Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2268,2,Mod(377,2268)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2268, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2268.377");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2268.x (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.1100711784\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 756) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 377.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2268.377 |
Dual form | 2268.2.x.h.1889.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1135\) | \(1541\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(5\) | 1.50000 | − | 2.59808i | 0.670820 | − | 1.16190i | −0.306851 | − | 0.951757i | \(-0.599275\pi\) |
0.977672 | − | 0.210138i | \(-0.0673912\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | − | 2.59808i | 0.188982 | − | 0.981981i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.50000 | + | 2.59808i | −1.35680 | + | 0.783349i | −0.989191 | − | 0.146631i | \(-0.953157\pi\) |
−0.367610 | + | 0.929980i | \(0.619824\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.00000 | − | 1.73205i | −0.832050 | − | 0.480384i | 0.0225039 | − | 0.999747i | \(-0.492836\pi\) |
−0.854554 | + | 0.519362i | \(0.826170\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.00000 | 1.45521 | 0.727607 | − | 0.685994i | \(-0.240633\pi\) | ||||
0.727607 | + | 0.685994i | \(0.240633\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.73205i | 0.397360i | 0.980064 | + | 0.198680i | \(0.0636654\pi\) | ||||
−0.980064 | + | 0.198680i | \(0.936335\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.50000 | − | 2.59808i | −0.938315 | − | 0.541736i | −0.0488832 | − | 0.998805i | \(-0.515566\pi\) |
−0.889432 | + | 0.457068i | \(0.848900\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | − | 3.46410i | −0.400000 | − | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.00000 | − | 5.19615i | 1.67126 | − | 0.964901i | 0.704323 | − | 0.709880i | \(-0.251251\pi\) |
0.966935 | − | 0.255021i | \(-0.0820825\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.50000 | − | 2.59808i | −0.808224 | − | 0.466628i | 0.0381148 | − | 0.999273i | \(-0.487865\pi\) |
−0.846339 | + | 0.532645i | \(0.821198\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.00000 | − | 5.19615i | −1.01419 | − | 0.878310i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | 0.164399 | 0.0821995 | − | 0.996616i | \(-0.473806\pi\) | ||||
0.0821995 | + | 0.996616i | \(0.473806\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.50000 | + | 2.59808i | −0.234261 | + | 0.405751i | −0.959058 | − | 0.283211i | \(-0.908600\pi\) |
0.724797 | + | 0.688963i | \(0.241934\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.00000 | − | 8.66025i | −0.762493 | − | 1.32068i | −0.941562 | − | 0.336840i | \(-0.890642\pi\) |
0.179069 | − | 0.983836i | \(-0.442691\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.00000 | − | 5.19615i | −0.437595 | − | 0.757937i | 0.559908 | − | 0.828554i | \(-0.310836\pi\) |
−0.997503 | + | 0.0706177i | \(0.977503\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.50000 | − | 2.59808i | −0.928571 | − | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.5885i | 2.10195i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.00000 | − | 5.19615i | 0.390567 | − | 0.676481i | −0.601958 | − | 0.798528i | \(-0.705612\pi\) |
0.992524 | + | 0.122047i | \(0.0389457\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.0000 | + | 6.92820i | −1.53644 | + | 0.887066i | −0.537400 | + | 0.843328i | \(0.680593\pi\) |
−0.999043 | + | 0.0437377i | \(0.986073\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.00000 | + | 5.19615i | −1.11631 | + | 0.644503i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | + | 1.73205i | −0.122169 | + | 0.211604i | −0.920623 | − | 0.390453i | \(-0.872318\pi\) |
0.798454 | + | 0.602056i | \(0.205652\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.19615i | 0.616670i | 0.951278 | + | 0.308335i | \(0.0997717\pi\) | ||||
−0.951278 | + | 0.308335i | \(0.900228\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 3.46410i | − | 0.405442i | −0.979236 | − | 0.202721i | \(-0.935021\pi\) | ||
0.979236 | − | 0.202721i | \(-0.0649785\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.50000 | + | 12.9904i | 0.512823 | + | 1.48039i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.00000 | − | 12.1244i | −0.787562 | − | 1.36410i | −0.927457 | − | 0.373930i | \(-0.878010\pi\) |
0.139895 | − | 0.990166i | \(-0.455323\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.00000 | + | 5.19615i | 0.329293 | + | 0.570352i | 0.982372 | − | 0.186938i | \(-0.0598564\pi\) |
−0.653079 | + | 0.757290i | \(0.726523\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.00000 | − | 15.5885i | 0.976187 | − | 1.69081i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.00000 | −0.953998 | −0.476999 | − | 0.878904i | \(-0.658275\pi\) | ||||
−0.476999 | + | 0.878904i | \(0.658275\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.00000 | + | 6.92820i | −0.628971 | + | 0.726273i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.50000 | + | 2.59808i | 0.461690 | + | 0.266557i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.00000 | + | 3.46410i | −0.609208 | + | 0.351726i | −0.772655 | − | 0.634826i | \(-0.781072\pi\) |
0.163448 | + | 0.986552i | \(0.447739\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.00000 | + | 15.5885i | 0.895533 | + | 1.55111i | 0.833143 | + | 0.553058i | \(0.186539\pi\) |
0.0623905 | + | 0.998052i | \(0.480128\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.50000 | + | 4.33013i | 0.738997 | + | 0.426660i | 0.821705 | − | 0.569914i | \(-0.193023\pi\) |
−0.0827075 | + | 0.996574i | \(0.526357\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.3923i | 1.00466i | 0.864675 | + | 0.502331i | \(0.167524\pi\) | ||||
−0.864675 | + | 0.502331i | \(0.832476\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.0000 | −1.05361 | −0.526804 | − | 0.849987i | \(-0.676610\pi\) | ||||
−0.526804 | + | 0.849987i | \(0.676610\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.5000 | + | 7.79423i | −1.25888 | + | 0.726816i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.00000 | − | 15.5885i | 0.275010 | − | 1.42899i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.00000 | − | 13.8564i | 0.727273 | − | 1.25967i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.00000 | 0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.00000 | 0.177471 | 0.0887357 | − | 0.996055i | \(-0.471717\pi\) | ||||
0.0887357 | + | 0.996055i | \(0.471717\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.00000 | + | 15.5885i | −0.786334 | + | 1.36197i | 0.141865 | + | 0.989886i | \(0.454690\pi\) |
−0.928199 | + | 0.372084i | \(0.878643\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.50000 | + | 0.866025i | 0.390199 | + | 0.0750939i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.00000 | − | 5.19615i | 0.768922 | − | 0.443937i | −0.0635680 | − | 0.997978i | \(-0.520248\pi\) |
0.832490 | + | 0.554040i | \(0.186915\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.0000 | − | 8.66025i | −1.27228 | − | 0.734553i | −0.296866 | − | 0.954919i | \(-0.595942\pi\) |
−0.975417 | + | 0.220366i | \(0.929275\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 18.0000 | 1.50524 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 31.1769i | − | 2.58910i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.00000 | − | 3.46410i | −0.162758 | − | 0.281905i | 0.773099 | − | 0.634285i | \(-0.218706\pi\) |
−0.935857 | + | 0.352381i | \(0.885372\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −13.5000 | + | 7.79423i | −1.08435 | + | 0.626048i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.00000 | + | 5.19615i | 0.718278 | + | 0.414698i | 0.814119 | − | 0.580699i | \(-0.197221\pi\) |
−0.0958404 | + | 0.995397i | \(0.530554\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.00000 | + | 10.3923i | −0.709299 | + | 0.819028i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.0000 | −0.783260 | −0.391630 | − | 0.920123i | \(-0.628089\pi\) | ||||
−0.391630 | + | 0.920123i | \(0.628089\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.00000 | − | 10.3923i | 0.464294 | − | 0.804181i | −0.534875 | − | 0.844931i | \(-0.679641\pi\) |
0.999169 | + | 0.0407502i | \(0.0129748\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.500000 | − | 0.866025i | −0.0384615 | − | 0.0666173i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.50000 | − | 7.79423i | −0.342129 | − | 0.592584i | 0.642699 | − | 0.766119i | \(-0.277815\pi\) |
−0.984828 | + | 0.173534i | \(0.944481\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.0000 | + | 3.46410i | −0.755929 | + | 0.261861i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 10.3923i | − | 0.776757i | −0.921500 | − | 0.388379i | \(-0.873035\pi\) | ||
0.921500 | − | 0.388379i | \(-0.126965\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.92820i | − | 0.514969i | −0.966282 | − | 0.257485i | \(-0.917106\pi\) | ||
0.966282 | − | 0.257485i | \(-0.0828937\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.50000 | − | 2.59808i | 0.110282 | − | 0.191014i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −27.0000 | + | 15.5885i | −1.97444 | + | 1.13994i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.50000 | − | 2.59808i | 0.325609 | − | 0.187990i | −0.328281 | − | 0.944580i | \(-0.606469\pi\) |
0.653890 | + | 0.756590i | \(0.273136\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.00000 | − | 1.73205i | 0.0719816 | − | 0.124676i | −0.827788 | − | 0.561041i | \(-0.810401\pi\) |
0.899770 | + | 0.436365i | \(0.143734\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 20.7846i | − | 1.48084i | −0.672143 | − | 0.740421i | \(-0.734626\pi\) | ||
0.672143 | − | 0.740421i | \(-0.265374\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.73205i | − | 0.122782i | −0.998114 | − | 0.0613909i | \(-0.980446\pi\) | ||
0.998114 | − | 0.0613909i | \(-0.0195536\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.00000 | − | 25.9808i | −0.631676 | − | 1.82349i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.50000 | + | 7.79423i | 0.314294 | + | 0.544373i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.50000 | − | 7.79423i | −0.311272 | − | 0.539138i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.0000 | − | 17.3205i | 0.688428 | − | 1.19239i | −0.283918 | − | 0.958849i | \(-0.591634\pi\) |
0.972346 | − | 0.233544i | \(-0.0750324\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −30.0000 | −2.04598 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.00000 | + | 10.3923i | −0.610960 | + | 0.705476i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.0000 | − | 10.3923i | −1.21081 | − | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.5000 | − | 12.9904i | 1.50671 | − | 0.869900i | 0.506742 | − | 0.862098i | \(-0.330850\pi\) |
0.999970 | − | 0.00780243i | \(-0.00248362\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.0000 | + | 10.3923i | 1.18947 | + | 0.686743i | 0.958187 | − | 0.286143i | \(-0.0923732\pi\) |
0.231287 | + | 0.972886i | \(0.425707\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 20.7846i | − | 1.36165i | −0.732448 | − | 0.680823i | \(-0.761622\pi\) | ||
0.732448 | − | 0.680823i | \(-0.238378\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.0000 | −1.17419 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.00000 | + | 5.19615i | 0.582162 | + | 0.336111i | 0.761992 | − | 0.647586i | \(-0.224222\pi\) |
−0.179830 | + | 0.983698i | \(0.557555\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.00000 | + | 1.73205i | −0.193247 | + | 0.111571i | −0.593502 | − | 0.804833i | \(-0.702255\pi\) |
0.400255 | + | 0.916404i | \(0.368922\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −16.5000 | + | 12.9904i | −1.05415 | + | 0.829925i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.00000 | − | 5.19615i | 0.190885 | − | 0.330623i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.0000 | 1.51487 | 0.757433 | − | 0.652913i | \(-0.226453\pi\) | ||||
0.757433 | + | 0.652913i | \(0.226453\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 27.0000 | 1.69748 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.50000 | − | 7.79423i | 0.280702 | − | 0.486191i | −0.690856 | − | 0.722993i | \(-0.742766\pi\) |
0.971558 | + | 0.236802i | \(0.0760993\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.500000 | − | 2.59808i | 0.0310685 | − | 0.161437i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.50000 | − | 2.59808i | 0.277482 | − | 0.160204i | −0.354801 | − | 0.934942i | \(-0.615451\pi\) |
0.632283 | + | 0.774738i | \(0.282118\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.0000 | 1.28039 | 0.640196 | − | 0.768211i | \(-0.278853\pi\) | ||||
0.640196 | + | 0.768211i | \(0.278853\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.46410i | 0.210429i | 0.994450 | + | 0.105215i | \(0.0335529\pi\) | ||||
−0.994450 | + | 0.105215i | \(0.966447\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 18.0000 | + | 10.3923i | 1.08544 | + | 0.626680i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.50000 | + | 16.4545i | 0.570800 | + | 0.988654i | 0.996484 | + | 0.0837823i | \(0.0267000\pi\) |
−0.425684 | + | 0.904872i | \(0.639967\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.00000 | + | 5.19615i | −0.536895 | + | 0.309976i | −0.743820 | − | 0.668380i | \(-0.766988\pi\) |
0.206925 | + | 0.978357i | \(0.433655\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.00000 | + | 5.19615i | 0.534994 | + | 0.308879i | 0.743048 | − | 0.669238i | \(-0.233379\pi\) |
−0.208053 | + | 0.978117i | \(0.566713\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.00000 | + | 5.19615i | 0.354169 | + | 0.306719i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.0000 | 1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.00000 | − | 5.19615i | 0.175262 | − | 0.303562i | −0.764990 | − | 0.644042i | \(-0.777256\pi\) |
0.940252 | + | 0.340480i | \(0.110589\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.00000 | − | 15.5885i | −0.524000 | − | 0.907595i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.00000 | + | 15.5885i | 0.520483 | + | 0.901504i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −25.0000 | + | 8.66025i | −1.44098 | + | 0.499169i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 41.5692i | 2.38025i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.5885i | 0.889680i | 0.895610 | + | 0.444840i | \(0.146740\pi\) | ||||
−0.895610 | + | 0.444840i | \(0.853260\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.00000 | + | 5.19615i | −0.170114 | + | 0.294647i | −0.938460 | − | 0.345389i | \(-0.887747\pi\) |
0.768345 | + | 0.640036i | \(0.221080\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.00000 | − | 1.73205i | 0.169570 | − | 0.0979013i | −0.412813 | − | 0.910816i | \(-0.635454\pi\) |
0.582383 | + | 0.812914i | \(0.302120\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 27.0000 | − | 15.5885i | 1.51647 | − | 0.875535i | 0.516658 | − | 0.856192i | \(-0.327176\pi\) |
0.999813 | − | 0.0193432i | \(-0.00615753\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −27.0000 | + | 46.7654i | −1.51171 | + | 2.61836i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.3923i | 0.578243i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.8564i | 0.768615i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.0000 | + | 5.19615i | −0.826977 | + | 0.286473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.00000 | − | 3.46410i | −0.109930 | − | 0.190404i | 0.805812 | − | 0.592172i | \(-0.201729\pi\) |
−0.915742 | + | 0.401768i | \(0.868396\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.00000 | + | 5.19615i | 0.163908 | + | 0.283896i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.5000 | − | 25.1147i | 0.789865 | − | 1.36809i | −0.136184 | − | 0.990684i | \(-0.543484\pi\) |
0.926049 | − | 0.377403i | \(-0.123183\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 27.0000 | 1.46213 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.50000 | + | 2.59808i | 0.241573 | + | 0.139472i | 0.615899 | − | 0.787825i | \(-0.288793\pi\) |
−0.374327 | + | 0.927297i | \(0.622126\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.0000 | − | 13.8564i | 1.28469 | − | 0.741716i | 0.306988 | − | 0.951713i | \(-0.400679\pi\) |
0.977702 | + | 0.209997i | \(0.0673454\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.50000 | − | 12.9904i | −0.399185 | − | 0.691408i | 0.594441 | − | 0.804139i | \(-0.297373\pi\) |
−0.993626 | + | 0.112731i | \(0.964040\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.5000 | + | 7.79423i | 0.716506 | + | 0.413675i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 10.3923i | − | 0.548485i | −0.961661 | − | 0.274242i | \(-0.911573\pi\) | ||
0.961661 | − | 0.274242i | \(-0.0884271\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.0000 | 0.842105 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.00000 | − | 5.19615i | −0.471082 | − | 0.271979i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.50000 | + | 0.866025i | −0.0782994 | + | 0.0452062i | −0.538639 | − | 0.842537i | \(-0.681061\pi\) |
0.460339 | + | 0.887743i | \(0.347728\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.5000 | + | 25.1147i | −0.750782 | + | 1.30039i | 0.196663 | + | 0.980471i | \(0.436990\pi\) |
−0.947444 | + | 0.319921i | \(0.896344\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −36.0000 | −1.85409 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.0000 | 0.513665 | 0.256833 | − | 0.966456i | \(-0.417321\pi\) | ||||
0.256833 | + | 0.966456i | \(0.417321\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.00000 | + | 10.3923i | −0.306586 | + | 0.531022i | −0.977613 | − | 0.210411i | \(-0.932520\pi\) |
0.671027 | + | 0.741433i | \(0.265853\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 40.5000 | + | 7.79423i | 2.06407 | + | 0.397231i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.0000 | + | 10.3923i | −0.912636 | + | 0.526911i | −0.881278 | − | 0.472597i | \(-0.843316\pi\) |
−0.0313578 | + | 0.999508i | \(0.509983\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −27.0000 | − | 15.5885i | −1.36545 | − | 0.788342i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −42.0000 | −2.11325 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 20.7846i | − | 1.04315i | −0.853206 | − | 0.521575i | \(-0.825345\pi\) | ||
0.853206 | − | 0.521575i | \(-0.174655\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.00000 | + | 5.19615i | 0.449439 | + | 0.259483i | 0.707593 | − | 0.706620i | \(-0.249781\pi\) |
−0.258154 | + | 0.966104i | \(0.583114\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.00000 | + | 15.5885i | 0.448322 | + | 0.776516i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.50000 | + | 2.59808i | −0.223057 | + | 0.128782i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.0000 | − | 8.66025i | −0.741702 | − | 0.428222i | 0.0809857 | − | 0.996715i | \(-0.474193\pi\) |
−0.822688 | + | 0.568493i | \(0.807527\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.0000 | − | 10.3923i | −0.590481 | − | 0.511372i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.0000 | 0.883585 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.0000 | + | 20.7846i | −0.586238 | + | 1.01539i | 0.408481 | + | 0.912767i | \(0.366058\pi\) |
−0.994720 | + | 0.102628i | \(0.967275\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.50000 | − | 4.33013i | −0.121843 | − | 0.211037i | 0.798652 | − | 0.601793i | \(-0.205547\pi\) |
−0.920494 | + | 0.390756i | \(0.872214\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12.0000 | − | 20.7846i | −0.582086 | − | 1.00820i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.0000 | + | 34.6410i | 0.580721 | + | 1.67640i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 36.3731i | − | 1.75203i | −0.482285 | − | 0.876014i | \(-0.660193\pi\) | ||
0.482285 | − | 0.876014i | \(-0.339807\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 10.3923i | − | 0.499422i | −0.968320 | − | 0.249711i | \(-0.919664\pi\) | ||
0.968320 | − | 0.249711i | \(-0.0803357\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.50000 | − | 7.79423i | 0.215264 | − | 0.372849i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.0000 | − | 15.5885i | 1.28864 | − | 0.743996i | 0.310228 | − | 0.950662i | \(-0.399595\pi\) |
0.978412 | + | 0.206666i | \(0.0662612\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.5000 | − | 7.79423i | 0.641404 | − | 0.370315i | −0.143751 | − | 0.989614i | \(-0.545916\pi\) |
0.785155 | + | 0.619299i | \(0.212583\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.5000 | + | 23.3827i | −0.639961 | + | 1.10845i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.7846i | 0.980886i | 0.871473 | + | 0.490443i | \(0.163165\pi\) | ||||
−0.871473 | + | 0.490443i | \(0.836835\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 15.5885i | − | 0.734032i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.00000 | + | 25.9808i | 0.421927 | + | 1.21800i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.50000 | + | 14.7224i | 0.397613 | + | 0.688686i | 0.993431 | − | 0.114433i | \(-0.0365053\pi\) |
−0.595818 | + | 0.803120i | \(0.703172\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.50000 | + | 12.9904i | 0.349310 | + | 0.605022i | 0.986127 | − | 0.165992i | \(-0.0530827\pi\) |
−0.636817 | + | 0.771015i | \(0.719749\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.00000 | − | 13.8564i | 0.371792 | − | 0.643962i | −0.618050 | − | 0.786139i | \(-0.712077\pi\) |
0.989841 | + | 0.142177i | \(0.0454103\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.0000 | 0.832941 | 0.416470 | − | 0.909149i | \(-0.363267\pi\) | ||||
0.416470 | + | 0.909149i | \(0.363267\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.00000 | + | 3.46410i | 0.184703 | + | 0.159957i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 45.0000 | + | 25.9808i | 2.06910 | + | 1.19460i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.00000 | − | 3.46410i | 0.275299 | − | 0.158944i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.0000 | + | 20.7846i | 0.548294 | + | 0.949673i | 0.998392 | + | 0.0566937i | \(0.0180558\pi\) |
−0.450098 | + | 0.892979i | \(0.648611\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.00000 | − | 1.73205i | −0.136788 | − | 0.0789747i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 20.7846i | 0.943781i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −26.0000 | −1.17817 | −0.589086 | − | 0.808070i | \(-0.700512\pi\) | ||||
−0.589086 | + | 0.808070i | \(0.700512\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.5000 | − | 7.79423i | −0.609246 | − | 0.351749i | 0.163424 | − | 0.986556i | \(-0.447746\pi\) |
−0.772670 | + | 0.634807i | \(0.781079\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 54.0000 | − | 31.1769i | 2.43204 | − | 1.40414i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.5000 | + | 2.59808i | 0.605558 | + | 0.116540i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.00000 | − | 12.1244i | 0.313363 | − | 0.542761i | −0.665725 | − | 0.746197i | \(-0.731878\pi\) |
0.979088 | + | 0.203436i | \(0.0652110\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.00000 | −0.267527 | −0.133763 | − | 0.991013i | \(-0.542706\pi\) | ||||
−0.133763 | + | 0.991013i | \(0.542706\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 54.0000 | 2.40297 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.0000 | − | 36.3731i | 0.930809 | − | 1.61221i | 0.148866 | − | 0.988857i | \(-0.452438\pi\) |
0.781943 | − | 0.623350i | \(-0.214229\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.00000 | − | 1.73205i | −0.398137 | − | 0.0766214i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 22.5000 | − | 12.9904i | 0.991468 | − | 0.572425i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 27.0000 | + | 15.5885i | 1.18746 | + | 0.685580i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.0000 | −1.44576 | −0.722878 | − | 0.690976i | \(-0.757181\pi\) | ||||
−0.722878 | + | 0.690976i | \(0.757181\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 12.1244i | − | 0.530161i | −0.964226 | − | 0.265081i | \(-0.914601\pi\) | ||
0.964226 | − | 0.265081i | \(-0.0853985\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −27.0000 | − | 15.5885i | −1.17614 | − | 0.679044i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.00000 | + | 3.46410i | 0.0869565 | + | 0.150613i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.00000 | − | 5.19615i | 0.389833 | − | 0.225070i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 27.0000 | + | 15.5885i | 1.16731 | + | 0.673948i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 36.0000 | − | 5.19615i | 1.55063 | − | 0.223814i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.0000 | 0.730887 | 0.365444 | − | 0.930834i | \(-0.380917\pi\) | ||||
0.365444 | + | 0.930834i | \(0.380917\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.5000 | + | 28.5788i | −0.706782 | + | 1.22418i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.0000 | + | 34.6410i | 0.855138 | + | 1.48114i | 0.876517 | + | 0.481371i | \(0.159861\pi\) |
−0.0213785 | + | 0.999771i | \(0.506805\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.00000 | + | 15.5885i | 0.383413 | + | 0.664091i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −35.0000 | + | 12.1244i | −1.48835 | + | 0.515580i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 20.7846i | − | 0.880672i | −0.897833 | − | 0.440336i | \(-0.854859\pi\) | ||
0.897833 | − | 0.440336i | \(-0.145141\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.6410i | 1.46516i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.00000 | + | 15.5885i | −0.379305 | + | 0.656975i | −0.990961 | − | 0.134148i | \(-0.957170\pi\) |
0.611656 | + | 0.791123i | \(0.290503\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −36.0000 | + | 20.7846i | −1.50920 | + | 0.871336i | −0.509256 | + | 0.860615i | \(0.670079\pi\) |
−0.999943 | + | 0.0107211i | \(0.996587\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0000 | + | 17.3205i | −0.418487 | + | 0.724841i | −0.995788 | − | 0.0916910i | \(-0.970773\pi\) |
0.577301 | + | 0.816532i | \(0.304106\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.7846i | 0.866778i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 34.6410i | − | 1.44212i | −0.692870 | − | 0.721062i | \(-0.743654\pi\) | ||
0.692870 | − | 0.721062i | \(-0.256346\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.0000 | − | 5.19615i | 0.622305 | − | 0.215573i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.0000 | − | 31.1769i | −0.742940 | − | 1.28681i | −0.951151 | − | 0.308725i | \(-0.900098\pi\) |
0.208212 | − | 0.978084i | \(-0.433236\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.50000 | − | 7.79423i | 0.185419 | − | 0.321156i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 39.0000 | 1.60154 | 0.800769 | − | 0.598973i | \(-0.204424\pi\) | ||||
0.800769 | + | 0.598973i | \(0.204424\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −36.0000 | − | 31.1769i | −1.47586 | − | 1.27813i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22.5000 | − | 12.9904i | −0.919325 | − | 0.530773i | −0.0359054 | − | 0.999355i | \(-0.511431\pi\) |
−0.883420 | + | 0.468583i | \(0.844765\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.00000 | + | 5.19615i | −0.367118 | + | 0.211955i | −0.672198 | − | 0.740371i | \(-0.734650\pi\) |
0.305081 | + | 0.952326i | \(0.401317\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −24.0000 | − | 41.5692i | −0.975739 | − | 1.69003i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.0000 | + | 8.66025i | 0.608831 | + | 0.351509i | 0.772508 | − | 0.635005i | \(-0.219002\pi\) |
−0.163677 | + | 0.986514i | \(0.552335\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.7846i | 0.840855i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.0000 | −0.767403 | −0.383701 | − | 0.923457i | \(-0.625351\pi\) | ||||
−0.383701 | + | 0.923457i | \(0.625351\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.0000 | − | 15.5885i | −1.08698 | − | 0.627568i | −0.154209 | − | 0.988038i | \(-0.549283\pi\) |
−0.932771 | + | 0.360471i | \(0.882616\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.5000 | + | 16.4545i | −1.14551 | + | 0.661361i | −0.947790 | − | 0.318897i | \(-0.896688\pi\) |
−0.197722 | + | 0.980258i | \(0.563354\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.50000 | + | 23.3827i | −0.180289 | + | 0.936808i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | − | 25.1147i | 0.580000 | − | 1.00459i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.00000 | 0.239236 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.0000 | 1.03504 | 0.517522 | − | 0.855670i | \(-0.326855\pi\) | ||||
0.517522 | + | 0.855670i | \(0.326855\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.00000 | − | 5.19615i | 0.119051 | − | 0.206203i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.0000 | + | 19.0526i | 0.594322 | + | 0.754890i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.0000 | + | 10.3923i | −0.710957 | + | 0.410471i | −0.811415 | − | 0.584470i | \(-0.801302\pi\) |
0.100458 | + | 0.994941i | \(0.467969\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.5000 | + | 23.3827i | 1.59716 | + | 0.922123i | 0.992030 | + | 0.125999i | \(0.0402137\pi\) |
0.605134 | + | 0.796124i | \(0.293120\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.0000 | 0.707653 | 0.353827 | − | 0.935311i | \(-0.384880\pi\) | ||||
0.353827 | + | 0.935311i | \(0.384880\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 31.1769i | 1.22380i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.00000 | − | 5.19615i | −0.352197 | − | 0.203341i | 0.313455 | − | 0.949603i | \(-0.398513\pi\) |
−0.665653 | + | 0.746262i | \(0.731847\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 27.0000 | + | 46.7654i | 1.05498 | + | 1.82727i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 31.5000 | − | 18.1865i | 1.22707 | − | 0.708447i | 0.260651 | − | 0.965433i | \(-0.416063\pi\) |
0.966415 | + | 0.256986i | \(0.0827296\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.0000 | − | 12.1244i | −0.816805 | − | 0.471583i | 0.0325082 | − | 0.999471i | \(-0.489650\pi\) |
−0.849314 | + | 0.527889i | \(0.822984\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.00000 | − | 10.3923i | 0.349005 | − | 0.402996i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −54.0000 | −2.09089 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 36.0000 | − | 62.3538i | 1.38976 | − | 2.40714i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.0000 | − | 19.0526i | −0.424019 | − | 0.734422i | 0.572309 | − | 0.820038i | \(-0.306048\pi\) |
−0.996328 | + | 0.0856156i | \(0.972714\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.5000 | + | 23.3827i | 0.518847 | + | 0.898670i | 0.999760 | + | 0.0219013i | \(0.00697196\pi\) |
−0.480913 | + | 0.876768i | \(0.659695\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.00000 | + | 17.3205i | 0.230259 | + | 0.664700i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.5885i | 0.596476i | 0.954492 | + | 0.298238i | \(0.0963989\pi\) | ||||
−0.954492 | + | 0.298238i | \(0.903601\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 31.1769i | − | 1.19121i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.00000 | + | 5.19615i | −0.342376 | + | 0.197671i | −0.661322 | − | 0.750102i | \(-0.730004\pi\) |
0.318946 | + | 0.947773i | \(0.396671\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −45.0000 | + | 25.9808i | −1.70695 | + | 0.985506i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.00000 | + | 15.5885i | −0.340899 | + | 0.590455i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 31.1769i | − | 1.17754i | −0.808302 | − | 0.588768i | \(-0.799613\pi\) | ||
0.808302 | − | 0.588768i | \(-0.200387\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.73205i | 0.0653255i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 45.0000 | − | 15.5885i | 1.69240 | − | 0.586264i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.5000 | + | 19.9186i | 0.431892 | + | 0.748058i | 0.997036 | − | 0.0769337i | \(-0.0245130\pi\) |
−0.565145 | + | 0.824992i | \(0.691180\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.5000 | + | 23.3827i | 0.505579 | + | 0.875688i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 27.0000 | − | 46.7654i | 1.00974 | − | 1.74893i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.00000 | −0.223762 | −0.111881 | − | 0.993722i | \(-0.535688\pi\) | ||||
−0.111881 | + | 0.993722i | \(0.535688\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.0000 | − | 17.3205i | 0.558629 | − | 0.645049i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −36.0000 | − | 20.7846i | −1.33701 | − | 0.771921i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27.0000 | + | 15.5885i | −1.00137 | + | 0.578144i | −0.908655 | − | 0.417548i | \(-0.862889\pi\) |
−0.0927199 | + | 0.995692i | \(0.529556\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30.0000 | − | 51.9615i | −1.10959 | − | 1.92187i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.00000 | − | 5.19615i | −0.332423 | − | 0.191924i | 0.324494 | − | 0.945888i | \(-0.394806\pi\) |
−0.656916 | + | 0.753964i | \(0.728139\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 10.3923i | − | 0.382805i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.0000 | −0.588570 | −0.294285 | − | 0.955718i | \(-0.595081\pi\) | ||||
−0.294285 | + | 0.955718i | \(0.595081\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.5000 | + | 18.1865i | 1.15562 | + | 0.667199i | 0.950251 | − | 0.311485i | \(-0.100826\pi\) |
0.205372 | + | 0.978684i | \(0.434160\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 27.0000 | + | 5.19615i | 0.986559 | + | 0.189863i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.00000 | − | 1.73205i | 0.0364905 | − | 0.0632034i | −0.847203 | − | 0.531269i | \(-0.821715\pi\) |
0.883694 | + | 0.468065i | \(0.155049\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.0000 | −0.436725 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.0000 | −0.944986 | −0.472493 | − | 0.881334i | \(-0.656646\pi\) | ||||
−0.472493 | + | 0.881334i | \(0.656646\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.00000 | − | 5.19615i | 0.108750 | − | 0.188360i | −0.806514 | − | 0.591215i | \(-0.798649\pi\) |
0.915264 | + | 0.402854i | \(0.131982\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.50000 | + | 28.5788i | −0.199113 | + | 1.03462i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18.0000 | + | 10.3923i | −0.649942 | + | 0.375244i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.00000 | + | 1.73205i | 0.108183 | + | 0.0624593i | 0.553115 | − | 0.833105i | \(-0.313439\pi\) |
−0.444932 | + | 0.895564i | \(0.646772\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −39.0000 | −1.40273 | −0.701366 | − | 0.712801i | \(-0.747426\pi\) | ||||
−0.701366 | + | 0.712801i | \(0.747426\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.7846i | 0.746605i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.50000 | − | 2.59808i | −0.161229 | − | 0.0930857i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.5000 | − | 23.3827i | −0.483068 | − | 0.836698i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 27.0000 | − | 15.5885i | 0.963671 | − | 0.556376i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.0000 | + | 19.0526i | 1.17632 | + | 0.679150i | 0.955161 | − | 0.296087i | \(-0.0956817\pi\) |
0.221162 | + | 0.975237i | \(0.429015\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 48.0000 | 1.70453 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22.5000 | + | 38.9711i | −0.796991 | + | 1.38043i | 0.124576 | + | 0.992210i | \(0.460243\pi\) |
−0.921567 | + | 0.388219i | \(0.873091\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.0000 | − | 31.1769i | −0.636794 | − | 1.10296i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.00000 | + | 15.5885i | 0.317603 | + | 0.550105i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.5000 | + | 38.9711i | 0.475812 | + | 1.37355i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 31.1769i | − | 1.09612i | −0.836438 | − | 0.548061i | \(-0.815366\pi\) | ||
0.836438 | − | 0.548061i | \(-0.184634\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 5.19615i | − | 0.182462i | −0.995830 | − | 0.0912308i | \(-0.970920\pi\) | ||
0.995830 | − | 0.0912308i | \(-0.0290801\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15.0000 | + | 25.9808i | −0.525427 | + | 0.910066i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.0000 | − | 8.66025i | 0.524784 | − | 0.302984i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.0000 | − | 15.5885i | 0.942306 | − | 0.544041i | 0.0516239 | − | 0.998667i | \(-0.483560\pi\) |
0.890683 | + | 0.454626i | \(0.150227\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.0000 | + | 17.3205i | −0.348578 | + | 0.603755i | −0.985997 | − | 0.166762i | \(-0.946669\pi\) |
0.637419 | + | 0.770517i | \(0.280002\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 46.7654i | − | 1.62619i | −0.582130 | − | 0.813096i | \(-0.697781\pi\) | ||
0.582130 | − | 0.813096i | \(-0.302219\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.0333i | 1.56407i | 0.623233 | + | 0.782036i | \(0.285819\pi\) | ||||
−0.623233 | + | 0.782036i | \(0.714181\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −39.0000 | − | 15.5885i | −1.35127 | − | 0.540108i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.0000 | − | 31.1769i | −0.622916 | − | 1.07892i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.0000 | − | 36.3731i | −0.725001 | − | 1.25574i | −0.958974 | − | 0.283495i | \(-0.908506\pi\) |
0.233973 | − | 0.972243i | \(-0.424827\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 39.5000 | − | 68.4160i | 1.36207 | − | 2.35917i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.00000 | −0.103203 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −32.0000 | − | 27.7128i | −1.09953 | − | 0.952224i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.50000 | − | 2.59808i | −0.154258 | − | 0.0890609i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −42.0000 | + | 24.2487i | −1.43805 | + | 0.830260i | −0.997714 | − | 0.0675719i | \(-0.978475\pi\) |
−0.440338 | + | 0.897832i | \(0.645141\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.5000 | + | 18.1865i | 0.358673 | + | 0.621240i | 0.987739 | − | 0.156112i | \(-0.0498959\pi\) |
−0.629066 | + | 0.777352i | \(0.716563\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.5000 | − | 14.7224i | −0.870049 | − | 0.502323i | −0.00268433 | − | 0.999996i | \(-0.500854\pi\) |
−0.867364 | + | 0.497674i | \(0.834188\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 10.3923i | − | 0.353758i | −0.984233 | − | 0.176879i | \(-0.943400\pi\) | ||
0.984233 | − | 0.176879i | \(-0.0566002\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −27.0000 | −0.918028 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 63.0000 | + | 36.3731i | 2.13713 | + | 1.23387i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.00000 | − | 3.46410i | 0.203302 | − | 0.117377i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.50000 | − | 7.79423i | 0.0507093 | − | 0.263493i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.00000 | + | 1.73205i | −0.0337676 | + | 0.0584872i | −0.882415 | − | 0.470471i | \(-0.844084\pi\) |
0.848648 | + | 0.528958i | \(0.177417\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.0000 | 0.909653 | 0.454827 | − | 0.890580i | \(-0.349701\pi\) | ||||
0.454827 | + | 0.890580i | \(0.349701\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.0000 | 0.942275 | 0.471138 | − | 0.882060i | \(-0.343844\pi\) | ||||
0.471138 | + | 0.882060i | \(0.343844\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.0000 | + | 36.3731i | −0.705111 | + | 1.22129i | 0.261540 | + | 0.965193i | \(0.415770\pi\) |
−0.966651 | + | 0.256096i | \(0.917564\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | − | 5.19615i | 0.0335389 | − | 0.174273i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.00000 | − | 5.19615i | 0.301174 | − | 0.173883i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −27.0000 | − | 15.5885i | −0.902510 | − | 0.521065i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −54.0000 | −1.80100 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.0000 | − | 10.3923i | −0.598340 | − | 0.345452i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.0000 | + | 27.7128i | 0.531271 | + | 0.920189i | 0.999334 | + | 0.0364935i | \(0.0116188\pi\) |
−0.468063 | + | 0.883695i | \(0.655048\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.00000 | − | 5.19615i | 0.298183 | − | 0.172156i | −0.343443 | − | 0.939173i | \(-0.611593\pi\) |
0.641626 | + | 0.767017i | \(0.278260\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.0000 | − | 15.5885i | −0.893570 | − | 0.515903i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 36.0000 | + | 31.1769i | 1.18882 | + | 1.02955i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.0000 | 0.527791 | 0.263896 | − | 0.964551i | \(-0.414993\pi\) | ||||
0.263896 | + | 0.964551i | \(0.414993\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.00000 | − | 15.5885i | 0.296239 | − | 0.513100i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.00000 | − | 3.46410i | −0.0657596 | − | 0.113899i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.0000 | + | 25.9808i | 0.492134 | + | 0.852401i | 0.999959 | − | 0.00905914i | \(-0.00288365\pi\) |
−0.507825 | + | 0.861460i | \(0.669550\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.50000 | − | 11.2583i | 0.147482 | − | 0.368977i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 93.5307i | 3.05878i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 55.4256i | − | 1.81068i | −0.424691 | − | 0.905338i | \(-0.639617\pi\) | ||
0.424691 | − | 0.905338i | \(-0.360383\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.5000 | + | 18.1865i | −0.342290 | + | 0.592864i | −0.984858 | − | 0.173365i | \(-0.944536\pi\) |
0.642567 | + | 0.766229i | \(0.277869\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.5000 | − | 7.79423i | 0.439620 | − | 0.253815i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.5000 | + | 12.9904i | −0.731152 | + | 0.422131i | −0.818843 | − | 0.574017i | \(-0.805384\pi\) |
0.0876916 | + | 0.996148i | \(0.472051\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.00000 | + | 10.3923i | −0.194768 | + | 0.337348i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.1769i | 1.00992i | 0.863143 | + | 0.504960i | \(0.168493\pi\) | ||||
−0.863143 | + | 0.504960i | \(0.831507\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 15.5885i | − | 0.504431i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.00000 | − | 25.9808i | −0.290625 | − | 0.838963i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.00000 | − | 3.46410i | −0.0645161 | − | 0.111745i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.00000 | − | 5.19615i | −0.0965734 | − | 0.167270i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.00000 | − | 13.8564i | 0.257263 | − | 0.445592i | −0.708245 | − | 0.705967i | \(-0.750513\pi\) |
0.965508 | + | 0.260375i | \(0.0838461\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.00000 | −0.192549 | −0.0962746 | − | 0.995355i | \(-0.530693\pi\) | ||||
−0.0962746 | + | 0.995355i | \(0.530693\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −30.0000 | + | 34.6410i | −0.961756 | + | 1.11054i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 36.0000 | + | 20.7846i | 1.15174 | + | 0.664959i | 0.949311 | − | 0.314338i | \(-0.101783\pi\) |
0.202431 | + | 0.979297i | \(0.435116\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 40.5000 | − | 23.3827i | 1.29439 | − | 0.747314i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.0000 | + | 36.3731i | 0.669796 | + | 1.16012i | 0.977961 | + | 0.208788i | \(0.0669518\pi\) |
−0.308165 | + | 0.951333i | \(0.599715\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −54.0000 | − | 31.1769i | −1.72058 | − | 0.993379i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 51.9615i | 1.65228i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.0000 | 0.317660 | 0.158830 | − | 0.987306i | \(-0.449228\pi\) | ||||
0.158830 | + | 0.987306i | \(0.449228\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.50000 | − | 2.59808i | −0.142660 | − | 0.0823646i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(998\) | 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 | 2268.2.x.h.377.1 | 2 | ||
3.2 | odd | 2 | 2268.2.x.b.377.1 | 2 | |||
7.6 | odd | 2 | 2268.2.x.a.377.1 | 2 | |||
9.2 | odd | 6 | 2268.2.x.a.1889.1 | 2 | |||
9.4 | even | 3 | 756.2.f.a.377.2 | yes | 2 | ||
9.5 | odd | 6 | 756.2.f.c.377.2 | yes | 2 | ||
9.7 | even | 3 | 2268.2.x.g.1889.1 | 2 | |||
21.20 | even | 2 | 2268.2.x.g.377.1 | 2 | |||
36.23 | even | 6 | 3024.2.k.d.1889.1 | 2 | |||
36.31 | odd | 6 | 3024.2.k.a.1889.1 | 2 | |||
63.13 | odd | 6 | 756.2.f.c.377.1 | yes | 2 | ||
63.20 | even | 6 | inner | 2268.2.x.h.1889.1 | 2 | ||
63.34 | odd | 6 | 2268.2.x.b.1889.1 | 2 | |||
63.41 | even | 6 | 756.2.f.a.377.1 | ✓ | 2 | ||
252.139 | even | 6 | 3024.2.k.d.1889.2 | 2 | |||
252.167 | odd | 6 | 3024.2.k.a.1889.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.f.a.377.1 | ✓ | 2 | 63.41 | even | 6 | ||
756.2.f.a.377.2 | yes | 2 | 9.4 | even | 3 | ||
756.2.f.c.377.1 | yes | 2 | 63.13 | odd | 6 | ||
756.2.f.c.377.2 | yes | 2 | 9.5 | odd | 6 | ||
2268.2.x.a.377.1 | 2 | 7.6 | odd | 2 | |||
2268.2.x.a.1889.1 | 2 | 9.2 | odd | 6 | |||
2268.2.x.b.377.1 | 2 | 3.2 | odd | 2 | |||
2268.2.x.b.1889.1 | 2 | 63.34 | odd | 6 | |||
2268.2.x.g.377.1 | 2 | 21.20 | even | 2 | |||
2268.2.x.g.1889.1 | 2 | 9.7 | even | 3 | |||
2268.2.x.h.377.1 | 2 | 1.1 | even | 1 | trivial | ||
2268.2.x.h.1889.1 | 2 | 63.20 | even | 6 | inner | ||
3024.2.k.a.1889.1 | 2 | 36.31 | odd | 6 | |||
3024.2.k.a.1889.2 | 2 | 252.167 | odd | 6 | |||
3024.2.k.d.1889.1 | 2 | 36.23 | even | 6 | |||
3024.2.k.d.1889.2 | 2 | 252.139 | even | 6 |