Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [600,2,Mod(349,600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 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("600.349");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 600.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.79102412128\) |
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: | no (minimal twist has level 24) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 349.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 600.349 |
Dual form | 600.2.d.c.349.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).
\(n\) | \(151\) | \(301\) | \(401\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 2.00000i | 1.00000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | − | 1.00000i | −0.408248 | − | 0.408248i | ||||
\(7\) | 2.00000i | 0.755929i | 0.925820 | + | 0.377964i | \(0.123376\pi\) | ||||
−0.925820 | + | 0.377964i | \(0.876624\pi\) | |||||||
\(8\) | −2.00000 | + | 2.00000i | −0.707107 | + | 0.707107i | ||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | − | 2.00000i | − | 0.577350i | ||||||
\(13\) | −4.00000 | −1.10940 | −0.554700 | − | 0.832050i | \(-0.687167\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | −2.00000 | + | 2.00000i | −0.534522 | + | 0.534522i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 2.00000i | 0.485071i | 0.970143 | + | 0.242536i | \(0.0779791\pi\) | ||||
−0.970143 | + | 0.242536i | \(0.922021\pi\) | |||||||
\(18\) | 1.00000 | + | 1.00000i | 0.235702 | + | 0.235702i | ||||
\(19\) | 4.00000i | 0.917663i | 0.888523 | + | 0.458831i | \(0.151732\pi\) | ||||
−0.888523 | + | 0.458831i | \(0.848268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 2.00000i | − | 0.436436i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000i | 0.834058i | 0.908893 | + | 0.417029i | \(0.136929\pi\) | ||||
−0.908893 | + | 0.417029i | \(0.863071\pi\) | |||||||
\(24\) | 2.00000 | − | 2.00000i | 0.408248 | − | 0.408248i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.00000 | − | 4.00000i | −0.784465 | − | 0.784465i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −4.00000 | −0.755929 | ||||||||
\(29\) | − | 6.00000i | − | 1.11417i | −0.830455 | − | 0.557086i | \(-0.811919\pi\) | ||
0.830455 | − | 0.557086i | \(-0.188081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 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 | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.00000i | 0.333333i | ||||||||
\(37\) | −8.00000 | −1.31519 | −0.657596 | − | 0.753371i | \(-0.728427\pi\) | ||||
−0.657596 | + | 0.753371i | \(0.728427\pi\) | |||||||
\(38\) | −4.00000 | + | 4.00000i | −0.648886 | + | 0.648886i | ||||
\(39\) | 4.00000 | 0.640513 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 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 | ||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.00000 | + | 4.00000i | −0.589768 | + | 0.589768i | ||||
\(47\) | 12.0000i | 1.75038i | 0.483779 | + | 0.875190i | \(0.339264\pi\) | ||||
−0.483779 | + | 0.875190i | \(0.660736\pi\) | |||||||
\(48\) | 4.00000 | 0.577350 | ||||||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 2.00000i | − | 0.280056i | ||||||
\(52\) | − | 8.00000i | − | 1.10940i | ||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | −1.00000 | − | 1.00000i | −0.136083 | − | 0.136083i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.00000 | − | 4.00000i | −0.534522 | − | 0.534522i | ||||
\(57\) | − | 4.00000i | − | 0.529813i | ||||||
\(58\) | 6.00000 | − | 6.00000i | 0.787839 | − | 0.787839i | ||||
\(59\) | 4.00000i | 0.520756i | 0.965507 | + | 0.260378i | \(0.0838471\pi\) | ||||
−0.965507 | + | 0.260378i | \(0.916153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 2.00000 | + | 2.00000i | 0.254000 | + | 0.254000i | ||||
\(63\) | 2.00000i | 0.251976i | ||||||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.0000 | 1.46603 | 0.733017 | − | 0.680211i | \(-0.238112\pi\) | ||||
0.733017 | + | 0.680211i | \(0.238112\pi\) | |||||||
\(68\) | −4.00000 | −0.485071 | ||||||||
\(69\) | − | 4.00000i | − | 0.481543i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 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 | ||||
\(73\) | − | 6.00000i | − | 0.702247i | −0.936329 | − | 0.351123i | \(-0.885800\pi\) | ||
0.936329 | − | 0.351123i | \(-0.114200\pi\) | |||||||
\(74\) | −8.00000 | − | 8.00000i | −0.929981 | − | 0.929981i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −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 | \(-0.690177\pi\) | ||||
−0.562544 | + | 0.826767i | \(0.690177\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.00000 | + | 2.00000i | 0.220863 | + | 0.220863i | ||||
\(83\) | 16.0000 | 1.75623 | 0.878114 | − | 0.478451i | \(-0.158802\pi\) | ||||
0.878114 | + | 0.478451i | \(0.158802\pi\) | |||||||
\(84\) | 4.00000 | 0.436436 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.00000 | − | 4.00000i | −0.431331 | − | 0.431331i | ||||
\(87\) | 6.00000i | 0.643268i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.0000 | 1.06000 | 0.529999 | − | 0.847998i | \(-0.322192\pi\) | ||||
0.529999 | + | 0.847998i | \(0.322192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 8.00000i | − | 0.838628i | ||||||
\(92\) | −8.00000 | −0.834058 | ||||||||
\(93\) | −2.00000 | −0.207390 | ||||||||
\(94\) | −12.0000 | + | 12.0000i | −1.23771 | + | 1.23771i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 4.00000 | + | 4.00000i | 0.408248 | + | 0.408248i | ||||
\(97\) | 2.00000i | 0.203069i | 0.994832 | + | 0.101535i | \(0.0323753\pi\) | ||||
−0.994832 | + | 0.101535i | \(0.967625\pi\) | |||||||
\(98\) | 3.00000 | + | 3.00000i | 0.303046 | + | 0.303046i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.0000i | 0.995037i | 0.867453 | + | 0.497519i | \(0.165755\pi\) | ||||
−0.867453 | + | 0.497519i | \(0.834245\pi\) | |||||||
\(102\) | 2.00000 | − | 2.00000i | 0.198030 | − | 0.198030i | ||||
\(103\) | − | 6.00000i | − | 0.591198i | −0.955312 | − | 0.295599i | \(-0.904481\pi\) | ||
0.955312 | − | 0.295599i | \(-0.0955191\pi\) | |||||||
\(104\) | 8.00000 | − | 8.00000i | 0.784465 | − | 0.784465i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | + | 6.00000i | 0.582772 | + | 0.582772i | ||||
\(107\) | 12.0000 | 1.16008 | 0.580042 | − | 0.814587i | \(-0.303036\pi\) | ||||
0.580042 | + | 0.814587i | \(0.303036\pi\) | |||||||
\(108\) | − | 2.00000i | − | 0.192450i | ||||||
\(109\) | 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 | ||||||||
\(112\) | − | 8.00000i | − | 0.755929i | ||||||
\(113\) | − | 6.00000i | − | 0.564433i | −0.959351 | − | 0.282216i | \(-0.908930\pi\) | ||
0.959351 | − | 0.282216i | \(-0.0910696\pi\) | |||||||
\(114\) | 4.00000 | − | 4.00000i | 0.374634 | − | 0.374634i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 12.0000 | 1.11417 | ||||||||
\(117\) | −4.00000 | −0.369800 | ||||||||
\(118\) | −4.00000 | + | 4.00000i | −0.368230 | + | 0.368230i | ||||
\(119\) | −4.00000 | −0.366679 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.0000 | 1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.00000 | −0.180334 | ||||||||
\(124\) | 4.00000i | 0.359211i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.00000 | + | 2.00000i | −0.178174 | + | 0.178174i | ||||
\(127\) | 2.00000i | 0.177471i | 0.996055 | + | 0.0887357i | \(0.0282826\pi\) | ||||
−0.996055 | + | 0.0887357i | \(0.971717\pi\) | |||||||
\(128\) | 8.00000 | − | 8.00000i | 0.707107 | − | 0.707107i | ||||
\(129\) | 4.00000 | 0.352180 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.0000i | 1.74741i | 0.486458 | + | 0.873704i | \(0.338289\pi\) | ||||
−0.486458 | + | 0.873704i | \(0.661711\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.00000 | −0.693688 | ||||||||
\(134\) | 12.0000 | + | 12.0000i | 1.03664 | + | 1.03664i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.00000 | − | 4.00000i | −0.342997 | − | 0.342997i | ||||
\(137\) | − | 18.0000i | − | 1.53784i | −0.639343 | − | 0.768922i | \(-0.720793\pi\) | ||
0.639343 | − | 0.768922i | \(-0.279207\pi\) | |||||||
\(138\) | 4.00000 | − | 4.00000i | 0.340503 | − | 0.340503i | ||||
\(139\) | 4.00000i | 0.339276i | 0.985506 | + | 0.169638i | \(0.0542598\pi\) | ||||
−0.985506 | + | 0.169638i | \(0.945740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 12.0000i | − | 1.01058i | ||||||
\(142\) | 12.0000 | + | 12.0000i | 1.00702 | + | 1.00702i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.00000 | −0.333333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.00000 | − | 6.00000i | 0.496564 | − | 0.496564i | ||||
\(147\) | −3.00000 | −0.247436 | ||||||||
\(148\) | − | 16.0000i | − | 1.31519i | ||||||
\(149\) | − | 6.00000i | − | 0.491539i | −0.969328 | − | 0.245770i | \(-0.920959\pi\) | ||
0.969328 | − | 0.245770i | \(-0.0790407\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −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 | ||||
\(153\) | 2.00000i | 0.161690i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 8.00000i | 0.640513i | ||||||||
\(157\) | −8.00000 | −0.638470 | −0.319235 | − | 0.947676i | \(-0.603426\pi\) | ||||
−0.319235 | + | 0.947676i | \(0.603426\pi\) | |||||||
\(158\) | −10.0000 | − | 10.0000i | −0.795557 | − | 0.795557i | ||||
\(159\) | −6.00000 | −0.475831 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.00000 | −0.630488 | ||||||||
\(162\) | 1.00000 | + | 1.00000i | 0.0785674 | + | 0.0785674i | ||||
\(163\) | −4.00000 | −0.313304 | −0.156652 | − | 0.987654i | \(-0.550070\pi\) | ||||
−0.156652 | + | 0.987654i | \(0.550070\pi\) | |||||||
\(164\) | 4.00000i | 0.312348i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 16.0000 | + | 16.0000i | 1.24184 | + | 1.24184i | ||||
\(167\) | − | 8.00000i | − | 0.619059i | −0.950890 | − | 0.309529i | \(-0.899829\pi\) | ||
0.950890 | − | 0.309529i | \(-0.100171\pi\) | |||||||
\(168\) | 4.00000 | + | 4.00000i | 0.308607 | + | 0.308607i | ||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.00000i | 0.305888i | ||||||||
\(172\) | − | 8.00000i | − | 0.609994i | ||||||
\(173\) | 6.00000 | 0.456172 | 0.228086 | − | 0.973641i | \(-0.426753\pi\) | ||||
0.228086 | + | 0.973641i | \(0.426753\pi\) | |||||||
\(174\) | −6.00000 | + | 6.00000i | −0.454859 | + | 0.454859i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 4.00000i | − | 0.300658i | ||||||
\(178\) | 10.0000 | + | 10.0000i | 0.749532 | + | 0.749532i | ||||
\(179\) | 4.00000i | 0.298974i | 0.988764 | + | 0.149487i | \(0.0477622\pi\) | ||||
−0.988764 | + | 0.149487i | \(0.952238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.0000i | 1.48659i | 0.668965 | + | 0.743294i | \(0.266738\pi\) | ||||
−0.668965 | + | 0.743294i | \(0.733262\pi\) | |||||||
\(182\) | 8.00000 | − | 8.00000i | 0.592999 | − | 0.592999i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.00000 | − | 8.00000i | −0.589768 | − | 0.589768i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.00000 | − | 2.00000i | −0.146647 | − | 0.146647i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −24.0000 | −1.75038 | ||||||||
\(189\) | − | 2.00000i | − | 0.145479i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.00000 | −0.578860 | −0.289430 | − | 0.957199i | \(-0.593466\pi\) | ||||
−0.289430 | + | 0.957199i | \(0.593466\pi\) | |||||||
\(192\) | 8.00000i | 0.577350i | ||||||||
\(193\) | − | 6.00000i | − | 0.431889i | −0.976406 | − | 0.215945i | \(-0.930717\pi\) | ||
0.976406 | − | 0.215945i | \(-0.0692831\pi\) | |||||||
\(194\) | −2.00000 | + | 2.00000i | −0.143592 | + | 0.143592i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.00000i | 0.428571i | ||||||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.0000 | −0.708881 | −0.354441 | − | 0.935079i | \(-0.615329\pi\) | ||||
−0.354441 | + | 0.935079i | \(0.615329\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.0000 | −0.846415 | ||||||||
\(202\) | −10.0000 | + | 10.0000i | −0.703598 | + | 0.703598i | ||||
\(203\) | 12.0000 | 0.842235 | ||||||||
\(204\) | 4.00000 | 0.280056 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.00000 | − | 6.00000i | 0.418040 | − | 0.418040i | ||||
\(207\) | 4.00000i | 0.278019i | ||||||||
\(208\) | 16.0000 | 1.10940 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 20.0000i | − | 1.37686i | −0.725304 | − | 0.688428i | \(-0.758301\pi\) | ||
0.725304 | − | 0.688428i | \(-0.241699\pi\) | |||||||
\(212\) | 12.0000i | 0.824163i | ||||||||
\(213\) | −12.0000 | −0.822226 | ||||||||
\(214\) | 12.0000 | + | 12.0000i | 0.820303 | + | 0.820303i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.00000 | − | 2.00000i | 0.136083 | − | 0.136083i | ||||
\(217\) | 4.00000i | 0.271538i | ||||||||
\(218\) | −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 | ||||
\(223\) | 14.0000i | 0.937509i | 0.883328 | + | 0.468755i | \(0.155297\pi\) | ||||
−0.883328 | + | 0.468755i | \(0.844703\pi\) | |||||||
\(224\) | 8.00000 | − | 8.00000i | 0.534522 | − | 0.534522i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.00000 | − | 6.00000i | 0.399114 | − | 0.399114i | ||||
\(227\) | −8.00000 | −0.530979 | −0.265489 | − | 0.964114i | \(-0.585534\pi\) | ||||
−0.265489 | + | 0.964114i | \(0.585534\pi\) | |||||||
\(228\) | 8.00000 | 0.529813 | ||||||||
\(229\) | 4.00000i | 0.264327i | 0.991228 | + | 0.132164i | \(0.0421925\pi\) | ||||
−0.991228 | + | 0.132164i | \(0.957808\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12.0000 | + | 12.0000i | 0.787839 | + | 0.787839i | ||||
\(233\) | 14.0000i | 0.917170i | 0.888650 | + | 0.458585i | \(0.151644\pi\) | ||||
−0.888650 | + | 0.458585i | \(0.848356\pi\) | |||||||
\(234\) | −4.00000 | − | 4.00000i | −0.261488 | − | 0.261488i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −8.00000 | −0.520756 | ||||||||
\(237\) | 10.0000 | 0.649570 | ||||||||
\(238\) | −4.00000 | − | 4.00000i | −0.259281 | − | 0.259281i | ||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 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 | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.00000 | − | 2.00000i | −0.127515 | − | 0.127515i | ||||
\(247\) | − | 16.0000i | − | 1.01806i | ||||||
\(248\) | −4.00000 | + | 4.00000i | −0.254000 | + | 0.254000i | ||||
\(249\) | −16.0000 | −1.01396 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | −4.00000 | −0.251976 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −2.00000 | + | 2.00000i | −0.125491 | + | 0.125491i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | − | 18.0000i | − | 1.12281i | −0.827541 | − | 0.561405i | \(-0.810261\pi\) | ||
0.827541 | − | 0.561405i | \(-0.189739\pi\) | |||||||
\(258\) | 4.00000 | + | 4.00000i | 0.249029 | + | 0.249029i | ||||
\(259\) | − | 16.0000i | − | 0.994192i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 6.00000i | − | 0.371391i | ||||||
\(262\) | −20.0000 | + | 20.0000i | −1.23560 | + | 1.23560i | ||||
\(263\) | − | 16.0000i | − | 0.986602i | −0.869859 | − | 0.493301i | \(-0.835790\pi\) | ||
0.869859 | − | 0.493301i | \(-0.164210\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −8.00000 | − | 8.00000i | −0.490511 | − | 0.490511i | ||||
\(267\) | −10.0000 | −0.611990 | ||||||||
\(268\) | 24.0000i | 1.46603i | ||||||||
\(269\) | − | 6.00000i | − | 0.365826i | −0.983129 | − | 0.182913i | \(-0.941447\pi\) | ||
0.983129 | − | 0.182913i | \(-0.0585527\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.0000 | −1.09342 | −0.546711 | − | 0.837321i | \(-0.684120\pi\) | ||||
−0.546711 | + | 0.837321i | \(0.684120\pi\) | |||||||
\(272\) | − | 8.00000i | − | 0.485071i | ||||||
\(273\) | 8.00000i | 0.484182i | ||||||||
\(274\) | 18.0000 | − | 18.0000i | 1.08742 | − | 1.08742i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 8.00000 | 0.481543 | ||||||||
\(277\) | −28.0000 | −1.68236 | −0.841178 | − | 0.540758i | \(-0.818138\pi\) | ||||
−0.841178 | + | 0.540758i | \(0.818138\pi\) | |||||||
\(278\) | −4.00000 | + | 4.00000i | −0.239904 | + | 0.239904i | ||||
\(279\) | 2.00000 | 0.119737 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −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 | ||||
\(283\) | −4.00000 | −0.237775 | −0.118888 | − | 0.992908i | \(-0.537933\pi\) | ||||
−0.118888 | + | 0.992908i | \(0.537933\pi\) | |||||||
\(284\) | 24.0000i | 1.42414i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.00000i | 0.236113i | ||||||||
\(288\) | −4.00000 | − | 4.00000i | −0.235702 | − | 0.235702i | ||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 2.00000i | − | 0.117242i | ||||||
\(292\) | 12.0000 | 0.702247 | ||||||||
\(293\) | 6.00000 | 0.350524 | 0.175262 | − | 0.984522i | \(-0.443923\pi\) | ||||
0.175262 | + | 0.984522i | \(0.443923\pi\) | |||||||
\(294\) | −3.00000 | − | 3.00000i | −0.174964 | − | 0.174964i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 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 | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 8.00000i | − | 0.461112i | ||||||
\(302\) | −18.0000 | − | 18.0000i | −1.03578 | − | 1.03578i | ||||
\(303\) | − | 10.0000i | − | 0.574485i | ||||||
\(304\) | − | 16.0000i | − | 0.917663i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.00000 | + | 2.00000i | −0.114332 | + | 0.114332i | ||||
\(307\) | 12.0000 | 0.684876 | 0.342438 | − | 0.939540i | \(-0.388747\pi\) | ||||
0.342438 | + | 0.939540i | \(0.388747\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.00000i | 0.341328i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −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 | ||||
\(313\) | 14.0000i | 0.791327i | 0.918396 | + | 0.395663i | \(0.129485\pi\) | ||||
−0.918396 | + | 0.395663i | \(0.870515\pi\) | |||||||
\(314\) | −8.00000 | − | 8.00000i | −0.451466 | − | 0.451466i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 20.0000i | − | 1.12509i | ||||||
\(317\) | 22.0000 | 1.23564 | 0.617822 | − | 0.786318i | \(-0.288015\pi\) | ||||
0.617822 | + | 0.786318i | \(0.288015\pi\) | |||||||
\(318\) | −6.00000 | − | 6.00000i | −0.336463 | − | 0.336463i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.0000 | −0.669775 | ||||||||
\(322\) | −8.00000 | − | 8.00000i | −0.445823 | − | 0.445823i | ||||
\(323\) | −8.00000 | −0.445132 | ||||||||
\(324\) | 2.00000i | 0.111111i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.00000 | − | 4.00000i | −0.221540 | − | 0.221540i | ||||
\(327\) | − | 4.00000i | − | 0.221201i | ||||||
\(328\) | −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 | \(-0.814761\pi\) | ||
0.835395 | − | 0.549650i | \(-0.185239\pi\) | |||||||
\(332\) | 32.0000i | 1.75623i | ||||||||
\(333\) | −8.00000 | −0.438397 | ||||||||
\(334\) | 8.00000 | − | 8.00000i | 0.437741 | − | 0.437741i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 8.00000i | 0.436436i | ||||||||
\(337\) | 2.00000i | 0.108947i | 0.998515 | + | 0.0544735i | \(0.0173480\pi\) | ||||
−0.998515 | + | 0.0544735i | \(0.982652\pi\) | |||||||
\(338\) | 3.00000 | + | 3.00000i | 0.163178 | + | 0.163178i | ||||
\(339\) | 6.00000i | 0.325875i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −4.00000 | + | 4.00000i | −0.216295 | + | 0.216295i | ||||
\(343\) | 20.0000i | 1.07990i | ||||||||
\(344\) | 8.00000 | − | 8.00000i | 0.431331 | − | 0.431331i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.00000 | + | 6.00000i | 0.322562 | + | 0.322562i | ||||
\(347\) | −8.00000 | −0.429463 | −0.214731 | − | 0.976673i | \(-0.568888\pi\) | ||||
−0.214731 | + | 0.976673i | \(0.568888\pi\) | |||||||
\(348\) | −12.0000 | −0.643268 | ||||||||
\(349\) | − | 16.0000i | − | 0.856460i | −0.903670 | − | 0.428230i | \(-0.859137\pi\) | ||
0.903670 | − | 0.428230i | \(-0.140863\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.00000 | 0.213504 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 6.00000i | − | 0.319348i | −0.987170 | − | 0.159674i | \(-0.948956\pi\) | ||
0.987170 | − | 0.159674i | \(-0.0510443\pi\) | |||||||
\(354\) | 4.00000 | − | 4.00000i | 0.212598 | − | 0.212598i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 20.0000i | 1.06000i | ||||||||
\(357\) | 4.00000 | 0.211702 | ||||||||
\(358\) | −4.00000 | + | 4.00000i | −0.211407 | + | 0.211407i | ||||
\(359\) | 20.0000 | 1.05556 | 0.527780 | − | 0.849381i | \(-0.323025\pi\) | ||||
0.527780 | + | 0.849381i | \(0.323025\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | −20.0000 | + | 20.0000i | −1.05118 | + | 1.05118i | ||||
\(363\) | −11.0000 | −0.577350 | ||||||||
\(364\) | 16.0000 | 0.838628 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 18.0000i | − | 0.939592i | −0.882775 | − | 0.469796i | \(-0.844327\pi\) | ||
0.882775 | − | 0.469796i | \(-0.155673\pi\) | |||||||
\(368\) | − | 16.0000i | − | 0.834058i | ||||||
\(369\) | 2.00000 | 0.104116 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.0000i | 0.623009i | ||||||||
\(372\) | − | 4.00000i | − | 0.207390i | ||||||
\(373\) | 16.0000 | 0.828449 | 0.414224 | − | 0.910175i | \(-0.364053\pi\) | ||||
0.414224 | + | 0.910175i | \(0.364053\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −24.0000 | − | 24.0000i | −1.23771 | − | 1.23771i | ||||
\(377\) | 24.0000i | 1.23606i | ||||||||
\(378\) | 2.00000 | − | 2.00000i | 0.102869 | − | 0.102869i | ||||
\(379\) | 4.00000i | 0.205466i | 0.994709 | + | 0.102733i | \(0.0327588\pi\) | ||||
−0.994709 | + | 0.102733i | \(0.967241\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 2.00000i | − | 0.102463i | ||||||
\(382\) | −8.00000 | − | 8.00000i | −0.409316 | − | 0.409316i | ||||
\(383\) | 24.0000i | 1.22634i | 0.789950 | + | 0.613171i | \(0.210106\pi\) | ||||
−0.789950 | + | 0.613171i | \(0.789894\pi\) | |||||||
\(384\) | −8.00000 | + | 8.00000i | −0.408248 | + | 0.408248i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.00000 | − | 6.00000i | 0.305392 | − | 0.305392i | ||||
\(387\) | −4.00000 | −0.203331 | ||||||||
\(388\) | −4.00000 | −0.203069 | ||||||||
\(389\) | 34.0000i | 1.72387i | 0.507020 | + | 0.861934i | \(0.330747\pi\) | ||||
−0.507020 | + | 0.861934i | \(0.669253\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.00000 | −0.404577 | ||||||||
\(392\) | −6.00000 | + | 6.00000i | −0.303046 | + | 0.303046i | ||||
\(393\) | − | 20.0000i | − | 1.00887i | ||||||
\(394\) | 2.00000 | + | 2.00000i | 0.100759 | + | 0.100759i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.0000 | 1.60603 | 0.803017 | − | 0.595956i | \(-0.203227\pi\) | ||||
0.803017 | + | 0.595956i | \(0.203227\pi\) | |||||||
\(398\) | −10.0000 | − | 10.0000i | −0.501255 | − | 0.501255i | ||||
\(399\) | 8.00000 | 0.400501 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −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 | ||||
\(403\) | −8.00000 | −0.398508 | ||||||||
\(404\) | −20.0000 | −0.995037 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 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 | \(-0.579522\pi\) | ||||
−0.247234 | + | 0.968956i | \(0.579522\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.0000i | 0.887875i | ||||||||
\(412\) | 12.0000 | 0.591198 | ||||||||
\(413\) | −8.00000 | −0.393654 | ||||||||
\(414\) | −4.00000 | + | 4.00000i | −0.196589 | + | 0.196589i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 16.0000 | + | 16.0000i | 0.784465 | + | 0.784465i | ||||
\(417\) | − | 4.00000i | − | 0.195881i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.0000i | 1.17248i | 0.810139 | + | 0.586238i | \(0.199392\pi\) | ||||
−0.810139 | + | 0.586238i | \(0.800608\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.0000i | 0.974740i | 0.873195 | + | 0.487370i | \(0.162044\pi\) | ||||
−0.873195 | + | 0.487370i | \(0.837956\pi\) | |||||||
\(422\) | 20.0000 | − | 20.0000i | 0.973585 | − | 0.973585i | ||||
\(423\) | 12.0000i | 0.583460i | ||||||||
\(424\) | −12.0000 | + | 12.0000i | −0.582772 | + | 0.582772i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −12.0000 | − | 12.0000i | −0.581402 | − | 0.581402i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 24.0000i | 1.16008i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.0000 | 0.578020 | 0.289010 | − | 0.957326i | \(-0.406674\pi\) | ||||
0.289010 | + | 0.957326i | \(0.406674\pi\) | |||||||
\(432\) | 4.00000 | 0.192450 | ||||||||
\(433\) | 14.0000i | 0.672797i | 0.941720 | + | 0.336399i | \(0.109209\pi\) | ||||
−0.941720 | + | 0.336399i | \(0.890791\pi\) | |||||||
\(434\) | −4.00000 | + | 4.00000i | −0.192006 | + | 0.192006i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.00000 | −0.383131 | ||||||||
\(437\) | −16.0000 | −0.765384 | ||||||||
\(438\) | −6.00000 | + | 6.00000i | −0.286691 | + | 0.286691i | ||||
\(439\) | 30.0000 | 1.43182 | 0.715911 | − | 0.698192i | \(-0.246012\pi\) | ||||
0.715911 | + | 0.698192i | \(0.246012\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.00000 | 0.142857 | ||||||||
\(442\) | 8.00000 | − | 8.00000i | 0.380521 | − | 0.380521i | ||||
\(443\) | −24.0000 | −1.14027 | −0.570137 | − | 0.821549i | \(-0.693110\pi\) | ||||
−0.570137 | + | 0.821549i | \(0.693110\pi\) | |||||||
\(444\) | 16.0000i | 0.759326i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −14.0000 | + | 14.0000i | −0.662919 | + | 0.662919i | ||||
\(447\) | 6.00000i | 0.283790i | ||||||||
\(448\) | 16.0000 | 0.755929 | ||||||||
\(449\) | −30.0000 | −1.41579 | −0.707894 | − | 0.706319i | \(-0.750354\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 12.0000 | 0.564433 | ||||||||
\(453\) | 18.0000 | 0.845714 | ||||||||
\(454\) | −8.00000 | − | 8.00000i | −0.375459 | − | 0.375459i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.00000 | + | 8.00000i | 0.374634 | + | 0.374634i | ||||
\(457\) | 22.0000i | 1.02912i | 0.857455 | + | 0.514558i | \(0.172044\pi\) | ||||
−0.857455 | + | 0.514558i | \(0.827956\pi\) | |||||||
\(458\) | −4.00000 | + | 4.00000i | −0.186908 | + | 0.186908i | ||||
\(459\) | − | 2.00000i | − | 0.0933520i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 30.0000i | − | 1.39724i | −0.715493 | − | 0.698620i | \(-0.753798\pi\) | ||
0.715493 | − | 0.698620i | \(-0.246202\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 26.0000i | − | 1.20832i | −0.796862 | − | 0.604161i | \(-0.793508\pi\) | ||
0.796862 | − | 0.604161i | \(-0.206492\pi\) | |||||||
\(464\) | 24.0000i | 1.11417i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.0000 | + | 14.0000i | −0.648537 | + | 0.648537i | ||||
\(467\) | −8.00000 | −0.370196 | −0.185098 | − | 0.982720i | \(-0.559260\pi\) | ||||
−0.185098 | + | 0.982720i | \(0.559260\pi\) | |||||||
\(468\) | − | 8.00000i | − | 0.369800i | ||||||
\(469\) | 24.0000i | 1.10822i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 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 | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 8.00000i | − | 0.366679i | ||||||
\(477\) | 6.00000 | 0.274721 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −20.0000 | −0.913823 | −0.456912 | − | 0.889512i | \(-0.651044\pi\) | ||||
−0.456912 | + | 0.889512i | \(0.651044\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 32.0000 | 1.45907 | ||||||||
\(482\) | 2.00000 | + | 2.00000i | 0.0910975 | + | 0.0910975i | ||||
\(483\) | 8.00000 | 0.364013 | ||||||||
\(484\) | 22.0000i | 1.00000i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | − | 1.00000i | −0.0453609 | − | 0.0453609i | ||||
\(487\) | − | 38.0000i | − | 1.72194i | −0.508652 | − | 0.860972i | \(-0.669856\pi\) | ||
0.508652 | − | 0.860972i | \(-0.330144\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.00000 | 0.180886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.0000i | 0.902587i | 0.892375 | + | 0.451294i | \(0.149037\pi\) | ||||
−0.892375 | + | 0.451294i | \(0.850963\pi\) | |||||||
\(492\) | − | 4.00000i | − | 0.180334i | ||||||
\(493\) | 12.0000 | 0.540453 | ||||||||
\(494\) | 16.0000 | − | 16.0000i | 0.719874 | − | 0.719874i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.00000 | −0.359211 | ||||||||
\(497\) | 24.0000i | 1.07655i | ||||||||
\(498\) | −16.0000 | − | 16.0000i | −0.716977 | − | 0.716977i | ||||
\(499\) | − | 36.0000i | − | 1.61158i | −0.592200 | − | 0.805791i | \(-0.701741\pi\) | ||
0.592200 | − | 0.805791i | \(-0.298259\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.00000i | 0.357414i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 36.0000i | − | 1.60516i | −0.596544 | − | 0.802580i | \(-0.703460\pi\) | ||
0.596544 | − | 0.802580i | \(-0.296540\pi\) | |||||||
\(504\) | −4.00000 | − | 4.00000i | −0.178174 | − | 0.178174i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.00000 | −0.133235 | ||||||||
\(508\) | −4.00000 | −0.177471 | ||||||||
\(509\) | − | 6.00000i | − | 0.265945i | −0.991120 | − | 0.132973i | \(-0.957548\pi\) | ||
0.991120 | − | 0.132973i | \(-0.0424523\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.0000 | 0.530849 | ||||||||
\(512\) | 16.0000 | + | 16.0000i | 0.707107 | + | 0.707107i | ||||
\(513\) | − | 4.00000i | − | 0.176604i | ||||||
\(514\) | 18.0000 | − | 18.0000i | 0.793946 | − | 0.793946i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 8.00000i | 0.352180i | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 16.0000 | − | 16.0000i | 0.703000 | − | 0.703000i | ||||
\(519\) | −6.00000 | −0.263371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 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 | ||||
\(523\) | 36.0000 | 1.57417 | 0.787085 | − | 0.616844i | \(-0.211589\pi\) | ||||
0.787085 | + | 0.616844i | \(0.211589\pi\) | |||||||
\(524\) | −40.0000 | −1.74741 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.0000 | − | 16.0000i | 0.697633 | − | 0.697633i | ||||
\(527\) | 4.00000i | 0.174243i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | 0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00000i | 0.173585i | ||||||||
\(532\) | − | 16.0000i | − | 0.693688i | ||||||
\(533\) | −8.00000 | −0.346518 | ||||||||
\(534\) | −10.0000 | − | 10.0000i | −0.432742 | − | 0.432742i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −24.0000 | + | 24.0000i | −1.03664 | + | 1.03664i | ||||
\(537\) | − | 4.00000i | − | 0.172613i | ||||||
\(538\) | 6.00000 | − | 6.00000i | 0.258678 | − | 0.258678i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 20.0000i | − | 0.859867i | −0.902861 | − | 0.429934i | \(-0.858537\pi\) | ||
0.902861 | − | 0.429934i | \(-0.141463\pi\) | |||||||
\(542\) | −18.0000 | − | 18.0000i | −0.773166 | − | 0.773166i | ||||
\(543\) | − | 20.0000i | − | 0.858282i | ||||||
\(544\) | 8.00000 | − | 8.00000i | 0.342997 | − | 0.342997i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −8.00000 | + | 8.00000i | −0.342368 | + | 0.342368i | ||||
\(547\) | −28.0000 | −1.19719 | −0.598597 | − | 0.801050i | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(548\) | 36.0000 | 1.53784 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.0000 | 1.02243 | ||||||||
\(552\) | 8.00000 | + | 8.00000i | 0.340503 | + | 0.340503i | ||||
\(553\) | − | 20.0000i | − | 0.850487i | ||||||
\(554\) | −28.0000 | − | 28.0000i | −1.18961 | − | 1.18961i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.00000 | −0.339276 | ||||||||
\(557\) | 42.0000 | 1.77960 | 0.889799 | − | 0.456354i | \(-0.150845\pi\) | ||||
0.889799 | + | 0.456354i | \(0.150845\pi\) | |||||||
\(558\) | 2.00000 | + | 2.00000i | 0.0846668 | + | 0.0846668i | ||||
\(559\) | 16.0000 | 0.676728 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −18.0000 | − | 18.0000i | −0.759284 | − | 0.759284i | ||||
\(563\) | −24.0000 | −1.01148 | −0.505740 | − | 0.862686i | \(-0.668780\pi\) | ||||
−0.505740 | + | 0.862686i | \(0.668780\pi\) | |||||||
\(564\) | 24.0000 | 1.01058 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.00000 | − | 4.00000i | −0.168133 | − | 0.168133i | ||||
\(567\) | 2.00000i | 0.0839921i | ||||||||
\(568\) | −24.0000 | + | 24.0000i | −1.00702 | + | 1.00702i | ||||
\(569\) | 30.0000 | 1.25767 | 0.628833 | − | 0.777541i | \(-0.283533\pi\) | ||||
0.628833 | + | 0.777541i | \(0.283533\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.0000i | 0.836974i | 0.908223 | + | 0.418487i | \(0.137439\pi\) | ||||
−0.908223 | + | 0.418487i | \(0.862561\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.00000 | 0.334205 | ||||||||
\(574\) | −4.00000 | + | 4.00000i | −0.166957 | + | 0.166957i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | − | 8.00000i | − | 0.333333i | ||||||
\(577\) | 42.0000i | 1.74848i | 0.485491 | + | 0.874241i | \(0.338641\pi\) | ||||
−0.485491 | + | 0.874241i | \(0.661359\pi\) | |||||||
\(578\) | 13.0000 | + | 13.0000i | 0.540729 | + | 0.540729i | ||||
\(579\) | 6.00000i | 0.249351i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 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 | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.00000 | + | 6.00000i | 0.247858 | + | 0.247858i | ||||
\(587\) | −28.0000 | −1.15568 | −0.577842 | − | 0.816149i | \(-0.696105\pi\) | ||||
−0.577842 | + | 0.816149i | \(0.696105\pi\) | |||||||
\(588\) | − | 6.00000i | − | 0.247436i | ||||||
\(589\) | 8.00000i | 0.329634i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.00000 | −0.0822690 | ||||||||
\(592\) | 32.0000 | 1.31519 | ||||||||
\(593\) | − | 6.00000i | − | 0.246390i | −0.992382 | − | 0.123195i | \(-0.960686\pi\) | ||
0.992382 | − | 0.123195i | \(-0.0393141\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.0000 | 0.491539 | ||||||||
\(597\) | 10.0000 | 0.409273 | ||||||||
\(598\) | 16.0000 | − | 16.0000i | 0.654289 | − | 0.654289i | ||||
\(599\) | 20.0000 | 0.817178 | 0.408589 | − | 0.912719i | \(-0.366021\pi\) | ||||
0.408589 | + | 0.912719i | \(0.366021\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 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 | ||||
\(603\) | 12.0000 | 0.488678 | ||||||||
\(604\) | − | 36.0000i | − | 1.46482i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 10.0000 | − | 10.0000i | 0.406222 | − | 0.406222i | ||||
\(607\) | 2.00000i | 0.0811775i | 0.999176 | + | 0.0405887i | \(0.0129233\pi\) | ||||
−0.999176 | + | 0.0405887i | \(0.987077\pi\) | |||||||
\(608\) | 16.0000 | − | 16.0000i | 0.648886 | − | 0.648886i | ||||
\(609\) | −12.0000 | −0.486265 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 48.0000i | − | 1.94187i | ||||||
\(612\) | −4.00000 | −0.161690 | ||||||||
\(613\) | 16.0000 | 0.646234 | 0.323117 | − | 0.946359i | \(-0.395269\pi\) | ||||
0.323117 | + | 0.946359i | \(0.395269\pi\) | |||||||
\(614\) | 12.0000 | + | 12.0000i | 0.484281 | + | 0.484281i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.00000i | 0.0805170i | 0.999189 | + | 0.0402585i | \(0.0128181\pi\) | ||||
−0.999189 | + | 0.0402585i | \(0.987182\pi\) | |||||||
\(618\) | −6.00000 | + | 6.00000i | −0.241355 | + | 0.241355i | ||||
\(619\) | − | 36.0000i | − | 1.44696i | −0.690344 | − | 0.723481i | \(-0.742541\pi\) | ||
0.690344 | − | 0.723481i | \(-0.257459\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 4.00000i | − | 0.160514i | ||||||
\(622\) | −8.00000 | − | 8.00000i | −0.320771 | − | 0.320771i | ||||
\(623\) | 20.0000i | 0.801283i | ||||||||
\(624\) | −16.0000 | −0.640513 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −14.0000 | + | 14.0000i | −0.559553 | + | 0.559553i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 16.0000i | − | 0.638470i | ||||||
\(629\) | − | 16.0000i | − | 0.637962i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 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 | ||||
\(633\) | 20.0000i | 0.794929i | ||||||||
\(634\) | 22.0000 | + | 22.0000i | 0.873732 | + | 0.873732i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 12.0000i | − | 0.475831i | ||||||
\(637\) | −12.0000 | −0.475457 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.0000 | 0.474713 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 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 | ||||
\(643\) | −4.00000 | −0.157745 | −0.0788723 | − | 0.996885i | \(-0.525132\pi\) | ||||
−0.0788723 | + | 0.996885i | \(0.525132\pi\) | |||||||
\(644\) | − | 16.0000i | − | 0.630488i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.00000 | − | 8.00000i | −0.314756 | − | 0.314756i | ||||
\(647\) | 12.0000i | 0.471769i | 0.971781 | + | 0.235884i | \(0.0757987\pi\) | ||||
−0.971781 | + | 0.235884i | \(0.924201\pi\) | |||||||
\(648\) | −2.00000 | + | 2.00000i | −0.0785674 | + | 0.0785674i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 4.00000i | − | 0.156772i | ||||||
\(652\) | − | 8.00000i | − | 0.313304i | ||||||
\(653\) | 6.00000 | 0.234798 | 0.117399 | − | 0.993085i | \(-0.462544\pi\) | ||||
0.117399 | + | 0.993085i | \(0.462544\pi\) | |||||||
\(654\) | 4.00000 | − | 4.00000i | 0.156412 | − | 0.156412i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −8.00000 | −0.312348 | ||||||||
\(657\) | − | 6.00000i | − | 0.234082i | ||||||
\(658\) | −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 | \(0.283720\pi\) | ||||
−0.628376 | + | 0.777910i | \(0.716280\pi\) | |||||||
\(662\) | 20.0000 | − | 20.0000i | 0.777322 | − | 0.777322i | ||||
\(663\) | 8.00000i | 0.310694i | ||||||||
\(664\) | −32.0000 | + | 32.0000i | −1.24184 | + | 1.24184i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.00000 | − | 8.00000i | −0.309994 | − | 0.309994i | ||||
\(667\) | 24.0000 | 0.929284 | ||||||||
\(668\) | 16.0000 | 0.619059 | ||||||||
\(669\) | − | 14.0000i | − | 0.541271i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −8.00000 | + | 8.00000i | −0.308607 | + | 0.308607i | ||||
\(673\) | 14.0000i | 0.539660i | 0.962908 | + | 0.269830i | \(0.0869676\pi\) | ||||
−0.962908 | + | 0.269830i | \(0.913032\pi\) | |||||||
\(674\) | −2.00000 | + | 2.00000i | −0.0770371 | + | 0.0770371i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.00000i | 0.230769i | ||||||||
\(677\) | −18.0000 | −0.691796 | −0.345898 | − | 0.938272i | \(-0.612426\pi\) | ||||
−0.345898 | + | 0.938272i | \(0.612426\pi\) | |||||||
\(678\) | −6.00000 | + | 6.00000i | −0.230429 | + | 0.230429i | ||||
\(679\) | −4.00000 | −0.153506 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.00000 | 0.306561 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.0000 | 0.612223 | 0.306111 | − | 0.951996i | \(-0.400972\pi\) | ||||
0.306111 | + | 0.951996i | \(0.400972\pi\) | |||||||
\(684\) | −8.00000 | −0.305888 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −20.0000 | + | 20.0000i | −0.763604 | + | 0.763604i | ||||
\(687\) | − | 4.00000i | − | 0.152610i | ||||||
\(688\) | 16.0000 | 0.609994 | ||||||||
\(689\) | −24.0000 | −0.914327 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.0000i | 0.760836i | 0.924815 | + | 0.380418i | \(0.124220\pi\) | ||||
−0.924815 | + | 0.380418i | \(0.875780\pi\) | |||||||
\(692\) | 12.0000i | 0.456172i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.00000 | − | 8.00000i | −0.303676 | − | 0.303676i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −12.0000 | − | 12.0000i | −0.454859 | − | 0.454859i | ||||
\(697\) | 4.00000i | 0.151511i | ||||||||
\(698\) | 16.0000 | − | 16.0000i | 0.605609 | − | 0.605609i | ||||
\(699\) | − | 14.0000i | − | 0.529529i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 50.0000i | − | 1.88847i | −0.329267 | − | 0.944237i | \(-0.606802\pi\) | ||
0.329267 | − | 0.944237i | \(-0.393198\pi\) | |||||||
\(702\) | 4.00000 | + | 4.00000i | 0.150970 | + | 0.150970i | ||||
\(703\) | − | 32.0000i | − | 1.20690i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.00000 | − | 6.00000i | 0.225813 | − | 0.225813i | ||||
\(707\) | −20.0000 | −0.752177 | ||||||||
\(708\) | 8.00000 | 0.300658 | ||||||||
\(709\) | 4.00000i | 0.150223i | 0.997175 | + | 0.0751116i | \(0.0239313\pi\) | ||||
−0.997175 | + | 0.0751116i | \(0.976069\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.0000 | −0.375029 | ||||||||
\(712\) | −20.0000 | + | 20.0000i | −0.749532 | + | 0.749532i | ||||
\(713\) | 8.00000i | 0.299602i | ||||||||
\(714\) | 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 | \(-0.378351\pi\) | ||||
0.372937 | + | 0.927857i | \(0.378351\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.0000 | 0.446903 | ||||||||
\(722\) | 3.00000 | + | 3.00000i | 0.111648 | + | 0.111648i | ||||
\(723\) | −2.00000 | −0.0743808 | ||||||||
\(724\) | −40.0000 | −1.48659 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −11.0000 | − | 11.0000i | −0.408248 | − | 0.408248i | ||||
\(727\) | 42.0000i | 1.55769i | 0.627214 | + | 0.778847i | \(0.284195\pi\) | ||||
−0.627214 | + | 0.778847i | \(0.715805\pi\) | |||||||
\(728\) | 16.0000 | + | 16.0000i | 0.592999 | + | 0.592999i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 8.00000i | − | 0.295891i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.00000 | −0.147743 | −0.0738717 | − | 0.997268i | \(-0.523536\pi\) | ||||
−0.0738717 | + | 0.997268i | \(0.523536\pi\) | |||||||
\(734\) | 18.0000 | − | 18.0000i | 0.664392 | − | 0.664392i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 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 | \(0.699856\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.0000i | 0.587775i | ||||||||
\(742\) | −12.0000 | + | 12.0000i | −0.440534 | + | 0.440534i | ||||
\(743\) | − | 16.0000i | − | 0.586983i | −0.955962 | − | 0.293492i | \(-0.905183\pi\) | ||
0.955962 | − | 0.293492i | \(-0.0948173\pi\) | |||||||
\(744\) | 4.00000 | − | 4.00000i | 0.146647 | − | 0.146647i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 16.0000 | + | 16.0000i | 0.585802 | + | 0.585802i | ||||
\(747\) | 16.0000 | 0.585409 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24.0000i | 0.876941i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.00000 | 0.0729810 | 0.0364905 | − | 0.999334i | \(-0.488382\pi\) | ||||
0.0364905 | + | 0.999334i | \(0.488382\pi\) | |||||||
\(752\) | − | 48.0000i | − | 1.75038i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −24.0000 | + | 24.0000i | −0.874028 | + | 0.874028i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.00000 | 0.145479 | ||||||||
\(757\) | 12.0000 | 0.436147 | 0.218074 | − | 0.975932i | \(-0.430023\pi\) | ||||
0.218074 | + | 0.975932i | \(0.430023\pi\) | |||||||
\(758\) | −4.00000 | + | 4.00000i | −0.145287 | + | 0.145287i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −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 | ||||
\(763\) | −8.00000 | −0.289619 | ||||||||
\(764\) | − | 16.0000i | − | 0.578860i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −24.0000 | + | 24.0000i | −0.867155 | + | 0.867155i | ||||
\(767\) | − | 16.0000i | − | 0.577727i | ||||||
\(768\) | −16.0000 | −0.577350 | ||||||||
\(769\) | −10.0000 | −0.360609 | −0.180305 | − | 0.983611i | \(-0.557708\pi\) | ||||
−0.180305 | + | 0.983611i | \(0.557708\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.0000i | 0.648254i | ||||||||
\(772\) | 12.0000 | 0.431889 | ||||||||
\(773\) | −34.0000 | −1.22290 | −0.611448 | − | 0.791285i | \(-0.709412\pi\) | ||||
−0.611448 | + | 0.791285i | \(0.709412\pi\) | |||||||
\(774\) | −4.00000 | − | 4.00000i | −0.143777 | − | 0.143777i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.00000 | − | 4.00000i | −0.143592 | − | 0.143592i | ||||
\(777\) | 16.0000i | 0.573997i | ||||||||
\(778\) | −34.0000 | + | 34.0000i | −1.21896 | + | 1.21896i | ||||
\(779\) | 8.00000i | 0.286630i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −8.00000 | − | 8.00000i | −0.286079 | − | 0.286079i | ||||
\(783\) | 6.00000i | 0.214423i | ||||||||
\(784\) | −12.0000 | −0.428571 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 20.0000 | − | 20.0000i | 0.713376 | − | 0.713376i | ||||
\(787\) | 12.0000 | 0.427754 | 0.213877 | − | 0.976861i | \(-0.431391\pi\) | ||||
0.213877 | + | 0.976861i | \(0.431391\pi\) | |||||||
\(788\) | 4.00000i | 0.142494i | ||||||||
\(789\) | 16.0000i | 0.569615i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.0000 | 0.426671 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 32.0000 | + | 32.0000i | 1.13564 | + | 1.13564i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 20.0000i | − | 0.708881i | ||||||
\(797\) | 2.00000 | 0.0708436 | 0.0354218 | − | 0.999372i | \(-0.488723\pi\) | ||||
0.0354218 | + | 0.999372i | \(0.488723\pi\) | |||||||
\(798\) | 8.00000 | + | 8.00000i | 0.283197 | + | 0.283197i | ||||
\(799\) | −24.0000 | −0.849059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.0000 | 0.353333 | ||||||||
\(802\) | −18.0000 | − | 18.0000i | −0.635602 | − | 0.635602i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | − | 24.0000i | − | 0.846415i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.00000 | − | 8.00000i | −0.281788 | − | 0.281788i | ||||
\(807\) | 6.00000i | 0.211210i | ||||||||
\(808\) | −20.0000 | − | 20.0000i | −0.703598 | − | 0.703598i | ||||
\(809\) | 30.0000 | 1.05474 | 0.527372 | − | 0.849635i | \(-0.323177\pi\) | ||||
0.527372 | + | 0.849635i | \(0.323177\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 20.0000i | − | 0.702295i | −0.936320 | − | 0.351147i | \(-0.885792\pi\) | ||
0.936320 | − | 0.351147i | \(-0.114208\pi\) | |||||||
\(812\) | 24.0000i | 0.842235i | ||||||||
\(813\) | 18.0000 | 0.631288 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 8.00000i | 0.280056i | ||||||||
\(817\) | − | 16.0000i | − | 0.559769i | ||||||
\(818\) | −10.0000 | − | 10.0000i | −0.349642 | − | 0.349642i | ||||
\(819\) | − | 8.00000i | − | 0.279543i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.0000i | 0.349002i | 0.984657 | + | 0.174501i | \(0.0558313\pi\) | ||||
−0.984657 | + | 0.174501i | \(0.944169\pi\) | |||||||
\(822\) | −18.0000 | + | 18.0000i | −0.627822 | + | 0.627822i | ||||
\(823\) | 14.0000i | 0.488009i | 0.969774 | + | 0.244005i | \(0.0784612\pi\) | ||||
−0.969774 | + | 0.244005i | \(0.921539\pi\) | |||||||
\(824\) | 12.0000 | + | 12.0000i | 0.418040 | + | 0.418040i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.00000 | − | 8.00000i | −0.278356 | − | 0.278356i | ||||
\(827\) | 12.0000 | 0.417281 | 0.208640 | − | 0.977992i | \(-0.433096\pi\) | ||||
0.208640 | + | 0.977992i | \(0.433096\pi\) | |||||||
\(828\) | −8.00000 | −0.278019 | ||||||||
\(829\) | 4.00000i | 0.138926i | 0.997585 | + | 0.0694629i | \(0.0221285\pi\) | ||||
−0.997585 | + | 0.0694629i | \(0.977871\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 28.0000 | 0.971309 | ||||||||
\(832\) | 32.0000i | 1.10940i | ||||||||
\(833\) | 6.00000i | 0.207888i | ||||||||
\(834\) | 4.00000 | − | 4.00000i | 0.138509 | − | 0.138509i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.00000 | −0.0691301 | ||||||||
\(838\) | −24.0000 | + | 24.0000i | −0.829066 | + | 0.829066i | ||||
\(839\) | −20.0000 | −0.690477 | −0.345238 | − | 0.938515i | \(-0.612202\pi\) | ||||
−0.345238 | + | 0.938515i | \(0.612202\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.00000 | −0.241379 | ||||||||
\(842\) | −20.0000 | + | 20.0000i | −0.689246 | + | 0.689246i | ||||
\(843\) | 18.0000 | 0.619953 | ||||||||
\(844\) | 40.0000 | 1.37686 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −12.0000 | + | 12.0000i | −0.412568 | + | 0.412568i | ||||
\(847\) | 22.0000i | 0.755929i | ||||||||
\(848\) | −24.0000 | −0.824163 | ||||||||
\(849\) | 4.00000 | 0.137280 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 32.0000i | − | 1.09695i | ||||||
\(852\) | − | 24.0000i | − | 0.822226i | ||||||
\(853\) | −24.0000 | −0.821744 | −0.410872 | − | 0.911693i | \(-0.634776\pi\) | ||||
−0.410872 | + | 0.911693i | \(0.634776\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −24.0000 | + | 24.0000i | −0.820303 | + | 0.820303i | ||||
\(857\) | − | 18.0000i | − | 0.614868i | −0.951569 | − | 0.307434i | \(-0.900530\pi\) | ||
0.951569 | − | 0.307434i | \(-0.0994704\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.0000i | 1.50126i | 0.660722 | + | 0.750630i | \(0.270250\pi\) | ||||
−0.660722 | + | 0.750630i | \(0.729750\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 4.00000i | − | 0.136320i | ||||||
\(862\) | 12.0000 | + | 12.0000i | 0.408722 | + | 0.408722i | ||||
\(863\) | 24.0000i | 0.816970i | 0.912765 | + | 0.408485i | \(0.133943\pi\) | ||||
−0.912765 | + | 0.408485i | \(0.866057\pi\) | |||||||
\(864\) | 4.00000 | + | 4.00000i | 0.136083 | + | 0.136083i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −14.0000 | + | 14.0000i | −0.475739 | + | 0.475739i | ||||
\(867\) | −13.0000 | −0.441503 | ||||||||
\(868\) | −8.00000 | −0.271538 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −48.0000 | −1.62642 | ||||||||
\(872\) | −8.00000 | − | 8.00000i | −0.270914 | − | 0.270914i | ||||
\(873\) | 2.00000i | 0.0676897i | ||||||||
\(874\) | −16.0000 | − | 16.0000i | −0.541208 | − | 0.541208i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −12.0000 | −0.405442 | ||||||||
\(877\) | 32.0000 | 1.08056 | 0.540282 | − | 0.841484i | \(-0.318318\pi\) | ||||
0.540282 | + | 0.841484i | \(0.318318\pi\) | |||||||
\(878\) | 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 | ||||
\(883\) | −4.00000 | −0.134611 | −0.0673054 | − | 0.997732i | \(-0.521440\pi\) | ||||
−0.0673054 | + | 0.997732i | \(0.521440\pi\) | |||||||
\(884\) | 16.0000 | 0.538138 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24.0000 | − | 24.0000i | −0.806296 | − | 0.806296i | ||||
\(887\) | − | 48.0000i | − | 1.61168i | −0.592132 | − | 0.805841i | \(-0.701714\pi\) | ||
0.592132 | − | 0.805841i | \(-0.298286\pi\) | |||||||
\(888\) | −16.0000 | + | 16.0000i | −0.536925 | + | 0.536925i | ||||
\(889\) | −4.00000 | −0.134156 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −28.0000 | −0.937509 | ||||||||
\(893\) | −48.0000 | −1.60626 | ||||||||
\(894\) | −6.00000 | + | 6.00000i | −0.200670 | + | 0.200670i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 16.0000 | + | 16.0000i | 0.534522 | + | 0.534522i | ||||
\(897\) | 16.0000i | 0.534224i | ||||||||
\(898\) | −30.0000 | − | 30.0000i | −1.00111 | − | 1.00111i | ||||
\(899\) | − | 12.0000i | − | 0.400222i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.0000i | 0.399778i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.00000i | 0.266223i | ||||||||
\(904\) | 12.0000 | + | 12.0000i | 0.399114 | + | 0.399114i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 18.0000 | + | 18.0000i | 0.598010 | + | 0.598010i | ||||
\(907\) | −28.0000 | −0.929725 | −0.464862 | − | 0.885383i | \(-0.653896\pi\) | ||||
−0.464862 | + | 0.885383i | \(0.653896\pi\) | |||||||
\(908\) | − | 16.0000i | − | 0.530979i | ||||||
\(909\) | 10.0000i | 0.331679i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.0000 | −1.59031 | −0.795155 | − | 0.606406i | \(-0.792611\pi\) | ||||
−0.795155 | + | 0.606406i | \(0.792611\pi\) | |||||||
\(912\) | 16.0000i | 0.529813i | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −22.0000 | + | 22.0000i | −0.727695 | + | 0.727695i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.00000 | −0.264327 | ||||||||
\(917\) | −40.0000 | −1.32092 | ||||||||
\(918\) | 2.00000 | − | 2.00000i | 0.0660098 | − | 0.0660098i | ||||
\(919\) | −30.0000 | −0.989609 | −0.494804 | − | 0.869004i | \(-0.664760\pi\) | ||||
−0.494804 | + | 0.869004i | \(0.664760\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.0000 | −0.395413 | ||||||||
\(922\) | 30.0000 | − | 30.0000i | 0.987997 | − | 0.987997i | ||||
\(923\) | −48.0000 | −1.57994 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 26.0000 | − | 26.0000i | 0.854413 | − | 0.854413i | ||||
\(927\) | − | 6.00000i | − | 0.197066i | ||||||
\(928\) | −24.0000 | + | 24.0000i | −0.787839 | + | 0.787839i | ||||
\(929\) | 50.0000 | 1.64045 | 0.820223 | − | 0.572043i | \(-0.193849\pi\) | ||||
0.820223 | + | 0.572043i | \(0.193849\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.0000i | 0.393284i | ||||||||
\(932\) | −28.0000 | −0.917170 | ||||||||
\(933\) | 8.00000 | 0.261908 | ||||||||
\(934\) | −8.00000 | − | 8.00000i | −0.261768 | − | 0.261768i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 8.00000 | − | 8.00000i | 0.261488 | − | 0.261488i | ||||
\(937\) | − | 38.0000i | − | 1.24141i | −0.784046 | − | 0.620703i | \(-0.786847\pi\) | ||
0.784046 | − | 0.620703i | \(-0.213153\pi\) | |||||||
\(938\) | −24.0000 | + | 24.0000i | −0.783628 | + | 0.783628i | ||||
\(939\) | − | 14.0000i | − | 0.456873i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 30.0000i | − | 0.977972i | −0.872292 | − | 0.488986i | \(-0.837367\pi\) | ||
0.872292 | − | 0.488986i | \(-0.162633\pi\) | |||||||
\(942\) | 8.00000 | + | 8.00000i | 0.260654 | + | 0.260654i | ||||
\(943\) | 8.00000i | 0.260516i | ||||||||
\(944\) | − | 16.0000i | − | 0.520756i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.0000 | 0.389948 | 0.194974 | − | 0.980808i | \(-0.437538\pi\) | ||||
0.194974 | + | 0.980808i | \(0.437538\pi\) | |||||||
\(948\) | 20.0000i | 0.649570i | ||||||||
\(949\) | 24.0000i | 0.779073i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.0000 | −0.713399 | ||||||||
\(952\) | 8.00000 | − | 8.00000i | 0.259281 | − | 0.259281i | ||||
\(953\) | − | 6.00000i | − | 0.194359i | −0.995267 | − | 0.0971795i | \(-0.969018\pi\) | ||
0.995267 | − | 0.0971795i | \(-0.0309821\pi\) | |||||||
\(954\) | 6.00000 | + | 6.00000i | 0.194257 | + | 0.194257i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −20.0000 | − | 20.0000i | −0.646171 | − | 0.646171i | ||||
\(959\) | 36.0000 | 1.16250 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 32.0000 | + | 32.0000i | 1.03172 | + | 1.03172i | ||||
\(963\) | 12.0000 | 0.386695 | ||||||||
\(964\) | 4.00000i | 0.128831i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 8.00000 | + | 8.00000i | 0.257396 | + | 0.257396i | ||||
\(967\) | 22.0000i | 0.707472i | 0.935345 | + | 0.353736i | \(0.115089\pi\) | ||||
−0.935345 | + | 0.353736i | \(0.884911\pi\) | |||||||
\(968\) | −22.0000 | + | 22.0000i | −0.707107 | + | 0.707107i | ||||
\(969\) | 8.00000 | 0.256997 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(972\) | − | 2.00000i | − | 0.0641500i | ||||||
\(973\) | −8.00000 | −0.256468 | ||||||||
\(974\) | 38.0000 | − | 38.0000i | 1.21760 | − | 1.21760i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.00000i | 0.0639857i | 0.999488 | + | 0.0319928i | \(0.0101854\pi\) | ||||
−0.999488 | + | 0.0319928i | \(0.989815\pi\) | |||||||
\(978\) | 4.00000 | + | 4.00000i | 0.127906 | + | 0.127906i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.00000i | 0.127710i | ||||||||
\(982\) | −20.0000 | + | 20.0000i | −0.638226 | + | 0.638226i | ||||
\(983\) | − | 16.0000i | − | 0.510321i | −0.966899 | − | 0.255160i | \(-0.917872\pi\) | ||
0.966899 | − | 0.255160i | \(-0.0821283\pi\) | |||||||
\(984\) | 4.00000 | − | 4.00000i | 0.127515 | − | 0.127515i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 12.0000 | + | 12.0000i | 0.382158 | + | 0.382158i | ||||
\(987\) | 24.0000 | 0.763928 | ||||||||
\(988\) | 32.0000 | 1.01806 | ||||||||
\(989\) | − | 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 | ||||
\(993\) | 20.0000i | 0.634681i | ||||||||
\(994\) | −24.0000 | + | 24.0000i | −0.761234 | + | 0.761234i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 32.0000i | − | 1.01396i | ||||||
\(997\) | −48.0000 | −1.52018 | −0.760088 | − | 0.649821i | \(-0.774844\pi\) | ||||
−0.760088 | + | 0.649821i | \(0.774844\pi\) | |||||||
\(998\) | 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 \(a_p\))