Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(257,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.ca (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 353.5 | ||
Root | \(-0.268067 - 1.71118i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.353 |
Dual form | 1008.2.ca.d.257.5 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.134439 | − | 1.72683i | 0.0776185 | − | 0.996983i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.842869 | + | 1.45989i | −0.376942 | + | 0.652883i | −0.990616 | − | 0.136677i | \(-0.956358\pi\) |
0.613673 | + | 0.789560i | \(0.289691\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.27938 | − | 1.34329i | 0.861524 | − | 0.507717i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.96385 | − | 0.464306i | −0.987951 | − | 0.154769i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.38216 | + | 1.95269i | −1.01976 | + | 0.588758i | −0.914034 | − | 0.405637i | \(-0.867050\pi\) |
−0.105725 | + | 0.994395i | \(0.533716\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.24391 | + | 3.02757i | −1.45440 | + | 0.839698i | −0.998727 | − | 0.0504496i | \(-0.983935\pi\) |
−0.455673 | + | 0.890147i | \(0.650601\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.40766 | + | 1.65175i | 0.621656 | + | 0.426481i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.201244 | + | 0.348565i | −0.0488088 | + | 0.0845393i | −0.889398 | − | 0.457134i | \(-0.848876\pi\) |
0.840589 | + | 0.541674i | \(0.182209\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.145617 | − | 0.0840718i | 0.0334067 | − | 0.0192874i | −0.483204 | − | 0.875508i | \(-0.660527\pi\) |
0.516610 | + | 0.856221i | \(0.327194\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.01319 | − | 4.11668i | −0.439315 | − | 0.898333i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.69373 | − | 4.44198i | −1.60425 | − | 0.926216i | −0.990623 | − | 0.136623i | \(-0.956375\pi\) |
−0.613630 | − | 0.789593i | \(-0.710291\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.07914 | + | 1.86913i | 0.215829 | + | 0.373827i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.20023 | + | 5.05563i | −0.230985 | + | 0.972957i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.15380 | − | 3.55290i | −1.14273 | − | 0.659757i | −0.195627 | − | 0.980678i | \(-0.562674\pi\) |
−0.947106 | + | 0.320921i | \(0.896007\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.28766i | − | 1.12930i | −0.825331 | − | 0.564649i | \(-0.809012\pi\) | ||
0.825331 | − | 0.564649i | \(-0.190988\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.91726 | + | 6.10292i | 0.507830 | + | 1.06238i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.0398441 | + | 4.45986i | 0.00673488 | + | 0.753855i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.13257 | + | 5.42578i | 0.514992 | + | 0.891992i | 0.999849 | + | 0.0173987i | \(0.00553846\pi\) |
−0.484857 | + | 0.874594i | \(0.661128\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.52310 | + | 9.46234i | 0.724276 | + | 1.51519i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.64707 | + | 2.85281i | 0.257229 | + | 0.445534i | 0.965499 | − | 0.260408i | \(-0.0838571\pi\) |
−0.708269 | + | 0.705942i | \(0.750524\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.80474 | + | 3.12590i | −0.275220 | + | 0.476695i | −0.970191 | − | 0.242343i | \(-0.922084\pi\) |
0.694971 | + | 0.719038i | \(0.255417\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.17597 | − | 3.93555i | 0.473446 | − | 0.586678i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.76965 | −1.27918 | −0.639592 | − | 0.768714i | \(-0.720897\pi\) | ||||
−0.639592 | + | 0.768714i | \(0.720897\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.39113 | − | 6.12374i | 0.484447 | − | 0.874820i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.574855 | + | 0.394374i | 0.0804958 | + | 0.0552234i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.94628 | + | 2.85574i | 0.679424 | + | 0.392266i | 0.799638 | − | 0.600482i | \(-0.205025\pi\) |
−0.120214 | + | 0.992748i | \(0.538358\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 6.58345i | − | 0.887712i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.125601 | − | 0.262757i | −0.0166362 | − | 0.0348030i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.50326 | −0.586275 | −0.293138 | − | 0.956070i | \(-0.594699\pi\) | ||||
−0.293138 | + | 0.956070i | \(0.594699\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 5.12315i | − | 0.655952i | −0.944686 | − | 0.327976i | \(-0.893634\pi\) | ||
0.944686 | − | 0.327976i | \(-0.106366\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.37944 | + | 2.92299i | −0.929722 | + | 0.368262i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 10.2074i | − | 1.26607i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.91041 | 0.722072 | 0.361036 | − | 0.932552i | \(-0.382423\pi\) | ||||
0.361036 | + | 0.932552i | \(0.382423\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.70486 | + | 12.6886i | −1.04794 | + | 1.52752i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.4308i | 1.35658i | 0.734792 | + | 0.678292i | \(0.237280\pi\) | ||||
−0.734792 | + | 0.678292i | \(0.762720\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.05559 | − | 3.49620i | −0.708753 | − | 0.409199i | 0.101846 | − | 0.994800i | \(-0.467525\pi\) |
−0.810599 | + | 0.585601i | \(0.800858\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.37275 | − | 1.61221i | 0.389451 | − | 0.186162i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.08619 | + | 8.99415i | −0.579625 | + | 1.02498i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.20794 | −0.135903 | −0.0679517 | − | 0.997689i | \(-0.521646\pi\) | ||||
−0.0679517 | + | 0.997689i | \(0.521646\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.56884 | + | 2.75227i | 0.952093 | + | 0.305808i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.181350 | + | 0.314108i | −0.0199058 | + | 0.0344779i | −0.875807 | − | 0.482662i | \(-0.839670\pi\) |
0.855901 | + | 0.517140i | \(0.173003\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.339244 | − | 0.587588i | −0.0367962 | − | 0.0637329i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.96255 | + | 10.1489i | −0.746464 | + | 1.08808i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.38526 | − | 2.39934i | −0.146837 | − | 0.254329i | 0.783220 | − | 0.621745i | \(-0.213576\pi\) |
−0.930057 | + | 0.367416i | \(0.880243\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.88594 | + | 13.9451i | −0.826671 | + | 1.46184i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.8577 | − | 0.845308i | −1.12589 | − | 0.0876544i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.283446i | 0.0290809i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.508914 | − | 0.293821i | −0.0516723 | − | 0.0298330i | 0.473941 | − | 0.880556i | \(-0.342831\pi\) |
−0.525614 | + | 0.850723i | \(0.676164\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.9309 | − | 4.21713i | 1.09859 | − | 0.423837i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.92329 | + | 11.9915i | 0.688893 | + | 1.19320i | 0.972196 | + | 0.234167i | \(0.0752364\pi\) |
−0.283303 | + | 0.959030i | \(0.591430\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.4610 | − | 6.03967i | −1.03075 | − | 0.595106i | −0.113554 | − | 0.993532i | \(-0.536223\pi\) |
−0.917201 | + | 0.398425i | \(0.869557\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.70676 | + | 0.530777i | 0.752103 | + | 0.0517985i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.9299 | − | 9.19711i | 1.54000 | − | 0.889118i | 0.541159 | − | 0.840920i | \(-0.317986\pi\) |
0.998838 | − | 0.0481978i | \(-0.0153478\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.51036 | + | 9.54422i | −0.527796 | + | 0.914170i | 0.471679 | + | 0.881771i | \(0.343648\pi\) |
−0.999475 | + | 0.0323997i | \(0.989685\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.79051 | − | 4.67997i | 0.929274 | − | 0.444203i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.36811 | + | 4.25398i | −0.693133 | + | 0.400181i | −0.804785 | − | 0.593567i | \(-0.797719\pi\) |
0.111652 | + | 0.993747i | \(0.464386\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.9696 | − | 7.48801i | 1.20942 | − | 0.698260i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 16.9479 | − | 6.53850i | 1.56683 | − | 0.604485i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.00951320 | + | 1.06484i | 0.000872074 | + | 0.0976137i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.12600 | − | 3.68234i | 0.193273 | − | 0.334758i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.14774 | − | 2.46067i | 0.464156 | − | 0.221871i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0670 | −1.07930 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.6312 | 0.943365 | 0.471682 | − | 0.881769i | \(-0.343647\pi\) | ||||
0.471682 | + | 0.881769i | \(0.343647\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.15525 | + | 3.53671i | 0.453894 | + | 0.311390i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.16740 | + | 5.48610i | −0.276737 | + | 0.479322i | −0.970572 | − | 0.240812i | \(-0.922586\pi\) |
0.693835 | + | 0.720134i | \(0.255920\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.218982 | − | 0.387237i | 0.0189882 | − | 0.0335777i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.36904 | − | 6.01345i | −0.548160 | − | 0.517555i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.4158 | − | 8.32296i | 1.23162 | − | 0.711078i | 0.264255 | − | 0.964453i | \(-0.414874\pi\) |
0.967368 | + | 0.253375i | \(0.0815406\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.24007 | + | 2.44800i | −0.359638 | + | 0.207637i | −0.668922 | − | 0.743333i | \(-0.733244\pi\) |
0.309284 | + | 0.950970i | \(0.399911\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.17898 | + | 15.1437i | −0.0992884 | + | 1.27533i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.8238 | − | 20.4795i | 0.988758 | − | 1.71258i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.3737 | − | 5.98926i | 0.861489 | − | 0.497381i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.1187 | − | 6.67916i | −0.834579 | − | 0.550888i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.57864 | − | 2.64348i | −0.375097 | − | 0.216562i | 0.300586 | − | 0.953755i | \(-0.402818\pi\) |
−0.675683 | + | 0.737192i | \(0.736151\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.29163 | − | 12.6295i | −0.593385 | − | 1.02777i | −0.993773 | − | 0.111427i | \(-0.964458\pi\) |
0.400388 | − | 0.916346i | \(-0.368875\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.758298 | − | 0.939655i | 0.0613047 | − | 0.0759666i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.17930 | + | 5.29967i | 0.737299 | + | 0.425680i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 17.8009i | − | 1.42066i | −0.703867 | − | 0.710332i | \(-0.748545\pi\) | ||
0.703867 | − | 0.710332i | \(-0.251455\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.59634 | − | 8.15744i | 0.443818 | − | 0.646927i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −23.5038 | + | 0.209981i | −1.85236 | + | 0.0165488i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.0482228 | − | 0.0835243i | −0.00377710 | − | 0.00654213i | 0.864131 | − | 0.503267i | \(-0.167869\pi\) |
−0.867908 | + | 0.496725i | \(0.834536\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −11.3685 | − | 0.885074i | −0.885034 | − | 0.0689029i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.47872 | − | 4.29327i | −0.191809 | − | 0.332224i | 0.754041 | − | 0.656828i | \(-0.228102\pi\) |
−0.945850 | + | 0.324604i | \(0.894769\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.8324 | − | 20.4943i | 0.910185 | − | 1.57649i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.470621 | + | 0.181566i | −0.0359893 | + | 0.0138847i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.8007 | −1.12527 | −0.562637 | − | 0.826704i | \(-0.690213\pi\) | ||||
−0.562637 | + | 0.826704i | \(0.690213\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.97057 | + | 2.81086i | 0.375740 | + | 0.212481i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.605415 | + | 7.77635i | −0.0455058 | + | 0.584506i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.592751 | + | 0.342225i | 0.0443043 | + | 0.0255791i | 0.521989 | − | 0.852952i | \(-0.325190\pi\) |
−0.477684 | + | 0.878532i | \(0.658524\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 7.84745i | − | 0.583297i | −0.956526 | − | 0.291648i | \(-0.905796\pi\) | ||
0.956526 | − | 0.291648i | \(-0.0942037\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.84678 | − | 0.688752i | −0.653973 | − | 0.0509140i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.5614 | −0.776489 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1.57187i | − | 0.114946i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.05541 | + | 13.1360i | 0.294987 | + | 0.955501i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.5946i | 1.41781i | 0.705302 | + | 0.708907i | \(0.250811\pi\) | ||||
−0.705302 | + | 0.708907i | \(0.749189\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.3623 | 1.32175 | 0.660875 | − | 0.750496i | \(-0.270186\pi\) | ||||
0.660875 | + | 0.750496i | \(0.270186\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −17.6264 | − | 1.37227i | −1.26225 | − | 0.0982705i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 5.92313i | − | 0.422006i | −0.977485 | − | 0.211003i | \(-0.932327\pi\) | ||
0.977485 | − | 0.211003i | \(-0.0676730\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.6268 | + | 7.86741i | 0.965975 | + | 0.557706i | 0.898007 | − | 0.439982i | \(-0.145015\pi\) |
0.0679681 | + | 0.997687i | \(0.478348\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.794591 | − | 10.2062i | 0.0560461 | − | 0.719893i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −18.7994 | + | 0.167953i | −1.31946 | + | 0.0117880i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.55306 | −0.387842 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 20.7406 | + | 16.7376i | 1.44157 | + | 1.16334i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.328332 | + | 0.568688i | −0.0227112 | + | 0.0393370i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.06619 | − | 8.77489i | −0.348771 | − | 0.604088i | 0.637261 | − | 0.770648i | \(-0.280067\pi\) |
−0.986031 | + | 0.166560i | \(0.946734\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 19.7390 | + | 1.53675i | 1.35249 | + | 0.105296i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.04231 | − | 5.26944i | −0.207484 | − | 0.359373i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.44616 | − | 14.3320i | −0.573363 | − | 0.972917i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.85143 | + | 9.98692i | −0.462977 | + | 0.674853i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 2.43712i | − | 0.163939i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.3944 | − | 7.73325i | −0.896955 | − | 0.517857i | −0.0207437 | − | 0.999785i | \(-0.506603\pi\) |
−0.876211 | + | 0.481928i | \(0.839937\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.33058 | − | 6.04089i | −0.155372 | − | 0.402726i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.0360 | − | 24.3110i | −0.931600 | − | 1.61358i | −0.780588 | − | 0.625046i | \(-0.785080\pi\) |
−0.151011 | − | 0.988532i | \(-0.548253\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.7453 | − | 8.51319i | −0.974396 | − | 0.562568i | −0.0738222 | − | 0.997271i | \(-0.523520\pi\) |
−0.900573 | + | 0.434704i | \(0.856853\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.8475 | + | 9.99212i | 0.976897 | + | 0.657433i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.0015 | − | 9.23847i | 1.04829 | − | 0.605233i | 0.126122 | − | 0.992015i | \(-0.459747\pi\) |
0.922171 | + | 0.386782i | \(0.126413\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.39166 | − | 12.8027i | 0.482179 | − | 0.835158i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.162394 | + | 2.08590i | −0.0105486 | + | 0.135493i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.06656 | − | 3.50253i | 0.392413 | − | 0.226560i | −0.290792 | − | 0.956786i | \(-0.593919\pi\) |
0.683205 | + | 0.730226i | \(0.260585\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.38459 | − | 3.10879i | 0.346852 | − | 0.200255i | −0.316446 | − | 0.948611i | \(-0.602490\pi\) |
0.663298 | + | 0.748355i | \(0.269156\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.90468 | − | 14.4269i | 0.378785 | − | 0.925485i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.08172 | + | 10.1122i | 0.388547 | + | 0.646044i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.509067 | + | 0.881730i | −0.0323912 | + | 0.0561031i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.518029 | + | 0.355389i | 0.0328288 | + | 0.0225219i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.81844 | −0.619734 | −0.309867 | − | 0.950780i | \(-0.600285\pi\) | ||||
−0.309867 | + | 0.950780i | \(0.600285\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 34.6952 | 2.18127 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.06027 | + | 0.506821i | −0.0663967 | + | 0.0317383i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.667904 | + | 1.15684i | −0.0416627 | + | 0.0721619i | −0.886105 | − | 0.463485i | \(-0.846599\pi\) |
0.844442 | + | 0.535647i | \(0.179932\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.4287 | + | 8.15944i | 0.896558 | + | 0.507003i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 16.5893 | + | 13.3875i | 1.02685 | + | 0.828667i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −17.6238 | + | 10.1751i | −1.08673 | + | 0.627424i | −0.932704 | − | 0.360643i | \(-0.882557\pi\) |
−0.154026 | + | 0.988067i | \(0.549224\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.33814 | + | 4.81402i | −0.512208 | + | 0.295723i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.32947 | + | 2.06954i | −0.264959 | + | 0.126654i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.3614 | − | 23.1426i | 0.814659 | − | 1.41103i | −0.0949131 | − | 0.995486i | \(-0.530257\pi\) |
0.909572 | − | 0.415546i | \(-0.136409\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.76517 | + | 2.17382i | −0.228718 | + | 0.132050i | −0.609980 | − | 0.792417i | \(-0.708823\pi\) |
0.381263 | + | 0.924467i | \(0.375489\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 23.0206 | + | 15.4924i | 1.39327 | + | 0.937643i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.29968 | − | 4.21447i | −0.440187 | − | 0.254142i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.19901 | + | 3.80880i | 0.132126 | + | 0.228849i | 0.924496 | − | 0.381192i | \(-0.124486\pi\) |
−0.792370 | + | 0.610041i | \(0.791153\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.91940 | + | 18.6357i | −0.174780 | + | 1.11569i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.62273 | + | 2.66893i | 0.275769 | + | 0.159215i | 0.631506 | − | 0.775371i | \(-0.282437\pi\) |
−0.355738 | + | 0.934586i | \(0.615770\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.9476i | 1.06687i | 0.845840 | + | 0.533437i | \(0.179100\pi\) | ||||
−0.845840 | + | 0.533437i | \(0.820900\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.489462 | + | 0.0381063i | 0.0289932 | + | 0.00225722i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.58645 | + | 4.29014i | 0.447814 | + | 0.253239i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.41900 | + | 14.5821i | 0.495235 | + | 0.857773i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.575796 | + | 0.839304i | −0.0337538 | + | 0.0492009i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.1126 | − | 22.7117i | −0.766048 | − | 1.32683i | −0.939691 | − | 0.342026i | \(-0.888887\pi\) |
0.173642 | − | 0.984809i | \(-0.444446\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.79566 | − | 6.57428i | 0.220992 | − | 0.382769i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.81271 | − | 19.4426i | −0.337287 | − | 1.12818i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 53.7936 | 3.11097 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.0853135 | + | 9.54939i | 0.00491739 | + | 0.550417i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 21.6380 | − | 10.3432i | 1.24307 | − | 0.594201i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.47924 | + | 4.31814i | 0.428260 | + | 0.247256i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.19520i | 0.410652i | 0.978694 | + | 0.205326i | \(0.0658254\pi\) | ||||
−0.978694 | + | 0.205326i | \(0.934175\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.8358 | + | 17.2524i | −0.673317 | + | 0.981454i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.17443 | −0.123301 | −0.0616503 | − | 0.998098i | \(-0.519636\pi\) | ||||
−0.0616503 | + | 0.998098i | \(0.519636\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.8784i | 0.671409i | 0.941967 | + | 0.335704i | \(0.108974\pi\) | ||||
−0.941967 | + | 0.335704i | \(0.891026\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.95265 | − | 13.2369i | 0.110019 | − | 0.745814i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.19801i | 0.460446i | 0.973138 | + | 0.230223i | \(0.0739456\pi\) | ||||
−0.973138 | + | 0.230223i | \(0.926054\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 27.7509 | 1.55375 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.7402 | − | 28.7445i | −0.766903 | − | 1.60436i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.0676757i | 0.00376558i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.3179 | − | 6.53438i | −0.627803 | − | 0.362462i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15.7404 | + | 10.7985i | 0.870446 | + | 0.597161i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −19.9893 | + | 11.7802i | −1.10205 | + | 0.649463i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.1708 | −0.943793 | −0.471897 | − | 0.881654i | \(-0.656430\pi\) | ||||
−0.471897 | + | 0.881654i | \(0.656430\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.76526 | − | 17.5357i | −0.370734 | − | 0.960949i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.98170 | + | 8.62856i | −0.272179 | + | 0.471428i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.95399 | + | 6.84850i | 0.215387 | + | 0.373062i | 0.953392 | − | 0.301733i | \(-0.0975653\pi\) |
−0.738005 | + | 0.674795i | \(0.764232\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.35532 | + | 13.2953i | 0.345173 | + | 0.722103i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.2779 | + | 21.2659i | 0.664883 | + | 1.15161i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.496303 | − | 18.5136i | −0.0267979 | − | 0.999641i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −11.1869 | − | 23.4029i | −0.602280 | − | 1.25997i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 0.512514i | − | 0.0275132i | −0.999905 | − | 0.0137566i | \(-0.995621\pi\) | ||
0.999905 | − | 0.0137566i | \(-0.00437900\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.74612 | + | 3.31752i | 0.307583 | + | 0.177583i | 0.645844 | − | 0.763469i | \(-0.276506\pi\) |
−0.338262 | + | 0.941052i | \(0.609839\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.01239 | − | 30.1451i | −0.481046 | − | 1.60903i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.03437 | + | 15.6480i | 0.480851 | + | 0.832858i | 0.999759 | − | 0.0219721i | \(-0.00699449\pi\) |
−0.518908 | + | 0.854830i | \(0.673661\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.6877 | − | 9.63465i | −0.885691 | − | 0.511354i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.84007 | + | 0.126729i | 0.0973869 | + | 0.00670719i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.52677 | + | 0.881479i | −0.0805796 | + | 0.0465227i | −0.539748 | − | 0.841826i | \(-0.681481\pi\) |
0.459169 | + | 0.888349i | \(0.348147\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.48586 | + | 16.4300i | −0.499256 | + | 0.864737i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.07294 | − | 4.16628i | −0.318747 | − | 0.218673i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.2081 | − | 5.89367i | 0.534318 | − | 0.308489i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.9614 | − | 16.7209i | 1.51177 | − | 0.872822i | 0.511867 | − | 0.859065i | \(-0.328954\pi\) |
0.999905 | − | 0.0137576i | \(-0.00437931\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.55710 | − | 9.22005i | −0.185175 | − | 0.479977i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.1105 | − | 0.134996i | 0.784500 | − | 0.00700867i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.7844 | + | 22.1433i | −0.661952 | + | 1.14653i | 0.318150 | + | 0.948040i | \(0.396938\pi\) |
−0.980102 | + | 0.198494i | \(0.936395\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.62228 | + | 20.8376i | −0.0837741 | + | 1.07605i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 43.0267 | 2.21599 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.7920 | −1.32485 | −0.662423 | − | 0.749130i | \(-0.730472\pi\) | ||||
−0.662423 | + | 0.749130i | \(0.730472\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.42925 | − | 18.3582i | 0.0732226 | − | 0.940519i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.4158 | + | 28.4330i | −0.838808 | + | 1.45286i | 0.0520838 | + | 0.998643i | \(0.483414\pi\) |
−0.890892 | + | 0.454215i | \(0.849920\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.84349 | − | 15.0062i | −0.450706 | − | 0.764785i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.80034 | − | 8.42674i | 0.345681 | − | 0.428355i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.4542 | + | 10.0772i | −0.884965 | + | 0.510935i | −0.872292 | − | 0.488985i | \(-0.837367\pi\) |
−0.0126730 | + | 0.999920i | \(0.504034\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.09663 | − | 1.78784i | 0.156603 | − | 0.0904150i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.04771 | + | 6.20709i | 0.456396 | + | 0.313106i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.01813 | − | 1.76346i | 0.0512278 | − | 0.0887291i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.2125 | + | 17.4432i | −1.51632 | + | 0.875449i | −0.516506 | + | 0.856284i | \(0.672768\pi\) |
−0.999816 | + | 0.0191652i | \(0.993899\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.639251 | − | 0.430204i | −0.0320026 | − | 0.0215372i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.36793 | + | 4.83122i | 0.417874 | + | 0.241260i | 0.694167 | − | 0.719814i | \(-0.255773\pi\) |
−0.276293 | + | 0.961073i | \(0.589106\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.0364 | + | 32.9719i | 0.948268 | + | 1.64245i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −11.2404 | + | 10.1898i | −0.558541 | + | 0.506334i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.1897 | − | 12.2339i | −1.05034 | − | 0.606412i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 37.0893i | 1.83395i | 0.398949 | + | 0.916973i | \(0.369375\pi\) | ||||
−0.398949 | + | 0.916973i | \(0.630625\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.4342 | − | 26.0125i | −0.613336 | − | 1.28310i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.2646 | + | 6.04920i | −0.505090 | + | 0.297662i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.305709 | − | 0.529504i | −0.0150067 | − | 0.0259923i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.65725 | + | 7.65097i | 0.179096 | + | 0.374669i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.84193 | − | 3.19031i | −0.0899841 | − | 0.155857i | 0.817520 | − | 0.575900i | \(-0.195348\pi\) |
−0.907504 | + | 0.420043i | \(0.862015\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.55139 | + | 14.8114i | −0.416769 | + | 0.721866i | −0.995612 | − | 0.0935732i | \(-0.970171\pi\) |
0.578843 | + | 0.815439i | \(0.303504\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 25.9919 | + | 4.07180i | 1.26377 | + | 0.197978i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.868685 | −0.0421374 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.88188 | − | 11.6776i | −0.333038 | − | 0.565118i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −33.7749 | − | 23.1709i | −1.63067 | − | 1.11870i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.3242 | − | 15.7756i | −1.31616 | − | 0.759885i | −0.333051 | − | 0.942909i | \(-0.608078\pi\) |
−0.983108 | + | 0.183024i | \(0.941411\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 10.0692i | − | 0.483893i | −0.970290 | − | 0.241947i | \(-0.922214\pi\) | ||
0.970290 | − | 0.241947i | \(-0.0777859\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.94777 | − | 18.7188i | −0.429013 | − | 0.897496i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.49378 | −0.0714572 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.9398i | 1.33350i | 0.745283 | + | 0.666748i | \(0.232314\pi\) | ||||
−0.745283 | + | 0.666748i | \(0.767686\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.8941 | + | 16.5753i | −0.614005 | + | 0.789302i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.8638i | 1.65643i | 0.560411 | + | 0.828215i | \(0.310643\pi\) | ||||
−0.560411 | + | 0.828215i | \(0.689357\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.67037 | 0.221397 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.18038 | + | 7.55113i | −0.245023 | + | 0.357156i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 23.2411i | − | 1.09682i | −0.836211 | − | 0.548408i | \(-0.815234\pi\) | ||
0.836211 | − | 0.548408i | \(-0.184766\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.1413 | − | 6.43244i | −0.524624 | − | 0.302892i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −22.7892 | + | 10.8935i | −1.07073 | + | 0.511820i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13.7115 | − | 23.2665i | −0.642805 | − | 1.09075i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.21876 | −0.290901 | −0.145451 | − | 0.989366i | \(-0.546463\pi\) | ||||
−0.145451 | + | 0.989366i | \(0.546463\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.52068 | − | 1.43577i | −0.0709790 | − | 0.0670162i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.17165 | + | 3.76140i | −0.101144 | + | 0.175186i | −0.912156 | − | 0.409843i | \(-0.865584\pi\) |
0.811012 | + | 0.585029i | \(0.198917\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.57451 | − | 6.19124i | −0.166122 | − | 0.287731i | 0.770931 | − | 0.636918i | \(-0.219791\pi\) |
−0.937053 | + | 0.349187i | \(0.886458\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10.3857 | − | 15.1386i | 0.481624 | − | 0.702034i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.944451 | − | 1.63584i | −0.0437040 | − | 0.0756975i | 0.843346 | − | 0.537371i | \(-0.180583\pi\) |
−0.887050 | + | 0.461673i | \(0.847249\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.4721 | − | 7.93941i | 0.622082 | − | 0.366608i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −30.7390 | − | 2.39314i | −1.41638 | − | 0.110270i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 14.0964i | − | 0.648152i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.314283 | + | 0.181451i | 0.0144203 | + | 0.00832555i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.3341 | − | 10.7606i | −0.610527 | − | 0.492693i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.22491 | + | 9.04981i | 0.238732 | + | 0.413497i | 0.960351 | − | 0.278794i | \(-0.0899348\pi\) |
−0.721618 | + | 0.692291i | \(0.756601\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −32.8539 | − | 18.9682i | −1.49801 | − | 0.864875i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.79723 | + | 40.6152i | −0.127278 | + | 1.84805i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.857895 | − | 0.495306i | 0.0389550 | − | 0.0224907i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.8298 | − | 20.4898i | 0.536060 | − | 0.928483i | −0.463052 | − | 0.886331i | \(-0.653246\pi\) |
0.999111 | − | 0.0421513i | \(-0.0134212\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.150715 | + | 0.0720434i | −0.00681557 | + | 0.00325792i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.6767 | − | 6.74152i | 0.526960 | − | 0.304241i | −0.212817 | − | 0.977092i | \(-0.568264\pi\) |
0.739778 | + | 0.672851i | \(0.234931\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.47683 | − | 1.43000i | 0.111551 | − | 0.0644039i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.05674 | + | 19.5124i | −0.137390 | + | 0.877016i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.3549 | + | 26.0551i | 0.688761 | + | 1.16873i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.04035 | + | 10.4622i | −0.270403 | + | 0.468352i | −0.968965 | − | 0.247197i | \(-0.920490\pi\) |
0.698562 | + | 0.715550i | \(0.253824\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.74697 | + | 3.70314i | −0.346109 | + | 0.165444i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.5283 | −0.915310 | −0.457655 | − | 0.889130i | \(-0.651310\pi\) | ||||
−0.457655 | + | 0.889130i | \(0.651310\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.3417 | −1.03869 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −33.7994 | − | 23.1877i | −1.50108 | − | 1.02980i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.09043 | − | 7.08483i | 0.181305 | − | 0.314029i | −0.761020 | − | 0.648728i | \(-0.775301\pi\) |
0.942325 | + | 0.334699i | \(0.108635\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.4994 | + | 0.165272i | −0.818365 | + | 0.00731121i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.250262 | + | 0.837090i | 0.0110493 | + | 0.0369584i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.6345 | − | 10.1813i | 0.777070 | − | 0.448642i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 29.6603 | − | 17.1244i | 1.30446 | − | 0.753131i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.98979 | + | 25.5582i | −0.0873421 | + | 1.12188i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.8746 | − | 24.0314i | 0.607856 | − | 1.05284i | −0.383738 | − | 0.923442i | \(-0.625363\pi\) |
0.991593 | − | 0.129395i | \(-0.0413034\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.8843 | + | 11.4802i | −0.869478 | + | 0.501993i | −0.867175 | − | 0.498004i | \(-0.834066\pi\) |
−0.00230311 | + | 0.999997i | \(0.500733\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.52210 | − | 8.20542i | 0.241004 | − | 0.358114i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.19166 | + | 1.26535i | 0.0954700 | + | 0.0551196i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.9623 | + | 48.4322i | 1.21575 | + | 2.10575i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.3470 | + | 2.09089i | 0.579211 | + | 0.0907370i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.2742 | − | 9.97325i | −0.748228 | − | 0.431990i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 31.0078i | 1.34058i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.670652 | − | 0.977569i | 0.0289408 | − | 0.0421852i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.488426 | + | 27.3333i | 0.0210380 | + | 1.17733i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.60405 | − | 4.51035i | −0.111957 | − | 0.193915i | 0.804602 | − | 0.593814i | \(-0.202379\pi\) |
−0.916559 | + | 0.399899i | \(0.869045\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.5512 | − | 1.05501i | −0.581537 | − | 0.0452746i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.28902 | − | 16.0890i | −0.397898 | − | 0.689179i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.6224 | + | 18.3985i | −0.454181 | + | 0.786664i | −0.998641 | − | 0.0521229i | \(-0.983401\pi\) |
0.544460 | + | 0.838787i | \(0.316735\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.37871 | + | 15.1843i | −0.101521 | + | 0.648048i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.19479 | −0.0509000 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.75334 | + | 1.62261i | −0.117084 | + | 0.0690005i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.41987 | + | 18.2377i | −0.0602700 | + | 0.774147i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.0945 | + | 6.40543i | 0.470090 | + | 0.271407i | 0.716277 | − | 0.697816i | \(-0.245844\pi\) |
−0.246187 | + | 0.969222i | \(0.579178\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 21.8559i | − | 0.924406i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.71434 | − | 0.211321i | −0.114600 | − | 0.00892197i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 37.4793 | 1.57956 | 0.789781 | − | 0.613388i | \(-0.210194\pi\) | ||||
0.789781 | + | 0.613388i | \(0.210194\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 14.3422i | − | 0.603380i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.2287 | − | 5.23699i | 0.975515 | − | 0.219933i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.86938i | 0.287979i | 0.989579 | + | 0.143990i | \(0.0459932\pi\) | ||||
−0.989579 | + | 0.143990i | \(0.954007\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.169582 | −0.00709678 | −0.00354839 | − | 0.999994i | \(-0.501129\pi\) | ||||
−0.00354839 | + | 0.999994i | \(0.501129\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 33.8364 | + | 2.63428i | 1.41354 | + | 0.110049i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 19.1741i | − | 0.799617i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.41193 | − | 3.12458i | −0.225302 | − | 0.130078i | 0.383101 | − | 0.923706i | \(-0.374856\pi\) |
−0.608403 | + | 0.793628i | \(0.708189\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.46862 | − | 31.7085i | 0.102592 | − | 1.31776i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.00857280 | + | 0.959578i | 0.000355660 | + | 0.0398100i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.3055 | −0.923799 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.73935 | + | 30.2532i | −0.195948 | + | 1.25082i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.7881 | − | 18.6855i | 0.445273 | − | 0.771235i | −0.552799 | − | 0.833315i | \(-0.686440\pi\) |
0.998071 | + | 0.0620801i | \(0.0197734\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.528615 | − | 0.915588i | −0.0217812 | − | 0.0377261i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.2282 | − | 0.796302i | −0.420733 | − | 0.0327555i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.13036 | − | 7.15399i | −0.169613 | − | 0.293779i | 0.768671 | − | 0.639645i | \(-0.220919\pi\) |
−0.938284 | + | 0.345866i | \(0.887585\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.56257 | − | 0.883632i | −0.0640591 | − | 0.0362254i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15.4176 | − | 22.4733i | 0.631001 | − | 0.919772i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 35.5206i | 1.45133i | 0.688047 | + | 0.725667i | \(0.258468\pi\) | ||||
−0.688047 | + | 0.725667i | \(0.741532\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.8981 | − | 20.7258i | −1.46432 | − | 0.845423i | −0.465109 | − | 0.885254i | \(-0.653985\pi\) |
−0.999206 | + | 0.0398308i | \(0.987318\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −17.5176 | − | 2.74424i | −0.713371 | − | 0.111754i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.58388 | + | 6.20746i | 0.145705 | + | 0.252369i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.09569 | + | 1.20995i | 0.0850616 | + | 0.0491103i | 0.541927 | − | 0.840425i | \(-0.317695\pi\) |
−0.456866 | + | 0.889536i | \(0.651028\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.23736 | + | 32.4859i | −0.0906622 | + | 1.31640i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 45.9873 | − | 26.5508i | 1.86045 | − | 1.07413i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.3228 | − | 36.9321i | 0.861219 | − | 1.49168i | −0.00953416 | − | 0.999955i | \(-0.503035\pi\) |
0.870753 | − | 0.491720i | \(-0.163632\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.746549 | + | 9.58916i | −0.0301038 | + | 0.386672i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.2535 | − | 7.65193i | 0.533567 | − | 0.308055i | −0.208901 | − | 0.977937i | \(-0.566989\pi\) |
0.742468 | + | 0.669882i | \(0.233655\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.9177 | + | 13.8089i | −0.961334 | + | 0.555026i | −0.896583 | − | 0.442875i | \(-0.853958\pi\) |
−0.0647505 | + | 0.997901i | \(0.520625\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 31.6913 | − | 33.5653i | 1.27173 | − | 1.34693i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.38054 | − | 3.60819i | −0.255631 | − | 0.144559i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.77517 | − | 8.27084i | 0.191007 | − | 0.330834i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.937885 | + | 0.643427i | 0.0374555 | + | 0.0256960i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.52164 | −0.100545 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.28775 | −0.329930 | −0.164965 | − | 0.986299i | \(-0.552751\pi\) | ||||
−0.164965 | + | 0.986299i | \(0.552751\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −15.8338 | + | 7.56873i | −0.629337 | + | 0.300830i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.96069 | + | 15.5204i | −0.355594 | + | 0.615907i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.757287 | + | 42.3793i | 0.0300048 | + | 1.67913i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.30738 | − | 33.8792i | 0.209957 | − | 1.34024i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.58307 | + | 4.95544i | −0.339011 | + | 0.195728i | −0.659835 | − | 0.751411i | \(-0.729374\pi\) |
0.320824 | + | 0.947139i | \(0.396040\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.83668 | − | 3.94716i | 0.269612 | − | 0.155661i | −0.359099 | − | 0.933299i | \(-0.616916\pi\) |
0.628711 | + | 0.777639i | \(0.283583\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.50841 | + | 4.54512i | −0.374393 | + | 0.178964i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.15966 | − | 3.74063i | 0.0849049 | − | 0.147060i | −0.820446 | − | 0.571724i | \(-0.806275\pi\) |
0.905351 | + | 0.424665i | \(0.139608\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.2308 | − | 8.79348i | 0.597859 | − | 0.345174i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −25.8843 | + | 12.6583i | −1.01448 | + | 0.496117i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 37.5853 | + | 21.6999i | 1.47082 | + | 0.849181i | 0.999463 | − | 0.0327591i | \(-0.0104294\pi\) |
0.471361 | + | 0.881940i | \(0.343763\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.33940 | − | 9.24812i | −0.208628 | − | 0.361354i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.3246 | + | 13.1739i | 0.636882 | + | 0.513961i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.34894 | + | 5.39761i | 0.364183 | + | 0.210261i | 0.670914 | − | 0.741535i | \(-0.265902\pi\) |
−0.306731 | + | 0.951796i | \(0.599235\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.92015i | 0.152476i | 0.997090 | + | 0.0762381i | \(0.0242909\pi\) | ||||
−0.997090 | + | 0.0762381i | \(0.975709\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.20848 | − | 0.327645i | −0.163444 | − | 0.0127247i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.380751 | + | 0.646081i | 0.0147649 | + | 0.0250539i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31.5638 | + | 54.6701i | 1.22216 | + | 2.11683i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.1547 | + | 22.0901i | −0.585915 | + | 0.854053i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.0039 | + | 17.3273i | 0.386197 | + | 0.668913i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.3404 | + | 21.3742i | −0.475687 | + | 0.823915i | −0.999612 | − | 0.0278497i | \(-0.991134\pi\) |
0.523925 | + | 0.851765i | \(0.324467\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −10.7449 | + | 3.21236i | −0.413571 | + | 0.123644i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.7265 | 0.565987 | 0.282994 | − | 0.959122i | \(-0.408672\pi\) | ||||
0.282994 | + | 0.959122i | \(0.408672\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.55469 | + | 0.0138895i | −0.0596637 | + | 0.000533031i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −43.8678 | + | 20.9693i | −1.68102 | + | 0.803545i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.60128 | − | 0.924499i | −0.0612712 | − | 0.0353750i | 0.469051 | − | 0.883171i | \(-0.344596\pi\) |
−0.530323 | + | 0.847796i | \(0.677929\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28.0606i | 1.07214i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.6831 | + | 24.3180i | −0.636502 | + | 0.927790i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −34.5838 | −1.31754 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 38.9842i | − | 1.48303i | −0.670938 | − | 0.741514i | \(-0.734108\pi\) | ||
0.670938 | − | 0.741514i | \(-0.265892\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 19.2507 | − | 24.2958i | 0.731275 | − | 0.922920i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 8.25339i | − | 0.313069i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.32585 | −0.0502202 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.8020 | − | 28.8738i | −0.522040 | − | 1.09211i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.4389i | 0.960813i | 0.877046 | + | 0.480406i | \(0.159511\pi\) | ||||
−0.877046 | + | 0.480406i | \(0.840489\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.912310 | + | 0.526722i | 0.0344084 | + | 0.0198657i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −21.1144 | − | 14.4853i | −0.795213 | − | 0.545548i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 31.8889 | + | 18.0331i | 1.19930 | + | 0.678206i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.2903 | −0.536685 | −0.268342 | − | 0.963324i | \(-0.586476\pi\) | ||||
−0.268342 | + | 0.963324i | \(0.586476\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.58014 | + | 0.560852i | 0.134266 | + | 0.0210336i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −27.9296 | + | 48.3756i | −1.04597 | + | 1.81168i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.9319 | + | 34.5230i | 0.745410 | + | 1.29109i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.23267 | − | 10.9468i | −0.195418 | − | 0.408814i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.7344 | − | 28.9848i | −0.624088 | − | 1.08095i | −0.988716 | − | 0.149799i | \(-0.952137\pi\) |
0.364629 | − | 0.931153i | \(-0.381196\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −31.9577 | + | 0.285507i | −1.19017 | + | 0.0106329i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.64445 | − | 9.71619i | −0.172729 | − | 0.361349i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 15.3364i | − | 0.569579i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.1354 | + | 7.00636i | 0.450076 | + | 0.259851i | 0.707862 | − | 0.706350i | \(-0.249660\pi\) |
−0.257786 | + | 0.966202i | \(0.582993\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −24.1189 | − | 12.1359i | −0.893292 | − | 0.449477i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.726384 | − | 1.25813i | −0.0268663 | − | 0.0465338i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.6491 | + | 13.6538i | 0.873501 | + | 0.504316i | 0.868510 | − | 0.495672i | \(-0.165078\pi\) |
0.00499085 | + | 0.999988i | \(0.498411\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 18.2796 | − | 9.14259i | 0.674254 | − | 0.337230i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −19.9899 | + | 11.5412i | −0.736339 | + | 0.425126i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26.3157 | + | 45.5801i | −0.968039 | + | 1.67669i | −0.266819 | + | 0.963747i | \(0.585973\pi\) |
−0.701220 | + | 0.712945i | \(0.747361\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.45416 | + | 0.997609i | 0.0534197 | + | 0.0366481i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.9523 | − | 17.8703i | 1.13553 | − | 0.655599i | 0.190211 | − | 0.981743i | \(-0.439083\pi\) |
0.945320 | + | 0.326144i | \(0.105750\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.71839 | − | 4.45621i | 0.282780 | − | 0.163263i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.683338 | − | 0.846768i | 0.0250020 | − | 0.0309816i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 23.9558 | − | 42.3621i | 0.875325 | − | 1.54788i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.5641 | + | 28.6899i | −0.604433 | + | 1.04691i | 0.387708 | + | 0.921782i | \(0.373267\pi\) |
−0.992141 | + | 0.125126i | \(0.960066\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.31998 | + | 16.9547i | −0.0481029 | + | 0.617865i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.5836 | 0.894687 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.6903 | −0.497584 | −0.248792 | − | 0.968557i | \(-0.580034\pi\) | ||||
−0.248792 | + | 0.968557i | \(0.580034\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.66440 | − | 59.9126i | 0.169307 | − | 2.17469i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.51737 | + | 11.2884i | −0.236255 | + | 0.409205i | −0.959637 | − | 0.281243i | \(-0.909253\pi\) |
0.723382 | + | 0.690448i | \(0.242587\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.260486 | + | 29.1569i | 0.00943021 | + | 1.05555i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.732649 | + | 1.89904i | 0.0264890 | + | 0.0686599i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 23.6147 | − | 13.6340i | 0.852678 | − | 0.492294i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.4866 | − | 10.6732i | 0.666642 | − | 0.384886i | −0.128161 | − | 0.991753i | \(-0.540907\pi\) |
0.794803 | + | 0.606867i | \(0.207574\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.90788 | + | 1.30888i | 0.0687104 | + | 0.0471381i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.73940 | − | 9.94093i | 0.206432 | − | 0.357550i | −0.744156 | − | 0.668006i | \(-0.767148\pi\) |
0.950588 | + | 0.310455i | \(0.100482\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.7525 | − | 6.78529i | 0.422161 | − | 0.243735i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 16.0297 | − | 23.8189i | 0.575063 | − | 0.854500i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.479682 | + | 0.276944i | 0.0171864 | + | 0.00992256i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.3208 | − | 38.6607i | −0.798701 | − | 1.38339i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 25.3482 | − | 26.8471i | 0.905870 | − | 0.959436i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 25.9873 | + | 15.0038i | 0.927528 | + | 0.535509i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 41.2006i | − | 1.46864i | −0.678802 | − | 0.734322i | \(-0.737500\pi\) | ||
0.678802 | − | 0.734322i | \(-0.262500\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15.2013 | + | 31.8012i | 0.541181 | + | 1.13215i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.0804 | + | 19.5939i | −0.393972 | + | 0.696681i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.5107 | + | 26.8653i | 0.550801 | + | 0.954016i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.19201 | + | 15.0457i | 0.255074 | + | 0.533616i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −25.0066 | − | 43.3127i | −0.885779 | − | 1.53421i | −0.844819 | − | 0.535053i | \(-0.820292\pi\) |
−0.0409600 | − | 0.999161i | \(-0.513042\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.76484 | − | 3.05679i | 0.0624355 | − | 0.108141i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.99168 | + | 7.75447i | 0.105706 | + | 0.273991i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 27.3079 | 0.963677 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 19.5041 | − | 34.4900i | 0.687428 | − | 1.21561i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −38.1670 | − | 26.1841i | −1.34354 | − | 0.921724i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −43.8995 | − | 25.3454i | −1.54343 | − | 0.891097i | −0.998619 | − | 0.0525356i | \(-0.983270\pi\) |
−0.544807 | − | 0.838562i | \(-0.683397\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.96566i | 0.314827i | 0.987533 | + | 0.157413i | \(0.0503155\pi\) | ||||
−0.987533 | + | 0.157413i | \(0.949684\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.24762 | + | 6.79403i | 0.113899 | + | 0.238277i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.162582 | 0.00569500 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.606910i | 0.0212331i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 29.8476 | − | 37.6697i | 1.04296 | − | 1.31629i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 32.5845i | − | 1.13721i | −0.822612 | − | 0.568603i | \(-0.807484\pi\) | ||
0.822612 | − | 0.568603i | \(-0.192516\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.1754 | 0.703271 | 0.351636 | − | 0.936137i | \(-0.385626\pi\) | ||||
0.351636 | + | 0.936137i | \(0.385626\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.25902 | + | 12.0387i | −0.287542 | + | 0.419133i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 0.253288i | − | 0.00880770i | −0.999990 | − | 0.00440385i | \(-0.998598\pi\) | ||
0.999990 | − | 0.00440385i | \(-0.00140179\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.10909 | − | 3.52708i | −0.212177 | − | 0.122501i | 0.390146 | − | 0.920753i | \(-0.372425\pi\) |
−0.602323 | + | 0.798253i | \(0.705758\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.87277 | − | 3.28526i | 0.238414 | − | 0.113964i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.45208 | + | 2.41439i | 0.0503114 | + | 0.0836538i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.35695 | 0.289204 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 31.7881 | + | 7.54666i | 1.09876 | + | 0.260851i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17.0936 | + | 29.6069i | −0.590136 | + | 1.02215i | 0.404078 | + | 0.914725i | \(0.367592\pi\) |
−0.994214 | + | 0.107420i | \(0.965741\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.7462 | + | 18.6130i | 0.370558 | + | 0.641826i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.23026 | − | 7.62383i | 0.180140 | − | 0.262579i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 19.9463 | + | 34.5480i | 0.686174 | + | 1.18849i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.100500 | − | 11.2493i | −0.00345323 | − | 0.386530i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 30.9924 | + | 2.41286i | 1.06366 | + | 0.0828092i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 55.6593i | − | 1.90798i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.7586 | + | 12.5623i | 0.745000 | + | 0.430126i | 0.823884 | − | 0.566758i | \(-0.191802\pi\) |
−0.0788844 | + | 0.996884i | \(0.525136\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.131606 | − | 0.840092i | 0.00450082 | − | 0.0287305i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.0954 | + | 36.5383i | 0.720604 | + | 1.24812i | 0.960758 | + | 0.277388i | \(0.0894688\pi\) |
−0.240154 | + | 0.970735i | \(0.577198\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.08139 | − | 2.35639i | −0.139255 | − | 0.0803990i | 0.428754 | − | 0.903421i | \(-0.358953\pi\) |
−0.568009 | + | 0.823022i | \(0.692286\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.42823 | − | 12.5237i | 0.287233 | − | 0.426807i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30.8409 | − | 17.8060i | 1.04984 | − | 0.606123i | 0.127232 | − | 0.991873i | \(-0.459391\pi\) |
0.922603 | + | 0.385750i | \(0.126057\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.4750 | − | 21.6074i | 0.424163 | − | 0.734672i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 26.3127 | − | 12.5777i | 0.893625 | − | 0.427162i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.08543 | − | 2.35873i | 0.138589 | − | 0.0800143i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.9937 | + | 17.8942i | −1.05018 | + | 0.606322i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.37192 | + | 1.10713i | 0.0464325 | + | 0.0374708i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −27.5053 | + | 16.2095i | −0.929847 | + | 0.547981i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.4532 | + | 35.4260i | −0.690655 | + | 1.19625i | 0.280969 | + | 0.959717i | \(0.409344\pi\) |
−0.971624 | + | 0.236532i | \(0.923989\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −40.9821 | + | 19.5899i | −1.38229 | + | 0.660750i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37.4443 | −1.26153 | −0.630765 | − | 0.775974i | \(-0.717259\pi\) | ||||
−0.630765 | + | 0.775974i | \(0.717259\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49.8357 | 1.67711 | 0.838553 | − | 0.544821i | \(-0.183402\pi\) | ||||
0.838553 | + | 0.544821i | \(0.183402\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.8423 | − | 7.43828i | −0.364461 | − | 0.250035i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.4482 | + | 25.0251i | −0.485124 | + | 0.840260i | −0.999854 | − | 0.0170929i | \(-0.994559\pi\) |
0.514730 | + | 0.857352i | \(0.327892\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.2325 | − | 14.2808i | 0.812731 | − | 0.478962i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −34.3555 | + | 7.42368i | −1.15095 | + | 0.248703i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.27701 | + | 0.737280i | −0.0427334 | + | 0.0246721i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.999223 | + | 0.576902i | −0.0334003 | + | 0.0192837i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.23198 | − | 92.8922i | 0.241469 | − | 3.10158i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −22.3394 | + | 38.6930i | −0.745062 | + | 1.29048i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.99082 | + | 1.14940i | −0.0663238 | + | 0.0382920i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 16.5016 | + | 1.13649i | 0.549139 | + | 0.0378200i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.4564 | + | 6.61437i | 0.380825 | + | 0.219869i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.43498 | − | 12.8778i | −0.246874 | − | 0.427599i | 0.715783 | − | 0.698323i | \(-0.246070\pi\) |
−0.962657 | + | 0.270724i | \(0.912737\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14.9519 | − | 38.7555i | −0.495923 | − | 1.28544i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.81616 | − | 4.51266i | −0.258961 | − | 0.149511i | 0.364899 | − | 0.931047i | \(-0.381103\pi\) |
−0.623861 | + | 0.781536i | \(0.714437\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1.41649i | − | 0.0468788i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.46218 | − | 12.3348i | 0.279751 | − | 0.407776i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.149729 | + | 16.7596i | 0.00494450 | + | 0.553452i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.2083 | − | 22.8774i | −0.435702 | − | 0.754657i | 0.561651 | − | 0.827374i | \(-0.310166\pi\) |
−0.997353 | + | 0.0727170i | \(0.976833\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.4249 | + | 0.967317i | 0.409413 | + | 0.0318742i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −34.6075 | − | 59.9420i | −1.13912 | − | 1.97302i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.76100 | + | 11.7104i | −0.222300 | + | 0.385036i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 28.2007 | + | 22.7578i | 0.926231 | + | 0.747464i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.2518 | 0.730058 | 0.365029 | − | 0.930996i | \(-0.381059\pi\) | ||||
0.365029 | + | 0.930996i | \(0.381059\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.0210289 | − | 1.17682i | −0.000689194 | − | 0.0385686i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.292329 | + | 3.75486i | −0.00957041 | + | 0.122929i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.29476 | + | 1.32488i | 0.0750465 | + | 0.0433281i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.6822i | 0.479647i | 0.970817 | + | 0.239823i | \(0.0770896\pi\) | ||||
−0.970817 | + | 0.239823i | \(0.922910\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20.5120 | + | 1.59693i | 0.669383 | + | 0.0521137i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 46.0792 | 1.50214 | 0.751070 | − | 0.660223i | \(-0.229538\pi\) | ||||
0.751070 | + | 0.660223i | \(0.229538\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 29.2650i | − | 0.952999i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −22.5953 | − | 5.15144i | −0.735024 | − | 0.167576i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 8.03805i | − | 0.261202i | −0.991435 | − | 0.130601i | \(-0.958309\pi\) | ||
0.991435 | − | 0.130601i | \(-0.0416906\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 42.3400 | 1.37441 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.1565 | + | 1.10213i | 0.459057 | + | 0.0357392i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 54.9348i | − | 1.77951i | −0.456437 | − | 0.889756i | \(-0.650875\pi\) | ||
0.456437 | − | 0.889756i | \(-0.349125\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −28.6060 | − | 16.5157i | −0.925667 | − | 0.534434i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.73080 | − | 47.9209i | 0.120600 | − | 1.54906i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 21.6789 | − | 38.3358i | 0.700047 | − | 1.23793i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.53466 | −0.275312 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −51.4840 | + | 19.8625i | −1.65905 | + | 0.640061i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15.4770 | + | 26.8070i | −0.498223 | + | 0.862948i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.5917 | + | 46.0582i | 0.855132 | + | 1.48113i | 0.876522 | + | 0.481361i | \(0.159857\pi\) |
−0.0213900 | + | 0.999771i | \(0.506809\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.116864 | + | 0.00909827i | 0.00375422 | + | 0.000292279i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.61403 | + | 13.1879i | 0.244346 | + | 0.423219i | 0.961947 | − | 0.273234i | \(-0.0880935\pi\) |
−0.717602 | + | 0.696454i | \(0.754760\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.37634 | + | 11.2756i | −0.204416 | + | 0.361479i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12.8053 | + | 18.6655i | −0.410098 | + | 0.597775i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1.72533i | − | 0.0551983i | −0.999619 | − | 0.0275992i | \(-0.991214\pi\) | ||
0.999619 | − | 0.0275992i | \(-0.00878620\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.37033 | + | 5.40997i | 0.299477 | + | 0.172903i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 20.7633 | − | 25.7292i | 0.662922 | − | 0.821469i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.1191 | + | 52.1679i | 0.960651 | + | 1.66390i | 0.720871 | + | 0.693070i | \(0.243742\pi\) |
0.239780 | + | 0.970827i | \(0.422925\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.64713 | + | 4.99242i | 0.275521 | + | 0.159072i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 17.6550 | + | 36.1018i | 0.561965 | + | 1.14913i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27.7703 | − | 16.0332i | 0.883044 | − | 0.509826i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.87312 | − | 4.97639i | 0.0912676 | − | 0.158080i | −0.816777 | − | 0.576953i | \(-0.804241\pi\) |
0.908045 | + | 0.418873i | \(0.137575\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.30843 | + | 29.6510i | −0.0732558 | + | 0.940946i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22.9711 | + | 13.2624i | −0.728234 | + | 0.420446i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.0224508 | − | 0.0129620i | 0.000711024 | − | 0.000410510i | −0.499644 | − | 0.866231i | \(-0.666536\pi\) |
0.500355 | + | 0.865820i | \(0.333203\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −31.1906 | + | 9.32495i | −0.986826 | + | 0.295028i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))