Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [867,2,Mod(616,867)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(867, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("867.616");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 867 = 3 \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 867.e (of order \(4\), 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: | \(6.92302985525\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.5473632256.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 49x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 51) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 829.1 | ||
Root | \(-1.81129 + 1.81129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 867.829 |
Dual form | 867.2.e.f.616.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/867\mathbb{Z}\right)^\times\).
\(n\) | \(290\) | \(292\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.56155i | − | 1.10418i | −0.833783 | − | 0.552092i | \(-0.813830\pi\) | ||
0.833783 | − | 0.552092i | \(-0.186170\pi\) | |||||||
\(3\) | −0.707107 | − | 0.707107i | −0.408248 | − | 0.408248i | ||||
\(4\) | −0.438447 | −0.219224 | ||||||||
\(5\) | 0.397078 | + | 0.397078i | 0.177579 | + | 0.177579i | 0.790299 | − | 0.612721i | \(-0.209925\pi\) |
−0.612721 | + | 0.790299i | \(0.709925\pi\) | |||||||
\(6\) | −1.10418 | + | 1.10418i | −0.450781 | + | 0.450781i | ||||
\(7\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(8\) | − | 2.43845i | − | 0.862121i | ||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0.620058 | − | 0.620058i | 0.196080 | − | 0.196080i | ||||
\(11\) | −1.81129 | + | 1.81129i | −0.546125 | + | 0.546125i | −0.925318 | − | 0.379193i | \(-0.876202\pi\) |
0.379193 | + | 0.925318i | \(0.376202\pi\) | |||||||
\(12\) | 0.310029 | + | 0.310029i | 0.0894977 | + | 0.0894977i | ||||
\(13\) | −4.56155 | −1.26515 | −0.632574 | − | 0.774500i | \(-0.718001\pi\) | ||||
−0.632574 | + | 0.774500i | \(0.718001\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 0.561553i | − | 0.144992i | ||||||
\(16\) | −4.68466 | −1.17116 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 1.56155 | 0.368062 | ||||||||
\(19\) | − | 7.68466i | − | 1.76298i | −0.472201 | − | 0.881491i | \(-0.656540\pi\) | ||
0.472201 | − | 0.881491i | \(-0.343460\pi\) | |||||||
\(20\) | −0.174098 | − | 0.174098i | −0.0389294 | − | 0.0389294i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.82843 | + | 2.82843i | 0.603023 | + | 0.603023i | ||||
\(23\) | −4.63972 | + | 4.63972i | −0.967448 | + | 0.967448i | −0.999487 | − | 0.0320385i | \(-0.989800\pi\) |
0.0320385 | + | 0.999487i | \(0.489800\pi\) | |||||||
\(24\) | −1.72424 | + | 1.72424i | −0.351960 | + | 0.351960i | ||||
\(25\) | − | 4.68466i | − | 0.936932i | ||||||
\(26\) | 7.12311i | 1.39696i | ||||||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.83095 | − | 5.83095i | −1.08278 | − | 1.08278i | −0.996249 | − | 0.0865315i | \(-0.972422\pi\) |
−0.0865315 | − | 0.996249i | \(-0.527578\pi\) | |||||||
\(30\) | −0.876894 | −0.160098 | ||||||||
\(31\) | −3.62258 | − | 3.62258i | −0.650635 | − | 0.650635i | 0.302511 | − | 0.953146i | \(-0.402175\pi\) |
−0.953146 | + | 0.302511i | \(0.902175\pi\) | |||||||
\(32\) | 2.43845i | 0.431061i | ||||||||
\(33\) | 2.56155 | 0.445909 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | − | 0.438447i | − | 0.0730745i | ||||||
\(37\) | 2.20837 | + | 2.20837i | 0.363054 | + | 0.363054i | 0.864936 | − | 0.501882i | \(-0.167359\pi\) |
−0.501882 | + | 0.864936i | \(0.667359\pi\) | |||||||
\(38\) | −12.0000 | −1.94666 | ||||||||
\(39\) | 3.22550 | + | 3.22550i | 0.516494 | + | 0.516494i | ||||
\(40\) | 0.968253 | − | 0.968253i | 0.153094 | − | 0.153094i | ||||
\(41\) | −0.397078 | + | 0.397078i | −0.0620131 | + | 0.0620131i | −0.737433 | − | 0.675420i | \(-0.763962\pi\) |
0.675420 | + | 0.737433i | \(0.263962\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.68466i | − | 1.17190i | −0.810347 | − | 0.585950i | \(-0.800722\pi\) | ||
0.810347 | − | 0.585950i | \(-0.199278\pi\) | |||||||
\(44\) | 0.794156 | − | 0.794156i | 0.119723 | − | 0.119723i | ||||
\(45\) | −0.397078 | + | 0.397078i | −0.0591929 | + | 0.0591929i | ||||
\(46\) | 7.24517 | + | 7.24517i | 1.06824 | + | 1.06824i | ||||
\(47\) | 2.87689 | 0.419638 | 0.209819 | − | 0.977740i | \(-0.432712\pi\) | ||||
0.209819 | + | 0.977740i | \(0.432712\pi\) | |||||||
\(48\) | 3.31255 | + | 3.31255i | 0.478126 | + | 0.478126i | ||||
\(49\) | 7.00000i | 1.00000i | ||||||||
\(50\) | −7.31534 | −1.03455 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.00000 | 0.277350 | ||||||||
\(53\) | 4.24621i | 0.583262i | 0.956531 | + | 0.291631i | \(0.0941979\pi\) | ||||
−0.956531 | + | 0.291631i | \(0.905802\pi\) | |||||||
\(54\) | −1.10418 | − | 1.10418i | −0.150260 | − | 0.150260i | ||||
\(55\) | −1.43845 | −0.193960 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.43387 | + | 5.43387i | −0.719734 | + | 0.719734i | ||||
\(58\) | −9.10534 | + | 9.10534i | −1.19559 | + | 1.19559i | ||||
\(59\) | − | 1.12311i | − | 0.146216i | −0.997324 | − | 0.0731079i | \(-0.976708\pi\) | ||
0.997324 | − | 0.0731079i | \(-0.0232918\pi\) | |||||||
\(60\) | 0.246211i | 0.0317857i | ||||||||
\(61\) | −0.620058 | + | 0.620058i | −0.0793903 | + | 0.0793903i | −0.745687 | − | 0.666297i | \(-0.767878\pi\) |
0.666297 | + | 0.745687i | \(0.267878\pi\) | |||||||
\(62\) | −5.65685 | + | 5.65685i | −0.718421 | + | 0.718421i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.56155 | −0.695194 | ||||||||
\(65\) | −1.81129 | − | 1.81129i | −0.224663 | − | 0.224663i | ||||
\(66\) | − | 4.00000i | − | 0.492366i | ||||||
\(67\) | 4.00000 | 0.488678 | 0.244339 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.56155 | 0.789918 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.24517 | + | 7.24517i | 0.859843 | + | 0.859843i | 0.991319 | − | 0.131476i | \(-0.0419717\pi\) |
−0.131476 | + | 0.991319i | \(0.541972\pi\) | |||||||
\(72\) | 2.43845 | 0.287374 | ||||||||
\(73\) | −3.00252 | − | 3.00252i | −0.351419 | − | 0.351419i | 0.509218 | − | 0.860637i | \(-0.329935\pi\) |
−0.860637 | + | 0.509218i | \(0.829935\pi\) | |||||||
\(74\) | 3.44849 | − | 3.44849i | 0.400878 | − | 0.400878i | ||||
\(75\) | −3.31255 | + | 3.31255i | −0.382501 | + | 0.382501i | ||||
\(76\) | 3.36932i | 0.386487i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.03680 | − | 5.03680i | 0.570305 | − | 0.570305i | ||||
\(79\) | 10.8677 | − | 10.8677i | 1.22272 | − | 1.22272i | 0.256055 | − | 0.966662i | \(-0.417577\pi\) |
0.966662 | − | 0.256055i | \(-0.0824228\pi\) | |||||||
\(80\) | −1.86017 | − | 1.86017i | −0.207974 | − | 0.207974i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0.620058 | + | 0.620058i | 0.0684739 | + | 0.0684739i | ||||
\(83\) | 9.12311i | 1.00139i | 0.865624 | + | 0.500695i | \(0.166922\pi\) | ||||
−0.865624 | + | 0.500695i | \(0.833078\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −12.0000 | −1.29399 | ||||||||
\(87\) | 8.24621i | 0.884087i | ||||||||
\(88\) | 4.41674 | + | 4.41674i | 0.470826 | + | 0.470826i | ||||
\(89\) | −7.12311 | −0.755048 | −0.377524 | − | 0.926000i | \(-0.623224\pi\) | ||||
−0.377524 | + | 0.926000i | \(0.623224\pi\) | |||||||
\(90\) | 0.620058 | + | 0.620058i | 0.0653598 | + | 0.0653598i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.03427 | − | 2.03427i | 0.212087 | − | 0.212087i | ||||
\(93\) | 5.12311i | 0.531241i | ||||||||
\(94\) | − | 4.49242i | − | 0.463358i | ||||||
\(95\) | 3.05141 | − | 3.05141i | 0.313068 | − | 0.313068i | ||||
\(96\) | 1.72424 | − | 1.72424i | 0.175980 | − | 0.175980i | ||||
\(97\) | 7.86522 | + | 7.86522i | 0.798592 | + | 0.798592i | 0.982874 | − | 0.184281i | \(-0.0589957\pi\) |
−0.184281 | + | 0.982874i | \(0.558996\pi\) | |||||||
\(98\) | 10.9309 | 1.10418 | ||||||||
\(99\) | −1.81129 | − | 1.81129i | −0.182042 | − | 0.182042i | ||||
\(100\) | 2.05398i | 0.205398i | ||||||||
\(101\) | 19.1231 | 1.90282 | 0.951410 | − | 0.307927i | \(-0.0996352\pi\) | ||||
0.951410 | + | 0.307927i | \(0.0996352\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.31534 | 0.425203 | 0.212602 | − | 0.977139i | \(-0.431806\pi\) | ||||
0.212602 | + | 0.977139i | \(0.431806\pi\) | |||||||
\(104\) | 11.1231i | 1.09071i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.63068 | 0.644029 | ||||||||
\(107\) | −5.43387 | − | 5.43387i | −0.525312 | − | 0.525312i | 0.393859 | − | 0.919171i | \(-0.371140\pi\) |
−0.919171 | + | 0.393859i | \(0.871140\pi\) | |||||||
\(108\) | −0.310029 | + | 0.310029i | −0.0298326 | + | 0.0298326i | ||||
\(109\) | 10.6937 | − | 10.6937i | 1.02427 | − | 1.02427i | 0.0245678 | − | 0.999698i | \(-0.492179\pi\) |
0.999698 | − | 0.0245678i | \(-0.00782096\pi\) | |||||||
\(110\) | 2.24621i | 0.214168i | ||||||||
\(111\) | − | 3.12311i | − | 0.296432i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.22550 | + | 3.22550i | −0.303430 | + | 0.303430i | −0.842354 | − | 0.538924i | \(-0.818831\pi\) |
0.538924 | + | 0.842354i | \(0.318831\pi\) | |||||||
\(114\) | 8.48528 | + | 8.48528i | 0.794719 | + | 0.794719i | ||||
\(115\) | −3.68466 | −0.343596 | ||||||||
\(116\) | 2.55656 | + | 2.55656i | 0.237371 | + | 0.237371i | ||||
\(117\) | − | 4.56155i | − | 0.421716i | ||||||
\(118\) | −1.75379 | −0.161449 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.36932 | −0.125001 | ||||||||
\(121\) | 4.43845i | 0.403495i | ||||||||
\(122\) | 0.968253 | + | 0.968253i | 0.0876615 | + | 0.0876615i | ||||
\(123\) | 0.561553 | 0.0506335 | ||||||||
\(124\) | 1.58831 | + | 1.58831i | 0.142635 | + | 0.142635i | ||||
\(125\) | 3.84556 | − | 3.84556i | 0.343958 | − | 0.343958i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 0.807764i | − | 0.0716775i | −0.999358 | − | 0.0358387i | \(-0.988590\pi\) | ||
0.999358 | − | 0.0358387i | \(-0.0114103\pi\) | |||||||
\(128\) | 13.5616i | 1.19868i | ||||||||
\(129\) | −5.43387 | + | 5.43387i | −0.478426 | + | 0.478426i | ||||
\(130\) | −2.82843 | + | 2.82843i | −0.248069 | + | 0.248069i | ||||
\(131\) | −13.1250 | − | 13.1250i | −1.14674 | − | 1.14674i | −0.987190 | − | 0.159546i | \(-0.948997\pi\) |
−0.159546 | − | 0.987190i | \(-0.551003\pi\) | |||||||
\(132\) | −1.12311 | −0.0977538 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 6.24621i | − | 0.539590i | ||||||
\(135\) | 0.561553 | 0.0483308 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.2462 | −1.38801 | −0.694004 | − | 0.719971i | \(-0.744155\pi\) | ||||
−0.694004 | + | 0.719971i | \(0.744155\pi\) | |||||||
\(138\) | − | 10.2462i | − | 0.872215i | ||||||
\(139\) | −6.45101 | − | 6.45101i | −0.547168 | − | 0.547168i | 0.378453 | − | 0.925621i | \(-0.376456\pi\) |
−0.925621 | + | 0.378453i | \(0.876456\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.03427 | − | 2.03427i | −0.171317 | − | 0.171317i | ||||
\(142\) | 11.3137 | − | 11.3137i | 0.949425 | − | 0.949425i | ||||
\(143\) | 8.26230 | − | 8.26230i | 0.690928 | − | 0.690928i | ||||
\(144\) | − | 4.68466i | − | 0.390388i | ||||||
\(145\) | − | 4.63068i | − | 0.384557i | ||||||
\(146\) | −4.68860 | + | 4.68860i | −0.388031 | + | 0.388031i | ||||
\(147\) | 4.94975 | − | 4.94975i | 0.408248 | − | 0.408248i | ||||
\(148\) | −0.968253 | − | 0.968253i | −0.0795899 | − | 0.0795899i | ||||
\(149\) | 4.24621 | 0.347863 | 0.173932 | − | 0.984758i | \(-0.444353\pi\) | ||||
0.173932 | + | 0.984758i | \(0.444353\pi\) | |||||||
\(150\) | 5.17273 | + | 5.17273i | 0.422351 | + | 0.422351i | ||||
\(151\) | − | 8.00000i | − | 0.651031i | −0.945537 | − | 0.325515i | \(-0.894462\pi\) | ||
0.945537 | − | 0.325515i | \(-0.105538\pi\) | |||||||
\(152\) | −18.7386 | −1.51990 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 2.87689i | − | 0.231078i | ||||||
\(156\) | −1.41421 | − | 1.41421i | −0.113228 | − | 0.113228i | ||||
\(157\) | 5.68466 | 0.453685 | 0.226843 | − | 0.973931i | \(-0.427160\pi\) | ||||
0.226843 | + | 0.973931i | \(0.427160\pi\) | |||||||
\(158\) | −16.9706 | − | 16.9706i | −1.35011 | − | 1.35011i | ||||
\(159\) | 3.00252 | − | 3.00252i | 0.238116 | − | 0.238116i | ||||
\(160\) | −0.968253 | + | 0.968253i | −0.0765471 | + | 0.0765471i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.56155i | 0.122687i | ||||||||
\(163\) | 4.86270 | − | 4.86270i | 0.380876 | − | 0.380876i | −0.490542 | − | 0.871418i | \(-0.663201\pi\) |
0.871418 | + | 0.490542i | \(0.163201\pi\) | |||||||
\(164\) | 0.174098 | − | 0.174098i | 0.0135947 | − | 0.0135947i | ||||
\(165\) | 1.01714 | + | 1.01714i | 0.0791839 | + | 0.0791839i | ||||
\(166\) | 14.2462 | 1.10572 | ||||||||
\(167\) | −0.571175 | − | 0.571175i | −0.0441989 | − | 0.0441989i | 0.684662 | − | 0.728861i | \(-0.259950\pi\) |
−0.728861 | + | 0.684662i | \(0.759950\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.80776 | 0.600597 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.68466 | 0.587661 | ||||||||
\(172\) | 3.36932i | 0.256908i | ||||||||
\(173\) | −13.2991 | − | 13.2991i | −1.01111 | − | 1.01111i | −0.999938 | − | 0.0111741i | \(-0.996443\pi\) |
−0.0111741 | − | 0.999938i | \(-0.503557\pi\) | |||||||
\(174\) | 12.8769 | 0.976195 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8.48528 | − | 8.48528i | 0.639602 | − | 0.639602i | ||||
\(177\) | −0.794156 | + | 0.794156i | −0.0596924 | + | 0.0596924i | ||||
\(178\) | 11.1231i | 0.833712i | ||||||||
\(179\) | − | 9.12311i | − | 0.681893i | −0.940083 | − | 0.340946i | \(-0.889253\pi\) | ||
0.940083 | − | 0.340946i | \(-0.110747\pi\) | |||||||
\(180\) | 0.174098 | − | 0.174098i | 0.0129765 | − | 0.0129765i | ||||
\(181\) | 4.24264 | − | 4.24264i | 0.315353 | − | 0.315353i | −0.531626 | − | 0.846979i | \(-0.678419\pi\) |
0.846979 | + | 0.531626i | \(0.178419\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.876894 | 0.0648219 | ||||||||
\(184\) | 11.3137 | + | 11.3137i | 0.834058 | + | 0.834058i | ||||
\(185\) | 1.75379i | 0.128941i | ||||||||
\(186\) | 8.00000 | 0.586588 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1.26137 | −0.0919946 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.76493 | − | 4.76493i | −0.345685 | − | 0.345685i | ||||
\(191\) | 13.1231 | 0.949555 | 0.474777 | − | 0.880106i | \(-0.342529\pi\) | ||||
0.474777 | + | 0.880106i | \(0.342529\pi\) | |||||||
\(192\) | 3.93261 | + | 3.93261i | 0.283812 | + | 0.283812i | ||||
\(193\) | −17.1447 | + | 17.1447i | −1.23410 | + | 1.23410i | −0.271725 | + | 0.962375i | \(0.587594\pi\) |
−0.962375 | + | 0.271725i | \(0.912406\pi\) | |||||||
\(194\) | 12.2820 | − | 12.2820i | 0.881793 | − | 0.881793i | ||||
\(195\) | 2.56155i | 0.183437i | ||||||||
\(196\) | − | 3.06913i | − | 0.219224i | ||||||
\(197\) | −14.0933 | + | 14.0933i | −1.00410 | + | 1.00410i | −0.00411116 | + | 0.999992i | \(0.501309\pi\) |
−0.999992 | + | 0.00411116i | \(0.998691\pi\) | |||||||
\(198\) | −2.82843 | + | 2.82843i | −0.201008 | + | 0.201008i | ||||
\(199\) | −11.3137 | − | 11.3137i | −0.802008 | − | 0.802008i | 0.181402 | − | 0.983409i | \(-0.441937\pi\) |
−0.983409 | + | 0.181402i | \(0.941937\pi\) | |||||||
\(200\) | −11.4233 | −0.807749 | ||||||||
\(201\) | −2.82843 | − | 2.82843i | −0.199502 | − | 0.199502i | ||||
\(202\) | − | 29.8617i | − | 2.10106i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.315342 | −0.0220244 | ||||||||
\(206\) | − | 6.73863i | − | 0.469503i | ||||||
\(207\) | −4.63972 | − | 4.63972i | −0.322483 | − | 0.322483i | ||||
\(208\) | 21.3693 | 1.48170 | ||||||||
\(209\) | 13.9192 | + | 13.9192i | 0.962808 | + | 0.962808i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.03932 | − | 8.03932i | 0.553450 | − | 0.553450i | −0.373985 | − | 0.927435i | \(-0.622009\pi\) |
0.927435 | + | 0.373985i | \(0.122009\pi\) | |||||||
\(212\) | − | 1.86174i | − | 0.127865i | ||||||
\(213\) | − | 10.2462i | − | 0.702059i | ||||||
\(214\) | −8.48528 | + | 8.48528i | −0.580042 | + | 0.580042i | ||||
\(215\) | 3.05141 | − | 3.05141i | 0.208104 | − | 0.208104i | ||||
\(216\) | −1.72424 | − | 1.72424i | −0.117320 | − | 0.117320i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −16.6987 | − | 16.6987i | −1.13098 | − | 1.13098i | ||||
\(219\) | 4.24621i | 0.286932i | ||||||||
\(220\) | 0.630683 | 0.0425206 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −4.87689 | −0.327316 | ||||||||
\(223\) | − | 13.9309i | − | 0.932880i | −0.884553 | − | 0.466440i | \(-0.845536\pi\) | ||
0.884553 | − | 0.466440i | \(-0.154464\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.68466 | 0.312311 | ||||||||
\(226\) | 5.03680 | + | 5.03680i | 0.335043 | + | 0.335043i | ||||
\(227\) | 16.3016 | − | 16.3016i | 1.08198 | − | 1.08198i | 0.0856515 | − | 0.996325i | \(-0.472703\pi\) |
0.996325 | − | 0.0856515i | \(-0.0272972\pi\) | |||||||
\(228\) | 2.38247 | − | 2.38247i | 0.157783 | − | 0.157783i | ||||
\(229\) | 6.00000i | 0.396491i | 0.980152 | + | 0.198246i | \(0.0635244\pi\) | ||||
−0.980152 | + | 0.198246i | \(0.936476\pi\) | |||||||
\(230\) | 5.75379i | 0.379394i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −14.2185 | + | 14.2185i | −0.933488 | + | 0.933488i | ||||
\(233\) | −0.397078 | − | 0.397078i | −0.0260134 | − | 0.0260134i | 0.693980 | − | 0.719994i | \(-0.255855\pi\) |
−0.719994 | + | 0.693980i | \(0.755855\pi\) | |||||||
\(234\) | −7.12311 | −0.465652 | ||||||||
\(235\) | 1.14235 | + | 1.14235i | 0.0745188 | + | 0.0745188i | ||||
\(236\) | 0.492423i | 0.0320540i | ||||||||
\(237\) | −15.3693 | −0.998344 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.2462 | 0.662772 | 0.331386 | − | 0.943495i | \(-0.392484\pi\) | ||||
0.331386 | + | 0.943495i | \(0.392484\pi\) | |||||||
\(240\) | 2.63068i | 0.169810i | ||||||||
\(241\) | −15.1104 | − | 15.1104i | −0.973346 | − | 0.973346i | 0.0263082 | − | 0.999654i | \(-0.491625\pi\) |
−0.999654 | + | 0.0263082i | \(0.991625\pi\) | |||||||
\(242\) | 6.93087 | 0.445533 | ||||||||
\(243\) | 0.707107 | + | 0.707107i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 0.271863 | − | 0.271863i | 0.0174042 | − | 0.0174042i | ||||
\(245\) | −2.77954 | + | 2.77954i | −0.177579 | + | 0.177579i | ||||
\(246\) | − | 0.876894i | − | 0.0559087i | ||||||
\(247\) | 35.0540i | 2.23043i | ||||||||
\(248\) | −8.83348 | + | 8.83348i | −0.560926 | + | 0.560926i | ||||
\(249\) | 6.45101 | − | 6.45101i | 0.408816 | − | 0.408816i | ||||
\(250\) | −6.00505 | − | 6.00505i | −0.379793 | − | 0.379793i | ||||
\(251\) | 24.4924 | 1.54595 | 0.772974 | − | 0.634438i | \(-0.218768\pi\) | ||||
0.772974 | + | 0.634438i | \(0.218768\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 16.8078i | − | 1.05670i | ||||||
\(254\) | −1.26137 | −0.0791452 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 10.0540 | 0.628373 | ||||||||
\(257\) | − | 9.36932i | − | 0.584442i | −0.956351 | − | 0.292221i | \(-0.905606\pi\) | ||
0.956351 | − | 0.292221i | \(-0.0943943\pi\) | |||||||
\(258\) | 8.48528 | + | 8.48528i | 0.528271 | + | 0.528271i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.794156 | + | 0.794156i | 0.0492514 | + | 0.0492514i | ||||
\(261\) | 5.83095 | − | 5.83095i | 0.360927 | − | 0.360927i | ||||
\(262\) | −20.4954 | + | 20.4954i | −1.26621 | + | 1.26621i | ||||
\(263\) | 12.4924i | 0.770316i | 0.922851 | + | 0.385158i | \(0.125853\pi\) | ||||
−0.922851 | + | 0.385158i | \(0.874147\pi\) | |||||||
\(264\) | − | 6.24621i | − | 0.384428i | ||||||
\(265\) | −1.68608 | + | 1.68608i | −0.103575 | + | 0.103575i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.03680 | + | 5.03680i | 0.308247 | + | 0.308247i | ||||
\(268\) | −1.75379 | −0.107130 | ||||||||
\(269\) | 14.5392 | + | 14.5392i | 0.886471 | + | 0.886471i | 0.994182 | − | 0.107711i | \(-0.0343520\pi\) |
−0.107711 | + | 0.994182i | \(0.534352\pi\) | |||||||
\(270\) | − | 0.876894i | − | 0.0533661i | ||||||
\(271\) | −0.807764 | −0.0490682 | −0.0245341 | − | 0.999699i | \(-0.507810\pi\) | ||||
−0.0245341 | + | 0.999699i | \(0.507810\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 25.3693i | 1.53262i | ||||||||
\(275\) | 8.48528 | + | 8.48528i | 0.511682 | + | 0.511682i | ||||
\(276\) | −2.87689 | −0.173169 | ||||||||
\(277\) | −4.24264 | − | 4.24264i | −0.254916 | − | 0.254916i | 0.568067 | − | 0.822982i | \(-0.307691\pi\) |
−0.822982 | + | 0.568067i | \(0.807691\pi\) | |||||||
\(278\) | −10.0736 | + | 10.0736i | −0.604174 | + | 0.604174i | ||||
\(279\) | 3.62258 | − | 3.62258i | 0.216878 | − | 0.216878i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 19.1231i | − | 1.14079i | −0.821371 | − | 0.570394i | \(-0.806790\pi\) | ||
0.821371 | − | 0.570394i | \(-0.193210\pi\) | |||||||
\(282\) | −3.17662 | + | 3.17662i | −0.189165 | + | 0.189165i | ||||
\(283\) | −2.38247 | + | 2.38247i | −0.141623 | + | 0.141623i | −0.774364 | − | 0.632741i | \(-0.781930\pi\) |
0.632741 | + | 0.774364i | \(0.281930\pi\) | |||||||
\(284\) | −3.17662 | − | 3.17662i | −0.188498 | − | 0.188498i | ||||
\(285\) | −4.31534 | −0.255619 | ||||||||
\(286\) | −12.9020 | − | 12.9020i | −0.762912 | − | 0.762912i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.43845 | −0.143687 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −7.23106 | −0.424622 | ||||||||
\(291\) | − | 11.1231i | − | 0.652048i | ||||||
\(292\) | 1.31645 | + | 1.31645i | 0.0770393 | + | 0.0770393i | ||||
\(293\) | 7.12311 | 0.416136 | 0.208068 | − | 0.978114i | \(-0.433282\pi\) | ||||
0.208068 | + | 0.978114i | \(0.433282\pi\) | |||||||
\(294\) | −7.72929 | − | 7.72929i | −0.450781 | − | 0.450781i | ||||
\(295\) | 0.445960 | − | 0.445960i | 0.0259648 | − | 0.0259648i | ||||
\(296\) | 5.38499 | − | 5.38499i | 0.312996 | − | 0.312996i | ||||
\(297\) | 2.56155i | 0.148636i | ||||||||
\(298\) | − | 6.63068i | − | 0.384105i | ||||||
\(299\) | 21.1643 | − | 21.1643i | 1.22396 | − | 1.22396i | ||||
\(300\) | 1.45238 | − | 1.45238i | 0.0838532 | − | 0.0838532i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −12.4924 | −0.718858 | ||||||||
\(303\) | −13.5221 | − | 13.5221i | −0.776823 | − | 0.776823i | ||||
\(304\) | 36.0000i | 2.06474i | ||||||||
\(305\) | −0.492423 | −0.0281960 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.492423 | −0.0281040 | −0.0140520 | − | 0.999901i | \(-0.504473\pi\) | ||||
−0.0140520 | + | 0.999901i | \(0.504473\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.05141 | − | 3.05141i | −0.173588 | − | 0.173588i | ||||
\(310\) | −4.49242 | −0.255152 | ||||||||
\(311\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(312\) | 7.86522 | − | 7.86522i | 0.445281 | − | 0.445281i | ||||
\(313\) | 5.38499 | − | 5.38499i | 0.304378 | − | 0.304378i | −0.538346 | − | 0.842724i | \(-0.680951\pi\) |
0.842724 | + | 0.538346i | \(0.180951\pi\) | |||||||
\(314\) | − | 8.87689i | − | 0.500952i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.76493 | + | 4.76493i | −0.268048 | + | 0.268048i | ||||
\(317\) | −12.7279 | + | 12.7279i | −0.714871 | + | 0.714871i | −0.967550 | − | 0.252679i | \(-0.918688\pi\) |
0.252679 | + | 0.967550i | \(0.418688\pi\) | |||||||
\(318\) | −4.68860 | − | 4.68860i | −0.262924 | − | 0.262924i | ||||
\(319\) | 21.1231 | 1.18267 | ||||||||
\(320\) | −2.20837 | − | 2.20837i | −0.123452 | − | 0.123452i | ||||
\(321\) | 7.68466i | 0.428916i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.438447 | 0.0243582 | ||||||||
\(325\) | 21.3693i | 1.18536i | ||||||||
\(326\) | −7.59336 | − | 7.59336i | −0.420557 | − | 0.420557i | ||||
\(327\) | −15.1231 | −0.836310 | ||||||||
\(328\) | 0.968253 | + | 0.968253i | 0.0534628 | + | 0.0534628i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.58831 | − | 1.58831i | 0.0874337 | − | 0.0874337i | ||||
\(331\) | − | 6.06913i | − | 0.333590i | −0.985992 | − | 0.166795i | \(-0.946658\pi\) | ||
0.985992 | − | 0.166795i | \(-0.0533417\pi\) | |||||||
\(332\) | − | 4.00000i | − | 0.219529i | ||||||
\(333\) | −2.20837 | + | 2.20837i | −0.121018 | + | 0.121018i | ||||
\(334\) | −0.891921 | + | 0.891921i | −0.0488037 | + | 0.0488037i | ||||
\(335\) | 1.58831 | + | 1.58831i | 0.0867787 | + | 0.0867787i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.1497 | + | 23.1497i | 1.26105 | + | 1.26105i | 0.950587 | + | 0.310458i | \(0.100482\pi\) |
0.310458 | + | 0.950587i | \(0.399518\pi\) | |||||||
\(338\) | − | 12.1922i | − | 0.663170i | ||||||
\(339\) | 4.56155 | 0.247750 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.1231 | 0.710656 | ||||||||
\(342\) | − | 12.0000i | − | 0.648886i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −18.7386 | −1.01032 | ||||||||
\(345\) | 2.60545 | + | 2.60545i | 0.140273 | + | 0.140273i | ||||
\(346\) | −20.7672 | + | 20.7672i | −1.11645 | + | 1.11645i | ||||
\(347\) | −17.3188 | + | 17.3188i | −0.929720 | + | 0.929720i | −0.997688 | − | 0.0679679i | \(-0.978348\pi\) |
0.0679679 | + | 0.997688i | \(0.478348\pi\) | |||||||
\(348\) | − | 3.61553i | − | 0.193813i | ||||||
\(349\) | 7.43845i | 0.398171i | 0.979982 | + | 0.199085i | \(0.0637971\pi\) | ||||
−0.979982 | + | 0.199085i | \(0.936203\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.22550 | + | 3.22550i | −0.172165 | + | 0.172165i | ||||
\(352\) | −4.41674 | − | 4.41674i | −0.235413 | − | 0.235413i | ||||
\(353\) | −22.4924 | −1.19715 | −0.598575 | − | 0.801066i | \(-0.704266\pi\) | ||||
−0.598575 | + | 0.801066i | \(0.704266\pi\) | |||||||
\(354\) | 1.24012 | + | 1.24012i | 0.0659114 | + | 0.0659114i | ||||
\(355\) | 5.75379i | 0.305379i | ||||||||
\(356\) | 3.12311 | 0.165524 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.2462 | −0.752936 | ||||||||
\(359\) | 2.24621i | 0.118550i | 0.998242 | + | 0.0592752i | \(0.0188790\pi\) | ||||
−0.998242 | + | 0.0592752i | \(0.981121\pi\) | |||||||
\(360\) | 0.968253 | + | 0.968253i | 0.0510314 | + | 0.0510314i | ||||
\(361\) | −40.0540 | −2.10810 | ||||||||
\(362\) | −6.62511 | − | 6.62511i | −0.348208 | − | 0.348208i | ||||
\(363\) | 3.13846 | − | 3.13846i | 0.164726 | − | 0.164726i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 2.38447i | − | 0.124809i | ||||||
\(366\) | − | 1.36932i | − | 0.0715753i | ||||||
\(367\) | 12.9020 | − | 12.9020i | 0.673480 | − | 0.673480i | −0.285037 | − | 0.958517i | \(-0.592006\pi\) |
0.958517 | + | 0.285037i | \(0.0920058\pi\) | |||||||
\(368\) | 21.7355 | − | 21.7355i | 1.13304 | − | 1.13304i | ||||
\(369\) | −0.397078 | − | 0.397078i | −0.0206710 | − | 0.0206710i | ||||
\(370\) | 2.73863 | 0.142375 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 2.24621i | − | 0.116461i | ||||||
\(373\) | 16.2462 | 0.841197 | 0.420598 | − | 0.907247i | \(-0.361820\pi\) | ||||
0.420598 | + | 0.907247i | \(0.361820\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.43845 | −0.280840 | ||||||||
\(376\) | − | 7.01515i | − | 0.361779i | ||||||
\(377\) | 26.5982 | + | 26.5982i | 1.36988 | + | 1.36988i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.48528 | + | 8.48528i | 0.435860 | + | 0.435860i | 0.890616 | − | 0.454756i | \(-0.150274\pi\) |
−0.454756 | + | 0.890616i | \(0.650274\pi\) | |||||||
\(380\) | −1.33788 | + | 1.33788i | −0.0686318 | + | 0.0686318i | ||||
\(381\) | −0.571175 | + | 0.571175i | −0.0292622 | + | 0.0292622i | ||||
\(382\) | − | 20.4924i | − | 1.04848i | ||||||
\(383\) | − | 10.2462i | − | 0.523557i | −0.965128 | − | 0.261778i | \(-0.915691\pi\) | ||
0.965128 | − | 0.261778i | \(-0.0843090\pi\) | |||||||
\(384\) | 9.58947 | − | 9.58947i | 0.489360 | − | 0.489360i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 26.7723 | + | 26.7723i | 1.36267 | + | 1.36267i | ||||
\(387\) | 7.68466 | 0.390633 | ||||||||
\(388\) | −3.44849 | − | 3.44849i | −0.175070 | − | 0.175070i | ||||
\(389\) | 21.8617i | 1.10843i | 0.832372 | + | 0.554217i | \(0.186982\pi\) | ||||
−0.832372 | + | 0.554217i | \(0.813018\pi\) | |||||||
\(390\) | 4.00000 | 0.202548 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 17.0691 | 0.862121 | ||||||||
\(393\) | 18.5616i | 0.936306i | ||||||||
\(394\) | 22.0074 | + | 22.0074i | 1.10871 | + | 1.10871i | ||||
\(395\) | 8.63068 | 0.434257 | ||||||||
\(396\) | 0.794156 | + | 0.794156i | 0.0399078 | + | 0.0399078i | ||||
\(397\) | 3.79668 | − | 3.79668i | 0.190550 | − | 0.190550i | −0.605384 | − | 0.795934i | \(-0.706980\pi\) |
0.795934 | + | 0.605384i | \(0.206980\pi\) | |||||||
\(398\) | −17.6670 | + | 17.6670i | −0.885564 | + | 0.885564i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 21.9460i | 1.09730i | ||||||||
\(401\) | 4.36786 | − | 4.36786i | 0.218120 | − | 0.218120i | −0.589586 | − | 0.807706i | \(-0.700709\pi\) |
0.807706 | + | 0.589586i | \(0.200709\pi\) | |||||||
\(402\) | −4.41674 | + | 4.41674i | −0.220287 | + | 0.220287i | ||||
\(403\) | 16.5246 | + | 16.5246i | 0.823149 | + | 0.823149i | ||||
\(404\) | −8.38447 | −0.417143 | ||||||||
\(405\) | −0.397078 | − | 0.397078i | −0.0197310 | − | 0.0197310i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.00000 | −0.396545 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.31534 | −0.114486 | −0.0572431 | − | 0.998360i | \(-0.518231\pi\) | ||||
−0.0572431 | + | 0.998360i | \(0.518231\pi\) | |||||||
\(410\) | 0.492423i | 0.0243190i | ||||||||
\(411\) | 11.4878 | + | 11.4878i | 0.566652 | + | 0.566652i | ||||
\(412\) | −1.89205 | −0.0932146 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −7.24517 | + | 7.24517i | −0.356080 | + | 0.356080i | ||||
\(415\) | −3.62258 | + | 3.62258i | −0.177826 | + | 0.177826i | ||||
\(416\) | − | 11.1231i | − | 0.545355i | ||||||
\(417\) | 9.12311i | 0.446760i | ||||||||
\(418\) | 21.7355 | − | 21.7355i | 1.06312 | − | 1.06312i | ||||
\(419\) | 22.9756 | − | 22.9756i | 1.12243 | − | 1.12243i | 0.131057 | − | 0.991375i | \(-0.458163\pi\) |
0.991375 | − | 0.131057i | \(-0.0418372\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.5616 | −1.39200 | −0.696002 | − | 0.718039i | \(-0.745040\pi\) | ||||
−0.696002 | + | 0.718039i | \(0.745040\pi\) | |||||||
\(422\) | −12.5538 | − | 12.5538i | −0.611111 | − | 0.611111i | ||||
\(423\) | 2.87689i | 0.139879i | ||||||||
\(424\) | 10.3542 | 0.502843 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −16.0000 | −0.775203 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2.38247 | + | 2.38247i | 0.115161 | + | 0.115161i | ||||
\(429\) | −11.6847 | −0.564141 | ||||||||
\(430\) | −4.76493 | − | 4.76493i | −0.229786 | − | 0.229786i | ||||
\(431\) | −16.9706 | + | 16.9706i | −0.817443 | + | 0.817443i | −0.985737 | − | 0.168294i | \(-0.946174\pi\) |
0.168294 | + | 0.985737i | \(0.446174\pi\) | |||||||
\(432\) | −3.31255 | + | 3.31255i | −0.159375 | + | 0.159375i | ||||
\(433\) | 14.3153i | 0.687951i | 0.938979 | + | 0.343976i | \(0.111774\pi\) | ||||
−0.938979 | + | 0.343976i | \(0.888226\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.27439 | + | 3.27439i | −0.156995 | + | 0.156995i | ||||
\(436\) | −4.68860 | + | 4.68860i | −0.224543 | + | 0.224543i | ||||
\(437\) | 35.6547 | + | 35.6547i | 1.70559 | + | 1.70559i | ||||
\(438\) | 6.63068 | 0.316826 | ||||||||
\(439\) | −4.06854 | − | 4.06854i | −0.194181 | − | 0.194181i | 0.603319 | − | 0.797500i | \(-0.293845\pi\) |
−0.797500 | + | 0.603319i | \(0.793845\pi\) | |||||||
\(440\) | 3.50758i | 0.167217i | ||||||||
\(441\) | −7.00000 | −0.333333 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.8769 | −1.08691 | −0.543457 | − | 0.839437i | \(-0.682885\pi\) | ||||
−0.543457 | + | 0.839437i | \(0.682885\pi\) | |||||||
\(444\) | 1.36932i | 0.0649849i | ||||||||
\(445\) | −2.82843 | − | 2.82843i | −0.134080 | − | 0.134080i | ||||
\(446\) | −21.7538 | −1.03007 | ||||||||
\(447\) | −3.00252 | − | 3.00252i | −0.142015 | − | 0.142015i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.00757 | − | 9.00757i | 0.425094 | − | 0.425094i | −0.461859 | − | 0.886953i | \(-0.652818\pi\) |
0.886953 | + | 0.461859i | \(0.152818\pi\) | |||||||
\(450\) | − | 7.31534i | − | 0.344849i | ||||||
\(451\) | − | 1.43845i | − | 0.0677338i | ||||||
\(452\) | 1.41421 | − | 1.41421i | 0.0665190 | − | 0.0665190i | ||||
\(453\) | −5.65685 | + | 5.65685i | −0.265782 | + | 0.265782i | ||||
\(454\) | −25.4558 | − | 25.4558i | −1.19470 | − | 1.19470i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 13.2502 | + | 13.2502i | 0.620498 | + | 0.620498i | ||||
\(457\) | 6.80776i | 0.318454i | 0.987242 | + | 0.159227i | \(0.0509001\pi\) | ||||
−0.987242 | + | 0.159227i | \(0.949100\pi\) | |||||||
\(458\) | 9.36932 | 0.437799 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.61553 | 0.0753244 | ||||||||
\(461\) | − | 8.24621i | − | 0.384064i | −0.981389 | − | 0.192032i | \(-0.938492\pi\) | ||
0.981389 | − | 0.192032i | \(-0.0615078\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.9848 | −1.16114 | −0.580572 | − | 0.814209i | \(-0.697171\pi\) | ||||
−0.580572 | + | 0.814209i | \(0.697171\pi\) | |||||||
\(464\) | 27.3160 | + | 27.3160i | 1.26811 | + | 1.26811i | ||||
\(465\) | −2.03427 | + | 2.03427i | −0.0943371 | + | 0.0943371i | ||||
\(466\) | −0.620058 | + | 0.620058i | −0.0287236 | + | 0.0287236i | ||||
\(467\) | − | 3.36932i | − | 0.155913i | −0.996957 | − | 0.0779567i | \(-0.975160\pi\) | ||
0.996957 | − | 0.0779567i | \(-0.0248396\pi\) | |||||||
\(468\) | 2.00000i | 0.0924500i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.78384 | − | 1.78384i | 0.0822825 | − | 0.0822825i | ||||
\(471\) | −4.01966 | − | 4.01966i | −0.185216 | − | 0.185216i | ||||
\(472\) | −2.73863 | −0.126056 | ||||||||
\(473\) | 13.9192 | + | 13.9192i | 0.640003 | + | 0.640003i | ||||
\(474\) | 24.0000i | 1.10236i | ||||||||
\(475\) | −36.0000 | −1.65179 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.24621 | −0.194421 | ||||||||
\(478\) | − | 16.0000i | − | 0.731823i | ||||||
\(479\) | −20.7184 | − | 20.7184i | −0.946646 | − | 0.946646i | 0.0520010 | − | 0.998647i | \(-0.483440\pi\) |
−0.998647 | + | 0.0520010i | \(0.983440\pi\) | |||||||
\(480\) | 1.36932 | 0.0625005 | ||||||||
\(481\) | −10.0736 | − | 10.0736i | −0.459316 | − | 0.459316i | ||||
\(482\) | −23.5957 | + | 23.5957i | −1.07475 | + | 1.07475i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 1.94602i | − | 0.0884557i | ||||||
\(485\) | 6.24621i | 0.283626i | ||||||||
\(486\) | 1.10418 | − | 1.10418i | 0.0500868 | − | 0.0500868i | ||||
\(487\) | −5.21089 | + | 5.21089i | −0.236128 | + | 0.236128i | −0.815245 | − | 0.579117i | \(-0.803398\pi\) |
0.579117 | + | 0.815245i | \(0.303398\pi\) | |||||||
\(488\) | 1.51198 | + | 1.51198i | 0.0684441 | + | 0.0684441i | ||||
\(489\) | −6.87689 | −0.310984 | ||||||||
\(490\) | 4.34041 | + | 4.34041i | 0.196080 | + | 0.196080i | ||||
\(491\) | − | 3.36932i | − | 0.152055i | −0.997106 | − | 0.0760276i | \(-0.975776\pi\) | ||
0.997106 | − | 0.0760276i | \(-0.0242237\pi\) | |||||||
\(492\) | −0.246211 | −0.0111001 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 54.7386 | 2.46281 | ||||||||
\(495\) | − | 1.43845i | − | 0.0646534i | ||||||
\(496\) | 16.9706 | + | 16.9706i | 0.762001 | + | 0.762001i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −10.0736 | − | 10.0736i | −0.451408 | − | 0.451408i | ||||
\(499\) | −8.03932 | + | 8.03932i | −0.359889 | + | 0.359889i | −0.863772 | − | 0.503883i | \(-0.831904\pi\) |
0.503883 | + | 0.863772i | \(0.331904\pi\) | |||||||
\(500\) | −1.68608 | + | 1.68608i | −0.0754036 | + | 0.0754036i | ||||
\(501\) | 0.807764i | 0.0360882i | ||||||||
\(502\) | − | 38.2462i | − | 1.70701i | ||||||
\(503\) | 17.9877 | − | 17.9877i | 0.802032 | − | 0.802032i | −0.181381 | − | 0.983413i | \(-0.558057\pi\) |
0.983413 | + | 0.181381i | \(0.0580567\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.59336 | + | 7.59336i | 0.337900 | + | 0.337900i | ||||
\(506\) | −26.2462 | −1.16679 | ||||||||
\(507\) | −5.52092 | − | 5.52092i | −0.245193 | − | 0.245193i | ||||
\(508\) | 0.354162i | 0.0157134i | ||||||||
\(509\) | 16.8769 | 0.748055 | 0.374028 | − | 0.927418i | \(-0.377977\pi\) | ||||
0.374028 | + | 0.927418i | \(0.377977\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 11.4233i | 0.504843i | ||||||||
\(513\) | −5.43387 | − | 5.43387i | −0.239911 | − | 0.239911i | ||||
\(514\) | −14.6307 | −0.645332 | ||||||||
\(515\) | 1.71353 | + | 1.71353i | 0.0755070 | + | 0.0755070i | ||||
\(516\) | 2.38247 | − | 2.38247i | 0.104882 | − | 0.104882i | ||||
\(517\) | −5.21089 | + | 5.21089i | −0.229175 | + | 0.229175i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.8078i | 0.825569i | ||||||||
\(520\) | −4.41674 | + | 4.41674i | −0.193687 | + | 0.193687i | ||||
\(521\) | −22.2303 | + | 22.2303i | −0.973929 | + | 0.973929i | −0.999669 | − | 0.0257398i | \(-0.991806\pi\) |
0.0257398 | + | 0.999669i | \(0.491806\pi\) | |||||||
\(522\) | −9.10534 | − | 9.10534i | −0.398530 | − | 0.398530i | ||||
\(523\) | 20.0000 | 0.874539 | 0.437269 | − | 0.899331i | \(-0.355946\pi\) | ||||
0.437269 | + | 0.899331i | \(0.355946\pi\) | |||||||
\(524\) | 5.75462 | + | 5.75462i | 0.251392 | + | 0.251392i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 19.5076 | 0.850571 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −12.0000 | −0.522233 | ||||||||
\(529\) | − | 20.0540i | − | 0.871912i | ||||||
\(530\) | 2.63290 | + | 2.63290i | 0.114366 | + | 0.114366i | ||||
\(531\) | 1.12311 | 0.0487386 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.81129 | − | 1.81129i | 0.0784557 | − | 0.0784557i | ||||
\(534\) | 7.86522 | − | 7.86522i | 0.340362 | − | 0.340362i | ||||
\(535\) | − | 4.31534i | − | 0.186568i | ||||||
\(536\) | − | 9.75379i | − | 0.421300i | ||||||
\(537\) | −6.45101 | + | 6.45101i | −0.278382 | + | 0.278382i | ||||
\(538\) | 22.7037 | − | 22.7037i | 0.978828 | − | 0.978828i | ||||
\(539\) | −12.6790 | − | 12.6790i | −0.546125 | − | 0.546125i | ||||
\(540\) | −0.246211 | −0.0105952 | ||||||||
\(541\) | −28.3606 | − | 28.3606i | −1.21932 | − | 1.21932i | −0.967871 | − | 0.251446i | \(-0.919094\pi\) |
−0.251446 | − | 0.967871i | \(-0.580906\pi\) | |||||||
\(542\) | 1.26137i | 0.0541803i | ||||||||
\(543\) | −6.00000 | −0.257485 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.49242 | 0.363775 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.7990 | + | 19.7990i | 0.846544 | + | 0.846544i | 0.989700 | − | 0.143156i | \(-0.0457252\pi\) |
−0.143156 | + | 0.989700i | \(0.545725\pi\) | |||||||
\(548\) | 7.12311 | 0.304284 | ||||||||
\(549\) | −0.620058 | − | 0.620058i | −0.0264634 | − | 0.0264634i | ||||
\(550\) | 13.2502 | − | 13.2502i | 0.564991 | − | 0.564991i | ||||
\(551\) | −44.8089 | + | 44.8089i | −1.90892 | + | 1.90892i | ||||
\(552\) | − | 16.0000i | − | 0.681005i | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −6.62511 | + | 6.62511i | −0.281474 | + | 0.281474i | ||||
\(555\) | 1.24012 | − | 1.24012i | 0.0526400 | − | 0.0526400i | ||||
\(556\) | 2.82843 | + | 2.82843i | 0.119952 | + | 0.119952i | ||||
\(557\) | 6.49242 | 0.275093 | 0.137546 | − | 0.990495i | \(-0.456078\pi\) | ||||
0.137546 | + | 0.990495i | \(0.456078\pi\) | |||||||
\(558\) | −5.65685 | − | 5.65685i | −0.239474 | − | 0.239474i | ||||
\(559\) | 35.0540i | 1.48263i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −29.8617 | −1.25964 | ||||||||
\(563\) | − | 22.8769i | − | 0.964146i | −0.876131 | − | 0.482073i | \(-0.839884\pi\) | ||
0.876131 | − | 0.482073i | \(-0.160116\pi\) | |||||||
\(564\) | 0.891921 | + | 0.891921i | 0.0375566 | + | 0.0375566i | ||||
\(565\) | −2.56155 | −0.107765 | ||||||||
\(566\) | 3.72035 | + | 3.72035i | 0.156378 | + | 0.156378i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 17.6670 | − | 17.6670i | 0.741289 | − | 0.741289i | ||||
\(569\) | 12.8769i | 0.539827i | 0.962885 | + | 0.269914i | \(0.0869952\pi\) | ||||
−0.962885 | + | 0.269914i | \(0.913005\pi\) | |||||||
\(570\) | 6.73863i | 0.282250i | ||||||||
\(571\) | −13.2502 | + | 13.2502i | −0.554504 | + | 0.554504i | −0.927738 | − | 0.373233i | \(-0.878249\pi\) |
0.373233 | + | 0.927738i | \(0.378249\pi\) | |||||||
\(572\) | −3.62258 | + | 3.62258i | −0.151468 | + | 0.151468i | ||||
\(573\) | −9.27944 | − | 9.27944i | −0.387654 | − | 0.387654i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 21.7355 | + | 21.7355i | 0.906433 | + | 0.906433i | ||||
\(576\) | − | 5.56155i | − | 0.231731i | ||||||
\(577\) | −41.0540 | −1.70910 | −0.854550 | − | 0.519370i | \(-0.826167\pi\) | ||||
−0.854550 | + | 0.519370i | \(0.826167\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 24.2462 | 1.00764 | ||||||||
\(580\) | 2.03031i | 0.0843040i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −17.3693 | −0.719981 | ||||||||
\(583\) | −7.69113 | − | 7.69113i | −0.318534 | − | 0.318534i | ||||
\(584\) | −7.32150 | + | 7.32150i | −0.302966 | + | 0.302966i | ||||
\(585\) | 1.81129 | − | 1.81129i | 0.0748877 | − | 0.0748877i | ||||
\(586\) | − | 11.1231i | − | 0.459491i | ||||||
\(587\) | 36.9848i | 1.52653i | 0.646087 | + | 0.763264i | \(0.276404\pi\) | ||||
−0.646087 | + | 0.763264i | \(0.723596\pi\) | |||||||
\(588\) | −2.17020 | + | 2.17020i | −0.0894977 | + | 0.0894977i | ||||
\(589\) | −27.8383 | + | 27.8383i | −1.14706 | + | 1.14706i | ||||
\(590\) | −0.696391 | − | 0.696391i | −0.0286699 | − | 0.0286699i | ||||
\(591\) | 19.9309 | 0.819846 | ||||||||
\(592\) | −10.3455 | − | 10.3455i | −0.425196 | − | 0.425196i | ||||
\(593\) | − | 44.2462i | − | 1.81697i | −0.417913 | − | 0.908487i | \(-0.637238\pi\) | ||
0.417913 | − | 0.908487i | \(-0.362762\pi\) | |||||||
\(594\) | 4.00000 | 0.164122 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.86174 | −0.0762598 | ||||||||
\(597\) | 16.0000i | 0.654836i | ||||||||
\(598\) | −33.0492 | − | 33.0492i | −1.35148 | − | 1.35148i | ||||
\(599\) | 41.6155 | 1.70036 | 0.850182 | − | 0.526489i | \(-0.176492\pi\) | ||||
0.850182 | + | 0.526489i | \(0.176492\pi\) | |||||||
\(600\) | 8.07749 | + | 8.07749i | 0.329762 | + | 0.329762i | ||||
\(601\) | 24.7380 | − | 24.7380i | 1.00908 | − | 1.00908i | 0.00912658 | − | 0.999958i | \(-0.497095\pi\) |
0.999958 | − | 0.00912658i | \(-0.00290512\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.00000i | 0.162893i | ||||||||
\(604\) | 3.50758i | 0.142721i | ||||||||
\(605\) | −1.76241 | + | 1.76241i | −0.0716521 | + | 0.0716521i | ||||
\(606\) | −21.1154 | + | 21.1154i | −0.857756 | + | 0.857756i | ||||
\(607\) | −10.8677 | − | 10.8677i | −0.441108 | − | 0.441108i | 0.451276 | − | 0.892384i | \(-0.350969\pi\) |
−0.892384 | + | 0.451276i | \(0.850969\pi\) | |||||||
\(608\) | 18.7386 | 0.759952 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.768944i | 0.0311336i | ||||||||
\(611\) | −13.1231 | −0.530904 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.31534 | 0.0935158 | 0.0467579 | − | 0.998906i | \(-0.485111\pi\) | ||||
0.0467579 | + | 0.998906i | \(0.485111\pi\) | |||||||
\(614\) | 0.768944i | 0.0310320i | ||||||||
\(615\) | 0.222980 | + | 0.222980i | 0.00899143 | + | 0.00899143i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.6249 | + | 19.6249i | 0.790068 | + | 0.790068i | 0.981505 | − | 0.191437i | \(-0.0613146\pi\) |
−0.191437 | + | 0.981505i | \(0.561315\pi\) | |||||||
\(618\) | −4.76493 | + | 4.76493i | −0.191674 | + | 0.191674i | ||||
\(619\) | 13.6962 | − | 13.6962i | 0.550496 | − | 0.550496i | −0.376088 | − | 0.926584i | \(-0.622731\pi\) |
0.926584 | + | 0.376088i | \(0.122731\pi\) | |||||||
\(620\) | 1.26137i | 0.0506577i | ||||||||
\(621\) | 6.56155i | 0.263306i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −15.1104 | − | 15.1104i | −0.604900 | − | 0.604900i | ||||
\(625\) | −20.3693 | −0.814773 | ||||||||
\(626\) | −8.40895 | − | 8.40895i | −0.336089 | − | 0.336089i | ||||
\(627\) | − | 19.6847i | − | 0.786130i | ||||||
\(628\) | −2.49242 | −0.0994585 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 11.6847i | − | 0.465159i | −0.972577 | − | 0.232579i | \(-0.925283\pi\) | ||
0.972577 | − | 0.232579i | \(-0.0747166\pi\) | |||||||
\(632\) | −26.5004 | − | 26.5004i | −1.05413 | − | 1.05413i | ||||
\(633\) | −11.3693 | −0.451890 | ||||||||
\(634\) | 19.8753 | + | 19.8753i | 0.789350 | + | 0.789350i | ||||
\(635\) | 0.320745 | − | 0.320745i | 0.0127284 | − | 0.0127284i | ||||
\(636\) | −1.31645 | + | 1.31645i | −0.0522006 | + | 0.0522006i | ||||
\(637\) | − | 31.9309i | − | 1.26515i | ||||||
\(638\) | − | 32.9848i | − | 1.30588i | ||||||
\(639\) | −7.24517 | + | 7.24517i | −0.286614 | + | 0.286614i | ||||
\(640\) | −5.38499 | + | 5.38499i | −0.212860 | + | 0.212860i | ||||
\(641\) | 0.0488825 | + | 0.0488825i | 0.00193074 | + | 0.00193074i | 0.708071 | − | 0.706141i | \(-0.249565\pi\) |
−0.706141 | + | 0.708071i | \(0.749565\pi\) | |||||||
\(642\) | 12.0000 | 0.473602 | ||||||||
\(643\) | −21.3873 | − | 21.3873i | −0.843433 | − | 0.843433i | 0.145871 | − | 0.989304i | \(-0.453402\pi\) |
−0.989304 | + | 0.145871i | \(0.953402\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.31534 | −0.169916 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.3693 | 0.604230 | 0.302115 | − | 0.953271i | \(-0.402307\pi\) | ||||
0.302115 | + | 0.953271i | \(0.402307\pi\) | |||||||
\(648\) | 2.43845i | 0.0957913i | ||||||||
\(649\) | 2.03427 | + | 2.03427i | 0.0798521 | + | 0.0798521i | ||||
\(650\) | 33.3693 | 1.30885 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.13204 | + | 2.13204i | −0.0834970 | + | 0.0834970i | ||||
\(653\) | 2.87731 | − | 2.87731i | 0.112598 | − | 0.112598i | −0.648563 | − | 0.761161i | \(-0.724630\pi\) |
0.761161 | + | 0.648563i | \(0.224630\pi\) | |||||||
\(654\) | 23.6155i | 0.923440i | ||||||||
\(655\) | − | 10.4233i | − | 0.407272i | ||||||
\(656\) | 1.86017 | − | 1.86017i | 0.0726276 | − | 0.0726276i | ||||
\(657\) | 3.00252 | − | 3.00252i | 0.117140 | − | 0.117140i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −47.8617 | −1.86443 | −0.932214 | − | 0.361907i | \(-0.882126\pi\) | ||||
−0.932214 | + | 0.361907i | \(0.882126\pi\) | |||||||
\(660\) | −0.445960 | − | 0.445960i | −0.0173590 | − | 0.0173590i | ||||
\(661\) | − | 25.6847i | − | 0.999017i | −0.866309 | − | 0.499509i | \(-0.833514\pi\) | ||
0.866309 | − | 0.499509i | \(-0.166486\pi\) | |||||||
\(662\) | −9.47727 | −0.368344 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 22.2462 | 0.863320 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.44849 | + | 3.44849i | 0.133626 | + | 0.133626i | ||||
\(667\) | 54.1080 | 2.09507 | ||||||||
\(668\) | 0.250430 | + | 0.250430i | 0.00968944 | + | 0.00968944i | ||||
\(669\) | −9.85061 | + | 9.85061i | −0.380847 | + | 0.380847i | ||||
\(670\) | 2.48023 | − | 2.48023i | 0.0958197 | − | 0.0958197i | ||||
\(671\) | − | 2.24621i | − | 0.0867140i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −34.4634 | + | 34.4634i | −1.32847 | + | 1.32847i | −0.421759 | + | 0.906708i | \(0.638587\pi\) |
−0.906708 | + | 0.421759i | \(0.861413\pi\) | |||||||
\(674\) | 36.1495 | − | 36.1495i | 1.39243 | − | 1.39243i | ||||
\(675\) | −3.31255 | − | 3.31255i | −0.127500 | − | 0.127500i | ||||
\(676\) | −3.42329 | −0.131665 | ||||||||
\(677\) | −9.67651 | − | 9.67651i | −0.371899 | − | 0.371899i | 0.496270 | − | 0.868168i | \(-0.334703\pi\) |
−0.868168 | + | 0.496270i | \(0.834703\pi\) | |||||||
\(678\) | − | 7.12311i | − | 0.273561i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.0540 | −0.883430 | ||||||||
\(682\) | − | 20.4924i | − | 0.784695i | ||||||
\(683\) | −3.84556 | − | 3.84556i | −0.147146 | − | 0.147146i | 0.629696 | − | 0.776842i | \(-0.283180\pi\) |
−0.776842 | + | 0.629696i | \(0.783180\pi\) | |||||||
\(684\) | −3.36932 | −0.128829 | ||||||||
\(685\) | −6.45101 | − | 6.45101i | −0.246480 | − | 0.246480i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.24264 | − | 4.24264i | 0.161867 | − | 0.161867i | ||||
\(688\) | 36.0000i | 1.37249i | ||||||||
\(689\) | − | 19.3693i | − | 0.737912i | ||||||
\(690\) | 4.06854 | − | 4.06854i | 0.154887 | − | 0.154887i | ||||
\(691\) | 26.1522 | − | 26.1522i | 0.994878 | − | 0.994878i | −0.00510905 | − | 0.999987i | \(-0.501626\pi\) |
0.999987 | + | 0.00510905i | \(0.00162627\pi\) | |||||||
\(692\) | 5.83095 | + | 5.83095i | 0.221660 | + | 0.221660i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 27.0442 | + | 27.0442i | 1.02658 | + | 1.02658i | ||||
\(695\) | − | 5.12311i | − | 0.194330i | ||||||
\(696\) | 20.1080 | 0.762190 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 11.6155 | 0.439654 | ||||||||
\(699\) | 0.561553i | 0.0212399i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.36932 | 0.353874 | 0.176937 | − | 0.984222i | \(-0.443381\pi\) | ||||
0.176937 | + | 0.984222i | \(0.443381\pi\) | |||||||
\(702\) | 5.03680 | + | 5.03680i | 0.190102 | + | 0.190102i | ||||
\(703\) | 16.9706 | − | 16.9706i | 0.640057 | − | 0.640057i | ||||
\(704\) | 10.0736 | − | 10.0736i | 0.379663 | − | 0.379663i | ||||
\(705\) | − | 1.61553i | − | 0.0608443i | ||||||
\(706\) | 35.1231i | 1.32188i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0.348195 | − | 0.348195i | 0.0130860 | − | 0.0130860i | ||||
\(709\) | −3.35072 | − | 3.35072i | −0.125839 | − | 0.125839i | 0.641382 | − | 0.767221i | \(-0.278361\pi\) |
−0.767221 | + | 0.641382i | \(0.778361\pi\) | |||||||
\(710\) | 8.98485 | 0.337195 | ||||||||
\(711\) | 10.8677 | + | 10.8677i | 0.407572 | + | 0.407572i | ||||
\(712\) | 17.3693i | 0.650943i | ||||||||
\(713\) | 33.6155 | 1.25891 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.56155 | 0.245388 | ||||||||
\(716\) | 4.00000i | 0.149487i | ||||||||
\(717\) | −7.24517 | − | 7.24517i | −0.270576 | − | 0.270576i | ||||
\(718\) | 3.50758 | 0.130902 | ||||||||
\(719\) | −6.22803 | − | 6.22803i | −0.232266 | − | 0.232266i | 0.581372 | − | 0.813638i | \(-0.302516\pi\) |
−0.813638 | + | 0.581372i | \(0.802516\pi\) | |||||||
\(720\) | 1.86017 | − | 1.86017i | 0.0693246 | − | 0.0693246i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 62.5464i | 2.32774i | ||||||||
\(723\) | 21.3693i | 0.794733i | ||||||||
\(724\) | −1.86017 | + | 1.86017i | −0.0691328 | + | 0.0691328i | ||||
\(725\) | −27.3160 | + | 27.3160i | −1.01449 | + | 1.01449i | ||||
\(726\) | −4.90086 | − | 4.90086i | −0.181888 | − | 0.181888i | ||||
\(727\) | 8.00000 | 0.296704 | 0.148352 | − | 0.988935i | \(-0.452603\pi\) | ||||
0.148352 | + | 0.988935i | \(0.452603\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | −3.72348 | −0.137812 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −0.384472 | −0.0142105 | ||||||||
\(733\) | 28.2462i | 1.04330i | 0.853160 | + | 0.521649i | \(0.174683\pi\) | ||||
−0.853160 | + | 0.521649i | \(0.825317\pi\) | |||||||
\(734\) | −20.1472 | − | 20.1472i | −0.743646 | − | 0.743646i | ||||
\(735\) | 3.93087 | 0.144992 | ||||||||
\(736\) | −11.3137 | − | 11.3137i | −0.417029 | − | 0.417029i | ||||
\(737\) | −7.24517 | + | 7.24517i | −0.266879 | + | 0.266879i | ||||
\(738\) | −0.620058 | + | 0.620058i | −0.0228246 | + | 0.0228246i | ||||
\(739\) | − | 8.31534i | − | 0.305885i | −0.988235 | − | 0.152942i | \(-0.951125\pi\) | ||
0.988235 | − | 0.152942i | \(-0.0488749\pi\) | |||||||
\(740\) | − | 0.768944i | − | 0.0282669i | ||||||
\(741\) | 24.7869 | − | 24.7869i | 0.910570 | − | 0.910570i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.17662 | + | 3.17662i | 0.116539 | + | 0.116539i | 0.762971 | − | 0.646432i | \(-0.223740\pi\) |
−0.646432 | + | 0.762971i | \(0.723740\pi\) | |||||||
\(744\) | 12.4924 | 0.457994 | ||||||||
\(745\) | 1.68608 | + | 1.68608i | 0.0617731 | + | 0.0617731i | ||||
\(746\) | − | 25.3693i | − | 0.928837i | ||||||
\(747\) | −9.12311 | −0.333797 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 8.49242i | 0.310099i | ||||||||
\(751\) | −0.445960 | − | 0.445960i | −0.0162733 | − | 0.0162733i | 0.698923 | − | 0.715197i | \(-0.253663\pi\) |
−0.715197 | + | 0.698923i | \(0.753663\pi\) | |||||||
\(752\) | −13.4773 | −0.491465 | ||||||||
\(753\) | −17.3188 | − | 17.3188i | −0.631131 | − | 0.631131i | ||||
\(754\) | 41.5345 | − | 41.5345i | 1.51260 | − | 1.51260i | ||||
\(755\) | 3.17662 | − | 3.17662i | 0.115609 | − | 0.115609i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 21.0540i | − | 0.765220i | −0.923910 | − | 0.382610i | \(-0.875025\pi\) | ||
0.923910 | − | 0.382610i | \(-0.124975\pi\) | |||||||
\(758\) | 13.2502 | − | 13.2502i | 0.481269 | − | 0.481269i | ||||
\(759\) | −11.8849 | + | 11.8849i | −0.431394 | + | 0.431394i | ||||
\(760\) | −7.44070 | − | 7.44070i | −0.269902 | − | 0.269902i | ||||
\(761\) | 32.2462 | 1.16892 | 0.584462 | − | 0.811421i | \(-0.301306\pi\) | ||||
0.584462 | + | 0.811421i | \(0.301306\pi\) | |||||||
\(762\) | 0.891921 | + | 0.891921i | 0.0323109 | + | 0.0323109i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −5.75379 | −0.208165 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.0000 | −0.578103 | ||||||||
\(767\) | 5.12311i | 0.184985i | ||||||||
\(768\) | −7.10923 | − | 7.10923i | −0.256532 | − | 0.256532i | ||||
\(769\) | 29.5464 | 1.06547 | 0.532735 | − | 0.846282i | \(-0.321164\pi\) | ||||
0.532735 | + | 0.846282i | \(0.321164\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.62511 | + | 6.62511i | −0.238597 | + | 0.238597i | ||||
\(772\) | 7.51703 | − | 7.51703i | 0.270544 | − | 0.270544i | ||||
\(773\) | − | 33.3693i | − | 1.20021i | −0.799921 | − | 0.600105i | \(-0.795125\pi\) | ||
0.799921 | − | 0.600105i | \(-0.204875\pi\) | |||||||
\(774\) | − | 12.0000i | − | 0.431331i | ||||||
\(775\) | −16.9706 | + | 16.9706i | −0.609601 | + | 0.609601i | ||||
\(776\) | 19.1789 | − | 19.1789i | 0.688484 | − | 0.688484i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 34.1383 | 1.22392 | ||||||||
\(779\) | 3.05141 | + | 3.05141i | 0.109328 | + | 0.109328i | ||||
\(780\) | − | 1.12311i | − | 0.0402136i | ||||||
\(781\) | −26.2462 | −0.939163 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.24621 | −0.294696 | ||||||||
\(784\) | − | 32.7926i | − | 1.17116i | ||||||
\(785\) | 2.25725 | + | 2.25725i | 0.0805648 | + | 0.0805648i | ||||
\(786\) | 28.9848 | 1.03386 | ||||||||
\(787\) | −4.41674 | − | 4.41674i | −0.157440 | − | 0.157440i | 0.623991 | − | 0.781431i | \(-0.285510\pi\) |
−0.781431 | + | 0.623991i | \(0.785510\pi\) | |||||||
\(788\) | 6.17915 | − | 6.17915i | 0.220123 | − | 0.220123i | ||||
\(789\) | 8.83348 | − | 8.83348i | 0.314480 | − | 0.314480i | ||||
\(790\) | − | 13.4773i | − | 0.479500i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −4.41674 | + | 4.41674i | −0.156942 | + | 0.156942i | ||||
\(793\) | 2.82843 | − | 2.82843i | 0.100440 | − | 0.100440i | ||||
\(794\) | −5.92872 | − | 5.92872i | −0.210402 | − | 0.210402i | ||||
\(795\) | 2.38447 | 0.0845685 | ||||||||
\(796\) | 4.96046 | + | 4.96046i | 0.175819 | + | 0.175819i | ||||
\(797\) | − | 31.6155i | − | 1.11988i | −0.828533 | − | 0.559940i | \(-0.810824\pi\) | ||
0.828533 | − | 0.559940i | \(-0.189176\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 11.4233 | 0.403874 | ||||||||
\(801\) | − | 7.12311i | − | 0.251683i | ||||||
\(802\) | −6.82064 | − | 6.82064i | −0.240845 | − | 0.240845i | ||||
\(803\) | 10.8769 | 0.383837 | ||||||||
\(804\) | 1.24012 | + | 1.24012i | 0.0437355 | + | 0.0437355i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 25.8040 | − | 25.8040i | 0.908909 | − | 0.908909i | ||||
\(807\) | − | 20.5616i | − | 0.723801i | ||||||
\(808\) | − | 46.6307i | − | 1.64046i | ||||||
\(809\) | −37.5148 | + | 37.5148i | −1.31895 | + | 1.31895i | −0.404344 | + | 0.914607i | \(0.632500\pi\) |
−0.914607 | + | 0.404344i | \(0.867500\pi\) | |||||||
\(810\) | −0.620058 | + | 0.620058i | −0.0217866 | + | 0.0217866i | ||||
\(811\) | 14.5881 | + | 14.5881i | 0.512257 | + | 0.512257i | 0.915218 | − | 0.402960i | \(-0.132019\pi\) |
−0.402960 | + | 0.915218i | \(0.632019\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.571175 | + | 0.571175i | 0.0200320 | + | 0.0200320i | ||||
\(814\) | 12.4924i | 0.437859i | ||||||||
\(815\) | 3.86174 | 0.135271 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −59.0540 | −2.06604 | ||||||||
\(818\) | 3.61553i | 0.126414i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.138261 | 0.00482827 | ||||||||
\(821\) | 11.7108 | + | 11.7108i | 0.408709 | + | 0.408709i | 0.881288 | − | 0.472579i | \(-0.156677\pi\) |
−0.472579 | + | 0.881288i | \(0.656677\pi\) | |||||||
\(822\) | 17.9388 | − | 17.9388i | 0.625688 | − | 0.625688i | ||||
\(823\) | −25.8040 | + | 25.8040i | −0.899472 | + | 0.899472i | −0.995389 | − | 0.0959171i | \(-0.969422\pi\) |
0.0959171 | + | 0.995389i | \(0.469422\pi\) | |||||||
\(824\) | − | 10.5227i | − | 0.366577i | ||||||
\(825\) | − | 12.0000i | − | 0.417786i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10.1988 | + | 10.1988i | −0.354647 | + | 0.354647i | −0.861835 | − | 0.507188i | \(-0.830685\pi\) |
0.507188 | + | 0.861835i | \(0.330685\pi\) | |||||||
\(828\) | 2.03427 | + | 2.03427i | 0.0706958 | + | 0.0706958i | ||||
\(829\) | −50.4924 | −1.75367 | −0.876837 | − | 0.480787i | \(-0.840351\pi\) | ||||
−0.876837 | + | 0.480787i | \(0.840351\pi\) | |||||||
\(830\) | 5.65685 | + | 5.65685i | 0.196352 | + | 0.196352i | ||||
\(831\) | 6.00000i | 0.208138i | ||||||||
\(832\) | 25.3693 | 0.879523 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 14.2462 | 0.493306 | ||||||||
\(835\) | − | 0.453602i | − | 0.0156976i | ||||||
\(836\) | −6.10281 | − | 6.10281i | −0.211070 | − | 0.211070i | ||||
\(837\) | −5.12311 | −0.177080 | ||||||||
\(838\) | −35.8776 | − | 35.8776i | −1.23937 | − | 1.23937i | ||||
\(839\) | 7.81634 | − | 7.81634i | 0.269850 | − | 0.269850i | −0.559190 | − | 0.829040i | \(-0.688888\pi\) |
0.829040 | + | 0.559190i | \(0.188888\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 39.0000i | 1.34483i | ||||||||
\(842\) | 44.6004i | 1.53703i | ||||||||
\(843\) | −13.5221 | + | 13.5221i | −0.465725 | + | 0.465725i | ||||
\(844\) | −3.52482 | + | 3.52482i | −0.121329 | + | 0.121329i | ||||
\(845\) | 3.10029 | + | 3.10029i | 0.106653 | + | 0.106653i | ||||
\(846\) | 4.49242 | 0.154453 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 19.8920i | − | 0.683096i | ||||||
\(849\) | 3.36932 | 0.115635 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20.4924 | −0.702471 | ||||||||
\(852\) | 4.49242i | 0.153908i | ||||||||
\(853\) | 14.6644 | + | 14.6644i | 0.502100 | + | 0.502100i | 0.912090 | − | 0.409990i | \(-0.134468\pi\) |
−0.409990 | + | 0.912090i | \(0.634468\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.05141 | + | 3.05141i | 0.104356 | + | 0.104356i | ||||
\(856\) | −13.2502 | + | 13.2502i | −0.452883 | + | 0.452883i | ||||
\(857\) | 4.24264 | − | 4.24264i | 0.144926 | − | 0.144926i | −0.630921 | − | 0.775847i | \(-0.717323\pi\) |
0.775847 | + | 0.630921i | \(0.217323\pi\) | |||||||
\(858\) | 18.2462i | 0.622915i | ||||||||
\(859\) | 12.0000i | 0.409435i | 0.978821 | + | 0.204717i | \(0.0656275\pi\) | ||||
−0.978821 | + | 0.204717i | \(0.934372\pi\) | |||||||
\(860\) | −1.33788 | + | 1.33788i | −0.0456214 | + | 0.0456214i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 26.5004 | + | 26.5004i | 0.902608 | + | 0.902608i | ||||
\(863\) | 26.2462 | 0.893431 | 0.446716 | − | 0.894676i | \(-0.352594\pi\) | ||||
0.446716 | + | 0.894676i | \(0.352594\pi\) | |||||||
\(864\) | 1.72424 | + | 1.72424i | 0.0586599 | + | 0.0586599i | ||||
\(865\) | − | 10.5616i | − | 0.359104i | ||||||
\(866\) | 22.3542 | 0.759625 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 39.3693i | 1.33551i | ||||||||
\(870\) | 5.11313 | + | 5.11313i | 0.173351 | + | 0.173351i | ||||
\(871\) | −18.2462 | −0.618249 | ||||||||
\(872\) | −26.0759 | − | 26.0759i | −0.883041 | − | 0.883041i | ||||
\(873\) | −7.86522 | + | 7.86522i | −0.266197 | + | 0.266197i | ||||
\(874\) | 55.6766 | − | 55.6766i | 1.88329 | − | 1.88329i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 1.86174i | − | 0.0629023i | ||||||
\(877\) | 24.0416 | − | 24.0416i | 0.811828 | − | 0.811828i | −0.173080 | − | 0.984908i | \(-0.555372\pi\) |
0.984908 | + | 0.173080i | \(0.0553718\pi\) | |||||||
\(878\) | −6.35324 | + | 6.35324i | −0.214412 | + | 0.214412i | ||||
\(879\) | −5.03680 | − | 5.03680i | −0.169887 | − | 0.169887i | ||||
\(880\) | 6.73863 | 0.227159 | ||||||||
\(881\) | 16.7965 | + | 16.7965i | 0.565887 | + | 0.565887i | 0.930974 | − | 0.365086i | \(-0.118961\pi\) |
−0.365086 | + | 0.930974i | \(0.618961\pi\) | |||||||
\(882\) | 10.9309i | 0.368062i | ||||||||
\(883\) | 38.4233 | 1.29305 | 0.646523 | − | 0.762894i | \(-0.276222\pi\) | ||||
0.646523 | + | 0.762894i | \(0.276222\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.630683 | −0.0212002 | ||||||||
\(886\) | 35.7235i | 1.20015i | ||||||||
\(887\) | 15.9534 | + | 15.9534i | 0.535664 | + | 0.535664i | 0.922252 | − | 0.386589i | \(-0.126347\pi\) |
−0.386589 | + | 0.922252i | \(0.626347\pi\) | |||||||
\(888\) | −7.61553 | −0.255560 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −4.41674 | + | 4.41674i | −0.148049 | + | 0.148049i | ||||
\(891\) | 1.81129 | − | 1.81129i | 0.0606805 | − | 0.0606805i | ||||
\(892\) | 6.10795i | 0.204509i | ||||||||
\(893\) | − | 22.1080i | − | 0.739814i | ||||||
\(894\) | −4.68860 | + | 4.68860i | −0.156810 | + | 0.156810i | ||||
\(895\) | 3.62258 | − | 3.62258i | 0.121090 | − | 0.121090i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −29.9309 | −0.999363 | ||||||||
\(898\) | −14.0658 | − | 14.0658i | −0.469382 | − | 0.469382i | ||||
\(899\) | 42.2462i | 1.40899i | ||||||||
\(900\) | −2.05398 | −0.0684658 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −2.24621 | −0.0747907 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.86522 | + | 7.86522i | 0.261593 | + | 0.261593i | ||||
\(905\) | 3.36932 | 0.112000 | ||||||||
\(906\) | 8.83348 | + | 8.83348i | 0.293473 | + | 0.293473i | ||||
\(907\) | 33.8434 | − | 33.8434i | 1.12375 | − | 1.12375i | 0.132578 | − | 0.991173i | \(-0.457675\pi\) |
0.991173 | − | 0.132578i | \(-0.0423254\pi\) | |||||||
\(908\) | −7.14740 | + | 7.14740i | −0.237195 | + | 0.237195i | ||||
\(909\) | 19.1231i | 0.634273i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.7184 | − | 20.7184i | 0.686430 | − | 0.686430i | −0.275011 | − | 0.961441i | \(-0.588682\pi\) |
0.961441 | + | 0.275011i | \(0.0886815\pi\) | |||||||
\(912\) | 25.4558 | − | 25.4558i | 0.842927 | − | 0.842927i | ||||
\(913\) | −16.5246 | − | 16.5246i | −0.546885 | − | 0.546885i | ||||
\(914\) | 10.6307 | 0.351632 | ||||||||
\(915\) | 0.348195 | + | 0.348195i | 0.0115110 | + | 0.0115110i | ||||
\(916\) | − | 2.63068i | − | 0.0869202i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.31534 | −0.142350 | −0.0711750 | − | 0.997464i | \(-0.522675\pi\) | ||||
−0.0711750 | + | 0.997464i | \(0.522675\pi\) | |||||||
\(920\) | 8.98485i | 0.296222i | ||||||||
\(921\) | 0.348195 | + | 0.348195i | 0.0114734 | + | 0.0114734i | ||||
\(922\) | −12.8769 | −0.424078 | ||||||||
\(923\) | −33.0492 | − | 33.0492i | −1.08783 | − | 1.08783i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.3455 | − | 10.3455i | 0.340156 | − | 0.340156i | ||||
\(926\) | 39.0152i | 1.28212i | ||||||||
\(927\) | 4.31534i | 0.141734i | ||||||||
\(928\) | 14.2185 | − | 14.2185i | 0.466744 | − | 0.466744i | ||||
\(929\) | 22.5785 | − | 22.5785i | 0.740778 | − | 0.740778i | −0.231950 | − | 0.972728i | \(-0.574511\pi\) |
0.972728 | + | 0.231950i | \(0.0745106\pi\) | |||||||
\(930\) | 3.17662 | + | 3.17662i | 0.104166 | + | 0.104166i | ||||
\(931\) | 53.7926 | 1.76298 | ||||||||
\(932\) | 0.174098 | + | 0.174098i | 0.00570276 | + | 0.00570276i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.26137 | −0.172157 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −11.1231 | −0.363570 | ||||||||
\(937\) | 22.0000i | 0.718709i | 0.933201 | + | 0.359354i | \(0.117003\pi\) | ||||
−0.933201 | + | 0.359354i | \(0.882997\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.61553 | −0.248523 | ||||||||
\(940\) | −0.500861 | − | 0.500861i | −0.0163363 | − | 0.0163363i | ||||
\(941\) | 21.2132 | − | 21.2132i | 0.691531 | − | 0.691531i | −0.271038 | − | 0.962569i | \(-0.587367\pi\) |
0.962569 | + | 0.271038i | \(0.0873669\pi\) | |||||||
\(942\) | −6.27691 | + | 6.27691i | −0.204513 | + | 0.204513i | ||||
\(943\) | − | 3.68466i | − | 0.119989i | ||||||
\(944\) | 5.26137i | 0.171243i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 21.7355 | − | 21.7355i | 0.706682 | − | 0.706682i | ||||
\(947\) | −8.48528 | − | 8.48528i | −0.275735 | − | 0.275735i | 0.555669 | − | 0.831404i | \(-0.312462\pi\) |
−0.831404 | + | 0.555669i | \(0.812462\pi\) | |||||||
\(948\) | 6.73863 | 0.218861 | ||||||||
\(949\) | 13.6962 | + | 13.6962i | 0.444597 | + | 0.444597i | ||||
\(950\) | 56.2159i | 1.82388i | ||||||||
\(951\) | 18.0000 | 0.583690 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −54.3542 | −1.76070 | −0.880352 | − | 0.474321i | \(-0.842694\pi\) | ||||
−0.880352 | + | 0.474321i | \(0.842694\pi\) | |||||||
\(954\) | 6.63068i | 0.214676i | ||||||||
\(955\) | 5.21089 | + | 5.21089i | 0.168621 | + | 0.168621i | ||||
\(956\) | −4.49242 | −0.145295 | ||||||||
\(957\) | −14.9363 | − | 14.9363i | −0.482822 | − | 0.482822i | ||||
\(958\) | −32.3528 | + | 32.3528i | −1.04527 | + | 1.04527i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 3.12311i | 0.100798i | ||||||||
\(961\) | − | 4.75379i | − | 0.153348i | ||||||
\(962\) | −15.7304 | + | 15.7304i | −0.507170 | + | 0.507170i | ||||
\(963\) | 5.43387 | − | 5.43387i | 0.175104 | − | 0.175104i | ||||
\(964\) | 6.62511 | + | 6.62511i | 0.213380 | + | 0.213380i | ||||
\(965\) | −13.6155 | −0.438299 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 46.5616i | − | 1.49732i | −0.662955 | − | 0.748659i | \(-0.730698\pi\) | ||
0.662955 | − | 0.748659i | \(-0.269302\pi\) | |||||||
\(968\) | 10.8229 | 0.347862 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 9.75379 | 0.313175 | ||||||||
\(971\) | 2.38447i | 0.0765213i | 0.999268 | + | 0.0382607i | \(0.0121817\pi\) | ||||
−0.999268 | + | 0.0382607i | \(0.987818\pi\) | |||||||
\(972\) | −0.310029 | − | 0.310029i | −0.00994418 | − | 0.00994418i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 8.13709 | + | 8.13709i | 0.260729 | + | 0.260729i | ||||
\(975\) | 15.1104 | − | 15.1104i | 0.483920 | − | 0.483920i | ||||
\(976\) | 2.90476 | − | 2.90476i | 0.0929791 | − | 0.0929791i | ||||
\(977\) | − | 8.24621i | − | 0.263820i | −0.991262 | − | 0.131910i | \(-0.957889\pi\) | ||
0.991262 | − | 0.131910i | \(-0.0421109\pi\) | |||||||
\(978\) | 10.7386i | 0.343384i | ||||||||
\(979\) | 12.9020 | − | 12.9020i | 0.412350 | − | 0.412350i | ||||
\(980\) | 1.21868 | − | 1.21868i | 0.0389294 | − | 0.0389294i | ||||
\(981\) | 10.6937 | + | 10.6937i | 0.341422 | + | 0.341422i | ||||
\(982\) | −5.26137 | −0.167897 | ||||||||
\(983\) | 1.46310 | + | 1.46310i | 0.0466655 | + | 0.0466655i | 0.730054 | − | 0.683389i | \(-0.239495\pi\) |
−0.683389 | + | 0.730054i | \(0.739495\pi\) | |||||||
\(984\) | − | 1.36932i | − | 0.0436522i | ||||||
\(985\) | −11.1922 | −0.356614 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 15.3693i | − | 0.488963i | ||||||
\(989\) | 35.6547 | + | 35.6547i | 1.13375 | + | 1.13375i | ||||
\(990\) | −2.24621 | −0.0713893 | ||||||||
\(991\) | 4.76493 | + | 4.76493i | 0.151363 | + | 0.151363i | 0.778727 | − | 0.627363i | \(-0.215866\pi\) |
−0.627363 | + | 0.778727i | \(0.715866\pi\) | |||||||
\(992\) | 8.83348 | − | 8.83348i | 0.280463 | − | 0.280463i | ||||
\(993\) | −4.29152 | + | 4.29152i | −0.136187 | + | 0.136187i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 8.98485i | − | 0.284839i | ||||||
\(996\) | −2.82843 | + | 2.82843i | −0.0896221 | + | 0.0896221i | ||||
\(997\) | −7.07107 | + | 7.07107i | −0.223943 | + | 0.223943i | −0.810157 | − | 0.586214i | \(-0.800618\pi\) |
0.586214 | + | 0.810157i | \(0.300618\pi\) | |||||||
\(998\) | 12.5538 | + | 12.5538i | 0.397384 | + | 0.397384i | ||||
\(999\) | 3.12311 | 0.0988107 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))