Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [484,2,Mod(9,484)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(484, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("484.9");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 484 = 2^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 484.e (of order \(5\), degree \(4\), 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: | \(3.86475945783\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 44) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 9.1 | ||
Root | \(-0.309017 - 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 484.9 |
Dual form | 484.2.e.a.269.1 |
$q$-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 \(\left(\mathbb{Z}/484\mathbb{Z}\right)^\times\).
\(n\) | \(243\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 | ||||||||
\(3\) | −0.809017 | + | 0.587785i | −0.467086 | + | 0.339358i | −0.796305 | − | 0.604896i | \(-0.793215\pi\) |
0.329218 | + | 0.944254i | \(0.393215\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.927051 | − | 2.85317i | −0.414590 | − | 1.27598i | −0.912617 | − | 0.408815i | \(-0.865942\pi\) |
0.498027 | − | 0.867161i | \(-0.334058\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.61803 | − | 1.17557i | −0.611559 | − | 0.444324i | 0.238404 | − | 0.971166i | \(-0.423376\pi\) |
−0.849963 | + | 0.526842i | \(0.823376\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.618034 | + | 1.90211i | −0.206011 | + | 0.634038i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.23607 | + | 3.80423i | −0.342824 | + | 1.05510i | 0.619915 | + | 0.784669i | \(0.287167\pi\) |
−0.962739 | + | 0.270434i | \(0.912833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.42705 | + | 1.76336i | 0.626662 | + | 0.455296i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.85410 | + | 5.70634i | 0.449686 | + | 1.38399i | 0.877262 | + | 0.480011i | \(0.159367\pi\) |
−0.427576 | + | 0.903979i | \(0.640633\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.47214 | + | 4.70228i | −1.48481 | + | 1.07878i | −0.508843 | + | 0.860859i | \(0.669927\pi\) |
−0.975967 | + | 0.217918i | \(0.930073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | 0.436436 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.00000 | −0.625543 | −0.312772 | − | 0.949828i | \(-0.601257\pi\) | ||||
−0.312772 | + | 0.949828i | \(0.601257\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.23607 | + | 2.35114i | −0.647214 | + | 0.470228i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.54508 | − | 4.75528i | −0.297352 | − | 0.915155i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.54508 | − | 4.75528i | 0.277505 | − | 0.854074i | −0.711040 | − | 0.703151i | \(-0.751776\pi\) |
0.988546 | − | 0.150923i | \(-0.0482244\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.85410 | + | 5.70634i | −0.313400 | + | 0.964547i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.809017 | + | 0.587785i | 0.133002 | + | 0.0966313i | 0.652297 | − | 0.757964i | \(-0.273806\pi\) |
−0.519295 | + | 0.854595i | \(0.673806\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.23607 | − | 3.80423i | −0.197929 | − | 0.609164i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.0000 | −1.52499 | −0.762493 | − | 0.646997i | \(-0.776025\pi\) | ||||
−0.762493 | + | 0.646997i | \(0.776025\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.00000 | 0.894427 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.927051 | − | 2.85317i | −0.132436 | − | 0.407596i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.85410 | − | 3.52671i | −0.679710 | − | 0.493838i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.85410 | + | 5.70634i | −0.254680 | + | 0.783826i | 0.739212 | + | 0.673473i | \(0.235198\pi\) |
−0.993892 | + | 0.110353i | \(0.964802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.47214 | − | 7.60845i | 0.327442 | − | 1.00776i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.42705 | − | 1.76336i | −0.315975 | − | 0.229569i | 0.418481 | − | 0.908226i | \(-0.362563\pi\) |
−0.734456 | + | 0.678656i | \(0.762563\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.23607 | − | 3.80423i | −0.158262 | − | 0.487081i | 0.840215 | − | 0.542254i | \(-0.182429\pi\) |
−0.998477 | + | 0.0551729i | \(0.982429\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.23607 | − | 2.35114i | 0.407706 | − | 0.296216i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.0000 | 1.48842 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | −0.122169 | −0.0610847 | − | 0.998133i | \(-0.519456\pi\) | ||||
−0.0610847 | + | 0.998133i | \(0.519456\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.42705 | − | 1.76336i | 0.292183 | − | 0.212283i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.63525 | + | 14.2658i | 0.550104 | + | 1.69304i | 0.708536 | + | 0.705675i | \(0.249356\pi\) |
−0.158432 | + | 0.987370i | \(0.550644\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.23607 | + | 2.35114i | 0.378753 | + | 0.275180i | 0.760831 | − | 0.648950i | \(-0.224791\pi\) |
−0.382078 | + | 0.924130i | \(0.624791\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.23607 | − | 3.80423i | 0.142729 | − | 0.439274i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.618034 | − | 1.90211i | 0.0695343 | − | 0.214004i | −0.910251 | − | 0.414057i | \(-0.864111\pi\) |
0.979785 | + | 0.200053i | \(0.0641114\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.85410 | + | 5.70634i | 0.203514 | + | 0.626352i | 0.999771 | + | 0.0213936i | \(0.00681031\pi\) |
−0.796257 | + | 0.604959i | \(0.793190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.5623 | − | 10.5801i | 1.57950 | − | 1.14758i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.00000 | −0.953998 | −0.476999 | − | 0.878904i | \(-0.658275\pi\) | ||||
−0.476999 | + | 0.878904i | \(0.658275\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.47214 | − | 4.70228i | 0.678464 | − | 0.492933i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.54508 | + | 4.75528i | 0.160218 | + | 0.493100i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 19.4164 | + | 14.1068i | 1.99208 | + | 1.44733i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.16312 | + | 6.65740i | −0.219631 | + | 0.675956i | 0.779161 | + | 0.626824i | \(0.215646\pi\) |
−0.998792 | + | 0.0491321i | \(0.984354\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.56231 | − | 17.1190i | 0.553470 | − | 1.70341i | −0.146480 | − | 0.989214i | \(-0.546794\pi\) |
0.699950 | − | 0.714192i | \(-0.253206\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.47214 | − | 4.70228i | −0.637719 | − | 0.463330i | 0.221347 | − | 0.975195i | \(-0.428955\pi\) |
−0.859066 | + | 0.511865i | \(0.828955\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.85410 | − | 5.70634i | −0.180942 | − | 0.556882i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.85410 | + | 3.52671i | −0.469264 | + | 0.340940i | −0.797154 | − | 0.603776i | \(-0.793662\pi\) |
0.327891 | + | 0.944716i | \(0.393662\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.00000 | −0.0949158 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.1353 | − | 8.81678i | 1.14159 | − | 0.829413i | 0.154249 | − | 0.988032i | \(-0.450704\pi\) |
0.987340 | + | 0.158619i | \(0.0507042\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.78115 | + | 8.55951i | 0.259344 | + | 0.798178i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.47214 | − | 4.70228i | −0.598349 | − | 0.434726i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.70820 | − | 11.4127i | 0.339930 | − | 1.04620i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.42705 | − | 1.76336i | −0.217082 | − | 0.157719i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.94427 | − | 15.2169i | −0.438733 | − | 1.35028i | −0.889212 | − | 0.457495i | \(-0.848747\pi\) |
0.450479 | − | 0.892787i | \(-0.351253\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.09017 | − | 5.87785i | 0.712300 | − | 0.517516i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.00000 | −0.524222 | −0.262111 | − | 0.965038i | \(-0.584419\pi\) | ||||
−0.262111 | + | 0.965038i | \(0.584419\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.0000 | 1.38738 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −12.1353 | + | 8.81678i | −1.04444 | + | 0.758827i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.78115 | + | 8.55951i | 0.237610 | + | 0.731288i | 0.996764 | + | 0.0803778i | \(0.0256127\pi\) |
−0.759155 | + | 0.650910i | \(0.774387\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.3262 | − | 8.22899i | −0.960679 | − | 0.697974i | −0.00737063 | − | 0.999973i | \(-0.502346\pi\) |
−0.953308 | + | 0.301999i | \(0.902346\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.42705 | + | 1.76336i | 0.200180 | + | 0.145439i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.85410 | + | 5.70634i | 0.151894 | + | 0.467482i | 0.997833 | − | 0.0657982i | \(-0.0209593\pi\) |
−0.845939 | + | 0.533280i | \(0.820959\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.09017 | − | 5.87785i | 0.658369 | − | 0.478333i | −0.207743 | − | 0.978183i | \(-0.566612\pi\) |
0.866112 | + | 0.499851i | \(0.166612\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −12.0000 | −0.970143 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.0000 | −1.20483 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.04508 | + | 2.93893i | −0.322833 | + | 0.234552i | −0.737383 | − | 0.675474i | \(-0.763939\pi\) |
0.414550 | + | 0.910026i | \(0.363939\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.85410 | − | 5.70634i | −0.147040 | − | 0.452542i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.85410 | + | 3.52671i | 0.382557 | + | 0.277944i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.23607 | + | 3.80423i | −0.0968163 | + | 0.297970i | −0.987723 | − | 0.156217i | \(-0.950070\pi\) |
0.890906 | + | 0.454187i | \(0.150070\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.70820 | + | 11.4127i | −0.286949 | + | 0.883140i | 0.698858 | + | 0.715260i | \(0.253692\pi\) |
−0.985808 | + | 0.167879i | \(0.946308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.42705 | − | 1.76336i | −0.186696 | − | 0.135643i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.94427 | − | 15.2169i | −0.378098 | − | 1.16367i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.5623 | + | 10.5801i | −1.10715 | + | 0.804393i | −0.982213 | − | 0.187772i | \(-0.939873\pi\) |
−0.124939 | + | 0.992164i | \(0.539873\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.00000 | 0.604743 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.00000 | 0.225494 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.28115 | − | 5.29007i | 0.544219 | − | 0.395398i | −0.281431 | − | 0.959582i | \(-0.590809\pi\) |
0.825649 | + | 0.564183i | \(0.190809\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.01722 | − | 12.3637i | −0.298598 | − | 0.918989i | −0.981989 | − | 0.188937i | \(-0.939496\pi\) |
0.683392 | − | 0.730052i | \(-0.260504\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.23607 | + | 2.35114i | 0.239217 | + | 0.173801i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.927051 | − | 2.85317i | 0.0681581 | − | 0.209769i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.09017 | + | 9.51057i | −0.224777 | + | 0.691792i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.9894 | + | 12.3435i | 1.22931 | + | 0.893144i | 0.996838 | − | 0.0794603i | \(-0.0253197\pi\) |
0.232469 | + | 0.972604i | \(0.425320\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.18034 | + | 19.0211i | 0.444871 | + | 1.36917i | 0.882626 | + | 0.470077i | \(0.155774\pi\) |
−0.437755 | + | 0.899094i | \(0.644226\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.70820 | + | 7.05342i | −0.695219 | + | 0.505106i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000 | 0.567105 | 0.283552 | − | 0.958957i | \(-0.408487\pi\) | ||||
0.283552 | + | 0.958957i | \(0.408487\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.809017 | − | 0.587785i | 0.0570637 | − | 0.0414592i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.85410 | − | 5.70634i | 0.128869 | − | 0.396618i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.18034 | − | 19.0211i | 0.425472 | − | 1.30947i | −0.477069 | − | 0.878866i | \(-0.658301\pi\) |
0.902541 | − | 0.430603i | \(-0.141699\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.1353 | − | 8.81678i | −0.831494 | − | 0.604116i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.27051 | + | 28.5317i | 0.632244 | + | 1.94585i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.09017 | + | 5.87785i | −0.549197 | + | 0.399015i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.00000 | −0.270295 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −24.0000 | −1.61441 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.7533 | + | 9.99235i | −0.920988 | + | 0.669137i | −0.943770 | − | 0.330603i | \(-0.892748\pi\) |
0.0227815 | + | 0.999740i | \(0.492748\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.47214 | − | 7.60845i | −0.164809 | − | 0.507230i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.85410 | − | 3.52671i | −0.322178 | − | 0.234076i | 0.414926 | − | 0.909855i | \(-0.363807\pi\) |
−0.737104 | + | 0.675779i | \(0.763807\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.01722 | + | 12.3637i | −0.265465 | + | 0.817019i | 0.726120 | + | 0.687568i | \(0.241321\pi\) |
−0.991586 | + | 0.129451i | \(0.958679\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.41641 | + | 22.8254i | −0.485865 | + | 1.49534i | 0.344859 | + | 0.938654i | \(0.387927\pi\) |
−0.830724 | + | 0.556684i | \(0.812073\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.618034 | + | 1.90211i | 0.0401456 | + | 0.123556i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.85410 | + | 3.52671i | −0.313986 | + | 0.228124i | −0.733605 | − | 0.679576i | \(-0.762164\pi\) |
0.419619 | + | 0.907700i | \(0.362164\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.00000 | 0.515325 | 0.257663 | − | 0.966235i | \(-0.417048\pi\) | ||||
0.257663 | + | 0.966235i | \(0.417048\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.0000 | 1.02640 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.28115 | + | 5.29007i | −0.465176 | + | 0.337970i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.88854 | − | 30.4338i | −0.629193 | − | 1.93646i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.85410 | − | 3.52671i | −0.307616 | − | 0.223496i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.78115 | + | 8.55951i | −0.175545 | + | 0.540271i | −0.999658 | − | 0.0261539i | \(-0.991674\pi\) |
0.824113 | + | 0.566425i | \(0.191674\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.56231 | + | 17.1190i | −0.348325 | + | 1.07203i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.5623 | + | 10.5801i | 0.908372 | + | 0.659971i | 0.940603 | − | 0.339510i | \(-0.110261\pi\) |
−0.0322308 | + | 0.999480i | \(0.510261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.618034 | − | 1.90211i | −0.0384028 | − | 0.118192i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.0000 | 1.10993 | 0.554964 | − | 0.831875i | \(-0.312732\pi\) | ||||
0.554964 | + | 0.831875i | \(0.312732\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.0000 | 1.10573 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.28115 | − | 5.29007i | 0.445599 | − | 0.323747i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.85410 | − | 5.70634i | −0.113047 | − | 0.347922i | 0.878488 | − | 0.477764i | \(-0.158553\pi\) |
−0.991535 | + | 0.129843i | \(0.958553\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.1803 | − | 11.7557i | −0.982886 | − | 0.714108i | −0.0245340 | − | 0.999699i | \(-0.507810\pi\) |
−0.958352 | + | 0.285591i | \(0.907810\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.47214 | + | 7.60845i | −0.149620 | + | 0.460484i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.09017 | + | 9.51057i | −0.185670 | + | 0.571434i | −0.999959 | − | 0.00902525i | \(-0.997127\pi\) |
0.814289 | + | 0.580460i | \(0.197127\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.09017 | + | 5.87785i | 0.484346 | + | 0.351898i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.56231 | − | 17.1190i | −0.331819 | − | 1.02123i | −0.968268 | − | 0.249916i | \(-0.919597\pi\) |
0.636448 | − | 0.771319i | \(-0.280403\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.23607 | − | 2.35114i | 0.192364 | − | 0.139761i | −0.487434 | − | 0.873160i | \(-0.662067\pi\) |
0.679799 | + | 0.733399i | \(0.262067\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −24.0000 | −1.42164 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.3713 | + | 11.1679i | −0.904195 | + | 0.656936i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.16312 | − | 6.65740i | −0.126804 | − | 0.390263i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.78115 | + | 8.55951i | −0.161925 | + | 0.498354i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.70820 | − | 11.4127i | 0.214451 | − | 0.660012i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.1803 | + | 11.7557i | 0.932619 | + | 0.677588i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.56231 | + | 17.1190i | 0.319546 | + | 0.983462i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.70820 | + | 7.05342i | −0.555890 | + | 0.403878i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.0000 | −0.913168 | −0.456584 | − | 0.889680i | \(-0.650927\pi\) | ||||
−0.456584 | + | 0.889680i | \(0.650927\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.00000 | 0.455104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.70820 | + | 7.05342i | −0.550502 | + | 0.399963i | −0.827970 | − | 0.560772i | \(-0.810505\pi\) |
0.277469 | + | 0.960735i | \(0.410505\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.309017 | − | 0.951057i | −0.0174667 | − | 0.0537569i | 0.941943 | − | 0.335772i | \(-0.108997\pi\) |
−0.959410 | + | 0.282015i | \(0.908997\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.70820 | − | 7.05342i | −0.546995 | − | 0.397415i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.1976 | − | 31.3849i | 0.572752 | − | 1.76275i | −0.0709570 | − | 0.997479i | \(-0.522605\pi\) |
0.643709 | − | 0.765270i | \(-0.277395\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.85410 | − | 5.70634i | 0.103486 | − | 0.318497i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −38.8328 | − | 28.2137i | −2.16072 | − | 1.56985i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.94427 | − | 15.2169i | −0.274259 | − | 0.844082i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.61803 | + | 1.17557i | −0.0894775 | + | 0.0650092i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.00000 | −0.384755 | −0.192377 | − | 0.981321i | \(-0.561620\pi\) | ||||
−0.192377 | + | 0.981321i | \(0.561620\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.61803 | + | 1.17557i | −0.0886677 | + | 0.0644209i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.927051 | + | 2.85317i | 0.0506502 | + | 0.155885i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.61803 | − | 1.17557i | −0.0881399 | − | 0.0640374i | 0.542843 | − | 0.839834i | \(-0.317348\pi\) |
−0.630982 | + | 0.775797i | \(0.717348\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.63525 | + | 14.2658i | −0.251752 | + | 0.774814i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.18034 | + | 19.0211i | −0.333707 | + | 1.02704i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.28115 | − | 5.29007i | −0.392004 | − | 0.284808i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.70820 | + | 11.4127i | 0.199067 | + | 0.612665i | 0.999905 | + | 0.0137839i | \(0.00438768\pi\) |
−0.800838 | + | 0.598881i | \(0.795612\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.3262 | + | 8.22899i | −0.606280 | + | 0.440488i | −0.848102 | − | 0.529833i | \(-0.822255\pi\) |
0.241823 | + | 0.970320i | \(0.422255\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 20.0000 | 1.06752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.0000 | −1.11772 | −0.558859 | − | 0.829263i | \(-0.688761\pi\) | ||||
−0.558859 | + | 0.829263i | \(0.688761\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 36.4058 | − | 26.4503i | 1.93222 | − | 1.40384i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.70820 | + | 11.4127i | 0.196259 | + | 0.604023i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.1246 | + | 21.1603i | 1.53714 | + | 1.11680i | 0.952098 | + | 0.305792i | \(0.0989211\pi\) |
0.585040 | + | 0.811005i | \(0.301079\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.9058 | − | 42.7975i | 0.731882 | − | 2.25250i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.70820 | − | 11.4127i | 0.194096 | − | 0.597367i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.3713 | + | 11.1679i | 0.802377 | + | 0.582961i | 0.911610 | − | 0.411055i | \(-0.134840\pi\) |
−0.109234 | + | 0.994016i | \(0.534840\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.70820 | − | 7.05342i | 0.504025 | − | 0.366195i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.0000 | −0.517780 | −0.258890 | − | 0.965907i | \(-0.583357\pi\) | ||||
−0.258890 | + | 0.965907i | \(0.583357\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.00000 | 0.154919 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.96149 | + | 27.5806i | 0.460321 | + | 1.41672i | 0.864773 | + | 0.502163i | \(0.167462\pi\) |
−0.404452 | + | 0.914559i | \(0.632538\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.9443 | + | 9.40456i | 0.663155 | + | 0.481810i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.34346 | + | 25.6785i | −0.426331 | + | 1.31211i | 0.475383 | + | 0.879779i | \(0.342309\pi\) |
−0.901714 | + | 0.432333i | \(0.857691\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.18034 | − | 19.0211i | 0.314164 | − | 0.966898i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.8435 | + | 15.8702i | 1.10751 | + | 0.804651i | 0.982269 | − | 0.187476i | \(-0.0600305\pi\) |
0.125238 | + | 0.992127i | \(0.460031\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.56231 | − | 17.1190i | −0.281298 | − | 0.865746i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.85410 | − | 3.52671i | 0.244857 | − | 0.177899i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.00000 | −0.301893 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −34.0000 | −1.70641 | −0.853206 | − | 0.521575i | \(-0.825345\pi\) | ||||
−0.853206 | + | 0.521575i | \(0.825345\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −12.9443 | + | 9.40456i | −0.648024 | + | 0.470817i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.56231 | + | 17.1190i | 0.277768 | + | 0.854883i | 0.988474 | + | 0.151393i | \(0.0483759\pi\) |
−0.710705 | + | 0.703490i | \(0.751624\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.1803 | + | 11.7557i | 0.806000 | + | 0.585593i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.927051 | + | 2.85317i | −0.0460655 | + | 0.141775i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.618034 | − | 1.90211i | 0.0305598 | − | 0.0940534i | −0.934613 | − | 0.355666i | \(-0.884254\pi\) |
0.965173 | + | 0.261612i | \(0.0842542\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.28115 | − | 5.29007i | −0.359153 | − | 0.260940i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.85410 | + | 5.70634i | 0.0912344 | + | 0.280791i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.5623 | − | 10.5801i | 0.714835 | − | 0.519358i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.0000 | 0.685583 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.0000 | 0.586238 | 0.293119 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293119 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.09017 | − | 5.87785i | 0.394291 | − | 0.286469i | −0.372921 | − | 0.927863i | \(-0.621644\pi\) |
0.767211 | + | 0.641394i | \(0.221644\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −19.4164 | − | 14.1068i | −0.941834 | − | 0.684283i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.47214 | + | 7.60845i | −0.119635 | + | 0.368199i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.56231 | − | 17.1190i | 0.267927 | − | 0.824594i | −0.723078 | − | 0.690767i | \(-0.757273\pi\) |
0.991005 | − | 0.133827i | \(-0.0427268\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.4615 | − | 17.0458i | −1.12749 | − | 0.819168i | −0.142160 | − | 0.989844i | \(-0.545405\pi\) |
−0.985327 | + | 0.170676i | \(0.945405\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 19.4164 | − | 14.1068i | 0.928813 | − | 0.674822i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.00000 | 0.381819 | 0.190910 | − | 0.981608i | \(-0.438856\pi\) | ||||
0.190910 | + | 0.981608i | \(0.438856\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.00000 | 0.285714 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.9894 | − | 12.3435i | 0.807189 | − | 0.586457i | −0.105825 | − | 0.994385i | \(-0.533748\pi\) |
0.913014 | + | 0.407928i | \(0.133748\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.34346 | + | 25.6785i | 0.395518 | + | 1.21728i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.85410 | − | 3.52671i | −0.229591 | − | 0.166808i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.927051 | − | 2.85317i | 0.0437502 | − | 0.134649i | −0.926795 | − | 0.375566i | \(-0.877448\pi\) |
0.970546 | + | 0.240917i | \(0.0774482\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.09017 | + | 9.51057i | −0.145189 | + | 0.446845i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −19.4164 | − | 14.1068i | −0.910255 | − | 0.661339i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.65248 | − | 26.6296i | −0.404746 | − | 1.24568i | −0.921107 | − | 0.389309i | \(-0.872714\pi\) |
0.516362 | − | 0.856371i | \(-0.327286\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 24.2705 | − | 17.6336i | 1.13285 | − | 0.823064i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.0000 | 0.558896 | 0.279448 | − | 0.960161i | \(-0.409849\pi\) | ||||
0.279448 | + | 0.960161i | \(0.409849\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.0000 | 1.06890 | 0.534450 | − | 0.845200i | \(-0.320519\pi\) | ||||
0.534450 | + | 0.845200i | \(0.320519\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 12.1353 | − | 8.81678i | 0.562759 | − | 0.408868i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.927051 | + | 2.85317i | 0.0428988 | + | 0.132029i | 0.970212 | − | 0.242257i | \(-0.0778878\pi\) |
−0.927313 | + | 0.374286i | \(0.877888\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.61803 | + | 1.17557i | 0.0747139 | + | 0.0542828i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.54508 | − | 4.75528i | 0.0711938 | − | 0.219112i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.88854 | − | 30.4338i | 0.453718 | − | 1.39640i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.70820 | − | 7.05342i | −0.444508 | − | 0.322954i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.70820 | − | 11.4127i | −0.169432 | − | 0.521459i | 0.829903 | − | 0.557907i | \(-0.188395\pi\) |
−0.999336 | + | 0.0364486i | \(0.988395\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.23607 | + | 2.35114i | −0.147552 | + | 0.107203i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.00000 | −0.273009 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.0000 | 0.953561 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.4615 | + | 17.0458i | −1.06314 | + | 0.772418i | −0.974667 | − | 0.223661i | \(-0.928199\pi\) |
−0.0884747 | + | 0.996078i | \(0.528199\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.23607 | − | 3.80423i | −0.0558969 | − | 0.172033i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.4164 | − | 14.1068i | −0.876250 | − | 0.636633i | 0.0560065 | − | 0.998430i | \(-0.482163\pi\) |
−0.932257 | + | 0.361797i | \(0.882163\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.27051 | − | 28.5317i | 0.415839 | − | 1.27982i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.23607 | + | 2.35114i | 0.144866 | + | 0.105252i | 0.657858 | − | 0.753142i | \(-0.271463\pi\) |
−0.512992 | + | 0.858394i | \(0.671463\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.70820 | − | 11.4127i | −0.165670 | − | 0.509881i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.2705 | − | 17.6336i | 1.08217 | − | 0.786241i | 0.104109 | − | 0.994566i | \(-0.466801\pi\) |
0.978060 | + | 0.208324i | \(0.0668010\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −54.0000 | −2.40297 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.00000 | 0.133235 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.9894 | − | 12.3435i | 0.753040 | − | 0.547116i | −0.143728 | − | 0.989617i | \(-0.545909\pi\) |
0.896768 | + | 0.442502i | \(0.145909\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.47214 | − | 7.60845i | −0.109361 | − | 0.336578i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 32.3607 | + | 23.5114i | 1.42876 | + | 1.03805i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.41641 | + | 22.8254i | −0.326806 | + | 1.00581i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.56231 | − | 17.1190i | 0.244158 | − | 0.751441i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.8435 | + | 15.8702i | 0.956979 | + | 0.695286i | 0.952447 | − | 0.304704i | \(-0.0985574\pi\) |
0.00453207 | + | 0.999990i | \(0.498557\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.47214 | + | 7.60845i | 0.108099 | + | 0.332694i | 0.990445 | − | 0.137906i | \(-0.0440373\pi\) |
−0.882346 | + | 0.470601i | \(0.844037\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.47214 | + | 4.70228i | −0.282467 | + | 0.205224i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 30.0000 | 1.30682 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.0000 | −0.608696 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.85410 | − | 3.52671i | 0.210650 | − | 0.153046i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.5623 | + | 10.5801i | 0.629583 | + | 0.457419i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.78115 | + | 8.55951i | −0.120016 | + | 0.369370i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.94427 | + | 15.2169i | −0.212571 | + | 0.654226i | 0.786746 | + | 0.617277i | \(0.211764\pi\) |
−0.999317 | + | 0.0369493i | \(0.988236\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.5172 | + | 7.64121i | 0.451337 | + | 0.327916i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.85410 | − | 5.70634i | −0.0794210 | − | 0.244433i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.47214 | + | 4.70228i | −0.276729 | + | 0.201055i | −0.717489 | − | 0.696570i | \(-0.754709\pi\) |
0.440761 | + | 0.897625i | \(0.354709\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.00000 | 0.341432 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.23607 | + | 2.35114i | −0.137612 | + | 0.0999807i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.927051 | + | 2.85317i | 0.0393511 | + | 0.121110i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.5623 | + | 10.5801i | 0.617025 | + | 0.448295i | 0.851881 | − | 0.523735i | \(-0.175462\pi\) |
−0.234856 | + | 0.972030i | \(0.575462\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.3607 | − | 38.0423i | 0.522801 | − | 1.60902i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.1246 | + | 34.2380i | −0.468846 | + | 1.44296i | 0.385233 | + | 0.922819i | \(0.374121\pi\) |
−0.854080 | + | 0.520142i | \(0.825879\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −36.4058 | − | 26.4503i | −1.53160 | − | 1.11277i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.618034 | + | 1.90211i | 0.0259550 | + | 0.0798812i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 44.0000 | 1.84134 | 0.920671 | − | 0.390339i | \(-0.127642\pi\) | ||||
0.920671 | + | 0.390339i | \(0.127642\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21.0000 | −0.877288 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.70820 | − | 7.05342i | 0.404860 | − | 0.294148i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.25329 | + | 16.1680i | 0.218697 | + | 0.673081i | 0.998870 | + | 0.0475174i | \(0.0151309\pi\) |
−0.780173 | + | 0.625564i | \(0.784869\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.1803 | − | 11.7557i | −0.672432 | − | 0.488550i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.70820 | − | 11.4127i | 0.153842 | − | 0.473478i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.41641 | + | 22.8254i | −0.306631 | + | 0.943712i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.70820 | + | 7.05342i | 0.400700 | + | 0.291126i | 0.769826 | − | 0.638254i | \(-0.220343\pi\) |
−0.369126 | + | 0.929379i | \(0.620343\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.3607 | + | 38.0423i | 0.509313 | + | 1.56750i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.85410 | + | 3.52671i | −0.199671 | + | 0.145070i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −36.0000 | −1.47834 | −0.739171 | − | 0.673517i | \(-0.764783\pi\) | ||||
−0.739171 | + | 0.673517i | \(0.764783\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −36.0000 | −1.47586 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.47214 | + | 4.70228i | −0.264887 | + | 0.192452i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.0344 | − | 15.2824i | −0.858013 | − | 0.623383i | 0.0693308 | − | 0.997594i | \(-0.477914\pi\) |
−0.927344 | + | 0.374211i | \(0.877914\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.618034 | − | 1.90211i | 0.0251683 | − | 0.0774600i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.32624 | − | 13.3148i | 0.175597 | − | 0.540431i | −0.824064 | − | 0.566497i | \(-0.808298\pi\) |
0.999660 | + | 0.0260665i | \(0.00829818\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.8885 | + | 18.8091i | −1.04563 | + | 0.759694i | −0.971376 | − | 0.237546i | \(-0.923657\pi\) |
−0.0742521 | + | 0.997239i | \(0.523657\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.0000 | 0.724653 | 0.362326 | − | 0.932051i | \(-0.381983\pi\) | ||||
0.362326 | + | 0.932051i | \(0.381983\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.7533 | + | 9.99235i | −0.552791 | + | 0.401626i | −0.828814 | − | 0.559525i | \(-0.810984\pi\) |
0.276022 | + | 0.961151i | \(0.410984\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.63525 | + | 14.2658i | 0.186006 | + | 0.572469i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.5623 | + | 10.5801i | 0.583426 | + | 0.423884i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.96149 | + | 27.5806i | −0.358460 | + | 1.10323i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.85410 | + | 5.70634i | −0.0739279 | + | 0.227527i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.7877 | + | 25.2748i | 1.38488 | + | 1.00617i | 0.996405 | + | 0.0847121i | \(0.0269971\pi\) |
0.388472 | + | 0.921460i | \(0.373003\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.18034 | + | 19.0211i | 0.245646 | + | 0.756022i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −38.8328 | + | 28.2137i | −1.54103 | + | 1.11963i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.0000 | 0.475457 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −30.0000 | −1.18678 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.5517 | + | 22.9236i | −1.24622 | + | 0.905429i | −0.997996 | − | 0.0632750i | \(-0.979845\pi\) |
−0.248220 | + | 0.968704i | \(0.579845\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.01722 | − | 12.3637i | −0.158424 | − | 0.487578i | 0.840068 | − | 0.542481i | \(-0.182515\pi\) |
−0.998492 | + | 0.0549031i | \(0.982515\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −24.2705 | − | 17.6336i | −0.955650 | − | 0.694321i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.927051 | − | 2.85317i | 0.0364461 | − | 0.112170i | −0.931178 | − | 0.364564i | \(-0.881218\pi\) |
0.967624 | + | 0.252394i | \(0.0812180\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.09017 | − | 9.51057i | 0.121113 | − | 0.372748i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.42705 | − | 1.76336i | −0.0949778 | − | 0.0690054i | 0.539283 | − | 0.842125i | \(-0.318695\pi\) |
−0.634261 | + | 0.773119i | \(0.718695\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.56231 | + | 17.1190i | 0.217337 | + | 0.668895i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.47214 | + | 4.70228i | −0.252502 | + | 0.183453i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −42.0000 | −1.63609 | −0.818044 | − | 0.575156i | \(-0.804941\pi\) | ||||
−0.818044 | + | 0.575156i | \(0.804941\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.0000 | 0.661223 | 0.330612 | − | 0.943767i | \(-0.392745\pi\) | ||||
0.330612 | + | 0.943767i | \(0.392745\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 19.4164 | − | 14.1068i | 0.754071 | − | 0.547865i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14.8328 | − | 45.6507i | −0.575192 | − | 1.77026i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.25329 | − | 16.1680i | 0.203104 | − | 0.625089i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.5066 | + | 32.3359i | −0.404999 | + | 1.24646i | 0.515897 | + | 0.856650i | \(0.327459\pi\) |
−0.920896 | + | 0.389808i | \(0.872541\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 16.1803 | + | 11.7557i | 0.622782 | + | 0.452477i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.9787 | − | 39.9444i | −0.498812 | − | 1.53519i | −0.810930 | − | 0.585143i | \(-0.801038\pi\) |
0.312117 | − | 0.950044i | \(-0.398962\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.3262 | − | 8.22899i | 0.434661 | − | 0.315800i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.00000 | 0.229920 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 48.0000 | 1.83667 | 0.918334 | − | 0.395805i | \(-0.129534\pi\) | ||||
0.918334 | + | 0.395805i | \(0.129534\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.8435 | − | 15.8702i | 0.834596 | − | 0.606369i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.01722 | − | 12.3637i | −0.153267 | − | 0.471706i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −19.4164 | − | 14.1068i | −0.739706 | − | 0.537428i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.309017 | + | 0.951057i | −0.0117556 | + | 0.0361799i | −0.956762 | − | 0.290871i | \(-0.906055\pi\) |
0.945007 | + | 0.327051i | \(0.106055\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.9787 | + | 39.9444i | −0.492311 | + | 1.51518i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.41641 | − | 22.8254i | −0.280514 | − | 0.863334i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.5623 | + | 10.5801i | −0.550011 | + | 0.399606i | −0.827789 | − | 0.561039i | \(-0.810402\pi\) |
0.277779 | + | 0.960645i | \(0.410402\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.00000 | −0.301726 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −29.1246 | + | 21.1603i | −1.09534 | + | 0.795814i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.4336 | − | 35.1891i | −0.429399 | − | 1.32155i | −0.898719 | − | 0.438526i | \(-0.855501\pi\) |
0.469320 | − | 0.883028i | \(-0.344499\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.23607 | + | 2.35114i | 0.121362 | + | 0.0881747i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.63525 | + | 14.2658i | −0.173592 | + | 0.534260i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.85410 | − | 5.70634i | 0.0692427 | − | 0.213107i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −36.4058 | − | 26.4503i | −1.35771 | − | 0.986431i | −0.998587 | − | 0.0531392i | \(-0.983077\pi\) |
−0.359119 | − | 0.933292i | \(-0.616923\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.94427 | + | 15.2169i | 0.184134 | + | 0.566707i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.47214 | + | 4.70228i | −0.240701 | + | 0.174880i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.0000 | 0.630495 | 0.315248 | − | 0.949009i | \(-0.397912\pi\) | ||||
0.315248 | + | 0.949009i | \(0.397912\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −10.5172 | + | 7.64121i | −0.389527 | + | 0.283008i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.5410 | − | 57.0634i | −0.685764 | − | 2.11057i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.23607 | + | 2.35114i | 0.119527 | + | 0.0868414i | 0.645943 | − | 0.763386i | \(-0.276464\pi\) |
−0.526416 | + | 0.850227i | \(0.676464\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.78115 | − | 8.55951i | 0.102584 | − | 0.315722i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.5066 | + | 32.3359i | −0.386491 | + | 1.18950i | 0.548902 | + | 0.835886i | \(0.315046\pi\) |
−0.935393 | + | 0.353610i | \(0.884954\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 25.8885 | + | 18.8091i | 0.951039 | + | 0.690971i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.70820 | + | 11.4127i | 0.136041 | + | 0.418691i | 0.995750 | − | 0.0920925i | \(-0.0293555\pi\) |
−0.859710 | + | 0.510783i | \(0.829356\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.5623 | − | 10.5801i | 0.533522 | − | 0.387626i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.0000 | −0.439057 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.0000 | 0.438470 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.3156 | + | 20.5725i | −1.03325 | + | 0.750701i | −0.968957 | − | 0.247230i | \(-0.920480\pi\) |
−0.0642940 | + | 0.997931i | \(0.520480\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.78115 | − | 8.55951i | −0.101351 | − | 0.311926i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −24.2705 | − | 17.6336i | −0.883294 | − | 0.641751i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.79837 | + | 20.9232i | −0.247091 | + | 0.760468i | 0.748194 | + | 0.663480i | \(0.230921\pi\) |
−0.995285 | + | 0.0969886i | \(0.969079\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.1246 | − | 34.2380i | 0.403267 | − | 1.24113i | −0.519067 | − | 0.854734i | \(-0.673720\pi\) |
0.922334 | − | 0.386394i | \(-0.126280\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.23607 | − | 2.35114i | −0.117154 | − | 0.0851170i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 11.1246 | + | 34.2380i | 0.402211 | + | 1.23788i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.70820 | − | 7.05342i | 0.350543 | − | 0.254684i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.0000 | 1.58668 | 0.793340 | − | 0.608778i | \(-0.208340\pi\) | ||||
0.793340 | + | 0.608778i | \(0.208340\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.0000 | −0.648254 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −33.9787 | + | 24.6870i | −1.22213 | + | 0.887929i | −0.996275 | − | 0.0862321i | \(-0.972517\pi\) |
−0.225854 | + | 0.974161i | \(0.572517\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.18034 | + | 19.0211i | 0.222004 | + | 0.683259i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.61803 | + | 1.17557i | 0.0580466 | + | 0.0421734i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.1353 | + | 8.81678i | 0.433126 | + | 0.314684i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.88854 | + | 30.4338i | 0.352489 | + | 1.08485i | 0.957451 | + | 0.288594i | \(0.0931879\pi\) |
−0.604963 | + | 0.796254i | \(0.706812\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.5623 | + | 10.5801i | −0.518432 | + | 0.376663i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −30.0000 | −1.06668 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.0000 | 0.568177 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14.5623 | + | 10.5801i | −0.516472 | + | 0.375239i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.78115 | + | 8.55951i | 0.0985135 | + | 0.303193i | 0.988153 | − | 0.153469i | \(-0.0490446\pi\) |
−0.889640 | + | 0.456663i | \(0.849045\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.56231 | − | 17.1190i | 0.196534 | − | 0.604871i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.56231 | − | 17.1190i | 0.196046 | − | 0.603366i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.85410 | + | 3.52671i | 0.170872 | + | 0.124146i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.41641 | − | 22.8254i | −0.260747 | − | 0.802497i | −0.992643 | − | 0.121080i | \(-0.961364\pi\) |
0.731896 | − | 0.681417i | \(-0.238636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30.7426 | + | 22.3358i | −1.07952 | + | 0.784317i | −0.977599 | − | 0.210475i | \(-0.932499\pi\) |
−0.101921 | + | 0.994792i | \(0.532499\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.0000 | 0.701431 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.0000 | 0.420342 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 64.7214 | − | 47.0228i | 2.26431 | − | 1.64512i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.94427 | + | 15.2169i | 0.172767 | + | 0.531722i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.2705 | − | 17.6336i | −0.847047 | − | 0.615415i | 0.0772835 | − | 0.997009i | \(-0.475375\pi\) |
−0.924330 | + | 0.381594i | \(0.875375\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.2877 | + | 40.8954i | −0.463181 | + | 1.42553i | 0.398074 | + | 0.917353i | \(0.369679\pi\) |
−0.861256 | + | 0.508172i | \(0.830321\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.1246 | + | 34.2380i | −0.386841 | + | 1.19057i | 0.548296 | + | 0.836285i | \(0.315277\pi\) |
−0.935136 | + | 0.354288i | \(0.884723\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.3713 | + | 11.1679i | 0.533868 | + | 0.387878i | 0.821803 | − | 0.569772i | \(-0.192969\pi\) |
−0.287935 | + | 0.957650i | \(0.592969\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.09017 | − | 9.51057i | −0.107197 | − | 0.329918i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.5623 | − | 10.5801i | 0.504554 | − | 0.366580i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 36.0000 | 1.24583 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −25.0000 | −0.864126 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31.5517 | − | 22.9236i | 1.08928 | − | 0.791411i | 0.110006 | − | 0.993931i | \(-0.464913\pi\) |
0.979278 | + | 0.202519i | \(0.0649129\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.96149 | − | 27.5806i | −0.309017 | − | 0.951057i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14.5623 | + | 10.5801i | 0.501552 | + | 0.364399i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.78115 | + | 8.55951i | −0.0956746 | + | 0.294456i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.23607 | + | 3.80423i | −0.0424217 | + | 0.130561i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.42705 | − | 1.76336i | −0.0831982 | − | 0.0604471i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.7426 | + | 36.1401i | 0.402061 | + | 1.23742i | 0.923325 | + | 0.384020i | \(0.125461\pi\) |
−0.521264 | + | 0.853395i | \(0.674539\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −38.8328 | + | 28.2137i | −1.32805 | + | 0.964888i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.0000 | 0.819824 | 0.409912 | − | 0.912125i | \(-0.365559\pi\) | ||||
0.409912 | + | 0.912125i | \(0.365559\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.0000 | −0.852989 | −0.426494 | − | 0.904490i | \(-0.640252\pi\) | ||||
−0.426494 | + | 0.904490i | \(0.640252\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.8328 | + | 45.6507i | 0.504915 | + | 1.55397i | 0.800914 | + | 0.598780i | \(0.204348\pi\) |
−0.295999 | + | 0.955188i | \(0.595652\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 43.6869 | + | 31.7404i | 1.48540 | + | 1.07921i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.87132 | − | 18.0701i | 0.199401 | − | 0.613692i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.23607 | − | 3.80423i | 0.0418826 | − | 0.128901i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11.3262 | − | 8.22899i | −0.383335 | − | 0.278509i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.85410 | + | 5.70634i | 0.0626801 | + | 0.192909i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 42.0689 | − | 30.5648i | 1.42057 | − | 1.03210i | 0.428887 | − | 0.903358i | \(-0.358906\pi\) |
0.991678 | − | 0.128743i | \(-0.0410942\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.0000 | −0.909653 | −0.454827 | − | 0.890580i | \(-0.650299\pi\) | ||||
−0.454827 | + | 0.890580i | \(0.650299\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.23607 | − | 2.35114i | 0.108902 | − | 0.0791222i | −0.532001 | − | 0.846744i | \(-0.678560\pi\) |
0.640904 | + | 0.767621i | \(0.278560\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.78115 | − | 8.55951i | −0.0934874 | − | 0.287725i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24.2705 | − | 17.6336i | −0.814924 | − | 0.592077i | 0.100330 | − | 0.994954i | \(-0.468010\pi\) |
−0.915254 | + | 0.402877i | \(0.868010\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.88854 | + | 30.4338i | −0.331651 | + | 1.02072i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.8435 | − | 15.8702i | −0.730146 | − | 0.530482i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.70820 | + | 11.4127i | 0.123813 | + | 0.381058i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.0000 | −1.19933 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −20.0000 | −0.665558 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −31.5517 | + | 22.9236i | −1.04881 | + | 0.762007i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.23607 | − | 3.80423i | −0.0410430 | − | 0.126317i | 0.928436 | − | 0.371493i | \(-0.121154\pi\) |
−0.969479 | + | 0.245176i | \(0.921154\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 29.1246 | + | 21.1603i | 0.966002 | + | 0.701842i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.70820 | − | 11.4127i | 0.122858 | − | 0.378119i | −0.870647 | − | 0.491909i | \(-0.836299\pi\) |
0.993505 | + | 0.113790i | \(0.0362992\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.70820 | − | 11.4127i | 0.122589 | − | 0.377292i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.70820 | + | 7.05342i | 0.320593 | + | 0.232925i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.5066 | − | 32.3359i | −0.346580 | − | 1.06666i | −0.960732 | − | 0.277476i | \(-0.910502\pi\) |
0.614152 | − | 0.789187i | \(-0.289498\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.9443 | − | 9.40456i | 0.426528 | − | 0.309891i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −60.0000 | −1.97492 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.00000 | −0.131519 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12.9443 | − | 9.40456i | 0.425146 | − | 0.308886i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.56231 | + | 17.1190i | 0.182493 | + | 0.561657i | 0.999896 | − | 0.0144098i | \(-0.00458693\pi\) |
−0.817403 | + | 0.576066i | \(0.804587\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.4164 | + | 14.1068i | 0.636347 | + | 0.462333i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.70820 | − | 11.4127i | 0.121401 | − | 0.373634i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.88854 | − | 30.4338i | 0.323045 | − | 0.994229i | −0.649271 | − | 0.760557i | \(-0.724926\pi\) |
0.972316 | − | 0.233672i | \(-0.0750742\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.809017 | + | 0.587785i | 0.0264013 | + | 0.0191816i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.27051 | − | 28.5317i | −0.302210 | − | 0.930107i | −0.980704 | − | 0.195500i | \(-0.937367\pi\) |
0.678494 | − | 0.734606i | \(-0.262633\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 30.0000 | 0.975900 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.0000 | 0.877382 | 0.438691 | − | 0.898638i | \(-0.355442\pi\) | ||||
0.438691 | + | 0.898638i | \(0.355442\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.9443 | + | 9.40456i | −0.420189 | + | 0.305285i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.1976 | + | 31.3849i | 0.330679 | + | 1.01772i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33.9787 | − | 24.6870i | −1.10068 | − | 0.799690i | −0.119508 | − | 0.992833i | \(-0.538132\pi\) |
−0.981171 | + | 0.193143i | \(0.938132\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.4681 | − | 59.9166i | 0.629972 | − | 1.93885i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.56231 | − | 17.1190i | 0.179616 | − | 0.552802i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.85410 | + | 3.52671i | 0.156584 | + | 0.113765i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.70820 | − | 11.4127i | −0.119495 | − | 0.367768i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 48.5410 | − | 35.2671i | 1.56259 | − | 1.13529i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.0000 | −0.514525 | −0.257263 | − | 0.966342i | \(-0.582821\pi\) | ||||
−0.257263 | + | 0.966342i | \(0.582821\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 48.0000 | 1.54198 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.1353 | − | 8.81678i | 0.389439 | − | 0.282944i | −0.375787 | − | 0.926706i | \(-0.622627\pi\) |
0.765226 | + | 0.643762i | \(0.222627\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.65248 | + | 26.6296i | 0.277386 | + | 0.853705i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 12.9443 | + | 9.40456i | 0.414548 | + | 0.301187i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.9058 | − | 42.7975i | 0.444885 | − | 1.36921i | −0.437725 | − | 0.899109i | \(-0.644216\pi\) |
0.882610 | − | 0.470106i | \(-0.155784\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.23607 | + | 3.80423i | −0.0394646 | + | 0.121460i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −36.4058 | − | 26.4503i | −1.16116 | − | 0.843635i | −0.171239 | − | 0.985230i | \(-0.554777\pi\) |
−0.989925 | + | 0.141595i | \(0.954777\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.56231 | − | 17.1190i | −0.177230 | − | 0.545457i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 30.0000 | 0.953945 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.0000 | −0.508257 | −0.254128 | − | 0.967170i | \(-0.581789\pi\) | ||||
−0.254128 | + | 0.967170i | \(0.581789\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.66312 | − | 4.11450i | 0.179714 | − | 0.130570i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.41641 | − | 22.8254i | −0.235116 | − | 0.723612i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.09017 | + | 5.87785i | 0.256218 | + | 0.186153i | 0.708478 | − | 0.705733i | \(-0.249382\pi\) |
−0.452260 | + | 0.891886i | \(0.649382\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.54508 | − | 4.75528i | 0.0488843 | − | 0.150450i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))