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 | 719.2 | ||
Character | \(\chi\) | \(=\) | 1152.719 |
Dual form | 1152.2.w.a.431.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{8}\right)\) |
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 | ||||||||
\(5\) | −1.78959 | − | 0.741273i | −0.800329 | − | 0.331507i | −0.0552409 | − | 0.998473i | \(-0.517593\pi\) |
−0.745088 | + | 0.666966i | \(0.767593\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.33709 | − | 2.33709i | 0.883337 | − | 0.883337i | −0.110535 | − | 0.993872i | \(-0.535256\pi\) |
0.993872 | + | 0.110535i | \(0.0352564\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.683332 | − | 0.283045i | −0.206032 | − | 0.0853413i | 0.277281 | − | 0.960789i | \(-0.410567\pi\) |
−0.483313 | + | 0.875448i | \(0.660567\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.43602 | + | 5.88107i | 0.675630 | + | 1.63112i | 0.771888 | + | 0.635759i | \(0.219313\pi\) |
−0.0962579 | + | 0.995356i | \(0.530687\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.967834 | −0.234734 | −0.117367 | − | 0.993089i | \(-0.537445\pi\) | ||||
−0.117367 | + | 0.993089i | \(0.537445\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.52772 | − | 1.04702i | 0.579899 | − | 0.240202i | −0.0733991 | − | 0.997303i | \(-0.523385\pi\) |
0.653298 | + | 0.757100i | \(0.273385\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.00283 | − | 5.00283i | 1.04316 | − | 1.04316i | 0.0441370 | − | 0.999025i | \(-0.485946\pi\) |
0.999025 | − | 0.0441370i | \(-0.0140538\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.882385 | − | 0.882385i | −0.176477 | − | 0.176477i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.563403 | + | 1.36018i | 0.104621 | + | 0.252578i | 0.967518 | − | 0.252802i | \(-0.0813522\pi\) |
−0.862897 | + | 0.505380i | \(0.831352\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.28582i | − | 1.30857i | −0.756247 | − | 0.654286i | \(-0.772969\pi\) | ||
0.756247 | − | 0.654286i | \(-0.227031\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.91486 | + | 2.45001i | −0.999793 | + | 0.414128i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.26572 | − | 7.88415i | 0.536881 | − | 1.29615i | −0.390008 | − | 0.920812i | \(-0.627528\pi\) |
0.926889 | − | 0.375335i | \(-0.122472\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.80014 | − | 6.80014i | −1.06200 | − | 1.06200i | −0.997946 | − | 0.0640576i | \(-0.979596\pi\) |
−0.0640576 | − | 0.997946i | \(-0.520404\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.36517 | + | 3.29581i | −0.208187 | + | 0.502607i | −0.993138 | − | 0.116951i | \(-0.962688\pi\) |
0.784951 | + | 0.619558i | \(0.212688\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 3.69279i | − | 0.538649i | −0.963050 | − | 0.269324i | \(-0.913200\pi\) | ||
0.963050 | − | 0.269324i | \(-0.0868004\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 3.92399i | − | 0.560570i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.85469 | + | 4.47761i | −0.254761 | + | 0.615047i | −0.998577 | − | 0.0533378i | \(-0.983014\pi\) |
0.743816 | + | 0.668385i | \(0.233014\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.01307 | + | 1.01307i | 0.136602 | + | 0.136602i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.05615 | − | 9.79242i | 0.528066 | − | 1.27486i | −0.404722 | − | 0.914440i | \(-0.632632\pi\) |
0.932788 | − | 0.360425i | \(-0.117368\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.8180 | − | 4.48097i | 1.38511 | − | 0.573730i | 0.439265 | − | 0.898358i | \(-0.355239\pi\) |
0.945842 | + | 0.324628i | \(0.105239\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 12.3305i | − | 1.52941i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.49290 | − | 3.60418i | −0.182387 | − | 0.440320i | 0.806071 | − | 0.591819i | \(-0.201590\pi\) |
−0.988457 | + | 0.151499i | \(0.951590\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.85675 | + | 9.85675i | 1.16978 | + | 1.16978i | 0.982261 | + | 0.187520i | \(0.0600450\pi\) |
0.187520 | + | 0.982261i | \(0.439955\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.81362 | + | 4.81362i | −0.563391 | + | 0.563391i | −0.930269 | − | 0.366878i | \(-0.880427\pi\) |
0.366878 | + | 0.930269i | \(0.380427\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.25851 | + | 0.935506i | −0.257381 | + | 0.106611i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.0160 | 1.23940 | 0.619700 | − | 0.784839i | \(-0.287254\pi\) | ||||
0.619700 | + | 0.784839i | \(0.287254\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.15064 | − | 2.77789i | −0.126299 | − | 0.304913i | 0.848064 | − | 0.529894i | \(-0.177768\pi\) |
−0.974363 | + | 0.224981i | \(0.927768\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.73203 | + | 0.717429i | 0.187865 | + | 0.0778161i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.82624 | − | 6.82624i | 0.723580 | − | 0.723580i | −0.245753 | − | 0.969333i | \(-0.579035\pi\) |
0.969333 | + | 0.245753i | \(0.0790352\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.4378 | + | 8.05140i | 2.03763 | + | 0.844016i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.29971 | −0.543739 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.67976 | 0.779762 | 0.389881 | − | 0.920865i | \(-0.372516\pi\) | ||||
0.389881 | + | 0.920865i | \(0.372516\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.05030 | + | 0.435049i | 0.104509 | + | 0.0432890i | 0.434325 | − | 0.900756i | \(-0.356987\pi\) |
−0.329816 | + | 0.944045i | \(0.606987\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.06356 | + | 7.06356i | −0.695993 | + | 0.695993i | −0.963544 | − | 0.267551i | \(-0.913786\pi\) |
0.267551 | + | 0.963544i | \(0.413786\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.1346 | − | 6.68316i | −1.55979 | − | 0.646086i | −0.574737 | − | 0.818338i | \(-0.694895\pi\) |
−0.985053 | + | 0.172253i | \(0.944895\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.771406 | + | 1.86234i | 0.0738873 | + | 0.178380i | 0.956508 | − | 0.291706i | \(-0.0942230\pi\) |
−0.882621 | + | 0.470086i | \(0.844223\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.726213 | 0.0683163 | 0.0341582 | − | 0.999416i | \(-0.489125\pi\) | ||||
0.0341582 | + | 0.999416i | \(0.489125\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.6615 | + | 5.24456i | −1.18069 | + | 0.489058i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.26192 | + | 2.26192i | −0.207350 | + | 0.207350i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.39135 | − | 7.39135i | −0.671941 | − | 0.671941i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.63138 | + | 11.1811i | 0.414243 | + | 1.00007i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 11.5686i | − | 1.02654i | −0.858226 | − | 0.513272i | \(-0.828433\pi\) | ||
0.858226 | − | 0.513272i | \(-0.171567\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.9241 | + | 7.42442i | −1.56604 | + | 0.648674i | −0.986125 | − | 0.166004i | \(-0.946913\pi\) |
−0.579913 | + | 0.814678i | \(0.696913\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.46054 | − | 8.35449i | 0.300067 | − | 0.724426i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.9867 | + | 15.9867i | 1.36584 | + | 1.36584i | 0.866283 | + | 0.499553i | \(0.166503\pi\) |
0.499553 | + | 0.866283i | \(0.333497\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.0365308 | + | 0.0881933i | −0.00309851 | + | 0.00748046i | −0.925421 | − | 0.378940i | \(-0.876289\pi\) |
0.922323 | + | 0.386421i | \(0.126289\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 4.70822i | − | 0.393721i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 2.85179i | − | 0.236828i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.79476 | + | 13.9898i | −0.474725 | + | 1.14609i | 0.487326 | + | 0.873220i | \(0.337972\pi\) |
−0.962051 | + | 0.272868i | \(0.912028\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.47087 | − | 7.47087i | −0.607971 | − | 0.607971i | 0.334445 | − | 0.942415i | \(-0.391451\pi\) |
−0.942415 | + | 0.334445i | \(0.891451\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.40078 | + | 13.0386i | −0.433801 | + | 1.04729i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.0372 | + | 4.57177i | −0.880867 | + | 0.364867i | −0.776833 | − | 0.629707i | \(-0.783175\pi\) |
−0.104034 | + | 0.994574i | \(0.533175\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 23.3841i | − | 1.84293i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.29972 | + | 7.96624i | 0.258454 | + | 0.623964i | 0.998837 | − | 0.0482221i | \(-0.0153555\pi\) |
−0.740382 | + | 0.672186i | \(0.765356\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.0751100 | − | 0.0751100i | −0.00581218 | − | 0.00581218i | 0.704195 | − | 0.710007i | \(-0.251308\pi\) |
−0.710007 | + | 0.704195i | \(0.751308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −19.4604 | + | 19.4604i | −1.49695 | + | 1.49695i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.0041 | − | 8.70018i | 1.59691 | − | 0.661463i | 0.605937 | − | 0.795512i | \(-0.292798\pi\) |
0.990975 | + | 0.134050i | \(0.0427982\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.12443 | −0.311777 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.35530 | + | 10.5146i | 0.325530 | + | 0.785900i | 0.998913 | + | 0.0466061i | \(0.0148406\pi\) |
−0.673383 | + | 0.739294i | \(0.735159\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.28737 | − | 1.77589i | −0.318677 | − | 0.132001i | 0.217610 | − | 0.976036i | \(-0.430174\pi\) |
−0.536288 | + | 0.844035i | \(0.680174\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.6886 | + | 11.6886i | −0.859364 | + | 0.859364i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.661352 | + | 0.273941i | 0.0483628 | + | 0.0200325i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.2718 | 1.61153 | 0.805766 | − | 0.592234i | \(-0.201754\pi\) | ||||
0.805766 | + | 0.592234i | \(0.201754\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.8858 | 0.783575 | 0.391787 | − | 0.920056i | \(-0.371857\pi\) | ||||
0.391787 | + | 0.920056i | \(0.371857\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.10110 | − | 2.52716i | −0.434686 | − | 0.180053i | 0.154601 | − | 0.987977i | \(-0.450591\pi\) |
−0.589286 | + | 0.807924i | \(0.700591\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.1086 | + | 10.1086i | −0.716582 | + | 0.716582i | −0.967904 | − | 0.251322i | \(-0.919135\pi\) |
0.251322 | + | 0.967904i | \(0.419135\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.49558 | + | 1.86213i | 0.315528 | + | 0.130696i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.12871 | + | 17.2102i | 0.497891 | + | 1.20201i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.02363 | −0.139977 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.8236 | + | 7.79698i | −1.29587 | + | 0.536766i | −0.920729 | − | 0.390202i | \(-0.872405\pi\) |
−0.375139 | + | 0.926969i | \(0.622405\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.88619 | − | 4.88619i | 0.333236 | − | 0.333236i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.0276 | − | 17.0276i | −1.15591 | − | 1.15591i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.35766 | − | 5.69190i | −0.158593 | − | 0.382879i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 14.8162i | − | 0.992164i | −0.868276 | − | 0.496082i | \(-0.834771\pi\) | ||
0.868276 | − | 0.496082i | \(-0.165229\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.9755 | − | 4.96040i | 0.794839 | − | 0.329233i | 0.0519519 | − | 0.998650i | \(-0.483456\pi\) |
0.742887 | + | 0.669416i | \(0.233456\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.65080 | + | 6.39960i | −0.175170 | + | 0.422897i | −0.986942 | − | 0.161077i | \(-0.948503\pi\) |
0.811772 | + | 0.583975i | \(0.198503\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.35926 | + | 8.35926i | 0.547634 | + | 0.547634i | 0.925756 | − | 0.378122i | \(-0.123430\pi\) |
−0.378122 | + | 0.925756i | \(0.623430\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.73736 | + | 6.60858i | −0.178566 | + | 0.431096i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.44122i | 0.157909i | 0.996878 | + | 0.0789547i | \(0.0251582\pi\) | ||||
−0.996878 | + | 0.0789547i | \(0.974842\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.86406i | 0.120074i | 0.998196 | + | 0.0600372i | \(0.0191219\pi\) | ||||
−0.998196 | + | 0.0600372i | \(0.980878\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.90874 | + | 7.02233i | −0.185833 | + | 0.448640i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.3152 | + | 12.3152i | 0.783595 | + | 0.783595i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.30926 | − | 15.2319i | 0.398237 | − | 0.961430i | −0.589847 | − | 0.807515i | \(-0.700812\pi\) |
0.988084 | − | 0.153915i | \(-0.0491881\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.83462 | + | 2.00257i | −0.303950 | + | 0.125900i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.84660i | 0.364701i | 0.983234 | + | 0.182350i | \(0.0583705\pi\) | ||||
−0.983234 | + | 0.182350i | \(0.941629\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.7937 | − | 26.0583i | −0.670687 | − | 1.61918i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.4239 | + | 11.4239i | 0.704427 | + | 0.704427i | 0.965358 | − | 0.260930i | \(-0.0840293\pi\) |
−0.260930 | + | 0.965358i | \(0.584029\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.63826 | − | 6.63826i | 0.407785 | − | 0.407785i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.42511 | + | 1.00451i | −0.147862 | + | 0.0612463i | −0.455387 | − | 0.890294i | \(-0.650499\pi\) |
0.307525 | + | 0.951540i | \(0.400499\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.6956 | 0.649711 | 0.324856 | − | 0.945764i | \(-0.394684\pi\) | ||||
0.324856 | + | 0.945764i | \(0.394684\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.353207 | + | 0.852716i | 0.0212992 | + | 0.0514207i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.7497 | − | 5.69533i | −0.826142 | − | 0.342199i | −0.0707678 | − | 0.997493i | \(-0.522545\pi\) |
−0.755374 | + | 0.655294i | \(0.772545\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.63475 | + | 1.63475i | −0.0975211 | + | 0.0975211i | −0.754184 | − | 0.656663i | \(-0.771967\pi\) |
0.656663 | + | 0.754184i | \(0.271967\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.75108 | + | 1.96796i | 0.282423 | + | 0.116983i | 0.519398 | − | 0.854532i | \(-0.326156\pi\) |
−0.236976 | + | 0.971516i | \(0.576156\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −31.7851 | −1.87622 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0633 | −0.944900 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.0434 | − | 5.40274i | −0.762001 | − | 0.315631i | −0.0323737 | − | 0.999476i | \(-0.510307\pi\) |
−0.729628 | + | 0.683845i | \(0.760307\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.5177 | + | 14.5177i | −0.845254 | + | 0.845254i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 41.6090 | + | 17.2350i | 2.40631 | + | 0.996726i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.51209 | + | 10.8931i | 0.260072 | + | 0.627870i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −22.6815 | −1.29874 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.7332 | + | 5.68846i | −0.783793 | + | 0.324658i | −0.738445 | − | 0.674313i | \(-0.764440\pi\) |
−0.0453480 | + | 0.998971i | \(0.514440\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.93693 | + | 1.93693i | −0.109833 | + | 0.109833i | −0.759888 | − | 0.650055i | \(-0.774746\pi\) |
0.650055 | + | 0.759888i | \(0.274746\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.8065 | + | 20.8065i | 1.17606 | + | 1.17606i | 0.980741 | + | 0.195315i | \(0.0625728\pi\) |
0.195315 | + | 0.980741i | \(0.437427\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.99169 | + | 16.8794i | 0.392692 | + | 0.948043i | 0.989351 | + | 0.145548i | \(0.0464945\pi\) |
−0.596659 | + | 0.802495i | \(0.703505\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1.08892i | − | 0.0609678i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.44642 | + | 1.01334i | −0.136122 | + | 0.0563837i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.03986 | − | 7.33887i | 0.168621 | − | 0.407087i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.63039 | − | 8.63039i | −0.475809 | − | 0.475809i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.57715 | + | 18.2929i | −0.416478 | + | 1.00547i | 0.566882 | + | 0.823799i | \(0.308150\pi\) |
−0.983360 | + | 0.181668i | \(0.941850\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.55664i | 0.412863i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.73391i | 0.366820i | 0.983037 | + | 0.183410i | \(0.0587135\pi\) | ||||
−0.983037 | + | 0.183410i | \(0.941286\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.06222 | + | 4.97863i | −0.111675 | + | 0.269608i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.18892 | + | 7.18892i | 0.388165 | + | 0.388165i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.79644 | − | 6.75121i | 0.150121 | − | 0.362424i | −0.830873 | − | 0.556462i | \(-0.812158\pi\) |
0.980994 | + | 0.194038i | \(0.0621585\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.16816 | + | 1.31229i | −0.169588 | + | 0.0702455i | −0.465862 | − | 0.884857i | \(-0.654256\pi\) |
0.296274 | + | 0.955103i | \(0.404256\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 29.8578i | 1.58917i | 0.607151 | + | 0.794586i | \(0.292312\pi\) | ||||
−0.607151 | + | 0.794586i | \(0.707688\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.3330 | − | 24.9461i | −0.548419 | − | 1.32400i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.44266 | + | 9.44266i | 0.498365 | + | 0.498365i | 0.910929 | − | 0.412564i | \(-0.135367\pi\) |
−0.412564 | + | 0.910929i | \(0.635367\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.14189 | + | 8.14189i | −0.428521 | + | 0.428521i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.1826 | − | 5.04620i | 0.637667 | − | 0.264130i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.8327 | −1.40065 | −0.700327 | − | 0.713822i | \(-0.746962\pi\) | ||||
−0.700327 | + | 0.713822i | \(0.746962\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.13001 | + | 14.7991i | 0.318254 | + | 0.768334i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.3312 | − | 5.10777i | −0.638487 | − | 0.264470i | 0.0398670 | − | 0.999205i | \(-0.487307\pi\) |
−0.678354 | + | 0.734735i | \(0.737307\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.62683 | + | 6.62683i | −0.341299 | + | 0.341299i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.26078 | + | 2.17909i | 0.270228 | + | 0.111932i | 0.513683 | − | 0.857980i | \(-0.328281\pi\) |
−0.243455 | + | 0.969912i | \(0.578281\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.14683 | −0.416283 | −0.208142 | − | 0.978099i | \(-0.566742\pi\) | ||||
−0.208142 | + | 0.978099i | \(0.566742\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.73527 | 0.241332 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.22236 | + | 3.40581i | 0.416890 | + | 0.172682i | 0.581261 | − | 0.813717i | \(-0.302559\pi\) |
−0.164371 | + | 0.986399i | \(0.552559\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.84191 | + | 4.84191i | −0.244866 | + | 0.244866i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −19.7142 | − | 8.16588i | −0.991927 | − | 0.410870i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.328403 | − | 0.792834i | −0.0164821 | − | 0.0397912i | 0.915424 | − | 0.402490i | \(-0.131855\pi\) |
−0.931906 | + | 0.362699i | \(0.881855\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.3098 | 0.864411 | 0.432206 | − | 0.901775i | \(-0.357735\pi\) | ||||
0.432206 | + | 0.901775i | \(0.357735\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 42.8484 | − | 17.7484i | 2.13443 | − | 0.884111i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.46314 | + | 4.46314i | −0.221230 | + | 0.221230i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.00972 | + | 5.00972i | 0.247715 | + | 0.247715i | 0.820032 | − | 0.572317i | \(-0.193955\pi\) |
−0.572317 | + | 0.820032i | \(0.693955\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.4062 | − | 32.3654i | −0.659675 | − | 1.59260i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.82422i | 0.285900i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.01103 | + | 2.90406i | −0.342511 | + | 0.141873i | −0.547307 | − | 0.836932i | \(-0.684347\pi\) |
0.204796 | + | 0.978805i | \(0.434347\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.94749 | − | 9.53009i | 0.192389 | − | 0.464468i | −0.798021 | − | 0.602630i | \(-0.794119\pi\) |
0.990410 | + | 0.138162i | \(0.0441195\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.854002 | + | 0.854002i | 0.0414252 | + | 0.0414252i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.8103 | − | 35.7552i | 0.716719 | − | 1.73031i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 11.8098i | − | 0.568858i | −0.958697 | − | 0.284429i | \(-0.908196\pi\) | ||
0.958697 | − | 0.284429i | \(-0.0918040\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.26662i | 0.156984i | 0.996915 | + | 0.0784919i | \(0.0250105\pi\) | ||||
−0.996915 | + | 0.0784919i | \(0.974990\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.40772 | − | 17.8838i | 0.354359 | − | 0.855499i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.7003 | − | 13.7003i | −0.653877 | − | 0.653877i | 0.300047 | − | 0.953924i | \(-0.402998\pi\) |
−0.953924 | + | 0.300047i | \(0.902998\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.53737 | − | 18.1968i | 0.358111 | − | 0.864557i | −0.637454 | − | 0.770488i | \(-0.720012\pi\) |
0.995566 | − | 0.0940692i | \(-0.0299875\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −17.2763 | + | 7.15607i | −0.818974 | + | 0.339230i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.46488i | 0.116325i | 0.998307 | + | 0.0581625i | \(0.0185241\pi\) | ||||
−0.998307 | + | 0.0581625i | \(0.981476\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.72200 | + | 6.57150i | 0.128174 | + | 0.309440i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −28.8174 | − | 28.8174i | −1.35098 | − | 1.35098i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.04617 | − | 3.04617i | 0.142494 | − | 0.142494i | −0.632261 | − | 0.774755i | \(-0.717873\pi\) |
0.774755 | + | 0.632261i | \(0.217873\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.85993 | + | 4.08412i | −0.459223 | + | 0.190216i | −0.600288 | − | 0.799784i | \(-0.704947\pi\) |
0.141065 | + | 0.990000i | \(0.454947\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.1511 | 1.30829 | 0.654147 | − | 0.756367i | \(-0.273028\pi\) | ||||
0.654147 | + | 0.756367i | \(0.273028\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.133756 | − | 0.322916i | −0.00618951 | − | 0.0149428i | 0.920755 | − | 0.390142i | \(-0.127574\pi\) |
−0.926944 | + | 0.375200i | \(0.877574\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.9123 | − | 4.93425i | −0.550060 | − | 0.227842i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.86573 | − | 1.86573i | 0.0857863 | − | 0.0857863i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.15430 | − | 1.30655i | −0.144729 | − | 0.0599487i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.3551 | −1.15850 | −0.579251 | − | 0.815149i | \(-0.696655\pi\) | ||||
−0.579251 | + | 0.815149i | \(0.696655\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 54.3226 | 2.47690 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.7436 | − | 5.69280i | −0.624066 | − | 0.258497i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.5211 | − | 15.5211i | 0.703327 | − | 0.703327i | −0.261796 | − | 0.965123i | \(-0.584315\pi\) |
0.965123 | + | 0.261796i | \(0.0843149\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.79527 | + | 3.22890i | 0.351795 | + | 0.145718i | 0.551581 | − | 0.834121i | \(-0.314025\pi\) |
−0.199786 | + | 0.979840i | \(0.564025\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.545281 | − | 1.31642i | −0.0245582 | − | 0.0592888i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 46.0722 | 2.06662 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.14784 | − | 0.889664i | 0.0961504 | − | 0.0398268i | −0.334090 | − | 0.942541i | \(-0.608429\pi\) |
0.430240 | + | 0.902714i | \(0.358429\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.4975 | − | 10.4975i | 0.468062 | − | 0.468062i | −0.433224 | − | 0.901286i | \(-0.642624\pi\) |
0.901286 | + | 0.433224i | \(0.142624\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.55712 | − | 1.55712i | −0.0692908 | − | 0.0692908i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.62373 | − | 20.8195i | −0.382240 | − | 0.922810i | −0.991532 | − | 0.129863i | \(-0.958546\pi\) |
0.609292 | − | 0.792946i | \(-0.291454\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.4997i | 0.995329i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.8769 | − | 7.40485i | 0.787750 | − | 0.326297i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.04523 | + | 2.52340i | −0.0459690 | + | 0.110979i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.6260 | + | 23.6260i | 1.03508 | + | 1.03508i | 0.999362 | + | 0.0357139i | \(0.0113705\pi\) |
0.0357139 | + | 0.999362i | \(0.488630\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.967311 | − | 2.33529i | 0.0422975 | − | 0.102115i | −0.901319 | − | 0.433156i | \(-0.857400\pi\) |
0.943616 | + | 0.331041i | \(0.107400\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.05147i | 0.307167i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 27.0566i | − | 1.17638i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 23.4268 | − | 56.5574i | 1.01473 | − | 2.44977i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.9203 | + | 23.9203i | 1.03416 | + | 1.03416i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.11067 | + | 2.68138i | −0.0478398 | + | 0.115495i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.3578 | − | 5.53299i | 0.574298 | − | 0.237882i | −0.0765813 | − | 0.997063i | \(-0.524400\pi\) |
0.650879 | + | 0.759181i | \(0.274400\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 3.90464i | − | 0.167257i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.5682 | + | 39.9992i | 0.708406 | + | 1.71024i | 0.703945 | + | 0.710254i | \(0.251420\pi\) |
0.00446097 | + | 0.999990i | \(0.498580\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.84825 | + | 2.84825i | 0.121340 | + | 0.121340i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 25.7454 | − | 25.7454i | 1.09481 | − | 1.09481i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.70924 | − | 2.36484i | 0.241908 | − | 0.100202i | −0.258436 | − | 0.966029i | \(-0.583207\pi\) |
0.500344 | + | 0.865827i | \(0.333207\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22.7085 | −0.960467 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.89410 | − | 14.2296i | −0.248407 | − | 0.599707i | 0.749662 | − | 0.661821i | \(-0.230216\pi\) |
−0.998069 | + | 0.0621133i | \(0.980216\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.29962 | − | 0.538322i | −0.0546756 | − | 0.0226474i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.242674 | − | 0.242674i | 0.0101734 | − | 0.0101734i | −0.702002 | − | 0.712175i | \(-0.747710\pi\) |
0.712175 | + | 0.702002i | \(0.247710\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25.8985 | − | 10.7275i | −1.08382 | − | 0.448933i | −0.231972 | − | 0.972722i | \(-0.574518\pi\) |
−0.851848 | + | 0.523789i | \(0.824518\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.82885 | −0.368188 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.7896 | 0.740589 | 0.370294 | − | 0.928914i | \(-0.379257\pi\) | ||||
0.370294 | + | 0.928914i | \(0.379257\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.18133 | − | 3.80303i | −0.380906 | − | 0.157776i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.53473 | − | 2.53473i | 0.104978 | − | 0.104978i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −30.9718 | − | 12.8289i | −1.27834 | − | 0.529507i | −0.362852 | − | 0.931847i | \(-0.618197\pi\) |
−0.915490 | + | 0.402340i | \(0.868197\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.62838 | − | 18.4165i | −0.314322 | − | 0.758840i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −41.4635 | −1.70270 | −0.851351 | − | 0.524596i | \(-0.824216\pi\) | ||||
−0.851351 | + | 0.524596i | \(0.824216\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.72460 | − | 2.37121i | 0.234686 | − | 0.0972100i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −32.9148 | + | 32.9148i | −1.34486 | + | 1.34486i | −0.453719 | + | 0.891145i | \(0.649903\pi\) |
−0.891145 | + | 0.453719i | \(0.850097\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.5748 | − | 12.5748i | −0.512936 | − | 0.512936i | 0.402489 | − | 0.915425i | \(-0.368145\pi\) |
−0.915425 | + | 0.402489i | \(0.868145\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.74848 | + | 18.7065i | 0.315021 | + | 0.760527i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 46.0240i | 1.86806i | 0.357198 | + | 0.934029i | \(0.383732\pi\) | ||||
−0.357198 | + | 0.934029i | \(0.616268\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.7176 | − | 8.99570i | 0.878598 | − | 0.363927i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.81762 | − | 9.21655i | 0.154192 | − | 0.372253i | −0.827841 | − | 0.560963i | \(-0.810431\pi\) |
0.982033 | + | 0.188711i | \(0.0604308\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.42700 | − | 9.42700i | −0.379517 | − | 0.379517i | 0.491411 | − | 0.870928i | \(-0.336481\pi\) |
−0.870928 | + | 0.491411i | \(0.836481\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.4213 | − | 25.1593i | 0.418868 | − | 1.01124i | −0.563808 | − | 0.825906i | \(-0.690664\pi\) |
0.982676 | − | 0.185332i | \(-0.0593359\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 31.9071i | − | 1.27833i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 17.2034i | − | 0.688136i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.16068 | + | 7.63055i | −0.126024 | + | 0.304250i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.7973 | − | 15.7973i | −0.628879 | − | 0.628879i | 0.318907 | − | 0.947786i | \(-0.396684\pi\) |
−0.947786 | + | 0.318907i | \(0.896684\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.57545 | + | 20.7030i | −0.340307 | + | 0.821573i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 23.0772 | − | 9.55891i | 0.914354 | − | 0.378738i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.2466i | 0.444215i | 0.975022 | + | 0.222107i | \(0.0712936\pi\) | ||||
−0.975022 | + | 0.222107i | \(0.928706\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.46309 | − | 10.7749i | −0.176007 | − | 0.424919i | 0.811115 | − | 0.584886i | \(-0.198861\pi\) |
−0.987122 | + | 0.159968i | \(0.948861\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.9908 | − | 22.9908i | −0.903861 | − | 0.903861i | 0.0919063 | − | 0.995768i | \(-0.470704\pi\) |
−0.995768 | + | 0.0919063i | \(0.970704\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.54340 | + | 5.54340i | −0.217597 | + | 0.217597i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.731559 | + | 0.303022i | −0.0286281 | + | 0.0118582i | −0.396952 | − | 0.917840i | \(-0.629932\pi\) |
0.368323 | + | 0.929698i | \(0.379932\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 37.5804 | 1.46839 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.48735 | + | 8.41921i | 0.135848 | + | 0.327966i | 0.977134 | − | 0.212624i | \(-0.0682010\pi\) |
−0.841286 | + | 0.540590i | \(0.818201\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.6551 | + | 9.38406i | 0.881182 | + | 0.364998i | 0.776955 | − | 0.629556i | \(-0.216763\pi\) |
0.104227 | + | 0.994554i | \(0.466763\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.3859 | + | 12.3859i | −0.480305 | + | 0.480305i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.62334 | + | 3.98612i | 0.372617 | + | 0.154343i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.66062 | −0.334340 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.3835 | −0.670084 | −0.335042 | − | 0.942203i | \(-0.608751\pi\) | ||||
−0.335042 | + | 0.942203i | \(0.608751\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 39.4502 | + | 16.3408i | 1.51620 | + | 0.628029i | 0.976825 | − | 0.214040i | \(-0.0686621\pi\) |
0.539371 | + | 0.842068i | \(0.318662\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.9483 | − | 17.9483i | 0.688793 | − | 0.688793i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 40.6471 | + | 16.8366i | 1.55532 | + | 0.644234i | 0.984268 | − | 0.176682i | \(-0.0565365\pi\) |
0.571049 | + | 0.820916i | \(0.306536\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.7591 | − | 40.4602i | −0.640334 | − | 1.54590i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −30.8512 | −1.17534 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.769203 | − | 0.318614i | 0.0292619 | − | 0.0121207i | −0.368005 | − | 0.929824i | \(-0.619959\pi\) |
0.397266 | + | 0.917703i | \(0.369959\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.130751 | − | 0.130751i | 0.00495965 | − | 0.00495965i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.58141 | + | 6.58141i | 0.249289 | + | 0.249289i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.7572 | − | 25.9701i | −0.406292 | − | 0.980876i | −0.986105 | − | 0.166126i | \(-0.946874\pi\) |
0.579812 | − | 0.814750i | \(-0.303126\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 23.3482i | − | 0.880595i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.47140 | − | 1.43790i | 0.130555 | − | 0.0540778i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.7081 | + | 33.0944i | −0.514820 | + | 1.24289i | 0.426229 | + | 0.904615i | \(0.359842\pi\) |
−0.941049 | + | 0.338270i | \(0.890158\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −36.4497 | − | 36.4497i | −1.36505 | − | 1.36505i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.49008 | + | 8.42579i | −0.130522 | + | 0.315107i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.7319i | 0.922345i | 0.887311 | + | 0.461172i | \(0.152571\pi\) | ||||
−0.887311 | + | 0.461172i | \(0.847429\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 33.0163i | 1.22959i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.703060 | − | 1.69734i | 0.0261110 | − | 0.0630375i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.89101 | − | 4.89101i | −0.181397 | − | 0.181397i | 0.610567 | − | 0.791965i | \(-0.290942\pi\) |
−0.791965 | + | 0.610567i | \(0.790942\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.32126 | − | 3.18980i | 0.0488685 | − | 0.117979i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.2058 | + | 4.22736i | −0.376958 | + | 0.156141i | −0.563114 | − | 0.826379i | \(-0.690397\pi\) |
0.186156 | + | 0.982520i | \(0.440397\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.88540i | 0.106285i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.71029 | − | 4.12900i | −0.0629139 | − | 0.151888i | 0.889296 | − | 0.457332i | \(-0.151195\pi\) |
−0.952210 | + | 0.305445i | \(0.901195\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.6977 | − | 12.6977i | −0.465832 | − | 0.465832i | 0.434729 | − | 0.900561i | \(-0.356844\pi\) |
−0.900561 | + | 0.434729i | \(0.856844\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.7405 | − | 20.7405i | 0.759873 | − | 0.759873i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −53.3272 | + | 22.0888i | −1.94853 | + | 0.807108i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.3864 | 0.926362 | 0.463181 | − | 0.886264i | \(-0.346708\pi\) | ||||
0.463181 | + | 0.886264i | \(0.346708\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.83185 | + | 18.9078i | 0.285030 | + | 0.688123i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 48.9351 | + | 20.2696i | 1.77858 | + | 0.736711i | 0.993023 | + | 0.117918i | \(0.0376220\pi\) |
0.785554 | + | 0.618793i | \(0.212378\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.18378 | − | 7.18378i | 0.260412 | − | 0.260412i | −0.564809 | − | 0.825221i | \(-0.691050\pi\) |
0.825221 | + | 0.564809i | \(0.191050\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.15530 | + | 2.54961i | 0.222837 | + | 0.0923020i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 67.4708 | 2.43623 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −48.6570 | −1.75462 | −0.877309 | − | 0.479926i | \(-0.840663\pi\) | ||||
−0.877309 | + | 0.479926i | \(0.840663\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.43579 | + | 3.08000i | 0.267447 | + | 0.110780i | 0.512377 | − | 0.858761i | \(-0.328765\pi\) |
−0.244930 | + | 0.969541i | \(0.578765\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.42890 | + | 6.42890i | −0.230933 | + | 0.230933i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −24.3087 | − | 10.0690i | −0.870951 | − | 0.360760i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.94552 | − | 9.52534i | −0.141182 | − | 0.340843i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 23.1411 | 0.825940 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.9915 | + | 6.20966i | −0.534388 | + | 0.221351i | −0.633524 | − | 0.773723i | \(-0.718392\pi\) |
0.0991360 | + | 0.995074i | \(0.468392\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.69722 | − | 1.69722i | 0.0603464 | − | 0.0603464i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 52.7058 | + | 52.7058i | 1.87164 | + | 1.87164i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.43692 | + | 5.88325i | 0.0863202 | + | 0.208395i | 0.961145 | − | 0.276044i | \(-0.0890236\pi\) |
−0.874825 | + | 0.484439i | \(0.839024\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.57401i | 0.126439i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.65177 | − | 1.92682i | 0.164157 | − | 0.0679962i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.3340 | + | 41.8480i | −0.610944 | + | 1.47495i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.30765 | + | 9.30765i | 0.327240 | + | 0.327240i | 0.851536 | − | 0.524296i | \(-0.175672\pi\) |
−0.524296 | + | 0.851536i | \(0.675672\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.10599 | − | 19.5696i | 0.284640 | − | 0.687181i | −0.715292 | − | 0.698825i | \(-0.753706\pi\) |
0.999932 | + | 0.0116440i | \(0.00370648\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 16.7023i | − | 0.585056i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.76026i | 0.341468i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.81353 | − | 9.20668i | 0.133093 | − | 0.321315i | −0.843257 | − | 0.537511i | \(-0.819365\pi\) |
0.976350 | + | 0.216195i | \(0.0693648\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.5761 | + | 16.5761i | 0.577808 | + | 0.577808i | 0.934299 | − | 0.356491i | \(-0.116027\pi\) |
−0.356491 | + | 0.934299i | \(0.616027\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.1677 | − | 26.9613i | 0.388340 | − | 0.937537i | −0.601951 | − | 0.798533i | \(-0.705610\pi\) |
0.990292 | − | 0.139004i | \(-0.0443901\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.82768 | − | 3.65654i | 0.306598 | − | 0.126997i | −0.224080 | − | 0.974571i | \(-0.571938\pi\) |
0.530678 | + | 0.847574i | \(0.321938\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.79777i | 0.131585i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.0787391 | + | 0.190093i | 0.00272488 | + | 0.00657844i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.55814 | + | 4.55814i | 0.157364 | + | 0.157364i | 0.781398 | − | 0.624033i | \(-0.214507\pi\) |
−0.624033 | + | 0.781398i | \(0.714507\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.9734 | − | 18.9734i | 0.654257 | − | 0.654257i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 49.2516 | − | 20.4007i | 1.69431 | − | 0.701805i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −34.5485 | −1.18710 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −23.1052 | − | 55.7809i | −0.792037 | − | 1.91215i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.7268 | + | 5.68583i | 0.469997 | + | 0.194679i | 0.605095 | − | 0.796153i | \(-0.293135\pi\) |
−0.135098 | + | 0.990832i | \(0.543135\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.1744 | − | 11.1744i | 0.381711 | − | 0.381711i | −0.490007 | − | 0.871718i | \(-0.663006\pi\) |
0.871718 | + | 0.490007i | \(0.163006\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39.1836 | − | 16.2304i | −1.33693 | − | 0.553773i | −0.404304 | − | 0.914625i | \(-0.632486\pi\) |
−0.932623 | + | 0.360851i | \(0.882486\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22.2298 | −0.756710 | −0.378355 | − | 0.925661i | \(-0.623510\pi\) | ||||
−0.378355 | + | 0.925661i | \(0.623510\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −44.0379 | −1.49733 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.52760 | − | 3.11803i | −0.255356 | − | 0.105772i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.5597 | − | 17.5597i | 0.594987 | − | 0.594987i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 36.9553 | + | 15.3074i | 1.24932 | + | 0.517484i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.13025 | + | 7.55709i | 0.105701 | + | 0.255185i | 0.967877 | − | 0.251424i | \(-0.0808989\pi\) |
−0.862176 | + | 0.506609i | \(0.830899\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.77921 | 0.161016 | 0.0805078 | − | 0.996754i | \(-0.474346\pi\) | ||||
0.0805078 | + | 0.996754i | \(0.474346\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 45.1752 | − | 18.7122i | 1.52027 | − | 0.629716i | 0.542622 | − | 0.839977i | \(-0.317431\pi\) |
0.977645 | + | 0.210261i | \(0.0674314\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.92890 | − | 6.92890i | 0.232650 | − | 0.232650i | −0.581148 | − | 0.813798i | \(-0.697396\pi\) |
0.813798 | + | 0.581148i | \(0.197396\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27.0368 | − | 27.0368i | −0.906784 | − | 0.906784i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.86641 | − | 9.33435i | −0.129385 | − | 0.312362i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 22.0453i | − | 0.736894i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.91000 | − | 4.10486i | 0.330517 | − | 0.136905i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.79503 | − | 4.33358i | 0.0598011 | − | 0.144373i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.35622 | + | 6.35622i | 0.211288 | + | 0.211288i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.4242 | + | 34.8230i | −0.478946 | + | 1.15628i | 0.481157 | + | 0.876634i | \(0.340217\pi\) |
−0.960104 | + | 0.279644i | \(0.909783\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44.7402i | 1.48231i | 0.671335 | + | 0.741154i | \(0.265721\pi\) | ||||
−0.671335 | + | 0.741154i | \(0.734279\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.22390i | 0.0736004i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −24.5388 | + | 59.2418i | −0.810342 | + | 1.95634i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.4709 | − | 25.4709i | −0.840207 | − | 0.840207i | 0.148678 | − | 0.988886i | \(-0.452498\pi\) |
−0.988886 | + | 0.148678i | \(0.952498\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −33.9570 | + | 81.9795i | −1.11771 | + | 2.69839i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.83848 | + | 4.07523i | −0.323487 | + | 0.133993i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.0747i | 0.757058i | 0.925589 | + | 0.378529i | \(0.123570\pi\) | ||||
−0.925589 | + | 0.378529i | \(0.876430\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.10848 | − | 9.91875i | −0.134650 | − | 0.325074i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.980484 | − | 0.980484i | −0.0320652 | − | 0.0320652i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.57961 | − | 6.57961i | 0.214947 | − | 0.214947i | −0.591418 | − | 0.806365i | \(-0.701432\pi\) |
0.806365 | + | 0.591418i | \(0.201432\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −40.5076 | + | 16.7788i | −1.32051 | + | 0.546973i | −0.927934 | − | 0.372746i | \(-0.878416\pi\) |
−0.392577 | + | 0.919719i | \(0.628416\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −68.0399 | −2.21569 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −21.7966 | − | 52.6218i | −0.708296 | − | 1.70998i | −0.704216 | − | 0.709986i | \(-0.748701\pi\) |
−0.00407986 | − | 0.999992i | \(-0.501299\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −40.0353 | − | 16.5831i | −1.29960 | − | 0.538312i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.5821 | − | 24.5821i | 0.796293 | − | 0.796293i | −0.186216 | − | 0.982509i | \(-0.559622\pi\) |
0.982509 | + | 0.186216i | \(0.0596224\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −39.8574 | − | 16.5095i | −1.28976 | − | 0.534234i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 74.7248 | 2.41299 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.0832 | −0.712362 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19.4811 | − | 8.06932i | −0.627118 | − | 0.259761i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.1878 | − | 19.1878i | 0.617037 | − | 0.617037i | −0.327734 | − | 0.944770i | \(-0.606285\pi\) |
0.944770 | + | 0.327734i | \(0.106285\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −35.5982 | − | 14.7453i | −1.14240 | − | 0.473198i | −0.270422 | − | 0.962742i | \(-0.587163\pi\) |
−0.871979 | + | 0.489544i | \(0.837163\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.120740 | + | 0.291492i | 0.00387074 | + | 0.00934479i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.7488 | 0.343885 | 0.171943 | − | 0.985107i | \(-0.444996\pi\) | ||||
0.171943 | + | 0.985107i | \(0.444996\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.59672 | + | 2.73245i | −0.210832 | + | 0.0873295i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.2745 | − | 15.2745i | 0.487181 | − | 0.487181i | −0.420234 | − | 0.907416i | \(-0.638052\pi\) |
0.907416 | + | 0.420234i | \(0.138052\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.04516 | + | 9.04516i | 0.288203 | + | 0.288203i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.65868 | + | 23.3181i | 0.307128 | + | 0.741473i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.5708i | 0.494622i | 0.968936 | + | 0.247311i | \(0.0795469\pi\) | ||||
−0.968936 | + | 0.247311i | \(0.920453\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 25.5836 | − | 10.5971i | 0.811053 | − | 0.335949i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.71754 | + | 4.14652i | −0.0543951 | + | 0.131321i | −0.948741 | − | 0.316055i | \(-0.897642\pi\) |
0.894346 | + | 0.447376i | \(0.147642\pi\) | |||||||
\(998\) | 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.a.719.2 | 32 | ||
3.2 | odd | 2 | 1152.2.w.b.719.7 | 32 | |||
4.3 | odd | 2 | 288.2.w.b.107.3 | yes | 32 | ||
12.11 | even | 2 | 288.2.w.a.107.6 | yes | 32 | ||
32.3 | odd | 8 | 1152.2.w.b.431.7 | 32 | |||
32.29 | even | 8 | 288.2.w.a.35.6 | ✓ | 32 | ||
96.29 | odd | 8 | 288.2.w.b.35.3 | yes | 32 | ||
96.35 | even | 8 | inner | 1152.2.w.a.431.2 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.2.w.a.35.6 | ✓ | 32 | 32.29 | even | 8 | ||
288.2.w.a.107.6 | yes | 32 | 12.11 | even | 2 | ||
288.2.w.b.35.3 | yes | 32 | 96.29 | odd | 8 | ||
288.2.w.b.107.3 | yes | 32 | 4.3 | odd | 2 | ||
1152.2.w.a.431.2 | 32 | 96.35 | even | 8 | inner | ||
1152.2.w.a.719.2 | 32 | 1.1 | even | 1 | trivial | ||
1152.2.w.b.431.7 | 32 | 32.3 | odd | 8 | |||
1152.2.w.b.719.7 | 32 | 3.2 | odd | 2 |