Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [200,2,Mod(101,200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("200.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 200 = 2^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 200.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.59700804043\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-7}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 101.1 | ||
Root | \(0.500000 - 1.32288i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 200.101 |
Dual form | 200.2.d.c.101.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/200\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(177\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 1.32288i | 0.353553 | − | 0.935414i | ||||
\(3\) | − | 2.64575i | − | 1.52753i | −0.645497 | − | 0.763763i | \(-0.723350\pi\) | ||
0.645497 | − | 0.763763i | \(-0.276650\pi\) | |||||||
\(4\) | −1.50000 | − | 1.32288i | −0.750000 | − | 0.661438i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.50000 | − | 1.32288i | −1.42887 | − | 0.540062i | ||||
\(7\) | 4.00000 | 1.51186 | 0.755929 | − | 0.654654i | \(-0.227186\pi\) | ||||
0.755929 | + | 0.654654i | \(0.227186\pi\) | |||||||
\(8\) | −2.50000 | + | 1.32288i | −0.883883 | + | 0.467707i | ||||
\(9\) | −4.00000 | −1.33333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.64575i | 0.797724i | 0.917011 | + | 0.398862i | \(0.130595\pi\) | ||||
−0.917011 | + | 0.398862i | \(0.869405\pi\) | |||||||
\(12\) | −3.50000 | + | 3.96863i | −1.01036 | + | 1.14564i | ||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | 2.00000 | − | 5.29150i | 0.534522 | − | 1.41421i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | + | 3.96863i | 0.125000 | + | 0.992157i | ||||
\(17\) | −3.00000 | −0.727607 | −0.363803 | − | 0.931476i | \(-0.618522\pi\) | ||||
−0.363803 | + | 0.931476i | \(0.618522\pi\) | |||||||
\(18\) | −2.00000 | + | 5.29150i | −0.471405 | + | 1.24722i | ||||
\(19\) | 2.64575i | 0.606977i | 0.952835 | + | 0.303488i | \(0.0981514\pi\) | ||||
−0.952835 | + | 0.303488i | \(0.901849\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 10.5830i | − | 2.30940i | ||||||
\(22\) | 3.50000 | + | 1.32288i | 0.746203 | + | 0.282038i | ||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | 3.50000 | + | 6.61438i | 0.714435 | + | 1.35015i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.64575i | 0.509175i | ||||||||
\(28\) | −6.00000 | − | 5.29150i | −1.13389 | − | 1.00000i | ||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | 5.50000 | + | 1.32288i | 0.972272 | + | 0.233854i | ||||
\(33\) | 7.00000 | 1.21854 | ||||||||
\(34\) | −1.50000 | + | 3.96863i | −0.257248 | + | 0.680614i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.00000 | + | 5.29150i | 1.00000 | + | 0.881917i | ||||
\(37\) | − | 10.5830i | − | 1.73984i | −0.493197 | − | 0.869918i | \(-0.664172\pi\) | ||
0.493197 | − | 0.869918i | \(-0.335828\pi\) | |||||||
\(38\) | 3.50000 | + | 1.32288i | 0.567775 | + | 0.214599i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.00000 | −0.780869 | −0.390434 | − | 0.920631i | \(-0.627675\pi\) | ||||
−0.390434 | + | 0.920631i | \(0.627675\pi\) | |||||||
\(42\) | −14.0000 | − | 5.29150i | −2.16025 | − | 0.816497i | ||||
\(43\) | − | 5.29150i | − | 0.806947i | −0.914991 | − | 0.403473i | \(-0.867803\pi\) | ||
0.914991 | − | 0.403473i | \(-0.132197\pi\) | |||||||
\(44\) | 3.50000 | − | 3.96863i | 0.527645 | − | 0.598293i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.00000 | − | 5.29150i | 0.294884 | − | 0.780189i | ||||
\(47\) | −8.00000 | −1.16692 | −0.583460 | − | 0.812142i | \(-0.698301\pi\) | ||||
−0.583460 | + | 0.812142i | \(0.698301\pi\) | |||||||
\(48\) | 10.5000 | − | 1.32288i | 1.51554 | − | 0.190941i | ||||
\(49\) | 9.00000 | 1.28571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.93725i | 1.11144i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.5830i | 1.45369i | 0.686803 | + | 0.726844i | \(0.259014\pi\) | ||||
−0.686803 | + | 0.726844i | \(0.740986\pi\) | |||||||
\(54\) | 3.50000 | + | 1.32288i | 0.476290 | + | 0.180021i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −10.0000 | + | 5.29150i | −1.33631 | + | 0.707107i | ||||
\(57\) | 7.00000 | 0.927173 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.29150i | 0.688895i | 0.938806 | + | 0.344447i | \(0.111934\pi\) | ||||
−0.938806 | + | 0.344447i | \(0.888066\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.5830i | 1.35501i | 0.735516 | + | 0.677507i | \(0.236940\pi\) | ||||
−0.735516 | + | 0.677507i | \(0.763060\pi\) | |||||||
\(62\) | 2.00000 | − | 5.29150i | 0.254000 | − | 0.672022i | ||||
\(63\) | −16.0000 | −2.01581 | ||||||||
\(64\) | 4.50000 | − | 6.61438i | 0.562500 | − | 0.826797i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.50000 | − | 9.26013i | 0.430820 | − | 1.13984i | ||||
\(67\) | 7.93725i | 0.969690i | 0.874600 | + | 0.484845i | \(0.161124\pi\) | ||||
−0.874600 | + | 0.484845i | \(0.838876\pi\) | |||||||
\(68\) | 4.50000 | + | 3.96863i | 0.545705 | + | 0.481267i | ||||
\(69\) | − | 10.5830i | − | 1.27404i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | 10.0000 | − | 5.29150i | 1.17851 | − | 0.623610i | ||||
\(73\) | −7.00000 | −0.819288 | −0.409644 | − | 0.912245i | \(-0.634347\pi\) | ||||
−0.409644 | + | 0.912245i | \(0.634347\pi\) | |||||||
\(74\) | −14.0000 | − | 5.29150i | −1.62747 | − | 0.615125i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.50000 | − | 3.96863i | 0.401478 | − | 0.455233i | ||||
\(77\) | 10.5830i | 1.20605i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000 | 0.450035 | 0.225018 | − | 0.974355i | \(-0.427756\pi\) | ||||
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.00000 | −0.555556 | ||||||||
\(82\) | −2.50000 | + | 6.61438i | −0.276079 | + | 0.730436i | ||||
\(83\) | 7.93725i | 0.871227i | 0.900134 | + | 0.435613i | \(0.143469\pi\) | ||||
−0.900134 | + | 0.435613i | \(0.856531\pi\) | |||||||
\(84\) | −14.0000 | + | 15.8745i | −1.52753 | + | 1.73205i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −7.00000 | − | 2.64575i | −0.754829 | − | 0.285299i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.50000 | − | 6.61438i | −0.373101 | − | 0.705095i | ||||
\(89\) | −1.00000 | −0.106000 | −0.0529999 | − | 0.998595i | \(-0.516878\pi\) | ||||
−0.0529999 | + | 0.998595i | \(0.516878\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.00000 | − | 5.29150i | −0.625543 | − | 0.551677i | ||||
\(93\) | − | 10.5830i | − | 1.09741i | ||||||
\(94\) | −4.00000 | + | 10.5830i | −0.412568 | + | 1.09155i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.50000 | − | 14.5516i | 0.357217 | − | 1.48517i | ||||
\(97\) | −2.00000 | −0.203069 | −0.101535 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101535 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(98\) | 4.50000 | − | 11.9059i | 0.454569 | − | 1.20268i | ||||
\(99\) | − | 10.5830i | − | 1.06363i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 10.5830i | − | 1.05305i | −0.850160 | − | 0.526524i | \(-0.823495\pi\) | ||
0.850160 | − | 0.526524i | \(-0.176505\pi\) | |||||||
\(102\) | 10.5000 | + | 3.96863i | 1.03965 | + | 0.392953i | ||||
\(103\) | 8.00000 | 0.788263 | 0.394132 | − | 0.919054i | \(-0.371045\pi\) | ||||
0.394132 | + | 0.919054i | \(0.371045\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 14.0000 | + | 5.29150i | 1.35980 | + | 0.513956i | ||||
\(107\) | − | 2.64575i | − | 0.255774i | −0.991789 | − | 0.127887i | \(-0.959180\pi\) | ||
0.991789 | − | 0.127887i | \(-0.0408196\pi\) | |||||||
\(108\) | 3.50000 | − | 3.96863i | 0.336788 | − | 0.381881i | ||||
\(109\) | 10.5830i | 1.01367i | 0.862044 | + | 0.506834i | \(0.169184\pi\) | ||||
−0.862044 | + | 0.506834i | \(0.830816\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −28.0000 | −2.65764 | ||||||||
\(112\) | 2.00000 | + | 15.8745i | 0.188982 | + | 1.50000i | ||||
\(113\) | −15.0000 | −1.41108 | −0.705541 | − | 0.708669i | \(-0.749296\pi\) | ||||
−0.705541 | + | 0.708669i | \(0.749296\pi\) | |||||||
\(114\) | 3.50000 | − | 9.26013i | 0.327805 | − | 0.867291i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.00000 | + | 2.64575i | 0.644402 | + | 0.243561i | ||||
\(119\) | −12.0000 | −1.10004 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.00000 | 0.363636 | ||||||||
\(122\) | 14.0000 | + | 5.29150i | 1.26750 | + | 0.479070i | ||||
\(123\) | 13.2288i | 1.19280i | ||||||||
\(124\) | −6.00000 | − | 5.29150i | −0.538816 | − | 0.475191i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −8.00000 | + | 21.1660i | −0.712697 | + | 1.88562i | ||||
\(127\) | 12.0000 | 1.06483 | 0.532414 | − | 0.846484i | \(-0.321285\pi\) | ||||
0.532414 | + | 0.846484i | \(0.321285\pi\) | |||||||
\(128\) | −6.50000 | − | 9.26013i | −0.574524 | − | 0.818488i | ||||
\(129\) | −14.0000 | −1.23263 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 15.8745i | − | 1.38696i | −0.720475 | − | 0.693481i | \(-0.756076\pi\) | ||
0.720475 | − | 0.693481i | \(-0.243924\pi\) | |||||||
\(132\) | −10.5000 | − | 9.26013i | −0.913908 | − | 0.805991i | ||||
\(133\) | 10.5830i | 0.917663i | ||||||||
\(134\) | 10.5000 | + | 3.96863i | 0.907062 | + | 0.342837i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.50000 | − | 3.96863i | 0.643120 | − | 0.340307i | ||||
\(137\) | −19.0000 | −1.62328 | −0.811640 | − | 0.584158i | \(-0.801425\pi\) | ||||
−0.811640 | + | 0.584158i | \(0.801425\pi\) | |||||||
\(138\) | −14.0000 | − | 5.29150i | −1.19176 | − | 0.450443i | ||||
\(139\) | − | 18.5203i | − | 1.57087i | −0.618945 | − | 0.785434i | \(-0.712440\pi\) | ||
0.618945 | − | 0.785434i | \(-0.287560\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 21.1660i | 1.78250i | ||||||||
\(142\) | 4.00000 | − | 10.5830i | 0.335673 | − | 0.888106i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.00000 | − | 15.8745i | −0.166667 | − | 1.32288i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.50000 | + | 9.26013i | −0.289662 | + | 0.766374i | ||||
\(147\) | − | 23.8118i | − | 1.96396i | ||||||
\(148\) | −14.0000 | + | 15.8745i | −1.15079 | + | 1.30488i | ||||
\(149\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000 | 0.325515 | 0.162758 | − | 0.986666i | \(-0.447961\pi\) | ||||
0.162758 | + | 0.986666i | \(0.447961\pi\) | |||||||
\(152\) | −3.50000 | − | 6.61438i | −0.283887 | − | 0.536497i | ||||
\(153\) | 12.0000 | 0.970143 | ||||||||
\(154\) | 14.0000 | + | 5.29150i | 1.12815 | + | 0.426401i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.5830i | 0.844616i | 0.906452 | + | 0.422308i | \(0.138780\pi\) | ||||
−0.906452 | + | 0.422308i | \(0.861220\pi\) | |||||||
\(158\) | 2.00000 | − | 5.29150i | 0.159111 | − | 0.420969i | ||||
\(159\) | 28.0000 | 2.22054 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.0000 | 1.26098 | ||||||||
\(162\) | −2.50000 | + | 6.61438i | −0.196419 | + | 0.519675i | ||||
\(163\) | − | 13.2288i | − | 1.03616i | −0.855333 | − | 0.518078i | \(-0.826648\pi\) | ||
0.855333 | − | 0.518078i | \(-0.173352\pi\) | |||||||
\(164\) | 7.50000 | + | 6.61438i | 0.585652 | + | 0.516496i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.5000 | + | 3.96863i | 0.814958 | + | 0.308025i | ||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 14.0000 | + | 26.4575i | 1.08012 | + | 2.04124i | ||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 10.5830i | − | 0.809303i | ||||||
\(172\) | −7.00000 | + | 7.93725i | −0.533745 | + | 0.605210i | ||||
\(173\) | − | 21.1660i | − | 1.60922i | −0.593802 | − | 0.804611i | \(-0.702374\pi\) | ||
0.593802 | − | 0.804611i | \(-0.297626\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −10.5000 | + | 1.32288i | −0.791467 | + | 0.0997155i | ||||
\(177\) | 14.0000 | 1.05230 | ||||||||
\(178\) | −0.500000 | + | 1.32288i | −0.0374766 | + | 0.0991537i | ||||
\(179\) | 23.8118i | 1.77977i | 0.456180 | + | 0.889887i | \(0.349217\pi\) | ||||
−0.456180 | + | 0.889887i | \(0.650783\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.5830i | 0.786629i | 0.919404 | + | 0.393314i | \(0.128672\pi\) | ||||
−0.919404 | + | 0.393314i | \(0.871328\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 28.0000 | 2.06982 | ||||||||
\(184\) | −10.0000 | + | 5.29150i | −0.737210 | + | 0.390095i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −14.0000 | − | 5.29150i | −1.02653 | − | 0.387992i | ||||
\(187\) | − | 7.93725i | − | 0.580429i | ||||||
\(188\) | 12.0000 | + | 10.5830i | 0.875190 | + | 0.771845i | ||||
\(189\) | 10.5830i | 0.769800i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.00000 | 0.289430 | 0.144715 | − | 0.989473i | \(-0.453773\pi\) | ||||
0.144715 | + | 0.989473i | \(0.453773\pi\) | |||||||
\(192\) | −17.5000 | − | 11.9059i | −1.26295 | − | 0.859233i | ||||
\(193\) | 5.00000 | 0.359908 | 0.179954 | − | 0.983675i | \(-0.442405\pi\) | ||||
0.179954 | + | 0.983675i | \(0.442405\pi\) | |||||||
\(194\) | −1.00000 | + | 2.64575i | −0.0717958 | + | 0.189954i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −13.5000 | − | 11.9059i | −0.964286 | − | 0.850420i | ||||
\(197\) | 10.5830i | 0.754008i | 0.926212 | + | 0.377004i | \(0.123046\pi\) | ||||
−0.926212 | + | 0.377004i | \(0.876954\pi\) | |||||||
\(198\) | −14.0000 | − | 5.29150i | −0.994937 | − | 0.376051i | ||||
\(199\) | −24.0000 | −1.70131 | −0.850657 | − | 0.525720i | \(-0.823796\pi\) | ||||
−0.850657 | + | 0.525720i | \(0.823796\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 21.0000 | 1.48123 | ||||||||
\(202\) | −14.0000 | − | 5.29150i | −0.985037 | − | 0.372309i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 10.5000 | − | 11.9059i | 0.735147 | − | 0.833578i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.00000 | − | 10.5830i | 0.278693 | − | 0.737353i | ||||
\(207\) | −16.0000 | −1.11208 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.00000 | −0.484200 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 7.93725i | − | 0.546423i | −0.961954 | − | 0.273212i | \(-0.911914\pi\) | ||
0.961954 | − | 0.273212i | \(-0.0880859\pi\) | |||||||
\(212\) | 14.0000 | − | 15.8745i | 0.961524 | − | 1.09027i | ||||
\(213\) | − | 21.1660i | − | 1.45027i | ||||||
\(214\) | −3.50000 | − | 1.32288i | −0.239255 | − | 0.0904299i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.50000 | − | 6.61438i | −0.238145 | − | 0.450051i | ||||
\(217\) | 16.0000 | 1.08615 | ||||||||
\(218\) | 14.0000 | + | 5.29150i | 0.948200 | + | 0.358386i | ||||
\(219\) | 18.5203i | 1.25148i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −14.0000 | + | 37.0405i | −0.939618 | + | 2.48600i | ||||
\(223\) | −16.0000 | −1.07144 | −0.535720 | − | 0.844396i | \(-0.679960\pi\) | ||||
−0.535720 | + | 0.844396i | \(0.679960\pi\) | |||||||
\(224\) | 22.0000 | + | 5.29150i | 1.46994 | + | 0.353553i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.50000 | + | 19.8431i | −0.498893 | + | 1.31995i | ||||
\(227\) | 15.8745i | 1.05363i | 0.849981 | + | 0.526814i | \(0.176614\pi\) | ||||
−0.849981 | + | 0.526814i | \(0.823386\pi\) | |||||||
\(228\) | −10.5000 | − | 9.26013i | −0.695379 | − | 0.613267i | ||||
\(229\) | 21.1660i | 1.39869i | 0.714785 | + | 0.699345i | \(0.246525\pi\) | ||||
−0.714785 | + | 0.699345i | \(0.753475\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 28.0000 | 1.84226 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.00000 | 0.393073 | 0.196537 | − | 0.980497i | \(-0.437031\pi\) | ||||
0.196537 | + | 0.980497i | \(0.437031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.00000 | − | 7.93725i | 0.455661 | − | 0.516671i | ||||
\(237\) | − | 10.5830i | − | 0.687440i | ||||||
\(238\) | −6.00000 | + | 15.8745i | −0.388922 | + | 1.02899i | ||||
\(239\) | −8.00000 | −0.517477 | −0.258738 | − | 0.965947i | \(-0.583307\pi\) | ||||
−0.258738 | + | 0.965947i | \(0.583307\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.0000 | −1.35273 | −0.676364 | − | 0.736567i | \(-0.736446\pi\) | ||||
−0.676364 | + | 0.736567i | \(0.736446\pi\) | |||||||
\(242\) | 2.00000 | − | 5.29150i | 0.128565 | − | 0.340151i | ||||
\(243\) | 21.1660i | 1.35780i | ||||||||
\(244\) | 14.0000 | − | 15.8745i | 0.896258 | − | 1.01626i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 17.5000 | + | 6.61438i | 1.11576 | + | 0.421717i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −10.0000 | + | 5.29150i | −0.635001 | + | 0.336011i | ||||
\(249\) | 21.0000 | 1.33082 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 7.93725i | − | 0.500995i | −0.968117 | − | 0.250498i | \(-0.919406\pi\) | ||
0.968117 | − | 0.250498i | \(-0.0805942\pi\) | |||||||
\(252\) | 24.0000 | + | 21.1660i | 1.51186 | + | 1.33333i | ||||
\(253\) | 10.5830i | 0.665348i | ||||||||
\(254\) | 6.00000 | − | 15.8745i | 0.376473 | − | 0.996055i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.5000 | + | 3.96863i | −0.968750 | + | 0.248039i | ||||
\(257\) | 14.0000 | 0.873296 | 0.436648 | − | 0.899632i | \(-0.356166\pi\) | ||||
0.436648 | + | 0.899632i | \(0.356166\pi\) | |||||||
\(258\) | −7.00000 | + | 18.5203i | −0.435801 | + | 1.15302i | ||||
\(259\) | − | 42.3320i | − | 2.63038i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −21.0000 | − | 7.93725i | −1.29738 | − | 0.490365i | ||||
\(263\) | 12.0000 | 0.739952 | 0.369976 | − | 0.929041i | \(-0.379366\pi\) | ||||
0.369976 | + | 0.929041i | \(0.379366\pi\) | |||||||
\(264\) | −17.5000 | + | 9.26013i | −1.07705 | + | 0.569922i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 14.0000 | + | 5.29150i | 0.858395 | + | 0.324443i | ||||
\(267\) | 2.64575i | 0.161917i | ||||||||
\(268\) | 10.5000 | − | 11.9059i | 0.641390 | − | 0.727267i | ||||
\(269\) | − | 21.1660i | − | 1.29051i | −0.763965 | − | 0.645257i | \(-0.776750\pi\) | ||
0.763965 | − | 0.645257i | \(-0.223250\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.0000 | −1.21491 | −0.607457 | − | 0.794353i | \(-0.707810\pi\) | ||||
−0.607457 | + | 0.794353i | \(0.707810\pi\) | |||||||
\(272\) | −1.50000 | − | 11.9059i | −0.0909509 | − | 0.721900i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.50000 | + | 25.1346i | −0.573916 | + | 1.51844i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −14.0000 | + | 15.8745i | −0.842701 | + | 0.955533i | ||||
\(277\) | − | 21.1660i | − | 1.27174i | −0.771795 | − | 0.635871i | \(-0.780641\pi\) | ||
0.771795 | − | 0.635871i | \(-0.219359\pi\) | |||||||
\(278\) | −24.5000 | − | 9.26013i | −1.46941 | − | 0.555386i | ||||
\(279\) | −16.0000 | −0.957895 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.0000 | −1.31241 | −0.656205 | − | 0.754583i | \(-0.727839\pi\) | ||||
−0.656205 | + | 0.754583i | \(0.727839\pi\) | |||||||
\(282\) | 28.0000 | + | 10.5830i | 1.66738 | + | 0.630209i | ||||
\(283\) | − | 13.2288i | − | 0.786368i | −0.919460 | − | 0.393184i | \(-0.871374\pi\) | ||
0.919460 | − | 0.393184i | \(-0.128626\pi\) | |||||||
\(284\) | −12.0000 | − | 10.5830i | −0.712069 | − | 0.627986i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.0000 | −1.18056 | ||||||||
\(288\) | −22.0000 | − | 5.29150i | −1.29636 | − | 0.311805i | ||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.29150i | 0.310193i | ||||||||
\(292\) | 10.5000 | + | 9.26013i | 0.614466 | + | 0.541908i | ||||
\(293\) | − | 10.5830i | − | 0.618266i | −0.951019 | − | 0.309133i | \(-0.899961\pi\) | ||
0.951019 | − | 0.309133i | \(-0.100039\pi\) | |||||||
\(294\) | −31.5000 | − | 11.9059i | −1.83712 | − | 0.694365i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 14.0000 | + | 26.4575i | 0.813733 | + | 1.53781i | ||||
\(297\) | −7.00000 | −0.406181 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 21.1660i | − | 1.21999i | ||||||
\(302\) | 2.00000 | − | 5.29150i | 0.115087 | − | 0.304492i | ||||
\(303\) | −28.0000 | −1.60856 | ||||||||
\(304\) | −10.5000 | + | 1.32288i | −0.602216 | + | 0.0758721i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.00000 | − | 15.8745i | 0.342997 | − | 0.907485i | ||||
\(307\) | − | 2.64575i | − | 0.151001i | −0.997146 | − | 0.0755005i | \(-0.975945\pi\) | ||
0.997146 | − | 0.0755005i | \(-0.0240554\pi\) | |||||||
\(308\) | 14.0000 | − | 15.8745i | 0.797724 | − | 0.904534i | ||||
\(309\) | − | 21.1660i | − | 1.20409i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.00000 | −0.226819 | −0.113410 | − | 0.993548i | \(-0.536177\pi\) | ||||
−0.113410 | + | 0.993548i | \(0.536177\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.00000 | 0.339140 | 0.169570 | − | 0.985518i | \(-0.445762\pi\) | ||||
0.169570 | + | 0.985518i | \(0.445762\pi\) | |||||||
\(314\) | 14.0000 | + | 5.29150i | 0.790066 | + | 0.298617i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.00000 | − | 5.29150i | −0.337526 | − | 0.297670i | ||||
\(317\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(318\) | 14.0000 | − | 37.0405i | 0.785081 | − | 2.07713i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.00000 | −0.390702 | ||||||||
\(322\) | 8.00000 | − | 21.1660i | 0.445823 | − | 1.17954i | ||||
\(323\) | − | 7.93725i | − | 0.441641i | ||||||
\(324\) | 7.50000 | + | 6.61438i | 0.416667 | + | 0.367465i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −17.5000 | − | 6.61438i | −0.969235 | − | 0.366337i | ||||
\(327\) | 28.0000 | 1.54840 | ||||||||
\(328\) | 12.5000 | − | 6.61438i | 0.690197 | − | 0.365218i | ||||
\(329\) | −32.0000 | −1.76422 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.64575i | 0.145424i | 0.997353 | + | 0.0727118i | \(0.0231653\pi\) | ||||
−0.997353 | + | 0.0727118i | \(0.976835\pi\) | |||||||
\(332\) | 10.5000 | − | 11.9059i | 0.576262 | − | 0.653420i | ||||
\(333\) | 42.3320i | 2.31978i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 42.0000 | − | 5.29150i | 2.29129 | − | 0.288675i | ||||
\(337\) | −15.0000 | −0.817102 | −0.408551 | − | 0.912735i | \(-0.633966\pi\) | ||||
−0.408551 | + | 0.912735i | \(0.633966\pi\) | |||||||
\(338\) | 6.50000 | − | 17.1974i | 0.353553 | − | 0.935414i | ||||
\(339\) | 39.6863i | 2.15546i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.5830i | 0.573102i | ||||||||
\(342\) | −14.0000 | − | 5.29150i | −0.757033 | − | 0.286132i | ||||
\(343\) | 8.00000 | 0.431959 | ||||||||
\(344\) | 7.00000 | + | 13.2288i | 0.377415 | + | 0.713247i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −28.0000 | − | 10.5830i | −1.50529 | − | 0.568946i | ||||
\(347\) | − | 2.64575i | − | 0.142031i | −0.997475 | − | 0.0710157i | \(-0.977376\pi\) | ||
0.997475 | − | 0.0710157i | \(-0.0226240\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 10.5830i | − | 0.566495i | −0.959047 | − | 0.283248i | \(-0.908588\pi\) | ||
0.959047 | − | 0.283248i | \(-0.0914118\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.50000 | + | 14.5516i | −0.186551 | + | 0.775605i | ||||
\(353\) | −18.0000 | −0.958043 | −0.479022 | − | 0.877803i | \(-0.659008\pi\) | ||||
−0.479022 | + | 0.877803i | \(0.659008\pi\) | |||||||
\(354\) | 7.00000 | − | 18.5203i | 0.372046 | − | 0.984341i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.50000 | + | 1.32288i | 0.0794998 | + | 0.0701123i | ||||
\(357\) | 31.7490i | 1.68034i | ||||||||
\(358\) | 31.5000 | + | 11.9059i | 1.66483 | + | 0.629245i | ||||
\(359\) | 36.0000 | 1.90001 | 0.950004 | − | 0.312239i | \(-0.101079\pi\) | ||||
0.950004 | + | 0.312239i | \(0.101079\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.0000 | 0.631579 | ||||||||
\(362\) | 14.0000 | + | 5.29150i | 0.735824 | + | 0.278115i | ||||
\(363\) | − | 10.5830i | − | 0.555464i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 14.0000 | − | 37.0405i | 0.731792 | − | 1.93614i | ||||
\(367\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(368\) | 2.00000 | + | 15.8745i | 0.104257 | + | 0.827516i | ||||
\(369\) | 20.0000 | 1.04116 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 42.3320i | 2.19777i | ||||||||
\(372\) | −14.0000 | + | 15.8745i | −0.725866 | + | 0.823055i | ||||
\(373\) | 10.5830i | 0.547967i | 0.961734 | + | 0.273984i | \(0.0883414\pi\) | ||||
−0.961734 | + | 0.273984i | \(0.911659\pi\) | |||||||
\(374\) | −10.5000 | − | 3.96863i | −0.542942 | − | 0.205213i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 20.0000 | − | 10.5830i | 1.03142 | − | 0.545777i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 14.0000 | + | 5.29150i | 0.720082 | + | 0.272166i | ||||
\(379\) | − | 7.93725i | − | 0.407709i | −0.979001 | − | 0.203855i | \(-0.934653\pi\) | ||
0.979001 | − | 0.203855i | \(-0.0653470\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 31.7490i | − | 1.62655i | ||||||
\(382\) | 2.00000 | − | 5.29150i | 0.102329 | − | 0.270737i | ||||
\(383\) | −36.0000 | −1.83951 | −0.919757 | − | 0.392488i | \(-0.871614\pi\) | ||||
−0.919757 | + | 0.392488i | \(0.871614\pi\) | |||||||
\(384\) | −24.5000 | + | 17.1974i | −1.25026 | + | 0.877600i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.50000 | − | 6.61438i | 0.127247 | − | 0.336663i | ||||
\(387\) | 21.1660i | 1.07593i | ||||||||
\(388\) | 3.00000 | + | 2.64575i | 0.152302 | + | 0.134318i | ||||
\(389\) | 10.5830i | 0.536580i | 0.963338 | + | 0.268290i | \(0.0864585\pi\) | ||||
−0.963338 | + | 0.268290i | \(0.913542\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.0000 | −0.606866 | ||||||||
\(392\) | −22.5000 | + | 11.9059i | −1.13642 | + | 0.601338i | ||||
\(393\) | −42.0000 | −2.11862 | ||||||||
\(394\) | 14.0000 | + | 5.29150i | 0.705310 | + | 0.266582i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −14.0000 | + | 15.8745i | −0.703526 | + | 0.797724i | ||||
\(397\) | − | 21.1660i | − | 1.06229i | −0.847280 | − | 0.531146i | \(-0.821762\pi\) | ||
0.847280 | − | 0.531146i | \(-0.178238\pi\) | |||||||
\(398\) | −12.0000 | + | 31.7490i | −0.601506 | + | 1.59143i | ||||
\(399\) | 28.0000 | 1.40175 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.0000 | 1.34832 | 0.674158 | − | 0.738587i | \(-0.264507\pi\) | ||||
0.674158 | + | 0.738587i | \(0.264507\pi\) | |||||||
\(402\) | 10.5000 | − | 27.7804i | 0.523692 | − | 1.38556i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −14.0000 | + | 15.8745i | −0.696526 | + | 0.789786i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 28.0000 | 1.38791 | ||||||||
\(408\) | −10.5000 | − | 19.8431i | −0.519827 | − | 0.982382i | ||||
\(409\) | 3.00000 | 0.148340 | 0.0741702 | − | 0.997246i | \(-0.476369\pi\) | ||||
0.0741702 | + | 0.997246i | \(0.476369\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 50.2693i | 2.47960i | ||||||||
\(412\) | −12.0000 | − | 10.5830i | −0.591198 | − | 0.521387i | ||||
\(413\) | 21.1660i | 1.04151i | ||||||||
\(414\) | −8.00000 | + | 21.1660i | −0.393179 | + | 1.04025i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −49.0000 | −2.39954 | ||||||||
\(418\) | −3.50000 | + | 9.26013i | −0.171191 | + | 0.452928i | ||||
\(419\) | − | 18.5203i | − | 0.904774i | −0.891822 | − | 0.452387i | \(-0.850573\pi\) | ||
0.891822 | − | 0.452387i | \(-0.149427\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.1660i | 1.03157i | 0.856719 | + | 0.515784i | \(0.172499\pi\) | ||||
−0.856719 | + | 0.515784i | \(0.827501\pi\) | |||||||
\(422\) | −10.5000 | − | 3.96863i | −0.511132 | − | 0.193190i | ||||
\(423\) | 32.0000 | 1.55589 | ||||||||
\(424\) | −14.0000 | − | 26.4575i | −0.679900 | − | 1.28489i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −28.0000 | − | 10.5830i | −1.35660 | − | 0.512748i | ||||
\(427\) | 42.3320i | 2.04859i | ||||||||
\(428\) | −3.50000 | + | 3.96863i | −0.169179 | + | 0.191831i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.0000 | 0.578020 | 0.289010 | − | 0.957326i | \(-0.406674\pi\) | ||||
0.289010 | + | 0.957326i | \(0.406674\pi\) | |||||||
\(432\) | −10.5000 | + | 1.32288i | −0.505181 | + | 0.0636469i | ||||
\(433\) | 37.0000 | 1.77811 | 0.889053 | − | 0.457804i | \(-0.151364\pi\) | ||||
0.889053 | + | 0.457804i | \(0.151364\pi\) | |||||||
\(434\) | 8.00000 | − | 21.1660i | 0.384012 | − | 1.01600i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.0000 | − | 15.8745i | 0.670478 | − | 0.760251i | ||||
\(437\) | 10.5830i | 0.506254i | ||||||||
\(438\) | 24.5000 | + | 9.26013i | 1.17066 | + | 0.442466i | ||||
\(439\) | 8.00000 | 0.381819 | 0.190910 | − | 0.981608i | \(-0.438856\pi\) | ||||
0.190910 | + | 0.981608i | \(0.438856\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −36.0000 | −1.71429 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.1033i | 1.38274i | 0.722502 | + | 0.691369i | \(0.242992\pi\) | ||||
−0.722502 | + | 0.691369i | \(0.757008\pi\) | |||||||
\(444\) | 42.0000 | + | 37.0405i | 1.99323 | + | 1.75787i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −8.00000 | + | 21.1660i | −0.378811 | + | 1.00224i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 18.0000 | − | 26.4575i | 0.850420 | − | 1.25000i | ||||
\(449\) | 27.0000 | 1.27421 | 0.637104 | − | 0.770778i | \(-0.280132\pi\) | ||||
0.637104 | + | 0.770778i | \(0.280132\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 13.2288i | − | 0.622918i | ||||||
\(452\) | 22.5000 | + | 19.8431i | 1.05831 | + | 0.933343i | ||||
\(453\) | − | 10.5830i | − | 0.497233i | ||||||
\(454\) | 21.0000 | + | 7.93725i | 0.985579 | + | 0.372514i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −17.5000 | + | 9.26013i | −0.819513 | + | 0.433645i | ||||
\(457\) | −27.0000 | −1.26301 | −0.631503 | − | 0.775373i | \(-0.717562\pi\) | ||||
−0.631503 | + | 0.775373i | \(0.717562\pi\) | |||||||
\(458\) | 28.0000 | + | 10.5830i | 1.30835 | + | 0.494511i | ||||
\(459\) | − | 7.93725i | − | 0.370479i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 42.3320i | − | 1.97160i | −0.167927 | − | 0.985799i | \(-0.553707\pi\) | ||
0.167927 | − | 0.985799i | \(-0.446293\pi\) | |||||||
\(462\) | 14.0000 | − | 37.0405i | 0.651339 | − | 1.72328i | ||||
\(463\) | −8.00000 | −0.371792 | −0.185896 | − | 0.982569i | \(-0.559519\pi\) | ||||
−0.185896 | + | 0.982569i | \(0.559519\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.00000 | − | 7.93725i | 0.138972 | − | 0.367686i | ||||
\(467\) | − | 26.4575i | − | 1.22431i | −0.790739 | − | 0.612154i | \(-0.790303\pi\) | ||
0.790739 | − | 0.612154i | \(-0.209697\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 31.7490i | 1.46603i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 28.0000 | 1.29017 | ||||||||
\(472\) | −7.00000 | − | 13.2288i | −0.322201 | − | 0.608903i | ||||
\(473\) | 14.0000 | 0.643721 | ||||||||
\(474\) | −14.0000 | − | 5.29150i | −0.643041 | − | 0.243047i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 18.0000 | + | 15.8745i | 0.825029 | + | 0.727607i | ||||
\(477\) | − | 42.3320i | − | 1.93825i | ||||||
\(478\) | −4.00000 | + | 10.5830i | −0.182956 | + | 0.484055i | ||||
\(479\) | 4.00000 | 0.182765 | 0.0913823 | − | 0.995816i | \(-0.470871\pi\) | ||||
0.0913823 | + | 0.995816i | \(0.470871\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −10.5000 | + | 27.7804i | −0.478262 | + | 1.26536i | ||||
\(483\) | − | 42.3320i | − | 1.92617i | ||||||
\(484\) | −6.00000 | − | 5.29150i | −0.272727 | − | 0.240523i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 28.0000 | + | 10.5830i | 1.27011 | + | 0.480055i | ||||
\(487\) | −12.0000 | −0.543772 | −0.271886 | − | 0.962329i | \(-0.587647\pi\) | ||||
−0.271886 | + | 0.962329i | \(0.587647\pi\) | |||||||
\(488\) | −14.0000 | − | 26.4575i | −0.633750 | − | 1.19768i | ||||
\(489\) | −35.0000 | −1.58275 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.29150i | 0.238802i | 0.992846 | + | 0.119401i | \(0.0380974\pi\) | ||||
−0.992846 | + | 0.119401i | \(0.961903\pi\) | |||||||
\(492\) | 17.5000 | − | 19.8431i | 0.788961 | − | 0.894598i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | + | 15.8745i | 0.0898027 | + | 0.712786i | ||||
\(497\) | 32.0000 | 1.43540 | ||||||||
\(498\) | 10.5000 | − | 27.7804i | 0.470516 | − | 1.24487i | ||||
\(499\) | 26.4575i | 1.18440i | 0.805791 | + | 0.592200i | \(0.201741\pi\) | ||||
−0.805791 | + | 0.592200i | \(0.798259\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −10.5000 | − | 3.96863i | −0.468638 | − | 0.177128i | ||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 40.0000 | − | 21.1660i | 1.78174 | − | 0.942809i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 14.0000 | + | 5.29150i | 0.622376 | + | 0.235236i | ||||
\(507\) | − | 34.3948i | − | 1.52753i | ||||||
\(508\) | −18.0000 | − | 15.8745i | −0.798621 | − | 0.704317i | ||||
\(509\) | − | 31.7490i | − | 1.40725i | −0.710571 | − | 0.703625i | \(-0.751563\pi\) | ||
0.710571 | − | 0.703625i | \(-0.248437\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −28.0000 | −1.23865 | ||||||||
\(512\) | −2.50000 | + | 22.4889i | −0.110485 | + | 0.993878i | ||||
\(513\) | −7.00000 | −0.309058 | ||||||||
\(514\) | 7.00000 | − | 18.5203i | 0.308757 | − | 0.816894i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 21.0000 | + | 18.5203i | 0.924473 | + | 0.815309i | ||||
\(517\) | − | 21.1660i | − | 0.930880i | ||||||
\(518\) | −56.0000 | − | 21.1660i | −2.46050 | − | 0.929981i | ||||
\(519\) | −56.0000 | −2.45813 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.00000 | 0.131432 | 0.0657162 | − | 0.997838i | \(-0.479067\pi\) | ||||
0.0657162 | + | 0.997838i | \(0.479067\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 2.64575i | − | 0.115691i | −0.998326 | − | 0.0578453i | \(-0.981577\pi\) | ||
0.998326 | − | 0.0578453i | \(-0.0184230\pi\) | |||||||
\(524\) | −21.0000 | + | 23.8118i | −0.917389 | + | 1.04022i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.00000 | − | 15.8745i | 0.261612 | − | 0.692161i | ||||
\(527\) | −12.0000 | −0.522728 | ||||||||
\(528\) | 3.50000 | + | 27.7804i | 0.152318 | + | 1.20899i | ||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 21.1660i | − | 0.918527i | ||||||
\(532\) | 14.0000 | − | 15.8745i | 0.606977 | − | 0.688247i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 3.50000 | + | 1.32288i | 0.151460 | + | 0.0572464i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −10.5000 | − | 19.8431i | −0.453531 | − | 0.857093i | ||||
\(537\) | 63.0000 | 2.71865 | ||||||||
\(538\) | −28.0000 | − | 10.5830i | −1.20717 | − | 0.456266i | ||||
\(539\) | 23.8118i | 1.02565i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 21.1660i | − | 0.909998i | −0.890492 | − | 0.454999i | \(-0.849640\pi\) | ||
0.890492 | − | 0.454999i | \(-0.150360\pi\) | |||||||
\(542\) | −10.0000 | + | 26.4575i | −0.429537 | + | 1.13645i | ||||
\(543\) | 28.0000 | 1.20160 | ||||||||
\(544\) | −16.5000 | − | 3.96863i | −0.707432 | − | 0.170153i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.5203i | 0.791869i | 0.918279 | + | 0.395935i | \(0.129579\pi\) | ||||
−0.918279 | + | 0.395935i | \(0.870421\pi\) | |||||||
\(548\) | 28.5000 | + | 25.1346i | 1.21746 | + | 1.07370i | ||||
\(549\) | − | 42.3320i | − | 1.80669i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 14.0000 | + | 26.4575i | 0.595880 | + | 1.12611i | ||||
\(553\) | 16.0000 | 0.680389 | ||||||||
\(554\) | −28.0000 | − | 10.5830i | −1.18961 | − | 0.449629i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −24.5000 | + | 27.7804i | −1.03903 | + | 1.17815i | ||||
\(557\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(558\) | −8.00000 | + | 21.1660i | −0.338667 | + | 0.896029i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −21.0000 | −0.886621 | ||||||||
\(562\) | −11.0000 | + | 29.1033i | −0.464007 | + | 1.22765i | ||||
\(563\) | 15.8745i | 0.669031i | 0.942390 | + | 0.334515i | \(0.108573\pi\) | ||||
−0.942390 | + | 0.334515i | \(0.891427\pi\) | |||||||
\(564\) | 28.0000 | − | 31.7490i | 1.17901 | − | 1.33687i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −17.5000 | − | 6.61438i | −0.735580 | − | 0.278023i | ||||
\(567\) | −20.0000 | −0.839921 | ||||||||
\(568\) | −20.0000 | + | 10.5830i | −0.839181 | + | 0.444053i | ||||
\(569\) | 11.0000 | 0.461144 | 0.230572 | − | 0.973055i | \(-0.425940\pi\) | ||||
0.230572 | + | 0.973055i | \(0.425940\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 37.0405i | − | 1.55010i | −0.631901 | − | 0.775049i | \(-0.717725\pi\) | ||
0.631901 | − | 0.775049i | \(-0.282275\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 10.5830i | − | 0.442111i | ||||||
\(574\) | −10.0000 | + | 26.4575i | −0.417392 | + | 1.10432i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −18.0000 | + | 26.4575i | −0.750000 | + | 1.10240i | ||||
\(577\) | −7.00000 | −0.291414 | −0.145707 | − | 0.989328i | \(-0.546546\pi\) | ||||
−0.145707 | + | 0.989328i | \(0.546546\pi\) | |||||||
\(578\) | −4.00000 | + | 10.5830i | −0.166378 | + | 0.440195i | ||||
\(579\) | − | 13.2288i | − | 0.549768i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 31.7490i | 1.31717i | ||||||||
\(582\) | 7.00000 | + | 2.64575i | 0.290159 | + | 0.109670i | ||||
\(583\) | −28.0000 | −1.15964 | ||||||||
\(584\) | 17.5000 | − | 9.26013i | 0.724155 | − | 0.383187i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.0000 | − | 5.29150i | −0.578335 | − | 0.218590i | ||||
\(587\) | 7.93725i | 0.327606i | 0.986493 | + | 0.163803i | \(0.0523761\pi\) | ||||
−0.986493 | + | 0.163803i | \(0.947624\pi\) | |||||||
\(588\) | −31.5000 | + | 35.7176i | −1.29904 | + | 1.47297i | ||||
\(589\) | 10.5830i | 0.436065i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 28.0000 | 1.15177 | ||||||||
\(592\) | 42.0000 | − | 5.29150i | 1.72619 | − | 0.217479i | ||||
\(593\) | 41.0000 | 1.68367 | 0.841834 | − | 0.539736i | \(-0.181476\pi\) | ||||
0.841834 | + | 0.539736i | \(0.181476\pi\) | |||||||
\(594\) | −3.50000 | + | 9.26013i | −0.143607 | + | 0.379948i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 63.4980i | 2.59880i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.0000 | −0.490307 | −0.245153 | − | 0.969484i | \(-0.578838\pi\) | ||||
−0.245153 | + | 0.969484i | \(0.578838\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.00000 | 0.285536 | 0.142768 | − | 0.989756i | \(-0.454400\pi\) | ||||
0.142768 | + | 0.989756i | \(0.454400\pi\) | |||||||
\(602\) | −28.0000 | − | 10.5830i | −1.14119 | − | 0.431331i | ||||
\(603\) | − | 31.7490i | − | 1.29292i | ||||||
\(604\) | −6.00000 | − | 5.29150i | −0.244137 | − | 0.215308i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −14.0000 | + | 37.0405i | −0.568711 | + | 1.50467i | ||||
\(607\) | −8.00000 | −0.324710 | −0.162355 | − | 0.986732i | \(-0.551909\pi\) | ||||
−0.162355 | + | 0.986732i | \(0.551909\pi\) | |||||||
\(608\) | −3.50000 | + | 14.5516i | −0.141944 | + | 0.590147i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −18.0000 | − | 15.8745i | −0.727607 | − | 0.641689i | ||||
\(613\) | − | 10.5830i | − | 0.427444i | −0.976895 | − | 0.213722i | \(-0.931441\pi\) | ||
0.976895 | − | 0.213722i | \(-0.0685586\pi\) | |||||||
\(614\) | −3.50000 | − | 1.32288i | −0.141249 | − | 0.0533869i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −14.0000 | − | 26.4575i | −0.564076 | − | 1.06600i | ||||
\(617\) | 6.00000 | 0.241551 | 0.120775 | − | 0.992680i | \(-0.461462\pi\) | ||||
0.120775 | + | 0.992680i | \(0.461462\pi\) | |||||||
\(618\) | −28.0000 | − | 10.5830i | −1.12633 | − | 0.425711i | ||||
\(619\) | 5.29150i | 0.212683i | 0.994330 | + | 0.106342i | \(0.0339137\pi\) | ||||
−0.994330 | + | 0.106342i | \(0.966086\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.5830i | 0.424681i | ||||||||
\(622\) | −2.00000 | + | 5.29150i | −0.0801927 | + | 0.212170i | ||||
\(623\) | −4.00000 | −0.160257 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3.00000 | − | 7.93725i | 0.119904 | − | 0.317236i | ||||
\(627\) | 18.5203i | 0.739628i | ||||||||
\(628\) | 14.0000 | − | 15.8745i | 0.558661 | − | 0.633462i | ||||
\(629\) | 31.7490i | 1.26592i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.0000 | 1.43314 | 0.716569 | − | 0.697517i | \(-0.245712\pi\) | ||||
0.716569 | + | 0.697517i | \(0.245712\pi\) | |||||||
\(632\) | −10.0000 | + | 5.29150i | −0.397779 | + | 0.210485i | ||||
\(633\) | −21.0000 | −0.834675 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −42.0000 | − | 37.0405i | −1.66541 | − | 1.46875i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −32.0000 | −1.26590 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.00000 | 0.0789953 | 0.0394976 | − | 0.999220i | \(-0.487424\pi\) | ||||
0.0394976 | + | 0.999220i | \(0.487424\pi\) | |||||||
\(642\) | −3.50000 | + | 9.26013i | −0.138134 | + | 0.365468i | ||||
\(643\) | 15.8745i | 0.626029i | 0.949748 | + | 0.313015i | \(0.101339\pi\) | ||||
−0.949748 | + | 0.313015i | \(0.898661\pi\) | |||||||
\(644\) | −24.0000 | − | 21.1660i | −0.945732 | − | 0.834058i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10.5000 | − | 3.96863i | −0.413117 | − | 0.156144i | ||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | 12.5000 | − | 6.61438i | 0.491046 | − | 0.259837i | ||||
\(649\) | −14.0000 | −0.549548 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 42.3320i | − | 1.65912i | ||||||
\(652\) | −17.5000 | + | 19.8431i | −0.685353 | + | 0.777117i | ||||
\(653\) | − | 31.7490i | − | 1.24243i | −0.783638 | − | 0.621217i | \(-0.786638\pi\) | ||
0.783638 | − | 0.621217i | \(-0.213362\pi\) | |||||||
\(654\) | 14.0000 | − | 37.0405i | 0.547443 | − | 1.44840i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.50000 | − | 19.8431i | −0.0976086 | − | 0.774744i | ||||
\(657\) | 28.0000 | 1.09238 | ||||||||
\(658\) | −16.0000 | + | 42.3320i | −0.623745 | + | 1.65027i | ||||
\(659\) | − | 7.93725i | − | 0.309192i | −0.987978 | − | 0.154596i | \(-0.950592\pi\) | ||
0.987978 | − | 0.154596i | \(-0.0494075\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.1660i | 0.823262i | 0.911351 | + | 0.411631i | \(0.135041\pi\) | ||||
−0.911351 | + | 0.411631i | \(0.864959\pi\) | |||||||
\(662\) | 3.50000 | + | 1.32288i | 0.136031 | + | 0.0514150i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.5000 | − | 19.8431i | −0.407479 | − | 0.770063i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 56.0000 | + | 21.1660i | 2.16996 | + | 0.820166i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 42.3320i | 1.63665i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.0000 | −1.08093 | ||||||||
\(672\) | 14.0000 | − | 58.2065i | 0.540062 | − | 2.24537i | ||||
\(673\) | −34.0000 | −1.31060 | −0.655302 | − | 0.755367i | \(-0.727459\pi\) | ||||
−0.655302 | + | 0.755367i | \(0.727459\pi\) | |||||||
\(674\) | −7.50000 | + | 19.8431i | −0.288889 | + | 0.764329i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −19.5000 | − | 17.1974i | −0.750000 | − | 0.661438i | ||||
\(677\) | − | 42.3320i | − | 1.62695i | −0.581599 | − | 0.813476i | \(-0.697573\pi\) | ||
0.581599 | − | 0.813476i | \(-0.302427\pi\) | |||||||
\(678\) | 52.5000 | + | 19.8431i | 2.01625 | + | 0.762071i | ||||
\(679\) | −8.00000 | −0.307012 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 42.0000 | 1.60944 | ||||||||
\(682\) | 14.0000 | + | 5.29150i | 0.536088 | + | 0.202622i | ||||
\(683\) | − | 23.8118i | − | 0.911132i | −0.890202 | − | 0.455566i | \(-0.849437\pi\) | ||
0.890202 | − | 0.455566i | \(-0.150563\pi\) | |||||||
\(684\) | −14.0000 | + | 15.8745i | −0.535303 | + | 0.606977i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 4.00000 | − | 10.5830i | 0.152721 | − | 0.404061i | ||||
\(687\) | 56.0000 | 2.13653 | ||||||||
\(688\) | 21.0000 | − | 2.64575i | 0.800617 | − | 0.100868i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.8118i | 0.905842i | 0.891551 | + | 0.452921i | \(0.149618\pi\) | ||||
−0.891551 | + | 0.452921i | \(0.850382\pi\) | |||||||
\(692\) | −28.0000 | + | 31.7490i | −1.06440 | + | 1.20692i | ||||
\(693\) | − | 42.3320i | − | 1.60806i | ||||||
\(694\) | −3.50000 | − | 1.32288i | −0.132858 | − | 0.0502157i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.0000 | 0.568166 | ||||||||
\(698\) | −14.0000 | − | 5.29150i | −0.529908 | − | 0.200286i | ||||
\(699\) | − | 15.8745i | − | 0.600429i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.1660i | 0.799429i | 0.916640 | + | 0.399715i | \(0.130891\pi\) | ||||
−0.916640 | + | 0.399715i | \(0.869109\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 28.0000 | 1.05604 | ||||||||
\(704\) | 17.5000 | + | 11.9059i | 0.659556 | + | 0.448720i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.00000 | + | 23.8118i | −0.338719 | + | 0.896167i | ||||
\(707\) | − | 42.3320i | − | 1.59206i | ||||||
\(708\) | −21.0000 | − | 18.5203i | −0.789228 | − | 0.696034i | ||||
\(709\) | 21.1660i | 0.794906i | 0.917622 | + | 0.397453i | \(0.130106\pi\) | ||||
−0.917622 | + | 0.397453i | \(0.869894\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.0000 | −0.600047 | ||||||||
\(712\) | 2.50000 | − | 1.32288i | 0.0936915 | − | 0.0495769i | ||||
\(713\) | 16.0000 | 0.599205 | ||||||||
\(714\) | 42.0000 | + | 15.8745i | 1.57181 | + | 0.594089i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 31.5000 | − | 35.7176i | 1.17721 | − | 1.33483i | ||||
\(717\) | 21.1660i | 0.790459i | ||||||||
\(718\) | 18.0000 | − | 47.6235i | 0.671754 | − | 1.77729i | ||||
\(719\) | 36.0000 | 1.34257 | 0.671287 | − | 0.741198i | \(-0.265742\pi\) | ||||
0.671287 | + | 0.741198i | \(0.265742\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 32.0000 | 1.19174 | ||||||||
\(722\) | 6.00000 | − | 15.8745i | 0.223297 | − | 0.590788i | ||||
\(723\) | 55.5608i | 2.06633i | ||||||||
\(724\) | 14.0000 | − | 15.8745i | 0.520306 | − | 0.589971i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −14.0000 | − | 5.29150i | −0.519589 | − | 0.196386i | ||||
\(727\) | −16.0000 | −0.593407 | −0.296704 | − | 0.954970i | \(-0.595887\pi\) | ||||
−0.296704 | + | 0.954970i | \(0.595887\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 41.0000 | 1.51852 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.8745i | 0.587140i | ||||||||
\(732\) | −42.0000 | − | 37.0405i | −1.55236 | − | 1.36906i | ||||
\(733\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 22.0000 | + | 5.29150i | 0.810931 | + | 0.195047i | ||||
\(737\) | −21.0000 | −0.773545 | ||||||||
\(738\) | 10.0000 | − | 26.4575i | 0.368105 | − | 0.973915i | ||||
\(739\) | − | 15.8745i | − | 0.583953i | −0.956425 | − | 0.291977i | \(-0.905687\pi\) | ||
0.956425 | − | 0.291977i | \(-0.0943129\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 56.0000 | + | 21.1660i | 2.05582 | + | 0.777029i | ||||
\(743\) | 36.0000 | 1.32071 | 0.660356 | − | 0.750953i | \(-0.270405\pi\) | ||||
0.660356 | + | 0.750953i | \(0.270405\pi\) | |||||||
\(744\) | 14.0000 | + | 26.4575i | 0.513265 | + | 0.969979i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 14.0000 | + | 5.29150i | 0.512576 | + | 0.193736i | ||||
\(747\) | − | 31.7490i | − | 1.16164i | ||||||
\(748\) | −10.5000 | + | 11.9059i | −0.383918 | + | 0.435322i | ||||
\(749\) | − | 10.5830i | − | 0.386695i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.00000 | 0.291924 | 0.145962 | − | 0.989290i | \(-0.453372\pi\) | ||||
0.145962 | + | 0.989290i | \(0.453372\pi\) | |||||||
\(752\) | −4.00000 | − | 31.7490i | −0.145865 | − | 1.15777i | ||||
\(753\) | −21.0000 | −0.765283 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 14.0000 | − | 15.8745i | 0.509175 | − | 0.577350i | ||||
\(757\) | 21.1660i | 0.769292i | 0.923064 | + | 0.384646i | \(0.125676\pi\) | ||||
−0.923064 | + | 0.384646i | \(0.874324\pi\) | |||||||
\(758\) | −10.5000 | − | 3.96863i | −0.381377 | − | 0.144147i | ||||
\(759\) | 28.0000 | 1.01634 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.0000 | −1.05125 | −0.525625 | − | 0.850717i | \(-0.676168\pi\) | ||||
−0.525625 | + | 0.850717i | \(0.676168\pi\) | |||||||
\(762\) | −42.0000 | − | 15.8745i | −1.52150 | − | 0.575073i | ||||
\(763\) | 42.3320i | 1.53252i | ||||||||
\(764\) | −6.00000 | − | 5.29150i | −0.217072 | − | 0.191440i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.0000 | + | 47.6235i | −0.650366 | + | 1.72071i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 10.5000 | + | 41.0091i | 0.378886 | + | 1.47979i | ||||
\(769\) | −21.0000 | −0.757279 | −0.378640 | − | 0.925544i | \(-0.623608\pi\) | ||||
−0.378640 | + | 0.925544i | \(0.623608\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 37.0405i | − | 1.33398i | ||||||
\(772\) | −7.50000 | − | 6.61438i | −0.269931 | − | 0.238057i | ||||
\(773\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(774\) | 28.0000 | + | 10.5830i | 1.00644 | + | 0.380398i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 5.00000 | − | 2.64575i | 0.179490 | − | 0.0949769i | ||||
\(777\) | −112.000 | −4.01798 | ||||||||
\(778\) | 14.0000 | + | 5.29150i | 0.501924 | + | 0.189710i | ||||
\(779\) | − | 13.2288i | − | 0.473969i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.1660i | 0.757379i | ||||||||
\(782\) | −6.00000 | + | 15.8745i | −0.214560 | + | 0.567671i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.50000 | + | 35.7176i | 0.160714 | + | 1.27563i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −21.0000 | + | 55.5608i | −0.749045 | + | 1.98179i | ||||
\(787\) | − | 26.4575i | − | 0.943108i | −0.881837 | − | 0.471554i | \(-0.843693\pi\) | ||
0.881837 | − | 0.471554i | \(-0.156307\pi\) | |||||||
\(788\) | 14.0000 | − | 15.8745i | 0.498729 | − | 0.565506i | ||||
\(789\) | − | 31.7490i | − | 1.13029i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −60.0000 | −2.13335 | ||||||||
\(792\) | 14.0000 | + | 26.4575i | 0.497468 | + | 0.940127i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −28.0000 | − | 10.5830i | −0.993683 | − | 0.375577i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 36.0000 | + | 31.7490i | 1.27599 | + | 1.12531i | ||||
\(797\) | 31.7490i | 1.12461i | 0.826931 | + | 0.562304i | \(0.190085\pi\) | ||||
−0.826931 | + | 0.562304i | \(0.809915\pi\) | |||||||
\(798\) | 14.0000 | − | 37.0405i | 0.495595 | − | 1.31122i | ||||
\(799\) | 24.0000 | 0.849059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.00000 | 0.141333 | ||||||||
\(802\) | 13.5000 | − | 35.7176i | 0.476702 | − | 1.26123i | ||||
\(803\) | − | 18.5203i | − | 0.653566i | ||||||
\(804\) | −31.5000 | − | 27.7804i | −1.11092 | − | 0.979739i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −56.0000 | −1.97129 | ||||||||
\(808\) | 14.0000 | + | 26.4575i | 0.492518 | + | 0.930772i | ||||
\(809\) | 10.0000 | 0.351581 | 0.175791 | − | 0.984428i | \(-0.443752\pi\) | ||||
0.175791 | + | 0.984428i | \(0.443752\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.29150i | 0.185810i | 0.995675 | + | 0.0929049i | \(0.0296153\pi\) | ||||
−0.995675 | + | 0.0929049i | \(0.970385\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 52.9150i | 1.85581i | ||||||||
\(814\) | 14.0000 | − | 37.0405i | 0.490700 | − | 1.29827i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −31.5000 | + | 3.96863i | −1.10272 | + | 0.138930i | ||||
\(817\) | 14.0000 | 0.489798 | ||||||||
\(818\) | 1.50000 | − | 3.96863i | 0.0524463 | − | 0.138760i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 10.5830i | − | 0.369349i | −0.982800 | − | 0.184675i | \(-0.940877\pi\) | ||
0.982800 | − | 0.184675i | \(-0.0591232\pi\) | |||||||
\(822\) | 66.5000 | + | 25.1346i | 2.31945 | + | 0.876671i | ||||
\(823\) | −24.0000 | −0.836587 | −0.418294 | − | 0.908312i | \(-0.637372\pi\) | ||||
−0.418294 | + | 0.908312i | \(0.637372\pi\) | |||||||
\(824\) | −20.0000 | + | 10.5830i | −0.696733 | + | 0.368676i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 28.0000 | + | 10.5830i | 0.974245 | + | 0.368230i | ||||
\(827\) | − | 13.2288i | − | 0.460009i | −0.973190 | − | 0.230004i | \(-0.926126\pi\) | ||
0.973190 | − | 0.230004i | \(-0.0738741\pi\) | |||||||
\(828\) | 24.0000 | + | 21.1660i | 0.834058 | + | 0.735570i | ||||
\(829\) | − | 21.1660i | − | 0.735126i | −0.929999 | − | 0.367563i | \(-0.880192\pi\) | ||
0.929999 | − | 0.367563i | \(-0.119808\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −56.0000 | −1.94262 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −27.0000 | −0.935495 | ||||||||
\(834\) | −24.5000 | + | 64.8209i | −0.848366 | + | 2.24456i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 10.5000 | + | 9.26013i | 0.363150 | + | 0.320268i | ||||
\(837\) | 10.5830i | 0.365802i | ||||||||
\(838\) | −24.5000 | − | 9.26013i | −0.846338 | − | 0.319886i | ||||
\(839\) | 40.0000 | 1.38095 | 0.690477 | − | 0.723355i | \(-0.257401\pi\) | ||||
0.690477 | + | 0.723355i | \(0.257401\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 28.0000 | + | 10.5830i | 0.964944 | + | 0.364714i | ||||
\(843\) | 58.2065i | 2.00474i | ||||||||
\(844\) | −10.5000 | + | 11.9059i | −0.361425 | + | 0.409817i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 16.0000 | − | 42.3320i | 0.550091 | − | 1.45540i | ||||
\(847\) | 16.0000 | 0.549767 | ||||||||
\(848\) | −42.0000 | + | 5.29150i | −1.44229 | + | 0.181711i | ||||
\(849\) | −35.0000 | −1.20120 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 42.3320i | − | 1.45112i | ||||||
\(852\) | −28.0000 | + | 31.7490i | −0.959264 | + | 1.08770i | ||||
\(853\) | 52.9150i | 1.81178i | 0.423517 | + | 0.905888i | \(0.360795\pi\) | ||||
−0.423517 | + | 0.905888i | \(0.639205\pi\) | |||||||
\(854\) | 56.0000 | + | 21.1660i | 1.91628 | + | 0.724286i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.50000 | + | 6.61438i | 0.119628 | + | 0.226075i | ||||
\(857\) | 21.0000 | 0.717346 | 0.358673 | − | 0.933463i | \(-0.383229\pi\) | ||||
0.358673 | + | 0.933463i | \(0.383229\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.64575i | 0.0902719i | 0.998981 | + | 0.0451359i | \(0.0143721\pi\) | ||||
−0.998981 | + | 0.0451359i | \(0.985628\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 52.9150i | 1.80334i | ||||||||
\(862\) | 6.00000 | − | 15.8745i | 0.204361 | − | 0.540688i | ||||
\(863\) | 24.0000 | 0.816970 | 0.408485 | − | 0.912765i | \(-0.366057\pi\) | ||||
0.408485 | + | 0.912765i | \(0.366057\pi\) | |||||||
\(864\) | −3.50000 | + | 14.5516i | −0.119072 | + | 0.495057i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 18.5000 | − | 48.9464i | 0.628656 | − | 1.66327i | ||||
\(867\) | 21.1660i | 0.718835i | ||||||||
\(868\) | −24.0000 | − | 21.1660i | −0.814613 | − | 0.718421i | ||||
\(869\) | 10.5830i | 0.359004i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −14.0000 | − | 26.4575i | −0.474100 | − | 0.895964i | ||||
\(873\) | 8.00000 | 0.270759 | ||||||||
\(874\) | 14.0000 | + | 5.29150i | 0.473557 | + | 0.178988i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 24.5000 | − | 27.7804i | 0.827778 | − | 0.938612i | ||||
\(877\) | 42.3320i | 1.42945i | 0.699405 | + | 0.714725i | \(0.253448\pi\) | ||||
−0.699405 | + | 0.714725i | \(0.746552\pi\) | |||||||
\(878\) | 4.00000 | − | 10.5830i | 0.134993 | − | 0.357159i | ||||
\(879\) | −28.0000 | −0.944417 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.0000 | −1.01073 | −0.505363 | − | 0.862907i | \(-0.668641\pi\) | ||||
−0.505363 | + | 0.862907i | \(0.668641\pi\) | |||||||
\(882\) | −18.0000 | + | 47.6235i | −0.606092 | + | 1.60357i | ||||
\(883\) | − | 44.9778i | − | 1.51362i | −0.653633 | − | 0.756811i | \(-0.726756\pi\) | ||
0.653633 | − | 0.756811i | \(-0.273244\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 38.5000 | + | 14.5516i | 1.29343 | + | 0.488872i | ||||
\(887\) | 56.0000 | 1.88030 | 0.940148 | − | 0.340766i | \(-0.110687\pi\) | ||||
0.940148 | + | 0.340766i | \(0.110687\pi\) | |||||||
\(888\) | 70.0000 | − | 37.0405i | 2.34905 | − | 1.24300i | ||||
\(889\) | 48.0000 | 1.60987 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 13.2288i | − | 0.443180i | ||||||
\(892\) | 24.0000 | + | 21.1660i | 0.803579 | + | 0.708690i | ||||
\(893\) | − | 21.1660i | − | 0.708294i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −26.0000 | − | 37.0405i | −0.868599 | − | 1.23744i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 13.5000 | − | 35.7176i | 0.450501 | − | 1.19191i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 31.7490i | − | 1.05771i | ||||||
\(902\) | −17.5000 | − | 6.61438i | −0.582686 | − | 0.220235i | ||||
\(903\) | −56.0000 | −1.86356 | ||||||||
\(904\) | 37.5000 | − | 19.8431i | 1.24723 | − | 0.659973i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −14.0000 | − | 5.29150i | −0.465119 | − | 0.175798i | ||||
\(907\) | − | 5.29150i | − | 0.175701i | −0.996134 | − | 0.0878507i | \(-0.972000\pi\) | ||
0.996134 | − | 0.0878507i | \(-0.0279999\pi\) | |||||||
\(908\) | 21.0000 | − | 23.8118i | 0.696909 | − | 0.790221i | ||||
\(909\) | 42.3320i | 1.40406i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.0000 | 1.59031 | 0.795155 | − | 0.606406i | \(-0.207389\pi\) | ||||
0.795155 | + | 0.606406i | \(0.207389\pi\) | |||||||
\(912\) | 3.50000 | + | 27.7804i | 0.115897 | + | 0.919901i | ||||
\(913\) | −21.0000 | −0.694999 | ||||||||
\(914\) | −13.5000 | + | 35.7176i | −0.446540 | + | 1.18143i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 28.0000 | − | 31.7490i | 0.925146 | − | 1.04902i | ||||
\(917\) | − | 63.4980i | − | 2.09689i | ||||||
\(918\) | −10.5000 | − | 3.96863i | −0.346552 | − | 0.130984i | ||||
\(919\) | 4.00000 | 0.131948 | 0.0659739 | − | 0.997821i | \(-0.478985\pi\) | ||||
0.0659739 | + | 0.997821i | \(0.478985\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.00000 | −0.230658 | ||||||||
\(922\) | −56.0000 | − | 21.1660i | −1.84426 | − | 0.697065i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −42.0000 | − | 37.0405i | −1.38170 | − | 1.21854i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −4.00000 | + | 10.5830i | −0.131448 | + | 0.347779i | ||||
\(927\) | −32.0000 | −1.05102 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.0000 | −0.459325 | −0.229663 | − | 0.973270i | \(-0.573762\pi\) | ||||
−0.229663 | + | 0.973270i | \(0.573762\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 23.8118i | 0.780399i | ||||||||
\(932\) | −9.00000 | − | 7.93725i | −0.294805 | − | 0.259993i | ||||
\(933\) | 10.5830i | 0.346472i | ||||||||
\(934\) | −35.0000 | − | 13.2288i | −1.14523 | − | 0.432858i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.00000 | −0.228680 | −0.114340 | − | 0.993442i | \(-0.536475\pi\) | ||||
−0.114340 | + | 0.993442i | \(0.536475\pi\) | |||||||
\(938\) | 42.0000 | + | 15.8745i | 1.37135 | + | 0.518321i | ||||
\(939\) | − | 15.8745i | − | 0.518045i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42.3320i | 1.37998i | 0.723817 | + | 0.689992i | \(0.242386\pi\) | ||||
−0.723817 | + | 0.689992i | \(0.757614\pi\) | |||||||
\(942\) | 14.0000 | − | 37.0405i | 0.456145 | − | 1.20685i | ||||
\(943\) | −20.0000 | −0.651290 | ||||||||
\(944\) | −21.0000 | + | 2.64575i | −0.683492 | + | 0.0861119i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.00000 | − | 18.5203i | 0.227590 | − | 0.602146i | ||||
\(947\) | 15.8745i | 0.515852i | 0.966165 | + | 0.257926i | \(0.0830391\pi\) | ||||
−0.966165 | + | 0.257926i | \(0.916961\pi\) | |||||||
\(948\) | −14.0000 | + | 15.8745i | −0.454699 | + | 0.515580i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 30.0000 | − | 15.8745i | 0.972306 | − | 0.514496i | ||||
\(953\) | 5.00000 | 0.161966 | 0.0809829 | − | 0.996715i | \(-0.474194\pi\) | ||||
0.0809829 | + | 0.996715i | \(0.474194\pi\) | |||||||
\(954\) | −56.0000 | − | 21.1660i | −1.81307 | − | 0.685275i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 12.0000 | + | 10.5830i | 0.388108 | + | 0.342279i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.00000 | − | 5.29150i | 0.0646171 | − | 0.170961i | ||||
\(959\) | −76.0000 | −2.45417 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.5830i | 0.341033i | ||||||||
\(964\) | 31.5000 | + | 27.7804i | 1.01455 | + | 0.894746i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −56.0000 | − | 21.1660i | −1.80177 | − | 0.681005i | ||||
\(967\) | 8.00000 | 0.257263 | 0.128631 | − | 0.991692i | \(-0.458942\pi\) | ||||
0.128631 | + | 0.991692i | \(0.458942\pi\) | |||||||
\(968\) | −10.0000 | + | 5.29150i | −0.321412 | + | 0.170075i | ||||
\(969\) | −21.0000 | −0.674617 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.8118i | 0.764156i | 0.924130 | + | 0.382078i | \(0.124791\pi\) | ||||
−0.924130 | + | 0.382078i | \(0.875209\pi\) | |||||||
\(972\) | 28.0000 | − | 31.7490i | 0.898100 | − | 1.01835i | ||||
\(973\) | − | 74.0810i | − | 2.37493i | ||||||
\(974\) | −6.00000 | + | 15.8745i | −0.192252 | + | 0.508652i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −42.0000 | + | 5.29150i | −1.34439 | + | 0.169377i | ||||
\(977\) | 37.0000 | 1.18373 | 0.591867 | − | 0.806035i | \(-0.298391\pi\) | ||||
0.591867 | + | 0.806035i | \(0.298391\pi\) | |||||||
\(978\) | −17.5000 | + | 46.3006i | −0.559588 | + | 1.48053i | ||||
\(979\) | − | 2.64575i | − | 0.0845586i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 42.3320i | − | 1.35156i | ||||||
\(982\) | 7.00000 | + | 2.64575i | 0.223379 | + | 0.0844293i | ||||
\(983\) | −28.0000 | −0.893061 | −0.446531 | − | 0.894768i | \(-0.647341\pi\) | ||||
−0.446531 | + | 0.894768i | \(0.647341\pi\) | |||||||
\(984\) | −17.5000 | − | 33.0719i | −0.557880 | − | 1.05429i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 84.6640i | 2.69489i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 21.1660i | − | 0.673040i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.0000 | 1.39771 | 0.698853 | − | 0.715265i | \(-0.253694\pi\) | ||||
0.698853 | + | 0.715265i | \(0.253694\pi\) | |||||||
\(992\) | 22.0000 | + | 5.29150i | 0.698501 | + | 0.168005i | ||||
\(993\) | 7.00000 | 0.222138 | ||||||||
\(994\) | 16.0000 | − | 42.3320i | 0.507489 | − | 1.34269i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −31.5000 | − | 27.7804i | −0.998116 | − | 0.880255i | ||||
\(997\) | 42.3320i | 1.34067i | 0.742059 | + | 0.670334i | \(0.233849\pi\) | ||||
−0.742059 | + | 0.670334i | \(0.766151\pi\) | |||||||
\(998\) | 35.0000 | + | 13.2288i | 1.10791 | + | 0.418749i | ||||
\(999\) | 28.0000 | 0.885881 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))