Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [68,2,Mod(13,68)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(68, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("68.13");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 68 = 2^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 68.e (of order \(4\), degree \(2\), 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: | \(0.542982733745\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{13})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 21.2 | ||
Root | \(-1.30278i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 68.21 |
Dual form | 68.2.e.a.13.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/68\mathbb{Z}\right)^\times\).
\(n\) | \(35\) | \(37\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.30278 | − | 1.30278i | 0.752158 | − | 0.752158i | −0.222724 | − | 0.974882i | \(-0.571495\pi\) |
0.974882 | + | 0.222724i | \(0.0714948\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | + | 1.00000i | −0.447214 | + | 0.447214i | −0.894427 | − | 0.447214i | \(-0.852416\pi\) |
0.447214 | + | 0.894427i | \(0.352416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.30278 | − | 1.30278i | −0.492403 | − | 0.492403i | 0.416660 | − | 0.909063i | \(-0.363201\pi\) |
−0.909063 | + | 0.416660i | \(0.863201\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 0.394449i | − | 0.131483i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.30278 | + | 3.30278i | 0.995824 | + | 0.995824i | 0.999991 | − | 0.00416699i | \(-0.00132640\pi\) |
−0.00416699 | + | 0.999991i | \(0.501326\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.60555 | −1.27735 | −0.638675 | − | 0.769477i | \(-0.720517\pi\) | ||||
−0.638675 | + | 0.769477i | \(0.720517\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.60555i | 0.672750i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.60555 | + | 2.00000i | −0.874475 | + | 0.485071i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 6.60555i | − | 1.51542i | −0.652593 | − | 0.757709i | \(-0.726319\pi\) | ||
0.652593 | − | 0.757709i | \(-0.273681\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.39445 | −0.740729 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.697224 | − | 0.697224i | −0.145381 | − | 0.145381i | 0.630670 | − | 0.776051i | \(-0.282780\pi\) |
−0.776051 | + | 0.630670i | \(0.782780\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000i | 0.600000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.39445 | + | 3.39445i | 0.653262 | + | 0.653262i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.60555 | − | 5.60555i | 1.04092 | − | 1.04092i | 0.0417987 | − | 0.999126i | \(-0.486691\pi\) |
0.999126 | − | 0.0417987i | \(-0.0133088\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.697224 | − | 0.697224i | 0.125225 | − | 0.125225i | −0.641717 | − | 0.766942i | \(-0.721777\pi\) |
0.766942 | + | 0.641717i | \(0.221777\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.60555 | 1.49803 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.60555 | 0.440419 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00000 | − | 3.00000i | 0.493197 | − | 0.493197i | −0.416115 | − | 0.909312i | \(-0.636609\pi\) |
0.909312 | + | 0.416115i | \(0.136609\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.00000 | + | 6.00000i | −0.960769 | + | 0.960769i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.00000 | + | 1.00000i | 0.156174 | + | 0.156174i | 0.780869 | − | 0.624695i | \(-0.214777\pi\) |
−0.624695 | + | 0.780869i | \(0.714777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 10.6056i | − | 1.61733i | −0.588268 | − | 0.808666i | \(-0.700190\pi\) | ||
0.588268 | − | 0.808666i | \(-0.299810\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.394449 | + | 0.394449i | 0.0588009 | + | 0.0588009i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.00000 | −0.583460 | −0.291730 | − | 0.956501i | \(-0.594231\pi\) | ||||
−0.291730 | + | 0.956501i | \(0.594231\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 3.60555i | − | 0.515079i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.09167 | + | 7.30278i | −0.292893 | + | 1.02259i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.21110i | 1.26524i | 0.774461 | + | 0.632621i | \(0.218021\pi\) | ||||
−0.774461 | + | 0.632621i | \(0.781979\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.60555 | −0.890692 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.60555 | − | 8.60555i | −1.13983 | − | 1.13983i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 1.39445i | − | 0.181542i | −0.995872 | − | 0.0907709i | \(-0.971067\pi\) | ||
0.995872 | − | 0.0907709i | \(-0.0289331\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.21110 | + | 8.21110i | 1.05132 | + | 1.05132i | 0.998610 | + | 0.0527143i | \(0.0167873\pi\) |
0.0527143 | + | 0.998610i | \(0.483213\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.513878 | + | 0.513878i | −0.0647426 | + | 0.0647426i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.60555 | − | 4.60555i | 0.571248 | − | 0.571248i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.21110 | −0.636638 | −0.318319 | − | 0.947984i | \(-0.603118\pi\) | ||||
−0.318319 | + | 0.947984i | \(0.603118\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.81665 | −0.218699 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.90833 | + | 7.90833i | −0.938546 | + | 0.938546i | −0.998218 | − | 0.0596723i | \(-0.980994\pi\) |
0.0596723 | + | 0.998218i | \(0.480994\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.00000 | + | 7.00000i | −0.819288 | + | 0.819288i | −0.986005 | − | 0.166717i | \(-0.946683\pi\) |
0.166717 | + | 0.986005i | \(0.446683\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.90833 | + | 3.90833i | 0.451295 | + | 0.451295i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 8.60555i | − | 0.980694i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.30278 | + | 3.30278i | 0.371591 | + | 0.371591i | 0.868057 | − | 0.496465i | \(-0.165369\pi\) |
−0.496465 | + | 0.868057i | \(0.665369\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 10.0278 | 1.11420 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 3.81665i | − | 0.418932i | −0.977816 | − | 0.209466i | \(-0.932827\pi\) | ||
0.977816 | − | 0.209466i | \(-0.0671726\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.60555 | − | 5.60555i | 0.174146 | − | 0.608007i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 14.6056i | − | 1.56588i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.8167 | −1.46456 | −0.732281 | − | 0.681002i | \(-0.761544\pi\) | ||||
−0.732281 | + | 0.681002i | \(0.761544\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.00000 | + | 6.00000i | 0.628971 | + | 0.628971i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 1.81665i | − | 0.188378i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.60555 | + | 6.60555i | 0.677715 | + | 0.677715i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.394449 | + | 0.394449i | −0.0400502 | + | 0.0400502i | −0.726848 | − | 0.686798i | \(-0.759016\pi\) |
0.686798 | + | 0.726848i | \(0.259016\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.30278 | − | 1.30278i | 0.130934 | − | 0.130934i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.39445 | 0.337760 | 0.168880 | − | 0.985637i | \(-0.445985\pi\) | ||||
0.168880 | + | 0.985637i | \(0.445985\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.21110 | 0.119333 | 0.0596667 | − | 0.998218i | \(-0.480996\pi\) | ||||
0.0596667 | + | 0.998218i | \(0.480996\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.39445 | − | 3.39445i | 0.331264 | − | 0.331264i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.30278 | − | 9.30278i | 0.899333 | − | 0.899333i | −0.0960438 | − | 0.995377i | \(-0.530619\pi\) |
0.995377 | + | 0.0960438i | \(0.0306189\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.21110 | + | 8.21110i | 0.786481 | + | 0.786481i | 0.980916 | − | 0.194435i | \(-0.0622872\pi\) |
−0.194435 | + | 0.980916i | \(0.562287\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 7.81665i | − | 0.741924i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.39445 | + | 2.39445i | 0.225251 | + | 0.225251i | 0.810705 | − | 0.585454i | \(-0.199084\pi\) |
−0.585454 | + | 0.810705i | \(0.699084\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.39445 | 0.130033 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.81665i | 0.167950i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.30278 | + | 2.09167i | 0.669444 | + | 0.191743i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.8167i | 0.983332i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.60555 | 0.234935 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.00000 | − | 8.00000i | −0.715542 | − | 0.715542i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.60555i | 0.586148i | 0.956090 | + | 0.293074i | \(0.0946782\pi\) | ||||
−0.956090 | + | 0.293074i | \(0.905322\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −13.8167 | − | 13.8167i | −1.21649 | − | 1.21649i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.69722 | + | 2.69722i | −0.235658 | + | 0.235658i | −0.815049 | − | 0.579392i | \(-0.803290\pi\) |
0.579392 | + | 0.815049i | \(0.303290\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.60555 | + | 8.60555i | −0.746196 | + | 0.746196i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.78890 | −0.584295 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.60555 | 0.393479 | 0.196739 | − | 0.980456i | \(-0.436965\pi\) | ||||
0.196739 | + | 0.980456i | \(0.436965\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.30278 | + | 3.30278i | −0.280138 | + | 0.280138i | −0.833164 | − | 0.553026i | \(-0.813473\pi\) |
0.553026 | + | 0.833164i | \(0.313473\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.21110 | + | 5.21110i | −0.438854 | + | 0.438854i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −15.2111 | − | 15.2111i | −1.27202 | − | 1.27202i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.2111i | 0.931031i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.69722 | − | 4.69722i | −0.387421 | − | 0.387421i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −20.4222 | −1.67305 | −0.836526 | − | 0.547927i | \(-0.815417\pi\) | ||||
−0.836526 | + | 0.547927i | \(0.815417\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2.60555i | − | 0.212037i | −0.994364 | − | 0.106018i | \(-0.966190\pi\) | ||
0.994364 | − | 0.106018i | \(-0.0338102\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.788897 | + | 1.42221i | 0.0637786 | + | 0.114978i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.39445i | 0.112005i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.4222 | 1.62987 | 0.814935 | − | 0.579553i | \(-0.196773\pi\) | ||||
0.814935 | + | 0.579553i | \(0.196773\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.0000 | + | 12.0000i | 0.951662 | + | 0.951662i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.81665i | 0.143172i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.697224 | − | 0.697224i | −0.0546108 | − | 0.0546108i | 0.679274 | − | 0.733885i | \(-0.262295\pi\) |
−0.733885 | + | 0.679274i | \(0.762295\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.60555 | + | 8.60555i | −0.669941 | + | 0.669941i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.09167 | − | 4.09167i | 0.316623 | − | 0.316623i | −0.530845 | − | 0.847469i | \(-0.678126\pi\) |
0.847469 | + | 0.530845i | \(0.178126\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.21110 | 0.631623 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.60555 | −0.199251 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.81665 | − | 6.81665i | 0.518261 | − | 0.518261i | −0.398784 | − | 0.917045i | \(-0.630568\pi\) |
0.917045 | + | 0.398784i | \(0.130568\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.90833 | − | 3.90833i | 0.295442 | − | 0.295442i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.81665 | − | 1.81665i | −0.136548 | − | 0.136548i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 21.0278i | 1.57169i | 0.618425 | + | 0.785844i | \(0.287771\pi\) | ||||
−0.618425 | + | 0.785844i | \(0.712229\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.0000 | − | 13.0000i | −0.966282 | − | 0.966282i | 0.0331674 | − | 0.999450i | \(-0.489441\pi\) |
−0.999450 | + | 0.0331674i | \(0.989441\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 21.3944 | 1.58152 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.00000i | 0.441129i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.5139 | − | 5.30278i | −1.35387 | − | 0.387777i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 8.84441i | − | 0.643336i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.2111 | 1.53478 | 0.767391 | − | 0.641180i | \(-0.221555\pi\) | ||||
0.767391 | + | 0.641180i | \(0.221555\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.21110 | + | 6.21110i | 0.447085 | + | 0.447085i | 0.894384 | − | 0.447299i | \(-0.147614\pi\) |
−0.447299 | + | 0.894384i | \(0.647614\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 12.0000i | − | 0.859338i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.3944 | − | 10.3944i | −0.740574 | − | 0.740574i | 0.232115 | − | 0.972688i | \(-0.425436\pi\) |
−0.972688 | + | 0.232115i | \(0.925436\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.1194 | − | 15.1194i | 1.07179 | − | 1.07179i | 0.0745723 | − | 0.997216i | \(-0.476241\pi\) |
0.997216 | − | 0.0745723i | \(-0.0237592\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.78890 | + | 6.78890i | −0.478852 | + | 0.478852i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −14.6056 | −1.02511 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.00000 | −0.139686 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.275019 | + | 0.275019i | −0.0191152 | + | 0.0191152i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.8167 | − | 21.8167i | 1.50909 | − | 1.50909i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.51388 | − | 2.51388i | −0.173063 | − | 0.173063i | 0.615261 | − | 0.788323i | \(-0.289051\pi\) |
−0.788323 | + | 0.615261i | \(0.789051\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 20.6056i | 1.41187i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.6056 | + | 10.6056i | 0.723293 | + | 0.723293i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.81665 | −0.123322 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 18.2389i | 1.23247i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.6056 | − | 9.21110i | 1.11701 | − | 0.619606i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.81665i | 0.255582i | 0.991801 | + | 0.127791i | \(0.0407887\pi\) | ||||
−0.991801 | + | 0.127791i | \(0.959211\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.18335 | 0.0788897 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.30278 | + | 3.30278i | 0.219213 | + | 0.219213i | 0.808167 | − | 0.588954i | \(-0.200460\pi\) |
−0.588954 | + | 0.808167i | \(0.700460\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 2.60555i | − | 0.172180i | −0.996287 | − | 0.0860898i | \(-0.972563\pi\) | ||
0.996287 | − | 0.0860898i | \(-0.0274372\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.2111 | − | 11.2111i | −0.737636 | − | 0.737636i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.60555 | + | 1.60555i | −0.105183 | + | 0.105183i | −0.757740 | − | 0.652557i | \(-0.773696\pi\) |
0.652557 | + | 0.757740i | \(0.273696\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.00000 | − | 4.00000i | 0.260931 | − | 0.260931i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.60555 | 0.558991 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −29.2111 | −1.88951 | −0.944755 | − | 0.327779i | \(-0.893700\pi\) | ||||
−0.944755 | + | 0.327779i | \(0.893700\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.00000 | − | 9.00000i | 0.579741 | − | 0.579741i | −0.355091 | − | 0.934832i | \(-0.615550\pi\) |
0.934832 | + | 0.355091i | \(0.115550\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.88057 | − | 2.88057i | 0.184789 | − | 0.184789i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.60555 | + | 3.60555i | 0.230350 | + | 0.230350i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 30.4222i | 1.93572i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.97224 | − | 4.97224i | −0.315103 | − | 0.315103i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 4.60555i | − | 0.289549i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.21110 | − | 9.39445i | −0.326332 | − | 0.588303i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 26.6056i | 1.65961i | 0.558054 | + | 0.829804i | \(0.311548\pi\) | ||||
−0.558054 | + | 0.829804i | \(0.688452\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.81665 | −0.485703 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.21110 | − | 2.21110i | −0.136864 | − | 0.136864i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 13.0278i | − | 0.803326i | −0.915788 | − | 0.401663i | \(-0.868432\pi\) | ||
0.915788 | − | 0.401663i | \(-0.131568\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.21110 | − | 9.21110i | −0.565834 | − | 0.565834i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −18.0000 | + | 18.0000i | −1.10158 | + | 1.10158i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.4222 | + | 11.4222i | −0.696424 | + | 0.696424i | −0.963637 | − | 0.267213i | \(-0.913897\pi\) |
0.267213 | + | 0.963637i | \(0.413897\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.2111 | −0.802517 | −0.401259 | − | 0.915965i | \(-0.631427\pi\) | ||||
−0.401259 | + | 0.915965i | \(0.631427\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 15.6333 | 0.946171 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.90833 | + | 9.90833i | −0.597495 | + | 0.597495i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.60555 | + | 3.60555i | −0.216637 | + | 0.216637i | −0.807079 | − | 0.590443i | \(-0.798953\pi\) |
0.590443 | + | 0.807079i | \(0.298953\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.275019 | − | 0.275019i | −0.0164650 | − | 0.0164650i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 10.4222i | − | 0.621737i | −0.950453 | − | 0.310868i | \(-0.899380\pi\) | ||
0.950453 | − | 0.310868i | \(-0.100620\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.1194 | − | 23.1194i | −1.37431 | − | 1.37431i | −0.853946 | − | 0.520361i | \(-0.825797\pi\) |
−0.520361 | − | 0.853946i | \(-0.674203\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 17.2111 | 1.01950 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 2.60555i | − | 0.153801i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.00000 | − | 14.4222i | 0.529412 | − | 0.848365i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.02776i | 0.0602481i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.6333 | 1.26383 | 0.631916 | − | 0.775037i | \(-0.282269\pi\) | ||||
0.631916 | + | 0.775037i | \(0.282269\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.39445 | + | 1.39445i | 0.0811879 | + | 0.0811879i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 22.4222i | 1.30107i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.21110 | + | 3.21110i | 0.185703 | + | 0.185703i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.8167 | + | 13.8167i | −0.796379 | + | 0.796379i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.42221 | − | 4.42221i | 0.254049 | − | 0.254049i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −16.4222 | −0.940333 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.78890 | 0.387463 | 0.193731 | − | 0.981055i | \(-0.437941\pi\) | ||||
0.193731 | + | 0.981055i | \(0.437941\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.57779 | − | 1.57779i | 0.0897576 | − | 0.0897576i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.09167 | − | 8.09167i | 0.458837 | − | 0.458837i | −0.439437 | − | 0.898274i | \(-0.644822\pi\) |
0.898274 | + | 0.439437i | \(0.144822\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.21110 | − | 8.21110i | −0.464119 | − | 0.464119i | 0.435884 | − | 0.900003i | \(-0.356436\pi\) |
−0.900003 | + | 0.435884i | \(0.856436\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 1.02776i | − | 0.0579075i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.3944 | + | 12.3944i | 0.696142 | + | 0.696142i | 0.963576 | − | 0.267434i | \(-0.0861759\pi\) |
−0.267434 | + | 0.963576i | \(0.586176\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 37.0278 | 2.07316 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 24.2389i | − | 1.35288i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.2111 | + | 23.8167i | 0.735085 | + | 1.32519i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 13.8167i | − | 0.766410i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 21.3944 | 1.18312 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.21110 | + | 5.21110i | 0.287297 | + | 0.287297i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 10.6056i | − | 0.582934i | −0.956581 | − | 0.291467i | \(-0.905857\pi\) | ||
0.956581 | − | 0.291467i | \(-0.0941433\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.18335 | − | 1.18335i | −0.0648470 | − | 0.0648470i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.21110 | − | 5.21110i | 0.284713 | − | 0.284713i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.78890 | + | 1.78890i | −0.0974475 | + | 0.0974475i | −0.754150 | − | 0.656702i | \(-0.771951\pi\) |
0.656702 | + | 0.754150i | \(0.271951\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.23886 | 0.338848 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.60555 | 0.249405 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.8167 | + | 13.8167i | −0.746029 | + | 0.746029i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.81665 | − | 1.81665i | 0.0978054 | − | 0.0978054i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.5139 | + | 12.5139i | 0.671780 | + | 0.671780i | 0.958126 | − | 0.286346i | \(-0.0924407\pi\) |
−0.286346 | + | 0.958126i | \(0.592441\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 19.6333i | − | 1.05095i | −0.850810 | − | 0.525473i | \(-0.823888\pi\) | ||
0.850810 | − | 0.525473i | \(-0.176112\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.6333 | − | 15.6333i | −0.834444 | − | 0.834444i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.7889 | −0.893583 | −0.446791 | − | 0.894638i | \(-0.647433\pi\) | ||||
−0.446791 | + | 0.894638i | \(0.647433\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 15.8167i | − | 0.839461i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 12.2389 | − | 6.78890i | 0.647749 | − | 0.359307i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.39445i | 0.495820i | 0.968783 | + | 0.247910i | \(0.0797437\pi\) | ||||
−0.968783 | + | 0.247910i | \(0.920256\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −24.6333 | −1.29649 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 14.0917 | + | 14.0917i | 0.739621 | + | 0.739621i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 14.0000i | − | 0.732793i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.90833 | + | 3.90833i | 0.204013 | + | 0.204013i | 0.801717 | − | 0.597704i | \(-0.203920\pi\) |
−0.597704 | + | 0.801717i | \(0.703920\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.394449 | − | 0.394449i | 0.0205342 | − | 0.0205342i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.0000 | − | 12.0000i | 0.623009 | − | 0.623009i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.0278 | −0.778108 | −0.389054 | − | 0.921215i | \(-0.627198\pi\) | ||||
−0.389054 | + | 0.921215i | \(0.627198\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −20.8444 | −1.07640 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −25.8167 | + | 25.8167i | −1.32963 | + | 1.32963i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.7250 | − | 11.7250i | 0.602272 | − | 0.602272i | −0.338643 | − | 0.940915i | \(-0.609968\pi\) |
0.940915 | + | 0.338643i | \(0.109968\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.60555 | + | 8.60555i | 0.440876 | + | 0.440876i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 26.6056i | − | 1.35948i | −0.733453 | − | 0.679740i | \(-0.762093\pi\) | ||
0.733453 | − | 0.679740i | \(-0.237907\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.60555 | + | 8.60555i | 0.438580 | + | 0.438580i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.18335 | −0.212651 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.8167i | 1.61317i | 0.591119 | + | 0.806584i | \(0.298686\pi\) | ||||
−0.591119 | + | 0.806584i | \(0.701314\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.90833 | + | 1.11943i | 0.197653 | + | 0.0566120i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.02776i | 0.354503i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.60555 | −0.332361 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.00000 | − | 9.00000i | −0.451697 | − | 0.451697i | 0.444220 | − | 0.895918i | \(-0.353481\pi\) |
−0.895918 | + | 0.444220i | \(0.853481\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 22.4222i | 1.12251i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.00000 | − | 7.00000i | −0.349563 | − | 0.349563i | 0.510384 | − | 0.859947i | \(-0.329503\pi\) |
−0.859947 | + | 0.510384i | \(0.829503\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.21110 | + | 3.21110i | −0.159956 | + | 0.159956i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10.0278 | + | 10.0278i | −0.498283 | + | 0.498283i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19.8167 | 0.982275 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.78890 | 0.434583 | 0.217292 | − | 0.976107i | \(-0.430278\pi\) | ||||
0.217292 | + | 0.976107i | \(0.430278\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.00000 | − | 6.00000i | 0.295958 | − | 0.295958i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.81665 | + | 1.81665i | −0.0893917 | + | 0.0893917i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.81665 | + | 3.81665i | 0.187352 | + | 0.187352i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.60555i | 0.421416i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.30278 | − | 1.30278i | −0.0636448 | − | 0.0636448i | 0.674568 | − | 0.738213i | \(-0.264330\pi\) |
−0.738213 | + | 0.674568i | \(0.764330\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.3944 | 0.555331 | 0.277666 | − | 0.960678i | \(-0.410439\pi\) | ||||
0.277666 | + | 0.960678i | \(0.410439\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.57779i | 0.0767150i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.00000 | − | 10.8167i | −0.291043 | − | 0.524685i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 21.3944i | − | 1.03535i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −39.6333 | −1.91351 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.1194 | − | 27.1194i | −1.30630 | − | 1.30630i | −0.924067 | − | 0.382230i | \(-0.875156\pi\) |
−0.382230 | − | 0.924067i | \(-0.624844\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.0278i | 1.01053i | 0.862964 | + | 0.505265i | \(0.168605\pi\) | ||||
−0.862964 | + | 0.505265i | \(0.831395\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.6056 | + | 14.6056i | 0.700283 | + | 0.700283i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.60555 | + | 4.60555i | −0.220313 | + | 0.220313i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.6972 | + | 22.6972i | −1.08328 | + | 1.08328i | −0.0870779 | + | 0.996202i | \(0.527753\pi\) |
−0.996202 | + | 0.0870779i | \(0.972247\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.42221 | −0.0677241 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.78890 | −0.132505 | −0.0662523 | − | 0.997803i | \(-0.521104\pi\) | ||||
−0.0662523 | + | 0.997803i | \(0.521104\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.8167 | − | 13.8167i | 0.654972 | − | 0.654972i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −26.6056 | + | 26.6056i | −1.25840 | + | 1.25840i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.81665 | + | 4.81665i | 0.227312 | + | 0.227312i | 0.811569 | − | 0.584257i | \(-0.198614\pi\) |
−0.584257 | + | 0.811569i | \(0.698614\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.60555i | 0.311043i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.39445 | − | 3.39445i | −0.159485 | − | 0.159485i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.0000 | −0.562569 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 29.3944i | − | 1.37501i | −0.726178 | − | 0.687507i | \(-0.758705\pi\) | ||
0.726178 | − | 0.687507i | \(-0.241295\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −19.0278 | − | 5.44996i | −0.888140 | − | 0.254382i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.7889i | 0.688788i | 0.938825 | + | 0.344394i | \(0.111916\pi\) | ||||
−0.938825 | + | 0.344394i | \(0.888084\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.63331 | 0.168854 | 0.0844271 | − | 0.996430i | \(-0.473094\pi\) | ||||
0.0844271 | + | 0.996430i | \(0.473094\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.81665 | + | 1.81665i | 0.0842453 | + | 0.0842453i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 34.2389i | − | 1.58439i | −0.610271 | − | 0.792193i | \(-0.708939\pi\) | ||
0.610271 | − | 0.792193i | \(-0.291061\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.78890 | + | 6.78890i | 0.313482 | + | 0.313482i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 26.6056 | − | 26.6056i | 1.22592 | − | 1.22592i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 35.0278 | − | 35.0278i | 1.61058 | − | 1.61058i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 19.8167 | 0.909250 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.63331 | 0.166358 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.69722 | − | 8.69722i | 0.397386 | − | 0.397386i | −0.479924 | − | 0.877310i | \(-0.659336\pi\) |
0.877310 | + | 0.479924i | \(0.159336\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.8167 | + | 13.8167i | −0.629985 | + | 0.629985i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.36669 | + | 2.36669i | 0.107688 | + | 0.107688i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 0.788897i | − | 0.0358220i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.3305 | + | 22.3305i | 1.01189 | + | 1.01189i | 0.999928 | + | 0.0119646i | \(0.00380853\pi\) |
0.0119646 | + | 0.999928i | \(0.496191\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.81665 | −0.0821519 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.8167i | 0.533278i | 0.963796 | + | 0.266639i | \(0.0859132\pi\) | ||||
−0.963796 | + | 0.266639i | \(0.914087\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.00000 | + | 31.4222i | −0.405340 | + | 1.41518i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.60555i | 0.117111i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 20.6056 | 0.924285 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.69722 | + | 6.69722i | 0.299809 | + | 0.299809i | 0.840939 | − | 0.541130i | \(-0.182003\pi\) |
−0.541130 | + | 0.840939i | \(0.682003\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 10.6611i | − | 0.476301i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.48612 | + | 9.48612i | 0.422965 | + | 0.422965i | 0.886223 | − | 0.463258i | \(-0.153320\pi\) |
−0.463258 | + | 0.886223i | \(0.653320\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.39445 | + | 3.39445i | −0.151051 | + | 0.151051i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.6972 | − | 10.6972i | 0.475080 | − | 0.475080i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.2111 | 0.496923 | 0.248462 | − | 0.968642i | \(-0.420075\pi\) | ||||
0.248462 | + | 0.968642i | \(0.420075\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.2389 | 0.806840 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 22.4222 | − | 22.4222i | 0.989965 | − | 0.989965i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.21110 | + | 1.21110i | −0.0533676 | + | 0.0533676i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.2111 | − | 13.2111i | −0.581024 | − | 0.581024i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 17.7611i | − | 0.779628i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.0000 | + | 13.0000i | 0.569540 | + | 0.569540i | 0.932000 | − | 0.362459i | \(-0.118063\pi\) |
−0.362459 | + | 0.932000i | \(0.618063\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.0000 | −0.524723 | −0.262362 | − | 0.964970i | \(-0.584501\pi\) | ||||
−0.262362 | + | 0.964970i | \(0.584501\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 10.1833i | − | 0.444438i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.11943 | + | 3.90833i | −0.0487631 | + | 0.170249i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 22.0278i | − | 0.957729i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.550039 | −0.0238696 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.60555 | − | 4.60555i | −0.199489 | − | 0.199489i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.6056i | 0.804388i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 27.3944 | + | 27.3944i | 1.18216 | + | 1.18216i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.9083 | − | 11.9083i | 0.512928 | − | 0.512928i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.00000 | − | 3.00000i | 0.128980 | − | 0.128980i | −0.639670 | − | 0.768650i | \(-0.720929\pi\) |
0.768650 | + | 0.639670i | \(0.220929\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −33.8722 | −1.45359 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.4222 | −0.703450 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.51388 | − | 6.51388i | 0.278513 | − | 0.278513i | −0.554002 | − | 0.832515i | \(-0.686900\pi\) |
0.832515 | + | 0.554002i | \(0.186900\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.23886 | − | 3.23886i | 0.138231 | − | 0.138231i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −37.0278 | − | 37.0278i | −1.57744 | − | 1.57744i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 8.60555i | − | 0.365945i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.81665 | + | 7.81665i | 0.331798 | + | 0.331798i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −28.6056 | −1.21206 | −0.606028 | − | 0.795443i | \(-0.707238\pi\) | ||||
−0.606028 | + | 0.795443i | \(0.707238\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 48.8444i | 2.06590i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −31.0278 | + | 17.2111i | −1.30999 | + | 0.726653i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.3944i | 0.564509i | 0.959340 | + | 0.282254i | \(0.0910822\pi\) | ||||
−0.959340 | + | 0.282254i | \(0.908918\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.78890 | −0.201470 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −13.0639 | − | 13.0639i | −0.548633 | − | 0.548633i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1.57779i | − | 0.0661446i | −0.999453 | − | 0.0330723i | \(-0.989471\pi\) | ||
0.999453 | − | 0.0330723i | \(-0.0105292\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.30278 | − | 1.30278i | −0.0545195 | − | 0.0545195i | 0.679321 | − | 0.733841i | \(-0.262274\pi\) |
−0.733841 | + | 0.679321i | \(0.762274\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 27.6333 | − | 27.6333i | 1.15440 | − | 1.15440i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.09167 | − | 2.09167i | 0.0872288 | − | 0.0872288i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.4500 | 1.39254 | 0.696270 | − | 0.717780i | \(-0.254842\pi\) | ||||
0.696270 | + | 0.717780i | \(0.254842\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16.1833 | 0.672557 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.97224 | + | 4.97224i | −0.206283 | + | 0.206283i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −30.4222 | + | 30.4222i | −1.25996 | + | 1.25996i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.81665 | − | 1.81665i | −0.0751094 | − | 0.0751094i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.60555i | 0.107543i | 0.998553 | + | 0.0537713i | \(0.0171242\pi\) | ||||
−0.998553 | + | 0.0537713i | \(0.982876\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.60555 | − | 4.60555i | −0.189768 | − | 0.189768i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −27.0833 | −1.11406 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 30.4222i | 1.24929i | 0.780909 | + | 0.624645i | \(0.214756\pi\) | ||||
−0.780909 | + | 0.624645i | \(0.785244\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.39445 | + | 5.21110i | −0.385135 | + | 0.213634i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 39.3944i | − | 1.61231i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −46.0555 | −1.88178 | −0.940889 | − | 0.338716i | \(-0.890007\pi\) | ||||
−0.940889 | + | 0.338716i | \(0.890007\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.2111 | + | 10.2111i | 0.416520 | + | 0.416520i | 0.884002 | − | 0.467483i | \(-0.154839\pi\) |
−0.467483 | + | 0.884002i | \(0.654839\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.05551i | 0.0837070i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.8167 | − | 10.8167i | −0.439760 | − | 0.439760i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.51388 | + | 8.51388i | −0.345568 | + | 0.345568i | −0.858456 | − | 0.512888i | \(-0.828576\pi\) |
0.512888 | + | 0.858456i | \(0.328576\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −19.0278 | + | 19.0278i | −0.771044 | + | 0.771044i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.4222 | 0.745283 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.5778 | 0.467623 | 0.233811 | − | 0.972282i | \(-0.424880\pi\) | ||||
0.233811 | + | 0.972282i | \(0.424880\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.60555 | + | 2.60555i | −0.105066 | + | 0.105066i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.60555 | + | 5.60555i | −0.225671 | + | 0.225671i | −0.810881 | − | 0.585210i | \(-0.801012\pi\) |
0.585210 | + | 0.810881i | \(0.301012\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.5139 | + | 32.5139i | 1.30684 | + | 1.30684i | 0.923681 | + | 0.383162i | \(0.125165\pi\) |
0.383162 | + | 0.923681i | \(0.374835\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 4.73338i | − | 0.189944i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18.0000 | + | 18.0000i | 0.721155 | + | 0.721155i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 56.8444i | − | 2.27015i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.81665 | + | 16.8167i | −0.192053 | + | 0.670524i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 26.2389i | − | 1.04455i | −0.852776 | − | 0.522276i | \(-0.825083\pi\) | ||
0.852776 | − | 0.522276i | \(-0.174917\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.55004 | −0.260341 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.60555 | − | 6.60555i | −0.262133 | − | 0.262133i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16.6056i | 0.657936i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.11943 | + | 3.11943i | 0.123403 | + | 0.123403i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.18335 | − | 9.18335i | 0.362720 | − | 0.362720i | −0.502093 | − | 0.864814i | \(-0.667437\pi\) |
0.864814 | + | 0.502093i | \(0.167437\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.1194 | + | 21.1194i | −0.832869 | + | 0.832869i | −0.987908 | − | 0.155039i | \(-0.950450\pi\) |
0.155039 | + | 0.987908i | \(0.450450\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 27.6333 | 1.08806 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.78890 | −0.109643 | −0.0548214 | − | 0.998496i | \(-0.517459\pi\) | ||||
−0.0548214 | + | 0.998496i | \(0.517459\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.60555 | − | 4.60555i | 0.180784 | − | 0.180784i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.36669 | + | 2.36669i | −0.0927580 | + | 0.0927580i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.18335 | + | 3.18335i | 0.124574 | + | 0.124574i | 0.766645 | − | 0.642071i | \(-0.221925\pi\) |
−0.642071 | + | 0.766645i | \(0.721925\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 5.39445i | − | 0.210779i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.76114 | + | 2.76114i | 0.107722 | + | 0.107722i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −32.0000 | −1.24654 | −0.623272 | − | 0.782006i | \(-0.714197\pi\) | ||||
−0.623272 | + | 0.782006i | \(0.714197\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.2111i | 0.513852i | 0.966431 | + | 0.256926i | \(0.0827097\pi\) | ||||
−0.966431 | + | 0.256926i | \(0.917290\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.63331 | − | 33.6333i | 0.374127 | − | 1.30621i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 17.2111i | − | 0.667418i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.81665 | −0.302662 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.97224 | + | 4.97224i | 0.192238 | + | 0.192238i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 54.2389i | 2.09387i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.60555 | − | 1.60555i | −0.0618895 | − | 0.0618895i | 0.675485 | − | 0.737374i | \(-0.263934\pi\) |
−0.737374 | + | 0.675485i | \(0.763934\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −10.1833 | + | 10.1833i | −0.391957 | + | 0.391957i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.0278 | − | 20.0278i | 0.769729 | − | 0.769729i | −0.208329 | − | 0.978059i | \(-0.566803\pi\) |
0.978059 | + | 0.208329i | \(0.0668026\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.02776 | 0.0394417 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.60555 | 0.329765 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.7250 | − | 31.7250i | 1.21392 | − | 1.21392i | 0.244197 | − | 0.969726i | \(-0.421476\pi\) |
0.969726 | − | 0.244197i | \(-0.0785244\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.60555 | + | 4.60555i | −0.175969 | + | 0.175969i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.39445 | − | 3.39445i | −0.129506 | − | 0.129506i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 42.4222i | − | 1.61616i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.5139 | + | 12.5139i | 0.476050 | + | 0.476050i | 0.903866 | − | 0.427816i | \(-0.140717\pi\) |
−0.427816 | + | 0.903866i | \(0.640717\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.39445 | −0.128944 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 6.60555i | − | 0.250563i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.60555 | − | 1.60555i | −0.212325 | − | 0.0608146i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.18335i | 0.158229i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.8167 | 0.521848 | 0.260924 | − | 0.965359i | \(-0.415973\pi\) | ||||
0.260924 | + | 0.965359i | \(0.415973\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.8167 | − | 19.8167i | −0.747399 | − | 0.747399i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 10.4222i | − | 0.392523i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.42221 | − | 4.42221i | −0.166314 | − | 0.166314i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.6056 | − | 21.6056i | 0.811414 | − | 0.811414i | −0.173432 | − | 0.984846i | \(-0.555486\pi\) |
0.984846 | + | 0.173432i | \(0.0554858\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.30278 | − | 1.30278i | 0.0488579 | − | 0.0488579i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.972244 | −0.0364108 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 30.4222 | 1.13773 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −38.0555 | + | 38.0555i | −1.42121 | + | 1.42121i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27.7250 | − | 27.7250i | 1.03397 | − | 1.03397i | 0.0345649 | − | 0.999402i | \(-0.488995\pi\) |
0.999402 | − | 0.0345649i | \(-0.0110045\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.57779 | − | 1.57779i | −0.0587602 | − | 0.0587602i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 23.4500i | − | 0.872113i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 16.8167 | + | 16.8167i | 0.624555 | + | 0.624555i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.4222 | 0.831594 | 0.415797 | − | 0.909458i | \(-0.363503\pi\) | ||||
0.415797 | + | 0.909458i | \(0.363503\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 22.5778i | 0.836215i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.2111 | + | 38.2389i | 0.784521 | + | 1.41432i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.0555i | 0.962382i | 0.876616 | + | 0.481191i | \(0.159796\pi\) | ||||
−0.876616 | + | 0.481191i | \(0.840204\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.39445 | 0.346519 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −17.2111 | − | 17.2111i | −0.633979 | − | 0.633979i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 44.6611i | − | 1.64288i | −0.570292 | − | 0.821442i | \(-0.693170\pi\) | ||
0.570292 | − | 0.821442i | \(-0.306830\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 39.6333 | + | 39.6333i | 1.45597 | + | 1.45597i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17.7250 | + | 17.7250i | −0.650266 | + | 0.650266i | −0.953057 | − | 0.302791i | \(-0.902082\pi\) |
0.302791 | + | 0.953057i | \(0.402082\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.4222 | − | 20.4222i | 0.748212 | − | 0.748212i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.50547 | −0.0550824 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −24.2389 | −0.885669 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.30278 | − | 5.30278i | 0.193501 | − | 0.193501i | −0.603706 | − | 0.797207i | \(-0.706310\pi\) |
0.797207 | + | 0.603706i | \(0.206310\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15.6333 | + | 15.6333i | −0.569709 | + | 0.569709i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.60555 | + | 2.60555i | 0.0948257 | + | 0.0948257i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.97224i | 0.108028i | 0.998540 | + | 0.0540140i | \(0.0172016\pi\) | ||||
−0.998540 | + | 0.0540140i | \(0.982798\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.00000 | − | 6.00000i | −0.217786 | − | 0.217786i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33.4500 | 1.21256 | 0.606280 | − | 0.795251i | \(-0.292661\pi\) | ||||
0.606280 | + | 0.795251i | \(0.292661\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 21.3944i | − | 0.774531i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.21110 | − | 0.633308i | −0.0799426 | − | 0.0228973i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.42221i | 0.231892i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.3944 | −0.410894 | −0.205447 | − | 0.978668i | \(-0.565865\pi\) | ||||
−0.205447 | + | 0.978668i | \(0.565865\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 34.6611 | + | 34.6611i | 1.24829 | + | 1.24829i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 21.3944i | − | 0.769505i | −0.923020 | − | 0.384752i | \(-0.874287\pi\) | ||
0.923020 | − | 0.384752i | \(-0.125713\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.09167 | + | 2.09167i | 0.0751351 | + | 0.0751351i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10.1833 | + | 10.1833i | −0.365326 | + | 0.365326i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.60555 | − | 6.60555i | 0.236668 | − | 0.236668i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −52.2389 | −1.86925 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 38.0555 | 1.35999 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.4222 | + | 20.4222i | −0.728900 | + | 0.728900i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.7250 | + | 17.7250i | −0.631827 | + | 0.631827i | −0.948526 | − | 0.316699i | \(-0.897426\pi\) |
0.316699 | + | 0.948526i | \(0.397426\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16.9722 | − | 16.9722i | −0.604228 | − | 0.604228i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 6.23886i | − | 0.221828i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −37.8167 | − | 37.8167i | −1.34291 | − | 1.34291i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −24.0000 | −0.851192 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 39.6333i | − | 1.40388i | −0.712234 | − | 0.701942i | \(-0.752317\pi\) | ||
0.712234 | − | 0.701942i | \(-0.247683\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.4222 | − | 8.00000i | 0.510221 | − | 0.283020i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.44996i | 0.192565i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −46.2389 | −1.63173 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.81665 | − | 1.81665i | −0.0640286 | − | 0.0640286i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 29.7611i | 1.04764i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.816654 | + | 0.816654i | 0.0287120 | + | 0.0287120i | 0.721317 | − | 0.692605i | \(-0.243537\pi\) |
−0.692605 | + | 0.721317i | \(0.743537\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.7250 | + | 21.7250i | −0.762867 | + | 0.762867i | −0.976840 | − | 0.213972i | \(-0.931360\pi\) |
0.213972 | + | 0.976840i | \(0.431360\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17.2111 | + | 17.2111i | −0.603620 | + | 0.603620i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.39445 | 0.0488454 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −70.0555 | −2.45093 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.36669 | − | 2.36669i | 0.0826989 | − | 0.0826989i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.81665 | + | 8.81665i | −0.307703 | + | 0.307703i | −0.844018 | − | 0.536315i | \(-0.819816\pi\) |
0.536315 | + | 0.844018i | \(0.319816\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.09167 | + | 2.09167i | 0.0729111 | + | 0.0729111i | 0.742622 | − | 0.669711i | \(-0.233582\pi\) |
−0.669711 | + | 0.742622i | \(0.733582\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 25.8167i | 0.898821i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.69722 | + | 2.69722i | 0.0937917 | + | 0.0937917i | 0.752446 | − | 0.658654i | \(-0.228874\pi\) |
−0.658654 | + | 0.752446i | \(0.728874\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.8444 | 1.34912 | 0.674561 | − | 0.738219i | \(-0.264333\pi\) | ||||
0.674561 | + | 0.738219i | \(0.264333\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.39445i | 0.325890i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.21110 | + | 13.0000i | 0.249850 | + | 0.450423i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.18335i | 0.283196i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.73338 | 0.163610 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.09167 | − | 4.09167i | −0.141260 | − | 0.141260i | 0.632940 | − | 0.774201i | \(-0.281848\pi\) |
−0.774201 | + | 0.632940i | \(0.781848\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 33.8444i | − | 1.16705i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.5778 | − | 13.5778i | −0.467644 | − | 0.467644i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.21110 | + | 8.21110i | −0.282471 | + | 0.282471i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.0917 | − | 14.0917i | 0.484196 | − | 0.484196i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −60.2389 | −2.06739 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.18335 | −0.143403 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.577795 | − | 0.577795i | 0.0197833 | − | 0.0197833i | −0.697146 | − | 0.716929i | \(-0.745547\pi\) |
0.716929 | + | 0.697146i | \(0.245547\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.60555 | − | 2.60555i | 0.0891080 | − | 0.0891080i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.6333 | + | 24.6333i | 0.841458 | + | 0.841458i | 0.989049 | − | 0.147591i | \(-0.0471519\pi\) |
−0.147591 | + | 0.989049i | \(0.547152\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 19.8167i | − | 0.676136i | −0.941122 | − | 0.338068i | \(-0.890227\pi\) | ||
0.941122 | − | 0.338068i | \(-0.109773\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.39445 | − | 3.39445i | −0.115683 | − | 0.115683i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 48.4777 | 1.65020 | 0.825100 | − | 0.564986i | \(-0.191119\pi\) | ||||
0.825100 | + | 0.564986i | \(0.191119\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.6333i | 0.463546i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.06392 | − | 30.5139i | −0.239903 | − | 1.03631i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.8167i | 0.740079i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.0000 | 0.813209 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.155590 | + | 0.155590i | 0.00526592 | + | 0.00526592i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 20.8444i | 0.704670i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.2111 | + | 16.2111i | 0.547410 | + | 0.547410i | 0.925691 | − | 0.378281i | \(-0.123485\pi\) |
−0.378281 | + | 0.925691i | \(0.623485\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 28.1833 | − | 28.1833i | 0.950601 | − | 0.950601i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.78890 | + | 9.78890i | −0.329796 | + | 0.329796i | −0.852509 | − | 0.522713i | \(-0.824920\pi\) |
0.522713 | + | 0.852509i | \(0.324920\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 54.4222 | 1.83145 | 0.915727 | − | 0.401802i | \(-0.131616\pi\) | ||||
0.915727 | + | 0.401802i | \(0.131616\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.63331 | 0.122132 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −15.3028 | + | 15.3028i | −0.513817 | + | 0.513817i | −0.915694 | − | 0.401877i | \(-0.868358\pi\) |
0.401877 | + | 0.915694i | \(0.368358\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.60555 | − | 8.60555i | 0.288621 | − | 0.288621i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 33.1194 | + | 33.1194i | 1.10954 | + | 1.10954i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26.4222i | 0.884185i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.0278 | − | 21.0278i | −0.702880 | − | 0.702880i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.36669 | 0.279356 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 7.81665i | − | 0.260700i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.4222 | − | 33.2111i | −0.613733 | − | 1.10642i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 36.0000i | 1.19800i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 26.0000 | 0.864269 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.5416 | − | 29.5416i | −0.980914 | − | 0.980914i | 0.0189074 | − | 0.999821i | \(-0.493981\pi\) |
−0.999821 | + | 0.0189074i | \(0.993981\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 1.33894i | − | 0.0444097i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.7250 | − | 27.7250i | −0.918570 | − | 0.918570i | 0.0783559 | − | 0.996925i | \(-0.475033\pi\) |
−0.996925 | + | 0.0783559i | \(0.975033\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.6056 | − | 12.6056i | 0.417183 | − | 0.417183i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −21.3944 | + | 21.3944i | −0.707279 | + | 0.707279i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.02776 | 0.232077 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.8444 | −0.555646 | −0.277823 | − | 0.960632i | \(-0.589613\pi\) | ||||
−0.277823 | + | 0.960632i | \(0.589613\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.84441 | − | 8.84441i | 0.291433 | − | 0.291433i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 36.4222 | − | 36.4222i | 1.19885 | − | 1.19885i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.00000 | + | 9.00000i | 0.295918 | + | 0.295918i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 0.477718i | − | 0.0156903i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.00000 | + | 1.00000i | 0.0328089 | + | 0.0328089i | 0.723321 | − | 0.690512i | \(-0.242615\pi\) |
−0.690512 | + | 0.723321i | \(0.742615\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −23.8167 | −0.780559 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 21.0833i | − | 0.690235i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 23.8167 | − | 13.2111i | 0.778888 | − | 0.432049i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 22.4222i | − | 0.732502i | −0.930516 | − | 0.366251i | \(-0.880641\pi\) | ||
0.930516 | − | 0.366251i | \(-0.119359\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −21.3944 | −0.698181 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.0278 | + | 20.0278i | 0.652886 | + | 0.652886i | 0.953687 | − | 0.300801i | \(-0.0972539\pi\) |
−0.300801 | + | 0.953687i | \(0.597254\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.39445i | − | 0.0454095i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.84441 | + | 8.84441i | 0.287709 | + | 0.287709i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −41.7250 | + | 41.7250i | −1.35588 | + | 1.35588i | −0.476948 | + | 0.878931i | \(0.658257\pi\) |
−0.878931 | + | 0.476948i | \(0.841743\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32.2389 | − | 32.2389i | 1.04652 | − | 1.04652i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 32.2944 | 1.04722 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.238859 | −0.00773740 | −0.00386870 | − | 0.999993i | \(-0.501231\pi\) | ||||
−0.00386870 | + | 0.999993i | \(0.501231\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −21.2111 | + | 21.2111i | −0.686375 | + | 0.686375i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 48.2389 | − | 48.2389i | 1.55934 | − | 1.55934i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.00000 | − | 6.00000i | −0.193750 | − | 0.193750i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.0278i | 0.968637i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.66947 | − | 3.66947i | −0.118247 | − | 0.118247i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.4222 | −0.399885 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.183346i | 0.00589602i | 0.999996 | + | 0.00294801i | \(0.000938381\pi\) | ||||
−0.999996 | + | 0.00294801i | \(0.999062\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 48.2389 | + | 13.8167i | 1.54966 | + | 0.443855i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.9722i | 0.608848i | 0.952537 | + | 0.304424i | \(0.0984640\pi\) | ||||
−0.952537 | + | 0.304424i | \(0.901536\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.60555 | 0.275881 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −18.0000 | − | 18.0000i | −0.576461 | − | 0.576461i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 40.8444i | − | 1.30673i | −0.757044 | − | 0.653364i | \(-0.773357\pi\) | ||
0.757044 | − | 0.653364i | \(-0.226643\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −45.6333 | − | 45.6333i | −1.45845 | − | 1.45845i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.23886 | − | 3.23886i | 0.103409 | − | 0.103409i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17.1194 | + | 17.1194i | −0.546025 | + | 0.546025i | −0.925289 | − | 0.379264i | \(-0.876177\pi\) |
0.379264 | + | 0.925289i | \(0.376177\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20.7889 | 0.662389 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13.5778 | 0.432186 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.39445 | + | 7.39445i | −0.235130 | + | 0.235130i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.48612 | + | 5.48612i | −0.174272 | + | 0.174272i | −0.788854 | − | 0.614581i | \(-0.789325\pi\) |
0.614581 | + | 0.788854i | \(0.289325\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13.8167 | − | 13.8167i | −0.438458 | − | 0.438458i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 30.2389i | 0.958636i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.2389 | − | 11.2389i | −0.355938 | − | 0.355938i | 0.506375 | − | 0.862313i | \(-0.330985\pi\) |
−0.862313 | + | 0.506375i | \(0.830985\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 20.3667 | 0.644374 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))