Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [144,2,Mod(35,144)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(144, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("144.35");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.l (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.14984578911\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4x^{14} + 6x^{12} - 12x^{10} + 33x^{8} - 48x^{6} + 96x^{4} - 256x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 107.2 | ||
Root | \(-1.36166 - 0.381939i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.107 |
Dual form | 144.2.l.a.35.2 |
$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.12697 | − | 0.854358i | −0.796891 | − | 0.604123i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.540143 | + | 1.92568i | 0.270072 | + | 0.962840i | ||||
\(5\) | 0.763878 | − | 0.763878i | 0.341617 | − | 0.341617i | −0.515358 | − | 0.856975i | \(-0.672341\pi\) |
0.856975 | + | 0.515358i | \(0.172341\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.33620 | 0.505038 | 0.252519 | − | 0.967592i | \(-0.418741\pi\) | ||||
0.252519 | + | 0.967592i | \(0.418741\pi\) | |||||||
\(8\) | 1.03649 | − | 2.63167i | 0.366456 | − | 0.930435i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.51350 | + | 0.208245i | −0.478610 | + | 0.0658530i | ||||
\(11\) | 1.95945 | + | 1.95945i | 0.590795 | + | 0.590795i | 0.937846 | − | 0.347051i | \(-0.112817\pi\) |
−0.347051 | + | 0.937846i | \(0.612817\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.18757 | − | 4.18757i | 1.16142 | − | 1.16142i | 0.177257 | − | 0.984165i | \(-0.443278\pi\) |
0.984165 | − | 0.177257i | \(-0.0567224\pi\) | |||||||
\(14\) | −1.50587 | − | 1.14160i | −0.402460 | − | 0.305105i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.41649 | + | 2.08029i | −0.854123 | + | 0.520072i | ||||
\(17\) | − | 4.03243i | − | 0.978009i | −0.872281 | − | 0.489004i | \(-0.837360\pi\) | ||
0.872281 | − | 0.489004i | \(-0.162640\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.26785 | − | 4.26785i | −0.979112 | − | 0.979112i | 0.0206739 | − | 0.999786i | \(-0.493419\pi\) |
−0.999786 | + | 0.0206739i | \(0.993419\pi\) | |||||||
\(20\) | 1.88359 | + | 1.05838i | 0.421183 | + | 0.236661i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.534176 | − | 3.88231i | −0.113887 | − | 0.827712i | ||||
\(23\) | 8.86408i | 1.84829i | 0.382044 | + | 0.924144i | \(0.375220\pi\) | ||||
−0.382044 | + | 0.924144i | \(0.624780\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.83298i | 0.766596i | ||||||||
\(26\) | −8.29696 | + | 1.14160i | −1.62717 | + | 0.223886i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.721742 | + | 2.57310i | 0.136396 | + | 0.486271i | ||||
\(29\) | 1.23934 | + | 1.23934i | 0.230140 | + | 0.230140i | 0.812751 | − | 0.582611i | \(-0.197969\pi\) |
−0.582611 | + | 0.812751i | \(0.697969\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.87835i | 0.516968i | 0.966016 | + | 0.258484i | \(0.0832229\pi\) | ||||
−0.966016 | + | 0.258484i | \(0.916777\pi\) | |||||||
\(32\) | 5.62761 | + | 0.574478i | 0.994830 | + | 0.101554i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.44514 | + | 4.54445i | −0.590837 | + | 0.779367i | ||||
\(35\) | 1.02070 | − | 1.02070i | 0.172529 | − | 0.172529i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.434870 | + | 0.434870i | 0.0714922 | + | 0.0714922i | 0.741949 | − | 0.670457i | \(-0.233902\pi\) |
−0.670457 | + | 0.741949i | \(0.733902\pi\) | |||||||
\(38\) | 1.16348 | + | 8.45604i | 0.188742 | + | 1.37175i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.21852 | − | 2.80203i | −0.192665 | − | 0.443040i | ||||
\(41\) | −7.81179 | −1.22000 | −0.609998 | − | 0.792403i | \(-0.708830\pi\) | ||||
−0.609998 | + | 0.792403i | \(0.708830\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.49678 | + | 5.49678i | −0.838251 | + | 0.838251i | −0.988629 | − | 0.150378i | \(-0.951951\pi\) |
0.150378 | + | 0.988629i | \(0.451951\pi\) | |||||||
\(44\) | −2.71489 | + | 4.83165i | −0.409284 | + | 0.728398i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.57310 | − | 9.98959i | 1.11659 | − | 1.47289i | ||||
\(47\) | −3.20723 | −0.467822 | −0.233911 | − | 0.972258i | \(-0.575152\pi\) | ||||
−0.233911 | + | 0.972258i | \(0.575152\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.21456 | −0.744937 | ||||||||
\(50\) | 3.27474 | − | 4.31967i | 0.463118 | − | 0.610894i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 10.3258 | + | 5.80203i | 1.43193 | + | 0.804597i | ||||
\(53\) | 4.06777 | − | 4.06777i | 0.558751 | − | 0.558751i | −0.370201 | − | 0.928952i | \(-0.620711\pi\) |
0.928952 | + | 0.370201i | \(0.120711\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.99355 | 0.403651 | ||||||||
\(56\) | 1.38497 | − | 3.51645i | 0.185074 | − | 0.469905i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.337865 | − | 2.45555i | −0.0443638 | − | 0.322430i | ||||
\(59\) | −4.71811 | − | 4.71811i | −0.614245 | − | 0.614245i | 0.329804 | − | 0.944049i | \(-0.393017\pi\) |
−0.944049 | + | 0.329804i | \(0.893017\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.26785 | − | 3.26785i | 0.418406 | − | 0.418406i | −0.466248 | − | 0.884654i | \(-0.654395\pi\) |
0.884654 | + | 0.466248i | \(0.154395\pi\) | |||||||
\(62\) | 2.45915 | − | 3.24383i | 0.312312 | − | 0.411967i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.85136 | − | 5.45542i | −0.731420 | − | 0.681927i | ||||
\(65\) | − | 6.39758i | − | 0.793522i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.44348 | − | 5.44348i | −0.665027 | − | 0.665027i | 0.291533 | − | 0.956561i | \(-0.405835\pi\) |
−0.956561 | + | 0.291533i | \(0.905835\pi\) | |||||||
\(68\) | 7.76518 | − | 2.17809i | 0.941666 | − | 0.264132i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.02234 | + | 0.278258i | −0.241716 | + | 0.0332582i | ||||
\(71\) | − | 3.76718i | − | 0.447082i | −0.974695 | − | 0.223541i | \(-0.928238\pi\) | ||
0.974695 | − | 0.223541i | \(-0.0717616\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.5357i | 1.23311i | 0.787312 | + | 0.616555i | \(0.211472\pi\) | ||||
−0.787312 | + | 0.616555i | \(0.788528\pi\) | |||||||
\(74\) | −0.118553 | − | 0.861623i | −0.0137815 | − | 0.100162i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.91327 | − | 10.5238i | 0.678298 | − | 1.20716i | ||||
\(77\) | 2.61822 | + | 2.61822i | 0.298374 | + | 0.298374i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.1995i | 1.26004i | 0.776578 | + | 0.630021i | \(0.216954\pi\) | ||||
−0.776578 | + | 0.630021i | \(0.783046\pi\) | |||||||
\(80\) | −1.02070 | + | 4.19887i | −0.114117 | + | 0.469447i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.80369 | + | 6.67407i | 0.972205 | + | 0.737028i | ||||
\(83\) | 9.73306 | − | 9.73306i | 1.06834 | − | 1.06834i | 0.0708558 | − | 0.997487i | \(-0.477427\pi\) |
0.997487 | − | 0.0708558i | \(-0.0225730\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.08029 | − | 3.08029i | −0.334104 | − | 0.334104i | ||||
\(86\) | 10.8909 | − | 1.49851i | 1.17440 | − | 0.161588i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 7.18757 | − | 3.12566i | 0.766197 | − | 0.333196i | ||||
\(89\) | −1.64130 | −0.173977 | −0.0869886 | − | 0.996209i | \(-0.527724\pi\) | ||||
−0.0869886 | + | 0.996209i | \(0.527724\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.59544 | − | 5.59544i | 0.586562 | − | 0.586562i | ||||
\(92\) | −17.0694 | + | 4.78787i | −1.77961 | + | 0.499170i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.61446 | + | 2.74012i | 0.372803 | + | 0.282622i | ||||
\(95\) | −6.52023 | −0.668962 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.70272 | −0.579024 | −0.289512 | − | 0.957174i | \(-0.593493\pi\) | ||||
−0.289512 | + | 0.957174i | \(0.593493\pi\) | |||||||
\(98\) | 5.87667 | + | 4.45510i | 0.593634 | + | 0.450033i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.38110 | + | 2.07036i | −0.738110 | + | 0.207036i | ||||
\(101\) | −6.68599 | + | 6.68599i | −0.665281 | + | 0.665281i | −0.956620 | − | 0.291339i | \(-0.905899\pi\) |
0.291339 | + | 0.956620i | \(0.405899\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.8784 | 1.07188 | 0.535938 | − | 0.844257i | \(-0.319958\pi\) | ||||
0.535938 | + | 0.844257i | \(0.319958\pi\) | |||||||
\(104\) | −6.67990 | − | 15.3607i | −0.655018 | − | 1.50624i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.05961 | + | 1.10894i | −0.782818 | + | 0.107710i | ||||
\(107\) | −1.31755 | − | 1.31755i | −0.127372 | − | 0.127372i | 0.640547 | − | 0.767919i | \(-0.278708\pi\) |
−0.767919 | + | 0.640547i | \(0.778708\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.51516 | + | 3.51516i | −0.336691 | + | 0.336691i | −0.855120 | − | 0.518429i | \(-0.826517\pi\) |
0.518429 | + | 0.855120i | \(0.326517\pi\) | |||||||
\(110\) | −3.37366 | − | 2.55757i | −0.321666 | − | 0.243855i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.56513 | + | 2.77969i | −0.431364 | + | 0.262656i | ||||
\(113\) | 16.3139i | 1.53469i | 0.641236 | + | 0.767344i | \(0.278422\pi\) | ||||
−0.641236 | + | 0.767344i | \(0.721578\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.77107 | + | 6.77107i | 0.631406 | + | 0.631406i | ||||
\(116\) | −1.71716 | + | 3.05600i | −0.159434 | + | 0.283742i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.28623 | + | 9.34814i | 0.118407 | + | 0.860566i | ||||
\(119\) | − | 5.38815i | − | 0.493931i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 3.32115i | − | 0.301922i | ||||||
\(122\) | −6.47470 | + | 0.890869i | −0.586192 | + | 0.0806555i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.54279 | + | 1.55472i | −0.497757 | + | 0.139618i | ||||
\(125\) | 6.74732 | + | 6.74732i | 0.603499 | + | 0.603499i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 20.7416i | − | 1.84052i | −0.391303 | − | 0.920262i | \(-0.627976\pi\) | ||
0.391303 | − | 0.920262i | \(-0.372024\pi\) | |||||||
\(128\) | 1.93345 | + | 11.1473i | 0.170895 | + | 0.985289i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.46582 | + | 7.20991i | −0.479384 | + | 0.632351i | ||||
\(131\) | −9.43621 | + | 9.43621i | −0.824446 | + | 0.824446i | −0.986742 | − | 0.162296i | \(-0.948110\pi\) |
0.162296 | + | 0.986742i | \(0.448110\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.70272 | − | 5.70272i | −0.494489 | − | 0.494489i | ||||
\(134\) | 1.48398 | + | 10.7854i | 0.128196 | + | 0.931713i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −10.6120 | − | 4.17959i | −0.909974 | − | 0.358397i | ||||
\(137\) | 12.8211 | 1.09538 | 0.547692 | − | 0.836680i | \(-0.315506\pi\) | ||||
0.547692 | + | 0.836680i | \(0.315506\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.44348 | − | 1.44348i | 0.122435 | − | 0.122435i | −0.643235 | − | 0.765669i | \(-0.722408\pi\) |
0.765669 | + | 0.643235i | \(0.222408\pi\) | |||||||
\(140\) | 2.51686 | + | 1.41421i | 0.212713 | + | 0.119523i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.21852 | + | 4.24551i | −0.270092 | + | 0.356275i | ||||
\(143\) | 16.4106 | 1.37232 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.89341 | 0.157239 | ||||||||
\(146\) | 9.00127 | − | 11.8735i | 0.744950 | − | 0.982655i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.602529 | + | 1.07231i | −0.0495276 | + | 0.0881436i | ||||
\(149\) | −6.42073 | + | 6.42073i | −0.526007 | + | 0.526007i | −0.919379 | − | 0.393372i | \(-0.871308\pi\) |
0.393372 | + | 0.919379i | \(0.371308\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.205945 | 0.0167596 | 0.00837978 | − | 0.999965i | \(-0.497333\pi\) | ||||
0.00837978 | + | 0.999965i | \(0.497333\pi\) | |||||||
\(152\) | −15.6552 | + | 6.80797i | −1.26980 | + | 0.552199i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.713769 | − | 5.18757i | −0.0575171 | − | 0.418026i | ||||
\(155\) | 2.19871 | + | 2.19871i | 0.176605 | + | 0.176605i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.26785 | + | 1.26785i | −0.101186 | + | 0.101186i | −0.755887 | − | 0.654702i | \(-0.772794\pi\) |
0.654702 | + | 0.755887i | \(0.272794\pi\) | |||||||
\(158\) | 9.56839 | − | 12.6216i | 0.761220 | − | 1.00412i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.73764 | − | 3.85997i | 0.374543 | − | 0.305158i | ||||
\(161\) | 11.8442i | 0.933456i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.169186 | + | 0.169186i | 0.0132517 | + | 0.0132517i | 0.713702 | − | 0.700450i | \(-0.247017\pi\) |
−0.700450 | + | 0.713702i | \(0.747017\pi\) | |||||||
\(164\) | −4.21949 | − | 15.0430i | −0.329486 | − | 1.17466i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −19.2844 | + | 2.65339i | −1.49676 | + | 0.205943i | ||||
\(167\) | − | 10.4503i | − | 0.808671i | −0.914611 | − | 0.404335i | \(-0.867503\pi\) | ||
0.914611 | − | 0.404335i | \(-0.132497\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 22.0714i | − | 1.69780i | ||||||
\(170\) | 0.839735 | + | 6.10307i | 0.0644048 | + | 0.468084i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −13.5541 | − | 7.61599i | −1.03349 | − | 0.580714i | ||||
\(173\) | 0.974085 | + | 0.974085i | 0.0740583 | + | 0.0740583i | 0.743166 | − | 0.669107i | \(-0.233323\pi\) |
−0.669107 | + | 0.743166i | \(0.733323\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.12165i | 0.387160i | ||||||||
\(176\) | −10.7706 | − | 2.61822i | −0.811867 | − | 0.197356i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.84970 | + | 1.40226i | 0.138641 | + | 0.105104i | ||||
\(179\) | 6.59560 | − | 6.59560i | 0.492979 | − | 0.492979i | −0.416265 | − | 0.909243i | \(-0.636661\pi\) |
0.909243 | + | 0.416265i | \(0.136661\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.1876 | + | 10.1876i | 0.757236 | + | 0.757236i | 0.975818 | − | 0.218583i | \(-0.0701433\pi\) |
−0.218583 | + | 0.975818i | \(0.570143\pi\) | |||||||
\(182\) | −11.0864 | + | 1.52541i | −0.821781 | + | 0.113071i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 23.3273 | + | 9.18757i | 1.71971 | + | 0.677316i | ||||
\(185\) | 0.664376 | 0.0488459 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.90133 | − | 7.90133i | 0.577803 | − | 0.577803i | ||||
\(188\) | −1.73236 | − | 6.17609i | −0.126345 | − | 0.450438i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.34814 | + | 5.57062i | 0.533090 | + | 0.404135i | ||||
\(191\) | −14.2297 | −1.02962 | −0.514812 | − | 0.857303i | \(-0.672138\pi\) | ||||
−0.514812 | + | 0.857303i | \(0.672138\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.53570 | 0.470450 | 0.235225 | − | 0.971941i | \(-0.424417\pi\) | ||||
0.235225 | + | 0.971941i | \(0.424417\pi\) | |||||||
\(194\) | 6.42682 | + | 4.87217i | 0.461419 | + | 0.349801i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.81661 | − | 10.0416i | −0.201186 | − | 0.717255i | ||||
\(197\) | 9.07713 | − | 9.07713i | 0.646718 | − | 0.646718i | −0.305480 | − | 0.952198i | \(-0.598817\pi\) |
0.952198 | + | 0.305480i | \(0.0988169\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.0865 | −0.715011 | −0.357505 | − | 0.933911i | \(-0.616373\pi\) | ||||
−0.357505 | + | 0.933911i | \(0.616373\pi\) | |||||||
\(200\) | 10.0871 | + | 3.97286i | 0.713268 | + | 0.280924i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 13.2472 | − | 1.82271i | 0.932068 | − | 0.128245i | ||||
\(203\) | 1.65601 | + | 1.65601i | 0.116229 | + | 0.116229i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.96725 | + | 5.96725i | −0.416771 | + | 0.416771i | ||||
\(206\) | −12.2596 | − | 9.29401i | −0.854169 | − | 0.647545i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.59544 | + | 23.0181i | −0.387974 | + | 1.59602i | ||||
\(209\) | − | 16.7252i | − | 1.15691i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.9792 | + | 17.9792i | 1.23774 | + | 1.23774i | 0.960923 | + | 0.276815i | \(0.0892789\pi\) |
0.276815 | + | 0.960923i | \(0.410721\pi\) | |||||||
\(212\) | 10.0304 | + | 5.63605i | 0.688891 | + | 0.387085i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.359185 | + | 2.61050i | 0.0245534 | + | 0.178450i | ||||
\(215\) | 8.39773i | 0.572721i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.84607i | 0.261088i | ||||||||
\(218\) | 6.96470 | − | 0.958288i | 0.471709 | − | 0.0649035i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.61695 | + | 5.76463i | 0.109015 | + | 0.388651i | ||||
\(221\) | −16.8861 | − | 16.8861i | −1.13588 | − | 1.13588i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 4.00861i | − | 0.268437i | −0.990952 | − | 0.134218i | \(-0.957148\pi\) | ||
0.990952 | − | 0.134218i | \(-0.0428523\pi\) | |||||||
\(224\) | 7.51963 | + | 0.767620i | 0.502427 | + | 0.0512888i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.9380 | − | 18.3854i | 0.927139 | − | 1.22298i | ||||
\(227\) | −13.7915 | + | 13.7915i | −0.915373 | + | 0.915373i | −0.996688 | − | 0.0813152i | \(-0.974088\pi\) |
0.0813152 | + | 0.996688i | \(0.474088\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.47840 | + | 3.47840i | 0.229859 | + | 0.229859i | 0.812634 | − | 0.582775i | \(-0.198033\pi\) |
−0.582775 | + | 0.812634i | \(0.698033\pi\) | |||||||
\(230\) | −1.84590 | − | 13.4158i | −0.121715 | − | 0.884609i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.54611 | − | 1.97697i | 0.298467 | − | 0.129794i | ||||
\(233\) | 3.23973 | 0.212241 | 0.106121 | − | 0.994353i | \(-0.466157\pi\) | ||||
0.106121 | + | 0.994353i | \(0.466157\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.44993 | + | 2.44993i | −0.159816 | + | 0.159816i | ||||
\(236\) | 6.53711 | − | 11.6340i | 0.425530 | − | 0.757310i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.60342 | + | 6.07231i | −0.298395 | + | 0.393610i | ||||
\(239\) | 24.2484 | 1.56850 | 0.784249 | − | 0.620446i | \(-0.213048\pi\) | ||||
0.784249 | + | 0.620446i | \(0.213048\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.5596 | 1.06670 | 0.533348 | − | 0.845896i | \(-0.320934\pi\) | ||||
0.533348 | + | 0.845896i | \(0.320934\pi\) | |||||||
\(242\) | −2.83745 | + | 3.74285i | −0.182398 | + | 0.240599i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.05795 | + | 4.52773i | 0.515857 | + | 0.289858i | ||||
\(245\) | −3.98329 | + | 3.98329i | −0.254483 | + | 0.254483i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −35.7438 | −2.27432 | ||||||||
\(248\) | 7.57487 | + | 2.98340i | 0.481005 | + | 0.189446i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.83943 | − | 13.3687i | −0.116336 | − | 0.845510i | ||||
\(251\) | −11.3957 | − | 11.3957i | −0.719287 | − | 0.719287i | 0.249172 | − | 0.968459i | \(-0.419842\pi\) |
−0.968459 | + | 0.249172i | \(0.919842\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.3687 | + | 17.3687i | −1.09196 | + | 1.09196i | ||||
\(254\) | −17.7208 | + | 23.3753i | −1.11190 | + | 1.46670i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.34482 | − | 14.2146i | 0.459051 | − | 0.888410i | ||||
\(257\) | 3.54316i | 0.221016i | 0.993875 | + | 0.110508i | \(0.0352478\pi\) | ||||
−0.993875 | + | 0.110508i | \(0.964752\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.581076 | + | 0.581076i | 0.0361063 | + | 0.0361063i | ||||
\(260\) | 12.3197 | − | 3.45561i | 0.764035 | − | 0.214308i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 18.6963 | − | 2.57246i | 1.15506 | − | 0.158927i | ||||
\(263\) | − | 21.0534i | − | 1.29821i | −0.760701 | − | 0.649103i | \(-0.775145\pi\) | ||
0.760701 | − | 0.649103i | \(-0.224855\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 6.21456i | − | 0.381757i | ||||||
\(266\) | 1.55465 | + | 11.2990i | 0.0953219 | + | 0.692786i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.54215 | − | 13.4227i | 0.460710 | − | 0.819920i | ||||
\(269\) | −20.4077 | − | 20.4077i | −1.24428 | − | 1.24428i | −0.958208 | − | 0.286072i | \(-0.907650\pi\) |
−0.286072 | − | 0.958208i | \(-0.592350\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 5.06279i | − | 0.307543i | −0.988106 | − | 0.153771i | \(-0.950858\pi\) | ||
0.988106 | − | 0.153771i | \(-0.0491419\pi\) | |||||||
\(272\) | 8.38862 | + | 13.7768i | 0.508635 | + | 0.835339i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.4491 | − | 10.9539i | −0.872902 | − | 0.661747i | ||||
\(275\) | −7.51052 | + | 7.51052i | −0.452901 | + | 0.452901i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.86642 | − | 5.86642i | −0.352479 | − | 0.352479i | 0.508552 | − | 0.861031i | \(-0.330181\pi\) |
−0.861031 | + | 0.508552i | \(0.830181\pi\) | |||||||
\(278\) | −2.86002 | + | 0.393517i | −0.171533 | + | 0.0236016i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.62819 | − | 3.74408i | −0.0973030 | − | 0.223752i | ||||
\(281\) | 4.77316 | 0.284743 | 0.142371 | − | 0.989813i | \(-0.454527\pi\) | ||||
0.142371 | + | 0.989813i | \(0.454527\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.0779 | + | 10.0779i | −0.599066 | + | 0.599066i | −0.940064 | − | 0.340998i | \(-0.889235\pi\) |
0.340998 | + | 0.940064i | \(0.389235\pi\) | |||||||
\(284\) | 7.25438 | − | 2.03481i | 0.430468 | − | 0.120744i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −18.4943 | − | 14.0205i | −1.09359 | − | 0.829052i | ||||
\(287\) | −10.4381 | −0.616144 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.739481 | 0.0434989 | ||||||||
\(290\) | −2.13383 | − | 1.61765i | −0.125303 | − | 0.0949919i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −20.2884 | + | 5.69079i | −1.18729 | + | 0.333028i | ||||
\(293\) | 11.7829 | − | 11.7829i | 0.688364 | − | 0.688364i | −0.273506 | − | 0.961870i | \(-0.588183\pi\) |
0.961870 | + | 0.273506i | \(0.0881834\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.20811 | −0.419673 | ||||||||
\(296\) | 1.59517 | − | 0.693694i | 0.0927177 | − | 0.0403202i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12.7216 | − | 1.75039i | 0.736943 | − | 0.101398i | ||||
\(299\) | 37.1189 | + | 37.1189i | 2.14664 | + | 2.14664i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.34482 | + | 7.34482i | −0.423348 | + | 0.423348i | ||||
\(302\) | −0.232095 | − | 0.175951i | −0.0133555 | − | 0.0101248i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 23.4594 | + | 5.70272i | 1.34549 | + | 0.327074i | ||||
\(305\) | − | 4.99248i | − | 0.285869i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.31322 | − | 4.31322i | −0.246169 | − | 0.246169i | 0.573228 | − | 0.819396i | \(-0.305691\pi\) |
−0.819396 | + | 0.573228i | \(0.805691\pi\) | |||||||
\(308\) | −3.62764 | + | 6.45607i | −0.206704 | + | 0.367869i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.599404 | − | 4.35638i | −0.0340438 | − | 0.247426i | ||||
\(311\) | 27.4434i | 1.55617i | 0.628156 | + | 0.778087i | \(0.283810\pi\) | ||||
−0.628156 | + | 0.778087i | \(0.716190\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 18.8568i | − | 1.06585i | −0.846162 | − | 0.532926i | \(-0.821092\pi\) | ||
0.846162 | − | 0.532926i | \(-0.178908\pi\) | |||||||
\(314\) | 2.51204 | − | 0.345637i | 0.141762 | − | 0.0195054i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −21.5667 | + | 6.04933i | −1.21322 | + | 0.340302i | ||||
\(317\) | −0.154552 | − | 0.154552i | −0.00868053 | − | 0.00868053i | 0.702753 | − | 0.711434i | \(-0.251954\pi\) |
−0.711434 | + | 0.702753i | \(0.751954\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.85685i | 0.271931i | ||||||||
\(320\) | −8.63700 | + | 0.302453i | −0.482823 | + | 0.0169076i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 10.1192 | − | 13.3481i | 0.563922 | − | 0.743863i | ||||
\(323\) | −17.2098 | + | 17.2098i | −0.957580 | + | 0.957580i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.0509 | + | 16.0509i | 0.890342 | + | 0.890342i | ||||
\(326\) | −0.0461227 | − | 0.335213i | −0.00255450 | − | 0.0185657i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8.09687 | + | 20.5580i | −0.447075 | + | 1.13513i | ||||
\(329\) | −4.28551 | −0.236268 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.3132 | + | 16.3132i | −0.896656 | + | 0.896656i | −0.995139 | − | 0.0984829i | \(-0.968601\pi\) |
0.0984829 | + | 0.995139i | \(0.468601\pi\) | |||||||
\(332\) | 24.0000 | + | 13.4855i | 1.31717 | + | 0.740114i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.92833 | + | 11.7773i | −0.488536 | + | 0.644423i | ||||
\(335\) | −8.31631 | −0.454369 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.89341 | 0.103141 | 0.0515704 | − | 0.998669i | \(-0.483577\pi\) | ||||
0.0515704 | + | 0.998669i | \(0.483577\pi\) | |||||||
\(338\) | −18.8569 | + | 24.8739i | −1.02568 | + | 1.35296i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.26785 | − | 7.59544i | 0.231457 | − | 0.411921i | ||||
\(341\) | −5.63998 | + | 5.63998i | −0.305422 | + | 0.305422i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.3211 | −0.881259 | ||||||||
\(344\) | 8.76832 | + | 20.1631i | 0.472756 | + | 1.08712i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.265551 | − | 1.92999i | −0.0142761 | − | 0.103757i | ||||
\(347\) | −19.7630 | − | 19.7630i | −1.06093 | − | 1.06093i | −0.998019 | − | 0.0629131i | \(-0.979961\pi\) |
−0.0629131 | − | 0.998019i | \(-0.520039\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.1008 | − | 18.1008i | 0.968915 | − | 0.968915i | −0.0306158 | − | 0.999531i | \(-0.509747\pi\) |
0.999531 | + | 0.0306158i | \(0.00974685\pi\) | |||||||
\(350\) | 4.37572 | − | 5.77197i | 0.233892 | − | 0.308525i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9.90133 | + | 12.1527i | 0.527743 | + | 0.647738i | ||||
\(353\) | − | 19.3695i | − | 1.03093i | −0.856910 | − | 0.515466i | \(-0.827619\pi\) | ||
0.856910 | − | 0.515466i | \(-0.172381\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.87766 | − | 2.87766i | −0.152730 | − | 0.152730i | ||||
\(356\) | −0.886536 | − | 3.16061i | −0.0469863 | − | 0.167512i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.0681 | + | 1.79807i | −0.690670 | + | 0.0950308i | ||||
\(359\) | − | 7.09236i | − | 0.374321i | −0.982329 | − | 0.187160i | \(-0.940072\pi\) | ||
0.982329 | − | 0.187160i | \(-0.0599284\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.4291i | 0.917322i | ||||||||
\(362\) | −2.77729 | − | 20.1850i | −0.145971 | − | 1.06090i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 13.7974 | + | 7.75270i | 0.723179 | + | 0.406352i | ||||
\(365\) | 8.04799 | + | 8.04799i | 0.421251 | + | 0.421251i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 1.65735i | − | 0.0865130i | −0.999064 | − | 0.0432565i | \(-0.986227\pi\) | ||
0.999064 | − | 0.0432565i | \(-0.0137733\pi\) | |||||||
\(368\) | −18.4398 | − | 30.2840i | −0.961242 | − | 1.57867i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.748734 | − | 0.567615i | −0.0389248 | − | 0.0295089i | ||||
\(371\) | 5.43537 | − | 5.43537i | 0.282190 | − | 0.282190i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.48241 | − | 3.48241i | −0.180312 | − | 0.180312i | 0.611180 | − | 0.791492i | \(-0.290695\pi\) |
−0.791492 | + | 0.611180i | \(0.790695\pi\) | |||||||
\(374\) | −15.6552 | + | 2.15403i | −0.809510 | + | 0.111382i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.32427 | + | 8.44036i | −0.171436 | + | 0.435278i | ||||
\(377\) | 10.3797 | 0.534579 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.1548 | − | 19.1548i | 0.983917 | − | 0.983917i | −0.0159558 | − | 0.999873i | \(-0.505079\pi\) |
0.999873 | + | 0.0159558i | \(0.00507910\pi\) | |||||||
\(380\) | −3.52186 | − | 12.5559i | −0.180668 | − | 0.644103i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 16.0365 | + | 12.1573i | 0.820498 | + | 0.622019i | ||||
\(383\) | 15.2907 | 0.781319 | 0.390660 | − | 0.920535i | \(-0.372247\pi\) | ||||
0.390660 | + | 0.920535i | \(0.372247\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.00000 | 0.203859 | ||||||||
\(386\) | −7.36557 | − | 5.58383i | −0.374898 | − | 0.284210i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.08029 | − | 10.9816i | −0.156378 | − | 0.557507i | ||||
\(389\) | −22.7144 | + | 22.7144i | −1.15166 | + | 1.15166i | −0.165445 | + | 0.986219i | \(0.552906\pi\) |
−0.986219 | + | 0.165445i | \(0.947094\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 35.7438 | 1.80764 | ||||||||
\(392\) | −5.40486 | + | 13.7230i | −0.272987 | + | 0.693116i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −17.9848 | + | 2.47457i | −0.906062 | + | 0.124667i | ||||
\(395\) | 8.55505 | + | 8.55505i | 0.430451 | + | 0.430451i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.45854 | − | 7.45854i | 0.374334 | − | 0.374334i | −0.494719 | − | 0.869053i | \(-0.664729\pi\) |
0.869053 | + | 0.494719i | \(0.164729\pi\) | |||||||
\(398\) | 11.3672 | + | 8.61746i | 0.569786 | + | 0.431954i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.97370 | − | 13.0953i | −0.398685 | − | 0.654767i | ||||
\(401\) | 11.5911i | 0.578834i | 0.957203 | + | 0.289417i | \(0.0934615\pi\) | ||||
−0.957203 | + | 0.289417i | \(0.906539\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.0533 | + | 12.0533i | 0.600417 | + | 0.600417i | ||||
\(404\) | −16.4865 | − | 9.26369i | −0.820233 | − | 0.460886i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.451456 | − | 3.28112i | −0.0224054 | − | 0.162839i | ||||
\(407\) | 1.70421i | 0.0844745i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 12.4659i | − | 0.616398i | −0.951322 | − | 0.308199i | \(-0.900274\pi\) | ||
0.951322 | − | 0.308199i | \(-0.0997262\pi\) | |||||||
\(410\) | 11.8231 | − | 1.62677i | 0.583902 | − | 0.0803404i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.87587 | + | 20.9482i | 0.289483 | + | 1.03205i | ||||
\(413\) | −6.30435 | − | 6.30435i | −0.310217 | − | 0.310217i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 14.8697i | − | 0.729927i | ||||||
\(416\) | 25.9716 | − | 21.1603i | 1.27336 | − | 1.03747i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −14.2894 | + | 18.8489i | −0.698915 | + | 0.921931i | ||||
\(419\) | 14.4096 | − | 14.4096i | 0.703953 | − | 0.703953i | −0.261304 | − | 0.965257i | \(-0.584152\pi\) |
0.965257 | + | 0.261304i | \(0.0841525\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.83630 | − | 5.83630i | −0.284444 | − | 0.284444i | 0.550434 | − | 0.834878i | \(-0.314462\pi\) |
−0.834878 | + | 0.550434i | \(0.814462\pi\) | |||||||
\(422\) | −4.90141 | − | 35.6228i | −0.238597 | − | 1.73409i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.48880 | − | 14.9212i | −0.315124 | − | 0.724640i | ||||
\(425\) | 15.4562 | 0.749738 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.36652 | − | 4.36652i | 0.211311 | − | 0.211311i | ||||
\(428\) | 1.82551 | − | 3.24884i | 0.0882395 | − | 0.157039i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.17467 | − | 9.46403i | 0.345993 | − | 0.456396i | ||||
\(431\) | 18.4510 | 0.888755 | 0.444377 | − | 0.895840i | \(-0.353425\pi\) | ||||
0.444377 | + | 0.895840i | \(0.353425\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.58166 | 0.316295 | 0.158147 | − | 0.987416i | \(-0.449448\pi\) | ||||
0.158147 | + | 0.987416i | \(0.449448\pi\) | |||||||
\(434\) | 3.28592 | − | 4.33442i | 0.157729 | − | 0.208059i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.66776 | − | 4.87038i | −0.415110 | − | 0.233249i | ||||
\(437\) | 37.8306 | − | 37.8306i | 1.80968 | − | 1.80968i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.68747 | 0.175993 | 0.0879966 | − | 0.996121i | \(-0.471954\pi\) | ||||
0.0879966 | + | 0.996121i | \(0.471954\pi\) | |||||||
\(440\) | 3.10280 | − | 7.87804i | 0.147920 | − | 0.375571i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.60342 | + | 33.4569i | 0.218962 | + | 1.59138i | ||||
\(443\) | −3.31861 | − | 3.31861i | −0.157672 | − | 0.157672i | 0.623862 | − | 0.781534i | \(-0.285563\pi\) |
−0.781534 | + | 0.623862i | \(0.785563\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.25375 | + | 1.25375i | −0.0594335 | + | 0.0594335i | ||||
\(446\) | −3.42479 | + | 4.51760i | −0.162169 | + | 0.213915i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7.81861 | − | 7.28955i | −0.369395 | − | 0.344399i | ||||
\(449\) | 20.3555i | 0.960635i | 0.877095 | + | 0.480318i | \(0.159479\pi\) | ||||
−0.877095 | + | 0.480318i | \(0.840521\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.3068 | − | 15.3068i | −0.720768 | − | 0.720768i | ||||
\(452\) | −31.4155 | + | 8.81187i | −1.47766 | + | 0.414475i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 27.3255 | − | 3.75978i | 1.28245 | − | 0.176455i | ||||
\(455\) | − | 8.54847i | − | 0.400758i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.0239i | 0.468897i | 0.972129 | + | 0.234448i | \(0.0753284\pi\) | ||||
−0.972129 | + | 0.234448i | \(0.924672\pi\) | |||||||
\(458\) | −0.948267 | − | 6.89186i | −0.0443096 | − | 0.322036i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.38158 | + | 16.6963i | −0.437418 | + | 0.778468i | ||||
\(461\) | 16.4043 | + | 16.4043i | 0.764026 | + | 0.764026i | 0.977048 | − | 0.213021i | \(-0.0683304\pi\) |
−0.213021 | + | 0.977048i | \(0.568330\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.997833i | 0.0463732i | 0.999731 | + | 0.0231866i | \(0.00738119\pi\) | ||||
−0.999731 | + | 0.0231866i | \(0.992619\pi\) | |||||||
\(464\) | −6.81239 | − | 1.65601i | −0.316257 | − | 0.0768786i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.65109 | − | 2.76789i | −0.169133 | − | 0.128220i | ||||
\(467\) | 9.73306 | − | 9.73306i | 0.450392 | − | 0.450392i | −0.445092 | − | 0.895485i | \(-0.646829\pi\) |
0.895485 | + | 0.445092i | \(0.146829\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.27361 | − | 7.27361i | −0.335864 | − | 0.335864i | ||||
\(470\) | 4.85413 | − | 0.667890i | 0.223904 | − | 0.0308075i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −17.3068 | + | 7.52620i | −0.796609 | + | 0.346422i | ||||
\(473\) | −21.5413 | −0.990469 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.3586 | − | 16.3586i | 0.750584 | − | 0.750584i | ||||
\(476\) | 10.3759 | − | 2.91038i | 0.475577 | − | 0.133397i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −27.3273 | − | 20.7168i | −1.24992 | − | 0.947565i | ||||
\(479\) | −37.0669 | −1.69363 | −0.846816 | − | 0.531886i | \(-0.821483\pi\) | ||||
−0.846816 | + | 0.531886i | \(0.821483\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.64210 | 0.166065 | ||||||||
\(482\) | −18.6622 | − | 14.1478i | −0.850041 | − | 0.644415i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.39546 | − | 1.79389i | 0.290703 | − | 0.0815406i | ||||
\(485\) | −4.35618 | + | 4.35618i | −0.197804 | + | 0.197804i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.1866 | 1.50383 | 0.751914 | − | 0.659261i | \(-0.229131\pi\) | ||||
0.751914 | + | 0.659261i | \(0.229131\pi\) | |||||||
\(488\) | −5.21280 | − | 11.9870i | −0.235972 | − | 0.542627i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 7.89221 | − | 1.08591i | 0.356534 | − | 0.0490563i | ||||
\(491\) | −10.2580 | − | 10.2580i | −0.462936 | − | 0.462936i | 0.436681 | − | 0.899617i | \(-0.356154\pi\) |
−0.899617 | + | 0.436681i | \(0.856154\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.99757 | − | 4.99757i | 0.225079 | − | 0.225079i | ||||
\(494\) | 40.2824 | + | 30.5380i | 1.81239 | + | 1.37397i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.98780 | − | 9.83387i | −0.268860 | − | 0.441554i | ||||
\(497\) | − | 5.03372i | − | 0.225793i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.19733 | + | 4.19733i | 0.187898 | + | 0.187898i | 0.794787 | − | 0.606889i | \(-0.207583\pi\) |
−0.606889 | + | 0.794787i | \(0.707583\pi\) | |||||||
\(500\) | −9.34866 | + | 16.6377i | −0.418085 | + | 0.744060i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.10664 | + | 22.5786i | 0.138656 | + | 1.00773i | ||||
\(503\) | 21.0655i | 0.939266i | 0.882862 | + | 0.469633i | \(0.155614\pi\) | ||||
−0.882862 | + | 0.469633i | \(0.844386\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.2146i | 0.454542i | ||||||||
\(506\) | 34.4131 | − | 4.73498i | 1.52985 | − | 0.210496i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 39.9418 | − | 11.2035i | 1.77213 | − | 0.497073i | ||||
\(509\) | 22.6424 | + | 22.6424i | 1.00361 | + | 1.00361i | 0.999993 | + | 0.00361481i | \(0.00115063\pi\) |
0.00361481 | + | 0.999993i | \(0.498849\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.0779i | 0.622768i | ||||||||
\(512\) | −20.4218 | + | 9.74434i | −0.902522 | + | 0.430643i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.02713 | − | 3.99305i | 0.133521 | − | 0.176126i | ||||
\(515\) | 8.30973 | − | 8.30973i | 0.366171 | − | 0.366171i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.28439 | − | 6.28439i | −0.276387 | − | 0.276387i | ||||
\(518\) | −0.158411 | − | 1.15130i | −0.00696016 | − | 0.0505854i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −16.8363 | − | 6.63105i | −0.738321 | − | 0.290791i | ||||
\(521\) | −38.3351 | −1.67949 | −0.839746 | − | 0.542980i | \(-0.817296\pi\) | ||||
−0.839746 | + | 0.542980i | \(0.817296\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.39811 | + | 5.39811i | −0.236043 | + | 0.236043i | −0.815209 | − | 0.579166i | \(-0.803378\pi\) |
0.579166 | + | 0.815209i | \(0.303378\pi\) | |||||||
\(524\) | −23.2680 | − | 13.0742i | −1.01647 | − | 0.571150i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.9871 | + | 23.7266i | −0.784275 | + | 1.03453i | ||||
\(527\) | 11.6068 | 0.505599 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −55.5719 | −2.41617 | ||||||||
\(530\) | −5.30946 | + | 7.00365i | −0.230628 | + | 0.304219i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.90133 | − | 14.0619i | 0.342566 | − | 0.609661i | ||||
\(533\) | −32.7124 | + | 32.7124i | −1.41693 | + | 1.41693i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.01289 | −0.0870249 | ||||||||
\(536\) | −19.9676 | + | 8.68331i | −0.862468 | + | 0.375062i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.56347 | + | 40.4345i | 0.239858 | + | 1.74325i | ||||
\(539\) | −10.2176 | − | 10.2176i | −0.440105 | − | 0.440105i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.51516 | − | 5.51516i | 0.237115 | − | 0.237115i | −0.578539 | − | 0.815654i | \(-0.696377\pi\) |
0.815654 | + | 0.578539i | \(0.196377\pi\) | |||||||
\(542\) | −4.32544 | + | 5.70564i | −0.185794 | + | 0.245078i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.31654 | − | 22.6930i | 0.0993210 | − | 0.972952i | ||||
\(545\) | 5.37030i | 0.230038i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.2535 | − | 23.2535i | −0.994247 | − | 0.994247i | 0.00573636 | − | 0.999984i | \(-0.498174\pi\) |
−0.999984 | + | 0.00573636i | \(0.998174\pi\) | |||||||
\(548\) | 6.92525 | + | 24.6894i | 0.295832 | + | 1.05468i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 14.8808 | − | 2.04749i | 0.634521 | − | 0.0873052i | ||||
\(551\) | − | 10.5787i | − | 0.450666i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.9648i | 0.636369i | ||||||||
\(554\) | 1.59928 | + | 11.6233i | 0.0679469 | + | 0.493828i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.55938 | + | 2.00000i | 0.150951 | + | 0.0848189i | ||||
\(557\) | 26.9066 | + | 26.9066i | 1.14007 | + | 1.14007i | 0.988437 | + | 0.151635i | \(0.0484537\pi\) |
0.151635 | + | 0.988437i | \(0.451546\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 46.0362i | 1.94712i | ||||||||
\(560\) | −1.36386 | + | 5.61054i | −0.0576336 | + | 0.237089i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.37922 | − | 4.07799i | −0.226909 | − | 0.172019i | ||||
\(563\) | 21.4144 | − | 21.4144i | 0.902508 | − | 0.902508i | −0.0931446 | − | 0.995653i | \(-0.529692\pi\) |
0.995653 | + | 0.0931446i | \(0.0296919\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.4619 | + | 12.4619i | 0.524275 | + | 0.524275i | ||||
\(566\) | 19.9676 | − | 2.74738i | 0.839300 | − | 0.115481i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.91396 | − | 3.90465i | −0.415980 | − | 0.163836i | ||||
\(569\) | −1.54807 | −0.0648986 | −0.0324493 | − | 0.999473i | \(-0.510331\pi\) | ||||
−0.0324493 | + | 0.999473i | \(0.510331\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.3384 | + | 12.3384i | −0.516345 | + | 0.516345i | −0.916463 | − | 0.400119i | \(-0.868969\pi\) |
0.400119 | + | 0.916463i | \(0.368969\pi\) | |||||||
\(572\) | 8.86408 | + | 31.6016i | 0.370626 | + | 1.32133i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 11.7635 | + | 8.91792i | 0.491000 | + | 0.372227i | ||||
\(575\) | −33.9759 | −1.41689 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.9648 | −1.03930 | −0.519650 | − | 0.854380i | \(-0.673937\pi\) | ||||
−0.519650 | + | 0.854380i | \(0.673937\pi\) | |||||||
\(578\) | −0.833376 | − | 0.631782i | −0.0346639 | − | 0.0262787i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.02271 | + | 3.64611i | 0.0424659 | + | 0.151396i | ||||
\(581\) | 13.0054 | − | 13.0054i | 0.539553 | − | 0.539553i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.9411 | 0.660215 | ||||||||
\(584\) | 27.7265 | + | 10.9202i | 1.14733 | + | 0.451881i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −23.3458 | + | 3.21221i | −0.964408 | + | 0.132695i | ||||
\(587\) | −3.99426 | − | 3.99426i | −0.164861 | − | 0.164861i | 0.619855 | − | 0.784716i | \(-0.287191\pi\) |
−0.784716 | + | 0.619855i | \(0.787191\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.2844 | − | 12.2844i | 0.506169 | − | 0.506169i | ||||
\(590\) | 8.12336 | + | 6.15831i | 0.334433 | + | 0.253534i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.39038 | − | 0.581076i | −0.0982442 | − | 0.0238821i | ||||
\(593\) | 21.0442i | 0.864183i | 0.901830 | + | 0.432092i | \(0.142224\pi\) | ||||
−0.901830 | + | 0.432092i | \(0.857776\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.11589 | − | 4.11589i | −0.168735 | − | 0.168735i | ||||
\(596\) | −15.8324 | − | 8.89616i | −0.648520 | − | 0.364401i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −10.1192 | − | 73.5449i | −0.413805 | − | 3.00748i | ||||
\(599\) | − | 12.7718i | − | 0.521840i | −0.965360 | − | 0.260920i | \(-0.915974\pi\) | ||
0.965360 | − | 0.260920i | \(-0.0840259\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 44.2967i | 1.80690i | 0.428691 | + | 0.903451i | \(0.358975\pi\) | ||||
−0.428691 | + | 0.903451i | \(0.641025\pi\) | |||||||
\(602\) | 14.5525 | − | 2.00232i | 0.593117 | − | 0.0816083i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.111240 | + | 0.396584i | 0.00452628 | + | 0.0161368i | ||||
\(605\) | −2.53695 | − | 2.53695i | −0.103142 | − | 0.103142i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 26.8784i | − | 1.09096i | −0.838124 | − | 0.545479i | \(-0.816348\pi\) | ||
0.838124 | − | 0.545479i | \(-0.183652\pi\) | |||||||
\(608\) | −21.5660 | − | 26.4696i | −0.874617 | − | 1.07348i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.26537 | + | 5.62640i | −0.172700 | + | 0.227806i | ||||
\(611\) | −13.4305 | + | 13.4305i | −0.543339 | + | 0.543339i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.6602 | − | 27.6602i | −1.11719 | − | 1.11719i | −0.992153 | − | 0.125033i | \(-0.960096\pi\) |
−0.125033 | − | 0.992153i | \(-0.539904\pi\) | |||||||
\(614\) | 1.17585 | + | 8.54593i | 0.0474536 | + | 0.344886i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.60406 | − | 4.17652i | 0.386958 | − | 0.168277i | ||||
\(617\) | 19.6148 | 0.789661 | 0.394831 | − | 0.918754i | \(-0.370803\pi\) | ||||
0.394831 | + | 0.918754i | \(0.370803\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.7854 | + | 11.7854i | −0.473697 | + | 0.473697i | −0.903109 | − | 0.429412i | \(-0.858721\pi\) |
0.429412 | + | 0.903109i | \(0.358721\pi\) | |||||||
\(620\) | −3.04640 | + | 5.42163i | −0.122346 | + | 0.217738i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 23.4465 | − | 30.9281i | 0.940120 | − | 1.24010i | ||||
\(623\) | −2.19311 | −0.0878651 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.85665 | −0.354266 | ||||||||
\(626\) | −16.1105 | + | 21.2512i | −0.643905 | + | 0.849368i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.12630 | − | 1.75666i | −0.124753 | − | 0.0700982i | ||||
\(629\) | 1.75359 | − | 1.75359i | 0.0699200 | − | 0.0699200i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.8195 | 0.749193 | 0.374596 | − | 0.927188i | \(-0.377781\pi\) | ||||
0.374596 | + | 0.927188i | \(0.377781\pi\) | |||||||
\(632\) | 29.4734 | + | 11.6082i | 1.17239 | + | 0.461750i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.0421335 | + | 0.306220i | 0.00167333 | + | 0.0121615i | ||||
\(635\) | −15.8441 | − | 15.8441i | −0.628753 | − | 0.628753i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −21.8363 | + | 21.8363i | −0.865186 | + | 0.865186i | ||||
\(638\) | 4.14949 | − | 5.47354i | 0.164280 | − | 0.216700i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 9.99208 | + | 7.03823i | 0.394972 | + | 0.278211i | ||||
\(641\) | − | 17.9718i | − | 0.709845i | −0.934896 | − | 0.354923i | \(-0.884507\pi\) | ||
0.934896 | − | 0.354923i | \(-0.115493\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.92589 | − | 9.92589i | −0.391439 | − | 0.391439i | 0.483761 | − | 0.875200i | \(-0.339270\pi\) |
−0.875200 | + | 0.483761i | \(0.839270\pi\) | |||||||
\(644\) | −22.8082 | + | 6.39758i | −0.898769 | + | 0.252100i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 34.0984 | − | 4.69168i | 1.34158 | − | 0.184591i | ||||
\(647\) | 13.6801i | 0.537820i | 0.963165 | + | 0.268910i | \(0.0866635\pi\) | ||||
−0.963165 | + | 0.268910i | \(0.913337\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 18.4897i | − | 0.725786i | ||||||
\(650\) | −4.37572 | − | 31.8021i | −0.171630 | − | 1.24738i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.234413 | + | 0.417182i | −0.00918033 | + | 0.0163381i | ||||
\(653\) | −31.1940 | − | 31.1940i | −1.22071 | − | 1.22071i | −0.967378 | − | 0.253336i | \(-0.918472\pi\) |
−0.253336 | − | 0.967378i | \(-0.581528\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.4162i | 0.563288i | ||||||||
\(656\) | 26.6889 | − | 16.2508i | 1.04203 | − | 0.634486i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.82966 | + | 3.66136i | 0.188280 | + | 0.142735i | ||||
\(659\) | 27.2397 | − | 27.2397i | 1.06111 | − | 1.06111i | 0.0631026 | − | 0.998007i | \(-0.479900\pi\) |
0.998007 | − | 0.0631026i | \(-0.0200995\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.0770 | − | 12.0770i | −0.469740 | − | 0.469740i | 0.432091 | − | 0.901830i | \(-0.357776\pi\) |
−0.901830 | + | 0.432091i | \(0.857776\pi\) | |||||||
\(662\) | 32.3219 | − | 4.44725i | 1.25623 | − | 0.172847i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15.5259 | − | 35.7025i | −0.602523 | − | 1.38552i | ||||
\(665\) | −8.71237 | −0.337851 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.9856 | + | 10.9856i | −0.425365 | + | 0.425365i | ||||
\(668\) | 20.1240 | − | 5.64467i | 0.778621 | − | 0.218399i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 9.37227 | + | 7.10511i | 0.362082 | + | 0.274494i | ||||
\(671\) | 12.8064 | 0.494384 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.0108 | 0.424434 | 0.212217 | − | 0.977223i | \(-0.431932\pi\) | ||||
0.212217 | + | 0.977223i | \(0.431932\pi\) | |||||||
\(674\) | −2.13383 | − | 1.61765i | −0.0821920 | − | 0.0623097i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 42.5025 | − | 11.9217i | 1.63471 | − | 0.458528i | ||||
\(677\) | −5.26708 | + | 5.26708i | −0.202430 | + | 0.202430i | −0.801040 | − | 0.598610i | \(-0.795720\pi\) |
0.598610 | + | 0.801040i | \(0.295720\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.62000 | −0.292429 | ||||||||
\(680\) | −11.2990 | + | 4.91360i | −0.433297 | + | 0.188428i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 11.1747 | − | 1.53755i | 0.427900 | − | 0.0588758i | ||||
\(683\) | −16.0080 | − | 16.0080i | −0.612528 | − | 0.612528i | 0.331076 | − | 0.943604i | \(-0.392588\pi\) |
−0.943604 | + | 0.331076i | \(0.892588\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.79379 | − | 9.79379i | 0.374201 | − | 0.374201i | ||||
\(686\) | 18.3935 | + | 13.9441i | 0.702268 | + | 0.532389i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.34482 | − | 30.2146i | 0.280019 | − | 1.15192i | ||||
\(689\) | − | 34.0681i | − | 1.29789i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.63348 | + | 7.63348i | 0.290391 | + | 0.290391i | 0.837235 | − | 0.546843i | \(-0.184171\pi\) |
−0.546843 | + | 0.837235i | \(0.684171\pi\) | |||||||
\(692\) | −1.34963 | + | 2.40192i | −0.0513053 | + | 0.0913074i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.38770 | + | 39.1570i | 0.204514 | + | 1.48638i | ||||
\(695\) | − | 2.20529i | − | 0.0836514i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 31.5005i | 1.19317i | ||||||||
\(698\) | −35.8638 | + | 4.93458i | −1.35746 | + | 0.186777i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −9.86265 | + | 2.76642i | −0.372773 | + | 0.104561i | ||||
\(701\) | 18.3494 | + | 18.3494i | 0.693049 | + | 0.693049i | 0.962902 | − | 0.269853i | \(-0.0869750\pi\) |
−0.269853 | + | 0.962902i | \(0.586975\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 3.71192i | − | 0.139998i | ||||||
\(704\) | −0.775831 | − | 22.1550i | −0.0292402 | − | 0.834999i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −16.5485 | + | 21.8289i | −0.622810 | + | 0.821541i | ||||
\(707\) | −8.93385 | + | 8.93385i | −0.335992 | + | 0.335992i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.8774 | + | 19.8774i | 0.746511 | + | 0.746511i | 0.973822 | − | 0.227311i | \(-0.0729934\pi\) |
−0.227311 | + | 0.973822i | \(0.572993\pi\) | |||||||
\(710\) | 0.784497 | + | 5.70161i | 0.0294416 | + | 0.213977i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.70119 | + | 4.31935i | −0.0637550 | + | 0.161875i | ||||
\(713\) | −25.5140 | −0.955505 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.5357 | − | 12.5357i | 0.468809 | − | 0.468809i | ||||
\(716\) | 16.2636 | + | 9.13845i | 0.607799 | + | 0.341520i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6.05942 | + | 7.99291i | −0.226136 | + | 0.298293i | ||||
\(719\) | 16.1176 | 0.601083 | 0.300542 | − | 0.953769i | \(-0.402833\pi\) | ||||
0.300542 | + | 0.953769i | \(0.402833\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.5357 | 0.541338 | ||||||||
\(722\) | 14.8907 | − | 19.6422i | 0.554175 | − | 0.731006i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −14.1153 | + | 25.1207i | −0.524589 | + | 0.933605i | ||||
\(725\) | −4.75038 | + | 4.75038i | −0.176425 | + | 0.176425i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.4536 | 0.610229 | 0.305115 | − | 0.952316i | \(-0.401305\pi\) | ||||
0.305115 | + | 0.952316i | \(0.401305\pi\) | |||||||
\(728\) | −8.92571 | − | 20.5250i | −0.330809 | − | 0.760707i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.19401 | − | 15.9457i | −0.0812040 | − | 0.590179i | ||||
\(731\) | 22.1654 | + | 22.1654i | 0.819816 | + | 0.819816i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.5995 | − | 24.5995i | 0.908602 | − | 0.908602i | −0.0875578 | − | 0.996159i | \(-0.527906\pi\) |
0.996159 | + | 0.0875578i | \(0.0279063\pi\) | |||||||
\(734\) | −1.41597 | + | 1.86779i | −0.0522644 | + | 0.0689414i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.09222 | + | 49.8836i | −0.187702 | + | 1.83873i | ||||
\(737\) | − | 21.3324i | − | 0.785790i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.06707 | + | 3.06707i | 0.112824 | + | 0.112824i | 0.761265 | − | 0.648441i | \(-0.224579\pi\) |
−0.648441 | + | 0.761265i | \(0.724579\pi\) | |||||||
\(740\) | 0.358858 | + | 1.27937i | 0.0131919 | + | 0.0470308i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −10.7693 | + | 1.48177i | −0.395353 | + | 0.0543975i | ||||
\(743\) | 1.16681i | 0.0428061i | 0.999771 | + | 0.0214031i | \(0.00681333\pi\) | ||||
−0.999771 | + | 0.0214031i | \(0.993187\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.80931i | 0.359385i | ||||||||
\(746\) | 0.949361 | + | 6.89981i | 0.0347586 | + | 0.252620i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 19.4833 | + | 10.9476i | 0.712380 | + | 0.400284i | ||||
\(749\) | −1.76051 | − | 1.76051i | −0.0643278 | − | 0.0643278i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.12809i | 0.0776552i | 0.999246 | + | 0.0388276i | \(0.0123623\pi\) | ||||
−0.999246 | + | 0.0388276i | \(0.987638\pi\) | |||||||
\(752\) | 10.9575 | − | 6.67195i | 0.399577 | − | 0.243301i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −11.6976 | − | 8.86795i | −0.426002 | − | 0.322952i | ||||
\(755\) | 0.157317 | − | 0.157317i | 0.00572534 | − | 0.00572534i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.1573 | + | 19.1573i | 0.696282 | + | 0.696282i | 0.963607 | − | 0.267324i | \(-0.0861395\pi\) |
−0.267324 | + | 0.963607i | \(0.586140\pi\) | |||||||
\(758\) | −37.9521 | + | 5.22191i | −1.37848 | + | 0.189668i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.75818 | + | 17.1591i | −0.245145 | + | 0.622426i | ||||
\(761\) | 10.2848 | 0.372824 | 0.186412 | − | 0.982472i | \(-0.440314\pi\) | ||||
0.186412 | + | 0.982472i | \(0.440314\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.69697 | + | 4.69697i | −0.170042 | + | 0.170042i | ||||
\(764\) | −7.68607 | − | 27.4018i | −0.278072 | − | 0.991363i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17.2322 | − | 13.0638i | −0.622626 | − | 0.472013i | ||||
\(767\) | −39.5147 | −1.42679 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.2860 | −0.551226 | −0.275613 | − | 0.961269i | \(-0.588881\pi\) | ||||
−0.275613 | + | 0.961269i | \(0.588881\pi\) | |||||||
\(770\) | −4.50790 | − | 3.41743i | −0.162453 | − | 0.123156i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.53022 | + | 12.5857i | 0.127055 | + | 0.452968i | ||||
\(773\) | 23.6903 | − | 23.6903i | 0.852081 | − | 0.852081i | −0.138308 | − | 0.990389i | \(-0.544166\pi\) |
0.990389 | + | 0.138308i | \(0.0441664\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.0327 | −0.396305 | ||||||||
\(776\) | −5.91084 | + | 15.0077i | −0.212187 | + | 0.538744i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 45.0047 | − | 6.19230i | 1.61350 | − | 0.222005i | ||||
\(779\) | 33.3396 | + | 33.3396i | 1.19451 | + | 1.19451i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.38158 | − | 7.38158i | 0.264134 | − | 0.264134i | ||||
\(782\) | −40.2824 | − | 30.5380i | −1.44049 | − | 1.09204i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 17.8155 | − | 10.8478i | 0.636267 | − | 0.387420i | ||||
\(785\) | 1.93697i | 0.0691333i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.3220 | − | 29.3220i | −1.04522 | − | 1.04522i | −0.998928 | − | 0.0462895i | \(-0.985260\pi\) |
−0.0462895 | − | 0.998928i | \(-0.514740\pi\) | |||||||
\(788\) | 22.3826 | + | 12.5767i | 0.797347 | + | 0.448026i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.33224 | − | 16.9504i | −0.0829775 | − | 0.603068i | ||||
\(791\) | 21.7988i | 0.775075i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 27.3687i | − | 0.971890i | ||||||
\(794\) | −14.7779 | + | 2.03332i | −0.524446 | + | 0.0721598i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.44814 | − | 19.4233i | −0.193104 | − | 0.688441i | ||||
\(797\) | −3.41153 | − | 3.41153i | −0.120843 | − | 0.120843i | 0.644099 | − | 0.764942i | \(-0.277232\pi\) |
−0.764942 | + | 0.644099i | \(0.777232\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.9329i | 0.457534i | ||||||||
\(800\) | −2.20196 | + | 21.5705i | −0.0778512 | + | 0.762633i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.90299 | − | 13.0629i | 0.349687 | − | 0.461268i | ||||
\(803\) | −20.6441 | + | 20.6441i | −0.728516 | + | 0.728516i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.04754 | + | 9.04754i | 0.318884 | + | 0.318884i | ||||
\(806\) | −3.28592 | − | 23.8816i | −0.115742 | − | 0.841193i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10.6653 | + | 24.5253i | 0.375205 | + | 0.862797i | ||||
\(809\) | −9.15877 | −0.322005 | −0.161003 | − | 0.986954i | \(-0.551473\pi\) | ||||
−0.161003 | + | 0.986954i | \(0.551473\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.91014 | + | 8.91014i | −0.312877 | + | 0.312877i | −0.846023 | − | 0.533146i | \(-0.821010\pi\) |
0.533146 | + | 0.846023i | \(0.321010\pi\) | |||||||
\(812\) | −2.29447 | + | 4.08344i | −0.0805201 | + | 0.143301i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.45601 | − | 1.92060i | 0.0510330 | − | 0.0673170i | ||||
\(815\) | 0.258474 | 0.00905397 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 46.9189 | 1.64148 | ||||||||
\(818\) | −10.6503 | + | 14.0487i | −0.372380 | + | 0.491202i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −14.7142 | − | 8.26785i | −0.513842 | − | 0.288726i | ||||
\(821\) | 27.0618 | − | 27.0618i | 0.944464 | − | 0.944464i | −0.0540734 | − | 0.998537i | \(-0.517221\pi\) |
0.998537 | + | 0.0540734i | \(0.0172205\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.6286 | 0.405348 | 0.202674 | − | 0.979246i | \(-0.435037\pi\) | ||||
0.202674 | + | 0.979246i | \(0.435037\pi\) | |||||||
\(824\) | 11.2753 | − | 28.6282i | 0.392795 | − | 0.997311i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.71867 | + | 12.4910i | 0.0598001 | + | 0.434618i | ||||
\(827\) | 8.57283 | + | 8.57283i | 0.298107 | + | 0.298107i | 0.840272 | − | 0.542165i | \(-0.182395\pi\) |
−0.542165 | + | 0.840272i | \(0.682395\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.5629 | − | 19.5629i | 0.679447 | − | 0.679447i | −0.280428 | − | 0.959875i | \(-0.590476\pi\) |
0.959875 | + | 0.280428i | \(0.0904763\pi\) | |||||||
\(830\) | −12.7041 | + | 16.7578i | −0.440965 | + | 0.581672i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −47.3479 | + | 1.65804i | −1.64149 | + | 0.0574822i | ||||
\(833\) | 21.0274i | 0.728555i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.98277 | − | 7.98277i | −0.276255 | − | 0.276255i | ||||
\(836\) | 32.2075 | − | 9.03403i | 1.11392 | − | 0.312448i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −28.5501 | + | 3.92828i | −0.986248 | + | 0.135700i | ||||
\(839\) | 14.8018i | 0.511015i | 0.966807 | + | 0.255508i | \(0.0822426\pi\) | ||||
−0.966807 | + | 0.255508i | \(0.917757\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 25.9281i | − | 0.894071i | ||||||
\(842\) | 1.59107 | + | 11.5637i | 0.0548319 | + | 0.398510i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −24.9108 | + | 44.3335i | −0.857466 | + | 1.52602i | ||||
\(845\) | −16.8599 | − | 16.8599i | −0.579997 | − | 0.579997i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 4.43773i | − | 0.152482i | ||||||
\(848\) | −5.43537 | + | 22.3596i | −0.186651 | + | 0.767833i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −17.4188 | − | 13.2052i | −0.597460 | − | 0.452934i | ||||
\(851\) | −3.85473 | + | 3.85473i | −0.132138 | + | 0.132138i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.2550 | − | 27.2550i | −0.933192 | − | 0.933192i | 0.0647119 | − | 0.997904i | \(-0.479387\pi\) |
−0.997904 | + | 0.0647119i | \(0.979387\pi\) | |||||||
\(854\) | −8.65153 | + | 1.19038i | −0.296049 | + | 0.0407341i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.83298 | + | 2.10172i | −0.165188 | + | 0.0718353i | ||||
\(857\) | 28.7462 | 0.981951 | 0.490976 | − | 0.871173i | \(-0.336640\pi\) | ||||
0.490976 | + | 0.871173i | \(0.336640\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.2578 | − | 29.2578i | 0.998264 | − | 0.998264i | −0.00173461 | − | 0.999998i | \(-0.500552\pi\) |
0.999998 | + | 0.00173461i | \(0.000552144\pi\) | |||||||
\(860\) | −16.1713 | + | 4.53598i | −0.551438 | + | 0.154676i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −20.7938 | − | 15.7638i | −0.708241 | − | 0.536917i | ||||
\(863\) | 40.6816 | 1.38482 | 0.692408 | − | 0.721506i | \(-0.256550\pi\) | ||||
0.692408 | + | 0.721506i | \(0.256550\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.48816 | 0.0505991 | ||||||||
\(866\) | −7.41737 | − | 5.62310i | −0.252052 | − | 0.191081i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.40630 | + | 2.07743i | −0.251386 | + | 0.0705125i | ||||
\(869\) | −21.9448 | + | 21.9448i | −0.744427 | + | 0.744427i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −45.5899 | −1.54475 | ||||||||
\(872\) | 5.60729 | + | 12.8942i | 0.189887 | + | 0.436652i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −74.9550 | + | 10.3132i | −2.53539 | + | 0.348850i | ||||
\(875\) | 9.01580 | + | 9.01580i | 0.304790 | + | 0.304790i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.9577 | + | 28.9577i | −0.977831 | + | 0.977831i | −0.999760 | − | 0.0219281i | \(-0.993020\pi\) |
0.0219281 | + | 0.999760i | \(0.493020\pi\) | |||||||
\(878\) | −4.15568 | − | 3.15042i | −0.140247 | − | 0.106321i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −10.2274 | + | 6.22745i | −0.344767 | + | 0.209927i | ||||
\(881\) | 17.2311i | 0.580531i | 0.956946 | + | 0.290266i | \(0.0937437\pi\) | ||||
−0.956946 | + | 0.290266i | \(0.906256\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.8129 | + | 24.8129i | 0.835019 | + | 0.835019i | 0.988198 | − | 0.153179i | \(-0.0489512\pi\) |
−0.153179 | + | 0.988198i | \(0.548951\pi\) | |||||||
\(884\) | 23.3963 | − | 41.6381i | 0.786902 | − | 1.40044i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.904706 | + | 6.57527i | 0.0303942 | + | 0.220901i | ||||
\(887\) | 39.0606i | 1.31153i | 0.754967 | + | 0.655763i | \(0.227653\pi\) | ||||
−0.754967 | + | 0.655763i | \(0.772347\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 27.7151i | − | 0.929534i | ||||||
\(890\) | 2.48410 | − | 0.341793i | 0.0832672 | − | 0.0114569i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.71931 | − | 2.16522i | 0.258462 | − | 0.0724971i | ||||
\(893\) | 13.6880 | + | 13.6880i | 0.458050 | + | 0.458050i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 10.0765i | − | 0.336819i | ||||||
\(896\) | 2.58349 | + | 14.8950i | 0.0863083 | + | 0.497608i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 17.3909 | − | 22.9401i | 0.580342 | − | 0.765522i | ||||
\(899\) | −3.56727 | + | 3.56727i | −0.118975 | + | 0.118975i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.4030 | − | 16.4030i | −0.546463 | − | 0.546463i | ||||
\(902\) | 4.17287 | + | 30.3278i | 0.138941 | + | 1.00981i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 42.9329 | + | 16.9093i | 1.42793 | + | 0.562395i | ||||
\(905\) | 15.5641 | 0.517369 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.366518 | − | 0.366518i | 0.0121700 | − | 0.0121700i | −0.700996 | − | 0.713166i | \(-0.747261\pi\) |
0.713166 | + | 0.700996i | \(0.247261\pi\) | |||||||
\(908\) | −34.0074 | − | 19.1086i | −1.12857 | − | 0.634142i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7.30346 | + | 9.63391i | −0.242107 | + | 0.319361i | ||||
\(911\) | 18.8950 | 0.626018 | 0.313009 | − | 0.949750i | \(-0.398663\pi\) | ||||
0.313009 | + | 0.949750i | \(0.398663\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 38.1428 | 1.26234 | ||||||||
\(914\) | 8.56398 | − | 11.2966i | 0.283271 | − | 0.373660i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.81945 | + | 8.57711i | −0.159239 | + | 0.283396i | ||||
\(917\) | −12.6087 | + | 12.6087i | −0.416376 | + | 0.416376i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −54.5805 | −1.80045 | −0.900223 | − | 0.435429i | \(-0.856597\pi\) | ||||
−0.900223 | + | 0.435429i | \(0.856597\pi\) | |||||||
\(920\) | 24.8374 | − | 10.8010i | 0.818865 | − | 0.356100i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.47208 | − | 32.5024i | −0.147280 | − | 1.07041i | ||||
\(923\) | −15.7753 | − | 15.7753i | −0.519250 | − | 0.519250i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.66685 | + | 1.66685i | −0.0548057 | + | 0.0548057i | ||||
\(926\) | 0.852507 | − | 1.12453i | 0.0280151 | − | 0.0369544i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.26256 | + | 7.68651i | 0.205579 | + | 0.252322i | ||||
\(929\) | − | 21.2118i | − | 0.695938i | −0.937506 | − | 0.347969i | \(-0.886871\pi\) | ||
0.937506 | − | 0.347969i | \(-0.113129\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.2550 | + | 22.2550i | 0.729377 | + | 0.729377i | ||||
\(932\) | 1.74992 | + | 6.23868i | 0.0573204 | + | 0.204355i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −19.2844 | + | 2.65339i | −0.631006 | + | 0.0868215i | ||||
\(935\) | − | 12.0713i | − | 0.394774i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 15.7395i | − | 0.514186i | −0.966387 | − | 0.257093i | \(-0.917235\pi\) | ||
0.966387 | − | 0.257093i | \(-0.0827647\pi\) | |||||||
\(938\) | 1.98290 | + | 14.4114i | 0.0647440 | + | 0.470550i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.04109 | − | 3.39447i | −0.197039 | − | 0.110715i | ||||
\(941\) | −1.43393 | − | 1.43393i | −0.0467447 | − | 0.0467447i | 0.683348 | − | 0.730093i | \(-0.260523\pi\) |
−0.730093 | + | 0.683348i | \(0.760523\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 69.2443i | − | 2.25491i | ||||||
\(944\) | 25.9344 | + | 6.30435i | 0.844092 | + | 0.205189i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 24.2765 | + | 18.4040i | 0.789296 | + | 0.598365i | ||||
\(947\) | −28.5461 | + | 28.5461i | −0.927623 | + | 0.927623i | −0.997552 | − | 0.0699288i | \(-0.977723\pi\) |
0.0699288 | + | 0.997552i | \(0.477723\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 44.1189 | + | 44.1189i | 1.43216 | + | 1.43216i | ||||
\(950\) | −32.4118 | + | 4.45962i | −1.05158 | + | 0.144689i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −14.1798 | − | 5.58479i | −0.459571 | − | 0.181004i | ||||
\(953\) | −14.6986 | −0.476136 | −0.238068 | − | 0.971249i | \(-0.576514\pi\) | ||||
−0.238068 | + | 0.971249i | \(0.576514\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.8697 | + | 10.8697i | −0.351737 | + | 0.351737i | ||||
\(956\) | 13.0976 | + | 46.6947i | 0.423607 | + | 1.51021i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 41.7735 | + | 31.6684i | 1.34964 | + | 1.02316i | ||||
\(959\) | 17.1317 | 0.553210 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.7151 | 0.732745 | ||||||||
\(962\) | −4.10455 | − | 3.11166i | −0.132336 | − | 0.100324i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8.94454 | + | 31.8884i | 0.288084 | + | 1.02706i | ||||
\(965\) | 4.99248 | − | 4.99248i | 0.160714 | − | 0.160714i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.34054 | −0.236056 | −0.118028 | − | 0.993010i | \(-0.537657\pi\) | ||||
−0.118028 | + | 0.993010i | \(0.537657\pi\) | |||||||
\(968\) | −8.74015 | − | 3.44235i | −0.280919 | − | 0.110641i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.63105 | − | 1.18757i | 0.277126 | − | 0.0381304i | ||||
\(971\) | 3.48251 | + | 3.48251i | 0.111759 | + | 0.111759i | 0.760775 | − | 0.649016i | \(-0.224819\pi\) |
−0.649016 | + | 0.760775i | \(0.724819\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.92879 | − | 1.92879i | 0.0618341 | − | 0.0618341i | ||||
\(974\) | −37.4005 | − | 28.3533i | −1.19839 | − | 0.908497i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.36652 | + | 17.9627i | −0.139769 | + | 0.574970i | ||||
\(977\) | 9.95013i | 0.318333i | 0.987252 | + | 0.159166i | \(0.0508806\pi\) | ||||
−0.987252 | + | 0.159166i | \(0.949119\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.21603 | − | 3.21603i | −0.102785 | − | 0.102785i | ||||
\(980\) | −9.82208 | − | 5.51899i | −0.313755 | − | 0.176298i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.79649 | + | 20.3245i | 0.0892395 | + | 0.648580i | ||||
\(983\) | 18.7648i | 0.598505i | 0.954174 | + | 0.299253i | \(0.0967373\pi\) | ||||
−0.954174 | + | 0.299253i | \(0.903263\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 13.8676i | − | 0.441859i | ||||||
\(986\) | −9.90184 | + | 1.36242i | −0.315339 | + | 0.0433882i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −19.3068 | − | 68.8312i | −0.614230 | − | 2.18981i | ||||
\(989\) | −48.7239 | − | 48.7239i | −1.54933 | − | 1.54933i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.18227i | 0.101088i | 0.998722 | + | 0.0505441i | \(0.0160955\pi\) | ||||
−0.998722 | + | 0.0505441i | \(0.983904\pi\) | |||||||
\(992\) | −1.65355 | + | 16.1982i | −0.0525003 | + | 0.514295i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.30060 | + | 5.67287i | −0.136407 | + | 0.179933i | ||||
\(995\) | −7.70483 | + | 7.70483i | −0.244259 | + | 0.244259i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.9944 | + | 26.9944i | 0.854923 | + | 0.854923i | 0.990735 | − | 0.135812i | \(-0.0433643\pi\) |
−0.135812 | + | 0.990735i | \(0.543364\pi\) | |||||||
\(998\) | −1.14426 | − | 8.31631i | −0.0362209 | − | 0.263248i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 144.2.l.a.107.2 | yes | 16 | |
3.2 | odd | 2 | inner | 144.2.l.a.107.7 | yes | 16 | |
4.3 | odd | 2 | 576.2.l.a.143.6 | 16 | |||
8.3 | odd | 2 | 1152.2.l.b.287.3 | 16 | |||
8.5 | even | 2 | 1152.2.l.a.287.3 | 16 | |||
12.11 | even | 2 | 576.2.l.a.143.3 | 16 | |||
16.3 | odd | 4 | inner | 144.2.l.a.35.7 | yes | 16 | |
16.5 | even | 4 | 1152.2.l.b.863.6 | 16 | |||
16.11 | odd | 4 | 1152.2.l.a.863.6 | 16 | |||
16.13 | even | 4 | 576.2.l.a.431.3 | 16 | |||
24.5 | odd | 2 | 1152.2.l.a.287.6 | 16 | |||
24.11 | even | 2 | 1152.2.l.b.287.6 | 16 | |||
48.5 | odd | 4 | 1152.2.l.b.863.3 | 16 | |||
48.11 | even | 4 | 1152.2.l.a.863.3 | 16 | |||
48.29 | odd | 4 | 576.2.l.a.431.6 | 16 | |||
48.35 | even | 4 | inner | 144.2.l.a.35.2 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.l.a.35.2 | ✓ | 16 | 48.35 | even | 4 | inner | |
144.2.l.a.35.7 | yes | 16 | 16.3 | odd | 4 | inner | |
144.2.l.a.107.2 | yes | 16 | 1.1 | even | 1 | trivial | |
144.2.l.a.107.7 | yes | 16 | 3.2 | odd | 2 | inner | |
576.2.l.a.143.3 | 16 | 12.11 | even | 2 | |||
576.2.l.a.143.6 | 16 | 4.3 | odd | 2 | |||
576.2.l.a.431.3 | 16 | 16.13 | even | 4 | |||
576.2.l.a.431.6 | 16 | 48.29 | odd | 4 | |||
1152.2.l.a.287.3 | 16 | 8.5 | even | 2 | |||
1152.2.l.a.287.6 | 16 | 24.5 | odd | 2 | |||
1152.2.l.a.863.3 | 16 | 48.11 | even | 4 | |||
1152.2.l.a.863.6 | 16 | 16.11 | odd | 4 | |||
1152.2.l.b.287.3 | 16 | 8.3 | odd | 2 | |||
1152.2.l.b.287.6 | 16 | 24.11 | even | 2 | |||
1152.2.l.b.863.3 | 16 | 48.5 | odd | 4 | |||
1152.2.l.b.863.6 | 16 | 16.5 | even | 4 |