Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [55,2,Mod(32,55)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(55, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("55.32");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 55 = 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 55.e (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.439177211117\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - 5x^{2} + 9 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{4}]$ |
Embedding invariants
Embedding label | 32.1 | ||
Root | \(-1.65831 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 55.32 |
Dual form | 55.2.e.b.43.1 |
$q$-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 \(\left(\mathbb{Z}/55\mathbb{Z}\right)^\times\).
\(n\) | \(12\) | \(46\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(3\) | −2.15831 | + | 2.15831i | −1.24610 | + | 1.24610i | −0.288675 | + | 0.957427i | \(0.593215\pi\) |
−0.957427 | + | 0.288675i | \(0.906785\pi\) | |||||||
\(4\) | 2.00000i | 1.00000i | ||||||||
\(5\) | 1.65831 | − | 1.50000i | 0.741620 | − | 0.670820i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 6.31662i | − | 2.10554i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.31662 | 1.00000 | ||||||||
\(12\) | −4.31662 | − | 4.31662i | −1.24610 | − | 1.24610i | ||||
\(13\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.341688 | + | 6.81662i | −0.0882234 | + | 1.76004i | ||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 3.00000 | + | 3.31662i | 0.670820 | + | 0.741620i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.84169 | − | 2.84169i | 0.592533 | − | 0.592533i | −0.345782 | − | 0.938315i | \(-0.612386\pi\) |
0.938315 | + | 0.345782i | \(0.112386\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | − | 4.97494i | 0.100000 | − | 0.994987i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 7.15831 | + | 7.15831i | 1.37762 | + | 1.37762i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.94987 | −1.78705 | −0.893525 | − | 0.449013i | \(-0.851776\pi\) | ||||
−0.893525 | + | 0.449013i | \(0.851776\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.15831 | + | 7.15831i | −1.24610 | + | 1.24610i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 12.6332 | 2.10554 | ||||||||
\(37\) | 1.47494 | + | 1.47494i | 0.242478 | + | 0.242478i | 0.817875 | − | 0.575396i | \(-0.195152\pi\) |
−0.575396 | + | 0.817875i | \(0.695152\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(44\) | 6.63325i | 1.00000i | ||||||||
\(45\) | −9.47494 | − | 10.4749i | −1.41244 | − | 1.56151i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.31662 | − | 9.31662i | −1.35897 | − | 1.35897i | −0.875190 | − | 0.483779i | \(-0.839264\pi\) |
−0.483779 | − | 0.875190i | \(-0.660736\pi\) | |||||||
\(48\) | 8.63325 | − | 8.63325i | 1.24610 | − | 1.24610i | ||||
\(49\) | 7.00000i | 1.00000i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.63325 | − | 3.63325i | 0.499065 | − | 0.499065i | −0.412082 | − | 0.911147i | \(-0.635198\pi\) |
0.911147 | + | 0.412082i | \(0.135198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.50000 | − | 4.97494i | 0.741620 | − | 0.670820i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 3.31662i | − | 0.431788i | −0.976417 | − | 0.215894i | \(-0.930733\pi\) | ||
0.976417 | − | 0.215894i | \(-0.0692665\pi\) | |||||||
\(60\) | −13.6332 | − | 0.683375i | −1.76004 | − | 0.0882234i | ||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.4749 | + | 11.4749i | 1.40189 | + | 1.40189i | 0.794101 | + | 0.607785i | \(0.207942\pi\) |
0.607785 | + | 0.794101i | \(0.292058\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.2665i | 1.47671i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.00000 | −0.356034 | −0.178017 | − | 0.984027i | \(-0.556968\pi\) | ||||
−0.178017 | + | 0.984027i | \(0.556968\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.65831 | + | 11.8166i | 1.11525 | + | 1.36447i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | −6.63325 | + | 6.00000i | −0.741620 | + | 0.670820i | ||||
\(81\) | −11.9499 | −1.32776 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.00000i | 0.953998i | 0.878904 | + | 0.476999i | \(0.158275\pi\) | ||||
−0.878904 | + | 0.476999i | \(0.841725\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.68338 | + | 5.68338i | 0.592533 | + | 0.592533i | ||||
\(93\) | 21.4749 | − | 21.4749i | 2.22685 | − | 2.22685i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.52506 | − | 3.52506i | −0.357916 | − | 0.357916i | 0.505128 | − | 0.863044i | \(-0.331445\pi\) |
−0.863044 | + | 0.505128i | \(0.831445\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 20.9499i | − | 2.10554i | ||||||
\(100\) | 9.94987 | + | 1.00000i | 0.994987 | + | 0.100000i | ||||
\(101\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.94987 | + | 7.94987i | −0.783324 | + | 0.783324i | −0.980390 | − | 0.197066i | \(-0.936859\pi\) |
0.197066 | + | 0.980390i | \(0.436859\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(108\) | −14.3166 | + | 14.3166i | −1.37762 | + | 1.37762i | ||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.36675 | −0.604305 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.1583 | + | 12.1583i | −1.14376 | + | 1.14376i | −0.156001 | + | 0.987757i | \(0.549860\pi\) |
−0.987757 | + | 0.156001i | \(0.950140\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.449874 | − | 8.97494i | 0.0419510 | − | 0.836917i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.0000 | 1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 19.8997i | − | 1.78705i | ||||||
\(125\) | −6.63325 | − | 9.00000i | −0.593296 | − | 0.804984i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | −14.3166 | − | 14.3166i | −1.24610 | − | 1.24610i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 22.6082 | + | 1.13325i | 1.94580 | + | 0.0975346i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.1082 | − | 10.1082i | −0.863601 | − | 0.863601i | 0.128154 | − | 0.991754i | \(-0.459095\pi\) |
−0.991754 | + | 0.128154i | \(0.959095\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 40.2164 | 3.38683 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 25.2665i | 2.10554i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −15.1082 | − | 15.1082i | −1.24610 | − | 1.24610i | ||||
\(148\) | −2.94987 | + | 2.94987i | −0.242478 | + | 0.242478i | ||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.5000 | + | 14.9248i | −1.32531 | + | 1.19879i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.4749 | + | 16.4749i | 1.31484 | + | 1.31484i | 0.917800 | + | 0.397043i | \(0.129964\pi\) |
0.397043 | + | 0.917800i | \(0.370036\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 15.6834i | 1.24377i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.9499 | + | 17.9499i | −1.40594 | + | 1.40594i | −0.626608 | + | 0.779334i | \(0.715557\pi\) |
−0.779334 | + | 0.626608i | \(0.784443\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.13325 | + | 22.6082i | −0.0882234 | + | 1.76004i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 13.0000i | − | 1.00000i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −13.2665 | −1.00000 | ||||||||
\(177\) | 7.15831 | + | 7.15831i | 0.538052 | + | 0.538052i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 21.0000i | − | 1.56961i | −0.619740 | − | 0.784807i | \(-0.712762\pi\) | ||
0.619740 | − | 0.784807i | \(-0.287238\pi\) | |||||||
\(180\) | 20.9499 | − | 18.9499i | 1.56151 | − | 1.41244i | ||||
\(181\) | −9.94987 | −0.739568 | −0.369784 | − | 0.929118i | \(-0.620568\pi\) | ||||
−0.369784 | + | 0.929118i | \(0.620568\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.65831 | + | 0.233501i | 0.342486 | + | 0.0171673i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 18.6332 | − | 18.6332i | 1.35897 | − | 1.35897i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.2164 | 1.67988 | 0.839939 | − | 0.542681i | \(-0.182591\pi\) | ||||
0.839939 | + | 0.542681i | \(0.182591\pi\) | |||||||
\(192\) | 17.2665 | + | 17.2665i | 1.24610 | + | 1.24610i | ||||
\(193\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −1.00000 | ||||||||
\(197\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 19.8997i | − | 1.41066i | −0.708881 | − | 0.705328i | \(-0.750800\pi\) | ||
0.708881 | − | 0.705328i | \(-0.249200\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −49.5330 | −3.49379 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −17.9499 | − | 17.9499i | −1.24760 | − | 1.24760i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | 7.26650 | + | 7.26650i | 0.499065 | + | 0.499065i | ||||
\(213\) | 6.47494 | − | 6.47494i | 0.443655 | − | 0.443655i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 9.94987 | + | 11.0000i | 0.670820 | + | 0.741620i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.4248 | − | 14.4248i | 0.965957 | − | 0.965957i | −0.0334825 | − | 0.999439i | \(-0.510660\pi\) |
0.999439 | + | 0.0334825i | \(0.0106598\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −31.4248 | − | 3.15831i | −2.09499 | − | 0.210554i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 29.8496i | 1.97252i | 0.165205 | + | 0.986259i | \(0.447172\pi\) | ||||
−0.165205 | + | 0.986259i | \(0.552828\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −29.4248 | − | 1.47494i | −1.91946 | − | 0.0962143i | ||||
\(236\) | 6.63325 | 0.431788 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 1.36675 | − | 27.2665i | 0.0882234 | − | 1.76004i | ||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.31662 | − | 4.31662i | 0.276912 | − | 0.276912i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.5000 | + | 11.6082i | 0.670820 | + | 0.741620i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.0000 | 1.70422 | 0.852112 | − | 0.523359i | \(-0.175321\pi\) | ||||
0.852112 | + | 0.523359i | \(0.175321\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.42481 | − | 9.42481i | 0.592533 | − | 0.592533i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 22.2665 | + | 22.2665i | 1.38895 | + | 1.38895i | 0.827541 | + | 0.561405i | \(0.189739\pi\) |
0.561405 | + | 0.827541i | \(0.310261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.575188 | − | 11.4749i | 0.0353335 | − | 0.704900i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −19.4248 | − | 19.4248i | −1.18878 | − | 1.18878i | ||||
\(268\) | −22.9499 | + | 22.9499i | −1.40189 | + | 1.40189i | ||||
\(269\) | 13.2665i | 0.808873i | 0.914566 | + | 0.404436i | \(0.132532\pi\) | ||||
−0.914566 | + | 0.404436i | \(0.867468\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.65831 | − | 16.5000i | 0.100000 | − | 0.994987i | ||||
\(276\) | −24.5330 | −1.47671 | ||||||||
\(277\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 62.8496i | 3.76271i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(284\) | − | 6.00000i | − | 0.356034i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.0000i | 1.00000i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.2164 | 0.892000 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.97494 | − | 5.50000i | −0.289652 | − | 0.320222i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 23.7414 | + | 23.7414i | 1.37762 | + | 1.37762i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −23.6332 | + | 19.3166i | −1.36447 | + | 1.11525i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 34.3166i | − | 1.95220i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0000 | 0.680458 | 0.340229 | − | 0.940343i | \(-0.389495\pi\) | ||||
0.340229 | + | 0.940343i | \(0.389495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.4248 | − | 24.4248i | 1.38057 | − | 1.38057i | 0.536972 | − | 0.843600i | \(-0.319568\pi\) |
0.843600 | − | 0.536972i | \(-0.180432\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25.1082 | − | 25.1082i | −1.41022 | − | 1.41022i | −0.758236 | − | 0.651981i | \(-0.773938\pi\) |
−0.651981 | − | 0.758236i | \(-0.726062\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −12.0000 | − | 13.2665i | −0.670820 | − | 0.741620i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | − | 23.8997i | − | 1.32776i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.94987 | −0.546895 | −0.273447 | − | 0.961887i | \(-0.588164\pi\) | ||||
−0.273447 | + | 0.961887i | \(0.588164\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.31662 | − | 9.31662i | 0.510548 | − | 0.510548i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 36.2414 | + | 1.81662i | 1.98008 | + | 0.0992528i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 52.4829i | − | 2.85048i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −33.0000 | −1.78705 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 18.3997 | + | 20.3417i | 0.990609 | + | 1.09516i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.7414 | + | 13.7414i | −0.731383 | + | 0.731383i | −0.970894 | − | 0.239511i | \(-0.923013\pi\) |
0.239511 | + | 0.970894i | \(0.423013\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.97494 | + | 4.50000i | −0.264042 | + | 0.238835i | ||||
\(356\) | −18.0000 | −0.953998 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −23.7414 | + | 23.7414i | −1.24610 | + | 1.24610i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.5251 | − | 13.5251i | −0.706003 | − | 0.706003i | 0.259690 | − | 0.965692i | \(-0.416380\pi\) |
−0.965692 | + | 0.259690i | \(0.916380\pi\) | |||||||
\(368\) | −11.3668 | + | 11.3668i | −0.592533 | + | 0.592533i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 42.9499 | + | 42.9499i | 2.22685 | + | 2.22685i | ||||
\(373\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 33.7414 | + | 5.10819i | 1.74240 | + | 0.263786i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.8496i | 1.53327i | 0.642082 | + | 0.766636i | \(0.278071\pi\) | ||||
−0.642082 | + | 0.766636i | \(0.721929\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.8417 | − | 17.8417i | 0.911668 | − | 0.911668i | −0.0847358 | − | 0.996403i | \(-0.527005\pi\) |
0.996403 | + | 0.0847358i | \(0.0270046\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.05013 | − | 7.05013i | 0.357916 | − | 0.357916i | ||||
\(389\) | − | 36.4829i | − | 1.84976i | −0.380265 | − | 0.924878i | \(-0.624167\pi\) | ||
0.380265 | − | 0.924878i | \(-0.375833\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 41.8997 | 2.10554 | ||||||||
\(397\) | −20.8997 | − | 20.8997i | −1.04893 | − | 1.04893i | −0.998740 | − | 0.0501886i | \(-0.984018\pi\) |
−0.0501886 | − | 0.998740i | \(-0.515982\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.00000 | + | 19.8997i | −0.100000 | + | 0.994987i | ||||
\(401\) | −26.5330 | −1.32499 | −0.662497 | − | 0.749064i | \(-0.730503\pi\) | ||||
−0.662497 | + | 0.749064i | \(0.730503\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −19.8166 | + | 17.9248i | −0.984696 | + | 0.890691i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.89181 | + | 4.89181i | 0.242478 | + | 0.242478i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 43.6332 | 2.15227 | ||||||||
\(412\) | −15.8997 | − | 15.8997i | −0.783324 | − | 0.783324i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.0000i | 1.17248i | 0.810139 | + | 0.586238i | \(0.199392\pi\) | ||||
−0.810139 | + | 0.586238i | \(0.800608\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 39.7995 | 1.93971 | 0.969854 | − | 0.243685i | \(-0.0783563\pi\) | ||||
0.969854 | + | 0.243685i | \(0.0783563\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −58.8496 | + | 58.8496i | −2.86137 | + | 2.86137i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(432\) | −28.6332 | − | 28.6332i | −1.37762 | − | 1.37762i | ||||
\(433\) | 29.4248 | − | 29.4248i | 1.41407 | − | 1.41407i | 0.696826 | − | 0.717241i | \(-0.254595\pi\) |
0.717241 | − | 0.696826i | \(-0.245405\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 44.2164 | 2.10554 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −28.7414 | + | 28.7414i | −1.36555 | + | 1.36555i | −0.498870 | + | 0.866677i | \(0.666252\pi\) |
−0.866677 | + | 0.498870i | \(0.833748\pi\) | |||||||
\(444\) | − | 12.7335i | − | 0.604305i | ||||||
\(445\) | 13.5000 | + | 14.9248i | 0.639961 | + | 0.707504i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 39.0000i | 1.84052i | 0.391303 | + | 0.920262i | \(0.372024\pi\) | ||||
−0.391303 | + | 0.920262i | \(0.627976\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −24.3166 | − | 24.3166i | −1.14376 | − | 1.14376i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 17.9499 | + | 0.899749i | 0.836917 | + | 0.0419510i | ||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.575188 | + | 0.575188i | −0.0267313 | + | 0.0267313i | −0.720346 | − | 0.693615i | \(-0.756017\pi\) |
0.693615 | + | 0.720346i | \(0.256017\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.39975 | − | 67.8246i | 0.157660 | − | 3.14529i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.0581 | + | 23.0581i | 1.06700 | + | 1.06700i | 0.997588 | + | 0.0694117i | \(0.0221122\pi\) |
0.0694117 | + | 0.997588i | \(0.477888\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −71.1161 | −3.27686 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −22.9499 | − | 22.9499i | −1.05080 | − | 1.05080i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 22.0000i | 1.00000i | ||||||||
\(485\) | −11.1332 | − | 0.558061i | −0.505535 | − | 0.0253403i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.4749 | + | 26.4749i | 1.19969 | + | 1.19969i | 0.974258 | + | 0.225436i | \(0.0723806\pi\) |
0.225436 | + | 0.974258i | \(0.427619\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 77.4829i | − | 3.50390i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −31.4248 | − | 34.7414i | −1.41244 | − | 1.56151i | ||||
\(496\) | 39.7995 | 1.78705 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 19.8997i | − | 0.890835i | −0.895323 | − | 0.445418i | \(-0.853055\pi\) | ||
0.895323 | − | 0.445418i | \(-0.146945\pi\) | |||||||
\(500\) | 18.0000 | − | 13.2665i | 0.804984 | − | 0.593296i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 28.0581 | + | 28.0581i | 1.24610 | + | 1.24610i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 3.31662i | − | 0.147007i | −0.997295 | − | 0.0735034i | \(-0.976582\pi\) | ||
0.997295 | − | 0.0735034i | \(-0.0234180\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.25856 | + | 25.1082i | −0.0554589 | + | 1.10640i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −30.8997 | − | 30.8997i | −1.35897 | − | 1.35897i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −43.1161 | −1.88895 | −0.944476 | − | 0.328581i | \(-0.893430\pi\) | ||||
−0.944476 | + | 0.328581i | \(0.893430\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 28.6332 | − | 28.6332i | 1.24610 | − | 1.24610i | ||||
\(529\) | 6.84962i | 0.297810i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −20.9499 | −0.909147 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 45.3246 | + | 45.3246i | 1.95590 | + | 1.95590i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 23.2164i | 1.00000i | ||||||||
\(540\) | −2.26650 | + | 45.2164i | −0.0975346 | + | 1.94580i | ||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 21.4749 | − | 21.4749i | 0.921578 | − | 0.921578i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(548\) | 20.2164 | − | 20.2164i | 0.863601 | − | 0.863601i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.5581 | + | 9.55013i | −0.448165 | + | 0.405380i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(564\) | 80.4327i | 3.38683i | ||||||||
\(565\) | −1.92481 | + | 38.3997i | −0.0809774 | + | 1.61549i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −50.1082 | + | 50.1082i | −2.09330 | + | 2.09330i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.7164 | − | 15.5581i | −0.530309 | − | 0.648816i | ||||
\(576\) | −50.5330 | −2.10554 | ||||||||
\(577\) | −18.5251 | − | 18.5251i | −0.771208 | − | 0.771208i | 0.207109 | − | 0.978318i | \(-0.433594\pi\) |
−0.978318 | + | 0.207109i | \(0.933594\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.0501 | − | 12.0501i | 0.499065 | − | 0.499065i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.6834 | + | 20.6834i | 0.853694 | + | 0.853694i | 0.990586 | − | 0.136892i | \(-0.0437113\pi\) |
−0.136892 | + | 0.990586i | \(0.543711\pi\) | |||||||
\(588\) | 30.2164 | − | 30.2164i | 1.24610 | − | 1.24610i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.89975 | − | 5.89975i | −0.242478 | − | 0.242478i | ||||
\(593\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 42.9499 | + | 42.9499i | 1.75782 | + | 1.75782i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 36.0000i | − | 1.47092i | −0.677568 | − | 0.735460i | \(-0.736966\pi\) | ||
0.677568 | − | 0.735460i | \(-0.263034\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 72.4829 | − | 72.4829i | 2.95173 | − | 2.95173i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 18.2414 | − | 16.5000i | 0.741620 | − | 0.670820i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.73350 | − | 7.73350i | −0.311339 | − | 0.311339i | 0.534089 | − | 0.845428i | \(-0.320655\pi\) |
−0.845428 | + | 0.534089i | \(0.820655\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 1.00000i | − | 0.0401934i | −0.999798 | − | 0.0200967i | \(-0.993603\pi\) | ||
0.999798 | − | 0.0200967i | \(-0.00639741\pi\) | |||||||
\(620\) | −29.8496 | − | 33.0000i | −1.19879 | − | 1.32531i | ||||
\(621\) | 40.6834 | 1.63257 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.5000 | − | 4.97494i | −0.980000 | − | 0.198997i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −32.9499 | + | 32.9499i | −1.31484 | + | 1.31484i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.00000 | 0.278666 | 0.139333 | − | 0.990246i | \(-0.455504\pi\) | ||||
0.139333 | + | 0.990246i | \(0.455504\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −31.3668 | −1.24377 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 18.9499i | 0.749645i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.2164 | 0.916992 | 0.458496 | − | 0.888697i | \(-0.348388\pi\) | ||||
0.458496 | + | 0.888697i | \(0.348388\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.57519 | + | 5.57519i | −0.219864 | + | 0.219864i | −0.808441 | − | 0.588577i | \(-0.799688\pi\) |
0.588577 | + | 0.808441i | \(0.299688\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.05806 | + | 8.05806i | 0.316795 | + | 0.316795i | 0.847535 | − | 0.530740i | \(-0.178086\pi\) |
−0.530740 | + | 0.847535i | \(0.678086\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 11.0000i | − | 0.431788i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −35.8997 | − | 35.8997i | −1.40594 | − | 1.40594i | ||||
\(653\) | −27.1583 | + | 27.1583i | −1.06279 | + | 1.06279i | −0.0648948 | + | 0.997892i | \(0.520671\pi\) |
−0.997892 | + | 0.0648948i | \(0.979329\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | −45.2164 | − | 2.26650i | −1.76004 | − | 0.0882234i | ||||
\(661\) | −13.0000 | −0.505641 | −0.252821 | − | 0.967513i | \(-0.581358\pi\) | ||||
−0.252821 | + | 0.967513i | \(0.581358\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 62.2665i | 2.40736i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 39.1913 | − | 32.0330i | 1.50847 | − | 1.23295i | ||||
\(676\) | 26.0000 | 1.00000 | ||||||||
\(677\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.2164 | − | 35.2164i | 1.34752 | − | 1.34752i | 0.459167 | − | 0.888350i | \(-0.348148\pi\) |
0.888350 | − | 0.459167i | \(-0.151852\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −31.9248 | − | 1.60025i | −1.21978 | − | 0.0611425i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −64.4248 | − | 64.4248i | −2.45796 | − | 2.45796i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.0000 | 0.646710 | 0.323355 | − | 0.946278i | \(-0.395189\pi\) | ||||
0.323355 | + | 0.946278i | \(0.395189\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | − | 26.5330i | − | 1.00000i | ||||||
\(705\) | 66.6913 | − | 60.3246i | 2.51174 | − | 2.27195i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −14.3166 | + | 14.3166i | −0.538052 | + | 0.538052i | ||||
\(709\) | 19.0000i | 0.713560i | 0.934188 | + | 0.356780i | \(0.116125\pi\) | ||||
−0.934188 | + | 0.356780i | \(0.883875\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −28.2744 | + | 28.2744i | −1.05889 | + | 1.05889i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 42.0000 | 1.56961 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 51.0000i | − | 1.90198i | −0.309223 | − | 0.950990i | \(-0.600069\pi\) | ||
0.309223 | − | 0.950990i | \(-0.399931\pi\) | |||||||
\(720\) | 37.8997 | + | 41.8997i | 1.41244 | + | 1.56151i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 19.8997i | − | 0.739568i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.4749 | + | 31.4749i | 1.16734 | + | 1.16734i | 0.982831 | + | 0.184510i | \(0.0590699\pi\) |
0.184510 | + | 0.982831i | \(0.440930\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 17.2164i | − | 0.637643i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −47.7164 | − | 2.39181i | −1.76004 | − | 0.0882234i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 38.0581 | + | 38.0581i | 1.40189 | + | 1.40189i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(740\) | −0.467002 | + | 9.31662i | −0.0171673 | + | 0.342486i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.0000 | −0.839282 | −0.419641 | − | 0.907690i | \(-0.637844\pi\) | ||||
−0.419641 | + | 0.907690i | \(0.637844\pi\) | |||||||
\(752\) | 37.2665 | + | 37.2665i | 1.35897 | + | 1.35897i | ||||
\(753\) | −58.2744 | + | 58.2744i | −2.12364 | + | 2.12364i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.899749 | − | 0.899749i | −0.0327019 | − | 0.0327019i | 0.690567 | − | 0.723269i | \(-0.257361\pi\) |
−0.723269 | + | 0.690567i | \(0.757361\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 40.6834i | 1.47671i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 46.4327i | 1.67988i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −34.5330 | + | 34.5330i | −1.24610 | + | 1.24610i | ||||
\(769\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −96.1161 | −3.46154 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 33.6332 | − | 33.6332i | 1.20970 | − | 1.20970i | 0.238581 | − | 0.971123i | \(-0.423318\pi\) |
0.971123 | − | 0.238581i | \(-0.0766824\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.97494 | + | 49.5000i | −0.178705 | + | 1.77809i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.94987 | −0.356034 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 28.0000i | − | 1.00000i | ||||||
\(785\) | 52.0330 | + | 2.60819i | 1.85714 | + | 0.0930902i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 23.5251 | + | 26.0079i | 0.834348 | + | 0.922406i | ||||
\(796\) | 39.7995 | 1.41066 | ||||||||
\(797\) | −26.6913 | − | 26.6913i | −0.945455 | − | 0.945455i | 0.0531327 | − | 0.998587i | \(-0.483079\pi\) |
−0.998587 | + | 0.0531327i | \(0.983079\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 56.8496 | 2.00868 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | − | 99.0660i | − | 3.49379i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −28.6332 | − | 28.6332i | −1.00794 | − | 1.00794i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.84169 | + | 56.6913i | −0.0995400 | + | 1.98581i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.4248 | − | 39.4248i | 1.37426 | − | 1.37426i | 0.520246 | − | 0.854016i | \(-0.325840\pi\) |
0.854016 | − | 0.520246i | \(-0.174160\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 32.0330 | + | 39.1913i | 1.11525 | + | 1.36447i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(828\) | 35.8997 | − | 35.8997i | 1.24760 | − | 1.24760i | ||||
\(829\) | 29.0000i | 1.00721i | 0.863934 | + | 0.503606i | \(0.167994\pi\) | ||||
−0.863934 | + | 0.503606i | \(0.832006\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −71.2243 | − | 71.2243i | −2.46187 | − | 2.46187i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 36.4829i | − | 1.25953i | −0.776786 | − | 0.629764i | \(-0.783151\pi\) | ||
0.776786 | − | 0.629764i | \(-0.216849\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19.5000 | − | 21.5581i | −0.670820 | − | 0.741620i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −14.5330 | + | 14.5330i | −0.499065 | + | 0.499065i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.38262 | 0.287353 | ||||||||
\(852\) | 12.9499 | + | 12.9499i | 0.443655 | + | 0.443655i | ||||
\(853\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 31.0000i | − | 1.05771i | −0.848713 | − | 0.528853i | \(-0.822622\pi\) | ||
0.848713 | − | 0.528853i | \(-0.177378\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.21637 | − | 5.21637i | 0.177567 | − | 0.177567i | −0.612727 | − | 0.790295i | \(-0.709928\pi\) |
0.790295 | + | 0.612727i | \(0.209928\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −36.6913 | − | 36.6913i | −1.24610 | − | 1.24610i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −22.2665 | + | 22.2665i | −0.753607 | + | 0.753607i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −22.0000 | + | 19.8997i | −0.741620 | + | 0.670820i | ||||
\(881\) | 57.0000 | 1.92038 | 0.960189 | − | 0.279350i | \(-0.0901189\pi\) | ||||
0.960189 | + | 0.279350i | \(0.0901189\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37.9499 | + | 37.9499i | −1.27711 | + | 1.27711i | −0.334840 | + | 0.942275i | \(0.608682\pi\) |
−0.942275 | + | 0.334840i | \(0.891318\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 22.6082 | + | 1.13325i | 0.759966 | + | 0.0380938i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −39.6332 | −1.32776 | ||||||||
\(892\) | 28.8496 | + | 28.8496i | 0.965957 | + | 0.965957i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.5000 | − | 34.8246i | −1.05293 | − | 1.16406i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 6.31662 | − | 62.8496i | 0.210554 | − | 2.09499i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −16.5000 | + | 14.9248i | −0.548479 | + | 0.496118i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.8496 | + | 33.8496i | 1.12396 | + | 1.12396i | 0.991140 | + | 0.132818i | \(0.0424025\pi\) |
0.132818 | + | 0.991140i | \(0.457597\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.63325 | 0.219769 | 0.109885 | − | 0.993944i | \(-0.464952\pi\) | ||||
0.109885 | + | 0.993944i | \(0.464952\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −59.6992 | −1.97252 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.07519 | − | 6.60025i | 0.265511 | − | 0.217015i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 50.2164 | + | 50.2164i | 1.64932 | + | 1.64932i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 53.0660i | − | 1.74104i | −0.492134 | − | 0.870519i | \(-0.663783\pi\) | ||
0.492134 | − | 0.870519i | \(-0.336217\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −25.8997 | + | 25.8997i | −0.847920 | + | 0.847920i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 105.433i | 3.44067i | ||||||||
\(940\) | 2.94987 | − | 58.8496i | 0.0962143 | − | 1.91946i | ||||
\(941\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 13.2665i | 0.431788i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −40.1082 | − | 40.1082i | −1.30334 | − | 1.30334i | −0.926126 | − | 0.377215i | \(-0.876882\pi\) |
−0.377215 | − | 0.926126i | \(-0.623118\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 108.383 | 3.51455 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 38.5000 | − | 34.8246i | 1.24583 | − | 1.12690i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 54.5330 | + | 2.73350i | 1.76004 | + | 0.0882234i | ||||
\(961\) | 68.0000 | 2.19355 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −43.1161 | −1.38366 | −0.691831 | − | 0.722059i | \(-0.743196\pi\) | ||||
−0.691831 | + | 0.722059i | \(0.743196\pi\) | |||||||
\(972\) | 8.63325 | + | 8.63325i | 0.276912 | + | 0.276912i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −41.6913 | − | 41.6913i | −1.33382 | − | 1.33382i | −0.901920 | − | 0.431903i | \(-0.857842\pi\) |
−0.431903 | − | 0.901920i | \(-0.642158\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 29.8496i | 0.953998i | ||||||||
\(980\) | −23.2164 | + | 21.0000i | −0.741620 | + | 0.670820i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −43.7414 | + | 43.7414i | −1.39514 | + | 1.39514i | −0.581811 | + | 0.813324i | \(0.697656\pi\) |
−0.813324 | + | 0.581811i | \(0.802344\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −59.6992 | −1.89641 | −0.948205 | − | 0.317660i | \(-0.897103\pi\) | ||||
−0.948205 | + | 0.317660i | \(0.897103\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 21.4749 | − | 21.4749i | 0.681487 | − | 0.681487i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −29.8496 | − | 33.0000i | −0.946297 | − | 1.04617i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 21.1161i | 0.668085i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))