Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,3,Mod(19,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.f (of order \(2\), degree \(1\), 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: | \(1.63488158616\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.389136420864.4 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 5x^{6} + 24x^{4} + 80x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 19.8 | ||
Root | \(1.52274 + 1.29664i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 60.19 |
Dual form | 60.3.f.b.19.7 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.52274 | + | 1.29664i | 0.761369 | + | 0.648319i | ||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | 0.637459 | + | 3.94888i | 0.159365 | + | 0.987220i | ||||
\(5\) | 4.27492 | + | 2.59328i | 0.854983 | + | 0.518655i | ||||
\(6\) | −2.63746 | − | 2.24584i | −0.439576 | − | 0.374307i | ||||
\(7\) | −0.837253 | −0.119608 | −0.0598038 | − | 0.998210i | \(-0.519048\pi\) | ||||
−0.0598038 | + | 0.998210i | \(0.519048\pi\) | |||||||
\(8\) | −4.14959 | + | 6.83966i | −0.518698 | + | 0.854957i | ||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 3.14704 | + | 9.49190i | 0.314704 | + | 0.949190i | ||||
\(11\) | − | 15.7955i | − | 1.43596i | −0.696066 | − | 0.717978i | \(-0.745068\pi\) | ||
0.696066 | − | 0.717978i | \(-0.254932\pi\) | |||||||
\(12\) | −1.10411 | − | 6.83966i | −0.0920092 | − | 0.569972i | ||||
\(13\) | − | 5.18655i | − | 0.398966i | −0.979901 | − | 0.199483i | \(-0.936074\pi\) | ||
0.979901 | − | 0.199483i | \(-0.0639262\pi\) | |||||||
\(14\) | −1.27492 | − | 1.08561i | −0.0910655 | − | 0.0775439i | ||||
\(15\) | −7.40437 | − | 4.49169i | −0.493625 | − | 0.299446i | ||||
\(16\) | −15.1873 | + | 5.03449i | −0.949206 | + | 0.314656i | ||||
\(17\) | − | 27.3586i | − | 1.60933i | −0.593728 | − | 0.804666i | \(-0.702344\pi\) | ||
0.593728 | − | 0.804666i | \(-0.297656\pi\) | |||||||
\(18\) | 4.56821 | + | 3.88991i | 0.253790 | + | 0.216106i | ||||
\(19\) | 17.9667i | 0.945618i | 0.881165 | + | 0.472809i | \(0.156760\pi\) | ||||
−0.881165 | + | 0.472809i | \(0.843240\pi\) | |||||||
\(20\) | −7.51545 | + | 18.5342i | −0.375773 | + | 0.926712i | ||||
\(21\) | 1.45017 | 0.0690555 | ||||||||
\(22\) | 20.4811 | − | 24.0524i | 0.930958 | − | 1.09329i | ||||
\(23\) | 19.1101 | 0.830874 | 0.415437 | − | 0.909622i | \(-0.363629\pi\) | ||||
0.415437 | + | 0.909622i | \(0.363629\pi\) | |||||||
\(24\) | 7.18729 | − | 11.8466i | 0.299471 | − | 0.493610i | ||||
\(25\) | 11.5498 | + | 22.1721i | 0.461993 | + | 0.886883i | ||||
\(26\) | 6.72508 | − | 7.89776i | 0.258657 | − | 0.303760i | ||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | −0.533714 | − | 3.30621i | −0.0190612 | − | 0.118079i | ||||
\(29\) | −45.6495 | −1.57412 | −0.787060 | − | 0.616876i | \(-0.788398\pi\) | ||||
−0.787060 | + | 0.616876i | \(0.788398\pi\) | |||||||
\(30\) | −5.45082 | − | 16.4405i | −0.181694 | − | 0.548015i | ||||
\(31\) | 13.6243i | 0.439493i | 0.975557 | + | 0.219747i | \(0.0705230\pi\) | ||||
−0.975557 | + | 0.219747i | \(0.929477\pi\) | |||||||
\(32\) | −29.6542 | − | 12.0262i | −0.926693 | − | 0.375819i | ||||
\(33\) | 27.3586i | 0.829050i | ||||||||
\(34\) | 35.4743 | − | 41.6600i | 1.04336 | − | 1.22529i | ||||
\(35\) | −3.57919 | − | 2.17123i | −0.102263 | − | 0.0620351i | ||||
\(36\) | 1.91238 | + | 11.8466i | 0.0531216 | + | 0.329073i | ||||
\(37\) | 15.5597i | 0.420531i | 0.977644 | + | 0.210266i | \(0.0674329\pi\) | ||||
−0.977644 | + | 0.210266i | \(0.932567\pi\) | |||||||
\(38\) | −23.2964 | + | 27.3586i | −0.613062 | + | 0.719964i | ||||
\(39\) | 8.98337i | 0.230343i | ||||||||
\(40\) | −35.4763 | + | 18.4780i | −0.886907 | + | 0.461949i | ||||
\(41\) | 13.2990 | 0.324366 | 0.162183 | − | 0.986761i | \(-0.448147\pi\) | ||||
0.162183 | + | 0.986761i | \(0.448147\pi\) | |||||||
\(42\) | 2.20822 | + | 1.88034i | 0.0525767 | + | 0.0447700i | ||||
\(43\) | −27.9430 | −0.649837 | −0.324918 | − | 0.945742i | \(-0.605337\pi\) | ||||
−0.324918 | + | 0.945742i | \(0.605337\pi\) | |||||||
\(44\) | 62.3746 | − | 10.0690i | 1.41760 | − | 0.228841i | ||||
\(45\) | 12.8248 | + | 7.77983i | 0.284994 | + | 0.172885i | ||||
\(46\) | 29.0997 | + | 24.7789i | 0.632601 | + | 0.538672i | ||||
\(47\) | 55.6558 | 1.18417 | 0.592083 | − | 0.805877i | \(-0.298306\pi\) | ||||
0.592083 | + | 0.805877i | \(0.298306\pi\) | |||||||
\(48\) | 26.3052 | − | 8.72000i | 0.548024 | − | 0.181667i | ||||
\(49\) | −48.2990 | −0.985694 | ||||||||
\(50\) | −11.1618 | + | 48.7382i | −0.223236 | + | 0.974764i | ||||
\(51\) | 47.3865i | 0.929148i | ||||||||
\(52\) | 20.4811 | − | 3.30621i | 0.393867 | − | 0.0635810i | ||||
\(53\) | 15.5597i | 0.293578i | 0.989168 | + | 0.146789i | \(0.0468939\pi\) | ||||
−0.989168 | + | 0.146789i | \(0.953106\pi\) | |||||||
\(54\) | −7.91238 | − | 6.73753i | −0.146525 | − | 0.124769i | ||||
\(55\) | 40.9621 | − | 67.5245i | 0.744766 | − | 1.22772i | ||||
\(56\) | 3.47425 | − | 5.72653i | 0.0620403 | − | 0.102259i | ||||
\(57\) | − | 31.1193i | − | 0.545953i | ||||||
\(58\) | −69.5122 | − | 59.1909i | −1.19849 | − | 1.02053i | ||||
\(59\) | 87.6625i | 1.48581i | 0.669400 | + | 0.742903i | \(0.266551\pi\) | ||||
−0.669400 | + | 0.742903i | \(0.733449\pi\) | |||||||
\(60\) | 13.0171 | − | 32.1022i | 0.216952 | − | 0.535037i | ||||
\(61\) | 38.0000 | 0.622951 | 0.311475 | − | 0.950254i | \(-0.399177\pi\) | ||||
0.311475 | + | 0.950254i | \(0.399177\pi\) | |||||||
\(62\) | −17.6658 | + | 20.7462i | −0.284932 | + | 0.334616i | ||||
\(63\) | −2.51176 | −0.0398692 | ||||||||
\(64\) | −29.5619 | − | 56.7635i | −0.461904 | − | 0.886930i | ||||
\(65\) | 13.4502 | − | 22.1721i | 0.206926 | − | 0.341109i | ||||
\(66\) | −35.4743 | + | 41.6600i | −0.537489 | + | 0.631212i | ||||
\(67\) | −92.2015 | −1.37614 | −0.688071 | − | 0.725643i | \(-0.741542\pi\) | ||||
−0.688071 | + | 0.725643i | \(0.741542\pi\) | |||||||
\(68\) | 108.036 | − | 17.4400i | 1.58876 | − | 0.256471i | ||||
\(69\) | −33.0997 | −0.479705 | ||||||||
\(70\) | −2.63487 | − | 7.94713i | −0.0376409 | − | 0.113530i | ||||
\(71\) | − | 130.707i | − | 1.84094i | −0.390816 | − | 0.920469i | \(-0.627807\pi\) | ||
0.390816 | − | 0.920469i | \(-0.372193\pi\) | |||||||
\(72\) | −12.4488 | + | 20.5190i | −0.172899 | + | 0.284986i | ||||
\(73\) | − | 54.7173i | − | 0.749552i | −0.927115 | − | 0.374776i | \(-0.877720\pi\) | ||
0.927115 | − | 0.374776i | \(-0.122280\pi\) | |||||||
\(74\) | −20.1752 | + | 23.6933i | −0.272638 | + | 0.320179i | ||||
\(75\) | −20.0049 | − | 38.4032i | −0.266732 | − | 0.512042i | ||||
\(76\) | −70.9485 | + | 11.4531i | −0.933533 | + | 0.150698i | ||||
\(77\) | 13.2249i | 0.171751i | ||||||||
\(78\) | −11.6482 | + | 13.6793i | −0.149336 | + | 0.175376i | ||||
\(79\) | − | 13.6243i | − | 0.172459i | −0.996275 | − | 0.0862297i | \(-0.972518\pi\) | ||
0.996275 | − | 0.0862297i | \(-0.0274819\pi\) | |||||||
\(80\) | −77.9803 | − | 17.8628i | −0.974753 | − | 0.223285i | ||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 20.2509 | + | 17.2440i | 0.246962 | + | 0.210293i | ||||
\(83\) | −59.0048 | −0.710901 | −0.355451 | − | 0.934695i | \(-0.615673\pi\) | ||||
−0.355451 | + | 0.934695i | \(0.615673\pi\) | |||||||
\(84\) | 0.924421 | + | 5.72653i | 0.0110050 | + | 0.0681730i | ||||
\(85\) | 70.9485 | − | 116.956i | 0.834688 | − | 1.37595i | ||||
\(86\) | −42.5498 | − | 36.2319i | −0.494766 | − | 0.421302i | ||||
\(87\) | 79.0673 | 0.908819 | ||||||||
\(88\) | 108.036 | + | 65.5448i | 1.22768 | + | 0.744828i | ||||
\(89\) | 39.8007 | 0.447198 | 0.223599 | − | 0.974681i | \(-0.428219\pi\) | ||||
0.223599 | + | 0.974681i | \(0.428219\pi\) | |||||||
\(90\) | 9.44111 | + | 28.4757i | 0.104901 | + | 0.316397i | ||||
\(91\) | 4.34246i | 0.0477193i | ||||||||
\(92\) | 12.1819 | + | 75.4635i | 0.132412 | + | 0.820255i | ||||
\(93\) | − | 23.5980i | − | 0.253741i | ||||||
\(94\) | 84.7492 | + | 72.1654i | 0.901587 | + | 0.767717i | ||||
\(95\) | −46.5927 | + | 76.8064i | −0.490450 | + | 0.808488i | ||||
\(96\) | 51.3625 | + | 20.8300i | 0.535026 | + | 0.216979i | ||||
\(97\) | 168.821i | 1.74043i | 0.492675 | + | 0.870214i | \(0.336019\pi\) | ||||
−0.492675 | + | 0.870214i | \(0.663981\pi\) | |||||||
\(98\) | −73.5467 | − | 62.6263i | −0.750477 | − | 0.639044i | ||||
\(99\) | − | 47.3865i | − | 0.478652i | ||||||
\(100\) | −80.1923 | + | 59.7427i | −0.801923 | + | 0.597427i | ||||
\(101\) | 44.5498 | 0.441087 | 0.220544 | − | 0.975377i | \(-0.429217\pi\) | ||||
0.220544 | + | 0.975377i | \(0.429217\pi\) | |||||||
\(102\) | −61.4432 | + | 72.1573i | −0.602384 | + | 0.707424i | ||||
\(103\) | 126.466 | 1.22782 | 0.613911 | − | 0.789375i | \(-0.289595\pi\) | ||||
0.613911 | + | 0.789375i | \(0.289595\pi\) | |||||||
\(104\) | 35.4743 | + | 21.5220i | 0.341099 | + | 0.206943i | ||||
\(105\) | 6.19934 | + | 3.76068i | 0.0590413 | + | 0.0358160i | ||||
\(106\) | −20.1752 | + | 23.6933i | −0.190333 | + | 0.223521i | ||||
\(107\) | −104.383 | −0.975546 | −0.487773 | − | 0.872971i | \(-0.662191\pi\) | ||||
−0.487773 | + | 0.872971i | \(0.662191\pi\) | |||||||
\(108\) | −3.31233 | − | 20.5190i | −0.0306697 | − | 0.189991i | ||||
\(109\) | −0.501656 | −0.00460235 | −0.00230117 | − | 0.999997i | \(-0.500732\pi\) | ||||
−0.00230117 | + | 0.999997i | \(0.500732\pi\) | |||||||
\(110\) | 149.929 | − | 49.7090i | 1.36300 | − | 0.451900i | ||||
\(111\) | − | 26.9501i | − | 0.242794i | ||||||
\(112\) | 12.7156 | − | 4.21515i | 0.113532 | − | 0.0376352i | ||||
\(113\) | 16.9855i | 0.150314i | 0.997172 | + | 0.0751572i | \(0.0239459\pi\) | ||||
−0.997172 | + | 0.0751572i | \(0.976054\pi\) | |||||||
\(114\) | 40.3505 | − | 47.3865i | 0.353952 | − | 0.415671i | ||||
\(115\) | 81.6941 | + | 49.5578i | 0.710384 | + | 0.430937i | ||||
\(116\) | −29.0997 | − | 180.264i | −0.250859 | − | 1.55400i | ||||
\(117\) | − | 15.5597i | − | 0.132989i | ||||||
\(118\) | −113.667 | + | 133.487i | −0.963276 | + | 1.13125i | ||||
\(119\) | 22.9061i | 0.192488i | ||||||||
\(120\) | 61.4467 | − | 32.0048i | 0.512056 | − | 0.266706i | ||||
\(121\) | −128.498 | −1.06197 | ||||||||
\(122\) | 57.8640 | + | 49.2723i | 0.474295 | + | 0.403871i | ||||
\(123\) | −23.0346 | −0.187273 | ||||||||
\(124\) | −53.8007 | + | 8.68492i | −0.433876 | + | 0.0700397i | ||||
\(125\) | −8.12376 | + | 124.736i | −0.0649901 | + | 0.997886i | ||||
\(126\) | −3.82475 | − | 3.25684i | −0.0303552 | − | 0.0258480i | ||||
\(127\) | −8.45598 | −0.0665825 | −0.0332913 | − | 0.999446i | \(-0.510599\pi\) | ||||
−0.0332913 | + | 0.999446i | \(0.510599\pi\) | |||||||
\(128\) | 28.5867 | − | 124.767i | 0.223334 | − | 0.974742i | ||||
\(129\) | 48.3987 | 0.375184 | ||||||||
\(130\) | 49.2302 | − | 16.3223i | 0.378694 | − | 0.125556i | ||||
\(131\) | 51.7290i | 0.394878i | 0.980315 | + | 0.197439i | \(0.0632624\pi\) | ||||
−0.980315 | + | 0.197439i | \(0.936738\pi\) | |||||||
\(132\) | −108.036 | + | 17.4400i | −0.818454 | + | 0.132121i | ||||
\(133\) | − | 15.0427i | − | 0.113103i | ||||||
\(134\) | −140.399 | − | 119.552i | −1.04775 | − | 0.892179i | ||||
\(135\) | −22.2131 | − | 13.4751i | −0.164542 | − | 0.0998153i | ||||
\(136\) | 187.124 | + | 113.527i | 1.37591 | + | 0.834757i | ||||
\(137\) | 53.8083i | 0.392762i | 0.980528 | + | 0.196381i | \(0.0629189\pi\) | ||||
−0.980528 | + | 0.196381i | \(0.937081\pi\) | |||||||
\(138\) | −50.4021 | − | 42.9183i | −0.365233 | − | 0.311002i | ||||
\(139\) | 13.6243i | 0.0980165i | 0.998798 | + | 0.0490082i | \(0.0156061\pi\) | ||||
−0.998798 | + | 0.0490082i | \(0.984394\pi\) | |||||||
\(140\) | 6.29234 | − | 15.5179i | 0.0449453 | − | 0.110842i | ||||
\(141\) | −96.3987 | −0.683679 | ||||||||
\(142\) | 169.479 | − | 199.032i | 1.19352 | − | 1.40163i | ||||
\(143\) | −81.9243 | −0.572897 | ||||||||
\(144\) | −45.5619 | + | 15.1035i | −0.316402 | + | 0.104885i | ||||
\(145\) | −195.148 | − | 118.382i | −1.34585 | − | 0.816426i | ||||
\(146\) | 70.9485 | − | 83.3200i | 0.485949 | − | 0.570685i | ||||
\(147\) | 83.6563 | 0.569091 | ||||||||
\(148\) | −61.4432 | + | 9.91864i | −0.415157 | + | 0.0670178i | ||||
\(149\) | −33.6495 | −0.225836 | −0.112918 | − | 0.993604i | \(-0.536020\pi\) | ||||
−0.112918 | + | 0.993604i | \(0.536020\pi\) | |||||||
\(150\) | 19.3328 | − | 84.4171i | 0.128885 | − | 0.562780i | ||||
\(151\) | 139.988i | 0.927076i | 0.886077 | + | 0.463538i | \(0.153420\pi\) | ||||
−0.886077 | + | 0.463538i | \(0.846580\pi\) | |||||||
\(152\) | −122.886 | − | 74.5546i | −0.808463 | − | 0.490490i | ||||
\(153\) | − | 82.0759i | − | 0.536444i | ||||||
\(154\) | −17.1478 | + | 20.1380i | −0.111350 | + | 0.130766i | ||||
\(155\) | −35.3315 | + | 58.2427i | −0.227945 | + | 0.375759i | ||||
\(156\) | −35.4743 | + | 5.72653i | −0.227399 | + | 0.0367085i | ||||
\(157\) | − | 21.2631i | − | 0.135434i | −0.997705 | − | 0.0677170i | \(-0.978428\pi\) | ||
0.997705 | − | 0.0677170i | \(-0.0215715\pi\) | |||||||
\(158\) | 17.6658 | − | 20.7462i | 0.111809 | − | 0.131305i | ||||
\(159\) | − | 26.9501i | − | 0.169498i | ||||||
\(160\) | −95.5819 | − | 128.313i | −0.597387 | − | 0.801953i | ||||
\(161\) | −16.0000 | −0.0993789 | ||||||||
\(162\) | 13.7046 | + | 11.6697i | 0.0845965 | + | 0.0720355i | ||||
\(163\) | 210.211 | 1.28964 | 0.644819 | − | 0.764335i | \(-0.276933\pi\) | ||||
0.644819 | + | 0.764335i | \(0.276933\pi\) | |||||||
\(164\) | 8.47757 | + | 52.5162i | 0.0516925 | + | 0.320221i | ||||
\(165\) | −70.9485 | + | 116.956i | −0.429991 | + | 0.708824i | ||||
\(166\) | −89.8488 | − | 76.5079i | −0.541258 | − | 0.460891i | ||||
\(167\) | 238.384 | 1.42745 | 0.713725 | − | 0.700426i | \(-0.247006\pi\) | ||||
0.713725 | + | 0.700426i | \(0.247006\pi\) | |||||||
\(168\) | −6.01759 | + | 9.91864i | −0.0358190 | + | 0.0590395i | ||||
\(169\) | 142.100 | 0.840826 | ||||||||
\(170\) | 259.685 | − | 86.0986i | 1.52756 | − | 0.506462i | ||||
\(171\) | 53.9002i | 0.315206i | ||||||||
\(172\) | −17.8125 | − | 110.343i | −0.103561 | − | 0.641532i | ||||
\(173\) | 2.33481i | 0.0134960i | 0.999977 | + | 0.00674800i | \(0.00214797\pi\) | ||||
−0.999977 | + | 0.00674800i | \(0.997852\pi\) | |||||||
\(174\) | 120.399 | + | 102.522i | 0.691946 | + | 0.589205i | ||||
\(175\) | −9.67014 | − | 18.5637i | −0.0552579 | − | 0.106078i | ||||
\(176\) | 79.5224 | + | 239.891i | 0.451832 | + | 1.36302i | ||||
\(177\) | − | 151.836i | − | 0.857830i | ||||||
\(178\) | 60.6060 | + | 51.6071i | 0.340483 | + | 0.289927i | ||||
\(179\) | − | 227.054i | − | 1.26846i | −0.773145 | − | 0.634229i | \(-0.781318\pi\) | ||
0.773145 | − | 0.634229i | \(-0.218682\pi\) | |||||||
\(180\) | −22.5464 | + | 55.6027i | −0.125258 | + | 0.308904i | ||||
\(181\) | 114.096 | 0.630367 | 0.315183 | − | 0.949031i | \(-0.397934\pi\) | ||||
0.315183 | + | 0.949031i | \(0.397934\pi\) | |||||||
\(182\) | −5.63060 | + | 6.61243i | −0.0309374 | + | 0.0363320i | ||||
\(183\) | −65.8179 | −0.359661 | ||||||||
\(184\) | −79.2990 | + | 130.707i | −0.430973 | + | 0.710362i | ||||
\(185\) | −40.3505 | + | 66.5163i | −0.218111 | + | 0.359547i | ||||
\(186\) | 30.5980 | − | 35.9335i | 0.164505 | − | 0.193191i | ||||
\(187\) | −432.144 | −2.31093 | ||||||||
\(188\) | 35.4783 | + | 219.778i | 0.188714 | + | 1.16903i | ||||
\(189\) | 4.35050 | 0.0230185 | ||||||||
\(190\) | −170.539 | + | 56.5420i | −0.897571 | + | 0.297589i | ||||
\(191\) | 139.392i | 0.729798i | 0.931047 | + | 0.364899i | \(0.118897\pi\) | ||||
−0.931047 | + | 0.364899i | \(0.881103\pi\) | |||||||
\(192\) | 51.2027 | + | 98.3173i | 0.266681 | + | 0.512069i | ||||
\(193\) | 182.046i | 0.943245i | 0.881801 | + | 0.471623i | \(0.156331\pi\) | ||||
−0.881801 | + | 0.471623i | \(0.843669\pi\) | |||||||
\(194\) | −218.900 | + | 257.071i | −1.12835 | + | 1.32511i | ||||
\(195\) | −23.2964 | + | 38.4032i | −0.119469 | + | 0.196939i | ||||
\(196\) | −30.7886 | − | 190.727i | −0.157085 | − | 0.973097i | ||||
\(197\) | − | 258.027i | − | 1.30978i | −0.755724 | − | 0.654890i | \(-0.772715\pi\) | ||
0.755724 | − | 0.654890i | \(-0.227285\pi\) | |||||||
\(198\) | 61.4432 | − | 72.1573i | 0.310319 | − | 0.364431i | ||||
\(199\) | − | 256.474i | − | 1.28881i | −0.764683 | − | 0.644407i | \(-0.777104\pi\) | ||
0.764683 | − | 0.644407i | \(-0.222896\pi\) | |||||||
\(200\) | −199.577 | − | 13.0080i | −0.997883 | − | 0.0650401i | ||||
\(201\) | 159.698 | 0.794516 | ||||||||
\(202\) | 67.8377 | + | 57.7650i | 0.335830 | + | 0.285965i | ||||
\(203\) | 38.2202 | 0.188277 | ||||||||
\(204\) | −187.124 | + | 30.2070i | −0.917273 | + | 0.148073i | ||||
\(205\) | 56.8522 | + | 34.4880i | 0.277328 | + | 0.168234i | ||||
\(206\) | 192.574 | + | 163.980i | 0.934825 | + | 0.796020i | ||||
\(207\) | 57.3303 | 0.276958 | ||||||||
\(208\) | 26.1117 | + | 78.7697i | 0.125537 | + | 0.378700i | ||||
\(209\) | 283.794 | 1.35787 | ||||||||
\(210\) | 4.56372 | + | 13.7648i | 0.0217320 | + | 0.0655468i | ||||
\(211\) | − | 211.855i | − | 1.00405i | −0.864852 | − | 0.502027i | \(-0.832588\pi\) | ||
0.864852 | − | 0.502027i | \(-0.167412\pi\) | |||||||
\(212\) | −61.4432 | + | 9.91864i | −0.289826 | + | 0.0467860i | ||||
\(213\) | 226.390i | 1.06287i | ||||||||
\(214\) | −158.949 | − | 135.348i | −0.742750 | − | 0.632465i | ||||
\(215\) | −119.454 | − | 72.4639i | −0.555600 | − | 0.337041i | ||||
\(216\) | 21.5619 | − | 35.5399i | 0.0998235 | − | 0.164537i | ||||
\(217\) | − | 11.4070i | − | 0.0525667i | ||||||
\(218\) | −0.763890 | − | 0.650466i | −0.00350408 | − | 0.00298379i | ||||
\(219\) | 94.7731i | 0.432754i | ||||||||
\(220\) | 292.758 | + | 118.710i | 1.33072 | + | 0.539593i | ||||
\(221\) | −141.897 | −0.642068 | ||||||||
\(222\) | 34.9446 | − | 41.0380i | 0.157408 | − | 0.184856i | ||||
\(223\) | −349.843 | −1.56880 | −0.784401 | − | 0.620255i | \(-0.787029\pi\) | ||||
−0.784401 | + | 0.620255i | \(0.787029\pi\) | |||||||
\(224\) | 24.8281 | + | 10.0690i | 0.110840 | + | 0.0449508i | ||||
\(225\) | 34.6495 | + | 66.5163i | 0.153998 | + | 0.295628i | ||||
\(226\) | −22.0241 | + | 25.8645i | −0.0974517 | + | 0.114445i | ||||
\(227\) | 185.554 | 0.817418 | 0.408709 | − | 0.912665i | \(-0.365979\pi\) | ||||
0.408709 | + | 0.912665i | \(0.365979\pi\) | |||||||
\(228\) | 122.886 | − | 19.8373i | 0.538976 | − | 0.0870056i | ||||
\(229\) | 263.897 | 1.15239 | 0.576194 | − | 0.817313i | \(-0.304537\pi\) | ||||
0.576194 | + | 0.817313i | \(0.304537\pi\) | |||||||
\(230\) | 60.1402 | + | 181.391i | 0.261479 | + | 0.788657i | ||||
\(231\) | − | 22.9061i | − | 0.0991607i | ||||||
\(232\) | 189.427 | − | 312.227i | 0.816494 | − | 1.34581i | ||||
\(233\) | − | 58.4780i | − | 0.250978i | −0.992095 | − | 0.125489i | \(-0.959950\pi\) | ||
0.992095 | − | 0.125489i | \(-0.0400500\pi\) | |||||||
\(234\) | 20.1752 | − | 23.6933i | 0.0862190 | − | 0.101253i | ||||
\(235\) | 237.924 | + | 144.331i | 1.01244 | + | 0.614174i | ||||
\(236\) | −346.169 | + | 55.8812i | −1.46682 | + | 0.236785i | ||||
\(237\) | 23.5980i | 0.0995694i | ||||||||
\(238\) | −29.7009 | + | 34.8800i | −0.124794 | + | 0.146555i | ||||
\(239\) | − | 113.337i | − | 0.474212i | −0.971484 | − | 0.237106i | \(-0.923801\pi\) | ||
0.971484 | − | 0.237106i | \(-0.0761989\pi\) | |||||||
\(240\) | 135.066 | + | 30.9393i | 0.562774 | + | 0.128914i | ||||
\(241\) | −77.7940 | −0.322797 | −0.161398 | − | 0.986889i | \(-0.551600\pi\) | ||||
−0.161398 | + | 0.986889i | \(0.551600\pi\) | |||||||
\(242\) | −195.669 | − | 166.616i | −0.808551 | − | 0.688495i | ||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | 24.2234 | + | 150.057i | 0.0992763 | + | 0.614989i | ||||
\(245\) | −206.474 | − | 125.253i | −0.842752 | − | 0.511235i | ||||
\(246\) | −35.0756 | − | 29.8675i | −0.142584 | − | 0.121413i | ||||
\(247\) | 93.1855 | 0.377269 | ||||||||
\(248\) | −93.1855 | − | 56.5351i | −0.375748 | − | 0.227964i | ||||
\(249\) | 102.199 | 0.410439 | ||||||||
\(250\) | −174.107 | + | 179.406i | −0.696430 | + | 0.717625i | ||||
\(251\) | 106.226i | 0.423212i | 0.977355 | + | 0.211606i | \(0.0678693\pi\) | ||||
−0.977355 | + | 0.211606i | \(0.932131\pi\) | |||||||
\(252\) | −1.60114 | − | 9.91864i | −0.00635374 | − | 0.0393597i | ||||
\(253\) | − | 301.854i | − | 1.19310i | ||||||
\(254\) | −12.8762 | − | 10.9644i | −0.0506939 | − | 0.0431667i | ||||
\(255\) | −122.886 | + | 202.574i | −0.481908 | + | 0.794406i | ||||
\(256\) | 205.308 | − | 152.921i | 0.801983 | − | 0.597346i | ||||
\(257\) | − | 381.078i | − | 1.48279i | −0.671067 | − | 0.741397i | \(-0.734164\pi\) | ||
0.671067 | − | 0.741397i | \(-0.265836\pi\) | |||||||
\(258\) | 73.6985 | + | 62.7556i | 0.285653 | + | 0.243239i | ||||
\(259\) | − | 13.0274i | − | 0.0502988i | ||||||
\(260\) | 96.1288 | + | 38.9793i | 0.369726 | + | 0.149920i | ||||
\(261\) | −136.949 | −0.524707 | ||||||||
\(262\) | −67.0738 | + | 78.7697i | −0.256007 | + | 0.300648i | ||||
\(263\) | 11.4914 | 0.0436934 | 0.0218467 | − | 0.999761i | \(-0.493045\pi\) | ||||
0.0218467 | + | 0.999761i | \(0.493045\pi\) | |||||||
\(264\) | −187.124 | − | 113.527i | −0.708802 | − | 0.430027i | ||||
\(265\) | −40.3505 | + | 66.5163i | −0.152266 | + | 0.251005i | ||||
\(266\) | 19.5050 | − | 22.9061i | 0.0733269 | − | 0.0861132i | ||||
\(267\) | −68.9368 | −0.258190 | ||||||||
\(268\) | −58.7746 | − | 364.093i | −0.219308 | − | 1.35855i | ||||
\(269\) | −77.9518 | −0.289784 | −0.144892 | − | 0.989447i | \(-0.546283\pi\) | ||||
−0.144892 | + | 0.989447i | \(0.546283\pi\) | |||||||
\(270\) | −16.3525 | − | 49.3214i | −0.0605647 | − | 0.182672i | ||||
\(271\) | − | 86.6851i | − | 0.319871i | −0.987127 | − | 0.159936i | \(-0.948871\pi\) | ||
0.987127 | − | 0.159936i | \(-0.0511287\pi\) | |||||||
\(272\) | 137.737 | + | 415.504i | 0.506386 | + | 1.52759i | ||||
\(273\) | − | 7.52136i | − | 0.0275508i | ||||||
\(274\) | −69.7700 | + | 81.9360i | −0.254635 | + | 0.299036i | ||||
\(275\) | 350.220 | − | 182.436i | 1.27353 | − | 0.663402i | ||||
\(276\) | −21.0997 | − | 130.707i | −0.0764481 | − | 0.473575i | ||||
\(277\) | 287.328i | 1.03729i | 0.854991 | + | 0.518643i | \(0.173563\pi\) | ||||
−0.854991 | + | 0.518643i | \(0.826437\pi\) | |||||||
\(278\) | −17.6658 | + | 20.7462i | −0.0635459 | + | 0.0746267i | ||||
\(279\) | 40.8729i | 0.146498i | ||||||||
\(280\) | 29.7026 | − | 15.4707i | 0.106081 | − | 0.0552526i | ||||
\(281\) | −224.598 | −0.799281 | −0.399641 | − | 0.916672i | \(-0.630865\pi\) | ||||
−0.399641 | + | 0.916672i | \(0.630865\pi\) | |||||||
\(282\) | −146.790 | − | 124.994i | −0.520531 | − | 0.443242i | ||||
\(283\) | 84.1224 | 0.297252 | 0.148626 | − | 0.988893i | \(-0.452515\pi\) | ||||
0.148626 | + | 0.988893i | \(0.452515\pi\) | |||||||
\(284\) | 516.145 | − | 83.3200i | 1.81741 | − | 0.293380i | ||||
\(285\) | 80.7010 | − | 133.033i | 0.283161 | − | 0.466781i | ||||
\(286\) | −124.749 | − | 106.226i | −0.436186 | − | 0.371420i | ||||
\(287\) | −11.1346 | −0.0387967 | ||||||||
\(288\) | −88.9625 | − | 36.0786i | −0.308898 | − | 0.125273i | ||||
\(289\) | −459.495 | −1.58995 | ||||||||
\(290\) | −143.661 | − | 433.301i | −0.495381 | − | 1.49414i | ||||
\(291\) | − | 292.407i | − | 1.00484i | ||||||
\(292\) | 216.072 | − | 34.8800i | 0.739972 | − | 0.119452i | ||||
\(293\) | 246.620i | 0.841706i | 0.907129 | + | 0.420853i | \(0.138269\pi\) | ||||
−0.907129 | + | 0.420853i | \(0.861731\pi\) | |||||||
\(294\) | 127.387 | + | 108.472i | 0.433288 | + | 0.368952i | ||||
\(295\) | −227.333 | + | 374.750i | −0.770621 | + | 1.27034i | ||||
\(296\) | −106.423 | − | 64.5661i | −0.359536 | − | 0.218129i | ||||
\(297\) | 82.0759i | 0.276350i | ||||||||
\(298\) | −51.2394 | − | 43.6312i | −0.171944 | − | 0.146414i | ||||
\(299\) | − | 99.1156i | − | 0.331490i | ||||||
\(300\) | 138.897 | − | 103.477i | 0.462991 | − | 0.344925i | ||||
\(301\) | 23.3954 | 0.0777255 | ||||||||
\(302\) | −181.514 | + | 213.166i | −0.601041 | + | 0.705846i | ||||
\(303\) | −77.1626 | −0.254662 | ||||||||
\(304\) | −90.4535 | − | 272.866i | −0.297544 | − | 0.897586i | ||||
\(305\) | 162.447 | + | 98.5445i | 0.532613 | + | 0.323097i | ||||
\(306\) | 106.423 | − | 124.980i | 0.347787 | − | 0.408432i | ||||
\(307\) | 115.811 | 0.377236 | 0.188618 | − | 0.982051i | \(-0.439599\pi\) | ||||
0.188618 | + | 0.982051i | \(0.439599\pi\) | |||||||
\(308\) | −52.2233 | + | 8.43030i | −0.169556 | + | 0.0273711i | ||||
\(309\) | −219.045 | −0.708883 | ||||||||
\(310\) | −129.320 | + | 42.8761i | −0.417162 | + | 0.138310i | ||||
\(311\) | 203.767i | 0.655201i | 0.944816 | + | 0.327600i | \(0.106240\pi\) | ||||
−0.944816 | + | 0.327600i | \(0.893760\pi\) | |||||||
\(312\) | −61.4432 | − | 37.2773i | −0.196933 | − | 0.119478i | ||||
\(313\) | 99.0614i | 0.316490i | 0.987400 | + | 0.158245i | \(0.0505836\pi\) | ||||
−0.987400 | + | 0.158245i | \(0.949416\pi\) | |||||||
\(314\) | 27.5706 | − | 32.3782i | 0.0878045 | − | 0.103115i | ||||
\(315\) | −10.7376 | − | 6.51369i | −0.0340875 | − | 0.0206784i | ||||
\(316\) | 53.8007 | − | 8.68492i | 0.170255 | − | 0.0274839i | ||||
\(317\) | 471.192i | 1.48641i | 0.669063 | + | 0.743206i | \(0.266696\pi\) | ||||
−0.669063 | + | 0.743206i | \(0.733304\pi\) | |||||||
\(318\) | 34.9446 | − | 41.0380i | 0.109889 | − | 0.129050i | ||||
\(319\) | 721.057i | 2.26037i | ||||||||
\(320\) | 20.8289 | − | 319.321i | 0.0650902 | − | 0.997879i | ||||
\(321\) | 180.797 | 0.563232 | ||||||||
\(322\) | −24.3638 | − | 20.7462i | −0.0756640 | − | 0.0644292i | ||||
\(323\) | 491.546 | 1.52181 | ||||||||
\(324\) | 5.73713 | + | 35.5399i | 0.0177072 | + | 0.109691i | ||||
\(325\) | 114.997 | − | 59.9038i | 0.353836 | − | 0.184319i | ||||
\(326\) | 320.096 | + | 272.568i | 0.981891 | + | 0.836098i | ||||
\(327\) | 0.868893 | 0.00265717 | ||||||||
\(328\) | −55.1854 | + | 90.9607i | −0.168248 | + | 0.277319i | ||||
\(329\) | −46.5980 | −0.141635 | ||||||||
\(330\) | −259.685 | + | 86.0986i | −0.786926 | + | 0.260905i | ||||
\(331\) | 270.695i | 0.817810i | 0.912577 | + | 0.408905i | \(0.134089\pi\) | ||||
−0.912577 | + | 0.408905i | \(0.865911\pi\) | |||||||
\(332\) | −37.6131 | − | 233.003i | −0.113293 | − | 0.701816i | ||||
\(333\) | 46.6790i | 0.140177i | ||||||||
\(334\) | 362.997 | + | 309.098i | 1.08682 | + | 0.925444i | ||||
\(335\) | −394.154 | − | 239.104i | −1.17658 | − | 0.713743i | ||||
\(336\) | −22.0241 | + | 7.30085i | −0.0655479 | + | 0.0217287i | ||||
\(337\) | 377.317i | 1.11964i | 0.828615 | + | 0.559818i | \(0.189129\pi\) | ||||
−0.828615 | + | 0.559818i | \(0.810871\pi\) | |||||||
\(338\) | 216.380 | + | 184.252i | 0.640179 | + | 0.545124i | ||||
\(339\) | − | 29.4198i | − | 0.0867841i | ||||||
\(340\) | 507.071 | + | 205.613i | 1.49139 | + | 0.604743i | ||||
\(341\) | 215.203 | 0.631093 | ||||||||
\(342\) | −69.8891 | + | 82.0759i | −0.204354 | + | 0.239988i | ||||
\(343\) | 81.4639 | 0.237504 | ||||||||
\(344\) | 115.952 | − | 191.121i | 0.337069 | − | 0.555583i | ||||
\(345\) | −141.498 | − | 85.8366i | −0.410140 | − | 0.248802i | ||||
\(346\) | −3.02740 | + | 3.55530i | −0.00874971 | + | 0.0102754i | ||||
\(347\) | −462.222 | −1.33205 | −0.666025 | − | 0.745929i | \(-0.732006\pi\) | ||||
−0.666025 | + | 0.745929i | \(0.732006\pi\) | |||||||
\(348\) | 50.4021 | + | 312.227i | 0.144834 | + | 0.897204i | ||||
\(349\) | 200.598 | 0.574779 | 0.287390 | − | 0.957814i | \(-0.407213\pi\) | ||||
0.287390 | + | 0.957814i | \(0.407213\pi\) | |||||||
\(350\) | 9.34526 | − | 40.8062i | 0.0267007 | − | 0.116589i | ||||
\(351\) | 26.9501i | 0.0767810i | ||||||||
\(352\) | −189.960 | + | 468.403i | −0.539660 | + | 1.33069i | ||||
\(353\) | − | 250.897i | − | 0.710757i | −0.934722 | − | 0.355379i | \(-0.884352\pi\) | ||
0.934722 | − | 0.355379i | \(-0.115648\pi\) | |||||||
\(354\) | 196.876 | − | 231.206i | 0.556148 | − | 0.653125i | ||||
\(355\) | 338.958 | − | 558.760i | 0.954812 | − | 1.57397i | ||||
\(356\) | 25.3713 | + | 157.168i | 0.0712676 | + | 0.441483i | ||||
\(357\) | − | 39.6746i | − | 0.111133i | ||||||
\(358\) | 294.407 | − | 345.744i | 0.822366 | − | 0.965764i | ||||
\(359\) | 215.601i | 0.600560i | 0.953851 | + | 0.300280i | \(0.0970801\pi\) | ||||
−0.953851 | + | 0.300280i | \(0.902920\pi\) | |||||||
\(360\) | −106.429 | + | 55.4339i | −0.295636 | + | 0.153983i | ||||
\(361\) | 38.1960 | 0.105806 | ||||||||
\(362\) | 173.739 | + | 147.942i | 0.479941 | + | 0.408679i | ||||
\(363\) | 222.566 | 0.613129 | ||||||||
\(364\) | −17.1478 | + | 2.76814i | −0.0471095 | + | 0.00760478i | ||||
\(365\) | 141.897 | − | 233.912i | 0.388759 | − | 0.640854i | ||||
\(366\) | −100.223 | − | 85.3420i | −0.273835 | − | 0.233175i | ||||
\(367\) | 67.0637 | 0.182735 | 0.0913675 | − | 0.995817i | \(-0.470876\pi\) | ||||
0.0913675 | + | 0.995817i | \(0.470876\pi\) | |||||||
\(368\) | −290.231 | + | 96.2097i | −0.788670 | + | 0.261439i | ||||
\(369\) | 39.8970 | 0.108122 | ||||||||
\(370\) | −147.691 | + | 48.9668i | −0.399164 | + | 0.132343i | ||||
\(371\) | − | 13.0274i | − | 0.0351142i | ||||||
\(372\) | 93.1855 | − | 15.0427i | 0.250499 | − | 0.0404374i | ||||
\(373\) | − | 567.402i | − | 1.52119i | −0.649230 | − | 0.760593i | \(-0.724909\pi\) | ||
0.649230 | − | 0.760593i | \(-0.275091\pi\) | |||||||
\(374\) | −658.042 | − | 560.334i | −1.75947 | − | 1.49822i | ||||
\(375\) | 14.0708 | − | 216.049i | 0.0375220 | − | 0.576130i | ||||
\(376\) | −230.949 | + | 380.667i | −0.614225 | + | 1.01241i | ||||
\(377\) | 236.764i | 0.628020i | ||||||||
\(378\) | 6.62466 | + | 5.64102i | 0.0175256 | + | 0.0149233i | ||||
\(379\) | − | 240.298i | − | 0.634031i | −0.948420 | − | 0.317016i | \(-0.897319\pi\) | ||
0.948420 | − | 0.317016i | \(-0.102681\pi\) | |||||||
\(380\) | −333.000 | − | 135.028i | −0.876316 | − | 0.355337i | ||||
\(381\) | 14.6462 | 0.0384414 | ||||||||
\(382\) | −180.740 | + | 212.257i | −0.473142 | + | 0.555646i | ||||
\(383\) | −670.068 | −1.74952 | −0.874762 | − | 0.484553i | \(-0.838982\pi\) | ||||
−0.874762 | + | 0.484553i | \(0.838982\pi\) | |||||||
\(384\) | −49.5137 | + | 216.103i | −0.128942 | + | 0.562768i | ||||
\(385\) | −34.2957 | + | 56.5351i | −0.0890797 | + | 0.146845i | ||||
\(386\) | −236.048 | + | 277.209i | −0.611524 | + | 0.718157i | ||||
\(387\) | −83.8290 | −0.216612 | ||||||||
\(388\) | −666.655 | + | 107.617i | −1.71818 | + | 0.277363i | ||||
\(389\) | −474.640 | −1.22015 | −0.610077 | − | 0.792342i | \(-0.708861\pi\) | ||||
−0.610077 | + | 0.792342i | \(0.708861\pi\) | |||||||
\(390\) | −85.2693 | + | 28.2710i | −0.218639 | + | 0.0724897i | ||||
\(391\) | − | 522.826i | − | 1.33715i | ||||||
\(392\) | 200.421 | − | 330.349i | 0.511278 | − | 0.842726i | ||||
\(393\) | − | 89.5973i | − | 0.227983i | ||||||
\(394\) | 334.567 | − | 392.907i | 0.849156 | − | 0.997226i | ||||
\(395\) | 35.3315 | − | 58.2427i | 0.0894469 | − | 0.147450i | ||||
\(396\) | 187.124 | − | 30.2070i | 0.472535 | − | 0.0762802i | ||||
\(397\) | − | 499.460i | − | 1.25809i | −0.777371 | − | 0.629043i | \(-0.783447\pi\) | ||
0.777371 | − | 0.629043i | \(-0.216553\pi\) | |||||||
\(398\) | 332.554 | − | 390.542i | 0.835562 | − | 0.981262i | ||||
\(399\) | 26.0548i | 0.0653001i | ||||||||
\(400\) | −287.036 | − | 278.586i | −0.717590 | − | 0.696466i | ||||
\(401\) | 344.694 | 0.859587 | 0.429793 | − | 0.902927i | \(-0.358586\pi\) | ||||
0.429793 | + | 0.902927i | \(0.358586\pi\) | |||||||
\(402\) | 243.178 | + | 207.070i | 0.604920 | + | 0.515100i | ||||
\(403\) | 70.6631 | 0.175343 | ||||||||
\(404\) | 28.3987 | + | 175.922i | 0.0702938 | + | 0.435450i | ||||
\(405\) | 38.4743 | + | 23.3395i | 0.0949982 | + | 0.0576284i | ||||
\(406\) | 58.1993 | + | 49.5578i | 0.143348 | + | 0.122063i | ||||
\(407\) | 245.773 | 0.603864 | ||||||||
\(408\) | −324.108 | − | 196.635i | −0.794382 | − | 0.481947i | ||||
\(409\) | −501.890 | −1.22712 | −0.613558 | − | 0.789650i | \(-0.710262\pi\) | ||||
−0.613558 | + | 0.789650i | \(0.710262\pi\) | |||||||
\(410\) | 41.8524 | + | 126.233i | 0.102079 | + | 0.307885i | ||||
\(411\) | − | 93.1988i | − | 0.226761i | ||||||
\(412\) | 80.6166 | + | 499.397i | 0.195671 | + | 1.21213i | ||||
\(413\) | − | 73.3957i | − | 0.177714i | ||||||
\(414\) | 87.2990 | + | 74.3367i | 0.210867 | + | 0.179557i | ||||
\(415\) | −252.241 | − | 153.016i | −0.607809 | − | 0.368713i | ||||
\(416\) | −62.3746 | + | 153.803i | −0.149939 | + | 0.369719i | ||||
\(417\) | − | 23.5980i | − | 0.0565898i | ||||||
\(418\) | 432.144 | + | 367.978i | 1.03384 | + | 0.880331i | ||||
\(419\) | 218.369i | 0.521167i | 0.965451 | + | 0.260584i | \(0.0839150\pi\) | ||||
−0.965451 | + | 0.260584i | \(0.916085\pi\) | |||||||
\(420\) | −10.8987 | + | 26.8777i | −0.0259492 | + | 0.0639946i | ||||
\(421\) | 281.698 | 0.669116 | 0.334558 | − | 0.942375i | \(-0.391413\pi\) | ||||
0.334558 | + | 0.942375i | \(0.391413\pi\) | |||||||
\(422\) | 274.700 | − | 322.600i | 0.650947 | − | 0.764455i | ||||
\(423\) | 166.967 | 0.394722 | ||||||||
\(424\) | −106.423 | − | 64.5661i | −0.250997 | − | 0.152279i | ||||
\(425\) | 606.598 | − | 315.988i | 1.42729 | − | 0.743501i | ||||
\(426\) | −293.547 | + | 344.733i | −0.689076 | + | 0.809233i | ||||
\(427\) | −31.8156 | −0.0745097 | ||||||||
\(428\) | −66.5401 | − | 412.197i | −0.155468 | − | 0.963078i | ||||
\(429\) | 141.897 | 0.330762 | ||||||||
\(430\) | −87.9376 | − | 265.232i | −0.204506 | − | 0.616819i | ||||
\(431\) | 441.081i | 1.02339i | 0.859167 | + | 0.511694i | \(0.170982\pi\) | ||||
−0.859167 | + | 0.511694i | \(0.829018\pi\) | |||||||
\(432\) | 78.9155 | − | 26.1600i | 0.182675 | − | 0.0605556i | ||||
\(433\) | 123.443i | 0.285089i | 0.989788 | + | 0.142544i | \(0.0455283\pi\) | ||||
−0.989788 | + | 0.142544i | \(0.954472\pi\) | |||||||
\(434\) | 14.7907 | − | 17.3698i | 0.0340800 | − | 0.0400227i | ||||
\(435\) | 338.006 | + | 205.043i | 0.777025 | + | 0.471364i | ||||
\(436\) | −0.319785 | − | 1.98098i | −0.000733451 | − | 0.00454353i | ||||
\(437\) | 343.346i | 0.785690i | ||||||||
\(438\) | −122.886 | + | 144.315i | −0.280563 | + | 0.329485i | ||||
\(439\) | − | 330.728i | − | 0.753368i | −0.926342 | − | 0.376684i | \(-0.877064\pi\) | ||
0.926342 | − | 0.376684i | \(-0.122936\pi\) | |||||||
\(440\) | 291.869 | + | 560.366i | 0.663338 | + | 1.27356i | ||||
\(441\) | −144.897 | −0.328565 | ||||||||
\(442\) | −216.072 | − | 183.989i | −0.488850 | − | 0.416265i | ||||
\(443\) | −154.952 | −0.349780 | −0.174890 | − | 0.984588i | \(-0.555957\pi\) | ||||
−0.174890 | + | 0.984588i | \(0.555957\pi\) | |||||||
\(444\) | 106.423 | − | 17.1796i | 0.239691 | − | 0.0386928i | ||||
\(445\) | 170.145 | + | 103.214i | 0.382347 | + | 0.231942i | ||||
\(446\) | −532.718 | − | 453.619i | −1.19444 | − | 1.01708i | ||||
\(447\) | 58.2826 | 0.130386 | ||||||||
\(448\) | 24.7508 | + | 47.5254i | 0.0552473 | + | 0.106084i | ||||
\(449\) | −95.8970 | −0.213579 | −0.106790 | − | 0.994282i | \(-0.534057\pi\) | ||||
−0.106790 | + | 0.994282i | \(0.534057\pi\) | |||||||
\(450\) | −33.4854 | + | 146.215i | −0.0744120 | + | 0.324921i | ||||
\(451\) | − | 210.065i | − | 0.465775i | ||||||
\(452\) | −67.0738 | + | 10.8276i | −0.148393 | + | 0.0239548i | ||||
\(453\) | − | 242.467i | − | 0.535247i | ||||||
\(454\) | 282.550 | + | 240.596i | 0.622356 | + | 0.529948i | ||||
\(455\) | −11.2612 | + | 18.5637i | −0.0247499 | + | 0.0407992i | ||||
\(456\) | 212.846 | + | 129.132i | 0.466767 | + | 0.283185i | ||||
\(457\) | − | 485.718i | − | 1.06284i | −0.847108 | − | 0.531420i | \(-0.821659\pi\) | ||
0.847108 | − | 0.531420i | \(-0.178341\pi\) | |||||||
\(458\) | 401.846 | + | 342.179i | 0.877393 | + | 0.747116i | ||||
\(459\) | 142.160i | 0.309716i | ||||||||
\(460\) | −143.621 | + | 354.191i | −0.312220 | + | 0.769981i | ||||
\(461\) | 353.650 | 0.767136 | 0.383568 | − | 0.923513i | \(-0.374695\pi\) | ||||
0.383568 | + | 0.923513i | \(0.374695\pi\) | |||||||
\(462\) | 29.7009 | − | 34.8800i | 0.0642878 | − | 0.0754978i | ||||
\(463\) | −421.720 | −0.910842 | −0.455421 | − | 0.890276i | \(-0.650511\pi\) | ||||
−0.455421 | + | 0.890276i | \(0.650511\pi\) | |||||||
\(464\) | 693.292 | − | 229.822i | 1.49416 | − | 0.495306i | ||||
\(465\) | 61.1960 | − | 100.879i | 0.131604 | − | 0.216945i | ||||
\(466\) | 75.8248 | − | 89.0466i | 0.162714 | − | 0.191087i | ||||
\(467\) | −640.974 | −1.37254 | −0.686268 | − | 0.727349i | \(-0.740752\pi\) | ||||
−0.686268 | + | 0.727349i | \(0.740752\pi\) | |||||||
\(468\) | 61.4432 | − | 9.91864i | 0.131289 | − | 0.0211937i | ||||
\(469\) | 77.1960 | 0.164597 | ||||||||
\(470\) | 175.151 | + | 528.279i | 0.372661 | + | 1.12400i | ||||
\(471\) | 36.8289i | 0.0781929i | ||||||||
\(472\) | −599.582 | − | 363.763i | −1.27030 | − | 0.770684i | ||||
\(473\) | 441.374i | 0.933137i | ||||||||
\(474\) | −30.5980 | + | 35.9335i | −0.0645528 | + | 0.0758091i | ||||
\(475\) | −398.360 | + | 207.513i | −0.838653 | + | 0.436869i | ||||
\(476\) | −90.4535 | + | 14.6017i | −0.190028 | + | 0.0306758i | ||||
\(477\) | 46.6790i | 0.0978595i | ||||||||
\(478\) | 146.957 | − | 172.582i | 0.307441 | − | 0.361050i | ||||
\(479\) | 221.137i | 0.461664i | 0.972994 | + | 0.230832i | \(0.0741448\pi\) | ||||
−0.972994 | + | 0.230832i | \(0.925855\pi\) | |||||||
\(480\) | 165.553 | + | 222.244i | 0.344901 | + | 0.463008i | ||||
\(481\) | 80.7010 | 0.167778 | ||||||||
\(482\) | −118.460 | − | 100.871i | −0.245767 | − | 0.209275i | ||||
\(483\) | 27.7128 | 0.0573764 | ||||||||
\(484\) | −81.9124 | − | 507.424i | −0.169240 | − | 1.04840i | ||||
\(485\) | −437.801 | + | 721.698i | −0.902682 | + | 1.48804i | ||||
\(486\) | −23.7371 | − | 20.2126i | −0.0488418 | − | 0.0415897i | ||||
\(487\) | 889.949 | 1.82741 | 0.913705 | − | 0.406377i | \(-0.133208\pi\) | ||||
0.913705 | + | 0.406377i | \(0.133208\pi\) | |||||||
\(488\) | −157.684 | + | 259.907i | −0.323123 | + | 0.532596i | ||||
\(489\) | −364.096 | −0.744573 | ||||||||
\(490\) | −151.999 | − | 458.449i | −0.310201 | − | 0.935611i | ||||
\(491\) | − | 552.843i | − | 1.12595i | −0.826473 | − | 0.562977i | \(-0.809656\pi\) | ||
0.826473 | − | 0.562977i | \(-0.190344\pi\) | |||||||
\(492\) | −14.6836 | − | 90.9607i | −0.0298447 | − | 0.184879i | ||||
\(493\) | 1248.91i | 2.53328i | ||||||||
\(494\) | 141.897 | + | 120.828i | 0.287241 | + | 0.244591i | ||||
\(495\) | 122.886 | − | 202.574i | 0.248255 | − | 0.409240i | ||||
\(496\) | −68.5914 | − | 206.916i | −0.138289 | − | 0.417169i | ||||
\(497\) | 109.435i | 0.220190i | ||||||||
\(498\) | 155.623 | + | 132.516i | 0.312495 | + | 0.266096i | ||||
\(499\) | 533.302i | 1.06874i | 0.845250 | + | 0.534371i | \(0.179451\pi\) | ||||
−0.845250 | + | 0.534371i | \(0.820549\pi\) | |||||||
\(500\) | −497.745 | + | 47.4341i | −0.995490 | + | 0.0948683i | ||||
\(501\) | −412.894 | −0.824139 | ||||||||
\(502\) | −137.737 | + | 161.755i | −0.274376 | + | 0.322220i | ||||
\(503\) | 574.914 | 1.14297 | 0.571485 | − | 0.820612i | \(-0.306367\pi\) | ||||
0.571485 | + | 0.820612i | \(0.306367\pi\) | |||||||
\(504\) | 10.4228 | − | 17.1796i | 0.0206801 | − | 0.0340865i | ||||
\(505\) | 190.447 | + | 115.530i | 0.377122 | + | 0.228772i | ||||
\(506\) | 391.395 | − | 459.644i | 0.773509 | − | 0.908388i | ||||
\(507\) | −246.124 | −0.485451 | ||||||||
\(508\) | −5.39034 | − | 33.3917i | −0.0106109 | − | 0.0657316i | ||||
\(509\) | 207.547 | 0.407753 | 0.203877 | − | 0.978997i | \(-0.434646\pi\) | ||||
0.203877 | + | 0.978997i | \(0.434646\pi\) | |||||||
\(510\) | −449.788 | + | 149.127i | −0.881938 | + | 0.292406i | ||||
\(511\) | 45.8122i | 0.0896521i | ||||||||
\(512\) | 510.913 | + | 33.3518i | 0.997876 | + | 0.0651403i | ||||
\(513\) | − | 93.3580i | − | 0.181984i | ||||||
\(514\) | 494.120 | − | 580.282i | 0.961324 | − | 1.12895i | ||||
\(515\) | 540.630 | + | 327.960i | 1.04977 | + | 0.636816i | ||||
\(516\) | 30.8522 | + | 191.121i | 0.0597910 | + | 0.370389i | ||||
\(517\) | − | 879.112i | − | 1.70041i | ||||||
\(518\) | 16.8918 | − | 19.8373i | 0.0326096 | − | 0.0382959i | ||||
\(519\) | − | 4.04401i | − | 0.00779192i | ||||||
\(520\) | 95.8369 | + | 184.000i | 0.184302 | + | 0.353845i | ||||
\(521\) | −712.900 | −1.36833 | −0.684165 | − | 0.729327i | \(-0.739833\pi\) | ||||
−0.684165 | + | 0.729327i | \(0.739833\pi\) | |||||||
\(522\) | −208.537 | − | 177.573i | −0.399495 | − | 0.340178i | ||||
\(523\) | 139.548 | 0.266822 | 0.133411 | − | 0.991061i | \(-0.457407\pi\) | ||||
0.133411 | + | 0.991061i | \(0.457407\pi\) | |||||||
\(524\) | −204.272 | + | 32.9751i | −0.389831 | + | 0.0629296i | ||||
\(525\) | 16.7492 | + | 32.1532i | 0.0319032 | + | 0.0612442i | ||||
\(526\) | 17.4983 | + | 14.9002i | 0.0332668 | + | 0.0283273i | ||||
\(527\) | 372.742 | 0.707290 | ||||||||
\(528\) | −137.737 | − | 415.504i | −0.260865 | − | 0.786939i | ||||
\(529\) | −163.804 | −0.309648 | ||||||||
\(530\) | −147.691 | + | 48.9668i | −0.278662 | + | 0.0923902i | ||||
\(531\) | 262.988i | 0.495268i | ||||||||
\(532\) | 59.4019 | − | 9.58911i | 0.111658 | − | 0.0180246i | ||||
\(533\) | − | 68.9760i | − | 0.129411i | ||||||
\(534\) | −104.973 | − | 89.3861i | −0.196578 | − | 0.167390i | ||||
\(535\) | −446.230 | − | 270.695i | −0.834075 | − | 0.505972i | ||||
\(536\) | 382.598 | − | 630.627i | 0.713802 | − | 1.17654i | ||||
\(537\) | 393.269i | 0.732345i | ||||||||
\(538\) | −118.700 | − | 101.075i | −0.220632 | − | 0.187872i | ||||
\(539\) | 762.908i | 1.41541i | ||||||||
\(540\) | 39.0514 | − | 96.3067i | 0.0723175 | − | 0.178346i | ||||
\(541\) | −946.688 | −1.74988 | −0.874942 | − | 0.484227i | \(-0.839101\pi\) | ||||
−0.874942 | + | 0.484227i | \(0.839101\pi\) | |||||||
\(542\) | 112.399 | − | 131.999i | 0.207379 | − | 0.243540i | ||||
\(543\) | −197.621 | −0.363942 | ||||||||
\(544\) | −329.021 | + | 811.298i | −0.604818 | + | 1.49136i | ||||
\(545\) | −2.14454 | − | 1.30093i | −0.00393493 | − | 0.00238703i | ||||
\(546\) | 9.75248 | − | 11.4531i | 0.0178617 | − | 0.0209763i | ||||
\(547\) | 50.3388 | 0.0920271 | 0.0460136 | − | 0.998941i | \(-0.485348\pi\) | ||||
0.0460136 | + | 0.998941i | \(0.485348\pi\) | |||||||
\(548\) | −212.483 | + | 34.3006i | −0.387742 | + | 0.0625923i | ||||
\(549\) | 114.000 | 0.207650 | ||||||||
\(550\) | 769.845 | + | 176.307i | 1.39972 | + | 0.320557i | ||||
\(551\) | − | 820.173i | − | 1.48852i | ||||||
\(552\) | 137.350 | − | 226.390i | 0.248822 | − | 0.410128i | ||||
\(553\) | 11.4070i | 0.0206275i | ||||||||
\(554\) | −372.561 | + | 437.525i | −0.672492 | + | 0.789757i | ||||
\(555\) | 69.8891 | − | 115.210i | 0.125926 | − | 0.207585i | ||||
\(556\) | −53.8007 | + | 8.68492i | −0.0967638 | + | 0.0156204i | ||||
\(557\) | − | 790.157i | − | 1.41859i | −0.704910 | − | 0.709297i | \(-0.749013\pi\) | ||
0.704910 | − | 0.709297i | \(-0.250987\pi\) | |||||||
\(558\) | −52.9973 | + | 62.2386i | −0.0949773 | + | 0.111539i | ||||
\(559\) | 144.928i | 0.259263i | ||||||||
\(560\) | 65.2892 | + | 14.9557i | 0.116588 | + | 0.0267066i | ||||
\(561\) | 748.495 | 1.33422 | ||||||||
\(562\) | −342.004 | − | 291.222i | −0.608548 | − | 0.518189i | ||||
\(563\) | −354.133 | −0.629010 | −0.314505 | − | 0.949256i | \(-0.601838\pi\) | ||||
−0.314505 | + | 0.949256i | \(0.601838\pi\) | |||||||
\(564\) | −61.4502 | − | 380.667i | −0.108954 | − | 0.674941i | ||||
\(565\) | −44.0482 | + | 72.6117i | −0.0779614 | + | 0.128516i | ||||
\(566\) | 128.096 | + | 109.076i | 0.226319 | + | 0.192714i | ||||
\(567\) | −7.53528 | −0.0132897 | ||||||||
\(568\) | 893.989 | + | 542.378i | 1.57392 | + | 0.954891i | ||||
\(569\) | 55.4983 | 0.0975366 | 0.0487683 | − | 0.998810i | \(-0.484470\pi\) | ||||
0.0487683 | + | 0.998810i | \(0.484470\pi\) | |||||||
\(570\) | 295.381 | − | 97.9336i | 0.518213 | − | 0.171813i | ||||
\(571\) | 791.134i | 1.38552i | 0.721167 | + | 0.692762i | \(0.243606\pi\) | ||||
−0.721167 | + | 0.692762i | \(0.756394\pi\) | |||||||
\(572\) | −52.2233 | − | 323.509i | −0.0912995 | − | 0.565575i | ||||
\(573\) | − | 241.433i | − | 0.421349i | ||||||
\(574\) | −16.9551 | − | 14.4376i | −0.0295386 | − | 0.0251526i | ||||
\(575\) | 220.719 | + | 423.711i | 0.383858 | + | 0.736888i | ||||
\(576\) | −88.6856 | − | 170.291i | −0.153968 | − | 0.295643i | ||||
\(577\) | − | 201.759i | − | 0.349668i | −0.984598 | − | 0.174834i | \(-0.944061\pi\) | ||
0.984598 | − | 0.174834i | \(-0.0559389\pi\) | |||||||
\(578\) | −699.690 | − | 595.799i | −1.21054 | − | 1.03079i | ||||
\(579\) | − | 315.313i | − | 0.544583i | ||||||
\(580\) | 343.077 | − | 846.079i | 0.591512 | − | 1.45876i | ||||
\(581\) | 49.4020 | 0.0850292 | ||||||||
\(582\) | 379.146 | − | 445.260i | 0.651454 | − | 0.765051i | ||||
\(583\) | 245.773 | 0.421566 | ||||||||
\(584\) | 374.248 | + | 227.054i | 0.640835 | + | 0.388791i | ||||
\(585\) | 40.3505 | − | 66.5163i | 0.0689752 | − | 0.113703i | ||||
\(586\) | −319.777 | + | 375.537i | −0.545694 | + | 0.640848i | ||||
\(587\) | −444.556 | −0.757335 | −0.378668 | − | 0.925533i | \(-0.623618\pi\) | ||||
−0.378668 | + | 0.925533i | \(0.623618\pi\) | |||||||
\(588\) | 53.3274 | + | 330.349i | 0.0906929 | + | 0.561818i | ||||
\(589\) | −244.784 | −0.415593 | ||||||||
\(590\) | −832.084 | + | 275.877i | −1.41031 | + | 0.467588i | ||||
\(591\) | 446.915i | 0.756202i | ||||||||
\(592\) | −78.3350 | − | 236.309i | −0.132323 | − | 0.399171i | ||||
\(593\) | − | 563.908i | − | 0.950942i | −0.879731 | − | 0.475471i | \(-0.842278\pi\) | ||
0.879731 | − | 0.475471i | \(-0.157722\pi\) | |||||||
\(594\) | −106.423 | + | 124.980i | −0.179163 | + | 0.210404i | ||||
\(595\) | −59.4019 | + | 97.9217i | −0.0998351 | + | 0.164574i | ||||
\(596\) | −21.4502 | − | 132.878i | −0.0359902 | − | 0.222949i | ||||
\(597\) | 444.226i | 0.744097i | ||||||||
\(598\) | 128.517 | − | 150.927i | 0.214911 | − | 0.252386i | ||||
\(599\) | − | 845.034i | − | 1.41074i | −0.708839 | − | 0.705371i | \(-0.750781\pi\) | ||
0.708839 | − | 0.705371i | \(-0.249219\pi\) | |||||||
\(600\) | 345.677 | + | 22.5306i | 0.576128 | + | 0.0375509i | ||||
\(601\) | 672.296 | 1.11863 | 0.559314 | − | 0.828956i | \(-0.311065\pi\) | ||||
0.559314 | + | 0.828956i | \(0.311065\pi\) | |||||||
\(602\) | 35.6250 | + | 30.3353i | 0.0591777 | + | 0.0503909i | ||||
\(603\) | −276.604 | −0.458714 | ||||||||
\(604\) | −552.797 | + | 89.2368i | −0.915227 | + | 0.147743i | ||||
\(605\) | −549.320 | − | 333.232i | −0.907967 | − | 0.550796i | ||||
\(606\) | −117.498 | − | 100.052i | −0.193892 | − | 0.165102i | ||||
\(607\) | 882.664 | 1.45414 | 0.727071 | − | 0.686562i | \(-0.240881\pi\) | ||||
0.727071 | + | 0.686562i | \(0.240881\pi\) | |||||||
\(608\) | 216.072 | − | 532.789i | 0.355381 | − | 0.876298i | ||||
\(609\) | −66.1993 | −0.108702 | ||||||||
\(610\) | 119.587 | + | 360.692i | 0.196045 | + | 0.591299i | ||||
\(611\) | − | 288.662i | − | 0.472442i | ||||||
\(612\) | 324.108 | − | 52.3200i | 0.529588 | − | 0.0854902i | ||||
\(613\) | 469.374i | 0.765701i | 0.923810 | + | 0.382850i | \(0.125057\pi\) | ||||
−0.923810 | + | 0.382850i | \(0.874943\pi\) | |||||||
\(614\) | 176.350 | + | 150.166i | 0.287216 | + | 0.244569i | ||||
\(615\) | −98.4708 | − | 59.7350i | −0.160115 | − | 0.0971300i | ||||
\(616\) | −90.4535 | − | 54.8777i | −0.146840 | − | 0.0890871i | ||||
\(617\) | − | 218.994i | − | 0.354934i | −0.984127 | − | 0.177467i | \(-0.943210\pi\) | ||
0.984127 | − | 0.177467i | \(-0.0567902\pi\) | |||||||
\(618\) | −333.548 | − | 284.022i | −0.539721 | − | 0.459582i | ||||
\(619\) | − | 879.610i | − | 1.42102i | −0.703689 | − | 0.710509i | \(-0.748465\pi\) | ||
0.703689 | − | 0.710509i | \(-0.251535\pi\) | |||||||
\(620\) | −252.516 | − | 102.393i | −0.407284 | − | 0.165149i | ||||
\(621\) | −99.2990 | −0.159902 | ||||||||
\(622\) | −264.213 | + | 310.284i | −0.424779 | + | 0.498849i | ||||
\(623\) | −33.3232 | −0.0534884 | ||||||||
\(624\) | −45.2267 | − | 136.433i | −0.0724787 | − | 0.218643i | ||||
\(625\) | −358.203 | + | 512.168i | −0.573124 | + | 0.819468i | ||||
\(626\) | −128.447 | + | 150.845i | −0.205187 | + | 0.240966i | ||||
\(627\) | −491.546 | −0.783964 | ||||||||
\(628\) | 83.9656 | − | 13.5544i | 0.133703 | − | 0.0215834i | ||||
\(629\) | 425.691 | 0.676774 | ||||||||
\(630\) | −7.90460 | − | 23.8414i | −0.0125470 | − | 0.0378435i | ||||
\(631\) | 635.566i | 1.00724i | 0.863926 | + | 0.503618i | \(0.167998\pi\) | ||||
−0.863926 | + | 0.503618i | \(0.832002\pi\) | |||||||
\(632\) | 93.1855 | + | 56.5351i | 0.147445 | + | 0.0894543i | ||||
\(633\) | 366.944i | 0.579691i | ||||||||
\(634\) | −610.966 | + | 717.502i | −0.963669 | + | 1.13171i | ||||
\(635\) | −36.1486 | − | 21.9287i | −0.0569270 | − | 0.0345334i | ||||
\(636\) | 106.423 | − | 17.1796i | 0.167331 | − | 0.0270119i | ||||
\(637\) | 250.505i | 0.393258i | ||||||||
\(638\) | −934.951 | + | 1097.98i | −1.46544 | + | 1.72097i | ||||
\(639\) | − | 392.120i | − | 0.613646i | ||||||
\(640\) | 445.761 | − | 459.235i | 0.696502 | − | 0.717555i | ||||
\(641\) | −296.309 | −0.462260 | −0.231130 | − | 0.972923i | \(-0.574242\pi\) | ||||
−0.231130 | + | 0.972923i | \(0.574242\pi\) | |||||||
\(642\) | 275.307 | + | 234.429i | 0.428827 | + | 0.365154i | ||||
\(643\) | −591.032 | −0.919179 | −0.459590 | − | 0.888131i | \(-0.652003\pi\) | ||||
−0.459590 | + | 0.888131i | \(0.652003\pi\) | |||||||
\(644\) | −10.1993 | − | 63.1821i | −0.0158375 | − | 0.0981088i | ||||
\(645\) | 206.900 | + | 125.511i | 0.320776 | + | 0.194591i | ||||
\(646\) | 748.495 | + | 637.357i | 1.15866 | + | 0.986621i | ||||
\(647\) | 166.507 | 0.257352 | 0.128676 | − | 0.991687i | \(-0.458927\pi\) | ||||
0.128676 | + | 0.991687i | \(0.458927\pi\) | |||||||
\(648\) | −37.3463 | + | 61.5569i | −0.0576331 | + | 0.0949953i | ||||
\(649\) | 1384.67 | 2.13355 | ||||||||
\(650\) | 252.783 | + | 57.8913i | 0.388897 | + | 0.0890635i | ||||
\(651\) | 19.7575i | 0.0303494i | ||||||||
\(652\) | 134.001 | + | 830.098i | 0.205523 | + | 1.27316i | ||||
\(653\) | − | 621.335i | − | 0.951509i | −0.879578 | − | 0.475754i | \(-0.842175\pi\) | ||
0.879578 | − | 0.475754i | \(-0.157825\pi\) | |||||||
\(654\) | 1.32310 | + | 1.12664i | 0.00202308 | + | 0.00172269i | ||||
\(655\) | −134.148 | + | 221.137i | −0.204806 | + | 0.337614i | ||||
\(656\) | −201.976 | + | 66.9538i | −0.307890 | + | 0.102064i | ||||
\(657\) | − | 164.152i | − | 0.249851i | ||||||
\(658\) | −70.9565 | − | 60.4208i | −0.107837 | − | 0.0918249i | ||||
\(659\) | − | 702.113i | − | 1.06542i | −0.846297 | − | 0.532711i | \(-0.821173\pi\) | ||
0.846297 | − | 0.532711i | \(-0.178827\pi\) | |||||||
\(660\) | −507.071 | − | 205.613i | −0.768290 | − | 0.311534i | ||||
\(661\) | 358.193 | 0.541895 | 0.270948 | − | 0.962594i | \(-0.412663\pi\) | ||||
0.270948 | + | 0.962594i | \(0.412663\pi\) | |||||||
\(662\) | −350.994 | + | 412.197i | −0.530202 | + | 0.622655i | ||||
\(663\) | 245.773 | 0.370698 | ||||||||
\(664\) | 244.846 | − | 403.573i | 0.368743 | − | 0.607790i | ||||
\(665\) | 39.0099 | − | 64.3064i | 0.0586616 | − | 0.0967013i | ||||
\(666\) | −60.5257 | + | 71.0798i | −0.0908795 | + | 0.106726i | ||||
\(667\) | −872.367 | −1.30790 | ||||||||
\(668\) | 151.960 | + | 941.351i | 0.227485 | + | 1.40921i | ||||
\(669\) | 605.945 | 0.905748 | ||||||||
\(670\) | −290.161 | − | 875.167i | −0.433077 | − | 1.30622i | ||||
\(671\) | − | 600.230i | − | 0.894530i | ||||||
\(672\) | −43.0035 | − | 17.4400i | −0.0639933 | − | 0.0259524i | ||||
\(673\) | − | 714.176i | − | 1.06118i | −0.847628 | − | 0.530592i | \(-0.821970\pi\) | ||
0.847628 | − | 0.530592i | \(-0.178030\pi\) | |||||||
\(674\) | −489.244 | + | 574.555i | −0.725882 | + | 0.852456i | ||||
\(675\) | −60.0147 | − | 115.210i | −0.0889107 | − | 0.170681i | ||||
\(676\) | 90.5827 | + | 561.134i | 0.133998 | + | 0.830081i | ||||
\(677\) | 509.833i | 0.753077i | 0.926401 | + | 0.376538i | \(0.122886\pi\) | ||||
−0.926401 | + | 0.376538i | \(0.877114\pi\) | |||||||
\(678\) | 38.1468 | − | 44.7986i | 0.0562638 | − | 0.0660747i | ||||
\(679\) | − | 141.346i | − | 0.208168i | ||||||
\(680\) | 505.532 | + | 970.582i | 0.743429 | + | 1.42733i | ||||
\(681\) | −321.389 | −0.471936 | ||||||||
\(682\) | 327.697 | + | 279.040i | 0.480494 | + | 0.409150i | ||||
\(683\) | 1263.93 | 1.85055 | 0.925275 | − | 0.379298i | \(-0.123834\pi\) | ||||
0.925275 | + | 0.379298i | \(0.123834\pi\) | |||||||
\(684\) | −212.846 | + | 34.3592i | −0.311178 | + | 0.0502327i | ||||
\(685\) | −139.540 | + | 230.026i | −0.203708 | + | 0.335805i | ||||
\(686\) | 124.048 | + | 105.629i | 0.180828 | + | 0.153978i | ||||
\(687\) | −457.083 | −0.665332 | ||||||||
\(688\) | 424.378 | − | 140.679i | 0.616829 | − | 0.204475i | ||||
\(689\) | 80.7010 | 0.117128 | ||||||||
\(690\) | −104.166 | − | 314.179i | −0.150965 | − | 0.455332i | ||||
\(691\) | 512.351i | 0.741463i | 0.928740 | + | 0.370731i | \(0.120893\pi\) | ||||
−0.928740 | + | 0.370731i | \(0.879107\pi\) | |||||||
\(692\) | −9.21987 | + | 1.48834i | −0.0133235 | + | 0.00215078i | ||||
\(693\) | 39.6746i | 0.0572504i | ||||||||
\(694\) | −703.842 | − | 599.334i | −1.01418 | − | 0.863594i | ||||
\(695\) | −35.3315 | + | 58.2427i | −0.0508368 | + | 0.0838024i | ||||
\(696\) | −328.096 | + | 540.793i | −0.471403 | + | 0.777002i | ||||
\(697\) | − | 363.843i | − | 0.522012i | ||||||
\(698\) | 305.458 | + | 260.103i | 0.437619 | + | 0.372640i | ||||
\(699\) | 101.287i | 0.144902i | ||||||||
\(700\) | 67.1413 | − | 50.0198i | 0.0959162 | − | 0.0714568i | ||||
\(701\) | 1092.03 | 1.55781 | 0.778907 | − | 0.627139i | \(-0.215774\pi\) | ||||
0.778907 | + | 0.627139i | \(0.215774\pi\) | |||||||
\(702\) | −34.9446 | + | 41.0380i | −0.0497786 | + | 0.0584586i | ||||
\(703\) | −279.556 | −0.397662 | ||||||||
\(704\) | −896.609 | + | 466.945i | −1.27359 | + | 0.663274i | ||||
\(705\) | −412.096 | − | 249.988i | −0.584534 | − | 0.354593i | ||||
\(706\) | 325.323 | − | 382.051i | 0.460798 | − | 0.541148i | ||||
\(707\) | −37.2995 | −0.0527574 | ||||||||
\(708\) | 599.582 | − | 96.7891i | 0.846867 | − | 0.136708i | ||||
\(709\) | 416.887 | 0.587993 | 0.293997 | − | 0.955806i | \(-0.405015\pi\) | ||||
0.293997 | + | 0.955806i | \(0.405015\pi\) | |||||||
\(710\) | 1240.65 | − | 411.338i | 1.74740 | − | 0.579350i | ||||
\(711\) | − | 40.8729i | − | 0.0574864i | ||||||
\(712\) | −165.156 | + | 272.223i | −0.231961 | + | 0.382336i | ||||
\(713\) | 260.362i | 0.365163i | ||||||||
\(714\) | 51.4435 | − | 60.4139i | 0.0720498 | − | 0.0846133i | ||||
\(715\) | −350.220 | − | 212.452i | −0.489818 | − | 0.297136i | ||||
\(716\) | 896.609 | − | 144.738i | 1.25225 | − | 0.202147i | ||||
\(717\) | 196.305i | 0.273787i | ||||||||
\(718\) | −279.556 | + | 328.304i | −0.389354 | + | 0.457247i | ||||
\(719\) | − | 395.268i | − | 0.549747i | −0.961480 | − | 0.274874i | \(-0.911364\pi\) | ||
0.961480 | − | 0.274874i | \(-0.0886361\pi\) | |||||||
\(720\) | −233.941 | − | 53.5884i | −0.324918 | − | 0.0744284i | ||||
\(721\) | −105.884 | −0.146857 | ||||||||
\(722\) | 58.1625 | + | 49.5264i | 0.0805575 | + | 0.0685962i | ||||
\(723\) | 134.743 | 0.186367 | ||||||||
\(724\) | 72.7317 | + | 450.553i | 0.100458 | + | 0.622310i | ||||
\(725\) | −527.244 | − | 1012.14i | −0.727233 | − | 1.39606i | ||||
\(726\) | 338.909 | + | 288.587i | 0.466817 | + | 0.397503i | ||||
\(727\) | 597.583 | 0.821985 | 0.410993 | − | 0.911639i | \(-0.365182\pi\) | ||||
0.410993 | + | 0.911639i | \(0.365182\pi\) | |||||||
\(728\) | −29.7009 | − | 18.0194i | −0.0407980 | − | 0.0247519i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 519.371 | − | 172.197i | 0.711467 | − | 0.235887i | ||||
\(731\) | 764.482i | 1.04580i | ||||||||
\(732\) | −41.9562 | − | 259.907i | −0.0573172 | − | 0.355064i | ||||
\(733\) | 23.8650i | 0.0325580i | 0.999867 | + | 0.0162790i | \(0.00518200\pi\) | ||||
−0.999867 | + | 0.0162790i | \(0.994818\pi\) | |||||||
\(734\) | 102.120 | + | 86.9574i | 0.139129 | + | 0.118471i | ||||
\(735\) | 357.624 | + | 216.944i | 0.486563 | + | 0.295162i | ||||
\(736\) | −566.694 | − | 229.822i | −0.769965 | − | 0.312258i | ||||
\(737\) | 1456.37i | 1.97608i | ||||||||
\(738\) | 60.7527 | + | 51.7320i | 0.0823207 | + | 0.0700976i | ||||
\(739\) | 125.767i | 0.170186i | 0.996373 | + | 0.0850928i | \(0.0271187\pi\) | ||||
−0.996373 | + | 0.0850928i | \(0.972881\pi\) | |||||||
\(740\) | −288.386 | − | 116.938i | −0.389711 | − | 0.158024i | ||||
\(741\) | −161.402 | −0.217816 | ||||||||
\(742\) | 16.8918 | − | 19.8373i | 0.0227652 | − | 0.0267349i | ||||
\(743\) | 148.841 | 0.200325 | 0.100162 | − | 0.994971i | \(-0.468064\pi\) | ||||
0.100162 | + | 0.994971i | \(0.468064\pi\) | |||||||
\(744\) | 161.402 | + | 97.9217i | 0.216938 | + | 0.131615i | ||||
\(745\) | −143.849 | − | 87.2625i | −0.193086 | − | 0.117131i | ||||
\(746\) | 735.715 | − | 864.004i | 0.986213 | − | 1.15818i | ||||
\(747\) | −177.014 | −0.236967 | ||||||||
\(748\) | −275.474 | − | 1706.48i | −0.368280 | − | 2.28140i | ||||
\(749\) | 87.3954 | 0.116683 | ||||||||
\(750\) | 301.563 | − | 310.741i | 0.402084 | − | 0.414321i | ||||
\(751\) | − | 463.390i | − | 0.617030i | −0.951219 | − | 0.308515i | \(-0.900168\pi\) | ||
0.951219 | − | 0.308515i | \(-0.0998321\pi\) | |||||||
\(752\) | −845.261 | + | 280.199i | −1.12402 | + | 0.372605i | ||||
\(753\) | − | 183.989i | − | 0.244341i | ||||||
\(754\) | −306.997 | + | 360.529i | −0.407157 | + | 0.478155i | ||||
\(755\) | −363.029 | + | 598.439i | −0.480833 | + | 0.792634i | ||||
\(756\) | 2.77326 | + | 17.1796i | 0.00366834 | + | 0.0227243i | ||||
\(757\) | 719.363i | 0.950281i | 0.879910 | + | 0.475141i | \(0.157603\pi\) | ||||
−0.879910 | + | 0.475141i | \(0.842397\pi\) | |||||||
\(758\) | 311.579 | − | 365.910i | 0.411054 | − | 0.482731i | ||||
\(759\) | 522.826i | 0.688836i | ||||||||
\(760\) | −331.989 | − | 637.393i | −0.436827 | − | 0.838675i | ||||
\(761\) | −1107.49 | −1.45530 | −0.727651 | − | 0.685947i | \(-0.759388\pi\) | ||||
−0.727651 | + | 0.685947i | \(0.759388\pi\) | |||||||
\(762\) | 22.3023 | + | 18.9908i | 0.0292681 | + | 0.0249223i | ||||
\(763\) | 0.420013 | 0.000550476 | ||||||||
\(764\) | −550.440 | + | 88.8563i | −0.720472 | + | 0.116304i | ||||
\(765\) | 212.846 | − | 350.868i | 0.278229 | − | 0.458651i | ||||
\(766\) | −1020.34 | − | 868.835i | −1.33203 | − | 1.13425i | ||||
\(767\) | 454.666 | 0.592785 | ||||||||
\(768\) | −355.603 | + | 264.866i | −0.463025 | + | 0.344878i | ||||
\(769\) | −231.691 | −0.301289 | −0.150644 | − | 0.988588i | \(-0.548135\pi\) | ||||
−0.150644 | + | 0.988588i | \(0.548135\pi\) | |||||||
\(770\) | −125.529 | + | 41.6191i | −0.163025 | + | 0.0540507i | ||||
\(771\) | 660.047i | 0.856092i | ||||||||
\(772\) | −718.879 | + | 116.047i | −0.931190 | + | 0.150320i | ||||
\(773\) | − | 519.956i | − | 0.672647i | −0.941746 | − | 0.336324i | \(-0.890816\pi\) | ||
0.941746 | − | 0.336324i | \(-0.109184\pi\) | |||||||
\(774\) | −127.650 | − | 108.696i | −0.164922 | − | 0.140434i | ||||
\(775\) | −302.079 | + | 157.358i | −0.389779 | + | 0.203043i | ||||
\(776\) | −1154.68 | − | 700.539i | −1.48799 | − | 0.902756i | ||||
\(777\) | 22.5641i | 0.0290400i | ||||||||
\(778\) | −722.751 | − | 615.436i | −0.928986 | − | 0.791049i | ||||
\(779\) | 238.940i | 0.306726i | ||||||||
\(780\) | −166.500 | − | 67.5141i | −0.213462 | − | 0.0865566i | ||||
\(781\) | −2064.58 | −2.64351 | ||||||||
\(782\) | 677.917 | − | 796.127i | 0.866901 | − | 1.01807i | ||||
\(783\) | 237.202 | 0.302940 | ||||||||
\(784\) | 733.531 | − | 243.161i | 0.935626 | − | 0.310154i | ||||
\(785\) | 55.1412 | − | 90.8982i | 0.0702436 | − | 0.115794i | ||||
\(786\) | 116.175 | − | 136.433i | 0.147806 | − | 0.173579i | ||||
\(787\) | 46.0288 | 0.0584864 | 0.0292432 | − | 0.999572i | \(-0.490690\pi\) | ||||
0.0292432 | + | 0.999572i | \(0.490690\pi\) | |||||||
\(788\) | 1018.92 | − | 164.481i | 1.29304 | − | 0.208733i | ||||
\(789\) | −19.9036 | −0.0252264 | ||||||||
\(790\) | 129.320 | − | 42.8761i | 0.163697 | − | 0.0542736i | ||||
\(791\) | − | 14.2212i | − | 0.0179788i | ||||||
\(792\) | 324.108 | + | 196.635i | 0.409227 | + | 0.248276i | ||||
\(793\) | − | 197.089i | − | 0.248536i | ||||||
\(794\) | 647.619 | − | 760.546i | 0.815641 | − | 0.957867i | ||||
\(795\) | 69.8891 | − | 115.210i | 0.0879108 | − | 0.144918i | ||||
\(796\) | 1012.78 | − | 163.491i | 1.27234 | − | 0.205391i | ||||
\(797\) | − | 15.3098i | − | 0.0192093i | −0.999954 | − | 0.00960463i | \(-0.996943\pi\) | ||
0.999954 | − | 0.00960463i | \(-0.00305730\pi\) | |||||||
\(798\) | −33.7836 | + | 39.6746i | −0.0423353 | + | 0.0497175i | ||||
\(799\) | − | 1522.67i | − | 1.90572i | ||||||
\(800\) | −75.8546 | − | 796.396i | −0.0948183 | − | 0.995495i | ||||
\(801\) | 119.402 | 0.149066 | ||||||||
\(802\) | 524.879 | + | 446.944i | 0.654463 | + | 0.557287i | ||||
\(803\) | −864.288 | −1.07632 | ||||||||
\(804\) | 101.801 | + | 630.627i | 0.126618 | + | 0.784362i | ||||
\(805\) | −68.3987 | − | 41.4924i | −0.0849673 | − | 0.0515434i | ||||
\(806\) | 107.601 | + | 91.6245i | 0.133500 | + | 0.113678i | ||||
\(807\) | 135.017 | 0.167307 | ||||||||
\(808\) | −184.863 | + | 304.706i | −0.228791 | + | 0.377111i | ||||
\(809\) | −313.093 | −0.387012 | −0.193506 | − | 0.981099i | \(-0.561986\pi\) | ||||
−0.193506 | + | 0.981099i | \(0.561986\pi\) | |||||||
\(810\) | 28.3233 | + | 85.4271i | 0.0349671 | + | 0.105466i | ||||
\(811\) | − | 1056.89i | − | 1.30319i | −0.758566 | − | 0.651596i | \(-0.774100\pi\) | ||
0.758566 | − | 0.651596i | \(-0.225900\pi\) | |||||||
\(812\) | 24.3638 | + | 150.927i | 0.0300047 | + | 0.185871i | ||||
\(813\) | 150.143i | 0.184678i | ||||||||
\(814\) | 374.248 | + | 318.678i | 0.459764 | + | 0.391497i | ||||
\(815\) | 898.635 | + | 545.136i | 1.10262 | + | 0.668878i | ||||
\(816\) | −238.567 | − | 719.673i | −0.292362 | − | 0.881953i | ||||
\(817\) | − | 502.045i | − | 0.614498i | ||||||
\(818\) | −764.247 | − | 650.770i | −0.934288 | − | 0.795563i | ||||
\(819\) | 13.0274i | 0.0159064i | ||||||||
\(820\) | −99.9481 | + | 246.487i | −0.121888 | + | 0.300594i | ||||
\(821\) | 308.659 | 0.375955 | 0.187978 | − | 0.982173i | \(-0.439807\pi\) | ||||
0.187978 | + | 0.982173i | \(0.439807\pi\) | |||||||
\(822\) | 120.845 | − | 141.917i | 0.147014 | − | 0.172649i | ||||
\(823\) | 109.680 | 0.133269 | 0.0666344 | − | 0.997777i | \(-0.478774\pi\) | ||||
0.0666344 | + | 0.997777i | \(0.478774\pi\) | |||||||
\(824\) | −524.780 | + | 864.982i | −0.636869 | + | 1.04974i | ||||
\(825\) | −606.598 | + | 315.988i | −0.735270 | + | 0.383015i | ||||
\(826\) | 95.1677 | − | 111.762i | 0.115215 | − | 0.135306i | ||||
\(827\) | −711.971 | −0.860908 | −0.430454 | − | 0.902613i | \(-0.641646\pi\) | ||||
−0.430454 | + | 0.902613i | \(0.641646\pi\) | |||||||
\(828\) | 36.5457 | + | 226.390i | 0.0441373 | + | 0.273418i | ||||
\(829\) | −118.688 | −0.143170 | −0.0715849 | − | 0.997435i | \(-0.522806\pi\) | ||||
−0.0715849 | + | 0.997435i | \(0.522806\pi\) | |||||||
\(830\) | −185.690 | − | 560.068i | −0.223723 | − | 0.674781i | ||||
\(831\) | − | 497.667i | − | 0.598877i | ||||||
\(832\) | −294.407 | + | 153.324i | −0.353854 | + | 0.184284i | ||||
\(833\) | 1321.40i | 1.58631i | ||||||||
\(834\) | 30.5980 | − | 35.9335i | 0.0366883 | − | 0.0430857i | ||||
\(835\) | 1019.07 | + | 618.196i | 1.22045 | + | 0.740355i | ||||
\(836\) | 180.907 | + | 1120.67i | 0.216396 | + | 1.34051i | ||||
\(837\) | − | 70.7939i | − | 0.0845805i | ||||||
\(838\) | −283.146 | + | 332.519i | −0.337883 | + | 0.396800i | ||||
\(839\) | 1413.67i | 1.68495i | 0.538736 | + | 0.842475i | \(0.318902\pi\) | ||||
−0.538736 | + | 0.842475i | \(0.681098\pi\) | |||||||
\(840\) | −51.4465 | + | 26.7961i | −0.0612458 | + | 0.0319001i | ||||
\(841\) | 1242.88 | 1.47786 | ||||||||
\(842\) | 428.952 | + | 365.260i | 0.509444 | + | 0.433800i | ||||
\(843\) | 389.015 | 0.461465 | ||||||||
\(844\) | 836.591 | − | 135.049i | 0.991222 | − | 0.160011i | ||||
\(845\) | 607.464 | + | 368.504i | 0.718893 | + | 0.436099i | ||||
\(846\) | 254.248 | + | 216.496i | 0.300529 | + | 0.255906i | ||||
\(847\) | 107.586 | 0.127020 | ||||||||
\(848\) | −78.3350 | − | 236.309i | −0.0923762 | − | 0.278666i | ||||
\(849\) | −145.704 | −0.171619 | ||||||||
\(850\) | 1333.41 | + | 305.372i | 1.56872 | + | 0.359261i | ||||
\(851\) | 297.347i | 0.349409i | ||||||||
\(852\) | −893.989 | + | 144.315i | −1.04928 | + | 0.169383i | ||||
\(853\) | − | 1308.03i | − | 1.53344i | −0.641979 | − | 0.766722i | \(-0.721886\pi\) | ||
0.641979 | − | 0.766722i | \(-0.278114\pi\) | |||||||
\(854\) | −48.4469 | − | 41.2534i | −0.0567293 | − | 0.0483060i | ||||
\(855\) | −139.778 | + | 230.419i | −0.163483 | + | 0.269496i | ||||
\(856\) | 433.148 | − | 713.947i | 0.506014 | − | 0.834050i | ||||
\(857\) | − | 719.755i | − | 0.839854i | −0.907558 | − | 0.419927i | \(-0.862056\pi\) | ||
0.907558 | − | 0.419927i | \(-0.137944\pi\) | |||||||
\(858\) | 216.072 | + | 183.989i | 0.251832 | + | 0.214440i | ||||
\(859\) | 1402.44i | 1.63264i | 0.577601 | + | 0.816319i | \(0.303989\pi\) | ||||
−0.577601 | + | 0.816319i | \(0.696011\pi\) | |||||||
\(860\) | 210.004 | − | 517.902i | 0.244191 | − | 0.602212i | ||||
\(861\) | 19.2858 | 0.0223993 | ||||||||
\(862\) | −571.922 | + | 671.650i | −0.663483 | + | 0.779176i | ||||
\(863\) | 72.4412 | 0.0839411 | 0.0419706 | − | 0.999119i | \(-0.486636\pi\) | ||||
0.0419706 | + | 0.999119i | \(0.486636\pi\) | |||||||
\(864\) | 154.088 | + | 62.4900i | 0.178342 | + | 0.0723264i | ||||
\(865\) | −6.05480 | + | 9.98111i | −0.00699977 | + | 0.0115389i | ||||
\(866\) | −160.061 | + | 187.972i | −0.184828 | + | 0.217058i | ||||
\(867\) | 795.869 | 0.917957 | ||||||||
\(868\) | 45.0448 | − | 7.27148i | 0.0518949 | − | 0.00837728i | ||||
\(869\) | −215.203 | −0.247644 | ||||||||
\(870\) | 248.827 | + | 750.499i | 0.286009 | + | 0.862642i | ||||
\(871\) | 478.208i | 0.549033i | ||||||||
\(872\) | 2.08166 | − | 3.43115i | 0.00238723 | − | 0.00393481i | ||||
\(873\) | 506.464i | 0.580142i | ||||||||
\(874\) | −445.196 | + | 522.826i | −0.509378 | + | 0.598200i | ||||
\(875\) | 6.80164 | − | 104.435i | 0.00777331 | − | 0.119355i | ||||
\(876\) | −374.248 | + | 60.4139i | −0.427223 | + | 0.0689657i | ||||
\(877\) | 1382.21i | 1.57606i | 0.615635 | + | 0.788032i | \(0.288900\pi\) | ||||
−0.615635 | + | 0.788032i | \(0.711100\pi\) | |||||||
\(878\) | 428.835 | − | 503.613i | 0.488423 | − | 0.573591i | ||||
\(879\) | − | 427.158i | − | 0.485959i | ||||||
\(880\) | −282.152 | + | 1231.74i | −0.320628 | + | 1.39970i | ||||
\(881\) | −1131.38 | −1.28419 | −0.642097 | − | 0.766623i | \(-0.721936\pi\) | ||||
−0.642097 | + | 0.766623i | \(0.721936\pi\) | |||||||
\(882\) | −220.640 | − | 187.879i | −0.250159 | − | 0.213015i | ||||
\(883\) | −1077.39 | −1.22014 | −0.610072 | − | 0.792346i | \(-0.708860\pi\) | ||||
−0.610072 | + | 0.792346i | \(0.708860\pi\) | |||||||
\(884\) | −90.4535 | − | 560.334i | −0.102323 | − | 0.633862i | ||||
\(885\) | 393.752 | − | 649.086i | 0.444918 | − | 0.733430i | ||||
\(886\) | −235.952 | − | 200.917i | −0.266311 | − | 0.226769i | ||||
\(887\) | −766.896 | −0.864595 | −0.432297 | − | 0.901731i | \(-0.642297\pi\) | ||||
−0.432297 | + | 0.901731i | \(0.642297\pi\) | |||||||
\(888\) | 184.330 | + | 111.832i | 0.207578 | + | 0.125937i | ||||
\(889\) | 7.07980 | 0.00796378 | ||||||||
\(890\) | 125.254 | + | 377.784i | 0.140735 | + | 0.424476i | ||||
\(891\) | − | 142.160i | − | 0.159551i | ||||||
\(892\) | −223.010 | − | 1381.49i | −0.250011 | − | 1.54875i | ||||
\(893\) | 999.954i | 1.11977i | ||||||||
\(894\) | 88.7492 | + | 75.5715i | 0.0992720 | + | 0.0845319i | ||||
\(895\) | 588.814 | − | 970.637i | 0.657893 | − | 1.08451i | ||||
\(896\) | −23.9344 | + | 104.462i | −0.0267124 | + | 0.116587i | ||||
\(897\) | 171.673i | 0.191386i | ||||||||
\(898\) | −146.026 | − | 124.344i | −0.162612 | − | 0.138467i | ||||
\(899\) | − | 621.942i | − | 0.691815i | ||||||
\(900\) | −240.577 | + | 179.228i | −0.267308 | + | 0.199142i | ||||
\(901\) | 425.691 | 0.472465 | ||||||||
\(902\) | 272.378 | − | 319.873i | 0.301971 | − | 0.354627i | ||||
\(903\) | −40.5220 | −0.0448748 | ||||||||
\(904\) | −116.175 | − | 70.4829i | −0.128512 | − | 0.0779678i | ||||
\(905\) | 487.752 | + | 295.883i | 0.538953 | + | 0.326943i | ||||
\(906\) | 314.392 | − | 369.214i | 0.347011 | − | 0.407521i | ||||
\(907\) | 1086.43 | 1.19783 | 0.598913 | − | 0.800814i | \(-0.295600\pi\) | ||||
0.598913 | + | 0.800814i | \(0.295600\pi\) | |||||||
\(908\) | 118.283 | + | 732.730i | 0.130268 | + | 0.806971i | ||||
\(909\) | 133.650 | 0.147029 | ||||||||
\(910\) | −41.2182 | + | 13.6659i | −0.0452947 | + | 0.0150174i | ||||
\(911\) | 237.746i | 0.260973i | 0.991450 | + | 0.130486i | \(0.0416539\pi\) | ||||
−0.991450 | + | 0.130486i | \(0.958346\pi\) | |||||||
\(912\) | 156.670 | + | 472.618i | 0.171787 | + | 0.518222i | ||||
\(913\) | 932.012i | 1.02082i | ||||||||
\(914\) | 629.801 | − | 739.621i | 0.689060 | − | 0.809214i | ||||
\(915\) | −281.366 | − | 170.684i | −0.307504 | − | 0.186540i | ||||
\(916\) | 168.223 | + | 1042.10i | 0.183650 | + | 1.13766i | ||||
\(917\) | − | 43.3103i | − | 0.0472304i | ||||||
\(918\) | −184.330 | + | 216.472i | −0.200795 | + | 0.235808i | ||||
\(919\) | 344.517i | 0.374882i | 0.982276 | + | 0.187441i | \(0.0600194\pi\) | ||||
−0.982276 | + | 0.187441i | \(0.939981\pi\) | |||||||
\(920\) | −677.955 | + | 353.116i | −0.736908 | + | 0.383821i | ||||
\(921\) | −200.591 | −0.217797 | ||||||||
\(922\) | 538.515 | + | 458.555i | 0.584073 | + | 0.497349i | ||||
\(923\) | −677.917 | −0.734471 | ||||||||
\(924\) | 90.4535 | − | 14.6017i | 0.0978934 | − | 0.0158027i | ||||
\(925\) | −344.990 | + | 179.711i | −0.372962 | + | 0.194283i | ||||
\(926\) | −642.169 | − | 546.818i | −0.693487 | − | 0.590516i | ||||
\(927\) | 379.397 | 0.409274 | ||||||||
\(928\) | 1353.70 | + | 548.991i | 1.45873 | + | 0.591585i | ||||
\(929\) | 1478.10 | 1.59106 | 0.795531 | − | 0.605913i | \(-0.207192\pi\) | ||||
0.795531 | + | 0.605913i | \(0.207192\pi\) | |||||||
\(930\) | 223.989 | − | 74.2636i | 0.240849 | − | 0.0798533i | ||||
\(931\) | − | 867.776i | − | 0.932090i | ||||||
\(932\) | 230.922 | − | 37.2773i | 0.247771 | − | 0.0399971i | ||||
\(933\) | − | 352.935i | − | 0.378280i | ||||||
\(934\) | −976.035 | − | 831.111i | −1.04501 | − | 0.889841i | ||||
\(935\) | −1847.38 | − | 1120.67i | −1.97581 | − | 1.19858i | ||||
\(936\) | 106.423 | + | 64.5661i | 0.113700 | + | 0.0689809i | ||||
\(937\) | − | 246.887i | − | 0.263486i | −0.991284 | − | 0.131743i | \(-0.957943\pi\) | ||
0.991284 | − | 0.131743i | \(-0.0420574\pi\) | |||||||
\(938\) | 117.549 | + | 100.095i | 0.125319 | + | 0.106711i | ||||
\(939\) | − | 171.579i | − | 0.182726i | ||||||
\(940\) | −418.279 | + | 1031.54i | −0.444977 | + | 1.09738i | ||||
\(941\) | 1658.64 | 1.76264 | 0.881318 | − | 0.472525i | \(-0.156657\pi\) | ||||
0.881318 | + | 0.472525i | \(0.156657\pi\) | |||||||
\(942\) | −47.7537 | + | 56.0807i | −0.0506940 | + | 0.0595336i | ||||
\(943\) | 254.145 | 0.269507 | ||||||||
\(944\) | −441.336 | − | 1331.36i | −0.467517 | − | 1.41033i | ||||
\(945\) | 18.5980 | + | 11.2820i | 0.0196804 | + | 0.0119387i | ||||
\(946\) | −572.302 | + | 672.097i | −0.604971 | + | 0.710462i | ||||
\(947\) | −6.00750 | −0.00634372 | −0.00317186 | − | 0.999995i | \(-0.501010\pi\) | ||||
−0.00317186 | + | 0.999995i | \(0.501010\pi\) | |||||||
\(948\) | −93.1855 | + | 15.0427i | −0.0982969 | + | 0.0158678i | ||||
\(949\) | −283.794 | −0.299045 | ||||||||
\(950\) | −875.667 | − | 200.541i | −0.921755 | − | 0.211096i | ||||
\(951\) | − | 816.129i | − | 0.858180i | ||||||
\(952\) | −156.670 | − | 95.0509i | −0.164569 | − | 0.0998434i | ||||
\(953\) | − | 1089.55i | − | 1.14329i | −0.820503 | − | 0.571643i | \(-0.806306\pi\) | ||
0.820503 | − | 0.571643i | \(-0.193694\pi\) | |||||||
\(954\) | −60.5257 | + | 71.0798i | −0.0634442 | + | 0.0745072i | ||||
\(955\) | −361.481 | + | 595.887i | −0.378514 | + | 0.623966i | ||||
\(956\) | 447.553 | − | 72.2475i | 0.468152 | − | 0.0755727i | ||||
\(957\) | − | 1248.91i | − | 1.30502i | ||||||
\(958\) | −286.735 | + | 336.734i | −0.299306 | + | 0.351497i | ||||
\(959\) | − | 45.0512i | − | 0.0469773i | ||||||
\(960\) | −36.0767 | + | 553.081i | −0.0375799 | + | 0.576126i | ||||
\(961\) | 775.379 | 0.806846 | ||||||||
\(962\) | 122.886 | + | 104.640i | 0.127741 | + | 0.108773i | ||||
\(963\) | −313.150 | −0.325182 | ||||||||
\(964\) | −49.5905 | − | 307.199i | −0.0514424 | − | 0.318671i | ||||
\(965\) | −472.096 | + | 778.233i | −0.489219 | + | 0.806459i | ||||
\(966\) | 42.1993 | + | 35.9335i | 0.0436846 | + | 0.0371982i | ||||
\(967\) | −1699.27 | −1.75726 | −0.878630 | − | 0.477502i | \(-0.841542\pi\) | ||||
−0.878630 | + | 0.477502i | \(0.841542\pi\) | |||||||
\(968\) | 533.215 | − | 878.885i | 0.550842 | − | 0.907939i | ||||
\(969\) | −851.382 | −0.878619 | ||||||||
\(970\) | −1602.44 | + | 531.287i | −1.65200 | + | 0.547719i | ||||
\(971\) | 197.851i | 0.203760i | 0.994797 | + | 0.101880i | \(0.0324857\pi\) | ||||
−0.994797 | + | 0.101880i | \(0.967514\pi\) | |||||||
\(972\) | −9.93700 | − | 61.5569i | −0.0102232 | − | 0.0633302i | ||||
\(973\) | − | 11.4070i | − | 0.0117235i | ||||||
\(974\) | 1355.16 | + | 1153.94i | 1.39133 | + | 1.18475i | ||||
\(975\) | −199.180 | + | 103.756i | −0.204287 | + | 0.106417i | ||||
\(976\) | −577.117 | + | 191.311i | −0.591309 | + | 0.196015i | ||||
\(977\) | − | 847.868i | − | 0.867828i | −0.900954 | − | 0.433914i | \(-0.857132\pi\) | ||
0.900954 | − | 0.433914i | \(-0.142868\pi\) | |||||||
\(978\) | −554.423 | − | 472.101i | −0.566895 | − | 0.482721i | ||||
\(979\) | − | 628.672i | − | 0.642157i | ||||||
\(980\) | 362.989 | − | 895.185i | 0.370397 | − | 0.913454i | ||||
\(981\) | −1.50497 | −0.00153412 | ||||||||
\(982\) | 716.837 | − | 841.835i | 0.729977 | − | 0.857266i | ||||
\(983\) | −96.0512 | −0.0977123 | −0.0488562 | − | 0.998806i | \(-0.515558\pi\) | ||||
−0.0488562 | + | 0.998806i | \(0.515558\pi\) | |||||||
\(984\) | 95.5839 | − | 157.549i | 0.0971381 | − | 0.160110i | ||||
\(985\) | 669.135 | − | 1103.04i | 0.679324 | − | 1.11984i | ||||
\(986\) | −1619.38 | + | 1901.76i | −1.64238 | + | 1.92876i | ||||
\(987\) | 80.7101 | 0.0817732 | ||||||||
\(988\) | 59.4019 | + | 367.978i | 0.0601234 | + | 0.372448i | ||||
\(989\) | −533.993 | −0.539933 | ||||||||
\(990\) | 449.788 | − | 149.127i | 0.454332 | − | 0.150633i | ||||
\(991\) | 1184.45i | 1.19520i | 0.801793 | + | 0.597602i | \(0.203880\pi\) | ||||
−0.801793 | + | 0.597602i | \(0.796120\pi\) | |||||||
\(992\) | 163.849 | − | 404.017i | 0.165170 | − | 0.407275i | ||||
\(993\) | − | 468.858i | − | 0.472163i | ||||||
\(994\) | −141.897 | + | 166.640i | −0.142754 | + | 0.167646i | ||||
\(995\) | 665.108 | − | 1096.40i | 0.668450 | − | 1.10191i | ||||
\(996\) | 65.1478 | + | 403.573i | 0.0654095 | + | 0.405194i | ||||
\(997\) | − | 1887.35i | − | 1.89303i | −0.322655 | − | 0.946517i | \(-0.604575\pi\) | ||
0.322655 | − | 0.946517i | \(-0.395425\pi\) | |||||||
\(998\) | −691.500 | + | 812.079i | −0.692886 | + | 0.813706i | ||||
\(999\) | − | 80.8504i | − | 0.0809313i |
(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 | 60.3.f.b.19.8 | yes | 8 | |
3.2 | odd | 2 | 180.3.f.h.19.1 | 8 | |||
4.3 | odd | 2 | inner | 60.3.f.b.19.2 | yes | 8 | |
5.2 | odd | 4 | 300.3.c.f.151.4 | 8 | |||
5.3 | odd | 4 | 300.3.c.f.151.5 | 8 | |||
5.4 | even | 2 | inner | 60.3.f.b.19.1 | ✓ | 8 | |
8.3 | odd | 2 | 960.3.j.e.319.1 | 8 | |||
8.5 | even | 2 | 960.3.j.e.319.5 | 8 | |||
12.11 | even | 2 | 180.3.f.h.19.7 | 8 | |||
15.2 | even | 4 | 900.3.c.r.451.5 | 8 | |||
15.8 | even | 4 | 900.3.c.r.451.4 | 8 | |||
15.14 | odd | 2 | 180.3.f.h.19.8 | 8 | |||
20.3 | even | 4 | 300.3.c.f.151.6 | 8 | |||
20.7 | even | 4 | 300.3.c.f.151.3 | 8 | |||
20.19 | odd | 2 | inner | 60.3.f.b.19.7 | yes | 8 | |
40.19 | odd | 2 | 960.3.j.e.319.6 | 8 | |||
40.29 | even | 2 | 960.3.j.e.319.2 | 8 | |||
60.23 | odd | 4 | 900.3.c.r.451.3 | 8 | |||
60.47 | odd | 4 | 900.3.c.r.451.6 | 8 | |||
60.59 | even | 2 | 180.3.f.h.19.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.3.f.b.19.1 | ✓ | 8 | 5.4 | even | 2 | inner | |
60.3.f.b.19.2 | yes | 8 | 4.3 | odd | 2 | inner | |
60.3.f.b.19.7 | yes | 8 | 20.19 | odd | 2 | inner | |
60.3.f.b.19.8 | yes | 8 | 1.1 | even | 1 | trivial | |
180.3.f.h.19.1 | 8 | 3.2 | odd | 2 | |||
180.3.f.h.19.2 | 8 | 60.59 | even | 2 | |||
180.3.f.h.19.7 | 8 | 12.11 | even | 2 | |||
180.3.f.h.19.8 | 8 | 15.14 | odd | 2 | |||
300.3.c.f.151.3 | 8 | 20.7 | even | 4 | |||
300.3.c.f.151.4 | 8 | 5.2 | odd | 4 | |||
300.3.c.f.151.5 | 8 | 5.3 | odd | 4 | |||
300.3.c.f.151.6 | 8 | 20.3 | even | 4 | |||
900.3.c.r.451.3 | 8 | 60.23 | odd | 4 | |||
900.3.c.r.451.4 | 8 | 15.8 | even | 4 | |||
900.3.c.r.451.5 | 8 | 15.2 | even | 4 | |||
900.3.c.r.451.6 | 8 | 60.47 | odd | 4 | |||
960.3.j.e.319.1 | 8 | 8.3 | odd | 2 | |||
960.3.j.e.319.2 | 8 | 40.29 | even | 2 | |||
960.3.j.e.319.5 | 8 | 8.5 | even | 2 | |||
960.3.j.e.319.6 | 8 | 40.19 | odd | 2 |