Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1568,2,Mod(815,1568)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1568, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1568.815");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1568 = 2^{5} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1568.q (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: | \(12.5205430369\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.144054149089536.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3x^{11} + x^{9} + 48x^{8} - 189x^{7} + 431x^{6} - 654x^{5} + 624x^{4} - 340x^{3} + 96x^{2} - 12x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1391.3 | ||
Root | \(0.609850 - 0.457915i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1568.1391 |
Dual form | 1568.2.q.g.815.3 |
$q$-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 \(\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(1471\) | \(1473\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | −0.416472 | + | 0.240450i | −0.240450 | + | 0.138824i | −0.615384 | − | 0.788228i | \(-0.710999\pi\) |
0.374933 | + | 0.927052i | \(0.377666\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.59713 | + | 2.76632i | −0.714260 | + | 1.23714i | 0.248984 | + | 0.968508i | \(0.419903\pi\) |
−0.963244 | + | 0.268628i | \(0.913430\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.38437 | + | 2.39779i | −0.461456 | + | 0.799265i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.800840 | − | 1.38709i | −0.241462 | − | 0.418225i | 0.719669 | − | 0.694318i | \(-0.244294\pi\) |
−0.961131 | + | 0.276093i | \(0.910960\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.38831 | 0.385047 | 0.192523 | − | 0.981292i | \(-0.438333\pi\) | ||||
0.192523 | + | 0.981292i | \(0.438333\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 1.53613i | − | 0.396626i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.48605 | + | 2.01267i | −0.845490 | + | 0.488144i | −0.859127 | − | 0.511763i | \(-0.828993\pi\) |
0.0136363 | + | 0.999907i | \(0.495659\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.56957 | − | 2.63824i | −1.04833 | − | 0.605255i | −0.126150 | − | 0.992011i | \(-0.540262\pi\) |
−0.922182 | + | 0.386756i | \(0.873595\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.83044 | + | 2.21151i | 0.798702 | + | 0.461131i | 0.843017 | − | 0.537887i | \(-0.180777\pi\) |
−0.0443149 | + | 0.999018i | \(0.514110\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.60168 | − | 4.50624i | −0.520336 | − | 0.901248i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 2.77419i | − | 0.533893i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.10613i | 0.948185i | 0.880475 | + | 0.474093i | \(0.157224\pi\) | ||||
−0.880475 | + | 0.474093i | \(0.842776\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.0579809 | − | 0.100426i | −0.0104137 | − | 0.0180370i | 0.860772 | − | 0.508991i | \(-0.169982\pi\) |
−0.871185 | + | 0.490954i | \(0.836648\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.667055 | + | 0.385124i | 0.116119 | + | 0.0670416i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.63087 | − | 2.67363i | −0.761310 | − | 0.439543i | 0.0684556 | − | 0.997654i | \(-0.478193\pi\) |
−0.829766 | + | 0.558111i | \(0.811526\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.578191 | + | 0.333819i | −0.0925847 | + | 0.0534538i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.21689i | − | 0.658568i | −0.944231 | − | 0.329284i | \(-0.893193\pi\) | ||
0.944231 | − | 0.329284i | \(-0.106807\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.42204 | − | 7.65920i | −0.659199 | − | 1.14177i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.05821 | − | 8.76108i | 0.737816 | − | 1.27794i | −0.215660 | − | 0.976468i | \(-0.569190\pi\) |
0.953477 | − | 0.301467i | \(-0.0974763\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.967895 | − | 1.67644i | 0.135532 | − | 0.234749i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.13514 | − | 3.54212i | 0.842726 | − | 0.486548i | −0.0154638 | − | 0.999880i | \(-0.504922\pi\) |
0.858190 | + | 0.513332i | \(0.171589\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.11619 | 0.689868 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.53747 | 0.336096 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.38856 | + | 2.53374i | −0.571342 | + | 0.329865i | −0.757685 | − | 0.652620i | \(-0.773670\pi\) |
0.186343 | + | 0.982485i | \(0.440336\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.21321 | − | 7.29750i | 0.539447 | − | 0.934349i | −0.459487 | − | 0.888184i | \(-0.651967\pi\) |
0.998934 | − | 0.0461646i | \(-0.0146999\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.21731 | + | 3.84050i | −0.275024 | + | 0.476355i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.01815 | − | 8.69169i | −0.613065 | − | 1.06186i | −0.990721 | − | 0.135913i | \(-0.956603\pi\) |
0.377656 | − | 0.925946i | \(-0.376730\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.12703 | −0.256064 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.29150i | 0.627986i | 0.949425 | + | 0.313993i | \(0.101667\pi\) | ||||
−0.949425 | + | 0.313993i | \(0.898333\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.30504 | + | 5.37227i | −1.08907 | + | 0.628776i | −0.933329 | − | 0.359021i | \(-0.883110\pi\) |
−0.155743 | + | 0.987798i | \(0.549777\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.16706 | + | 1.25115i | 0.250230 | + | 0.144470i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.3349 | − | 5.96688i | −1.16277 | − | 0.671327i | −0.210805 | − | 0.977528i | \(-0.567609\pi\) |
−0.951967 | + | 0.306201i | \(0.900942\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.48605 | − | 6.03801i | −0.387338 | − | 0.670890i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 14.9789i | − | 1.64415i | −0.569382 | − | 0.822073i | \(-0.692818\pi\) | ||
0.569382 | − | 0.822073i | \(-0.307182\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 12.8580i | − | 1.39465i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.22777 | − | 2.12656i | −0.131631 | − | 0.227992i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.50000 | − | 0.866025i | −0.159000 | − | 0.0917985i | 0.418389 | − | 0.908268i | \(-0.362595\pi\) |
−0.577389 | + | 0.816469i | \(0.695928\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.0482949 | + | 0.0278831i | 0.00500795 | + | 0.00289134i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 14.5965 | − | 8.42726i | 1.49756 | − | 0.864619i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 2.87198i | − | 0.291606i | −0.989314 | − | 0.145803i | \(-0.953423\pi\) | ||
0.989314 | − | 0.145803i | \(-0.0465765\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.43462 | 0.445696 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.40310 | + | 5.89434i | 0.338621 | + | 0.586509i | 0.984174 | − | 0.177207i | \(-0.0567062\pi\) |
−0.645553 | + | 0.763716i | \(0.723373\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.02471 | + | 12.1672i | −0.692165 | + | 1.19887i | 0.278962 | + | 0.960302i | \(0.410010\pi\) |
−0.971127 | + | 0.238563i | \(0.923324\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.56957 | + | 4.45063i | −0.248410 | + | 0.430259i | −0.963085 | − | 0.269198i | \(-0.913241\pi\) |
0.714675 | + | 0.699457i | \(0.246575\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.45182 | + | 1.41556i | −0.234842 | + | 0.135586i | −0.612804 | − | 0.790235i | \(-0.709958\pi\) |
0.377962 | + | 0.925821i | \(0.376625\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.57151 | 0.244077 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.43695 | −0.135177 | −0.0675887 | − | 0.997713i | \(-0.521531\pi\) | ||||
−0.0675887 | + | 0.997713i | \(0.521531\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.2355 | + | 7.06415i | −1.14096 | + | 0.658735i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.92193 | + | 3.32887i | −0.177682 | + | 0.307754i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.21731 | − | 7.30460i | 0.383392 | − | 0.664054i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.01395 | + | 1.75622i | 0.0914251 | + | 0.158353i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.649581 | 0.0581003 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 4.92077i | − | 0.436647i | −0.975876 | − | 0.218324i | \(-0.929941\pi\) | ||
0.975876 | − | 0.218324i | \(-0.0700589\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.41647 | − | 1.97250i | −0.298499 | − | 0.172338i | 0.343270 | − | 0.939237i | \(-0.388466\pi\) |
−0.641768 | + | 0.766899i | \(0.721799\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.67429 | + | 4.43075i | 0.660498 | + | 0.381339i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.0514223 | + | 0.0890661i | 0.00439331 | + | 0.00760943i | 0.868214 | − | 0.496190i | \(-0.165268\pi\) |
−0.863820 | + | 0.503800i | \(0.831935\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.9789i | 1.27049i | 0.772310 | + | 0.635246i | \(0.219101\pi\) | ||||
−0.772310 | + | 0.635246i | \(0.780899\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.86500i | 0.409707i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.11181 | − | 1.92571i | −0.0929743 | − | 0.161036i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.1252 | − | 8.15518i | −1.17303 | − | 0.677251i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.79164 | + | 5.65320i | 0.802162 | + | 0.463129i | 0.844227 | − | 0.535986i | \(-0.180060\pi\) |
−0.0420645 | + | 0.999115i | \(0.513393\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.8351 | + | 7.41032i | −1.04450 | + | 0.603044i | −0.921105 | − | 0.389314i | \(-0.872712\pi\) |
−0.123397 | + | 0.992357i | \(0.539379\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 11.1451i | − | 0.901028i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.370413 | 0.0297523 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.369362 | + | 0.639755i | 0.0294783 | + | 0.0510580i | 0.880388 | − | 0.474254i | \(-0.157282\pi\) |
−0.850910 | + | 0.525312i | \(0.823949\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.70341 | + | 2.95039i | −0.135089 | + | 0.233981i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.35226 | + | 7.53834i | −0.340895 | + | 0.590448i | −0.984599 | − | 0.174826i | \(-0.944064\pi\) |
0.643704 | + | 0.765275i | \(0.277397\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.13075 | + | 1.23019i | −0.165879 | + | 0.0957703i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.38831 | −0.107430 | −0.0537152 | − | 0.998556i | \(-0.517106\pi\) | ||||
−0.0537152 | + | 0.998556i | \(0.517106\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0726 | −0.851739 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.6519 | − | 7.30460i | 0.967518 | − | 0.558597i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.485324 | + | 0.840606i | −0.0368985 | + | 0.0639101i | −0.883885 | − | 0.467704i | \(-0.845081\pi\) |
0.846986 | + | 0.531615i | \(0.178414\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.21848 | − | 2.11046i | 0.0915864 | − | 0.158632i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.13495 | − | 12.3581i | −0.533291 | − | 0.923687i | −0.999244 | − | 0.0388779i | \(-0.987622\pi\) |
0.465953 | − | 0.884810i | \(-0.345712\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.3218 | 1.13886 | 0.569429 | − | 0.822041i | \(-0.307164\pi\) | ||||
0.569429 | + | 0.822041i | \(0.307164\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.05228i | 0.299553i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 14.7922 | − | 8.54031i | 1.08755 | − | 0.627896i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.58353 | + | 3.22365i | 0.408308 | + | 0.235737i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.16564 | − | 1.25033i | −0.156700 | − | 0.0904709i | 0.419599 | − | 0.907709i | \(-0.362171\pi\) |
−0.576300 | + | 0.817238i | \(0.695504\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.55026 | + | 2.68512i | 0.111590 | + | 0.193279i | 0.916411 | − | 0.400237i | \(-0.131072\pi\) |
−0.804822 | + | 0.593517i | \(0.797739\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 2.13261i | − | 0.152720i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.6891i | 1.11780i | 0.829233 | + | 0.558902i | \(0.188777\pi\) | ||||
−0.829233 | + | 0.558902i | \(0.811223\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.91290 | − | 10.2414i | −0.419154 | − | 0.725997i | 0.576700 | − | 0.816956i | \(-0.304340\pi\) |
−0.995855 | + | 0.0909591i | \(0.971007\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.17984 | + | 2.41323i | 0.294823 | + | 0.170216i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.6653 | + | 6.73495i | 0.814738 | + | 0.470389i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.6055 | + | 6.12307i | −0.737131 | + | 0.425583i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.45124i | 0.584585i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.0726 | −0.693427 | −0.346713 | − | 0.937971i | \(-0.612702\pi\) | ||||
−0.346713 | + | 0.937971i | \(0.612702\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.27234 | − | 2.20376i | −0.0871796 | − | 0.150999i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.58353 | − | 4.47480i | 0.174579 | − | 0.302379i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.83970 | + | 2.79420i | −0.325553 | + | 0.187958i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.3086 | −1.62783 | −0.813913 | − | 0.580987i | \(-0.802667\pi\) | ||||
−0.813913 | + | 0.580987i | \(0.802667\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.4067 | 0.960448 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.4048 | + | 7.16194i | −0.823339 | + | 0.475355i | −0.851566 | − | 0.524247i | \(-0.824347\pi\) |
0.0282277 | + | 0.999602i | \(0.491014\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.32502 | − | 9.22321i | 0.351887 | − | 0.609487i | −0.634693 | − | 0.772765i | \(-0.718873\pi\) |
0.986580 | + | 0.163278i | \(0.0522066\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.318991 | − | 0.552509i | 0.0208978 | − | 0.0361961i | −0.855387 | − | 0.517989i | \(-0.826681\pi\) |
0.876285 | + | 0.481793i | \(0.160014\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.1573 | + | 27.9853i | 1.05399 | + | 1.82556i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.73896 | 0.372785 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.73540i | 0.306307i | 0.988202 | + | 0.153154i | \(0.0489430\pi\) | ||||
−0.988202 | + | 0.153154i | \(0.951057\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.1380 | − | 5.85317i | 0.653045 | − | 0.377036i | −0.136577 | − | 0.990629i | \(-0.543610\pi\) |
0.789622 | + | 0.613594i | \(0.210277\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.1112 | + | 5.83773i | 0.648636 | + | 0.374490i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.34397 | − | 3.66269i | −0.403657 | − | 0.233051i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.60168 | + | 6.23829i | 0.228247 | + | 0.395336i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.5631i | 0.729858i | 0.931035 | + | 0.364929i | \(0.118907\pi\) | ||||
−0.931035 | + | 0.364929i | \(0.881093\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 7.08425i | − | 0.445383i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.09172 | + | 5.35501i | 0.193611 | + | 0.335344i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.4302 | + | 11.7954i | 1.27440 | + | 0.735777i | 0.975813 | − | 0.218605i | \(-0.0701506\pi\) |
0.298589 | + | 0.954382i | \(0.403484\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.2435 | − | 7.06876i | −0.757851 | − | 0.437546i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.24833 | − | 5.33953i | 0.570277 | − | 0.329249i | −0.186983 | − | 0.982363i | \(-0.559871\pi\) |
0.757260 | + | 0.653114i | \(0.226538\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 22.6290i | 1.39009i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.832945 | 0.0509754 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.6690 | + | 20.2113i | 0.711471 | + | 1.23230i | 0.964305 | + | 0.264794i | \(0.0853040\pi\) |
−0.252834 | + | 0.967510i | \(0.581363\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.81961 | − | 11.8119i | 0.414262 | − | 0.717522i | −0.581089 | − | 0.813840i | \(-0.697373\pi\) |
0.995351 | + | 0.0963179i | \(0.0307066\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.16706 | + | 7.21755i | −0.251283 | + | 0.435235i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.396180 | + | 0.228735i | −0.0238042 | + | 0.0137433i | −0.511855 | − | 0.859072i | \(-0.671041\pi\) |
0.488051 | + | 0.872815i | \(0.337708\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.321068 | 0.0192218 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.43695 | 0.0857215 | 0.0428608 | − | 0.999081i | \(-0.486353\pi\) | ||||
0.0428608 | + | 0.999081i | \(0.486353\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.0428 | − | 15.6132i | 1.60753 | − | 0.928108i | 0.617609 | − | 0.786486i | \(-0.288102\pi\) |
0.989921 | − | 0.141622i | \(-0.0452318\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.05268 | + | 7.01945i | −0.240060 | + | 0.415796i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.398321 | + | 0.689912i | −0.0234306 | + | 0.0405831i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.690570 | + | 1.19610i | 0.0404819 | + | 0.0701168i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −31.3006 | −1.82860 | −0.914299 | − | 0.405040i | \(-0.867258\pi\) | ||||
−0.914299 | + | 0.405040i | \(0.867258\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 16.1869i | − | 0.942437i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.84806 | + | 2.22168i | −0.223287 | + | 0.128915i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.31783 | + | 3.07025i | 0.307538 | + | 0.177557i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.83459 | − | 1.63655i | −0.162843 | − | 0.0940175i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.4581 | + | 23.3102i | 0.770611 | + | 1.33474i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.7215i | 0.840202i | 0.907477 | + | 0.420101i | \(0.138005\pi\) | ||||
−0.907477 | + | 0.420101i | \(0.861995\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 6.75638i | − | 0.384357i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.79025 | + | 13.4931i | 0.441745 | + | 0.765124i | 0.997819 | − | 0.0660082i | \(-0.0210263\pi\) |
−0.556074 | + | 0.831133i | \(0.687693\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.3329 | − | 6.54308i | −0.640576 | − | 0.369837i | 0.144260 | − | 0.989540i | \(-0.453920\pi\) |
−0.784836 | + | 0.619703i | \(0.787253\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −20.3971 | − | 11.7763i | −1.14562 | − | 0.661422i | −0.197801 | − | 0.980242i | \(-0.563380\pi\) |
−0.947815 | + | 0.318821i | \(0.896713\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.08269 | − | 4.08919i | 0.396555 | − | 0.228951i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 2.47142i | − | 0.137941i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 21.2397 | 1.18181 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.61193 | − | 6.25604i | −0.200354 | − | 0.347023i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.680744 | − | 1.17908i | 0.0376452 | − | 0.0652035i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.5277 | − | 28.6268i | 0.908445 | − | 1.57347i | 0.0922207 | − | 0.995739i | \(-0.470603\pi\) |
0.816225 | − | 0.577735i | \(-0.196063\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.8217 | − | 7.40258i | 0.702622 | − | 0.405659i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 32.0587 | 1.75155 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.5096 | −0.844860 | −0.422430 | − | 0.906396i | \(-0.638823\pi\) | ||||
−0.422430 | + | 0.906396i | \(0.638823\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.598452 | − | 0.345516i | 0.0325035 | − | 0.0187659i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.0928668 | + | 0.160850i | −0.00502902 | + | 0.00871052i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.39716 | − | 5.88405i | 0.182897 | − | 0.316786i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.2494 | + | 19.4846i | 0.603900 | + | 1.04599i | 0.992224 | + | 0.124463i | \(0.0397209\pi\) |
−0.388324 | + | 0.921523i | \(0.626946\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.4735 | −1.52415 | −0.762077 | − | 0.647486i | \(-0.775820\pi\) | ||||
−0.762077 | + | 0.647486i | \(0.775820\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 3.85142i | − | 0.205574i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.29108 | − | 4.78686i | 0.441290 | − | 0.254779i | −0.262855 | − | 0.964835i | \(-0.584664\pi\) |
0.704145 | + | 0.710057i | \(0.251331\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.6380 | − | 8.45124i | −0.776903 | − | 0.448545i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.25225 | − | 1.87769i | −0.171647 | − | 0.0991006i | 0.411715 | − | 0.911313i | \(-0.364930\pi\) |
−0.583362 | + | 0.812212i | \(0.698263\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.42067 | + | 7.65683i | 0.232667 | + | 0.402991i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.05622i | 0.212896i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 34.3209i | − | 1.79644i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.41302 | + | 14.5718i | 0.439156 | + | 0.760640i | 0.997625 | − | 0.0688852i | \(-0.0219442\pi\) |
−0.558469 | + | 0.829526i | \(0.688611\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.1112 | + | 5.83773i | 0.526370 | + | 0.303900i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.1354 | + | 6.42901i | 0.576568 | + | 0.332882i | 0.759768 | − | 0.650194i | \(-0.225312\pi\) |
−0.183200 | + | 0.983076i | \(0.558646\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.270533 | + | 0.156192i | −0.0139702 | + | 0.00806572i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.08888i | 0.365096i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.5822 | −1.31407 | −0.657034 | − | 0.753861i | \(-0.728189\pi\) | ||||
−0.657034 | + | 0.753861i | \(0.728189\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.18320 | + | 2.04936i | 0.0606172 | + | 0.104992i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.4846 | + | 23.3561i | −0.689033 | + | 1.19344i | 0.283118 | + | 0.959085i | \(0.408631\pi\) |
−0.972151 | + | 0.234355i | \(0.924702\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −27.7043 | + | 15.9951i | −1.40466 | + | 0.810983i | −0.994867 | − | 0.101195i | \(-0.967734\pi\) |
−0.409796 | + | 0.912177i | \(0.634400\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.8041 | −0.900394 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.89716 | 0.0956988 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 33.0126 | − | 19.0598i | 1.66104 | − | 0.959004i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.51929 | + | 14.7558i | −0.427571 | + | 0.740575i | −0.996657 | − | 0.0817035i | \(-0.973964\pi\) |
0.569086 | + | 0.822278i | \(0.307297\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.94858 | − | 5.10709i | 0.147245 | − | 0.255036i | −0.782963 | − | 0.622068i | \(-0.786293\pi\) |
0.930208 | + | 0.367032i | \(0.119626\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.0804953 | − | 0.139422i | −0.00400976 | − | 0.00694510i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 22.2707 | 1.10664 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.56461i | 0.424532i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.207751 | − | 0.119945i | 0.0102726 | − | 0.00593090i | −0.494855 | − | 0.868976i | \(-0.664779\pi\) |
0.505128 | + | 0.863045i | \(0.331445\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.0428320 | − | 0.0247290i | −0.00211274 | − | 0.00121979i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 41.4364 | + | 23.9233i | 2.03403 | + | 1.17435i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.60168 | − | 6.23829i | −0.176375 | − | 0.305490i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 29.4140i | − | 1.43697i | −0.695544 | − | 0.718484i | \(-0.744837\pi\) | ||
0.695544 | − | 0.718484i | \(-0.255163\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.1265i | 1.56575i | 0.622180 | + | 0.782874i | \(0.286247\pi\) | ||||
−0.622180 | + | 0.782874i | \(0.713753\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 14.0049 | + | 24.2571i | 0.680939 | + | 1.17942i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 18.1391 | + | 10.4726i | 0.879878 | + | 0.507998i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.926077 | + | 0.534671i | 0.0447114 | + | 0.0258141i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −32.7662 | + | 18.9176i | −1.57829 | + | 0.911228i | −0.583196 | + | 0.812332i | \(0.698198\pi\) |
−0.995098 | + | 0.0988962i | \(0.968469\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.4835i | 1.22466i | 0.790602 | + | 0.612330i | \(0.209768\pi\) | ||||
−0.790602 | + | 0.612330i | \(0.790232\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.84367 | 0.376075 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.6690 | − | 20.2113i | −0.558204 | − | 0.966837i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.9804 | − | 20.7506i | 0.571792 | − | 0.990373i | −0.424590 | − | 0.905386i | \(-0.639582\pi\) |
0.996382 | − | 0.0849871i | \(-0.0270849\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.13495 | − | 8.89399i | 0.243969 | − | 0.422566i | −0.717872 | − | 0.696175i | \(-0.754884\pi\) |
0.961841 | + | 0.273608i | \(0.0882172\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.79140 | − | 2.76632i | 0.227134 | − | 0.131136i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.43726 | −0.257174 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.5096 | 0.543170 | 0.271585 | − | 0.962414i | \(-0.412452\pi\) | ||||
0.271585 | + | 0.962414i | \(0.412452\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.84923 | + | 3.37705i | −0.275429 | + | 0.159019i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.56363 | − | 6.17239i | 0.167434 | − | 0.290004i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.3050 | + | 26.5091i | −0.715939 | + | 1.24004i | 0.246657 | + | 0.969103i | \(0.420668\pi\) |
−0.962596 | + | 0.270941i | \(0.912665\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.58353 | + | 9.67095i | 0.260617 | + | 0.451401i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.3671 | 0.808866 | 0.404433 | − | 0.914568i | \(-0.367469\pi\) | ||||
0.404433 | + | 0.914568i | \(0.367469\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.7288i | 1.00983i | 0.863171 | + | 0.504913i | \(0.168475\pi\) | ||||
−0.863171 | + | 0.504913i | \(0.831525\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.154267 | + | 0.0890661i | −0.00715396 | + | 0.00413034i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.585859 | − | 0.338246i | −0.0271103 | − | 0.0156521i | 0.486384 | − | 0.873745i | \(-0.338316\pi\) |
−0.513494 | + | 0.858093i | \(0.671649\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.307659 | − | 0.177627i | −0.0141762 | − | 0.00818461i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 27.4555i | 1.25974i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 19.6144i | 0.898082i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.3839 | − | 24.9136i | −0.657217 | − | 1.13833i | −0.981333 | − | 0.192316i | \(-0.938400\pi\) |
0.324116 | − | 0.946017i | \(-0.394933\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.42907 | − | 3.71182i | −0.293140 | − | 0.169245i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.94483 | + | 4.58695i | 0.360756 | + | 0.208283i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.58745 | + | 0.916514i | −0.0719342 | + | 0.0415312i | −0.535536 | − | 0.844513i | \(-0.679890\pi\) |
0.463602 | + | 0.886044i | \(0.346557\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 4.18601i | − | 0.189298i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.4370 | −0.606401 | −0.303201 | − | 0.952927i | \(-0.598055\pi\) | ||||
−0.303201 | + | 0.952927i | \(0.598055\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.2770 | − | 17.8002i | −0.462851 | − | 0.801682i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.08269 | + | 12.2676i | −0.318343 | + | 0.551387i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.68404 | + | 9.84505i | −0.254453 | + | 0.440725i | −0.964747 | − | 0.263180i | \(-0.915229\pi\) |
0.710294 | + | 0.703905i | \(0.248562\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.578191 | − | 0.333819i | 0.0258317 | − | 0.0149139i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.2022 | 0.588656 | 0.294328 | − | 0.955704i | \(-0.404904\pi\) | ||||
0.294328 | + | 0.955704i | \(0.404904\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.7408 | −0.967454 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.61144 | − | 2.66241i | 0.204801 | − | 0.118242i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.2178 | + | 22.8940i | −0.585870 | + | 1.01476i | 0.408896 | + | 0.912581i | \(0.365914\pi\) |
−0.994766 | + | 0.102176i | \(0.967420\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.31899 | + | 12.6769i | −0.323141 | + | 0.559697i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −22.4388 | − | 38.8652i | −0.988773 | − | 1.71260i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.2033 | −0.712619 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 0.466786i | − | 0.0204896i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.4163 | − | 6.01384i | 0.456345 | − | 0.263471i | −0.254161 | − | 0.967162i | \(-0.581799\pi\) |
0.710506 | + | 0.703691i | \(0.248466\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.43276 | + | 1.40455i | 0.106377 | + | 0.0614168i | 0.552245 | − | 0.833682i | \(-0.313771\pi\) |
−0.445868 | + | 0.895099i | \(0.647105\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.404248 | + | 0.233393i | 0.0176093 | + | 0.0101668i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.71848 | − | 2.97649i | −0.0747164 | − | 0.129413i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 14.0305i | − | 0.608872i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 5.85434i | − | 0.253580i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.20791 | − | 14.2165i | −0.354859 | − | 0.614634i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.94302 | + | 3.43120i | 0.256460 | + | 0.148067i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.68628 | − | 0.973573i | −0.0724988 | − | 0.0418572i | 0.463312 | − | 0.886195i | \(-0.346661\pi\) |
−0.535811 | + | 0.844338i | \(0.679994\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.38109 | + | 3.68413i | −0.273839 | + | 0.158101i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 9.04336i | − | 0.387375i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.4561 | −1.21669 | −0.608347 | − | 0.793671i | \(-0.708167\pi\) | ||||
−0.608347 | + | 0.793671i | \(0.708167\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.6653 | + | 20.2048i | 0.497862 | + | 0.862321i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.4712 | − | 23.3329i | 0.573894 | − | 0.994013i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.10704 | + | 7.11361i | −0.174334 | + | 0.301956i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.96630 | + | 4.59935i | −0.337543 | + | 0.194881i | −0.659185 | − | 0.751981i | \(-0.729099\pi\) |
0.321642 | + | 0.946861i | \(0.395765\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.10051 | −0.130904 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23.5533 | + | 13.5985i | −0.992653 | + | 0.573108i | −0.906066 | − | 0.423136i | \(-0.860929\pi\) |
−0.0865866 | + | 0.996244i | \(0.527596\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.29501 | − | 3.97508i | 0.0965518 | − | 0.167233i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.7699 | − | 20.3861i | 0.493420 | − | 0.854628i | −0.506551 | − | 0.862210i | \(-0.669080\pi\) |
0.999971 | + | 0.00758149i | \(0.00241329\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.1713 | + | 26.2774i | 0.634897 | + | 1.09967i | 0.986537 | + | 0.163539i | \(0.0522909\pi\) |
−0.351640 | + | 0.936135i | \(0.614376\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.20257 | 0.0502382 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 23.0145i | − | 0.959772i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.7760 | + | 14.3044i | −1.03144 | + | 0.595500i | −0.917396 | − | 0.397976i | \(-0.869713\pi\) |
−0.114041 | + | 0.993476i | \(0.536380\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.29128 | − | 0.745520i | −0.0536637 | − | 0.0309828i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.82652 | − | 5.67335i | −0.406973 | − | 0.234966i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.13915 | − | 10.6333i | −0.253823 | − | 0.439634i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.2362i | 0.628867i | 0.949280 | + | 0.314433i | \(0.101814\pi\) | ||||
−0.949280 | + | 0.314433i | \(0.898186\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.611872i | 0.0252117i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.77246 | − | 6.53409i | −0.155178 | − | 0.268777i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.2934 | − | 10.5617i | −0.751221 | − | 0.433717i | 0.0749142 | − | 0.997190i | \(-0.476132\pi\) |
−0.826135 | + | 0.563473i | \(0.809465\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.92512 | + | 2.84352i | 0.201572 | + | 0.116378i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.1795 | − | 16.8468i | 1.19224 | − | 0.688341i | 0.233427 | − | 0.972374i | \(-0.425006\pi\) |
0.958814 | + | 0.284033i | \(0.0916726\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 24.3960i | − | 0.995132i | −0.867426 | − | 0.497566i | \(-0.834227\pi\) | ||
0.867426 | − | 0.497566i | \(-0.165773\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 27.7879 | 1.13161 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.4712 | + | 23.3329i | 0.547683 | + | 0.948616i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.08757 | + | 7.07987i | −0.165909 | + | 0.287363i | −0.936978 | − | 0.349389i | \(-0.886389\pi\) |
0.771069 | + | 0.636752i | \(0.219723\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.02235 | − | 12.1631i | 0.284094 | − | 0.492065i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.7221 | − | 8.49981i | 0.594620 | − | 0.343304i | −0.172302 | − | 0.985044i | \(-0.555121\pi\) |
0.766922 | + | 0.641740i | \(0.221787\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.47768 | −0.261205 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 39.6548 | 1.59644 | 0.798221 | − | 0.602365i | \(-0.205775\pi\) | ||||
0.798221 | + | 0.602365i | \(0.205775\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.4719 | + | 7.20065i | −0.501288 | + | 0.289419i | −0.729245 | − | 0.684252i | \(-0.760129\pi\) |
0.227957 | + | 0.973671i | \(0.426795\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.13514 | − | 10.6264i | 0.246195 | − | 0.426422i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.9709 | − | 20.7343i | 0.478837 | − | 0.829370i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.03211 | − | 3.51971i | −0.0811545 | − | 0.140564i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21.5246 | 0.858241 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 36.6698i | − | 1.45980i | −0.683553 | − | 0.729900i | \(-0.739566\pi\) | ||
0.683553 | − | 0.729900i | \(-0.260434\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.19496 | − | 2.42196i | 0.166735 | − | 0.0962644i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13.6124 | + | 7.85913i | 0.540192 | + | 0.311880i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.6879 | − | 7.32538i | −0.501927 | − | 0.289788i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.13798 | − | 15.8274i | −0.360929 | − | 0.625147i | 0.627185 | − | 0.778870i | \(-0.284207\pi\) |
−0.988114 | + | 0.153723i | \(0.950874\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 13.6340i | − | 0.537671i | −0.963186 | − | 0.268836i | \(-0.913361\pi\) | ||
0.963186 | − | 0.268836i | \(-0.0866389\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.74153 | − | 15.1408i | −0.343665 | − | 0.595245i | 0.641445 | − | 0.767169i | \(-0.278335\pi\) |
−0.985110 | + | 0.171923i | \(0.945002\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.02907 | + | 4.05824i | 0.275915 | + | 0.159300i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.40495 | − | 4.85260i | −0.328911 | − | 0.189897i | 0.326446 | − | 0.945216i | \(-0.394149\pi\) |
−0.655358 | + | 0.755319i | \(0.727482\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.9131 | − | 6.30070i | 0.426411 | − | 0.246189i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 29.7488i | − | 1.16061i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.9465 | 1.12760 | 0.563798 | − | 0.825913i | \(-0.309340\pi\) | ||||
0.563798 | + | 0.825913i | \(0.309340\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.43683 | + | 11.1489i | 0.250364 | + | 0.433643i | 0.963626 | − | 0.267254i | \(-0.0861164\pi\) |
−0.713262 | + | 0.700897i | \(0.752783\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.34373 | − | 2.32742i | 0.0521863 | − | 0.0903893i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.2922 | + | 19.5587i | −0.437238 | + | 0.757318i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.1239 | − | 5.84502i | 0.391412 | − | 0.225982i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.4964 | −0.521024 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.6548 | −0.911825 | −0.455912 | − | 0.890025i | \(-0.650687\pi\) | ||||
−0.455912 | + | 0.890025i | \(0.650687\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −12.5012 | + | 7.21755i | −0.481170 | + | 0.277804i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.80224 | − | 3.12157i | 0.0692657 | − | 0.119972i | −0.829313 | − | 0.558785i | \(-0.811268\pi\) |
0.898578 | + | 0.438813i | \(0.144601\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.44419 | − | 5.96550i | 0.131981 | − | 0.228599i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.80924 | − | 6.59779i | −0.145756 | − | 0.252457i | 0.783899 | − | 0.620889i | \(-0.213228\pi\) |
−0.929655 | + | 0.368432i | \(0.879895\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.328514 | −0.0125519 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.12162i | 0.195402i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.51745 | − | 4.91755i | 0.324489 | − | 0.187344i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.9707 | − | 25.9639i | −1.71077 | − | 0.987712i | −0.933526 | − | 0.358509i | \(-0.883285\pi\) |
−0.777241 | − | 0.629203i | \(-0.783381\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −41.4364 | − | 23.9233i | −1.57177 | − | 0.907462i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.48721 | + | 14.7003i | 0.321476 | + | 0.556813i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.306806i | 0.0116045i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 0.741474i | − | 0.0280051i | −0.999902 | − | 0.0140025i | \(-0.995543\pi\) | ||
0.999902 | − | 0.0140025i | \(-0.00445729\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.1074 | + | 24.4347i | 0.532071 | + | 0.921574i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13.4581 | − | 7.77006i | −0.506863 | − | 0.292637i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.6491 | − | 20.5820i | −1.33883 | − | 0.772974i | −0.352196 | − | 0.935926i | \(-0.614565\pi\) |
−0.986634 | + | 0.162952i | \(0.947898\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 28.6147 | − | 16.5207i | 1.07314 | − | 0.619575i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 0.512901i | − | 0.0192083i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.10284 | 0.265631 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.13863 | − | 1.97216i | −0.0425229 | − | 0.0736518i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.02471 | + | 12.1672i | −0.261978 | + | 0.453758i | −0.966767 | − | 0.255658i | \(-0.917708\pi\) |
0.704790 | + | 0.709416i | \(0.251041\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.81479 | + | 4.87536i | −0.104683 | + | 0.181317i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 23.0095 | − | 13.2845i | 0.854550 | − | 0.493375i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.2022 | −0.489642 | −0.244821 | − | 0.969568i | \(-0.578729\pi\) | ||||
−0.244821 | + | 0.969568i | \(0.578729\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.3015 | 0.566724 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.9797 | − | 43.2661i | 0.922646 | − | 1.59807i | 0.127342 | − | 0.991859i | \(-0.459356\pi\) |
0.795304 | − | 0.606211i | \(-0.207311\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.03747 | + | 13.9213i | −0.296064 | + | 0.512798i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.2718 | − | 31.6476i | −0.672138 | − | 1.16418i | −0.977297 | − | 0.211875i | \(-0.932043\pi\) |
0.305159 | − | 0.952301i | \(-0.401290\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.52278 | 0.129413 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.1330i | 0.555177i | 0.960700 | + | 0.277589i | \(0.0895352\pi\) | ||||
−0.960700 | + | 0.277589i | \(0.910465\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −31.2771 | + | 18.0579i | −1.14591 | + | 0.661589i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 35.9163 | + | 20.7363i | 1.31411 | + | 0.758701i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.9997 | + | 6.92806i | 0.437877 | + | 0.252808i | 0.702697 | − | 0.711490i | \(-0.251979\pi\) |
−0.264820 | + | 0.964298i | \(0.585312\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.78036 | − | 4.81572i | −0.101322 | − | 0.175495i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 47.3412i | − | 1.72292i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 46.6967i | − | 1.69722i | −0.529019 | − | 0.848610i | \(-0.677440\pi\) | ||
0.529019 | − | 0.848610i | \(-0.322560\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.70341 | + | 2.95039i | 0.0618299 | + | 0.107093i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −40.7899 | − | 23.5501i | −1.47863 | − | 0.853689i | −0.478925 | − | 0.877856i | \(-0.658974\pi\) |
−0.999708 | + | 0.0241662i | \(0.992307\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 30.8309 | + | 17.8002i | 1.11469 | + | 0.643568i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.09267 | + | 3.51761i | −0.219994 | + | 0.127013i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.3071i | 0.624110i | 0.950064 | + | 0.312055i | \(0.101017\pi\) | ||||
−0.950064 | + | 0.312055i | \(0.898983\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.3448 | −0.408574 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.5389 | − | 23.4501i | −0.486960 | − | 0.843440i | 0.512927 | − | 0.858432i | \(-0.328561\pi\) |
−0.999888 | + | 0.0149920i | \(0.995228\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.301696 | + | 0.522552i | −0.0108372 | + | 0.0187706i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.1252 | + | 19.2694i | −0.398601 | + | 0.690398i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.33982 | − | 4.23764i | 0.262639 | − | 0.151635i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14.1654 | 0.506230 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.35969 | −0.0842208 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −46.9684 | + | 27.1172i | −1.67424 | + | 0.966624i | −0.709023 | + | 0.705186i | \(0.750864\pi\) |
−0.965220 | + | 0.261439i | \(0.915803\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.56778 | + | 4.44753i | −0.0914155 | + | 0.158336i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.84923 | − | 10.1312i | 0.207712 | − | 0.359768i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.44115 | − | 9.42435i | −0.192978 | − | 0.334247i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20.1437 | 0.713527 | 0.356763 | − | 0.934195i | \(-0.383880\pi\) | ||||
0.356763 | + | 0.934195i | \(0.383880\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 40.7221i | 1.44064i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.15310 | − | 2.39779i | 0.146743 | − | 0.0847219i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.9037 | + | 8.60465i | 0.525940 | + | 0.303651i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.71963 | − | 5.61163i | −0.342147 | − | 0.197539i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17.2771 | − | 29.9249i | −0.607432 | − | 1.05210i | −0.991662 | − | 0.128865i | \(-0.958867\pi\) |
0.384231 | − | 0.923237i | \(-0.374467\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.6340i | 0.478754i | 0.970927 | + | 0.239377i | \(0.0769431\pi\) | ||||
−0.970927 | + | 0.239377i | \(0.923057\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.55911i | 0.230038i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.9023 | − | 24.0795i | −0.486976 | − | 0.843468i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.7311 | + | 16.0106i | 0.967822 | + | 0.558772i | 0.898572 | − | 0.438827i | \(-0.144606\pi\) |
0.0692505 | + | 0.997599i | \(0.477939\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26.8399 | + | 15.4960i | −0.935580 | + | 0.540158i | −0.888572 | − | 0.458737i | \(-0.848302\pi\) |
−0.0470083 | + | 0.998894i | \(0.514969\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 4.00788i | − | 0.139537i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.0191 | 0.383172 | 0.191586 | − | 0.981476i | \(-0.438637\pi\) | ||||
0.191586 | + | 0.981476i | \(0.438637\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.9836 | − | 32.8806i | −0.659328 | − | 1.14199i | −0.980790 | − | 0.195067i | \(-0.937508\pi\) |
0.321462 | − | 0.946922i | \(-0.395826\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.109999 | − | 0.190524i | 0.00381582 | − | 0.00660919i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.21731 | − | 3.84050i | 0.0767332 | − | 0.132906i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.278601 | + | 0.160850i | −0.00962984 | + | 0.00555979i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.32984 | 0.287578 | 0.143789 | − | 0.989608i | \(-0.454071\pi\) | ||||
0.143789 | + | 0.989608i | \(0.454071\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.92739 | 0.100945 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.598452 | + | 0.345516i | −0.0206118 | + | 0.0119002i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 17.6844 | − | 30.6304i | 0.608363 | − | 1.05372i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.50840 | + | 13.0049i | −0.257687 | + | 0.446328i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.8255 | − | 20.4824i | −0.405374 | − | 0.702128i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.94153 | −0.237673 | −0.118837 | − | 0.992914i | \(-0.537917\pi\) | ||||
−0.118837 | + | 0.992914i | \(0.537917\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 46.6657i | 1.59593i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.91744 | + | 1.10704i | −0.0654986 | + | 0.0378156i | −0.532392 | − | 0.846498i | \(-0.678707\pi\) |
0.466893 | + | 0.884314i | \(0.345373\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.26337 | + | 3.03881i | 0.179584 | + | 0.103683i | 0.587097 | − | 0.809516i | \(-0.300271\pi\) |
−0.407513 | + | 0.913199i | \(0.633604\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.64747 | − | 4.41527i | −0.260323 | − | 0.150298i | 0.364159 | − | 0.931337i | \(-0.381357\pi\) |
−0.624482 | + | 0.781039i | \(0.714690\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.55026 | − | 2.68512i | −0.0527103 | − | 0.0912969i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 0.383106i | − | 0.0130110i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19.1141i | 0.648400i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.96673 | − | 12.0667i | −0.236059 | − | 0.408866i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.88643 | + | 3.97588i | 0.233070 | + | 0.134563i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.3059 | + | 5.95011i | 0.348005 | + | 0.200921i | 0.663806 | − | 0.747905i | \(-0.268940\pi\) |
−0.315801 | + | 0.948825i | \(0.602273\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.0358 | − | 7.52623i | 0.439687 | − | 0.253854i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 53.9142i | − | 1.81642i | −0.418519 | − | 0.908208i | \(-0.637451\pi\) | ||
0.418519 | − | 0.908208i | \(-0.362549\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.1987 | −0.376866 | −0.188433 | − | 0.982086i | \(-0.560341\pi\) | ||||
−0.188433 | + | 0.982086i | \(0.560341\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.89215 | + | 6.74139i | 0.130833 | + | 0.226609i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.1832 | + | 31.4942i | −0.610531 | + | 1.05747i | 0.380620 | + | 0.924732i | \(0.375711\pi\) |
−0.991151 | + | 0.132740i | \(0.957623\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.58353 | + | 9.67095i | −0.187055 | + | 0.323989i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −46.2278 | + | 26.6896i | −1.54695 | + | 0.893134i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 45.5819 | 1.52364 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.95297 | −0.0985968 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.512788 | − | 0.296058i | 0.0171024 | − | 0.00987410i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.2583 | + | 24.6960i | −0.475011 | + | 0.822744i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −24.4709 | + | 42.3849i | −0.813441 | + | 1.40892i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.92370 | − | 15.4563i | −0.296307 | − | 0.513218i | 0.678981 | − | 0.734156i | \(-0.262422\pi\) |
−0.975288 | + | 0.220937i | \(0.929088\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18.8446 | −0.625034 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 11.1458i | − | 0.369278i | −0.982806 | − | 0.184639i | \(-0.940888\pi\) | ||
0.982806 | − | 0.184639i | \(-0.0591116\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.7771 | + | 11.9957i | −0.687623 | + | 0.396999i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11.2099 | − | 6.47203i | −0.370587 | − | 0.213959i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.2802 | + | 16.3276i | 0.932879 | + | 0.538598i | 0.887721 | − | 0.460382i | \(-0.152288\pi\) |
0.0451579 | + | 0.998980i | \(0.485621\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.53980 | − | 6.13111i | −0.116640 | − | 0.202027i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.34623i | 0.241804i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27.8238i | 0.914839i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −19.4496 | − | 33.6876i | −0.638807 | − | 1.10645i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.3027 | + | 13.4538i | 0.764537 | + | 0.441406i | 0.830922 | − | 0.556388i | \(-0.187813\pi\) |
−0.0663853 | + | 0.997794i | \(0.521147\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.48885 | − | 3.74634i | −0.212435 | − | 0.122650i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −17.8353 | + | 10.2972i | −0.583276 | + | 0.336755i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.6476i | 1.06655i | 0.845942 | + | 0.533275i | \(0.179039\pi\) | ||||
−0.845942 | + | 0.533275i | \(0.820961\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.29315 | 0.205369 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.32087 | − | 10.9481i | −0.206055 | − | 0.356897i | 0.744414 | − | 0.667719i | \(-0.232729\pi\) |
−0.950468 | + | 0.310822i | \(0.899396\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.32569 | − | 16.1526i | 0.303686 | − | 0.526000i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −21.1271 | + | 36.5931i | −0.686537 | + | 1.18912i | 0.286414 | + | 0.958106i | \(0.407537\pi\) |
−0.972951 | + | 0.231011i | \(0.925797\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.9182 | + | 7.45835i | −0.419344 | + | 0.242108i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.3264 | 0.367285 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −44.4561 | −1.44007 | −0.720037 | − | 0.693936i | \(-0.755875\pi\) | ||||
−0.720037 | + | 0.693936i | \(0.755875\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.91764 | − | 3.99390i | 0.223850 | − | 0.129240i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.96650 | + | 3.40607i | −0.0635678 | + | 0.110103i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.4933 | − | 26.8351i | 0.499783 | − | 0.865650i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.11447 | − | 12.3226i | −0.229261 | − | 0.397091i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.90388 | −0.318817 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 25.7160i | − | 0.826972i | −0.910510 | − | 0.413486i | \(-0.864311\pi\) | ||
0.910510 | − | 0.413486i | \(-0.135689\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.84573 | + | 5.10709i | −0.284166 | + | 0.164063i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −40.2746 | − | 23.2526i | −1.29247 | − | 0.746210i | −0.313381 | − | 0.949627i | \(-0.601462\pi\) |
−0.979092 | + | 0.203417i | \(0.934795\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.00854 | + | 1.73698i | 0.0963503 | + | 0.0556278i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17.1348 | − | 29.6783i | −0.548189 | − | 0.949492i | −0.998399 | − | 0.0565688i | \(-0.981984\pi\) |
0.450209 | − | 0.892923i | \(-0.351349\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.77419i | 0.0886635i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 7.83862i | − | 0.250268i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.777334 | + | 1.34638i | 0.0247931 | + | 0.0429429i | 0.878156 | − | 0.478375i | \(-0.158774\pi\) |
−0.853363 | + | 0.521318i | \(0.825441\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −43.4012 | − | 25.0577i | −1.38288 | − | 0.798404i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.6482 | − | 13.0759i | 0.719443 | − | 0.415371i | −0.0951047 | − | 0.995467i | \(-0.530319\pi\) |
0.814548 | + | 0.580097i | \(0.196985\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15.8964i | 0.504457i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 37.7748 | 1.19754 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.1467 | + | 31.4310i | 0.574711 | + | 0.995429i | 0.996073 | + | 0.0885360i | \(0.0282188\pi\) |
−0.421362 | + | 0.906893i | \(0.638448\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.41717 | + | 12.8469i | −0.234669 | + | 0.406458i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))