Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,4,Mod(13,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 8]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.13");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.i (of order \(9\), degree \(6\), 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: | \(6.37220628062\) |
Analytic rank: | \(0\) |
Dimension: | \(54\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{9})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 13.3 | ||
Character | \(\chi\) | \(=\) | 108.13 |
Dual form | 108.4.i.a.25.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{4}{9}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −4.40211 | − | 2.76069i | −0.847187 | − | 0.531294i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −14.9393 | − | 12.5356i | −1.33621 | − | 1.12122i | −0.982582 | − | 0.185831i | \(-0.940502\pi\) |
−0.353631 | − | 0.935385i | \(-0.615053\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 23.5233 | + | 8.56177i | 1.27014 | + | 0.462292i | 0.887158 | − | 0.461465i | \(-0.152676\pi\) |
0.382978 | + | 0.923757i | \(0.374898\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 11.7572 | + | 24.3057i | 0.435453 | + | 0.900211i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −39.5319 | + | 33.1712i | −1.08358 | + | 0.909227i | −0.996213 | − | 0.0869492i | \(-0.972288\pi\) |
−0.0873623 | + | 0.996177i | \(0.527844\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −10.2025 | + | 57.8615i | −0.217668 | + | 1.23445i | 0.658550 | + | 0.752537i | \(0.271170\pi\) |
−0.876217 | + | 0.481917i | \(0.839941\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 31.1578 | + | 96.4258i | 0.536327 | + | 1.65980i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.52013 | + | 6.09704i | −0.0502210 | + | 0.0869853i | −0.890043 | − | 0.455876i | \(-0.849326\pi\) |
0.839822 | + | 0.542862i | \(0.182659\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −42.6669 | − | 73.9012i | −0.515182 | − | 0.892321i | −0.999845 | − | 0.0176203i | \(-0.994391\pi\) |
0.484663 | − | 0.874701i | \(-0.338942\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −79.9157 | − | 102.630i | −0.830431 | − | 1.06646i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 32.2883 | − | 11.7520i | 0.292721 | − | 0.106542i | −0.191486 | − | 0.981495i | \(-0.561331\pi\) |
0.484206 | + | 0.874954i | \(0.339108\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 44.3365 | + | 251.445i | 0.354692 | + | 2.01156i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 15.3437 | − | 139.455i | 0.109367 | − | 0.994001i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 37.0590 | + | 210.172i | 0.237300 | + | 1.34579i | 0.837717 | + | 0.546105i | \(0.183890\pi\) |
−0.600417 | + | 0.799687i | \(0.704999\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −133.967 | + | 48.7600i | −0.776168 | + | 0.282502i | −0.699574 | − | 0.714560i | \(-0.746627\pi\) |
−0.0765940 | + | 0.997062i | \(0.524405\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 265.599 | − | 36.8883i | 1.40106 | − | 0.194589i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −244.095 | − | 422.784i | −1.17884 | − | 2.04182i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −65.2996 | + | 113.102i | −0.290140 | + | 0.502538i | −0.973843 | − | 0.227223i | \(-0.927035\pi\) |
0.683702 | + | 0.729761i | \(0.260369\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 204.650 | − | 226.547i | 0.840263 | − | 0.930168i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.52460 | + | 48.3454i | −0.0324712 | + | 0.184153i | −0.996729 | − | 0.0808109i | \(-0.974249\pi\) |
0.964258 | + | 0.264964i | \(0.0853601\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 126.716 | − | 106.327i | 0.449394 | − | 0.377086i | −0.389817 | − | 0.920892i | \(-0.627462\pi\) |
0.839211 | + | 0.543806i | \(0.183017\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 129.041 | − | 510.494i | 0.427473 | − | 1.69111i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −470.489 | − | 171.244i | −1.46017 | − | 0.531458i | −0.514757 | − | 0.857336i | \(-0.672118\pi\) |
−0.945412 | + | 0.325878i | \(0.894340\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 217.287 | + | 182.325i | 0.633489 | + | 0.531560i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 32.3280 | − | 17.1219i | 0.0887613 | − | 0.0470107i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −347.277 | −0.900042 | −0.450021 | − | 0.893018i | \(-0.648584\pi\) | ||||
−0.450021 | + | 0.893018i | \(0.648584\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1006.40 | 2.46733 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −16.1935 | + | 443.112i | −0.0376295 | + | 1.02968i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −172.501 | − | 144.746i | −0.380640 | − | 0.319395i | 0.432314 | − | 0.901723i | \(-0.357697\pi\) |
−0.812954 | + | 0.582329i | \(0.802142\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −577.795 | − | 210.300i | −1.21277 | − | 0.441413i | −0.345107 | − | 0.938563i | \(-0.612158\pi\) |
−0.867664 | + | 0.497150i | \(0.834380\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 68.4686 | + | 672.412i | 0.136924 | + | 1.34470i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 877.746 | − | 736.517i | 1.67494 | − | 1.40544i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −162.166 | + | 919.690i | −0.295698 | + | 1.67698i | 0.368656 | + | 0.929566i | \(0.379818\pi\) |
−0.664353 | + | 0.747419i | \(0.731293\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −174.580 | − | 37.4043i | −0.304594 | − | 0.0652601i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 46.7209 | − | 80.9229i | 0.0780950 | − | 0.135265i | −0.824333 | − | 0.566105i | \(-0.808450\pi\) |
0.902428 | + | 0.430841i | \(0.141783\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −133.977 | − | 232.055i | −0.214806 | − | 0.372055i | 0.738406 | − | 0.674356i | \(-0.235579\pi\) |
−0.953213 | + | 0.302301i | \(0.902245\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 498.985 | − | 1229.29i | 0.768238 | − | 1.89261i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1213.92 | + | 441.832i | −1.79662 | + | 0.653915i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −155.815 | − | 883.669i | −0.221905 | − | 1.25849i | −0.868514 | − | 0.495665i | \(-0.834924\pi\) |
0.646608 | − | 0.762822i | \(-0.276187\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −452.535 | + | 571.536i | −0.620761 | + | 0.784000i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.17283 | + | 35.0079i | 0.00816333 | + | 0.0462966i | 0.988617 | − | 0.150452i | \(-0.0480729\pi\) |
−0.980454 | + | 0.196748i | \(0.936962\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 129.018 | − | 46.9588i | 0.164635 | − | 0.0599223i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 417.081 | − | 1027.51i | 0.513975 | − | 1.26621i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 361.721 | + | 626.519i | 0.430813 | + | 0.746189i | 0.996943 | − | 0.0781261i | \(-0.0248937\pi\) |
−0.566131 | + | 0.824315i | \(0.691560\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −735.394 | + | 1273.74i | −0.847146 | + | 1.46730i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 724.350 | + | 155.194i | 0.807651 | + | 0.173041i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −288.980 | + | 1638.89i | −0.312092 | + | 1.76996i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1214.37 | + | 1018.98i | −1.27114 | + | 1.06662i | −0.276744 | + | 0.960944i | \(0.589255\pi\) |
−0.994401 | + | 0.105673i | \(0.966300\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1271.04 | − | 570.850i | −1.29034 | − | 0.579521i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1643.15 | + | 598.056i | 1.61880 | + | 0.589196i | 0.983153 | − | 0.182782i | \(-0.0585103\pi\) |
0.635649 | + | 0.771978i | \(0.280732\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 717.798 | + | 602.304i | 0.686667 | + | 0.576182i | 0.917946 | − | 0.396705i | \(-0.129846\pi\) |
−0.231279 | + | 0.972888i | \(0.574291\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −92.6420 | + | 2535.01i | −0.0861041 | + | 2.35611i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.1019 | −0.0145480 | −0.00727398 | − | 0.999974i | \(-0.502315\pi\) | ||||
−0.00727398 | + | 0.999974i | \(0.502315\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1665.12 | 1.46321 | 0.731603 | − | 0.681731i | \(-0.238772\pi\) | ||||
0.731603 | + | 0.681731i | \(0.238772\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 599.696 | − | 317.617i | 0.512799 | − | 0.271594i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −632.247 | − | 530.518i | −0.526343 | − | 0.441654i | 0.340493 | − | 0.940247i | \(-0.389406\pi\) |
−0.866836 | + | 0.498593i | \(0.833850\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −629.683 | − | 229.186i | −0.510593 | − | 0.185841i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1526.32 | + | 432.311i | −1.20605 | + | 0.341600i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −135.006 | + | 113.284i | −0.104000 | + | 0.0872664i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 231.317 | − | 1311.87i | 0.173792 | − | 0.985625i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 170.993 | − | 189.288i | 0.125349 | − | 0.138761i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1270.78 | − | 2201.05i | 0.909295 | − | 1.57495i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1130.88 | − | 1958.74i | −0.790151 | − | 1.36858i | −0.925873 | − | 0.377835i | \(-0.876669\pi\) |
0.135722 | − | 0.990747i | \(-0.456665\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −851.352 | + | 118.242i | −0.581065 | + | 0.0807024i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1343.42 | − | 488.966i | 0.895996 | − | 0.326116i | 0.147349 | − | 0.989085i | \(-0.452926\pi\) |
0.748647 | + | 0.662969i | \(0.230704\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −370.939 | − | 2103.70i | −0.241839 | − | 1.37153i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1977.37 | + | 1891.01i | −1.26063 | + | 1.20557i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 260.376 | + | 1476.67i | 0.162375 | + | 0.920877i | 0.951729 | + | 0.306938i | \(0.0993046\pi\) |
−0.789354 | + | 0.613938i | \(0.789584\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −54.1508 | + | 19.7093i | −0.0330433 | + | 0.0120268i | −0.358489 | − | 0.933534i | \(-0.616708\pi\) |
0.325446 | + | 0.945561i | \(0.394486\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1598.40 | + | 2052.71i | 0.954676 | + | 1.22602i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1516.01 | − | 2625.81i | −0.886540 | − | 1.53553i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2080.99 | − | 3604.38i | 1.19184 | − | 2.06433i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −453.178 | − | 1402.48i | −0.254269 | − | 0.786900i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −236.688 | + | 1342.32i | −0.130136 | + | 0.738037i | 0.847988 | + | 0.530015i | \(0.177814\pi\) |
−0.978124 | + | 0.208022i | \(0.933297\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 897.782 | − | 753.329i | 0.483844 | − | 0.405993i | −0.367970 | − | 0.929838i | \(-0.619947\pi\) |
0.851814 | + | 0.523844i | \(0.175503\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −189.580 | − | 13.8749i | −0.100174 | − | 0.00733150i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2612.61 | + | 950.913i | 1.35387 | + | 0.492769i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −977.108 | − | 819.891i | −0.496699 | − | 0.416780i | 0.359721 | − | 0.933060i | \(-0.382872\pi\) |
−0.856420 | + | 0.516280i | \(0.827316\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1528.76 | + | 958.724i | 0.762504 | + | 0.478187i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 860.144 | 0.421049 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1616.42 | 0.776736 | 0.388368 | − | 0.921504i | \(-0.373039\pi\) | ||||
0.388368 | + | 0.921504i | \(0.373039\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4430.29 | − | 2778.35i | −2.09029 | − | 1.31088i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 424.273 | + | 356.007i | 0.196594 | + | 0.164962i | 0.735771 | − | 0.677231i | \(-0.236820\pi\) |
−0.539177 | + | 0.842193i | \(0.681264\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1179.36 | − | 429.252i | −0.536805 | − | 0.195381i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1294.58 | − | 1905.92i | 0.578940 | − | 0.852337i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 539.141 | − | 452.393i | 0.236937 | − | 0.198814i | −0.516586 | − | 0.856235i | \(-0.672797\pi\) |
0.753523 | + | 0.657421i | \(0.228353\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1109.87 | + | 6294.40i | −0.479420 | + | 2.71892i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 359.773 | + | 1113.41i | 0.152781 | + | 0.472819i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −585.812 | + | 1014.66i | −0.244612 | + | 0.423681i | −0.962023 | − | 0.272970i | \(-0.911994\pi\) |
0.717410 | + | 0.696651i | \(0.245327\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −386.512 | − | 669.458i | −0.158725 | − | 0.274919i | 0.775684 | − | 0.631121i | \(-0.217405\pi\) |
−0.934409 | + | 0.356202i | \(0.884072\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1962.95 | + | 2520.88i | 0.792925 | + | 1.01830i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2393.33 | − | 871.102i | 0.951143 | − | 0.346188i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −63.0889 | − | 357.795i | −0.0246712 | − | 0.139917i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1554.91 | − | 3149.06i | 0.598430 | − | 1.21196i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −98.8386 | − | 560.541i | −0.0374435 | − | 0.212353i | 0.960346 | − | 0.278812i | \(-0.0899407\pi\) |
−0.997789 | + | 0.0664597i | \(0.978830\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4565.75 | + | 1661.80i | −1.70285 | + | 0.619787i | −0.996145 | − | 0.0877221i | \(-0.972041\pi\) |
−0.706705 | + | 0.707509i | \(0.749819\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5897.23 | + | 819.049i | −2.16569 | + | 0.300786i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −946.267 | − | 1638.98i | −0.342227 | − | 0.592754i | 0.642619 | − | 0.766186i | \(-0.277848\pi\) |
−0.984846 | + | 0.173431i | \(0.944514\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1950.36 | − | 3378.12i | 0.694759 | − | 1.20336i | −0.275502 | − | 0.961300i | \(-0.588844\pi\) |
0.970262 | − | 0.242058i | \(-0.0778225\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3252.85 | − | 3600.89i | 1.14148 | − | 1.26362i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −927.696 | + | 5261.22i | −0.320746 | + | 1.81904i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 733.389 | − | 615.386i | 0.249864 | − | 0.209661i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 665.261 | + | 646.619i | 0.223376 | + | 0.217117i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4138.10 | + | 1506.15i | 1.36956 | + | 0.498480i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1142.91 | + | 959.011i | 0.372895 | + | 0.312896i | 0.809906 | − | 0.586560i | \(-0.199518\pi\) |
−0.437011 | + | 0.899456i | \(0.643963\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −429.073 | + | 227.250i | −0.138026 | + | 0.0731030i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3225.91 | −1.02328 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3568.81 | −1.11644 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −50.8488 | + | 1391.40i | −0.0156897 | + | 0.429326i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −316.870 | − | 265.885i | −0.0964478 | − | 0.0809293i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1925.56 | − | 700.848i | −0.578230 | − | 0.210459i | 0.0363147 | − | 0.999340i | \(-0.488438\pi\) |
−0.614545 | + | 0.788882i | \(0.710660\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5590.27 | + | 4033.92i | −1.65638 | + | 1.19524i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1243.19 | + | 1043.16i | −0.363496 | + | 0.305009i | −0.806182 | − | 0.591667i | \(-0.798470\pi\) |
0.442686 | + | 0.896677i | \(0.354026\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 651.857 | − | 3696.86i | 0.188104 | − | 1.06679i | −0.733797 | − | 0.679369i | \(-0.762254\pi\) |
0.921901 | − | 0.387425i | \(-0.126635\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6563.59 | + | 1406.27i | 1.86949 | + | 0.400544i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −48.1965 | + | 83.4788i | −0.0135513 | + | 0.0234716i | −0.872722 | − | 0.488218i | \(-0.837647\pi\) |
0.859170 | + | 0.511690i | \(0.170980\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4882.15 | + | 8456.12i | 1.35522 | + | 2.34731i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1753.62 | + | 4320.17i | −0.480632 | + | 1.18407i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4215.25 | + | 1534.22i | −1.14084 | + | 0.415233i | −0.842218 | − | 0.539137i | \(-0.818751\pi\) |
−0.298626 | + | 0.954370i | \(0.596528\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 420.948 | + | 2387.32i | 0.112513 | + | 0.638093i | 0.987952 | + | 0.154764i | \(0.0494616\pi\) |
−0.875438 | + | 0.483330i | \(0.839427\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3569.94 | − | 1266.66i | 0.942436 | − | 0.334388i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −960.563 | − | 5447.62i | −0.250482 | − | 1.42055i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4711.35 | − | 1714.79i | 1.21367 | − | 0.441739i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 69.4722 | − | 171.150i | 0.0176812 | − | 0.0435590i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1200.00 | − | 2078.47i | −0.301767 | − | 0.522677i | 0.674769 | − | 0.738029i | \(-0.264243\pi\) |
−0.976536 | + | 0.215352i | \(0.930910\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −886.591 | + | 1535.62i | −0.220314 | + | 0.381595i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −697.591 | − | 149.461i | −0.171313 | − | 0.0367043i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −65.0046 | + | 368.659i | −0.0157777 | + | 0.0894799i | −0.991680 | − | 0.128729i | \(-0.958910\pi\) |
0.975902 | + | 0.218209i | \(0.0700214\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2504.42 | + | 2101.45i | −0.600837 | + | 0.504162i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4672.67 | + | 3371.79i | −1.10816 | + | 0.799649i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3775.09 | − | 1374.02i | −0.885102 | − | 0.322151i | −0.140835 | − | 0.990033i | \(-0.544979\pi\) |
−0.744267 | + | 0.667882i | \(0.767201\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5188.09 | + | 4353.32i | 1.20265 | + | 1.00914i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 137.285 | − | 3756.60i | 0.0314670 | − | 0.861050i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3102.46 | 0.703198 | 0.351599 | − | 0.936151i | \(-0.385638\pi\) | ||||
0.351599 | + | 0.936151i | \(0.385638\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −146.797 | −0.0329050 | −0.0164525 | − | 0.999865i | \(-0.505237\pi\) | ||||
−0.0164525 | + | 0.999865i | \(0.505237\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6753.69 | − | 3576.96i | 1.49726 | − | 0.792994i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10093.4 | − | 8469.40i | −2.21330 | − | 1.85718i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4020.61 | − | 1463.38i | −0.872111 | − | 0.317423i | −0.133090 | − | 0.991104i | \(-0.542490\pi\) |
−0.739022 | + | 0.673681i | \(0.764712\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2760.23 | − | 2682.88i | −0.592296 | − | 0.575699i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3809.81 | + | 3196.81i | −0.808805 | + | 0.678668i | −0.950322 | − | 0.311268i | \(-0.899246\pi\) |
0.141517 | + | 0.989936i | \(0.454802\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −185.085 | + | 1049.67i | −0.0388770 | + | 0.220482i | −0.998056 | − | 0.0623156i | \(-0.980151\pi\) |
0.959180 | + | 0.282798i | \(0.0912626\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5796.58 | − | 6416.79i | 1.20477 | − | 1.33368i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −614.448 | + | 1064.26i | −0.126375 | + | 0.218889i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2431.72 | + | 4211.86i | 0.494956 | + | 0.857288i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8158.90 | − | 1133.17i | 1.64358 | − | 0.228273i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6323.47 | − | 2301.56i | 1.26082 | − | 0.458902i | 0.376778 | − | 0.926304i | \(-0.377032\pi\) |
0.884045 | + | 0.467402i | \(0.154810\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 762.579 | + | 4324.80i | 0.150505 | + | 0.853559i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4019.31 | + | 6021.88i | 0.785266 | + | 1.17651i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 350.565 | + | 1988.15i | 0.0678049 | + | 0.384541i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3891.11 | − | 1416.25i | 0.745116 | − | 0.271200i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5582.27 | − | 7168.92i | −1.05839 | − | 1.35922i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5995.63 | + | 10384.7i | 1.12560 | + | 1.94960i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −419.639 | + | 726.835i | −0.0780132 | + | 0.135123i | −0.902393 | − | 0.430915i | \(-0.858191\pi\) |
0.824379 | + | 0.566038i | \(0.191524\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1497.06 | − | 4633.03i | −0.275614 | − | 0.852957i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −782.999 | + | 4440.61i | −0.142765 | + | 0.809658i | 0.826370 | + | 0.563127i | \(0.190402\pi\) |
−0.969135 | + | 0.246531i | \(0.920709\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3326.13 | − | 2790.96i | 0.600652 | − | 0.504007i | −0.291003 | − | 0.956722i | \(-0.593989\pi\) |
0.891655 | + | 0.452715i | \(0.149545\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7406.20 | − | 10903.7i | 1.32474 | − | 1.95032i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8805.07 | − | 3204.78i | −1.56007 | − | 0.567819i | −0.589317 | − | 0.807902i | \(-0.700603\pi\) |
−0.970752 | + | 0.240083i | \(0.922825\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8436.68 | − | 7079.22i | −1.48076 | − | 1.24251i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 70.8825 | + | 44.4524i | 0.0123249 | + | 0.00772925i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 600.772 | 0.103492 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15001.3 | −2.56038 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7330.05 | − | 4596.87i | −1.23961 | − | 0.777393i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9601.29 | − | 8056.44i | −1.60893 | − | 1.35005i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7052.64 | + | 2566.95i | 1.17114 | + | 0.426261i | 0.853066 | − | 0.521804i | \(-0.174741\pi\) |
0.318077 | + | 0.948065i | \(0.396963\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3516.77 | − | 257.384i | −0.578733 | − | 0.0423561i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 13951.5 | − | 11706.7i | 2.27538 | − | 1.90927i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 595.457 | − | 3377.01i | 0.0962511 | − | 0.545867i | −0.898106 | − | 0.439780i | \(-0.855057\pi\) |
0.994357 | − | 0.106087i | \(-0.0338323\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1318.63 | + | 4080.84i | 0.211263 | + | 0.653807i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3678.55 | − | 6371.43i | 0.584178 | − | 1.01183i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −742.883 | − | 1286.71i | −0.116944 | − | 0.202553i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2139.23 | + | 2747.26i | 0.333832 | + | 0.428717i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10147.3 | − | 3693.32i | 1.56984 | − | 0.571377i | 0.596880 | − | 0.802331i | \(-0.296407\pi\) |
0.972965 | + | 0.230954i | \(0.0741848\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −221.987 | − | 1258.95i | −0.0340479 | − | 0.193095i | 0.963040 | − | 0.269359i | \(-0.0868119\pi\) |
−0.997088 | + | 0.0762641i | \(0.975701\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7912.51 | + | 2310.60i | 1.20324 | + | 0.351370i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1599.06 | + | 9068.74i | 0.241104 | + | 1.36737i | 0.829370 | + | 0.558700i | \(0.188699\pi\) |
−0.588267 | + | 0.808667i | \(0.700189\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1712.39 | + | 623.260i | −0.256012 | + | 0.0931809i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 907.054 | − | 125.978i | 0.134472 | − | 0.0186764i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −331.332 | − | 573.884i | −0.0487104 | − | 0.0843689i | 0.840642 | − | 0.541591i | \(-0.182178\pi\) |
−0.889353 | + | 0.457222i | \(0.848844\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −211.429 | + | 366.206i | −0.0308250 | + | 0.0533905i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4639.94 | + | 5136.39i | −0.670891 | + | 0.742674i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −907.419 | + | 5146.23i | −0.130127 | + | 0.737989i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4961.59 | + | 4163.27i | −0.705702 | + | 0.592155i | −0.923390 | − | 0.383864i | \(-0.874593\pi\) |
0.217687 | + | 0.976019i | \(0.430149\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1275.29 | + | 361.211i | −0.179916 | + | 0.0509591i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8169.10 | − | 2973.31i | −1.14318 | − | 0.416082i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5459.75 | + | 4581.27i | 0.757896 | + | 0.635950i | 0.937578 | − | 0.347775i | \(-0.113063\pi\) |
−0.179682 | + | 0.983725i | \(0.557507\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11670.5 | + | 6181.07i | −1.60710 | + | 0.851170i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12539.0 | −1.71297 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7451.59 | 1.00993 | 0.504964 | − | 0.863140i | \(-0.331506\pi\) | ||||
0.504964 | + | 0.863140i | \(0.331506\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −429.205 | + | 11744.6i | −0.0577135 | + | 1.57925i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10198.1 | + | 8557.21i | 1.36057 | + | 1.14165i | 0.975806 | + | 0.218637i | \(0.0701610\pi\) |
0.384762 | + | 0.923016i | \(0.374283\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 23673.8 | + | 8616.56i | 3.13384 | + | 1.14063i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4074.18 | + | 1829.80i | 0.535148 | + | 0.240346i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10703.4 | + | 8981.22i | −1.39508 | + | 1.17061i | −0.431839 | + | 0.901951i | \(0.642135\pi\) |
−0.963236 | + | 0.268656i | \(0.913420\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −42.0066 | + | 238.232i | −0.00543316 | + | 0.0308130i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7263.79 | − | 1556.29i | −0.932340 | − | 0.199756i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8749.53 | + | 15154.6i | −1.11452 | + | 1.93041i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4359.70 | − | 7551.22i | −0.551151 | − | 0.954622i | −0.998192 | − | 0.0601082i | \(-0.980855\pi\) |
0.447041 | − | 0.894514i | \(-0.352478\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4174.74 | + | 10284.8i | −0.523806 | + | 1.29043i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12751.4 | − | 4641.12i | 1.58796 | − | 0.577971i | 0.611046 | − | 0.791595i | \(-0.290749\pi\) |
0.976916 | + | 0.213624i | \(0.0685267\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1454.52 | − | 8249.02i | −0.179789 | − | 1.01963i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13925.1 | − | 2865.56i | 1.70850 | − | 0.351583i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1170.32 | − | 6637.22i | −0.142532 | − | 0.808341i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8465.11 | + | 3081.05i | −1.02341 | + | 0.372489i | −0.798566 | − | 0.601907i | \(-0.794408\pi\) |
−0.224839 | + | 0.974396i | \(0.572186\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2930.41 | − | 7219.27i | 0.351694 | − | 0.866424i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2818.51 | − | 4881.81i | −0.335811 | − | 0.581642i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 346.626 | − | 600.374i | 0.0410005 | − | 0.0710149i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 292.789 | + | 62.7309i | 0.0343836 | + | 0.00736677i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 769.338 | − | 4363.13i | 0.0897008 | − | 0.508718i | −0.906542 | − | 0.422115i | \(-0.861288\pi\) |
0.996243 | − | 0.0866031i | \(-0.0276012\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −472.103 | + | 396.141i | −0.0546529 | + | 0.0458592i | −0.669705 | − | 0.742627i | \(-0.733579\pi\) |
0.615052 | + | 0.788487i | \(0.289135\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1369.44 | − | 13448.9i | −0.157410 | − | 1.54589i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1689.14 | − | 614.796i | −0.192789 | − | 0.0701694i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11791.1 | − | 9893.89i | −1.33632 | − | 1.12131i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −575.376 | + | 15744.3i | −0.0647539 | + | 1.77190i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9458.47 | 1.05707 | 0.528537 | − | 0.848910i | \(-0.322741\pi\) | ||||
0.528537 | + | 0.848910i | \(0.322741\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5691.49 | 0.631676 | 0.315838 | − | 0.948813i | \(-0.397714\pi\) | ||||
0.315838 | + | 0.948813i | \(0.397714\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −19111.3 | + | 10121.9i | −2.10648 | + | 1.11566i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2246.13 | − | 1884.72i | −0.245874 | − | 0.206313i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12777.3 | − | 4650.57i | −1.38913 | − | 0.505602i | −0.464198 | − | 0.885732i | \(-0.653657\pi\) |
−0.924933 | + | 0.380129i | \(0.875880\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1876.85 | + | 7424.94i | −0.202662 | + | 0.801743i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8689.72 | + | 7291.54i | −0.931966 | + | 0.782013i | −0.976169 | − | 0.217010i | \(-0.930370\pi\) |
0.0442031 | + | 0.999023i | \(0.485925\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2449.91 | − | 13894.1i | 0.260982 | − | 1.48010i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4747.67 | − | 5255.65i | 0.502364 | − | 0.556115i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2603.29 | − | 4509.03i | 0.273623 | − | 0.473930i | −0.696163 | − | 0.717883i | \(-0.745111\pi\) |
0.969787 | + | 0.243954i | \(0.0784444\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1266.68 | − | 2193.96i | −0.132252 | − | 0.229067i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6031.84 | + | 837.745i | −0.625609 | + | 0.0868889i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 26953.3 | − | 9810.21i | 2.77713 | − | 1.01079i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2794.59 | + | 15848.9i | 0.286051 | + | 1.62228i | 0.701506 | + | 0.712664i | \(0.252512\pi\) |
−0.415454 | + | 0.909614i | \(0.636377\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 796.248 | + | 584.449i | 0.0809710 | + | 0.0594330i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2417.98 | + | 13713.0i | 0.244287 | + | 1.38542i | 0.822143 | + | 0.569282i | \(0.192779\pi\) |
−0.577855 | + | 0.816139i | \(0.696110\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −683.331 | + | 248.712i | −0.0685898 | + | 0.0249646i | −0.376087 | − | 0.926584i | \(-0.622731\pi\) |
0.307497 | + | 0.951549i | \(0.400508\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8875.84 | − | 11398.6i | −0.885177 | − | 1.13677i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6275.96 | + | 10870.3i | 0.621877 | + | 1.07712i | 0.989136 | + | 0.147004i | \(0.0469630\pi\) |
−0.367259 | + | 0.930119i | \(0.619704\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11688.8 | + | 20245.7i | −1.15083 | + | 1.99330i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2037.88 | + | 6306.74i | 0.199364 | + | 0.616984i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1482.31 | + | 8406.62i | −0.144095 | + | 0.817203i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16690.4 | − | 14004.9i | 1.61222 | − | 1.35282i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4083.02 | − | 8440.83i | −0.391926 | − | 0.810228i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8706.20 | + | 3168.80i | 0.830472 | + | 0.302267i | 0.722053 | − | 0.691838i | \(-0.243199\pi\) |
0.108420 | + | 0.994105i | \(0.465421\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5878.05 | − | 4932.27i | −0.557206 | − | 0.467551i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3786.45 | − | 2374.59i | −0.356707 | − | 0.223701i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 30915.4 | 2.89443 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7806.10 | −0.726341 | −0.363170 | − | 0.931723i | \(-0.618306\pi\) | ||||
−0.363170 | + | 0.931723i | \(0.618306\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7115.67 | − | 4462.43i | −0.658041 | − | 0.412675i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4101.97 | − | 3441.96i | −0.377025 | − | 0.316361i | 0.434508 | − | 0.900668i | \(-0.356922\pi\) |
−0.811533 | + | 0.584306i | \(0.801367\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1411.88 | − | 513.882i | −0.128982 | − | 0.0469454i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11832.5 | + | 24461.3i | 1.07440 | + | 2.22112i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1791.87 | − | 1503.56i | 0.161723 | − | 0.135702i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 256.588 | − | 1455.18i | 0.0230190 | − | 0.130547i | −0.971133 | − | 0.238540i | \(-0.923331\pi\) |
0.994152 | + | 0.107993i | \(0.0344423\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −884.874 | − | 2738.47i | −0.0789087 | − | 0.244203i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6261.59 | + | 10845.4i | −0.555051 | + | 0.961376i | 0.442849 | + | 0.896596i | \(0.353968\pi\) |
−0.997900 | + | 0.0647801i | \(0.979365\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17050.5 | − | 29532.3i | −1.50245 | − | 2.60232i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4006.65 | + | 5145.46i | 0.350970 | + | 0.450726i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 980.124 | − | 356.736i | 0.0853502 | − | 0.0310649i | −0.298992 | − | 0.954256i | \(-0.596650\pi\) |
0.384342 | + | 0.923191i | \(0.374428\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1164.78 | − | 6605.78i | −0.100835 | − | 0.571864i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10960.5 | + | 4816.17i | −0.943313 | + | 0.414501i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3173.18 | − | 17996.0i | −0.271509 | − | 1.53980i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24279.7 | − | 8837.10i | 2.06542 | − | 0.751751i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3622.28 | + | 503.088i | −0.306359 | + | 0.0425493i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4911.87 | + | 8507.61i | 0.413038 | + | 0.715403i | 0.995220 | − | 0.0976552i | \(-0.0311342\pi\) |
−0.582182 | + | 0.813058i | \(0.697801\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −904.471 | + | 1566.59i | −0.0756209 | + | 0.130979i | −0.901356 | − | 0.433079i | \(-0.857427\pi\) |
0.825735 | + | 0.564058i | \(0.190761\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 22262.6 | − | 24644.7i | 1.85071 | − | 2.04873i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 174.289 | − | 988.444i | 0.0144064 | − | 0.0817027i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8416.04 | + | 7061.89i | −0.691710 | + | 0.580414i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1490.01 | − | 5894.57i | 0.121772 | − | 0.481738i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2710.37 | − | 986.492i | −0.220261 | − | 0.0801683i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 240.552 | + | 201.847i | 0.0194392 | + | 0.0163114i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5379.96 | − | 2849.39i | 0.432332 | − | 0.228976i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −14637.7 | −1.16974 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5724.91 | 0.454960 | 0.227480 | − | 0.973783i | \(-0.426951\pi\) | ||||
0.227480 | + | 0.973783i | \(0.426951\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −146.694 | + | 4014.07i | −0.0115934 | + | 0.317238i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −24875.7 | − | 20873.2i | −1.95516 | − | 1.64057i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6752.26 | + | 2457.62i | 0.527798 | + | 0.192103i | 0.592155 | − | 0.805824i | \(-0.298277\pi\) |
−0.0643567 | + | 0.997927i | \(0.520500\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1681.77 | − | 16516.3i | −0.130740 | − | 1.28397i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13950.8 | − | 11706.1i | 1.07863 | − | 0.905075i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3900.50 | − | 22120.8i | 0.299939 | − | 1.70104i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −12940.6 | − | 2772.55i | −0.989723 | − | 0.212051i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −800.454 | + | 1386.43i | −0.0608910 | + | 0.105466i | −0.894864 | − | 0.446339i | \(-0.852728\pi\) |
0.833973 | + | 0.551805i | \(0.186061\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4859.42 | + | 8416.77i | 0.367677 | + | 0.636836i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −710.034 | + | 1749.22i | −0.0534361 | + | 0.131644i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12290.5 | + | 4473.39i | −0.920042 | + | 0.334868i | −0.758255 | − | 0.651958i | \(-0.773948\pi\) |
−0.161787 | + | 0.986826i | \(0.551726\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2794.98 | + | 15851.1i | 0.208117 | + | 1.18029i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −15538.5 | + | 9569.88i | −1.15089 | + | 0.708813i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3956.96 | − | 22441.0i | −0.291537 | − | 1.65339i | −0.680955 | − | 0.732325i | \(-0.738435\pi\) |
0.389419 | − | 0.921061i | \(-0.372676\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10197.6 | − | 3711.63i | 0.747386 | − | 0.272026i | 0.0598805 | − | 0.998206i | \(-0.480928\pi\) |
0.687505 | + | 0.726179i | \(0.258706\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1112.38 | + | 2740.43i | −0.0811001 | + | 0.199796i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4386.52 | + | 7597.68i | 0.318140 | + | 0.551035i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10891.7 | + | 18865.0i | −0.785835 | + | 1.36111i | 0.142664 | + | 0.989771i | \(0.454433\pi\) |
−0.928499 | + | 0.371335i | \(0.878900\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 24686.7 | + | 5289.18i | 1.77192 | + | 0.379639i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −154.524 | + | 876.350i | −0.0110340 | + | 0.0625768i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13728.5 | − | 11519.6i | 0.975263 | − | 0.818343i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 28221.4 | + | 12674.9i | 1.99455 | + | 0.895796i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9679.74 | − | 3523.14i | −0.680623 | − | 0.247726i | −0.0215079 | − | 0.999769i | \(-0.506847\pi\) |
−0.659115 | + | 0.752042i | \(0.729069\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9319.39 | + | 7819.90i | 0.651950 | + | 0.547051i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −359.139 | + | 9827.33i | −0.0249966 | + | 0.683997i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4017.02 | 0.278178 | 0.139089 | − | 0.990280i | \(-0.455583\pi\) | ||||
0.139089 | + | 0.990280i | \(0.455583\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3436.98 | 0.236811 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −17911.6 | + | 9486.54i | −1.22793 | + | 0.650349i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3884.65 | − | 3259.61i | −0.264979 | − | 0.222344i | 0.500611 | − | 0.865672i | \(-0.333109\pi\) |
−0.765590 | + | 0.643328i | \(0.777553\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6769.34 | − | 2463.84i | −0.459446 | − | 0.167225i | 0.101919 | − | 0.994793i | \(-0.467502\pi\) |
−0.561366 | + | 0.827568i | \(0.689724\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −24260.3 | + | 6871.44i | −1.63840 | + | 0.464057i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −19900.7 | + | 16698.7i | −1.33732 | + | 1.12215i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −829.608 | + | 4704.94i | −0.0554741 | + | 0.314609i | −0.999900 | − | 0.0141141i | \(-0.995507\pi\) |
0.944426 | + | 0.328723i | \(0.106618\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 18608.4 | − | 20599.4i | 1.23818 | − | 1.37066i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14708.6 | − | 25476.1i | 0.973892 | − | 1.68683i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9124.06 | + | 15803.3i | 0.601170 | + | 1.04126i | 0.992644 | + | 0.121068i | \(0.0386319\pi\) |
−0.391474 | + | 0.920189i | \(0.628035\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4927.35 | + | 684.345i | −0.323073 | + | 0.0448707i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9238.38 | − | 3362.50i | 0.602793 | − | 0.219399i | −0.0225540 | − | 0.999746i | \(-0.507180\pi\) |
0.625347 | + | 0.780347i | \(0.284958\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2028.41 | − | 11503.7i | −0.131710 | − | 0.746966i | −0.977094 | − | 0.212807i | \(-0.931739\pi\) |
0.845384 | − | 0.534159i | \(-0.179372\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1143.44 | − | 4683.07i | −0.0738886 | − | 0.302617i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3144.74 | + | 17834.7i | 0.202234 | + | 1.14692i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16585.3 | + | 6036.55i | −1.06146 | + | 0.386339i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −14058.4 | − | 18054.2i | −0.895436 | − | 1.14995i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −459.726 | − | 796.269i | −0.0291423 | − | 0.0504759i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5452.85 | + | 9444.62i | −0.344017 | + | 0.595855i | −0.985175 | − | 0.171554i | \(-0.945121\pi\) |
0.641158 | + | 0.767409i | \(0.278454\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2383.67 | − | 7376.88i | −0.149672 | − | 0.463199i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7659.36 | + | 43438.4i | −0.478665 | + | 2.71465i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12766.5 | + | 10712.4i | −0.794077 | + | 0.666309i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2516.20 | + | 184.155i | 0.155773 | + | 0.0114007i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19546.8 | + | 7114.47i | 1.20445 | + | 0.438385i | 0.864776 | − | 0.502158i | \(-0.167460\pi\) |
0.339676 | + | 0.940542i | \(0.389682\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6541.99 | + | 5489.38i | 0.401230 | + | 0.336672i | 0.820969 | − | 0.570973i | \(-0.193434\pi\) |
−0.419739 | + | 0.907645i | \(0.637878\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14200.8 | + | 8905.73i | 0.866911 | + | 0.543663i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17690.0 | −1.07491 | −0.537454 | − | 0.843293i | \(-0.680614\pi\) | ||||
−0.537454 | + | 0.843293i | \(0.680614\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11620.7 | 0.702854 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15710.3 | + | 9852.38i | 0.945832 | + | 0.593157i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10827.1 | − | 9085.01i | −0.648847 | − | 0.544447i | 0.257874 | − | 0.966179i | \(-0.416978\pi\) |
−0.906721 | + | 0.421732i | \(0.861422\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −26199.3 | − | 9535.77i | −1.56289 | − | 0.568845i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4065.07 | − | 5984.74i | 0.241390 | − | 0.355383i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7705.44 | + | 6465.63i | −0.455480 | + | 0.382193i | −0.841465 | − | 0.540312i | \(-0.818306\pi\) |
0.385985 | + | 0.922505i | \(0.373862\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3544.49 | + | 20101.8i | −0.208570 | + | 1.18286i | 0.683153 | + | 0.730275i | \(0.260608\pi\) |
−0.891723 | + | 0.452582i | \(0.850503\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 660.872 | + | 2045.24i | 0.0387121 | + | 0.119805i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −20829.5 | + | 36077.8i | −1.21464 | + | 2.10382i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3666.51 | + | 6350.58i | 0.212845 | + | 0.368659i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6541.74 | + | 8401.09i | 0.378054 | + | 0.485508i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29817.3 | − | 10852.6i | 1.71547 | − | 0.624381i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2017.24 | + | 11440.4i | 0.115541 | + | 0.655265i | 0.986481 | + | 0.163876i | \(0.0523996\pi\) |
−0.870940 | + | 0.491389i | \(0.836489\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 35745.4 | − | 2324.82i | 2.03828 | − | 0.132566i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3453.35 | − | 19584.9i | −0.196046 | − | 1.11183i | −0.910921 | − | 0.412580i | \(-0.864628\pi\) |
0.714876 | − | 0.699252i | \(-0.246483\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −37290.3 | + | 13572.6i | −2.10762 | + | 0.767109i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8352.52 | − | 1160.06i | 0.469999 | − | 0.0652768i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5188.26 | − | 8986.33i | −0.290664 | − | 0.503444i | 0.683303 | − | 0.730135i | \(-0.260543\pi\) |
−0.973967 | + | 0.226690i | \(0.927209\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14621.0 | − | 25324.3i | 0.815533 | − | 1.41255i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13075.4 | + | 14474.4i | −0.726141 | + | 0.803835i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3543.12 | − | 20094.0i | 0.195910 | − | 1.11106i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23664.3 | + | 19856.7i | −1.30279 | + | 1.09317i | −0.313140 | + | 0.949707i | \(0.601381\pi\) |
−0.989655 | + | 0.143468i | \(0.954175\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −25011.4 | − | 24310.6i | −1.37100 | − | 1.33259i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1056.04 | + | 384.368i | 0.0576374 | + | 0.0209783i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −264.756 | − | 222.157i | −0.0143879 | − | 0.0120729i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 442.625 | − | 234.428i | 0.0239508 | − | 0.0126851i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28142.8 | −1.51632 | −0.758158 | − | 0.652071i | \(-0.773901\pi\) | ||||
−0.758158 | + | 0.652071i | \(0.773901\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11144.5 | 0.597900 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1852.94 | − | 50702.9i | 0.0989866 | − | 2.70863i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 33531.7 | + | 28136.5i | 1.78372 | + | 1.49672i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20208.5 | + | 7355.30i | 1.07045 | + | 0.389611i | 0.816344 | − | 0.577566i | \(-0.195997\pi\) |
0.254103 | + | 0.967177i | \(0.418220\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 19646.3 | − | 14176.7i | 1.03628 | − | 0.747774i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3752.54 | + | 3148.76i | −0.197102 | + | 0.165388i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10267.8 | + | 58231.9i | −0.537057 | + | 3.04580i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 22791.5 | + | 4883.14i | 1.18712 | + | 0.254343i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18578.1 | − | 32178.3i | 0.963626 | − | 1.66905i | 0.250366 | − | 0.968151i | \(-0.419449\pi\) |
0.713261 | − | 0.700899i | \(-0.247217\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11728.2 | + | 20313.8i | 0.605797 | + | 1.04927i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4737.57 | − | 11671.3i | 0.243696 | − | 0.600362i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −51203.6 | + | 18636.6i | −2.62297 | + | 0.954683i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2772.11 | − | 15721.4i | −0.141419 | − | 0.802029i | −0.970173 | − | 0.242415i | \(-0.922060\pi\) |
0.828753 | − | 0.559614i | \(-0.189051\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19212.1 | − | 4279.51i | −0.976078 | − | 0.217422i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 202.225 | + | 1146.87i | 0.0102320 | + | 0.0580283i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31627.8 | − | 11511.6i | 1.59372 | − | 0.580067i | 0.615592 | − | 0.788065i | \(-0.288917\pi\) |
0.978129 | + | 0.207998i | \(0.0666948\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −10810.7 | + | 26632.9i | −0.542527 | + | 1.33656i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −24096.5 | − | 41736.4i | −1.20435 | − | 2.08600i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14420.2 | − | 24976.5i | 0.717801 | − | 1.24327i | −0.244068 | − | 0.969758i | \(-0.578482\pi\) |
0.961869 | − | 0.273510i | \(-0.0881845\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −25473.9 | − | 5457.85i | −1.26290 | − | 0.270579i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1573.69 | + | 8924.86i | −0.0777028 | + | 0.440675i | 0.920991 | + | 0.389583i | \(0.127381\pi\) |
−0.998694 | + | 0.0510912i | \(0.983730\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20362.8 | − | 17086.4i | 1.00139 | − | 0.840264i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −778.316 | + | 561.631i | −0.0381219 | + | 0.0275087i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −378.770 | − | 137.861i | −0.0184779 | − | 0.00672541i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4600.11 | + | 3859.95i | 0.223516 | + | 0.187552i | 0.747668 | − | 0.664072i | \(-0.231173\pi\) |
−0.524152 | + | 0.851625i | \(0.675618\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −455.441 | + | 12462.5i | −0.0220414 | + | 0.603132i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22855.7 | −1.10172 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25006.2 | −1.20061 | −0.600307 | − | 0.799770i | \(-0.704955\pi\) | ||||
−0.600307 | + | 0.799770i | \(0.704955\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8142.24 | − | 4312.38i | 0.389387 | − | 0.206231i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16281.6 | − | 13661.8i | −0.775566 | − | 0.650777i | 0.166562 | − | 0.986031i | \(-0.446733\pi\) |
−0.942128 | + | 0.335254i | \(0.891178\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 39169.0 | + | 14256.4i | 1.85847 | + | 0.676429i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2658.26 | + | 2583.77i | 0.125634 | + | 0.122113i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10135.2 | − | 8504.41i | 0.477131 | − | 0.400360i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 598.520 | − | 3394.38i | 0.0280666 | − | 0.159173i | −0.967553 | − | 0.252667i | \(-0.918692\pi\) |
0.995620 | + | 0.0934935i | \(0.0298034\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1303.91 | − | 1443.42i | 0.0609068 | − | 0.0674236i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9004.85 | − | 15596.8i | 0.418993 | − | 0.725718i | −0.576845 | − | 0.816853i | \(-0.695716\pi\) |
0.995838 | + | 0.0911359i | \(0.0290498\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18200.1 | − | 31523.5i | −0.843569 | − | 1.46110i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 16826.2 | − | 2336.94i | 0.776880 | − | 0.107899i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3936.50 | − | 1432.77i | 0.181052 | − | 0.0658977i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 837.347 | + | 4748.83i | 0.0383644 | + | 0.217575i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 29878.1 | − | 1943.22i | 1.36367 | − | 0.0886909i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4319.52 | + | 24497.2i | 0.196395 | + | 1.11381i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16461.5 | + | 5991.50i | −0.745603 | + | 0.271377i | −0.686754 | − | 0.726890i | \(-0.740965\pi\) |
−0.0588488 | + | 0.998267i | \(0.518743\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12825.1 | + | 16470.4i | 0.578690 | + | 0.743172i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10330.3 | − | 17892.7i | −0.464354 | − | 0.804285i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18063.3 | − | 31286.5i | 0.808885 | − | 1.40103i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10820.4 | − | 33486.5i | −0.482717 | − | 1.49389i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1312.20 | − | 7441.84i | 0.0583192 | − | 0.330745i | −0.941664 | − | 0.336555i | \(-0.890738\pi\) |
0.999983 | + | 0.00581003i | \(0.00184940\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2700.27 | − | 2265.79i | 0.119560 | − | 0.100323i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10975.1 | + | 16158.0i | −0.484130 | + | 0.712753i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12993.9 | + | 4729.41i | 0.571041 | + | 0.207842i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12850.0 | − | 10782.4i | −0.562610 | − | 0.472086i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13657.4 | − | 8564.91i | −0.595740 | − | 0.373605i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 38981.7 | 1.69410 | 0.847048 | − | 0.531517i | \(-0.178378\pi\) | ||||
0.847048 | + | 0.531517i | \(0.178378\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3470.10 | −0.150249 | −0.0751244 | − | 0.997174i | \(-0.523935\pi\) | ||||
−0.0751244 | + | 0.997174i | \(0.523935\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 646.215 | + | 405.259i | 0.0278767 | + | 0.0174822i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −24148.2 | − | 20262.8i | −1.03788 | − | 0.870888i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13264.3 | − | 4827.80i | −0.568002 | − | 0.206736i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −39605.4 | − | 2898.62i | −1.68977 | − | 0.123670i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18661.9 | − | 15659.2i | 0.793305 | − | 0.665662i | −0.153256 | − | 0.988187i | \(-0.548976\pi\) |
0.946561 | + | 0.322524i | \(0.104531\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6973.29 | − | 39547.5i | 0.295351 | − | 1.67502i | −0.370423 | − | 0.928863i | \(-0.620787\pi\) |
0.665774 | − | 0.746154i | \(-0.268102\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 21051.1 | + | 65148.1i | 0.888371 | + | 2.74929i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4564.78 | + | 7906.43i | −0.191938 | + | 0.332447i | −0.945893 | − | 0.324480i | \(-0.894811\pi\) |
0.753954 | + | 0.656927i | \(0.228144\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11850.3 | + | 20525.3i | 0.496475 | + | 0.859920i | 0.999992 | − | 0.00406556i | \(-0.00129411\pi\) |
−0.503517 | + | 0.863985i | \(0.667961\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13659.2 | + | 17541.6i | 0.570197 | + | 0.732264i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1876.52 | + | 682.998i | −0.0780523 | + | 0.0284087i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1875.59 | − | 10637.0i | −0.0777336 | − | 0.440849i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4744.25 | + | 19430.5i | 0.195920 | + | 0.802408i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5839.10 | + | 33115.2i | 0.240272 | + | 1.36265i | 0.831222 | + | 0.555941i | \(0.187642\pi\) |
−0.590950 | + | 0.806708i | \(0.701247\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19880.8 | + | 7236.01i | −0.815153 | + | 0.296692i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 25596.6 | − | 3555.04i | 1.04578 | − | 0.145246i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12237.9 | + | 21196.7i | 0.498221 | + | 0.862945i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16673.2 | − | 28878.9i | 0.676386 | − | 1.17154i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3712.58 | − | 4109.81i | 0.150077 | − | 0.166135i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −779.238 | + | 4419.28i | −0.0313889 | + | 0.178015i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20152.9 | + | 16910.3i | −0.808937 | + | 0.678778i | −0.950354 | − | 0.311172i | \(-0.899279\pi\) |
0.141417 | + | 0.989950i | \(0.454834\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −43231.9 | + | 12244.9i | −1.72924 | + | 0.489786i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 151.335 | + | 55.0813i | 0.00603208 | + | 0.00219550i | 0.345034 | − | 0.938590i | \(-0.387867\pi\) |
−0.339002 | + | 0.940786i | \(0.610089\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37816.0 | + | 31731.4i | 1.50206 | + | 1.26038i | 0.877675 | + | 0.479256i | \(0.159094\pi\) |
0.624382 | + | 0.781119i | \(0.285351\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5642.95 | − | 2988.68i | 0.223358 | − | 0.118297i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19390.7 | 0.764853 | 0.382426 | − | 0.923986i | \(-0.375089\pi\) | ||||
0.382426 | + | 0.923986i | \(0.375089\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13725.4 | −0.539512 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 922.917 | − | 25254.3i | 0.0361521 | − | 0.989251i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 35472.0 | + | 29764.6i | 1.38470 | + | 1.16190i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −51560.1 | − | 18766.4i | −2.00580 | − | 0.730050i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −39044.7 | − | 17535.8i | −1.51370 | − | 0.679837i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 48737.7 | − | 40895.8i | 1.88301 | − | 1.58004i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4605.11 | + | 26116.9i | −0.177313 | + | 1.00559i | 0.758127 | + | 0.652107i | \(0.226115\pi\) |
−0.935440 | + | 0.353486i | \(0.884996\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −34190.5 | − | 7325.40i | −1.31197 | − | 0.281092i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4444.25 | − | 7697.66i | 0.169955 | − | 0.294371i | −0.768449 | − | 0.639911i | \(-0.778971\pi\) |
0.938404 | + | 0.345540i | \(0.112304\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9393.58 | + | 16270.2i | 0.358006 | + | 0.620084i | 0.987628 | − | 0.156818i | \(-0.0501235\pi\) |
−0.629622 | + | 0.776902i | \(0.716790\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8582.46 | − | 21143.5i | 0.325984 | − | 0.803087i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16935.5 | + | 6164.02i | −0.641081 | + | 0.233334i | −0.642047 | − | 0.766665i | \(-0.721915\pi\) |
0.000966332 | 1.00000i | \(0.499692\pi\) | ||||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9831.68 | − | 55758.2i | −0.370915 | − | 2.10357i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1068.95 | − | 37605.1i | −0.0401922 | − | 1.41394i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7419.17 | + | 42076.2i | 0.278021 | + | 1.57674i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21470.9 | − | 7814.77i | 0.801892 | − | 0.291865i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3945.43 | − | 9719.86i | 0.146861 | − | 0.361802i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15212.7 | − | 26349.1i | −0.564373 | − | 0.977523i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1222.46 | − | 2117.37i | 0.0452010 | − | 0.0782904i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −21038.9 | − | 4507.65i | −0.775340 | − | 0.166119i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2617.82 | + | 14846.4i | −0.0961538 | + | 0.545315i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23612.4 | + | 19813.2i | −0.864430 | + | 0.725343i | −0.962918 | − | 0.269795i | \(-0.913044\pi\) |
0.0984877 | + | 0.995138i | \(0.468599\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4782.66 | + | 46969.3i | 0.174511 | + | 1.71383i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43762.2 | − | 15928.1i | −1.59155 | − | 0.579278i | −0.613878 | − | 0.789401i | \(-0.710391\pi\) |
−0.977675 | + | 0.210123i | \(0.932614\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1405.28 | − | 1179.17i | −0.0509397 | − | 0.0427435i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2275.54 | − | 62266.8i | 0.0822153 | − | 2.24970i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 35788.1 | 1.28880 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3405.86 | 0.122251 | 0.0611256 | − | 0.998130i | \(-0.480531\pi\) | ||||
0.0611256 | + | 0.998130i | \(0.480531\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3853.86 | − | 2041.12i | 0.137882 | − | 0.0730264i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4205.65 | + | 3528.96i | 0.149979 | + | 0.125847i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −31334.1 | − | 11404.7i | −1.11379 | − | 0.405388i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6200.11 | + | 24528.0i | −0.219675 | + | 0.869046i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23801.4 | + | 19971.7i | −0.840580 | + | 0.705330i | −0.957694 | − | 0.287788i | \(-0.907080\pi\) |
0.117114 | + | 0.993118i | \(0.462636\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4203.11 | − | 23837.0i | 0.147961 | − | 0.839126i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15706.0 | − | 17386.4i | 0.551115 | − | 0.610082i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3542.66 | + | 6136.06i | −0.123912 | + | 0.214621i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14196.9 | + | 24589.8i | 0.494976 | + | 0.857324i | 0.999983 | − | 0.00579118i | \(-0.00184340\pi\) |
−0.505007 | + | 0.863115i | \(0.668510\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22347.0 | + | 3103.70i | −0.776641 | + | 0.107865i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8174.57 | + | 2975.30i | −0.283192 | + | 0.103073i | −0.479711 | − | 0.877427i | \(-0.659258\pi\) |
0.196519 | + | 0.980500i | \(0.437036\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 292.909 | + | 1661.17i | 0.0101150 | + | 0.0573650i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −62704.5 | + | 27553.0i | −2.15850 | + | 0.948465i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1821.30 | + | 10329.1i | 0.0624967 | + | 0.354436i | 0.999979 | + | 0.00640472i | \(0.00203870\pi\) |
−0.937483 | + | 0.348032i | \(0.886850\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14794.0 | − | 5384.57i | 0.506041 | − | 0.184184i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 29913.5 | + | 38415.9i | 1.01999 | + | 1.30990i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16369.0 | + | 28351.9i | 0.556393 | + | 0.963701i | 0.997794 | + | 0.0663907i | \(0.0211484\pi\) |
−0.441401 | + | 0.897310i | \(0.645518\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5550.13 | + | 9613.10i | −0.188061 | + | 0.325731i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 17595.7 | + | 54454.5i | 0.594347 | + | 1.83936i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6517.98 | + | 36965.3i | −0.219475 | + | 1.24470i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7251.59 | + | 6084.80i | −0.243415 | + | 0.204250i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −189.314 | − | 391.369i | −0.00633495 | − | 0.0130962i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 89040.8 | + | 32408.2i | 2.97028 | + | 1.08109i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12731.9 | − | 10683.3i | −0.423403 | − | 0.355277i | 0.406053 | − | 0.913850i | \(-0.366905\pi\) |
−0.829456 | + | 0.558572i | \(0.811349\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2644.67 | − | 1658.54i | −0.0876769 | − | 0.0549846i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30671.4 | −1.01369 | −0.506844 | − | 0.862038i | \(-0.669188\pi\) | ||||
−0.506844 | + | 0.862038i | \(0.669188\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1442.55 | −0.0475293 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 66037.5 | + | 41413.9i | 2.16912 | + | 1.36032i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7083.39 | + | 5943.67i | 0.231953 | + | 0.194631i | 0.751355 | − | 0.659899i | \(-0.229401\pi\) |
−0.519402 | + | 0.854530i | \(0.673845\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −35081.9 | − | 12768.8i | −1.14527 | − | 0.416845i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19577.2 | + | 40471.9i | 0.637158 | + | 1.31720i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 39119.3 | − | 32825.0i | 1.26929 | − | 1.06506i | 0.274662 | − | 0.961541i | \(-0.411434\pi\) |
0.994627 | − | 0.103519i | \(-0.0330104\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6409.00 | + | 36347.3i | −0.207318 | + | 1.17576i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 20024.7 | + | 61971.5i | 0.645788 | + | 1.99856i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2841.88 | − | 4922.28i | 0.0913715 | − | 0.158260i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19142.6 | + | 33156.0i | 0.613609 | + | 1.06280i | 0.990627 | + | 0.136595i | \(0.0436160\pi\) |
−0.377018 | + | 0.926206i | \(0.623051\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −23960.0 | − | 30770.1i | −0.765707 | − | 0.983344i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −71483.6 | + | 26017.9i | −2.27757 | + | 0.828968i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1194.72 | + | 6775.57i | 0.0379509 | + | 0.215230i | 0.997886 | − | 0.0649932i | \(-0.0207026\pi\) |
−0.959935 | + | 0.280223i | \(0.909591\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 14770.7 | + | 10841.7i | 0.467792 | + | 0.343361i |
(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 | 108.4.i.a.13.3 | ✓ | 54 | |
3.2 | odd | 2 | 324.4.i.a.253.9 | 54 | |||
27.2 | odd | 18 | 324.4.i.a.73.9 | 54 | |||
27.25 | even | 9 | inner | 108.4.i.a.25.3 | yes | 54 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.4.i.a.13.3 | ✓ | 54 | 1.1 | even | 1 | trivial | |
108.4.i.a.25.3 | yes | 54 | 27.25 | even | 9 | inner | |
324.4.i.a.73.9 | 54 | 27.2 | odd | 18 | |||
324.4.i.a.253.9 | 54 | 3.2 | odd | 2 |