Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [24,2,Mod(13,24)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(24, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("24.13");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 24 = 2^{3} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 24.d (of order \(2\), degree \(1\), 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: | \(0.191640964851\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 13.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 24.13 |
Dual form | 24.2.d.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 \(\left(\mathbb{Z}/24\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(13\) | \(17\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.00000i | −0.707107 | − | 0.707107i | ||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 2.00000i | 1.00000i | ||||||||
\(5\) | 2.00000i | 0.894427i | 0.894427 | + | 0.447214i | \(0.147584\pi\) | ||||
−0.894427 | + | 0.447214i | \(0.852416\pi\) | |||||||
\(6\) | −1.00000 | + | 1.00000i | −0.408248 | + | 0.408248i | ||||
\(7\) | −2.00000 | −0.755929 | −0.377964 | − | 0.925820i | \(-0.623376\pi\) | ||||
−0.377964 | + | 0.925820i | \(0.623376\pi\) | |||||||
\(8\) | 2.00000 | − | 2.00000i | 0.707107 | − | 0.707107i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 2.00000 | − | 2.00000i | 0.632456 | − | 0.632456i | ||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | 2.00000 | 0.577350 | ||||||||
\(13\) | − | 4.00000i | − | 1.10940i | −0.832050 | − | 0.554700i | \(-0.812833\pi\) | ||
0.832050 | − | 0.554700i | \(-0.187167\pi\) | |||||||
\(14\) | 2.00000 | + | 2.00000i | 0.534522 | + | 0.534522i | ||||
\(15\) | 2.00000 | 0.516398 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 1.00000 | + | 1.00000i | 0.235702 | + | 0.235702i | ||||
\(19\) | 4.00000i | 0.917663i | 0.888523 | + | 0.458831i | \(0.151732\pi\) | ||||
−0.888523 | + | 0.458831i | \(0.848268\pi\) | |||||||
\(20\) | −4.00000 | −0.894427 | ||||||||
\(21\) | 2.00000i | 0.436436i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | −2.00000 | − | 2.00000i | −0.408248 | − | 0.408248i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.00000 | + | 4.00000i | −0.784465 | + | 0.784465i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | − | 4.00000i | − | 0.755929i | ||||||
\(29\) | − | 6.00000i | − | 1.11417i | −0.830455 | − | 0.557086i | \(-0.811919\pi\) | ||
0.830455 | − | 0.557086i | \(-0.188081\pi\) | |||||||
\(30\) | −2.00000 | − | 2.00000i | −0.365148 | − | 0.365148i | ||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | 4.00000 | + | 4.00000i | 0.707107 | + | 0.707107i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.00000 | + | 2.00000i | 0.342997 | + | 0.342997i | ||||
\(35\) | − | 4.00000i | − | 0.676123i | ||||||
\(36\) | − | 2.00000i | − | 0.333333i | ||||||
\(37\) | 8.00000i | 1.31519i | 0.753371 | + | 0.657596i | \(0.228427\pi\) | ||||
−0.753371 | + | 0.657596i | \(0.771573\pi\) | |||||||
\(38\) | 4.00000 | − | 4.00000i | 0.648886 | − | 0.648886i | ||||
\(39\) | −4.00000 | −0.640513 | ||||||||
\(40\) | 4.00000 | + | 4.00000i | 0.632456 | + | 0.632456i | ||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 2.00000 | − | 2.00000i | 0.308607 | − | 0.308607i | ||||
\(43\) | − | 4.00000i | − | 0.609994i | −0.952353 | − | 0.304997i | \(-0.901344\pi\) | ||
0.952353 | − | 0.304997i | \(-0.0986555\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 2.00000i | − | 0.298142i | ||||||
\(46\) | −4.00000 | − | 4.00000i | −0.589768 | − | 0.589768i | ||||
\(47\) | −12.0000 | −1.75038 | −0.875190 | − | 0.483779i | \(-0.839264\pi\) | ||||
−0.875190 | + | 0.483779i | \(0.839264\pi\) | |||||||
\(48\) | 4.00000i | 0.577350i | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | −1.00000 | − | 1.00000i | −0.141421 | − | 0.141421i | ||||
\(51\) | 2.00000i | 0.280056i | ||||||||
\(52\) | 8.00000 | 1.10940 | ||||||||
\(53\) | 6.00000i | 0.824163i | 0.911147 | + | 0.412082i | \(0.135198\pi\) | ||||
−0.911147 | + | 0.412082i | \(0.864802\pi\) | |||||||
\(54\) | 1.00000 | − | 1.00000i | 0.136083 | − | 0.136083i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.00000 | + | 4.00000i | −0.534522 | + | 0.534522i | ||||
\(57\) | 4.00000 | 0.529813 | ||||||||
\(58\) | −6.00000 | + | 6.00000i | −0.787839 | + | 0.787839i | ||||
\(59\) | 4.00000i | 0.520756i | 0.965507 | + | 0.260378i | \(0.0838471\pi\) | ||||
−0.965507 | + | 0.260378i | \(0.916153\pi\) | |||||||
\(60\) | 4.00000i | 0.516398i | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | −2.00000 | − | 2.00000i | −0.254000 | − | 0.254000i | ||||
\(63\) | 2.00000 | 0.251976 | ||||||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | 8.00000 | 0.992278 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 12.0000i | − | 1.46603i | −0.680211 | − | 0.733017i | \(-0.738112\pi\) | ||
0.680211 | − | 0.733017i | \(-0.261888\pi\) | |||||||
\(68\) | − | 4.00000i | − | 0.485071i | ||||||
\(69\) | − | 4.00000i | − | 0.481543i | ||||||
\(70\) | −4.00000 | + | 4.00000i | −0.478091 | + | 0.478091i | ||||
\(71\) | 12.0000 | 1.42414 | 0.712069 | − | 0.702109i | \(-0.247758\pi\) | ||||
0.712069 | + | 0.702109i | \(0.247758\pi\) | |||||||
\(72\) | −2.00000 | + | 2.00000i | −0.235702 | + | 0.235702i | ||||
\(73\) | −6.00000 | −0.702247 | −0.351123 | − | 0.936329i | \(-0.614200\pi\) | ||||
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | 8.00000 | − | 8.00000i | 0.929981 | − | 0.929981i | ||||
\(75\) | − | 1.00000i | − | 0.115470i | ||||||
\(76\) | −8.00000 | −0.917663 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.00000 | + | 4.00000i | 0.452911 | + | 0.452911i | ||||
\(79\) | 10.0000 | 1.12509 | 0.562544 | − | 0.826767i | \(-0.309823\pi\) | ||||
0.562544 | + | 0.826767i | \(0.309823\pi\) | |||||||
\(80\) | − | 8.00000i | − | 0.894427i | ||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.00000 | − | 2.00000i | −0.220863 | − | 0.220863i | ||||
\(83\) | 16.0000i | 1.75623i | 0.478451 | + | 0.878114i | \(0.341198\pi\) | ||||
−0.478451 | + | 0.878114i | \(0.658802\pi\) | |||||||
\(84\) | −4.00000 | −0.436436 | ||||||||
\(85\) | − | 4.00000i | − | 0.433861i | ||||||
\(86\) | −4.00000 | + | 4.00000i | −0.431331 | + | 0.431331i | ||||
\(87\) | −6.00000 | −0.643268 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.0000 | −1.06000 | −0.529999 | − | 0.847998i | \(-0.677808\pi\) | ||||
−0.529999 | + | 0.847998i | \(0.677808\pi\) | |||||||
\(90\) | −2.00000 | + | 2.00000i | −0.210819 | + | 0.210819i | ||||
\(91\) | 8.00000i | 0.838628i | ||||||||
\(92\) | 8.00000i | 0.834058i | ||||||||
\(93\) | − | 2.00000i | − | 0.207390i | ||||||
\(94\) | 12.0000 | + | 12.0000i | 1.23771 | + | 1.23771i | ||||
\(95\) | −8.00000 | −0.820783 | ||||||||
\(96\) | 4.00000 | − | 4.00000i | 0.408248 | − | 0.408248i | ||||
\(97\) | −2.00000 | −0.203069 | −0.101535 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101535 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(98\) | 3.00000 | + | 3.00000i | 0.303046 | + | 0.303046i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.00000i | 0.200000i | ||||||||
\(101\) | − | 10.0000i | − | 0.995037i | −0.867453 | − | 0.497519i | \(-0.834245\pi\) | ||
0.867453 | − | 0.497519i | \(-0.165755\pi\) | |||||||
\(102\) | 2.00000 | − | 2.00000i | 0.198030 | − | 0.198030i | ||||
\(103\) | −6.00000 | −0.591198 | −0.295599 | − | 0.955312i | \(-0.595519\pi\) | ||||
−0.295599 | + | 0.955312i | \(0.595519\pi\) | |||||||
\(104\) | −8.00000 | − | 8.00000i | −0.784465 | − | 0.784465i | ||||
\(105\) | −4.00000 | −0.390360 | ||||||||
\(106\) | 6.00000 | − | 6.00000i | 0.582772 | − | 0.582772i | ||||
\(107\) | − | 12.0000i | − | 1.16008i | −0.814587 | − | 0.580042i | \(-0.803036\pi\) | ||
0.814587 | − | 0.580042i | \(-0.196964\pi\) | |||||||
\(108\) | −2.00000 | −0.192450 | ||||||||
\(109\) | 4.00000i | 0.383131i | 0.981480 | + | 0.191565i | \(0.0613564\pi\) | ||||
−0.981480 | + | 0.191565i | \(0.938644\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.00000 | 0.759326 | ||||||||
\(112\) | 8.00000 | 0.755929 | ||||||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | −4.00000 | − | 4.00000i | −0.374634 | − | 0.374634i | ||||
\(115\) | 8.00000i | 0.746004i | ||||||||
\(116\) | 12.0000 | 1.11417 | ||||||||
\(117\) | 4.00000i | 0.369800i | ||||||||
\(118\) | 4.00000 | − | 4.00000i | 0.368230 | − | 0.368230i | ||||
\(119\) | 4.00000 | 0.366679 | ||||||||
\(120\) | 4.00000 | − | 4.00000i | 0.365148 | − | 0.365148i | ||||
\(121\) | 11.0000 | 1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 2.00000i | − | 0.180334i | ||||||
\(124\) | 4.00000i | 0.359211i | ||||||||
\(125\) | 12.0000i | 1.07331i | ||||||||
\(126\) | −2.00000 | − | 2.00000i | −0.178174 | − | 0.178174i | ||||
\(127\) | −2.00000 | −0.177471 | −0.0887357 | − | 0.996055i | \(-0.528283\pi\) | ||||
−0.0887357 | + | 0.996055i | \(0.528283\pi\) | |||||||
\(128\) | −8.00000 | + | 8.00000i | −0.707107 | + | 0.707107i | ||||
\(129\) | −4.00000 | −0.352180 | ||||||||
\(130\) | −8.00000 | − | 8.00000i | −0.701646 | − | 0.701646i | ||||
\(131\) | − | 20.0000i | − | 1.74741i | −0.486458 | − | 0.873704i | \(-0.661711\pi\) | ||
0.486458 | − | 0.873704i | \(-0.338289\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 8.00000i | − | 0.693688i | ||||||
\(134\) | −12.0000 | + | 12.0000i | −1.03664 | + | 1.03664i | ||||
\(135\) | −2.00000 | −0.172133 | ||||||||
\(136\) | −4.00000 | + | 4.00000i | −0.342997 | + | 0.342997i | ||||
\(137\) | 18.0000 | 1.53784 | 0.768922 | − | 0.639343i | \(-0.220793\pi\) | ||||
0.768922 | + | 0.639343i | \(0.220793\pi\) | |||||||
\(138\) | −4.00000 | + | 4.00000i | −0.340503 | + | 0.340503i | ||||
\(139\) | 4.00000i | 0.339276i | 0.985506 | + | 0.169638i | \(0.0542598\pi\) | ||||
−0.985506 | + | 0.169638i | \(0.945740\pi\) | |||||||
\(140\) | 8.00000 | 0.676123 | ||||||||
\(141\) | 12.0000i | 1.01058i | ||||||||
\(142\) | −12.0000 | − | 12.0000i | −1.00702 | − | 1.00702i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 4.00000 | 0.333333 | ||||||||
\(145\) | 12.0000 | 0.996546 | ||||||||
\(146\) | 6.00000 | + | 6.00000i | 0.496564 | + | 0.496564i | ||||
\(147\) | 3.00000i | 0.247436i | ||||||||
\(148\) | −16.0000 | −1.31519 | ||||||||
\(149\) | − | 6.00000i | − | 0.491539i | −0.969328 | − | 0.245770i | \(-0.920959\pi\) | ||
0.969328 | − | 0.245770i | \(-0.0790407\pi\) | |||||||
\(150\) | −1.00000 | + | 1.00000i | −0.0816497 | + | 0.0816497i | ||||
\(151\) | −18.0000 | −1.46482 | −0.732410 | − | 0.680864i | \(-0.761604\pi\) | ||||
−0.732410 | + | 0.680864i | \(0.761604\pi\) | |||||||
\(152\) | 8.00000 | + | 8.00000i | 0.648886 | + | 0.648886i | ||||
\(153\) | 2.00000 | 0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.00000i | 0.321288i | ||||||||
\(156\) | − | 8.00000i | − | 0.640513i | ||||||
\(157\) | 8.00000i | 0.638470i | 0.947676 | + | 0.319235i | \(0.103426\pi\) | ||||
−0.947676 | + | 0.319235i | \(0.896574\pi\) | |||||||
\(158\) | −10.0000 | − | 10.0000i | −0.795557 | − | 0.795557i | ||||
\(159\) | 6.00000 | 0.475831 | ||||||||
\(160\) | −8.00000 | + | 8.00000i | −0.632456 | + | 0.632456i | ||||
\(161\) | −8.00000 | −0.630488 | ||||||||
\(162\) | −1.00000 | − | 1.00000i | −0.0785674 | − | 0.0785674i | ||||
\(163\) | − | 4.00000i | − | 0.313304i | −0.987654 | − | 0.156652i | \(-0.949930\pi\) | ||
0.987654 | − | 0.156652i | \(-0.0500701\pi\) | |||||||
\(164\) | 4.00000i | 0.312348i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 16.0000 | − | 16.0000i | 1.24184 | − | 1.24184i | ||||
\(167\) | 8.00000 | 0.619059 | 0.309529 | − | 0.950890i | \(-0.399829\pi\) | ||||
0.309529 | + | 0.950890i | \(0.399829\pi\) | |||||||
\(168\) | 4.00000 | + | 4.00000i | 0.308607 | + | 0.308607i | ||||
\(169\) | −3.00000 | −0.230769 | ||||||||
\(170\) | −4.00000 | + | 4.00000i | −0.306786 | + | 0.306786i | ||||
\(171\) | − | 4.00000i | − | 0.305888i | ||||||
\(172\) | 8.00000 | 0.609994 | ||||||||
\(173\) | 6.00000i | 0.456172i | 0.973641 | + | 0.228086i | \(0.0732467\pi\) | ||||
−0.973641 | + | 0.228086i | \(0.926753\pi\) | |||||||
\(174\) | 6.00000 | + | 6.00000i | 0.454859 | + | 0.454859i | ||||
\(175\) | −2.00000 | −0.151186 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.00000 | 0.300658 | ||||||||
\(178\) | 10.0000 | + | 10.0000i | 0.749532 | + | 0.749532i | ||||
\(179\) | 4.00000i | 0.298974i | 0.988764 | + | 0.149487i | \(0.0477622\pi\) | ||||
−0.988764 | + | 0.149487i | \(0.952238\pi\) | |||||||
\(180\) | 4.00000 | 0.298142 | ||||||||
\(181\) | − | 20.0000i | − | 1.48659i | −0.668965 | − | 0.743294i | \(-0.733262\pi\) | ||
0.668965 | − | 0.743294i | \(-0.266738\pi\) | |||||||
\(182\) | 8.00000 | − | 8.00000i | 0.592999 | − | 0.592999i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.00000 | − | 8.00000i | 0.589768 | − | 0.589768i | ||||
\(185\) | −16.0000 | −1.17634 | ||||||||
\(186\) | −2.00000 | + | 2.00000i | −0.146647 | + | 0.146647i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 24.0000i | − | 1.75038i | ||||||
\(189\) | − | 2.00000i | − | 0.145479i | ||||||
\(190\) | 8.00000 | + | 8.00000i | 0.580381 | + | 0.580381i | ||||
\(191\) | −8.00000 | −0.578860 | −0.289430 | − | 0.957199i | \(-0.593466\pi\) | ||||
−0.289430 | + | 0.957199i | \(0.593466\pi\) | |||||||
\(192\) | −8.00000 | −0.577350 | ||||||||
\(193\) | −6.00000 | −0.431889 | −0.215945 | − | 0.976406i | \(-0.569283\pi\) | ||||
−0.215945 | + | 0.976406i | \(0.569283\pi\) | |||||||
\(194\) | 2.00000 | + | 2.00000i | 0.143592 | + | 0.143592i | ||||
\(195\) | − | 8.00000i | − | 0.572892i | ||||||
\(196\) | − | 6.00000i | − | 0.428571i | ||||||
\(197\) | − | 2.00000i | − | 0.142494i | −0.997459 | − | 0.0712470i | \(-0.977302\pi\) | ||
0.997459 | − | 0.0712470i | \(-0.0226979\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.0000 | 0.708881 | 0.354441 | − | 0.935079i | \(-0.384671\pi\) | ||||
0.354441 | + | 0.935079i | \(0.384671\pi\) | |||||||
\(200\) | 2.00000 | − | 2.00000i | 0.141421 | − | 0.141421i | ||||
\(201\) | −12.0000 | −0.846415 | ||||||||
\(202\) | −10.0000 | + | 10.0000i | −0.703598 | + | 0.703598i | ||||
\(203\) | 12.0000i | 0.842235i | ||||||||
\(204\) | −4.00000 | −0.280056 | ||||||||
\(205\) | 4.00000i | 0.279372i | ||||||||
\(206\) | 6.00000 | + | 6.00000i | 0.418040 | + | 0.418040i | ||||
\(207\) | −4.00000 | −0.278019 | ||||||||
\(208\) | 16.0000i | 1.10940i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 4.00000 | + | 4.00000i | 0.276026 | + | 0.276026i | ||||
\(211\) | 20.0000i | 1.37686i | 0.725304 | + | 0.688428i | \(0.241699\pi\) | ||||
−0.725304 | + | 0.688428i | \(0.758301\pi\) | |||||||
\(212\) | −12.0000 | −0.824163 | ||||||||
\(213\) | − | 12.0000i | − | 0.822226i | ||||||
\(214\) | −12.0000 | + | 12.0000i | −0.820303 | + | 0.820303i | ||||
\(215\) | 8.00000 | 0.545595 | ||||||||
\(216\) | 2.00000 | + | 2.00000i | 0.136083 | + | 0.136083i | ||||
\(217\) | −4.00000 | −0.271538 | ||||||||
\(218\) | 4.00000 | − | 4.00000i | 0.270914 | − | 0.270914i | ||||
\(219\) | 6.00000i | 0.405442i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.00000i | 0.538138i | ||||||||
\(222\) | −8.00000 | − | 8.00000i | −0.536925 | − | 0.536925i | ||||
\(223\) | 14.0000 | 0.937509 | 0.468755 | − | 0.883328i | \(-0.344703\pi\) | ||||
0.468755 | + | 0.883328i | \(0.344703\pi\) | |||||||
\(224\) | −8.00000 | − | 8.00000i | −0.534522 | − | 0.534522i | ||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 6.00000 | + | 6.00000i | 0.399114 | + | 0.399114i | ||||
\(227\) | 8.00000i | 0.530979i | 0.964114 | + | 0.265489i | \(0.0855335\pi\) | ||||
−0.964114 | + | 0.265489i | \(0.914466\pi\) | |||||||
\(228\) | 8.00000i | 0.529813i | ||||||||
\(229\) | 4.00000i | 0.264327i | 0.991228 | + | 0.132164i | \(0.0421925\pi\) | ||||
−0.991228 | + | 0.132164i | \(0.957808\pi\) | |||||||
\(230\) | 8.00000 | − | 8.00000i | 0.527504 | − | 0.527504i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −12.0000 | − | 12.0000i | −0.787839 | − | 0.787839i | ||||
\(233\) | 14.0000 | 0.917170 | 0.458585 | − | 0.888650i | \(-0.348356\pi\) | ||||
0.458585 | + | 0.888650i | \(0.348356\pi\) | |||||||
\(234\) | 4.00000 | − | 4.00000i | 0.261488 | − | 0.261488i | ||||
\(235\) | − | 24.0000i | − | 1.56559i | ||||||
\(236\) | −8.00000 | −0.520756 | ||||||||
\(237\) | − | 10.0000i | − | 0.649570i | ||||||
\(238\) | −4.00000 | − | 4.00000i | −0.259281 | − | 0.259281i | ||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | −8.00000 | −0.516398 | ||||||||
\(241\) | 2.00000 | 0.128831 | 0.0644157 | − | 0.997923i | \(-0.479482\pi\) | ||||
0.0644157 | + | 0.997923i | \(0.479482\pi\) | |||||||
\(242\) | −11.0000 | − | 11.0000i | −0.707107 | − | 0.707107i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 6.00000i | − | 0.383326i | ||||||
\(246\) | −2.00000 | + | 2.00000i | −0.127515 | + | 0.127515i | ||||
\(247\) | 16.0000 | 1.01806 | ||||||||
\(248\) | 4.00000 | − | 4.00000i | 0.254000 | − | 0.254000i | ||||
\(249\) | 16.0000 | 1.01396 | ||||||||
\(250\) | 12.0000 | − | 12.0000i | 0.758947 | − | 0.758947i | ||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | 4.00000i | 0.251976i | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 2.00000 | + | 2.00000i | 0.125491 | + | 0.125491i | ||||
\(255\) | −4.00000 | −0.250490 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 18.0000 | 1.12281 | 0.561405 | − | 0.827541i | \(-0.310261\pi\) | ||||
0.561405 | + | 0.827541i | \(0.310261\pi\) | |||||||
\(258\) | 4.00000 | + | 4.00000i | 0.249029 | + | 0.249029i | ||||
\(259\) | − | 16.0000i | − | 0.994192i | ||||||
\(260\) | 16.0000i | 0.992278i | ||||||||
\(261\) | 6.00000i | 0.371391i | ||||||||
\(262\) | −20.0000 | + | 20.0000i | −1.23560 | + | 1.23560i | ||||
\(263\) | −16.0000 | −0.986602 | −0.493301 | − | 0.869859i | \(-0.664210\pi\) | ||||
−0.493301 | + | 0.869859i | \(0.664210\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.0000 | −0.737154 | ||||||||
\(266\) | −8.00000 | + | 8.00000i | −0.490511 | + | 0.490511i | ||||
\(267\) | 10.0000i | 0.611990i | ||||||||
\(268\) | 24.0000 | 1.46603 | ||||||||
\(269\) | − | 6.00000i | − | 0.365826i | −0.983129 | − | 0.182913i | \(-0.941447\pi\) | ||
0.983129 | − | 0.182913i | \(-0.0585527\pi\) | |||||||
\(270\) | 2.00000 | + | 2.00000i | 0.121716 | + | 0.121716i | ||||
\(271\) | −18.0000 | −1.09342 | −0.546711 | − | 0.837321i | \(-0.684120\pi\) | ||||
−0.546711 | + | 0.837321i | \(0.684120\pi\) | |||||||
\(272\) | 8.00000 | 0.485071 | ||||||||
\(273\) | 8.00000 | 0.484182 | ||||||||
\(274\) | −18.0000 | − | 18.0000i | −1.08742 | − | 1.08742i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 8.00000 | 0.481543 | ||||||||
\(277\) | 28.0000i | 1.68236i | 0.540758 | + | 0.841178i | \(0.318138\pi\) | ||||
−0.540758 | + | 0.841178i | \(0.681862\pi\) | |||||||
\(278\) | 4.00000 | − | 4.00000i | 0.239904 | − | 0.239904i | ||||
\(279\) | −2.00000 | −0.119737 | ||||||||
\(280\) | −8.00000 | − | 8.00000i | −0.478091 | − | 0.478091i | ||||
\(281\) | −18.0000 | −1.07379 | −0.536895 | − | 0.843649i | \(-0.680403\pi\) | ||||
−0.536895 | + | 0.843649i | \(0.680403\pi\) | |||||||
\(282\) | 12.0000 | − | 12.0000i | 0.714590 | − | 0.714590i | ||||
\(283\) | − | 4.00000i | − | 0.237775i | −0.992908 | − | 0.118888i | \(-0.962067\pi\) | ||
0.992908 | − | 0.118888i | \(-0.0379328\pi\) | |||||||
\(284\) | 24.0000i | 1.42414i | ||||||||
\(285\) | 8.00000i | 0.473879i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.00000 | −0.236113 | ||||||||
\(288\) | −4.00000 | − | 4.00000i | −0.235702 | − | 0.235702i | ||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | −12.0000 | − | 12.0000i | −0.704664 | − | 0.704664i | ||||
\(291\) | 2.00000i | 0.117242i | ||||||||
\(292\) | − | 12.0000i | − | 0.702247i | ||||||
\(293\) | 6.00000i | 0.350524i | 0.984522 | + | 0.175262i | \(0.0560772\pi\) | ||||
−0.984522 | + | 0.175262i | \(0.943923\pi\) | |||||||
\(294\) | 3.00000 | − | 3.00000i | 0.174964 | − | 0.174964i | ||||
\(295\) | −8.00000 | −0.465778 | ||||||||
\(296\) | 16.0000 | + | 16.0000i | 0.929981 | + | 0.929981i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.00000 | + | 6.00000i | −0.347571 | + | 0.347571i | ||||
\(299\) | − | 16.0000i | − | 0.925304i | ||||||
\(300\) | 2.00000 | 0.115470 | ||||||||
\(301\) | 8.00000i | 0.461112i | ||||||||
\(302\) | 18.0000 | + | 18.0000i | 1.03578 | + | 1.03578i | ||||
\(303\) | −10.0000 | −0.574485 | ||||||||
\(304\) | − | 16.0000i | − | 0.917663i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.00000 | − | 2.00000i | −0.114332 | − | 0.114332i | ||||
\(307\) | − | 12.0000i | − | 0.684876i | −0.939540 | − | 0.342438i | \(-0.888747\pi\) | ||
0.939540 | − | 0.342438i | \(-0.111253\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.00000i | 0.341328i | ||||||||
\(310\) | 4.00000 | − | 4.00000i | 0.227185 | − | 0.227185i | ||||
\(311\) | −8.00000 | −0.453638 | −0.226819 | − | 0.973937i | \(-0.572833\pi\) | ||||
−0.226819 | + | 0.973937i | \(0.572833\pi\) | |||||||
\(312\) | −8.00000 | + | 8.00000i | −0.452911 | + | 0.452911i | ||||
\(313\) | 14.0000 | 0.791327 | 0.395663 | − | 0.918396i | \(-0.370515\pi\) | ||||
0.395663 | + | 0.918396i | \(0.370515\pi\) | |||||||
\(314\) | 8.00000 | − | 8.00000i | 0.451466 | − | 0.451466i | ||||
\(315\) | 4.00000i | 0.225374i | ||||||||
\(316\) | 20.0000i | 1.12509i | ||||||||
\(317\) | − | 22.0000i | − | 1.23564i | −0.786318 | − | 0.617822i | \(-0.788015\pi\) | ||
0.786318 | − | 0.617822i | \(-0.211985\pi\) | |||||||
\(318\) | −6.00000 | − | 6.00000i | −0.336463 | − | 0.336463i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 16.0000 | 0.894427 | ||||||||
\(321\) | −12.0000 | −0.669775 | ||||||||
\(322\) | 8.00000 | + | 8.00000i | 0.445823 | + | 0.445823i | ||||
\(323\) | − | 8.00000i | − | 0.445132i | ||||||
\(324\) | 2.00000i | 0.111111i | ||||||||
\(325\) | − | 4.00000i | − | 0.221880i | ||||||
\(326\) | −4.00000 | + | 4.00000i | −0.221540 | + | 0.221540i | ||||
\(327\) | 4.00000 | 0.221201 | ||||||||
\(328\) | 4.00000 | − | 4.00000i | 0.220863 | − | 0.220863i | ||||
\(329\) | 24.0000 | 1.32316 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.0000i | 1.09930i | 0.835395 | + | 0.549650i | \(0.185239\pi\) | ||||
−0.835395 | + | 0.549650i | \(0.814761\pi\) | |||||||
\(332\) | −32.0000 | −1.75623 | ||||||||
\(333\) | − | 8.00000i | − | 0.438397i | ||||||
\(334\) | −8.00000 | − | 8.00000i | −0.437741 | − | 0.437741i | ||||
\(335\) | 24.0000 | 1.31126 | ||||||||
\(336\) | − | 8.00000i | − | 0.436436i | ||||||
\(337\) | −2.00000 | −0.108947 | −0.0544735 | − | 0.998515i | \(-0.517348\pi\) | ||||
−0.0544735 | + | 0.998515i | \(0.517348\pi\) | |||||||
\(338\) | 3.00000 | + | 3.00000i | 0.163178 | + | 0.163178i | ||||
\(339\) | 6.00000i | 0.325875i | ||||||||
\(340\) | 8.00000 | 0.433861 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −4.00000 | + | 4.00000i | −0.216295 | + | 0.216295i | ||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | −8.00000 | − | 8.00000i | −0.431331 | − | 0.431331i | ||||
\(345\) | 8.00000 | 0.430706 | ||||||||
\(346\) | 6.00000 | − | 6.00000i | 0.322562 | − | 0.322562i | ||||
\(347\) | 8.00000i | 0.429463i | 0.976673 | + | 0.214731i | \(0.0688876\pi\) | ||||
−0.976673 | + | 0.214731i | \(0.931112\pi\) | |||||||
\(348\) | − | 12.0000i | − | 0.643268i | ||||||
\(349\) | − | 16.0000i | − | 0.856460i | −0.903670 | − | 0.428230i | \(-0.859137\pi\) | ||
0.903670 | − | 0.428230i | \(-0.140863\pi\) | |||||||
\(350\) | 2.00000 | + | 2.00000i | 0.106904 | + | 0.106904i | ||||
\(351\) | 4.00000 | 0.213504 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.00000 | −0.319348 | −0.159674 | − | 0.987170i | \(-0.551044\pi\) | ||||
−0.159674 | + | 0.987170i | \(0.551044\pi\) | |||||||
\(354\) | −4.00000 | − | 4.00000i | −0.212598 | − | 0.212598i | ||||
\(355\) | 24.0000i | 1.27379i | ||||||||
\(356\) | − | 20.0000i | − | 1.06000i | ||||||
\(357\) | − | 4.00000i | − | 0.211702i | ||||||
\(358\) | 4.00000 | − | 4.00000i | 0.211407 | − | 0.211407i | ||||
\(359\) | −20.0000 | −1.05556 | −0.527780 | − | 0.849381i | \(-0.676975\pi\) | ||||
−0.527780 | + | 0.849381i | \(0.676975\pi\) | |||||||
\(360\) | −4.00000 | − | 4.00000i | −0.210819 | − | 0.210819i | ||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | −20.0000 | + | 20.0000i | −1.05118 | + | 1.05118i | ||||
\(363\) | − | 11.0000i | − | 0.577350i | ||||||
\(364\) | −16.0000 | −0.838628 | ||||||||
\(365\) | − | 12.0000i | − | 0.628109i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.0000 | 0.939592 | 0.469796 | − | 0.882775i | \(-0.344327\pi\) | ||||
0.469796 | + | 0.882775i | \(0.344327\pi\) | |||||||
\(368\) | −16.0000 | −0.834058 | ||||||||
\(369\) | −2.00000 | −0.104116 | ||||||||
\(370\) | 16.0000 | + | 16.0000i | 0.831800 | + | 0.831800i | ||||
\(371\) | − | 12.0000i | − | 0.623009i | ||||||
\(372\) | 4.00000 | 0.207390 | ||||||||
\(373\) | 16.0000i | 0.828449i | 0.910175 | + | 0.414224i | \(0.135947\pi\) | ||||
−0.910175 | + | 0.414224i | \(0.864053\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.0000 | 0.619677 | ||||||||
\(376\) | −24.0000 | + | 24.0000i | −1.23771 | + | 1.23771i | ||||
\(377\) | −24.0000 | −1.23606 | ||||||||
\(378\) | −2.00000 | + | 2.00000i | −0.102869 | + | 0.102869i | ||||
\(379\) | 4.00000i | 0.205466i | 0.994709 | + | 0.102733i | \(0.0327588\pi\) | ||||
−0.994709 | + | 0.102733i | \(0.967241\pi\) | |||||||
\(380\) | − | 16.0000i | − | 0.820783i | ||||||
\(381\) | 2.00000i | 0.102463i | ||||||||
\(382\) | 8.00000 | + | 8.00000i | 0.409316 | + | 0.409316i | ||||
\(383\) | 24.0000 | 1.22634 | 0.613171 | − | 0.789950i | \(-0.289894\pi\) | ||||
0.613171 | + | 0.789950i | \(0.289894\pi\) | |||||||
\(384\) | 8.00000 | + | 8.00000i | 0.408248 | + | 0.408248i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.00000 | + | 6.00000i | 0.305392 | + | 0.305392i | ||||
\(387\) | 4.00000i | 0.203331i | ||||||||
\(388\) | − | 4.00000i | − | 0.203069i | ||||||
\(389\) | 34.0000i | 1.72387i | 0.507020 | + | 0.861934i | \(0.330747\pi\) | ||||
−0.507020 | + | 0.861934i | \(0.669253\pi\) | |||||||
\(390\) | −8.00000 | + | 8.00000i | −0.405096 | + | 0.405096i | ||||
\(391\) | −8.00000 | −0.404577 | ||||||||
\(392\) | −6.00000 | + | 6.00000i | −0.303046 | + | 0.303046i | ||||
\(393\) | −20.0000 | −1.00887 | ||||||||
\(394\) | −2.00000 | + | 2.00000i | −0.100759 | + | 0.100759i | ||||
\(395\) | 20.0000i | 1.00631i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 32.0000i | − | 1.60603i | −0.595956 | − | 0.803017i | \(-0.703227\pi\) | ||
0.595956 | − | 0.803017i | \(-0.296773\pi\) | |||||||
\(398\) | −10.0000 | − | 10.0000i | −0.501255 | − | 0.501255i | ||||
\(399\) | −8.00000 | −0.400501 | ||||||||
\(400\) | −4.00000 | −0.200000 | ||||||||
\(401\) | −18.0000 | −0.898877 | −0.449439 | − | 0.893311i | \(-0.648376\pi\) | ||||
−0.449439 | + | 0.893311i | \(0.648376\pi\) | |||||||
\(402\) | 12.0000 | + | 12.0000i | 0.598506 | + | 0.598506i | ||||
\(403\) | − | 8.00000i | − | 0.398508i | ||||||
\(404\) | 20.0000 | 0.995037 | ||||||||
\(405\) | 2.00000i | 0.0993808i | ||||||||
\(406\) | 12.0000 | − | 12.0000i | 0.595550 | − | 0.595550i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 4.00000 | + | 4.00000i | 0.198030 | + | 0.198030i | ||||
\(409\) | 10.0000 | 0.494468 | 0.247234 | − | 0.968956i | \(-0.420478\pi\) | ||||
0.247234 | + | 0.968956i | \(0.420478\pi\) | |||||||
\(410\) | 4.00000 | − | 4.00000i | 0.197546 | − | 0.197546i | ||||
\(411\) | − | 18.0000i | − | 0.887875i | ||||||
\(412\) | − | 12.0000i | − | 0.591198i | ||||||
\(413\) | − | 8.00000i | − | 0.393654i | ||||||
\(414\) | 4.00000 | + | 4.00000i | 0.196589 | + | 0.196589i | ||||
\(415\) | −32.0000 | −1.57082 | ||||||||
\(416\) | 16.0000 | − | 16.0000i | 0.784465 | − | 0.784465i | ||||
\(417\) | 4.00000 | 0.195881 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.0000i | 1.17248i | 0.810139 | + | 0.586238i | \(0.199392\pi\) | ||||
−0.810139 | + | 0.586238i | \(0.800608\pi\) | |||||||
\(420\) | − | 8.00000i | − | 0.390360i | ||||||
\(421\) | − | 20.0000i | − | 0.974740i | −0.873195 | − | 0.487370i | \(-0.837956\pi\) | ||
0.873195 | − | 0.487370i | \(-0.162044\pi\) | |||||||
\(422\) | 20.0000 | − | 20.0000i | 0.973585 | − | 0.973585i | ||||
\(423\) | 12.0000 | 0.583460 | ||||||||
\(424\) | 12.0000 | + | 12.0000i | 0.582772 | + | 0.582772i | ||||
\(425\) | −2.00000 | −0.0970143 | ||||||||
\(426\) | −12.0000 | + | 12.0000i | −0.581402 | + | 0.581402i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 24.0000 | 1.16008 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.00000 | − | 8.00000i | −0.385794 | − | 0.385794i | ||||
\(431\) | 12.0000 | 0.578020 | 0.289010 | − | 0.957326i | \(-0.406674\pi\) | ||||
0.289010 | + | 0.957326i | \(0.406674\pi\) | |||||||
\(432\) | − | 4.00000i | − | 0.192450i | ||||||
\(433\) | 14.0000 | 0.672797 | 0.336399 | − | 0.941720i | \(-0.390791\pi\) | ||||
0.336399 | + | 0.941720i | \(0.390791\pi\) | |||||||
\(434\) | 4.00000 | + | 4.00000i | 0.192006 | + | 0.192006i | ||||
\(435\) | − | 12.0000i | − | 0.575356i | ||||||
\(436\) | −8.00000 | −0.383131 | ||||||||
\(437\) | 16.0000i | 0.765384i | ||||||||
\(438\) | 6.00000 | − | 6.00000i | 0.286691 | − | 0.286691i | ||||
\(439\) | −30.0000 | −1.43182 | −0.715911 | − | 0.698192i | \(-0.753988\pi\) | ||||
−0.715911 | + | 0.698192i | \(0.753988\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.00000 | 0.142857 | ||||||||
\(442\) | 8.00000 | − | 8.00000i | 0.380521 | − | 0.380521i | ||||
\(443\) | − | 24.0000i | − | 1.14027i | −0.821549 | − | 0.570137i | \(-0.806890\pi\) | ||
0.821549 | − | 0.570137i | \(-0.193110\pi\) | |||||||
\(444\) | 16.0000i | 0.759326i | ||||||||
\(445\) | − | 20.0000i | − | 0.948091i | ||||||
\(446\) | −14.0000 | − | 14.0000i | −0.662919 | − | 0.662919i | ||||
\(447\) | −6.00000 | −0.283790 | ||||||||
\(448\) | 16.0000i | 0.755929i | ||||||||
\(449\) | 30.0000 | 1.41579 | 0.707894 | − | 0.706319i | \(-0.249646\pi\) | ||||
0.707894 | + | 0.706319i | \(0.249646\pi\) | |||||||
\(450\) | 1.00000 | + | 1.00000i | 0.0471405 | + | 0.0471405i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 12.0000i | − | 0.564433i | ||||||
\(453\) | 18.0000i | 0.845714i | ||||||||
\(454\) | 8.00000 | − | 8.00000i | 0.375459 | − | 0.375459i | ||||
\(455\) | −16.0000 | −0.750092 | ||||||||
\(456\) | 8.00000 | − | 8.00000i | 0.374634 | − | 0.374634i | ||||
\(457\) | −22.0000 | −1.02912 | −0.514558 | − | 0.857455i | \(-0.672044\pi\) | ||||
−0.514558 | + | 0.857455i | \(0.672044\pi\) | |||||||
\(458\) | 4.00000 | − | 4.00000i | 0.186908 | − | 0.186908i | ||||
\(459\) | − | 2.00000i | − | 0.0933520i | ||||||
\(460\) | −16.0000 | −0.746004 | ||||||||
\(461\) | 30.0000i | 1.39724i | 0.715493 | + | 0.698620i | \(0.246202\pi\) | ||||
−0.715493 | + | 0.698620i | \(0.753798\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.0000 | −1.20832 | −0.604161 | − | 0.796862i | \(-0.706492\pi\) | ||||
−0.604161 | + | 0.796862i | \(0.706492\pi\) | |||||||
\(464\) | 24.0000i | 1.11417i | ||||||||
\(465\) | 4.00000 | 0.185496 | ||||||||
\(466\) | −14.0000 | − | 14.0000i | −0.648537 | − | 0.648537i | ||||
\(467\) | 8.00000i | 0.370196i | 0.982720 | + | 0.185098i | \(0.0592602\pi\) | ||||
−0.982720 | + | 0.185098i | \(0.940740\pi\) | |||||||
\(468\) | −8.00000 | −0.369800 | ||||||||
\(469\) | 24.0000i | 1.10822i | ||||||||
\(470\) | −24.0000 | + | 24.0000i | −1.10704 | + | 1.10704i | ||||
\(471\) | 8.00000 | 0.368621 | ||||||||
\(472\) | 8.00000 | + | 8.00000i | 0.368230 | + | 0.368230i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −10.0000 | + | 10.0000i | −0.459315 | + | 0.459315i | ||||
\(475\) | 4.00000i | 0.183533i | ||||||||
\(476\) | 8.00000i | 0.366679i | ||||||||
\(477\) | − | 6.00000i | − | 0.274721i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.0000 | 0.913823 | 0.456912 | − | 0.889512i | \(-0.348956\pi\) | ||||
0.456912 | + | 0.889512i | \(0.348956\pi\) | |||||||
\(480\) | 8.00000 | + | 8.00000i | 0.365148 | + | 0.365148i | ||||
\(481\) | 32.0000 | 1.45907 | ||||||||
\(482\) | −2.00000 | − | 2.00000i | −0.0910975 | − | 0.0910975i | ||||
\(483\) | 8.00000i | 0.364013i | ||||||||
\(484\) | 22.0000i | 1.00000i | ||||||||
\(485\) | − | 4.00000i | − | 0.181631i | ||||||
\(486\) | −1.00000 | + | 1.00000i | −0.0453609 | + | 0.0453609i | ||||
\(487\) | 38.0000 | 1.72194 | 0.860972 | − | 0.508652i | \(-0.169856\pi\) | ||||
0.860972 | + | 0.508652i | \(0.169856\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.00000 | −0.180886 | ||||||||
\(490\) | −6.00000 | + | 6.00000i | −0.271052 | + | 0.271052i | ||||
\(491\) | − | 20.0000i | − | 0.902587i | −0.892375 | − | 0.451294i | \(-0.850963\pi\) | ||
0.892375 | − | 0.451294i | \(-0.149037\pi\) | |||||||
\(492\) | 4.00000 | 0.180334 | ||||||||
\(493\) | 12.0000i | 0.540453i | ||||||||
\(494\) | −16.0000 | − | 16.0000i | −0.719874 | − | 0.719874i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.00000 | −0.359211 | ||||||||
\(497\) | −24.0000 | −1.07655 | ||||||||
\(498\) | −16.0000 | − | 16.0000i | −0.716977 | − | 0.716977i | ||||
\(499\) | − | 36.0000i | − | 1.61158i | −0.592200 | − | 0.805791i | \(-0.701741\pi\) | ||
0.592200 | − | 0.805791i | \(-0.298259\pi\) | |||||||
\(500\) | −24.0000 | −1.07331 | ||||||||
\(501\) | − | 8.00000i | − | 0.357414i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −36.0000 | −1.60516 | −0.802580 | − | 0.596544i | \(-0.796540\pi\) | ||||
−0.802580 | + | 0.596544i | \(0.796540\pi\) | |||||||
\(504\) | 4.00000 | − | 4.00000i | 0.178174 | − | 0.178174i | ||||
\(505\) | 20.0000 | 0.889988 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.00000i | 0.133235i | ||||||||
\(508\) | − | 4.00000i | − | 0.177471i | ||||||
\(509\) | − | 6.00000i | − | 0.265945i | −0.991120 | − | 0.132973i | \(-0.957548\pi\) | ||
0.991120 | − | 0.132973i | \(-0.0424523\pi\) | |||||||
\(510\) | 4.00000 | + | 4.00000i | 0.177123 | + | 0.177123i | ||||
\(511\) | 12.0000 | 0.530849 | ||||||||
\(512\) | −16.0000 | − | 16.0000i | −0.707107 | − | 0.707107i | ||||
\(513\) | −4.00000 | −0.176604 | ||||||||
\(514\) | −18.0000 | − | 18.0000i | −0.793946 | − | 0.793946i | ||||
\(515\) | − | 12.0000i | − | 0.528783i | ||||||
\(516\) | − | 8.00000i | − | 0.352180i | ||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −16.0000 | + | 16.0000i | −0.703000 | + | 0.703000i | ||||
\(519\) | 6.00000 | 0.263371 | ||||||||
\(520\) | 16.0000 | − | 16.0000i | 0.701646 | − | 0.701646i | ||||
\(521\) | 42.0000 | 1.84005 | 0.920027 | − | 0.391856i | \(-0.128167\pi\) | ||||
0.920027 | + | 0.391856i | \(0.128167\pi\) | |||||||
\(522\) | 6.00000 | − | 6.00000i | 0.262613 | − | 0.262613i | ||||
\(523\) | 36.0000i | 1.57417i | 0.616844 | + | 0.787085i | \(0.288411\pi\) | ||||
−0.616844 | + | 0.787085i | \(0.711589\pi\) | |||||||
\(524\) | 40.0000 | 1.74741 | ||||||||
\(525\) | 2.00000i | 0.0872872i | ||||||||
\(526\) | 16.0000 | + | 16.0000i | 0.697633 | + | 0.697633i | ||||
\(527\) | −4.00000 | −0.174243 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 12.0000 | + | 12.0000i | 0.521247 | + | 0.521247i | ||||
\(531\) | − | 4.00000i | − | 0.173585i | ||||||
\(532\) | 16.0000 | 0.693688 | ||||||||
\(533\) | − | 8.00000i | − | 0.346518i | ||||||
\(534\) | 10.0000 | − | 10.0000i | 0.432742 | − | 0.432742i | ||||
\(535\) | 24.0000 | 1.03761 | ||||||||
\(536\) | −24.0000 | − | 24.0000i | −1.03664 | − | 1.03664i | ||||
\(537\) | 4.00000 | 0.172613 | ||||||||
\(538\) | −6.00000 | + | 6.00000i | −0.258678 | + | 0.258678i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | − | 4.00000i | − | 0.172133i | ||||||
\(541\) | 20.0000i | 0.859867i | 0.902861 | + | 0.429934i | \(0.141463\pi\) | ||||
−0.902861 | + | 0.429934i | \(0.858537\pi\) | |||||||
\(542\) | 18.0000 | + | 18.0000i | 0.773166 | + | 0.773166i | ||||
\(543\) | −20.0000 | −0.858282 | ||||||||
\(544\) | −8.00000 | − | 8.00000i | −0.342997 | − | 0.342997i | ||||
\(545\) | −8.00000 | −0.342682 | ||||||||
\(546\) | −8.00000 | − | 8.00000i | −0.342368 | − | 0.342368i | ||||
\(547\) | 28.0000i | 1.19719i | 0.801050 | + | 0.598597i | \(0.204275\pi\) | ||||
−0.801050 | + | 0.598597i | \(0.795725\pi\) | |||||||
\(548\) | 36.0000i | 1.53784i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.0000 | 1.02243 | ||||||||
\(552\) | −8.00000 | − | 8.00000i | −0.340503 | − | 0.340503i | ||||
\(553\) | −20.0000 | −0.850487 | ||||||||
\(554\) | 28.0000 | − | 28.0000i | 1.18961 | − | 1.18961i | ||||
\(555\) | 16.0000i | 0.679162i | ||||||||
\(556\) | −8.00000 | −0.339276 | ||||||||
\(557\) | − | 42.0000i | − | 1.77960i | −0.456354 | − | 0.889799i | \(-0.650845\pi\) | ||
0.456354 | − | 0.889799i | \(-0.349155\pi\) | |||||||
\(558\) | 2.00000 | + | 2.00000i | 0.0846668 | + | 0.0846668i | ||||
\(559\) | −16.0000 | −0.676728 | ||||||||
\(560\) | 16.0000i | 0.676123i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18.0000 | + | 18.0000i | 0.759284 | + | 0.759284i | ||||
\(563\) | − | 24.0000i | − | 1.01148i | −0.862686 | − | 0.505740i | \(-0.831220\pi\) | ||
0.862686 | − | 0.505740i | \(-0.168780\pi\) | |||||||
\(564\) | −24.0000 | −1.01058 | ||||||||
\(565\) | − | 12.0000i | − | 0.504844i | ||||||
\(566\) | −4.00000 | + | 4.00000i | −0.168133 | + | 0.168133i | ||||
\(567\) | −2.00000 | −0.0839921 | ||||||||
\(568\) | 24.0000 | − | 24.0000i | 1.00702 | − | 1.00702i | ||||
\(569\) | −30.0000 | −1.25767 | −0.628833 | − | 0.777541i | \(-0.716467\pi\) | ||||
−0.628833 | + | 0.777541i | \(0.716467\pi\) | |||||||
\(570\) | 8.00000 | − | 8.00000i | 0.335083 | − | 0.335083i | ||||
\(571\) | − | 20.0000i | − | 0.836974i | −0.908223 | − | 0.418487i | \(-0.862561\pi\) | ||
0.908223 | − | 0.418487i | \(-0.137439\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.00000i | 0.334205i | ||||||||
\(574\) | 4.00000 | + | 4.00000i | 0.166957 | + | 0.166957i | ||||
\(575\) | 4.00000 | 0.166812 | ||||||||
\(576\) | 8.00000i | 0.333333i | ||||||||
\(577\) | −42.0000 | −1.74848 | −0.874241 | − | 0.485491i | \(-0.838641\pi\) | ||||
−0.874241 | + | 0.485491i | \(0.838641\pi\) | |||||||
\(578\) | 13.0000 | + | 13.0000i | 0.540729 | + | 0.540729i | ||||
\(579\) | 6.00000i | 0.249351i | ||||||||
\(580\) | 24.0000i | 0.996546i | ||||||||
\(581\) | − | 32.0000i | − | 1.32758i | ||||||
\(582\) | 2.00000 | − | 2.00000i | 0.0829027 | − | 0.0829027i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −12.0000 | + | 12.0000i | −0.496564 | + | 0.496564i | ||||
\(585\) | −8.00000 | −0.330759 | ||||||||
\(586\) | 6.00000 | − | 6.00000i | 0.247858 | − | 0.247858i | ||||
\(587\) | 28.0000i | 1.15568i | 0.816149 | + | 0.577842i | \(0.196105\pi\) | ||||
−0.816149 | + | 0.577842i | \(0.803895\pi\) | |||||||
\(588\) | −6.00000 | −0.247436 | ||||||||
\(589\) | 8.00000i | 0.329634i | ||||||||
\(590\) | 8.00000 | + | 8.00000i | 0.329355 | + | 0.329355i | ||||
\(591\) | −2.00000 | −0.0822690 | ||||||||
\(592\) | − | 32.0000i | − | 1.31519i | ||||||
\(593\) | −6.00000 | −0.246390 | −0.123195 | − | 0.992382i | \(-0.539314\pi\) | ||||
−0.123195 | + | 0.992382i | \(0.539314\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.00000i | 0.327968i | ||||||||
\(596\) | 12.0000 | 0.491539 | ||||||||
\(597\) | − | 10.0000i | − | 0.409273i | ||||||
\(598\) | −16.0000 | + | 16.0000i | −0.654289 | + | 0.654289i | ||||
\(599\) | −20.0000 | −0.817178 | −0.408589 | − | 0.912719i | \(-0.633979\pi\) | ||||
−0.408589 | + | 0.912719i | \(0.633979\pi\) | |||||||
\(600\) | −2.00000 | − | 2.00000i | −0.0816497 | − | 0.0816497i | ||||
\(601\) | 2.00000 | 0.0815817 | 0.0407909 | − | 0.999168i | \(-0.487012\pi\) | ||||
0.0407909 | + | 0.999168i | \(0.487012\pi\) | |||||||
\(602\) | 8.00000 | − | 8.00000i | 0.326056 | − | 0.326056i | ||||
\(603\) | 12.0000i | 0.488678i | ||||||||
\(604\) | − | 36.0000i | − | 1.46482i | ||||||
\(605\) | 22.0000i | 0.894427i | ||||||||
\(606\) | 10.0000 | + | 10.0000i | 0.406222 | + | 0.406222i | ||||
\(607\) | −2.00000 | −0.0811775 | −0.0405887 | − | 0.999176i | \(-0.512923\pi\) | ||||
−0.0405887 | + | 0.999176i | \(0.512923\pi\) | |||||||
\(608\) | −16.0000 | + | 16.0000i | −0.648886 | + | 0.648886i | ||||
\(609\) | 12.0000 | 0.486265 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 48.0000i | 1.94187i | ||||||||
\(612\) | 4.00000i | 0.161690i | ||||||||
\(613\) | 16.0000i | 0.646234i | 0.946359 | + | 0.323117i | \(0.104731\pi\) | ||||
−0.946359 | + | 0.323117i | \(0.895269\pi\) | |||||||
\(614\) | −12.0000 | + | 12.0000i | −0.484281 | + | 0.484281i | ||||
\(615\) | 4.00000 | 0.161296 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.00000 | −0.0805170 | −0.0402585 | − | 0.999189i | \(-0.512818\pi\) | ||||
−0.0402585 | + | 0.999189i | \(0.512818\pi\) | |||||||
\(618\) | 6.00000 | − | 6.00000i | 0.241355 | − | 0.241355i | ||||
\(619\) | − | 36.0000i | − | 1.44696i | −0.690344 | − | 0.723481i | \(-0.742541\pi\) | ||
0.690344 | − | 0.723481i | \(-0.257459\pi\) | |||||||
\(620\) | −8.00000 | −0.321288 | ||||||||
\(621\) | 4.00000i | 0.160514i | ||||||||
\(622\) | 8.00000 | + | 8.00000i | 0.320771 | + | 0.320771i | ||||
\(623\) | 20.0000 | 0.801283 | ||||||||
\(624\) | 16.0000 | 0.640513 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | −14.0000 | − | 14.0000i | −0.559553 | − | 0.559553i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −16.0000 | −0.638470 | ||||||||
\(629\) | − | 16.0000i | − | 0.637962i | ||||||
\(630\) | 4.00000 | − | 4.00000i | 0.159364 | − | 0.159364i | ||||
\(631\) | 22.0000 | 0.875806 | 0.437903 | − | 0.899022i | \(-0.355721\pi\) | ||||
0.437903 | + | 0.899022i | \(0.355721\pi\) | |||||||
\(632\) | 20.0000 | − | 20.0000i | 0.795557 | − | 0.795557i | ||||
\(633\) | 20.0000 | 0.794929 | ||||||||
\(634\) | −22.0000 | + | 22.0000i | −0.873732 | + | 0.873732i | ||||
\(635\) | − | 4.00000i | − | 0.158735i | ||||||
\(636\) | 12.0000i | 0.475831i | ||||||||
\(637\) | 12.0000i | 0.475457i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.0000 | −0.474713 | ||||||||
\(640\) | −16.0000 | − | 16.0000i | −0.632456 | − | 0.632456i | ||||
\(641\) | 22.0000 | 0.868948 | 0.434474 | − | 0.900684i | \(-0.356934\pi\) | ||||
0.434474 | + | 0.900684i | \(0.356934\pi\) | |||||||
\(642\) | 12.0000 | + | 12.0000i | 0.473602 | + | 0.473602i | ||||
\(643\) | − | 4.00000i | − | 0.157745i | −0.996885 | − | 0.0788723i | \(-0.974868\pi\) | ||
0.996885 | − | 0.0788723i | \(-0.0251319\pi\) | |||||||
\(644\) | − | 16.0000i | − | 0.630488i | ||||||
\(645\) | − | 8.00000i | − | 0.315000i | ||||||
\(646\) | −8.00000 | + | 8.00000i | −0.314756 | + | 0.314756i | ||||
\(647\) | −12.0000 | −0.471769 | −0.235884 | − | 0.971781i | \(-0.575799\pi\) | ||||
−0.235884 | + | 0.971781i | \(0.575799\pi\) | |||||||
\(648\) | 2.00000 | − | 2.00000i | 0.0785674 | − | 0.0785674i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −4.00000 | + | 4.00000i | −0.156893 | + | 0.156893i | ||||
\(651\) | 4.00000i | 0.156772i | ||||||||
\(652\) | 8.00000 | 0.313304 | ||||||||
\(653\) | 6.00000i | 0.234798i | 0.993085 | + | 0.117399i | \(0.0374557\pi\) | ||||
−0.993085 | + | 0.117399i | \(0.962544\pi\) | |||||||
\(654\) | −4.00000 | − | 4.00000i | −0.156412 | − | 0.156412i | ||||
\(655\) | 40.0000 | 1.56293 | ||||||||
\(656\) | −8.00000 | −0.312348 | ||||||||
\(657\) | 6.00000 | 0.234082 | ||||||||
\(658\) | −24.0000 | − | 24.0000i | −0.935617 | − | 0.935617i | ||||
\(659\) | − | 36.0000i | − | 1.40236i | −0.712984 | − | 0.701180i | \(-0.752657\pi\) | ||
0.712984 | − | 0.701180i | \(-0.247343\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 40.0000i | − | 1.55582i | −0.628376 | − | 0.777910i | \(-0.716280\pi\) | ||
0.628376 | − | 0.777910i | \(-0.283720\pi\) | |||||||
\(662\) | 20.0000 | − | 20.0000i | 0.777322 | − | 0.777322i | ||||
\(663\) | 8.00000 | 0.310694 | ||||||||
\(664\) | 32.0000 | + | 32.0000i | 1.24184 | + | 1.24184i | ||||
\(665\) | 16.0000 | 0.620453 | ||||||||
\(666\) | −8.00000 | + | 8.00000i | −0.309994 | + | 0.309994i | ||||
\(667\) | − | 24.0000i | − | 0.929284i | ||||||
\(668\) | 16.0000i | 0.619059i | ||||||||
\(669\) | − | 14.0000i | − | 0.541271i | ||||||
\(670\) | −24.0000 | − | 24.0000i | −0.927201 | − | 0.927201i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −8.00000 | + | 8.00000i | −0.308607 | + | 0.308607i | ||||
\(673\) | 14.0000 | 0.539660 | 0.269830 | − | 0.962908i | \(-0.413032\pi\) | ||||
0.269830 | + | 0.962908i | \(0.413032\pi\) | |||||||
\(674\) | 2.00000 | + | 2.00000i | 0.0770371 | + | 0.0770371i | ||||
\(675\) | 1.00000i | 0.0384900i | ||||||||
\(676\) | − | 6.00000i | − | 0.230769i | ||||||
\(677\) | 18.0000i | 0.691796i | 0.938272 | + | 0.345898i | \(0.112426\pi\) | ||||
−0.938272 | + | 0.345898i | \(0.887574\pi\) | |||||||
\(678\) | 6.00000 | − | 6.00000i | 0.230429 | − | 0.230429i | ||||
\(679\) | 4.00000 | 0.153506 | ||||||||
\(680\) | −8.00000 | − | 8.00000i | −0.306786 | − | 0.306786i | ||||
\(681\) | 8.00000 | 0.306561 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.0000i | 0.612223i | 0.951996 | + | 0.306111i | \(0.0990280\pi\) | ||||
−0.951996 | + | 0.306111i | \(0.900972\pi\) | |||||||
\(684\) | 8.00000 | 0.305888 | ||||||||
\(685\) | 36.0000i | 1.37549i | ||||||||
\(686\) | −20.0000 | − | 20.0000i | −0.763604 | − | 0.763604i | ||||
\(687\) | 4.00000 | 0.152610 | ||||||||
\(688\) | 16.0000i | 0.609994i | ||||||||
\(689\) | 24.0000 | 0.914327 | ||||||||
\(690\) | −8.00000 | − | 8.00000i | −0.304555 | − | 0.304555i | ||||
\(691\) | − | 20.0000i | − | 0.760836i | −0.924815 | − | 0.380418i | \(-0.875780\pi\) | ||
0.924815 | − | 0.380418i | \(-0.124220\pi\) | |||||||
\(692\) | −12.0000 | −0.456172 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.00000 | − | 8.00000i | 0.303676 | − | 0.303676i | ||||
\(695\) | −8.00000 | −0.303457 | ||||||||
\(696\) | −12.0000 | + | 12.0000i | −0.454859 | + | 0.454859i | ||||
\(697\) | −4.00000 | −0.151511 | ||||||||
\(698\) | −16.0000 | + | 16.0000i | −0.605609 | + | 0.605609i | ||||
\(699\) | − | 14.0000i | − | 0.529529i | ||||||
\(700\) | − | 4.00000i | − | 0.151186i | ||||||
\(701\) | 50.0000i | 1.88847i | 0.329267 | + | 0.944237i | \(0.393198\pi\) | ||||
−0.329267 | + | 0.944237i | \(0.606802\pi\) | |||||||
\(702\) | −4.00000 | − | 4.00000i | −0.150970 | − | 0.150970i | ||||
\(703\) | −32.0000 | −1.20690 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −24.0000 | −0.903892 | ||||||||
\(706\) | 6.00000 | + | 6.00000i | 0.225813 | + | 0.225813i | ||||
\(707\) | 20.0000i | 0.752177i | ||||||||
\(708\) | 8.00000i | 0.300658i | ||||||||
\(709\) | 4.00000i | 0.150223i | 0.997175 | + | 0.0751116i | \(0.0239313\pi\) | ||||
−0.997175 | + | 0.0751116i | \(0.976069\pi\) | |||||||
\(710\) | 24.0000 | − | 24.0000i | 0.900704 | − | 0.900704i | ||||
\(711\) | −10.0000 | −0.375029 | ||||||||
\(712\) | −20.0000 | + | 20.0000i | −0.749532 | + | 0.749532i | ||||
\(713\) | 8.00000 | 0.299602 | ||||||||
\(714\) | −4.00000 | + | 4.00000i | −0.149696 | + | 0.149696i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.00000 | −0.298974 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 20.0000 | + | 20.0000i | 0.746393 | + | 0.746393i | ||||
\(719\) | −20.0000 | −0.745874 | −0.372937 | − | 0.927857i | \(-0.621649\pi\) | ||||
−0.372937 | + | 0.927857i | \(0.621649\pi\) | |||||||
\(720\) | 8.00000i | 0.298142i | ||||||||
\(721\) | 12.0000 | 0.446903 | ||||||||
\(722\) | −3.00000 | − | 3.00000i | −0.111648 | − | 0.111648i | ||||
\(723\) | − | 2.00000i | − | 0.0743808i | ||||||
\(724\) | 40.0000 | 1.48659 | ||||||||
\(725\) | − | 6.00000i | − | 0.222834i | ||||||
\(726\) | −11.0000 | + | 11.0000i | −0.408248 | + | 0.408248i | ||||
\(727\) | −42.0000 | −1.55769 | −0.778847 | − | 0.627214i | \(-0.784195\pi\) | ||||
−0.778847 | + | 0.627214i | \(0.784195\pi\) | |||||||
\(728\) | 16.0000 | + | 16.0000i | 0.592999 | + | 0.592999i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −12.0000 | + | 12.0000i | −0.444140 | + | 0.444140i | ||||
\(731\) | 8.00000i | 0.295891i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 4.00000i | − | 0.147743i | −0.997268 | − | 0.0738717i | \(-0.976464\pi\) | ||
0.997268 | − | 0.0738717i | \(-0.0235355\pi\) | |||||||
\(734\) | −18.0000 | − | 18.0000i | −0.664392 | − | 0.664392i | ||||
\(735\) | −6.00000 | −0.221313 | ||||||||
\(736\) | 16.0000 | + | 16.0000i | 0.589768 | + | 0.589768i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 2.00000 | + | 2.00000i | 0.0736210 | + | 0.0736210i | ||||
\(739\) | 44.0000i | 1.61857i | 0.587419 | + | 0.809283i | \(0.300144\pi\) | ||||
−0.587419 | + | 0.809283i | \(0.699856\pi\) | |||||||
\(740\) | − | 32.0000i | − | 1.17634i | ||||||
\(741\) | − | 16.0000i | − | 0.587775i | ||||||
\(742\) | −12.0000 | + | 12.0000i | −0.440534 | + | 0.440534i | ||||
\(743\) | −16.0000 | −0.586983 | −0.293492 | − | 0.955962i | \(-0.594817\pi\) | ||||
−0.293492 | + | 0.955962i | \(0.594817\pi\) | |||||||
\(744\) | −4.00000 | − | 4.00000i | −0.146647 | − | 0.146647i | ||||
\(745\) | 12.0000 | 0.439646 | ||||||||
\(746\) | 16.0000 | − | 16.0000i | 0.585802 | − | 0.585802i | ||||
\(747\) | − | 16.0000i | − | 0.585409i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24.0000i | 0.876941i | ||||||||
\(750\) | −12.0000 | − | 12.0000i | −0.438178 | − | 0.438178i | ||||
\(751\) | 2.00000 | 0.0729810 | 0.0364905 | − | 0.999334i | \(-0.488382\pi\) | ||||
0.0364905 | + | 0.999334i | \(0.488382\pi\) | |||||||
\(752\) | 48.0000 | 1.75038 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 24.0000 | + | 24.0000i | 0.874028 | + | 0.874028i | ||||
\(755\) | − | 36.0000i | − | 1.31017i | ||||||
\(756\) | 4.00000 | 0.145479 | ||||||||
\(757\) | − | 12.0000i | − | 0.436147i | −0.975932 | − | 0.218074i | \(-0.930023\pi\) | ||
0.975932 | − | 0.218074i | \(-0.0699773\pi\) | |||||||
\(758\) | 4.00000 | − | 4.00000i | 0.145287 | − | 0.145287i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −16.0000 | + | 16.0000i | −0.580381 | + | 0.580381i | ||||
\(761\) | −38.0000 | −1.37750 | −0.688749 | − | 0.724999i | \(-0.741840\pi\) | ||||
−0.688749 | + | 0.724999i | \(0.741840\pi\) | |||||||
\(762\) | 2.00000 | − | 2.00000i | 0.0724524 | − | 0.0724524i | ||||
\(763\) | − | 8.00000i | − | 0.289619i | ||||||
\(764\) | − | 16.0000i | − | 0.578860i | ||||||
\(765\) | 4.00000i | 0.144620i | ||||||||
\(766\) | −24.0000 | − | 24.0000i | −0.867155 | − | 0.867155i | ||||
\(767\) | 16.0000 | 0.577727 | ||||||||
\(768\) | − | 16.0000i | − | 0.577350i | ||||||
\(769\) | 10.0000 | 0.360609 | 0.180305 | − | 0.983611i | \(-0.442292\pi\) | ||||
0.180305 | + | 0.983611i | \(0.442292\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 18.0000i | − | 0.648254i | ||||||
\(772\) | − | 12.0000i | − | 0.431889i | ||||||
\(773\) | − | 34.0000i | − | 1.22290i | −0.791285 | − | 0.611448i | \(-0.790588\pi\) | ||
0.791285 | − | 0.611448i | \(-0.209412\pi\) | |||||||
\(774\) | 4.00000 | − | 4.00000i | 0.143777 | − | 0.143777i | ||||
\(775\) | 2.00000 | 0.0718421 | ||||||||
\(776\) | −4.00000 | + | 4.00000i | −0.143592 | + | 0.143592i | ||||
\(777\) | −16.0000 | −0.573997 | ||||||||
\(778\) | 34.0000 | − | 34.0000i | 1.21896 | − | 1.21896i | ||||
\(779\) | 8.00000i | 0.286630i | ||||||||
\(780\) | 16.0000 | 0.572892 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 8.00000 | + | 8.00000i | 0.286079 | + | 0.286079i | ||||
\(783\) | 6.00000 | 0.214423 | ||||||||
\(784\) | 12.0000 | 0.428571 | ||||||||
\(785\) | −16.0000 | −0.571064 | ||||||||
\(786\) | 20.0000 | + | 20.0000i | 0.713376 | + | 0.713376i | ||||
\(787\) | − | 12.0000i | − | 0.427754i | −0.976861 | − | 0.213877i | \(-0.931391\pi\) | ||
0.976861 | − | 0.213877i | \(-0.0686091\pi\) | |||||||
\(788\) | 4.00000 | 0.142494 | ||||||||
\(789\) | 16.0000i | 0.569615i | ||||||||
\(790\) | 20.0000 | − | 20.0000i | 0.711568 | − | 0.711568i | ||||
\(791\) | 12.0000 | 0.426671 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −32.0000 | + | 32.0000i | −1.13564 | + | 1.13564i | ||||
\(795\) | 12.0000i | 0.425596i | ||||||||
\(796\) | 20.0000i | 0.708881i | ||||||||
\(797\) | − | 2.00000i | − | 0.0708436i | −0.999372 | − | 0.0354218i | \(-0.988723\pi\) | ||
0.999372 | − | 0.0354218i | \(-0.0112775\pi\) | |||||||
\(798\) | 8.00000 | + | 8.00000i | 0.283197 | + | 0.283197i | ||||
\(799\) | 24.0000 | 0.849059 | ||||||||
\(800\) | 4.00000 | + | 4.00000i | 0.141421 | + | 0.141421i | ||||
\(801\) | 10.0000 | 0.353333 | ||||||||
\(802\) | 18.0000 | + | 18.0000i | 0.635602 | + | 0.635602i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | − | 24.0000i | − | 0.846415i | ||||||
\(805\) | − | 16.0000i | − | 0.563926i | ||||||
\(806\) | −8.00000 | + | 8.00000i | −0.281788 | + | 0.281788i | ||||
\(807\) | −6.00000 | −0.211210 | ||||||||
\(808\) | −20.0000 | − | 20.0000i | −0.703598 | − | 0.703598i | ||||
\(809\) | −30.0000 | −1.05474 | −0.527372 | − | 0.849635i | \(-0.676823\pi\) | ||||
−0.527372 | + | 0.849635i | \(0.676823\pi\) | |||||||
\(810\) | 2.00000 | − | 2.00000i | 0.0702728 | − | 0.0702728i | ||||
\(811\) | 20.0000i | 0.702295i | 0.936320 | + | 0.351147i | \(0.114208\pi\) | ||||
−0.936320 | + | 0.351147i | \(0.885792\pi\) | |||||||
\(812\) | −24.0000 | −0.842235 | ||||||||
\(813\) | 18.0000i | 0.631288i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.00000 | 0.280228 | ||||||||
\(816\) | − | 8.00000i | − | 0.280056i | ||||||
\(817\) | 16.0000 | 0.559769 | ||||||||
\(818\) | −10.0000 | − | 10.0000i | −0.349642 | − | 0.349642i | ||||
\(819\) | − | 8.00000i | − | 0.279543i | ||||||
\(820\) | −8.00000 | −0.279372 | ||||||||
\(821\) | − | 10.0000i | − | 0.349002i | −0.984657 | − | 0.174501i | \(-0.944169\pi\) | ||
0.984657 | − | 0.174501i | \(-0.0558313\pi\) | |||||||
\(822\) | −18.0000 | + | 18.0000i | −0.627822 | + | 0.627822i | ||||
\(823\) | 14.0000 | 0.488009 | 0.244005 | − | 0.969774i | \(-0.421539\pi\) | ||||
0.244005 | + | 0.969774i | \(0.421539\pi\) | |||||||
\(824\) | −12.0000 | + | 12.0000i | −0.418040 | + | 0.418040i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.00000 | + | 8.00000i | −0.278356 | + | 0.278356i | ||||
\(827\) | − | 12.0000i | − | 0.417281i | −0.977992 | − | 0.208640i | \(-0.933096\pi\) | ||
0.977992 | − | 0.208640i | \(-0.0669038\pi\) | |||||||
\(828\) | − | 8.00000i | − | 0.278019i | ||||||
\(829\) | 4.00000i | 0.138926i | 0.997585 | + | 0.0694629i | \(0.0221285\pi\) | ||||
−0.997585 | + | 0.0694629i | \(0.977871\pi\) | |||||||
\(830\) | 32.0000 | + | 32.0000i | 1.11074 | + | 1.11074i | ||||
\(831\) | 28.0000 | 0.971309 | ||||||||
\(832\) | −32.0000 | −1.10940 | ||||||||
\(833\) | 6.00000 | 0.207888 | ||||||||
\(834\) | −4.00000 | − | 4.00000i | −0.138509 | − | 0.138509i | ||||
\(835\) | 16.0000i | 0.553703i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.00000i | 0.0691301i | ||||||||
\(838\) | 24.0000 | − | 24.0000i | 0.829066 | − | 0.829066i | ||||
\(839\) | 20.0000 | 0.690477 | 0.345238 | − | 0.938515i | \(-0.387798\pi\) | ||||
0.345238 | + | 0.938515i | \(0.387798\pi\) | |||||||
\(840\) | −8.00000 | + | 8.00000i | −0.276026 | + | 0.276026i | ||||
\(841\) | −7.00000 | −0.241379 | ||||||||
\(842\) | −20.0000 | + | 20.0000i | −0.689246 | + | 0.689246i | ||||
\(843\) | 18.0000i | 0.619953i | ||||||||
\(844\) | −40.0000 | −1.37686 | ||||||||
\(845\) | − | 6.00000i | − | 0.206406i | ||||||
\(846\) | −12.0000 | − | 12.0000i | −0.412568 | − | 0.412568i | ||||
\(847\) | −22.0000 | −0.755929 | ||||||||
\(848\) | − | 24.0000i | − | 0.824163i | ||||||
\(849\) | −4.00000 | −0.137280 | ||||||||
\(850\) | 2.00000 | + | 2.00000i | 0.0685994 | + | 0.0685994i | ||||
\(851\) | 32.0000i | 1.09695i | ||||||||
\(852\) | 24.0000 | 0.822226 | ||||||||
\(853\) | − | 24.0000i | − | 0.821744i | −0.911693 | − | 0.410872i | \(-0.865224\pi\) | ||
0.911693 | − | 0.410872i | \(-0.134776\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.00000 | 0.273594 | ||||||||
\(856\) | −24.0000 | − | 24.0000i | −0.820303 | − | 0.820303i | ||||
\(857\) | 18.0000 | 0.614868 | 0.307434 | − | 0.951569i | \(-0.400530\pi\) | ||||
0.307434 | + | 0.951569i | \(0.400530\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.0000i | 1.50126i | 0.660722 | + | 0.750630i | \(0.270250\pi\) | ||||
−0.660722 | + | 0.750630i | \(0.729750\pi\) | |||||||
\(860\) | 16.0000i | 0.545595i | ||||||||
\(861\) | 4.00000i | 0.136320i | ||||||||
\(862\) | −12.0000 | − | 12.0000i | −0.408722 | − | 0.408722i | ||||
\(863\) | 24.0000 | 0.816970 | 0.408485 | − | 0.912765i | \(-0.366057\pi\) | ||||
0.408485 | + | 0.912765i | \(0.366057\pi\) | |||||||
\(864\) | −4.00000 | + | 4.00000i | −0.136083 | + | 0.136083i | ||||
\(865\) | −12.0000 | −0.408012 | ||||||||
\(866\) | −14.0000 | − | 14.0000i | −0.475739 | − | 0.475739i | ||||
\(867\) | 13.0000i | 0.441503i | ||||||||
\(868\) | − | 8.00000i | − | 0.271538i | ||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −12.0000 | + | 12.0000i | −0.406838 | + | 0.406838i | ||||
\(871\) | −48.0000 | −1.62642 | ||||||||
\(872\) | 8.00000 | + | 8.00000i | 0.270914 | + | 0.270914i | ||||
\(873\) | 2.00000 | 0.0676897 | ||||||||
\(874\) | 16.0000 | − | 16.0000i | 0.541208 | − | 0.541208i | ||||
\(875\) | − | 24.0000i | − | 0.811348i | ||||||
\(876\) | −12.0000 | −0.405442 | ||||||||
\(877\) | − | 32.0000i | − | 1.08056i | −0.841484 | − | 0.540282i | \(-0.818318\pi\) | ||
0.841484 | − | 0.540282i | \(-0.181682\pi\) | |||||||
\(878\) | 30.0000 | + | 30.0000i | 1.01245 | + | 1.01245i | ||||
\(879\) | 6.00000 | 0.202375 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.00000 | 0.0673817 | 0.0336909 | − | 0.999432i | \(-0.489274\pi\) | ||||
0.0336909 | + | 0.999432i | \(0.489274\pi\) | |||||||
\(882\) | −3.00000 | − | 3.00000i | −0.101015 | − | 0.101015i | ||||
\(883\) | − | 4.00000i | − | 0.134611i | −0.997732 | − | 0.0673054i | \(-0.978560\pi\) | ||
0.997732 | − | 0.0673054i | \(-0.0214402\pi\) | |||||||
\(884\) | −16.0000 | −0.538138 | ||||||||
\(885\) | 8.00000i | 0.268917i | ||||||||
\(886\) | −24.0000 | + | 24.0000i | −0.806296 | + | 0.806296i | ||||
\(887\) | 48.0000 | 1.61168 | 0.805841 | − | 0.592132i | \(-0.201714\pi\) | ||||
0.805841 | + | 0.592132i | \(0.201714\pi\) | |||||||
\(888\) | 16.0000 | − | 16.0000i | 0.536925 | − | 0.536925i | ||||
\(889\) | 4.00000 | 0.134156 | ||||||||
\(890\) | −20.0000 | + | 20.0000i | −0.670402 | + | 0.670402i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 28.0000i | 0.937509i | ||||||||
\(893\) | − | 48.0000i | − | 1.60626i | ||||||
\(894\) | 6.00000 | + | 6.00000i | 0.200670 | + | 0.200670i | ||||
\(895\) | −8.00000 | −0.267411 | ||||||||
\(896\) | 16.0000 | − | 16.0000i | 0.534522 | − | 0.534522i | ||||
\(897\) | −16.0000 | −0.534224 | ||||||||
\(898\) | −30.0000 | − | 30.0000i | −1.00111 | − | 1.00111i | ||||
\(899\) | − | 12.0000i | − | 0.400222i | ||||||
\(900\) | − | 2.00000i | − | 0.0666667i | ||||||
\(901\) | − | 12.0000i | − | 0.399778i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.00000 | 0.266223 | ||||||||
\(904\) | −12.0000 | + | 12.0000i | −0.399114 | + | 0.399114i | ||||
\(905\) | 40.0000 | 1.32964 | ||||||||
\(906\) | 18.0000 | − | 18.0000i | 0.598010 | − | 0.598010i | ||||
\(907\) | 28.0000i | 0.929725i | 0.885383 | + | 0.464862i | \(0.153896\pi\) | ||||
−0.885383 | + | 0.464862i | \(0.846104\pi\) | |||||||
\(908\) | −16.0000 | −0.530979 | ||||||||
\(909\) | 10.0000i | 0.331679i | ||||||||
\(910\) | 16.0000 | + | 16.0000i | 0.530395 | + | 0.530395i | ||||
\(911\) | −48.0000 | −1.59031 | −0.795155 | − | 0.606406i | \(-0.792611\pi\) | ||||
−0.795155 | + | 0.606406i | \(0.792611\pi\) | |||||||
\(912\) | −16.0000 | −0.529813 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 22.0000 | + | 22.0000i | 0.727695 | + | 0.727695i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.00000 | −0.264327 | ||||||||
\(917\) | 40.0000i | 1.32092i | ||||||||
\(918\) | −2.00000 | + | 2.00000i | −0.0660098 | + | 0.0660098i | ||||
\(919\) | 30.0000 | 0.989609 | 0.494804 | − | 0.869004i | \(-0.335240\pi\) | ||||
0.494804 | + | 0.869004i | \(0.335240\pi\) | |||||||
\(920\) | 16.0000 | + | 16.0000i | 0.527504 | + | 0.527504i | ||||
\(921\) | −12.0000 | −0.395413 | ||||||||
\(922\) | 30.0000 | − | 30.0000i | 0.987997 | − | 0.987997i | ||||
\(923\) | − | 48.0000i | − | 1.57994i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.00000i | 0.263038i | ||||||||
\(926\) | 26.0000 | + | 26.0000i | 0.854413 | + | 0.854413i | ||||
\(927\) | 6.00000 | 0.197066 | ||||||||
\(928\) | 24.0000 | − | 24.0000i | 0.787839 | − | 0.787839i | ||||
\(929\) | −50.0000 | −1.64045 | −0.820223 | − | 0.572043i | \(-0.806151\pi\) | ||||
−0.820223 | + | 0.572043i | \(0.806151\pi\) | |||||||
\(930\) | −4.00000 | − | 4.00000i | −0.131165 | − | 0.131165i | ||||
\(931\) | − | 12.0000i | − | 0.393284i | ||||||
\(932\) | 28.0000i | 0.917170i | ||||||||
\(933\) | 8.00000i | 0.261908i | ||||||||
\(934\) | 8.00000 | − | 8.00000i | 0.261768 | − | 0.261768i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 8.00000 | + | 8.00000i | 0.261488 | + | 0.261488i | ||||
\(937\) | 38.0000 | 1.24141 | 0.620703 | − | 0.784046i | \(-0.286847\pi\) | ||||
0.620703 | + | 0.784046i | \(0.286847\pi\) | |||||||
\(938\) | 24.0000 | − | 24.0000i | 0.783628 | − | 0.783628i | ||||
\(939\) | − | 14.0000i | − | 0.456873i | ||||||
\(940\) | 48.0000 | 1.56559 | ||||||||
\(941\) | 30.0000i | 0.977972i | 0.872292 | + | 0.488986i | \(0.162633\pi\) | ||||
−0.872292 | + | 0.488986i | \(0.837367\pi\) | |||||||
\(942\) | −8.00000 | − | 8.00000i | −0.260654 | − | 0.260654i | ||||
\(943\) | 8.00000 | 0.260516 | ||||||||
\(944\) | − | 16.0000i | − | 0.520756i | ||||||
\(945\) | 4.00000 | 0.130120 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 12.0000i | − | 0.389948i | −0.980808 | − | 0.194974i | \(-0.937538\pi\) | ||
0.980808 | − | 0.194974i | \(-0.0624622\pi\) | |||||||
\(948\) | 20.0000 | 0.649570 | ||||||||
\(949\) | 24.0000i | 0.779073i | ||||||||
\(950\) | 4.00000 | − | 4.00000i | 0.129777 | − | 0.129777i | ||||
\(951\) | −22.0000 | −0.713399 | ||||||||
\(952\) | 8.00000 | − | 8.00000i | 0.259281 | − | 0.259281i | ||||
\(953\) | −6.00000 | −0.194359 | −0.0971795 | − | 0.995267i | \(-0.530982\pi\) | ||||
−0.0971795 | + | 0.995267i | \(0.530982\pi\) | |||||||
\(954\) | −6.00000 | + | 6.00000i | −0.194257 | + | 0.194257i | ||||
\(955\) | − | 16.0000i | − | 0.517748i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −20.0000 | − | 20.0000i | −0.646171 | − | 0.646171i | ||||
\(959\) | −36.0000 | −1.16250 | ||||||||
\(960\) | − | 16.0000i | − | 0.516398i | ||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | −32.0000 | − | 32.0000i | −1.03172 | − | 1.03172i | ||||
\(963\) | 12.0000i | 0.386695i | ||||||||
\(964\) | 4.00000i | 0.128831i | ||||||||
\(965\) | − | 12.0000i | − | 0.386294i | ||||||
\(966\) | 8.00000 | − | 8.00000i | 0.257396 | − | 0.257396i | ||||
\(967\) | −22.0000 | −0.707472 | −0.353736 | − | 0.935345i | \(-0.615089\pi\) | ||||
−0.353736 | + | 0.935345i | \(0.615089\pi\) | |||||||
\(968\) | 22.0000 | − | 22.0000i | 0.707107 | − | 0.707107i | ||||
\(969\) | −8.00000 | −0.256997 | ||||||||
\(970\) | −4.00000 | + | 4.00000i | −0.128432 | + | 0.128432i | ||||
\(971\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(972\) | 2.00000 | 0.0641500 | ||||||||
\(973\) | − | 8.00000i | − | 0.256468i | ||||||
\(974\) | −38.0000 | − | 38.0000i | −1.21760 | − | 1.21760i | ||||
\(975\) | −4.00000 | −0.128103 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.00000 | −0.0639857 | −0.0319928 | − | 0.999488i | \(-0.510185\pi\) | ||||
−0.0319928 | + | 0.999488i | \(0.510185\pi\) | |||||||
\(978\) | 4.00000 | + | 4.00000i | 0.127906 | + | 0.127906i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 12.0000 | 0.383326 | ||||||||
\(981\) | − | 4.00000i | − | 0.127710i | ||||||
\(982\) | −20.0000 | + | 20.0000i | −0.638226 | + | 0.638226i | ||||
\(983\) | −16.0000 | −0.510321 | −0.255160 | − | 0.966899i | \(-0.582128\pi\) | ||||
−0.255160 | + | 0.966899i | \(0.582128\pi\) | |||||||
\(984\) | −4.00000 | − | 4.00000i | −0.127515 | − | 0.127515i | ||||
\(985\) | 4.00000 | 0.127451 | ||||||||
\(986\) | 12.0000 | − | 12.0000i | 0.382158 | − | 0.382158i | ||||
\(987\) | − | 24.0000i | − | 0.763928i | ||||||
\(988\) | 32.0000i | 1.01806i | ||||||||
\(989\) | − | 16.0000i | − | 0.508770i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.00000 | 0.0635321 | 0.0317660 | − | 0.999495i | \(-0.489887\pi\) | ||||
0.0317660 | + | 0.999495i | \(0.489887\pi\) | |||||||
\(992\) | 8.00000 | + | 8.00000i | 0.254000 | + | 0.254000i | ||||
\(993\) | 20.0000 | 0.634681 | ||||||||
\(994\) | 24.0000 | + | 24.0000i | 0.761234 | + | 0.761234i | ||||
\(995\) | 20.0000i | 0.634043i | ||||||||
\(996\) | 32.0000i | 1.01396i | ||||||||
\(997\) | 48.0000i | 1.52018i | 0.649821 | + | 0.760088i | \(0.274844\pi\) | ||||
−0.649821 | + | 0.760088i | \(0.725156\pi\) | |||||||
\(998\) | −36.0000 | + | 36.0000i | −1.13956 | + | 1.13956i | ||||
\(999\) | −8.00000 | −0.253109 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))