Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1800,2,Mod(901,1800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1800.901");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1800.k (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: | \(14.3730723638\) |
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: | no (minimal twist has level 200) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 901.1 | ||
Root | \(0.500000 - 1.32288i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1800.901 |
Dual form | 1800.2.k.f.901.2 |
$q$-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 \(\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1001\) | \(1351\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 1.32288i | 0.353553 | − | 0.935414i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.50000 | − | 1.32288i | −0.750000 | − | 0.661438i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.00000 | −1.51186 | −0.755929 | − | 0.654654i | \(-0.772814\pi\) | ||||
−0.755929 | + | 0.654654i | \(0.772814\pi\) | |||||||
\(8\) | −2.50000 | + | 1.32288i | −0.883883 | + | 0.467707i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.64575i | − | 0.797724i | −0.917011 | − | 0.398862i | \(-0.869405\pi\) | ||
0.917011 | − | 0.398862i | \(-0.130595\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 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 | \(0.618522\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.64575i | 0.606977i | 0.952835 | + | 0.303488i | \(0.0981514\pi\) | ||||
−0.952835 | + | 0.303488i | \(0.901849\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.50000 | − | 1.32288i | −0.746203 | − | 0.282038i | ||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 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 | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.50000 | + | 3.96863i | −0.257248 | + | 0.680614i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.5830i | 1.73984i | 0.493197 | + | 0.869918i | \(0.335828\pi\) | ||||
−0.493197 | + | 0.869918i | \(0.664172\pi\) | |||||||
\(38\) | 3.50000 | + | 1.32288i | 0.567775 | + | 0.214599i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.00000 | 0.780869 | 0.390434 | − | 0.920631i | \(-0.372325\pi\) | ||||
0.390434 | + | 0.920631i | \(0.372325\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.29150i | 0.806947i | 0.914991 | + | 0.403473i | \(0.132197\pi\) | ||||
−0.914991 | + | 0.403473i | \(0.867803\pi\) | |||||||
\(44\) | −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 | \(0.698301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.00000 | 1.28571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.5830i | 1.45369i | 0.686803 | + | 0.726844i | \(0.259014\pi\) | ||||
−0.686803 | + | 0.726844i | \(0.740986\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 10.0000 | − | 5.29150i | 1.33631 | − | 0.707107i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 5.29150i | − | 0.688895i | −0.938806 | − | 0.344447i | \(-0.888066\pi\) | ||
0.938806 | − | 0.344447i | \(-0.111934\pi\) | |||||||
\(60\) | 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 | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.50000 | − | 6.61438i | 0.562500 | − | 0.826797i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 7.93725i | − | 0.969690i | −0.874600 | − | 0.484845i | \(-0.838876\pi\) | ||
0.874600 | − | 0.484845i | \(-0.161124\pi\) | |||||||
\(68\) | 4.50000 | + | 3.96863i | 0.545705 | + | 0.481267i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.00000 | 0.819288 | 0.409644 | − | 0.912245i | \(-0.365653\pi\) | ||||
0.409644 | + | 0.912245i | \(0.365653\pi\) | |||||||
\(74\) | 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 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.50000 | − | 6.61438i | 0.276079 | − | 0.730436i | ||||
\(83\) | 7.93725i | 0.871227i | 0.900134 | + | 0.435613i | \(0.143469\pi\) | ||||
−0.900134 | + | 0.435613i | \(0.856531\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 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 | \(-0.483122\pi\) | ||||
0.0529999 | + | 0.998595i | \(0.483122\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.00000 | − | 5.29150i | −0.625543 | − | 0.551677i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.00000 | + | 10.5830i | −0.412568 | + | 1.09155i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.00000 | 0.203069 | 0.101535 | − | 0.994832i | \(-0.467625\pi\) | ||||
0.101535 | + | 0.994832i | \(0.467625\pi\) | |||||||
\(98\) | 4.50000 | − | 11.9059i | 0.454569 | − | 1.20268i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.5830i | 1.05305i | 0.850160 | + | 0.526524i | \(0.176505\pi\) | ||||
−0.850160 | + | 0.526524i | \(0.823495\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.00000 | −0.788263 | −0.394132 | − | 0.919054i | \(-0.628955\pi\) | ||||
−0.394132 | + | 0.919054i | \(0.628955\pi\) | |||||||
\(104\) | 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 | \(-0.0408196\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.5830i | 1.01367i | 0.862044 | + | 0.506834i | \(0.169184\pi\) | ||||
−0.862044 | + | 0.506834i | \(0.830816\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.00000 | − | 15.8745i | −0.188982 | − | 1.50000i | ||||
\(113\) | −15.0000 | −1.41108 | −0.705541 | − | 0.708669i | \(-0.749296\pi\) | ||||
−0.705541 | + | 0.708669i | \(0.749296\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 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 | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.00000 | − | 5.29150i | −0.538816 | − | 0.475191i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.0000 | −1.06483 | −0.532414 | − | 0.846484i | \(-0.678715\pi\) | ||||
−0.532414 | + | 0.846484i | \(0.678715\pi\) | |||||||
\(128\) | −6.50000 | − | 9.26013i | −0.574524 | − | 0.818488i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.8745i | 1.38696i | 0.720475 | + | 0.693481i | \(0.243924\pi\) | ||||
−0.720475 | + | 0.693481i | \(0.756076\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 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 | \(0.801425\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 18.5203i | − | 1.57087i | −0.618945 | − | 0.785434i | \(-0.712440\pi\) | ||
0.618945 | − | 0.785434i | \(-0.287560\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.00000 | + | 10.5830i | −0.335673 | + | 0.888106i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.50000 | − | 9.26013i | 0.289662 | − | 0.766374i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 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 | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 14.0000 | + | 5.29150i | 1.12815 | + | 0.426401i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 10.5830i | − | 0.844616i | −0.906452 | − | 0.422308i | \(-0.861220\pi\) | ||
0.906452 | − | 0.422308i | \(-0.138780\pi\) | |||||||
\(158\) | 2.00000 | − | 5.29150i | 0.159111 | − | 0.420969i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.0000 | −1.26098 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.2288i | 1.03616i | 0.855333 | + | 0.518078i | \(0.173352\pi\) | ||||
−0.855333 | + | 0.518078i | \(0.826648\pi\) | |||||||
\(164\) | −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 | \(0.5\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 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 | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.500000 | − | 1.32288i | 0.0374766 | − | 0.0991537i | ||||
\(179\) | − | 23.8118i | − | 1.77977i | −0.456180 | − | 0.889887i | \(-0.650783\pi\) | ||
0.456180 | − | 0.889887i | \(-0.349217\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.5830i | 0.786629i | 0.919404 | + | 0.393314i | \(0.128672\pi\) | ||||
−0.919404 | + | 0.393314i | \(0.871328\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −10.0000 | + | 5.29150i | −0.737210 | + | 0.390095i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.93725i | 0.580429i | ||||||||
\(188\) | 12.0000 | + | 10.5830i | 0.875190 | + | 0.771845i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.00000 | −0.289430 | −0.144715 | − | 0.989473i | \(-0.546227\pi\) | ||||
−0.144715 | + | 0.989473i | \(0.546227\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.00000 | −0.359908 | −0.179954 | − | 0.983675i | \(-0.557595\pi\) | ||||
−0.179954 | + | 0.983675i | \(0.557595\pi\) | |||||||
\(194\) | 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 | \(0.876954\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.0000 | −1.70131 | −0.850657 | − | 0.525720i | \(-0.823796\pi\) | ||||
−0.850657 | + | 0.525720i | \(0.823796\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 14.0000 | + | 5.29150i | 0.985037 | + | 0.372309i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.00000 | + | 10.5830i | −0.278693 | + | 0.737353i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 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 | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.50000 | − | 1.32288i | −0.239255 | − | 0.0904299i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.0000 | −1.08615 | ||||||||
\(218\) | 14.0000 | + | 5.29150i | 0.948200 | + | 0.358386i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.0000 | 1.07144 | 0.535720 | − | 0.844396i | \(-0.320040\pi\) | ||||
0.535720 | + | 0.844396i | \(0.320040\pi\) | |||||||
\(224\) | −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 | \(0.823386\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.1660i | 1.39869i | 0.714785 | + | 0.699345i | \(0.246525\pi\) | ||||
−0.714785 | + | 0.699345i | \(0.753475\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 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 | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.00000 | − | 15.8745i | 0.388922 | − | 1.02899i | ||||
\(239\) | 8.00000 | 0.517477 | 0.258738 | − | 0.965947i | \(-0.416693\pi\) | ||||
0.258738 | + | 0.965947i | \(0.416693\pi\) | |||||||
\(240\) | 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 | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 14.0000 | − | 15.8745i | 0.896258 | − | 1.01626i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −10.0000 | + | 5.29150i | −0.635001 | + | 0.336011i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.93725i | 0.500995i | 0.968117 | + | 0.250498i | \(0.0805942\pi\) | ||||
−0.968117 | + | 0.250498i | \(0.919406\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 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 | \(0.356166\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 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 | \(0.379366\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −14.0000 | − | 5.29150i | −0.858395 | − | 0.324443i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −10.5000 | + | 11.9059i | −0.641390 | + | 0.727267i | ||||
\(269\) | 21.1660i | 1.29051i | 0.763965 | + | 0.645257i | \(0.223250\pi\) | ||||
−0.763965 | + | 0.645257i | \(0.776750\pi\) | |||||||
\(270\) | 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 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.1660i | 1.27174i | 0.771795 | + | 0.635871i | \(0.219359\pi\) | ||||
−0.771795 | + | 0.635871i | \(0.780641\pi\) | |||||||
\(278\) | −24.5000 | − | 9.26013i | −1.46941 | − | 0.555386i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.0000 | 1.31241 | 0.656205 | − | 0.754583i | \(-0.272161\pi\) | ||||
0.656205 | + | 0.754583i | \(0.272161\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.2288i | 0.786368i | 0.919460 | + | 0.393184i | \(0.128626\pi\) | ||||
−0.919460 | + | 0.393184i | \(0.871374\pi\) | |||||||
\(284\) | 12.0000 | + | 10.5830i | 0.712069 | + | 0.627986i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.0000 | −1.18056 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −10.5000 | − | 9.26013i | −0.614466 | − | 0.541908i | ||||
\(293\) | − | 10.5830i | − | 0.618266i | −0.951019 | − | 0.309133i | \(-0.899961\pi\) | ||
0.951019 | − | 0.309133i | \(-0.100039\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −14.0000 | − | 26.4575i | −0.813733 | − | 1.53781i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 21.1660i | − | 1.21999i | ||||||
\(302\) | 2.00000 | − | 5.29150i | 0.115087 | − | 0.304492i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −10.5000 | + | 1.32288i | −0.602216 | + | 0.0758721i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.64575i | 0.151001i | 0.997146 | + | 0.0755005i | \(0.0240554\pi\) | ||||
−0.997146 | + | 0.0755005i | \(0.975945\pi\) | |||||||
\(308\) | 14.0000 | − | 15.8745i | 0.797724 | − | 0.904534i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.00000 | 0.226819 | 0.113410 | − | 0.993548i | \(-0.463823\pi\) | ||||
0.113410 | + | 0.993548i | \(0.463823\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.00000 | −0.339140 | −0.169570 | − | 0.985518i | \(-0.554238\pi\) | ||||
−0.169570 | + | 0.985518i | \(0.554238\pi\) | |||||||
\(314\) | −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 | \(\pi\) | |||||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.00000 | + | 21.1660i | −0.445823 | + | 1.17954i | ||||
\(323\) | − | 7.93725i | − | 0.441641i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 17.5000 | + | 6.61438i | 0.969235 | + | 0.366337i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −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 | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.0000 | 0.817102 | 0.408551 | − | 0.912735i | \(-0.366034\pi\) | ||||
0.408551 | + | 0.912735i | \(0.366034\pi\) | |||||||
\(338\) | 6.50000 | − | 17.1974i | 0.353553 | − | 0.935414i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 10.5830i | − | 0.573102i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −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 | \(0.659008\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.50000 | − | 1.32288i | −0.0794998 | − | 0.0701123i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −31.5000 | − | 11.9059i | −1.66483 | − | 0.629245i | ||||
\(359\) | −36.0000 | −1.90001 | −0.950004 | − | 0.312239i | \(-0.898921\pi\) | ||||
−0.950004 | + | 0.312239i | \(0.898921\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.0000 | 0.631579 | ||||||||
\(362\) | 14.0000 | + | 5.29150i | 0.735824 | + | 0.278115i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(368\) | 2.00000 | + | 15.8745i | 0.104257 | + | 0.827516i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 42.3320i | − | 2.19777i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 10.5830i | − | 0.547967i | −0.961734 | − | 0.273984i | \(-0.911659\pi\) | ||
0.961734 | − | 0.273984i | \(-0.0883414\pi\) | |||||||
\(374\) | 10.5000 | + | 3.96863i | 0.542942 | + | 0.205213i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 20.0000 | − | 10.5830i | 1.03142 | − | 0.545777i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 7.93725i | − | 0.407709i | −0.979001 | − | 0.203855i | \(-0.934653\pi\) | ||
0.979001 | − | 0.203855i | \(-0.0653470\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.00000 | + | 5.29150i | −0.102329 | + | 0.270737i | ||||
\(383\) | −36.0000 | −1.83951 | −0.919757 | − | 0.392488i | \(-0.871614\pi\) | ||||
−0.919757 | + | 0.392488i | \(0.871614\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.50000 | + | 6.61438i | −0.127247 | + | 0.336663i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.00000 | − | 2.64575i | −0.152302 | − | 0.134318i | ||||
\(389\) | − | 10.5830i | − | 0.536580i | −0.963338 | − | 0.268290i | \(-0.913542\pi\) | ||
0.963338 | − | 0.268290i | \(-0.0864585\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.0000 | −0.606866 | ||||||||
\(392\) | −22.5000 | + | 11.9059i | −1.13642 | + | 0.601338i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 14.0000 | + | 5.29150i | 0.705310 | + | 0.266582i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.1660i | 1.06229i | 0.847280 | + | 0.531146i | \(0.178238\pi\) | ||||
−0.847280 | + | 0.531146i | \(0.821762\pi\) | |||||||
\(398\) | −12.0000 | + | 31.7490i | −0.601506 | + | 1.59143i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.0000 | −1.34832 | −0.674158 | − | 0.738587i | \(-0.735493\pi\) | ||||
−0.674158 | + | 0.738587i | \(0.735493\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 14.0000 | − | 15.8745i | 0.696526 | − | 0.789786i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 28.0000 | 1.38791 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.00000 | 0.148340 | 0.0741702 | − | 0.997246i | \(-0.476369\pi\) | ||||
0.0741702 | + | 0.997246i | \(0.476369\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.0000 | + | 10.5830i | 0.591198 | + | 0.521387i | ||||
\(413\) | 21.1660i | 1.04151i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.50000 | − | 9.26013i | 0.171191 | − | 0.452928i | ||||
\(419\) | 18.5203i | 0.904774i | 0.891822 | + | 0.452387i | \(0.149427\pi\) | ||||
−0.891822 | + | 0.452387i | \(0.850573\pi\) | |||||||
\(420\) | 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 | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −14.0000 | − | 26.4575i | −0.679900 | − | 1.28489i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 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 | \(-0.593326\pi\) | ||||
−0.289010 | + | 0.957326i | \(0.593326\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −37.0000 | −1.77811 | −0.889053 | − | 0.457804i | \(-0.848636\pi\) | ||||
−0.889053 | + | 0.457804i | \(0.848636\pi\) | |||||||
\(434\) | −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 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.00000 | 0.381819 | 0.190910 | − | 0.981608i | \(-0.438856\pi\) | ||||
0.190910 | + | 0.981608i | \(0.438856\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.1033i | 1.38274i | 0.722502 | + | 0.691369i | \(0.242992\pi\) | ||||
−0.722502 | + | 0.691369i | \(0.757008\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 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 | \(-0.719868\pi\) | ||||
−0.637104 | + | 0.770778i | \(0.719868\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 13.2288i | − | 0.622918i | ||||||
\(452\) | 22.5000 | + | 19.8431i | 1.05831 | + | 0.933343i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 21.0000 | + | 7.93725i | 0.985579 | + | 0.372514i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.0000 | 1.26301 | 0.631503 | − | 0.775373i | \(-0.282438\pi\) | ||||
0.631503 | + | 0.775373i | \(0.282438\pi\) | |||||||
\(458\) | 28.0000 | + | 10.5830i | 1.30835 | + | 0.494511i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 42.3320i | 1.97160i | 0.167927 | + | 0.985799i | \(0.446293\pi\) | ||||
−0.167927 | + | 0.985799i | \(0.553707\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.00000 | 0.371792 | 0.185896 | − | 0.982569i | \(-0.440481\pi\) | ||||
0.185896 | + | 0.982569i | \(0.440481\pi\) | |||||||
\(464\) | 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 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.00000 | + | 13.2288i | 0.322201 | + | 0.608903i | ||||
\(473\) | 14.0000 | 0.643721 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −18.0000 | − | 15.8745i | −0.825029 | − | 0.727607i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.00000 | − | 10.5830i | 0.182956 | − | 0.484055i | ||||
\(479\) | −4.00000 | −0.182765 | −0.0913823 | − | 0.995816i | \(-0.529129\pi\) | ||||
−0.0913823 | + | 0.995816i | \(0.529129\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −10.5000 | + | 27.7804i | −0.478262 | + | 1.26536i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.00000 | − | 5.29150i | −0.272727 | − | 0.240523i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.0000 | 0.543772 | 0.271886 | − | 0.962329i | \(-0.412353\pi\) | ||||
0.271886 | + | 0.962329i | \(0.412353\pi\) | |||||||
\(488\) | −14.0000 | − | 26.4575i | −0.633750 | − | 1.19768i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 5.29150i | − | 0.238802i | −0.992846 | − | 0.119401i | \(-0.961903\pi\) | ||
0.992846 | − | 0.119401i | \(-0.0380974\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | + | 15.8745i | 0.0898027 | + | 0.712786i | ||||
\(497\) | 32.0000 | 1.43540 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 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 | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −14.0000 | − | 5.29150i | −0.622376 | − | 0.235236i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 18.0000 | + | 15.8745i | 0.798621 | + | 0.704317i | ||||
\(509\) | 31.7490i | 1.40725i | 0.710571 | + | 0.703625i | \(0.248437\pi\) | ||||
−0.710571 | + | 0.703625i | \(0.751563\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −28.0000 | −1.23865 | ||||||||
\(512\) | −2.50000 | + | 22.4889i | −0.110485 | + | 0.993878i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.00000 | − | 18.5203i | 0.308757 | − | 0.816894i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.1660i | 0.930880i | ||||||||
\(518\) | −56.0000 | − | 21.1660i | −2.46050 | − | 0.929981i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.00000 | −0.131432 | −0.0657162 | − | 0.997838i | \(-0.520933\pi\) | ||||
−0.0657162 | + | 0.997838i | \(0.520933\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.64575i | 0.115691i | 0.998326 | + | 0.0578453i | \(0.0184230\pi\) | ||||
−0.998326 | + | 0.0578453i | \(0.981577\pi\) | |||||||
\(524\) | 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 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −14.0000 | + | 15.8745i | −0.606977 | + | 0.688247i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 10.5000 | + | 19.8431i | 0.453531 | + | 0.857093i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 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 | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −16.5000 | − | 3.96863i | −0.707432 | − | 0.170153i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 18.5203i | − | 0.791869i | −0.918279 | − | 0.395935i | \(-0.870421\pi\) | ||
0.918279 | − | 0.395935i | \(-0.129579\pi\) | |||||||
\(548\) | 28.5000 | + | 25.1346i | 1.21746 | + | 1.07370i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −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 | \(\pi\) | |||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 11.0000 | − | 29.1033i | 0.464007 | − | 1.22765i | ||||
\(563\) | 15.8745i | 0.669031i | 0.942390 | + | 0.334515i | \(0.108573\pi\) | ||||
−0.942390 | + | 0.334515i | \(0.891427\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 17.5000 | + | 6.61438i | 0.735580 | + | 0.278023i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 20.0000 | − | 10.5830i | 0.839181 | − | 0.444053i | ||||
\(569\) | −11.0000 | −0.461144 | −0.230572 | − | 0.973055i | \(-0.574060\pi\) | ||||
−0.230572 | + | 0.973055i | \(0.574060\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 37.0405i | − | 1.55010i | −0.631901 | − | 0.775049i | \(-0.717725\pi\) | ||
0.631901 | − | 0.775049i | \(-0.282275\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −10.0000 | + | 26.4575i | −0.417392 | + | 1.10432i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.00000 | 0.291414 | 0.145707 | − | 0.989328i | \(-0.453454\pi\) | ||||
0.145707 | + | 0.989328i | \(0.453454\pi\) | |||||||
\(578\) | −4.00000 | + | 10.5830i | −0.166378 | + | 0.440195i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 31.7490i | − | 1.31717i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 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 | \(0.947624\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.5830i | 0.436065i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −42.0000 | + | 5.29150i | −1.72619 | + | 0.217479i | ||||
\(593\) | 41.0000 | 1.68367 | 0.841834 | − | 0.539736i | \(-0.181476\pi\) | ||||
0.841834 | + | 0.539736i | \(0.181476\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.0000 | 0.490307 | 0.245153 | − | 0.969484i | \(-0.421162\pi\) | ||||
0.245153 | + | 0.969484i | \(0.421162\pi\) | |||||||
\(600\) | 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 | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.00000 | − | 5.29150i | −0.244137 | − | 0.215308i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.00000 | 0.324710 | 0.162355 | − | 0.986732i | \(-0.448091\pi\) | ||||
0.162355 | + | 0.986732i | \(0.448091\pi\) | |||||||
\(608\) | −3.50000 | + | 14.5516i | −0.141944 | + | 0.590147i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.5830i | 0.427444i | 0.976895 | + | 0.213722i | \(0.0685586\pi\) | ||||
−0.976895 | + | 0.213722i | \(0.931441\pi\) | |||||||
\(614\) | 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 | \(0.461462\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.29150i | 0.212683i | 0.994330 | + | 0.106342i | \(0.0339137\pi\) | ||||
−0.994330 | + | 0.106342i | \(0.966086\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 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 | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −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 | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.00000 | −0.0789953 | −0.0394976 | − | 0.999220i | \(-0.512576\pi\) | ||||
−0.0394976 | + | 0.999220i | \(0.512576\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 15.8745i | − | 0.626029i | −0.949748 | − | 0.313015i | \(-0.898661\pi\) | ||
0.949748 | − | 0.313015i | \(-0.101339\pi\) | |||||||
\(644\) | 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 | \(0.5\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.0000 | −0.549548 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17.5000 | − | 19.8431i | 0.685353 | − | 0.777117i | ||||
\(653\) | − | 31.7490i | − | 1.24243i | −0.783638 | − | 0.621217i | \(-0.786638\pi\) | ||
0.783638 | − | 0.621217i | \(-0.213362\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.50000 | + | 19.8431i | 0.0976086 | + | 0.774744i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 16.0000 | − | 42.3320i | 0.623745 | − | 1.65027i | ||||
\(659\) | 7.93725i | 0.309192i | 0.987978 | + | 0.154596i | \(0.0494075\pi\) | ||||
−0.987978 | + | 0.154596i | \(0.950592\pi\) | |||||||
\(660\) | 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 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 28.0000 | 1.08093 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.0000 | 1.31060 | 0.655302 | − | 0.755367i | \(-0.272541\pi\) | ||||
0.655302 | + | 0.755367i | \(0.272541\pi\) | |||||||
\(674\) | 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 | \(-0.302427\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.00000 | −0.307012 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −14.0000 | − | 5.29150i | −0.536088 | − | 0.202622i | ||||
\(683\) | − | 23.8118i | − | 0.911132i | −0.890202 | − | 0.455566i | \(-0.849437\pi\) | ||
0.890202 | − | 0.455566i | \(-0.150563\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −4.00000 | + | 10.5830i | −0.152721 | + | 0.404061i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −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 | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −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 | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 21.1660i | − | 0.799429i | −0.916640 | − | 0.399715i | \(-0.869109\pi\) | ||
0.916640 | − | 0.399715i | \(-0.130891\pi\) | |||||||
\(702\) | 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 | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.1660i | 0.794906i | 0.917622 | + | 0.397453i | \(0.130106\pi\) | ||||
−0.917622 | + | 0.397453i | \(0.869894\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.50000 | + | 1.32288i | −0.0936915 | + | 0.0495769i | ||||
\(713\) | 16.0000 | 0.599205 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −31.5000 | + | 35.7176i | −1.17721 | + | 1.33483i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −18.0000 | + | 47.6235i | −0.671754 | + | 1.77729i | ||||
\(719\) | −36.0000 | −1.34257 | −0.671287 | − | 0.741198i | \(-0.734258\pi\) | ||||
−0.671287 | + | 0.741198i | \(0.734258\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 32.0000 | 1.19174 | ||||||||
\(722\) | 6.00000 | − | 15.8745i | 0.223297 | − | 0.590788i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.0000 | − | 15.8745i | 0.520306 | − | 0.589971i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.0000 | 0.593407 | 0.296704 | − | 0.954970i | \(-0.404113\pi\) | ||||
0.296704 | + | 0.954970i | \(0.404113\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 15.8745i | − | 0.587140i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 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 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 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 | \(0.270405\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −14.0000 | − | 5.29150i | −0.512576 | − | 0.193736i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 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 | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 21.1660i | − | 0.769292i | −0.923064 | − | 0.384646i | \(-0.874324\pi\) | ||
0.923064 | − | 0.384646i | \(-0.125676\pi\) | |||||||
\(758\) | −10.5000 | − | 3.96863i | −0.381377 | − | 0.144147i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.0000 | 1.05125 | 0.525625 | − | 0.850717i | \(-0.323832\pi\) | ||||
0.525625 | + | 0.850717i | \(0.323832\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 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 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.0000 | −0.757279 | −0.378640 | − | 0.925544i | \(-0.623608\pi\) | ||||
−0.378640 | + | 0.925544i | \(0.623608\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.50000 | + | 6.61438i | 0.269931 | + | 0.238057i | ||||
\(773\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.00000 | + | 2.64575i | −0.179490 | + | 0.0949769i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −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 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.4575i | 0.943108i | 0.881837 | + | 0.471554i | \(0.156307\pi\) | ||||
−0.881837 | + | 0.471554i | \(0.843693\pi\) | |||||||
\(788\) | 14.0000 | − | 15.8745i | 0.498729 | − | 0.565506i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 60.0000 | 2.13335 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 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 | \(0.809915\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.0000 | 0.849059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −13.5000 | + | 35.7176i | −0.476702 | + | 1.26123i | ||||
\(803\) | − | 18.5203i | − | 0.653566i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −14.0000 | − | 26.4575i | −0.492518 | − | 0.930772i | ||||
\(809\) | −10.0000 | −0.351581 | −0.175791 | − | 0.984428i | \(-0.556248\pi\) | ||||
−0.175791 | + | 0.984428i | \(0.556248\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.29150i | 0.185810i | 0.995675 | + | 0.0929049i | \(0.0296153\pi\) | ||||
−0.995675 | + | 0.0929049i | \(0.970385\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 14.0000 | − | 37.0405i | 0.490700 | − | 1.29827i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −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 | \(0.0591232\pi\) | ||||
−0.982800 | + | 0.184675i | \(0.940877\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.0000 | 0.836587 | 0.418294 | − | 0.908312i | \(-0.362628\pi\) | ||||
0.418294 | + | 0.908312i | \(0.362628\pi\) | |||||||
\(824\) | 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 | \(-0.0738741\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 21.1660i | − | 0.735126i | −0.929999 | − | 0.367563i | \(-0.880192\pi\) | ||
0.929999 | − | 0.367563i | \(-0.119808\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −27.0000 | −0.935495 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −10.5000 | − | 9.26013i | −0.363150 | − | 0.320268i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 24.5000 | + | 9.26013i | 0.846338 | + | 0.319886i | ||||
\(839\) | −40.0000 | −1.38095 | −0.690477 | − | 0.723355i | \(-0.742599\pi\) | ||||
−0.690477 | + | 0.723355i | \(0.742599\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 28.0000 | + | 10.5830i | 0.964944 | + | 0.364714i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.5000 | + | 11.9059i | −0.361425 | + | 0.409817i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16.0000 | −0.549767 | ||||||||
\(848\) | −42.0000 | + | 5.29150i | −1.44229 | + | 0.181711i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 42.3320i | 1.45112i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 52.9150i | − | 1.81178i | −0.423517 | − | 0.905888i | \(-0.639205\pi\) | ||
0.423517 | − | 0.905888i | \(-0.360795\pi\) | |||||||
\(854\) | −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 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.00000 | + | 15.8745i | −0.204361 | + | 0.540688i | ||||
\(863\) | 24.0000 | 0.816970 | 0.408485 | − | 0.912765i | \(-0.366057\pi\) | ||||
0.408485 | + | 0.912765i | \(0.366057\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −18.5000 | + | 48.9464i | −0.628656 | + | 1.66327i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 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 | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 14.0000 | + | 5.29150i | 0.473557 | + | 0.178988i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 42.3320i | − | 1.42945i | −0.699405 | − | 0.714725i | \(-0.746552\pi\) | ||
0.699405 | − | 0.714725i | \(-0.253448\pi\) | |||||||
\(878\) | 4.00000 | − | 10.5830i | 0.134993 | − | 0.357159i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.0000 | 1.01073 | 0.505363 | − | 0.862907i | \(-0.331359\pi\) | ||||
0.505363 | + | 0.862907i | \(0.331359\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.9778i | 1.51362i | 0.653633 | + | 0.756811i | \(0.273244\pi\) | ||||
−0.653633 | + | 0.756811i | \(0.726756\pi\) | |||||||
\(884\) | 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 | \(0.110687\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 48.0000 | 1.60987 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −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 | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 37.5000 | − | 19.8431i | 1.24723 | − | 0.659973i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.29150i | 0.175701i | 0.996134 | + | 0.0878507i | \(0.0279999\pi\) | ||||
−0.996134 | + | 0.0878507i | \(0.972000\pi\) | |||||||
\(908\) | 21.0000 | − | 23.8118i | 0.696909 | − | 0.790221i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.0000 | −1.59031 | −0.795155 | − | 0.606406i | \(-0.792611\pi\) | ||||
−0.795155 | + | 0.606406i | \(0.792611\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 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 | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.00000 | 0.131948 | 0.0659739 | − | 0.997821i | \(-0.478985\pi\) | ||||
0.0659739 | + | 0.997821i | \(0.478985\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 56.0000 | + | 21.1660i | 1.84426 | + | 0.697065i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 4.00000 | − | 10.5830i | 0.131448 | − | 0.347779i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.0000 | 0.459325 | 0.229663 | − | 0.973270i | \(-0.426238\pi\) | ||||
0.229663 | + | 0.973270i | \(0.426238\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 23.8118i | 0.780399i | ||||||||
\(932\) | −9.00000 | − | 7.93725i | −0.294805 | − | 0.259993i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −35.0000 | − | 13.2288i | −1.14523 | − | 0.432858i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.00000 | 0.228680 | 0.114340 | − | 0.993442i | \(-0.463525\pi\) | ||||
0.114340 | + | 0.993442i | \(0.463525\pi\) | |||||||
\(938\) | 42.0000 | + | 15.8745i | 1.37135 | + | 0.518321i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 42.3320i | − | 1.37998i | −0.723817 | − | 0.689992i | \(-0.757614\pi\) | ||
0.723817 | − | 0.689992i | \(-0.242386\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 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 | \(0.916961\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 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 | \(0.474194\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 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 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 31.5000 | + | 27.7804i | 1.01455 | + | 0.894746i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.00000 | −0.257263 | −0.128631 | − | 0.991692i | \(-0.541058\pi\) | ||||
−0.128631 | + | 0.991692i | \(0.541058\pi\) | |||||||
\(968\) | −10.0000 | + | 5.29150i | −0.321412 | + | 0.170075i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 23.8118i | − | 0.764156i | −0.924130 | − | 0.382078i | \(-0.875209\pi\) | ||
0.924130 | − | 0.382078i | \(-0.124791\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 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 | \(0.298391\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2.64575i | − | 0.0845586i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.00000 | − | 2.64575i | −0.223379 | − | 0.0844293i | ||||
\(983\) | −28.0000 | −0.893061 | −0.446531 | − | 0.894768i | \(-0.647341\pi\) | ||||
−0.446531 | + | 0.894768i | \(0.647341\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 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 | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 16.0000 | − | 42.3320i | 0.507489 | − | 1.34269i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 42.3320i | − | 1.34067i | −0.742059 | − | 0.670334i | \(-0.766151\pi\) | ||
0.742059 | − | 0.670334i | \(-0.233849\pi\) | |||||||
\(998\) | 35.0000 | + | 13.2288i | 1.10791 | + | 0.418749i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))