Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [288,3,Mod(19,288)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(288, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 7, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("288.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 288 = 2^{5} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 288.u (of order \(8\), degree \(4\), 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: | \(7.84743161358\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 163.2 | ||
Character | \(\chi\) | \(=\) | 288.163 |
Dual form | 288.3.u.a.235.2 |
$q$-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 \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{3}{8}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.20513 | − | 1.59614i | −0.602567 | − | 0.798069i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.09531 | + | 3.84712i | −0.273827 | + | 0.961779i | ||||
\(5\) | 0.642823 | + | 1.55191i | 0.128565 | + | 0.310382i | 0.975034 | − | 0.222055i | \(-0.0712763\pi\) |
−0.846470 | + | 0.532437i | \(0.821276\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.95044 | − | 4.95044i | −0.707206 | − | 0.707206i | 0.258741 | − | 0.965947i | \(-0.416692\pi\) |
−0.965947 | + | 0.258741i | \(0.916692\pi\) | |||||||
\(8\) | 7.46052 | − | 2.88803i | 0.932564 | − | 0.361004i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.70238 | − | 2.89629i | 0.170238 | − | 0.289629i | ||||
\(11\) | 4.27221 | + | 10.3140i | 0.388383 | + | 0.937640i | 0.990283 | + | 0.139068i | \(0.0444106\pi\) |
−0.601900 | + | 0.798572i | \(0.705589\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.68327 | − | 4.06379i | 0.129483 | − | 0.312599i | −0.845821 | − | 0.533467i | \(-0.820889\pi\) |
0.975304 | + | 0.220868i | \(0.0708890\pi\) | |||||||
\(14\) | −1.93564 | + | 13.8675i | −0.138260 | + | 0.990538i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −13.6006 | − | 8.42755i | −0.850038 | − | 0.526722i | ||||
\(17\) | − | 28.6469i | − | 1.68511i | −0.538609 | − | 0.842556i | \(-0.681050\pi\) | ||
0.538609 | − | 0.842556i | \(-0.318950\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 17.5460 | + | 7.26778i | 0.923473 | + | 0.382515i | 0.793199 | − | 0.608963i | \(-0.208414\pi\) |
0.130274 | + | 0.991478i | \(0.458414\pi\) | |||||||
\(20\) | −6.67447 | + | 0.773195i | −0.333724 | + | 0.0386597i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 11.3140 | − | 19.2488i | 0.514274 | − | 0.874947i | ||||
\(23\) | 24.3334 | − | 24.3334i | 1.05797 | − | 1.05797i | 0.0597590 | − | 0.998213i | \(-0.480967\pi\) |
0.998213 | − | 0.0597590i | \(-0.0190332\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 15.6825 | − | 15.6825i | 0.627298 | − | 0.627298i | ||||
\(26\) | −8.51493 | + | 2.21067i | −0.327497 | + | 0.0850256i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 24.4672 | − | 13.6227i | 0.873828 | − | 0.486524i | ||||
\(29\) | −8.57286 | − | 3.55100i | −0.295616 | − | 0.122448i | 0.229946 | − | 0.973203i | \(-0.426145\pi\) |
−0.525562 | + | 0.850755i | \(0.676145\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.73273i | 0.184927i | 0.995716 | + | 0.0924634i | \(0.0294741\pi\) | ||||
−0.995716 | + | 0.0924634i | \(0.970526\pi\) | |||||||
\(32\) | 2.93903 | + | 31.8647i | 0.0918446 | + | 0.995773i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −45.7244 | + | 34.5233i | −1.34483 | + | 1.01539i | ||||
\(35\) | 4.50039 | − | 10.8649i | 0.128583 | − | 0.310426i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −26.1364 | − | 63.0989i | −0.706390 | − | 1.70538i | −0.708831 | − | 0.705379i | \(-0.750777\pi\) |
0.00244114 | − | 0.999997i | \(-0.499223\pi\) | |||||||
\(38\) | −9.54487 | − | 36.7644i | −0.251181 | − | 0.967485i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 9.27775 | + | 9.72157i | 0.231944 | + | 0.243039i | ||||
\(41\) | 14.2561 | + | 14.2561i | 0.347711 | + | 0.347711i | 0.859256 | − | 0.511545i | \(-0.170927\pi\) |
−0.511545 | + | 0.859256i | \(0.670927\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.1365 | − | 24.4717i | −0.235733 | − | 0.569109i | 0.761100 | − | 0.648634i | \(-0.224660\pi\) |
−0.996833 | + | 0.0795253i | \(0.974660\pi\) | |||||||
\(44\) | −44.3587 | + | 5.13867i | −1.00815 | + | 0.116788i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −68.1643 | − | 9.51443i | −1.48183 | − | 0.206835i | ||||
\(47\) | −57.9804 | −1.23363 | −0.616813 | − | 0.787110i | \(-0.711576\pi\) | ||||
−0.616813 | + | 0.787110i | \(0.711576\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.0137567i | 0.000280749i | ||||||||
\(50\) | −43.9308 | − | 6.13190i | −0.878616 | − | 0.122638i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 13.7902 | + | 10.9268i | 0.265195 | + | 0.210132i | ||||
\(53\) | 46.3830 | − | 19.2124i | 0.875150 | − | 0.362499i | 0.100536 | − | 0.994933i | \(-0.467944\pi\) |
0.774614 | + | 0.632434i | \(0.217944\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −13.2602 | + | 13.2602i | −0.241094 | + | 0.241094i | ||||
\(56\) | −51.2299 | − | 22.6358i | −0.914819 | − | 0.404211i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.66357 | + | 17.9629i | 0.0804064 | + | 0.309705i | ||||
\(59\) | 27.6347 | − | 11.4467i | 0.468384 | − | 0.194011i | −0.135992 | − | 0.990710i | \(-0.543422\pi\) |
0.604377 | + | 0.796699i | \(0.293422\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 76.3985 | + | 31.6453i | 1.25243 | + | 0.518775i | 0.907579 | − | 0.419881i | \(-0.137928\pi\) |
0.344855 | + | 0.938656i | \(0.387928\pi\) | |||||||
\(62\) | 9.15022 | − | 6.90870i | 0.147584 | − | 0.111431i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 47.3186 | − | 43.0924i | 0.739353 | − | 0.673318i | ||||
\(65\) | 7.38868 | 0.113672 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −36.1949 | + | 87.3821i | −0.540222 | + | 1.30421i | 0.384345 | + | 0.923190i | \(0.374427\pi\) |
−0.924566 | + | 0.381021i | \(0.875573\pi\) | |||||||
\(68\) | 110.208 | + | 31.3771i | 1.62070 | + | 0.461429i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −22.7654 | + | 5.91042i | −0.325221 | + | 0.0844346i | ||||
\(71\) | 5.39666 | + | 5.39666i | 0.0760092 | + | 0.0760092i | 0.744089 | − | 0.668080i | \(-0.232884\pi\) |
−0.668080 | + | 0.744089i | \(0.732884\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −25.4031 | − | 25.4031i | −0.347988 | − | 0.347988i | 0.511372 | − | 0.859360i | \(-0.329137\pi\) |
−0.859360 | + | 0.511372i | \(0.829137\pi\) | |||||||
\(74\) | −69.2166 | + | 117.760i | −0.935360 | + | 1.59135i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −47.1782 | + | 59.5410i | −0.620766 | + | 0.783434i | ||||
\(77\) | 29.9097 | − | 72.2084i | 0.388438 | − | 0.937771i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 50.1674 | 0.635030 | 0.317515 | − | 0.948253i | \(-0.397152\pi\) | ||||
0.317515 | + | 0.948253i | \(0.397152\pi\) | |||||||
\(80\) | 4.33602 | − | 26.5244i | 0.0542003 | − | 0.331554i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.57420 | − | 39.9353i | 0.0679781 | − | 0.487016i | ||||
\(83\) | 100.805 | + | 41.7550i | 1.21452 | + | 0.503072i | 0.895665 | − | 0.444730i | \(-0.146700\pi\) |
0.318859 | + | 0.947802i | \(0.396700\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 44.4574 | − | 18.4149i | 0.523029 | − | 0.216646i | ||||
\(86\) | −26.8443 | + | 45.6709i | −0.312143 | + | 0.531057i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 61.6601 | + | 64.6097i | 0.700683 | + | 0.734202i | ||||
\(89\) | −10.6266 | + | 10.6266i | −0.119400 | + | 0.119400i | −0.764282 | − | 0.644882i | \(-0.776906\pi\) |
0.644882 | + | 0.764282i | \(0.276906\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −28.4505 | + | 11.7846i | −0.312643 | + | 0.129501i | ||||
\(92\) | 66.9607 | + | 120.266i | 0.727834 | + | 1.30724i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 69.8741 | + | 92.5446i | 0.743341 | + | 0.984517i | ||||
\(95\) | 31.9017i | 0.335807i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.3055 | −0.147479 | −0.0737395 | − | 0.997278i | \(-0.523493\pi\) | ||||
−0.0737395 | + | 0.997278i | \(0.523493\pi\) | |||||||
\(98\) | 0.0219576 | − | 0.0165786i | 0.000224057 | − | 0.000169170i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 43.1551 | + | 77.5094i | 0.431551 | + | 0.775094i | ||||
\(101\) | −51.6638 | − | 124.728i | −0.511523 | − | 1.23493i | −0.942997 | − | 0.332801i | \(-0.892006\pi\) |
0.431474 | − | 0.902125i | \(-0.357994\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.87593 | + | 4.87593i | 0.0473392 | + | 0.0473392i | 0.730380 | − | 0.683041i | \(-0.239343\pi\) |
−0.683041 | + | 0.730380i | \(0.739343\pi\) | |||||||
\(104\) | 0.821771 | − | 35.1793i | 0.00790164 | − | 0.338262i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −86.5634 | − | 50.8800i | −0.816635 | − | 0.480000i | ||||
\(107\) | 4.55603 | + | 10.9992i | 0.0425797 | + | 0.102797i | 0.943739 | − | 0.330692i | \(-0.107282\pi\) |
−0.901159 | + | 0.433489i | \(0.857282\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.0098 | − | 26.5800i | 0.101007 | − | 0.243853i | −0.865295 | − | 0.501263i | \(-0.832869\pi\) |
0.966302 | + | 0.257410i | \(0.0828690\pi\) | |||||||
\(110\) | 37.1454 | + | 5.18478i | 0.337685 | + | 0.0471344i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 25.6089 | + | 109.049i | 0.228651 | + | 0.973653i | ||||
\(113\) | 120.275i | 1.06438i | 0.846624 | + | 0.532191i | \(0.178631\pi\) | ||||
−0.846624 | + | 0.532191i | \(0.821369\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 53.4052 | + | 22.1212i | 0.464393 | + | 0.192358i | ||||
\(116\) | 23.0510 | − | 29.0914i | 0.198716 | − | 0.250788i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −51.5739 | − | 30.3140i | −0.437067 | − | 0.256898i | ||||
\(119\) | −141.815 | + | 141.815i | −1.19172 | + | 1.19172i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.56759 | + | 2.56759i | −0.0212197 | + | 0.0212197i | ||||
\(122\) | −41.5601 | − | 160.079i | −0.340657 | − | 1.31212i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −22.0545 | − | 6.27910i | −0.177859 | − | 0.0506379i | ||||
\(125\) | 73.2166 | + | 30.3273i | 0.585733 | + | 0.242619i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 128.040i | 1.00819i | 0.863648 | + | 0.504095i | \(0.168174\pi\) | ||||
−0.863648 | + | 0.504095i | \(0.831826\pi\) | |||||||
\(128\) | −125.807 | − | 23.5949i | −0.982863 | − | 0.184335i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −8.90435 | − | 11.7933i | −0.0684950 | − | 0.0907181i | ||||
\(131\) | −20.1358 | + | 48.6121i | −0.153708 | + | 0.371084i | −0.981911 | − | 0.189345i | \(-0.939364\pi\) |
0.828203 | + | 0.560429i | \(0.189364\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −50.8816 | − | 122.839i | −0.382569 | − | 0.923602i | ||||
\(134\) | 183.093 | − | 47.5351i | 1.36637 | − | 0.354740i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −82.7331 | − | 213.721i | −0.608331 | − | 1.57148i | ||||
\(137\) | 1.66083 | + | 1.66083i | 0.0121228 | + | 0.0121228i | 0.713142 | − | 0.701019i | \(-0.247271\pi\) |
−0.701019 | + | 0.713142i | \(0.747271\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 75.6997 | + | 182.755i | 0.544602 | + | 1.31479i | 0.921445 | + | 0.388508i | \(0.127009\pi\) |
−0.376843 | + | 0.926277i | \(0.622991\pi\) | |||||||
\(140\) | 36.8692 | + | 29.2139i | 0.263352 | + | 0.208671i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.11011 | − | 15.1175i | 0.0148599 | − | 0.106461i | ||||
\(143\) | 49.1053 | 0.343394 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 15.5870i | − | 0.107496i | ||||||
\(146\) | −9.93270 | + | 71.1609i | −0.0680322 | + | 0.487404i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 271.376 | − | 31.4372i | 1.83362 | − | 0.212413i | ||||
\(149\) | 16.1203 | − | 6.67724i | 0.108190 | − | 0.0448137i | −0.327932 | − | 0.944701i | \(-0.606352\pi\) |
0.436122 | + | 0.899888i | \(0.356352\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −127.344 | + | 127.344i | −0.843335 | + | 0.843335i | −0.989291 | − | 0.145956i | \(-0.953374\pi\) |
0.145956 | + | 0.989291i | \(0.453374\pi\) | |||||||
\(152\) | 151.892 | + | 3.54811i | 0.999287 | + | 0.0233429i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −151.300 | + | 39.2808i | −0.982465 | + | 0.255070i | ||||
\(155\) | −8.89669 | + | 3.68513i | −0.0573980 | + | 0.0237750i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −236.255 | − | 97.8598i | −1.50481 | − | 0.623311i | −0.530328 | − | 0.847793i | \(-0.677931\pi\) |
−0.974478 | + | 0.224482i | \(0.927931\pi\) | |||||||
\(158\) | −60.4584 | − | 80.0740i | −0.382648 | − | 0.506797i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −47.5620 | + | 25.0445i | −0.297262 | + | 0.156528i | ||||
\(161\) | −240.922 | −1.49641 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 38.0947 | − | 91.9687i | 0.233710 | − | 0.564225i | −0.762898 | − | 0.646518i | \(-0.776224\pi\) |
0.996608 | + | 0.0822932i | \(0.0262244\pi\) | |||||||
\(164\) | −70.4599 | + | 39.2302i | −0.429634 | + | 0.239209i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −54.8373 | − | 211.220i | −0.330345 | − | 1.27241i | ||||
\(167\) | −223.831 | − | 223.831i | −1.34031 | − | 1.34031i | −0.895750 | − | 0.444558i | \(-0.853361\pi\) |
−0.444558 | − | 0.895750i | \(-0.646639\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 105.820 | + | 105.820i | 0.626154 | + | 0.626154i | ||||
\(170\) | −82.9698 | − | 48.7678i | −0.488058 | − | 0.286869i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 105.248 | − | 12.1923i | 0.611907 | − | 0.0708855i | ||||
\(173\) | −13.2654 | + | 32.0254i | −0.0766784 | + | 0.185118i | −0.957571 | − | 0.288199i | \(-0.906944\pi\) |
0.880892 | + | 0.473317i | \(0.156944\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −155.270 | −0.887259 | ||||||||
\(176\) | 28.8173 | − | 176.281i | 0.163735 | − | 1.00160i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 29.7680 | + | 4.15504i | 0.167236 | + | 0.0233429i | ||||
\(179\) | 13.8305 | + | 5.72877i | 0.0772652 | + | 0.0320043i | 0.420981 | − | 0.907069i | \(-0.361686\pi\) |
−0.343716 | + | 0.939074i | \(0.611686\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 153.596 | − | 63.6217i | 0.848599 | − | 0.351501i | 0.0843605 | − | 0.996435i | \(-0.473115\pi\) |
0.764238 | + | 0.644934i | \(0.223115\pi\) | |||||||
\(182\) | 53.0964 | + | 31.2089i | 0.291739 | + | 0.171477i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 111.264 | − | 251.815i | 0.604695 | − | 1.36856i | ||||
\(185\) | 81.1228 | − | 81.1228i | 0.438502 | − | 0.438502i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 295.465 | − | 122.386i | 1.58003 | − | 0.654469i | ||||
\(188\) | 63.5063 | − | 223.057i | 0.337800 | − | 1.18647i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 50.9195 | − | 38.4458i | 0.267997 | − | 0.202346i | ||||
\(191\) | 2.00135i | 0.0104783i | 0.999986 | + | 0.00523914i | \(0.00166768\pi\) | ||||
−0.999986 | + | 0.00523914i | \(0.998332\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −107.502 | −0.557003 | −0.278502 | − | 0.960436i | \(-0.589838\pi\) | ||||
−0.278502 | + | 0.960436i | \(0.589838\pi\) | |||||||
\(194\) | 17.2400 | + | 22.8335i | 0.0888659 | + | 0.117698i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.0529236 | − | 0.0150678i | −0.000270018 | − | 7.68765e-5i | ||||
\(197\) | −35.9828 | − | 86.8701i | −0.182654 | − | 0.440965i | 0.805858 | − | 0.592109i | \(-0.201704\pi\) |
−0.988512 | + | 0.151144i | \(0.951704\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −228.742 | − | 228.742i | −1.14946 | − | 1.14946i | −0.986659 | − | 0.162799i | \(-0.947948\pi\) |
−0.162799 | − | 0.986659i | \(-0.552052\pi\) | |||||||
\(200\) | 71.7079 | − | 162.291i | 0.358539 | − | 0.811453i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −136.820 | + | 232.776i | −0.677329 | + | 1.15236i | ||||
\(203\) | 24.8605 | + | 60.0185i | 0.122465 | + | 0.295658i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.9601 | + | 31.2885i | −0.0632200 | + | 0.152627i | ||||
\(206\) | 1.90651 | − | 13.6588i | 0.00925489 | − | 0.0663049i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −57.1413 | + | 41.0841i | −0.274718 | + | 0.197520i | ||||
\(209\) | 212.019i | 1.01445i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −244.800 | − | 101.400i | −1.16019 | − | 0.480567i | −0.282252 | − | 0.959340i | \(-0.591082\pi\) |
−0.877938 | + | 0.478773i | \(0.841082\pi\) | |||||||
\(212\) | 23.1090 | + | 199.484i | 0.109005 | + | 0.940963i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 12.0657 | − | 20.5276i | 0.0563816 | − | 0.0959233i | ||||
\(215\) | 31.4619 | − | 31.4619i | 0.146335 | − | 0.146335i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 28.3796 | − | 28.3796i | 0.130781 | − | 0.130781i | ||||
\(218\) | −55.6935 | + | 14.4593i | −0.255475 | + | 0.0663270i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −36.4895 | − | 65.5375i | −0.165861 | − | 0.297898i | ||||
\(221\) | −116.415 | − | 48.2206i | −0.526764 | − | 0.218193i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 110.575i | − | 0.495853i | −0.968779 | − | 0.247927i | \(-0.920251\pi\) | ||
0.968779 | − | 0.247927i | \(-0.0797492\pi\) | |||||||
\(224\) | 143.195 | − | 172.294i | 0.639264 | − | 0.769170i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 191.976 | − | 144.948i | 0.849449 | − | 0.641361i | ||||
\(227\) | −153.333 | + | 370.178i | −0.675475 | + | 1.63074i | 0.0966861 | + | 0.995315i | \(0.469176\pi\) |
−0.772161 | + | 0.635427i | \(0.780824\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.0559 | − | 58.0760i | −0.105047 | − | 0.253607i | 0.862612 | − | 0.505865i | \(-0.168827\pi\) |
−0.967660 | + | 0.252258i | \(0.918827\pi\) | |||||||
\(230\) | −29.0520 | − | 111.901i | −0.126313 | − | 0.486526i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −74.2134 | − | 1.73359i | −0.319885 | − | 0.00747236i | ||||
\(233\) | 104.978 | + | 104.978i | 0.450547 | + | 0.450547i | 0.895536 | − | 0.444989i | \(-0.146792\pi\) |
−0.444989 | + | 0.895536i | \(0.646792\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −37.2711 | − | 89.9804i | −0.158600 | − | 0.382895i | ||||
\(236\) | 13.7682 | + | 118.851i | 0.0583397 | + | 0.503608i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 397.262 | + | 55.4501i | 1.66917 | + | 0.232984i | ||||
\(239\) | −122.643 | −0.513151 | −0.256576 | − | 0.966524i | \(-0.582594\pi\) | ||||
−0.256576 | + | 0.966524i | \(0.582594\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 188.784i | 0.783335i | 0.920107 | + | 0.391668i | \(0.128102\pi\) | ||||
−0.920107 | + | 0.391668i | \(0.871898\pi\) | |||||||
\(242\) | 7.19251 | + | 1.00394i | 0.0297211 | + | 0.00414850i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −205.423 | + | 259.253i | −0.841897 | + | 1.06251i | ||||
\(245\) | −0.0213492 | + | 0.00884311i | −8.71395e−5 | + | 3.60943e-5i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 59.0694 | − | 59.0694i | 0.239147 | − | 0.239147i | ||||
\(248\) | 16.5563 | + | 42.7691i | 0.0667592 | + | 0.172456i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −39.8292 | − | 153.412i | −0.159317 | − | 0.613649i | ||||
\(251\) | 355.365 | − | 147.197i | 1.41580 | − | 0.586443i | 0.461997 | − | 0.886881i | \(-0.347133\pi\) |
0.953801 | + | 0.300439i | \(0.0971330\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 354.932 | + | 147.018i | 1.40289 | + | 0.581098i | ||||
\(254\) | 204.370 | − | 154.305i | 0.804604 | − | 0.607501i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 113.953 | + | 229.239i | 0.445129 | + | 0.895467i | ||||
\(257\) | −84.4316 | −0.328528 | −0.164264 | − | 0.986416i | \(-0.552525\pi\) | ||||
−0.164264 | + | 0.986416i | \(0.552525\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −182.981 | + | 441.754i | −0.706489 | + | 1.70561i | ||||
\(260\) | −8.09287 | + | 28.4251i | −0.0311264 | + | 0.109327i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 101.858 | − | 26.4446i | 0.388770 | − | 0.100933i | ||||
\(263\) | 37.2079 | + | 37.2079i | 0.141475 | + | 0.141475i | 0.774297 | − | 0.632822i | \(-0.218104\pi\) |
−0.632822 | + | 0.774297i | \(0.718104\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 59.6320 | + | 59.6320i | 0.225027 | + | 0.225027i | ||||
\(266\) | −134.749 | + | 229.252i | −0.506575 | + | 0.861848i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −296.525 | − | 234.956i | −1.10644 | − | 0.876702i | ||||
\(269\) | 90.5201 | − | 218.535i | 0.336506 | − | 0.812398i | −0.661540 | − | 0.749910i | \(-0.730097\pi\) |
0.998046 | − | 0.0624874i | \(-0.0199033\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 312.612 | 1.15355 | 0.576775 | − | 0.816903i | \(-0.304311\pi\) | ||||
0.576775 | + | 0.816903i | \(0.304311\pi\) | |||||||
\(272\) | −241.423 | + | 389.615i | −0.887585 | + | 1.43241i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.649390 | − | 4.65243i | 0.00237004 | − | 0.0169797i | ||||
\(275\) | 228.748 | + | 94.7506i | 0.831812 | + | 0.344548i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −199.434 | + | 82.6083i | −0.719978 | + | 0.298225i | −0.712426 | − | 0.701747i | \(-0.752404\pi\) |
−0.00755172 | + | 0.999971i | \(0.502404\pi\) | |||||||
\(278\) | 200.474 | − | 341.071i | 0.721130 | − | 1.22688i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.19708 | − | 94.0550i | 0.00784672 | − | 0.335911i | ||||
\(281\) | −237.700 | + | 237.700i | −0.845909 | + | 0.845909i | −0.989620 | − | 0.143711i | \(-0.954096\pi\) |
0.143711 | + | 0.989620i | \(0.454096\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 58.7408 | − | 24.3312i | 0.207565 | − | 0.0859761i | −0.276479 | − | 0.961020i | \(-0.589168\pi\) |
0.484044 | + | 0.875044i | \(0.339168\pi\) | |||||||
\(284\) | −26.6726 | + | 14.8506i | −0.0939174 | + | 0.0522907i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −59.1785 | − | 78.3788i | −0.206918 | − | 0.274052i | ||||
\(287\) | − | 141.148i | − | 0.491807i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −531.645 | −1.83960 | ||||||||
\(290\) | −24.8790 | + | 18.7844i | −0.0857895 | + | 0.0647738i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 125.553 | − | 69.9045i | 0.429976 | − | 0.239399i | ||||
\(293\) | −47.5607 | − | 114.822i | −0.162323 | − | 0.391883i | 0.821701 | − | 0.569919i | \(-0.193026\pi\) |
−0.984024 | + | 0.178036i | \(0.943026\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 35.5284 | + | 35.5284i | 0.120435 | + | 0.120435i | ||||
\(296\) | −377.223 | − | 395.268i | −1.27440 | − | 1.33536i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −30.0849 | − | 17.6832i | −0.100956 | − | 0.0593396i | ||||
\(299\) | −57.9258 | − | 139.845i | −0.193732 | − | 0.467710i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −70.9655 | + | 171.326i | −0.235766 | + | 0.569189i | ||||
\(302\) | 356.724 | + | 49.7918i | 1.18120 | + | 0.164874i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −177.386 | − | 246.716i | −0.583508 | − | 0.811565i | ||||
\(305\) | 138.906i | 0.455429i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 407.254 | + | 168.690i | 1.32656 | + | 0.549480i | 0.929673 | − | 0.368387i | \(-0.120090\pi\) |
0.396889 | + | 0.917867i | \(0.370090\pi\) | |||||||
\(308\) | 245.034 | + | 194.156i | 0.795564 | + | 0.630378i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 16.6037 | + | 9.75926i | 0.0535602 | + | 0.0314815i | ||||
\(311\) | −149.458 | + | 149.458i | −0.480572 | + | 0.480572i | −0.905314 | − | 0.424742i | \(-0.860365\pi\) |
0.424742 | + | 0.905314i | \(0.360365\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 295.452 | − | 295.452i | 0.943937 | − | 0.943937i | −0.0545726 | − | 0.998510i | \(-0.517380\pi\) |
0.998510 | + | 0.0545726i | \(0.0173796\pi\) | |||||||
\(314\) | 128.521 | + | 495.029i | 0.409301 | + | 1.57652i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −54.9486 | + | 193.000i | −0.173888 | + | 0.610758i | ||||
\(317\) | 222.852 | + | 92.3084i | 0.703004 | + | 0.291194i | 0.705406 | − | 0.708803i | \(-0.250765\pi\) |
−0.00240221 | + | 0.999997i | \(0.500765\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 103.591i | − | 0.324738i | ||||||
\(320\) | 97.2930 | + | 45.7335i | 0.304041 | + | 0.142917i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 290.343 | + | 384.544i | 0.901686 | + | 1.19424i | ||||
\(323\) | 208.199 | − | 502.638i | 0.644580 | − | 1.55615i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −37.3323 | − | 90.1281i | −0.114868 | − | 0.277317i | ||||
\(326\) | −192.704 | + | 50.0302i | −0.591116 | + | 0.153467i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 147.530 | + | 65.1860i | 0.449788 | + | 0.198738i | ||||
\(329\) | 287.029 | + | 287.029i | 0.872427 | + | 0.872427i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −200.624 | − | 484.350i | −0.606115 | − | 1.46329i | −0.867192 | − | 0.497974i | \(-0.834077\pi\) |
0.261076 | − | 0.965318i | \(-0.415923\pi\) | |||||||
\(332\) | −271.049 | + | 342.076i | −0.816413 | + | 1.03035i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −87.5189 | + | 627.012i | −0.262033 | + | 1.87728i | ||||
\(335\) | −158.876 | −0.474257 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 248.089i | 0.736169i | 0.929792 | + | 0.368085i | \(0.119986\pi\) | ||||
−0.929792 | + | 0.368085i | \(0.880014\pi\) | |||||||
\(338\) | 41.3760 | − | 296.431i | 0.122414 | − | 0.877014i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 22.1496 | + | 191.203i | 0.0651460 | + | 0.562361i | ||||
\(341\) | −59.1276 | + | 24.4914i | −0.173395 | + | 0.0718224i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −242.504 | + | 242.504i | −0.707007 | + | 0.707007i | ||||
\(344\) | −146.299 | − | 153.297i | −0.425286 | − | 0.445631i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 67.1035 | − | 17.4216i | 0.193941 | − | 0.0503514i | ||||
\(347\) | 101.462 | − | 42.0270i | 0.292398 | − | 0.121115i | −0.231662 | − | 0.972796i | \(-0.574416\pi\) |
0.524061 | + | 0.851681i | \(0.324416\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 489.895 | + | 202.921i | 1.40371 | + | 0.581436i | 0.950712 | − | 0.310076i | \(-0.100354\pi\) |
0.452998 | + | 0.891512i | \(0.350354\pi\) | |||||||
\(350\) | 187.121 | + | 247.833i | 0.534632 | + | 0.708093i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −316.098 | + | 166.446i | −0.898006 | + | 0.472859i | ||||
\(353\) | 185.627 | 0.525856 | 0.262928 | − | 0.964815i | \(-0.415312\pi\) | ||||
0.262928 | + | 0.964815i | \(0.415312\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.90604 | + | 11.8442i | −0.0138198 | + | 0.0333640i | ||||
\(356\) | −29.2424 | − | 52.5211i | −0.0821415 | − | 0.147531i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.52366 | − | 28.9793i | −0.0210158 | − | 0.0809476i | ||||
\(359\) | −222.847 | − | 222.847i | −0.620743 | − | 0.620743i | 0.324978 | − | 0.945722i | \(-0.394643\pi\) |
−0.945722 | + | 0.324978i | \(0.894643\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.224842 | − | 0.224842i | −0.000622830 | − | 0.000622830i | ||||
\(362\) | −286.653 | − | 168.488i | −0.791859 | − | 0.465437i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −14.1746 | − | 122.360i | −0.0389413 | − | 0.336154i | ||||
\(365\) | 23.0937 | − | 55.7530i | 0.0632703 | − | 0.152748i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 532.771 | 1.45169 | 0.725846 | − | 0.687857i | \(-0.241448\pi\) | ||||
0.725846 | + | 0.687857i | \(0.241448\pi\) | |||||||
\(368\) | −536.019 | + | 125.878i | −1.45657 | + | 0.342060i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −227.247 | − | 31.7193i | −0.614181 | − | 0.0857279i | ||||
\(371\) | −324.726 | − | 134.506i | −0.875273 | − | 0.362550i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −277.629 | + | 114.998i | −0.744313 | + | 0.308305i | −0.722419 | − | 0.691456i | \(-0.756970\pi\) |
−0.0218944 | + | 0.999760i | \(0.506970\pi\) | |||||||
\(374\) | −551.419 | − | 324.112i | −1.47438 | − | 0.866609i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −432.564 | + | 167.449i | −1.15043 | + | 0.445343i | ||||
\(377\) | −28.8610 | + | 28.8610i | −0.0765543 | + | 0.0765543i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 306.344 | − | 126.892i | 0.808296 | − | 0.334807i | 0.0600223 | − | 0.998197i | \(-0.480883\pi\) |
0.748274 | + | 0.663390i | \(0.230883\pi\) | |||||||
\(380\) | −122.730 | − | 34.9421i | −0.322972 | − | 0.0919530i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.19443 | − | 2.41190i | 0.00836239 | − | 0.00631387i | ||||
\(383\) | 163.336i | 0.426465i | 0.977001 | + | 0.213233i | \(0.0683992\pi\) | ||||
−0.977001 | + | 0.213233i | \(0.931601\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 131.288 | 0.341007 | ||||||||
\(386\) | 129.554 | + | 171.587i | 0.335632 | + | 0.444527i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 15.6689 | − | 55.0348i | 0.0403837 | − | 0.141842i | ||||
\(389\) | 27.0717 | + | 65.3568i | 0.0695930 | + | 0.168012i | 0.954849 | − | 0.297092i | \(-0.0960168\pi\) |
−0.885256 | + | 0.465104i | \(0.846017\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −697.075 | − | 697.075i | −1.78280 | − | 1.78280i | ||||
\(392\) | 0.0397297 | + | 0.102632i | 0.000101351 | + | 0.000261816i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −95.2925 | + | 162.124i | −0.241859 | + | 0.411481i | ||||
\(395\) | 32.2487 | + | 77.8553i | 0.0816423 | + | 0.197102i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −153.949 | + | 371.666i | −0.387781 | + | 0.936187i | 0.602628 | + | 0.798022i | \(0.294120\pi\) |
−0.990409 | + | 0.138165i | \(0.955880\pi\) | |||||||
\(398\) | −89.4390 | + | 640.769i | −0.224721 | + | 1.60997i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −345.456 | + | 81.1263i | −0.863639 | + | 0.202816i | ||||
\(401\) | − | 287.838i | − | 0.717801i | −0.933376 | − | 0.358900i | \(-0.883152\pi\) | ||
0.933376 | − | 0.358900i | \(-0.116848\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23.2966 | + | 9.64976i | 0.0578079 | + | 0.0239448i | ||||
\(404\) | 536.429 | − | 62.1419i | 1.32779 | − | 0.153816i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 65.8375 | − | 112.011i | 0.162161 | − | 0.275889i | ||||
\(407\) | 539.144 | − | 539.144i | 1.32468 | − | 1.32468i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −134.641 | + | 134.641i | −0.329195 | + | 0.329195i | −0.852280 | − | 0.523085i | \(-0.824781\pi\) |
0.523085 | + | 0.852280i | \(0.324781\pi\) | |||||||
\(410\) | 65.5593 | − | 17.0207i | 0.159901 | − | 0.0415138i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −24.0989 | + | 13.4176i | −0.0584925 | + | 0.0325671i | ||||
\(413\) | −193.470 | − | 80.1378i | −0.468450 | − | 0.194038i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 183.282i | 0.441644i | ||||||||
\(416\) | 134.439 | + | 41.6936i | 0.323170 | + | 0.100225i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 338.412 | − | 255.512i | 0.809598 | − | 0.611272i | ||||
\(419\) | −94.1979 | + | 227.414i | −0.224816 | + | 0.542754i | −0.995532 | − | 0.0944249i | \(-0.969899\pi\) |
0.770716 | + | 0.637179i | \(0.219899\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −151.850 | − | 366.598i | −0.360689 | − | 0.870779i | −0.995200 | − | 0.0978656i | \(-0.968798\pi\) |
0.634511 | − | 0.772914i | \(-0.281202\pi\) | |||||||
\(422\) | 133.169 | + | 512.935i | 0.315567 | + | 1.21549i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 290.555 | − | 277.290i | 0.685270 | − | 0.653986i | ||||
\(425\) | −449.254 | − | 449.254i | −1.05707 | − | 1.05707i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −221.548 | − | 534.864i | −0.518848 | − | 1.25261i | ||||
\(428\) | −47.3056 | + | 5.48005i | −0.110527 | + | 0.0128039i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −88.1333 | − | 12.3017i | −0.204961 | − | 0.0286087i | ||||
\(431\) | 691.406 | 1.60419 | 0.802095 | − | 0.597196i | \(-0.203719\pi\) | ||||
0.802095 | + | 0.597196i | \(0.203719\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 580.011i | 1.33952i | 0.742579 | + | 0.669758i | \(0.233602\pi\) | ||||
−0.742579 | + | 0.669758i | \(0.766398\pi\) | |||||||
\(434\) | −79.4988 | − | 11.0965i | −0.183177 | − | 0.0255680i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 90.1971 | + | 71.4691i | 0.206874 | + | 0.163920i | ||||
\(437\) | 603.802 | − | 250.103i | 1.38170 | − | 0.572318i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 411.067 | − | 411.067i | 0.936371 | − | 0.936371i | −0.0617227 | − | 0.998093i | \(-0.519659\pi\) |
0.998093 | + | 0.0617227i | \(0.0196594\pi\) | |||||||
\(440\) | −60.6321 | + | 137.224i | −0.137800 | + | 0.311872i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 63.3287 | + | 243.926i | 0.143278 | + | 0.551869i | ||||
\(443\) | 34.4767 | − | 14.2807i | 0.0778256 | − | 0.0322364i | −0.343431 | − | 0.939178i | \(-0.611589\pi\) |
0.421257 | + | 0.906941i | \(0.361589\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −23.3226 | − | 9.66052i | −0.0524102 | − | 0.0217090i | ||||
\(446\) | −176.493 | + | 133.258i | −0.395725 | + | 0.298785i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −447.574 | − | 20.9216i | −0.999049 | − | 0.0467001i | ||||
\(449\) | −185.456 | −0.413043 | −0.206521 | − | 0.978442i | \(-0.566214\pi\) | ||||
−0.206521 | + | 0.978442i | \(0.566214\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −86.1331 | + | 207.944i | −0.190982 | + | 0.461073i | ||||
\(452\) | −462.712 | − | 131.738i | −1.02370 | − | 0.291456i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 775.642 | − | 201.374i | 1.70846 | − | 0.443555i | ||||
\(455\) | −36.5772 | − | 36.5772i | −0.0803895 | − | 0.0803895i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 386.211 | + | 386.211i | 0.845100 | + | 0.845100i | 0.989517 | − | 0.144417i | \(-0.0461306\pi\) |
−0.144417 | + | 0.989517i | \(0.546131\pi\) | |||||||
\(458\) | −63.7067 | + | 108.386i | −0.139098 | + | 0.236650i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −143.598 | + | 181.227i | −0.312169 | + | 0.393971i | ||||
\(461\) | −268.824 | + | 648.999i | −0.583133 | + | 1.40781i | 0.306826 | + | 0.951766i | \(0.400733\pi\) |
−0.889958 | + | 0.456042i | \(0.849267\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 49.4705 | 0.106848 | 0.0534238 | − | 0.998572i | \(-0.482987\pi\) | ||||
0.0534238 | + | 0.998572i | \(0.482987\pi\) | |||||||
\(464\) | 86.6700 | + | 120.544i | 0.186789 | + | 0.259793i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 41.0466 | − | 294.070i | 0.0880828 | − | 0.631052i | ||||
\(467\) | 192.753 | + | 79.8411i | 0.412748 | + | 0.170966i | 0.579388 | − | 0.815052i | \(-0.303292\pi\) |
−0.166640 | + | 0.986018i | \(0.553292\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 611.761 | − | 253.400i | 1.30439 | − | 0.540297i | ||||
\(470\) | −98.7044 | + | 167.928i | −0.210009 | + | 0.357294i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 173.111 | − | 165.208i | 0.366760 | − | 0.350016i | ||||
\(473\) | 209.097 | − | 209.097i | 0.442065 | − | 0.442065i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 389.141 | − | 161.187i | 0.819244 | − | 0.339342i | ||||
\(476\) | −390.247 | − | 700.909i | −0.819847 | − | 1.47250i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 147.801 | + | 195.755i | 0.309208 | + | 0.409530i | ||||
\(479\) | 256.988i | 0.536509i | 0.963348 | + | 0.268254i | \(0.0864468\pi\) | ||||
−0.963348 | + | 0.268254i | \(0.913553\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −300.415 | −0.624564 | ||||||||
\(482\) | 301.325 | − | 227.510i | 0.625155 | − | 0.472012i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.06551 | − | 12.6901i | −0.0145982 | − | 0.0262192i | ||||
\(485\) | −9.19588 | − | 22.2008i | −0.0189606 | − | 0.0457749i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.7898 | − | 10.7898i | −0.0221557 | − | 0.0221557i | 0.695942 | − | 0.718098i | \(-0.254987\pi\) |
−0.718098 | + | 0.695942i | \(0.754987\pi\) | |||||||
\(488\) | 661.365 | + | 15.4492i | 1.35526 | + | 0.0316581i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.0398434 | + | 0.0234191i | 8.13131e−5 | + | 4.77940e-5i | ||||
\(491\) | −58.0314 | − | 140.100i | −0.118190 | − | 0.285336i | 0.853702 | − | 0.520761i | \(-0.174352\pi\) |
−0.971893 | + | 0.235425i | \(0.924352\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −101.725 | + | 245.586i | −0.206339 | + | 0.498146i | ||||
\(494\) | −165.469 | − | 23.0964i | −0.334958 | − | 0.0467538i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 48.3128 | − | 77.9686i | 0.0974049 | − | 0.157195i | ||||
\(497\) | − | 53.4317i | − | 0.107508i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −72.1133 | − | 29.8703i | −0.144516 | − | 0.0598603i | 0.309253 | − | 0.950980i | \(-0.399921\pi\) |
−0.453769 | + | 0.891119i | \(0.649921\pi\) | |||||||
\(500\) | −196.867 | + | 248.455i | −0.393735 | + | 0.496910i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −663.210 | − | 389.820i | −1.32113 | − | 0.776533i | ||||
\(503\) | −151.600 | + | 151.600i | −0.301393 | + | 0.301393i | −0.841559 | − | 0.540166i | \(-0.818361\pi\) |
0.540166 | + | 0.841559i | \(0.318361\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 160.355 | − | 160.355i | 0.317535 | − | 0.317535i | ||||
\(506\) | −193.080 | − | 743.697i | −0.381582 | − | 1.46976i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −492.585 | − | 140.243i | −0.969656 | − | 0.276069i | ||||
\(509\) | 562.711 | + | 233.082i | 1.10552 | + | 0.457922i | 0.859393 | − | 0.511315i | \(-0.170842\pi\) |
0.246128 | + | 0.969237i | \(0.420842\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 251.513i | 0.492198i | ||||||||
\(512\) | 228.569 | − | 458.149i | 0.446424 | − | 0.894822i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 101.751 | + | 134.764i | 0.197960 | + | 0.262188i | ||||
\(515\) | −4.43266 | + | 10.7014i | −0.00860710 | + | 0.0207794i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −247.705 | − | 598.012i | −0.479119 | − | 1.15670i | ||||
\(518\) | 925.616 | − | 240.311i | 1.78690 | − | 0.463920i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 55.1234 | − | 21.3387i | 0.106006 | − | 0.0410360i | ||||
\(521\) | 224.985 | + | 224.985i | 0.431833 | + | 0.431833i | 0.889252 | − | 0.457418i | \(-0.151226\pi\) |
−0.457418 | + | 0.889252i | \(0.651226\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.30771 | − | 22.4708i | −0.0177968 | − | 0.0429652i | 0.914731 | − | 0.404063i | \(-0.132402\pi\) |
−0.932528 | + | 0.361097i | \(0.882402\pi\) | |||||||
\(524\) | −164.961 | − | 130.710i | −0.314812 | − | 0.249446i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14.5484 | − | 104.229i | 0.0276586 | − | 0.198155i | ||||
\(527\) | 164.225 | 0.311622 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 655.224i | − | 1.23861i | ||||||
\(530\) | 23.3163 | − | 167.045i | 0.0439931 | − | 0.315180i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 528.307 | − | 61.2010i | 0.993059 | − | 0.115039i | ||||
\(533\) | 81.9309 | − | 33.9369i | 0.153717 | − | 0.0636715i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.1411 | + | 14.1411i | −0.0264320 | + | 0.0264320i | ||||
\(536\) | −17.6702 | + | 756.447i | −0.0329669 | + | 1.41128i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −457.901 | + | 118.881i | −0.851116 | + | 0.220969i | ||||
\(539\) | −0.141887 | + | 0.0587715i | −0.000263241 | + | 0.000109038i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −357.866 | − | 148.233i | −0.661490 | − | 0.273998i | 0.0265752 | − | 0.999647i | \(-0.491540\pi\) |
−0.688066 | + | 0.725649i | \(0.741540\pi\) | |||||||
\(542\) | −376.739 | − | 498.972i | −0.695091 | − | 0.920613i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 912.826 | − | 84.1940i | 1.67799 | − | 0.154768i | ||||
\(545\) | 48.3271 | 0.0886735 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 187.175 | − | 451.879i | 0.342184 | − | 0.826105i | −0.655311 | − | 0.755360i | \(-0.727462\pi\) |
0.997494 | − | 0.0707454i | \(-0.0225378\pi\) | |||||||
\(548\) | −8.20852 | + | 4.57029i | −0.0149791 | + | 0.00833994i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −124.437 | − | 479.301i | −0.226249 | − | 0.871456i | ||||
\(551\) | −124.611 | − | 124.611i | −0.226155 | − | 0.226155i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −248.351 | − | 248.351i | −0.449097 | − | 0.449097i | ||||
\(554\) | 372.199 | + | 218.770i | 0.671839 | + | 0.394892i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −785.995 | + | 91.0524i | −1.41366 | + | 0.163763i | ||||
\(557\) | −307.716 | + | 742.891i | −0.552452 | + | 1.33374i | 0.363181 | + | 0.931719i | \(0.381691\pi\) |
−0.915632 | + | 0.402017i | \(0.868309\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −116.510 | −0.208426 | ||||||||
\(560\) | −152.773 | + | 109.842i | −0.272808 | + | 0.196146i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 665.863 | + | 92.9417i | 1.18481 | + | 0.165377i | ||||
\(563\) | −706.303 | − | 292.560i | −1.25454 | − | 0.519646i | −0.346307 | − | 0.938121i | \(-0.612565\pi\) |
−0.908228 | + | 0.418476i | \(0.862565\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −186.656 | + | 77.3156i | −0.330365 | + | 0.136842i | ||||
\(566\) | −109.626 | − | 64.4360i | −0.193686 | − | 0.113844i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 55.8475 | + | 24.6761i | 0.0983231 | + | 0.0434439i | ||||
\(569\) | 552.550 | − | 552.550i | 0.971089 | − | 0.971089i | −0.0285048 | − | 0.999594i | \(-0.509075\pi\) |
0.999594 | + | 0.0285048i | \(0.00907459\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −476.739 | + | 197.472i | −0.834919 | + | 0.345835i | −0.758848 | − | 0.651268i | \(-0.774237\pi\) |
−0.0760707 | + | 0.997102i | \(0.524237\pi\) | |||||||
\(572\) | −53.7854 | + | 188.914i | −0.0940304 | + | 0.330269i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −225.292 | + | 170.103i | −0.392495 | + | 0.296346i | ||||
\(575\) | − | 763.214i | − | 1.32733i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −188.090 | −0.325980 | −0.162990 | − | 0.986628i | \(-0.552114\pi\) | ||||
−0.162990 | + | 0.986628i | \(0.552114\pi\) | |||||||
\(578\) | 640.703 | + | 848.578i | 1.10848 | + | 1.46813i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 59.9650 | + | 17.0725i | 0.103388 | + | 0.0294354i | ||||
\(581\) | −292.326 | − | 705.737i | −0.503143 | − | 1.21469i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 396.316 | + | 396.316i | 0.679787 | + | 0.679787i | ||||
\(584\) | −262.885 | − | 116.155i | −0.450146 | − | 0.198896i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −125.954 | + | 214.289i | −0.214939 | + | 0.365681i | ||||
\(587\) | −229.302 | − | 553.585i | −0.390634 | − | 0.943075i | −0.989802 | − | 0.142451i | \(-0.954502\pi\) |
0.599167 | − | 0.800624i | \(-0.295498\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −41.6642 | + | 100.586i | −0.0707372 | + | 0.170775i | ||||
\(590\) | 13.8917 | − | 99.5246i | 0.0235453 | − | 0.168686i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −176.298 | + | 1078.45i | −0.297800 | + | 1.82170i | ||||
\(593\) | 378.708i | 0.638630i | 0.947649 | + | 0.319315i | \(0.103453\pi\) | ||||
−0.947649 | + | 0.319315i | \(0.896547\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −311.246 | − | 128.922i | −0.523102 | − | 0.216676i | ||||
\(596\) | 8.03146 | + | 69.3302i | 0.0134756 | + | 0.116326i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −153.404 | + | 260.990i | −0.256528 | + | 0.436438i | ||||
\(599\) | −745.316 | + | 745.316i | −1.24427 | + | 1.24427i | −0.286055 | + | 0.958213i | \(0.592344\pi\) |
−0.958213 | + | 0.286055i | \(0.907656\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 130.996 | − | 130.996i | 0.217963 | − | 0.217963i | −0.589676 | − | 0.807640i | \(-0.700745\pi\) |
0.807640 | + | 0.589676i | \(0.200745\pi\) | |||||||
\(602\) | 358.983 | − | 93.1999i | 0.596316 | − | 0.154817i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −350.425 | − | 629.386i | −0.580174 | − | 1.04203i | ||||
\(605\) | −5.63517 | − | 2.33416i | −0.00931433 | − | 0.00385812i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 732.344i | 1.20650i | 0.797553 | + | 0.603249i | \(0.206127\pi\) | ||||
−0.797553 | + | 0.603249i | \(0.793873\pi\) | |||||||
\(608\) | −180.018 | + | 580.458i | −0.296082 | + | 0.954701i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 221.713 | − | 167.400i | 0.363464 | − | 0.274427i | ||||
\(611\) | −97.5969 | + | 235.620i | −0.159733 | + | 0.385630i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 208.204 | + | 502.648i | 0.339647 | + | 0.819981i | 0.997749 | + | 0.0670521i | \(0.0213594\pi\) |
−0.658102 | + | 0.752928i | \(0.728641\pi\) | |||||||
\(614\) | −221.543 | − | 853.328i | −0.360819 | − | 1.38979i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 14.6018 | − | 625.092i | 0.0237043 | − | 1.01476i | ||||
\(617\) | −209.834 | − | 209.834i | −0.340087 | − | 0.340087i | 0.516313 | − | 0.856400i | \(-0.327304\pi\) |
−0.856400 | + | 0.516313i | \(0.827304\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 175.433 | + | 423.533i | 0.283414 | + | 0.684222i | 0.999911 | − | 0.0133688i | \(-0.00425556\pi\) |
−0.716497 | + | 0.697590i | \(0.754256\pi\) | |||||||
\(620\) | −4.43252 | − | 38.2629i | −0.00714922 | − | 0.0617144i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 418.672 | + | 58.4386i | 0.673106 | + | 0.0939527i | ||||
\(623\) | 105.213 | 0.168881 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 421.338i | − | 0.674141i | ||||||
\(626\) | −827.642 | − | 115.523i | −1.32211 | − | 0.184541i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 635.249 | − | 801.712i | 1.01154 | − | 1.27661i | ||||
\(629\) | −1807.59 | + | 748.727i | −2.87375 | + | 1.19035i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 232.756 | − | 232.756i | 0.368868 | − | 0.368868i | −0.498196 | − | 0.867064i | \(-0.666004\pi\) |
0.867064 | + | 0.498196i | \(0.166004\pi\) | |||||||
\(632\) | 374.274 | − | 144.885i | 0.592206 | − | 0.229248i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −121.230 | − | 466.947i | −0.191214 | − | 0.736509i | ||||
\(635\) | −198.707 | + | 82.3071i | −0.312924 | + | 0.129617i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.0559042 | + | 0.0231563i | 8.77618e−5 | + | 3.63521e-5i | ||||
\(638\) | −165.346 | + | 124.842i | −0.259163 | + | 0.195676i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −44.2541 | − | 210.408i | −0.0691470 | − | 0.328762i | ||||
\(641\) | 123.632 | 0.192873 | 0.0964366 | − | 0.995339i | \(-0.469256\pi\) | ||||
0.0964366 | + | 0.995339i | \(0.469256\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −351.513 | + | 848.628i | −0.546677 | + | 1.31979i | 0.373260 | + | 0.927727i | \(0.378240\pi\) |
−0.919936 | + | 0.392068i | \(0.871760\pi\) | |||||||
\(644\) | 263.883 | − | 926.854i | 0.409756 | − | 1.43921i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1053.19 | + | 273.431i | −1.63032 | + | 0.423268i | ||||
\(647\) | 191.561 | + | 191.561i | 0.296076 | + | 0.296076i | 0.839475 | − | 0.543399i | \(-0.182863\pi\) |
−0.543399 | + | 0.839475i | \(0.682863\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 236.122 | + | 236.122i | 0.363825 | + | 0.363825i | ||||
\(650\) | −98.8664 | + | 168.204i | −0.152102 | + | 0.258775i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 312.089 | + | 247.289i | 0.478664 | + | 0.379277i | ||||
\(653\) | 89.1964 | − | 215.339i | 0.136595 | − | 0.329769i | −0.840750 | − | 0.541424i | \(-0.817885\pi\) |
0.977344 | + | 0.211655i | \(0.0678853\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −88.3853 | −0.134939 | ||||||||
\(656\) | −73.7479 | − | 314.037i | −0.112421 | − | 0.478714i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 112.229 | − | 804.045i | 0.170561 | − | 1.22195i | ||||
\(659\) | 911.099 | + | 377.389i | 1.38255 | + | 0.572670i | 0.945161 | − | 0.326604i | \(-0.105904\pi\) |
0.437386 | + | 0.899274i | \(0.355904\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −496.993 | + | 205.861i | −0.751880 | + | 0.311439i | −0.725509 | − | 0.688213i | \(-0.758395\pi\) |
−0.0263718 | + | 0.999652i | \(0.508395\pi\) | |||||||
\(662\) | −531.310 | + | 903.930i | −0.802582 | + | 1.36545i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 872.650 | + | 20.3847i | 1.31423 | + | 0.0306998i | ||||
\(665\) | 157.928 | − | 157.928i | 0.237485 | − | 0.237485i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −295.014 | + | 122.199i | −0.442300 | + | 0.183207i | ||||
\(668\) | 1106.27 | − | 615.941i | 1.65609 | − | 0.922068i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 191.467 | + | 253.588i | 0.285772 | + | 0.378490i | ||||
\(671\) | 923.172i | 1.37582i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 374.150 | 0.555944 | 0.277972 | − | 0.960589i | \(-0.410338\pi\) | ||||
0.277972 | + | 0.960589i | \(0.410338\pi\) | |||||||
\(674\) | 395.984 | − | 298.980i | 0.587514 | − | 0.443591i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −523.008 | + | 291.197i | −0.773680 | + | 0.430764i | ||||
\(677\) | −12.3571 | − | 29.8326i | −0.0182527 | − | 0.0440659i | 0.914490 | − | 0.404608i | \(-0.132592\pi\) |
−0.932743 | + | 0.360542i | \(0.882592\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 70.8184 | + | 70.8184i | 0.104298 | + | 0.104298i | ||||
\(680\) | 278.493 | − | 265.779i | 0.409548 | − | 0.390851i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 110.348 | + | 64.8603i | 0.161801 | + | 0.0951030i | ||||
\(683\) | −22.0894 | − | 53.3285i | −0.0323417 | − | 0.0780799i | 0.906883 | − | 0.421382i | \(-0.138455\pi\) |
−0.939225 | + | 0.343302i | \(0.888455\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.50984 | + | 3.64508i | −0.00220415 | + | 0.00532128i | ||||
\(686\) | 679.318 | + | 94.8198i | 0.990260 | + | 0.138221i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −68.3737 | + | 418.256i | −0.0993803 | + | 0.607930i | ||||
\(689\) | − | 220.830i | − | 0.320508i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −622.510 | − | 257.852i | −0.900883 | − | 0.373158i | −0.116323 | − | 0.993211i | \(-0.537111\pi\) |
−0.784560 | + | 0.620053i | \(0.787111\pi\) | |||||||
\(692\) | −108.676 | − | 86.1111i | −0.157046 | − | 0.124438i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −189.356 | − | 111.299i | −0.272848 | − | 0.160374i | ||||
\(695\) | −234.958 | + | 234.958i | −0.338069 | + | 0.338069i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 408.394 | − | 408.394i | 0.585932 | − | 0.585932i | ||||
\(698\) | −266.499 | − | 1026.49i | −0.381803 | − | 1.47061i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 170.069 | − | 597.343i | 0.242955 | − | 0.853347i | ||||
\(701\) | 34.0835 | + | 14.1179i | 0.0486213 | + | 0.0201396i | 0.406862 | − | 0.913490i | \(-0.366623\pi\) |
−0.358240 | + | 0.933629i | \(0.616623\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1297.09i | − | 1.84507i | ||||||
\(704\) | 646.611 | + | 303.946i | 0.918482 | + | 0.431741i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −223.706 | − | 296.286i | −0.316863 | − | 0.419669i | ||||
\(707\) | −361.698 | + | 873.215i | −0.511595 | + | 1.23510i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 285.114 | + | 688.325i | 0.402135 | + | 0.970840i | 0.987147 | + | 0.159815i | \(0.0510898\pi\) |
−0.585012 | + | 0.811025i | \(0.698910\pi\) | |||||||
\(710\) | 24.8174 | − | 6.44316i | 0.0349541 | − | 0.00907487i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −48.5900 | + | 109.970i | −0.0682444 | + | 0.154452i | ||||
\(713\) | 139.497 | + | 139.497i | 0.195647 | + | 0.195647i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 31.5660 | + | 76.2071i | 0.0441483 | + | 0.106583i | ||||
\(716\) | −37.1878 | + | 46.9327i | −0.0519383 | + | 0.0655484i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −87.1339 | + | 624.254i | −0.121356 | + | 0.869435i | ||||
\(719\) | 478.037 | 0.664863 | 0.332432 | − | 0.943127i | \(-0.392131\pi\) | ||||
0.332432 | + | 0.943127i | \(0.392131\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 48.2761i | − | 0.0669571i | ||||||
\(722\) | −0.0879139 | + | 0.629843i | −0.000121764 | + | 0.000872358i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 76.5249 | + | 660.588i | 0.105697 | + | 0.912415i | ||||
\(725\) | −190.132 | + | 78.7553i | −0.262251 | + | 0.108628i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −408.395 | + | 408.395i | −0.561753 | + | 0.561753i | −0.929805 | − | 0.368052i | \(-0.880025\pi\) |
0.368052 | + | 0.929805i | \(0.380025\pi\) | |||||||
\(728\) | −178.221 | + | 170.085i | −0.244809 | + | 0.233633i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −116.820 | + | 30.3292i | −0.160028 | + | 0.0415468i | ||||
\(731\) | −701.038 | + | 290.379i | −0.959012 | + | 0.397236i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 747.573 | + | 309.655i | 1.01988 | + | 0.422449i | 0.829050 | − | 0.559174i | \(-0.188882\pi\) |
0.190831 | + | 0.981623i | \(0.438882\pi\) | |||||||
\(734\) | −642.060 | − | 850.376i | −0.874741 | − | 1.15855i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 846.892 | + | 703.860i | 1.15067 | + | 0.956331i | ||||
\(737\) | −1055.89 | −1.43269 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −348.876 | + | 842.261i | −0.472092 | + | 1.13973i | 0.491145 | + | 0.871078i | \(0.336579\pi\) |
−0.963237 | + | 0.268653i | \(0.913421\pi\) | |||||||
\(740\) | 223.234 | + | 400.943i | 0.301668 | + | 0.541815i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 176.648 | + | 680.405i | 0.238071 | + | 0.916988i | ||||
\(743\) | 345.072 | + | 345.072i | 0.464430 | + | 0.464430i | 0.900104 | − | 0.435674i | \(-0.143490\pi\) |
−0.435674 | + | 0.900104i | \(0.643490\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.7250 | + | 20.7250i | 0.0278187 | + | 0.0278187i | ||||
\(746\) | 518.132 | + | 304.546i | 0.694547 | + | 0.408239i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 147.207 | + | 1270.74i | 0.196801 | + | 1.69885i | ||||
\(749\) | 31.8967 | − | 77.0054i | 0.0425857 | − | 0.102811i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 642.659 | 0.855737 | 0.427869 | − | 0.903841i | \(-0.359265\pi\) | ||||
0.427869 | + | 0.903841i | \(0.359265\pi\) | |||||||
\(752\) | 788.568 | + | 488.632i | 1.04863 | + | 0.649777i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 80.8474 | + | 11.2847i | 0.107225 | + | 0.0149665i | ||||
\(755\) | −279.485 | − | 115.767i | −0.370179 | − | 0.153333i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 241.802 | − | 100.158i | 0.319422 | − | 0.132309i | −0.217211 | − | 0.976125i | \(-0.569696\pi\) |
0.536633 | + | 0.843816i | \(0.319696\pi\) | |||||||
\(758\) | −571.723 | − | 336.046i | −0.754252 | − | 0.443332i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 92.1330 | + | 238.003i | 0.121228 | + | 0.313162i | ||||
\(761\) | 253.025 | − | 253.025i | 0.332490 | − | 0.332490i | −0.521042 | − | 0.853531i | \(-0.674456\pi\) |
0.853531 | + | 0.521042i | \(0.174456\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −186.086 | + | 77.0793i | −0.243887 | + | 0.101021i | ||||
\(764\) | −7.69944 | − | 2.19210i | −0.0100778 | − | 0.00286923i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 260.707 | − | 196.842i | 0.340349 | − | 0.256974i | ||||
\(767\) | − | 131.569i | − | 0.171537i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1066.22 | −1.38650 | −0.693248 | − | 0.720699i | \(-0.743821\pi\) | ||||
−0.693248 | + | 0.720699i | \(0.743821\pi\) | |||||||
\(770\) | −158.219 | − | 209.553i | −0.205479 | − | 0.272147i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 117.747 | − | 413.571i | 0.152522 | − | 0.535714i | ||||
\(773\) | 497.702 | + | 1201.56i | 0.643857 | + | 1.55441i | 0.821435 | + | 0.570302i | \(0.193174\pi\) |
−0.177578 | + | 0.984107i | \(0.556826\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 89.9033 | + | 89.9033i | 0.116004 | + | 0.116004i | ||||
\(776\) | −106.726 | + | 41.3146i | −0.137534 | + | 0.0532404i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 71.6934 | − | 121.974i | 0.0921509 | − | 0.156779i | ||||
\(779\) | 146.527 | + | 353.749i | 0.188097 | + | 0.454106i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.6056 | + | 78.7170i | −0.0417486 | + | 0.100790i | ||||
\(782\) | −272.559 | + | 1952.70i | −0.348541 | + | 2.49705i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.115935 | − | 0.187099i | 0.000147876 | − | 0.000238647i | ||||
\(785\) | − | 429.553i | − | 0.547201i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 307.578 | + | 127.403i | 0.390823 | + | 0.161884i | 0.569437 | − | 0.822035i | \(-0.307161\pi\) |
−0.178614 | + | 0.983919i | \(0.557161\pi\) | |||||||
\(788\) | 373.612 | − | 43.2805i | 0.474126 | − | 0.0549245i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 85.4037 | − | 145.299i | 0.108106 | − | 0.183923i | ||||
\(791\) | 595.415 | − | 595.415i | 0.752737 | − | 0.752737i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 257.199 | − | 257.199i | 0.324337 | − | 0.324337i | ||||
\(794\) | 778.760 | − | 202.183i | 0.980806 | − | 0.254639i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1130.54 | − | 629.455i | 1.42028 | − | 0.790772i | ||||
\(797\) | 367.115 | + | 152.064i | 0.460621 | + | 0.190795i | 0.600912 | − | 0.799315i | \(-0.294804\pi\) |
−0.140292 | + | 0.990110i | \(0.544804\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1660.96i | 2.07880i | ||||||||
\(800\) | 545.809 | + | 453.626i | 0.682261 | + | 0.567033i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −459.429 | + | 346.883i | −0.572854 | + | 0.432523i | ||||
\(803\) | 153.481 | − | 370.536i | 0.191134 | − | 0.461439i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −154.870 | − | 373.889i | −0.192385 | − | 0.464459i | ||||
\(806\) | −12.6732 | − | 48.8138i | −0.0157235 | − | 0.0605630i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −745.655 | − | 781.325i | −0.922841 | − | 0.966986i | ||||
\(809\) | −318.547 | − | 318.547i | −0.393754 | − | 0.393754i | 0.482269 | − | 0.876023i | \(-0.339813\pi\) |
−0.876023 | + | 0.482269i | \(0.839813\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 187.929 | + | 453.701i | 0.231725 | + | 0.559434i | 0.996380 | − | 0.0850055i | \(-0.0270908\pi\) |
−0.764655 | + | 0.644439i | \(0.777091\pi\) | |||||||
\(812\) | −258.128 | + | 29.9025i | −0.317891 | + | 0.0368257i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1510.29 | − | 210.807i | −1.85539 | − | 0.258977i | ||||
\(815\) | 167.215 | 0.205172 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 503.050i | − | 0.615728i | ||||||
\(818\) | 377.165 | + | 52.6450i | 0.461082 | + | 0.0643582i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −106.175 | − | 84.1295i | −0.129482 | − | 0.102597i | ||||
\(821\) | 1296.86 | − | 537.177i | 1.57961 | − | 0.654295i | 0.591257 | − | 0.806483i | \(-0.298632\pi\) |
0.988352 | + | 0.152188i | \(0.0486318\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1104.17 | + | 1104.17i | −1.34164 | + | 1.34164i | −0.447215 | + | 0.894426i | \(0.647584\pi\) |
−0.894426 | + | 0.447215i | \(0.852416\pi\) | |||||||
\(824\) | 50.4588 | + | 22.2951i | 0.0612364 | + | 0.0270572i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 105.246 | + | 405.381i | 0.127416 | + | 0.490776i | ||||
\(827\) | −193.766 | + | 80.2605i | −0.234300 | + | 0.0970502i | −0.496744 | − | 0.867897i | \(-0.665471\pi\) |
0.262445 | + | 0.964947i | \(0.415471\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −282.707 | − | 117.101i | −0.341021 | − | 0.141256i | 0.205599 | − | 0.978636i | \(-0.434086\pi\) |
−0.546620 | + | 0.837381i | \(0.684086\pi\) | |||||||
\(830\) | 292.543 | − | 220.879i | 0.352462 | − | 0.266120i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −95.4679 | − | 264.829i | −0.114745 | − | 0.318304i | ||||
\(833\) | 0.394087 | 0.000473093 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 203.483 | − | 491.251i | 0.243692 | − | 0.588324i | ||||
\(836\) | −815.663 | − | 232.226i | −0.975674 | − | 0.277783i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 476.505 | − | 123.711i | 0.568622 | − | 0.147627i | ||||
\(839\) | 922.254 | + | 922.254i | 1.09923 | + | 1.09923i | 0.994501 | + | 0.104729i | \(0.0333975\pi\) |
0.104729 | + | 0.994501i | \(0.466603\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −533.792 | − | 533.792i | −0.634711 | − | 0.634711i | ||||
\(842\) | −402.141 | + | 684.173i | −0.477603 | + | 0.812557i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 658.227 | − | 830.711i | 0.779890 | − | 0.984255i | ||||
\(845\) | −96.1999 | + | 232.247i | −0.113846 | + | 0.274849i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.4214 | 0.0300134 | ||||||||
\(848\) | −792.750 | − | 129.594i | −0.934847 | − | 0.152823i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −175.660 | + | 1258.48i | −0.206659 | + | 1.48057i | ||||
\(851\) | −2171.39 | − | 899.421i | −2.55158 | − | 1.05690i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 319.646 | − | 132.402i | 0.374731 | − | 0.155219i | −0.187366 | − | 0.982290i | \(-0.559995\pi\) |
0.562097 | + | 0.827072i | \(0.309995\pi\) | |||||||
\(854\) | −586.722 | + | 998.204i | −0.687028 | + | 1.16886i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 65.7565 | + | 68.9020i | 0.0768183 | + | 0.0804930i | ||||
\(857\) | 154.384 | − | 154.384i | 0.180145 | − | 0.180145i | −0.611274 | − | 0.791419i | \(-0.709343\pi\) |
0.791419 | + | 0.611274i | \(0.209343\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 598.422 | − | 247.875i | 0.696650 | − | 0.288562i | −0.00611778 | − | 0.999981i | \(-0.501947\pi\) |
0.702768 | + | 0.711419i | \(0.251947\pi\) | |||||||
\(860\) | 86.5772 | + | 155.498i | 0.100671 | + | 0.180812i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −833.236 | − | 1103.58i | −0.966632 | − | 1.28025i | ||||
\(863\) | 687.121i | 0.796201i | 0.917342 | + | 0.398101i | \(0.130330\pi\) | ||||
−0.917342 | + | 0.398101i | \(0.869670\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −58.2279 | −0.0673155 | ||||||||
\(866\) | 925.777 | − | 698.990i | 1.06903 | − | 0.807148i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 78.0951 | + | 140.264i | 0.0899713 | + | 0.161594i | ||||
\(869\) | 214.326 | + | 517.428i | 0.246635 | + | 0.595429i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 294.176 | + | 294.176i | 0.337745 | + | 0.337745i | ||||
\(872\) | 5.37495 | − | 230.097i | 0.00616393 | − | 0.263872i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1126.86 | − | 662.343i | −1.28931 | − | 0.757830i | ||||
\(875\) | −212.321 | − | 512.588i | −0.242653 | − | 0.585815i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 146.136 | − | 352.804i | 0.166632 | − | 0.402285i | −0.818402 | − | 0.574646i | \(-0.805140\pi\) |
0.985034 | + | 0.172361i | \(0.0551397\pi\) | |||||||
\(878\) | −1151.51 | − | 160.729i | −1.31151 | − | 0.183062i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 292.098 | − | 68.5958i | 0.331929 | − | 0.0779497i | ||||
\(881\) | − | 1060.30i | − | 1.20352i | −0.798675 | − | 0.601762i | \(-0.794466\pi\) | ||
0.798675 | − | 0.601762i | \(-0.205534\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 281.886 | + | 116.761i | 0.319237 | + | 0.132232i | 0.536547 | − | 0.843870i | \(-0.319728\pi\) |
−0.217310 | + | 0.976103i | \(0.569728\pi\) | |||||||
\(884\) | 313.020 | − | 395.045i | 0.354095 | − | 0.446884i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −64.3431 | − | 37.8194i | −0.0726220 | − | 0.0426856i | ||||
\(887\) | 934.058 | − | 934.058i | 1.05305 | − | 1.05305i | 0.0545418 | − | 0.998511i | \(-0.482630\pi\) |
0.998511 | − | 0.0545418i | \(-0.0173698\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 633.855 | − | 633.855i | 0.712998 | − | 0.712998i | ||||
\(890\) | 12.6873 | + | 48.8682i | 0.0142554 | + | 0.0549081i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 425.396 | + | 121.114i | 0.476901 | + | 0.135778i | ||||
\(893\) | −1017.32 | − | 421.389i | −1.13922 | − | 0.471880i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 25.1462i | 0.0280964i | ||||||||
\(896\) | 505.993 | + | 739.603i | 0.564724 | + | 0.825450i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 223.499 | + | 296.014i | 0.248886 | + | 0.329636i | ||||
\(899\) | 20.3569 | − | 49.1459i | 0.0226439 | − | 0.0546673i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −550.377 | − | 1328.73i | −0.610851 | − | 1.47473i | ||||
\(902\) | 435.709 | − | 113.120i | 0.483047 | − | 0.125410i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 347.358 | + | 897.314i | 0.384246 | + | 0.992604i | ||||
\(905\) | 197.470 | + | 197.470i | 0.218199 | + | 0.218199i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −312.448 | − | 754.317i | −0.344485 | − | 0.831661i | −0.997251 | − | 0.0741012i | \(-0.976391\pi\) |
0.652765 | − | 0.757560i | \(-0.273609\pi\) | |||||||
\(908\) | −1256.17 | − | 995.348i | −1.38345 | − | 1.09620i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −14.3018 | + | 102.463i | −0.0157163 | + | 0.112596i | ||||
\(911\) | −678.215 | −0.744473 | −0.372236 | − | 0.928138i | \(-0.621409\pi\) | ||||
−0.372236 | + | 0.928138i | \(0.621409\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1218.10i | 1.33417i | ||||||||
\(914\) | 151.010 | − | 1081.88i | 0.165219 | − | 1.18368i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 249.774 | − | 28.9347i | 0.272679 | − | 0.0315881i | ||||
\(917\) | 340.332 | − | 140.970i | 0.371137 | − | 0.153730i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 456.147 | − | 456.147i | 0.496352 | − | 0.496352i | −0.413949 | − | 0.910300i | \(-0.635851\pi\) |
0.910300 | + | 0.413949i | \(0.135851\pi\) | |||||||
\(920\) | 462.317 | + | 10.7995i | 0.502519 | + | 0.0117386i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1359.86 | − | 353.050i | 1.47490 | − | 0.382918i | ||||
\(923\) | 31.0149 | − | 12.8468i | 0.0336023 | − | 0.0139185i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1399.43 | − | 579.663i | −1.51290 | − | 0.626662i | ||||
\(926\) | −59.6185 | − | 78.9616i | −0.0643828 | − | 0.0852718i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 87.9557 | − | 283.609i | 0.0947799 | − | 0.305613i | ||||
\(929\) | 1356.05 | 1.45969 | 0.729845 | − | 0.683613i | \(-0.239592\pi\) | ||||
0.729845 | + | 0.683613i | \(0.239592\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.0999806 | + | 0.241375i | −0.000107391 | + | 0.000259264i | ||||
\(932\) | −518.843 | + | 288.878i | −0.556699 | + | 0.309955i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −104.856 | − | 403.880i | −0.112266 | − | 0.432420i | ||||
\(935\) | 379.863 | + | 379.863i | 0.406271 | + | 0.406271i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.1043 | + | 38.1043i | 0.0406663 | + | 0.0406663i | 0.727148 | − | 0.686481i | \(-0.240846\pi\) |
−0.686481 | + | 0.727148i | \(0.740846\pi\) | |||||||
\(938\) | −1141.71 | − | 671.073i | −1.21718 | − | 0.715430i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 386.988 | − | 44.8301i | 0.411690 | − | 0.0476916i | ||||
\(941\) | −283.674 | + | 684.849i | −0.301460 | + | 0.727789i | 0.698466 | + | 0.715643i | \(0.253866\pi\) |
−0.999926 | + | 0.0121459i | \(0.996134\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 693.800 | 0.735737 | ||||||||
\(944\) | −472.315 | − | 77.2110i | −0.500334 | − | 0.0817913i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −585.736 | − | 81.7575i | −0.619171 | − | 0.0864244i | ||||
\(947\) | 187.436 | + | 77.6384i | 0.197926 | + | 0.0819836i | 0.479445 | − | 0.877572i | \(-0.340838\pi\) |
−0.281519 | + | 0.959556i | \(0.590838\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −145.993 | + | 60.4723i | −0.153839 | + | 0.0637222i | ||||
\(950\) | −726.244 | − | 426.870i | −0.764467 | − | 0.449337i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −648.446 | + | 1467.58i | −0.681141 | + | 1.54157i | ||||
\(953\) | −960.541 | + | 960.541i | −1.00791 | + | 1.00791i | −0.00794427 | + | 0.999968i | \(0.502529\pi\) |
−0.999968 | + | 0.00794427i | \(0.997471\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.10592 | + | 1.28652i | −0.00325227 | + | 0.00134714i | ||||
\(956\) | 134.332 | − | 471.822i | 0.140515 | − | 0.493538i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 410.188 | − | 309.705i | 0.428171 | − | 0.323282i | ||||
\(959\) | − | 16.4437i | − | 0.0171467i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 928.136 | 0.965802 | ||||||||
\(962\) | 362.040 | + | 479.504i | 0.376341 | + | 0.498445i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −726.273 | − | 206.776i | −0.753395 | − | 0.214498i | ||||
\(965\) | −69.1045 | − | 166.833i | −0.0716109 | − | 0.172884i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 183.282 | + | 183.282i | 0.189537 | + | 0.189537i | 0.795496 | − | 0.605959i | \(-0.207211\pi\) |
−0.605959 | + | 0.795496i | \(0.707211\pi\) | |||||||
\(968\) | −11.7403 | + | 26.5708i | −0.0121284 | + | 0.0274492i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −24.3533 | + | 41.4328i | −0.0251065 | + | 0.0427142i | ||||
\(971\) | 344.446 | + | 831.566i | 0.354733 | + | 0.856401i | 0.996022 | + | 0.0891022i | \(0.0283998\pi\) |
−0.641289 | + | 0.767299i | \(0.721600\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 529.972 | − | 1279.47i | 0.544678 | − | 1.31497i | ||||
\(974\) | −4.21887 | + | 30.2253i | −0.00433148 | + | 0.0310321i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −772.374 | − | 1074.25i | −0.791366 | − | 1.10066i | ||||
\(977\) | − | 1484.89i | − | 1.51985i | −0.650010 | − | 0.759926i | \(-0.725235\pi\) | ||
0.650010 | − | 0.759926i | \(-0.274765\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −155.002 | − | 64.2040i | −0.158327 | − | 0.0655812i | ||||
\(980\) | −0.0106366 | − | 0.0918186i | −1.08537e−5 | − | 9.36925e-5i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −153.683 | + | 261.465i | −0.156500 | + | 0.266258i | ||||
\(983\) | −32.2811 | + | 32.2811i | −0.0328394 | + | 0.0328394i | −0.723336 | − | 0.690496i | \(-0.757392\pi\) |
0.690496 | + | 0.723336i | \(0.257392\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 111.684 | − | 111.684i | 0.113385 | − | 0.113385i | ||||
\(986\) | 514.581 | − | 133.597i | 0.521888 | − | 0.135494i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 162.548 | + | 291.946i | 0.164522 | + | 0.295492i | ||||
\(989\) | −842.133 | − | 348.823i | −0.851500 | − | 0.352703i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1236.65i | − | 1.24789i | −0.781470 | − | 0.623943i | \(-0.785530\pi\) | ||
0.781470 | − | 0.623943i | \(-0.214470\pi\) | |||||||
\(992\) | −182.672 | + | 16.8487i | −0.184145 | + | 0.0169845i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −85.2843 | + | 64.3923i | −0.0857991 | + | 0.0647810i | ||||
\(995\) | 207.947 | − | 502.028i | 0.208992 | − | 0.504551i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 234.577 | + | 566.319i | 0.235283 | + | 0.568023i | 0.996784 | − | 0.0801409i | \(-0.0255370\pi\) |
−0.761501 | + | 0.648164i | \(0.775537\pi\) | |||||||
\(998\) | 39.2290 | + | 151.100i | 0.0393077 | + | 0.151403i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 288.3.u.a.163.2 | 28 | ||
3.2 | odd | 2 | 32.3.h.a.3.6 | ✓ | 28 | ||
12.11 | even | 2 | 128.3.h.a.47.3 | 28 | |||
24.5 | odd | 2 | 256.3.h.b.95.3 | 28 | |||
24.11 | even | 2 | 256.3.h.a.95.5 | 28 | |||
32.11 | odd | 8 | inner | 288.3.u.a.235.2 | 28 | ||
96.5 | odd | 8 | 256.3.h.a.159.5 | 28 | |||
96.11 | even | 8 | 32.3.h.a.11.6 | yes | 28 | ||
96.53 | odd | 8 | 128.3.h.a.79.3 | 28 | |||
96.59 | even | 8 | 256.3.h.b.159.3 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.3.h.a.3.6 | ✓ | 28 | 3.2 | odd | 2 | ||
32.3.h.a.11.6 | yes | 28 | 96.11 | even | 8 | ||
128.3.h.a.47.3 | 28 | 12.11 | even | 2 | |||
128.3.h.a.79.3 | 28 | 96.53 | odd | 8 | |||
256.3.h.a.95.5 | 28 | 24.11 | even | 2 | |||
256.3.h.a.159.5 | 28 | 96.5 | odd | 8 | |||
256.3.h.b.95.3 | 28 | 24.5 | odd | 2 | |||
256.3.h.b.159.3 | 28 | 96.59 | even | 8 | |||
288.3.u.a.163.2 | 28 | 1.1 | even | 1 | trivial | ||
288.3.u.a.235.2 | 28 | 32.11 | odd | 8 | inner |