Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,2,Mod(143,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 1, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.w (of order \(8\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.19876631285\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 288) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 431.4 | ||
Character | \(\chi\) | \(=\) | 1152.431 |
Dual form | 1152.2.w.b.719.4 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{8}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.0913223 | + | 0.0378270i | −0.0408406 | + | 0.0169167i | −0.403010 | − | 0.915195i | \(-0.632036\pi\) |
0.362170 | + | 0.932112i | \(0.382036\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.05457 | + | 3.05457i | 1.15452 | + | 1.15452i | 0.985636 | + | 0.168884i | \(0.0540163\pi\) |
0.168884 | + | 0.985636i | \(0.445984\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.25649 | − | 2.17731i | 1.58489 | − | 0.656483i | 0.595712 | − | 0.803198i | \(-0.296870\pi\) |
0.989179 | + | 0.146715i | \(0.0468699\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.57202 | + | 3.79519i | −0.436000 | + | 1.05260i | 0.541317 | + | 0.840818i | \(0.317926\pi\) |
−0.977318 | + | 0.211779i | \(0.932074\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.56471 | −0.622034 | −0.311017 | − | 0.950404i | \(-0.600670\pi\) | ||||
−0.311017 | + | 0.950404i | \(0.600670\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.64058 | − | 1.09376i | −0.605791 | − | 0.250927i | 0.0586367 | − | 0.998279i | \(-0.481325\pi\) |
−0.664428 | + | 0.747353i | \(0.731325\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.03079 | + | 4.03079i | 0.840477 | + | 0.840477i | 0.988921 | − | 0.148443i | \(-0.0474263\pi\) |
−0.148443 | + | 0.988921i | \(0.547426\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.52863 | + | 3.52863i | −0.705725 | + | 0.705725i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.06984 | − | 4.99704i | 0.384360 | − | 0.927927i | −0.606752 | − | 0.794892i | \(-0.707528\pi\) |
0.991111 | − | 0.133035i | \(-0.0424723\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.44203i | − | 0.258996i | −0.991580 | − | 0.129498i | \(-0.958663\pi\) | ||
0.991580 | − | 0.129498i | \(-0.0413366\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.394496 | − | 0.163406i | −0.0666820 | − | 0.0276206i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.07758 | − | 5.01573i | −0.341552 | − | 0.824581i | −0.997559 | − | 0.0698256i | \(-0.977756\pi\) |
0.656007 | − | 0.754755i | \(-0.272244\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.296726 | − | 0.296726i | 0.0463409 | − | 0.0463409i | −0.683557 | − | 0.729897i | \(-0.739568\pi\) |
0.729897 | + | 0.683557i | \(0.239568\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.72382 | + | 6.57588i | 0.415378 | + | 1.00281i | 0.983669 | + | 0.179984i | \(0.0576047\pi\) |
−0.568291 | + | 0.822828i | \(0.692395\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.42367i | 1.08285i | 0.840748 | + | 0.541427i | \(0.182116\pi\) | ||||
−0.840748 | + | 0.541427i | \(0.817884\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.6608i | 1.66583i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.53235 | + | 3.69941i | 0.210484 | + | 0.508153i | 0.993498 | − | 0.113851i | \(-0.0363187\pi\) |
−0.783014 | + | 0.622004i | \(0.786319\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.397674 | + | 0.397674i | −0.0536223 | + | 0.0536223i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.988255 | − | 2.38586i | −0.128660 | − | 0.310612i | 0.846402 | − | 0.532544i | \(-0.178764\pi\) |
−0.975062 | + | 0.221931i | \(0.928764\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.4346 | + | 4.32215i | 1.33601 | + | 0.553395i | 0.932365 | − | 0.361519i | \(-0.117742\pi\) |
0.403649 | + | 0.914914i | \(0.367742\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 0.406051i | − | 0.0503644i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.690522 | − | 1.66707i | 0.0843606 | − | 0.203665i | −0.876070 | − | 0.482184i | \(-0.839844\pi\) |
0.960431 | + | 0.278519i | \(0.0898437\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.97957 | − | 2.97957i | 0.353610 | − | 0.353610i | −0.507841 | − | 0.861451i | \(-0.669556\pi\) |
0.861451 | + | 0.507841i | \(0.169556\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.22401 | + | 9.22401i | 1.07959 | + | 1.07959i | 0.996546 | + | 0.0830429i | \(0.0264638\pi\) |
0.0830429 | + | 0.996546i | \(0.473536\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 22.7071 | + | 9.40558i | 2.58771 | + | 1.07187i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.12181 | 0.126213 | 0.0631065 | − | 0.998007i | \(-0.479899\pi\) | ||||
0.0631065 | + | 0.998007i | \(0.479899\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.13529 | − | 9.98348i | 0.453907 | − | 1.09583i | −0.516916 | − | 0.856036i | \(-0.672920\pi\) |
0.970824 | − | 0.239794i | \(-0.0770798\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.234216 | − | 0.0970152i | 0.0254042 | − | 0.0105228i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.0590 | − | 12.0590i | −1.27825 | − | 1.27825i | −0.941644 | − | 0.336609i | \(-0.890720\pi\) |
−0.336609 | − | 0.941644i | \(-0.609280\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −16.3945 | + | 6.79084i | −1.71862 | + | 0.711874i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.282518 | 0.0289857 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.5545 | −1.88393 | −0.941963 | − | 0.335717i | \(-0.891022\pi\) | ||||
−0.941963 | + | 0.335717i | \(0.891022\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.24603 | − | 2.17298i | 0.521999 | − | 0.216219i | −0.106096 | − | 0.994356i | \(-0.533835\pi\) |
0.628095 | + | 0.778137i | \(0.283835\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.0095 | + | 11.0095i | 1.08479 | + | 1.08479i | 0.996055 | + | 0.0887398i | \(0.0282839\pi\) |
0.0887398 | + | 0.996055i | \(0.471716\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.182628 | + | 0.0756468i | −0.0176553 | + | 0.00731305i | −0.391494 | − | 0.920181i | \(-0.628041\pi\) |
0.373838 | + | 0.927494i | \(0.378041\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.10265 | − | 5.07626i | 0.201398 | − | 0.486217i | −0.790621 | − | 0.612305i | \(-0.790242\pi\) |
0.992019 | + | 0.126088i | \(0.0402423\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.91777 | 0.556697 | 0.278348 | − | 0.960480i | \(-0.410213\pi\) | ||||
0.278348 | + | 0.960480i | \(0.410213\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.520573 | − | 0.215629i | −0.0485437 | − | 0.0201075i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.83410 | − | 7.83410i | −0.718151 | − | 0.718151i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.1118 | − | 15.1118i | 1.37380 | − | 1.37380i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.377900 | − | 0.912331i | 0.0338004 | − | 0.0816014i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.70061i | 0.860790i | 0.902641 | + | 0.430395i | \(0.141626\pi\) | ||||
−0.902641 | + | 0.430395i | \(0.858374\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.7327 | − | 5.27407i | −1.11246 | − | 0.460798i | −0.250678 | − | 0.968070i | \(-0.580654\pi\) |
−0.861786 | + | 0.507273i | \(0.830654\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.72486 | − | 11.4068i | −0.409698 | − | 0.989098i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.62861 | + | 5.62861i | −0.480884 | + | 0.480884i | −0.905414 | − | 0.424530i | \(-0.860439\pi\) |
0.424530 | + | 0.905414i | \(0.360439\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.202389 | − | 0.488610i | −0.0171664 | − | 0.0414434i | 0.915064 | − | 0.403309i | \(-0.132140\pi\) |
−0.932230 | + | 0.361865i | \(0.882140\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 23.3722i | 1.95448i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.534637i | 0.0443992i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.35052 | + | 3.26046i | 0.110639 | + | 0.267107i | 0.969495 | − | 0.245110i | \(-0.0788242\pi\) |
−0.858856 | + | 0.512217i | \(0.828824\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.6492 | − | 13.6492i | 1.11076 | − | 1.11076i | 0.117709 | − | 0.993048i | \(-0.462445\pi\) |
0.993048 | − | 0.117709i | \(-0.0375552\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.0545476 | + | 0.131690i | 0.00438137 | + | 0.0105776i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.4587 | − | 6.40321i | −1.23374 | − | 0.511032i | −0.331987 | − | 0.943284i | \(-0.607719\pi\) |
−0.901753 | + | 0.432252i | \(0.857719\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 24.6247i | 1.94070i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.04288 | − | 14.5888i | 0.473315 | − | 1.14268i | −0.489374 | − | 0.872074i | \(-0.662775\pi\) |
0.962689 | − | 0.270609i | \(-0.0872252\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.58872 | + | 6.58872i | −0.509850 | + | 0.509850i | −0.914480 | − | 0.404630i | \(-0.867400\pi\) |
0.404630 | + | 0.914480i | \(0.367400\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.73986 | − | 2.73986i | −0.210759 | − | 0.210759i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.8204 | − | 7.38143i | −1.35486 | − | 0.561200i | −0.417216 | − | 0.908807i | \(-0.636994\pi\) |
−0.937640 | + | 0.347608i | \(0.886994\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −21.5569 | −1.62955 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.07369 | − | 9.83475i | 0.304482 | − | 0.735084i | −0.695383 | − | 0.718639i | \(-0.744765\pi\) |
0.999865 | − | 0.0164446i | \(-0.00523471\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.06280 | − | 3.33972i | 0.599303 | − | 0.248239i | −0.0623442 | − | 0.998055i | \(-0.519858\pi\) |
0.661647 | + | 0.749815i | \(0.269858\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.379459 | + | 0.379459i | 0.0278984 | + | 0.0278984i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.4814 | + | 5.58417i | −0.985856 | + | 0.408355i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.0520 | −0.944411 | −0.472205 | − | 0.881489i | \(-0.656542\pi\) | ||||
−0.472205 | + | 0.881489i | \(0.656542\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.05926 | −0.220210 | −0.110105 | − | 0.993920i | \(-0.535119\pi\) | ||||
−0.110105 | + | 0.993920i | \(0.535119\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.46774 | + | 2.26481i | −0.389560 | + | 0.161361i | −0.568862 | − | 0.822433i | \(-0.692616\pi\) |
0.179302 | + | 0.983794i | \(0.442616\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.48835 | + | 4.48835i | 0.318170 | + | 0.318170i | 0.848064 | − | 0.529894i | \(-0.177768\pi\) |
−0.529894 | + | 0.848064i | \(0.677768\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 21.5863 | − | 8.94133i | 1.51506 | − | 0.627559i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.0158735 | + | 0.0383220i | −0.00110865 | + | 0.00267652i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.2617 | −1.12484 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.322439 | − | 0.133558i | −0.0221976 | − | 0.00919454i | 0.371557 | − | 0.928410i | \(-0.378824\pi\) |
−0.393755 | + | 0.919216i | \(0.628824\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.497491 | − | 0.497491i | −0.0339286 | − | 0.0339286i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.40478 | − | 4.40478i | 0.299016 | − | 0.299016i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.03178 | − | 9.73358i | 0.271207 | − | 0.654752i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 19.1612i | − | 1.28313i | −0.767068 | − | 0.641566i | \(-0.778285\pi\) | ||
0.767068 | − | 0.641566i | \(-0.221715\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.4451 | − | 8.05441i | −1.29061 | − | 0.534590i | −0.371446 | − | 0.928455i | \(-0.621138\pi\) |
−0.919169 | + | 0.393864i | \(0.871138\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.97193 | − | 16.8317i | −0.460718 | − | 1.11227i | −0.968103 | − | 0.250552i | \(-0.919388\pi\) |
0.507385 | − | 0.861719i | \(-0.330612\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.7768 | − | 16.7768i | 1.09909 | − | 1.09909i | 0.104569 | − | 0.994518i | \(-0.466654\pi\) |
0.994518 | − | 0.104569i | \(-0.0333462\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.280815 | − | 0.677947i | −0.0183183 | − | 0.0442244i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 9.10976i | − | 0.589261i | −0.955611 | − | 0.294631i | \(-0.904803\pi\) | ||
0.955611 | − | 0.294631i | \(-0.0951966\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.39995i | 0.476673i | 0.971183 | + | 0.238336i | \(0.0766020\pi\) | ||||
−0.971183 | + | 0.238336i | \(0.923398\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.441093 | − | 1.06489i | −0.0281804 | − | 0.0680336i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.30210 | − | 8.30210i | 0.528250 | − | 0.528250i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.84250 | + | 11.6908i | 0.305656 | + | 0.737919i | 0.999836 | + | 0.0181174i | \(0.00576726\pi\) |
−0.694180 | + | 0.719802i | \(0.744233\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 29.9641 | + | 12.4115i | 1.88382 | + | 0.780306i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 6.02571i | − | 0.375873i | −0.982181 | − | 0.187937i | \(-0.939820\pi\) | ||
0.982181 | − | 0.187937i | \(-0.0601800\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.97478 | − | 21.6670i | 0.557666 | − | 1.34632i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.79218 | − | 6.79218i | 0.418824 | − | 0.418824i | −0.465974 | − | 0.884798i | \(-0.654296\pi\) |
0.884798 | + | 0.465974i | \(0.154296\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.279875 | − | 0.279875i | −0.0171926 | − | 0.0171926i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.8548 | + | 5.73883i | 0.844740 | + | 0.349903i | 0.762721 | − | 0.646728i | \(-0.223863\pi\) |
0.0820193 | + | 0.996631i | \(0.473863\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.62497 | −0.341692 | −0.170846 | − | 0.985298i | \(-0.554650\pi\) | ||||
−0.170846 | + | 0.985298i | \(0.554650\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.8653 | + | 26.2311i | −0.655201 | + | 1.58179i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.00843 | + | 0.417706i | −0.0605908 | + | 0.0250975i | −0.412773 | − | 0.910834i | \(-0.635440\pi\) |
0.352182 | + | 0.935931i | \(0.385440\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.7589 | − | 21.7589i | −1.29803 | − | 1.29803i | −0.929693 | − | 0.368335i | \(-0.879928\pi\) |
−0.368335 | − | 0.929693i | \(-0.620072\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.3614 | − | 9.26239i | 1.32925 | − | 0.550592i | 0.398807 | − | 0.917035i | \(-0.369424\pi\) |
0.930441 | + | 0.366443i | \(0.119424\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.81274 | 0.107003 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.4223 | −0.613074 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −29.2423 | + | 12.1126i | −1.70835 | + | 0.707623i | −0.708355 | + | 0.705856i | \(0.750562\pi\) |
−0.999998 | + | 0.00176683i | \(0.999438\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.180500 | + | 0.180500i | 0.0105091 | + | 0.0105091i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −21.6341 | + | 8.96114i | −1.25113 | + | 0.518236i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.7664 | + | 28.4066i | −0.678204 | + | 1.63733i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.11641 | −0.0639252 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.7854 | − | 5.71009i | −0.786773 | − | 0.325892i | −0.0471275 | − | 0.998889i | \(-0.515007\pi\) |
−0.739645 | + | 0.672997i | \(0.765007\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.4220 | + | 11.4220i | 0.647684 | + | 0.647684i | 0.952433 | − | 0.304749i | \(-0.0985725\pi\) |
−0.304749 | + | 0.952433i | \(0.598573\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.24707 | − | 2.24707i | 0.127012 | − | 0.127012i | −0.640743 | − | 0.767755i | \(-0.721374\pi\) |
0.767755 | + | 0.640743i | \(0.221374\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.05906 | + | 2.55679i | −0.0594826 | + | 0.143604i | −0.950826 | − | 0.309724i | \(-0.899763\pi\) |
0.891344 | + | 0.453328i | \(0.149763\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 30.7736i | − | 1.72299i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.77233 | + | 2.80519i | 0.376823 | + | 0.156085i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.84475 | − | 18.9389i | −0.435148 | − | 1.05054i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −22.6761 | + | 22.6761i | −1.25018 | + | 1.25018i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.123439 | + | 0.298008i | 0.00678481 | + | 0.0163800i | 0.927236 | − | 0.374478i | \(-0.122178\pi\) |
−0.920451 | + | 0.390858i | \(0.872178\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.178361i | 0.00974489i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 16.5067i | − | 0.899179i | −0.893235 | − | 0.449590i | \(-0.851570\pi\) | ||
0.893235 | − | 0.449590i | \(-0.148430\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.13974 | − | 7.58001i | −0.170027 | − | 0.410481i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.2368 | + | 14.2368i | −0.768716 | + | 0.768716i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.96248 | + | 14.3947i | 0.320083 | + | 0.772748i | 0.999248 | + | 0.0387633i | \(0.0123418\pi\) |
−0.679166 | + | 0.733985i | \(0.737658\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.57618 | + | 0.652873i | 0.0843707 | + | 0.0349475i | 0.424470 | − | 0.905442i | \(-0.360461\pi\) |
−0.340099 | + | 0.940390i | \(0.610461\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 18.7091i | − | 0.995786i | −0.867239 | − | 0.497893i | \(-0.834107\pi\) | ||
0.867239 | − | 0.497893i | \(-0.165893\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.159393 | + | 0.384810i | −0.00845972 | + | 0.0204236i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.5065 | − | 23.5065i | 1.24062 | − | 1.24062i | 0.280882 | − | 0.959742i | \(-0.409373\pi\) |
0.959742 | − | 0.280882i | \(-0.0906270\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.65868 | − | 7.65868i | −0.403088 | − | 0.403088i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.19127 | − | 0.493442i | −0.0623542 | − | 0.0258279i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.95190 | 0.154088 | 0.0770440 | − | 0.997028i | \(-0.475452\pi\) | ||||
0.0770440 | + | 0.997028i | \(0.475452\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.61945 | + | 15.9808i | −0.343665 | + | 0.829680i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.7552 | + | 8.18287i | −1.02289 | + | 0.423693i | −0.830140 | − | 0.557556i | \(-0.811739\pi\) |
−0.192746 | + | 0.981249i | \(0.561739\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.7109 | + | 15.7109i | 0.809152 | + | 0.809152i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.26476 | + | 1.76652i | −0.219066 | + | 0.0907402i | −0.489518 | − | 0.871993i | \(-0.662827\pi\) |
0.270451 | + | 0.962734i | \(0.412827\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.45328 | −0.483040 | −0.241520 | − | 0.970396i | \(-0.577646\pi\) | ||||
−0.241520 | + | 0.970396i | \(0.577646\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.42945 | −0.123816 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.8554 | + | 8.63860i | −1.05741 | + | 0.437994i | −0.842532 | − | 0.538646i | \(-0.818936\pi\) |
−0.214880 | + | 0.976640i | \(0.568936\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.3378 | − | 10.3378i | −0.522806 | − | 0.522806i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.102446 | + | 0.0424345i | −0.00515461 | + | 0.00213511i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.29268 | − | 7.94922i | 0.165255 | − | 0.398960i | −0.819460 | − | 0.573137i | \(-0.805726\pi\) |
0.984714 | + | 0.174177i | \(0.0557264\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.5903 | 1.62748 | 0.813740 | − | 0.581229i | \(-0.197428\pi\) | ||||
0.813740 | + | 0.581229i | \(0.197428\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.47278 | + | 2.26690i | 0.272619 | + | 0.112922i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.8416 | − | 21.8416i | −1.08265 | − | 1.08265i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.41708 | − | 5.41708i | 0.267858 | − | 0.267858i | −0.560379 | − | 0.828236i | \(-0.689344\pi\) |
0.828236 | + | 0.560379i | \(0.189344\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.26908 | − | 10.3065i | 0.210068 | − | 0.507149i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.06814i | 0.0524329i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.0298 | + | 9.12504i | 1.07623 | + | 0.445787i | 0.849184 | − | 0.528097i | \(-0.177094\pi\) |
0.227042 | + | 0.973885i | \(0.427094\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.82553 | + | 6.82144i | 0.137708 | + | 0.332457i | 0.977656 | − | 0.210210i | \(-0.0674147\pi\) |
−0.839948 | + | 0.542667i | \(0.817415\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.04991 | − | 9.04991i | 0.438985 | − | 0.438985i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.6709 | + | 45.0756i | 0.903549 | + | 2.18136i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 6.73112i | − | 0.324226i | −0.986772 | − | 0.162113i | \(-0.948169\pi\) | ||
0.986772 | − | 0.162113i | \(-0.0518310\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 12.1160i | − | 0.582257i | −0.956684 | − | 0.291129i | \(-0.905969\pi\) | ||
0.956684 | − | 0.291129i | \(-0.0940308\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.23489 | − | 15.0524i | −0.298255 | − | 0.720052i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.0767 | + | 14.0767i | −0.671843 | + | 0.671843i | −0.958141 | − | 0.286298i | \(-0.907575\pi\) |
0.286298 | + | 0.958141i | \(0.407575\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.5313 | − | 35.0817i | −0.690404 | − | 1.66678i | −0.743965 | − | 0.668218i | \(-0.767057\pi\) |
0.0535615 | − | 0.998565i | \(-0.482943\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.55741 | + | 0.645102i | 0.0738285 | + | 0.0305808i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.9809i | 1.22611i | 0.790039 | + | 0.613056i | \(0.210060\pi\) | ||||
−0.790039 | + | 0.613056i | \(0.789940\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.913674 | − | 2.20580i | 0.0430232 | − | 0.103867i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.24031 | − | 1.24031i | 0.0581467 | − | 0.0581467i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.23785 | + | 6.23785i | 0.291794 | + | 0.291794i | 0.837789 | − | 0.545994i | \(-0.183848\pi\) |
−0.545994 | + | 0.837789i | \(0.683848\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.3278 | − | 9.66269i | −1.08648 | − | 0.450036i | −0.233704 | − | 0.972308i | \(-0.575085\pi\) |
−0.852779 | + | 0.522271i | \(0.825085\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.99595 | −0.185707 | −0.0928537 | − | 0.995680i | \(-0.529599\pi\) | ||||
−0.0928537 | + | 0.995680i | \(0.529599\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.26272 | − | 17.5338i | 0.336079 | − | 0.811366i | −0.662006 | − | 0.749499i | \(-0.730294\pi\) |
0.998084 | − | 0.0618671i | \(-0.0197055\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.20142 | − | 2.98293i | 0.332531 | − | 0.137739i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 28.6354 | + | 28.6354i | 1.31666 | + | 1.31666i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.1771 | − | 5.45814i | 0.604607 | − | 0.250437i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.7665 | 0.994537 | 0.497268 | − | 0.867597i | \(-0.334336\pi\) | ||||
0.497268 | + | 0.867597i | \(0.334336\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.3017 | 1.01687 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.69444 | − | 0.701861i | 0.0769407 | − | 0.0318699i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.10128 | + | 9.10128i | 0.412419 | + | 0.412419i | 0.882580 | − | 0.470162i | \(-0.155804\pi\) |
−0.470162 | + | 0.882580i | \(0.655804\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.2645 | − | 6.32276i | 0.688876 | − | 0.285342i | −0.0106556 | − | 0.999943i | \(-0.503392\pi\) |
0.699532 | + | 0.714601i | \(0.253392\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.30855 | + | 12.8160i | −0.239085 | + | 0.577202i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 18.2026 | 0.816500 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.2595 | + | 13.3623i | 1.44413 | + | 0.598180i | 0.960796 | − | 0.277255i | \(-0.0894246\pi\) |
0.483337 | + | 0.875434i | \(0.339425\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.34111 | − | 7.34111i | −0.327324 | − | 0.327324i | 0.524244 | − | 0.851568i | \(-0.324348\pi\) |
−0.851568 | + | 0.524244i | \(0.824348\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.396882 | + | 0.396882i | −0.0176610 | + | 0.0176610i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.55299 | + | 18.2345i | −0.334780 | + | 0.808231i | 0.663419 | + | 0.748248i | \(0.269105\pi\) |
−0.998199 | + | 0.0599832i | \(0.980895\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 56.3508i | 2.49281i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.42186 | − | 0.588955i | −0.0626548 | − | 0.0259525i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.1636 | + | 39.0225i | 0.710876 | + | 1.71621i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.3209 | − | 26.3209i | 1.15314 | − | 1.15314i | 0.167218 | − | 0.985920i | \(-0.446522\pi\) |
0.985920 | − | 0.167218i | \(-0.0534785\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.50275 | − | 13.2848i | −0.240619 | − | 0.580905i | 0.756726 | − | 0.653732i | \(-0.226798\pi\) |
−0.997345 | + | 0.0728276i | \(0.976798\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.69839i | 0.161104i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.49450i | 0.412805i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.659674 | + | 1.59259i | 0.0285737 | + | 0.0689829i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.0138165 | − | 0.0138165i | 0.000597339 | − | 0.000597339i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 25.3892 | + | 61.2950i | 1.09359 | + | 2.64016i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.34772 | + | 0.558245i | 0.0579431 | + | 0.0240008i | 0.411467 | − | 0.911425i | \(-0.365017\pi\) |
−0.353524 | + | 0.935426i | \(0.615017\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.543113i | 0.0232644i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.11417 | + | 7.51828i | −0.133152 | + | 0.321458i | −0.976367 | − | 0.216119i | \(-0.930660\pi\) |
0.843215 | + | 0.537577i | \(0.180660\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.9312 | + | 10.9312i | −0.465683 | + | 0.465683i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.42664 | + | 3.42664i | 0.145715 | + | 0.145715i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.3810 | + | 4.29993i | 0.439855 | + | 0.182194i | 0.591610 | − | 0.806224i | \(-0.298492\pi\) |
−0.151755 | + | 0.988418i | \(0.548492\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −29.2386 | −1.23666 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.95005 | + | 4.70784i | −0.0821848 | + | 0.198412i | −0.959630 | − | 0.281265i | \(-0.909246\pi\) |
0.877445 | + | 0.479677i | \(0.159246\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.540424 | + | 0.223851i | −0.0227358 | + | 0.00941749i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.12423 | + | 3.12423i | 0.130974 | + | 0.130974i | 0.769555 | − | 0.638581i | \(-0.220478\pi\) |
−0.638581 | + | 0.769555i | \(0.720478\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.4029 | + | 13.8360i | −1.39787 | + | 0.579017i | −0.949198 | − | 0.314680i | \(-0.898103\pi\) |
−0.448672 | + | 0.893697i | \(0.648103\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −28.4463 | −1.18629 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.0315 | −0.584141 | −0.292070 | − | 0.956397i | \(-0.594344\pi\) | ||||
−0.292070 | + | 0.956397i | \(0.594344\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 43.1268 | − | 17.8637i | 1.78920 | − | 0.741112i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.1095 | + | 16.1095i | 0.667188 | + | 0.667188i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.0165 | + | 4.97740i | −0.495975 | + | 0.205439i | −0.616627 | − | 0.787255i | \(-0.711501\pi\) |
0.120652 | + | 0.992695i | \(0.461501\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.57724 | + | 3.80780i | −0.0649891 | + | 0.156898i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.6528 | 0.724914 | 0.362457 | − | 0.932000i | \(-0.381938\pi\) | ||||
0.362457 | + | 0.932000i | \(0.381938\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.01177 | + | 0.419088i | 0.0414785 | + | 0.0171809i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.25995 | + | 5.25995i | 0.214916 | + | 0.214916i | 0.806352 | − | 0.591436i | \(-0.201439\pi\) |
−0.591436 | + | 0.806352i | \(0.701439\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.54574 | − | 6.54574i | 0.267006 | − | 0.267006i | −0.560886 | − | 0.827893i | \(-0.689540\pi\) |
0.827893 | + | 0.560886i | \(0.189540\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.808413 | + | 1.95168i | −0.0328667 | + | 0.0793472i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.72276i | 0.0699248i | 0.999389 | + | 0.0349624i | \(0.0111311\pi\) | ||||
−0.999389 | + | 0.0349624i | \(0.988869\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −28.1743 | − | 11.6702i | −1.13981 | − | 0.472125i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.6267 | + | 40.1405i | 0.671547 | + | 1.62126i | 0.778982 | + | 0.627046i | \(0.215736\pi\) |
−0.107435 | + | 0.994212i | \(0.534264\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.78933 | − | 7.78933i | 0.313587 | − | 0.313587i | −0.532711 | − | 0.846297i | \(-0.678827\pi\) |
0.846297 | + | 0.532711i | \(0.178827\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.0171 | − | 26.5976i | −0.442814 | − | 1.06905i | −0.974957 | − | 0.222394i | \(-0.928613\pi\) |
0.532143 | − | 0.846655i | \(-0.321387\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 73.6703i | − | 2.95154i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 24.8535i | − | 0.994141i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.32840 | + | 12.8639i | 0.212457 | + | 0.512917i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.0548 | − | 21.0548i | 0.838177 | − | 0.838177i | −0.150442 | − | 0.988619i | \(-0.548070\pi\) |
0.988619 | + | 0.150442i | \(0.0480696\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.366944 | − | 0.885882i | −0.0145617 | − | 0.0351552i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −44.2551 | − | 18.3311i | −1.75345 | − | 0.726303i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.65123i | 0.223210i | 0.993753 | + | 0.111605i | \(0.0355992\pi\) | ||||
−0.993753 | + | 0.111605i | \(0.964401\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.0022 | + | 41.0470i | −0.670502 | + | 1.61874i | 0.110256 | + | 0.993903i | \(0.464833\pi\) |
−0.780759 | + | 0.624833i | \(0.785167\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.0151270 | + | 0.0151270i | −0.000594703 | + | 0.000594703i | −0.707404 | − | 0.706809i | \(-0.750134\pi\) |
0.706809 | + | 0.707404i | \(0.250134\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.3895 | − | 10.3895i | −0.407824 | − | 0.407824i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −28.8575 | − | 11.9531i | −1.12928 | − | 0.467763i | −0.261744 | − | 0.965137i | \(-0.584297\pi\) |
−0.867536 | + | 0.497375i | \(0.834297\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.36228 | 0.0532289 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.25678 | + | 17.5194i | −0.282684 | + | 0.682459i | −0.999896 | − | 0.0143952i | \(-0.995418\pi\) |
0.717212 | + | 0.696855i | \(0.245418\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.6310 | + | 6.47456i | −0.607974 | + | 0.251831i | −0.665362 | − | 0.746521i | \(-0.731723\pi\) |
0.0573877 | + | 0.998352i | \(0.481723\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.862971 | + | 0.862971i | 0.0334646 | + | 0.0334646i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.4851 | − | 11.7989i | 1.10295 | − | 0.456856i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 64.2600 | 2.48073 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.5987 | 1.02530 | 0.512652 | − | 0.858596i | \(-0.328663\pi\) | ||||
0.512652 | + | 0.858596i | \(0.328663\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.3000 | − | 10.8938i | 1.01079 | − | 0.418683i | 0.185047 | − | 0.982730i | \(-0.440756\pi\) |
0.825743 | + | 0.564047i | \(0.190756\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −56.6761 | − | 56.6761i | −2.17503 | − | 2.17503i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.9528 | + | 12.4069i | −1.14611 | + | 0.474735i | −0.873228 | − | 0.487312i | \(-0.837978\pi\) |
−0.272884 | + | 0.962047i | \(0.587978\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.301105 | − | 0.726931i | 0.0115046 | − | 0.0277746i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.4489 | −0.626652 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.94272 | + | 4.11841i | 0.378239 | + | 0.156672i | 0.563699 | − | 0.825980i | \(-0.309378\pi\) |
−0.185460 | + | 0.982652i | \(0.559378\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.0369653 | + | 0.0369653i | 0.00140217 | + | 0.00140217i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.761018 | + | 0.761018i | −0.0288256 | + | 0.0288256i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.59430 | + | 13.5058i | −0.211294 | + | 0.510108i | −0.993623 | − | 0.112757i | \(-0.964032\pi\) |
0.782329 | + | 0.622866i | \(0.214032\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.5168i | 0.585228i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 22.6619 | + | 9.38686i | 0.852288 | + | 0.353029i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.92207 | + | 11.8829i | 0.184852 | + | 0.446273i | 0.988955 | − | 0.148218i | \(-0.0473537\pi\) |
−0.804102 | + | 0.594491i | \(0.797354\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.81252 | − | 5.81252i | 0.217680 | − | 0.217680i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.884098 | − | 2.13440i | −0.0330634 | − | 0.0798221i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.1029i | 0.600537i | 0.953855 | + | 0.300268i | \(0.0970762\pi\) | ||||
−0.953855 | + | 0.300268i | \(0.902924\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 67.2584i | 2.50483i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10.3290 | + | 24.9364i | 0.383609 | + | 0.926113i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.0560 | + | 21.0560i | −0.780923 | + | 0.780923i | −0.979987 | − | 0.199064i | \(-0.936210\pi\) |
0.199064 | + | 0.979987i | \(0.436210\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.98581 | − | 16.8652i | −0.258379 | − | 0.623783i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 41.2426 | + | 17.0832i | 1.52333 | + | 0.630984i | 0.978255 | − | 0.207404i | \(-0.0665015\pi\) |
0.545074 | + | 0.838388i | \(0.316501\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 10.2664i | − | 0.378168i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.2262 | + | 27.1024i | −0.412962 | + | 0.996977i | 0.571377 | + | 0.820688i | \(0.306409\pi\) |
−0.984338 | + | 0.176290i | \(0.943591\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.8059 | − | 15.8059i | 0.579863 | − | 0.579863i | −0.355003 | − | 0.934865i | \(-0.615520\pi\) |
0.934865 | + | 0.355003i | \(0.115520\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.246666 | − | 0.246666i | −0.00903715 | − | 0.00903715i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.788918 | − | 0.326780i | −0.0288264 | − | 0.0119403i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.4955 | 0.455969 | 0.227984 | − | 0.973665i | \(-0.426787\pi\) | ||||
0.227984 | + | 0.973665i | \(0.426787\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.730170 | + | 1.76279i | −0.0265736 | + | 0.0641544i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.0398 | − | 12.4429i | 1.09182 | − | 0.452245i | 0.237176 | − | 0.971467i | \(-0.423778\pi\) |
0.854639 | + | 0.519222i | \(0.173778\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.5032 | − | 15.5032i | −0.561992 | − | 0.561992i | 0.367881 | − | 0.929873i | \(-0.380083\pi\) |
−0.929873 | + | 0.367881i | \(0.880083\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21.9285 | − | 9.08308i | 0.793865 | − | 0.328830i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.6084 | 0.383046 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.08253 | −0.255403 | −0.127701 | − | 0.991813i | \(-0.540760\pi\) | ||||
−0.127701 | + | 0.991813i | \(0.540760\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30.3534 | + | 12.5728i | −1.09173 | + | 0.452211i | −0.854611 | − | 0.519268i | \(-0.826204\pi\) |
−0.237123 | + | 0.971480i | \(0.576204\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.08838 | + | 5.08838i | 0.182780 | + | 0.182780i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.10808 | + | 0.458981i | −0.0397011 | + | 0.0164447i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.17464 | − | 22.1495i | 0.328294 | − | 0.792573i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.65394 | 0.0590316 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.1276 | + | 15.3788i | 1.32346 | + | 0.548194i | 0.928782 | − | 0.370627i | \(-0.120857\pi\) |
0.394675 | + | 0.918821i | \(0.370857\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.0763 | + | 18.0763i | 0.642718 | + | 0.642718i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.8068 | + | 32.8068i | −1.16500 | + | 1.16500i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.87919 | + | 4.53677i | −0.0665644 | + | 0.160701i | −0.953661 | − | 0.300883i | \(-0.902719\pi\) |
0.887097 | + | 0.461584i | \(0.152719\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 19.0396i | − | 0.673572i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 68.5694 | + | 28.4024i | 2.41976 | + | 1.00230i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.931476 | − | 2.24878i | −0.0328302 | − | 0.0792592i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30.6738 | + | 30.6738i | −1.07843 | + | 1.07843i | −0.0817820 | + | 0.996650i | \(0.526061\pi\) |
−0.996650 | + | 0.0817820i | \(0.973939\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.57082 | + | 6.20650i | 0.0902736 | + | 0.217940i | 0.962567 | − | 0.271042i | \(-0.0873683\pi\) |
−0.872294 | + | 0.488982i | \(0.837368\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.56087i | 0.0546748i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 20.3434i | − | 0.711724i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.97965 | − | 21.6788i | −0.313392 | − | 0.756595i | −0.999575 | − | 0.0291659i | \(-0.990715\pi\) |
0.686183 | − | 0.727429i | \(-0.259285\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.8793 | + | 17.8793i | −0.623234 | + | 0.623234i | −0.946357 | − | 0.323123i | \(-0.895267\pi\) |
0.323123 | + | 0.946357i | \(0.395267\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15.5945 | − | 37.6486i | −0.542275 | − | 1.30917i | −0.923114 | − | 0.384527i | \(-0.874365\pi\) |
0.380838 | − | 0.924642i | \(-0.375635\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −46.3584 | − | 19.2023i | −1.61009 | − | 0.666922i | −0.617296 | − | 0.786731i | \(-0.711772\pi\) |
−0.992797 | + | 0.119808i | \(0.961772\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 29.9067i | − | 1.03620i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.352466 | − | 0.850928i | 0.0121976 | − | 0.0294476i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −33.5966 | + | 33.5966i | −1.15988 | + | 1.15988i | −0.175383 | + | 0.984500i | \(0.556116\pi\) |
−0.984500 | + | 0.175383i | \(0.943884\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.180047 | − | 0.180047i | −0.00620852 | − | 0.00620852i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.353851 | + | 0.146570i | 0.0121729 | + | 0.00504216i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 92.3203 | 3.17216 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.8430 | − | 28.5916i | 0.405974 | − | 0.980108i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.0647873 | + | 0.0268358i | −0.00221827 | + | 0.000918839i | −0.383792 | − | 0.923419i | \(-0.625382\pi\) |
0.381574 | + | 0.924338i | \(0.375382\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.9971 | + | 22.9971i | 0.785567 | + | 0.785567i | 0.980764 | − | 0.195197i | \(-0.0625347\pi\) |
−0.195197 | + | 0.980764i | \(0.562535\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.9596 | − | 6.19647i | 0.510415 | − | 0.211421i | −0.112586 | − | 0.993642i | \(-0.535913\pi\) |
0.623001 | + | 0.782221i | \(0.285913\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −20.2047 | −0.687775 | −0.343888 | − | 0.939011i | \(-0.611744\pi\) | ||||
−0.343888 | + | 0.939011i | \(0.611744\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.90661 | 0.0648268 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.89676 | − | 2.44252i | 0.200034 | − | 0.0828567i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.24133 | + | 5.24133i | 0.177596 | + | 0.177596i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.94110 | − | 1.63246i | 0.133234 | − | 0.0551872i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.55444 | − | 20.6523i | 0.288863 | − | 0.697377i | −0.711121 | − | 0.703070i | \(-0.751812\pi\) |
0.999984 | + | 0.00569289i | \(0.00181211\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.9972 | −1.01063 | −0.505315 | − | 0.862935i | \(-0.668624\pi\) | ||||
−0.505315 | + | 0.862935i | \(0.668624\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.2360 | − | 11.6957i | −0.950217 | − | 0.393593i | −0.146905 | − | 0.989151i | \(-0.546931\pi\) |
−0.803312 | + | 0.595558i | \(0.796931\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.07846 | + | 4.07846i | 0.136941 | + | 0.136941i | 0.772254 | − | 0.635313i | \(-0.219129\pi\) |
−0.635313 | + | 0.772254i | \(0.719129\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −29.6312 | + | 29.6312i | −0.993799 | + | 0.993799i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.11975 | − | 19.6028i | 0.271717 | − | 0.655983i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.05223i | 0.0351721i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.20588 | − | 2.98477i | −0.240329 | − | 0.0995477i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.93003 | − | 9.48792i | −0.130928 | − | 0.316088i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.609982 | + | 0.609982i | −0.0202765 | + | 0.0202765i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.3711 | − | 32.2808i | −0.443981 | − | 1.07187i | −0.974539 | − | 0.224217i | \(-0.928018\pi\) |
0.530558 | − | 0.847649i | \(-0.321982\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.1517i | 0.998971i | 0.866322 | + | 0.499486i | \(0.166478\pi\) | ||||
−0.866322 | + | 0.499486i | \(0.833522\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 61.4819i | − | 2.03475i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −22.7830 | − | 55.0031i | −0.752362 | − | 1.81636i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.45081 | − | 1.45081i | 0.0478579 | − | 0.0478579i | −0.682773 | − | 0.730631i | \(-0.739226\pi\) |
0.730631 | + | 0.682773i | \(0.239226\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.62411 | + | 15.9920i | 0.218035 | + | 0.526383i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25.0296 | + | 10.3676i | 0.822969 | + | 0.340885i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 52.1840i | − | 1.71210i | −0.516890 | − | 0.856052i | \(-0.672911\pi\) | ||
0.516890 | − | 0.856052i | \(-0.327089\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.7542 | − | 30.7914i | 0.418002 | − | 1.00915i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.01992 | − | 1.01992i | 0.0333549 | − | 0.0333549i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.45171 | + | 1.45171i | 0.0474253 | + | 0.0474253i | 0.730422 | − | 0.682996i | \(-0.239324\pi\) |
−0.682996 | + | 0.730422i | \(0.739324\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.19665 | + | 1.32409i | 0.104208 | + | 0.0431642i | 0.434178 | − | 0.900827i | \(-0.357039\pi\) |
−0.329971 | + | 0.943991i | \(0.607039\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.39208 | 0.0778969 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.34992 | − | 10.5016i | 0.141353 | − | 0.341257i | −0.837310 | − | 0.546729i | \(-0.815873\pi\) |
0.978663 | + | 0.205472i | \(0.0658728\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −49.5073 | + | 20.5066i | −1.60707 | + | 0.665672i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.74508 | − | 8.74508i | −0.283281 | − | 0.283281i | 0.551135 | − | 0.834416i | \(-0.314195\pi\) |
−0.834416 | + | 0.551135i | \(0.814195\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.19194 | − | 0.493718i | 0.0385703 | − | 0.0159763i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −34.3860 | −1.11038 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.9206 | 0.932921 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.279378 | − | 0.115722i | 0.00899351 | − | 0.00372523i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.3193 | − | 30.3193i | −0.975003 | − | 0.975003i | 0.0246926 | − | 0.999695i | \(-0.492139\pi\) |
−0.999695 | + | 0.0246926i | \(0.992139\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.2589 | − | 20.8179i | 1.61288 | − | 0.668078i | 0.619722 | − | 0.784822i | \(-0.287246\pi\) |
0.993162 | + | 0.116743i | \(0.0372455\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.874284 | − | 2.11071i | 0.0280283 | − | 0.0676662i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −28.6269 | −0.915857 | −0.457928 | − | 0.888989i | \(-0.651408\pi\) | ||||
−0.457928 | + | 0.888989i | \(0.651408\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −89.6443 | − | 37.1319i | −2.86505 | − | 1.18674i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.81670 | + | 3.81670i | 0.121734 | + | 0.121734i | 0.765349 | − | 0.643615i | \(-0.222566\pi\) |
−0.643615 | + | 0.765349i | \(0.722566\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.413656 | − | 0.413656i | 0.0131802 | − | 0.0131802i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15.5268 | + | 37.4851i | −0.493725 | + | 1.19196i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 27.6845i | − | 0.879426i | −0.898138 | − | 0.439713i | \(-0.855080\pi\) | ||
0.898138 | − | 0.439713i | \(-0.144920\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.579667 | − | 0.240106i | −0.0183767 | − | 0.00761187i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.51070 | − | 13.3040i | −0.174526 | − | 0.421342i | 0.812277 | − | 0.583273i | \(-0.198228\pi\) |
−0.986802 | + | 0.161930i | \(0.948228\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1152.2.w.b.431.4 | 32 | ||
3.2 | odd | 2 | 1152.2.w.a.431.5 | 32 | |||
4.3 | odd | 2 | 288.2.w.a.35.3 | ✓ | 32 | ||
12.11 | even | 2 | 288.2.w.b.35.6 | yes | 32 | ||
32.11 | odd | 8 | 1152.2.w.a.719.5 | 32 | |||
32.21 | even | 8 | 288.2.w.b.107.6 | yes | 32 | ||
96.11 | even | 8 | inner | 1152.2.w.b.719.4 | 32 | ||
96.53 | odd | 8 | 288.2.w.a.107.3 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.2.w.a.35.3 | ✓ | 32 | 4.3 | odd | 2 | ||
288.2.w.a.107.3 | yes | 32 | 96.53 | odd | 8 | ||
288.2.w.b.35.6 | yes | 32 | 12.11 | even | 2 | ||
288.2.w.b.107.6 | yes | 32 | 32.21 | even | 8 | ||
1152.2.w.a.431.5 | 32 | 3.2 | odd | 2 | |||
1152.2.w.a.719.5 | 32 | 32.11 | odd | 8 | |||
1152.2.w.b.431.4 | 32 | 1.1 | even | 1 | trivial | ||
1152.2.w.b.719.4 | 32 | 96.11 | even | 8 | inner |