Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(451,1050)]
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, 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("1050.451");
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.p (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 92 x^{14} - 112 x^{13} + 5846 x^{12} - 7728 x^{11} + 197216 x^{10} - 298200 x^{9} + \cdots + 101626561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{4}\cdot 7 \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 901.6 | ||
Root | \(-2.63284 - 4.56021i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.901 |
Dual form | 1050.3.p.i.451.6 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 1.22474i | 0.353553 | − | 0.612372i | ||||
\(3\) | 1.50000 | − | 0.866025i | 0.500000 | − | 0.288675i | ||||
\(4\) | −1.00000 | − | 1.73205i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 2.44949i | − | 0.408248i | ||||||
\(7\) | −1.94434 | − | 6.72455i | −0.277762 | − | 0.960650i | ||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.263223 | + | 0.455915i | 0.0239293 | + | 0.0414468i | 0.877742 | − | 0.479133i | \(-0.159049\pi\) |
−0.853813 | + | 0.520580i | \(0.825716\pi\) | |||||||
\(12\) | −3.00000 | − | 1.73205i | −0.250000 | − | 0.144338i | ||||
\(13\) | − | 4.22307i | − | 0.324851i | −0.986721 | − | 0.162426i | \(-0.948068\pi\) | ||
0.986721 | − | 0.162426i | \(-0.0519318\pi\) | |||||||
\(14\) | −9.61071 | − | 2.37366i | −0.686479 | − | 0.169547i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.125000 | + | 0.216506i | ||||
\(17\) | 28.8825 | − | 16.6753i | 1.69897 | − | 0.980900i | 0.752228 | − | 0.658903i | \(-0.228979\pi\) |
0.946741 | − | 0.321997i | \(-0.104354\pi\) | |||||||
\(18\) | −2.12132 | − | 3.67423i | −0.117851 | − | 0.204124i | ||||
\(19\) | 2.75133 | + | 1.58848i | 0.144807 | + | 0.0836044i | 0.570653 | − | 0.821191i | \(-0.306690\pi\) |
−0.425846 | + | 0.904796i | \(0.640023\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.74014 | − | 8.40298i | −0.416197 | − | 0.400142i | ||||
\(22\) | 0.744507 | 0.0338412 | ||||||||
\(23\) | 5.52954 | − | 9.57744i | 0.240415 | − | 0.416410i | −0.720418 | − | 0.693540i | \(-0.756050\pi\) |
0.960832 | + | 0.277130i | \(0.0893832\pi\) | |||||||
\(24\) | −4.24264 | + | 2.44949i | −0.176777 | + | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.17218 | − | 2.98616i | −0.198930 | − | 0.114852i | ||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | −9.70292 | + | 10.0922i | −0.346533 | + | 0.360437i | ||||
\(29\) | −56.1302 | −1.93552 | −0.967762 | − | 0.251866i | \(-0.918956\pi\) | ||||
−0.967762 | + | 0.251866i | \(0.918956\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.63817 | + | 0.945800i | −0.0528443 | + | 0.0305097i | −0.526189 | − | 0.850367i | \(-0.676380\pi\) |
0.473345 | + | 0.880877i | \(0.343046\pi\) | |||||||
\(32\) | 2.82843 | + | 4.89898i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0.789668 | + | 0.455915i | 0.0239293 | + | 0.0138156i | ||||
\(34\) | − | 47.1649i | − | 1.38720i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | −4.87682 | + | 8.44690i | −0.131806 | + | 0.228294i | −0.924373 | − | 0.381491i | \(-0.875411\pi\) |
0.792567 | + | 0.609785i | \(0.208744\pi\) | |||||||
\(38\) | 3.89097 | − | 2.24645i | 0.102394 | − | 0.0591172i | ||||
\(39\) | −3.65729 | − | 6.33460i | −0.0937765 | − | 0.162426i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.07377i | − | 0.0993603i | −0.998765 | − | 0.0496802i | \(-0.984180\pi\) | ||
0.998765 | − | 0.0496802i | \(-0.0158202\pi\) | |||||||
\(42\) | −16.4717 | + | 4.76263i | −0.392184 | + | 0.113396i | ||||
\(43\) | −46.3519 | −1.07795 | −0.538975 | − | 0.842322i | \(-0.681188\pi\) | ||||
−0.538975 | + | 0.842322i | \(0.681188\pi\) | |||||||
\(44\) | 0.526446 | − | 0.911831i | 0.0119647 | − | 0.0207234i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.81995 | − | 13.5445i | −0.169999 | − | 0.294447i | ||||
\(47\) | −54.7969 | − | 31.6370i | −1.16589 | − | 0.673127i | −0.213182 | − | 0.977012i | \(-0.568383\pi\) |
−0.952709 | + | 0.303885i | \(0.901716\pi\) | |||||||
\(48\) | 6.92820i | 0.144338i | ||||||||
\(49\) | −41.4391 | + | 26.1496i | −0.845696 | + | 0.533665i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 28.8825 | − | 50.0259i | 0.566323 | − | 0.980900i | ||||
\(52\) | −7.31457 | + | 4.22307i | −0.140665 | + | 0.0812129i | ||||
\(53\) | −23.2606 | − | 40.2885i | −0.438878 | − | 0.760160i | 0.558725 | − | 0.829353i | \(-0.311291\pi\) |
−0.997603 | + | 0.0691934i | \(0.977957\pi\) | |||||||
\(54\) | −6.36396 | − | 3.67423i | −0.117851 | − | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 5.49942 | + | 19.0199i | 0.0982038 | + | 0.339641i | ||||
\(57\) | 5.50267 | 0.0965380 | ||||||||
\(58\) | −39.6900 | + | 68.7452i | −0.684311 | + | 1.18526i | ||||
\(59\) | −43.7614 | + | 25.2657i | −0.741719 | + | 0.428231i | −0.822694 | − | 0.568485i | \(-0.807530\pi\) |
0.0809752 | + | 0.996716i | \(0.474197\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 89.4583 | + | 51.6488i | 1.46653 | + | 0.846702i | 0.999299 | − | 0.0374335i | \(-0.0119182\pi\) |
0.467231 | + | 0.884135i | \(0.345252\pi\) | |||||||
\(62\) | 2.67513i | 0.0431472i | ||||||||
\(63\) | −20.3874 | − | 5.03529i | −0.323609 | − | 0.0799252i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.11676 | − | 0.644762i | 0.0169206 | − | 0.00976912i | ||||
\(67\) | 4.36948 | + | 7.56816i | 0.0652161 | + | 0.112958i | 0.896790 | − | 0.442457i | \(-0.145893\pi\) |
−0.831574 | + | 0.555414i | \(0.812560\pi\) | |||||||
\(68\) | −57.7649 | − | 33.3506i | −0.849484 | − | 0.490450i | ||||
\(69\) | − | 19.1549i | − | 0.277607i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 29.0608 | 0.409307 | 0.204653 | − | 0.978835i | \(-0.434393\pi\) | ||||
0.204653 | + | 0.978835i | \(0.434393\pi\) | |||||||
\(72\) | −4.24264 | + | 7.34847i | −0.0589256 | + | 0.102062i | ||||
\(73\) | −14.4912 | + | 8.36647i | −0.198509 | + | 0.114609i | −0.595960 | − | 0.803014i | \(-0.703228\pi\) |
0.397451 | + | 0.917623i | \(0.369895\pi\) | |||||||
\(74\) | 6.89686 | + | 11.9457i | 0.0932008 | + | 0.161429i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 6.35393i | − | 0.0836044i | ||||||
\(77\) | 2.55403 | − | 2.65651i | 0.0331692 | − | 0.0345001i | ||||
\(78\) | −10.3444 | −0.132620 | ||||||||
\(79\) | 66.1473 | − | 114.571i | 0.837308 | − | 1.45026i | −0.0548297 | − | 0.998496i | \(-0.517462\pi\) |
0.892137 | − | 0.451764i | \(-0.149205\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −4.98933 | − | 2.88059i | −0.0608455 | − | 0.0351292i | ||||
\(83\) | 12.4838i | 0.150407i | 0.997168 | + | 0.0752033i | \(0.0239606\pi\) | ||||
−0.997168 | + | 0.0752033i | \(0.976039\pi\) | |||||||
\(84\) | −5.81425 | + | 23.5413i | −0.0692173 | + | 0.280254i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −32.7757 | + | 56.7692i | −0.381113 | + | 0.660107i | ||||
\(87\) | −84.1953 | + | 48.6102i | −0.967762 | + | 0.558738i | ||||
\(88\) | −0.744507 | − | 1.28952i | −0.00846030 | − | 0.0146537i | ||||
\(89\) | −59.1101 | − | 34.1272i | −0.664158 | − | 0.383452i | 0.129701 | − | 0.991553i | \(-0.458598\pi\) |
−0.793860 | + | 0.608101i | \(0.791931\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −28.3982 | + | 8.21107i | −0.312068 | + | 0.0902315i | ||||
\(92\) | −22.1182 | −0.240415 | ||||||||
\(93\) | −1.63817 | + | 2.83740i | −0.0176148 | + | 0.0305097i | ||||
\(94\) | −77.4945 | + | 44.7415i | −0.824409 | + | 0.475973i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 8.48528 | + | 4.89898i | 0.0883883 | + | 0.0510310i | ||||
\(97\) | − | 149.281i | − | 1.53898i | −0.638659 | − | 0.769490i | \(-0.720510\pi\) | ||
0.638659 | − | 0.769490i | \(-0.279490\pi\) | |||||||
\(98\) | 2.72468 | + | 69.2429i | 0.0278029 | + | 0.706560i | ||||
\(99\) | 1.57934 | 0.0159529 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 83.7839 | − | 48.3726i | 0.829543 | − | 0.478937i | −0.0241531 | − | 0.999708i | \(-0.507689\pi\) |
0.853696 | + | 0.520771i | \(0.174356\pi\) | |||||||
\(102\) | −40.8460 | − | 70.7473i | −0.400451 | − | 0.693601i | ||||
\(103\) | −90.7268 | − | 52.3811i | −0.880843 | − | 0.508555i | −0.00990642 | − | 0.999951i | \(-0.503153\pi\) |
−0.870936 | + | 0.491396i | \(0.836487\pi\) | |||||||
\(104\) | 11.9446i | 0.114852i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −65.7908 | −0.620668 | ||||||||
\(107\) | −62.3022 | + | 107.911i | −0.582263 | + | 1.00851i | 0.412947 | + | 0.910755i | \(0.364499\pi\) |
−0.995211 | + | 0.0977548i | \(0.968834\pi\) | |||||||
\(108\) | −9.00000 | + | 5.19615i | −0.0833333 | + | 0.0481125i | ||||
\(109\) | −42.3042 | − | 73.2731i | −0.388112 | − | 0.672230i | 0.604083 | − | 0.796921i | \(-0.293539\pi\) |
−0.992196 | + | 0.124691i | \(0.960206\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 16.8938i | 0.152196i | ||||||||
\(112\) | 27.1832 | + | 6.71372i | 0.242707 | + | 0.0599439i | ||||
\(113\) | 116.241 | 1.02868 | 0.514340 | − | 0.857586i | \(-0.328037\pi\) | ||||
0.514340 | + | 0.857586i | \(0.328037\pi\) | |||||||
\(114\) | 3.89097 | − | 6.73936i | 0.0341313 | − | 0.0591172i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 56.1302 | + | 97.2204i | 0.483881 | + | 0.838107i | ||||
\(117\) | −10.9719 | − | 6.33460i | −0.0937765 | − | 0.0541419i | ||||
\(118\) | 71.4621i | 0.605611i | ||||||||
\(119\) | −168.291 | − | 161.799i | −1.41421 | − | 1.35966i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 60.3614 | − | 104.549i | 0.498855 | − | 0.864042i | ||||
\(122\) | 126.513 | − | 73.0424i | 1.03699 | − | 0.598708i | ||||
\(123\) | −3.52799 | − | 6.11066i | −0.0286829 | − | 0.0496802i | ||||
\(124\) | 3.27635 | + | 1.89160i | 0.0264222 | + | 0.0152548i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −20.5830 | + | 21.4089i | −0.163357 | + | 0.169912i | ||||
\(127\) | 81.3744 | 0.640743 | 0.320372 | − | 0.947292i | \(-0.396192\pi\) | ||||
0.320372 | + | 0.947292i | \(0.396192\pi\) | |||||||
\(128\) | 5.65685 | − | 9.79796i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −69.5278 | + | 40.1419i | −0.538975 | + | 0.311178i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 208.389 | + | 120.313i | 1.59075 | + | 0.918421i | 0.993178 | + | 0.116608i | \(0.0372020\pi\) |
0.597574 | + | 0.801814i | \(0.296131\pi\) | |||||||
\(132\) | − | 1.82366i | − | 0.0138156i | ||||||
\(133\) | 5.33231 | − | 21.5900i | 0.0400926 | − | 0.162331i | ||||
\(134\) | 12.3588 | 0.0922295 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −81.6919 | + | 47.1649i | −0.600676 | + | 0.346800i | ||||
\(137\) | 116.831 | + | 202.357i | 0.852778 | + | 1.47706i | 0.878691 | + | 0.477391i | \(0.158418\pi\) |
−0.0259125 | + | 0.999664i | \(0.508249\pi\) | |||||||
\(138\) | −23.4598 | − | 13.5445i | −0.169999 | − | 0.0981489i | ||||
\(139\) | 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 | ||||||||
\(142\) | 20.5491 | − | 35.5920i | 0.144712 | − | 0.250648i | ||||
\(143\) | 1.92536 | − | 1.11161i | 0.0134641 | − | 0.00777348i | ||||
\(144\) | 6.00000 | + | 10.3923i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 23.6640i | 0.162082i | ||||||||
\(147\) | −39.5125 | + | 75.1117i | −0.268792 | + | 0.510964i | ||||
\(148\) | 19.5073 | 0.131806 | ||||||||
\(149\) | −72.0402 | + | 124.777i | −0.483491 | + | 0.837431i | −0.999820 | − | 0.0189590i | \(-0.993965\pi\) |
0.516329 | + | 0.856390i | \(0.327298\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −46.7563 | − | 80.9842i | −0.309644 | − | 0.536319i | 0.668640 | − | 0.743586i | \(-0.266877\pi\) |
−0.978285 | + | 0.207267i | \(0.933543\pi\) | |||||||
\(152\) | −7.78195 | − | 4.49291i | −0.0511970 | − | 0.0295586i | ||||
\(153\) | − | 100.052i | − | 0.653933i | ||||||
\(154\) | −1.44757 | − | 5.00647i | −0.00939982 | − | 0.0325095i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7.31457 | + | 12.6692i | −0.0468883 | + | 0.0812129i | ||||
\(157\) | 148.286 | − | 85.6127i | 0.944494 | − | 0.545304i | 0.0531280 | − | 0.998588i | \(-0.483081\pi\) |
0.891366 | + | 0.453284i | \(0.149748\pi\) | |||||||
\(158\) | −93.5464 | − | 162.027i | −0.592066 | − | 1.02549i | ||||
\(159\) | −69.7817 | − | 40.2885i | −0.438878 | − | 0.253387i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −75.1553 | − | 18.5619i | −0.466803 | − | 0.115291i | ||||
\(162\) | −12.7279 | −0.0785674 | ||||||||
\(163\) | 46.5064 | − | 80.5515i | 0.285316 | − | 0.494181i | −0.687370 | − | 0.726307i | \(-0.741235\pi\) |
0.972686 | + | 0.232126i | \(0.0745682\pi\) | |||||||
\(164\) | −7.05598 | + | 4.07377i | −0.0430243 | + | 0.0248401i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.2894 | + | 8.82735i | 0.0921049 | + | 0.0531768i | ||||
\(167\) | 104.991i | 0.628688i | 0.949309 | + | 0.314344i | \(0.101784\pi\) | ||||
−0.949309 | + | 0.314344i | \(0.898216\pi\) | |||||||
\(168\) | 24.7208 | + | 23.7672i | 0.147148 | + | 0.141471i | ||||
\(169\) | 151.166 | 0.894472 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.25400 | − | 4.76545i | 0.0482690 | − | 0.0278681i | ||||
\(172\) | 46.3519 | + | 80.2838i | 0.269488 | + | 0.466766i | ||||
\(173\) | −176.805 | − | 102.079i | −1.02200 | − | 0.590049i | −0.107314 | − | 0.994225i | \(-0.534225\pi\) |
−0.914681 | + | 0.404176i | \(0.867558\pi\) | |||||||
\(174\) | 137.490i | 0.790174i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.10578 | −0.0119647 | ||||||||
\(177\) | −43.7614 | + | 75.7970i | −0.247240 | + | 0.428231i | ||||
\(178\) | −83.5943 | + | 48.2632i | −0.469631 | + | 0.271141i | ||||
\(179\) | 97.9495 | + | 169.653i | 0.547204 | + | 0.947785i | 0.998465 | + | 0.0553926i | \(0.0176410\pi\) |
−0.451261 | + | 0.892392i | \(0.649026\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 119.031i | − | 0.657632i | −0.944394 | − | 0.328816i | \(-0.893350\pi\) | ||
0.944394 | − | 0.328816i | \(-0.106650\pi\) | |||||||
\(182\) | −10.0241 | + | 40.5867i | −0.0550776 | + | 0.223004i | ||||
\(183\) | 178.917 | 0.977687 | ||||||||
\(184\) | −15.6399 | + | 27.0891i | −0.0849994 | + | 0.147223i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.31673 | + | 4.01269i | 0.0124555 | + | 0.0215736i | ||||
\(187\) | 15.2050 | + | 8.77864i | 0.0813104 | + | 0.0469446i | ||||
\(188\) | 126.548i | 0.673127i | ||||||||
\(189\) | −34.9418 | + | 10.1031i | −0.184877 | + | 0.0534554i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 32.8657 | − | 56.9250i | 0.172072 | − | 0.298037i | −0.767072 | − | 0.641561i | \(-0.778287\pi\) |
0.939144 | + | 0.343524i | \(0.111621\pi\) | |||||||
\(192\) | 12.0000 | − | 6.92820i | 0.0625000 | − | 0.0360844i | ||||
\(193\) | −48.4350 | − | 83.8919i | −0.250959 | − | 0.434673i | 0.712831 | − | 0.701335i | \(-0.247412\pi\) |
−0.963790 | + | 0.266662i | \(0.914079\pi\) | |||||||
\(194\) | −182.831 | − | 105.558i | −0.942429 | − | 0.544112i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 86.7315 | + | 45.6251i | 0.442508 | + | 0.232781i | ||||
\(197\) | −186.672 | −0.947574 | −0.473787 | − | 0.880640i | \(-0.657113\pi\) | ||||
−0.473787 | + | 0.880640i | \(0.657113\pi\) | |||||||
\(198\) | 1.11676 | − | 1.93428i | 0.00564020 | − | 0.00976912i | ||||
\(199\) | 99.8454 | − | 57.6458i | 0.501736 | − | 0.289677i | −0.227694 | − | 0.973733i | \(-0.573119\pi\) |
0.729430 | + | 0.684055i | \(0.239785\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.1084 | + | 7.56816i | 0.0652161 | + | 0.0376525i | ||||
\(202\) | − | 136.818i | − | 0.677319i | ||||||
\(203\) | 109.136 | + | 377.450i | 0.537616 | + | 1.85936i | ||||
\(204\) | −115.530 | −0.566323 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −128.307 | + | 74.0781i | −0.622850 | + | 0.359602i | ||||
\(207\) | −16.5886 | − | 28.7323i | −0.0801382 | − | 0.138803i | ||||
\(208\) | 14.6291 | + | 8.44614i | 0.0703324 | + | 0.0406064i | ||||
\(209\) | 1.67250i | 0.00800239i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 139.433 | 0.660819 | 0.330409 | − | 0.943838i | \(-0.392813\pi\) | ||||
0.330409 | + | 0.943838i | \(0.392813\pi\) | |||||||
\(212\) | −46.5211 | + | 80.5769i | −0.219439 | + | 0.380080i | ||||
\(213\) | 43.5912 | − | 25.1674i | 0.204653 | − | 0.118157i | ||||
\(214\) | 88.1086 | + | 152.609i | 0.411722 | + | 0.713124i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 14.6969i | 0.0680414i | ||||||||
\(217\) | 9.54524 | + | 9.17703i | 0.0439873 | + | 0.0422905i | ||||
\(218\) | −119.654 | −0.548874 | ||||||||
\(219\) | −14.4912 | + | 25.0994i | −0.0661697 | + | 0.114609i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −70.4209 | − | 121.973i | −0.318647 | − | 0.551912i | ||||
\(222\) | 20.6906 | + | 11.9457i | 0.0932008 | + | 0.0538095i | ||||
\(223\) | − | 258.055i | − | 1.15720i | −0.815612 | − | 0.578599i | \(-0.803600\pi\) | ||
0.815612 | − | 0.578599i | \(-0.196400\pi\) | |||||||
\(224\) | 27.4440 | − | 28.5452i | 0.122518 | − | 0.127434i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 82.1947 | − | 142.365i | 0.363693 | − | 0.629935i | ||||
\(227\) | −286.682 | + | 165.516i | −1.26292 | + | 0.729146i | −0.973638 | − | 0.228099i | \(-0.926749\pi\) |
−0.289280 | + | 0.957245i | \(0.593416\pi\) | |||||||
\(228\) | −5.50267 | − | 9.53090i | −0.0241345 | − | 0.0418022i | ||||
\(229\) | 211.516 | + | 122.119i | 0.923653 | + | 0.533271i | 0.884799 | − | 0.465974i | \(-0.154296\pi\) |
0.0388541 | + | 0.999245i | \(0.487629\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.53044 | − | 6.19662i | 0.00662529 | − | 0.0268252i | ||||
\(232\) | 158.760 | 0.684311 | ||||||||
\(233\) | 105.745 | − | 183.155i | 0.453840 | − | 0.786074i | −0.544781 | − | 0.838579i | \(-0.683387\pi\) |
0.998621 | + | 0.0525044i | \(0.0167204\pi\) | |||||||
\(234\) | −15.5165 | + | 8.95848i | −0.0663100 | + | 0.0382841i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 87.5228 | + | 50.5313i | 0.370859 | + | 0.214116i | ||||
\(237\) | − | 229.141i | − | 0.966840i | ||||||
\(238\) | −317.162 | + | 91.7044i | −1.33262 | + | 0.385313i | ||||
\(239\) | 344.134 | 1.43989 | 0.719946 | − | 0.694030i | \(-0.244167\pi\) | ||||
0.719946 | + | 0.694030i | \(0.244167\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −148.392 | + | 85.6742i | −0.615735 | + | 0.355495i | −0.775207 | − | 0.631708i | \(-0.782354\pi\) |
0.159472 | + | 0.987203i | \(0.449021\pi\) | |||||||
\(242\) | −85.3639 | − | 147.855i | −0.352744 | − | 0.610970i | ||||
\(243\) | −13.5000 | − | 7.79423i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | − | 206.595i | − | 0.846702i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −9.97867 | −0.0405637 | ||||||||
\(247\) | 6.70827 | − | 11.6191i | 0.0271590 | − | 0.0470408i | ||||
\(248\) | 4.63346 | − | 2.67513i | 0.0186833 | − | 0.0107868i | ||||
\(249\) | 10.8112 | + | 18.7256i | 0.0434187 | + | 0.0752033i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 327.538i | − | 1.30493i | −0.757818 | − | 0.652467i | \(-0.773734\pi\) | ||
0.757818 | − | 0.652467i | \(-0.226266\pi\) | |||||||
\(252\) | 11.6660 | + | 40.3473i | 0.0462937 | + | 0.160108i | ||||
\(253\) | 5.82200 | 0.0230119 | ||||||||
\(254\) | 57.5404 | − | 99.6629i | 0.226537 | − | 0.392374i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 190.836 | + | 110.179i | 0.742552 | + | 0.428713i | 0.822997 | − | 0.568046i | \(-0.192301\pi\) |
−0.0804442 | + | 0.996759i | \(0.525634\pi\) | |||||||
\(258\) | 113.538i | 0.440072i | ||||||||
\(259\) | 66.2837 | + | 16.3708i | 0.255922 | + | 0.0632077i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −84.1953 | + | 145.831i | −0.322587 | + | 0.558738i | ||||
\(262\) | 294.706 | − | 170.149i | 1.12483 | − | 0.649422i | ||||
\(263\) | 66.5976 | + | 115.350i | 0.253223 | + | 0.438594i | 0.964411 | − | 0.264407i | \(-0.0851761\pi\) |
−0.711189 | + | 0.703001i | \(0.751843\pi\) | |||||||
\(264\) | −2.23352 | − | 1.28952i | −0.00846030 | − | 0.00488456i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −22.6718 | − | 21.7972i | −0.0852322 | − | 0.0819443i | ||||
\(267\) | −118.220 | −0.442772 | ||||||||
\(268\) | 8.73896 | − | 15.1363i | 0.0326080 | − | 0.0564788i | ||||
\(269\) | −22.9633 | + | 13.2578i | −0.0853653 | + | 0.0492857i | −0.542075 | − | 0.840330i | \(-0.682361\pi\) |
0.456710 | + | 0.889616i | \(0.349028\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −92.6776 | − | 53.5074i | −0.341984 | − | 0.197444i | 0.319165 | − | 0.947699i | \(-0.396598\pi\) |
−0.661149 | + | 0.750255i | \(0.729931\pi\) | |||||||
\(272\) | 133.402i | 0.490450i | ||||||||
\(273\) | −35.4864 | + | 36.9102i | −0.129987 | + | 0.135202i | ||||
\(274\) | 330.447 | 1.20601 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −33.1772 | + | 19.1549i | −0.120207 | + | 0.0694017i | ||||
\(277\) | 220.191 | + | 381.381i | 0.794912 | + | 1.37683i | 0.922895 | + | 0.385052i | \(0.125816\pi\) |
−0.127983 | + | 0.991776i | \(0.540850\pi\) | |||||||
\(278\) | 259.023 | + | 149.547i | 0.931737 | + | 0.537939i | ||||
\(279\) | 5.67480i | 0.0203398i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 322.069 | 1.14615 | 0.573076 | − | 0.819502i | \(-0.305750\pi\) | ||||
0.573076 | + | 0.819502i | \(0.305750\pi\) | |||||||
\(282\) | −77.4945 | + | 134.224i | −0.274803 | + | 0.475973i | ||||
\(283\) | 59.3514 | − | 34.2665i | 0.209722 | − | 0.121083i | −0.391460 | − | 0.920195i | \(-0.628030\pi\) |
0.601182 | + | 0.799112i | \(0.294697\pi\) | |||||||
\(284\) | −29.0608 | − | 50.3347i | −0.102327 | − | 0.177235i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 3.14410i | − | 0.0109934i | ||||||
\(287\) | −27.3943 | + | 7.92079i | −0.0954505 | + | 0.0275986i | ||||
\(288\) | 16.9706 | 0.0589256 | ||||||||
\(289\) | 411.631 | − | 712.966i | 1.42433 | − | 2.46701i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −129.281 | − | 223.922i | −0.444265 | − | 0.769490i | ||||
\(292\) | 28.9823 | + | 16.7329i | 0.0992545 | + | 0.0573046i | ||||
\(293\) | − | 147.510i | − | 0.503448i | −0.967799 | − | 0.251724i | \(-0.919003\pi\) | ||
0.967799 | − | 0.251724i | \(-0.0809975\pi\) | |||||||
\(294\) | 64.0531 | + | 101.505i | 0.217868 | + | 0.345254i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 13.7937 | − | 23.8914i | 0.0466004 | − | 0.0807143i | ||||
\(297\) | 2.36901 | − | 1.36775i | 0.00797645 | − | 0.00460521i | ||||
\(298\) | 101.880 | + | 176.462i | 0.341880 | + | 0.592153i | ||||
\(299\) | −40.4462 | − | 23.3516i | −0.135272 | − | 0.0780991i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 90.1237 | + | 311.695i | 0.299414 | + | 1.03553i | ||||
\(302\) | −132.247 | −0.437903 | ||||||||
\(303\) | 83.7839 | − | 145.118i | 0.276514 | − | 0.478937i | ||||
\(304\) | −11.0053 | + | 6.35393i | −0.0362018 | + | 0.0209011i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −122.538 | − | 70.7473i | −0.400451 | − | 0.231200i | ||||
\(307\) | − | 376.010i | − | 1.22479i | −0.790553 | − | 0.612394i | \(-0.790207\pi\) | ||
0.790553 | − | 0.612394i | \(-0.209793\pi\) | |||||||
\(308\) | −7.15524 | − | 1.76720i | −0.0232313 | − | 0.00573767i | ||||
\(309\) | −181.454 | −0.587228 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −337.599 | + | 194.913i | −1.08553 | + | 0.626730i | −0.932383 | − | 0.361473i | \(-0.882274\pi\) |
−0.153146 | + | 0.988204i | \(0.548941\pi\) | |||||||
\(312\) | 10.3444 | + | 17.9170i | 0.0331550 | + | 0.0574262i | ||||
\(313\) | 123.890 | + | 71.5282i | 0.395816 | + | 0.228524i | 0.684677 | − | 0.728847i | \(-0.259943\pi\) |
−0.288861 | + | 0.957371i | \(0.593277\pi\) | |||||||
\(314\) | − | 242.149i | − | 0.771176i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −264.589 | −0.837308 | ||||||||
\(317\) | 192.222 | − | 332.938i | 0.606378 | − | 1.05028i | −0.385454 | − | 0.922727i | \(-0.625955\pi\) |
0.991832 | − | 0.127551i | \(-0.0407117\pi\) | |||||||
\(318\) | −98.6862 | + | 56.9765i | −0.310334 | + | 0.179171i | ||||
\(319\) | −14.7747 | − | 25.5906i | −0.0463158 | − | 0.0802214i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 215.821i | 0.672340i | ||||||||
\(322\) | −75.8764 | + | 78.9208i | −0.235641 | + | 0.245096i | ||||
\(323\) | 105.954 | 0.328030 | ||||||||
\(324\) | −9.00000 | + | 15.5885i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −65.7700 | − | 113.917i | −0.201749 | − | 0.349439i | ||||
\(327\) | −126.913 | − | 73.2731i | −0.388112 | − | 0.224077i | ||||
\(328\) | 11.5224i | 0.0351292i | ||||||||
\(329\) | −106.201 | + | 429.997i | −0.322799 | + | 1.30698i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −96.9539 | + | 167.929i | −0.292912 | + | 0.507338i | −0.974497 | − | 0.224400i | \(-0.927958\pi\) |
0.681585 | + | 0.731739i | \(0.261291\pi\) | |||||||
\(332\) | 21.6225 | − | 12.4838i | 0.0651280 | − | 0.0376017i | ||||
\(333\) | 14.6305 | + | 25.3407i | 0.0439353 | + | 0.0760982i | ||||
\(334\) | 128.587 | + | 74.2397i | 0.384991 | + | 0.222275i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 46.5890 | − | 13.4708i | 0.138658 | − | 0.0400916i | ||||
\(337\) | −125.477 | −0.372337 | −0.186168 | − | 0.982518i | \(-0.559607\pi\) | ||||
−0.186168 | + | 0.982518i | \(0.559607\pi\) | |||||||
\(338\) | 106.890 | − | 185.139i | 0.316243 | − | 0.547750i | ||||
\(339\) | 174.361 | − | 100.668i | 0.514340 | − | 0.296954i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.862410 | − | 0.497912i | −0.00252906 | − | 0.00146015i | ||||
\(342\) | − | 13.4787i | − | 0.0394115i | ||||||
\(343\) | 256.416 | + | 227.816i | 0.747568 | + | 0.664186i | ||||
\(344\) | 131.103 | 0.381113 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −250.040 | + | 144.361i | −0.722660 | + | 0.417228i | ||||
\(347\) | −251.798 | − | 436.128i | −0.725644 | − | 1.25685i | −0.958708 | − | 0.284391i | \(-0.908209\pi\) |
0.233065 | − | 0.972461i | \(-0.425125\pi\) | |||||||
\(348\) | 168.391 | + | 97.2204i | 0.483881 | + | 0.279369i | ||||
\(349\) | − | 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 | ||||||||
\(352\) | −1.48901 | + | 2.57905i | −0.00423015 | + | 0.00732684i | ||||
\(353\) | −28.5012 | + | 16.4552i | −0.0807399 | + | 0.0466152i | −0.539826 | − | 0.841776i | \(-0.681510\pi\) |
0.459087 | + | 0.888392i | \(0.348177\pi\) | |||||||
\(354\) | 61.8880 | + | 107.193i | 0.174825 | + | 0.302805i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 136.509i | 0.383452i | ||||||||
\(357\) | −392.559 | − | 96.9543i | −1.09960 | − | 0.271581i | ||||
\(358\) | 277.043 | 0.773863 | ||||||||
\(359\) | −133.898 | + | 231.919i | −0.372976 | + | 0.646013i | −0.990022 | − | 0.140914i | \(-0.954996\pi\) |
0.617046 | + | 0.786927i | \(0.288329\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −175.453 | − | 303.894i | −0.486021 | − | 0.841812i | ||||
\(362\) | −145.783 | − | 84.1679i | −0.402716 | − | 0.232508i | ||||
\(363\) | − | 209.098i | − | 0.576028i | ||||||
\(364\) | 42.6202 | + | 40.9761i | 0.117089 | + | 0.112572i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 126.513 | − | 219.127i | 0.345665 | − | 0.598708i | ||||
\(367\) | 137.458 | − | 79.3613i | 0.374545 | − | 0.216243i | −0.300897 | − | 0.953657i | \(-0.597286\pi\) |
0.675442 | + | 0.737413i | \(0.263953\pi\) | |||||||
\(368\) | 22.1182 | + | 38.3098i | 0.0601037 | + | 0.104103i | ||||
\(369\) | −10.5840 | − | 6.11066i | −0.0286829 | − | 0.0165601i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −225.695 | + | 234.751i | −0.608343 | + | 0.632752i | ||||
\(372\) | 6.55270 | 0.0176148 | ||||||||
\(373\) | 207.172 | − | 358.832i | 0.555421 | − | 0.962017i | −0.442450 | − | 0.896793i | \(-0.645891\pi\) |
0.997871 | − | 0.0652235i | \(-0.0207760\pi\) | |||||||
\(374\) | 21.5032 | − | 12.4149i | 0.0574951 | − | 0.0331948i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 154.989 | + | 89.4829i | 0.412205 | + | 0.237986i | ||||
\(377\) | 237.042i | 0.628758i | ||||||||
\(378\) | −12.3339 | + | 49.9387i | −0.0326293 | + | 0.132113i | ||||
\(379\) | −72.8000 | −0.192084 | −0.0960422 | − | 0.995377i | \(-0.530618\pi\) | ||||
−0.0960422 | + | 0.995377i | \(0.530618\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 122.062 | − | 70.4723i | 0.320372 | − | 0.184967i | ||||
\(382\) | −46.4791 | − | 80.5042i | −0.121673 | − | 0.210744i | ||||
\(383\) | 246.830 | + | 142.507i | 0.644464 | + | 0.372082i | 0.786332 | − | 0.617804i | \(-0.211977\pi\) |
−0.141868 | + | 0.989886i | \(0.545311\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −136.995 | −0.354909 | ||||||||
\(387\) | −69.5278 | + | 120.426i | −0.179658 | + | 0.311178i | ||||
\(388\) | −258.562 | + | 149.281i | −0.666398 | + | 0.384745i | ||||
\(389\) | 48.5692 | + | 84.1242i | 0.124856 | + | 0.216258i | 0.921677 | − | 0.387959i | \(-0.126820\pi\) |
−0.796820 | + | 0.604216i | \(0.793486\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 368.827i | − | 0.943291i | ||||||
\(392\) | 117.207 | − | 73.9622i | 0.298999 | − | 0.188679i | ||||
\(393\) | 416.777 | 1.06050 | ||||||||
\(394\) | −131.997 | + | 228.626i | −0.335018 | + | 0.580268i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.57934 | − | 2.73549i | −0.00398822 | − | 0.00690781i | ||||
\(397\) | 685.636 | + | 395.852i | 1.72704 | + | 0.997108i | 0.901520 | + | 0.432737i | \(0.142452\pi\) |
0.825522 | + | 0.564371i | \(0.190881\pi\) | |||||||
\(398\) | − | 163.047i | − | 0.409665i | ||||||
\(399\) | −10.6990 | − | 37.0030i | −0.0268146 | − | 0.0927392i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −251.613 | + | 435.807i | −0.627464 | + | 1.08680i | 0.360594 | + | 0.932723i | \(0.382574\pi\) |
−0.988059 | + | 0.154077i | \(0.950759\pi\) | |||||||
\(402\) | 18.5381 | − | 10.7030i | 0.0461147 | − | 0.0266244i | ||||
\(403\) | 3.99418 | + | 6.91812i | 0.00991112 | + | 0.0171666i | ||||
\(404\) | −167.568 | − | 96.7453i | −0.414772 | − | 0.239468i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 539.451 | + | 133.234i | 1.32870 | + | 0.328162i | ||||
\(407\) | −5.13476 | −0.0126161 | ||||||||
\(408\) | −81.6919 | + | 141.495i | −0.200225 | + | 0.346800i | ||||
\(409\) | 649.395 | − | 374.928i | 1.58776 | − | 0.916696i | 0.594088 | − | 0.804400i | \(-0.297513\pi\) |
0.993675 | − | 0.112296i | \(-0.0358204\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 350.492 | + | 202.357i | 0.852778 | + | 0.492352i | ||||
\(412\) | 209.525i | 0.508555i | ||||||||
\(413\) | 254.987 | + | 245.151i | 0.617402 | + | 0.593585i | ||||
\(414\) | −46.9197 | −0.113333 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 20.6887 | − | 11.9446i | 0.0497325 | − | 0.0287131i | ||||
\(417\) | 183.157 | + | 317.237i | 0.439225 | + | 0.760760i | ||||
\(418\) | 2.04839 | + | 1.18264i | 0.00490044 | + | 0.00282927i | ||||
\(419\) | 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 | \(0.365214\pi\) | |||||||
\(422\) | 98.5939 | − | 170.770i | 0.233635 | − | 0.404667i | ||||
\(423\) | −164.391 | + | 94.9110i | −0.388630 | + | 0.224376i | ||||
\(424\) | 65.7908 | + | 113.953i | 0.155167 | + | 0.268757i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 71.1841i | − | 0.167099i | ||||||
\(427\) | 173.378 | − | 701.990i | 0.406037 | − | 1.64400i | ||||
\(428\) | 249.209 | 0.582263 | ||||||||
\(429\) | 1.92536 | − | 3.33482i | 0.00448802 | − | 0.00777348i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −247.300 | − | 428.336i | −0.573782 | − | 0.993819i | −0.996173 | − | 0.0874056i | \(-0.972142\pi\) |
0.422391 | − | 0.906414i | \(-0.361191\pi\) | |||||||
\(432\) | 18.0000 | + | 10.3923i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | 730.022i | 1.68596i | 0.537943 | + | 0.842981i | \(0.319201\pi\) | ||||
−0.537943 | + | 0.842981i | \(0.680799\pi\) | |||||||
\(434\) | 17.9890 | − | 5.20135i | 0.0414494 | − | 0.0119847i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −84.6085 | + | 146.546i | −0.194056 | + | 0.336115i | ||||
\(437\) | 30.4272 | − | 17.5672i | 0.0696275 | − | 0.0401994i | ||||
\(438\) | 20.4936 | + | 35.4959i | 0.0467890 | + | 0.0810410i | ||||
\(439\) | −321.631 | − | 185.694i | −0.732645 | − | 0.422993i | 0.0867437 | − | 0.996231i | \(-0.472354\pi\) |
−0.819389 | + | 0.573238i | \(0.805687\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.77993 | + | 146.886i | 0.0131064 | + | 0.333076i | ||||
\(442\) | −199.180 | −0.450635 | ||||||||
\(443\) | 204.354 | − | 353.951i | 0.461295 | − | 0.798987i | −0.537731 | − | 0.843117i | \(-0.680718\pi\) |
0.999026 | + | 0.0441299i | \(0.0140515\pi\) | |||||||
\(444\) | 29.2609 | − | 16.8938i | 0.0659029 | − | 0.0380491i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −316.052 | − | 182.473i | −0.708636 | − | 0.409131i | ||||
\(447\) | 249.555i | 0.558288i | ||||||||
\(448\) | −15.5547 | − | 53.7964i | −0.0347203 | − | 0.120081i | ||||
\(449\) | 725.469 | 1.61574 | 0.807872 | − | 0.589358i | \(-0.200619\pi\) | ||||
0.807872 | + | 0.589358i | \(0.200619\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.85730 | − | 1.07231i | 0.00411817 | − | 0.00237763i | ||||
\(452\) | −116.241 | − | 201.335i | −0.257170 | − | 0.445432i | ||||
\(453\) | −140.269 | − | 80.9842i | −0.309644 | − | 0.178773i | ||||
\(454\) | 468.150i | 1.03117i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −15.5639 | −0.0341313 | ||||||||
\(457\) | 200.765 | − | 347.736i | 0.439311 | − | 0.760909i | −0.558325 | − | 0.829622i | \(-0.688556\pi\) |
0.997636 | + | 0.0687128i | \(0.0218892\pi\) | |||||||
\(458\) | 299.129 | − | 172.702i | 0.653121 | − | 0.377080i | ||||
\(459\) | −86.6474 | − | 150.078i | −0.188774 | − | 0.326967i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 653.050i | − | 1.41659i | −0.705915 | − | 0.708297i | \(-0.749464\pi\) | ||
0.705915 | − | 0.708297i | \(-0.250536\pi\) | |||||||
\(462\) | −6.50709 | − | 6.25607i | −0.0140846 | − | 0.0135413i | ||||
\(463\) | 869.580 | 1.87814 | 0.939072 | − | 0.343722i | \(-0.111688\pi\) | ||||
0.939072 | + | 0.343722i | \(0.111688\pi\) | |||||||
\(464\) | 112.260 | − | 194.441i | 0.241941 | − | 0.419053i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −149.546 | − | 259.021i | −0.320913 | − | 0.555838i | ||||
\(467\) | −640.168 | − | 369.601i | −1.37081 | − | 0.791437i | −0.379779 | − | 0.925077i | \(-0.624000\pi\) |
−0.991030 | + | 0.133641i | \(0.957333\pi\) | |||||||
\(468\) | 25.3384i | 0.0541419i | ||||||||
\(469\) | 42.3967 | − | 44.0978i | 0.0903981 | − | 0.0940252i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 148.286 | − | 256.838i | 0.314831 | − | 0.545304i | ||||
\(472\) | 123.776 | − | 71.4621i | 0.262237 | − | 0.151403i | ||||
\(473\) | −12.2009 | − | 21.1325i | −0.0257947 | − | 0.0446777i | ||||
\(474\) | −280.639 | − | 162.027i | −0.592066 | − | 0.341829i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −111.953 | + | 453.288i | −0.235196 | + | 0.952285i | ||||
\(477\) | −139.563 | −0.292586 | ||||||||
\(478\) | 243.339 | − | 421.476i | 0.509078 | − | 0.881750i | ||||
\(479\) | −525.006 | + | 303.112i | −1.09605 | + | 0.632802i | −0.935180 | − | 0.354174i | \(-0.884762\pi\) |
−0.160866 | + | 0.986976i | \(0.551429\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 35.6718 | + | 20.5951i | 0.0741618 | + | 0.0428173i | ||||
\(482\) | 242.323i | 0.502745i | ||||||||
\(483\) | −128.808 | + | 37.2435i | −0.266683 | + | 0.0771088i | ||||
\(484\) | −241.446 | −0.498855 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −19.0919 | + | 11.0227i | −0.0392837 | + | 0.0226805i | ||||
\(487\) | 324.788 | + | 562.549i | 0.666916 | + | 1.15513i | 0.978762 | + | 0.205000i | \(0.0657193\pi\) |
−0.311846 | + | 0.950133i | \(0.600947\pi\) | |||||||
\(488\) | −253.026 | − | 146.085i | −0.518497 | − | 0.299354i | ||||
\(489\) | − | 161.103i | − | 0.329454i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 266.629 | 0.543033 | 0.271516 | − | 0.962434i | \(-0.412475\pi\) | ||||
0.271516 | + | 0.962434i | \(0.412475\pi\) | |||||||
\(492\) | −7.05598 | + | 12.2213i | −0.0143414 | + | 0.0248401i | ||||
\(493\) | −1621.18 | + | 935.988i | −3.28839 | + | 1.89856i | ||||
\(494\) | −9.48693 | − | 16.4318i | −0.0192043 | − | 0.0332628i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 7.56640i | − | 0.0152548i | ||||||
\(497\) | −56.5039 | − | 195.421i | −0.113690 | − | 0.393200i | ||||
\(498\) | 30.5788 | 0.0614033 | ||||||||
\(499\) | 340.553 | − | 589.855i | 0.682471 | − | 1.18207i | −0.291754 | − | 0.956493i | \(-0.594239\pi\) |
0.974225 | − | 0.225581i | \(-0.0724279\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 90.9247 | + | 157.486i | 0.181487 | + | 0.314344i | ||||
\(502\) | −401.151 | − | 231.604i | −0.799105 | − | 0.461364i | ||||
\(503\) | 453.326i | 0.901245i | 0.892715 | + | 0.450622i | \(0.148798\pi\) | ||||
−0.892715 | + | 0.450622i | \(0.851202\pi\) | |||||||
\(504\) | 57.6643 | + | 14.2419i | 0.114413 | + | 0.0282578i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.11678 | − | 7.13047i | 0.00813592 | − | 0.0140918i | ||||
\(507\) | 226.749 | − | 130.913i | 0.447236 | − | 0.258212i | ||||
\(508\) | −81.3744 | − | 140.945i | −0.160186 | − | 0.277450i | ||||
\(509\) | −43.5300 | − | 25.1321i | −0.0855206 | − | 0.0493754i | 0.456630 | − | 0.889657i | \(-0.349056\pi\) |
−0.542150 | + | 0.840281i | \(0.682390\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 84.4364 | + | 81.1792i | 0.165238 | + | 0.158863i | ||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 8.25400 | − | 14.2963i | 0.0160897 | − | 0.0278681i | ||||
\(514\) | 269.883 | − | 155.817i | 0.525064 | − | 0.303146i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 139.056 | + | 80.2838i | 0.269488 | + | 0.155589i | ||||
\(517\) | − | 33.3103i | − | 0.0644300i | ||||||
\(518\) | 66.9197 | − | 69.6048i | 0.129189 | − | 0.134372i | ||||
\(519\) | −353.610 | −0.681330 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −89.2971 | + | 51.5557i | −0.171396 | + | 0.0989553i | −0.583244 | − | 0.812297i | \(-0.698217\pi\) |
0.411848 | + | 0.911252i | \(0.364883\pi\) | |||||||
\(522\) | 119.070 | + | 206.236i | 0.228104 | + | 0.395087i | ||||
\(523\) | 317.716 | + | 183.434i | 0.607488 | + | 0.350733i | 0.771982 | − | 0.635645i | \(-0.219266\pi\) |
−0.164494 | + | 0.986378i | \(0.552599\pi\) | |||||||
\(524\) | − | 481.253i | − | 0.918421i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 188.366 | 0.358111 | ||||||||
\(527\) | −31.5430 | + | 54.6341i | −0.0598539 | + | 0.103670i | ||||
\(528\) | −3.15867 | + | 1.82366i | −0.00598234 | + | 0.00345390i | ||||
\(529\) | 203.348 | + | 352.210i | 0.384402 | + | 0.665803i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 151.594i | 0.285488i | ||||||||
\(532\) | −42.7273 | + | 12.3542i | −0.0803145 | + | 0.0232222i | ||||
\(533\) | −17.2038 | −0.0322773 | ||||||||
\(534\) | −83.5943 | + | 144.790i | −0.156544 | + | 0.271141i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −12.3588 | − | 21.4060i | −0.0230574 | − | 0.0399365i | ||||
\(537\) | 293.848 | + | 169.653i | 0.547204 | + | 0.315928i | ||||
\(538\) | 37.4988i | 0.0697005i | ||||||||
\(539\) | −22.8297 | − | 12.0096i | −0.0423557 | − | 0.0222812i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 266.559 | − | 461.693i | 0.492714 | − | 0.853407i | −0.507250 | − | 0.861799i | \(-0.669338\pi\) |
0.999965 | + | 0.00839227i | \(0.00267137\pi\) | |||||||
\(542\) | −131.066 | + | 75.6709i | −0.241819 | + | 0.139614i | ||||
\(543\) | −103.084 | − | 178.547i | −0.189842 | − | 0.328816i | ||||
\(544\) | 163.384 | + | 94.3297i | 0.300338 | + | 0.173400i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 20.1129 | + | 69.5612i | 0.0368369 | + | 0.127401i | ||||
\(547\) | −69.6218 | −0.127279 | −0.0636396 | − | 0.997973i | \(-0.520271\pi\) | ||||
−0.0636396 | + | 0.997973i | \(0.520271\pi\) | |||||||
\(548\) | 233.661 | − | 404.713i | 0.426389 | − | 0.738528i | ||||
\(549\) | 268.375 | − | 154.946i | 0.488843 | − | 0.282234i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −154.433 | − | 89.1619i | −0.280277 | − | 0.161818i | ||||
\(552\) | 54.1782i | 0.0981489i | ||||||||
\(553\) | −899.048 | − | 222.047i | −1.62576 | − | 0.401532i | ||||
\(554\) | 622.793 | 1.12418 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 366.314 | − | 211.491i | 0.658838 | − | 0.380380i | ||||
\(557\) | 8.43122 | + | 14.6033i | 0.0151368 | + | 0.0262178i | 0.873495 | − | 0.486834i | \(-0.161848\pi\) |
−0.858358 | + | 0.513052i | \(0.828515\pi\) | |||||||
\(558\) | 6.95018 | + | 4.01269i | 0.0124555 | + | 0.00719120i | ||||
\(559\) | 195.747i | 0.350174i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 30.4101 | 0.0542069 | ||||||||
\(562\) | 227.737 | − | 394.452i | 0.405226 | − | 0.701872i | ||||
\(563\) | −793.093 | + | 457.892i | −1.40869 | + | 0.813308i | −0.995262 | − | 0.0972290i | \(-0.969002\pi\) |
−0.413428 | + | 0.910537i | \(0.635669\pi\) | |||||||
\(564\) | 109.594 | + | 189.822i | 0.194315 | + | 0.336564i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 96.9204i | − | 0.171237i | ||||||
\(567\) | −43.6632 | + | 45.4151i | −0.0770073 | + | 0.0800971i | ||||
\(568\) | −82.1963 | −0.144712 | ||||||||
\(569\) | −203.828 | + | 353.040i | −0.358221 | + | 0.620456i | −0.987664 | − | 0.156590i | \(-0.949950\pi\) |
0.629443 | + | 0.777047i | \(0.283283\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 447.910 | + | 775.803i | 0.784431 | + | 1.35867i | 0.929339 | + | 0.369229i | \(0.120378\pi\) |
−0.144908 | + | 0.989445i | \(0.546289\pi\) | |||||||
\(572\) | −3.85072 | − | 2.22322i | −0.00673203 | − | 0.00388674i | ||||
\(573\) | − | 113.850i | − | 0.198691i | ||||||
\(574\) | −9.66974 | + | 39.1519i | −0.0168462 | + | 0.0682088i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 12.0000 | − | 20.7846i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | −590.115 | + | 340.703i | −1.02273 | + | 0.590473i | −0.914893 | − | 0.403695i | \(-0.867726\pi\) |
−0.107836 | + | 0.994169i | \(0.534392\pi\) | |||||||
\(578\) | −582.134 | − | 1008.29i | −1.00715 | − | 1.74444i | ||||
\(579\) | −145.305 | − | 83.8919i | −0.250959 | − | 0.144891i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 83.9476 | − | 24.2726i | 0.144488 | − | 0.0417773i | ||||
\(582\) | −365.662 | −0.628286 | ||||||||
\(583\) | 12.2454 | − | 21.2097i | 0.0210041 | − | 0.0363802i | ||||
\(584\) | 40.9872 | − | 23.6640i | 0.0701835 | − | 0.0405205i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −180.662 | − | 104.305i | −0.308297 | − | 0.177996i | ||||
\(587\) | 833.001i | 1.41908i | 0.704665 | + | 0.709541i | \(0.251097\pi\) | ||||
−0.704665 | + | 0.709541i | \(0.748903\pi\) | |||||||
\(588\) | 169.610 | − | 6.67408i | 0.288452 | − | 0.0113505i | ||||
\(589\) | −6.00955 | −0.0102030 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −280.008 | + | 161.663i | −0.473787 | + | 0.273541i | ||||
\(592\) | −19.5073 | − | 33.7876i | −0.0329515 | − | 0.0570736i | ||||
\(593\) | −270.842 | − | 156.371i | −0.456731 | − | 0.263694i | 0.253938 | − | 0.967221i | \(-0.418274\pi\) |
−0.710669 | + | 0.703527i | \(0.751608\pi\) | |||||||
\(594\) | − | 3.86857i | − | 0.00651274i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 288.161 | 0.483491 | ||||||||
\(597\) | 99.8454 | − | 172.937i | 0.167245 | − | 0.289677i | ||||
\(598\) | −57.1996 | + | 33.0242i | −0.0956514 | + | 0.0552244i | ||||
\(599\) | −107.121 | − | 185.540i | −0.178834 | − | 0.309749i | 0.762648 | − | 0.646814i | \(-0.223899\pi\) |
−0.941481 | + | 0.337065i | \(0.890566\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 176.849i | 0.294257i | 0.989117 | + | 0.147129i | \(0.0470031\pi\) | ||||
−0.989117 | + | 0.147129i | \(0.952997\pi\) | |||||||
\(602\) | 445.474 | + | 110.023i | 0.739991 | + | 0.182763i | ||||
\(603\) | 26.2169 | 0.0434774 | ||||||||
\(604\) | −93.5125 | + | 161.968i | −0.154822 | + | 0.268160i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −118.488 | − | 205.228i | −0.195525 | − | 0.338660i | ||||
\(607\) | −32.1304 | − | 18.5505i | −0.0529331 | − | 0.0305609i | 0.473300 | − | 0.880901i | \(-0.343063\pi\) |
−0.526233 | + | 0.850340i | \(0.676396\pi\) | |||||||
\(608\) | 17.9716i | 0.0295586i | ||||||||
\(609\) | 490.586 | + | 471.661i | 0.805559 | + | 0.774484i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −133.605 | + | 231.411i | −0.218666 | + | 0.378741i | ||||
\(612\) | −173.295 | + | 100.052i | −0.283161 | + | 0.163483i | ||||
\(613\) | −449.860 | − | 779.180i | −0.733866 | − | 1.27109i | −0.955219 | − | 0.295899i | \(-0.904381\pi\) |
0.221353 | − | 0.975194i | \(-0.428953\pi\) | |||||||
\(614\) | −460.516 | − | 265.879i | −0.750027 | − | 0.433028i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.22389 | + | 7.51374i | −0.0117271 | + | 0.0121976i | ||||
\(617\) | 626.244 | 1.01498 | 0.507491 | − | 0.861657i | \(-0.330573\pi\) | ||||
0.507491 | + | 0.861657i | \(0.330573\pi\) | |||||||
\(618\) | −128.307 | + | 222.234i | −0.207617 | + | 0.359602i | ||||
\(619\) | −776.375 | + | 448.240i | −1.25424 | + | 0.724136i | −0.971949 | − | 0.235193i | \(-0.924428\pi\) |
−0.282291 | + | 0.959329i | \(0.591094\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −49.7658 | − | 28.7323i | −0.0801382 | − | 0.0462678i | ||||
\(622\) | 551.298i | 0.886331i | ||||||||
\(623\) | −114.560 | + | 463.843i | −0.183885 | + | 0.744532i | ||||
\(624\) | 29.2583 | 0.0468883 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 175.207 | − | 101.156i | 0.279884 | − | 0.161591i | ||||
\(627\) | 1.44843 | + | 2.50875i | 0.00231009 | + | 0.00400120i | ||||
\(628\) | −296.571 | − | 171.225i | −0.472247 | − | 0.272652i | ||||
\(629\) | 325.290i | 0.517153i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −500.730 | −0.793550 | −0.396775 | − | 0.917916i | \(-0.629871\pi\) | ||||
−0.396775 | + | 0.917916i | \(0.629871\pi\) | |||||||
\(632\) | −187.093 | + | 324.054i | −0.296033 | + | 0.512744i | ||||
\(633\) | 209.149 | − | 120.752i | 0.330409 | − | 0.190762i | ||||
\(634\) | −271.843 | − | 470.846i | −0.428774 | − | 0.742659i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 161.154i | 0.253387i | ||||||||
\(637\) | 110.431 | + | 175.000i | 0.173362 | + | 0.274726i | ||||
\(638\) | −41.7893 | −0.0655005 | ||||||||
\(639\) | 43.5912 | − | 75.5021i | 0.0682178 | − | 0.118157i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −310.289 | − | 537.436i | −0.484070 | − | 0.838434i | 0.515763 | − | 0.856732i | \(-0.327509\pi\) |
−0.999833 | + | 0.0182978i | \(0.994175\pi\) | |||||||
\(642\) | 264.326 | + | 152.609i | 0.411722 | + | 0.237708i | ||||
\(643\) | − | 1127.93i | − | 1.75417i | −0.480334 | − | 0.877086i | \(-0.659484\pi\) | ||
0.480334 | − | 0.877086i | \(-0.340516\pi\) | |||||||
\(644\) | 43.0051 | + | 148.735i | 0.0667782 | + | 0.230954i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 74.9206 | − | 129.766i | 0.115976 | − | 0.200877i | ||||
\(647\) | 117.130 | − | 67.6248i | 0.181035 | − | 0.104521i | −0.406744 | − | 0.913542i | \(-0.633336\pi\) |
0.587779 | + | 0.809022i | \(0.300003\pi\) | |||||||
\(648\) | 12.7279 | + | 22.0454i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | −23.0380 | − | 13.3010i | −0.0354977 | − | 0.0204946i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 22.2654 | + | 5.49912i | 0.0342018 | + | 0.00844719i | ||||
\(652\) | −186.026 | −0.285316 | ||||||||
\(653\) | −195.145 | + | 338.001i | −0.298843 | + | 0.517612i | −0.975872 | − | 0.218345i | \(-0.929934\pi\) |
0.677028 | + | 0.735957i | \(0.263267\pi\) | |||||||
\(654\) | −179.482 | + | 103.624i | −0.274437 | + | 0.158446i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 14.1120 | + | 8.14755i | 0.0215121 | + | 0.0124200i | ||||
\(657\) | 50.1988i | 0.0764061i | ||||||||
\(658\) | 451.542 | + | 434.123i | 0.686233 | + | 0.659761i | ||||
\(659\) | −864.853 | −1.31237 | −0.656186 | − | 0.754599i | \(-0.727831\pi\) | ||||
−0.656186 | + | 0.754599i | \(0.727831\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −873.134 | + | 504.104i | −1.32093 | + | 0.762638i | −0.983877 | − | 0.178848i | \(-0.942763\pi\) |
−0.337052 | + | 0.941486i | \(0.609430\pi\) | |||||||
\(662\) | 137.113 | + | 237.487i | 0.207120 | + | 0.358742i | ||||
\(663\) | −211.263 | − | 121.973i | −0.318647 | − | 0.183971i | ||||
\(664\) | − | 35.3094i | − | 0.0531768i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 41.3812 | 0.0621339 | ||||||||
\(667\) | −310.374 | + | 537.584i | −0.465328 | + | 0.805973i | ||||
\(668\) | 181.849 | − | 104.991i | 0.272230 | − | 0.157172i | ||||
\(669\) | −223.482 | − | 387.083i | −0.334054 | − | 0.578599i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 54.3806i | 0.0810441i | ||||||||
\(672\) | 16.4452 | − | 66.5850i | 0.0244720 | − | 0.0990848i | ||||
\(673\) | 109.959 | 0.163386 | 0.0816928 | − | 0.996658i | \(-0.473967\pi\) | ||||
0.0816928 | + | 0.996658i | \(0.473967\pi\) | |||||||
\(674\) | −88.7259 | + | 153.678i | −0.131641 | + | 0.228009i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −151.166 | − | 261.827i | −0.223618 | − | 0.387318i | ||||
\(677\) | −146.213 | − | 84.4163i | −0.215972 | − | 0.124692i | 0.388112 | − | 0.921612i | \(-0.373128\pi\) |
−0.604084 | + | 0.796921i | \(0.706461\pi\) | |||||||
\(678\) | − | 284.731i | − | 0.419957i | ||||||
\(679\) | −1003.85 | + | 290.253i | −1.47842 | + | 0.427471i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −286.682 | + | 496.548i | −0.420973 | + | 0.729146i | ||||
\(682\) | −1.21963 | + | 0.704155i | −0.00178832 | + | 0.00103248i | ||||
\(683\) | −218.065 | − | 377.700i | −0.319276 | − | 0.553002i | 0.661061 | − | 0.750332i | \(-0.270106\pi\) |
−0.980337 | + | 0.197330i | \(0.936773\pi\) | |||||||
\(684\) | −16.5080 | − | 9.53090i | −0.0241345 | − | 0.0139341i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 460.329 | − | 152.954i | 0.671034 | − | 0.222965i | ||||
\(687\) | 423.033 | 0.615768 | ||||||||
\(688\) | 92.7038 | − | 160.568i | 0.134744 | − | 0.233383i | ||||
\(689\) | −170.141 | + | 98.2309i | −0.246939 | + | 0.142570i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −59.2770 | − | 34.2236i | −0.0857843 | − | 0.0495276i | 0.456494 | − | 0.889726i | \(-0.349105\pi\) |
−0.542279 | + | 0.840199i | \(0.682438\pi\) | |||||||
\(692\) | 408.314i | 0.590049i | ||||||||
\(693\) | −3.07076 | − | 10.6203i | −0.00443112 | − | 0.0153251i | ||||
\(694\) | −712.193 | −1.02622 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 238.140 | − | 137.490i | 0.342156 | − | 0.197544i | ||||
\(697\) | −67.9314 | − | 117.661i | −0.0974625 | − | 0.168810i | ||||
\(698\) | −58.5039 | − | 33.7772i | −0.0838164 | − | 0.0483914i | ||||
\(699\) | − | 366.311i | − | 0.524050i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1283.41 | 1.83083 | 0.915414 | − | 0.402514i | \(-0.131864\pi\) | ||||
0.915414 | + | 0.402514i | \(0.131864\pi\) | |||||||
\(702\) | −15.5165 | + | 26.8754i | −0.0221033 | + | 0.0382841i | ||||
\(703\) | −26.8355 | + | 15.4935i | −0.0381728 | + | 0.0220391i | ||||
\(704\) | 2.10578 | + | 3.64732i | 0.00299117 | + | 0.00518086i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 46.5422i | 0.0659238i | ||||||||
\(707\) | −488.188 | − | 469.356i | −0.690507 | − | 0.663870i | ||||
\(708\) | 175.046 | 0.247240 | ||||||||
\(709\) | −86.2000 | + | 149.303i | −0.121580 | + | 0.210582i | −0.920391 | − | 0.391000i | \(-0.872129\pi\) |
0.798811 | + | 0.601582i | \(0.205463\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −198.442 | − | 343.712i | −0.279103 | − | 0.483420i | ||||
\(712\) | 167.189 | + | 96.5264i | 0.234815 | + | 0.135571i | ||||
\(713\) | 20.9194i | 0.0293399i | ||||||||
\(714\) | −396.325 | + | 412.227i | −0.555077 | + | 0.577349i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 195.899 | − | 339.307i | 0.273602 | − | 0.473892i | ||||
\(717\) | 516.201 | − | 298.029i | 0.719946 | − | 0.415661i | ||||
\(718\) | 189.361 | + | 327.983i | 0.263734 | + | 0.456801i | ||||
\(719\) | −435.015 | − | 251.156i | −0.605028 | − | 0.349313i | 0.165989 | − | 0.986128i | \(-0.446918\pi\) |
−0.771017 | + | 0.636815i | \(0.780252\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −175.836 | + | 711.943i | −0.243878 | + | 0.987439i | ||||
\(722\) | −496.257 | −0.687337 | ||||||||
\(723\) | −148.392 | + | 257.023i | −0.205245 | + | 0.355495i | ||||
\(724\) | −206.168 | + | 119.031i | −0.284763 | + | 0.164408i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −256.092 | − | 147.855i | −0.352744 | − | 0.203657i | ||||
\(727\) | − | 748.693i | − | 1.02984i | −0.857238 | − | 0.514920i | \(-0.827822\pi\) | ||
0.857238 | − | 0.514920i | \(-0.172178\pi\) | |||||||
\(728\) | 80.3223 | − | 23.2244i | 0.110333 | − | 0.0319017i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1338.76 | + | 772.931i | −1.83140 | + | 1.05736i | ||||
\(732\) | −178.917 | − | 309.893i | −0.244422 | − | 0.423351i | ||||
\(733\) | 812.761 | + | 469.248i | 1.10881 | + | 0.640175i | 0.938522 | − | 0.345219i | \(-0.112195\pi\) |
0.170293 | + | 0.985394i | \(0.445529\pi\) | |||||||
\(734\) | − | 224.468i | − | 0.305814i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 62.5596 | 0.0849994 | ||||||||
\(737\) | −2.30029 | + | 3.98422i | −0.00312116 | + | 0.00540600i | ||||
\(738\) | −14.9680 | + | 8.64178i | −0.0202818 | + | 0.0117097i | ||||
\(739\) | −106.820 | − | 185.018i | −0.144547 | − | 0.250363i | 0.784657 | − | 0.619931i | \(-0.212839\pi\) |
−0.929204 | + | 0.369567i | \(0.879506\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 23.2381i | − | 0.0313605i | ||||||
\(742\) | 127.919 | + | 442.413i | 0.172398 | + | 0.596244i | ||||
\(743\) | −544.013 | −0.732184 | −0.366092 | − | 0.930579i | \(-0.619304\pi\) | ||||
−0.366092 | + | 0.930579i | \(0.619304\pi\) | |||||||
\(744\) | 4.63346 | − | 8.02538i | 0.00622776 | − | 0.0107868i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −292.985 | − | 507.465i | −0.392742 | − | 0.680249i | ||||
\(747\) | 32.4337 | + | 18.7256i | 0.0434187 | + | 0.0250678i | ||||
\(748\) | − | 35.1146i | − | 0.0469446i | ||||||
\(749\) | 846.786 | + | 209.140i | 1.13056 | + | 0.279225i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −294.705 | + | 510.443i | −0.392416 | + | 0.679685i | −0.992768 | − | 0.120051i | \(-0.961694\pi\) |
0.600351 | + | 0.799736i | \(0.295027\pi\) | |||||||
\(752\) | 219.187 | − | 126.548i | 0.291473 | − | 0.168282i | ||||
\(753\) | −283.656 | − | 491.307i | −0.376702 | − | 0.652467i | ||||
\(754\) | 290.316 | + | 167.614i | 0.385034 | + | 0.222299i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 52.4408 | + | 50.4179i | 0.0693662 | + | 0.0666903i | ||||
\(757\) | 448.997 | 0.593127 | 0.296564 | − | 0.955013i | \(-0.404159\pi\) | ||||
0.296564 | + | 0.955013i | \(0.404159\pi\) | |||||||
\(758\) | −51.4774 | + | 89.1614i | −0.0679121 | + | 0.117627i | ||||
\(759\) | 8.73300 | − | 5.04200i | 0.0115059 | − | 0.00664295i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 371.914 | + | 214.725i | 0.488718 | + | 0.282161i | 0.724042 | − | 0.689756i | \(-0.242282\pi\) |
−0.235325 | + | 0.971917i | \(0.575615\pi\) | |||||||
\(762\) | − | 199.326i | − | 0.261582i | ||||||
\(763\) | −410.475 | + | 426.944i | −0.537975 | + | 0.559560i | ||||
\(764\) | −131.463 | −0.172072 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 349.070 | − | 201.536i | 0.455705 | − | 0.263101i | ||||
\(767\) | 106.699 | + | 184.807i | 0.139112 | + | 0.240948i | ||||
\(768\) | −24.0000 | − | 13.8564i | −0.0312500 | − | 0.0180422i | ||||
\(769\) | − | 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 | ||||||||
\(772\) | −96.8700 | + | 167.784i | −0.125479 | + | 0.217337i | ||||
\(773\) | −1076.93 | + | 621.768i | −1.39319 | + | 0.804357i | −0.993667 | − | 0.112367i | \(-0.964157\pi\) |
−0.399520 | + | 0.916724i | \(0.630823\pi\) | |||||||
\(774\) | 98.3272 | + | 170.308i | 0.127038 | + | 0.220036i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 422.231i | 0.544112i | ||||||||
\(777\) | 113.603 | − | 32.8472i | 0.146207 | − | 0.0422744i | ||||
\(778\) | 137.374 | 0.176574 | ||||||||
\(779\) | 6.47112 | − | 11.2083i | 0.00830696 | − | 0.0143881i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.64946 | + | 13.2493i | 0.00979444 | + | 0.0169645i | ||||
\(782\) | −451.719 | − | 260.800i | −0.577645 | − | 0.333504i | ||||
\(783\) | 291.661i | 0.372492i | ||||||||
\(784\) | −7.70657 | − | 195.848i | −0.00982981 | − | 0.249807i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 294.706 | − | 510.446i | 0.374944 | − | 0.649422i | ||||
\(787\) | −165.088 | + | 95.3138i | −0.209769 | + | 0.121110i | −0.601204 | − | 0.799096i | \(-0.705312\pi\) |
0.391435 | + | 0.920206i | \(0.371979\pi\) | |||||||
\(788\) | 186.672 | + | 323.325i | 0.236893 | + | 0.410311i | ||||
\(789\) | 199.793 | + | 115.350i | 0.253223 | + | 0.146198i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −226.011 | − | 781.667i | −0.285729 | − | 0.988202i | ||||
\(792\) | −4.46704 | −0.00564020 | ||||||||
\(793\) | 218.116 | − | 377.789i | 0.275052 | − | 0.476405i | ||||
\(794\) | 969.635 | − | 559.819i | 1.22120 | − | 0.705062i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −199.691 | − | 115.292i | −0.250868 | − | 0.144839i | ||||
\(797\) | 387.796i | 0.486570i | 0.969955 | + | 0.243285i | \(0.0782250\pi\) | ||||
−0.969955 | + | 0.243285i | \(0.921775\pi\) | |||||||
\(798\) | −52.8845 | − | 13.0614i | −0.0662713 | − | 0.0163677i | ||||
\(799\) | −2110.23 | −2.64108 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −177.330 | + | 102.382i | −0.221386 | + | 0.127817i | ||||
\(802\) | 355.835 | + | 616.324i | 0.443684 | + | 0.768484i | ||||
\(803\) | −7.62881 | − | 4.40449i | −0.00950038 | − | 0.00548505i | ||||
\(804\) | − | 30.2726i | − | 0.0376525i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 11.2972 | 0.0140164 | ||||||||
\(807\) | −22.9633 | + | 39.7735i | −0.0284551 | + | 0.0492857i | ||||
\(808\) | −236.977 | + | 136.818i | −0.293288 | + | 0.169330i | ||||
\(809\) | −182.613 | − | 316.295i | −0.225727 | − | 0.390970i | 0.730811 | − | 0.682580i | \(-0.239142\pi\) |
−0.956537 | + | 0.291610i | \(0.905809\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 944.189i | 1.16423i | 0.813107 | + | 0.582114i | \(0.197774\pi\) | ||||
−0.813107 | + | 0.582114i | \(0.802226\pi\) | |||||||
\(812\) | 544.627 | − | 566.479i | 0.670723 | − | 0.697635i | ||||
\(813\) | −185.355 | −0.227989 | ||||||||
\(814\) | −3.63082 | + | 6.28877i | −0.00446047 | + | 0.00772576i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 115.530 | + | 200.104i | 0.141581 | + | 0.245225i | ||||
\(817\) | −127.529 | − | 73.6292i | −0.156095 | − | 0.0901214i | ||||
\(818\) | − | 1060.46i | − | 1.29640i | ||||||
\(819\) | −21.2644 | + | 86.0974i | −0.0259638 | + | 0.105125i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 342.337 | − | 592.946i | 0.416976 | − | 0.722224i | −0.578657 | − | 0.815571i | \(-0.696423\pi\) |
0.995634 | + | 0.0933467i | \(0.0297565\pi\) | |||||||
\(822\) | 495.670 | − | 286.175i | 0.603005 | − | 0.348145i | ||||
\(823\) | −522.835 | − | 905.578i | −0.635280 | − | 1.10034i | −0.986456 | − | 0.164028i | \(-0.947551\pi\) |
0.351176 | − | 0.936310i | \(-0.385782\pi\) | |||||||
\(824\) | 256.614 | + | 148.156i | 0.311425 | + | 0.179801i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 480.550 | − | 138.946i | 0.581780 | − | 0.168216i | ||||
\(827\) | −830.505 | −1.00424 | −0.502119 | − | 0.864798i | \(-0.667446\pi\) | ||||
−0.502119 | + | 0.864798i | \(0.667446\pi\) | |||||||
\(828\) | −33.1772 | + | 57.4646i | −0.0400691 | + | 0.0694017i | ||||
\(829\) | −621.983 | + | 359.102i | −0.750280 | + | 0.433175i | −0.825795 | − | 0.563970i | \(-0.809273\pi\) |
0.0755148 | + | 0.997145i | \(0.475940\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 660.572 | + | 381.381i | 0.794912 | + | 0.458943i | ||||
\(832\) | − | 33.7846i | − | 0.0406064i | ||||||
\(833\) | −760.812 | + | 1446.27i | −0.913339 | + | 1.73622i | ||||
\(834\) | 518.046 | 0.621158 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.89685 | − | 1.67250i | 0.00346514 | − | 0.00200060i | ||||
\(837\) | 4.91452 | + | 8.51220i | 0.00587159 | + | 0.0101699i | ||||
\(838\) | 570.436 | + | 329.342i | 0.680712 | + | 0.393009i | ||||
\(839\) | − | 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 | ||||||||
\(842\) | 244.645 | − | 423.737i | 0.290552 | − | 0.503251i | ||||
\(843\) | 483.103 | − | 278.920i | 0.573076 | − | 0.330866i | ||||
\(844\) | −139.433 | − | 241.505i | −0.165205 | − | 0.286143i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 268.449i | 0.317315i | ||||||||
\(847\) | −820.408 | − | 202.625i | −0.968605 | − | 0.239226i | ||||
\(848\) | 186.084 | 0.219439 | ||||||||
\(849\) | 59.3514 | − | 102.800i | 0.0699074 | − | 0.121083i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 53.9331 | + | 93.4149i | 0.0633761 | + | 0.109771i | ||||
\(852\) | −87.1823 | − | 50.3347i | −0.102327 | − | 0.0590783i | ||||
\(853\) | 21.9601i | 0.0257445i | 0.999917 | + | 0.0128723i | \(0.00409748\pi\) | ||||
−0.999917 | + | 0.0128723i | \(0.995903\pi\) | |||||||
\(854\) | −737.162 | − | 708.725i | −0.863187 | − | 0.829889i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 176.217 | − | 305.217i | 0.205861 | − | 0.356562i | ||||
\(857\) | 1399.33 | − | 807.903i | 1.63282 | − | 0.942711i | 0.649607 | − | 0.760271i | \(-0.274934\pi\) |
0.983217 | − | 0.182441i | \(-0.0583997\pi\) | |||||||
\(858\) | −2.72287 | − | 4.71615i | −0.00317351 | − | 0.00549668i | ||||
\(859\) | 772.149 | + | 445.801i | 0.898893 | + | 0.518976i | 0.876841 | − | 0.480781i | \(-0.159647\pi\) |
0.0220523 | + | 0.999757i | \(0.492980\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −34.2318 | + | 35.6053i | −0.0397582 | + | 0.0413535i | ||||
\(862\) | −699.470 | −0.811450 | ||||||||
\(863\) | −448.173 | + | 776.259i | −0.519320 | + | 0.899489i | 0.480428 | + | 0.877034i | \(0.340481\pi\) |
−0.999748 | + | 0.0224544i | \(0.992852\pi\) | |||||||
\(864\) | 25.4558 | − | 14.6969i | 0.0294628 | − | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 894.090 | + | 516.203i | 1.03244 | + | 0.596078i | ||||
\(867\) | − | 1425.93i | − | 1.64467i | ||||||
\(868\) | 6.34984 | − | 25.7099i | 0.00731548 | − | 0.0296197i | ||||
\(869\) | 69.6459 | 0.0801449 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.9609 | − | 18.4526i | 0.0366944 | − | 0.0211855i | ||||
\(872\) | 119.654 | + | 207.248i | 0.137218 | + | 0.237669i | ||||
\(873\) | −387.844 | − | 223.922i | −0.444265 | − | 0.256497i | ||||
\(874\) | − | 49.6874i | − | 0.0568506i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 57.9646 | 0.0661697 | ||||||||
\(877\) | −168.885 | + | 292.517i | −0.192571 | + | 0.333543i | −0.946102 | − | 0.323870i | \(-0.895016\pi\) |
0.753530 | + | 0.657413i | \(0.228349\pi\) | |||||||
\(878\) | −454.855 | + | 262.611i | −0.518059 | + | 0.299101i | ||||
\(879\) | −127.748 | − | 221.265i | −0.145333 | − | 0.251724i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 301.377i | 0.342085i | 0.985264 | + | 0.171042i | \(0.0547135\pi\) | ||||
−0.985264 | + | 0.171042i | \(0.945287\pi\) | |||||||
\(882\) | 183.985 | + | 96.7854i | 0.208600 | + | 0.109734i | ||||
\(883\) | −38.3679 | −0.0434518 | −0.0217259 | − | 0.999764i | \(-0.506916\pi\) | ||||
−0.0217259 | + | 0.999764i | \(0.506916\pi\) | |||||||
\(884\) | −140.842 | + | 243.945i | −0.159323 | + | 0.275956i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −289.000 | − | 500.563i | −0.326185 | − | 0.564969i | ||||
\(887\) | −572.834 | − | 330.726i | −0.645811 | − | 0.372859i | 0.141038 | − | 0.990004i | \(-0.454956\pi\) |
−0.786849 | + | 0.617145i | \(0.788289\pi\) | |||||||
\(888\) | − | 47.7829i | − | 0.0538095i | ||||||
\(889\) | −158.219 | − | 547.206i | −0.177974 | − | 0.615530i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.36901 | − | 4.10324i | 0.00265882 | − | 0.00460521i | ||||
\(892\) | −446.965 | + | 258.055i | −0.501082 | + | 0.289300i | ||||
\(893\) | −100.510 | − | 174.088i | −0.112553 | − | 0.194947i | ||||
\(894\) | 305.641 | + | 176.462i | 0.341880 | + | 0.197384i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −76.8857 | − | 18.9893i | −0.0858099 | − | 0.0211934i | ||||
\(897\) | −80.8924 | −0.0901810 | ||||||||
\(898\) | 512.984 | − | 888.515i | 0.571252 | − | 0.989437i | ||||
\(899\) | 91.9510 | − | 53.0880i | 0.102281 | − | 0.0590522i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1343.64 | − | 775.753i | −1.49128 | − | 0.860991i | ||||
\(902\) | − | 3.03295i | − | 0.00336247i | ||||||
\(903\) | 405.122 | + | 389.494i | 0.448640 | + | 0.431333i | ||||
\(904\) | −328.779 | −0.363693 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −198.370 | + | 114.529i | −0.218951 | + | 0.126412i | ||||
\(907\) | −484.152 | − | 838.576i | −0.533795 | − | 0.924560i | −0.999221 | − | 0.0394729i | \(-0.987432\pi\) |
0.465426 | − | 0.885087i | \(-0.345901\pi\) | |||||||
\(908\) | 573.365 | + | 331.032i | 0.631459 | + | 0.364573i | ||||
\(909\) | − | 290.236i | − | 0.319291i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 220.674 | 0.242233 | 0.121116 | − | 0.992638i | \(-0.461353\pi\) | ||||
0.121116 | + | 0.992638i | \(0.461353\pi\) | |||||||
\(912\) | −11.0053 | + | 19.0618i | −0.0120673 | + | 0.0209011i | ||||
\(913\) | −5.69153 | + | 3.28601i | −0.00623388 | + | 0.00359913i | ||||
\(914\) | −283.925 | − | 491.772i | −0.310640 | − | 0.538044i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 488.476i | − | 0.533271i | ||||||
\(917\) | 403.874 | − | 1635.25i | 0.440430 | − | 1.78326i | ||||
\(918\) | −245.076 | −0.266967 | ||||||||
\(919\) | 574.019 | − | 994.231i | 0.624613 | − | 1.08186i | −0.364002 | − | 0.931398i | \(-0.618590\pi\) |
0.988616 | − | 0.150464i | \(-0.0480766\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −325.634 | − | 564.015i | −0.353566 | − | 0.612394i | ||||
\(922\) | −799.819 | − | 461.776i | −0.867483 | − | 0.500841i | ||||
\(923\) | − | 122.726i | − | 0.132964i | ||||||
\(924\) | −12.2633 | + | 3.54581i | −0.0132720 | + | 0.00383746i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 614.886 | − | 1065.01i | 0.664024 | − | 1.15012i | ||||
\(927\) | −272.180 | + | 157.143i | −0.293614 | + | 0.169518i | ||||
\(928\) | −158.760 | − | 274.981i | −0.171078 | − | 0.296315i | ||||
\(929\) | −264.398 | − | 152.650i | −0.284605 | − | 0.164317i | 0.350901 | − | 0.936412i | \(-0.385875\pi\) |
−0.635506 | + | 0.772096i | \(0.719209\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −155.551 | + | 6.12088i | −0.167079 | + | 0.00657452i | ||||
\(932\) | −422.979 | −0.453840 | ||||||||
\(933\) | −337.599 | + | 584.739i | −0.361843 | + | 0.626730i | ||||
\(934\) | −905.334 | + | 522.695i | −0.969308 | + | 0.559630i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 31.0331 | + | 17.9170i | 0.0331550 | + | 0.0191421i | ||||
\(937\) | 12.4049i | 0.0132390i | 0.999978 | + | 0.00661948i | \(0.00210706\pi\) | ||||
−0.999978 | + | 0.00661948i | \(0.997893\pi\) | |||||||
\(938\) | −24.0296 | − | 83.1070i | −0.0256179 | − | 0.0886002i | ||||
\(939\) | 247.781 | 0.263877 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −250.409 | + | 144.573i | −0.266109 | + | 0.153638i | −0.627118 | − | 0.778924i | \(-0.715766\pi\) |
0.361009 | + | 0.932562i | \(0.382432\pi\) | |||||||
\(942\) | −209.708 | − | 363.224i | −0.222619 | − | 0.385588i | ||||
\(943\) | −39.0163 | − | 22.5261i | −0.0413747 | − | 0.0238877i | ||||
\(944\) | − | 202.125i | − | 0.214116i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −34.5093 | −0.0364792 | ||||||||
\(947\) | −713.478 | + | 1235.78i | −0.753409 | + | 1.30494i | 0.192752 | + | 0.981247i | \(0.438259\pi\) |
−0.946161 | + | 0.323695i | \(0.895075\pi\) | |||||||
\(948\) | −396.884 | + | 229.141i | −0.418654 | + | 0.241710i | ||||
\(949\) | 35.3322 | + | 61.1972i | 0.0372310 | + | 0.0644859i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 665.876i | − | 0.700186i | ||||||
\(952\) | 475.999 | + | 457.637i | 0.499999 | + | 0.480711i | ||||
\(953\) | 668.525 | 0.701495 | 0.350747 | − | 0.936470i | \(-0.385928\pi\) | ||||
0.350747 | + | 0.936470i | \(0.385928\pi\) | |||||||
\(954\) | −98.6862 | + | 170.929i | −0.103445 | + | 0.179171i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −344.134 | − | 596.058i | −0.359973 | − | 0.623491i | ||||
\(957\) | −44.3242 | − | 25.5906i | −0.0463158 | − | 0.0267405i | ||||
\(958\) | 857.331i | 0.894918i | ||||||||
\(959\) | 1133.60 | − | 1179.08i | 1.18206 | − | 1.22949i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −478.711 | + | 829.152i | −0.498138 | + | 0.862801i | ||||
\(962\) | 50.4476 | − | 29.1259i | 0.0524403 | − | 0.0302764i | ||||
\(963\) | 186.907 | + | 323.732i | 0.194088 | + | 0.336170i | ||||
\(964\) | 296.784 | + | 171.348i | 0.307867 | + | 0.177747i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −45.4671 | + | 184.092i | −0.0470674 | + | 0.190571i | ||||
\(967\) | −1647.14 | −1.70335 | −0.851676 | − | 0.524069i | \(-0.824414\pi\) | ||||
−0.851676 | + | 0.524069i | \(0.824414\pi\) | |||||||
\(968\) | −170.728 | + | 295.709i | −0.176372 | + | 0.305485i | ||||
\(969\) | 158.931 | − | 91.7586i | 0.164015 | − | 0.0946941i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1138.76 | + | 657.466i | 1.17277 | + | 0.677102i | 0.954332 | − | 0.298748i | \(-0.0965690\pi\) |
0.218443 | + | 0.975850i | \(0.429902\pi\) | |||||||
\(972\) | 31.1769i | 0.0320750i | ||||||||
\(973\) | 1422.18 | − | 411.210i | 1.46165 | − | 0.422621i | ||||
\(974\) | 918.639 | 0.943161 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −357.833 | + | 206.595i | −0.366633 | + | 0.211675i | ||||
\(977\) | 778.021 | + | 1347.57i | 0.796337 | + | 1.37930i | 0.921987 | + | 0.387221i | \(0.126565\pi\) |
−0.125650 | + | 0.992075i | \(0.540102\pi\) | |||||||
\(978\) | −197.310 | − | 113.917i | −0.201749 | − | 0.116480i | ||||
\(979\) | − | 35.9323i | − | 0.0367030i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −253.825 | −0.258741 | ||||||||
\(982\) | 188.535 | − | 326.553i | 0.191991 | − | 0.332538i | ||||
\(983\) | 1188.87 | − | 686.397i | 1.20944 | − | 0.698268i | 0.246799 | − | 0.969067i | \(-0.420621\pi\) |
0.962636 | + | 0.270799i | \(0.0872879\pi\) | |||||||
\(984\) | 9.97867 | + | 17.2836i | 0.0101409 | + | 0.0175646i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2647.37i | 2.68496i | ||||||||
\(987\) | 213.087 | + | 736.968i | 0.215894 | + | 0.746675i | ||||
\(988\) | −26.8331 | −0.0271590 | ||||||||
\(989\) | −256.304 | + | 443.932i | −0.259155 | + | 0.448870i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −321.812 | − | 557.395i | −0.324735 | − | 0.562457i | 0.656724 | − | 0.754131i | \(-0.271942\pi\) |
−0.981459 | + | 0.191674i | \(0.938608\pi\) | |||||||
\(992\) | −9.26691 | − | 5.35025i | −0.00934165 | − | 0.00539340i | ||||
\(993\) | 335.858i | 0.338226i | ||||||||
\(994\) | −279.295 | − | 68.9803i | −0.280981 | − | 0.0693967i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 21.6225 | − | 37.4513i | 0.0217093 | − | 0.0376017i | ||||
\(997\) | −610.431 | + | 352.433i | −0.612268 | + | 0.353493i | −0.773853 | − | 0.633366i | \(-0.781673\pi\) |
0.161584 | + | 0.986859i | \(0.448340\pi\) | |||||||
\(998\) | −481.615 | − | 834.181i | −0.482580 | − | 0.835853i | ||||
\(999\) | 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.p.i.901.6 | 16 | ||
5.2 | odd | 4 | 1050.3.q.e.649.12 | 32 | |||
5.3 | odd | 4 | 1050.3.q.e.649.4 | 32 | |||
5.4 | even | 2 | 210.3.o.b.61.4 | yes | 16 | ||
7.3 | odd | 6 | inner | 1050.3.p.i.451.6 | 16 | ||
15.14 | odd | 2 | 630.3.v.c.271.6 | 16 | |||
35.3 | even | 12 | 1050.3.q.e.199.12 | 32 | |||
35.9 | even | 6 | 1470.3.f.d.391.9 | 16 | |||
35.17 | even | 12 | 1050.3.q.e.199.4 | 32 | |||
35.19 | odd | 6 | 1470.3.f.d.391.15 | 16 | |||
35.24 | odd | 6 | 210.3.o.b.31.4 | ✓ | 16 | ||
105.59 | even | 6 | 630.3.v.c.451.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.o.b.31.4 | ✓ | 16 | 35.24 | odd | 6 | ||
210.3.o.b.61.4 | yes | 16 | 5.4 | even | 2 | ||
630.3.v.c.271.6 | 16 | 15.14 | odd | 2 | |||
630.3.v.c.451.6 | 16 | 105.59 | even | 6 | |||
1050.3.p.i.451.6 | 16 | 7.3 | odd | 6 | inner | ||
1050.3.p.i.901.6 | 16 | 1.1 | even | 1 | trivial | ||
1050.3.q.e.199.4 | 32 | 35.17 | even | 12 | |||
1050.3.q.e.199.12 | 32 | 35.3 | even | 12 | |||
1050.3.q.e.649.4 | 32 | 5.3 | odd | 4 | |||
1050.3.q.e.649.12 | 32 | 5.2 | odd | 4 | |||
1470.3.f.d.391.9 | 16 | 35.9 | even | 6 | |||
1470.3.f.d.391.15 | 16 | 35.19 | odd | 6 |