Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [350,2,Mod(51,350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(350, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("350.51");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 350 = 2 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 350.e (of order \(3\), 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: | \(2.79476407074\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 70) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 51.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 350.51 |
Dual form | 350.2.e.b.151.1 |
$q$-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 \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | −1.00000 | − | 1.73205i | −0.577350 | − | 1.00000i | −0.995782 | − | 0.0917517i | \(-0.970753\pi\) |
0.418432 | − | 0.908248i | \(-0.362580\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.00000 | 0.816497 | ||||||||
\(7\) | 2.00000 | + | 1.73205i | 0.755929 | + | 0.654654i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50000 | − | 2.59808i | −0.452267 | − | 0.783349i | 0.546259 | − | 0.837616i | \(-0.316051\pi\) |
−0.998526 | + | 0.0542666i | \(0.982718\pi\) | |||||||
\(12\) | −1.00000 | + | 1.73205i | −0.288675 | + | 0.500000i | ||||
\(13\) | 1.00000 | 0.277350 | 0.138675 | − | 0.990338i | \(-0.455716\pi\) | ||||
0.138675 | + | 0.990338i | \(0.455716\pi\) | |||||||
\(14\) | −2.50000 | + | 0.866025i | −0.668153 | + | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −3.00000 | − | 5.19615i | −0.727607 | − | 1.26025i | −0.957892 | − | 0.287129i | \(-0.907299\pi\) |
0.230285 | − | 0.973123i | \(-0.426034\pi\) | |||||||
\(18\) | −0.500000 | − | 0.866025i | −0.117851 | − | 0.204124i | ||||
\(19\) | 0.500000 | − | 0.866025i | 0.114708 | − | 0.198680i | −0.802955 | − | 0.596040i | \(-0.796740\pi\) |
0.917663 | + | 0.397360i | \(0.130073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | − | 5.19615i | 0.218218 | − | 1.13389i | ||||
\(22\) | 3.00000 | 0.639602 | ||||||||
\(23\) | 4.50000 | − | 7.79423i | 0.938315 | − | 1.62521i | 0.169701 | − | 0.985496i | \(-0.445720\pi\) |
0.768613 | − | 0.639713i | \(-0.220947\pi\) | |||||||
\(24\) | −1.00000 | − | 1.73205i | −0.204124 | − | 0.353553i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.500000 | + | 0.866025i | −0.0980581 | + | 0.169842i | ||||
\(27\) | −4.00000 | −0.769800 | ||||||||
\(28\) | 0.500000 | − | 2.59808i | 0.0944911 | − | 0.490990i | ||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | − | 6.92820i | −0.718421 | − | 1.24434i | −0.961625 | − | 0.274367i | \(-0.911532\pi\) |
0.243204 | − | 0.969975i | \(-0.421802\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −3.00000 | + | 5.19615i | −0.522233 | + | 0.904534i | ||||
\(34\) | 6.00000 | 1.02899 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −3.50000 | + | 6.06218i | −0.575396 | + | 0.996616i | 0.420602 | + | 0.907245i | \(0.361819\pi\) |
−0.995998 | + | 0.0893706i | \(0.971514\pi\) | |||||||
\(38\) | 0.500000 | + | 0.866025i | 0.0811107 | + | 0.140488i | ||||
\(39\) | −1.00000 | − | 1.73205i | −0.160128 | − | 0.277350i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.00000 | 0.468521 | 0.234261 | − | 0.972174i | \(-0.424733\pi\) | ||||
0.234261 | + | 0.972174i | \(0.424733\pi\) | |||||||
\(42\) | 4.00000 | + | 3.46410i | 0.617213 | + | 0.534522i | ||||
\(43\) | −2.00000 | −0.304997 | −0.152499 | − | 0.988304i | \(-0.548732\pi\) | ||||
−0.152499 | + | 0.988304i | \(0.548732\pi\) | |||||||
\(44\) | −1.50000 | + | 2.59808i | −0.226134 | + | 0.391675i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.50000 | + | 7.79423i | 0.663489 | + | 1.14920i | ||||
\(47\) | 4.50000 | − | 7.79423i | 0.656392 | − | 1.13691i | −0.325150 | − | 0.945662i | \(-0.605415\pi\) |
0.981543 | − | 0.191243i | \(-0.0612518\pi\) | |||||||
\(48\) | 2.00000 | 0.288675 | ||||||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.00000 | + | 10.3923i | −0.840168 | + | 1.45521i | ||||
\(52\) | −0.500000 | − | 0.866025i | −0.0693375 | − | 0.120096i | ||||
\(53\) | 4.50000 | + | 7.79423i | 0.618123 | + | 1.07062i | 0.989828 | + | 0.142269i | \(0.0454398\pi\) |
−0.371706 | + | 0.928351i | \(0.621227\pi\) | |||||||
\(54\) | 2.00000 | − | 3.46410i | 0.272166 | − | 0.471405i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.00000 | + | 1.73205i | 0.267261 | + | 0.231455i | ||||
\(57\) | −2.00000 | −0.264906 | ||||||||
\(58\) | −3.00000 | + | 5.19615i | −0.393919 | + | 0.682288i | ||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.00000 | + | 6.92820i | −0.512148 | + | 0.887066i | 0.487753 | + | 0.872982i | \(0.337817\pi\) |
−0.999901 | + | 0.0140840i | \(0.995517\pi\) | |||||||
\(62\) | 8.00000 | 1.01600 | ||||||||
\(63\) | −2.50000 | + | 0.866025i | −0.314970 | + | 0.109109i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.00000 | − | 5.19615i | −0.369274 | − | 0.639602i | ||||
\(67\) | 4.00000 | + | 6.92820i | 0.488678 | + | 0.846415i | 0.999915 | − | 0.0130248i | \(-0.00414604\pi\) |
−0.511237 | + | 0.859440i | \(0.670813\pi\) | |||||||
\(68\) | −3.00000 | + | 5.19615i | −0.363803 | + | 0.630126i | ||||
\(69\) | −18.0000 | −2.16695 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | −2.00000 | − | 3.46410i | −0.234082 | − | 0.405442i | 0.724923 | − | 0.688830i | \(-0.241875\pi\) |
−0.959006 | + | 0.283387i | \(0.908542\pi\) | |||||||
\(74\) | −3.50000 | − | 6.06218i | −0.406867 | − | 0.704714i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 1.50000 | − | 7.79423i | 0.170941 | − | 0.888235i | ||||
\(78\) | 2.00000 | 0.226455 | ||||||||
\(79\) | 5.00000 | − | 8.66025i | 0.562544 | − | 0.974355i | −0.434730 | − | 0.900561i | \(-0.643156\pi\) |
0.997274 | − | 0.0737937i | \(-0.0235106\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.50000 | + | 9.52628i | 0.611111 | + | 1.05848i | ||||
\(82\) | −1.50000 | + | 2.59808i | −0.165647 | + | 0.286910i | ||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | −5.00000 | + | 1.73205i | −0.545545 | + | 0.188982i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.00000 | − | 1.73205i | 0.107833 | − | 0.186772i | ||||
\(87\) | −6.00000 | − | 10.3923i | −0.643268 | − | 1.11417i | ||||
\(88\) | −1.50000 | − | 2.59808i | −0.159901 | − | 0.276956i | ||||
\(89\) | −3.00000 | + | 5.19615i | −0.317999 | + | 0.550791i | −0.980071 | − | 0.198650i | \(-0.936344\pi\) |
0.662071 | + | 0.749441i | \(0.269678\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | + | 1.73205i | 0.209657 | + | 0.181568i | ||||
\(92\) | −9.00000 | −0.938315 | ||||||||
\(93\) | −8.00000 | + | 13.8564i | −0.829561 | + | 1.43684i | ||||
\(94\) | 4.50000 | + | 7.79423i | 0.464140 | + | 0.803913i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | + | 1.73205i | −0.102062 | + | 0.176777i | ||||
\(97\) | 10.0000 | 1.01535 | 0.507673 | − | 0.861550i | \(-0.330506\pi\) | ||||
0.507673 | + | 0.861550i | \(0.330506\pi\) | |||||||
\(98\) | −6.50000 | − | 2.59808i | −0.656599 | − | 0.262445i | ||||
\(99\) | 3.00000 | 0.301511 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | − | 10.3923i | −0.597022 | − | 1.03407i | −0.993258 | − | 0.115924i | \(-0.963017\pi\) |
0.396236 | − | 0.918149i | \(-0.370316\pi\) | |||||||
\(102\) | −6.00000 | − | 10.3923i | −0.594089 | − | 1.02899i | ||||
\(103\) | −2.00000 | + | 3.46410i | −0.197066 | + | 0.341328i | −0.947576 | − | 0.319531i | \(-0.896475\pi\) |
0.750510 | + | 0.660859i | \(0.229808\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.00000 | −0.874157 | ||||||||
\(107\) | −6.00000 | + | 10.3923i | −0.580042 | + | 1.00466i | 0.415432 | + | 0.909624i | \(0.363630\pi\) |
−0.995474 | + | 0.0950377i | \(0.969703\pi\) | |||||||
\(108\) | 2.00000 | + | 3.46410i | 0.192450 | + | 0.333333i | ||||
\(109\) | 8.00000 | + | 13.8564i | 0.766261 | + | 1.32720i | 0.939577 | + | 0.342337i | \(0.111218\pi\) |
−0.173316 | + | 0.984866i | \(0.555448\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.0000 | 1.32882 | ||||||||
\(112\) | −2.50000 | + | 0.866025i | −0.236228 | + | 0.0818317i | ||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | 1.00000 | − | 1.73205i | 0.0936586 | − | 0.162221i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.00000 | − | 5.19615i | −0.278543 | − | 0.482451i | ||||
\(117\) | −0.500000 | + | 0.866025i | −0.0462250 | + | 0.0800641i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.00000 | − | 15.5885i | 0.275010 | − | 1.42899i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | −4.00000 | − | 6.92820i | −0.362143 | − | 0.627250i | ||||
\(123\) | −3.00000 | − | 5.19615i | −0.270501 | − | 0.468521i | ||||
\(124\) | −4.00000 | + | 6.92820i | −0.359211 | + | 0.622171i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.500000 | − | 2.59808i | 0.0445435 | − | 0.231455i | ||||
\(127\) | 1.00000 | 0.0887357 | 0.0443678 | − | 0.999015i | \(-0.485873\pi\) | ||||
0.0443678 | + | 0.999015i | \(0.485873\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 2.00000 | + | 3.46410i | 0.176090 | + | 0.304997i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.50000 | + | 2.59808i | −0.131056 | + | 0.226995i | −0.924084 | − | 0.382190i | \(-0.875170\pi\) |
0.793028 | + | 0.609185i | \(0.208503\pi\) | |||||||
\(132\) | 6.00000 | 0.522233 | ||||||||
\(133\) | 2.50000 | − | 0.866025i | 0.216777 | − | 0.0750939i | ||||
\(134\) | −8.00000 | −0.691095 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.00000 | − | 5.19615i | −0.257248 | − | 0.445566i | ||||
\(137\) | 6.00000 | + | 10.3923i | 0.512615 | + | 0.887875i | 0.999893 | + | 0.0146279i | \(0.00465636\pi\) |
−0.487278 | + | 0.873247i | \(0.662010\pi\) | |||||||
\(138\) | 9.00000 | − | 15.5885i | 0.766131 | − | 1.32698i | ||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −18.0000 | −1.51587 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.50000 | − | 2.59808i | −0.125436 | − | 0.217262i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.00000 | 0.331042 | ||||||||
\(147\) | 11.0000 | − | 8.66025i | 0.907265 | − | 0.714286i | ||||
\(148\) | 7.00000 | 0.575396 | ||||||||
\(149\) | 3.00000 | − | 5.19615i | 0.245770 | − | 0.425685i | −0.716578 | − | 0.697507i | \(-0.754293\pi\) |
0.962348 | + | 0.271821i | \(0.0876260\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.00000 | + | 8.66025i | 0.406894 | + | 0.704761i | 0.994540 | − | 0.104357i | \(-0.0332784\pi\) |
−0.587646 | + | 0.809118i | \(0.699945\pi\) | |||||||
\(152\) | 0.500000 | − | 0.866025i | 0.0405554 | − | 0.0702439i | ||||
\(153\) | 6.00000 | 0.485071 | ||||||||
\(154\) | 6.00000 | + | 5.19615i | 0.483494 | + | 0.418718i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.00000 | + | 1.73205i | −0.0800641 | + | 0.138675i | ||||
\(157\) | 11.5000 | + | 19.9186i | 0.917800 | + | 1.58968i | 0.802749 | + | 0.596316i | \(0.203370\pi\) |
0.115050 | + | 0.993360i | \(0.463297\pi\) | |||||||
\(158\) | 5.00000 | + | 8.66025i | 0.397779 | + | 0.688973i | ||||
\(159\) | 9.00000 | − | 15.5885i | 0.713746 | − | 1.23625i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 22.5000 | − | 7.79423i | 1.77325 | − | 0.614271i | ||||
\(162\) | −11.0000 | −0.864242 | ||||||||
\(163\) | 10.0000 | − | 17.3205i | 0.783260 | − | 1.35665i | −0.146772 | − | 0.989170i | \(-0.546888\pi\) |
0.930033 | − | 0.367477i | \(-0.119778\pi\) | |||||||
\(164\) | −1.50000 | − | 2.59808i | −0.117130 | − | 0.202876i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.00000 | −0.232147 | −0.116073 | − | 0.993241i | \(-0.537031\pi\) | ||||
−0.116073 | + | 0.993241i | \(0.537031\pi\) | |||||||
\(168\) | 1.00000 | − | 5.19615i | 0.0771517 | − | 0.400892i | ||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.500000 | + | 0.866025i | 0.0382360 | + | 0.0662266i | ||||
\(172\) | 1.00000 | + | 1.73205i | 0.0762493 | + | 0.132068i | ||||
\(173\) | 4.50000 | − | 7.79423i | 0.342129 | − | 0.592584i | −0.642699 | − | 0.766119i | \(-0.722185\pi\) |
0.984828 | + | 0.173534i | \(0.0555188\pi\) | |||||||
\(174\) | 12.0000 | 0.909718 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.00000 | 0.226134 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.00000 | − | 5.19615i | −0.224860 | − | 0.389468i | ||||
\(179\) | 1.50000 | + | 2.59808i | 0.112115 | + | 0.194189i | 0.916623 | − | 0.399753i | \(-0.130904\pi\) |
−0.804508 | + | 0.593942i | \(0.797571\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | −2.50000 | + | 0.866025i | −0.185312 | + | 0.0641941i | ||||
\(183\) | 16.0000 | 1.18275 | ||||||||
\(184\) | 4.50000 | − | 7.79423i | 0.331744 | − | 0.574598i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −8.00000 | − | 13.8564i | −0.586588 | − | 1.01600i | ||||
\(187\) | −9.00000 | + | 15.5885i | −0.658145 | + | 1.13994i | ||||
\(188\) | −9.00000 | −0.656392 | ||||||||
\(189\) | −8.00000 | − | 6.92820i | −0.581914 | − | 0.503953i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.00000 | + | 10.3923i | −0.434145 | + | 0.751961i | −0.997225 | − | 0.0744412i | \(-0.976283\pi\) |
0.563081 | + | 0.826402i | \(0.309616\pi\) | |||||||
\(192\) | −1.00000 | − | 1.73205i | −0.0721688 | − | 0.125000i | ||||
\(193\) | −8.00000 | − | 13.8564i | −0.575853 | − | 0.997406i | −0.995948 | − | 0.0899262i | \(-0.971337\pi\) |
0.420096 | − | 0.907480i | \(-0.361996\pi\) | |||||||
\(194\) | −5.00000 | + | 8.66025i | −0.358979 | + | 0.621770i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.50000 | − | 4.33013i | 0.392857 | − | 0.309295i | ||||
\(197\) | −15.0000 | −1.06871 | −0.534353 | − | 0.845262i | \(-0.679445\pi\) | ||||
−0.534353 | + | 0.845262i | \(0.679445\pi\) | |||||||
\(198\) | −1.50000 | + | 2.59808i | −0.106600 | + | 0.184637i | ||||
\(199\) | 8.00000 | + | 13.8564i | 0.567105 | + | 0.982255i | 0.996850 | + | 0.0793045i | \(0.0252700\pi\) |
−0.429745 | + | 0.902950i | \(0.641397\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.00000 | − | 13.8564i | 0.564276 | − | 0.977356i | ||||
\(202\) | 12.0000 | 0.844317 | ||||||||
\(203\) | 12.0000 | + | 10.3923i | 0.842235 | + | 0.729397i | ||||
\(204\) | 12.0000 | 0.840168 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.00000 | − | 3.46410i | −0.139347 | − | 0.241355i | ||||
\(207\) | 4.50000 | + | 7.79423i | 0.312772 | + | 0.541736i | ||||
\(208\) | −0.500000 | + | 0.866025i | −0.0346688 | + | 0.0600481i | ||||
\(209\) | −3.00000 | −0.207514 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.0000 | 1.58339 | 0.791693 | − | 0.610920i | \(-0.209200\pi\) | ||||
0.791693 | + | 0.610920i | \(0.209200\pi\) | |||||||
\(212\) | 4.50000 | − | 7.79423i | 0.309061 | − | 0.535310i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.00000 | − | 10.3923i | −0.410152 | − | 0.710403i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.00000 | −0.272166 | ||||||||
\(217\) | 4.00000 | − | 20.7846i | 0.271538 | − | 1.41095i | ||||
\(218\) | −16.0000 | −1.08366 | ||||||||
\(219\) | −4.00000 | + | 6.92820i | −0.270295 | + | 0.468165i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.00000 | − | 5.19615i | −0.201802 | − | 0.349531i | ||||
\(222\) | −7.00000 | + | 12.1244i | −0.469809 | + | 0.813733i | ||||
\(223\) | −8.00000 | −0.535720 | −0.267860 | − | 0.963458i | \(-0.586316\pi\) | ||||
−0.267860 | + | 0.963458i | \(0.586316\pi\) | |||||||
\(224\) | 0.500000 | − | 2.59808i | 0.0334077 | − | 0.173591i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.00000 | − | 10.3923i | −0.398234 | − | 0.689761i | 0.595274 | − | 0.803523i | \(-0.297043\pi\) |
−0.993508 | + | 0.113761i | \(0.963710\pi\) | |||||||
\(228\) | 1.00000 | + | 1.73205i | 0.0662266 | + | 0.114708i | ||||
\(229\) | 2.00000 | − | 3.46410i | 0.132164 | − | 0.228914i | −0.792347 | − | 0.610071i | \(-0.791141\pi\) |
0.924510 | + | 0.381157i | \(0.124474\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15.0000 | + | 5.19615i | −0.986928 | + | 0.341882i | ||||
\(232\) | 6.00000 | 0.393919 | ||||||||
\(233\) | −3.00000 | + | 5.19615i | −0.196537 | + | 0.340411i | −0.947403 | − | 0.320043i | \(-0.896303\pi\) |
0.750867 | + | 0.660454i | \(0.229636\pi\) | |||||||
\(234\) | −0.500000 | − | 0.866025i | −0.0326860 | − | 0.0566139i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −20.0000 | −1.29914 | ||||||||
\(238\) | 12.0000 | + | 10.3923i | 0.777844 | + | 0.673633i | ||||
\(239\) | −6.00000 | −0.388108 | −0.194054 | − | 0.980991i | \(-0.562164\pi\) | ||||
−0.194054 | + | 0.980991i | \(0.562164\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.500000 | + | 0.866025i | 0.0322078 | + | 0.0557856i | 0.881680 | − | 0.471848i | \(-0.156413\pi\) |
−0.849472 | + | 0.527633i | \(0.823079\pi\) | |||||||
\(242\) | 1.00000 | + | 1.73205i | 0.0642824 | + | 0.111340i | ||||
\(243\) | 5.00000 | − | 8.66025i | 0.320750 | − | 0.555556i | ||||
\(244\) | 8.00000 | 0.512148 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.00000 | 0.382546 | ||||||||
\(247\) | 0.500000 | − | 0.866025i | 0.0318142 | − | 0.0551039i | ||||
\(248\) | −4.00000 | − | 6.92820i | −0.254000 | − | 0.439941i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.0000 | −0.946792 | −0.473396 | − | 0.880850i | \(-0.656972\pi\) | ||||
−0.473396 | + | 0.880850i | \(0.656972\pi\) | |||||||
\(252\) | 2.00000 | + | 1.73205i | 0.125988 | + | 0.109109i | ||||
\(253\) | −27.0000 | −1.69748 | ||||||||
\(254\) | −0.500000 | + | 0.866025i | −0.0313728 | + | 0.0543393i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(258\) | −4.00000 | −0.249029 | ||||||||
\(259\) | −17.5000 | + | 6.06218i | −1.08740 | + | 0.376685i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.00000 | + | 5.19615i | −0.185695 | + | 0.321634i | ||||
\(262\) | −1.50000 | − | 2.59808i | −0.0926703 | − | 0.160510i | ||||
\(263\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(264\) | −3.00000 | + | 5.19615i | −0.184637 | + | 0.319801i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.500000 | + | 2.59808i | −0.0306570 | + | 0.159298i | ||||
\(267\) | 12.0000 | 0.734388 | ||||||||
\(268\) | 4.00000 | − | 6.92820i | 0.244339 | − | 0.423207i | ||||
\(269\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | − | 13.8564i | 0.485965 | − | 0.841717i | −0.513905 | − | 0.857847i | \(-0.671801\pi\) |
0.999870 | + | 0.0161307i | \(0.00513477\pi\) | |||||||
\(272\) | 6.00000 | 0.363803 | ||||||||
\(273\) | 1.00000 | − | 5.19615i | 0.0605228 | − | 0.314485i | ||||
\(274\) | −12.0000 | −0.724947 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 9.00000 | + | 15.5885i | 0.541736 | + | 0.938315i | ||||
\(277\) | −5.00000 | − | 8.66025i | −0.300421 | − | 0.520344i | 0.675810 | − | 0.737075i | \(-0.263794\pi\) |
−0.976231 | + | 0.216731i | \(0.930460\pi\) | |||||||
\(278\) | 2.00000 | − | 3.46410i | 0.119952 | − | 0.207763i | ||||
\(279\) | 8.00000 | 0.478947 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.0000 | −1.61068 | −0.805342 | − | 0.592810i | \(-0.798019\pi\) | ||||
−0.805342 | + | 0.592810i | \(0.798019\pi\) | |||||||
\(282\) | 9.00000 | − | 15.5885i | 0.535942 | − | 0.928279i | ||||
\(283\) | 7.00000 | + | 12.1244i | 0.416107 | + | 0.720718i | 0.995544 | − | 0.0942988i | \(-0.0300609\pi\) |
−0.579437 | + | 0.815017i | \(0.696728\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.00000 | 0.177394 | ||||||||
\(287\) | 6.00000 | + | 5.19615i | 0.354169 | + | 0.306719i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −9.50000 | + | 16.4545i | −0.558824 | + | 0.967911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.0000 | − | 17.3205i | −0.586210 | − | 1.01535i | ||||
\(292\) | −2.00000 | + | 3.46410i | −0.117041 | + | 0.202721i | ||||
\(293\) | 9.00000 | 0.525786 | 0.262893 | − | 0.964825i | \(-0.415323\pi\) | ||||
0.262893 | + | 0.964825i | \(0.415323\pi\) | |||||||
\(294\) | 2.00000 | + | 13.8564i | 0.116642 | + | 0.808122i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.50000 | + | 6.06218i | −0.203433 | + | 0.352357i | ||||
\(297\) | 6.00000 | + | 10.3923i | 0.348155 | + | 0.603023i | ||||
\(298\) | 3.00000 | + | 5.19615i | 0.173785 | + | 0.301005i | ||||
\(299\) | 4.50000 | − | 7.79423i | 0.260242 | − | 0.450752i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.00000 | − | 3.46410i | −0.230556 | − | 0.199667i | ||||
\(302\) | −10.0000 | −0.575435 | ||||||||
\(303\) | −12.0000 | + | 20.7846i | −0.689382 | + | 1.19404i | ||||
\(304\) | 0.500000 | + | 0.866025i | 0.0286770 | + | 0.0496700i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.00000 | + | 5.19615i | −0.171499 | + | 0.297044i | ||||
\(307\) | −14.0000 | −0.799022 | −0.399511 | − | 0.916728i | \(-0.630820\pi\) | ||||
−0.399511 | + | 0.916728i | \(0.630820\pi\) | |||||||
\(308\) | −7.50000 | + | 2.59808i | −0.427352 | + | 0.148039i | ||||
\(309\) | 8.00000 | 0.455104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0000 | + | 20.7846i | 0.680458 | + | 1.17859i | 0.974841 | + | 0.222900i | \(0.0715523\pi\) |
−0.294384 | + | 0.955687i | \(0.595114\pi\) | |||||||
\(312\) | −1.00000 | − | 1.73205i | −0.0566139 | − | 0.0980581i | ||||
\(313\) | −14.0000 | + | 24.2487i | −0.791327 | + | 1.37062i | 0.133819 | + | 0.991006i | \(0.457276\pi\) |
−0.925146 | + | 0.379612i | \(0.876057\pi\) | |||||||
\(314\) | −23.0000 | −1.29797 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.0000 | −0.562544 | ||||||||
\(317\) | 3.00000 | − | 5.19615i | 0.168497 | − | 0.291845i | −0.769395 | − | 0.638774i | \(-0.779442\pi\) |
0.937892 | + | 0.346929i | \(0.112775\pi\) | |||||||
\(318\) | 9.00000 | + | 15.5885i | 0.504695 | + | 0.874157i | ||||
\(319\) | −9.00000 | − | 15.5885i | −0.503903 | − | 0.872786i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 24.0000 | 1.33955 | ||||||||
\(322\) | −4.50000 | + | 23.3827i | −0.250775 | + | 1.30307i | ||||
\(323\) | −6.00000 | −0.333849 | ||||||||
\(324\) | 5.50000 | − | 9.52628i | 0.305556 | − | 0.529238i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10.0000 | + | 17.3205i | 0.553849 | + | 0.959294i | ||||
\(327\) | 16.0000 | − | 27.7128i | 0.884802 | − | 1.53252i | ||||
\(328\) | 3.00000 | 0.165647 | ||||||||
\(329\) | 22.5000 | − | 7.79423i | 1.24047 | − | 0.429710i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.50000 | − | 6.06218i | 0.192377 | − | 0.333207i | −0.753660 | − | 0.657264i | \(-0.771714\pi\) |
0.946038 | + | 0.324057i | \(0.105047\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.50000 | − | 6.06218i | −0.191799 | − | 0.332205i | ||||
\(334\) | 1.50000 | − | 2.59808i | 0.0820763 | − | 0.142160i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.00000 | + | 3.46410i | 0.218218 | + | 0.188982i | ||||
\(337\) | 22.0000 | 1.19842 | 0.599208 | − | 0.800593i | \(-0.295482\pi\) | ||||
0.599208 | + | 0.800593i | \(0.295482\pi\) | |||||||
\(338\) | 6.00000 | − | 10.3923i | 0.326357 | − | 0.565267i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.0000 | + | 20.7846i | −0.649836 | + | 1.12555i | ||||
\(342\) | −1.00000 | −0.0540738 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | −2.00000 | −0.107833 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.50000 | + | 7.79423i | 0.241921 | + | 0.419020i | ||||
\(347\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(348\) | −6.00000 | + | 10.3923i | −0.321634 | + | 0.557086i | ||||
\(349\) | 26.0000 | 1.39175 | 0.695874 | − | 0.718164i | \(-0.255017\pi\) | ||||
0.695874 | + | 0.718164i | \(0.255017\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.00000 | −0.213504 | ||||||||
\(352\) | −1.50000 | + | 2.59808i | −0.0799503 | + | 0.138478i | ||||
\(353\) | 6.00000 | + | 10.3923i | 0.319348 | + | 0.553127i | 0.980352 | − | 0.197256i | \(-0.0632029\pi\) |
−0.661004 | + | 0.750382i | \(0.729870\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | −30.0000 | + | 10.3923i | −1.58777 | + | 0.550019i | ||||
\(358\) | −3.00000 | −0.158555 | ||||||||
\(359\) | −9.00000 | + | 15.5885i | −0.475002 | + | 0.822727i | −0.999590 | − | 0.0286287i | \(-0.990886\pi\) |
0.524588 | + | 0.851356i | \(0.324219\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | + | 15.5885i | 0.473684 | + | 0.820445i | ||||
\(362\) | −1.00000 | + | 1.73205i | −0.0525588 | + | 0.0910346i | ||||
\(363\) | −4.00000 | −0.209946 | ||||||||
\(364\) | 0.500000 | − | 2.59808i | 0.0262071 | − | 0.136176i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −8.00000 | + | 13.8564i | −0.418167 | + | 0.724286i | ||||
\(367\) | −9.50000 | − | 16.4545i | −0.495896 | − | 0.858917i | 0.504093 | − | 0.863649i | \(-0.331827\pi\) |
−0.999989 | + | 0.00473247i | \(0.998494\pi\) | |||||||
\(368\) | 4.50000 | + | 7.79423i | 0.234579 | + | 0.406302i | ||||
\(369\) | −1.50000 | + | 2.59808i | −0.0780869 | + | 0.135250i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.50000 | + | 23.3827i | −0.233628 | + | 1.21397i | ||||
\(372\) | 16.0000 | 0.829561 | ||||||||
\(373\) | 1.00000 | − | 1.73205i | 0.0517780 | − | 0.0896822i | −0.838975 | − | 0.544170i | \(-0.816844\pi\) |
0.890753 | + | 0.454488i | \(0.150178\pi\) | |||||||
\(374\) | −9.00000 | − | 15.5885i | −0.465379 | − | 0.806060i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.50000 | − | 7.79423i | 0.232070 | − | 0.401957i | ||||
\(377\) | 6.00000 | 0.309016 | ||||||||
\(378\) | 10.0000 | − | 3.46410i | 0.514344 | − | 0.178174i | ||||
\(379\) | 23.0000 | 1.18143 | 0.590715 | − | 0.806880i | \(-0.298846\pi\) | ||||
0.590715 | + | 0.806880i | \(0.298846\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.00000 | − | 1.73205i | −0.0512316 | − | 0.0887357i | ||||
\(382\) | −6.00000 | − | 10.3923i | −0.306987 | − | 0.531717i | ||||
\(383\) | 10.5000 | − | 18.1865i | 0.536525 | − | 0.929288i | −0.462563 | − | 0.886586i | \(-0.653070\pi\) |
0.999088 | − | 0.0427020i | \(-0.0135966\pi\) | |||||||
\(384\) | 2.00000 | 0.102062 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 16.0000 | 0.814379 | ||||||||
\(387\) | 1.00000 | − | 1.73205i | 0.0508329 | − | 0.0880451i | ||||
\(388\) | −5.00000 | − | 8.66025i | −0.253837 | − | 0.439658i | ||||
\(389\) | 6.00000 | + | 10.3923i | 0.304212 | + | 0.526911i | 0.977086 | − | 0.212847i | \(-0.0682735\pi\) |
−0.672874 | + | 0.739758i | \(0.734940\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −54.0000 | −2.73090 | ||||||||
\(392\) | 1.00000 | + | 6.92820i | 0.0505076 | + | 0.349927i | ||||
\(393\) | 6.00000 | 0.302660 | ||||||||
\(394\) | 7.50000 | − | 12.9904i | 0.377845 | − | 0.654446i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.50000 | − | 2.59808i | −0.0753778 | − | 0.130558i | ||||
\(397\) | 7.00000 | − | 12.1244i | 0.351320 | − | 0.608504i | −0.635161 | − | 0.772380i | \(-0.719066\pi\) |
0.986481 | + | 0.163876i | \(0.0523996\pi\) | |||||||
\(398\) | −16.0000 | −0.802008 | ||||||||
\(399\) | −4.00000 | − | 3.46410i | −0.200250 | − | 0.173422i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.5000 | − | 23.3827i | 0.674158 | − | 1.16768i | −0.302556 | − | 0.953131i | \(-0.597840\pi\) |
0.976714 | − | 0.214544i | \(-0.0688266\pi\) | |||||||
\(402\) | 8.00000 | + | 13.8564i | 0.399004 | + | 0.691095i | ||||
\(403\) | −4.00000 | − | 6.92820i | −0.199254 | − | 0.345118i | ||||
\(404\) | −6.00000 | + | 10.3923i | −0.298511 | + | 0.517036i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15.0000 | + | 5.19615i | −0.744438 | + | 0.257881i | ||||
\(407\) | 21.0000 | 1.04093 | ||||||||
\(408\) | −6.00000 | + | 10.3923i | −0.297044 | + | 0.514496i | ||||
\(409\) | −13.0000 | − | 22.5167i | −0.642809 | − | 1.11338i | −0.984803 | − | 0.173675i | \(-0.944436\pi\) |
0.341994 | − | 0.939702i | \(-0.388898\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.0000 | − | 20.7846i | 0.591916 | − | 1.02523i | ||||
\(412\) | 4.00000 | 0.197066 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −9.00000 | −0.442326 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.500000 | − | 0.866025i | −0.0245145 | − | 0.0424604i | ||||
\(417\) | 4.00000 | + | 6.92820i | 0.195881 | + | 0.339276i | ||||
\(418\) | 1.50000 | − | 2.59808i | 0.0733674 | − | 0.127076i | ||||
\(419\) | −9.00000 | −0.439679 | −0.219839 | − | 0.975536i | \(-0.570553\pi\) | ||||
−0.219839 | + | 0.975536i | \(0.570553\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.00000 | 0.0974740 | 0.0487370 | − | 0.998812i | \(-0.484480\pi\) | ||||
0.0487370 | + | 0.998812i | \(0.484480\pi\) | |||||||
\(422\) | −11.5000 | + | 19.9186i | −0.559811 | + | 0.969622i | ||||
\(423\) | 4.50000 | + | 7.79423i | 0.218797 | + | 0.378968i | ||||
\(424\) | 4.50000 | + | 7.79423i | 0.218539 | + | 0.378521i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −20.0000 | + | 6.92820i | −0.967868 | + | 0.335279i | ||||
\(428\) | 12.0000 | 0.580042 | ||||||||
\(429\) | −3.00000 | + | 5.19615i | −0.144841 | + | 0.250873i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.00000 | − | 10.3923i | −0.289010 | − | 0.500580i | 0.684564 | − | 0.728953i | \(-0.259993\pi\) |
−0.973574 | + | 0.228373i | \(0.926659\pi\) | |||||||
\(432\) | 2.00000 | − | 3.46410i | 0.0962250 | − | 0.166667i | ||||
\(433\) | 40.0000 | 1.92228 | 0.961139 | − | 0.276066i | \(-0.0890309\pi\) | ||||
0.961139 | + | 0.276066i | \(0.0890309\pi\) | |||||||
\(434\) | 16.0000 | + | 13.8564i | 0.768025 | + | 0.665129i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.00000 | − | 13.8564i | 0.383131 | − | 0.663602i | ||||
\(437\) | −4.50000 | − | 7.79423i | −0.215264 | − | 0.372849i | ||||
\(438\) | −4.00000 | − | 6.92820i | −0.191127 | − | 0.331042i | ||||
\(439\) | −13.0000 | + | 22.5167i | −0.620456 | + | 1.07466i | 0.368945 | + | 0.929451i | \(0.379719\pi\) |
−0.989401 | + | 0.145210i | \(0.953614\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.50000 | − | 2.59808i | −0.309524 | − | 0.123718i | ||||
\(442\) | 6.00000 | 0.285391 | ||||||||
\(443\) | 6.00000 | − | 10.3923i | 0.285069 | − | 0.493753i | −0.687557 | − | 0.726130i | \(-0.741317\pi\) |
0.972626 | + | 0.232377i | \(0.0746503\pi\) | |||||||
\(444\) | −7.00000 | − | 12.1244i | −0.332205 | − | 0.575396i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.00000 | − | 6.92820i | 0.189405 | − | 0.328060i | ||||
\(447\) | −12.0000 | −0.567581 | ||||||||
\(448\) | 2.00000 | + | 1.73205i | 0.0944911 | + | 0.0818317i | ||||
\(449\) | 21.0000 | 0.991051 | 0.495526 | − | 0.868593i | \(-0.334975\pi\) | ||||
0.495526 | + | 0.868593i | \(0.334975\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.50000 | − | 7.79423i | −0.211897 | − | 0.367016i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.0000 | − | 17.3205i | 0.469841 | − | 0.813788i | ||||
\(454\) | 12.0000 | 0.563188 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.00000 | −0.0936586 | ||||||||
\(457\) | 7.00000 | − | 12.1244i | 0.327446 | − | 0.567153i | −0.654558 | − | 0.756012i | \(-0.727145\pi\) |
0.982004 | + | 0.188858i | \(0.0604787\pi\) | |||||||
\(458\) | 2.00000 | + | 3.46410i | 0.0934539 | + | 0.161867i | ||||
\(459\) | 12.0000 | + | 20.7846i | 0.560112 | + | 0.970143i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.0000 | −1.39724 | −0.698620 | − | 0.715493i | \(-0.746202\pi\) | ||||
−0.698620 | + | 0.715493i | \(0.746202\pi\) | |||||||
\(462\) | 3.00000 | − | 15.5885i | 0.139573 | − | 0.725241i | ||||
\(463\) | 1.00000 | 0.0464739 | 0.0232370 | − | 0.999730i | \(-0.492603\pi\) | ||||
0.0232370 | + | 0.999730i | \(0.492603\pi\) | |||||||
\(464\) | −3.00000 | + | 5.19615i | −0.139272 | + | 0.241225i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.00000 | − | 5.19615i | −0.138972 | − | 0.240707i | ||||
\(467\) | −3.00000 | + | 5.19615i | −0.138823 | + | 0.240449i | −0.927052 | − | 0.374934i | \(-0.877665\pi\) |
0.788228 | + | 0.615383i | \(0.210999\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | −4.00000 | + | 20.7846i | −0.184703 | + | 0.959744i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 23.0000 | − | 39.8372i | 1.05978 | − | 1.83560i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.00000 | + | 5.19615i | 0.137940 | + | 0.238919i | ||||
\(474\) | 10.0000 | − | 17.3205i | 0.459315 | − | 0.795557i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −15.0000 | + | 5.19615i | −0.687524 | + | 0.238165i | ||||
\(477\) | −9.00000 | −0.412082 | ||||||||
\(478\) | 3.00000 | − | 5.19615i | 0.137217 | − | 0.237666i | ||||
\(479\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.50000 | + | 6.06218i | −0.159586 | + | 0.276412i | ||||
\(482\) | −1.00000 | −0.0455488 | ||||||||
\(483\) | −36.0000 | − | 31.1769i | −1.63806 | − | 1.41860i | ||||
\(484\) | −2.00000 | −0.0909091 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 5.00000 | + | 8.66025i | 0.226805 | + | 0.392837i | ||||
\(487\) | −8.00000 | − | 13.8564i | −0.362515 | − | 0.627894i | 0.625859 | − | 0.779936i | \(-0.284748\pi\) |
−0.988374 | + | 0.152042i | \(0.951415\pi\) | |||||||
\(488\) | −4.00000 | + | 6.92820i | −0.181071 | + | 0.313625i | ||||
\(489\) | −40.0000 | −1.80886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.0000 | 1.62466 | 0.812329 | − | 0.583200i | \(-0.198200\pi\) | ||||
0.812329 | + | 0.583200i | \(0.198200\pi\) | |||||||
\(492\) | −3.00000 | + | 5.19615i | −0.135250 | + | 0.234261i | ||||
\(493\) | −18.0000 | − | 31.1769i | −0.810679 | − | 1.40414i | ||||
\(494\) | 0.500000 | + | 0.866025i | 0.0224961 | + | 0.0389643i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.00000 | 0.359211 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.00000 | − | 3.46410i | 0.0895323 | − | 0.155074i | −0.817781 | − | 0.575529i | \(-0.804796\pi\) |
0.907314 | + | 0.420455i | \(0.138129\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.00000 | + | 5.19615i | 0.134030 | + | 0.232147i | ||||
\(502\) | 7.50000 | − | 12.9904i | 0.334741 | − | 0.579789i | ||||
\(503\) | −24.0000 | −1.07011 | −0.535054 | − | 0.844818i | \(-0.679709\pi\) | ||||
−0.535054 | + | 0.844818i | \(0.679709\pi\) | |||||||
\(504\) | −2.50000 | + | 0.866025i | −0.111359 | + | 0.0385758i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 13.5000 | − | 23.3827i | 0.600148 | − | 1.03949i | ||||
\(507\) | 12.0000 | + | 20.7846i | 0.532939 | + | 0.923077i | ||||
\(508\) | −0.500000 | − | 0.866025i | −0.0221839 | − | 0.0384237i | ||||
\(509\) | 21.0000 | − | 36.3731i | 0.930809 | − | 1.61221i | 0.148866 | − | 0.988857i | \(-0.452438\pi\) |
0.781943 | − | 0.623350i | \(-0.214229\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.00000 | − | 10.3923i | 0.0884748 | − | 0.459728i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −2.00000 | + | 3.46410i | −0.0883022 | + | 0.152944i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.00000 | − | 3.46410i | 0.0880451 | − | 0.152499i | ||||
\(517\) | −27.0000 | −1.18746 | ||||||||
\(518\) | 3.50000 | − | 18.1865i | 0.153781 | − | 0.799070i | ||||
\(519\) | −18.0000 | −0.790112 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.50000 | + | 12.9904i | 0.328581 | + | 0.569119i | 0.982231 | − | 0.187678i | \(-0.0600963\pi\) |
−0.653650 | + | 0.756797i | \(0.726763\pi\) | |||||||
\(522\) | −3.00000 | − | 5.19615i | −0.131306 | − | 0.227429i | ||||
\(523\) | −14.0000 | + | 24.2487i | −0.612177 | + | 1.06032i | 0.378695 | + | 0.925521i | \(0.376373\pi\) |
−0.990873 | + | 0.134801i | \(0.956961\pi\) | |||||||
\(524\) | 3.00000 | 0.131056 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −24.0000 | + | 41.5692i | −1.04546 | + | 1.81078i | ||||
\(528\) | −3.00000 | − | 5.19615i | −0.130558 | − | 0.226134i | ||||
\(529\) | −29.0000 | − | 50.2295i | −1.26087 | − | 2.18389i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.00000 | − | 1.73205i | −0.0867110 | − | 0.0750939i | ||||
\(533\) | 3.00000 | 0.129944 | ||||||||
\(534\) | −6.00000 | + | 10.3923i | −0.259645 | + | 0.449719i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.00000 | + | 6.92820i | 0.172774 | + | 0.299253i | ||||
\(537\) | 3.00000 | − | 5.19615i | 0.129460 | − | 0.224231i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16.5000 | − | 12.9904i | 0.710705 | − | 0.559535i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.00000 | + | 6.92820i | −0.171973 | + | 0.297867i | −0.939110 | − | 0.343617i | \(-0.888348\pi\) |
0.767136 | + | 0.641484i | \(0.221681\pi\) | |||||||
\(542\) | 8.00000 | + | 13.8564i | 0.343629 | + | 0.595184i | ||||
\(543\) | −2.00000 | − | 3.46410i | −0.0858282 | − | 0.148659i | ||||
\(544\) | −3.00000 | + | 5.19615i | −0.128624 | + | 0.222783i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 4.00000 | + | 3.46410i | 0.171184 | + | 0.148250i | ||||
\(547\) | −8.00000 | −0.342055 | −0.171028 | − | 0.985266i | \(-0.554709\pi\) | ||||
−0.171028 | + | 0.985266i | \(0.554709\pi\) | |||||||
\(548\) | 6.00000 | − | 10.3923i | 0.256307 | − | 0.443937i | ||||
\(549\) | −4.00000 | − | 6.92820i | −0.170716 | − | 0.295689i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.00000 | − | 5.19615i | 0.127804 | − | 0.221364i | ||||
\(552\) | −18.0000 | −0.766131 | ||||||||
\(553\) | 25.0000 | − | 8.66025i | 1.06311 | − | 0.368271i | ||||
\(554\) | 10.0000 | 0.424859 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.00000 | + | 3.46410i | 0.0848189 | + | 0.146911i | ||||
\(557\) | −4.50000 | − | 7.79423i | −0.190671 | − | 0.330252i | 0.754802 | − | 0.655953i | \(-0.227733\pi\) |
−0.945473 | + | 0.325701i | \(0.894400\pi\) | |||||||
\(558\) | −4.00000 | + | 6.92820i | −0.169334 | + | 0.293294i | ||||
\(559\) | −2.00000 | −0.0845910 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 36.0000 | 1.51992 | ||||||||
\(562\) | 13.5000 | − | 23.3827i | 0.569463 | − | 0.986339i | ||||
\(563\) | 21.0000 | + | 36.3731i | 0.885044 | + | 1.53294i | 0.845663 | + | 0.533718i | \(0.179206\pi\) |
0.0393818 | + | 0.999224i | \(0.487461\pi\) | |||||||
\(564\) | 9.00000 | + | 15.5885i | 0.378968 | + | 0.656392i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −14.0000 | −0.588464 | ||||||||
\(567\) | −5.50000 | + | 28.5788i | −0.230978 | + | 1.20020i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.5000 | + | 18.1865i | −0.440183 | + | 0.762419i | −0.997703 | − | 0.0677445i | \(-0.978420\pi\) |
0.557520 | + | 0.830164i | \(0.311753\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0000 | − | 17.3205i | −0.418487 | − | 0.724841i | 0.577301 | − | 0.816532i | \(-0.304106\pi\) |
−0.995788 | + | 0.0916910i | \(0.970773\pi\) | |||||||
\(572\) | −1.50000 | + | 2.59808i | −0.0627182 | + | 0.108631i | ||||
\(573\) | 24.0000 | 1.00261 | ||||||||
\(574\) | −7.50000 | + | 2.59808i | −0.313044 | + | 0.108442i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 22.0000 | + | 38.1051i | 0.915872 | + | 1.58634i | 0.805620 | + | 0.592433i | \(0.201833\pi\) |
0.110252 | + | 0.993904i | \(0.464834\pi\) | |||||||
\(578\) | −9.50000 | − | 16.4545i | −0.395148 | − | 0.684416i | ||||
\(579\) | −16.0000 | + | 27.7128i | −0.664937 | + | 1.15171i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 20.0000 | 0.829027 | ||||||||
\(583\) | 13.5000 | − | 23.3827i | 0.559113 | − | 0.968412i | ||||
\(584\) | −2.00000 | − | 3.46410i | −0.0827606 | − | 0.143346i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.50000 | + | 7.79423i | −0.185893 | + | 0.321977i | ||||
\(587\) | 24.0000 | 0.990586 | 0.495293 | − | 0.868726i | \(-0.335061\pi\) | ||||
0.495293 | + | 0.868726i | \(0.335061\pi\) | |||||||
\(588\) | −13.0000 | − | 5.19615i | −0.536111 | − | 0.214286i | ||||
\(589\) | −8.00000 | −0.329634 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.0000 | + | 25.9808i | 0.617018 | + | 1.06871i | ||||
\(592\) | −3.50000 | − | 6.06218i | −0.143849 | − | 0.249154i | ||||
\(593\) | 12.0000 | − | 20.7846i | 0.492781 | − | 0.853522i | −0.507184 | − | 0.861838i | \(-0.669314\pi\) |
0.999965 | + | 0.00831589i | \(0.00264706\pi\) | |||||||
\(594\) | −12.0000 | −0.492366 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.00000 | −0.245770 | ||||||||
\(597\) | 16.0000 | − | 27.7128i | 0.654836 | − | 1.13421i | ||||
\(598\) | 4.50000 | + | 7.79423i | 0.184019 | + | 0.318730i | ||||
\(599\) | 21.0000 | + | 36.3731i | 0.858037 | + | 1.48616i | 0.873799 | + | 0.486287i | \(0.161649\pi\) |
−0.0157622 | + | 0.999876i | \(0.505017\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.0000 | 1.06056 | 0.530281 | − | 0.847822i | \(-0.322086\pi\) | ||||
0.530281 | + | 0.847822i | \(0.322086\pi\) | |||||||
\(602\) | 5.00000 | − | 1.73205i | 0.203785 | − | 0.0705931i | ||||
\(603\) | −8.00000 | −0.325785 | ||||||||
\(604\) | 5.00000 | − | 8.66025i | 0.203447 | − | 0.352381i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −12.0000 | − | 20.7846i | −0.487467 | − | 0.844317i | ||||
\(607\) | −0.500000 | + | 0.866025i | −0.0202944 | + | 0.0351509i | −0.875994 | − | 0.482322i | \(-0.839794\pi\) |
0.855700 | + | 0.517472i | \(0.173127\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 6.00000 | − | 31.1769i | 0.243132 | − | 1.26335i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.50000 | − | 7.79423i | 0.182051 | − | 0.315321i | ||||
\(612\) | −3.00000 | − | 5.19615i | −0.121268 | − | 0.210042i | ||||
\(613\) | 14.5000 | + | 25.1147i | 0.585649 | + | 1.01437i | 0.994794 | + | 0.101905i | \(0.0324938\pi\) |
−0.409145 | + | 0.912470i | \(0.634173\pi\) | |||||||
\(614\) | 7.00000 | − | 12.1244i | 0.282497 | − | 0.489299i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.50000 | − | 7.79423i | 0.0604367 | − | 0.314038i | ||||
\(617\) | 18.0000 | 0.724653 | 0.362326 | − | 0.932051i | \(-0.381983\pi\) | ||||
0.362326 | + | 0.932051i | \(0.381983\pi\) | |||||||
\(618\) | −4.00000 | + | 6.92820i | −0.160904 | + | 0.278693i | ||||
\(619\) | −11.5000 | − | 19.9186i | −0.462224 | − | 0.800595i | 0.536847 | − | 0.843679i | \(-0.319615\pi\) |
−0.999071 | + | 0.0430838i | \(0.986282\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.0000 | + | 31.1769i | −0.722315 | + | 1.25109i | ||||
\(622\) | −24.0000 | −0.962312 | ||||||||
\(623\) | −15.0000 | + | 5.19615i | −0.600962 | + | 0.208179i | ||||
\(624\) | 2.00000 | 0.0800641 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −14.0000 | − | 24.2487i | −0.559553 | − | 0.969173i | ||||
\(627\) | 3.00000 | + | 5.19615i | 0.119808 | + | 0.207514i | ||||
\(628\) | 11.5000 | − | 19.9186i | 0.458900 | − | 0.794838i | ||||
\(629\) | 42.0000 | 1.67465 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.0000 | 0.796187 | 0.398094 | − | 0.917345i | \(-0.369672\pi\) | ||||
0.398094 | + | 0.917345i | \(0.369672\pi\) | |||||||
\(632\) | 5.00000 | − | 8.66025i | 0.198889 | − | 0.344486i | ||||
\(633\) | −23.0000 | − | 39.8372i | −0.914168 | − | 1.58339i | ||||
\(634\) | 3.00000 | + | 5.19615i | 0.119145 | + | 0.206366i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −18.0000 | −0.713746 | ||||||||
\(637\) | 1.00000 | + | 6.92820i | 0.0396214 | + | 0.274505i | ||||
\(638\) | 18.0000 | 0.712627 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.5000 | − | 23.3827i | −0.533218 | − | 0.923561i | −0.999247 | − | 0.0387913i | \(-0.987649\pi\) |
0.466029 | − | 0.884769i | \(-0.345684\pi\) | |||||||
\(642\) | −12.0000 | + | 20.7846i | −0.473602 | + | 0.820303i | ||||
\(643\) | −2.00000 | −0.0788723 | −0.0394362 | − | 0.999222i | \(-0.512556\pi\) | ||||
−0.0394362 | + | 0.999222i | \(0.512556\pi\) | |||||||
\(644\) | −18.0000 | − | 15.5885i | −0.709299 | − | 0.614271i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.00000 | − | 5.19615i | 0.118033 | − | 0.204440i | ||||
\(647\) | 16.5000 | + | 28.5788i | 0.648682 | + | 1.12355i | 0.983438 | + | 0.181245i | \(0.0580128\pi\) |
−0.334756 | + | 0.942305i | \(0.608654\pi\) | |||||||
\(648\) | 5.50000 | + | 9.52628i | 0.216060 | + | 0.374228i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −40.0000 | + | 13.8564i | −1.56772 | + | 0.543075i | ||||
\(652\) | −20.0000 | −0.783260 | ||||||||
\(653\) | −4.50000 | + | 7.79423i | −0.176099 | + | 0.305012i | −0.940541 | − | 0.339680i | \(-0.889681\pi\) |
0.764442 | + | 0.644692i | \(0.223014\pi\) | |||||||
\(654\) | 16.0000 | + | 27.7128i | 0.625650 | + | 1.08366i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.50000 | + | 2.59808i | −0.0585652 | + | 0.101438i | ||||
\(657\) | 4.00000 | 0.156055 | ||||||||
\(658\) | −4.50000 | + | 23.3827i | −0.175428 | + | 0.911552i | ||||
\(659\) | −24.0000 | −0.934907 | −0.467454 | − | 0.884018i | \(-0.654829\pi\) | ||||
−0.467454 | + | 0.884018i | \(0.654829\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.0000 | + | 24.2487i | 0.544537 | + | 0.943166i | 0.998636 | + | 0.0522143i | \(0.0166279\pi\) |
−0.454099 | + | 0.890951i | \(0.650039\pi\) | |||||||
\(662\) | 3.50000 | + | 6.06218i | 0.136031 | + | 0.235613i | ||||
\(663\) | −6.00000 | + | 10.3923i | −0.233021 | + | 0.403604i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.00000 | 0.271244 | ||||||||
\(667\) | 27.0000 | − | 46.7654i | 1.04544 | − | 1.81076i | ||||
\(668\) | 1.50000 | + | 2.59808i | 0.0580367 | + | 0.100523i | ||||
\(669\) | 8.00000 | + | 13.8564i | 0.309298 | + | 0.535720i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.0000 | 0.926510 | ||||||||
\(672\) | −5.00000 | + | 1.73205i | −0.192879 | + | 0.0668153i | ||||
\(673\) | 34.0000 | 1.31060 | 0.655302 | − | 0.755367i | \(-0.272541\pi\) | ||||
0.655302 | + | 0.755367i | \(0.272541\pi\) | |||||||
\(674\) | −11.0000 | + | 19.0526i | −0.423704 | + | 0.733877i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.00000 | + | 10.3923i | 0.230769 | + | 0.399704i | ||||
\(677\) | −4.50000 | + | 7.79423i | −0.172949 | + | 0.299557i | −0.939450 | − | 0.342687i | \(-0.888663\pi\) |
0.766501 | + | 0.642244i | \(0.221996\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.0000 | + | 17.3205i | 0.767530 | + | 0.664700i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.0000 | + | 20.7846i | −0.459841 | + | 0.796468i | ||||
\(682\) | −12.0000 | − | 20.7846i | −0.459504 | − | 0.795884i | ||||
\(683\) | 6.00000 | + | 10.3923i | 0.229584 | + | 0.397650i | 0.957685 | − | 0.287819i | \(-0.0929302\pi\) |
−0.728101 | + | 0.685470i | \(0.759597\pi\) | |||||||
\(684\) | 0.500000 | − | 0.866025i | 0.0191180 | − | 0.0331133i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.50000 | − | 16.4545i | −0.324532 | − | 0.628235i | ||||
\(687\) | −8.00000 | −0.305219 | ||||||||
\(688\) | 1.00000 | − | 1.73205i | 0.0381246 | − | 0.0660338i | ||||
\(689\) | 4.50000 | + | 7.79423i | 0.171436 | + | 0.296936i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.0000 | + | 27.7128i | −0.608669 | + | 1.05425i | 0.382791 | + | 0.923835i | \(0.374963\pi\) |
−0.991460 | + | 0.130410i | \(0.958371\pi\) | |||||||
\(692\) | −9.00000 | −0.342129 | ||||||||
\(693\) | 6.00000 | + | 5.19615i | 0.227921 | + | 0.197386i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −6.00000 | − | 10.3923i | −0.227429 | − | 0.393919i | ||||
\(697\) | −9.00000 | − | 15.5885i | −0.340899 | − | 0.590455i | ||||
\(698\) | −13.0000 | + | 22.5167i | −0.492057 | + | 0.852268i | ||||
\(699\) | 12.0000 | 0.453882 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.0000 | −1.13308 | −0.566542 | − | 0.824033i | \(-0.691719\pi\) | ||||
−0.566542 | + | 0.824033i | \(0.691719\pi\) | |||||||
\(702\) | 2.00000 | − | 3.46410i | 0.0754851 | − | 0.130744i | ||||
\(703\) | 3.50000 | + | 6.06218i | 0.132005 | + | 0.228639i | ||||
\(704\) | −1.50000 | − | 2.59808i | −0.0565334 | − | 0.0979187i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.0000 | −0.451626 | ||||||||
\(707\) | 6.00000 | − | 31.1769i | 0.225653 | − | 1.17253i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.0000 | − | 39.8372i | 0.863783 | − | 1.49612i | −0.00446726 | − | 0.999990i | \(-0.501422\pi\) |
0.868250 | − | 0.496126i | \(-0.165245\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.00000 | + | 8.66025i | 0.187515 | + | 0.324785i | ||||
\(712\) | −3.00000 | + | 5.19615i | −0.112430 | + | 0.194734i | ||||
\(713\) | −72.0000 | −2.69642 | ||||||||
\(714\) | 6.00000 | − | 31.1769i | 0.224544 | − | 1.16677i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.50000 | − | 2.59808i | 0.0560576 | − | 0.0970947i | ||||
\(717\) | 6.00000 | + | 10.3923i | 0.224074 | + | 0.388108i | ||||
\(718\) | −9.00000 | − | 15.5885i | −0.335877 | − | 0.581756i | ||||
\(719\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.0000 | + | 3.46410i | −0.372419 | + | 0.129010i | ||||
\(722\) | −18.0000 | −0.669891 | ||||||||
\(723\) | 1.00000 | − | 1.73205i | 0.0371904 | − | 0.0644157i | ||||
\(724\) | −1.00000 | − | 1.73205i | −0.0371647 | − | 0.0643712i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.00000 | − | 3.46410i | 0.0742270 | − | 0.128565i | ||||
\(727\) | 1.00000 | 0.0370879 | 0.0185440 | − | 0.999828i | \(-0.494097\pi\) | ||||
0.0185440 | + | 0.999828i | \(0.494097\pi\) | |||||||
\(728\) | 2.00000 | + | 1.73205i | 0.0741249 | + | 0.0641941i | ||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.00000 | + | 10.3923i | 0.221918 | + | 0.384373i | ||||
\(732\) | −8.00000 | − | 13.8564i | −0.295689 | − | 0.512148i | ||||
\(733\) | −21.5000 | + | 37.2391i | −0.794121 | + | 1.37546i | 0.129275 | + | 0.991609i | \(0.458735\pi\) |
−0.923396 | + | 0.383849i | \(0.874598\pi\) | |||||||
\(734\) | 19.0000 | 0.701303 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.00000 | −0.331744 | ||||||||
\(737\) | 12.0000 | − | 20.7846i | 0.442026 | − | 0.765611i | ||||
\(738\) | −1.50000 | − | 2.59808i | −0.0552158 | − | 0.0956365i | ||||
\(739\) | −17.5000 | − | 30.3109i | −0.643748 | − | 1.11500i | −0.984589 | − | 0.174883i | \(-0.944045\pi\) |
0.340841 | − | 0.940121i | \(-0.389288\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.00000 | −0.0734718 | ||||||||
\(742\) | −18.0000 | − | 15.5885i | −0.660801 | − | 0.572270i | ||||
\(743\) | 45.0000 | 1.65089 | 0.825445 | − | 0.564483i | \(-0.190924\pi\) | ||||
0.825445 | + | 0.564483i | \(0.190924\pi\) | |||||||
\(744\) | −8.00000 | + | 13.8564i | −0.293294 | + | 0.508001i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.00000 | + | 1.73205i | 0.0366126 | + | 0.0634149i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 18.0000 | 0.658145 | ||||||||
\(749\) | −30.0000 | + | 10.3923i | −1.09618 | + | 0.379727i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.00000 | − | 8.66025i | 0.182453 | − | 0.316017i | −0.760263 | − | 0.649616i | \(-0.774930\pi\) |
0.942715 | + | 0.333599i | \(0.108263\pi\) | |||||||
\(752\) | 4.50000 | + | 7.79423i | 0.164098 | + | 0.284226i | ||||
\(753\) | 15.0000 | + | 25.9808i | 0.546630 | + | 0.946792i | ||||
\(754\) | −3.00000 | + | 5.19615i | −0.109254 | + | 0.189233i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.00000 | + | 10.3923i | −0.0727393 | + | 0.377964i | ||||
\(757\) | −38.0000 | −1.38113 | −0.690567 | − | 0.723269i | \(-0.742639\pi\) | ||||
−0.690567 | + | 0.723269i | \(0.742639\pi\) | |||||||
\(758\) | −11.5000 | + | 19.9186i | −0.417699 | + | 0.723476i | ||||
\(759\) | 27.0000 | + | 46.7654i | 0.980038 | + | 1.69748i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.5000 | − | 23.3827i | 0.489375 | − | 0.847622i | −0.510551 | − | 0.859848i | \(-0.670558\pi\) |
0.999925 | + | 0.0122260i | \(0.00389175\pi\) | |||||||
\(762\) | 2.00000 | 0.0724524 | ||||||||
\(763\) | −8.00000 | + | 41.5692i | −0.289619 | + | 1.50491i | ||||
\(764\) | 12.0000 | 0.434145 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10.5000 | + | 18.1865i | 0.379380 | + | 0.657106i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | + | 1.73205i | −0.0360844 | + | 0.0625000i | ||||
\(769\) | 23.0000 | 0.829401 | 0.414701 | − | 0.909958i | \(-0.363886\pi\) | ||||
0.414701 | + | 0.909958i | \(0.363886\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.00000 | + | 13.8564i | −0.287926 | + | 0.498703i | ||||
\(773\) | −25.5000 | − | 44.1673i | −0.917171 | − | 1.58859i | −0.803691 | − | 0.595047i | \(-0.797133\pi\) |
−0.113480 | − | 0.993540i | \(-0.536200\pi\) | |||||||
\(774\) | 1.00000 | + | 1.73205i | 0.0359443 | + | 0.0622573i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 10.0000 | 0.358979 | ||||||||
\(777\) | 28.0000 | + | 24.2487i | 1.00449 | + | 0.869918i | ||||
\(778\) | −12.0000 | −0.430221 | ||||||||
\(779\) | 1.50000 | − | 2.59808i | 0.0537431 | − | 0.0930857i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 27.0000 | − | 46.7654i | 0.965518 | − | 1.67233i | ||||
\(783\) | −24.0000 | −0.857690 | ||||||||
\(784\) | −6.50000 | − | 2.59808i | −0.232143 | − | 0.0927884i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.00000 | + | 5.19615i | −0.107006 | + | 0.185341i | ||||
\(787\) | −11.0000 | − | 19.0526i | −0.392108 | − | 0.679150i | 0.600620 | − | 0.799535i | \(-0.294921\pi\) |
−0.992727 | + | 0.120384i | \(0.961587\pi\) | |||||||
\(788\) | 7.50000 | + | 12.9904i | 0.267176 | + | 0.462763i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.00000 | 0.106600 | ||||||||
\(793\) | −4.00000 | + | 6.92820i | −0.142044 | + | 0.246028i | ||||
\(794\) | 7.00000 | + | 12.1244i | 0.248421 | + | 0.430277i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.00000 | − | 13.8564i | 0.283552 | − | 0.491127i | ||||
\(797\) | −6.00000 | −0.212531 | −0.106265 | − | 0.994338i | \(-0.533889\pi\) | ||||
−0.106265 | + | 0.994338i | \(0.533889\pi\) | |||||||
\(798\) | 5.00000 | − | 1.73205i | 0.176998 | − | 0.0613139i | ||||
\(799\) | −54.0000 | −1.91038 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.00000 | − | 5.19615i | −0.106000 | − | 0.183597i | ||||
\(802\) | 13.5000 | + | 23.3827i | 0.476702 | + | 0.825671i | ||||
\(803\) | −6.00000 | + | 10.3923i | −0.211735 | + | 0.366736i | ||||
\(804\) | −16.0000 | −0.564276 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.00000 | 0.281788 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.00000 | − | 10.3923i | −0.211079 | − | 0.365600i | ||||
\(809\) | 4.50000 | + | 7.79423i | 0.158212 | + | 0.274030i | 0.934224 | − | 0.356687i | \(-0.116094\pi\) |
−0.776012 | + | 0.630718i | \(0.782761\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.0000 | −0.877869 | −0.438934 | − | 0.898519i | \(-0.644644\pi\) | ||||
−0.438934 | + | 0.898519i | \(0.644644\pi\) | |||||||
\(812\) | 3.00000 | − | 15.5885i | 0.105279 | − | 0.547048i | ||||
\(813\) | −32.0000 | −1.12229 | ||||||||
\(814\) | −10.5000 | + | 18.1865i | −0.368025 | + | 0.637438i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −6.00000 | − | 10.3923i | −0.210042 | − | 0.363803i | ||||
\(817\) | −1.00000 | + | 1.73205i | −0.0349856 | + | 0.0605968i | ||||
\(818\) | 26.0000 | 0.909069 | ||||||||
\(819\) | −2.50000 | + | 0.866025i | −0.0873571 | + | 0.0302614i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.0000 | + | 25.9808i | −0.523504 | + | 0.906735i | 0.476122 | + | 0.879379i | \(0.342042\pi\) |
−0.999626 | + | 0.0273557i | \(0.991291\pi\) | |||||||
\(822\) | 12.0000 | + | 20.7846i | 0.418548 | + | 0.724947i | ||||
\(823\) | −2.00000 | − | 3.46410i | −0.0697156 | − | 0.120751i | 0.829060 | − | 0.559159i | \(-0.188876\pi\) |
−0.898776 | + | 0.438408i | \(0.855543\pi\) | |||||||
\(824\) | −2.00000 | + | 3.46410i | −0.0696733 | + | 0.120678i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.00000 | −0.208640 | −0.104320 | − | 0.994544i | \(-0.533267\pi\) | ||||
−0.104320 | + | 0.994544i | \(0.533267\pi\) | |||||||
\(828\) | 4.50000 | − | 7.79423i | 0.156386 | − | 0.270868i | ||||
\(829\) | −7.00000 | − | 12.1244i | −0.243120 | − | 0.421096i | 0.718481 | − | 0.695546i | \(-0.244838\pi\) |
−0.961601 | + | 0.274450i | \(0.911504\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.0000 | + | 17.3205i | −0.346896 | + | 0.600842i | ||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 33.0000 | − | 25.9808i | 1.14338 | − | 0.900180i | ||||
\(834\) | −8.00000 | −0.277017 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.50000 | + | 2.59808i | 0.0518786 | + | 0.0898563i | ||||
\(837\) | 16.0000 | + | 27.7128i | 0.553041 | + | 0.957895i | ||||
\(838\) | 4.50000 | − | 7.79423i | 0.155450 | − | 0.269247i | ||||
\(839\) | −30.0000 | −1.03572 | −0.517858 | − | 0.855467i | \(-0.673270\pi\) | ||||
−0.517858 | + | 0.855467i | \(0.673270\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | −1.00000 | + | 1.73205i | −0.0344623 | + | 0.0596904i | ||||
\(843\) | 27.0000 | + | 46.7654i | 0.929929 | + | 1.61068i | ||||
\(844\) | −11.5000 | − | 19.9186i | −0.395846 | − | 0.685626i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9.00000 | −0.309426 | ||||||||
\(847\) | 5.00000 | − | 1.73205i | 0.171802 | − | 0.0595140i | ||||
\(848\) | −9.00000 | −0.309061 | ||||||||
\(849\) | 14.0000 | − | 24.2487i | 0.480479 | − | 0.832214i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 31.5000 | + | 54.5596i | 1.07981 | + | 1.87028i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.0000 | 0.650548 | 0.325274 | − | 0.945620i | \(-0.394544\pi\) | ||||
0.325274 | + | 0.945620i | \(0.394544\pi\) | |||||||
\(854\) | 4.00000 | − | 20.7846i | 0.136877 | − | 0.711235i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.00000 | + | 10.3923i | −0.205076 | + | 0.355202i | ||||
\(857\) | −9.00000 | − | 15.5885i | −0.307434 | − | 0.532492i | 0.670366 | − | 0.742030i | \(-0.266137\pi\) |
−0.977800 | + | 0.209539i | \(0.932804\pi\) | |||||||
\(858\) | −3.00000 | − | 5.19615i | −0.102418 | − | 0.177394i | ||||
\(859\) | −16.0000 | + | 27.7128i | −0.545913 | + | 0.945549i | 0.452636 | + | 0.891695i | \(0.350484\pi\) |
−0.998549 | + | 0.0538535i | \(0.982850\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.00000 | − | 15.5885i | 0.102240 | − | 0.531253i | ||||
\(862\) | 12.0000 | 0.408722 | ||||||||
\(863\) | −1.50000 | + | 2.59808i | −0.0510606 | + | 0.0884395i | −0.890426 | − | 0.455128i | \(-0.849593\pi\) |
0.839365 | + | 0.543568i | \(0.182927\pi\) | |||||||
\(864\) | 2.00000 | + | 3.46410i | 0.0680414 | + | 0.117851i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −20.0000 | + | 34.6410i | −0.679628 | + | 1.17715i | ||||
\(867\) | 38.0000 | 1.29055 | ||||||||
\(868\) | −20.0000 | + | 6.92820i | −0.678844 | + | 0.235159i | ||||
\(869\) | −30.0000 | −1.01768 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.00000 | + | 6.92820i | 0.135535 | + | 0.234753i | ||||
\(872\) | 8.00000 | + | 13.8564i | 0.270914 | + | 0.469237i | ||||
\(873\) | −5.00000 | + | 8.66025i | −0.169224 | + | 0.293105i | ||||
\(874\) | 9.00000 | 0.304430 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.00000 | 0.270295 | ||||||||
\(877\) | −6.50000 | + | 11.2583i | −0.219489 | + | 0.380167i | −0.954652 | − | 0.297724i | \(-0.903772\pi\) |
0.735163 | + | 0.677891i | \(0.237106\pi\) | |||||||
\(878\) | −13.0000 | − | 22.5167i | −0.438729 | − | 0.759900i | ||||
\(879\) | −9.00000 | − | 15.5885i | −0.303562 | − | 0.525786i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.0000 | 1.11180 | 0.555899 | − | 0.831250i | \(-0.312374\pi\) | ||||
0.555899 | + | 0.831250i | \(0.312374\pi\) | |||||||
\(882\) | 5.50000 | − | 4.33013i | 0.185195 | − | 0.145803i | ||||
\(883\) | −8.00000 | −0.269221 | −0.134611 | − | 0.990899i | \(-0.542978\pi\) | ||||
−0.134611 | + | 0.990899i | \(0.542978\pi\) | |||||||
\(884\) | −3.00000 | + | 5.19615i | −0.100901 | + | 0.174766i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.00000 | + | 10.3923i | 0.201574 | + | 0.349136i | ||||
\(887\) | −24.0000 | + | 41.5692i | −0.805841 | + | 1.39576i | 0.109881 | + | 0.993945i | \(0.464953\pi\) |
−0.915722 | + | 0.401813i | \(0.868380\pi\) | |||||||
\(888\) | 14.0000 | 0.469809 | ||||||||
\(889\) | 2.00000 | + | 1.73205i | 0.0670778 | + | 0.0580911i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 16.5000 | − | 28.5788i | 0.552771 | − | 0.957427i | ||||
\(892\) | 4.00000 | + | 6.92820i | 0.133930 | + | 0.231973i | ||||
\(893\) | −4.50000 | − | 7.79423i | −0.150587 | − | 0.260824i | ||||
\(894\) | 6.00000 | − | 10.3923i | 0.200670 | − | 0.347571i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.50000 | + | 0.866025i | −0.0835191 | + | 0.0289319i | ||||
\(897\) | −18.0000 | −0.601003 | ||||||||
\(898\) | −10.5000 | + | 18.1865i | −0.350390 | + | 0.606892i | ||||
\(899\) | −24.0000 | − | 41.5692i | −0.800445 | − | 1.38641i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27.0000 | − | 46.7654i | 0.899500 | − | 1.55798i | ||||
\(902\) | 9.00000 | 0.299667 | ||||||||
\(903\) | −2.00000 | + | 10.3923i | −0.0665558 | + | 0.345834i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 10.0000 | + | 17.3205i | 0.332228 | + | 0.575435i | ||||
\(907\) | −5.00000 | − | 8.66025i | −0.166022 | − | 0.287559i | 0.770996 | − | 0.636841i | \(-0.219759\pi\) |
−0.937018 | + | 0.349281i | \(0.886426\pi\) | |||||||
\(908\) | −6.00000 | + | 10.3923i | −0.199117 | + | 0.344881i | ||||
\(909\) | 12.0000 | 0.398015 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.0000 | −0.993944 | −0.496972 | − | 0.867766i | \(-0.665555\pi\) | ||||
−0.496972 | + | 0.867766i | \(0.665555\pi\) | |||||||
\(912\) | 1.00000 | − | 1.73205i | 0.0331133 | − | 0.0573539i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 7.00000 | + | 12.1244i | 0.231539 | + | 0.401038i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.00000 | −0.132164 | ||||||||
\(917\) | −7.50000 | + | 2.59808i | −0.247672 | + | 0.0857960i | ||||
\(918\) | −24.0000 | −0.792118 | ||||||||
\(919\) | 11.0000 | − | 19.0526i | 0.362857 | − | 0.628486i | −0.625573 | − | 0.780165i | \(-0.715135\pi\) |
0.988430 | + | 0.151680i | \(0.0484682\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.0000 | + | 24.2487i | 0.461316 | + | 0.799022i | ||||
\(922\) | 15.0000 | − | 25.9808i | 0.493999 | − | 0.855631i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 12.0000 | + | 10.3923i | 0.394771 | + | 0.341882i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −0.500000 | + | 0.866025i | −0.0164310 | + | 0.0284594i | ||||
\(927\) | −2.00000 | − | 3.46410i | −0.0656886 | − | 0.113776i | ||||
\(928\) | −3.00000 | − | 5.19615i | −0.0984798 | − | 0.170572i | ||||
\(929\) | −28.5000 | + | 49.3634i | −0.935055 | + | 1.61956i | −0.160518 | + | 0.987033i | \(0.551317\pi\) |
−0.774536 | + | 0.632529i | \(0.782017\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.50000 | + | 2.59808i | 0.213029 | + | 0.0851485i | ||||
\(932\) | 6.00000 | 0.196537 | ||||||||
\(933\) | 24.0000 | − | 41.5692i | 0.785725 | − | 1.36092i | ||||
\(934\) | −3.00000 | − | 5.19615i | −0.0981630 | − | 0.170023i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.500000 | + | 0.866025i | −0.0163430 | + | 0.0283069i | ||||
\(937\) | 10.0000 | 0.326686 | 0.163343 | − | 0.986569i | \(-0.447772\pi\) | ||||
0.163343 | + | 0.986569i | \(0.447772\pi\) | |||||||
\(938\) | −16.0000 | − | 13.8564i | −0.522419 | − | 0.452428i | ||||
\(939\) | 56.0000 | 1.82749 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.0000 | − | 41.5692i | −0.782378 | − | 1.35512i | −0.930553 | − | 0.366157i | \(-0.880673\pi\) |
0.148176 | − | 0.988961i | \(-0.452660\pi\) | |||||||
\(942\) | 23.0000 | + | 39.8372i | 0.749380 | + | 1.29797i | ||||
\(943\) | 13.5000 | − | 23.3827i | 0.439620 | − | 0.761445i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.00000 | −0.195077 | ||||||||
\(947\) | 3.00000 | − | 5.19615i | 0.0974869 | − | 0.168852i | −0.813157 | − | 0.582045i | \(-0.802253\pi\) |
0.910644 | + | 0.413192i | \(0.135586\pi\) | |||||||
\(948\) | 10.0000 | + | 17.3205i | 0.324785 | + | 0.562544i | ||||
\(949\) | −2.00000 | − | 3.46410i | −0.0649227 | − | 0.112449i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.0000 | −0.389127 | ||||||||
\(952\) | 3.00000 | − | 15.5885i | 0.0972306 | − | 0.505225i | ||||
\(953\) | −36.0000 | −1.16615 | −0.583077 | − | 0.812417i | \(-0.698151\pi\) | ||||
−0.583077 | + | 0.812417i | \(0.698151\pi\) | |||||||
\(954\) | 4.50000 | − | 7.79423i | 0.145693 | − | 0.252347i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.00000 | + | 5.19615i | 0.0970269 | + | 0.168056i | ||||
\(957\) | −18.0000 | + | 31.1769i | −0.581857 | + | 1.00781i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.00000 | + | 31.1769i | −0.193750 | + | 1.00676i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.5000 | + | 28.5788i | −0.532258 | + | 0.921898i | ||||
\(962\) | −3.50000 | − | 6.06218i | −0.112845 | − | 0.195452i | ||||
\(963\) | −6.00000 | − | 10.3923i | −0.193347 | − | 0.334887i | ||||
\(964\) | 0.500000 | − | 0.866025i | 0.0161039 | − | 0.0278928i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 45.0000 | − | 15.5885i | 1.44785 | − | 0.501550i | ||||
\(967\) | −32.0000 | −1.02905 | −0.514525 | − | 0.857475i | \(-0.672032\pi\) | ||||
−0.514525 | + | 0.857475i | \(0.672032\pi\) | |||||||
\(968\) | 1.00000 | − | 1.73205i | 0.0321412 | − | 0.0556702i | ||||
\(969\) | 6.00000 | + | 10.3923i | 0.192748 | + | 0.333849i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.5000 | − | 38.9711i | 0.722059 | − | 1.25064i | −0.238114 | − | 0.971237i | \(-0.576529\pi\) |
0.960173 | − | 0.279406i | \(-0.0901376\pi\) | |||||||
\(972\) | −10.0000 | −0.320750 | ||||||||
\(973\) | −8.00000 | − | 6.92820i | −0.256468 | − | 0.222108i | ||||
\(974\) | 16.0000 | 0.512673 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.00000 | − | 6.92820i | −0.128037 | − | 0.221766i | ||||
\(977\) | −21.0000 | − | 36.3731i | −0.671850 | − | 1.16368i | −0.977379 | − | 0.211495i | \(-0.932167\pi\) |
0.305530 | − | 0.952183i | \(-0.401167\pi\) | |||||||
\(978\) | 20.0000 | − | 34.6410i | 0.639529 | − | 1.10770i | ||||
\(979\) | 18.0000 | 0.575282 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.0000 | −0.510841 | ||||||||
\(982\) | −18.0000 | + | 31.1769i | −0.574403 | + | 0.994895i | ||||
\(983\) | 1.50000 | + | 2.59808i | 0.0478426 | + | 0.0828658i | 0.888955 | − | 0.457995i | \(-0.151432\pi\) |
−0.841112 | + | 0.540860i | \(0.818099\pi\) | |||||||
\(984\) | −3.00000 | − | 5.19615i | −0.0956365 | − | 0.165647i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 36.0000 | 1.14647 | ||||||||
\(987\) | −36.0000 | − | 31.1769i | −1.14589 | − | 0.992372i | ||||
\(988\) | −1.00000 | −0.0318142 | ||||||||
\(989\) | −9.00000 | + | 15.5885i | −0.286183 | + | 0.495684i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.0000 | − | 38.1051i | −0.698853 | − | 1.21045i | −0.968864 | − | 0.247592i | \(-0.920361\pi\) |
0.270011 | − | 0.962857i | \(-0.412973\pi\) | |||||||
\(992\) | −4.00000 | + | 6.92820i | −0.127000 | + | 0.219971i | ||||
\(993\) | −14.0000 | −0.444277 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.0000 | − | 19.0526i | −0.348373 | − | 0.603401i | 0.637587 | − | 0.770378i | \(-0.279933\pi\) |
−0.985961 | + | 0.166978i | \(0.946599\pi\) | |||||||
\(998\) | 2.00000 | + | 3.46410i | 0.0633089 | + | 0.109654i | ||||
\(999\) | 14.0000 | − | 24.2487i | 0.442940 | − | 0.767195i |
(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 | 350.2.e.b.51.1 | 2 | ||
5.2 | odd | 4 | 350.2.j.d.149.1 | 4 | |||
5.3 | odd | 4 | 350.2.j.d.149.2 | 4 | |||
5.4 | even | 2 | 70.2.e.d.51.1 | yes | 2 | ||
7.2 | even | 3 | 2450.2.a.bf.1.1 | 1 | |||
7.4 | even | 3 | inner | 350.2.e.b.151.1 | 2 | ||
7.5 | odd | 6 | 2450.2.a.v.1.1 | 1 | |||
15.14 | odd | 2 | 630.2.k.d.541.1 | 2 | |||
20.19 | odd | 2 | 560.2.q.b.401.1 | 2 | |||
35.2 | odd | 12 | 2450.2.c.q.99.2 | 2 | |||
35.4 | even | 6 | 70.2.e.d.11.1 | ✓ | 2 | ||
35.9 | even | 6 | 490.2.a.a.1.1 | 1 | |||
35.12 | even | 12 | 2450.2.c.e.99.2 | 2 | |||
35.18 | odd | 12 | 350.2.j.d.249.1 | 4 | |||
35.19 | odd | 6 | 490.2.a.d.1.1 | 1 | |||
35.23 | odd | 12 | 2450.2.c.q.99.1 | 2 | |||
35.24 | odd | 6 | 490.2.e.g.361.1 | 2 | |||
35.32 | odd | 12 | 350.2.j.d.249.2 | 4 | |||
35.33 | even | 12 | 2450.2.c.e.99.1 | 2 | |||
35.34 | odd | 2 | 490.2.e.g.471.1 | 2 | |||
105.44 | odd | 6 | 4410.2.a.x.1.1 | 1 | |||
105.74 | odd | 6 | 630.2.k.d.361.1 | 2 | |||
105.89 | even | 6 | 4410.2.a.bg.1.1 | 1 | |||
140.19 | even | 6 | 3920.2.a.e.1.1 | 1 | |||
140.39 | odd | 6 | 560.2.q.b.81.1 | 2 | |||
140.79 | odd | 6 | 3920.2.a.bh.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.2.e.d.11.1 | ✓ | 2 | 35.4 | even | 6 | ||
70.2.e.d.51.1 | yes | 2 | 5.4 | even | 2 | ||
350.2.e.b.51.1 | 2 | 1.1 | even | 1 | trivial | ||
350.2.e.b.151.1 | 2 | 7.4 | even | 3 | inner | ||
350.2.j.d.149.1 | 4 | 5.2 | odd | 4 | |||
350.2.j.d.149.2 | 4 | 5.3 | odd | 4 | |||
350.2.j.d.249.1 | 4 | 35.18 | odd | 12 | |||
350.2.j.d.249.2 | 4 | 35.32 | odd | 12 | |||
490.2.a.a.1.1 | 1 | 35.9 | even | 6 | |||
490.2.a.d.1.1 | 1 | 35.19 | odd | 6 | |||
490.2.e.g.361.1 | 2 | 35.24 | odd | 6 | |||
490.2.e.g.471.1 | 2 | 35.34 | odd | 2 | |||
560.2.q.b.81.1 | 2 | 140.39 | odd | 6 | |||
560.2.q.b.401.1 | 2 | 20.19 | odd | 2 | |||
630.2.k.d.361.1 | 2 | 105.74 | odd | 6 | |||
630.2.k.d.541.1 | 2 | 15.14 | odd | 2 | |||
2450.2.a.v.1.1 | 1 | 7.5 | odd | 6 | |||
2450.2.a.bf.1.1 | 1 | 7.2 | even | 3 | |||
2450.2.c.e.99.1 | 2 | 35.33 | even | 12 | |||
2450.2.c.e.99.2 | 2 | 35.12 | even | 12 | |||
2450.2.c.q.99.1 | 2 | 35.23 | odd | 12 | |||
2450.2.c.q.99.2 | 2 | 35.2 | odd | 12 | |||
3920.2.a.e.1.1 | 1 | 140.19 | even | 6 | |||
3920.2.a.bh.1.1 | 1 | 140.79 | odd | 6 | |||
4410.2.a.x.1.1 | 1 | 105.44 | odd | 6 | |||
4410.2.a.bg.1.1 | 1 | 105.89 | even | 6 |