Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1872,2,Mod(433,1872)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1872, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1872.433");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1872.by (of order \(6\), 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: | \(14.9479952584\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 156) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 433.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1872.433 |
Dual form | 1872.2.by.b.1297.1 |
$q$-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 \(\left(\mathbb{Z}/1872\mathbb{Z}\right)^\times\).
\(n\) | \(145\) | \(209\) | \(469\) | \(703\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.73205i | − | 0.774597i | −0.921954 | − | 0.387298i | \(-0.873408\pi\) | ||
0.921954 | − | 0.387298i | \(-0.126592\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.00000 | + | 1.73205i | −1.13389 | + | 0.654654i | −0.944911 | − | 0.327327i | \(-0.893852\pi\) |
−0.188982 | + | 0.981981i | \(0.560519\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.00000 | + | 1.73205i | 0.904534 | + | 0.522233i | 0.878668 | − | 0.477432i | \(-0.158432\pi\) |
0.0258656 | + | 0.999665i | \(0.491766\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.50000 | − | 2.59808i | −0.693375 | − | 0.720577i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.50000 | + | 2.59808i | 0.363803 | + | 0.630126i | 0.988583 | − | 0.150675i | \(-0.0481447\pi\) |
−0.624780 | + | 0.780801i | \(0.714811\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.00000 | − | 1.73205i | 0.688247 | − | 0.397360i | −0.114708 | − | 0.993399i | \(-0.536593\pi\) |
0.802955 | + | 0.596040i | \(0.203260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.00000 | + | 5.19615i | −0.625543 | + | 1.08347i | 0.362892 | + | 0.931831i | \(0.381789\pi\) |
−0.988436 | + | 0.151642i | \(0.951544\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | 0.400000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.50000 | − | 7.79423i | 0.835629 | − | 1.44735i | −0.0578882 | − | 0.998323i | \(-0.518437\pi\) |
0.893517 | − | 0.449029i | \(-0.148230\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.00000 | + | 5.19615i | 0.507093 | + | 0.878310i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.50000 | − | 2.59808i | −0.739795 | − | 0.427121i | 0.0821995 | − | 0.996616i | \(-0.473806\pi\) |
−0.821995 | + | 0.569495i | \(0.807139\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.50000 | + | 4.33013i | 1.17130 | + | 0.676252i | 0.953987 | − | 0.299849i | \(-0.0969363\pi\) |
0.217317 | + | 0.976101i | \(0.430270\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000 | + | 1.73205i | 0.152499 | + | 0.264135i | 0.932145 | − | 0.362084i | \(-0.117935\pi\) |
−0.779647 | + | 0.626219i | \(0.784601\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 3.46410i | − | 0.505291i | −0.967559 | − | 0.252646i | \(-0.918699\pi\) | ||
0.967559 | − | 0.252646i | \(-0.0813007\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.50000 | − | 4.33013i | 0.357143 | − | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.00000 | 1.23625 | 0.618123 | − | 0.786082i | \(-0.287894\pi\) | ||||
0.618123 | + | 0.786082i | \(0.287894\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.00000 | − | 5.19615i | 0.404520 | − | 0.700649i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.0000 | − | 6.92820i | 1.56227 | − | 0.901975i | 0.565240 | − | 0.824927i | \(-0.308784\pi\) |
0.997027 | − | 0.0770484i | \(-0.0245496\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.50000 | + | 9.52628i | 0.704203 | + | 1.21972i | 0.966978 | + | 0.254858i | \(0.0820288\pi\) |
−0.262776 | + | 0.964857i | \(0.584638\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.50000 | + | 4.33013i | −0.558156 | + | 0.537086i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.00000 | − | 5.19615i | −1.09952 | − | 0.634811i | −0.163429 | − | 0.986555i | \(-0.552255\pi\) |
−0.936096 | + | 0.351744i | \(0.885589\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.00000 | − | 5.19615i | 1.06810 | − | 0.616670i | 0.140441 | − | 0.990089i | \(-0.455148\pi\) |
0.927663 | + | 0.373419i | \(0.121815\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 5.19615i | − | 0.608164i | −0.952646 | − | 0.304082i | \(-0.901650\pi\) | ||
0.952646 | − | 0.304082i | \(-0.0983496\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.0000 | −1.36753 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.46410i | 0.380235i | 0.981761 | + | 0.190117i | \(0.0608868\pi\) | ||||
−0.981761 | + | 0.190117i | \(0.939113\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.50000 | − | 2.59808i | 0.488094 | − | 0.281801i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.00000 | + | 3.46410i | 0.635999 | + | 0.367194i | 0.783072 | − | 0.621932i | \(-0.213652\pi\) |
−0.147073 | + | 0.989126i | \(0.546985\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.0000 | + | 3.46410i | 1.25794 | + | 0.363137i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.00000 | − | 5.19615i | −0.307794 | − | 0.533114i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.00000 | − | 3.46410i | 0.609208 | − | 0.351726i | −0.163448 | − | 0.986552i | \(-0.552261\pi\) |
0.772655 | + | 0.634826i | \(0.218928\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.50000 | − | 2.59808i | 0.149256 | − | 0.258518i | −0.781697 | − | 0.623658i | \(-0.785646\pi\) |
0.930953 | + | 0.365140i | \(0.118979\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.0000 | −1.37946 | −0.689730 | − | 0.724066i | \(-0.742271\pi\) | ||||
−0.689730 | + | 0.724066i | \(0.742271\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.00000 | − | 15.5885i | 0.870063 | − | 1.50699i | 0.00813215 | − | 0.999967i | \(-0.497411\pi\) |
0.861931 | − | 0.507026i | \(-0.169255\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.8564i | 1.32720i | 0.748086 | + | 0.663602i | \(0.230973\pi\) | ||||
−0.748086 | + | 0.663602i | \(0.769027\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.50000 | + | 2.59808i | 0.141108 | + | 0.244406i | 0.927914 | − | 0.372794i | \(-0.121600\pi\) |
−0.786806 | + | 0.617200i | \(0.788267\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.00000 | + | 5.19615i | 0.839254 | + | 0.484544i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.00000 | − | 5.19615i | −0.825029 | − | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.500000 | + | 0.866025i | 0.0454545 | + | 0.0787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 12.1244i | − | 1.08444i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000 | − | 13.8564i | 0.709885 | − | 1.22956i | −0.255014 | − | 0.966937i | \(-0.582080\pi\) |
0.964899 | − | 0.262620i | \(-0.0845865\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.0000 | −1.04844 | −0.524222 | − | 0.851581i | \(-0.675644\pi\) | ||||
−0.524222 | + | 0.851581i | \(0.675644\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.00000 | + | 10.3923i | −0.520266 | + | 0.901127i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.5000 | + | 7.79423i | −1.15338 | + | 0.665906i | −0.949709 | − | 0.313133i | \(-0.898621\pi\) |
−0.203674 | + | 0.979039i | \(0.565288\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.00000 | − | 3.46410i | −0.169638 | − | 0.293821i | 0.768655 | − | 0.639664i | \(-0.220926\pi\) |
−0.938293 | + | 0.345843i | \(0.887593\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.00000 | − | 12.1244i | −0.250873 | − | 1.01389i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.5000 | − | 7.79423i | −1.12111 | − | 0.647275i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.50000 | − | 4.33013i | 0.614424 | − | 0.354738i | −0.160271 | − | 0.987073i | \(-0.551237\pi\) |
0.774695 | + | 0.632335i | \(0.217903\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.3205i | 1.40952i | 0.709444 | + | 0.704761i | \(0.248946\pi\) | ||||
−0.709444 | + | 0.704761i | \(0.751054\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 23.0000 | 1.83560 | 0.917800 | − | 0.397043i | \(-0.129964\pi\) | ||||
0.917800 | + | 0.397043i | \(0.129964\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 20.7846i | − | 1.63806i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.0000 | − | 6.92820i | 0.939913 | − | 0.542659i | 0.0499796 | − | 0.998750i | \(-0.484084\pi\) |
0.889933 | + | 0.456091i | \(0.150751\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.00000 | + | 3.46410i | 0.464294 | + | 0.268060i | 0.713848 | − | 0.700301i | \(-0.246951\pi\) |
−0.249554 | + | 0.968361i | \(0.580284\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.500000 | + | 12.9904i | −0.0384615 | + | 0.999260i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 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 | ||||||||
\(175\) | −6.00000 | + | 3.46410i | −0.453557 | + | 0.261861i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.00000 | + | 15.5885i | −0.672692 | + | 1.16514i | 0.304446 | + | 0.952529i | \(0.401529\pi\) |
−0.977138 | + | 0.212607i | \(0.931805\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.0000 | −0.966282 | −0.483141 | − | 0.875542i | \(-0.660504\pi\) | ||||
−0.483141 | + | 0.875542i | \(0.660504\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.50000 | + | 7.79423i | −0.330847 | + | 0.573043i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.3923i | 0.759961i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.50000 | + | 0.866025i | 0.107972 | + | 0.0623379i | 0.553014 | − | 0.833172i | \(-0.313478\pi\) |
−0.445041 | + | 0.895510i | \(0.646811\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.00000 | − | 3.46410i | −0.427482 | − | 0.246807i | 0.270791 | − | 0.962638i | \(-0.412715\pi\) |
−0.698273 | + | 0.715831i | \(0.746048\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.00000 | + | 8.66025i | 0.354441 | + | 0.613909i | 0.987022 | − | 0.160585i | \(-0.0513380\pi\) |
−0.632581 | + | 0.774494i | \(0.718005\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 31.1769i | 2.18819i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.50000 | − | 12.9904i | 0.523823 | − | 0.907288i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.0000 | 0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | + | 6.92820i | −0.275371 | + | 0.476957i | −0.970229 | − | 0.242190i | \(-0.922134\pi\) |
0.694857 | + | 0.719148i | \(0.255467\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.00000 | − | 1.73205i | 0.204598 | − | 0.118125i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.00000 | − | 10.3923i | 0.201802 | − | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.0000 | − | 6.92820i | −0.803579 | − | 0.463947i | 0.0411418 | − | 0.999153i | \(-0.486900\pi\) |
−0.844721 | + | 0.535207i | \(0.820234\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.00000 | − | 5.19615i | 0.597351 | − | 0.344881i | −0.170648 | − | 0.985332i | \(-0.554586\pi\) |
0.767999 | + | 0.640451i | \(0.221253\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 6.92820i | − | 0.457829i | −0.973447 | − | 0.228914i | \(-0.926482\pi\) | ||
0.973447 | − | 0.228914i | \(-0.0735176\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.0000 | −1.17922 | −0.589610 | − | 0.807688i | \(-0.700718\pi\) | ||||
−0.589610 | + | 0.807688i | \(0.700718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.00000 | −0.391397 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 10.3923i | − | 0.672222i | −0.941822 | − | 0.336111i | \(-0.890888\pi\) | ||
0.941822 | − | 0.336111i | \(-0.109112\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.5000 | − | 12.9904i | 1.44935 | − | 0.836784i | 0.450910 | − | 0.892570i | \(-0.351100\pi\) |
0.998443 | + | 0.0557856i | \(0.0177663\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.50000 | − | 4.33013i | −0.479157 | − | 0.276642i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.0000 | − | 3.46410i | −0.763542 | − | 0.220416i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.0000 | + | 20.7846i | 0.757433 | + | 1.31191i | 0.944156 | + | 0.329500i | \(0.106880\pi\) |
−0.186722 | + | 0.982413i | \(0.559786\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.0000 | + | 10.3923i | −1.13165 | + | 0.653359i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.50000 | + | 2.59808i | −0.0935674 | + | 0.162064i | −0.909010 | − | 0.416775i | \(-0.863160\pi\) |
0.815442 | + | 0.578838i | \(0.196494\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.0000 | 1.11847 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.00000 | + | 5.19615i | −0.184988 | + | 0.320408i | −0.943572 | − | 0.331166i | \(-0.892558\pi\) |
0.758585 | + | 0.651575i | \(0.225891\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 15.5885i | − | 0.957591i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.0000 | + | 25.9808i | 0.914566 | + | 1.58408i | 0.807535 | + | 0.589819i | \(0.200801\pi\) |
0.107031 | + | 0.994256i | \(0.465866\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.00000 | − | 3.46410i | −0.364474 | − | 0.210429i | 0.306568 | − | 0.951849i | \(-0.400819\pi\) |
−0.671042 | + | 0.741420i | \(0.734153\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.00000 | + | 3.46410i | 0.361814 | + | 0.208893i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.50000 | + | 16.4545i | 0.570800 | + | 0.988654i | 0.996484 | + | 0.0837823i | \(0.0267000\pi\) |
−0.425684 | + | 0.904872i | \(0.639967\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 29.4449i | − | 1.75653i | −0.478171 | − | 0.878267i | \(-0.658700\pi\) | ||
0.478171 | − | 0.878267i | \(-0.341300\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.00000 | + | 12.1244i | −0.416107 | + | 0.720718i | −0.995544 | − | 0.0942988i | \(-0.969939\pi\) |
0.579437 | + | 0.815017i | \(0.303272\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −30.0000 | −1.77084 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.50000 | + | 0.866025i | −0.0876309 | + | 0.0505937i | −0.543175 | − | 0.839619i | \(-0.682778\pi\) |
0.455544 | + | 0.890213i | \(0.349445\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.0000 | − | 20.7846i | −0.698667 | − | 1.21013i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 21.0000 | − | 5.19615i | 1.21446 | − | 0.300501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.00000 | − | 3.46410i | −0.345834 | − | 0.199667i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.5000 | − | 9.52628i | 0.944787 | − | 0.545473i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.3205i | 0.988534i | 0.869310 | + | 0.494267i | \(0.164563\pi\) | ||||
−0.869310 | + | 0.494267i | \(0.835437\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.0000 | −1.02069 | −0.510343 | − | 0.859971i | \(-0.670482\pi\) | ||||
−0.510343 | + | 0.859971i | \(0.670482\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.0000 | −0.791327 | −0.395663 | − | 0.918396i | \(-0.629485\pi\) | ||||
−0.395663 | + | 0.918396i | \(0.629485\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.73205i | 0.0972817i | 0.998816 | + | 0.0486408i | \(0.0154890\pi\) | ||||
−0.998816 | + | 0.0486408i | \(0.984511\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 27.0000 | − | 15.5885i | 1.51171 | − | 0.872786i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.00000 | + | 5.19615i | 0.500773 | + | 0.289122i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.00000 | − | 5.19615i | −0.277350 | − | 0.288231i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.00000 | + | 10.3923i | 0.330791 | + | 0.572946i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.0000 | + | 6.92820i | −0.659580 | + | 0.380808i | −0.792117 | − | 0.610370i | \(-0.791021\pi\) |
0.132537 | + | 0.991178i | \(0.457688\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.00000 | + | 15.5885i | −0.491723 | + | 0.851688i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.0000 | −1.25289 | −0.626445 | − | 0.779466i | \(-0.715491\pi\) | ||||
−0.626445 | + | 0.779466i | \(0.715491\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 6.92820i | − | 0.374088i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.00000 | − | 15.5885i | −0.483145 | − | 0.836832i | 0.516667 | − | 0.856186i | \(-0.327172\pi\) |
−0.999813 | + | 0.0193540i | \(0.993839\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.0000 | − | 6.92820i | −0.642345 | − | 0.370858i | 0.143172 | − | 0.989698i | \(-0.454270\pi\) |
−0.785517 | + | 0.618840i | \(0.787603\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.5000 | + | 12.9904i | 1.19755 | + | 0.691408i | 0.960009 | − | 0.279968i | \(-0.0903240\pi\) |
0.237545 | + | 0.971377i | \(0.423657\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.00000 | − | 15.5885i | −0.477670 | − | 0.827349i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.46410i | 0.182828i | 0.995813 | + | 0.0914141i | \(0.0291387\pi\) | ||||
−0.995813 | + | 0.0914141i | \(0.970861\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.50000 | + | 6.06218i | −0.184211 | + | 0.319062i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.00000 | −0.471082 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.00000 | − | 1.73205i | 0.0521996 | − | 0.0904123i | −0.838745 | − | 0.544524i | \(-0.816710\pi\) |
0.890945 | + | 0.454112i | \(0.150043\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −27.0000 | + | 15.5885i | −1.40177 | + | 0.809312i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.5000 | − | 26.8468i | −0.802560 | − | 1.39007i | −0.917926 | − | 0.396751i | \(-0.870138\pi\) |
0.115367 | − | 0.993323i | \(-0.463196\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −31.5000 | + | 7.79423i | −1.62233 | + | 0.401423i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.0000 | − | 6.92820i | −0.616399 | − | 0.355878i | 0.159067 | − | 0.987268i | \(-0.449151\pi\) |
−0.775466 | + | 0.631390i | \(0.782485\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.0000 | − | 6.92820i | 0.613171 | − | 0.354015i | −0.161034 | − | 0.986949i | \(-0.551483\pi\) |
0.774206 | + | 0.632934i | \(0.218150\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 20.7846i | 1.05928i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −21.0000 | −1.06474 | −0.532371 | − | 0.846511i | \(-0.678699\pi\) | ||||
−0.532371 | + | 0.846511i | \(0.678699\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.0000 | −0.910299 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 13.8564i | − | 0.697191i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.0000 | + | 13.8564i | −1.20453 | + | 0.695433i | −0.961558 | − | 0.274601i | \(-0.911454\pi\) |
−0.242967 | + | 0.970034i | \(0.578121\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −31.5000 | − | 18.1865i | −1.57303 | − | 0.908192i | −0.995794 | − | 0.0916181i | \(-0.970796\pi\) |
−0.577241 | − | 0.816574i | \(-0.695871\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.00000 | − | 15.5885i | −0.446113 | − | 0.772691i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.5000 | + | 6.06218i | −0.519192 | + | 0.299755i | −0.736604 | − | 0.676324i | \(-0.763572\pi\) |
0.217412 | + | 0.976080i | \(0.430238\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −24.0000 | + | 41.5692i | −1.18096 | + | 2.04549i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.00000 | 0.294528 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 12.1244i | − | 0.590905i | −0.955357 | − | 0.295452i | \(-0.904530\pi\) | ||
0.955357 | − | 0.295452i | \(-0.0954704\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.00000 | + | 5.19615i | 0.145521 | + | 0.252050i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −33.0000 | − | 19.0526i | −1.59698 | − | 0.922018i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.0000 | − | 15.5885i | −1.30054 | − | 0.750870i | −0.320047 | − | 0.947402i | \(-0.603699\pi\) |
−0.980497 | + | 0.196532i | \(0.937032\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.5000 | + | 25.1147i | 0.696826 | + | 1.20694i | 0.969561 | + | 0.244848i | \(0.0787382\pi\) |
−0.272736 | + | 0.962089i | \(0.587929\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.7846i | 0.994263i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.00000 | + | 8.66025i | −0.238637 | + | 0.413331i | −0.960323 | − | 0.278889i | \(-0.910034\pi\) |
0.721686 | + | 0.692220i | \(0.243367\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.0000 | 1.14027 | 0.570137 | − | 0.821549i | \(-0.306890\pi\) | ||||
0.570137 | + | 0.821549i | \(0.306890\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.00000 | − | 10.3923i | 0.284427 | − | 0.492642i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.00000 | − | 3.46410i | 0.283158 | − | 0.163481i | −0.351694 | − | 0.936115i | \(-0.614394\pi\) |
0.634852 | + | 0.772634i | \(0.281061\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.0000 | + | 25.9808i | 0.706322 | + | 1.22339i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.00000 | − | 20.7846i | 0.281284 | − | 0.974398i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.50000 | + | 4.33013i | 0.350835 | + | 0.202555i | 0.665053 | − | 0.746796i | \(-0.268409\pi\) |
−0.314218 | + | 0.949351i | \(0.601742\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.50000 | + | 2.59808i | −0.209586 | + | 0.121004i | −0.601119 | − | 0.799160i | \(-0.705278\pi\) |
0.391533 | + | 0.920164i | \(0.371945\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 3.46410i | − | 0.160990i | −0.996755 | − | 0.0804952i | \(-0.974350\pi\) | ||
0.996755 | − | 0.0804952i | \(-0.0256502\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.00000 | −0.277647 | −0.138823 | − | 0.990317i | \(-0.544332\pi\) | ||||
−0.138823 | + | 0.990317i | \(0.544332\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 36.0000 | 1.66233 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.92820i | 0.318559i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.00000 | − | 3.46410i | 0.275299 | − | 0.158944i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.00000 | + | 3.46410i | 0.274147 | + | 0.158279i | 0.630771 | − | 0.775969i | \(-0.282739\pi\) |
−0.356624 | + | 0.934248i | \(0.616072\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.50000 | + | 18.1865i | 0.205182 | + | 0.829235i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.00000 | − | 10.3923i | −0.272446 | − | 0.471890i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.0000 | − | 8.66025i | 0.679715 | − | 0.392434i | −0.120033 | − | 0.992770i | \(-0.538300\pi\) |
0.799748 | + | 0.600336i | \(0.204967\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.0000 | + | 25.9808i | −0.676941 | + | 1.17250i | 0.298957 | + | 0.954267i | \(0.403361\pi\) |
−0.975898 | + | 0.218229i | \(0.929972\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.0000 | 1.21602 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18.0000 | + | 31.1769i | −0.807410 | + | 1.39848i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.00000 | − | 5.19615i | −0.133763 | − | 0.231685i | 0.791361 | − | 0.611349i | \(-0.209373\pi\) |
−0.925124 | + | 0.379664i | \(0.876040\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.50000 | − | 2.59808i | −0.200247 | − | 0.115613i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.50000 | − | 0.866025i | −0.0664863 | − | 0.0383859i | 0.466388 | − | 0.884580i | \(-0.345555\pi\) |
−0.532875 | + | 0.846194i | \(0.678888\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.00000 | + | 15.5885i | 0.398137 | + | 0.689593i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 24.2487i | 1.06853i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.00000 | − | 10.3923i | 0.263880 | − | 0.457053i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.00000 | 0.394297 | 0.197149 | − | 0.980374i | \(-0.436832\pi\) | ||||
0.197149 | + | 0.980374i | \(0.436832\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.00000 | + | 8.66025i | −0.218635 | + | 0.378686i | −0.954391 | − | 0.298560i | \(-0.903494\pi\) |
0.735756 | + | 0.677247i | \(0.236827\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | − | 11.2583i | −0.282609 | − | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.50000 | − | 30.3109i | −0.324861 | − | 1.31291i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −27.0000 | − | 15.5885i | −1.16731 | − | 0.673948i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.0000 | − | 8.66025i | 0.646096 | − | 0.373024i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.73205i | 0.0744667i | 0.999307 | + | 0.0372333i | \(0.0118545\pi\) | ||||
−0.999307 | + | 0.0372333i | \(0.988146\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24.0000 | 1.02805 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.0000 | 1.45374 | 0.726868 | − | 0.686778i | \(-0.240975\pi\) | ||||
0.726868 | + | 0.686778i | \(0.240975\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 31.1769i | − | 1.32818i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24.0000 | + | 13.8564i | −1.02058 | + | 0.589234i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.50000 | − | 0.866025i | −0.0635570 | − | 0.0366947i | 0.467885 | − | 0.883789i | \(-0.345016\pi\) |
−0.531442 | + | 0.847095i | \(0.678350\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.00000 | − | 6.92820i | 0.0845910 | − | 0.293032i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.0000 | − | 20.7846i | −0.505740 | − | 0.875967i | −0.999978 | − | 0.00664037i | \(-0.997886\pi\) |
0.494238 | − | 0.869326i | \(-0.335447\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.50000 | − | 2.59808i | 0.189316 | − | 0.109302i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.00000 | − | 5.19615i | 0.125767 | − | 0.217834i | −0.796266 | − | 0.604947i | \(-0.793194\pi\) |
0.922032 | + | 0.387113i | \(0.126528\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.0000 | 1.08807 | 0.544033 | − | 0.839064i | \(-0.316897\pi\) | ||||
0.544033 | + | 0.839064i | \(0.316897\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.00000 | + | 10.3923i | −0.250217 | + | 0.433389i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.66025i | 0.360531i | 0.983618 | + | 0.180266i | \(0.0576957\pi\) | ||||
−0.983618 | + | 0.180266i | \(0.942304\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.00000 | − | 10.3923i | −0.248922 | − | 0.431145i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 27.0000 | + | 15.5885i | 1.11823 | + | 0.645608i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.0000 | + | 10.3923i | 0.742940 | + | 0.428936i | 0.823137 | − | 0.567843i | \(-0.192222\pi\) |
−0.0801976 | + | 0.996779i | \(0.525555\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 12.1244i | − | 0.497888i | −0.968518 | − | 0.248944i | \(-0.919917\pi\) | ||
0.968518 | − | 0.248944i | \(-0.0800834\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.00000 | + | 15.5885i | −0.368964 | + | 0.639064i | ||||
\(596\) | 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 | ||||||||
\(601\) | −18.5000 | + | 32.0429i | −0.754631 | + | 1.30706i | 0.190927 | + | 0.981604i | \(0.438851\pi\) |
−0.945558 | + | 0.325455i | \(0.894483\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.50000 | − | 0.866025i | 0.0609837 | − | 0.0352089i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.00000 | + | 6.92820i | 0.162355 | + | 0.281207i | 0.935713 | − | 0.352763i | \(-0.114758\pi\) |
−0.773358 | + | 0.633970i | \(0.781424\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.00000 | + | 8.66025i | −0.364101 | + | 0.350356i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.50000 | − | 2.59808i | −0.181753 | − | 0.104935i | 0.406363 | − | 0.913712i | \(-0.366797\pi\) |
−0.588116 | + | 0.808776i | \(0.700130\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.5000 | − | 12.9904i | 0.905816 | − | 0.522973i | 0.0267333 | − | 0.999643i | \(-0.491490\pi\) |
0.879083 | + | 0.476670i | \(0.158156\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 13.8564i | − | 0.556936i | −0.960446 | − | 0.278468i | \(-0.910173\pi\) | ||
0.960446 | − | 0.278468i | \(-0.0898266\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −24.0000 | −0.961540 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 15.5885i | − | 0.621552i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.0000 | + | 13.8564i | −0.955425 | + | 0.551615i | −0.894762 | − | 0.446543i | \(-0.852655\pi\) |
−0.0606630 | + | 0.998158i | \(0.519321\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −24.0000 | − | 13.8564i | −0.952411 | − | 0.549875i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.5000 | + | 4.33013i | −0.693375 | + | 0.171566i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.5000 | − | 18.1865i | −0.414725 | − | 0.718325i | 0.580674 | − | 0.814136i | \(-0.302789\pi\) |
−0.995400 | + | 0.0958109i | \(0.969456\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.00000 | − | 3.46410i | 0.236617 | − | 0.136611i | −0.377004 | − | 0.926212i | \(-0.623046\pi\) |
0.613621 | + | 0.789601i | \(0.289712\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 48.0000 | 1.88416 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.00000 | − | 5.19615i | 0.117399 | − | 0.203341i | −0.801337 | − | 0.598213i | \(-0.795878\pi\) |
0.918736 | + | 0.394872i | \(0.129211\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.7846i | 0.812122i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.00000 | − | 10.3923i | −0.233727 | − | 0.404827i | 0.725175 | − | 0.688565i | \(-0.241759\pi\) |
−0.958902 | + | 0.283738i | \(0.908425\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.5000 | − | 6.06218i | −0.408403 | − | 0.235791i | 0.281701 | − | 0.959502i | \(-0.409102\pi\) |
−0.690103 | + | 0.723711i | \(0.742435\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 18.0000 | + | 10.3923i | 0.698010 | + | 0.402996i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 27.0000 | + | 46.7654i | 1.04544 | + | 1.81076i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 38.1051i | 1.47103i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.50000 | + | 4.33013i | −0.0963679 | + | 0.166914i | −0.910179 | − | 0.414216i | \(-0.864056\pi\) |
0.813811 | + | 0.581130i | \(0.197389\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.0000 | 1.15299 | 0.576497 | − | 0.817099i | \(-0.304419\pi\) | ||||
0.576497 | + | 0.817099i | \(0.304419\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.0000 | + | 20.7846i | −0.460518 | + | 0.797640i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.0000 | + | 6.92820i | −0.459167 | + | 0.265100i | −0.711694 | − | 0.702490i | \(-0.752072\pi\) |
0.252527 | + | 0.967590i | \(0.418738\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.5000 | + | 23.3827i | 0.515808 | + | 0.893407i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −22.5000 | − | 23.3827i | −0.857182 | − | 0.890809i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.00000 | + | 5.19615i | 0.342376 | + | 0.197671i | 0.661322 | − | 0.750102i | \(-0.269996\pi\) |
−0.318946 | + | 0.947773i | \(0.603329\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.00000 | + | 3.46410i | −0.227593 | + | 0.131401i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.9808i | 0.984092i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.00000 | −0.226617 | −0.113308 | − | 0.993560i | \(-0.536145\pi\) | ||||
−0.113308 | + | 0.993560i | \(0.536145\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.0000 | −0.678883 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.3923i | 0.390843i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.5000 | − | 7.79423i | 0.507003 | − | 0.292718i | −0.224598 | − | 0.974452i | \(-0.572107\pi\) |
0.731601 | + | 0.681733i | \(0.238773\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −21.0000 | + | 5.19615i | −0.785355 | + | 0.194325i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.0000 | + | 31.1769i | 0.671287 | + | 1.16270i | 0.977539 | + | 0.210752i | \(0.0675914\pi\) |
−0.306253 | + | 0.951950i | \(0.599075\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 42.0000 | − | 24.2487i | 1.56416 | − | 0.903069i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.00000 | − | 15.5885i | 0.334252 | − | 0.578941i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.0000 | −0.370879 | −0.185440 | − | 0.982656i | \(-0.559371\pi\) | ||||
−0.185440 | + | 0.982656i | \(0.559371\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.00000 | + | 5.19615i | −0.110959 | + | 0.192187i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 36.3731i | − | 1.34347i | −0.740792 | − | 0.671735i | \(-0.765549\pi\) | ||
0.740792 | − | 0.671735i | \(-0.234451\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.0000 | − | 31.1769i | −0.663039 | − | 1.14842i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.0000 | − | 13.8564i | −0.882854 | − | 0.509716i | −0.0112558 | − | 0.999937i | \(-0.503583\pi\) |
−0.871598 | + | 0.490221i | \(0.836916\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.0000 | + | 20.7846i | 1.32071 | + | 0.762513i | 0.983842 | − | 0.179038i | \(-0.0572985\pi\) |
0.336870 | + | 0.941551i | \(0.390632\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.50000 | − | 12.9904i | −0.274779 | − | 0.475931i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 62.3538i | 2.27836i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.0000 | − | 22.5167i | 0.474377 | − | 0.821645i | −0.525193 | − | 0.850983i | \(-0.676007\pi\) |
0.999570 | + | 0.0293387i | \(0.00934013\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 30.0000 | 1.09181 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.00000 | − | 1.73205i | 0.0363456 | − | 0.0629525i | −0.847280 | − | 0.531146i | \(-0.821762\pi\) |
0.883626 | + | 0.468193i | \(0.155095\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.0000 | + | 10.3923i | −0.652499 | + | 0.376721i | −0.789413 | − | 0.613862i | \(-0.789615\pi\) |
0.136914 | + | 0.990583i | \(0.456282\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −24.0000 | − | 41.5692i | −0.868858 | − | 1.50491i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −48.0000 | − | 13.8564i | −1.73318 | − | 0.500326i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.0000 | − | 17.3205i | −1.08183 | − | 0.624593i | −0.150439 | − | 0.988619i | \(-0.548069\pi\) |
−0.931389 | + | 0.364026i | \(0.881402\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 30.0000 | 1.07486 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.0000 | 1.28818 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 39.8372i | − | 1.42185i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.0000 | − | 20.7846i | 1.28326 | − | 0.740891i | 0.305818 | − | 0.952090i | \(-0.401070\pi\) |
0.977443 | + | 0.211199i | \(0.0677367\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.00000 | − | 5.19615i | −0.320003 | − | 0.184754i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.0000 | − | 38.1051i | 0.390621 | − | 1.35315i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.00000 | + | 15.5885i | 0.318796 | + | 0.552171i | 0.980237 | − | 0.197826i | \(-0.0633881\pi\) |
−0.661441 | + | 0.749997i | \(0.730055\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.00000 | − | 5.19615i | 0.318397 | − | 0.183827i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.00000 | − | 15.5885i | 0.317603 | − | 0.550105i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −36.0000 | −1.26883 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.5000 | + | 18.1865i | −0.369160 | + | 0.639404i | −0.989434 | − | 0.144981i | \(-0.953688\pi\) |
0.620274 | + | 0.784385i | \(0.287021\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 6.92820i | − | 0.243282i | −0.992574 | − | 0.121641i | \(-0.961184\pi\) | ||
0.992574 | − | 0.121641i | \(-0.0388157\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.0000 | − | 20.7846i | −0.420342 | − | 0.728053i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.00000 | + | 3.46410i | 0.209913 | + | 0.121194i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.0000 | − | 13.8564i | −0.837606 | − | 0.483592i | 0.0188439 | − | 0.999822i | \(-0.494001\pi\) |
−0.856450 | + | 0.516231i | \(0.827335\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.0000 | − | 34.6410i | −0.697156 | − | 1.20751i | −0.969448 | − | 0.245295i | \(-0.921115\pi\) |
0.272292 | − | 0.962215i | \(-0.412218\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 27.7128i | − | 0.963669i | −0.876262 | − | 0.481834i | \(-0.839971\pi\) | ||
0.876262 | − | 0.481834i | \(-0.160029\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.50000 | − | 9.52628i | 0.191023 | − | 0.330861i | −0.754567 | − | 0.656223i | \(-0.772153\pi\) |
0.945589 | + | 0.325362i | \(0.105486\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15.0000 | 0.519719 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.00000 | − | 10.3923i | 0.207639 | − | 0.359641i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 36.0000 | − | 20.7846i | 1.24286 | − | 0.717564i | 0.273183 | − | 0.961962i | \(-0.411924\pi\) |
0.969675 | + | 0.244398i | \(0.0785902\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.0000 | − | 45.0333i | −0.896552 | − | 1.55287i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 22.5000 | + | 0.866025i | 0.774024 | + | 0.0297922i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.00000 | − | 1.73205i | −0.103081 | − | 0.0595140i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 27.0000 | − | 15.5885i | 0.925548 | − | 0.534365i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 43.3013i | − | 1.48261i | −0.671170 | − | 0.741304i | \(-0.734208\pi\) | ||
0.671170 | − | 0.741304i | \(-0.265792\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.00000 | 0.102478 | 0.0512390 | − | 0.998686i | \(-0.483683\pi\) | ||||
0.0512390 | + | 0.998686i | \(0.483683\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.0000 | 0.477674 | 0.238837 | − | 0.971060i | \(-0.423234\pi\) | ||||
0.238837 | + | 0.971060i | \(0.423234\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 38.1051i | 1.29711i | 0.761166 | + | 0.648557i | \(0.224627\pi\) | ||||
−0.761166 | + | 0.648557i | \(0.775373\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 27.0000 | − | 15.5885i | 0.918028 | − | 0.530023i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.0000 | + | 13.8564i | 0.814144 | + | 0.470046i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.00000 | + | 36.3731i | 0.304953 | + | 1.23245i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 21.0000 | + | 36.3731i | 0.709930 | + | 1.22963i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.5000 | + | 18.1865i | −1.06368 | + | 0.614116i | −0.926448 | − | 0.376423i | \(-0.877154\pi\) |
−0.137232 | + | 0.990539i | \(0.543820\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.50000 | − | 7.79423i | 0.151609 | − | 0.262594i | −0.780210 | − | 0.625517i | \(-0.784888\pi\) |
0.931819 | + | 0.362923i | \(0.118221\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.0000 | −0.538443 | −0.269221 | − | 0.963078i | \(-0.586766\pi\) | ||||
−0.269221 | + | 0.963078i | \(0.586766\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 55.4256i | 1.85892i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.00000 | − | 10.3923i | −0.200782 | − | 0.347765i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 27.0000 | + | 15.5885i | 0.902510 | + | 0.521065i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.5000 | + | 23.3827i | 0.449750 | + | 0.778990i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 22.5167i | 0.748479i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.0000 | − | 24.2487i | 0.464862 | − | 0.805165i | −0.534333 | − | 0.845274i | \(-0.679437\pi\) |
0.999195 | + | 0.0401089i | \(0.0127705\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.00000 | + | 10.3923i | −0.198571 | + | 0.343935i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 36.0000 | − | 20.7846i | 1.18882 | − | 0.686368i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.0000 | − | 27.7128i | −0.527791 | − | 0.914161i | −0.999475 | − | 0.0323936i | \(-0.989687\pi\) |
0.471684 | − | 0.881768i | \(-0.343646\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −36.0000 | − | 10.3923i | −1.18495 | − | 0.342067i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.00000 | − | 5.19615i | −0.295918 | − | 0.170848i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 49.5000 | − | 28.5788i | 1.62404 | − | 0.937641i | 0.638219 | − | 0.769855i | \(-0.279671\pi\) |
0.985823 | − | 0.167786i | \(-0.0536619\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 17.3205i | − | 0.567657i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 18.0000 | 0.588663 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41.0000 | −1.33941 | −0.669706 | − | 0.742627i | \(-0.733580\pi\) | ||||
−0.669706 | + | 0.742627i | \(0.733580\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −45.0000 | + | 25.9808i | −1.46540 | + | 0.846050i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.0000 | − | 6.92820i | −0.389948 | − | 0.225136i | 0.292190 | − | 0.956360i | \(-0.405616\pi\) |
−0.682137 | + | 0.731224i | \(0.738949\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.5000 | + | 12.9904i | −0.438229 | + | 0.421686i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.0000 | + | 46.7654i | 0.874616 | + | 1.51488i | 0.857171 | + | 0.515031i | \(0.172220\pi\) |
0.0174443 | + | 0.999848i | \(0.494447\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 27.0000 | − | 46.7654i | 0.871875 | − | 1.51013i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.0000 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.50000 | − | 2.59808i | 0.0482867 | − | 0.0836350i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 45.0333i | − | 1.44817i | −0.689709 | − | 0.724087i | \(-0.742261\pi\) | ||
0.689709 | − | 0.724087i | \(-0.257739\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.0000 | + | 20.7846i | 0.385098 | + | 0.667010i | 0.991783 | − | 0.127933i | \(-0.0408342\pi\) |
−0.606685 | + | 0.794943i | \(0.707501\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.0000 | + | 6.92820i | 0.384702 | + | 0.222108i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.50000 | + | 4.33013i | 0.239946 | + | 0.138533i | 0.615152 | − | 0.788409i | \(-0.289095\pi\) |
−0.375206 | + | 0.926942i | \(0.622428\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.0000 | + | 20.7846i | 0.383522 | + | 0.664279i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 20.7846i | − | 0.662926i | −0.943468 | − | 0.331463i | \(-0.892458\pi\) | ||
0.943468 | − | 0.331463i | \(-0.107542\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.00000 | + | 10.3923i | −0.191176 | + | 0.331126i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.0000 | −0.381578 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.00000 | − | 1.73205i | 0.0317660 | − | 0.0550204i | −0.849705 | − | 0.527258i | \(-0.823220\pi\) |
0.881471 | + | 0.472237i | \(0.156554\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.0000 | − | 8.66025i | 0.475532 | − | 0.274549i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.5000 | + | 47.6314i | 0.870934 | + | 1.50850i | 0.861032 | + | 0.508551i | \(0.169818\pi\) |
0.00990158 | + | 0.999951i | \(0.496848\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))