 0.257935i | ||||
\(685\) | −5168.00 | −0.288262 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12540.0 | 0.696406 | ||||||||
\(688\) | 1312.00 | − | 2272.45i | 0.0727028 | − | 0.125925i | ||||
\(689\) | 956.000 | + | 1655.84i | 0.0528602 | + | 0.0915566i | ||||
\(690\) | 2016.00 | + | 3491.81i | 0.111229 | + | 0.192654i | ||||
\(691\) | −7358.00 | + | 12744.4i | −0.405082 | + | 0.701622i | −0.994331 | − | 0.106329i | \(-0.966090\pi\) |
0.589249 | + | 0.807951i | \(0.299424\pi\) | |||||||
\(692\) | 1376.00 | 0.0755891 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7968.00 | 0.435823 | ||||||||
\(695\) | 12048.0 | − | 20867.7i | 0.657564 | − | 1.13893i | ||||
\(696\) | −696.000 | − | 1205.51i | −0.0379049 | − | 0.0656532i | ||||
\(697\) | 17640.0 | + | 30553.4i | 0.958626 | + | 1.66039i | ||||
\(698\) | 180.000 | − | 311.769i | 0.00976089 | − | 0.0169064i | ||||
\(699\) | 3966.00 | 0.214604 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28202.0 | 1.51951 | 0.759754 | − | 0.650211i | \(-0.225319\pi\) | ||||
0.759754 | + | 0.650211i | \(0.225319\pi\) | |||||||
\(702\) | 108.000 | − | 187.061i | 0.00580655 | − | 0.0100572i | ||||
\(703\) | −16428.0 | − | 28454.1i | −0.881357 | − | 1.52655i | ||||
\(704\) | −1280.00 | − | 2217.03i | −0.0685253 | − | 0.118689i | ||||
\(705\) | 5856.00 | − | 10142.9i | 0.312836 | − | 0.541849i | ||||
\(706\) | −20856.0 | −1.11179 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 6576.00 | 0.349070 | ||||||||
\(709\) | −11057.0 | + | 19151.3i | −0.585690 | + | 1.01445i | 0.409099 | + | 0.912490i | \(0.365843\pi\) |
−0.994789 | + | 0.101955i | \(0.967490\pi\) | |||||||
\(710\) | 4192.00 | + | 7260.76i | 0.221582 | + | 0.383791i | ||||
\(711\) | −5472.00 | − | 9477.78i | −0.288630 | − | 0.499922i | ||||
\(712\) | −2416.00 | + | 4184.63i | −0.127168 | + | 0.220261i | ||||
\(713\) | 11424.0 | 0.600045 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1280.00 | 0.0669501 | ||||||||
\(716\) | −2784.00 | + | 4822.03i | −0.145311 | + | 0.251687i | ||||
\(717\) | 3618.00 | + | 6266.56i | 0.188447 | + | 0.326400i | ||||
\(718\) | 8684.00 | + | 15041.1i | 0.451370 | + | 0.781797i | ||||
\(719\) | −4644.00 | + | 8043.64i | −0.240879 | + | 0.417215i | −0.960965 | − | 0.276670i | \(-0.910769\pi\) |
0.720086 | + | 0.693885i | \(0.244102\pi\) | |||||||
\(720\) | −1152.00 | −0.0596285 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −30090.0 | −1.55102 | ||||||||
\(723\) | 6504.00 | − | 11265.3i | 0.334559 | − | 0.579474i | ||||
\(724\) | 8104.00 | + | 14036.5i | 0.415998 | + | 0.720530i | ||||
\(725\) | 1769.00 | + | 3064.00i | 0.0906193 | + | 0.156957i | ||||
\(726\) | −807.000 | + | 1397.77i | −0.0412542 | + | 0.0714544i | ||||
\(727\) | −23848.0 | −1.21661 | −0.608304 | − | 0.793704i | \(-0.708150\pi\) | ||||
−0.608304 | + | 0.793704i | \(0.708150\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 3520.00 | − | 6096.82i | 0.178467 | − | 0.309114i | ||||
\(731\) | 6888.00 | + | 11930.4i | 0.348511 | + | 0.603640i | ||||
\(732\) | −4152.00 | − | 7191.47i | −0.209648 | − | 0.363121i | ||||
\(733\) | −17378.0 | + | 30099.6i | −0.875677 | + | 1.51672i | −0.0196367 | + | 0.999807i | \(0.506251\pi\) |
−0.856040 | + | 0.516909i | \(0.827082\pi\) | |||||||
\(734\) | 11296.0 | 0.568042 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2688.00 | −0.134621 | ||||||||
\(737\) | 18160.0 | − | 31454.0i | 0.907642 | − | 1.57208i | ||||
\(738\) | −3780.00 | − | 6547.15i | −0.188542 | − | 0.326564i | ||||
\(739\) | −13022.0 | − | 22554.8i | −0.648203 | − | 1.12272i | −0.983552 | − | 0.180626i | \(-0.942187\pi\) |
0.335349 | − | 0.942094i | \(-0.391146\pi\) | |||||||
\(740\) | −3552.00 | + | 6152.24i | −0.176452 | + | 0.305623i | ||||
\(741\) | −1776.00 | −0.0880472 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36204.0 | 1.78761 | 0.893806 | − | 0.448454i | \(-0.148025\pi\) | ||||
0.893806 | + | 0.448454i | \(0.148025\pi\) | |||||||
\(744\) | −1632.00 | + | 2826.71i | −0.0804194 | + | 0.139290i | ||||
\(745\) | −12680.0 | − | 21962.4i | −0.623569 | − | 1.08005i | ||||
\(746\) | −2546.00 | − | 4409.80i | −0.124954 | − | 0.216427i | ||||
\(747\) | −3078.00 | + | 5331.25i | −0.150761 | + | 0.261125i | ||||
\(748\) | 13440.0 | 0.656972 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 8928.00 | 0.434673 | ||||||||
\(751\) | 5712.00 | − | 9893.47i | 0.277542 | − | 0.480716i | −0.693232 | − | 0.720715i | \(-0.743814\pi\) |
0.970773 | + | 0.239999i | \(0.0771470\pi\) | |||||||
\(752\) | 3904.00 | + | 6761.93i | 0.189314 | + | 0.327902i | ||||
\(753\) | −1146.00 | − | 1984.93i | −0.0554616 | − | 0.0960623i | ||||
\(754\) | −232.000 | + | 401.836i | −0.0112055 | + | 0.0194085i | ||||
\(755\) | 15040.0 | 0.724982 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16622.0 | −0.798067 | −0.399034 | − | 0.916936i | \(-0.630654\pi\) | ||||
−0.399034 | + | 0.916936i | \(0.630654\pi\) | |||||||
\(758\) | 8268.00 | − | 14320.6i | 0.396184 | − | 0.686210i | ||||
\(759\) | 5040.00 | + | 8729.54i | 0.241028 | + | 0.417473i | ||||
\(760\) | 4736.00 | + | 8202.99i | 0.226043 | + | 0.391518i | ||||
\(761\) | −19262.0 | + | 33362.8i | −0.917539 | + | 1.58922i | −0.114397 | + | 0.993435i | \(0.536494\pi\) |
−0.803141 | + | 0.595789i | \(0.796840\pi\) | |||||||
\(762\) | −1104.00 | −0.0524852 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −12432.0 | −0.588709 | ||||||||
\(765\) | 3024.00 | − | 5237.72i | 0.142919 | − | 0.247543i | ||||
\(766\) | 10872.0 | + | 18830.9i | 0.512822 | + | 0.888233i | ||||
\(767\) | −1096.00 | − | 1898.33i | −0.0515962 | − | 0.0893672i | ||||
\(768\) | 384.000 | − | 665.108i | 0.0180422 | − | 0.0312500i | ||||
\(769\) | 18440.0 | 0.864712 | 0.432356 | − | 0.901703i | \(-0.357682\pi\) | ||||
0.432356 | + | 0.901703i | \(0.357682\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12900.0 | 0.602571 | ||||||||
\(772\) | −100.000 | + | 173.205i | −0.00466202 | + | 0.00807485i | ||||
\(773\) | −6984.00 | − | 12096.6i | −0.324964 | − | 0.562854i | 0.656541 | − | 0.754290i | \(-0.272019\pi\) |
−0.981505 | + | 0.191436i | \(0.938685\pi\) | |||||||
\(774\) | −1476.00 | − | 2556.51i | −0.0685449 | − | 0.118723i | ||||
\(775\) | 4148.00 | − | 7184.55i | 0.192259 | − | 0.333002i | ||||
\(776\) | −6656.00 | −0.307908 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −20868.0 | −0.961638 | ||||||||
\(779\) | −31080.0 | + | 53832.1i | −1.42947 | + | 2.47591i | ||||
\(780\) | 192.000 | + | 332.554i | 0.00881372 | + | 0.0152658i | ||||
\(781\) | 10480.0 | + | 18151.9i | 0.480159 | + | 0.831659i | ||||
\(782\) | 7056.00 | − | 12221.4i | 0.322662 | − | 0.558868i | ||||
\(783\) | −1566.00 | −0.0714742 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4832.00 | 0.219696 | ||||||||
\(786\) | −4356.00 | + | 7544.81i | −0.197676 | + | 0.342385i | ||||
\(787\) | 5458.00 | + | 9453.53i | 0.247213 | + | 0.428186i | 0.962752 | − | 0.270388i | \(-0.0871519\pi\) |
−0.715538 | + | 0.698573i | \(0.753819\pi\) | |||||||
\(788\) | 324.000 | + | 561.184i | 0.0146472 | + | 0.0253698i | ||||
\(789\) | −5790.00 | + | 10028.6i | −0.261254 | + | 0.452505i | ||||
\(790\) | 19456.0 | 0.876220 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2880.00 | −0.129213 | ||||||||
\(793\) | −1384.00 | + | 2397.16i | −0.0619764 | + | 0.107346i | ||||
\(794\) | 3044.00 | + | 5272.36i | 0.136055 | + | 0.235654i | ||||
\(795\) | −5736.00 | − | 9935.04i | −0.255893 | − | 0.443220i | ||||
\(796\) | 3088.00 | − | 5348.57i | 0.137502 | − | 0.238160i | ||||
\(797\) | −12360.0 | −0.549327 | −0.274664 | − | 0.961540i | \(-0.588566\pi\) | ||||
−0.274664 | + | 0.961540i | \(0.588566\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −40992.0 | −1.81501 | ||||||||
\(800\) | −976.000 | + | 1690.48i | −0.0431335 | + | 0.0747094i | ||||
\(801\) | 2718.00 | + | 4707.71i | 0.119895 | + | 0.207664i | ||||
\(802\) | 8910.00 | + | 15432.6i | 0.392298 | + | 0.679480i | ||||
\(803\) | 8800.00 | − | 15242.0i | 0.386731 | − | 0.669838i | ||||
\(804\) | 10896.0 | 0.477951 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1088.00 | 0.0475474 | ||||||||
\(807\) | 4200.00 | − | 7274.61i | 0.183206 | − | 0.317322i | ||||
\(808\) | −1856.00 | − | 3214.69i | −0.0808092 | − | 0.139966i | ||||
\(809\) | −1701.00 | − | 2946.22i | −0.0739233 | − | 0.128039i | 0.826694 | − | 0.562651i | \(-0.190219\pi\) |
−0.900618 | + | 0.434612i | \(0.856885\pi\) | |||||||
\(810\) | −648.000 | + | 1122.37i | −0.0281091 | + | 0.0486864i | ||||
\(811\) | −292.000 | −0.0126430 | −0.00632152 | − | 0.999980i | \(-0.502012\pi\) | ||||
−0.00632152 | + | 0.999980i | \(0.502012\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14640.0 | −0.631546 | ||||||||
\(814\) | −8880.00 | + | 15380.6i | −0.382363 | + | 0.662273i | ||||
\(815\) | 4464.00 | + | 7731.87i | 0.191861 | + | 0.332314i | ||||
\(816\) | 2016.00 | + | 3491.81i | 0.0864879 | + | 0.149801i | ||||
\(817\) | −12136.0 | + | 21020.2i | −0.519688 | + | 0.900126i | ||||
\(818\) | 11232.0 | 0.480095 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13440.0 | 0.572372 | ||||||||
\(821\) | −3455.00 | + | 5984.24i | −0.146870 | + | 0.254386i | −0.930069 | − | 0.367385i | \(-0.880253\pi\) |
0.783199 | + | 0.621771i | \(0.213587\pi\) | |||||||
\(822\) | −1938.00 | − | 3356.71i | −0.0822330 | − | 0.142432i | ||||
\(823\) | −284.000 | − | 491.902i | −0.0120287 | − | 0.0208343i | 0.859948 | − | 0.510381i | \(-0.170496\pi\) |
−0.871977 | + | 0.489547i | \(0.837162\pi\) | |||||||
\(824\) | 2528.00 | − | 4378.62i | 0.106877 | − | 0.185117i | ||||
\(825\) | 7320.00 | 0.308909 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12144.0 | −0.510627 | −0.255313 | − | 0.966858i | \(-0.582179\pi\) | ||||
−0.255313 | + | 0.966858i | \(0.582179\pi\) | |||||||
\(828\) | −1512.00 | + | 2618.86i | −0.0634609 | + | 0.109918i | ||||
\(829\) | 7414.00 | + | 12841.4i | 0.310614 | + | 0.537999i | 0.978495 | − | 0.206269i | \(-0.0661321\pi\) |
−0.667882 | + | 0.744268i | \(0.732799\pi\) | |||||||
\(830\) | −5472.00 | − | 9477.78i | −0.228838 | − | 0.396360i | ||||
\(831\) | −10011.0 | + | 17339.6i | −0.417903 | + | 0.723830i | ||||
\(832\) | −256.000 | −0.0106673 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 18072.0 | 0.750338 | ||||||||
\(835\) | 7136.00 | − | 12359.9i | 0.295750 | − | 0.512254i | ||||
\(836\) | 11840.0 | + | 20507.5i | 0.489827 | + | 0.848404i | ||||
\(837\) | 1836.00 | + | 3180.05i | 0.0758201 | + | 0.131324i | ||||
\(838\) | 8932.00 | − | 15470.7i | 0.368199 | − | 0.637739i | ||||
\(839\) | 22824.0 | 0.939180 | 0.469590 | − | 0.882885i | \(-0.344402\pi\) | ||||
0.469590 | + | 0.882885i | \(0.344402\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21025.0 | −0.862069 | ||||||||
\(842\) | −5538.00 | + | 9592.10i | −0.226665 | + | 0.392596i | ||||
\(843\) | −14103.0 | − | 24427.1i | −0.576196 | − | 0.998001i | ||||
\(844\) | 2408.00 | + | 4170.78i | 0.0982071 | + | 0.170100i | ||||
\(845\) | −8724.00 | + | 15110.4i | −0.355165 | + | 0.615164i | ||||
\(846\) | 8784.00 | 0.356974 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 7648.00 | 0.309709 | ||||||||
\(849\) | 13650.0 | − | 23642.5i | 0.551787 | − | 0.955722i | ||||
\(850\) | −5124.00 | − | 8875.03i | −0.206767 | − | 0.358131i | ||||
\(851\) | 9324.00 | + | 16149.6i | 0.375585 | + | 0.650532i | ||||
\(852\) | −3144.00 | + | 5445.57i | −0.126422 | + | 0.218970i | ||||
\(853\) | 41780.0 | 1.67705 | 0.838523 | − | 0.544866i | \(-0.183420\pi\) | ||||
0.838523 | + | 0.544866i | \(0.183420\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10656.0 | 0.426231 | ||||||||
\(856\) | −640.000 | + | 1108.51i | −0.0255546 | + | 0.0442619i | ||||
\(857\) | −10710.0 | − | 18550.3i | −0.426892 | − | 0.739399i | 0.569703 | − | 0.821851i | \(-0.307058\pi\) |
−0.996595 | + | 0.0824518i | \(0.973725\pi\) | |||||||
\(858\) | 480.000 | + | 831.384i | 0.0190990 | + | 0.0330804i | ||||
\(859\) | −9066.00 | + | 15702.8i | −0.360102 | + | 0.623716i | −0.987977 | − | 0.154599i | \(-0.950592\pi\) |
0.627875 | + | 0.778314i | \(0.283925\pi\) | |||||||
\(860\) | 5248.00 | 0.208088 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13400.0 | 0.529473 | ||||||||
\(863\) | −12018.0 | + | 20815.8i | −0.474041 | + | 0.821063i | −0.999558 | − | 0.0297197i | \(-0.990539\pi\) |
0.525517 | + | 0.850783i | \(0.323872\pi\) | |||||||
\(864\) | −432.000 | − | 748.246i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | 1376.00 | + | 2383.30i | 0.0540872 | + | 0.0936817i | ||||
\(866\) | 5048.00 | − | 8743.39i | 0.198081 | − | 0.343086i | ||||
\(867\) | −6429.00 | −0.251834 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 48640.0 | 1.89873 | ||||||||
\(870\) | 1392.00 | − | 2411.01i | 0.0542451 | − | 0.0939552i | ||||
\(871\) | −1816.00 | − | 3145.40i | −0.0706462 | − | 0.122363i | ||||
\(872\) | −8792.00 | − | 15228.2i | −0.341439 | − | 0.591389i | ||||
\(873\) | −3744.00 | + | 6484.80i | −0.145149 | + | 0.251406i | ||||
\(874\) | 24864.0 | 0.962285 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5280.00 | 0.203647 | ||||||||
\(877\) | 2187.00 | − | 3788.00i | 0.0842072 | − | 0.145851i | −0.820846 | − | 0.571150i | \(-0.806498\pi\) |
0.905053 | + | 0.425299i | \(0.139831\pi\) | |||||||
\(878\) | 1344.00 | + | 2327.88i | 0.0516604 | + | 0.0894784i | ||||
\(879\) | −8928.00 | − | 15463.7i | −0.342587 | − | 0.593378i | ||||
\(880\) | 2560.00 | − | 4434.05i | 0.0980654 | − | 0.169854i | ||||
\(881\) | 46348.0 | 1.77242 | 0.886211 | − | 0.463282i | \(-0.153328\pi\) | ||||
0.886211 | + | 0.463282i | \(0.153328\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20660.0 | −0.787389 | −0.393694 | − | 0.919241i | \(-0.628803\pi\) | ||||
−0.393694 | + | 0.919241i | \(0.628803\pi\) | |||||||
\(884\) | 672.000 | − | 1163.94i | 0.0255677 | − | 0.0442845i | ||||
\(885\) | 6576.00 | + | 11390.0i | 0.249774 | + | 0.432621i | ||||
\(886\) | −4392.00 | − | 7607.17i | −0.166537 | − | 0.288451i | ||||
\(887\) | −900.000 | + | 1558.85i | −0.0340688 | + | 0.0590089i | −0.882557 | − | 0.470205i | \(-0.844180\pi\) |
0.848488 | + | 0.529214i | \(0.177513\pi\) | |||||||
\(888\) | −5328.00 | −0.201347 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −9664.00 | −0.363975 | ||||||||
\(891\) | −1620.00 | + | 2805.92i | −0.0609114 | + | 0.105502i | ||||
\(892\) | 4000.00 | + | 6928.20i | 0.150146 | + | 0.260060i | ||||
\(893\) | −36112.0 | − | 62547.8i | −1.35324 | − | 2.34388i | ||||
\(894\) | 9510.00 | − | 16471.8i | 0.355774 | − | 0.616219i | ||||
\(895\) | −11136.0 | −0.415906 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1008.00 | 0.0375208 | ||||||||
\(898\) | 3666.00 | − | 6349.70i | 0.136232 | − | 0.235960i | ||||
\(899\) | −3944.00 | − | 6831.21i | −0.146318 | − | 0.253430i | ||||
\(900\) | 1098.00 | + | 1901.79i | 0.0406667 | + | 0.0704367i | ||||
\(901\) | −20076.0 | + | 34772.7i | −0.742318 | + | 1.28573i | ||||
\(902\) | 33600.0 | 1.24031 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6160.00 | −0.226636 | ||||||||
\(905\) | −16208.0 | + | 28073.1i | −0.595328 | + | 1.03114i | ||||
\(906\) | 5640.00 | + | 9768.77i | 0.206817 | + | 0.358218i | ||||
\(907\) | 20998.0 | + | 36369.6i | 0.768718 | + | 1.33146i | 0.938258 | + | 0.345935i | \(0.112438\pi\) |
−0.169540 | + | 0.985523i | \(0.554228\pi\) | |||||||
\(908\) | 776.000 | − | 1344.07i | 0.0283617 | − | 0.0491240i | ||||
\(909\) | −4176.00 | −0.152375 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41308.0 | −1.50230 | −0.751150 | − | 0.660132i | \(-0.770500\pi\) | ||||
−0.751150 | + | 0.660132i | \(0.770500\pi\) | |||||||
\(912\) | −3552.00 | + | 6152.24i | −0.128968 | + | 0.223378i | ||||
\(913\) | −13680.0 | − | 23694.5i | −0.495884 | − | 0.858896i | ||||
\(914\) | 26.0000 | + | 45.0333i | 0.000940923 | + | 0.00162973i | ||||
\(915\) | 8304.00 | − | 14382.9i | 0.300024 | − | 0.519656i | ||||
\(916\) | −16720.0 | −0.603105 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 4536.00 | 0.163083 | ||||||||
\(919\) | −1968.00 | + | 3408.68i | −0.0706402 | + | 0.122352i | −0.899182 | − | 0.437575i | \(-0.855838\pi\) |
0.828542 | + | 0.559927i | \(0.189171\pi\) | |||||||
\(920\) | −2688.00 | − | 4655.75i | −0.0963269 | − | 0.166843i | ||||
\(921\) | 4506.00 | + | 7804.62i | 0.161214 | + | 0.279230i | ||||
\(922\) | −7656.00 | + | 13260.6i | −0.273467 | + | 0.473659i | ||||
\(923\) | 2096.00 | 0.0747461 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13542.0 | 0.481360 | ||||||||
\(926\) | 12608.0 | − | 21837.7i | 0.447435 | − | 0.774980i | ||||
\(927\) | −2844.00 | − | 4925.95i | −0.100765 | − | 0.174530i | ||||
\(928\) | 928.000 | + | 1607.34i | 0.0328266 | + | 0.0568574i | ||||
\(929\) | −3606.00 | + | 6245.78i | −0.127351 | + | 0.220578i | −0.922649 | − | 0.385640i | \(-0.873981\pi\) |
0.795299 | + | 0.606218i | \(0.207314\pi\) | |||||||
\(930\) | −6528.00 | −0.230174 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −5288.00 | −0.185852 | ||||||||
\(933\) | −1032.00 | + | 1787.48i | −0.0362124 | + | 0.0627217i | ||||
\(934\) | 3068.00 | + | 5313.93i | 0.107482 | + | 0.186164i | ||||
\(935\) | 13440.0 | + | 23278.8i | 0.470091 | + | 0.814221i | ||||
\(936\) | −144.000 | + | 249.415i | −0.00502862 | + | 0.00870982i | ||||
\(937\) | 38976.0 | 1.35890 | 0.679451 | − | 0.733721i | \(-0.262218\pi\) | ||||
0.679451 | + | 0.733721i | \(0.262218\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16776.0 | 0.583029 | ||||||||
\(940\) | −7808.00 | + | 13523.9i | −0.270924 | + | 0.469255i | ||||
\(941\) | 26772.0 | + | 46370.5i | 0.927463 | + | 1.60641i | 0.787552 | + | 0.616248i | \(0.211348\pi\) |
0.139910 | + | 0.990164i | \(0.455319\pi\) | |||||||
\(942\) | 1812.00 | + | 3138.48i | 0.0626732 | + | 0.108553i | ||||
\(943\) | 17640.0 | − | 30553.4i | 0.609160 | − | 1.05510i | ||||
\(944\) | −8768.00 | −0.302303 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13120.0 | 0.450918 | ||||||||
\(947\) | 10696.0 | − | 18526.0i | 0.367026 | − | 0.635707i | −0.622073 | − | 0.782959i | \(-0.713709\pi\) |
0.989099 | + | 0.147252i | \(0.0470428\pi\) | |||||||
\(948\) | 7296.00 | + | 12637.0i | 0.249961 | + | 0.432945i | ||||
\(949\) | −880.000 | − | 1524.20i | −0.0301012 | − | 0.0521368i | ||||
\(950\) | 9028.00 | − | 15637.0i | 0.308323 | − | 0.534031i | ||||
\(951\) | 8766.00 | 0.298903 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21162.0 | 0.719312 | 0.359656 | − | 0.933085i | \(-0.382894\pi\) | ||||
0.359656 | + | 0.933085i | \(0.382894\pi\) | |||||||
\(954\) | 4302.00 | − | 7451.28i | 0.145998 | − | 0.252876i | ||||
\(955\) | −12432.0 | − | 21532.9i | −0.421246 | − | 0.729620i | ||||
\(956\) | −4824.00 | − | 8355.41i | −0.163200 | − | 0.282671i | ||||
\(957\) | 3480.00 | − | 6027.54i | 0.117547 | − | 0.203597i | ||||
\(958\) | 12912.0 | 0.435457 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1536.00 | 0.0516398 | ||||||||
\(961\) | 5647.50 | − | 9781.76i | 0.189571 | − | 0.328346i | ||||
\(962\) | 888.000 | + | 1538.06i | 0.0297612 | + | 0.0515479i | ||||
\(963\) | 720.000 | + | 1247.08i | 0.0240931 | + | 0.0417305i | ||||
\(964\) | −8672.00 | + | 15020.3i | −0.289737 | + | 0.501839i | ||||
\(965\) | −400.000 | −0.0133435 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8224.00 | 0.273491 | 0.136746 | − | 0.990606i | \(-0.456336\pi\) | ||||
0.136746 | + | 0.990606i | \(0.456336\pi\) | |||||||
\(968\) | 1076.00 | − | 1863.69i | 0.0357272 | − | 0.0618814i | ||||
\(969\) | −18648.0 | − | 32299.3i | −0.618225 | − | 1.07080i | ||||
\(970\) | −6656.00 | − | 11528.5i | −0.220321 | − | 0.381607i | ||||
\(971\) | −4070.00 | + | 7049.45i | −0.134513 | + | 0.232984i | −0.925411 | − | 0.378964i | \(-0.876280\pi\) |
0.790898 | + | 0.611948i | \(0.209614\pi\) | |||||||
\(972\) | −972.000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −23792.0 | −0.782695 | ||||||||
\(975\) | 366.000 | − | 633.931i | 0.0120219 | − | 0.0208226i | ||||
\(976\) | 5536.00 | + | 9588.63i | 0.181560 | + | 0.314472i | ||||
\(977\) | −16079.0 | − | 27849.6i | −0.526523 | − | 0.911964i | −0.999522 | − | 0.0309016i | \(-0.990162\pi\) |
0.473000 | − | 0.881063i | \(-0.343171\pi\) | |||||||
\(978\) | −3348.00 | + | 5798.91i | −0.109465 | + | 0.189600i | ||||
\(979\) | −24160.0 | −0.788720 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −19782.0 | −0.643823 | ||||||||
\(982\) | −264.000 | + | 457.261i | −0.00857900 | + | 0.0148593i | ||||
\(983\) | −20708.0 | − | 35867.3i | −0.671905 | − | 1.16377i | −0.977363 | − | 0.211568i | \(-0.932143\pi\) |
0.305458 | − | 0.952205i | \(-0.401190\pi\) | |||||||
\(984\) | 5040.00 | + | 8729.54i | 0.163282 | + | 0.282812i | ||||
\(985\) | −648.000 | + | 1122.37i | −0.0209614 | + | 0.0363062i | ||||
\(986\) | −9744.00 | −0.314718 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2368.00 | 0.0762511 | ||||||||
\(989\) | 6888.00 | − | 11930.4i | 0.221462 | − | 0.383583i | ||||
\(990\) | −2880.00 | − | 4988.31i | −0.0924570 | − | 0.160140i | ||||
\(991\) | −6148.00 | − | 10648.6i | −0.197071 | − | 0.341338i | 0.750506 | − | 0.660863i | \(-0.229810\pi\) |
−0.947578 | + | 0.319526i | \(0.896476\pi\) | |||||||
\(992\) | 2176.00 | − | 3768.94i | 0.0696452 | − | 0.120629i | ||||
\(993\) | 22476.0 | 0.718282 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12352.0 | 0.393552 | ||||||||
\(996\) | 4104.00 | − | 7108.34i | 0.130562 | − | 0.226141i | ||||
\(997\) | 28826.0 | + | 49928.1i | 0.915676 | + | 1.58600i | 0.805909 | + | 0.592039i | \(0.201677\pi\) |
0.109766 | + | 0.993957i | \(0.464990\pi\) | |||||||
\(998\) | −2628.00 | − | 4551.83i | −0.0833546 | − | 0.144374i | ||||
\(999\) | −2997.00 | + | 5190.96i | −0.0949158 | + | 0.164399i |
(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 | 294.4.e.j.79.1 | 2 | ||
3.2 | odd | 2 | 882.4.g.c.667.1 | 2 | |||
7.2 | even | 3 | 294.4.a.b.1.1 | ✓ | 1 | ||
7.3 | odd | 6 | 294.4.e.f.67.1 | 2 | |||
7.4 | even | 3 | inner | 294.4.e.j.67.1 | 2 | ||
7.5 | odd | 6 | 294.4.a.f.1.1 | yes | 1 | ||
7.6 | odd | 2 | 294.4.e.f.79.1 | 2 | |||
21.2 | odd | 6 | 882.4.a.q.1.1 | 1 | |||
21.5 | even | 6 | 882.4.a.j.1.1 | 1 | |||
21.11 | odd | 6 | 882.4.g.c.361.1 | 2 | |||
21.17 | even | 6 | 882.4.g.j.361.1 | 2 | |||
21.20 | even | 2 | 882.4.g.j.667.1 | 2 | |||
28.19 | even | 6 | 2352.4.a.m.1.1 | 1 | |||
28.23 | odd | 6 | 2352.4.a.z.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
294.4.a.b.1.1 | ✓ | 1 | 7.2 | even | 3 | ||
294.4.a.f.1.1 | yes | 1 | 7.5 | odd | 6 | ||
294.4.e.f.67.1 | 2 | 7.3 | odd | 6 | |||
294.4.e.f.79.1 | 2 | 7.6 | odd | 2 | |||
294.4.e.j.67.1 | 2 | 7.4 | even | 3 | inner | ||
294.4.e.j.79.1 | 2 | 1.1 | even | 1 | trivial | ||
882.4.a.j.1.1 | 1 | 21.5 | even | 6 | |||
882.4.a.q.1.1 | 1 | 21.2 | odd | 6 | |||
882.4.g.c.361.1 | 2 | 21.11 | odd | 6 | |||
882.4.g.c.667.1 | 2 | 3.2 | odd | 2 | |||
882.4.g.j.361.1 | 2 | 21.17 | even | 6 | |||
882.4.g.j.667.1 | 2 | 21.20 | even | 2 | |||
2352.4.a.m.1.1 | 1 | 28.19 | even | 6 | |||
2352.4.a.z.1.1 | 1 | 28.23 | odd | 6 |