Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [156,2,Mod(49,156)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(156, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("156.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 156 = 2^{2} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 156.q (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.24566627153\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 121.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 156.121 |
Dual form | 156.2.q.a.49.1 |
$q$-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 \(\left(\mathbb{Z}/156\mathbb{Z}\right)^\times\).
\(n\) | \(53\) | \(79\) | \(145\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.73205i | 0.774597i | 0.921954 | + | 0.387298i | \(0.126592\pi\) | ||||
−0.921954 | + | 0.387298i | \(0.873408\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.00000 | − | 1.73205i | 1.13389 | − | 0.654654i | 0.188982 | − | 0.981981i | \(-0.439481\pi\) |
0.944911 | + | 0.327327i | \(0.106148\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 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 | ||||||||
\(15\) | 1.50000 | + | 0.866025i | 0.387298 | + | 0.223607i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.50000 | − | 2.59808i | −0.363803 | − | 0.630126i | 0.624780 | − | 0.780801i | \(-0.285189\pi\) |
−0.988583 | + | 0.150675i | \(0.951855\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.00000 | + | 1.73205i | −0.688247 | + | 0.397360i | −0.802955 | − | 0.596040i | \(-0.796740\pi\) |
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 3.46410i | − | 0.755929i | ||||||
\(22\) | 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 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.50000 | + | 7.79423i | −0.835629 | + | 1.44735i | 0.0578882 | + | 0.998323i | \(0.481563\pi\) |
−0.893517 | + | 0.449029i | \(0.851770\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.00000 | − | 1.73205i | 0.522233 | − | 0.301511i | ||||
\(34\) | 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 | ||||||||
\(39\) | −3.50000 | + | 0.866025i | −0.560449 | + | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.50000 | − | 4.33013i | −1.17130 | − | 0.676252i | −0.217317 | − | 0.976101i | \(-0.569730\pi\) |
−0.953987 | + | 0.299849i | \(0.903064\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.00000 | − | 1.73205i | −0.152499 | − | 0.264135i | 0.779647 | − | 0.626219i | \(-0.215399\pi\) |
−0.932145 | + | 0.362084i | \(0.882065\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.50000 | − | 0.866025i | 0.223607 | − | 0.129099i | ||||
\(46\) | 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 | ||||||||
\(51\) | −3.00000 | −0.420084 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.00000 | −1.23625 | −0.618123 | − | 0.786082i | \(-0.712106\pi\) | ||||
−0.618123 | + | 0.786082i | \(0.712106\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.00000 | + | 5.19615i | −0.404520 | + | 0.700649i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.46410i | 0.458831i | ||||||||
\(58\) | 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 | ||||||||
\(63\) | −3.00000 | − | 1.73205i | −0.377964 | − | 0.218218i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.50000 | − | 4.33013i | 0.558156 | − | 0.537086i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.00000 | + | 5.19615i | 1.09952 | + | 0.634811i | 0.936096 | − | 0.351744i | \(-0.114411\pi\) |
0.163429 | + | 0.986555i | \(0.447745\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.00000 | + | 5.19615i | 0.361158 | + | 0.625543i | ||||
\(70\) | 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 | ||||||||
\(75\) | 1.00000 | − | 1.73205i | 0.115470 | − | 0.200000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.0000 | 1.36753 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.00000 | −0.900070 | −0.450035 | − | 0.893011i | \(-0.648589\pi\) | ||||
−0.450035 | + | 0.893011i | \(0.648589\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 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 | ||||||||
\(87\) | 4.50000 | + | 7.79423i | 0.482451 | + | 0.835629i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.00000 | − | 3.46410i | −0.635999 | − | 0.367194i | 0.147073 | − | 0.989126i | \(-0.453015\pi\) |
−0.783072 | + | 0.621932i | \(0.786348\pi\) | |||||||
\(90\) | 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 | ||||||||
\(99\) | − | 3.46410i | − | 0.348155i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.50000 | + | 2.59808i | −0.149256 | + | 0.258518i | −0.930953 | − | 0.365140i | \(-0.881021\pi\) |
0.781697 | + | 0.623658i | \(0.214354\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.0000 | 1.37946 | 0.689730 | − | 0.724066i | \(-0.257729\pi\) | ||||
0.689730 | + | 0.724066i | \(0.257729\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.00000 | 0.585540 | ||||||||
\(106\) | 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 | ||||||||
\(111\) | −4.50000 | + | 2.59808i | −0.427121 | + | 0.246598i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.50000 | − | 2.59808i | −0.141108 | − | 0.244406i | 0.786806 | − | 0.617200i | \(-0.211733\pi\) |
−0.927914 | + | 0.372794i | \(0.878400\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.00000 | − | 5.19615i | −0.839254 | − | 0.484544i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | + | 3.46410i | −0.0924500 | + | 0.320256i | ||||
\(118\) | 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 | ||||||||
\(123\) | −7.50000 | + | 4.33013i | −0.676252 | + | 0.390434i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1244i | 1.08444i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.00000 | + | 13.8564i | −0.709885 | + | 1.22956i | 0.255014 | + | 0.966937i | \(0.417920\pi\) |
−0.964899 | + | 0.262620i | \(0.915413\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.00000 | −0.176090 | ||||||||
\(130\) | 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 | ||||||||
\(135\) | − | 1.73205i | − | 0.149071i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.5000 | − | 7.79423i | 1.15338 | − | 0.665906i | 0.203674 | − | 0.979039i | \(-0.434712\pi\) |
0.949709 | + | 0.313133i | \(0.101379\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.00000 | + | 3.46410i | 0.169638 | + | 0.293821i | 0.938293 | − | 0.345843i | \(-0.112407\pi\) |
−0.768655 | + | 0.639664i | \(0.779074\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.00000 | − | 1.73205i | −0.252646 | − | 0.145865i | ||||
\(142\) | 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 | ||||||||
\(147\) | −2.50000 | − | 4.33013i | −0.206197 | − | 0.357143i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.50000 | + | 4.33013i | −0.614424 | + | 0.354738i | −0.774695 | − | 0.632335i | \(-0.782097\pi\) |
0.160271 | + | 0.987073i | \(0.448763\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 17.3205i | − | 1.40952i | −0.709444 | − | 0.704761i | \(-0.751054\pi\) | ||
0.709444 | − | 0.704761i | \(-0.248946\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.50000 | + | 2.59808i | −0.121268 | + | 0.210042i | ||||
\(154\) | 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 | ||||||||
\(159\) | −4.50000 | + | 7.79423i | −0.356873 | + | 0.618123i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20.7846i | 1.63806i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.0000 | + | 6.92820i | −0.939913 | + | 0.542659i | −0.889933 | − | 0.456091i | \(-0.849249\pi\) |
−0.0499796 | + | 0.998750i | \(0.515916\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.00000 | + | 5.19615i | 0.233550 | + | 0.404520i | ||||
\(166\) | 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 | ||||||||
\(171\) | 3.00000 | + | 1.73205i | 0.229416 | + | 0.132453i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.00000 | − | 15.5885i | −0.684257 | − | 1.18517i | −0.973670 | − | 0.227964i | \(-0.926793\pi\) |
0.289412 | − | 0.957205i | \(-0.406540\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.00000 | − | 3.46410i | 0.453557 | − | 0.261861i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 13.8564i | − | 1.04151i | ||||||
\(178\) | 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 | ||||||||
\(183\) | 11.0000 | 0.813143 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.50000 | − | 7.79423i | 0.330847 | − | 0.573043i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 10.3923i | − | 0.759961i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.00000 | + | 1.73205i | −0.218218 | + | 0.125988i | ||||
\(190\) | 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 | ||||||||
\(195\) | −1.50000 | − | 6.06218i | −0.107417 | − | 0.434122i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.00000 | + | 3.46410i | 0.427482 | + | 0.246807i | 0.698273 | − | 0.715831i | \(-0.253952\pi\) |
−0.270791 | + | 0.962638i | \(0.587285\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.00000 | − | 8.66025i | −0.354441 | − | 0.613909i | 0.632581 | − | 0.774494i | \(-0.281995\pi\) |
−0.987022 | + | 0.160585i | \(0.948662\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.00000 | − | 5.19615i | 0.634811 | − | 0.366508i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 31.1769i | 2.18819i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.50000 | − | 12.9904i | 0.523823 | − | 0.907288i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.00000 | 0.417029 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.0000 | −0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | − | 6.92820i | 0.275371 | − | 0.476957i | −0.694857 | − | 0.719148i | \(-0.744533\pi\) |
0.970229 | + | 0.242190i | \(0.0778659\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 10.3923i | − | 0.712069i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.00000 | − | 1.73205i | 0.204598 | − | 0.118125i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.50000 | − | 2.59808i | −0.304082 | − | 0.175562i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.00000 | + | 10.3923i | −0.201802 | + | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.0000 | + | 6.92820i | 0.803579 | + | 0.463947i | 0.844721 | − | 0.535207i | \(-0.179766\pi\) |
−0.0411418 | + | 0.999153i | \(0.513100\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.00000 | − | 1.73205i | −0.0666667 | − | 0.115470i | ||||
\(226\) | 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 | ||||||||
\(231\) | 6.00000 | − | 10.3923i | 0.394771 | − | 0.683763i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.0000 | 1.17922 | 0.589610 | − | 0.807688i | \(-0.299282\pi\) | ||||
0.589610 | + | 0.807688i | \(0.299282\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.00000 | 0.391397 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.00000 | + | 6.92820i | −0.259828 | + | 0.450035i | ||||
\(238\) | 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 | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 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 | ||||||||
\(249\) | 3.00000 | + | 1.73205i | 0.190117 | + | 0.109764i | ||||
\(250\) | 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 | ||||||||
\(255\) | − | 5.19615i | − | 0.325396i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.50000 | − | 2.59808i | 0.0935674 | − | 0.162064i | −0.815442 | − | 0.578838i | \(-0.803506\pi\) |
0.909010 | + | 0.416775i | \(0.136840\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18.0000 | −1.11847 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.00000 | 0.557086 | ||||||||
\(262\) | 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 | ||||||||
\(267\) | −6.00000 | + | 3.46410i | −0.367194 | + | 0.212000i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.0000 | − | 25.9808i | −0.914566 | − | 1.58408i | −0.807535 | − | 0.589819i | \(-0.799199\pi\) |
−0.107031 | − | 0.994256i | \(-0.534134\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.00000 | + | 3.46410i | 0.364474 | + | 0.210429i | 0.671042 | − | 0.741420i | \(-0.265847\pi\) |
−0.306568 | + | 0.951849i | \(0.599181\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.00000 | + | 8.66025i | −0.544705 | + | 0.524142i | ||||
\(274\) | 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 | \(0.341300\pi\) | ||||
−0.478171 | + | 0.878267i | \(0.658700\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.00000 | − | 12.1244i | 0.416107 | − | 0.720718i | −0.579437 | − | 0.815017i | \(-0.696728\pi\) |
0.995544 | + | 0.0942988i | \(0.0300609\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.00000 | −0.355409 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −30.0000 | −1.77084 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 6.92820i | − | 0.406138i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.50000 | − | 0.866025i | 0.0876309 | − | 0.0505937i | −0.455544 | − | 0.890213i | \(-0.650555\pi\) |
0.543175 | + | 0.839619i | \(0.317222\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.0000 | + | 20.7846i | 0.698667 | + | 1.21013i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.00000 | − | 1.73205i | −0.174078 | − | 0.100504i | ||||
\(298\) | 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 | ||||||||
\(303\) | 1.50000 | + | 2.59808i | 0.0861727 | + | 0.149256i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −16.5000 | + | 9.52628i | −0.944787 | + | 0.545473i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 17.3205i | − | 0.988534i | −0.869310 | − | 0.494267i | \(-0.835437\pi\) | ||
0.869310 | − | 0.494267i | \(-0.164563\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.00000 | − | 12.1244i | 0.398216 | − | 0.689730i | ||||
\(310\) | 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 | ||||||||
\(315\) | 3.00000 | − | 5.19615i | 0.169031 | − | 0.292770i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 1.73205i | − | 0.0972817i | −0.998816 | − | 0.0486408i | \(-0.984511\pi\) | ||
0.998816 | − | 0.0486408i | \(-0.0154890\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −27.0000 | + | 15.5885i | −1.51171 | + | 0.872786i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.00000 | − | 15.5885i | −0.502331 | − | 0.870063i | ||||
\(322\) | 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 | ||||||||
\(327\) | 12.0000 | + | 6.92820i | 0.663602 | + | 0.383131i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.00000 | − | 10.3923i | −0.330791 | − | 0.572946i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.0000 | − | 6.92820i | 0.659580 | − | 0.380808i | −0.132537 | − | 0.991178i | \(-0.542312\pi\) |
0.792117 | + | 0.610370i | \(0.208979\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.19615i | 0.284747i | ||||||||
\(334\) | 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 | ||||||||
\(339\) | −3.00000 | −0.162938 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.92820i | 0.374088i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.00000 | + | 5.19615i | −0.484544 | + | 0.279751i | ||||
\(346\) | 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 | ||||||||
\(351\) | 2.50000 | + | 2.59808i | 0.133440 | + | 0.138675i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.5000 | − | 12.9904i | −1.19755 | − | 0.691408i | −0.237545 | − | 0.971377i | \(-0.576343\pi\) |
−0.960009 | + | 0.279968i | \(0.909676\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.00000 | + | 15.5885i | 0.477670 | + | 0.827349i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.00000 | + | 5.19615i | −0.476331 | + | 0.275010i | ||||
\(358\) | 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 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.00000 | 0.471082 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.00000 | + | 1.73205i | −0.0521996 | + | 0.0904123i | −0.890945 | − | 0.454112i | \(-0.849957\pi\) |
0.838745 | + | 0.544524i | \(0.183290\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.66025i | 0.450835i | ||||||||
\(370\) | 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 | ||||||||
\(375\) | 10.5000 | + | 6.06218i | 0.542218 | + | 0.313050i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 31.5000 | − | 7.79423i | 1.62233 | − | 0.401423i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.0000 | + | 6.92820i | 0.616399 | + | 0.355878i | 0.775466 | − | 0.631390i | \(-0.217515\pi\) |
−0.159067 | + | 0.987268i | \(0.550849\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.00000 | + | 13.8564i | 0.409852 | + | 0.709885i | ||||
\(382\) | 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 | ||||||||
\(387\) | −1.00000 | + | 1.73205i | −0.0508329 | + | 0.0880451i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.0000 | 1.06474 | 0.532371 | − | 0.846511i | \(-0.321301\pi\) | ||||
0.532371 | + | 0.846511i | \(0.321301\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.0000 | 0.910299 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.00000 | + | 10.3923i | −0.302660 | + | 0.524222i | ||||
\(394\) | 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 | ||||||||
\(399\) | 6.00000 | + | 10.3923i | 0.300376 | + | 0.520266i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.5000 | + | 18.1865i | 1.57303 | + | 0.908192i | 0.995794 | + | 0.0916181i | \(0.0292039\pi\) |
0.577241 | + | 0.816574i | \(0.304129\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.50000 | − | 0.866025i | −0.0745356 | − | 0.0430331i | ||||
\(406\) | 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 | ||||||||
\(411\) | − | 15.5885i | − | 0.768922i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 24.0000 | − | 41.5692i | 1.18096 | − | 2.04549i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.00000 | −0.294528 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.00000 | 0.195881 | ||||||||
\(418\) | 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 | ||||||||
\(423\) | −3.00000 | + | 1.73205i | −0.145865 | + | 0.0842152i | ||||
\(424\) | 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 | ||||||||
\(429\) | −12.0000 | − | 3.46410i | −0.579365 | − | 0.167248i | ||||
\(430\) | 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 | ||||||||
\(435\) | −13.5000 | + | 7.79423i | −0.647275 | + | 0.373705i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 20.7846i | − | 0.994263i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.00000 | − | 8.66025i | 0.238637 | − | 0.413331i | −0.721686 | − | 0.692220i | \(-0.756633\pi\) |
0.960323 | + | 0.278889i | \(0.0899661\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.00000 | −0.238095 | ||||||||
\(442\) | 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 | ||||||||
\(447\) | 8.66025i | 0.409616i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.00000 | + | 3.46410i | −0.283158 | + | 0.163481i | −0.634852 | − | 0.772634i | \(-0.718939\pi\) |
0.351694 | + | 0.936115i | \(0.385606\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.0000 | − | 25.9808i | −0.706322 | − | 1.22339i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15.0000 | − | 8.66025i | −0.704761 | − | 0.406894i | ||||
\(454\) | 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 | ||||||||
\(459\) | 1.50000 | + | 2.59808i | 0.0700140 | + | 0.121268i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.50000 | − | 2.59808i | 0.209586 | − | 0.121004i | −0.391533 | − | 0.920164i | \(-0.628055\pi\) |
0.601119 | + | 0.799160i | \(0.294722\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.46410i | 0.160990i | 0.996755 | + | 0.0804952i | \(0.0256502\pi\) | ||||
−0.996755 | + | 0.0804952i | \(0.974350\pi\) | |||||||
\(464\) | 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 | ||||||||
\(471\) | 11.5000 | − | 19.9186i | 0.529892 | − | 0.917800i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 6.92820i | − | 0.318559i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.00000 | + | 3.46410i | −0.275299 | + | 0.158944i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.50000 | + | 7.79423i | 0.206041 | + | 0.356873i | ||||
\(478\) | 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 | ||||||||
\(483\) | 18.0000 | + | 10.3923i | 0.819028 | + | 0.472866i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.00000 | + | 10.3923i | 0.272446 | + | 0.471890i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.0000 | + | 8.66025i | −0.679715 | + | 0.392434i | −0.799748 | − | 0.600336i | \(-0.795033\pi\) |
0.120033 | + | 0.992770i | \(0.461700\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.8564i | 0.626608i | ||||||||
\(490\) | 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 | ||||||||
\(495\) | 6.00000 | 0.269680 | ||||||||
\(496\) | 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 | ||||||||
\(501\) | 6.00000 | − | 3.46410i | 0.268060 | − | 0.154765i | ||||
\(502\) | 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 | ||||||||
\(507\) | 11.0000 | + | 6.92820i | 0.488527 | + | 0.307692i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.50000 | + | 0.866025i | 0.0664863 | + | 0.0383859i | 0.532875 | − | 0.846194i | \(-0.321112\pi\) |
−0.466388 | + | 0.884580i | \(0.654445\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.00000 | − | 15.5885i | −0.398137 | − | 0.689593i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.00000 | − | 1.73205i | 0.132453 | − | 0.0764719i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 24.2487i | 1.06853i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.00000 | − | 10.3923i | 0.263880 | − | 0.457053i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.0000 | −0.790112 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.00000 | −0.394297 | −0.197149 | − | 0.980374i | \(-0.563168\pi\) | ||||
−0.197149 | + | 0.980374i | \(0.563168\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.00000 | − | 8.66025i | 0.218635 | − | 0.378686i | −0.735756 | − | 0.677247i | \(-0.763173\pi\) |
0.954391 | + | 0.298560i | \(0.0965063\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 6.92820i | − | 0.302372i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | − | 11.2583i | −0.282609 | − | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.0000 | − | 6.92820i | −0.520756 | − | 0.300658i | ||||
\(532\) | 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 | ||||||||
\(537\) | 9.00000 | + | 15.5885i | 0.388379 | + | 0.672692i | ||||
\(538\) | 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 | ||||||||
\(543\) | −6.50000 | + | 11.2583i | −0.278942 | + | 0.483141i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −24.0000 | −1.02805 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.0000 | −1.45374 | −0.726868 | − | 0.686778i | \(-0.759025\pi\) | ||||
−0.726868 | + | 0.686778i | \(0.759025\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.50000 | − | 9.52628i | 0.234734 | − | 0.406572i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 31.1769i | − | 1.32818i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24.0000 | + | 13.8564i | −1.02058 | + | 0.589234i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.50000 | − | 7.79423i | −0.191014 | − | 0.330847i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.50000 | + | 0.866025i | 0.0635570 | + | 0.0366947i | 0.531442 | − | 0.847095i | \(-0.321650\pi\) |
−0.467885 | + | 0.883789i | \(0.654984\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.00000 | + | 6.92820i | −0.0845910 | + | 0.293032i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.00000 | − | 5.19615i | −0.379980 | − | 0.219382i | ||||
\(562\) | 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 | ||||||||
\(567\) | 3.46410i | 0.145479i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.00000 | + | 5.19615i | −0.125767 | + | 0.217834i | −0.922032 | − | 0.387113i | \(-0.873472\pi\) |
0.796266 | + | 0.604947i | \(0.206806\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.0000 | −1.08807 | −0.544033 | − | 0.839064i | \(-0.683103\pi\) | ||||
−0.544033 | + | 0.839064i | \(0.683103\pi\) | |||||||
\(572\) | 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 | ||||||||
\(579\) | 1.50000 | − | 0.866025i | 0.0623379 | − | 0.0359908i | ||||
\(580\) | 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 | ||||||||
\(585\) | −6.00000 | − | 1.73205i | −0.248069 | − | 0.0716115i | ||||
\(586\) | 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 | ||||||||
\(591\) | 6.00000 | − | 3.46410i | 0.246807 | − | 0.142494i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.1244i | 0.497888i | 0.968518 | + | 0.248944i | \(0.0800834\pi\) | ||||
−0.968518 | + | 0.248944i | \(0.919917\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.00000 | − | 15.5885i | 0.368964 | − | 0.639064i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10.0000 | −0.409273 | ||||||||
\(598\) | 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 | ||||||||
\(603\) | − | 10.3923i | − | 0.423207i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.50000 | + | 0.866025i | −0.0609837 | + | 0.0352089i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.00000 | − | 6.92820i | −0.162355 | − | 0.281207i | 0.773358 | − | 0.633970i | \(-0.218576\pi\) |
−0.935713 | + | 0.352763i | \(0.885242\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 27.0000 | + | 15.5885i | 1.09410 | + | 0.631676i | ||||
\(610\) | 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 | ||||||||
\(615\) | −7.50000 | − | 12.9904i | −0.302429 | − | 0.523823i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.5000 | + | 12.9904i | −0.905816 | + | 0.522973i | −0.879083 | − | 0.476670i | \(-0.841844\pi\) |
−0.0267333 | + | 0.999643i | \(0.508510\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.8564i | 0.556936i | 0.960446 | + | 0.278468i | \(0.0898266\pi\) | ||||
−0.960446 | + | 0.278468i | \(0.910173\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.00000 | − | 5.19615i | 0.120386 | − | 0.208514i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −24.0000 | −0.961540 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.00000 | + | 10.3923i | −0.239617 | + | 0.415029i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.5885i | 0.621552i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.0000 | − | 13.8564i | 0.955425 | − | 0.551615i | 0.0606630 | − | 0.998158i | \(-0.480679\pi\) |
0.894762 | + | 0.446543i | \(0.147345\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.00000 | − | 6.92820i | −0.158986 | − | 0.275371i | ||||
\(634\) | 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 | ||||||||
\(639\) | −9.00000 | − | 5.19615i | −0.356034 | − | 0.205557i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.5000 | + | 18.1865i | 0.414725 | + | 0.718325i | 0.995400 | − | 0.0958109i | \(-0.0305444\pi\) |
−0.580674 | + | 0.814136i | \(0.697211\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.00000 | + | 3.46410i | −0.236617 | + | 0.136611i | −0.613621 | − | 0.789601i | \(-0.710288\pi\) |
0.377004 | + | 0.926212i | \(0.376954\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 3.46410i | − | 0.136399i | ||||||
\(646\) | 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 | −0.918736 | − | 0.394872i | \(-0.870789\pi\) |
0.801337 | + | 0.598213i | \(0.204122\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 20.7846i | − | 0.812122i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.50000 | + | 2.59808i | −0.175562 | + | 0.101361i | ||||
\(658\) | 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 | ||||||||
\(663\) | 7.50000 | + | 7.79423i | 0.291276 | + | 0.302703i | ||||
\(664\) | 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 | ||||||||
\(669\) | 12.0000 | − | 6.92820i | 0.463947 | − | 0.267860i | ||||
\(670\) | 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 | ||||||||
\(675\) | −2.00000 | −0.0769800 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −30.0000 | −1.15299 | −0.576497 | − | 0.817099i | \(-0.695581\pi\) | ||||
−0.576497 | + | 0.817099i | \(0.695581\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.0000 | − | 20.7846i | 0.460518 | − | 0.797640i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 10.3923i | − | 0.398234i | ||||||
\(682\) | 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 | ||||||||
\(687\) | −6.00000 | − | 3.46410i | −0.228914 | − | 0.132164i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.5000 | + | 23.3827i | 0.857182 | + | 0.890809i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.00000 | − | 5.19615i | −0.342376 | − | 0.197671i | 0.318946 | − | 0.947773i | \(-0.396671\pi\) |
−0.661322 | + | 0.750102i | \(0.730004\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.00000 | − | 10.3923i | −0.227921 | − | 0.394771i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.00000 | + | 3.46410i | −0.227593 | + | 0.131401i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.9808i | 0.984092i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.00000 | − | 15.5885i | 0.340411 | − | 0.589610i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.00000 | 0.226617 | 0.113308 | − | 0.993560i | \(-0.463855\pi\) | ||||
0.113308 | + | 0.993560i | \(0.463855\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.0000 | 0.678883 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.00000 | − | 5.19615i | 0.112987 | − | 0.195698i | ||||
\(706\) | 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 | ||||||||
\(711\) | 4.00000 | + | 6.92820i | 0.150012 | + | 0.259828i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 21.0000 | − | 5.19615i | 0.785355 | − | 0.194325i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.00000 | − | 5.19615i | −0.336111 | − | 0.194054i | ||||
\(718\) | 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 | ||||||||
\(723\) | − | 25.9808i | − | 0.966235i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.00000 | + | 15.5885i | −0.334252 | + | 0.578941i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.0000 | 0.370879 | 0.185440 | − | 0.982656i | \(-0.440629\pi\) | ||||
0.185440 | + | 0.982656i | \(0.440629\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 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 | ||||||||
\(735\) | 7.50000 | − | 4.33013i | 0.276642 | − | 0.159719i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18.0000 | + | 31.1769i | 0.663039 | + | 1.14842i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.0000 | + | 13.8564i | 0.882854 | + | 0.509716i | 0.871598 | − | 0.490221i | \(-0.163084\pi\) |
0.0112558 | + | 0.999937i | \(0.496417\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.00000 | − | 8.66025i | 0.330623 | − | 0.318142i | ||||
\(742\) | 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 | ||||||||
\(747\) | 3.00000 | − | 1.73205i | 0.109764 | − | 0.0633724i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 62.3538i | − | 2.27836i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.0000 | + | 22.5167i | −0.474377 | + | 0.821645i | −0.999570 | − | 0.0293387i | \(-0.990660\pi\) |
0.525193 | + | 0.850983i | \(0.323993\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24.0000 | 0.874609 | ||||||||
\(754\) | 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 | ||||||||
\(759\) | 20.7846i | 0.754434i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.0000 | − | 10.3923i | 0.652499 | − | 0.376721i | −0.136914 | − | 0.990583i | \(-0.543718\pi\) |
0.789413 | + | 0.613862i | \(0.210385\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 24.0000 | + | 41.5692i | 0.868858 | + | 1.50491i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.50000 | − | 2.59808i | −0.162698 | − | 0.0939336i | ||||
\(766\) | 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 | ||||||||
\(771\) | −1.50000 | − | 2.59808i | −0.0540212 | − | 0.0935674i | ||||
\(772\) | 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 | ||||||||
\(777\) | −9.00000 | + | 15.5885i | −0.322873 | + | 0.559233i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 30.0000 | 1.07486 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.0000 | 1.28818 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.50000 | − | 7.79423i | 0.160817 | − | 0.278543i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 39.8372i | 1.42185i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −36.0000 | + | 20.7846i | −1.28326 | + | 0.740891i | −0.977443 | − | 0.211199i | \(-0.932263\pi\) |
−0.305818 | + | 0.952090i | \(0.598930\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.00000 | + | 5.19615i | 0.106803 | + | 0.184988i | ||||
\(790\) | 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 | ||||||||
\(795\) | −13.5000 | − | 7.79423i | −0.478796 | − | 0.276433i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.00000 | − | 15.5885i | −0.318796 | − | 0.552171i | 0.661441 | − | 0.749997i | \(-0.269945\pi\) |
−0.980237 | + | 0.197826i | \(0.936612\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.00000 | + | 5.19615i | −0.318397 | + | 0.183827i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.92820i | 0.244796i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.00000 | − | 15.5885i | 0.317603 | − | 0.550105i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −36.0000 | −1.26883 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −30.0000 | −1.05605 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.5000 | − | 18.1865i | 0.369160 | − | 0.639404i | −0.620274 | − | 0.784385i | \(-0.712979\pi\) |
0.989434 | + | 0.144981i | \(0.0463120\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.92820i | 0.243282i | 0.992574 | + | 0.121641i | \(0.0388157\pi\) | ||||
−0.992574 | + | 0.121641i | \(0.961184\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.00000 | − | 3.46410i | 0.210429 | − | 0.121491i | ||||
\(814\) | 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 | ||||||||
\(819\) | 3.00000 | + | 12.1244i | 0.104828 | + | 0.423659i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.0000 | + | 13.8564i | 0.837606 | + | 0.483592i | 0.856450 | − | 0.516231i | \(-0.172665\pi\) |
−0.0188439 | + | 0.999822i | \(0.505999\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.0000 | + | 34.6410i | 0.697156 | + | 1.20751i | 0.969448 | + | 0.245295i | \(0.0788849\pi\) |
−0.272292 | + | 0.962215i | \(0.587782\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.00000 | − | 3.46410i | 0.208893 | − | 0.120605i | ||||
\(826\) | 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 | ||||||||
\(831\) | 19.0000 | 0.659103 | ||||||||
\(832\) | 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 | ||||||||
\(843\) | 25.5000 | + | 14.7224i | 0.878267 | + | 0.507067i | ||||
\(844\) | 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 | ||||||||
\(849\) | −7.00000 | − | 12.1244i | −0.240239 | − | 0.416107i | ||||
\(850\) | 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 | ||||||||
\(855\) | −3.00000 | + | 5.19615i | −0.102598 | + | 0.177705i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.00000 | −0.102478 | −0.0512390 | − | 0.998686i | \(-0.516317\pi\) | ||||
−0.0512390 | + | 0.998686i | \(0.516317\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.0000 | −0.477674 | −0.238837 | − | 0.971060i | \(-0.576766\pi\) | ||||
−0.238837 | + | 0.971060i | \(0.576766\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.0000 | + | 25.9808i | −0.511199 | + | 0.885422i | ||||
\(862\) | 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 | ||||||||
\(867\) | −4.00000 | − | 6.92820i | −0.135847 | − | 0.235294i | ||||
\(868\) | 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 | ||||||||
\(873\) | −6.00000 | − | 3.46410i | −0.203069 | − | 0.117242i | ||||
\(874\) | 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 | ||||||||
\(879\) | − | 1.73205i | − | 0.0584206i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.50000 | + | 7.79423i | −0.151609 | + | 0.262594i | −0.931819 | − | 0.362923i | \(-0.881779\pi\) |
0.780210 | + | 0.625517i | \(0.215112\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.0000 | 0.538443 | 0.269221 | − | 0.963078i | \(-0.413234\pi\) | ||||
0.269221 | + | 0.963078i | \(0.413234\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 24.0000 | 0.806751 | ||||||||
\(886\) | 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 | ||||||||
\(891\) | −3.00000 | + | 1.73205i | −0.100504 | + | 0.0580259i | ||||
\(892\) | 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 | ||||||||
\(897\) | 6.00000 | − | 20.7846i | 0.200334 | − | 0.693978i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.5000 | + | 23.3827i | 0.449750 | + | 0.778990i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.00000 | + | 3.46410i | −0.199667 | + | 0.115278i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 22.5167i | − | 0.748479i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.0000 | + | 24.2487i | −0.464862 | + | 0.805165i | −0.999195 | − | 0.0401089i | \(-0.987230\pi\) |
0.534333 | + | 0.845274i | \(0.320563\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.00000 | 0.0995037 | ||||||||
\(910\) | 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 | ||||||||
\(915\) | 19.0526i | 0.629858i | ||||||||
\(916\) | 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 | \(0.0103130\pi\) |
−0.471684 | + | 0.881768i | \(0.656354\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.0000 | − | 8.66025i | −0.494267 | − | 0.285365i | ||||
\(922\) | 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 | ||||||||
\(927\) | −7.00000 | − | 12.1244i | −0.229910 | − | 0.398216i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −49.5000 | + | 28.5788i | −1.62404 | + | 0.937641i | −0.638219 | + | 0.769855i | \(0.720329\pi\) |
−0.985823 | + | 0.167786i | \(0.946338\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.3205i | 0.567657i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.00000 | + | 15.5885i | −0.294647 | + | 0.510343i | ||||
\(934\) | 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 | ||||||||
\(939\) | −7.00000 | + | 12.1244i | −0.228436 | + | 0.395663i | ||||
\(940\) | 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 | ||||||||
\(945\) | −3.00000 | − | 5.19615i | −0.0975900 | − | 0.169031i | ||||
\(946\) | 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 | ||||||||
\(951\) | −1.50000 | − | 0.866025i | −0.0486408 | − | 0.0280828i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27.0000 | − | 46.7654i | −0.874616 | − | 1.51488i | −0.857171 | − | 0.515031i | \(-0.827780\pi\) |
−0.0174443 | − | 0.999848i | \(-0.505553\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 31.1769i | 1.00781i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 27.0000 | − | 46.7654i | 0.871875 | − | 1.51013i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.0000 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −18.0000 | −0.580042 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.50000 | + | 2.59808i | −0.0482867 | + | 0.0836350i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.0333i | 1.44817i | 0.689709 | + | 0.724087i | \(0.257739\pi\) | ||||
−0.689709 | + | 0.724087i | \(0.742261\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.00000 | − | 5.19615i | 0.289122 | − | 0.166924i | ||||
\(970\) | 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 | ||||||||
\(975\) | −7.00000 | + | 1.73205i | −0.224179 | + | 0.0554700i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.50000 | − | 4.33013i | −0.239946 | − | 0.138533i | 0.375206 | − | 0.926942i | \(-0.377572\pi\) |
−0.615152 | + | 0.788409i | \(0.710905\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.0000 | − | 20.7846i | −0.383522 | − | 0.664279i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.0000 | − | 6.92820i | 0.383131 | − | 0.221201i | ||||
\(982\) | 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 | ||||||||
\(987\) | −12.0000 | −0.381964 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.0000 | 0.381578 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.00000 | + | 1.73205i | −0.0317660 | + | 0.0550204i | −0.881471 | − | 0.472237i | \(-0.843446\pi\) |
0.849705 | + | 0.527258i | \(0.176780\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 13.8564i | − | 0.439720i | ||||||
\(994\) | 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 | ||||||||
\(999\) | 4.50000 | + | 2.59808i | 0.142374 | + | 0.0821995i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))