Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(199,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.199");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.q (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 199.4 | ||
Character | \(\chi\) | \(=\) | 1050.199 |
Dual form | 1050.3.q.e.649.4 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22474 | + | 0.707107i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0.866025 | − | 1.50000i | 0.288675 | − | 0.500000i | ||||
\(4\) | 1.00000 | − | 1.73205i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.44949i | 0.408248i | ||||||||
\(7\) | −6.72455 | − | 1.94434i | −0.960650 | − | 0.277762i | ||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | −1.50000 | − | 2.59808i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.263223 | − | 0.455915i | 0.0239293 | − | 0.0414468i | −0.853813 | − | 0.520580i | \(-0.825716\pi\) |
0.877742 | + | 0.479133i | \(0.159049\pi\) | |||||||
\(12\) | −1.73205 | − | 3.00000i | −0.144338 | − | 0.250000i | ||||
\(13\) | 4.22307 | 0.324851 | 0.162426 | − | 0.986721i | \(-0.448068\pi\) | ||||
0.162426 | + | 0.986721i | \(0.448068\pi\) | |||||||
\(14\) | 9.61071 | − | 2.37366i | 0.686479 | − | 0.169547i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.125000 | − | 0.216506i | ||||
\(17\) | −16.6753 | + | 28.8825i | −0.980900 | + | 1.69897i | −0.321997 | + | 0.946741i | \(0.604354\pi\) |
−0.658903 | + | 0.752228i | \(0.728979\pi\) | |||||||
\(18\) | 3.67423 | + | 2.12132i | 0.204124 | + | 0.117851i | ||||
\(19\) | −2.75133 | + | 1.58848i | −0.144807 | + | 0.0836044i | −0.570653 | − | 0.821191i | \(-0.693310\pi\) |
0.425846 | + | 0.904796i | \(0.359977\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.74014 | + | 8.40298i | −0.416197 | + | 0.400142i | ||||
\(22\) | 0.744507i | 0.0338412i | ||||||||
\(23\) | 9.57744 | − | 5.52954i | 0.416410 | − | 0.240415i | −0.277130 | − | 0.960832i | \(-0.589383\pi\) |
0.693540 | + | 0.720418i | \(0.256050\pi\) | |||||||
\(24\) | 4.24264 | + | 2.44949i | 0.176777 | + | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.17218 | + | 2.98616i | −0.198930 | + | 0.114852i | ||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | −10.0922 | + | 9.70292i | −0.360437 | + | 0.346533i | ||||
\(29\) | 56.1302 | 1.93552 | 0.967762 | − | 0.251866i | \(-0.0810442\pi\) | ||||
0.967762 | + | 0.251866i | \(0.0810442\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.63817 | − | 0.945800i | −0.0528443 | − | 0.0305097i | 0.473345 | − | 0.880877i | \(-0.343046\pi\) |
−0.526189 | + | 0.850367i | \(0.676380\pi\) | |||||||
\(32\) | 4.89898 | + | 2.82843i | 0.153093 | + | 0.0883883i | ||||
\(33\) | −0.455915 | − | 0.789668i | −0.0138156 | − | 0.0239293i | ||||
\(34\) | − | 47.1649i | − | 1.38720i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | 8.44690 | − | 4.87682i | 0.228294 | − | 0.131806i | −0.381491 | − | 0.924373i | \(-0.624589\pi\) |
0.609785 | + | 0.792567i | \(0.291256\pi\) | |||||||
\(38\) | 2.24645 | − | 3.89097i | 0.0591172 | − | 0.102394i | ||||
\(39\) | 3.65729 | − | 6.33460i | 0.0937765 | − | 0.162426i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.07377i | 0.0993603i | 0.998765 | + | 0.0496802i | \(0.0158202\pi\) | ||||
−0.998765 | + | 0.0496802i | \(0.984180\pi\) | |||||||
\(42\) | 4.76263 | − | 16.4717i | 0.113396 | − | 0.392184i | ||||
\(43\) | 46.3519i | 1.07795i | 0.842322 | + | 0.538975i | \(0.181188\pi\) | ||||
−0.842322 | + | 0.538975i | \(0.818812\pi\) | |||||||
\(44\) | −0.526446 | − | 0.911831i | −0.0119647 | − | 0.0207234i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.81995 | + | 13.5445i | −0.169999 | + | 0.294447i | ||||
\(47\) | −31.6370 | − | 54.7969i | −0.673127 | − | 1.16589i | −0.977012 | − | 0.213182i | \(-0.931617\pi\) |
0.303885 | − | 0.952709i | \(-0.401716\pi\) | |||||||
\(48\) | −6.92820 | −0.144338 | ||||||||
\(49\) | 41.4391 | + | 26.1496i | 0.845696 | + | 0.533665i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 28.8825 | + | 50.0259i | 0.566323 | + | 0.980900i | ||||
\(52\) | 4.22307 | − | 7.31457i | 0.0812129 | − | 0.140665i | ||||
\(53\) | 40.2885 | + | 23.2606i | 0.760160 | + | 0.438878i | 0.829353 | − | 0.558725i | \(-0.188709\pi\) |
−0.0691934 | + | 0.997603i | \(0.522043\pi\) | |||||||
\(54\) | 6.36396 | − | 3.67423i | 0.117851 | − | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 5.49942 | − | 19.0199i | 0.0982038 | − | 0.339641i | ||||
\(57\) | 5.50267i | 0.0965380i | ||||||||
\(58\) | −68.7452 | + | 39.6900i | −1.18526 | + | 0.684311i | ||||
\(59\) | 43.7614 | + | 25.2657i | 0.741719 | + | 0.428231i | 0.822694 | − | 0.568485i | \(-0.192470\pi\) |
−0.0809752 | + | 0.996716i | \(0.525803\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 89.4583 | − | 51.6488i | 1.46653 | − | 0.846702i | 0.467231 | − | 0.884135i | \(-0.345252\pi\) |
0.999299 | + | 0.0374335i | \(0.0119182\pi\) | |||||||
\(62\) | 2.67513 | 0.0431472 | ||||||||
\(63\) | 5.03529 | + | 20.3874i | 0.0799252 | + | 0.323609i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.11676 | + | 0.644762i | 0.0169206 | + | 0.00976912i | ||||
\(67\) | 7.56816 | + | 4.36948i | 0.112958 | + | 0.0652161i | 0.555414 | − | 0.831574i | \(-0.312560\pi\) |
−0.442457 | + | 0.896790i | \(0.645893\pi\) | |||||||
\(68\) | 33.3506 | + | 57.7649i | 0.490450 | + | 0.849484i | ||||
\(69\) | − | 19.1549i | − | 0.277607i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 29.0608 | 0.409307 | 0.204653 | − | 0.978835i | \(-0.434393\pi\) | ||||
0.204653 | + | 0.978835i | \(0.434393\pi\) | |||||||
\(72\) | 7.34847 | − | 4.24264i | 0.102062 | − | 0.0589256i | ||||
\(73\) | −8.36647 | + | 14.4912i | −0.114609 | + | 0.198509i | −0.917623 | − | 0.397451i | \(-0.869895\pi\) |
0.803014 | + | 0.595960i | \(0.203228\pi\) | |||||||
\(74\) | −6.89686 | + | 11.9457i | −0.0932008 | + | 0.161429i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.35393i | 0.0836044i | ||||||||
\(77\) | −2.65651 | + | 2.55403i | −0.0345001 | + | 0.0331692i | ||||
\(78\) | 10.3444i | 0.132620i | ||||||||
\(79\) | −66.1473 | − | 114.571i | −0.837308 | − | 1.45026i | −0.892137 | − | 0.451764i | \(-0.850795\pi\) |
0.0548297 | − | 0.998496i | \(-0.482538\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −2.88059 | − | 4.98933i | −0.0351292 | − | 0.0608455i | ||||
\(83\) | −12.4838 | −0.150407 | −0.0752033 | − | 0.997168i | \(-0.523961\pi\) | ||||
−0.0752033 | + | 0.997168i | \(0.523961\pi\) | |||||||
\(84\) | 5.81425 | + | 23.5413i | 0.0692173 | + | 0.280254i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −32.7757 | − | 56.7692i | −0.381113 | − | 0.660107i | ||||
\(87\) | 48.6102 | − | 84.1953i | 0.558738 | − | 0.967762i | ||||
\(88\) | 1.28952 | + | 0.744507i | 0.0146537 | + | 0.00846030i | ||||
\(89\) | 59.1101 | − | 34.1272i | 0.664158 | − | 0.383452i | −0.129701 | − | 0.991553i | \(-0.541402\pi\) |
0.793860 | + | 0.608101i | \(0.208069\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −28.3982 | − | 8.21107i | −0.312068 | − | 0.0902315i | ||||
\(92\) | − | 22.1182i | − | 0.240415i | ||||||
\(93\) | −2.83740 | + | 1.63817i | −0.0305097 | + | 0.0176148i | ||||
\(94\) | 77.4945 | + | 44.7415i | 0.824409 | + | 0.475973i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 8.48528 | − | 4.89898i | 0.0883883 | − | 0.0510310i | ||||
\(97\) | −149.281 | −1.53898 | −0.769490 | − | 0.638659i | \(-0.779490\pi\) | ||||
−0.769490 | + | 0.638659i | \(0.779490\pi\) | |||||||
\(98\) | −69.2429 | − | 2.72468i | −0.706560 | − | 0.0278029i | ||||
\(99\) | −1.57934 | −0.0159529 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 83.7839 | + | 48.3726i | 0.829543 | + | 0.478937i | 0.853696 | − | 0.520771i | \(-0.174356\pi\) |
−0.0241531 | + | 0.999708i | \(0.507689\pi\) | |||||||
\(102\) | −70.7473 | − | 40.8460i | −0.693601 | − | 0.400451i | ||||
\(103\) | 52.3811 | + | 90.7268i | 0.508555 | + | 0.880843i | 0.999951 | + | 0.00990642i | \(0.00315336\pi\) |
−0.491396 | + | 0.870936i | \(0.663513\pi\) | |||||||
\(104\) | 11.9446i | 0.114852i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −65.7908 | −0.620668 | ||||||||
\(107\) | 107.911 | − | 62.3022i | 1.00851 | − | 0.582263i | 0.0977548 | − | 0.995211i | \(-0.468834\pi\) |
0.910755 | + | 0.412947i | \(0.135501\pi\) | |||||||
\(108\) | −5.19615 | + | 9.00000i | −0.0481125 | + | 0.0833333i | ||||
\(109\) | 42.3042 | − | 73.2731i | 0.388112 | − | 0.672230i | −0.604083 | − | 0.796921i | \(-0.706461\pi\) |
0.992196 | + | 0.124691i | \(0.0397940\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 16.8938i | − | 0.152196i | ||||||
\(112\) | 6.71372 | + | 27.1832i | 0.0599439 | + | 0.242707i | ||||
\(113\) | − | 116.241i | − | 1.02868i | −0.857586 | − | 0.514340i | \(-0.828037\pi\) | ||
0.857586 | − | 0.514340i | \(-0.171963\pi\) | |||||||
\(114\) | −3.89097 | − | 6.73936i | −0.0341313 | − | 0.0591172i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 56.1302 | − | 97.2204i | 0.483881 | − | 0.838107i | ||||
\(117\) | −6.33460 | − | 10.9719i | −0.0541419 | − | 0.0937765i | ||||
\(118\) | −71.4621 | −0.605611 | ||||||||
\(119\) | 168.291 | − | 161.799i | 1.41421 | − | 1.35966i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 60.3614 | + | 104.549i | 0.498855 | + | 0.864042i | ||||
\(122\) | −73.0424 | + | 126.513i | −0.598708 | + | 1.03699i | ||||
\(123\) | 6.11066 | + | 3.52799i | 0.0496802 | + | 0.0286829i | ||||
\(124\) | −3.27635 | + | 1.89160i | −0.0264222 | + | 0.0152548i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −20.5830 | − | 21.4089i | −0.163357 | − | 0.169912i | ||||
\(127\) | 81.3744i | 0.640743i | 0.947292 | + | 0.320372i | \(0.103808\pi\) | ||||
−0.947292 | + | 0.320372i | \(0.896192\pi\) | |||||||
\(128\) | 9.79796 | − | 5.65685i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 69.5278 | + | 40.1419i | 0.538975 | + | 0.311178i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 208.389 | − | 120.313i | 1.59075 | − | 0.918421i | 0.597574 | − | 0.801814i | \(-0.296131\pi\) |
0.993178 | − | 0.116608i | \(-0.0372020\pi\) | |||||||
\(132\) | −1.82366 | −0.0138156 | ||||||||
\(133\) | 21.5900 | − | 5.33231i | 0.162331 | − | 0.0400926i | ||||
\(134\) | −12.3588 | −0.0922295 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −81.6919 | − | 47.1649i | −0.600676 | − | 0.346800i | ||||
\(137\) | 202.357 | + | 116.831i | 1.47706 | + | 0.852778i | 0.999664 | − | 0.0259125i | \(-0.00824914\pi\) |
0.477391 | + | 0.878691i | \(0.341582\pi\) | |||||||
\(138\) | 13.5445 | + | 23.4598i | 0.0981489 | + | 0.169999i | ||||
\(139\) | 211.491i | 1.52152i | 0.649033 | + | 0.760760i | \(0.275174\pi\) | ||||
−0.649033 | + | 0.760760i | \(0.724826\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −109.594 | −0.777261 | ||||||||
\(142\) | −35.5920 | + | 20.5491i | −0.250648 | + | 0.144712i | ||||
\(143\) | 1.11161 | − | 1.92536i | 0.00777348 | − | 0.0134641i | ||||
\(144\) | −6.00000 | + | 10.3923i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 23.6640i | − | 0.162082i | ||||||
\(147\) | 75.1117 | − | 39.5125i | 0.510964 | − | 0.268792i | ||||
\(148\) | − | 19.5073i | − | 0.131806i | ||||||
\(149\) | 72.0402 | + | 124.777i | 0.483491 | + | 0.837431i | 0.999820 | − | 0.0189590i | \(-0.00603520\pi\) |
−0.516329 | + | 0.856390i | \(0.672702\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −46.7563 | + | 80.9842i | −0.309644 | + | 0.536319i | −0.978285 | − | 0.207267i | \(-0.933543\pi\) |
0.668640 | + | 0.743586i | \(0.266877\pi\) | |||||||
\(152\) | −4.49291 | − | 7.78195i | −0.0295586 | − | 0.0511970i | ||||
\(153\) | 100.052 | 0.653933 | ||||||||
\(154\) | 1.44757 | − | 5.00647i | 0.00939982 | − | 0.0325095i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7.31457 | − | 12.6692i | −0.0468883 | − | 0.0812129i | ||||
\(157\) | −85.6127 | + | 148.286i | −0.545304 | + | 0.944494i | 0.453284 | + | 0.891366i | \(0.350252\pi\) |
−0.998588 | + | 0.0531280i | \(0.983081\pi\) | |||||||
\(158\) | 162.027 | + | 93.5464i | 1.02549 | + | 0.592066i | ||||
\(159\) | 69.7817 | − | 40.2885i | 0.438878 | − | 0.253387i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −75.1553 | + | 18.5619i | −0.466803 | + | 0.115291i | ||||
\(162\) | − | 12.7279i | − | 0.0785674i | ||||||
\(163\) | 80.5515 | − | 46.5064i | 0.494181 | − | 0.285316i | −0.232126 | − | 0.972686i | \(-0.574568\pi\) |
0.726307 | + | 0.687370i | \(0.241235\pi\) | |||||||
\(164\) | 7.05598 | + | 4.07377i | 0.0430243 | + | 0.0248401i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.2894 | − | 8.82735i | 0.0921049 | − | 0.0531768i | ||||
\(167\) | 104.991 | 0.628688 | 0.314344 | − | 0.949309i | \(-0.398216\pi\) | ||||
0.314344 | + | 0.949309i | \(0.398216\pi\) | |||||||
\(168\) | −23.7672 | − | 24.7208i | −0.141471 | − | 0.147148i | ||||
\(169\) | −151.166 | −0.894472 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.25400 | + | 4.76545i | 0.0482690 | + | 0.0278681i | ||||
\(172\) | 80.2838 | + | 46.3519i | 0.466766 | + | 0.269488i | ||||
\(173\) | 102.079 | + | 176.805i | 0.590049 | + | 1.02200i | 0.994225 | + | 0.107314i | \(0.0342251\pi\) |
−0.404176 | + | 0.914681i | \(0.632442\pi\) | |||||||
\(174\) | 137.490i | 0.790174i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.10578 | −0.0119647 | ||||||||
\(177\) | 75.7970 | − | 43.7614i | 0.428231 | − | 0.247240i | ||||
\(178\) | −48.2632 | + | 83.5943i | −0.271141 | + | 0.469631i | ||||
\(179\) | −97.9495 | + | 169.653i | −0.547204 | + | 0.947785i | 0.451261 | + | 0.892392i | \(0.350974\pi\) |
−0.998465 | + | 0.0553926i | \(0.982359\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 119.031i | 0.657632i | 0.944394 | + | 0.328816i | \(0.106650\pi\) | ||||
−0.944394 | + | 0.328816i | \(0.893350\pi\) | |||||||
\(182\) | 40.5867 | − | 10.0241i | 0.223004 | − | 0.0550776i | ||||
\(183\) | − | 178.917i | − | 0.977687i | ||||||
\(184\) | 15.6399 | + | 27.0891i | 0.0849994 | + | 0.147223i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.31673 | − | 4.01269i | 0.0124555 | − | 0.0215736i | ||||
\(187\) | 8.77864 | + | 15.2050i | 0.0469446 | + | 0.0813104i | ||||
\(188\) | −126.548 | −0.673127 | ||||||||
\(189\) | 34.9418 | + | 10.1031i | 0.184877 | + | 0.0534554i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 32.8657 | + | 56.9250i | 0.172072 | + | 0.298037i | 0.939144 | − | 0.343524i | \(-0.111621\pi\) |
−0.767072 | + | 0.641561i | \(0.778287\pi\) | |||||||
\(192\) | −6.92820 | + | 12.0000i | −0.0360844 | + | 0.0625000i | ||||
\(193\) | 83.8919 | + | 48.4350i | 0.434673 | + | 0.250959i | 0.701335 | − | 0.712831i | \(-0.252588\pi\) |
−0.266662 | + | 0.963790i | \(0.585921\pi\) | |||||||
\(194\) | 182.831 | − | 105.558i | 0.942429 | − | 0.544112i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 86.7315 | − | 45.6251i | 0.442508 | − | 0.232781i | ||||
\(197\) | − | 186.672i | − | 0.947574i | −0.880640 | − | 0.473787i | \(-0.842887\pi\) | ||
0.880640 | − | 0.473787i | \(-0.157113\pi\) | |||||||
\(198\) | 1.93428 | − | 1.11676i | 0.00976912 | − | 0.00564020i | ||||
\(199\) | −99.8454 | − | 57.6458i | −0.501736 | − | 0.289677i | 0.227694 | − | 0.973733i | \(-0.426881\pi\) |
−0.729430 | + | 0.684055i | \(0.760215\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.1084 | − | 7.56816i | 0.0652161 | − | 0.0376525i | ||||
\(202\) | −136.818 | −0.677319 | ||||||||
\(203\) | −377.450 | − | 109.136i | −1.85936 | − | 0.537616i | ||||
\(204\) | 115.530 | 0.566323 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −128.307 | − | 74.0781i | −0.622850 | − | 0.359602i | ||||
\(207\) | −28.7323 | − | 16.5886i | −0.138803 | − | 0.0801382i | ||||
\(208\) | −8.44614 | − | 14.6291i | −0.0406064 | − | 0.0703324i | ||||
\(209\) | 1.67250i | 0.00800239i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 139.433 | 0.660819 | 0.330409 | − | 0.943838i | \(-0.392813\pi\) | ||||
0.330409 | + | 0.943838i | \(0.392813\pi\) | |||||||
\(212\) | 80.5769 | − | 46.5211i | 0.380080 | − | 0.219439i | ||||
\(213\) | 25.1674 | − | 43.5912i | 0.118157 | − | 0.204653i | ||||
\(214\) | −88.1086 | + | 152.609i | −0.411722 | + | 0.713124i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 14.6969i | − | 0.0680414i | ||||||
\(217\) | 9.17703 | + | 9.54524i | 0.0422905 | + | 0.0439873i | ||||
\(218\) | 119.654i | 0.548874i | ||||||||
\(219\) | 14.4912 | + | 25.0994i | 0.0661697 | + | 0.114609i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −70.4209 | + | 121.973i | −0.318647 | + | 0.551912i | ||||
\(222\) | 11.9457 | + | 20.6906i | 0.0538095 | + | 0.0932008i | ||||
\(223\) | 258.055 | 1.15720 | 0.578599 | − | 0.815612i | \(-0.303600\pi\) | ||||
0.578599 | + | 0.815612i | \(0.303600\pi\) | |||||||
\(224\) | −27.4440 | − | 28.5452i | −0.122518 | − | 0.127434i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 82.1947 | + | 142.365i | 0.363693 | + | 0.629935i | ||||
\(227\) | 165.516 | − | 286.682i | 0.729146 | − | 1.26292i | −0.228099 | − | 0.973638i | \(-0.573251\pi\) |
0.957245 | − | 0.289280i | \(-0.0934158\pi\) | |||||||
\(228\) | 9.53090 | + | 5.50267i | 0.0418022 | + | 0.0241345i | ||||
\(229\) | −211.516 | + | 122.119i | −0.923653 | + | 0.533271i | −0.884799 | − | 0.465974i | \(-0.845704\pi\) |
−0.0388541 | + | 0.999245i | \(0.512371\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.53044 | + | 6.19662i | 0.00662529 | + | 0.0268252i | ||||
\(232\) | 158.760i | 0.684311i | ||||||||
\(233\) | 183.155 | − | 105.745i | 0.786074 | − | 0.453840i | −0.0525044 | − | 0.998621i | \(-0.516720\pi\) |
0.838579 | + | 0.544781i | \(0.183387\pi\) | |||||||
\(234\) | 15.5165 | + | 8.95848i | 0.0663100 | + | 0.0382841i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 87.5228 | − | 50.5313i | 0.370859 | − | 0.214116i | ||||
\(237\) | −229.141 | −0.966840 | ||||||||
\(238\) | −91.7044 | + | 317.162i | −0.385313 | + | 1.33262i | ||||
\(239\) | −344.134 | −1.43989 | −0.719946 | − | 0.694030i | \(-0.755833\pi\) | ||||
−0.719946 | + | 0.694030i | \(0.755833\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −148.392 | − | 85.6742i | −0.615735 | − | 0.355495i | 0.159472 | − | 0.987203i | \(-0.449021\pi\) |
−0.775207 | + | 0.631708i | \(0.782354\pi\) | |||||||
\(242\) | −147.855 | − | 85.3639i | −0.610970 | − | 0.352744i | ||||
\(243\) | 7.79423 | + | 13.5000i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | − | 206.595i | − | 0.846702i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −9.97867 | −0.0405637 | ||||||||
\(247\) | −11.6191 | + | 6.70827i | −0.0470408 | + | 0.0271590i | ||||
\(248\) | 2.67513 | − | 4.63346i | 0.0107868 | − | 0.0186833i | ||||
\(249\) | −10.8112 | + | 18.7256i | −0.0434187 | + | 0.0752033i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 327.538i | 1.30493i | 0.757818 | + | 0.652467i | \(0.226266\pi\) | ||||
−0.757818 | + | 0.652467i | \(0.773734\pi\) | |||||||
\(252\) | 40.3473 | + | 11.6660i | 0.160108 | + | 0.0462937i | ||||
\(253\) | − | 5.82200i | − | 0.0230119i | ||||||
\(254\) | −57.5404 | − | 99.6629i | −0.226537 | − | 0.392374i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 110.179 | + | 190.836i | 0.428713 | + | 0.742552i | 0.996759 | − | 0.0804442i | \(-0.0256339\pi\) |
−0.568046 | + | 0.822997i | \(0.692301\pi\) | |||||||
\(258\) | −113.538 | −0.440072 | ||||||||
\(259\) | −66.2837 | + | 16.3708i | −0.255922 | + | 0.0632077i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −84.1953 | − | 145.831i | −0.322587 | − | 0.558738i | ||||
\(262\) | −170.149 | + | 294.706i | −0.649422 | + | 1.12483i | ||||
\(263\) | −115.350 | − | 66.5976i | −0.438594 | − | 0.253223i | 0.264407 | − | 0.964411i | \(-0.414824\pi\) |
−0.703001 | + | 0.711189i | \(0.748157\pi\) | |||||||
\(264\) | 2.23352 | − | 1.28952i | 0.00846030 | − | 0.00488456i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −22.6718 | + | 21.7972i | −0.0852322 | + | 0.0819443i | ||||
\(267\) | − | 118.220i | − | 0.442772i | ||||||
\(268\) | 15.1363 | − | 8.73896i | 0.0564788 | − | 0.0326080i | ||||
\(269\) | 22.9633 | + | 13.2578i | 0.0853653 | + | 0.0492857i | 0.542075 | − | 0.840330i | \(-0.317639\pi\) |
−0.456710 | + | 0.889616i | \(0.650972\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −92.6776 | + | 53.5074i | −0.341984 | + | 0.197444i | −0.661149 | − | 0.750255i | \(-0.729931\pi\) |
0.319165 | + | 0.947699i | \(0.396598\pi\) | |||||||
\(272\) | 133.402 | 0.490450 | ||||||||
\(273\) | −36.9102 | + | 35.4864i | −0.135202 | + | 0.129987i | ||||
\(274\) | −330.447 | −1.20601 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −33.1772 | − | 19.1549i | −0.120207 | − | 0.0694017i | ||||
\(277\) | 381.381 | + | 220.191i | 1.37683 | + | 0.794912i | 0.991776 | − | 0.127983i | \(-0.0408503\pi\) |
0.385052 | + | 0.922895i | \(0.374184\pi\) | |||||||
\(278\) | −149.547 | − | 259.023i | −0.537939 | − | 0.931737i | ||||
\(279\) | 5.67480i | 0.0203398i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 322.069 | 1.14615 | 0.573076 | − | 0.819502i | \(-0.305750\pi\) | ||||
0.573076 | + | 0.819502i | \(0.305750\pi\) | |||||||
\(282\) | 134.224 | − | 77.4945i | 0.475973 | − | 0.274803i | ||||
\(283\) | 34.2665 | − | 59.3514i | 0.121083 | − | 0.209722i | −0.799112 | − | 0.601182i | \(-0.794697\pi\) |
0.920195 | + | 0.391460i | \(0.128030\pi\) | |||||||
\(284\) | 29.0608 | − | 50.3347i | 0.102327 | − | 0.177235i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.14410i | 0.0109934i | ||||||||
\(287\) | 7.92079 | − | 27.3943i | 0.0275986 | − | 0.0954505i | ||||
\(288\) | − | 16.9706i | − | 0.0589256i | ||||||
\(289\) | −411.631 | − | 712.966i | −1.42433 | − | 2.46701i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −129.281 | + | 223.922i | −0.444265 | + | 0.769490i | ||||
\(292\) | 16.7329 | + | 28.9823i | 0.0573046 | + | 0.0992545i | ||||
\(293\) | 147.510 | 0.503448 | 0.251724 | − | 0.967799i | \(-0.419003\pi\) | ||||
0.251724 | + | 0.967799i | \(0.419003\pi\) | |||||||
\(294\) | −64.0531 | + | 101.505i | −0.217868 | + | 0.345254i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 13.7937 | + | 23.8914i | 0.0466004 | + | 0.0807143i | ||||
\(297\) | −1.36775 | + | 2.36901i | −0.00460521 | + | 0.00797645i | ||||
\(298\) | −176.462 | − | 101.880i | −0.592153 | − | 0.341880i | ||||
\(299\) | 40.4462 | − | 23.3516i | 0.135272 | − | 0.0780991i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 90.1237 | − | 311.695i | 0.299414 | − | 1.03553i | ||||
\(302\) | − | 132.247i | − | 0.437903i | ||||||
\(303\) | 145.118 | − | 83.7839i | 0.478937 | − | 0.276514i | ||||
\(304\) | 11.0053 | + | 6.35393i | 0.0362018 | + | 0.0209011i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −122.538 | + | 70.7473i | −0.400451 | + | 0.231200i | ||||
\(307\) | −376.010 | −1.22479 | −0.612394 | − | 0.790553i | \(-0.709793\pi\) | ||||
−0.612394 | + | 0.790553i | \(0.709793\pi\) | |||||||
\(308\) | 1.76720 | + | 7.15524i | 0.00573767 | + | 0.0232313i | ||||
\(309\) | 181.454 | 0.587228 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −337.599 | − | 194.913i | −1.08553 | − | 0.626730i | −0.153146 | − | 0.988204i | \(-0.548941\pi\) |
−0.932383 | + | 0.361473i | \(0.882274\pi\) | |||||||
\(312\) | 17.9170 | + | 10.3444i | 0.0574262 | + | 0.0331550i | ||||
\(313\) | −71.5282 | − | 123.890i | −0.228524 | − | 0.395816i | 0.728847 | − | 0.684677i | \(-0.240057\pi\) |
−0.957371 | + | 0.288861i | \(0.906723\pi\) | |||||||
\(314\) | − | 242.149i | − | 0.771176i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −264.589 | −0.837308 | ||||||||
\(317\) | −332.938 | + | 192.222i | −1.05028 | + | 0.606378i | −0.922727 | − | 0.385454i | \(-0.874045\pi\) |
−0.127551 | + | 0.991832i | \(0.540712\pi\) | |||||||
\(318\) | −56.9765 | + | 98.6862i | −0.179171 | + | 0.310334i | ||||
\(319\) | 14.7747 | − | 25.5906i | 0.0463158 | − | 0.0802214i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 215.821i | − | 0.672340i | ||||||
\(322\) | 78.9208 | − | 75.8764i | 0.245096 | − | 0.235641i | ||||
\(323\) | − | 105.954i | − | 0.328030i | ||||||
\(324\) | 9.00000 | + | 15.5885i | 0.0277778 | + | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −65.7700 | + | 113.917i | −0.201749 | + | 0.349439i | ||||
\(327\) | −73.2731 | − | 126.913i | −0.224077 | − | 0.388112i | ||||
\(328\) | −11.5224 | −0.0351292 | ||||||||
\(329\) | 106.201 | + | 429.997i | 0.322799 | + | 1.30698i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −96.9539 | − | 167.929i | −0.292912 | − | 0.507338i | 0.681585 | − | 0.731739i | \(-0.261291\pi\) |
−0.974497 | + | 0.224400i | \(0.927958\pi\) | |||||||
\(332\) | −12.4838 | + | 21.6225i | −0.0376017 | + | 0.0651280i | ||||
\(333\) | −25.3407 | − | 14.6305i | −0.0760982 | − | 0.0439353i | ||||
\(334\) | −128.587 | + | 74.2397i | −0.384991 | + | 0.222275i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 46.5890 | + | 13.4708i | 0.138658 | + | 0.0400916i | ||||
\(337\) | − | 125.477i | − | 0.372337i | −0.982518 | − | 0.186168i | \(-0.940393\pi\) | ||
0.982518 | − | 0.186168i | \(-0.0596070\pi\) | |||||||
\(338\) | 185.139 | − | 106.890i | 0.547750 | − | 0.316243i | ||||
\(339\) | −174.361 | − | 100.668i | −0.514340 | − | 0.296954i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.862410 | + | 0.497912i | −0.00252906 | + | 0.00146015i | ||||
\(342\) | −13.4787 | −0.0394115 | ||||||||
\(343\) | −227.816 | − | 256.416i | −0.664186 | − | 0.747568i | ||||
\(344\) | −131.103 | −0.381113 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −250.040 | − | 144.361i | −0.722660 | − | 0.417228i | ||||
\(347\) | −436.128 | − | 251.798i | −1.25685 | − | 0.725644i | −0.284391 | − | 0.958708i | \(-0.591791\pi\) |
−0.972461 | + | 0.233065i | \(0.925125\pi\) | |||||||
\(348\) | −97.2204 | − | 168.391i | −0.279369 | − | 0.483881i | ||||
\(349\) | − | 47.7682i | − | 0.136872i | −0.997656 | − | 0.0684358i | \(-0.978199\pi\) | ||
0.997656 | − | 0.0684358i | \(-0.0218008\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −21.9437 | −0.0625177 | ||||||||
\(352\) | 2.57905 | − | 1.48901i | 0.00732684 | − | 0.00423015i | ||||
\(353\) | −16.4552 | + | 28.5012i | −0.0466152 | + | 0.0807399i | −0.888392 | − | 0.459087i | \(-0.848177\pi\) |
0.841776 | + | 0.539826i | \(0.181510\pi\) | |||||||
\(354\) | −61.8880 | + | 107.193i | −0.174825 | + | 0.302805i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 136.509i | − | 0.383452i | ||||||
\(357\) | −96.9543 | − | 392.559i | −0.271581 | − | 1.09960i | ||||
\(358\) | − | 277.043i | − | 0.773863i | ||||||
\(359\) | 133.898 | + | 231.919i | 0.372976 | + | 0.646013i | 0.990022 | − | 0.140914i | \(-0.0450040\pi\) |
−0.617046 | + | 0.786927i | \(0.711671\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −175.453 | + | 303.894i | −0.486021 | + | 0.841812i | ||||
\(362\) | −84.1679 | − | 145.783i | −0.232508 | − | 0.402716i | ||||
\(363\) | 209.098 | 0.576028 | ||||||||
\(364\) | −42.6202 | + | 40.9761i | −0.117089 | + | 0.112572i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 126.513 | + | 219.127i | 0.345665 | + | 0.598708i | ||||
\(367\) | −79.3613 | + | 137.458i | −0.216243 | + | 0.374545i | −0.953657 | − | 0.300897i | \(-0.902714\pi\) |
0.737413 | + | 0.675442i | \(0.236047\pi\) | |||||||
\(368\) | −38.3098 | − | 22.1182i | −0.104103 | − | 0.0601037i | ||||
\(369\) | 10.5840 | − | 6.11066i | 0.0286829 | − | 0.0165601i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −225.695 | − | 234.751i | −0.608343 | − | 0.632752i | ||||
\(372\) | 6.55270i | 0.0176148i | ||||||||
\(373\) | 358.832 | − | 207.172i | 0.962017 | − | 0.555421i | 0.0652235 | − | 0.997871i | \(-0.479224\pi\) |
0.896793 | + | 0.442450i | \(0.145891\pi\) | |||||||
\(374\) | −21.5032 | − | 12.4149i | −0.0574951 | − | 0.0331948i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 154.989 | − | 89.4829i | 0.412205 | − | 0.237986i | ||||
\(377\) | 237.042 | 0.628758 | ||||||||
\(378\) | −49.9387 | + | 12.3339i | −0.132113 | + | 0.0326293i | ||||
\(379\) | 72.8000 | 0.192084 | 0.0960422 | − | 0.995377i | \(-0.469382\pi\) | ||||
0.0960422 | + | 0.995377i | \(0.469382\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 122.062 | + | 70.4723i | 0.320372 | + | 0.184967i | ||||
\(382\) | −80.5042 | − | 46.4791i | −0.210744 | − | 0.121673i | ||||
\(383\) | −142.507 | − | 246.830i | −0.372082 | − | 0.644464i | 0.617804 | − | 0.786332i | \(-0.288023\pi\) |
−0.989886 | + | 0.141868i | \(0.954689\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −136.995 | −0.354909 | ||||||||
\(387\) | 120.426 | − | 69.5278i | 0.311178 | − | 0.179658i | ||||
\(388\) | −149.281 | + | 258.562i | −0.384745 | + | 0.666398i | ||||
\(389\) | −48.5692 | + | 84.1242i | −0.124856 | + | 0.216258i | −0.921677 | − | 0.387959i | \(-0.873180\pi\) |
0.796820 | + | 0.604216i | \(0.206514\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 368.827i | 0.943291i | ||||||||
\(392\) | −73.9622 | + | 117.207i | −0.188679 | + | 0.298999i | ||||
\(393\) | − | 416.777i | − | 1.06050i | ||||||
\(394\) | 131.997 | + | 228.626i | 0.335018 | + | 0.580268i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.57934 | + | 2.73549i | −0.00398822 | + | 0.00690781i | ||||
\(397\) | 395.852 | + | 685.636i | 0.997108 | + | 1.72704i | 0.564371 | + | 0.825522i | \(0.309119\pi\) |
0.432737 | + | 0.901520i | \(0.357548\pi\) | |||||||
\(398\) | 163.047 | 0.409665 | ||||||||
\(399\) | 10.6990 | − | 37.0030i | 0.0268146 | − | 0.0927392i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −251.613 | − | 435.807i | −0.627464 | − | 1.08680i | −0.988059 | − | 0.154077i | \(-0.950759\pi\) |
0.360594 | − | 0.932723i | \(-0.382574\pi\) | |||||||
\(402\) | −10.7030 | + | 18.5381i | −0.0266244 | + | 0.0461147i | ||||
\(403\) | −6.91812 | − | 3.99418i | −0.0171666 | − | 0.00991112i | ||||
\(404\) | 167.568 | − | 96.7453i | 0.414772 | − | 0.239468i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 539.451 | − | 133.234i | 1.32870 | − | 0.328162i | ||||
\(407\) | − | 5.13476i | − | 0.0126161i | ||||||
\(408\) | −141.495 | + | 81.6919i | −0.346800 | + | 0.200225i | ||||
\(409\) | −649.395 | − | 374.928i | −1.58776 | − | 0.916696i | −0.993675 | − | 0.112296i | \(-0.964180\pi\) |
−0.594088 | − | 0.804400i | \(-0.702487\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 350.492 | − | 202.357i | 0.852778 | − | 0.492352i | ||||
\(412\) | 209.525 | 0.508555 | ||||||||
\(413\) | −245.151 | − | 254.987i | −0.593585 | − | 0.617402i | ||||
\(414\) | 46.9197 | 0.113333 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 20.6887 | + | 11.9446i | 0.0497325 | + | 0.0287131i | ||||
\(417\) | 317.237 | + | 183.157i | 0.760760 | + | 0.439225i | ||||
\(418\) | −1.18264 | − | 2.04839i | −0.00282927 | − | 0.00490044i | ||||
\(419\) | 465.759i | 1.11160i | 0.831317 | + | 0.555799i | \(0.187587\pi\) | ||||
−0.831317 | + | 0.555799i | \(0.812413\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 345.980 | 0.821805 | 0.410902 | − | 0.911679i | \(-0.365214\pi\) | ||||
0.410902 | + | 0.911679i | \(0.365214\pi\) | |||||||
\(422\) | −170.770 | + | 98.5939i | −0.404667 | + | 0.233635i | ||||
\(423\) | −94.9110 | + | 164.391i | −0.224376 | + | 0.388630i | ||||
\(424\) | −65.7908 | + | 113.953i | −0.155167 | + | 0.268757i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 71.1841i | 0.167099i | ||||||||
\(427\) | −701.990 | + | 173.378i | −1.64400 | + | 0.406037i | ||||
\(428\) | − | 249.209i | − | 0.582263i | ||||||
\(429\) | −1.92536 | − | 3.33482i | −0.00448802 | − | 0.00777348i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −247.300 | + | 428.336i | −0.573782 | + | 0.993819i | 0.422391 | + | 0.906414i | \(0.361191\pi\) |
−0.996173 | + | 0.0874056i | \(0.972142\pi\) | |||||||
\(432\) | 10.3923 | + | 18.0000i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | −730.022 | −1.68596 | −0.842981 | − | 0.537943i | \(-0.819201\pi\) | ||||
−0.842981 | + | 0.537943i | \(0.819201\pi\) | |||||||
\(434\) | −17.9890 | − | 5.20135i | −0.0414494 | − | 0.0119847i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −84.6085 | − | 146.546i | −0.194056 | − | 0.336115i | ||||
\(437\) | −17.5672 | + | 30.4272i | −0.0401994 | + | 0.0696275i | ||||
\(438\) | −35.4959 | − | 20.4936i | −0.0810410 | − | 0.0467890i | ||||
\(439\) | 321.631 | − | 185.694i | 0.732645 | − | 0.422993i | −0.0867437 | − | 0.996231i | \(-0.527646\pi\) |
0.819389 | + | 0.573238i | \(0.194313\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.77993 | − | 146.886i | 0.0131064 | − | 0.333076i | ||||
\(442\) | − | 199.180i | − | 0.450635i | ||||||
\(443\) | 353.951 | − | 204.354i | 0.798987 | − | 0.461295i | −0.0441299 | − | 0.999026i | \(-0.514052\pi\) |
0.843117 | + | 0.537731i | \(0.180718\pi\) | |||||||
\(444\) | −29.2609 | − | 16.8938i | −0.0659029 | − | 0.0380491i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −316.052 | + | 182.473i | −0.708636 | + | 0.409131i | ||||
\(447\) | 249.555 | 0.558288 | ||||||||
\(448\) | 53.7964 | + | 15.5547i | 0.120081 | + | 0.0347203i | ||||
\(449\) | −725.469 | −1.61574 | −0.807872 | − | 0.589358i | \(-0.799381\pi\) | ||||
−0.807872 | + | 0.589358i | \(0.799381\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.85730 | + | 1.07231i | 0.00411817 | + | 0.00237763i | ||||
\(452\) | −201.335 | − | 116.241i | −0.445432 | − | 0.257170i | ||||
\(453\) | 80.9842 | + | 140.269i | 0.178773 | + | 0.309644i | ||||
\(454\) | 468.150i | 1.03117i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −15.5639 | −0.0341313 | ||||||||
\(457\) | −347.736 | + | 200.765i | −0.760909 | + | 0.439311i | −0.829622 | − | 0.558325i | \(-0.811444\pi\) |
0.0687128 | + | 0.997636i | \(0.478111\pi\) | |||||||
\(458\) | 172.702 | − | 299.129i | 0.377080 | − | 0.653121i | ||||
\(459\) | 86.6474 | − | 150.078i | 0.188774 | − | 0.326967i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 653.050i | 1.41659i | 0.705915 | + | 0.708297i | \(0.250536\pi\) | ||||
−0.705915 | + | 0.708297i | \(0.749464\pi\) | |||||||
\(462\) | −6.25607 | − | 6.50709i | −0.0135413 | − | 0.0140846i | ||||
\(463\) | − | 869.580i | − | 1.87814i | −0.343722 | − | 0.939072i | \(-0.611688\pi\) | ||
0.343722 | − | 0.939072i | \(-0.388312\pi\) | |||||||
\(464\) | −112.260 | − | 194.441i | −0.241941 | − | 0.419053i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −149.546 | + | 259.021i | −0.320913 | + | 0.555838i | ||||
\(467\) | −369.601 | − | 640.168i | −0.791437 | − | 1.37081i | −0.925077 | − | 0.379779i | \(-0.876000\pi\) |
0.133641 | − | 0.991030i | \(-0.457333\pi\) | |||||||
\(468\) | −25.3384 | −0.0541419 | ||||||||
\(469\) | −42.3967 | − | 44.0978i | −0.0903981 | − | 0.0940252i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 148.286 | + | 256.838i | 0.314831 | + | 0.545304i | ||||
\(472\) | −71.4621 | + | 123.776i | −0.151403 | + | 0.262237i | ||||
\(473\) | 21.1325 | + | 12.2009i | 0.0446777 | + | 0.0257947i | ||||
\(474\) | 280.639 | − | 162.027i | 0.592066 | − | 0.341829i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −111.953 | − | 453.288i | −0.235196 | − | 0.952285i | ||||
\(477\) | − | 139.563i | − | 0.292586i | ||||||
\(478\) | 421.476 | − | 243.339i | 0.881750 | − | 0.509078i | ||||
\(479\) | 525.006 | + | 303.112i | 1.09605 | + | 0.632802i | 0.935180 | − | 0.354174i | \(-0.115238\pi\) |
0.160866 | + | 0.986976i | \(0.448571\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 35.6718 | − | 20.5951i | 0.0741618 | − | 0.0428173i | ||||
\(482\) | 242.323 | 0.502745 | ||||||||
\(483\) | −37.2435 | + | 128.808i | −0.0771088 | + | 0.266683i | ||||
\(484\) | 241.446 | 0.498855 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −19.0919 | − | 11.0227i | −0.0392837 | − | 0.0226805i | ||||
\(487\) | 562.549 | + | 324.788i | 1.15513 | + | 0.666916i | 0.950133 | − | 0.311846i | \(-0.100947\pi\) |
0.205000 | + | 0.978762i | \(0.434281\pi\) | |||||||
\(488\) | 146.085 | + | 253.026i | 0.299354 | + | 0.518497i | ||||
\(489\) | − | 161.103i | − | 0.329454i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 266.629 | 0.543033 | 0.271516 | − | 0.962434i | \(-0.412475\pi\) | ||||
0.271516 | + | 0.962434i | \(0.412475\pi\) | |||||||
\(492\) | 12.2213 | − | 7.05598i | 0.0248401 | − | 0.0143414i | ||||
\(493\) | −935.988 | + | 1621.18i | −1.89856 | + | 3.28839i | ||||
\(494\) | 9.48693 | − | 16.4318i | 0.0192043 | − | 0.0332628i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.56640i | 0.0152548i | ||||||||
\(497\) | −195.421 | − | 56.5039i | −0.393200 | − | 0.113690i | ||||
\(498\) | − | 30.5788i | − | 0.0614033i | ||||||
\(499\) | −340.553 | − | 589.855i | −0.682471 | − | 1.18207i | −0.974225 | − | 0.225581i | \(-0.927572\pi\) |
0.291754 | − | 0.956493i | \(-0.405761\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 90.9247 | − | 157.486i | 0.181487 | − | 0.314344i | ||||
\(502\) | −231.604 | − | 401.151i | −0.461364 | − | 0.799105i | ||||
\(503\) | −453.326 | −0.901245 | −0.450622 | − | 0.892715i | \(-0.648798\pi\) | ||||
−0.450622 | + | 0.892715i | \(0.648798\pi\) | |||||||
\(504\) | −57.6643 | + | 14.2419i | −0.114413 | + | 0.0282578i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.11678 | + | 7.13047i | 0.00813592 | + | 0.0140918i | ||||
\(507\) | −130.913 | + | 226.749i | −0.258212 | + | 0.447236i | ||||
\(508\) | 140.945 | + | 81.3744i | 0.277450 | + | 0.160186i | ||||
\(509\) | 43.5300 | − | 25.1321i | 0.0855206 | − | 0.0493754i | −0.456630 | − | 0.889657i | \(-0.650944\pi\) |
0.542150 | + | 0.840281i | \(0.317610\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 84.4364 | − | 81.1792i | 0.165238 | − | 0.158863i | ||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | 14.2963 | − | 8.25400i | 0.0278681 | − | 0.0160897i | ||||
\(514\) | −269.883 | − | 155.817i | −0.525064 | − | 0.303146i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 139.056 | − | 80.2838i | 0.269488 | − | 0.155589i | ||||
\(517\) | −33.3103 | −0.0644300 | ||||||||
\(518\) | 69.6048 | − | 66.9197i | 0.134372 | − | 0.129189i | ||||
\(519\) | 353.610 | 0.681330 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −89.2971 | − | 51.5557i | −0.171396 | − | 0.0989553i | 0.411848 | − | 0.911252i | \(-0.364883\pi\) |
−0.583244 | + | 0.812297i | \(0.698217\pi\) | |||||||
\(522\) | 206.236 | + | 119.070i | 0.395087 | + | 0.228104i | ||||
\(523\) | −183.434 | − | 317.716i | −0.350733 | − | 0.607488i | 0.635645 | − | 0.771982i | \(-0.280734\pi\) |
−0.986378 | + | 0.164494i | \(0.947401\pi\) | |||||||
\(524\) | − | 481.253i | − | 0.918421i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 188.366 | 0.358111 | ||||||||
\(527\) | 54.6341 | − | 31.5430i | 0.103670 | − | 0.0598539i | ||||
\(528\) | −1.82366 | + | 3.15867i | −0.00345390 | + | 0.00598234i | ||||
\(529\) | −203.348 | + | 352.210i | −0.384402 | + | 0.665803i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 151.594i | − | 0.285488i | ||||||
\(532\) | 12.3542 | − | 42.7273i | 0.0232222 | − | 0.0803145i | ||||
\(533\) | 17.2038i | 0.0322773i | ||||||||
\(534\) | 83.5943 | + | 144.790i | 0.156544 | + | 0.271141i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −12.3588 | + | 21.4060i | −0.0230574 | + | 0.0399365i | ||||
\(537\) | 169.653 | + | 293.848i | 0.315928 | + | 0.547204i | ||||
\(538\) | −37.4988 | −0.0697005 | ||||||||
\(539\) | 22.8297 | − | 12.0096i | 0.0423557 | − | 0.0222812i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 266.559 | + | 461.693i | 0.492714 | + | 0.853407i | 0.999965 | − | 0.00839227i | \(-0.00267137\pi\) |
−0.507250 | + | 0.861799i | \(0.669338\pi\) | |||||||
\(542\) | 75.6709 | − | 131.066i | 0.139614 | − | 0.241819i | ||||
\(543\) | 178.547 | + | 103.084i | 0.328816 | + | 0.189842i | ||||
\(544\) | −163.384 | + | 94.3297i | −0.300338 | + | 0.173400i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 20.1129 | − | 69.5612i | 0.0368369 | − | 0.127401i | ||||
\(547\) | − | 69.6218i | − | 0.127279i | −0.997973 | − | 0.0636396i | \(-0.979729\pi\) | ||
0.997973 | − | 0.0636396i | \(-0.0202708\pi\) | |||||||
\(548\) | 404.713 | − | 233.661i | 0.738528 | − | 0.426389i | ||||
\(549\) | −268.375 | − | 154.946i | −0.488843 | − | 0.282234i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −154.433 | + | 89.1619i | −0.280277 | + | 0.161818i | ||||
\(552\) | 54.1782 | 0.0981489 | ||||||||
\(553\) | 222.047 | + | 899.048i | 0.401532 | + | 1.62576i | ||||
\(554\) | −622.793 | −1.12418 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 366.314 | + | 211.491i | 0.658838 | + | 0.380380i | ||||
\(557\) | 14.6033 | + | 8.43122i | 0.0262178 | + | 0.0151368i | 0.513052 | − | 0.858358i | \(-0.328515\pi\) |
−0.486834 | + | 0.873495i | \(0.661848\pi\) | |||||||
\(558\) | −4.01269 | − | 6.95018i | −0.00719120 | − | 0.0124555i | ||||
\(559\) | 195.747i | 0.350174i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 30.4101 | 0.0542069 | ||||||||
\(562\) | −394.452 | + | 227.737i | −0.701872 | + | 0.405226i | ||||
\(563\) | −457.892 | + | 793.093i | −0.813308 | + | 1.40869i | 0.0972290 | + | 0.995262i | \(0.469002\pi\) |
−0.910537 | + | 0.413428i | \(0.864331\pi\) | |||||||
\(564\) | −109.594 | + | 189.822i | −0.194315 | + | 0.336564i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 96.9204i | 0.171237i | ||||||||
\(567\) | 45.4151 | − | 43.6632i | 0.0800971 | − | 0.0770073i | ||||
\(568\) | 82.1963i | 0.144712i | ||||||||
\(569\) | 203.828 | + | 353.040i | 0.358221 | + | 0.620456i | 0.987664 | − | 0.156590i | \(-0.0500502\pi\) |
−0.629443 | + | 0.777047i | \(0.716717\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 447.910 | − | 775.803i | 0.784431 | − | 1.35867i | −0.144908 | − | 0.989445i | \(-0.546289\pi\) |
0.929339 | − | 0.369229i | \(-0.120378\pi\) | |||||||
\(572\) | −2.22322 | − | 3.85072i | −0.00388674 | − | 0.00673203i | ||||
\(573\) | 113.850 | 0.198691 | ||||||||
\(574\) | 9.66974 | + | 39.1519i | 0.0168462 | + | 0.0682088i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 12.0000 | + | 20.7846i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | 340.703 | − | 590.115i | 0.590473 | − | 1.02273i | −0.403695 | − | 0.914893i | \(-0.632274\pi\) |
0.994169 | − | 0.107836i | \(-0.0343922\pi\) | |||||||
\(578\) | 1008.29 | + | 582.134i | 1.74444 | + | 1.00715i | ||||
\(579\) | 145.305 | − | 83.8919i | 0.250959 | − | 0.144891i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 83.9476 | + | 24.2726i | 0.144488 | + | 0.0417773i | ||||
\(582\) | − | 365.662i | − | 0.628286i | ||||||
\(583\) | 21.2097 | − | 12.2454i | 0.0363802 | − | 0.0210041i | ||||
\(584\) | −40.9872 | − | 23.6640i | −0.0701835 | − | 0.0405205i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −180.662 | + | 104.305i | −0.308297 | + | 0.177996i | ||||
\(587\) | 833.001 | 1.41908 | 0.709541 | − | 0.704665i | \(-0.248903\pi\) | ||||
0.709541 | + | 0.704665i | \(0.248903\pi\) | |||||||
\(588\) | 6.67408 | − | 169.610i | 0.0113505 | − | 0.288452i | ||||
\(589\) | 6.00955 | 0.0102030 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −280.008 | − | 161.663i | −0.473787 | − | 0.273541i | ||||
\(592\) | −33.7876 | − | 19.5073i | −0.0570736 | − | 0.0329515i | ||||
\(593\) | 156.371 | + | 270.842i | 0.263694 | + | 0.456731i | 0.967221 | − | 0.253938i | \(-0.0817258\pi\) |
−0.703527 | + | 0.710669i | \(0.748392\pi\) | |||||||
\(594\) | − | 3.86857i | − | 0.00651274i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 288.161 | 0.483491 | ||||||||
\(597\) | −172.937 | + | 99.8454i | −0.289677 | + | 0.167245i | ||||
\(598\) | −33.0242 | + | 57.1996i | −0.0552244 | + | 0.0956514i | ||||
\(599\) | 107.121 | − | 185.540i | 0.178834 | − | 0.309749i | −0.762648 | − | 0.646814i | \(-0.776101\pi\) |
0.941481 | + | 0.337065i | \(0.109434\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 176.849i | − | 0.294257i | −0.989117 | − | 0.147129i | \(-0.952997\pi\) | ||
0.989117 | − | 0.147129i | \(-0.0470031\pi\) | |||||||
\(602\) | 110.023 | + | 445.474i | 0.182763 | + | 0.739991i | ||||
\(603\) | − | 26.2169i | − | 0.0434774i | ||||||
\(604\) | 93.5125 | + | 161.968i | 0.154822 | + | 0.268160i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −118.488 | + | 205.228i | −0.195525 | + | 0.338660i | ||||
\(607\) | −18.5505 | − | 32.1304i | −0.0305609 | − | 0.0529331i | 0.850340 | − | 0.526233i | \(-0.176396\pi\) |
−0.880901 | + | 0.473300i | \(0.843063\pi\) | |||||||
\(608\) | −17.9716 | −0.0295586 | ||||||||
\(609\) | −490.586 | + | 471.661i | −0.805559 | + | 0.774484i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −133.605 | − | 231.411i | −0.218666 | − | 0.378741i | ||||
\(612\) | 100.052 | − | 173.295i | 0.163483 | − | 0.283161i | ||||
\(613\) | 779.180 | + | 449.860i | 1.27109 | + | 0.733866i | 0.975194 | − | 0.221353i | \(-0.0710475\pi\) |
0.295899 | + | 0.955219i | \(0.404381\pi\) | |||||||
\(614\) | 460.516 | − | 265.879i | 0.750027 | − | 0.433028i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.22389 | − | 7.51374i | −0.0117271 | − | 0.0121976i | ||||
\(617\) | 626.244i | 1.01498i | 0.861657 | + | 0.507491i | \(0.169427\pi\) | ||||
−0.861657 | + | 0.507491i | \(0.830573\pi\) | |||||||
\(618\) | −222.234 | + | 128.307i | −0.359602 | + | 0.207617i | ||||
\(619\) | 776.375 | + | 448.240i | 1.25424 | + | 0.724136i | 0.971949 | − | 0.235193i | \(-0.0755722\pi\) |
0.282291 | + | 0.959329i | \(0.408906\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −49.7658 | + | 28.7323i | −0.0801382 | + | 0.0462678i | ||||
\(622\) | 551.298 | 0.886331 | ||||||||
\(623\) | −463.843 | + | 114.560i | −0.744532 | + | 0.183885i | ||||
\(624\) | −29.2583 | −0.0468883 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 175.207 | + | 101.156i | 0.279884 | + | 0.161591i | ||||
\(627\) | 2.50875 | + | 1.44843i | 0.00400120 | + | 0.00231009i | ||||
\(628\) | 171.225 | + | 296.571i | 0.272652 | + | 0.472247i | ||||
\(629\) | 325.290i | 0.517153i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −500.730 | −0.793550 | −0.396775 | − | 0.917916i | \(-0.629871\pi\) | ||||
−0.396775 | + | 0.917916i | \(0.629871\pi\) | |||||||
\(632\) | 324.054 | − | 187.093i | 0.512744 | − | 0.296033i | ||||
\(633\) | 120.752 | − | 209.149i | 0.190762 | − | 0.330409i | ||||
\(634\) | 271.843 | − | 470.846i | 0.428774 | − | 0.742659i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 161.154i | − | 0.253387i | ||||||
\(637\) | 175.000 | + | 110.431i | 0.274726 | + | 0.173362i | ||||
\(638\) | 41.7893i | 0.0655005i | ||||||||
\(639\) | −43.5912 | − | 75.5021i | −0.0682178 | − | 0.118157i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −310.289 | + | 537.436i | −0.484070 | + | 0.838434i | −0.999833 | − | 0.0182978i | \(-0.994175\pi\) |
0.515763 | + | 0.856732i | \(0.327509\pi\) | |||||||
\(642\) | 152.609 | + | 264.326i | 0.237708 | + | 0.411722i | ||||
\(643\) | 1127.93 | 1.75417 | 0.877086 | − | 0.480334i | \(-0.159484\pi\) | ||||
0.877086 | + | 0.480334i | \(0.159484\pi\) | |||||||
\(644\) | −43.0051 | + | 148.735i | −0.0667782 | + | 0.230954i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 74.9206 | + | 129.766i | 0.115976 | + | 0.200877i | ||||
\(647\) | −67.6248 | + | 117.130i | −0.104521 | + | 0.181035i | −0.913542 | − | 0.406744i | \(-0.866664\pi\) |
0.809022 | + | 0.587779i | \(0.199997\pi\) | |||||||
\(648\) | −22.0454 | − | 12.7279i | −0.0340207 | − | 0.0196419i | ||||
\(649\) | 23.0380 | − | 13.3010i | 0.0354977 | − | 0.0204946i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 22.2654 | − | 5.49912i | 0.0342018 | − | 0.00844719i | ||||
\(652\) | − | 186.026i | − | 0.285316i | ||||||
\(653\) | −338.001 | + | 195.145i | −0.517612 | + | 0.298843i | −0.735957 | − | 0.677028i | \(-0.763267\pi\) |
0.218345 | + | 0.975872i | \(0.429934\pi\) | |||||||
\(654\) | 179.482 | + | 103.624i | 0.274437 | + | 0.158446i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 14.1120 | − | 8.14755i | 0.0215121 | − | 0.0124200i | ||||
\(657\) | 50.1988 | 0.0764061 | ||||||||
\(658\) | −434.123 | − | 451.542i | −0.659761 | − | 0.686233i | ||||
\(659\) | 864.853 | 1.31237 | 0.656186 | − | 0.754599i | \(-0.272169\pi\) | ||||
0.656186 | + | 0.754599i | \(0.272169\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −873.134 | − | 504.104i | −1.32093 | − | 0.762638i | −0.337052 | − | 0.941486i | \(-0.609430\pi\) |
−0.983877 | + | 0.178848i | \(0.942763\pi\) | |||||||
\(662\) | 237.487 | + | 137.113i | 0.358742 | + | 0.207120i | ||||
\(663\) | 121.973 | + | 211.263i | 0.183971 | + | 0.318647i | ||||
\(664\) | − | 35.3094i | − | 0.0531768i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 41.3812 | 0.0621339 | ||||||||
\(667\) | 537.584 | − | 310.374i | 0.805973 | − | 0.465328i | ||||
\(668\) | 104.991 | − | 181.849i | 0.157172 | − | 0.272230i | ||||
\(669\) | 223.482 | − | 387.083i | 0.334054 | − | 0.578599i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 54.3806i | − | 0.0810441i | ||||||
\(672\) | −66.5850 | + | 16.4452i | −0.0990848 | + | 0.0244720i | ||||
\(673\) | − | 109.959i | − | 0.163386i | −0.996658 | − | 0.0816928i | \(-0.973967\pi\) | ||
0.996658 | − | 0.0816928i | \(-0.0260327\pi\) | |||||||
\(674\) | 88.7259 | + | 153.678i | 0.131641 | + | 0.228009i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −151.166 | + | 261.827i | −0.223618 | + | 0.387318i | ||||
\(677\) | −84.4163 | − | 146.213i | −0.124692 | − | 0.215972i | 0.796921 | − | 0.604084i | \(-0.206461\pi\) |
−0.921612 | + | 0.388112i | \(0.873128\pi\) | |||||||
\(678\) | 284.731 | 0.419957 | ||||||||
\(679\) | 1003.85 | + | 290.253i | 1.47842 | + | 0.427471i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −286.682 | − | 496.548i | −0.420973 | − | 0.729146i | ||||
\(682\) | 0.704155 | − | 1.21963i | 0.00103248 | − | 0.00178832i | ||||
\(683\) | 377.700 | + | 218.065i | 0.553002 | + | 0.319276i | 0.750332 | − | 0.661061i | \(-0.229894\pi\) |
−0.197330 | + | 0.980337i | \(0.563227\pi\) | |||||||
\(684\) | 16.5080 | − | 9.53090i | 0.0241345 | − | 0.0139341i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 460.329 | + | 152.954i | 0.671034 | + | 0.222965i | ||||
\(687\) | 423.033i | 0.615768i | ||||||||
\(688\) | 160.568 | − | 92.7038i | 0.233383 | − | 0.134744i | ||||
\(689\) | 170.141 | + | 98.2309i | 0.246939 | + | 0.142570i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −59.2770 | + | 34.2236i | −0.0857843 | + | 0.0495276i | −0.542279 | − | 0.840199i | \(-0.682438\pi\) |
0.456494 | + | 0.889726i | \(0.349105\pi\) | |||||||
\(692\) | 408.314 | 0.590049 | ||||||||
\(693\) | 10.6203 | + | 3.07076i | 0.0153251 | + | 0.00443112i | ||||
\(694\) | 712.193 | 1.02622 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 238.140 | + | 137.490i | 0.342156 | + | 0.197544i | ||||
\(697\) | −117.661 | − | 67.9314i | −0.168810 | − | 0.0974625i | ||||
\(698\) | 33.7772 | + | 58.5039i | 0.0483914 | + | 0.0838164i | ||||
\(699\) | − | 366.311i | − | 0.524050i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1283.41 | 1.83083 | 0.915414 | − | 0.402514i | \(-0.131864\pi\) | ||||
0.915414 | + | 0.402514i | \(0.131864\pi\) | |||||||
\(702\) | 26.8754 | − | 15.5165i | 0.0382841 | − | 0.0221033i | ||||
\(703\) | −15.4935 | + | 26.8355i | −0.0220391 | + | 0.0381728i | ||||
\(704\) | −2.10578 | + | 3.64732i | −0.00299117 | + | 0.00518086i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 46.5422i | − | 0.0659238i | ||||||
\(707\) | −469.356 | − | 488.188i | −0.663870 | − | 0.690507i | ||||
\(708\) | − | 175.046i | − | 0.247240i | ||||||
\(709\) | 86.2000 | + | 149.303i | 0.121580 | + | 0.210582i | 0.920391 | − | 0.391000i | \(-0.127871\pi\) |
−0.798811 | + | 0.601582i | \(0.794537\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −198.442 | + | 343.712i | −0.279103 | + | 0.483420i | ||||
\(712\) | 96.5264 | + | 167.189i | 0.135571 | + | 0.234815i | ||||
\(713\) | −20.9194 | −0.0293399 | ||||||||
\(714\) | 396.325 | + | 412.227i | 0.555077 | + | 0.577349i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 195.899 | + | 339.307i | 0.273602 | + | 0.473892i | ||||
\(717\) | −298.029 | + | 516.201i | −0.415661 | + | 0.719946i | ||||
\(718\) | −327.983 | − | 189.361i | −0.456801 | − | 0.263734i | ||||
\(719\) | 435.015 | − | 251.156i | 0.605028 | − | 0.349313i | −0.165989 | − | 0.986128i | \(-0.553082\pi\) |
0.771017 | + | 0.636815i | \(0.219748\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −175.836 | − | 711.943i | −0.243878 | − | 0.987439i | ||||
\(722\) | − | 496.257i | − | 0.687337i | ||||||
\(723\) | −257.023 | + | 148.392i | −0.355495 | + | 0.205245i | ||||
\(724\) | 206.168 | + | 119.031i | 0.284763 | + | 0.164408i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −256.092 | + | 147.855i | −0.352744 | + | 0.203657i | ||||
\(727\) | −748.693 | −1.02984 | −0.514920 | − | 0.857238i | \(-0.672178\pi\) | ||||
−0.514920 | + | 0.857238i | \(0.672178\pi\) | |||||||
\(728\) | 23.2244 | − | 80.3223i | 0.0319017 | − | 0.110333i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1338.76 | − | 772.931i | −1.83140 | − | 1.05736i | ||||
\(732\) | −309.893 | − | 178.917i | −0.423351 | − | 0.244422i | ||||
\(733\) | −469.248 | − | 812.761i | −0.640175 | − | 1.10881i | −0.985394 | − | 0.170293i | \(-0.945529\pi\) |
0.345219 | − | 0.938522i | \(-0.387805\pi\) | |||||||
\(734\) | − | 224.468i | − | 0.305814i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 62.5596 | 0.0849994 | ||||||||
\(737\) | 3.98422 | − | 2.30029i | 0.00540600 | − | 0.00312116i | ||||
\(738\) | −8.64178 | + | 14.9680i | −0.0117097 | + | 0.0202818i | ||||
\(739\) | 106.820 | − | 185.018i | 0.144547 | − | 0.250363i | −0.784657 | − | 0.619931i | \(-0.787161\pi\) |
0.929204 | + | 0.369567i | \(0.120494\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 23.2381i | 0.0313605i | ||||||||
\(742\) | 442.413 | + | 127.919i | 0.596244 | + | 0.172398i | ||||
\(743\) | 544.013i | 0.732184i | 0.930579 | + | 0.366092i | \(0.119304\pi\) | ||||
−0.930579 | + | 0.366092i | \(0.880696\pi\) | |||||||
\(744\) | −4.63346 | − | 8.02538i | −0.00622776 | − | 0.0107868i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −292.985 | + | 507.465i | −0.392742 | + | 0.680249i | ||||
\(747\) | 18.7256 | + | 32.4337i | 0.0250678 | + | 0.0434187i | ||||
\(748\) | 35.1146 | 0.0469446 | ||||||||
\(749\) | −846.786 | + | 209.140i | −1.13056 | + | 0.279225i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −294.705 | − | 510.443i | −0.392416 | − | 0.679685i | 0.600351 | − | 0.799736i | \(-0.295027\pi\) |
−0.992768 | + | 0.120051i | \(0.961694\pi\) | |||||||
\(752\) | −126.548 | + | 219.187i | −0.168282 | + | 0.291473i | ||||
\(753\) | 491.307 | + | 283.656i | 0.652467 | + | 0.376702i | ||||
\(754\) | −290.316 | + | 167.614i | −0.385034 | + | 0.222299i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 52.4408 | − | 50.4179i | 0.0693662 | − | 0.0666903i | ||||
\(757\) | 448.997i | 0.593127i | 0.955013 | + | 0.296564i | \(0.0958406\pi\) | ||||
−0.955013 | + | 0.296564i | \(0.904159\pi\) | |||||||
\(758\) | −89.1614 | + | 51.4774i | −0.117627 | + | 0.0679121i | ||||
\(759\) | −8.73300 | − | 5.04200i | −0.0115059 | − | 0.00664295i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 371.914 | − | 214.725i | 0.488718 | − | 0.282161i | −0.235325 | − | 0.971917i | \(-0.575615\pi\) |
0.724042 | + | 0.689756i | \(0.242282\pi\) | |||||||
\(762\) | −199.326 | −0.261582 | ||||||||
\(763\) | −426.944 | + | 410.475i | −0.559560 | + | 0.537975i | ||||
\(764\) | 131.463 | 0.172072 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 349.070 | + | 201.536i | 0.455705 | + | 0.263101i | ||||
\(767\) | 184.807 | + | 106.699i | 0.240948 | + | 0.139112i | ||||
\(768\) | 13.8564 | + | 24.0000i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | − | 32.5790i | − | 0.0423655i | −0.999776 | − | 0.0211827i | \(-0.993257\pi\) | ||
0.999776 | − | 0.0211827i | \(-0.00674318\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 381.672 | 0.495035 | ||||||||
\(772\) | 167.784 | − | 96.8700i | 0.217337 | − | 0.125479i | ||||
\(773\) | −621.768 | + | 1076.93i | −0.804357 | + | 1.39319i | 0.112367 | + | 0.993667i | \(0.464157\pi\) |
−0.916724 | + | 0.399520i | \(0.869177\pi\) | |||||||
\(774\) | −98.3272 | + | 170.308i | −0.127038 | + | 0.220036i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 422.231i | − | 0.544112i | ||||||
\(777\) | −32.8472 | + | 113.603i | −0.0422744 | + | 0.146207i | ||||
\(778\) | − | 137.374i | − | 0.176574i | ||||||
\(779\) | −6.47112 | − | 11.2083i | −0.00830696 | − | 0.0143881i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.64946 | − | 13.2493i | 0.00979444 | − | 0.0169645i | ||||
\(782\) | −260.800 | − | 451.719i | −0.333504 | − | 0.577645i | ||||
\(783\) | −291.661 | −0.372492 | ||||||||
\(784\) | 7.70657 | − | 195.848i | 0.00982981 | − | 0.249807i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 294.706 | + | 510.446i | 0.374944 | + | 0.649422i | ||||
\(787\) | 95.3138 | − | 165.088i | 0.121110 | − | 0.209769i | −0.799096 | − | 0.601204i | \(-0.794688\pi\) |
0.920206 | + | 0.391435i | \(0.128021\pi\) | |||||||
\(788\) | −323.325 | − | 186.672i | −0.410311 | − | 0.236893i | ||||
\(789\) | −199.793 | + | 115.350i | −0.253223 | + | 0.146198i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −226.011 | + | 781.667i | −0.285729 | + | 0.988202i | ||||
\(792\) | − | 4.46704i | − | 0.00564020i | ||||||
\(793\) | 377.789 | − | 218.116i | 0.476405 | − | 0.275052i | ||||
\(794\) | −969.635 | − | 559.819i | −1.22120 | − | 0.705062i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −199.691 | + | 115.292i | −0.250868 | + | 0.144839i | ||||
\(797\) | 387.796 | 0.486570 | 0.243285 | − | 0.969955i | \(-0.421775\pi\) | ||||
0.243285 | + | 0.969955i | \(0.421775\pi\) | |||||||
\(798\) | 13.0614 | + | 52.8845i | 0.0163677 | + | 0.0662713i | ||||
\(799\) | 2110.23 | 2.64108 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −177.330 | − | 102.382i | −0.221386 | − | 0.127817i | ||||
\(802\) | 616.324 | + | 355.835i | 0.768484 | + | 0.443684i | ||||
\(803\) | 4.40449 | + | 7.62881i | 0.00548505 | + | 0.00950038i | ||||
\(804\) | − | 30.2726i | − | 0.0376525i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 11.2972 | 0.0140164 | ||||||||
\(807\) | 39.7735 | − | 22.9633i | 0.0492857 | − | 0.0284551i | ||||
\(808\) | −136.818 | + | 236.977i | −0.169330 | + | 0.293288i | ||||
\(809\) | 182.613 | − | 316.295i | 0.225727 | − | 0.390970i | −0.730811 | − | 0.682580i | \(-0.760858\pi\) |
0.956537 | + | 0.291610i | \(0.0941911\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 944.189i | − | 1.16423i | −0.813107 | − | 0.582114i | \(-0.802226\pi\) | ||
0.813107 | − | 0.582114i | \(-0.197774\pi\) | |||||||
\(812\) | −566.479 | + | 544.627i | −0.697635 | + | 0.670723i | ||||
\(813\) | 185.355i | 0.227989i | ||||||||
\(814\) | 3.63082 | + | 6.28877i | 0.00446047 | + | 0.00772576i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 115.530 | − | 200.104i | 0.141581 | − | 0.245225i | ||||
\(817\) | −73.6292 | − | 127.529i | −0.0901214 | − | 0.156095i | ||||
\(818\) | 1060.46 | 1.29640 | ||||||||
\(819\) | 21.2644 | + | 86.0974i | 0.0259638 | + | 0.105125i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 342.337 | + | 592.946i | 0.416976 | + | 0.722224i | 0.995634 | − | 0.0933467i | \(-0.0297565\pi\) |
−0.578657 | + | 0.815571i | \(0.696423\pi\) | |||||||
\(822\) | −286.175 | + | 495.670i | −0.348145 | + | 0.603005i | ||||
\(823\) | 905.578 | + | 522.835i | 1.10034 | + | 0.635280i | 0.936310 | − | 0.351176i | \(-0.114218\pi\) |
0.164028 | + | 0.986456i | \(0.447551\pi\) | |||||||
\(824\) | −256.614 | + | 148.156i | −0.311425 | + | 0.179801i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 480.550 | + | 138.946i | 0.581780 | + | 0.168216i | ||||
\(827\) | − | 830.505i | − | 1.00424i | −0.864798 | − | 0.502119i | \(-0.832554\pi\) | ||
0.864798 | − | 0.502119i | \(-0.167446\pi\) | |||||||
\(828\) | −57.4646 | + | 33.1772i | −0.0694017 | + | 0.0400691i | ||||
\(829\) | 621.983 | + | 359.102i | 0.750280 | + | 0.433175i | 0.825795 | − | 0.563970i | \(-0.190727\pi\) |
−0.0755148 | + | 0.997145i | \(0.524060\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 660.572 | − | 381.381i | 0.794912 | − | 0.458943i | ||||
\(832\) | −33.7846 | −0.0406064 | ||||||||
\(833\) | −1446.27 | + | 760.812i | −1.73622 | + | 0.913339i | ||||
\(834\) | −518.046 | −0.621158 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.89685 | + | 1.67250i | 0.00346514 | + | 0.00200060i | ||||
\(837\) | 8.51220 | + | 4.91452i | 0.0101699 | + | 0.00587159i | ||||
\(838\) | −329.342 | − | 570.436i | −0.393009 | − | 0.680712i | ||||
\(839\) | − | 55.2900i | − | 0.0658999i | −0.999457 | − | 0.0329499i | \(-0.989510\pi\) | ||
0.999457 | − | 0.0329499i | \(-0.0104902\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2309.60 | 2.74625 | ||||||||
\(842\) | −423.737 | + | 244.645i | −0.503251 | + | 0.290552i | ||||
\(843\) | 278.920 | − | 483.103i | 0.330866 | − | 0.573076i | ||||
\(844\) | 139.433 | − | 241.505i | 0.165205 | − | 0.286143i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 268.449i | − | 0.317315i | ||||||
\(847\) | −202.625 | − | 820.408i | −0.239226 | − | 0.968605i | ||||
\(848\) | − | 186.084i | − | 0.219439i | ||||||
\(849\) | −59.3514 | − | 102.800i | −0.0699074 | − | 0.121083i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 53.9331 | − | 93.4149i | 0.0633761 | − | 0.109771i | ||||
\(852\) | −50.3347 | − | 87.1823i | −0.0590783 | − | 0.102327i | ||||
\(853\) | −21.9601 | −0.0257445 | −0.0128723 | − | 0.999917i | \(-0.504097\pi\) | ||||
−0.0128723 | + | 0.999917i | \(0.504097\pi\) | |||||||
\(854\) | 737.162 | − | 708.725i | 0.863187 | − | 0.829889i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 176.217 | + | 305.217i | 0.205861 | + | 0.356562i | ||||
\(857\) | −807.903 | + | 1399.33i | −0.942711 | + | 1.63282i | −0.182441 | + | 0.983217i | \(0.558400\pi\) |
−0.760271 | + | 0.649607i | \(0.774934\pi\) | |||||||
\(858\) | 4.71615 | + | 2.72287i | 0.00549668 | + | 0.00317351i | ||||
\(859\) | −772.149 | + | 445.801i | −0.898893 | + | 0.518976i | −0.876841 | − | 0.480781i | \(-0.840353\pi\) |
−0.0220523 | + | 0.999757i | \(0.507020\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −34.2318 | − | 35.6053i | −0.0397582 | − | 0.0413535i | ||||
\(862\) | − | 699.470i | − | 0.811450i | ||||||
\(863\) | −776.259 | + | 448.173i | −0.899489 | + | 0.519320i | −0.877034 | − | 0.480428i | \(-0.840481\pi\) |
−0.0224544 | + | 0.999748i | \(0.507148\pi\) | |||||||
\(864\) | −25.4558 | − | 14.6969i | −0.0294628 | − | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 894.090 | − | 516.203i | 1.03244 | − | 0.596078i | ||||
\(867\) | −1425.93 | −1.64467 | ||||||||
\(868\) | 25.7099 | − | 6.34984i | 0.0296197 | − | 0.00731548i | ||||
\(869\) | −69.6459 | −0.0801449 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.9609 | + | 18.4526i | 0.0366944 | + | 0.0211855i | ||||
\(872\) | 207.248 | + | 119.654i | 0.237669 | + | 0.137218i | ||||
\(873\) | 223.922 | + | 387.844i | 0.256497 | + | 0.444265i | ||||
\(874\) | − | 49.6874i | − | 0.0568506i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 57.9646 | 0.0661697 | ||||||||
\(877\) | 292.517 | − | 168.885i | 0.333543 | − | 0.192571i | −0.323870 | − | 0.946102i | \(-0.604984\pi\) |
0.657413 | + | 0.753530i | \(0.271651\pi\) | |||||||
\(878\) | −262.611 | + | 454.855i | −0.299101 | + | 0.518059i | ||||
\(879\) | 127.748 | − | 221.265i | 0.145333 | − | 0.251724i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 301.377i | − | 0.342085i | −0.985264 | − | 0.171042i | \(-0.945287\pi\) | ||
0.985264 | − | 0.171042i | \(-0.0547135\pi\) | |||||||
\(882\) | 96.7854 | + | 183.985i | 0.109734 | + | 0.208600i | ||||
\(883\) | 38.3679i | 0.0434518i | 0.999764 | + | 0.0217259i | \(0.00691611\pi\) | ||||
−0.999764 | + | 0.0217259i | \(0.993084\pi\) | |||||||
\(884\) | 140.842 | + | 243.945i | 0.159323 | + | 0.275956i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −289.000 | + | 500.563i | −0.326185 | + | 0.564969i | ||||
\(887\) | −330.726 | − | 572.834i | −0.372859 | − | 0.645811i | 0.617145 | − | 0.786849i | \(-0.288289\pi\) |
−0.990004 | + | 0.141038i | \(0.954956\pi\) | |||||||
\(888\) | 47.7829 | 0.0538095 | ||||||||
\(889\) | 158.219 | − | 547.206i | 0.177974 | − | 0.615530i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.36901 | + | 4.10324i | 0.00265882 | + | 0.00460521i | ||||
\(892\) | 258.055 | − | 446.965i | 0.289300 | − | 0.501082i | ||||
\(893\) | 174.088 | + | 100.510i | 0.194947 | + | 0.112553i | ||||
\(894\) | −305.641 | + | 176.462i | −0.341880 | + | 0.197384i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −76.8857 | + | 18.9893i | −0.0858099 | + | 0.0211934i | ||||
\(897\) | − | 80.8924i | − | 0.0901810i | ||||||
\(898\) | 888.515 | − | 512.984i | 0.989437 | − | 0.571252i | ||||
\(899\) | −91.9510 | − | 53.0880i | −0.102281 | − | 0.0590522i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1343.64 | + | 775.753i | −1.49128 | + | 0.860991i | ||||
\(902\) | −3.03295 | −0.00336247 | ||||||||
\(903\) | −389.494 | − | 405.122i | −0.431333 | − | 0.448640i | ||||
\(904\) | 328.779 | 0.363693 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −198.370 | − | 114.529i | −0.218951 | − | 0.126412i | ||||
\(907\) | −838.576 | − | 484.152i | −0.924560 | − | 0.533795i | −0.0394729 | − | 0.999221i | \(-0.512568\pi\) |
−0.885087 | + | 0.465426i | \(0.845901\pi\) | |||||||
\(908\) | −331.032 | − | 573.365i | −0.364573 | − | 0.631459i | ||||
\(909\) | − | 290.236i | − | 0.319291i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 220.674 | 0.242233 | 0.121116 | − | 0.992638i | \(-0.461353\pi\) | ||||
0.121116 | + | 0.992638i | \(0.461353\pi\) | |||||||
\(912\) | 19.0618 | − | 11.0053i | 0.0209011 | − | 0.0120673i | ||||
\(913\) | −3.28601 | + | 5.69153i | −0.00359913 | + | 0.00623388i | ||||
\(914\) | 283.925 | − | 491.772i | 0.310640 | − | 0.538044i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 488.476i | 0.533271i | ||||||||
\(917\) | −1635.25 | + | 403.874i | −1.78326 | + | 0.440430i | ||||
\(918\) | 245.076i | 0.266967i | ||||||||
\(919\) | −574.019 | − | 994.231i | −0.624613 | − | 1.08186i | −0.988616 | − | 0.150464i | \(-0.951923\pi\) |
0.364002 | − | 0.931398i | \(-0.381410\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −325.634 | + | 564.015i | −0.353566 | + | 0.612394i | ||||
\(922\) | −461.776 | − | 799.819i | −0.500841 | − | 0.867483i | ||||
\(923\) | 122.726 | 0.132964 | ||||||||
\(924\) | 12.2633 | + | 3.54581i | 0.0132720 | + | 0.00383746i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 614.886 | + | 1065.01i | 0.664024 | + | 1.15012i | ||||
\(927\) | 157.143 | − | 272.180i | 0.169518 | − | 0.293614i | ||||
\(928\) | 274.981 | + | 158.760i | 0.296315 | + | 0.171078i | ||||
\(929\) | 264.398 | − | 152.650i | 0.284605 | − | 0.164317i | −0.350901 | − | 0.936412i | \(-0.614125\pi\) |
0.635506 | + | 0.772096i | \(0.280791\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −155.551 | − | 6.12088i | −0.167079 | − | 0.00657452i | ||||
\(932\) | − | 422.979i | − | 0.453840i | ||||||
\(933\) | −584.739 | + | 337.599i | −0.626730 | + | 0.361843i | ||||
\(934\) | 905.334 | + | 522.695i | 0.969308 | + | 0.559630i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 31.0331 | − | 17.9170i | 0.0331550 | − | 0.0191421i | ||||
\(937\) | 12.4049 | 0.0132390 | 0.00661948 | − | 0.999978i | \(-0.497893\pi\) | ||||
0.00661948 | + | 0.999978i | \(0.497893\pi\) | |||||||
\(938\) | 83.1070 | + | 24.0296i | 0.0886002 | + | 0.0256179i | ||||
\(939\) | −247.781 | −0.263877 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −250.409 | − | 144.573i | −0.266109 | − | 0.153638i | 0.361009 | − | 0.932562i | \(-0.382432\pi\) |
−0.627118 | + | 0.778924i | \(0.715766\pi\) | |||||||
\(942\) | −363.224 | − | 209.708i | −0.385588 | − | 0.222619i | ||||
\(943\) | 22.5261 | + | 39.0163i | 0.0238877 | + | 0.0413747i | ||||
\(944\) | − | 202.125i | − | 0.214116i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −34.5093 | −0.0364792 | ||||||||
\(947\) | 1235.78 | − | 713.478i | 1.30494 | − | 0.753409i | 0.323695 | − | 0.946161i | \(-0.395075\pi\) |
0.981247 | + | 0.192752i | \(0.0617414\pi\) | |||||||
\(948\) | −229.141 | + | 396.884i | −0.241710 | + | 0.418654i | ||||
\(949\) | −35.3322 | + | 61.1972i | −0.0372310 | + | 0.0644859i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 665.876i | 0.700186i | ||||||||
\(952\) | 457.637 | + | 475.999i | 0.480711 | + | 0.499999i | ||||
\(953\) | − | 668.525i | − | 0.701495i | −0.936470 | − | 0.350747i | \(-0.885928\pi\) | ||
0.936470 | − | 0.350747i | \(-0.114072\pi\) | |||||||
\(954\) | 98.6862 | + | 170.929i | 0.103445 | + | 0.179171i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −344.134 | + | 596.058i | −0.359973 | + | 0.623491i | ||||
\(957\) | −25.5906 | − | 44.3242i | −0.0267405 | − | 0.0463158i | ||||
\(958\) | −857.331 | −0.894918 | ||||||||
\(959\) | −1133.60 | − | 1179.08i | −1.18206 | − | 1.22949i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −478.711 | − | 829.152i | −0.498138 | − | 0.862801i | ||||
\(962\) | −29.1259 | + | 50.4476i | −0.0302764 | + | 0.0524403i | ||||
\(963\) | −323.732 | − | 186.907i | −0.336170 | − | 0.194088i | ||||
\(964\) | −296.784 | + | 171.348i | −0.307867 | + | 0.177747i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −45.4671 | − | 184.092i | −0.0470674 | − | 0.190571i | ||||
\(967\) | − | 1647.14i | − | 1.70335i | −0.524069 | − | 0.851676i | \(-0.675586\pi\) | ||
0.524069 | − | 0.851676i | \(-0.324414\pi\) | |||||||
\(968\) | −295.709 | + | 170.728i | −0.305485 | + | 0.176372i | ||||
\(969\) | −158.931 | − | 91.7586i | −0.164015 | − | 0.0946941i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1138.76 | − | 657.466i | 1.17277 | − | 0.677102i | 0.218443 | − | 0.975850i | \(-0.429902\pi\) |
0.954332 | + | 0.298748i | \(0.0965690\pi\) | |||||||
\(972\) | 31.1769 | 0.0320750 | ||||||||
\(973\) | 411.210 | − | 1422.18i | 0.422621 | − | 1.46165i | ||||
\(974\) | −918.639 | −0.943161 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −357.833 | − | 206.595i | −0.366633 | − | 0.211675i | ||||
\(977\) | 1347.57 | + | 778.021i | 1.37930 | + | 0.796337i | 0.992075 | − | 0.125650i | \(-0.0401017\pi\) |
0.387221 | + | 0.921987i | \(0.373435\pi\) | |||||||
\(978\) | 113.917 | + | 197.310i | 0.116480 | + | 0.201749i | ||||
\(979\) | − | 35.9323i | − | 0.0367030i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −253.825 | −0.258741 | ||||||||
\(982\) | −326.553 | + | 188.535i | −0.332538 | + | 0.191991i | ||||
\(983\) | 686.397 | − | 1188.87i | 0.698268 | − | 1.20944i | −0.270799 | − | 0.962636i | \(-0.587288\pi\) |
0.969067 | − | 0.246799i | \(-0.0793788\pi\) | |||||||
\(984\) | −9.97867 | + | 17.2836i | −0.0101409 | + | 0.0175646i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 2647.37i | − | 2.68496i | ||||||
\(987\) | 736.968 | + | 213.087i | 0.746675 | + | 0.215894i | ||||
\(988\) | 26.8331i | 0.0271590i | ||||||||
\(989\) | 256.304 | + | 443.932i | 0.259155 | + | 0.448870i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −321.812 | + | 557.395i | −0.324735 | + | 0.562457i | −0.981459 | − | 0.191674i | \(-0.938608\pi\) |
0.656724 | + | 0.754131i | \(0.271942\pi\) | |||||||
\(992\) | −5.35025 | − | 9.26691i | −0.00539340 | − | 0.00934165i | ||||
\(993\) | −335.858 | −0.338226 | ||||||||
\(994\) | 279.295 | − | 68.9803i | 0.280981 | − | 0.0693967i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 21.6225 | + | 37.4513i | 0.0217093 | + | 0.0376017i | ||||
\(997\) | 352.433 | − | 610.431i | 0.353493 | − | 0.612268i | −0.633366 | − | 0.773853i | \(-0.718327\pi\) |
0.986859 | + | 0.161584i | \(0.0516604\pi\) | |||||||
\(998\) | 834.181 | + | 481.615i | 0.835853 | + | 0.482580i | ||||
\(999\) | −43.8914 | + | 25.3407i | −0.0439353 | + | 0.0253661i |
(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 | 1050.3.q.e.199.4 | 32 | ||
5.2 | odd | 4 | 210.3.o.b.31.4 | ✓ | 16 | ||
5.3 | odd | 4 | 1050.3.p.i.451.6 | 16 | |||
5.4 | even | 2 | inner | 1050.3.q.e.199.12 | 32 | ||
7.5 | odd | 6 | inner | 1050.3.q.e.649.12 | 32 | ||
15.2 | even | 4 | 630.3.v.c.451.6 | 16 | |||
35.12 | even | 12 | 210.3.o.b.61.4 | yes | 16 | ||
35.17 | even | 12 | 1470.3.f.d.391.9 | 16 | |||
35.19 | odd | 6 | inner | 1050.3.q.e.649.4 | 32 | ||
35.32 | odd | 12 | 1470.3.f.d.391.15 | 16 | |||
35.33 | even | 12 | 1050.3.p.i.901.6 | 16 | |||
105.47 | odd | 12 | 630.3.v.c.271.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.o.b.31.4 | ✓ | 16 | 5.2 | odd | 4 | ||
210.3.o.b.61.4 | yes | 16 | 35.12 | even | 12 | ||
630.3.v.c.271.6 | 16 | 105.47 | odd | 12 | |||
630.3.v.c.451.6 | 16 | 15.2 | even | 4 | |||
1050.3.p.i.451.6 | 16 | 5.3 | odd | 4 | |||
1050.3.p.i.901.6 | 16 | 35.33 | even | 12 | |||
1050.3.q.e.199.4 | 32 | 1.1 | even | 1 | trivial | ||
1050.3.q.e.199.12 | 32 | 5.4 | even | 2 | inner | ||
1050.3.q.e.649.4 | 32 | 35.19 | odd | 6 | inner | ||
1050.3.q.e.649.12 | 32 | 7.5 | odd | 6 | inner | ||
1470.3.f.d.391.9 | 16 | 35.17 | even | 12 | |||
1470.3.f.d.391.15 | 16 | 35.32 | odd | 12 |