Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(226,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("441.226");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.e (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: | \(3.52140272914\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 226.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.226 |
Dual form | 441.2.e.a.361.1 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | −0.986869 | − | 0.161521i | \(-0.948360\pi\) |
0.633316 | + | 0.773893i | \(0.281693\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −1.00000 | + | 1.73205i | −0.447214 | + | 0.774597i | −0.998203 | − | 0.0599153i | \(-0.980917\pi\) |
0.550990 | + | 0.834512i | \(0.314250\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.00000 | −1.06066 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.00000 | − | 1.73205i | −0.316228 | − | 0.547723i | ||||
\(11\) | 2.00000 | + | 3.46410i | 0.603023 | + | 1.04447i | 0.992361 | + | 0.123371i | \(0.0393705\pi\) |
−0.389338 | + | 0.921095i | \(0.627296\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | −3.00000 | − | 5.19615i | −0.727607 | − | 1.26025i | −0.957892 | − | 0.287129i | \(-0.907299\pi\) |
0.230285 | − | 0.973123i | \(-0.426034\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | + | 3.46410i | −0.458831 | + | 0.794719i | −0.998899 | − | 0.0469020i | \(-0.985065\pi\) |
0.540068 | + | 0.841621i | \(0.318398\pi\) | |||||||
\(20\) | −2.00000 | −0.447214 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.00000 | −0.852803 | ||||||||
\(23\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | 1.00000 | − | 1.73205i | 0.196116 | − | 0.339683i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(32\) | −2.50000 | − | 4.33013i | −0.441942 | − | 0.765466i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.00000 | 1.02899 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.00000 | + | 5.19615i | −0.493197 | + | 0.854242i | −0.999969 | − | 0.00783774i | \(-0.997505\pi\) |
0.506772 | + | 0.862080i | \(0.330838\pi\) | |||||||
\(38\) | −2.00000 | − | 3.46410i | −0.324443 | − | 0.561951i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.00000 | − | 5.19615i | 0.474342 | − | 0.821584i | ||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | −2.00000 | + | 3.46410i | −0.301511 | + | 0.522233i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.00000 | − | 1.73205i | −0.138675 | − | 0.240192i | ||||
\(53\) | 3.00000 | + | 5.19615i | 0.412082 | + | 0.713746i | 0.995117 | − | 0.0987002i | \(-0.0314685\pi\) |
−0.583036 | + | 0.812447i | \(0.698135\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.00000 | −1.07872 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.00000 | + | 1.73205i | −0.131306 | + | 0.227429i | ||||
\(59\) | 6.00000 | + | 10.3923i | 0.781133 | + | 1.35296i | 0.931282 | + | 0.364299i | \(0.118692\pi\) |
−0.150148 | + | 0.988663i | \(0.547975\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00000 | − | 1.73205i | 0.128037 | − | 0.221766i | −0.794879 | − | 0.606768i | \(-0.792466\pi\) |
0.922916 | + | 0.385002i | \(0.125799\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | 2.00000 | − | 3.46410i | 0.248069 | − | 0.429669i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.00000 | − | 3.46410i | −0.244339 | − | 0.423207i | 0.717607 | − | 0.696449i | \(-0.245238\pi\) |
−0.961946 | + | 0.273241i | \(0.911904\pi\) | |||||||
\(68\) | 3.00000 | − | 5.19615i | 0.363803 | − | 0.630126i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.00000 | + | 5.19615i | 0.351123 | + | 0.608164i | 0.986447 | − | 0.164083i | \(-0.0524664\pi\) |
−0.635323 | + | 0.772246i | \(0.719133\pi\) | |||||||
\(74\) | −3.00000 | − | 5.19615i | −0.348743 | − | 0.604040i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.00000 | −0.458831 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | − | 13.8564i | 0.900070 | − | 1.55897i | 0.0726692 | − | 0.997356i | \(-0.476848\pi\) |
0.827401 | − | 0.561611i | \(-0.189818\pi\) | |||||||
\(80\) | 1.00000 | + | 1.73205i | 0.111803 | + | 0.193649i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.00000 | − | 1.73205i | 0.110432 | − | 0.191273i | ||||
\(83\) | 12.0000 | 1.31717 | 0.658586 | − | 0.752506i | \(-0.271155\pi\) | ||||
0.658586 | + | 0.752506i | \(0.271155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.0000 | 1.30158 | ||||||||
\(86\) | 2.00000 | − | 3.46410i | 0.215666 | − | 0.373544i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.00000 | − | 10.3923i | −0.639602 | − | 1.10782i | ||||
\(89\) | −7.00000 | + | 12.1244i | −0.741999 | + | 1.28518i | 0.209585 | + | 0.977790i | \(0.432789\pi\) |
−0.951584 | + | 0.307389i | \(0.900545\pi\) | |||||||
\(90\) | 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 | ||||||||
\(97\) | 18.0000 | 1.82762 | 0.913812 | − | 0.406138i | \(-0.133125\pi\) | ||||
0.913812 | + | 0.406138i | \(0.133125\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | 7.00000 | + | 12.1244i | 0.696526 | + | 1.20642i | 0.969664 | + | 0.244443i | \(0.0786053\pi\) |
−0.273138 | + | 0.961975i | \(0.588061\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.00000 | + | 6.92820i | −0.394132 | + | 0.682656i | −0.992990 | − | 0.118199i | \(-0.962288\pi\) |
0.598858 | + | 0.800855i | \(0.295621\pi\) | |||||||
\(104\) | 6.00000 | 0.588348 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | 2.00000 | − | 3.46410i | 0.193347 | − | 0.334887i | −0.753010 | − | 0.658009i | \(-0.771399\pi\) |
0.946357 | + | 0.323122i | \(0.104732\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.00000 | + | 15.5885i | 0.862044 | + | 1.49310i | 0.869953 | + | 0.493135i | \(0.164149\pi\) |
−0.00790932 | + | 0.999969i | \(0.502518\pi\) | |||||||
\(110\) | 4.00000 | − | 6.92820i | 0.381385 | − | 0.660578i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.0000 | 1.31701 | 0.658505 | − | 0.752577i | \(-0.271189\pi\) | ||||
0.658505 | + | 0.752577i | \(0.271189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.00000 | + | 1.73205i | 0.0928477 | + | 0.160817i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.0000 | −1.10469 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.50000 | + | 4.33013i | −0.227273 | + | 0.393648i | ||||
\(122\) | 1.00000 | + | 1.73205i | 0.0905357 | + | 0.156813i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | 1.50000 | − | 2.59808i | 0.132583 | − | 0.229640i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.00000 | + | 3.46410i | 0.175412 | + | 0.303822i | ||||
\(131\) | 2.00000 | − | 3.46410i | 0.174741 | − | 0.302660i | −0.765331 | − | 0.643637i | \(-0.777425\pi\) |
0.940072 | + | 0.340977i | \(0.110758\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.00000 | 0.345547 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.00000 | + | 15.5885i | 0.771744 | + | 1.33670i | ||||
\(137\) | −3.00000 | − | 5.19615i | −0.256307 | − | 0.443937i | 0.708942 | − | 0.705266i | \(-0.249173\pi\) |
−0.965250 | + | 0.261329i | \(0.915839\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.0000 | 1.01783 | 0.508913 | − | 0.860818i | \(-0.330047\pi\) | ||||
0.508913 | + | 0.860818i | \(0.330047\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.00000 | − | 6.92820i | −0.334497 | − | 0.579365i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.00000 | + | 3.46410i | −0.166091 | + | 0.287678i | ||||
\(146\) | −6.00000 | −0.496564 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.00000 | −0.493197 | ||||||||
\(149\) | 3.00000 | − | 5.19615i | 0.245770 | − | 0.425685i | −0.716578 | − | 0.697507i | \(-0.754293\pi\) |
0.962348 | + | 0.271821i | \(0.0876260\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.00000 | − | 6.92820i | −0.325515 | − | 0.563809i | 0.656101 | − | 0.754673i | \(-0.272204\pi\) |
−0.981617 | + | 0.190864i | \(0.938871\pi\) | |||||||
\(152\) | 6.00000 | − | 10.3923i | 0.486664 | − | 0.842927i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.00000 | + | 1.73205i | 0.0798087 | + | 0.138233i | 0.903167 | − | 0.429289i | \(-0.141236\pi\) |
−0.823359 | + | 0.567521i | \(0.807902\pi\) | |||||||
\(158\) | 8.00000 | + | 13.8564i | 0.636446 | + | 1.10236i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 10.0000 | 0.790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.00000 | + | 3.46410i | −0.156652 | + | 0.271329i | −0.933659 | − | 0.358162i | \(-0.883403\pi\) |
0.777007 | + | 0.629492i | \(0.216737\pi\) | |||||||
\(164\) | −1.00000 | − | 1.73205i | −0.0780869 | − | 0.135250i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.00000 | + | 10.3923i | −0.465690 | + | 0.806599i | ||||
\(167\) | 8.00000 | 0.619059 | 0.309529 | − | 0.950890i | \(-0.399829\pi\) | ||||
0.309529 | + | 0.950890i | \(0.399829\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | −6.00000 | + | 10.3923i | −0.460179 | + | 0.797053i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.00000 | − | 3.46410i | −0.152499 | − | 0.264135i | ||||
\(173\) | −5.00000 | + | 8.66025i | −0.380143 | + | 0.658427i | −0.991082 | − | 0.133250i | \(-0.957459\pi\) |
0.610939 | + | 0.791677i | \(0.290792\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.00000 | 0.301511 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.00000 | − | 12.1244i | −0.524672 | − | 0.908759i | ||||
\(179\) | −2.00000 | − | 3.46410i | −0.149487 | − | 0.258919i | 0.781551 | − | 0.623841i | \(-0.214429\pi\) |
−0.931038 | + | 0.364922i | \(0.881096\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −26.0000 | −1.93256 | −0.966282 | − | 0.257485i | \(-0.917106\pi\) | ||||
−0.966282 | + | 0.257485i | \(0.917106\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.00000 | − | 10.3923i | −0.441129 | − | 0.764057i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.0000 | − | 20.7846i | 0.877527 | − | 1.51992i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.00000 | 0.580381 | ||||||||
\(191\) | −4.00000 | + | 6.92820i | −0.289430 | + | 0.501307i | −0.973674 | − | 0.227946i | \(-0.926799\pi\) |
0.684244 | + | 0.729253i | \(0.260132\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.00000 | − | 1.73205i | −0.0719816 | − | 0.124676i | 0.827788 | − | 0.561041i | \(-0.189599\pi\) |
−0.899770 | + | 0.436365i | \(0.856266\pi\) | |||||||
\(194\) | −9.00000 | + | 15.5885i | −0.646162 | + | 1.11919i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.0000 | −1.56744 | −0.783718 | − | 0.621117i | \(-0.786679\pi\) | ||||
−0.783718 | + | 0.621117i | \(0.786679\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.0000 | − | 20.7846i | −0.850657 | − | 1.47338i | −0.880616 | − | 0.473831i | \(-0.842871\pi\) |
0.0299585 | − | 0.999551i | \(-0.490462\pi\) | |||||||
\(200\) | −1.50000 | − | 2.59808i | −0.106066 | − | 0.183712i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −14.0000 | −0.985037 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.00000 | − | 3.46410i | 0.139686 | − | 0.241943i | ||||
\(206\) | −4.00000 | − | 6.92820i | −0.278693 | − | 0.482711i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.00000 | + | 1.73205i | −0.0693375 | + | 0.120096i | ||||
\(209\) | −16.0000 | −1.10674 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | −3.00000 | + | 5.19615i | −0.206041 | + | 0.356873i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.00000 | + | 3.46410i | 0.136717 | + | 0.236801i | ||||
\(215\) | 4.00000 | − | 6.92820i | 0.272798 | − | 0.472500i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −18.0000 | −1.21911 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.00000 | − | 6.92820i | −0.269680 | − | 0.467099i | ||||
\(221\) | 6.00000 | + | 10.3923i | 0.403604 | + | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.0000 | 1.07144 | 0.535720 | − | 0.844396i | \(-0.320040\pi\) | ||||
0.535720 | + | 0.844396i | \(0.320040\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.00000 | + | 12.1244i | −0.465633 | + | 0.806500i | ||||
\(227\) | −6.00000 | − | 10.3923i | −0.398234 | − | 0.689761i | 0.595274 | − | 0.803523i | \(-0.297043\pi\) |
−0.993508 | + | 0.113761i | \(0.963710\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.00000 | − | 8.66025i | 0.330409 | − | 0.572286i | −0.652183 | − | 0.758062i | \(-0.726147\pi\) |
0.982592 | + | 0.185776i | \(0.0594799\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.00000 | −0.393919 | ||||||||
\(233\) | −3.00000 | + | 5.19615i | −0.196537 | + | 0.340411i | −0.947403 | − | 0.320043i | \(-0.896303\pi\) |
0.750867 | + | 0.660454i | \(0.229636\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.00000 | + | 10.3923i | −0.390567 | + | 0.676481i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.0000 | −1.55243 | −0.776215 | − | 0.630468i | \(-0.782863\pi\) | ||||
−0.776215 | + | 0.630468i | \(0.782863\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | − | 1.73205i | −0.0644157 | − | 0.111571i | 0.832019 | − | 0.554747i | \(-0.187185\pi\) |
−0.896435 | + | 0.443176i | \(0.853852\pi\) | |||||||
\(242\) | −2.50000 | − | 4.33013i | −0.160706 | − | 0.278351i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.00000 | 0.128037 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.00000 | − | 6.92820i | 0.254514 | − | 0.440831i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.00000 | − | 10.3923i | 0.379473 | − | 0.657267i | ||||
\(251\) | 20.0000 | 1.26239 | 0.631194 | − | 0.775625i | \(-0.282565\pi\) | ||||
0.631194 | + | 0.775625i | \(0.282565\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.50000 | + | 14.7224i | 0.531250 | + | 0.920152i | ||||
\(257\) | 13.0000 | − | 22.5167i | 0.810918 | − | 1.40455i | −0.101305 | − | 0.994855i | \(-0.532302\pi\) |
0.912222 | − | 0.409695i | \(-0.134365\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.00000 | 0.248069 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.00000 | + | 3.46410i | 0.123560 | + | 0.214013i | ||||
\(263\) | 8.00000 | + | 13.8564i | 0.493301 | + | 0.854423i | 0.999970 | − | 0.00771799i | \(-0.00245674\pi\) |
−0.506669 | + | 0.862141i | \(0.669123\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.0000 | −0.737154 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.00000 | − | 3.46410i | 0.122169 | − | 0.211604i | ||||
\(269\) | 3.00000 | + | 5.19615i | 0.182913 | + | 0.316815i | 0.942871 | − | 0.333157i | \(-0.108114\pi\) |
−0.759958 | + | 0.649972i | \(0.774781\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | + | 13.8564i | −0.485965 | + | 0.841717i | −0.999870 | − | 0.0161307i | \(-0.994865\pi\) |
0.513905 | + | 0.857847i | \(0.328199\pi\) | |||||||
\(272\) | −6.00000 | −0.363803 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.00000 | 0.362473 | ||||||||
\(275\) | −2.00000 | + | 3.46410i | −0.120605 | + | 0.208893i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.0000 | − | 19.0526i | −0.660926 | − | 1.14476i | −0.980373 | − | 0.197153i | \(-0.936830\pi\) |
0.319447 | − | 0.947604i | \(-0.396503\pi\) | |||||||
\(278\) | −6.00000 | + | 10.3923i | −0.359856 | + | 0.623289i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.0000 | 1.31241 | 0.656205 | − | 0.754583i | \(-0.272161\pi\) | ||||
0.656205 | + | 0.754583i | \(0.272161\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.0000 | + | 17.3205i | 0.594438 | + | 1.02960i | 0.993626 | + | 0.112728i | \(0.0359589\pi\) |
−0.399188 | + | 0.916869i | \(0.630708\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.00000 | 0.473050 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.50000 | + | 16.4545i | −0.558824 | + | 0.967911i | ||||
\(290\) | −2.00000 | − | 3.46410i | −0.117444 | − | 0.203419i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.00000 | + | 5.19615i | −0.175562 | + | 0.304082i | ||||
\(293\) | −14.0000 | −0.817889 | −0.408944 | − | 0.912559i | \(-0.634103\pi\) | ||||
−0.408944 | + | 0.912559i | \(0.634103\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −24.0000 | −1.39733 | ||||||||
\(296\) | 9.00000 | − | 15.5885i | 0.523114 | − | 0.906061i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.00000 | + | 5.19615i | 0.173785 | + | 0.301005i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8.00000 | 0.460348 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.00000 | + | 3.46410i | 0.114708 | + | 0.198680i | ||||
\(305\) | 2.00000 | + | 3.46410i | 0.114520 | + | 0.198354i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.00000 | 0.228292 | 0.114146 | − | 0.993464i | \(-0.463587\pi\) | ||||
0.114146 | + | 0.993464i | \(0.463587\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.0000 | − | 20.7846i | −0.680458 | − | 1.17859i | −0.974841 | − | 0.222900i | \(-0.928448\pi\) |
0.294384 | − | 0.955687i | \(-0.404886\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.0000 | + | 22.5167i | −0.734803 | + | 1.27272i | 0.220006 | + | 0.975499i | \(0.429392\pi\) |
−0.954810 | + | 0.297218i | \(0.903941\pi\) | |||||||
\(314\) | −2.00000 | −0.112867 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.0000 | 0.900070 | ||||||||
\(317\) | −9.00000 | + | 15.5885i | −0.505490 | + | 0.875535i | 0.494489 | + | 0.869184i | \(0.335355\pi\) |
−0.999980 | + | 0.00635137i | \(0.997978\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.00000 | + | 6.92820i | 0.223957 | + | 0.387905i | ||||
\(320\) | −7.00000 | + | 12.1244i | −0.391312 | + | 0.677772i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 24.0000 | 1.33540 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | − | 1.73205i | −0.0554700 | − | 0.0960769i | ||||
\(326\) | −2.00000 | − | 3.46410i | −0.110770 | − | 0.191859i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.00000 | 0.331295 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.00000 | − | 3.46410i | 0.109930 | − | 0.190404i | −0.805812 | − | 0.592172i | \(-0.798271\pi\) |
0.915742 | + | 0.401768i | \(0.131604\pi\) | |||||||
\(332\) | 6.00000 | + | 10.3923i | 0.329293 | + | 0.570352i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.00000 | + | 6.92820i | −0.218870 | + | 0.379094i | ||||
\(335\) | 8.00000 | 0.437087 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.0000 | −0.762629 | −0.381314 | − | 0.924445i | \(-0.624528\pi\) | ||||
−0.381314 | + | 0.924445i | \(0.624528\pi\) | |||||||
\(338\) | 4.50000 | − | 7.79423i | 0.244768 | − | 0.423950i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.00000 | + | 10.3923i | 0.325396 | + | 0.563602i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 12.0000 | 0.646997 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.00000 | − | 8.66025i | −0.268802 | − | 0.465578i | ||||
\(347\) | −14.0000 | − | 24.2487i | −0.751559 | − | 1.30174i | −0.947067 | − | 0.321037i | \(-0.895969\pi\) |
0.195507 | − | 0.980702i | \(-0.437365\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.00000 | −0.107058 | −0.0535288 | − | 0.998566i | \(-0.517047\pi\) | ||||
−0.0535288 | + | 0.998566i | \(0.517047\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10.0000 | − | 17.3205i | 0.533002 | − | 0.923186i | ||||
\(353\) | 5.00000 | + | 8.66025i | 0.266123 | + | 0.460939i | 0.967857 | − | 0.251500i | \(-0.0809239\pi\) |
−0.701734 | + | 0.712439i | \(0.747591\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −14.0000 | −0.741999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.00000 | 0.211407 | ||||||||
\(359\) | 16.0000 | − | 27.7128i | 0.844448 | − | 1.46263i | −0.0416523 | − | 0.999132i | \(-0.513262\pi\) |
0.886100 | − | 0.463494i | \(-0.153404\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.50000 | + | 2.59808i | 0.0789474 | + | 0.136741i | ||||
\(362\) | 13.0000 | − | 22.5167i | 0.683265 | − | 1.18345i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.0000 | −0.628109 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 12.0000 | 0.623850 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.00000 | − | 8.66025i | 0.258890 | − | 0.448411i | −0.707055 | − | 0.707159i | \(-0.749977\pi\) |
0.965945 | + | 0.258748i | \(0.0833099\pi\) | |||||||
\(374\) | 12.0000 | + | 20.7846i | 0.620505 | + | 1.07475i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.00000 | −0.206010 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.0000 | 0.616399 | 0.308199 | − | 0.951322i | \(-0.400274\pi\) | ||||
0.308199 | + | 0.951322i | \(0.400274\pi\) | |||||||
\(380\) | 4.00000 | − | 6.92820i | 0.205196 | − | 0.355409i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.00000 | − | 6.92820i | −0.204658 | − | 0.354478i | ||||
\(383\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.00000 | 0.101797 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.00000 | + | 15.5885i | 0.456906 | + | 0.791384i | ||||
\(389\) | 3.00000 | + | 5.19615i | 0.152106 | + | 0.263455i | 0.932002 | − | 0.362454i | \(-0.118061\pi\) |
−0.779895 | + | 0.625910i | \(0.784728\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 11.0000 | − | 19.0526i | 0.554172 | − | 0.959854i | ||||
\(395\) | 16.0000 | + | 27.7128i | 0.805047 | + | 1.39438i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.00000 | − | 15.5885i | 0.451697 | − | 0.782362i | −0.546795 | − | 0.837267i | \(-0.684152\pi\) |
0.998492 | + | 0.0549046i | \(0.0174855\pi\) | |||||||
\(398\) | 24.0000 | 1.20301 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −15.0000 | + | 25.9808i | −0.749064 | + | 1.29742i | 0.199207 | + | 0.979957i | \(0.436163\pi\) |
−0.948272 | + | 0.317460i | \(0.897170\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −7.00000 | + | 12.1244i | −0.348263 | + | 0.603209i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.0000 | −1.18964 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.0000 | + | 19.0526i | 0.543915 | + | 0.942088i | 0.998674 | + | 0.0514740i | \(0.0163919\pi\) |
−0.454759 | + | 0.890614i | \(0.650275\pi\) | |||||||
\(410\) | 2.00000 | + | 3.46410i | 0.0987730 | + | 0.171080i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.00000 | −0.394132 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.0000 | + | 20.7846i | −0.589057 | + | 1.02028i | ||||
\(416\) | 5.00000 | + | 8.66025i | 0.245145 | + | 0.424604i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8.00000 | − | 13.8564i | 0.391293 | − | 0.677739i | ||||
\(419\) | 12.0000 | 0.586238 | 0.293119 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293119 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 38.0000 | 1.85201 | 0.926003 | − | 0.377515i | \(-0.123221\pi\) | ||||
0.926003 | + | 0.377515i | \(0.123221\pi\) | |||||||
\(422\) | −2.00000 | + | 3.46410i | −0.0973585 | + | 0.168630i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.00000 | − | 15.5885i | −0.437079 | − | 0.757042i | ||||
\(425\) | 3.00000 | − | 5.19615i | 0.145521 | − | 0.252050i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4.00000 | 0.193347 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.00000 | + | 6.92820i | 0.192897 | + | 0.334108i | ||||
\(431\) | −12.0000 | − | 20.7846i | −0.578020 | − | 1.00116i | −0.995706 | − | 0.0925683i | \(-0.970492\pi\) |
0.417687 | − | 0.908591i | \(-0.362841\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.0000 | −0.672797 | −0.336399 | − | 0.941720i | \(-0.609209\pi\) | ||||
−0.336399 | + | 0.941720i | \(0.609209\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.00000 | + | 15.5885i | −0.431022 | + | 0.746552i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.0000 | − | 20.7846i | 0.572729 | − | 0.991995i | −0.423556 | − | 0.905870i | \(-0.639218\pi\) |
0.996284 | − | 0.0861252i | \(-0.0274485\pi\) | |||||||
\(440\) | 24.0000 | 1.14416 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12.0000 | −0.570782 | ||||||||
\(443\) | 18.0000 | − | 31.1769i | 0.855206 | − | 1.48126i | −0.0212481 | − | 0.999774i | \(-0.506764\pi\) |
0.876454 | − | 0.481486i | \(-0.159903\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.0000 | − | 24.2487i | −0.663664 | − | 1.14950i | ||||
\(446\) | −8.00000 | + | 13.8564i | −0.378811 | + | 0.656120i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.0000 | 1.41579 | 0.707894 | − | 0.706319i | \(-0.249646\pi\) | ||||
0.707894 | + | 0.706319i | \(0.249646\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.00000 | − | 6.92820i | −0.188353 | − | 0.326236i | ||||
\(452\) | 7.00000 | + | 12.1244i | 0.329252 | + | 0.570282i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 12.0000 | 0.563188 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.00000 | + | 8.66025i | −0.233890 | + | 0.405110i | −0.958950 | − | 0.283577i | \(-0.908479\pi\) |
0.725059 | + | 0.688686i | \(0.241812\pi\) | |||||||
\(458\) | 5.00000 | + | 8.66025i | 0.233635 | + | 0.404667i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.0000 | 0.465746 | 0.232873 | − | 0.972507i | \(-0.425187\pi\) | ||||
0.232873 | + | 0.972507i | \(0.425187\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.0000 | 0.743583 | 0.371792 | − | 0.928316i | \(-0.378744\pi\) | ||||
0.371792 | + | 0.928316i | \(0.378744\pi\) | |||||||
\(464\) | 1.00000 | − | 1.73205i | 0.0464238 | − | 0.0804084i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.00000 | − | 5.19615i | −0.138972 | − | 0.240707i | ||||
\(467\) | 18.0000 | − | 31.1769i | 0.832941 | − | 1.44270i | −0.0627555 | − | 0.998029i | \(-0.519989\pi\) |
0.895696 | − | 0.444667i | \(-0.146678\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −18.0000 | − | 31.1769i | −0.828517 | − | 1.43503i | ||||
\(473\) | −8.00000 | − | 13.8564i | −0.367840 | − | 0.637118i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.00000 | −0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12.0000 | − | 20.7846i | 0.548867 | − | 0.950666i | ||||
\(479\) | −8.00000 | − | 13.8564i | −0.365529 | − | 0.633115i | 0.623332 | − | 0.781958i | \(-0.285779\pi\) |
−0.988861 | + | 0.148842i | \(0.952445\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.00000 | − | 10.3923i | 0.273576 | − | 0.473848i | ||||
\(482\) | 2.00000 | 0.0910975 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.00000 | −0.227273 | ||||||||
\(485\) | −18.0000 | + | 31.1769i | −0.817338 | + | 1.41567i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.00000 | + | 6.92820i | 0.181257 | + | 0.313947i | 0.942309 | − | 0.334744i | \(-0.108650\pi\) |
−0.761052 | + | 0.648691i | \(0.775317\pi\) | |||||||
\(488\) | −3.00000 | + | 5.19615i | −0.135804 | + | 0.235219i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.0000 | −0.902587 | −0.451294 | − | 0.892375i | \(-0.649037\pi\) | ||||
−0.451294 | + | 0.892375i | \(0.649037\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.00000 | − | 10.3923i | −0.270226 | − | 0.468046i | ||||
\(494\) | 4.00000 | + | 6.92820i | 0.179969 | + | 0.311715i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.00000 | + | 3.46410i | −0.0895323 | + | 0.155074i | −0.907314 | − | 0.420455i | \(-0.861871\pi\) |
0.817781 | + | 0.575529i | \(0.195204\pi\) | |||||||
\(500\) | −6.00000 | − | 10.3923i | −0.268328 | − | 0.464758i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −10.0000 | + | 17.3205i | −0.446322 | + | 0.773052i | ||||
\(503\) | −24.0000 | −1.07011 | −0.535054 | − | 0.844818i | \(-0.679709\pi\) | ||||
−0.535054 | + | 0.844818i | \(0.679709\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −28.0000 | −1.24598 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.00000 | + | 8.66025i | −0.221621 | + | 0.383859i | −0.955300 | − | 0.295637i | \(-0.904468\pi\) |
0.733679 | + | 0.679496i | \(0.237801\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −11.0000 | −0.486136 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 13.0000 | + | 22.5167i | 0.573405 | + | 0.993167i | ||||
\(515\) | −8.00000 | − | 13.8564i | −0.352522 | − | 0.610586i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.00000 | + | 10.3923i | −0.263117 | + | 0.455733i | ||||
\(521\) | 9.00000 | + | 15.5885i | 0.394297 | + | 0.682943i | 0.993011 | − | 0.118020i | \(-0.0376547\pi\) |
−0.598714 | + | 0.800963i | \(0.704321\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.0000 | − | 17.3205i | 0.437269 | − | 0.757373i | −0.560208 | − | 0.828352i | \(-0.689279\pi\) |
0.997478 | + | 0.0709788i | \(0.0226123\pi\) | |||||||
\(524\) | 4.00000 | 0.174741 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.0000 | −0.697633 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.5000 | + | 19.9186i | 0.500000 | + | 0.866025i | ||||
\(530\) | 6.00000 | − | 10.3923i | 0.260623 | − | 0.451413i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.00000 | 0.173259 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.00000 | + | 6.92820i | 0.172935 | + | 0.299532i | ||||
\(536\) | 6.00000 | + | 10.3923i | 0.259161 | + | 0.448879i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6.00000 | −0.258678 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.0000 | − | 29.4449i | 0.730887 | − | 1.26593i | −0.225617 | − | 0.974216i | \(-0.572440\pi\) |
0.956504 | − | 0.291718i | \(-0.0942267\pi\) | |||||||
\(542\) | −8.00000 | − | 13.8564i | −0.343629 | − | 0.595184i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −15.0000 | + | 25.9808i | −0.643120 | + | 1.11392i | ||||
\(545\) | −36.0000 | −1.54207 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.00000 | 0.171028 | 0.0855138 | − | 0.996337i | \(-0.472747\pi\) | ||||
0.0855138 | + | 0.996337i | \(0.472747\pi\) | |||||||
\(548\) | 3.00000 | − | 5.19615i | 0.128154 | − | 0.221969i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.00000 | − | 3.46410i | −0.0852803 | − | 0.147710i | ||||
\(551\) | −4.00000 | + | 6.92820i | −0.170406 | + | 0.295151i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 22.0000 | 0.934690 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.00000 | + | 10.3923i | 0.254457 | + | 0.440732i | ||||
\(557\) | −1.00000 | − | 1.73205i | −0.0423714 | − | 0.0733893i | 0.844062 | − | 0.536246i | \(-0.180158\pi\) |
−0.886433 | + | 0.462856i | \(0.846825\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.00000 | 0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −11.0000 | + | 19.0526i | −0.464007 | + | 0.803684i | ||||
\(563\) | 2.00000 | + | 3.46410i | 0.0842900 | + | 0.145994i | 0.905088 | − | 0.425223i | \(-0.139804\pi\) |
−0.820798 | + | 0.571218i | \(0.806471\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.0000 | + | 24.2487i | −0.588984 | + | 1.02015i | ||||
\(566\) | −20.0000 | −0.840663 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.00000 | − | 8.66025i | 0.209611 | − | 0.363057i | −0.741981 | − | 0.670421i | \(-0.766114\pi\) |
0.951592 | + | 0.307364i | \(0.0994469\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.00000 | + | 3.46410i | 0.0836974 | + | 0.144968i | 0.904835 | − | 0.425762i | \(-0.139994\pi\) |
−0.821138 | + | 0.570730i | \(0.806660\pi\) | |||||||
\(572\) | 4.00000 | − | 6.92820i | 0.167248 | − | 0.289683i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.0000 | − | 29.4449i | −0.707719 | − | 1.22581i | −0.965701 | − | 0.259656i | \(-0.916391\pi\) |
0.257982 | − | 0.966150i | \(-0.416942\pi\) | |||||||
\(578\) | −9.50000 | − | 16.4545i | −0.395148 | − | 0.684416i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.00000 | −0.166091 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.0000 | + | 20.7846i | −0.496989 | + | 0.860811i | ||||
\(584\) | −9.00000 | − | 15.5885i | −0.372423 | − | 0.645055i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.00000 | − | 12.1244i | 0.289167 | − | 0.500853i | ||||
\(587\) | −28.0000 | −1.15568 | −0.577842 | − | 0.816149i | \(-0.696105\pi\) | ||||
−0.577842 | + | 0.816149i | \(0.696105\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 12.0000 | − | 20.7846i | 0.494032 | − | 0.855689i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.00000 | + | 5.19615i | 0.123299 | + | 0.213561i | ||||
\(593\) | −3.00000 | + | 5.19615i | −0.123195 | + | 0.213380i | −0.921026 | − | 0.389501i | \(-0.872647\pi\) |
0.797831 | + | 0.602881i | \(0.205981\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.00000 | 0.245770 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.0000 | + | 41.5692i | 0.980613 | + | 1.69847i | 0.660006 | + | 0.751260i | \(0.270554\pi\) |
0.320607 | + | 0.947212i | \(0.396113\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.00000 | −0.244745 | −0.122373 | − | 0.992484i | \(-0.539050\pi\) | ||||
−0.122373 | + | 0.992484i | \(0.539050\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.00000 | − | 6.92820i | 0.162758 | − | 0.281905i | ||||
\(605\) | −5.00000 | − | 8.66025i | −0.203279 | − | 0.352089i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.00000 | − | 13.8564i | 0.324710 | − | 0.562414i | −0.656744 | − | 0.754114i | \(-0.728067\pi\) |
0.981454 | + | 0.191700i | \(0.0614000\pi\) | |||||||
\(608\) | 20.0000 | 0.811107 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.00000 | −0.161955 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.0000 | + | 22.5167i | 0.525065 | + | 0.909439i | 0.999574 | + | 0.0291886i | \(0.00929235\pi\) |
−0.474509 | + | 0.880251i | \(0.657374\pi\) | |||||||
\(614\) | −2.00000 | + | 3.46410i | −0.0807134 | + | 0.139800i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.00000 | 0.241551 | 0.120775 | − | 0.992680i | \(-0.461462\pi\) | ||||
0.120775 | + | 0.992680i | \(0.461462\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.0000 | + | 17.3205i | 0.401934 | + | 0.696170i | 0.993959 | − | 0.109749i | \(-0.0350048\pi\) |
−0.592025 | + | 0.805919i | \(0.701671\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24.0000 | 0.962312 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50000 | − | 16.4545i | 0.380000 | − | 0.658179i | ||||
\(626\) | −13.0000 | − | 22.5167i | −0.519584 | − | 0.899947i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.00000 | + | 1.73205i | −0.0399043 | + | 0.0691164i | ||||
\(629\) | 36.0000 | 1.43541 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.0000 | −1.59237 | −0.796187 | − | 0.605050i | \(-0.793153\pi\) | ||||
−0.796187 | + | 0.605050i | \(0.793153\pi\) | |||||||
\(632\) | −24.0000 | + | 41.5692i | −0.954669 | + | 1.65353i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9.00000 | − | 15.5885i | −0.357436 | − | 0.619097i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −8.00000 | −0.316723 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.00000 | + | 5.19615i | 0.118585 | + | 0.205396i | ||||
\(641\) | 9.00000 | + | 15.5885i | 0.355479 | + | 0.615707i | 0.987200 | − | 0.159489i | \(-0.0509845\pi\) |
−0.631721 | + | 0.775196i | \(0.717651\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.0000 | 0.788723 | 0.394362 | − | 0.918955i | \(-0.370966\pi\) | ||||
0.394362 | + | 0.918955i | \(0.370966\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.0000 | + | 20.7846i | −0.472134 | + | 0.817760i | ||||
\(647\) | −20.0000 | − | 34.6410i | −0.786281 | − | 1.36188i | −0.928231 | − | 0.372005i | \(-0.878670\pi\) |
0.141950 | − | 0.989874i | \(-0.454663\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.0000 | + | 41.5692i | −0.942082 | + | 1.63173i | ||||
\(650\) | 2.00000 | 0.0784465 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.00000 | −0.156652 | ||||||||
\(653\) | −9.00000 | + | 15.5885i | −0.352197 | + | 0.610023i | −0.986634 | − | 0.162951i | \(-0.947899\pi\) |
0.634437 | + | 0.772975i | \(0.281232\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.00000 | + | 6.92820i | 0.156293 | + | 0.270707i | ||||
\(656\) | −1.00000 | + | 1.73205i | −0.0390434 | + | 0.0676252i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.0000 | −0.467454 | −0.233727 | − | 0.972302i | \(-0.575092\pi\) | ||||
−0.233727 | + | 0.972302i | \(0.575092\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.0000 | − | 19.0526i | −0.427850 | − | 0.741059i | 0.568831 | − | 0.822454i | \(-0.307396\pi\) |
−0.996682 | + | 0.0813955i | \(0.974062\pi\) | |||||||
\(662\) | 2.00000 | + | 3.46410i | 0.0777322 | + | 0.134636i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −36.0000 | −1.39707 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 4.00000 | + | 6.92820i | 0.154765 | + | 0.268060i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.00000 | + | 6.92820i | −0.154533 | + | 0.267660i | ||||
\(671\) | 8.00000 | 0.308837 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.0000 | 1.31060 | 0.655302 | − | 0.755367i | \(-0.272541\pi\) | ||||
0.655302 | + | 0.755367i | \(0.272541\pi\) | |||||||
\(674\) | 7.00000 | − | 12.1244i | 0.269630 | − | 0.467013i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.50000 | − | 7.79423i | −0.173077 | − | 0.299778i | ||||
\(677\) | −9.00000 | + | 15.5885i | −0.345898 | + | 0.599113i | −0.985517 | − | 0.169580i | \(-0.945759\pi\) |
0.639618 | + | 0.768693i | \(0.279092\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −36.0000 | −1.38054 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.00000 | − | 10.3923i | −0.229584 | − | 0.397650i | 0.728101 | − | 0.685470i | \(-0.240403\pi\) |
−0.957685 | + | 0.287819i | \(0.907070\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.0000 | 0.458496 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.00000 | + | 3.46410i | −0.0762493 | + | 0.132068i | ||||
\(689\) | −6.00000 | − | 10.3923i | −0.228582 | − | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.0000 | + | 17.3205i | −0.380418 | + | 0.658903i | −0.991122 | − | 0.132956i | \(-0.957553\pi\) |
0.610704 | + | 0.791859i | \(0.290887\pi\) | |||||||
\(692\) | −10.0000 | −0.380143 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 28.0000 | 1.06287 | ||||||||
\(695\) | −12.0000 | + | 20.7846i | −0.455186 | + | 0.788405i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.00000 | + | 10.3923i | 0.227266 | + | 0.393637i | ||||
\(698\) | 1.00000 | − | 1.73205i | 0.0378506 | − | 0.0655591i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.0000 | −1.13308 | −0.566542 | − | 0.824033i | \(-0.691719\pi\) | ||||
−0.566542 | + | 0.824033i | \(0.691719\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.0000 | − | 20.7846i | −0.452589 | − | 0.783906i | ||||
\(704\) | 14.0000 | + | 24.2487i | 0.527645 | + | 0.913908i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.0000 | −0.376355 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.00000 | + | 5.19615i | −0.112667 | + | 0.195146i | −0.916845 | − | 0.399244i | \(-0.869273\pi\) |
0.804178 | + | 0.594389i | \(0.202606\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 21.0000 | − | 36.3731i | 0.787008 | − | 1.36314i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.0000 | 0.598366 | ||||||||
\(716\) | 2.00000 | − | 3.46410i | 0.0747435 | − | 0.129460i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 16.0000 | + | 27.7128i | 0.597115 | + | 1.03423i | ||||
\(719\) | −24.0000 | + | 41.5692i | −0.895049 | + | 1.55027i | −0.0613050 | + | 0.998119i | \(0.519526\pi\) |
−0.833744 | + | 0.552151i | \(0.813807\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −3.00000 | −0.111648 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −13.0000 | − | 22.5167i | −0.483141 | − | 0.836825i | ||||
\(725\) | 1.00000 | + | 1.73205i | 0.0371391 | + | 0.0643268i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.0000 | −1.48352 | −0.741759 | − | 0.670667i | \(-0.766008\pi\) | ||||
−0.741759 | + | 0.670667i | \(0.766008\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.00000 | − | 10.3923i | 0.222070 | − | 0.384636i | ||||
\(731\) | 12.0000 | + | 20.7846i | 0.443836 | + | 0.768747i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.00000 | − | 15.5885i | 0.332423 | − | 0.575773i | −0.650564 | − | 0.759452i | \(-0.725467\pi\) |
0.982986 | + | 0.183679i | \(0.0588007\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.00000 | − | 13.8564i | 0.294684 | − | 0.510407i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.0000 | − | 31.1769i | −0.662141 | − | 1.14686i | −0.980052 | − | 0.198741i | \(-0.936315\pi\) |
0.317911 | − | 0.948120i | \(-0.397019\pi\) | |||||||
\(740\) | 6.00000 | − | 10.3923i | 0.220564 | − | 0.382029i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.00000 | + | 10.3923i | 0.219823 | + | 0.380745i | ||||
\(746\) | 5.00000 | + | 8.66025i | 0.183063 | + | 0.317074i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 24.0000 | 0.877527 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.0000 | − | 27.7128i | 0.583848 | − | 1.01125i | −0.411170 | − | 0.911559i | \(-0.634880\pi\) |
0.995018 | − | 0.0996961i | \(-0.0317870\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.00000 | − | 3.46410i | 0.0728357 | − | 0.126155i | ||||
\(755\) | 16.0000 | 0.582300 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.0000 | −0.363456 | −0.181728 | − | 0.983349i | \(-0.558169\pi\) | ||||
−0.181728 | + | 0.983349i | \(0.558169\pi\) | |||||||
\(758\) | −6.00000 | + | 10.3923i | −0.217930 | + | 0.377466i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 12.0000 | + | 20.7846i | 0.435286 | + | 0.753937i | ||||
\(761\) | 9.00000 | − | 15.5885i | 0.326250 | − | 0.565081i | −0.655515 | − | 0.755182i | \(-0.727548\pi\) |
0.981764 | + | 0.190101i | \(0.0608816\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −8.00000 | −0.289430 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.0000 | − | 20.7846i | −0.433295 | − | 0.750489i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.00000 | 0.0721218 | 0.0360609 | − | 0.999350i | \(-0.488519\pi\) | ||||
0.0360609 | + | 0.999350i | \(0.488519\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.00000 | − | 1.73205i | 0.0359908 | − | 0.0623379i | ||||
\(773\) | 7.00000 | + | 12.1244i | 0.251773 | + | 0.436083i | 0.964014 | − | 0.265852i | \(-0.0856532\pi\) |
−0.712241 | + | 0.701935i | \(0.752320\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −54.0000 | −1.93849 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.00000 | −0.215110 | ||||||||
\(779\) | 4.00000 | − | 6.92820i | 0.143315 | − | 0.248229i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.00000 | −0.142766 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.0000 | + | 38.1051i | 0.784215 | + | 1.35830i | 0.929467 | + | 0.368906i | \(0.120268\pi\) |
−0.145251 | + | 0.989395i | \(0.546399\pi\) | |||||||
\(788\) | −11.0000 | − | 19.0526i | −0.391859 | − | 0.678719i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −32.0000 | −1.13851 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.00000 | + | 3.46410i | −0.0710221 | + | 0.123014i | ||||
\(794\) | 9.00000 | + | 15.5885i | 0.319398 | + | 0.553214i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.0000 | − | 20.7846i | 0.425329 | − | 0.736691i | ||||
\(797\) | 26.0000 | 0.920967 | 0.460484 | − | 0.887668i | \(-0.347676\pi\) | ||||
0.460484 | + | 0.887668i | \(0.347676\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 2.50000 | − | 4.33013i | 0.0883883 | − | 0.153093i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −15.0000 | − | 25.9808i | −0.529668 | − | 0.917413i | ||||
\(803\) | −12.0000 | + | 20.7846i | −0.423471 | + | 0.733473i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −21.0000 | − | 36.3731i | −0.738777 | − | 1.27960i | ||||
\(809\) | 21.0000 | + | 36.3731i | 0.738321 | + | 1.27881i | 0.953251 | + | 0.302180i | \(0.0977142\pi\) |
−0.214930 | + | 0.976629i | \(0.568952\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.0000 | 1.54505 | 0.772524 | − | 0.634985i | \(-0.218994\pi\) | ||||
0.772524 | + | 0.634985i | \(0.218994\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 12.0000 | − | 20.7846i | 0.420600 | − | 0.728500i | ||||
\(815\) | −4.00000 | − | 6.92820i | −0.140114 | − | 0.242684i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.00000 | − | 13.8564i | 0.279885 | − | 0.484774i | ||||
\(818\) | −22.0000 | −0.769212 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.00000 | 0.139686 | ||||||||
\(821\) | 19.0000 | − | 32.9090i | 0.663105 | − | 1.14853i | −0.316691 | − | 0.948529i | \(-0.602572\pi\) |
0.979795 | − | 0.200002i | \(-0.0640949\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.0000 | − | 20.7846i | −0.418294 | − | 0.724506i | 0.577474 | − | 0.816409i | \(-0.304038\pi\) |
−0.995768 | + | 0.0919029i | \(0.970705\pi\) | |||||||
\(824\) | 12.0000 | − | 20.7846i | 0.418040 | − | 0.724066i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.0000 | 0.417281 | 0.208640 | − | 0.977992i | \(-0.433096\pi\) | ||||
0.208640 | + | 0.977992i | \(0.433096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.00000 | − | 12.1244i | −0.243120 | − | 0.421096i | 0.718481 | − | 0.695546i | \(-0.244838\pi\) |
−0.961601 | + | 0.274450i | \(0.911504\pi\) | |||||||
\(830\) | −12.0000 | − | 20.7846i | −0.416526 | − | 0.721444i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −14.0000 | −0.485363 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.00000 | + | 13.8564i | −0.276851 | + | 0.479521i | ||||
\(836\) | −8.00000 | − | 13.8564i | −0.276686 | − | 0.479234i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.00000 | + | 10.3923i | −0.207267 | + | 0.358996i | ||||
\(839\) | 8.00000 | 0.276191 | 0.138095 | − | 0.990419i | \(-0.455902\pi\) | ||||
0.138095 | + | 0.990419i | \(0.455902\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | −19.0000 | + | 32.9090i | −0.654783 | + | 1.13412i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.00000 | + | 3.46410i | 0.0688428 | + | 0.119239i | ||||
\(845\) | 9.00000 | − | 15.5885i | 0.309609 | − | 0.536259i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.00000 | 0.206041 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.00000 | + | 5.19615i | 0.102899 | + | 0.178227i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.0000 | −0.342393 | −0.171197 | − | 0.985237i | \(-0.554763\pi\) | ||||
−0.171197 | + | 0.985237i | \(0.554763\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.00000 | + | 10.3923i | −0.205076 | + | 0.355202i | ||||
\(857\) | −7.00000 | − | 12.1244i | −0.239115 | − | 0.414160i | 0.721345 | − | 0.692576i | \(-0.243524\pi\) |
−0.960461 | + | 0.278416i | \(0.910191\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.0000 | + | 38.1051i | −0.750630 | + | 1.30013i | 0.196887 | + | 0.980426i | \(0.436917\pi\) |
−0.947518 | + | 0.319704i | \(0.896417\pi\) | |||||||
\(860\) | 8.00000 | 0.272798 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 24.0000 | 0.817443 | ||||||||
\(863\) | −12.0000 | + | 20.7846i | −0.408485 | + | 0.707516i | −0.994720 | − | 0.102624i | \(-0.967276\pi\) |
0.586235 | + | 0.810141i | \(0.300609\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.0000 | − | 17.3205i | −0.340010 | − | 0.588915i | ||||
\(866\) | 7.00000 | − | 12.1244i | 0.237870 | − | 0.412002i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 64.0000 | 2.17105 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.00000 | + | 6.92820i | 0.135535 | + | 0.234753i | ||||
\(872\) | −27.0000 | − | 46.7654i | −0.914335 | − | 1.58368i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.0000 | + | 39.8372i | −0.776655 | + | 1.34521i | 0.157205 | + | 0.987566i | \(0.449752\pi\) |
−0.933860 | + | 0.357640i | \(0.883582\pi\) | |||||||
\(878\) | 12.0000 | + | 20.7846i | 0.404980 | + | 0.701447i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.00000 | + | 6.92820i | −0.134840 | + | 0.233550i | ||||
\(881\) | 6.00000 | 0.202145 | 0.101073 | − | 0.994879i | \(-0.467773\pi\) | ||||
0.101073 | + | 0.994879i | \(0.467773\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.0000 | −0.942275 | −0.471138 | − | 0.882060i | \(-0.656156\pi\) | ||||
−0.471138 | + | 0.882060i | \(0.656156\pi\) | |||||||
\(884\) | −6.00000 | + | 10.3923i | −0.201802 | + | 0.349531i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 18.0000 | + | 31.1769i | 0.604722 | + | 1.04741i | ||||
\(887\) | 4.00000 | − | 6.92820i | 0.134307 | − | 0.232626i | −0.791026 | − | 0.611783i | \(-0.790453\pi\) |
0.925332 | + | 0.379157i | \(0.123786\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 28.0000 | 0.938562 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.00000 | + | 13.8564i | 0.267860 | + | 0.463947i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.00000 | 0.267411 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15.0000 | + | 25.9808i | −0.500556 | + | 0.866989i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.0000 | − | 31.1769i | 0.599667 | − | 1.03865i | ||||
\(902\) | 8.00000 | 0.266371 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −42.0000 | −1.39690 | ||||||||
\(905\) | 26.0000 | − | 45.0333i | 0.864269 | − | 1.49696i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.00000 | + | 3.46410i | 0.0664089 | + | 0.115024i | 0.897318 | − | 0.441384i | \(-0.145512\pi\) |
−0.830909 | + | 0.556408i | \(0.812179\pi\) | |||||||
\(908\) | 6.00000 | − | 10.3923i | 0.199117 | − | 0.344881i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.0000 | 0.795155 | 0.397578 | − | 0.917568i | \(-0.369851\pi\) | ||||
0.397578 | + | 0.917568i | \(0.369851\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.0000 | + | 41.5692i | 0.794284 | + | 1.37574i | ||||
\(914\) | −5.00000 | − | 8.66025i | −0.165385 | − | 0.286456i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.0000 | 0.330409 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.00000 | + | 6.92820i | −0.131948 | + | 0.228540i | −0.924427 | − | 0.381358i | \(-0.875456\pi\) |
0.792480 | + | 0.609898i | \(0.208790\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.00000 | + | 8.66025i | −0.164666 | + | 0.285210i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.00000 | −0.197279 | ||||||||
\(926\) | −8.00000 | + | 13.8564i | −0.262896 | + | 0.455350i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.00000 | − | 8.66025i | −0.164133 | − | 0.284287i | ||||
\(929\) | 13.0000 | − | 22.5167i | 0.426516 | − | 0.738748i | −0.570045 | − | 0.821614i | \(-0.693074\pi\) |
0.996561 | + | 0.0828661i | \(0.0264074\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −6.00000 | −0.196537 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 18.0000 | + | 31.1769i | 0.588978 | + | 1.02014i | ||||
\(935\) | 24.0000 | + | 41.5692i | 0.784884 | + | 1.35946i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.0000 | 1.37208 | 0.686040 | − | 0.727564i | \(-0.259347\pi\) | ||||
0.686040 | + | 0.727564i | \(0.259347\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.0000 | + | 32.9090i | 0.619382 | + | 1.07280i | 0.989599 | + | 0.143856i | \(0.0459502\pi\) |
−0.370216 | + | 0.928946i | \(0.620716\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 12.0000 | 0.390567 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.0000 | 0.520205 | ||||||||
\(947\) | 22.0000 | − | 38.1051i | 0.714904 | − | 1.23825i | −0.248093 | − | 0.968736i | \(-0.579804\pi\) |
0.962997 | − | 0.269514i | \(-0.0868629\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.00000 | − | 10.3923i | −0.194768 | − | 0.337348i | ||||
\(950\) | 2.00000 | − | 3.46410i | 0.0648886 | − | 0.112390i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.0000 | −0.842223 | −0.421111 | − | 0.907009i | \(-0.638360\pi\) | ||||
−0.421111 | + | 0.907009i | \(0.638360\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.00000 | − | 13.8564i | −0.258874 | − | 0.448383i | ||||
\(956\) | −12.0000 | − | 20.7846i | −0.388108 | − | 0.672222i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 16.0000 | 0.516937 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.5000 | − | 26.8468i | 0.500000 | − | 0.866025i | ||||
\(962\) | 6.00000 | + | 10.3923i | 0.193448 | + | 0.335061i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.00000 | − | 1.73205i | 0.0322078 | − | 0.0557856i | ||||
\(965\) | 4.00000 | 0.128765 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.0000 | 1.28631 | 0.643157 | − | 0.765735i | \(-0.277624\pi\) | ||||
0.643157 | + | 0.765735i | \(0.277624\pi\) | |||||||
\(968\) | 7.50000 | − | 12.9904i | 0.241059 | − | 0.417527i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −18.0000 | − | 31.1769i | −0.577945 | − | 1.00103i | ||||
\(971\) | 6.00000 | − | 10.3923i | 0.192549 | − | 0.333505i | −0.753545 | − | 0.657396i | \(-0.771658\pi\) |
0.946094 | + | 0.323891i | \(0.104991\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −8.00000 | −0.256337 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.00000 | − | 1.73205i | −0.0320092 | − | 0.0554416i | ||||
\(977\) | −15.0000 | − | 25.9808i | −0.479893 | − | 0.831198i | 0.519841 | − | 0.854263i | \(-0.325991\pi\) |
−0.999734 | + | 0.0230645i | \(0.992658\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −56.0000 | −1.78977 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 10.0000 | − | 17.3205i | 0.319113 | − | 0.552720i | ||||
\(983\) | 12.0000 | + | 20.7846i | 0.382741 | + | 0.662926i | 0.991453 | − | 0.130465i | \(-0.0416470\pi\) |
−0.608712 | + | 0.793391i | \(0.708314\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22.0000 | − | 38.1051i | 0.700978 | − | 1.21413i | ||||
\(986\) | 12.0000 | 0.382158 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.00000 | 0.254514 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.00000 | + | 13.8564i | 0.254128 | + | 0.440163i | 0.964658 | − | 0.263504i | \(-0.0848781\pi\) |
−0.710530 | + | 0.703667i | \(0.751545\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 48.0000 | 1.52170 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.0000 | + | 22.5167i | 0.411714 | + | 0.713110i | 0.995077 | − | 0.0991016i | \(-0.0315969\pi\) |
−0.583363 | + | 0.812211i | \(0.698264\pi\) | |||||||
\(998\) | −2.00000 | − | 3.46410i | −0.0633089 | − | 0.109654i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))