Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,2,Mod(961,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2352.961");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.7808145554\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1537.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.1537 |
Dual form | 2352.2.q.n.961.1 |
$q$-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 \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1471\) | \(1765\) | \(2257\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | − | 1.73205i | −0.447214 | − | 0.774597i | 0.550990 | − | 0.834512i | \(-0.314250\pi\) |
−0.998203 | + | 0.0599153i | \(0.980917\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | + | 3.46410i | −0.603023 | + | 1.04447i | 0.389338 | + | 0.921095i | \(0.372704\pi\) |
−0.992361 | + | 0.123371i | \(0.960630\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.00000 | −1.66410 | −0.832050 | − | 0.554700i | \(-0.812833\pi\) | ||||
−0.832050 | + | 0.554700i | \(0.812833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.00000 | −0.516398 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | − | 1.73205i | 0.242536 | − | 0.420084i | −0.718900 | − | 0.695113i | \(-0.755354\pi\) |
0.961436 | + | 0.275029i | \(0.0886875\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | + | 3.46410i | 0.458831 | + | 0.794719i | 0.998899 | − | 0.0469020i | \(-0.0149348\pi\) |
−0.540068 | + | 0.841621i | \(0.681602\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000 | + | 6.92820i | 0.834058 | + | 1.44463i | 0.894795 | + | 0.446476i | \(0.147321\pi\) |
−0.0607377 | + | 0.998154i | \(0.519345\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.00000 | + | 3.46410i | 0.348155 | + | 0.603023i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.00000 | + | 8.66025i | 0.821995 | + | 1.42374i | 0.904194 | + | 0.427121i | \(0.140472\pi\) |
−0.0821995 | + | 0.996616i | \(0.526194\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.00000 | + | 5.19615i | −0.480384 | + | 0.832050i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000 | 0.609994 | 0.304997 | − | 0.952353i | \(-0.401344\pi\) | ||||
0.304997 | + | 0.952353i | \(0.401344\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | + | 1.73205i | −0.149071 | + | 0.258199i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.00000 | − | 1.73205i | −0.140028 | − | 0.242536i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.00000 | + | 5.19615i | −0.412082 | + | 0.713746i | −0.995117 | − | 0.0987002i | \(-0.968532\pi\) |
0.583036 | + | 0.812447i | \(0.301865\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.00000 | 1.07872 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.00000 | 0.529813 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.00000 | + | 3.46410i | −0.260378 | + | 0.450988i | −0.966342 | − | 0.257260i | \(-0.917180\pi\) |
0.705965 | + | 0.708247i | \(0.250514\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.00000 | + | 5.19615i | 0.384111 | + | 0.665299i | 0.991645 | − | 0.128994i | \(-0.0411748\pi\) |
−0.607535 | + | 0.794293i | \(0.707841\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.00000 | + | 10.3923i | 0.744208 | + | 1.28901i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000 | − | 3.46410i | 0.244339 | − | 0.423207i | −0.717607 | − | 0.696449i | \(-0.754762\pi\) |
0.961946 | + | 0.273241i | \(0.0880957\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.00000 | 0.963087 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.00000 | − | 8.66025i | 0.585206 | − | 1.01361i | −0.409644 | − | 0.912245i | \(-0.634347\pi\) |
0.994850 | − | 0.101361i | \(-0.0323196\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.500000 | − | 0.866025i | −0.0577350 | − | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.00000 | −0.439057 | −0.219529 | − | 0.975606i | \(-0.570452\pi\) | ||||
−0.219529 | + | 0.975606i | \(0.570452\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.00000 | −0.433861 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.00000 | + | 1.73205i | −0.107211 | + | 0.185695i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.00000 | − | 5.19615i | −0.317999 | − | 0.550791i | 0.662071 | − | 0.749441i | \(-0.269678\pi\) |
−0.980071 | + | 0.198650i | \(0.936344\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.00000 | − | 6.92820i | 0.410391 | − | 0.710819i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.0000 | 1.42148 | 0.710742 | − | 0.703452i | \(-0.248359\pi\) | ||||
0.710742 | + | 0.703452i | \(0.248359\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.00000 | 0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.00000 | + | 1.73205i | −0.0995037 | + | 0.172345i | −0.911479 | − | 0.411346i | \(-0.865059\pi\) |
0.811976 | + | 0.583691i | \(0.198392\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.00000 | − | 6.92820i | −0.394132 | − | 0.682656i | 0.598858 | − | 0.800855i | \(-0.295621\pi\) |
−0.992990 | + | 0.118199i | \(0.962288\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.00000 | + | 10.3923i | 0.580042 | + | 1.00466i | 0.995474 | + | 0.0950377i | \(0.0302972\pi\) |
−0.415432 | + | 0.909624i | \(0.636370\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.00000 | − | 1.73205i | 0.0957826 | − | 0.165900i | −0.814152 | − | 0.580651i | \(-0.802798\pi\) |
0.909935 | + | 0.414751i | \(0.136131\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.0000 | 0.949158 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.0000 | −1.31701 | −0.658505 | − | 0.752577i | \(-0.728811\pi\) | ||||
−0.658505 | + | 0.752577i | \(0.728811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.00000 | − | 13.8564i | 0.746004 | − | 1.29212i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.00000 | + | 5.19615i | 0.277350 | + | 0.480384i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.50000 | − | 4.33013i | −0.227273 | − | 0.393648i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.00000 | − | 5.19615i | 0.270501 | − | 0.468521i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.00000 | − | 3.46410i | 0.176090 | − | 0.304997i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.0000 | + | 17.3205i | 0.873704 | + | 1.51330i | 0.858137 | + | 0.513421i | \(0.171622\pi\) |
0.0155672 | + | 0.999879i | \(0.495045\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | + | 1.73205i | 0.0860663 | + | 0.149071i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.00000 | + | 8.66025i | −0.427179 | + | 0.739895i | −0.996621 | − | 0.0821359i | \(-0.973826\pi\) |
0.569442 | + | 0.822031i | \(0.307159\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.0000 | − | 20.7846i | 1.00349 | − | 1.73810i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.00000 | + | 3.46410i | 0.166091 | + | 0.287678i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.00000 | − | 5.19615i | −0.245770 | − | 0.425685i | 0.716578 | − | 0.697507i | \(-0.245707\pi\) |
−0.962348 | + | 0.271821i | \(0.912374\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.00000 | + | 6.92820i | −0.325515 | + | 0.563809i | −0.981617 | − | 0.190864i | \(-0.938871\pi\) |
0.656101 | + | 0.754673i | \(0.272204\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.00000 | −0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.00000 | + | 8.66025i | −0.399043 | + | 0.691164i | −0.993608 | − | 0.112884i | \(-0.963991\pi\) |
0.594565 | + | 0.804048i | \(0.297324\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.00000 | + | 5.19615i | 0.237915 | + | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.0000 | + | 17.3205i | 0.783260 | + | 1.35665i | 0.930033 | + | 0.367477i | \(0.119778\pi\) |
−0.146772 | + | 0.989170i | \(0.546888\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.00000 | − | 6.92820i | 0.311400 | − | 0.539360i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.00000 | −0.619059 | −0.309529 | − | 0.950890i | \(-0.600171\pi\) | ||||
−0.309529 | + | 0.950890i | \(0.600171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.0000 | 1.76923 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.00000 | − | 3.46410i | 0.152944 | − | 0.264906i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.0000 | + | 19.0526i | 0.836315 | + | 1.44854i | 0.892956 | + | 0.450145i | \(0.148628\pi\) |
−0.0566411 | + | 0.998395i | \(0.518039\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.00000 | + | 3.46410i | 0.150329 | + | 0.260378i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.00000 | + | 10.3923i | −0.448461 | + | 0.776757i | −0.998286 | − | 0.0585225i | \(-0.981361\pi\) |
0.549825 | + | 0.835280i | \(0.314694\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.0000 | 1.33793 | 0.668965 | − | 0.743294i | \(-0.266738\pi\) | ||||
0.668965 | + | 0.743294i | \(0.266738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.00000 | 0.443533 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.0000 | − | 17.3205i | 0.735215 | − | 1.27343i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.00000 | + | 6.92820i | 0.292509 | + | 0.506640i | ||||
\(188\) | 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 | ||||||||
\(193\) | −1.00000 | + | 1.73205i | −0.0719816 | + | 0.124676i | −0.899770 | − | 0.436365i | \(-0.856266\pi\) |
0.827788 | + | 0.561041i | \(0.189599\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 12.0000 | 0.859338 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.0000 | −0.712470 | −0.356235 | − | 0.934396i | \(-0.615940\pi\) | ||||
−0.356235 | + | 0.934396i | \(0.615940\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.00000 | + | 6.92820i | −0.283552 | + | 0.491127i | −0.972257 | − | 0.233915i | \(-0.924846\pi\) |
0.688705 | + | 0.725042i | \(0.258180\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.00000 | − | 3.46410i | −0.141069 | − | 0.244339i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.00000 | − | 10.3923i | −0.419058 | − | 0.725830i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.00000 | − | 6.92820i | 0.278019 | − | 0.481543i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.0000 | −1.10674 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.0000 | −1.37686 | −0.688428 | − | 0.725304i | \(-0.741699\pi\) | ||||
−0.688428 | + | 0.725304i | \(0.741699\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.00000 | + | 6.92820i | −0.274075 | + | 0.474713i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.00000 | − | 6.92820i | −0.272798 | − | 0.472500i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.00000 | − | 8.66025i | −0.337869 | − | 0.585206i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.00000 | + | 10.3923i | −0.403604 | + | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.0000 | −1.07144 | −0.535720 | − | 0.844396i | \(-0.679960\pi\) | ||||
−0.535720 | + | 0.844396i | \(0.679960\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.00000 | + | 10.3923i | −0.398234 | + | 0.689761i | −0.993508 | − | 0.113761i | \(-0.963710\pi\) |
0.595274 | + | 0.803523i | \(0.297043\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.00000 | − | 1.73205i | −0.0660819 | − | 0.114457i | 0.831092 | − | 0.556136i | \(-0.187717\pi\) |
−0.897173 | + | 0.441679i | \(0.854383\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.0000 | + | 19.0526i | 0.720634 | + | 1.24817i | 0.960746 | + | 0.277429i | \(0.0894825\pi\) |
−0.240112 | + | 0.970745i | \(0.577184\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | − | 1.73205i | 0.0644157 | − | 0.111571i | −0.832019 | − | 0.554747i | \(-0.812815\pi\) |
0.896435 | + | 0.443176i | \(0.146148\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.0000 | − | 20.7846i | −0.763542 | − | 1.32249i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.00000 | + | 3.46410i | −0.126745 | + | 0.219529i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −32.0000 | −2.01182 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.00000 | + | 3.46410i | −0.125245 | + | 0.216930i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.0000 | − | 25.9808i | −0.935674 | − | 1.62064i | −0.773427 | − | 0.633885i | \(-0.781459\pi\) |
−0.162247 | − | 0.986750i | \(-0.551874\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00000 | + | 1.73205i | 0.0618984 | + | 0.107211i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.0000 | + | 20.7846i | −0.739952 | + | 1.28163i | 0.212565 | + | 0.977147i | \(0.431818\pi\) |
−0.952517 | + | 0.304487i | \(0.901515\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.0000 | 0.737154 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.00000 | −0.367194 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.0000 | − | 19.0526i | 0.670682 | − | 1.16166i | −0.307029 | − | 0.951700i | \(-0.599335\pi\) |
0.977711 | − | 0.209955i | \(-0.0673317\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.00000 | + | 3.46410i | 0.120605 | + | 0.208893i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.00000 | − | 8.66025i | 0.300421 | − | 0.520344i | −0.675810 | − | 0.737075i | \(-0.736206\pi\) |
0.976231 | + | 0.216731i | \(0.0695395\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.0000 | 1.55103 | 0.775515 | − | 0.631329i | \(-0.217490\pi\) | ||||
0.775515 | + | 0.631329i | \(0.217490\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.00000 | + | 3.46410i | −0.118888 | + | 0.205919i | −0.919327 | − | 0.393494i | \(-0.871266\pi\) |
0.800439 | + | 0.599414i | \(0.204600\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.00000 | − | 6.92820i | −0.236940 | − | 0.410391i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | + | 11.2583i | 0.382353 | + | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.00000 | − | 12.1244i | 0.410347 | − | 0.710742i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −30.0000 | −1.75262 | −0.876309 | − | 0.481749i | \(-0.840002\pi\) | ||||
−0.876309 | + | 0.481749i | \(0.840002\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.00000 | 0.465778 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.00000 | − | 3.46410i | 0.116052 | − | 0.201008i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −24.0000 | − | 41.5692i | −1.38796 | − | 2.40401i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.00000 | + | 1.73205i | 0.0574485 | + | 0.0995037i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.00000 | − | 10.3923i | 0.343559 | − | 0.595062i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.0000 | 1.59804 | 0.799022 | − | 0.601302i | \(-0.205351\pi\) | ||||
0.799022 | + | 0.601302i | \(0.205351\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.00000 | −0.455104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.00000 | − | 6.92820i | 0.226819 | − | 0.392862i | −0.730044 | − | 0.683400i | \(-0.760501\pi\) |
0.956864 | + | 0.290537i | \(0.0938340\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.00000 | + | 8.66025i | 0.282617 | + | 0.489506i | 0.972028 | − | 0.234863i | \(-0.0754642\pi\) |
−0.689412 | + | 0.724370i | \(0.742131\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.00000 | + | 15.5885i | 0.505490 | + | 0.875535i | 0.999980 | + | 0.00635137i | \(0.00202172\pi\) |
−0.494489 | + | 0.869184i | \(0.664645\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.00000 | − | 6.92820i | 0.223957 | − | 0.387905i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.0000 | 0.669775 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.00000 | 0.445132 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.00000 | + | 5.19615i | −0.166410 | + | 0.288231i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.00000 | − | 1.73205i | −0.0553001 | − | 0.0957826i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.00000 | − | 3.46410i | −0.109930 | − | 0.190404i | 0.805812 | − | 0.592172i | \(-0.201729\pi\) |
−0.915742 | + | 0.401768i | \(0.868396\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.00000 | − | 8.66025i | 0.273998 | − | 0.474579i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.00000 | −0.437087 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.0000 | 0.980522 | 0.490261 | − | 0.871576i | \(-0.336901\pi\) | ||||
0.490261 | + | 0.871576i | \(0.336901\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.00000 | + | 12.1244i | −0.380188 | + | 0.658505i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.00000 | − | 13.8564i | −0.430706 | − | 0.746004i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.00000 | − | 10.3923i | 0.322097 | − | 0.557888i | −0.658824 | − | 0.752297i | \(-0.728946\pi\) |
0.980921 | + | 0.194409i | \(0.0622790\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.0000 | −1.17763 | −0.588817 | − | 0.808267i | \(-0.700406\pi\) | ||||
−0.588817 | + | 0.808267i | \(0.700406\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.00000 | 0.320256 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.0000 | + | 25.9808i | −0.798369 | + | 1.38282i | 0.122308 | + | 0.992492i | \(0.460970\pi\) |
−0.920677 | + | 0.390324i | \(0.872363\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.00000 | + | 13.8564i | 0.424596 | + | 0.735422i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.00000 | − | 6.92820i | −0.211112 | − | 0.365657i | 0.740951 | − | 0.671559i | \(-0.234375\pi\) |
−0.952063 | + | 0.305903i | \(0.901042\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.50000 | − | 2.59808i | 0.0789474 | − | 0.136741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.00000 | −0.262432 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −20.0000 | −1.04685 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.0000 | + | 27.7128i | −0.835193 | + | 1.44660i | 0.0586798 | + | 0.998277i | \(0.481311\pi\) |
−0.893873 | + | 0.448320i | \(0.852022\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.00000 | − | 5.19615i | −0.156174 | − | 0.270501i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.0000 | − | 19.0526i | −0.569558 | − | 0.986504i | −0.996610 | − | 0.0822766i | \(-0.973781\pi\) |
0.427051 | − | 0.904227i | \(-0.359552\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.00000 | + | 10.3923i | −0.309839 | + | 0.536656i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.0000 | 0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.0000 | 1.02733 | 0.513665 | − | 0.857991i | \(-0.328287\pi\) | ||||
0.513665 | + | 0.857991i | \(0.328287\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.00000 | + | 13.8564i | 0.408781 | + | 0.708029i | 0.994753 | − | 0.102302i | \(-0.0326207\pi\) |
−0.585973 | + | 0.810331i | \(0.699287\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.00000 | − | 3.46410i | −0.101666 | − | 0.176090i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.0000 | − | 22.5167i | 0.659126 | − | 1.14164i | −0.321716 | − | 0.946836i | \(-0.604260\pi\) |
0.980842 | − | 0.194804i | \(-0.0624070\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.0000 | 0.809155 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.0000 | 1.00887 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.00000 | + | 5.19615i | 0.150566 | + | 0.260787i | 0.931436 | − | 0.363906i | \(-0.118557\pi\) |
−0.780870 | + | 0.624694i | \(0.785224\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.00000 | − | 15.5885i | −0.449439 | − | 0.778450i | 0.548911 | − | 0.835881i | \(-0.315043\pi\) |
−0.998350 | + | 0.0574304i | \(0.981709\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.00000 | 0.0993808 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −40.0000 | −1.98273 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.0000 | + | 19.0526i | −0.543915 | + | 0.942088i | 0.454759 | + | 0.890614i | \(0.349725\pi\) |
−0.998674 | + | 0.0514740i | \(0.983608\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.00000 | + | 8.66025i | 0.246632 | + | 0.427179i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.00000 | + | 6.92820i | 0.196352 | + | 0.340092i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.00000 | − | 3.46410i | 0.0979404 | − | 0.169638i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −36.0000 | −1.75872 | −0.879358 | − | 0.476162i | \(-0.842028\pi\) | ||||
−0.879358 | + | 0.476162i | \(0.842028\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.00000 | 0.292422 | 0.146211 | − | 0.989253i | \(-0.453292\pi\) | ||||
0.146211 | + | 0.989253i | \(0.453292\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.00000 | − | 1.73205i | −0.0485071 | − | 0.0840168i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.0000 | − | 20.7846i | −0.579365 | − | 1.00349i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.00000 | −0.0961139 | −0.0480569 | − | 0.998845i | \(-0.515303\pi\) | ||||
−0.0480569 | + | 0.998845i | \(0.515303\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.00000 | 0.191785 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.0000 | + | 27.7128i | −0.765384 | + | 1.32568i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.0000 | + | 20.7846i | 0.572729 | + | 0.991995i | 0.996284 | + | 0.0861252i | \(0.0274485\pi\) |
−0.423556 | + | 0.905870i | \(0.639218\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.00000 | − | 3.46410i | −0.0950229 | − | 0.164584i | 0.814595 | − | 0.580030i | \(-0.196959\pi\) |
−0.909618 | + | 0.415445i | \(0.863626\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.00000 | + | 10.3923i | −0.284427 | + | 0.492642i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.00000 | −0.283790 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 34.0000 | 1.60456 | 0.802280 | − | 0.596948i | \(-0.203620\pi\) | ||||
0.802280 | + | 0.596948i | \(0.203620\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.0000 | + | 20.7846i | −0.565058 | + | 0.978709i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.00000 | + | 6.92820i | 0.187936 | + | 0.325515i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.00000 | − | 8.66025i | −0.233890 | − | 0.405110i | 0.725059 | − | 0.688686i | \(-0.241812\pi\) |
−0.958950 | + | 0.283577i | \(0.908479\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.00000 | + | 1.73205i | −0.0466760 | + | 0.0808452i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.0000 | −1.02464 | −0.512321 | − | 0.858794i | \(-0.671214\pi\) | ||||
−0.512321 | + | 0.858794i | \(0.671214\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.0000 | 1.48717 | 0.743583 | − | 0.668644i | \(-0.233125\pi\) | ||||
0.743583 | + | 0.668644i | \(0.233125\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.0000 | − | 24.2487i | −0.647843 | − | 1.12210i | −0.983637 | − | 0.180161i | \(-0.942338\pi\) |
0.335794 | − | 0.941935i | \(-0.390995\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.00000 | + | 8.66025i | 0.230388 | + | 0.399043i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.00000 | + | 13.8564i | −0.367840 | + | 0.637118i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.00000 | 0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.00000 | 0.274721 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.00000 | − | 13.8564i | 0.365529 | − | 0.633115i | −0.623332 | − | 0.781958i | \(-0.714221\pi\) |
0.988861 | + | 0.148842i | \(0.0475547\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −30.0000 | − | 51.9615i | −1.36788 | − | 2.36924i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.0000 | − | 24.2487i | −0.635707 | − | 1.10108i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.00000 | − | 6.92820i | 0.181257 | − | 0.313947i | −0.761052 | − | 0.648691i | \(-0.775317\pi\) |
0.942309 | + | 0.334744i | \(0.108650\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 20.0000 | 0.904431 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.0000 | −0.541552 | −0.270776 | − | 0.962642i | \(-0.587280\pi\) | ||||
−0.270776 | + | 0.962642i | \(0.587280\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.00000 | + | 3.46410i | −0.0900755 | + | 0.156015i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.00000 | − | 6.92820i | −0.179787 | − | 0.311400i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.0000 | − | 38.1051i | −0.984855 | − | 1.70582i | −0.642578 | − | 0.766220i | \(-0.722135\pi\) |
−0.342277 | − | 0.939599i | \(-0.611198\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.00000 | + | 6.92820i | −0.178707 | + | 0.309529i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.0000 | 1.07011 | 0.535054 | − | 0.844818i | \(-0.320291\pi\) | ||||
0.535054 | + | 0.844818i | \(0.320291\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.00000 | 0.177998 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.5000 | − | 19.9186i | 0.510733 | − | 0.884615i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.00000 | + | 5.19615i | 0.132973 | + | 0.230315i | 0.924821 | − | 0.380402i | \(-0.124214\pi\) |
−0.791849 | + | 0.610718i | \(0.790881\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.00000 | − | 3.46410i | −0.0883022 | − | 0.152944i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.00000 | + | 13.8564i | −0.352522 | + | 0.610586i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22.0000 | 0.965693 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.00000 | + | 5.19615i | −0.131432 | + | 0.227648i | −0.924229 | − | 0.381839i | \(-0.875291\pi\) |
0.792797 | + | 0.609486i | \(0.208624\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.0000 | − | 17.3205i | −0.437269 | − | 0.757373i | 0.560208 | − | 0.828352i | \(-0.310721\pi\) |
−0.997478 | + | 0.0709788i | \(0.977388\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.5000 | + | 35.5070i | −0.891304 | + | 1.54378i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00000 | 0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −36.0000 | −1.55933 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.0000 | − | 20.7846i | 0.518805 | − | 0.898597i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.00000 | + | 10.3923i | 0.258919 | + | 0.448461i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.0000 | − | 25.9808i | −0.644900 | − | 1.11700i | −0.984325 | − | 0.176367i | \(-0.943566\pi\) |
0.339424 | − | 0.940633i | \(-0.389768\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.00000 | − | 15.5885i | 0.386227 | − | 0.668965i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.00000 | −0.171341 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.0000 | 0.513083 | 0.256541 | − | 0.966533i | \(-0.417417\pi\) | ||||
0.256541 | + | 0.966533i | \(0.417417\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.00000 | − | 5.19615i | 0.128037 | − | 0.221766i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.00000 | − | 6.92820i | −0.170406 | − | 0.295151i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.0000 | − | 17.3205i | −0.424476 | − | 0.735215i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.00000 | − | 1.73205i | 0.0423714 | − | 0.0733893i | −0.844062 | − | 0.536246i | \(-0.819842\pi\) |
0.886433 | + | 0.462856i | \(0.153175\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −24.0000 | −1.01509 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.00000 | 0.337760 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.0000 | + | 38.1051i | −0.927189 | + | 1.60594i | −0.139188 | + | 0.990266i | \(0.544449\pi\) |
−0.788002 | + | 0.615673i | \(0.788884\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.0000 | + | 24.2487i | 0.588984 | + | 1.02015i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.00000 | + | 5.19615i | 0.125767 | + | 0.217834i | 0.922032 | − | 0.387113i | \(-0.126528\pi\) |
−0.796266 | + | 0.604947i | \(0.793194\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.00000 | − | 10.3923i | 0.251092 | − | 0.434904i | −0.712735 | − | 0.701434i | \(-0.752544\pi\) |
0.963827 | + | 0.266529i | \(0.0858769\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.00000 | 0.333623 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.0000 | − | 29.4449i | 0.707719 | − | 1.22581i | −0.257982 | − | 0.966150i | \(-0.583058\pi\) |
0.965701 | − | 0.259656i | \(-0.0836092\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.00000 | + | 1.73205i | 0.0415586 | + | 0.0719816i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.0000 | − | 20.7846i | −0.496989 | − | 0.860811i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.00000 | − | 10.3923i | 0.248069 | − | 0.429669i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.0000 | −1.15568 | −0.577842 | − | 0.816149i | \(-0.696105\pi\) | ||||
−0.577842 | + | 0.816149i | \(0.696105\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.00000 | + | 8.66025i | −0.205673 | + | 0.356235i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.00000 | + | 15.5885i | 0.369586 | + | 0.640141i | 0.989501 | − | 0.144528i | \(-0.0461663\pi\) |
−0.619915 | + | 0.784669i | \(0.712833\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.00000 | + | 6.92820i | 0.163709 | + | 0.283552i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.0000 | − | 20.7846i | 0.490307 | − | 0.849236i | −0.509631 | − | 0.860393i | \(-0.670218\pi\) |
0.999938 | + | 0.0111569i | \(0.00355143\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.0000 | −1.06056 | −0.530281 | − | 0.847822i | \(-0.677914\pi\) | ||||
−0.530281 | + | 0.847822i | \(0.677914\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.00000 | −0.162893 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.00000 | + | 8.66025i | −0.203279 | + | 0.352089i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.0000 | − | 41.5692i | −0.974130 | − | 1.68724i | −0.682777 | − | 0.730627i | \(-0.739228\pi\) |
−0.291353 | − | 0.956616i | \(-0.594105\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.0000 | − | 36.3731i | 0.848182 | − | 1.46909i | −0.0346469 | − | 0.999400i | \(-0.511031\pi\) |
0.882829 | − | 0.469695i | \(-0.155636\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −12.0000 | −0.483887 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.0000 | −0.885687 | −0.442843 | − | 0.896599i | \(-0.646030\pi\) | ||||
−0.442843 | + | 0.896599i | \(0.646030\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.0000 | − | 38.1051i | 0.884255 | − | 1.53157i | 0.0376891 | − | 0.999290i | \(-0.488000\pi\) |
0.846566 | − | 0.532284i | \(-0.178666\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.00000 | − | 6.92820i | −0.160514 | − | 0.278019i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50000 | + | 16.4545i | 0.380000 | + | 0.658179i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.00000 | + | 13.8564i | −0.319489 | + | 0.553372i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.0000 | 0.797452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.00000 | −0.318475 | −0.159237 | − | 0.987240i | \(-0.550904\pi\) | ||||
−0.159237 | + | 0.987240i | \(0.550904\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.0000 | + | 17.3205i | −0.397464 | + | 0.688428i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.00000 | + | 6.92820i | 0.158238 | + | 0.274075i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.00000 | + | 1.73205i | −0.0394976 | + | 0.0684119i | −0.885098 | − | 0.465404i | \(-0.845909\pi\) |
0.845601 | + | 0.533816i | \(0.179242\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.00000 | −0.157745 | −0.0788723 | − | 0.996885i | \(-0.525132\pi\) | ||||
−0.0788723 | + | 0.996885i | \(0.525132\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.00000 | −0.315000 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.0000 | + | 20.7846i | −0.471769 | + | 0.817127i | −0.999478 | − | 0.0322975i | \(-0.989718\pi\) |
0.527710 | + | 0.849425i | \(0.323051\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.00000 | − | 13.8564i | −0.314027 | − | 0.543912i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.00000 | + | 15.5885i | 0.352197 | + | 0.610023i | 0.986634 | − | 0.162951i | \(-0.0521013\pi\) |
−0.634437 | + | 0.772975i | \(0.718768\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.0000 | − | 34.6410i | 0.781465 | − | 1.35354i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.0000 | −0.390137 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.0000 | 1.09073 | 0.545363 | − | 0.838200i | \(-0.316392\pi\) | ||||
0.545363 | + | 0.838200i | \(0.316392\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.00000 | + | 1.73205i | −0.0388955 | + | 0.0673690i | −0.884818 | − | 0.465937i | \(-0.845717\pi\) |
0.845922 | + | 0.533306i | \(0.179051\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.00000 | + | 10.3923i | 0.233021 | + | 0.403604i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.00000 | − | 13.8564i | −0.309761 | − | 0.536522i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.00000 | + | 13.8564i | −0.309298 | + | 0.535720i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.0000 | −0.926510 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.00000 | 0.0770943 | 0.0385472 | − | 0.999257i | \(-0.487727\pi\) | ||||
0.0385472 | + | 0.999257i | \(0.487727\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.500000 | + | 0.866025i | −0.0192450 | + | 0.0333333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.00000 | − | 15.5885i | −0.345898 | − | 0.599113i | 0.639618 | − | 0.768693i | \(-0.279092\pi\) |
−0.985517 | + | 0.169580i | \(0.945759\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.00000 | + | 10.3923i | 0.229920 | + | 0.398234i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.00000 | − | 10.3923i | 0.229584 | − | 0.397650i | −0.728101 | − | 0.685470i | \(-0.759597\pi\) |
0.957685 | + | 0.287819i | \(0.0929302\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.0000 | 0.764161 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.00000 | −0.0763048 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.0000 | − | 31.1769i | 0.685745 | − | 1.18775i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.00000 | + | 3.46410i | 0.0760836 | + | 0.131781i | 0.901557 | − | 0.432660i | \(-0.142425\pi\) |
−0.825473 | + | 0.564441i | \(0.809092\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.00000 | − | 6.92820i | −0.151729 | − | 0.262802i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.00000 | − | 10.3923i | 0.227266 | − | 0.393637i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 22.0000 | 0.832116 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.00000 | −0.0755390 | −0.0377695 | − | 0.999286i | \(-0.512025\pi\) | ||||
−0.0377695 | + | 0.999286i | \(0.512025\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.0000 | + | 34.6410i | −0.754314 | + | 1.30651i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.00000 | + | 8.66025i | 0.187779 | + | 0.325243i | 0.944509 | − | 0.328484i | \(-0.106538\pi\) |
−0.756730 | + | 0.653727i | \(0.773204\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −48.0000 | −1.79510 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.00000 | − | 1.73205i | −0.0371904 | − | 0.0644157i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.00000 | + | 1.73205i | −0.0371391 | + | 0.0643268i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.00000 | −0.296704 | −0.148352 | − | 0.988935i | \(-0.547397\pi\) | ||||
−0.148352 | + | 0.988935i | \(0.547397\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.00000 | − | 6.92820i | 0.147945 | − | 0.256249i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.00000 | + | 5.19615i | 0.110808 | + | 0.191924i | 0.916096 | − | 0.400959i | \(-0.131323\pi\) |
−0.805289 | + | 0.592883i | \(0.797990\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.00000 | + | 13.8564i | 0.294684 | + | 0.510407i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.00000 | + | 10.3923i | −0.220714 | + | 0.382287i | −0.955025 | − | 0.296526i | \(-0.904172\pi\) |
0.734311 | + | 0.678813i | \(0.237505\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −24.0000 | −0.881662 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.0000 | −0.880475 | −0.440237 | − | 0.897881i | \(-0.645106\pi\) | ||||
−0.440237 | + | 0.897881i | \(0.645106\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.00000 | + | 10.3923i | −0.219823 | + | 0.380745i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.00000 | + | 3.46410i | 0.0731762 | + | 0.126745i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.0000 | + | 41.5692i | 0.875772 | + | 1.51688i | 0.855938 | + | 0.517079i | \(0.172981\pi\) |
0.0198348 | + | 0.999803i | \(0.493686\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.00000 | + | 10.3923i | −0.218652 | + | 0.378717i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.0000 | 0.582300 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.00000 | 0.218074 | 0.109037 | − | 0.994038i | \(-0.465223\pi\) | ||||
0.109037 | + | 0.994038i | \(0.465223\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −16.0000 | + | 27.7128i | −0.580763 | + | 1.00591i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.0000 | − | 19.0526i | −0.398750 | − | 0.690655i | 0.594822 | − | 0.803857i | \(-0.297222\pi\) |
−0.993572 | + | 0.113203i | \(0.963889\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.00000 | + | 3.46410i | 0.0723102 | + | 0.125245i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.0000 | − | 20.7846i | 0.433295 | − | 0.750489i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.0000 | 0.504853 | 0.252426 | − | 0.967616i | \(-0.418771\pi\) | ||||
0.252426 | + | 0.967616i | \(0.418771\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −30.0000 | −1.08042 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.00000 | + | 1.73205i | −0.0359675 | + | 0.0622975i | −0.883449 | − | 0.468528i | \(-0.844785\pi\) |
0.847481 | + | 0.530825i | \(0.178118\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.0000 | + | 20.7846i | 0.429945 | + | 0.744686i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.0000 | − | 27.7128i | 0.572525 | − | 0.991642i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.00000 | 0.0714742 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.0000 | 0.713831 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.0000 | − | 31.1769i | 0.641631 | − | 1.11134i | −0.343438 | − | 0.939175i | \(-0.611592\pi\) |
0.985069 | − | 0.172162i | \(-0.0550751\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.0000 | + | 20.7846i | 0.427211 | + | 0.739952i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.0000 | − | 31.1769i | −0.639199 | − | 1.10712i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.00000 | − | 10.3923i | 0.212798 | − | 0.368577i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.00000 | −0.212531 | −0.106265 | − | 0.994338i | \(-0.533889\pi\) | ||||
−0.106265 | + | 0.994338i | \(0.533889\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.00000 | + | 5.19615i | −0.106000 | + | 0.183597i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20.0000 | + | 34.6410i | 0.705785 | + | 1.22245i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11.0000 | − | 19.0526i | −0.387218 | − | 0.670682i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.00000 | + | 8.66025i | −0.175791 | + | 0.304478i | −0.940435 | − | 0.339975i | \(-0.889582\pi\) |
0.764644 | + | 0.644453i | \(0.222915\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −44.0000 | −1.54505 | −0.772524 | − | 0.634985i | \(-0.781006\pi\) | ||||
−0.772524 | + | 0.634985i | \(0.781006\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20.0000 | − | 34.6410i | 0.700569 | − | 1.21342i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.00000 | + | 13.8564i | 0.279885 | + | 0.484774i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.0000 | − | 32.9090i | −0.663105 | − | 1.14853i | −0.979795 | − | 0.200002i | \(-0.935905\pi\) |
0.316691 | − | 0.948529i | \(-0.397428\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.0000 | + | 48.4974i | −0.976019 | + | 1.69051i | −0.299487 | + | 0.954100i | \(0.596815\pi\) |
−0.676532 | + | 0.736413i | \(0.736518\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.00000 | 0.139262 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.0000 | 1.25184 | 0.625921 | − | 0.779886i | \(-0.284723\pi\) | ||||
0.625921 | + | 0.779886i | \(0.284723\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.0000 | + | 22.5167i | −0.451509 | + | 0.782036i | −0.998480 | − | 0.0551154i | \(-0.982447\pi\) |
0.546971 | + | 0.837151i | \(0.315781\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.00000 | − | 8.66025i | −0.173448 | − | 0.300421i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.00000 | + | 13.8564i | 0.276851 | + | 0.479521i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 56.0000 | 1.93333 | 0.966667 | − | 0.256036i | \(-0.0824164\pi\) | ||||
0.966667 | + | 0.256036i | \(0.0824164\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.0000 | − | 22.5167i | 0.447744 | − | 0.775515i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −23.0000 | − | 39.8372i | −0.791224 | − | 1.37044i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.00000 | + | 3.46410i | 0.0686398 | + | 0.118888i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −40.0000 | + | 69.2820i | −1.37118 | + | 2.37496i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.0000 | −0.479351 | −0.239675 | − | 0.970853i | \(-0.577041\pi\) | ||||
−0.239675 | + | 0.970853i | \(0.577041\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.00000 | −0.273594 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.0000 | − | 36.3731i | 0.717346 | − | 1.24248i | −0.244701 | − | 0.969599i | \(-0.578690\pi\) |
0.962048 | − | 0.272882i | \(-0.0879768\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.0000 | − | 17.3205i | −0.341196 | − | 0.590968i | 0.643459 | − | 0.765480i | \(-0.277499\pi\) |
−0.984655 | + | 0.174512i | \(0.944165\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16.0000 | − | 27.7128i | −0.544646 | − | 0.943355i | −0.998629 | − | 0.0523446i | \(-0.983331\pi\) |
0.453983 | − | 0.891010i | \(-0.350003\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.0000 | − | 38.1051i | 0.748022 | − | 1.29561i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.0000 | 0.441503 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.0000 | + | 20.7846i | −0.406604 | + | 0.704260i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.00000 | − | 12.1244i | −0.236914 | − | 0.410347i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.00000 | + | 1.73205i | 0.0337676 | + | 0.0584872i | 0.882415 | − | 0.470471i | \(-0.155916\pi\) |
−0.848648 | + | 0.528958i | \(0.822583\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.0000 | + | 25.9808i | −0.505937 | + | 0.876309i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.0000 | −0.606435 | −0.303218 | − | 0.952921i | \(-0.598061\pi\) | ||||
−0.303218 | + | 0.952921i | \(0.598061\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.0000 | −0.673054 | −0.336527 | − | 0.941674i | \(-0.609252\pi\) | ||||
−0.336527 | + | 0.941674i | \(0.609252\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.00000 | − | 6.92820i | 0.134459 | − | 0.232889i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.0000 | + | 20.7846i | 0.402921 | + | 0.697879i | 0.994077 | − | 0.108678i | \(-0.0346618\pi\) |
−0.591156 | + | 0.806557i | \(0.701328\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.00000 | − | 3.46410i | −0.0670025 | − | 0.116052i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.0000 | 0.802232 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −48.0000 | −1.60267 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.00000 | + | 10.3923i | 0.199889 | + | 0.346218i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.0000 | − | 31.1769i | −0.598340 | − | 1.03636i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.00000 | − | 10.3923i | 0.199227 | − | 0.345071i | −0.749051 | − | 0.662512i | \(-0.769490\pi\) |
0.948278 | + | 0.317441i | \(0.102824\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.00000 | 0.0663358 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.00000 | − | 13.8564i | 0.264761 | − | 0.458580i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.00000 | − | 10.3923i | −0.198354 | − | 0.343559i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.0000 | + | 34.6410i | 0.659739 | + | 1.14270i | 0.980683 | + | 0.195603i | \(0.0626666\pi\) |
−0.320944 | + | 0.947098i | \(0.604000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.0000 | − | 24.2487i | 0.461316 | − | 0.799022i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 48.0000 | 1.57994 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.0000 | 0.328798 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.00000 | + | 6.92820i | −0.131377 | + | 0.227552i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.00000 | + | 15.5885i | 0.295280 | + | 0.511441i | 0.975050 | − | 0.221985i | \(-0.0712536\pi\) |
−0.679770 | + | 0.733426i | \(0.737920\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.00000 | − | 6.92820i | −0.130954 | − | 0.226819i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.00000 | − | 13.8564i | 0.261628 | − | 0.453153i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.0000 | 0.718709 | 0.359354 | − | 0.933201i | \(-0.382997\pi\) | ||||
0.359354 | + | 0.933201i | \(0.382997\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.0000 | 0.326338 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.0000 | + | 22.5167i | −0.423788 | + | 0.734022i | −0.996306 | − | 0.0858697i | \(-0.972633\pi\) |
0.572518 | + | 0.819892i | \(0.305966\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.0000 | + | 41.5692i | 0.781548 | + | 1.35368i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.00000 | + | 3.46410i | 0.0649913 | + | 0.112568i | 0.896690 | − | 0.442659i | \(-0.145965\pi\) |
−0.831699 | + | 0.555227i | \(0.812631\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.0000 | + | 51.9615i | −0.973841 | + | 1.68674i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.0000 | 0.583690 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.0000 | 0.842223 | 0.421111 | − | 0.907009i | \(-0.361640\pi\) | ||||
0.421111 | + | 0.907009i | \(0.361640\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.00000 | − | 6.92820i | −0.129302 | − | 0.223957i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.5000 | + | 26.8468i | 0.500000 | + | 0.866025i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.00000 | − | 10.3923i | 0.193347 | − | 0.334887i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.00000 | 0.128765 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.00000 | −0.257263 | −0.128631 | − | 0.991692i | \(-0.541058\pi\) | ||||
−0.128631 | + | 0.991692i | \(0.541058\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.00000 | − | 6.92820i | 0.128499 | − | 0.222566i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.00000 | + | 10.3923i | 0.192549 | + | 0.333505i | 0.946094 | − | 0.323891i | \(-0.104991\pi\) |
−0.753545 | + | 0.657396i | \(0.771658\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.00000 | + | 5.19615i | 0.0960769 | + | 0.166410i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.00000 | + | 15.5885i | −0.287936 | + | 0.498719i | −0.973317 | − | 0.229465i | \(-0.926302\pi\) |
0.685381 | + | 0.728184i | \(0.259636\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.0000 | 0.767043 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.00000 | −0.0638551 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.0000 | − | 20.7846i | 0.382741 | − | 0.662926i | −0.608712 | − | 0.793391i | \(-0.708314\pi\) |
0.991453 | + | 0.130465i | \(0.0416470\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.0000 | + | 17.3205i | 0.318626 | + | 0.551877i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.0000 | + | 27.7128i | 0.508770 | + | 0.881216i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.00000 | + | 13.8564i | −0.254128 | + | 0.440163i | −0.964658 | − | 0.263504i | \(-0.915122\pi\) |
0.710530 | + | 0.703667i | \(0.248455\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.00000 | −0.126936 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.0000 | 0.507234 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.00000 | − | 12.1244i | 0.221692 | − | 0.383982i | −0.733630 | − | 0.679549i | \(-0.762175\pi\) |
0.955322 | + | 0.295567i | \(0.0955086\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.00000 | − | 8.66025i | −0.158193 | − | 0.273998i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))