Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [720,2,Mod(241,720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(720, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("720.241");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.74922894553\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 90) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 481.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 720.481 |
Dual form | 720.2.q.c.241.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(271\) | \(577\) | \(641\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.50000 | − | 0.866025i | 0.866025 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | − | 3.46410i | −0.755929 | − | 1.30931i | −0.944911 | − | 0.327327i | \(-0.893852\pi\) |
0.188982 | − | 0.981981i | \(-0.439481\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.50000 | + | 2.59808i | 0.452267 | + | 0.783349i | 0.998526 | − | 0.0542666i | \(-0.0172821\pi\) |
−0.546259 | + | 0.837616i | \(0.683949\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | − | 3.46410i | 0.554700 | − | 0.960769i | −0.443227 | − | 0.896410i | \(-0.646166\pi\) |
0.997927 | − | 0.0643593i | \(-0.0205004\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.73205i | 0.447214i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.00000 | 0.727607 | 0.363803 | − | 0.931476i | \(-0.381478\pi\) | ||||
0.363803 | + | 0.931476i | \(0.381478\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.00000 | −1.14708 | −0.573539 | − | 0.819178i | \(-0.694430\pi\) | ||||
−0.573539 | + | 0.819178i | \(0.694430\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.00000 | − | 3.46410i | −1.30931 | − | 0.755929i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.00000 | − | 5.19615i | 0.625543 | − | 1.08347i | −0.362892 | − | 0.931831i | \(-0.618211\pi\) |
0.988436 | − | 0.151642i | \(-0.0484560\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.00000 | − | 5.19615i | −0.557086 | − | 0.964901i | −0.997738 | − | 0.0672232i | \(-0.978586\pi\) |
0.440652 | − | 0.897678i | \(-0.354747\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00000 | − | 1.73205i | 0.179605 | − | 0.311086i | −0.762140 | − | 0.647412i | \(-0.775851\pi\) |
0.941745 | + | 0.336327i | \(0.109185\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.50000 | + | 2.59808i | 0.783349 | + | 0.452267i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.00000 | 0.676123 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 6.92820i | − | 1.10940i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.50000 | − | 2.59808i | 0.234261 | − | 0.405751i | −0.724797 | − | 0.688963i | \(-0.758066\pi\) |
0.959058 | + | 0.283211i | \(0.0913998\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.50000 | + | 9.52628i | 0.838742 | + | 1.45274i | 0.890947 | + | 0.454108i | \(0.150042\pi\) |
−0.0522047 | + | 0.998636i | \(0.516625\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.50000 | + | 2.59808i | 0.223607 | + | 0.387298i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.50000 | + | 7.79423i | −0.642857 | + | 1.11346i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.50000 | − | 2.59808i | 0.630126 | − | 0.363803i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.00000 | −0.404520 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.50000 | + | 4.33013i | −0.993399 | + | 0.573539i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.50000 | + | 2.59808i | −0.195283 | + | 0.338241i | −0.946993 | − | 0.321253i | \(-0.895896\pi\) |
0.751710 | + | 0.659494i | \(0.229229\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.00000 | + | 8.66025i | 0.640184 | + | 1.10883i | 0.985391 | + | 0.170305i | \(0.0544754\pi\) |
−0.345207 | + | 0.938527i | \(0.612191\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −12.0000 | −1.51186 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.00000 | + | 3.46410i | 0.248069 | + | 0.429669i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.50000 | − | 4.33013i | 0.305424 | − | 0.529009i | −0.671932 | − | 0.740613i | \(-0.734535\pi\) |
0.977356 | + | 0.211604i | \(0.0678686\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 10.3923i | − | 1.25109i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.00000 | −0.819288 | −0.409644 | − | 0.912245i | \(-0.634347\pi\) | ||||
−0.409644 | + | 0.912245i | \(0.634347\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.50000 | − | 0.866025i | −0.173205 | − | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.00000 | − | 10.3923i | 0.683763 | − | 1.18431i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.00000 | + | 12.1244i | 0.787562 | + | 1.36410i | 0.927457 | + | 0.373930i | \(0.121990\pi\) |
−0.139895 | + | 0.990166i | \(0.544677\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.00000 | + | 10.3923i | 0.658586 | + | 1.14070i | 0.980982 | + | 0.194099i | \(0.0621783\pi\) |
−0.322396 | + | 0.946605i | \(0.604488\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.50000 | + | 2.59808i | −0.162698 | + | 0.281801i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.00000 | − | 5.19615i | −0.964901 | − | 0.557086i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −16.0000 | −1.67726 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 3.46410i | − | 0.359211i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.50000 | − | 4.33013i | 0.256495 | − | 0.444262i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.50000 | − | 9.52628i | −0.558440 | − | 0.967247i | −0.997627 | − | 0.0688512i | \(-0.978067\pi\) |
0.439187 | − | 0.898396i | \(-0.355267\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.00000 | 0.904534 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | + | 10.3923i | 0.597022 | + | 1.03407i | 0.993258 | + | 0.115924i | \(0.0369830\pi\) |
−0.396236 | + | 0.918149i | \(0.629684\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.00000 | + | 3.46410i | −0.197066 | + | 0.341328i | −0.947576 | − | 0.319531i | \(-0.896475\pi\) |
0.750510 | + | 0.660859i | \(0.229808\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.00000 | − | 3.46410i | 0.585540 | − | 0.338062i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.00000 | 0.870063 | 0.435031 | − | 0.900415i | \(-0.356737\pi\) | ||||
0.435031 | + | 0.900415i | \(0.356737\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.00000 | −0.383131 | −0.191565 | − | 0.981480i | \(-0.561356\pi\) | ||||
−0.191565 | + | 0.981480i | \(0.561356\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.00000 | + | 3.46410i | −0.569495 | + | 0.328798i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.00000 | + | 15.5885i | −0.846649 | + | 1.46644i | 0.0375328 | + | 0.999295i | \(0.488050\pi\) |
−0.884182 | + | 0.467143i | \(0.845283\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.00000 | + | 5.19615i | 0.279751 | + | 0.484544i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.00000 | − | 10.3923i | −0.554700 | − | 0.960769i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.00000 | − | 10.3923i | −0.550019 | − | 0.952661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 5.19615i | − | 0.468521i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.00000 | −0.177471 | −0.0887357 | − | 0.996055i | \(-0.528283\pi\) | ||||
−0.0887357 | + | 0.996055i | \(0.528283\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 16.5000 | + | 9.52628i | 1.45274 | + | 0.838742i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.00000 | − | 10.3923i | 0.524222 | − | 0.907980i | −0.475380 | − | 0.879781i | \(-0.657689\pi\) |
0.999602 | − | 0.0281993i | \(-0.00897729\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.0000 | + | 17.3205i | 0.867110 | + | 1.50188i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.50000 | + | 2.59808i | 0.387298 | + | 0.223607i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.50000 | + | 7.79423i | 0.384461 | + | 0.665906i | 0.991694 | − | 0.128618i | \(-0.0410540\pi\) |
−0.607233 | + | 0.794524i | \(0.707721\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.500000 | + | 0.866025i | −0.0424094 | + | 0.0734553i | −0.886451 | − | 0.462822i | \(-0.846837\pi\) |
0.844042 | + | 0.536278i | \(0.180170\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.0000 | 1.00349 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.00000 | 0.498273 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 15.5885i | 1.28571i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.00000 | − | 8.66025i | −0.406894 | − | 0.704761i | 0.587646 | − | 0.809118i | \(-0.300055\pi\) |
−0.994540 | + | 0.104357i | \(0.966722\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.50000 | − | 7.79423i | 0.363803 | − | 0.630126i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.00000 | + | 1.73205i | 0.0803219 | + | 0.139122i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.00000 | + | 6.92820i | −0.319235 | + | 0.552931i | −0.980329 | − | 0.197372i | \(-0.936759\pi\) |
0.661094 | + | 0.750303i | \(0.270093\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.00000 | − | 5.19615i | 0.713746 | − | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −24.0000 | −1.89146 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.0000 | 1.25322 | 0.626608 | − | 0.779334i | \(-0.284443\pi\) | ||||
0.626608 | + | 0.779334i | \(0.284443\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.50000 | + | 2.59808i | −0.350325 | + | 0.202260i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.00000 | + | 15.5885i | −0.696441 | + | 1.20627i | 0.273252 | + | 0.961943i | \(0.411901\pi\) |
−0.969693 | + | 0.244328i | \(0.921432\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.50000 | − | 2.59808i | −0.115385 | − | 0.199852i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.50000 | + | 12.9904i | −0.573539 | + | 0.993399i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.00000 | + | 15.5885i | 0.684257 | + | 1.18517i | 0.973670 | + | 0.227964i | \(0.0732068\pi\) |
−0.289412 | + | 0.957205i | \(0.593460\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.00000 | + | 3.46410i | −0.151186 | + | 0.261861i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.19615i | 0.390567i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.0000 | −1.18927 | −0.594635 | − | 0.803996i | \(-0.702704\pi\) | ||||
−0.594635 | + | 0.803996i | \(0.702704\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.0000 | + | 8.66025i | 1.10883 | + | 0.640184i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.00000 | − | 3.46410i | 0.147043 | − | 0.254686i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.50000 | + | 7.79423i | 0.329073 | + | 0.569970i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −18.0000 | + | 10.3923i | −1.30931 | + | 0.755929i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.50000 | − | 11.2583i | 0.467880 | − | 0.810392i | −0.531446 | − | 0.847092i | \(-0.678351\pi\) |
0.999326 | + | 0.0366998i | \(0.0116845\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.00000 | + | 3.46410i | 0.429669 | + | 0.248069i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.0000 | −1.41776 | −0.708881 | − | 0.705328i | \(-0.750800\pi\) | ||||
−0.708881 | + | 0.705328i | \(0.750800\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 8.66025i | − | 0.610847i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.0000 | + | 20.7846i | −0.842235 | + | 1.45879i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.50000 | + | 2.59808i | 0.104765 | + | 0.181458i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.00000 | − | 15.5885i | −0.625543 | − | 1.08347i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.50000 | − | 12.9904i | −0.518786 | − | 0.898563i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.00000 | + | 3.46410i | −0.137686 | + | 0.238479i | −0.926620 | − | 0.375999i | \(-0.877300\pi\) |
0.788935 | + | 0.614477i | \(0.210633\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.00000 | + | 5.19615i | −0.616670 | + | 0.356034i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.0000 | −0.750194 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.00000 | −0.543075 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.5000 | + | 6.06218i | −0.709524 | + | 0.409644i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.00000 | − | 10.3923i | 0.403604 | − | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.0000 | − | 19.0526i | −0.736614 | − | 1.27585i | −0.954011 | − | 0.299770i | \(-0.903090\pi\) |
0.217397 | − | 0.976083i | \(-0.430243\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.00000 | −0.200000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.50000 | − | 2.59808i | −0.0995585 | − | 0.172440i | 0.811943 | − | 0.583736i | \(-0.198410\pi\) |
−0.911502 | + | 0.411296i | \(0.865076\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0000 | + | 17.3205i | −0.660819 | + | 1.14457i | 0.319582 | + | 0.947559i | \(0.396457\pi\) |
−0.980401 | + | 0.197013i | \(0.936876\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 20.7846i | − | 1.36753i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 21.0000 | 1.37576 | 0.687878 | − | 0.725826i | \(-0.258542\pi\) | ||||
0.687878 | + | 0.725826i | \(0.258542\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 21.0000 | + | 12.1244i | 1.36410 | + | 0.787562i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.00000 | − | 5.19615i | 0.194054 | − | 0.336111i | −0.752536 | − | 0.658551i | \(-0.771170\pi\) |
0.946590 | + | 0.322440i | \(0.104503\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.50000 | − | 14.7224i | −0.547533 | − | 0.948355i | −0.998443 | − | 0.0557856i | \(-0.982234\pi\) |
0.450910 | − | 0.892570i | \(-0.351100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.5000 | − | 7.79423i | −0.866025 | − | 0.500000i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.50000 | − | 7.79423i | −0.287494 | − | 0.497955i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.0000 | + | 17.3205i | −0.636285 | + | 1.10208i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 18.0000 | + | 10.3923i | 1.14070 | + | 0.658586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.0000 | 1.32551 | 0.662754 | − | 0.748837i | \(-0.269387\pi\) | ||||
0.662754 | + | 0.748837i | \(0.269387\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.0000 | 1.13165 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.19615i | 0.325396i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.50000 | + | 7.79423i | −0.280702 | + | 0.486191i | −0.971558 | − | 0.236802i | \(-0.923901\pi\) |
0.690856 | + | 0.722993i | \(0.257234\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.00000 | + | 13.8564i | 0.497096 | + | 0.860995i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −18.0000 | −1.11417 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.0000 | + | 20.7846i | 0.739952 | + | 1.28163i | 0.952517 | + | 0.304487i | \(0.0984850\pi\) |
−0.212565 | + | 0.977147i | \(0.568182\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.00000 | + | 5.19615i | −0.184289 | + | 0.319197i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.00000 | − | 5.19615i | 0.550791 | − | 0.317999i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.00000 | 0.365826 | 0.182913 | − | 0.983129i | \(-0.441447\pi\) | ||||
0.182913 | + | 0.983129i | \(0.441447\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.0000 | 0.971931 | 0.485965 | − | 0.873978i | \(-0.338468\pi\) | ||||
0.485965 | + | 0.873978i | \(0.338468\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −24.0000 | + | 13.8564i | −1.45255 | + | 0.838628i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.50000 | − | 2.59808i | 0.0904534 | − | 0.156670i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.0000 | + | 19.0526i | 0.660926 | + | 1.14476i | 0.980373 | + | 0.197153i | \(0.0631696\pi\) |
−0.319447 | + | 0.947604i | \(0.603497\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.00000 | − | 5.19615i | −0.179605 | − | 0.311086i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.00000 | + | 5.19615i | 0.178965 | + | 0.309976i | 0.941526 | − | 0.336939i | \(-0.109392\pi\) |
−0.762561 | + | 0.646916i | \(0.776058\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.0000 | − | 17.3205i | 0.594438 | − | 1.02960i | −0.399188 | − | 0.916869i | \(-0.630708\pi\) |
0.993626 | − | 0.112728i | \(-0.0359589\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 8.66025i | − | 0.512989i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.0000 | −0.708338 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.5000 | − | 9.52628i | −0.967247 | − | 0.558440i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.00000 | − | 15.5885i | 0.525786 | − | 0.910687i | −0.473763 | − | 0.880652i | \(-0.657105\pi\) |
0.999549 | − | 0.0300351i | \(-0.00956192\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.50000 | − | 2.59808i | −0.0873334 | − | 0.151266i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.5000 | − | 7.79423i | 0.783349 | − | 0.452267i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.0000 | − | 20.7846i | −0.693978 | − | 1.20201i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 22.0000 | − | 38.1051i | 1.26806 | − | 2.19634i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 18.0000 | + | 10.3923i | 1.03407 | + | 0.597022i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.0000 | −0.572598 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.00000 | 0.399511 | 0.199756 | − | 0.979846i | \(-0.435985\pi\) | ||||
0.199756 | + | 0.979846i | \(0.435985\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.92820i | 0.394132i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.00000 | + | 5.19615i | −0.170114 | + | 0.294647i | −0.938460 | − | 0.345389i | \(-0.887747\pi\) |
0.768345 | + | 0.640036i | \(0.221080\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.500000 | + | 0.866025i | 0.0282617 | + | 0.0489506i | 0.879810 | − | 0.475325i | \(-0.157669\pi\) |
−0.851549 | + | 0.524276i | \(0.824336\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.00000 | − | 10.3923i | 0.338062 | − | 0.585540i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.0000 | − | 20.7846i | −0.673987 | − | 1.16738i | −0.976764 | − | 0.214318i | \(-0.931247\pi\) |
0.302777 | − | 0.953062i | \(-0.402086\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.00000 | − | 15.5885i | 0.503903 | − | 0.872786i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.5000 | − | 7.79423i | 0.753497 | − | 0.435031i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.0000 | −0.834622 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.00000 | −0.221880 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.00000 | + | 3.46410i | −0.331801 | + | 0.191565i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.00000 | − | 3.46410i | −0.109930 | − | 0.190404i | 0.805812 | − | 0.592172i | \(-0.201729\pi\) |
−0.915742 | + | 0.401768i | \(0.868396\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.00000 | + | 10.3923i | −0.328798 | + | 0.569495i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.50000 | + | 4.33013i | 0.136590 | + | 0.236580i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.5000 | − | 26.8468i | 0.844339 | − | 1.46244i | −0.0418554 | − | 0.999124i | \(-0.513327\pi\) |
0.886194 | − | 0.463314i | \(-0.153340\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 31.1769i | 1.69330i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.00000 | 0.324918 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.00000 | 0.431959 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9.00000 | + | 5.19615i | 0.484544 | + | 0.279751i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.5000 | − | 18.1865i | 0.563670 | − | 0.976304i | −0.433503 | − | 0.901152i | \(-0.642722\pi\) |
0.997172 | − | 0.0751519i | \(-0.0239442\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.00000 | + | 13.8564i | 0.428230 | + | 0.741716i | 0.996716 | − | 0.0809766i | \(-0.0258039\pi\) |
−0.568486 | + | 0.822693i | \(0.692471\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18.0000 | − | 10.3923i | −0.960769 | − | 0.554700i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.50000 | − | 7.79423i | −0.239511 | − | 0.414845i | 0.721063 | − | 0.692869i | \(-0.243654\pi\) |
−0.960574 | + | 0.278024i | \(0.910320\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.00000 | − | 5.19615i | 0.159223 | − | 0.275783i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −18.0000 | − | 10.3923i | −0.952661 | − | 0.550019i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.0000 | 1.26667 | 0.633336 | − | 0.773877i | \(-0.281685\pi\) | ||||
0.633336 | + | 0.773877i | \(0.281685\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.00000 | 0.315789 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 3.46410i | − | 0.181818i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.50000 | − | 6.06218i | 0.183198 | − | 0.317309i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.00000 | + | 6.92820i | 0.208798 | + | 0.361649i | 0.951336 | − | 0.308155i | \(-0.0997115\pi\) |
−0.742538 | + | 0.669804i | \(0.766378\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.50000 | − | 7.79423i | −0.234261 | − | 0.405751i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.0000 | − | 20.7846i | −0.623009 | − | 1.07908i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.00000 | − | 8.66025i | 0.258890 | − | 0.448411i | −0.707055 | − | 0.707159i | \(-0.749977\pi\) |
0.965945 | + | 0.258748i | \(0.0833099\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.50000 | − | 0.866025i | 0.0774597 | − | 0.0447214i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −24.0000 | −1.23606 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.0000 | −1.48963 | −0.744815 | − | 0.667271i | \(-0.767462\pi\) | ||||
−0.744815 | + | 0.667271i | \(0.767462\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.00000 | + | 1.73205i | −0.153695 | + | 0.0887357i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.00000 | − | 10.3923i | 0.306586 | − | 0.531022i | −0.671027 | − | 0.741433i | \(-0.734147\pi\) |
0.977613 | + | 0.210411i | \(0.0674801\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.00000 | + | 10.3923i | 0.305788 | + | 0.529641i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 33.0000 | 1.67748 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.0000 | − | 31.1769i | −0.912636 | − | 1.58073i | −0.810326 | − | 0.585980i | \(-0.800710\pi\) |
−0.102311 | − | 0.994753i | \(-0.532624\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.00000 | − | 15.5885i | 0.455150 | − | 0.788342i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 20.7846i | − | 1.04844i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.0000 | −0.704416 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.00000 | 0.401508 | 0.200754 | − | 0.979642i | \(-0.435661\pi\) | ||||
0.200754 | + | 0.979642i | \(0.435661\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 30.0000 | + | 17.3205i | 1.50188 | + | 0.867110i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.5000 | + | 28.5788i | −0.823971 | + | 1.42716i | 0.0787327 | + | 0.996896i | \(0.474913\pi\) |
−0.902703 | + | 0.430263i | \(0.858421\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.00000 | − | 6.92820i | −0.199254 | − | 0.345118i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.00000 | 0.447214 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.00000 | − | 10.3923i | −0.297409 | − | 0.515127i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.5000 | − | 26.8468i | 0.766426 | − | 1.32749i | −0.173064 | − | 0.984911i | \(-0.555367\pi\) |
0.939490 | − | 0.342578i | \(-0.111300\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.5000 | + | 7.79423i | 0.665906 | + | 0.384461i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.0000 | 0.590481 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.0000 | −0.589057 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.73205i | 0.0848189i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.00000 | − | 1.73205i | −0.0487370 | − | 0.0844150i | 0.840628 | − | 0.541613i | \(-0.182186\pi\) |
−0.889365 | + | 0.457198i | \(0.848853\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.50000 | − | 2.59808i | −0.0727607 | − | 0.126025i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.0000 | − | 34.6410i | 0.967868 | − | 1.67640i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 18.0000 | − | 10.3923i | 0.869048 | − | 0.501745i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.0000 | −1.15604 | −0.578020 | − | 0.816023i | \(-0.696174\pi\) | ||||
−0.578020 | + | 0.816023i | \(0.696174\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.0000 | −0.624740 | −0.312370 | − | 0.949960i | \(-0.601123\pi\) | ||||
−0.312370 | + | 0.949960i | \(0.601123\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.00000 | − | 5.19615i | 0.431517 | − | 0.249136i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.0000 | + | 25.9808i | −0.717547 | + | 1.24283i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.00000 | − | 8.66025i | −0.238637 | − | 0.413331i | 0.721686 | − | 0.692220i | \(-0.243367\pi\) |
−0.960323 | + | 0.278889i | \(0.910034\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.5000 | + | 23.3827i | 0.642857 | + | 1.11346i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.50000 | + | 2.59808i | 0.0712672 | + | 0.123438i | 0.899457 | − | 0.437009i | \(-0.143962\pi\) |
−0.828190 | + | 0.560448i | \(0.810629\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.00000 | + | 5.19615i | −0.142214 | + | 0.246321i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.0000 | −0.707894 | −0.353947 | − | 0.935266i | \(-0.615161\pi\) | ||||
−0.353947 | + | 0.935266i | \(0.615161\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.00000 | 0.423793 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15.0000 | − | 8.66025i | −0.704761 | − | 0.406894i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.00000 | − | 13.8564i | 0.375046 | − | 0.649598i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.500000 | + | 0.866025i | 0.0233890 | + | 0.0405110i | 0.877483 | − | 0.479608i | \(-0.159221\pi\) |
−0.854094 | + | 0.520119i | \(0.825888\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 15.5885i | − | 0.727607i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.0000 | − | 17.3205i | 0.464739 | − | 0.804952i | −0.534450 | − | 0.845200i | \(-0.679481\pi\) |
0.999190 | + | 0.0402476i | \(0.0128147\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.00000 | + | 1.73205i | 0.139122 | + | 0.0803219i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.0000 | −0.971764 | −0.485882 | − | 0.874024i | \(-0.661502\pi\) | ||||
−0.485882 | + | 0.874024i | \(0.661502\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −20.0000 | −0.923514 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.8564i | 0.638470i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −16.5000 | + | 28.5788i | −0.758671 | + | 1.31406i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.50000 | + | 4.33013i | 0.114708 | + | 0.198680i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.00000 | − | 15.5885i | 0.412082 | − | 0.713746i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.00000 | − | 5.19615i | −0.137073 | − | 0.237418i | 0.789314 | − | 0.613990i | \(-0.210436\pi\) |
−0.926388 | + | 0.376571i | \(0.877103\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.00000 | + | 13.8564i | −0.364769 | + | 0.631798i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −36.0000 | + | 20.7846i | −1.63806 | + | 0.945732i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11.0000 | 0.499484 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.00000 | −0.0906287 | −0.0453143 | − | 0.998973i | \(-0.514429\pi\) | ||||
−0.0453143 | + | 0.998973i | \(0.514429\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.0000 | − | 13.8564i | 1.08532 | − | 0.626608i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.5000 | + | 28.5788i | −0.744635 | + | 1.28974i | 0.205731 | + | 0.978609i | \(0.434043\pi\) |
−0.950365 | + | 0.311136i | \(0.899290\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.00000 | − | 15.5885i | −0.405340 | − | 0.702069i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.50000 | + | 7.79423i | −0.202260 | + | 0.350325i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.0000 | + | 20.7846i | 0.538274 | + | 0.932317i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.5000 | + | 26.8468i | −0.693875 | + | 1.20183i | 0.276683 | + | 0.960961i | \(0.410765\pi\) |
−0.970558 | + | 0.240866i | \(0.922569\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 31.1769i | 1.39288i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.00000 | −0.267527 | −0.133763 | − | 0.991013i | \(-0.542706\pi\) | ||||
−0.133763 | + | 0.991013i | \(0.542706\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.0000 | −0.533993 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.50000 | − | 2.59808i | −0.199852 | − | 0.115385i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.00000 | − | 10.3923i | 0.265945 | − | 0.460631i | −0.701866 | − | 0.712309i | \(-0.747649\pi\) |
0.967811 | + | 0.251679i | \(0.0809826\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.0000 | + | 24.2487i | 0.619324 | + | 1.07270i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 25.9808i | 1.14708i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.00000 | − | 3.46410i | −0.0881305 | − | 0.152647i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 27.0000 | + | 15.5885i | 1.18517 | + | 0.684257i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.00000 | −0.131432 | −0.0657162 | − | 0.997838i | \(-0.520933\pi\) | ||||
−0.0657162 | + | 0.997838i | \(0.520933\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.0000 | −0.874539 | −0.437269 | − | 0.899331i | \(-0.644054\pi\) | ||||
−0.437269 | + | 0.899331i | \(0.644054\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.92820i | 0.302372i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.00000 | − | 5.19615i | 0.130682 | − | 0.226348i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | − | 11.2583i | −0.282609 | − | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.50000 | + | 7.79423i | 0.195283 | + | 0.338241i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.00000 | − | 10.3923i | −0.259889 | − | 0.450141i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.50000 | + | 7.79423i | −0.194552 | + | 0.336974i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −27.0000 | −1.16297 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.00000 | 0.343947 | 0.171973 | − | 0.985102i | \(-0.444986\pi\) | ||||
0.171973 | + | 0.985102i | \(0.444986\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −24.0000 | + | 13.8564i | −1.02994 | + | 0.594635i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.00000 | − | 3.46410i | 0.0856706 | − | 0.148386i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.500000 | − | 0.866025i | −0.0213785 | − | 0.0370286i | 0.855138 | − | 0.518400i | \(-0.173472\pi\) |
−0.876517 | + | 0.481371i | \(0.840139\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 30.0000 | 1.28037 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.0000 | + | 25.9808i | 0.639021 | + | 1.10682i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28.0000 | − | 48.4974i | 1.19068 | − | 2.06232i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 6.92820i | − | 0.294086i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.0000 | −0.508456 | −0.254228 | − | 0.967144i | \(-0.581821\pi\) | ||||
−0.254228 | + | 0.967144i | \(0.581821\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 44.0000 | 1.86100 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.5000 | + | 7.79423i | 0.569970 | + | 0.329073i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.50000 | + | 2.59808i | −0.0632175 | + | 0.109496i | −0.895902 | − | 0.444252i | \(-0.853470\pi\) |
0.832684 | + | 0.553748i | \(0.186803\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.00000 | − | 15.5885i | −0.378633 | − | 0.655811i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −18.0000 | + | 31.1769i | −0.755929 | + | 1.30931i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.5000 | + | 33.7750i | 0.817483 | + | 1.41592i | 0.907532 | + | 0.419984i | \(0.137964\pi\) |
−0.0900490 | + | 0.995937i | \(0.528702\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.5000 | − | 25.1147i | 0.606806 | − | 1.05102i | −0.384957 | − | 0.922934i | \(-0.625784\pi\) |
0.991763 | − | 0.128085i | \(-0.0408829\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.00000 | −0.250217 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.00000 | −0.291414 | −0.145707 | − | 0.989328i | \(-0.546546\pi\) | ||||
−0.145707 | + | 0.989328i | \(0.546546\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 22.5167i | − | 0.935760i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 24.0000 | − | 41.5692i | 0.995688 | − | 1.72458i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.00000 | + | 15.5885i | 0.372742 | + | 0.645608i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12.0000 | 0.496139 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.5000 | + | 33.7750i | 0.804851 | + | 1.39404i | 0.916392 | + | 0.400283i | \(0.131088\pi\) |
−0.111540 | + | 0.993760i | \(0.535578\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.00000 | + | 8.66025i | −0.206021 | + | 0.356840i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.0000 | −0.739171 | −0.369586 | − | 0.929197i | \(-0.620500\pi\) | ||||
−0.369586 | + | 0.929197i | \(0.620500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.0000 | 0.491952 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −30.0000 | + | 17.3205i | −1.22782 | + | 0.708881i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.5000 | + | 21.6506i | 0.509886 | + | 0.883148i | 0.999934 | + | 0.0114528i | \(0.00364562\pi\) |
−0.490049 | + | 0.871695i | \(0.663021\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.50000 | − | 12.9904i | −0.305424 | − | 0.529009i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.00000 | + | 1.73205i | 0.0406558 | + | 0.0704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.00000 | − | 6.92820i | 0.162355 | − | 0.281207i | −0.773358 | − | 0.633970i | \(-0.781424\pi\) |
0.935713 | + | 0.352763i | \(0.114758\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 41.5692i | 1.68447i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.00000 | 0.0807792 | 0.0403896 | − | 0.999184i | \(-0.487140\pi\) | ||||
0.0403896 | + | 0.999184i | \(0.487140\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.50000 | + | 2.59808i | 0.181458 | + | 0.104765i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.5000 | − | 33.7750i | 0.785040 | − | 1.35973i | −0.143934 | − | 0.989587i | \(-0.545975\pi\) |
0.928975 | − | 0.370143i | \(-0.120691\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.50000 | − | 16.4545i | −0.381837 | − | 0.661361i | 0.609488 | − | 0.792796i | \(-0.291375\pi\) |
−0.991325 | + | 0.131434i | \(0.958042\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −27.0000 | − | 15.5885i | −1.08347 | − | 0.625543i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.0000 | − | 20.7846i | −0.480770 | − | 0.832718i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −22.5000 | − | 12.9904i | −0.898563 | − | 0.518786i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.0000 | −0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.0000 | 1.35352 | 0.676759 | − | 0.736204i | \(-0.263384\pi\) | ||||
0.676759 | + | 0.736204i | \(0.263384\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.92820i | 0.275371i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.00000 | − | 1.73205i | 0.0396838 | − | 0.0687343i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.0000 | + | 31.1769i | 0.713186 | + | 1.23527i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.00000 | + | 15.5885i | −0.356034 | + | 0.616670i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.50000 | − | 7.79423i | −0.177739 | − | 0.307854i | 0.763367 | − | 0.645966i | \(-0.223545\pi\) |
−0.941106 | + | 0.338112i | \(0.890212\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.5000 | − | 19.9186i | 0.453516 | − | 0.785512i | −0.545086 | − | 0.838380i | \(-0.683503\pi\) |
0.998602 | + | 0.0528680i | \(0.0168363\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.5000 | + | 9.52628i | −0.649687 | + | 0.375097i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.00000 | −0.235884 | −0.117942 | − | 0.993020i | \(-0.537630\pi\) | ||||
−0.117942 | + | 0.993020i | \(0.537630\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.00000 | −0.353281 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.0000 | + | 6.92820i | −0.470317 | + | 0.271538i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.0000 | + | 36.3731i | −0.821794 | + | 1.42339i | 0.0825519 | + | 0.996587i | \(0.473693\pi\) |
−0.904345 | + | 0.426801i | \(0.859640\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.00000 | + | 10.3923i | 0.234439 | + | 0.406061i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.5000 | + | 18.1865i | −0.409644 | + | 0.709524i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.0000 | − | 31.1769i | −0.701180 | − | 1.21448i | −0.968052 | − | 0.250748i | \(-0.919323\pi\) |
0.266872 | − | 0.963732i | \(-0.414010\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.0000 | + | 27.7128i | −0.622328 | + | 1.07790i | 0.366723 | + | 0.930330i | \(0.380480\pi\) |
−0.989051 | + | 0.147573i | \(0.952854\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 20.7846i | − | 0.807207i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −20.0000 | −0.775567 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −36.0000 | −1.39393 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −33.0000 | − | 19.0526i | −1.27585 | − | 0.736614i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.0000 | + | 25.9808i | −0.579069 | + | 1.00298i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.00000 | − | 12.1244i | −0.269830 | − | 0.467360i | 0.698988 | − | 0.715134i | \(-0.253634\pi\) |
−0.968818 | + | 0.247774i | \(0.920301\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.50000 | + | 2.59808i | −0.173205 | + | 0.100000i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.0000 | + | 31.1769i | 0.691796 | + | 1.19823i | 0.971249 | + | 0.238067i | \(0.0765137\pi\) |
−0.279453 | + | 0.960159i | \(0.590153\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.0000 | + | 38.1051i | −0.844283 | + | 1.46234i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.50000 | − | 2.59808i | −0.172440 | − | 0.0995585i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.0000 | 0.803543 | 0.401771 | − | 0.915740i | \(-0.368395\pi\) | ||||
0.401771 | + | 0.915740i | \(0.368395\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.00000 | −0.343872 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 34.6410i | 1.32164i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.0000 | − | 20.7846i | 0.457164 | − | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.00000 | + | 6.92820i | 0.152167 | + | 0.263561i | 0.932024 | − | 0.362397i | \(-0.118041\pi\) |
−0.779857 | + | 0.625958i | \(0.784708\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −18.0000 | − | 31.1769i | −0.683763 | − | 1.18431i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.500000 | − | 0.866025i | −0.0189661 | − | 0.0328502i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.50000 | − | 7.79423i | 0.170450 | − | 0.295227i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 31.5000 | − | 18.1865i | 1.19144 | − | 0.687878i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.0000 | 1.58632 | 0.793159 | − | 0.609015i | \(-0.208435\pi\) | ||||
0.793159 | + | 0.609015i | \(0.208435\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.0000 | 0.754314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 24.0000 | − | 41.5692i | 0.902613 | − | 1.56337i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.0000 | + | 29.4449i | 0.638448 | + | 1.10583i | 0.985773 | + | 0.168080i | \(0.0537568\pi\) |
−0.347325 | + | 0.937745i | \(0.612910\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 42.0000 | 1.57512 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.00000 | − | 10.3923i | −0.224702 | − | 0.389195i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.00000 | + | 10.3923i | −0.224387 | + | 0.388650i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 10.3923i | − | 0.388108i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.0000 | 0.595871 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −25.5000 | − | 14.7224i | −0.948355 | − | 0.547533i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.00000 | + | 5.19615i | −0.111417 | + | 0.192980i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.0000 | − | 24.2487i | −0.519231 | − | 0.899335i | −0.999750 | − | 0.0223506i | \(-0.992885\pi\) |
0.480519 | − | 0.876984i | \(-0.340448\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.5000 | + | 28.5788i | 0.610275 | + | 1.05703i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.0000 | + | 27.7128i | −0.590973 | + | 1.02360i | 0.403128 | + | 0.915144i | \(0.367923\pi\) |
−0.994102 | + | 0.108453i | \(0.965410\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −13.5000 | − | 7.79423i | −0.497955 | − | 0.287494i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15.0000 | 0.552532 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.0000 | −1.06678 | −0.533391 | − | 0.845869i | \(-0.679083\pi\) | ||||
−0.533391 | + | 0.845869i | \(0.679083\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 34.6410i | 1.27257i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.00000 | + | 5.19615i | −0.110059 | + | 0.190628i | −0.915794 | − | 0.401648i | \(-0.868437\pi\) |
0.805735 | + | 0.592277i | \(0.201771\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 36.0000 | 1.31717 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.0000 | − | 31.1769i | −0.657706 | − | 1.13918i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.0000 | + | 24.2487i | −0.510867 | + | 0.884848i | 0.489053 | + | 0.872254i | \(0.337342\pi\) |
−0.999921 | + | 0.0125942i | \(0.995991\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 31.5000 | − | 18.1865i | 1.14792 | − | 0.662754i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.0000 | 0.363937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.0000 | 1.38113 | 0.690567 | − | 0.723269i | \(-0.257361\pi\) | ||||
0.690567 | + | 0.723269i | \(0.257361\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 27.0000 | − | 15.5885i | 0.980038 | − | 0.565825i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.00000 | + | 15.5885i | −0.326250 | + | 0.565081i | −0.981764 | − | 0.190101i | \(-0.939118\pi\) |
0.655515 | + | 0.755182i | \(0.272452\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.00000 | + | 13.8564i | 0.289619 | + | 0.501636i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.50000 | + | 7.79423i | 0.162698 | + | 0.281801i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.00000 | + | 10.3923i | 0.216647 | + | 0.375244i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.0000 | + | 43.3013i | −0.901523 | + | 1.56148i | −0.0760054 | + | 0.997107i | \(0.524217\pi\) |
−0.825518 | + | 0.564376i | \(0.809117\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.5885i | 0.561405i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30.0000 | −1.07903 | −0.539513 | − | 0.841978i | \(-0.681391\pi\) | ||||
−0.539513 | + | 0.841978i | \(0.681391\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.00000 | −0.0718421 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 24.0000 | + | 13.8564i | 0.860995 | + | 0.497096i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.50000 | + | 12.9904i | −0.268715 | + | 0.465429i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.00000 | − | 15.5885i | −0.322045 | − | 0.557799i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −27.0000 | + | 15.5885i | −0.964901 | + | 0.557086i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.00000 | − | 6.92820i | −0.142766 | − | 0.247278i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.00000 | + | 3.46410i | −0.0712923 | + | 0.123482i | −0.899468 | − | 0.436987i | \(-0.856046\pi\) |
0.828176 | + | 0.560469i | \(0.189379\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 36.0000 | + | 20.7846i | 1.28163 | + | 0.739952i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 72.0000 | 2.56003 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 40.0000 | 1.42044 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.3923i | 0.368577i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.0000 | − | 41.5692i | 0.850124 | − | 1.47246i | −0.0309726 | − | 0.999520i | \(-0.509860\pi\) |
0.881096 | − | 0.472937i | \(-0.156806\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.00000 | − | 15.5885i | 0.317999 | − | 0.550791i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.5000 | − | 18.1865i | −0.370537 | − | 0.641789i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.0000 | − | 20.7846i | 0.422944 | − | 0.732561i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.00000 | − | 5.19615i | 0.316815 | − | 0.182913i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39.0000 | −1.37117 | −0.685583 | − | 0.727994i | \(-0.740453\pi\) | ||||
−0.685583 | + | 0.727994i | \(0.740453\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35.0000 | −1.22902 | −0.614508 | − | 0.788911i | \(-0.710645\pi\) | ||||
−0.614508 | + | 0.788911i | \(0.710645\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 24.0000 | − | 13.8564i | 0.841717 | − | 0.485965i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.00000 | + | 13.8564i | −0.280228 | + | 0.485369i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −27.5000 | − | 47.6314i | −0.962103 | − | 1.66641i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −24.0000 | + | 41.5692i | −0.838628 | + | 1.45255i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.0000 | + | 41.5692i | 0.837606 | + | 1.45078i | 0.891891 | + | 0.452250i | \(0.149379\pi\) |
−0.0542853 | + | 0.998525i | \(0.517288\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.00000 | + | 3.46410i | −0.0697156 | + | 0.120751i | −0.898776 | − | 0.438408i | \(-0.855543\pi\) |
0.829060 | + | 0.559159i | \(0.188876\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 5.19615i | − | 0.180907i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.0000 | 1.25184 | 0.625921 | − | 0.779886i | \(-0.284723\pi\) | ||||
0.625921 | + | 0.779886i | \(0.284723\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 44.0000 | 1.52818 | 0.764092 | − | 0.645108i | \(-0.223188\pi\) | ||||
0.764092 | + | 0.645108i | \(0.223188\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 33.0000 | + | 19.0526i | 1.14476 | + | 0.660926i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13.5000 | + | 23.3827i | −0.467747 | + | 0.810162i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.00000 | − | 15.5885i | −0.311458 | − | 0.539461i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.00000 | − | 5.19615i | −0.311086 | − | 0.179605i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.0000 | − | 25.9808i | −0.517858 | − | 0.896956i | −0.999785 | − | 0.0207443i | \(-0.993396\pi\) |
0.481927 | − | 0.876211i | \(-0.339937\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50000 | + | 6.06218i | −0.120690 | + | 0.209041i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.00000 | + | 5.19615i | 0.309976 | + | 0.178965i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.00000 | 0.103203 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.00000 | −0.274883 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 34.6410i | − | 1.18888i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.0000 | + | 20.7846i | −0.411355 | + | 0.712487i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.0000 | − | 38.1051i | −0.753266 | − | 1.30469i | −0.946232 | − | 0.323489i | \(-0.895144\pi\) |
0.192966 | − | 0.981205i | \(-0.438189\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.50000 | − | 12.9904i | −0.256495 | − | 0.444262i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.00000 | + | 15.5885i | 0.307434 | + | 0.532492i | 0.977800 | − | 0.209539i | \(-0.0671963\pi\) |
−0.670366 | + | 0.742030i | \(0.733863\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.50000 | + | 16.4545i | −0.324136 | + | 0.561420i | −0.981337 | − | 0.192295i | \(-0.938407\pi\) |
0.657201 | + | 0.753715i | \(0.271740\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −18.0000 | + | 10.3923i | −0.613438 | + | 0.354169i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.00000 | 0.204242 | 0.102121 | − | 0.994772i | \(-0.467437\pi\) | ||||
0.102121 | + | 0.994772i | \(0.467437\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.0000 | −0.612018 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.0000 | + | 6.92820i | −0.407541 | + | 0.235294i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21.0000 | + | 36.3731i | −0.712376 | + | 1.23387i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.0000 | − | 17.3205i | −0.338837 | − | 0.586883i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −33.0000 | −1.11688 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.00000 | − | 3.46410i | −0.0676123 | − | 0.117108i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.00000 | + | 1.73205i | −0.0337676 | + | 0.0584872i | −0.882415 | − | 0.470471i | \(-0.844084\pi\) |
0.848648 | + | 0.528958i | \(0.177417\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 31.1769i | − | 1.05157i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.0000 | 1.01073 | 0.505363 | − | 0.862907i | \(-0.331359\pi\) | ||||
0.505363 | + | 0.862907i | \(0.331359\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −41.0000 | −1.37976 | −0.689880 | − | 0.723924i | \(-0.742337\pi\) | ||||
−0.689880 | + | 0.723924i | \(0.742337\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.50000 | − | 2.59808i | −0.151266 | − | 0.0873334i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.0000 | + | 36.3731i | −0.705111 | + | 1.22129i | 0.261540 | + | 0.965193i | \(0.415770\pi\) |
−0.966651 | + | 0.256096i | \(0.917564\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.00000 | + | 6.92820i | 0.134156 | + | 0.232364i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.5000 | − | 23.3827i | 0.452267 | − | 0.783349i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −36.0000 | − | 20.7846i | −1.20201 | − | 0.693978i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.0000 | −0.400222 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.0000 | 0.599667 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 76.2102i | − | 2.53612i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.00000 | − | 13.8564i | 0.265929 | − | 0.460603i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.50000 | + | 4.33013i | 0.0830111 | + | 0.143780i | 0.904542 | − | 0.426385i | \(-0.140213\pi\) |
−0.821531 | + | 0.570164i | \(0.806880\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 36.0000 | 1.19404 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.0000 | − | 25.9808i | −0.496972 | − | 0.860781i | 0.503022 | − | 0.864274i | \(-0.332222\pi\) |
−0.999994 | + | 0.00349271i | \(0.998888\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.0000 | + | 31.1769i | −0.595713 | + | 1.03181i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −15.0000 | + | 8.66025i | −0.495885 | + | 0.286299i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −48.0000 | −1.58510 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.0000 | 1.12156 | 0.560778 | − | 0.827966i | \(-0.310502\pi\) | ||||
0.560778 | + | 0.827966i | \(0.310502\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.5000 | − | 6.06218i | 0.345987 | − | 0.199756i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.0000 | + | 20.7846i | −0.394985 | + | 0.684134i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.00000 | + | 3.46410i | 0.0657596 | + | 0.113899i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.00000 | + | 10.3923i | 0.197066 | + | 0.341328i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.0000 | − | 25.9808i | −0.492134 | − | 0.852401i | 0.507825 | − | 0.861460i | \(-0.330450\pi\) |
−0.999959 | + | 0.00905914i | \(0.997116\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.5000 | − | 38.9711i | 0.737408 | − | 1.27723i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.3923i | 0.340229i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.00000 | −0.294331 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.0000 | −0.326686 | −0.163343 | − | 0.986569i | \(-0.552228\pi\) | ||||
−0.163343 | + | 0.986569i | \(0.552228\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.50000 | + | 0.866025i | 0.0489506 | + | 0.0282617i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.0000 | + | 20.7846i | −0.391189 | + | 0.677559i | −0.992607 | − | 0.121376i | \(-0.961269\pi\) |
0.601418 | + | 0.798935i | \(0.294603\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.00000 | − | 15.5885i | −0.293080 | − | 0.507630i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 20.7846i | − | 0.676123i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.5000 | + | 23.3827i | 0.438691 | + | 0.759835i | 0.997589 | − | 0.0694014i | \(-0.0221089\pi\) |
−0.558898 | + | 0.829237i | \(0.688776\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.0000 | + | 24.2487i | −0.454459 | + | 0.787146i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −36.0000 | − | 20.7846i | −1.16738 | − | 0.673987i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 51.0000 | 1.65205 | 0.826026 | − | 0.563632i | \(-0.190596\pi\) | ||||
0.826026 | + | 0.563632i | \(0.190596\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 31.1769i | − | 1.00781i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.0000 | − | 31.1769i | 0.581250 | − | 1.00676i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5000 | + | 23.3827i | 0.435484 | + | 0.754280i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.5000 | − | 23.3827i | 0.435031 | − | 0.753497i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.50000 | + | 11.2583i | 0.209242 | + | 0.362418i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.0000 | + | 19.0526i | −0.353736 | + | 0.612689i | −0.986901 | − | 0.161328i | \(-0.948422\pi\) |
0.633165 | + | 0.774017i | \(0.281756\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −22.5000 | + | 12.9904i | −0.722804 | + | 0.417311i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −60.0000 | −1.92549 | −0.962746 | − | 0.270408i | \(-0.912841\pi\) | ||||
−0.962746 | + | 0.270408i | \(0.912841\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.00000 | 0.128234 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.00000 | + | 3.46410i | −0.192154 | + | 0.110940i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.50000 | − | 7.79423i | 0.143968 | − | 0.249359i | −0.785020 | − | 0.619471i | \(-0.787347\pi\) |
0.928987 | + | 0.370111i | \(0.120681\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.00000 | + | 15.5885i | 0.287641 | + | 0.498209i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.00000 | + | 10.3923i | −0.191565 | + | 0.331801i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.0000 | + | 31.1769i | 0.574111 | + | 0.994389i | 0.996138 | + | 0.0878058i | \(0.0279855\pi\) |
−0.422027 | + | 0.906583i | \(0.638681\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 66.0000 | 2.09868 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.0000 | −0.635321 | −0.317660 | − | 0.948205i | \(-0.602897\pi\) | ||||
−0.317660 | + | 0.948205i | \(0.602897\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.00000 | − | 3.46410i | −0.190404 | − | 0.109930i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.0000 | − | 17.3205i | 0.317021 | − | 0.549097i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.0000 | − | 22.5167i | −0.411714 | − | 0.713110i | 0.583363 | − | 0.812211i | \(-0.301736\pi\) |
−0.995077 | + | 0.0991016i | \(0.968403\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 20.7846i | 0.657596i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))